From 089d6219a1430b1dc58f9567fe370cef6fcdda90 Mon Sep 17 00:00:00 2001
From: krahets <krahets@163.com>
Date: Thu, 15 Jun 2023 01:59:09 +0800
Subject: [PATCH] deploy

---
 .DS_Store                                     | Bin 12292 -> 12292 bytes
 .../hash_collision_chaining.png               | Bin 86607 -> 0 bytes
 .../hash_collision_linear_probing.png         | Bin 58163 -> 0 bytes
 .../hash_table_chaining.png                   | Bin 0 -> 91610 bytes
 .../hash_table_linear_probing.png             | Bin 0 -> 68495 bytes
 chapter_hashing/hash_collision/index.html     |  17 +-
 .../hash_map.assets/hash_collision.png        | Bin 81300 -> 91972 bytes
 .../hash_map.assets/hash_function.png         | Bin 90233 -> 100007 bytes
 chapter_hashing/hash_map.assets/hash_map.png  | Bin 66528 -> 0 bytes
 .../hash_map.assets/hash_table_lookup.png     | Bin 0 -> 61522 bytes
 chapter_hashing/hash_map/index.html           |  44 ++---
 search/search_index.json                      |   2 +-
 sitemap.xml                                   | 152 +++++++++---------
 sitemap.xml.gz                                | Bin 763 -> 763 bytes
 14 files changed, 102 insertions(+), 113 deletions(-)
 delete mode 100644 chapter_hashing/hash_collision.assets/hash_collision_chaining.png
 delete mode 100644 chapter_hashing/hash_collision.assets/hash_collision_linear_probing.png
 create mode 100644 chapter_hashing/hash_collision.assets/hash_table_chaining.png
 create mode 100644 chapter_hashing/hash_collision.assets/hash_table_linear_probing.png
 delete mode 100644 chapter_hashing/hash_map.assets/hash_map.png
 create mode 100644 chapter_hashing/hash_map.assets/hash_table_lookup.png

diff --git a/.DS_Store b/.DS_Store
index 48e8be2d8e7d8963ef53a1accc6ca2dccfec4427..886ed5efbbff7ba96e863b309feaccfeb1dde8bd 100644
GIT binary patch
delta 785
zcmZokXi3<xU4U62`QPLZ0xFa532?DjGo1U-Aaiu`djWkUw(?{TL0)Eo4Gfd}1l1<j
z3Gy+W>jE;3*rN>~${B^!C%+TqLE@V-U0|4;C!{txPKcLT@mMX8ZN&aU=?>WRhd|}$
zgm{qnCd^7e(;I}9CR+*fGG~QL0NE;&^MtwB&5v+=1i7eQSRaY4JoyGtU9JGb<N^_+
z$x<SGObHf1rpe?u5ia)2FHFE%@<r^C*v6Azi10B6O#UvS#q9fP&Ey{<GLs!dc{uVD
z!a%AW!2$*70t-ZWnfw<_UN3r=N%g|yJ~1Ws*jj6dC&a`jpA+Lj;;S+mOlB9CV;0@y
zIaxzohTZ!R*yPFH;<9jdzPKEd=z-1s;_Eq?KF3UUP&D9>KH&;7&=JT{n><gEiybO3
zdA*_$Gb_-G21+)Q6_j|HrRui;*&ginyOY2!s8{lYv(GDeF-tuF28XiC<OF42W`($m
zKz0DfTECeP!wZz%CiAIqu|owW%c}%2D|}#>Y@=!*kdtm0oSdIqzyJb5ALf7rg>&;=
zT#|C~lYl}TfmddOZM0T3oUEbB!;awFF$)(kOy*OQ+dNBkHY2k>U(RG6br}(4%^Sa+
mhByHtkpedrSwf&71IY~r1q>4>=xqL=?!rnZyC#277XbifmKOW~

delta 795
zcmZokXi3<xU4U72)2_)M1XL#96X0TA)D}2-zM9nJ^8)<5DK1Gl`AG~63>*ki-pL+<
zyv%9>43ql=)h5>o@-c0f1u~7;`?mz%`T69?WJV$N$?pVtkocxd2N)*j38_tv6XInS
z5M2jk8?i@Cjsz=z2vmMfhzE&p!YnX>VRD18(qt=PUS<b}d>~t8a-J|3d&SoJH;11d
znOrZdkHl7<d;_S?@d3l+0uiIhQX+gzk{Ljz$>cZ@F82Ou{a|bIMeLE-#*<%&@G&w>
z{w|`$Y`gWu<R2n3lO05PI2LEF2B~%g3lyLWED+^ovimT3z35#gww}p-VoL0io8H_8
z`T3!k_~dh9JV<<1MuExf;&ROV(`6@Xh|91)(BA`gy0^G2oSiQ&$Hc#2bHDg{PNqZK
zCp#z_a5!K64l>XY$Wfa-PmzlqDlmDyq7gF-(2E92Hj@>Uc$vjLVu5TA_BAK@!TzgP
z@`SU`D|s=CF8~IIvdiQIWnN~vTLwUO00+C3J;)7?K#tpFJ{2x@`3bsU&GITi%<=&Y
zlWkND1ai_1gOl@f3xKiCz`(hGIY>}AH{S)G6e1t!fi+pH8cx<w<zYwg?U=cM$%0Q!
zZu2bF*^JEE=65FZsLO~TYu5SZ4+&t11R{YUO9&KXAh|)OfnnkVoy{NAU0CU4*W?fC
FA^-{>GBp4I

diff --git a/chapter_hashing/hash_collision.assets/hash_collision_chaining.png b/chapter_hashing/hash_collision.assets/hash_collision_chaining.png
deleted file mode 100644
index 6653bfa1251dbe52a5c67787fb8259d889567499..0000000000000000000000000000000000000000
GIT binary patch
literal 0
HcmV?d00001

literal 86607
zcmeEug;!N=6Yn{PMnJlyL+LIl2}uzpq`SL2B^61fTafN<4&B||-6aio^L}x^_4@t;
zcdZMDwKr>aJTdc|d44m``64eTfr?Cs3<7~rr6k2Zf<SP<DP$NC0vv=%rNO`fZ2wV0
z1XMIgyaW8>Z>S<=^zI#q4md{y!GSSBFi)2NzaTK-UpGJ9A`K?`@A*gY%YR=3JTu4?
z1pC+ZAdnhxeEQJ={+{mn*AXTS{C}UA2Kmp`aG*4p|C~dHfvZ8@VsAWv1CouTsyzsV
z*8cPdj;2Q=0@@9d5__ZQ0^UzX@K6@7>y&ygNllKlBm6QwKucUW@@Lx5GP<vhnp2t!
zKb<u{Ro7k~E=(*m?$*Va*P1iu`&5X_*NsMMi6BM5lY>XGMvu-m0#=SIiI?fOZkx95
zPG1kkvm0+FKN5?koHenpP0h~E`XV4jfd2k*dF?BF|H8t;qM)#_u(;UT>~&g_?bY>l
zIy|q85?yHh4ZX1xCK>qe9}qbI=SSGAV0mmri`OC|B79E!_}JK)-xIa#*>K?K=;`zG
z^N9!v@9ytMqWCIe$Q6vgGrWaR3IF|bgY<HN4k>A3WONjhn3xy?0|N(VqKLs#0wj79
z6CK^cpa^?mE&&SJc?tje+}V#>$_G~RZyzWfSjP92n?kNO6`7B%q*u0FGMQhYGIc!H
z1zl^BjI{Lf1u7z<{O%`upA&wj5tPH#2>*(&GOypA;{JUwfZ>^@O&kA(nHc3W-{B|O
zH<IN&WV*b$Y2@OEg^7tyYFTNw2f5mxDW`p((heivOjCVyo$+orL9RPuS8T6$#tf#P
z>W{G^^QET()rJtRfAe?o9N=JKOZT<qW@TmN;219xr-#&JWo1=VU}NGvwNU(WwE#^q
zsKW49Klz^z0taEqv#De<5B~Ij$Fy7p1Hnf)U0Yi#6^w}oZ$j{!mR48wJ~ST_hU|SZ
zC>d>}aEr!LnaIIu(~GI=fc=NgZd2)KYl`gtB>Ckl4j*#ZL2%|uZMlQcBnisU`0xQk
z?el8DjnbhuRRmH;NI9_y3KHuJq>5}N@tZuE<OO}!zbgfxCg>2Ox{p-Z20uZVQ8BRR
zESTtxy+{QdHqz2xodl1?+5Jj)adt=Zw14?BP82Jz=2b}BO#gjCf%#oVMhYIr`IUQ~
zwXHSIfV3X+UIi!Ot)c1G`nrK(8yxuCi|~@o^7yq+B54~135wBXSb8yeu}J^Wpc)Z~
zbP!$77g#o1$uMaXqE<#1d)vV7fN>>v%495Pjqklz<%3q?xwx15eO8<?m11L5uG+-n
zN5i;3m7dJEk0vcTDJmu}O?U&-xR9{p7qNULdU-@$WMt&W<s?ub&0Cyq%!LpU9z`{)
z9#xVy0?xb&jv@Ac7<!%<AH?^$3SZ<AKlWf4er4w<sM1^)9+fuXfVFmT;5badf=*0K
z<Va!{Crwae?m}TCWq#46&zAImsQ%}ck)>4>@zb{|^t`76G?BoNDt(=ig9Wx2QOA4U
z%ECfSr=l)&%XaxACQrt<q{6D~fgc=0f7&C}GCD+!^DFX!q~d&QdV2w8EqX&lqst_f
zkGZ+|1gfQJW`{<fe{UBfFIAB7KMc1GgYQ}0*txdl!0yLH792iizv%IR{SLn@^zEA)
zw^zE43<GH>n0A52s+e{m|M&nBFh;s`OoHjh=y3lT@XWJ(SrQ$KFaxLOv3jM_%O86s
z1rs8PYuDrdzyTlFq<6wpd59k?ektYJy@Ho)`i(LZqP_`H`T1*r?xUq7yAg#t;qpJ-
zs38o(RQjSI6>K6tM&U+HeyVK8gs6j2F^izc%c?o?(oj(f&*9s<KhZP7hX711M@{|{
z$I#}BsH>Aw7&eQmPo+2`ee{+RtI~7<74ttKmLaTIQm?85{h(1{KJhCfOz7;-s7b*L
zk_g#y8B3|Gf4YSew!b}h<JbB!1402Gtxt#GI-RIe0+V)!|37HGKBoMr(ihd~+|ei&
zBppXG8N0}gyY5{ktbdqr9Tmt=<4S3jR~n_)NgyuzAonUelsP5BKhb*G9JT^;YBbzD
zM*k3ut1?SRRXA|MnYPdThkE<yBB^{;rq)ps`PK|zvZ(9VjTF@nZNFmzBmZzf5g^34
z9+hAX%P=WWUuFCaXFZklKPVQ9Aefz%K9<6rIRU0Xsk8G4hw&ef7W^7kY@IIGT@Iu!
zZJ^XDr`aI>caH-MK_CT))jZdxL*zS%tKRtKm?_F1JpdtTkb@%|xA>u-RPab?{{f2q
zu+l(WSD+F8KO5VHo(6J4k(d<u<J~$o5Ns$sDOrNVAEIS^Koqvpt@bAzqR9C`rk7#F
z&i)h;ivl86V%2AV^uVVDNghPx;bTJbr$`@B9`rhp()>>s!@>hb*719eK0x_Lmu*l0
zQJ0MY<DW_dPb&<zI0pZ8{ZkZ1E)3qs4=V`x!(O4wurGa31%)}n{}izTq8DwEm48|s
zei8_-qy-^(^G{9U2?Rv?JY~3l&dC1*lLbpSFZeIDKqI$V?~csMqEXy9I$Fw*cpfy~
zBh3^Jf`_z`59u+mP|UjR?(OyU_37*B0ijpLb=4>*C#Sf$c+AB#-H^wBd#_Cc41Hh5
zP}6sx=NKw=4yKNdoP5OC*ymSk;d}enCu?1MySw{%a*~q4-@YjtR#`7KSuOC@He7Ee
zj*X6vGiu9$)`~Rie;+M*uZ41_@Yw40L{W>t=$9Jy#Vpi2KgVZD^L~6-Sy`#Atqs9r
z?$pdQ9!h!f;)P`@QHo~06C><dFb1W(l(4YR{b_>?go#pKOI>+RK9TtQs8z_z+RLlO
zqU3sNaoX!!&2y=o1>;}Pu+Imm?@%R!g2c{c4ztf*;r^wCq*OpZ{QL%)zWX?1^4M>p
zBn4I7OwP|UR1*>rkwYzTo}r<Ig@h<Le=63}R8h%cDx|sjeel}z#=-H~;lS*yTCHMe
zUcF$VN{P-JFE7EmX1k5vf&zvPa2ptmqGvu?;LG3i_;4E%60*U>MoB@TD5d^I!2S0!
zZc?YV_r0T$QI^Ly9*?Wz2G=tS0gCHz!JC&HRrhQ_mp+N;3|7@@AE?Km$J<y=wyPs7
z(JA44!nN+ZEy~P0e_*}L@2$qO@b(<ot3g3S@j8sz`uJM&G>DyFOIbaTkZq0q(WB2k
z&xqz<hTRXCWg>Wm8Y#jj8&jpy3@0hbt>AIl@3{re-fZRGLG_Z=UeUx|Obl-Rb^kaf
zKEF!|;&O&WxS0@Z@Qt{XkWh2acUsDH!S`t@^@kecfzL@t(VN6xerj;Jt%PTJ2VtTa
z9vy8s>4xV}`>14Bck`p7iPL&dJ4S$cC-*+f;fq|9gVj#06xi#<U7eU?q-@{W;m?I^
zb2;@*%Iv0{`K{)>a;5y|MOA9>@oj8@;{Fwnnmv<i{ePh&GZ`>RaDLrPPbTX#f^@z+
z@vNmE2M31*`%u;JaC0D$+Vf)K6D=+6nz@LS)R*=4uC9E&D$HHm?X8gvi8;DX4@?^Y
z-$vTsN-2duob12aYhB%VM_5@{iTT^h<nQFq+{|BmzmZ#X)*~Ig4LgdCO6GIAVe(GQ
z+#n_*nPX4S&P-LmF&<BAG>;El^s>CjkGYOIi=BIL3xL#=6f6&EKe&1npH!pOG7c}@
z4N1DBPmyS>ZEbmvK@<BeR7&&(?K*$g@G-55{0LPg$d9FtrsXD{K_|rK`?aK)4|i_x
z6SHOpE29oYnkX~7;m3@<$I!{?n&@bdL)f;(RxahQ+AcX#qKK#$q%(uoj2?;G(ZgeG
zbY9mF#p>$nw=|bBBN!~!U6==j)b26koa0&x_QZPVRL!}+Oc$$a&C!ZnZ*H=gDSL(0
zdB>=hM_~KC?Oh#=P56PaWXAG=tvfwT?3kyhB4Djk&i6cOyfjc^%y*8@rMB6hX64yB
z*?PfNT7g4Gsi%sZnVr40u|bZSdhiv8-tG5(t`B9Yb*dDRN%&y$YyHv6b)5rxSKL^e
z$Ii}9Gnu^e8r!w;5{h0zIeo_vBupC;U*=1O57Br(aF!8bS6Wu?zuz9w%?6xr>L(H<
z5N%ne=6@yk1?@au-&oHkeOP!az`7$uCGkKzy69+2c(}0@Blt;86ZumW^6uoUP2SD8
zM555=Zf-1S3GwyI8T!)8U&zaAIJCzMf~ebg(BmNQ#-lyWfY;u32k$9G-<fl)C-*!y
zJ3b=3y6R;})JCXy5qWN`{umIB=ZsRnRz=PpX<t=Zlsi)qNAZKopY=Qsd(OdO4DWT*
zRY#`wG#>P7ntX{yt7*+}<4ywA=WOuC`Pg)=)ZA-T7~Ej9^_iX17^H!uQ{nI1cC3qz
zLCb8A`HcU&&wGqC(C^$8BV#FOBGSCuUhOL<<=5A<=Ea(w6e=G+d{8zQ%@RGYD(r1!
zApJ0~<awFwfP7X_IhGgwd7)}x{h}4qFz?6)+uXAwDm=RA2dJ|`w+96UrC~QO9~l|h
z&dzRG3Jn!iDVof;vhoK=&~X<Vt^^ltOpc-?LkHnU;6yKmKLg~dJC{=BqSuT-J$`}D
z+3&o}?Q%QUUfYQ!WI8Mu84a=Ore?6ex!41VWHV<tM_caNPzM_DsO~6uSf<B$!D(OR
z8HUrXrSc%uocP=QVo#0wT*a>Jlxmz=I&9aAsc!uj4zuOh)mHJ2=Q|a7d}LxCSI|~8
zg7Q}(p)CDu0zV@aF0lC5{w68UbV&^IV&oqaF(LZR<{E)qq;ShJ%~Xj>$;w#xY$)@^
zoA=0m!RdDcsLhpX-{Ps3F92WN=oLKk2J;vRlKnollTF4cYfZ157z}P+owIJXMCj$5
z((tSNkqJ^R<#RpFoM^Rj?og@h9b+%uuNq{6@)r1Wj57-==}gdX&-o!d@72&tz9_**
z;z<H=?A8-4Mw($zd9?YMqO;l|-OteG7Mq>8xMFY=jus)xRXLE;h*9UAJ_@Y87vB)a
zam>nvHR@Vwx-ob3<YW_th#nGoHqU6*?qe*$oKEjD3dF02S<Wb#oN5YrEnp>64tCr$
z-5;n27zXT~)V&=myAD3_avC{O%Hld1yzzEIIn1%E>vU}N?uXeOmHXLHb$5FtWKt=t
z;X*7@Us;XLjb=@krLJ#z&{2=K5a+32u0CB`C0lRmk1P}KUEraLX>2ysO}K#BuC+8?
zvJ0hC3Lov<Dcy;I;HR&BBop9T8>~K3d~b@?9C!BYfO_<~_WiM=Ck;86HC3TuX`hLS
zD1k6Tgwox)2l;ra5+n$Z)^-`xF{JmBHLa~4t-9bl@85<WF*o39WJamdB5L9k6*a3+
zY~82m;kfPjkoHM)tW=tMwN+Uzvqp>i<zZz3T>X{aH7kSbucW#dLn?$pEh?5+d~-n=
zG~(8_pyx}a`aun#t5M%z^MgCx_52}He0g<F_EcD6@w6KYN2!h4+<orzX5HW2GqVZl
z$z%=+uYZMY^VwO1mm-RKUbT^uRp1-eIUh1n2N|Gr_|0Z3x*b;WE|EMaYpT)6M>C#W
zhriaA8t*pkGd@@sp75^esqi41PoK4nS?&_lu$w-8a}uDosb5sUg;gi#Zc4i_o38Xy
zHHLT2Ws(gm<#&%Kt#{>7{(CNOHhz7cp93FgpzmX)#iX_^aoWQKrSF@Qf7gRw!3+mz
z4|-z4Tn;NOHG6I!)Npojyj<ev*=*S#_iawP%*5t;%{*U=$eYWWi{<uS#oZ+IH&&hp
zr%y#^*R%5MafZEUUizh_tCSf{$1g5M1rLQx2ed36_+kaaf#4TOf-0Q4kFOS~!PXRj
z^Lv-k(*!s_o;YFEcvE!@l24LpGIPFH>o5qizMo?dM3U3JN{vrv%JCi|8ZQ^!OY4u4
zc<tL6lcJ*R<}9np-x89(7Q9}^s@%ZA9dH8zuJN*=V5iPZ?fwg;LXY1w#&iR)NHspf
zvR!dKp4kjDXVw(~*D=;!XIUJ`LM)pDoq=7Au0!h5j$|Lz99}5eUS1uZ%_)BsaaD&*
z!~Isbge<mV;n3>*UZ6aj#C0**f4<zM%qt-s&al{sZ?5{dKAV~&OO<x{P`XPh*-y;I
z&P$`ZFxpIkm$Wss^c(LYjmvhhv1q_dW{KAWS1*qB3m+dtR_V;SAv=rk(Ng14k#}}h
zI(%twxaJu?MdYu;bCt2*iuCr%%lt)KH7^2QQ&Tin0i0qNeOM5D5Ew(_L}lMhY-;6&
z-;ia6Q`RO2He0XkP!mQf?_%R4#jD%d-6>^K4Ngz!`Ao*)8-jcZMHTFZ4WsJgYfwvn
zcl+-Vqw0NaJ@o1-)R%#d=hq<X+wfy1Bo{1jV>4ny?$AE49`bR<iUVR+fDX(I4?=q}
zTWg<P)y!_x?}LZo-cJ$8_4+jt(c>!9W<Z`)-fZh{&yLwB**S7h=+_s~D{++!FmLGd
zwcZdV9_R%u+aqrE_DZ|by?P}@bGeE^?YyC^6y4)agRq*~G3O!Z_ec%qMz3)l9-#0k
z^(d{n&WbTQaBFQF4eD)>|Iy+<D*X7{ctT|NTzdakp~7hGui632F=<g4(Xq8r#%DTJ
zbeo52n|u8&eD7cKa_Hy8KPRx0<1P9C>SIWRElDL+cAuOqfMto1KKwo|;Vxs$$4@ms
zIB%qc6qD}dctO95NlIxax4FFKQ2FX6V_CL^H1;mG&O8Q)K=yv?I+NKOuMA#DOj7zD
z?-wxPsXntln-w)rKc>Bize|K`jw!LvHQrhL73IU!q4&ww@=&kG)%m_YqL)>db<HiM
z&F*;pO>MwgOVz7(^sQOhb#nwlHzJ{33@I|)<&9`>iH6HO82ZxA%9({;zA@$@?#T!1
z*li{oPkjNFi&`+?DB9yzgCNu2h?qTnf#n(VH?~_zNRv3Ien*($jRSd#a{VfX(<*_G
z7eCk9o0@&@B@Y-p3JU!d#UIf{vpCSPtapB*qnL&&DshH1_SoS5j7dI=m7R{>Av2A`
z+AR{<#kU4*6!8=AlBW!?_R7jJqjhEn`NzjL?K1g<ilUM_j3#0V=Js(k;A(VeR7b=|
z718MeM_ZCSSq;4zgIbLWa}1}ONDk#5xAitsiqM_1xJx2jV)$!C4O<9r1idm&UwKGM
zv}P<BHYven@VLH{pr$=trr@|;La8cipA5rD1>;gh*g|j-CBu=Kee0m}o5WY9=YwVi
zWmN{E3Z4(~9+qgMtGa;=LK=46`?ySFdSjK5ZNMUj?ZZqNl^wc-<rb4w9|i#?Sb`}|
zG?MNEAvU_p88op}8{_;S?ofZZ>*3^zw6Cf^4(S`q&KFgzl}u0Pw)(4K&?j%Zb6yE<
zvCYm5q7U}c+1RSQD5)@HDMOr24?<^ELv2IX`Dnqx59bJ*N8xq!NHYS@R?guJ1FCM|
z@Je02l=@d<LS2YOk=j@a@aM^3ij9pX4Yi_tM4zYuSW0?;8el;OyLe6&YZp7xc6M~=
z+Un%!$s*jZhA<nHy<}iwWV}Bgdr#_hrK>(^E}90o6h<t0OB|ynC5U{(6tHl*yFRnU
zo4v?Nw1PNMYo7?L9@ZaqIyJ?-CeigZsqDu|3E)<lSSr>QVsME`NI-UMw9VLImLb04
zw_R|Yl2UU|5pb_kgL7*OL^Z+y1Gf3y2L?%F>BwzcU}JeeuBUTWvd=!oTs%#=Hr@1q
zv7p+YIB73&Pz02kD|p|&^?sZ6c~rlgR5u;0j&>eB&(S&SbfEDHS49Q5H?Ov%qMS8M
z?uEW~{hnjLeJ5XkRK_6l!h^G<bhl0|+=yW<1zzSX`&sITa1*SEOJ(c(jmc&cys<Ep
z&>H9Q##sdF(08^ch3U?EN0AF})fNM=+ocD4Qw~q!g%Ypq_a!*JyYOaPJ?qXfLfwF6
zp~A$kxD)fy@hss>1$5~2GP1e!z=9y&nBPR$yX_J6E&b(6C8?X6hbeWVNzQTd&$Dc#
zWdv4>Ev9}Gb;E2Ue4I3><;mrk?ui1Yvk6lX_6on>$#+YN`HPu7(*Z&Od}S1?@H3)!
z=FfmNo|Y^?2!$ZTYEptpDL{<=uQIk-hyztnrwg`hSiXYBHrK2XP1ID63C?6TY_a97
zwC*a?GueI+@ptl6a7q$FhAfs|^sx!1z%0F{q9-Hcd$EKa!>k>~@p<S(39^KZKFV(~
z&2mtn*%ELKP2{qS;`nM>eI1aEhk)#H+=7q?`aD;N2FrgZ4Pxh0vpLy^K#tq>uIc;l
z+O-NytQ<DCzo<?n=kcO)XPw@J9dSO4F{buLwN}Y~mM(SNV>=y***9>P8j{8<nJ!Bh
z&-1(se|%VLiFyWZoK<%kWe@T=`mLLVlgaQL7JtuHAw+*{-&Q5qwaO^Ird_a+M>I{X
zQC&p~7F@u8{1Peon`7qlWd0h9B{o<T%4LGZolnZm6s$v-5}~M}73QAzo*PTQG%q~C
zsqiJ3l`fkbF*Db`tjd#>MS|*vN}%SZO-EUrl;OPuiB6%<)j;frQXcj}SIvTMeq=U&
zVzf6~U8n<!Dof-aP~Sh>K`pE+%qpP?KUD^@mxP7@+?)H!a+x{RvM4N>#g8EL6s-a-
zi{`TkgO`Dg#-(gnG&dq&a=Rw{RLoQg5kqx$K52U@EsW9td9<r(eHH3}AOT2Rbm(*B
zVD?W$kDnR4+dhSN9UJQQ$Fbt0iM?5qft^1+EqvqZgE4t{<Q<7(VrC|?Utu>QDxz=8
zP;-A$s=q&7`dfBI0MkYgT*H?hJB+5~Zi=eDsgs*2(Rt6pkhA7_H1A&3Q?aP7Xmb9d
z?GW0a%1{M+xwfhql5P_b-jnk@oIOBzZ8)${I&5#q*sO2ZB>ULjoIZ{KgixtEh@<th
z^^=k6qi4Pu{PgR^vZ7Qaf@tCMngWi%(6opz#UP_poc2qr&4{j~IV~gsavxU9+brK{
z$y}WD9mLSi;O@HNxQq}+?++^}KNsX{ZJ4{n9XbuSj(JQ8Wj;%ZT@Ih8FI9F#$TaZ@
znU)@5Sk2s!jpk;UqM<EDWW{uL(eP(gI6EN|k04?Tp`B&@PRygT=Jo}1A}v?7SXQ$<
zi}2xoTGVBY7-$3BiYzRd)e4dSka7=ghj>F1<=byQiI)T1OFuY+FmRuFhID-Ir&6}H
zEp;1~gOKRFc6OCP^te5!j(G`iVnqY(PE8qaL#1V9+Yt{J8`a&PJ!l<J!=vqfGBut5
z=sPTVd9<Xh?lP1ja3x93Yc%$)vIB582$;}aF%@_zb#i5#&gXWEN%t{ak1;LPc`}uP
zxEhhcvC7wyI@~(t1nDY6JE7JOpX%W-D6A*mzEQZ<^nQ%H{RMB(RC5PcAb3AK9VA~K
z|9h-TkDl>{g^yv@%r`rWAI`P7@uK6m>oaFYf4}pdp62mQ8N&1q_pqbVerGK-+)9xR
z6_NrOhf$e6?Rig+OYenqiNZeYA~kF%pRSVyRETu?4L3gzaVp)z&4hM|7aJE=6dY7=
z;S@<E!@9r8w!PzI!t?vBVYZR}o+c1N?#2vWx#>-OQ>8paMn>suw`<Uht9d3P4;aM?
zV{t*g%j#KIdJ_3yX?4s*7bCl&u%Qj(5nB*!Lmc4s@t!l)zl8v4Mbe!WMt}Wbw#+KP
zUqrk;#%WVRB!`WzG@oM9^%v9Be36xHHc=o4E@+QtUUf1_ML@wPdlsd8Kwk*zOe0g#
z<P0G9+AFMP(W2{OAg6cF?+5P8<G`ZQc?kjNm;38xuPoV*rDZl7xpzA=W5s*yNQOUb
zI{4lL{!p{T-k0H)AzYv9)$gk7oou1#o;K~HN8~|alZMtZ5wR8APYHrs8!;qa9;<7!
z1m$_Aw@9Y5F&|r7<;tqQ=TW^Ju1Mlc5h1SWRr~_-j`iYbw?<J-CAeJ@S#5O<VTKGb
z-k;f53uaT)8NObX4+V8jibWgK@6OF%xn`fqll;~vOXFvK_UWz;Ag^wZsJ+FSu-zRm
z@~u72;F(5Rgci>wJj#V{Xs7P5>EjPxPWx7D_+C%P#3TB89edKJkG%ZyE>jrCjp%#K
zMvE>%TVybDNXoEzYcCAF(Cj&Rl{RwK^!w>Dob_&>yi0&YFpBc|gb5fxudZRXBoq%x
zhdY_M`3_S{yV9zJAb`>`NHwdjeN@$kZqegxKpIBWfm~J%XP9Q0HRek}w|~B>dx&X1
zEI=TJ)i`W?@5(gy$c9Gfid(%}DpcqG&|K5s-3^_cm0s1;H9nZvywY8!u9{aw((+ti
z6RzPDXjGQ)jklup0jV8)t&b>U3mqF}iS|Ap|KNy+CTihwHqlf(&Y(B{*{9a~{9a)$
zMxjm@ib`sAgC0NJNowKYEmn>3Sbg|7{B_(X)T4Rv@dDr+Yxh&lx*0I$aPKsf6^vqz
zGG!QStLwLa;-mKkl9@BI7jEt|%zqfKQaH&u%s|(;Z_j+Z8o1M53xPfsd9Hog8!V)!
zf$%W!C{C1YU0J~qoOxAmShq1=&7DN9M%oJTsk&l%=~z5NDP}wEI0=hXdNb}Ax>dzd
zy}=b5h<m7!qo#<2l=3Oo2&sTsQ$ahFvyIwYWlA@y#{MdK&wffDiG$&iQ-7Gz=)G#=
z4{&r#rJ4^wjTAmnBaQ|$%$Uc#5Ea^<u$u|Lwd0kxz8J>(l|Z6Qmhoana6z)ZEVv+u
zkt@yZ@%~b&$9Apr*RNkIegVA%JT__4l;Gw%OsE+Wy%Gpx1Rbg(@GK;C1<Im}Ts?tP
za*TL7ak>zv#xRGLp9kcHjnVNZEU_nH-wq6UoH)2@@?st@=<ev`(B#XFI9Wpd-)}Dt
zNN}rmcF7U3yc=hx^9`{(tg3ai1UJSx<Rv>JZ*9Tolf(_*COFNNG5Ay_N4n;1{@B=8
z?Q8v%;)gW)cyaXDaO#!`j}d=@aZ<*~suy@f<hi82)Km$u$_yW9;(zM2`B5rn$k(C{
zpc---%VQ?0CEuD2&)&oqKb&4Wr>3h^*I22*-AvTW(lg2+p0|AxvcQEDnw3Xi*^Jd1
z-dW(3BnY{$3rvTov}RXtS$}7-=zseb8#H;->TY)iCAg9|xloP%lHTsK`Vs!q2KyUG
zlQ0nQ;JuCaqynds`FJ0#&?%CLpA(cJ$cbNJ+6w>9d6f|dgF;FPF%0?ob=jrePFlrL
z$^j$BvvZKI7s=vTlA1db9K%L@VYUY^DVA-emMSR7hVkV~bedo}39-6Wm?OT)vX8MU
z#Lt|`<CM_g3C#ud;jB47;&Yy`=)1ARa41kmx&Wci1b(4bBcVEz=@HvI$RL?dZdF-k
ziJB@I69p3uLtX8~ywjV}msyz)>j|kZVbG`QuH$y@W%qt?=?|myy#Fc}D02)jbTLy2
z{uKauD<$~TvYGqb{m8oExK!#i$PmT-I1ho9VB*wPfcF*atCxYnGcX+pH&hoRXWbjo
zNXUqT!2`pO3|<G$6}X0lW-4X3OKeM5n{U_^w>br|goX8Hw!*nQGjX6833)8ec+uU9
zeZf=+!Wyf4Fo=DN&G%8aLknCIxB>9E^Ww0l53Bd14j&yx*P9fmEVu50hzhsw>N;lu
za@Tk(w=!rlr>E_4_NMrJ8l}K0^mIBHAA%od?l804J2cCuTkbF1w`^w33dExCfvMRG
zihDr?#G(<&$qTgyP*@#{OJp!gD2K@~S$q5D))qY&Wd}|d#h97DQzZcZ8FR~Cy+IEq
zL#uy>{{(4)6V$Yln66qOs@fm4+C%=X+G>Fgyo;!<xQj<Jo2!sbCy$;pTa4c=u_7LV
zyWstJZ&t@i;!E|Gj8BZYNsm~_ix|nHTUZxXCJ{+Ti5-h-`7I<a<Tjt#i}UB6<iVoQ
zH1pPO%GwVlTDq^|ptg;i0SVviY{9eJfadR&85n0M1T>>E0{NIzMw%hgc3<rk(JF{>
zGt8!_b9&Wj^!Pe;I@bJXpIZr5_2feEiO>Y>+log#Wr!H;(PusP&siDLEL~;nO4h~^
zESZ!Q-9tMsP_dtf-nY=I3qCB$kMWJ#Jbu*{pkwG&R*DKobgDVQs}3Ob^OFTBhfBs)
zXtX{SOMqy_wWk*~CKSfx^G9QlzTF}az4Owy(DPpkjXS;X&GT+JZp1qYfGZCpAIES=
zo~$}4-YB0XMxkb!!z~LN*<^qBzZRlRPG(yIAo3LUS91V_qNAhZX7a^-ga`#6@9ftp
zu@X;oA~UzQw|B;}FZX8@)cchQ!zoqN7A6kg=d;DLP=Yj(yKaZmMOPL&s*w&fuNF^S
zAs+_hOH?9>f_@iek|zoQ43>-M+N$hri12gK%U;9;oVO9|oeK=#W2u&zAXkp$?;hPR
zn<IUOKbwC#u=hK#@46sFP@O1p1xWAPhv_4I5#|PuVAsLd$&Yts&*WNTVm8};1(i;o
z6t!vwNuw>WUE#`pWPIJ+h|2bOzTy37au=@O_AatN)>%he192I(mdFUT`I+y0tRfPB
zsCB`;cG~gfa}c;j>!fCKA<wLhYR-652o-!6l=#5T%65`5K&mvUw8**2^wLK0bTQC5
z-6b{QlwRYfUvt8x;yclSA=(EI*-fQ9_-N?IkIYQo820IYFrOdwN0}=Wia*d$GOc}5
zNR4TYBV_y%$CCIF-CTQM=>)Dx+92B?1Y~7tdA)GH)aUoinF-4Fsrq@Nz+Qtp|4+*=
zMz!W!cgI1o{G_*Q??`*}OrI8xR~6pX$JN0u-e-y2DNPRq9Or$n-p`oIEwom{029hu
zK=&O9^Y{hi;BoNc1@8VUfa8+Dg3b;O%K_0;2ZSz<^8V(cZC~Lf#X+yi)!ic$=DChO
zN&94PYWDQ$We9VV52({fGREF*CBL0*B*G>*;jL?qxrGk>JE$f~Y`Iw&k~$D5vzp^U
z8S#om&QDi6LNJuVO54ct2wCXyneM}d9`NBJzNDG-Q>3sNB4?fg>Bho5?V4bqHmH<3
zitFtQ(l_WZ%oDAj3U<4)+VSOK5vLRQ3#8fJKw>38BI3F7x!}ag#m7U>Rco=q-Xxsk
zkBj`rn=6_UCY14oT-;4l{`u}2sHk7+fh^+(!;&JL@k)j@s(AF!_ZpX^DmC~w@^)#V
zq>uYsYwn>E=fyMdGI=DoU-H?yC}wdVI)TL18=lhpRwDqYOLL;t*3=HsBw0J~6JM~=
z;zDX<e)Mo63);A7O{~$q)GA;O_%e*1-}jrbQGYtwW|yMZd2Iwx7*7~0+460x0=Iz5
z;?f>Qx|VT`{##CSNq1HGm~a`7z~E{d8g8z{Rq5qMZ?i>aTPrJ5-s!Bx$m`ZA<~yTV
z>k*F8X#@ZdbqrUz?Hou{>HwN2@FN7wV6BT(vBBFH`TWvOIhKLySOBiPsg#a$b={Ha
z;afIKFut@0A+$uTs+Ab?*bOKJ(GqIkCque|1)I?Fctw}Pd3GX80lD5lXT0iubm3Kz
z0l6d|jN3z<7c@DqUik#1ky}|eUMLrQDDZ?0V5E<P1ZQ#0IY``+jfv>2v<4i<%LJF{
zL56rIEjxSXyIXV$)vM(eL?Co{q?E_G5aUW^T#pV({RgfXw@EKQsEaNWcbLDwKalJ0
zwuoVdEvYh!jw$pj#dmabtLruR3`;DjqrT`IQ~BzGzM4$)i8PjXZmd6lYr$SMjiJ4f
zpRe7*|Nf4HlUu-h@2qSnB1bzIigWvpP7<xJw#5dbKawT1aB6I#v$5!(ie3+1$^Il#
zY;5f@X|eY6EPCdSxuI)%3s>z~xomMy9d64USBToYaPx9UfRF#Z?*n-Hutq{;sABqA
z`OU@`R0%HORf<qlYifk=)+<h(VO=l^2&>gCKbjO47mk^5UF$55ElWsyaR&`N^q?`~
zKx*JMc0_j7mi6OpZ|r&qs9|HxEi~3ceXFpmY8BV$AWy0_kID(<tr|Q8u7m+MYbpVr
zzLdKv@8<sJ(z{)D*UgAI22w@N>GyXotr;<J%k@=sK6nReIiFKYH=_An_Lk?4mEijH
zc0M&<VfwylU*kq=IFbGgVPG^yLvld|ifG;wyqcAQQ0at&jQmBKNcdgkk#!@fw$)*|
zM4e5Oy=p?fv_!oBh~j4Ydw<6ALp6~Ye_JvU0fFfx=GQkGF9h7i8AxL(CD^?BqrSSL
zt;X2fG4)HfBLuVRcS2j9J@THecy&>z93Oto#(S<$^V=T@Ykf%7Bh%+lvs4cb9+5ZL
zsB2B-Hvt4+8XuwQjj&K6caJ%y4Y%*uM0Wb*4;+=eYU__nKtf9fjmE|){0MDlVzvdF
zGBnfxBc}k_91F;m80lT~32687$<FFUb^1?}?}(P(Vla_UKX9xK0T>DX_)fjd+D^M1
zxzhO{b0t@+)Ef@B@}a9YHZ|p@BFFaiMrAdNqq4hce5cj>;zBQ+Yrl^OZw{rwSH9#v
z@2eS=za=3x(&~Jtm7Ng}A07xE?mi0l+_u)f$NA~td03b47MB#Sa<SWpdgM!|cqx!^
z7|*3sr}#@?jUMDtr4mNOB!BhQFq)ySb|5=XX3LrzNu2omt=!=v?^&VslGx2*WV!A2
zB)4@@w`!@wQS4Ls266IywoIxYbx>L-dEiMOvLCW{{VYyyA=(&{efeYU;p6xQ^Oj)l
zC>=S*DNo;magjGXJ->I^wf={~(ii&Po^948so#HeZAEnrS#SCikB5hb!Q9>LB@!B>
z7es`tO<*vFue42p+uikrl`>=_{x{=njwB3Oa2R_h6U!uCbLu#y85<w}N;81+1HDhF
z4i3f7%03NUf|XMJF1>)2;-(wqk&+0l-q5rFINJ1hP+*Rz5_;#Xo~$}G=u?9~w`jrd
zoiPO4onFh7Xv43oZD6T8faX|+X}_4#wywGzk02L~c+Snn!7gZ-#uA7mF=xL?+Ycjw
zUEx}EU|uO2bwJS|3W*g3kq->htp>HXFCY}(2pS;qCk@lqT-@$7cVQ08J0DrQJZJYk
z;2?`EnuV~#FEmgX^BVn<&eBF`PWd7L#HyqTg5&*#$e{?O{vGj6(}M5S-b}O5oS2!9
zrJ|uC-|kcj-LFLnQKS)yoG*@C?s!jn_0$FO@#LT2fCg8(iW*B8oWz26><z><fAKG}
z@({D(jEob7TYLt+-2{ksC_<j~U==Tg&%2v)QF>e?KL$mS*#bw|B~JTNz3?2OoA>PW
zfnUmO5`z$eg!ooQ#-}S%J#Q4o`Lk~Ed48S@wLk9?U`wCkO!d4hZtS|mjlo-0t%T(m
zMa&@?^Q`y<>P#|_)mKI}9ivmAUS|@4Cku4OJ`@&&G_UMcl^;$muDPS<7MVdmfy#rO
zQHTSdU*k)o<k0oNB3)sFg*<+>?owXOVR*wXe`|)bT`m^o^$WQBWpcqRl1kAr7zILd
zp#b+ki2K{mF;{_dmikf-zEqa6gy5Hlob;iuzT1RRhx?qHhp7;%opLN=-cdDiDj0>t
za77CrVm-IZ49P52!n|w5XUI1!slzcNd!KI;XDSOpwC)snS1vKwqzmP>b=)8SPyl!D
zm+#HOy2oe8o|GCl_eFRTsC`)04w&`z_#ENq@j2tUZ&#U8I9)g_BoiovnPaXc-Ru&%
z(Oc0z(9Ad8t}wif86dIco<y!v6E>zHPO<jB<(lssTDrkgKZ}Vy(r&te=JoscBXsiT
zWUJjVew}HMx%Bw*!mYk5_15DHLMijO?`l$0&%FU2#kx+O<p)<?r(R*|3ws&+YT~(X
z_o0TfEWKnu2;E<id(0}2*@QC9)|RB#mgd%CB$axdZXfEWF*5d956mGS6)9faBuud|
z9rKC`n91llGRdwp<<fO@h23P?(;w@OmN^BV$!*>1PxJ|_y7RL=Nc>XzwfcKXS&ueU
z2aJ!DxMJ^RvM+iJKlkbzk39o2YBh@&%Uc)wiWJMZuRZ<2UnK<GaC581(5)kVSdl6M
zv>hTUb!^@m#3w}xa}Yd?LJ62qk#+RZNDC?cQxSRW0zvc-Y#Mc<%y#isjuo6u>XW48
z!`owjv!c;i{^<dczo-$@P3t4#c{Fz~A+ZSPD=2+7Mi&k(Hz_*8XAYo->pc-o{w##`
zp-0@thT@6a*0eHJz4@a+R2XvjRAYs<Yw`Whg2@elY0wNyLIo7;Z#9!OegFaYI;Z^I
zf9nGOdlCzjusZSDaY_F1u4ObJ0y#_@<odG|S>ve~b)$QR?C&p%@Ocg7j_UpR=Kd_q
zwc!QaUM!`t-=77d|G!iJnX>;sQ~%LJK>d6VO@3JZOPhI8pmq96-s<ke7Y}+Gr%IZX
zFP1>&4me<fURHvvHy(B#W%&t)um7!D%lA*DoA<XFQ9#d&Y02D>jCXcC+ki#gZe!Dw
z)_hA;0{piu6cbVVw)e$f&sGP4B+Xyjk^(8viP2HqMIfRmhS4ygC+3!x14Bd4feJ1Z
zly=^<gX7D~E^phnGIqbu&g^ya3%>qkg-~Bu%m;gVGol2{hvOVr1q#kq-{^9>YV@n3
zlAHRUv)tS%KPH6|qPgfAGt?P$Gye51K}j;G5QvZm$_(|pLDPL^uCAuGK0iPIjbo4p
zC~8eiNU)K6|9*>D=Q*K5g7nj{C?noEhQ8XrUit9Fx_=*SN9MvjAQHhymzb0!zU0Cf
zhNX<<al`t(s}8LR+h3Lml#rTOnHE{*SXx>B9!Hz5N`y>v5iR~z^4*5zb0a|OBaz_I
z%-;|WGGOtzO+?=1+MIIJKANWd7d}v8<yfD#5-4Fq-+FDB5IsF}n}SSEL{nU~8wN?z
z;B_*TgvWv7uk954iJ&{^;udTc==XkX)Z}*%(iM;Ig=<zoabT8>Q%-m@;=bU&;esc?
z=aSd=l~3~N&ytT%Z?ZuJtG<jo^U@TZ(=6=1qClS2gfG$jH%1*3KCOh<f9xav9c_4`
zKtI!7s3wDVe}cH6WW%ukzT<y(?QA{4o1lKxADhmobU?sk;qhS;{uC{H0HQ(Te%wE6
z?NOeXMv$K{)}NxJC#LKA+YIFI&5ZB?1E5HxgKqK<qBFo1yiR3R|DQJhyB91V054%s
zAn*PZ0r@;+oh^2wXaCms|LFoe;2$h}-lQS@DH;SS^!GhFEqwoU9U#D7P+1T;{y}sN
zh?0lm82{!{fPe9Qgwwzl|9O)YjZGPyx5Nk^{s)ctBO`@|U)M|@cD_XJNPRHnad%5a
zrbp)5uoPiN?tRAJ$P8a9#7M(P&Bw_}L(R!IKt`jPLg2y86rPxz-LSb(GA6M|0loy1
z7f#IHRdP?de@F}3sW0DFznojq#9dZ^csb!Z;>WQ$$@eOy%+=P`Z^~ctd0hF7i*XjW
z<$N2-V0+8k;5DV#?c7F?)VQ`_15Yq11qpkq(RvwG5cD(x{NX-4ULAYS!l@k+@M`E$
z*-%zLbj8A5pNJ8lY%L}w+xycte57Q5>sD7kN_GU_51MN|{Tb>?wBEI5z_Nt8)hLtl
zV8s)TVon2=0P>7Z*iw_CPc0>RE6nTl$}^eOZuLSOk%OnY_H*+^fz38>Yx;n2;OG=V
zF@hlVGD4H~3d%SMHrfEt#A5%vv5Y0uiDxvD&~9MBL;3kCLZ2F$Bq`jQA~3?fBla?^
zh>+ysmFmuEA=o(c#lq+EU91c9op|g^#Sh}-giiV<94LNZK5>0HaaB3-4&PHd{<7wu
z{i@xw`Oa_Oa%1;=4IBJ=nAt0R$8OR#^KfPxp6@|PYtcwlGJ{x*u!Kt4%n!Ws+mn7H
zW(X5K={Ix&maKC)^U8~H?ybrBmtIH`HQ#KR&oes%j8`0)_7F>}iFi>Z!`f(Lv`@*l
zzOGdX+ZY6i1UMn}3g6k42prz%K<Wn%bBq_Fd_tZdsO4#I+}MXG&At`)+ld!_E%Z2j
z*N`!5yb!HyB#bm9d6d`h1K)`N=kX5uV|K30IL||$=Bas;WKYf0Z{n@^3j6J8s|%0*
z8=1eFCk`~P{oY*Z8)M&fduZJ!av#)QlzgYWD9MI|@{Y#3PXsXRKd6leU2;v|F+2z2
zHLRnCkfYXBS<85$XMOL&w1t|{3JdePtmL4Icm2dXV|HF_#Ldr6Pv^H!D+A!A@r9au
zNisEB;<OoMNPWu<B`hY^Zane<U0~VVYjJM7utrp;0*8}9J$(f9;!LQX3?IOxhWZ?|
zmLVe<tvC41)z_}nuV2ip<BY?NAm-~NPVg;Xd3yA*{o*Z*v6a~@``N~VvMIGEjGD?d
zy6Wy6BE?74u`2uWm2KuO2JE)Ty~xcfOW2Ll<`?ykn$oMany*oEyrLt~x9CtuLTV>#
zejH>eHjQ8^FQMX_u21<L1&%CI%!)#+o-F-0c^dc$1eVPpRqgAe_o+~94Bn!u+{WMS
zTzwyl*DY9QEL_|0dG%7JM~g`3@M)YQt{daD^7lVrw)%|Xy<H6r;Q93S>rAkR@^2z`
zux$}1rksxcY;I-m=>k+!e9`A=S`Ll@j-QGQP}ysmCxq}B!ayf2jwew_k<x#_33(%8
zQ8gpaD3C(W8;I21*ex8nfjAVSaZ*h*(Bc)@VTo5(5slog^r1M08a0a2nqgH_H!seA
z*_d->lI*P-C(PSc#ae3ULQPSe(z5}!fko7L&a0=9w}5p8$de}o_dtD81s_;h+gdjI
z={Sb<Viie=!Xv_6Jl)Pt4wV8-)v#j=97Ib4bITc;55-l7gjCwCxIc1L&SuC0E6oED
z;>{|Vzt&FFzwKVH*Y*F9hWeC9#)bwGq7nXO&HzQ@)2~(asWsxVgujyf;FKg|9qSA1
zwwrRXfj!Mo*-UxCM*WKFnz*?X6b={%O;G$_n*@RV4<-WnZ>yBdX`T4l%5v4__`4Mg
zXQJMklp1EW*z;37%q*igCT!V04P!E8pB~k62XK3%i_Hw@lLr`<fnH%L{GwHRjaqYB
z&NxqEkXOj$BG%MGJFI4CvhJ8yNVuOK@4?OQux!GG#Pby4v*(n_{pkYR0C3`(j~FKV
zQ)K+KNex~JK*qm&3mu-PF(ASu6#GN8jPm3i(|Y;-To<57kPX}5j{N&gYZ$>up;94I
zGGC?9o})1r(J>XgEGf@3tDZjGNgiF}>x`cKu^GLw5xb#!5HYByoa*Re6zmPHe6{oO
zpzL!7BbqhToxcBD-?syN^O@!-vu_Wq<sQj?Bm|f<8TR2nw#O$YCqJLw&5zY`qH-E3
z)h>?~iw2p0AM=BO6jWUpwtV<&hfFZ?m)`xPc>G9w-0{-PoAs04wXWVUU6o2hszUo=
zN8Iv)B?4Xy-#4FVe<e)ZY3}qyl~)?YHvsDw7Bs-iu6=`J1mY!|SH7E@o2#p<W7+S!
zy1Hm-Xl`!jz6Iyz<<T)Pi245b@gq1GF;>m=TPHmA^Sbn*3eclHTblPr@9E0D_M!lH
z+zKa_N73J%P28x`1eu&3ZKbGv&pitV-l!R~61^#D{Lgm*lxHV7^H$ieiZ&uh-os5O
zx%bNP7Be#EyXu^#d1>CLI_)0kwi!WGw$f<DX%++=oK)oF#(Ak6B`0R`o;SHaIvkkx
zDJLcPRj+n=GP}hq*<TC{U_-wK7PbeUV@#dbaPg2`d4R`?(L4s@%FoUMHv`Y&vmSSe
z9g;gLIA3!L)YyN%X-p?XevXo4e;!c>u)LB`lP8D7MNt8GO(+g*7>NL%_rqOh=UY<-
zDk_7`{`lc)BTH^hPDYgyGH&iq8<z)jmw`l9B^fbFQpHjzQUq*;M-C3zRq4OC<1->!
z1XkT(;bDzv4L_w6YB;+5s>)ug3&*<v@GZ)nuG-uJKB+UKK8#67y{S?sgf6!{j_&Al
zdrmvmMDMmg6|#=FsPWH&qW$T3{n^&8L5+2?3Eu5=-}LgJMJz(>+0oImdKYJX`?cZm
z^vLwcOO(b-(xs;P`Pl-?))`Z8p(~$vU6H+~>=(w=j9Us9j<YgZj7aT4UGEP$JAgR9
z`6XHm$?@6Q(M+weq6xMLeAZ>7?c!nWE=ICnQF&b6B;1#>n{suT5G7GjKHAmflRcZm
z$`9AFPr=YvzyQ+&{W^j3n$Mv5+Oy38KLj3L-dgjiqMH7pp~wC5p~I%zLw|qRLOApu
zi7;X$WaQnYW}(5?PW#i<)}#*&@m!V(RdLSQ<Zc*e--LDqXC7>oJaPEuSaa6i7eA=V
z3(FT@X{mux*lZ@#p}7ePM^>)cO}S0(7S1)N5$p_(ahOoPklHA-lIF*V8nKDhZvV{c
z=lfjFmicqCDwH-2t5>U@Aq5Mp8#|=ufHH~RuSPQ4$5_zM28x-<n#FcA4MQ8T+>Tz?
z4k;%0g*P88x|M~!DU9uW!A=&l=@E}V0|zF%vLt)HBw*llS#v1g`r!4zSh$r%xc#I*
zOas02^o`m39A1hqQng+WEDgCq8|d1A?;HU5j%k!@`+7r;zo0rvOb00Gm2b|?%`G<?
zAOyPqjeva^y`crznlMon3^L8pUY`d_Qohr?OJLD$^#Nz0&osJUDl00Q$hbKZrZiS_
zHC=CZa*N&nEUyf$47L)dAg2JcsW_5`y^tMh+sJANJ-s}Pv-;Gta20&Do?{@j$B>oh
z_(o4&LqsKQC**ib0&R8v6;*}vw`i$CrjmB`#9^UrzbFI<L@!1BKC2^B^d33J*Rr|+
zC-T#8bMuu+?<4JkapoJuPb`BizAdNqB5r>{$C-50J~q%jn5P&XohBb(hmJuIV9P#*
zxkNb0i{YxOfhtQHW~?w61T+o~jkp+~;>pUORc5}?-I)s5z6qpP_35V4{pO=8tW(l`
zM@}|ljP71SPFA+=wh-RO8&GA+R8L#&GL4sII^rrkuOnlnYr%fh&`>XDd9+ao>7fsJ
zX@Xa=w@ULBIi$*}Zks;54+ZGSiRDpGy24hLeAp0i@wXr9yHQA8m^K4@k%Y<c<*cbc
zSN8*kg82|Mjaj?&bS(koUzG46A713n+Q$GoBLJb5OM*f&gN=dJrvz{JETejr!{IzZ
zzHSSW#>bD4p%Q*=MMZzHa1w#_)B2+(QQdaQjBoQ%9;Ez~#C#bF@O)wN#yIW4eZdik
zNr?%Gd3*Vh_)DI|gMDZWiR1Q|M(={E7bdh(s5R|jZ>~{8xUccKqf>G$&4B7oGaU`c
z&$K1pnki2Bnk*d2B}SrmV<omEf@VCJZEw-+b;eW>o|(Vt^6$`@JnYF^<&>CA$>A^B
zow~NtsigYy>Sg|GKjYG4o~CrNa~<Q6u+oL%Fhs6K9sZ;@(3xU{tOq^n>-}}#GXF*A
z06f9=ztlDf9OU>!$r1oy&rBrm1fX2n3kWA?)_@`fC1uAweHreaTA^BHUPFV%p)^iZ
zSXfx+uWbVcTmgseVQQHeXz08gyOt+WpN1pa(Kn_;0oO<|Y|oEVCThfpUMW_#3+etR
zv4>ZOYohm}(QYHE{f3AL?VUjg36R?A3Pz*y+6sIKk6?v<curhf^ac}q+YBo8FO6eU
z^XL*7Lz|C3a*+xa=c|T4JeMUDvg_pd0ty;@gO~j6^b}Wjfgy8>RDCJkvecFV8fX|X
z$fa3<AD!#8MJja2o}-1eKRi7DO|@mvdeV`R=i&mIbHBfvnm@QNSnBS0Xy%yv<o*;U
zfXpnQ169Bhb&jI#Y3J|}71=B&$9P3AngQeHeQWMqx$%(W-XysMl1_mz{Z0wXm=*)#
z_qV!Y@AMf-Em<=?54N!<cV<bjM$8NLzt%R*9_pK#X!IV^VAj?>O!Ku%_9eVEt121P
zn@vbgAW7CqNYWUQPgSrw<+BoSJVmfPAZMCQgtd`2`^w`bevkYyvv{7|W8HyCWOa{d
zXfuU(bb8$9*GQ*fSkRES^yK)|R5K0g4)Hme_gE|<u?^)K5wfyOEB6n}fF;d^1GAnk
z^>tkEywK!%hs2ACP`pj)9NBQWX>Wm|V|paPU>%~Z5-5wRP_uXJL%;@H90^0a16tjn
z9*F=lM+)HJIG;kew)ny)NDlxxFvudIaUIAYsk#GsIH1;q0u}fclzDNHg9!hqZm~Fy
zs%L?6f)3proF8yRXS2~<?2J&G^7U;bmep#U-zdm@ueyz!3X+jb9^Y1!#JlUc)m(Az
zeiO%`>=9jGGp;JDUVb(@U2Y(zes?xG`n_!bEVtZIf{wmULR=Kz+r_21EfI|YO{3Q2
z@Rzc?M9C{V-IaM5H<ES(Ie`wvczOrKBc7%V7_UK6+B`X+6kJch#vci4PJ40;Soda3
zMwaj+^dvqD{RY)_?<9dUdFfsfhi54v<l(lXRCHD;EnG>7FITsLr1<gPkygpeb;7JU
zN<#~E8v7uC^U)9A=uWLBZ*O{idwuVAUS8!x@W#f6bV7w&z!gq!sCH)qQMbpF*L#o3
z{aOY>HJq;B6_)0slqNo@_nX<E5cryk2Q8{J_mu*l{x)Uk&+pl?td=HUWagu#BaU-n
zyi*nhx5H|VdCm#x>-F5JfV2un97S8H)Tn<ylB5NXQ54f~zkG8|ffb8oy1%F~>#O~J
z`{uZs?y6#PEQL`Cnk02g9*XXB&rF%F<8Q$^4Q5?3$x&+ov9rY$Rh;x8$bC!~Ei!b>
zAG?Z!yv;Lr+=mTG;Wn<z$d$88R4|}?2ro$Av51pCX6SZh9NNa$%&X~~VmYC(!RaMg
z^5<(h9Fz^ze?w?y>K#K~?#pQzBaJMkB7Y%5<gS%<NmNSCOU+A5_g)8!a~QgB_4GIZ
zPPy&gIz-$R*=L|yB*01vKL-~<3WG5F09A5%?hEWkaexn7I+&|o<2UNZ|6=x*@Y)U!
z$>3{mVL`zUrLzCS-CIW06(w7v$O#gHySoIJV8Pu2gb+M<aCZn!aJS&@?(P=c-46tJ
zcl$Q!+ugVC{oZ(g-*_2}!GWC3KD%m3Rn1v*{kYnvL^cf}JtBvlJ}K#}{(e-<-dHRv
zClHcdWN}0XDg=zm>p`aZMgLPs+aDBCU*AzZ3uNx6542}p!>YSlcM7G__BBnH$G)J>
z=UpR#CgCdtY1$8hdrGN4!*w8SF0X=5!hUdUTSOLp-&@<SW1?T>dn<lSxQbE$jtiu_
z=kocTeijD3(i3emsrEPA!H0B2LPRi5CRbdV-W6w?{{SB;*bLf*w8Tb5czq^J$fyQ@
zrTDqd#>S@AHTik8w`Z;C<J6=qpx{(gFG=oscfK``Z*smlkQF1J`q2+cn!31aHMQfg
znFn@kA8!eB<(rG~?<W0&l51=`A*E;k7Q`@yymqJuitA2X;awoavsHO@`!pLb2l<99
zlyl!+w7eZtFr$ZF$GC4rcs6<rKVS5QDt=Pa2U$GFzTDZn?na5zeu?T)ciD;;F5lo8
zD7Y|w1$*IdE{jk!0`{AqHRMfX)MfS6xmxU4Z#3S1@4XU)x^NCDmXi#B78>JAO-_vs
z%RfalknuKI*xwyDR@0)Zx41DW9M>3g<|Ar;qPE;iZ6WGIh)DJuH`9)YpKWuNs>>D4
z*Qtc4_2Wtt3x8zfD^sKRwv%x{?<j@!vEuYL$L_`T-nqgHI;x5m%^D5ZWvIOkYJn9O
zh7v$)prD~q2SQPdDb0|H`QO>Cpa1qz9Xz&NX~M+D7I^~NvjJA%hOqRXINI$i_yVw+
z$T1rDB<^tpfU<wCDYW{xm$emYF%Inyo)4bq<d}OyQ?fCekQ@`y^A+Ts?$PHZS!<Ee
zQPn91nsC?DQolu3(!$VeX}s*Yyd0iB?T-yd6{|(ky5u3fTUOS%Z&n`HV?C*2r%m%K
zQsZ*UR0~nJ(07#Cp{zMR`e_-^b$8R|x$}$A>}dQWy~BLR_o)nQC5%op>Z@JiOF}Uo
zQHXA(z!NG}#UF;(H=?X+VLam|)FBJhYoT-cs*9(Et@(NrRk_^SL^OO}$Yk?#`*|Lm
zA(V~zjBZR*+`At`7ETJYkNFe%=s76Ng;v*(@})oT+~!O#H6<BNedU-w;n%;H8~h2Z
z(G|cNjmY!iLn!e2JqVD$$S?$y(LyXDS=rbo#Fdn0?ynA_c9-hQ55p)B0f`D7pnpg*
zyXEmIOz#w4-_p9><0&VUDFvMzU2H0=x_e4uO=9Wb_XCy%(_)#eGNG2kO=L6b8$Q=v
zK3a5*MK`<erA?y3Ml46<qmmJ(8ZV8Fxo_wMl4sfra{!W0qBX#%F;%}Co<hF$P{J<z
zc2iXJr%NCD5$aU-`}O!jWb>`0??|w9{k}OSRdBJMBoK8J>_Ss=x1v|AT|Henv@5U+
zKI$+~It=*g!y9WOPlvwgu4I|~<z_8JX@q}((itv~Q~$03lL?03s9$eQl1bpw!Qjbn
z;p!hDTy&+n#!bKR-O<_iIujX-qcbVXaK}FSBZgNAp?AVSy^I7}hz(e)ze(s!7bpOE
zhtTi^5VzrDV)|Jd=Tx$tR_J!ui1+mLyu)P$(dk$$))Z!BK*;HH`6@splNQ!i)oi)5
zX=*u5$Tg}y?QU2Q%bvJqm;CZ;x0f-K#y(8+thy)j1M;-$D7`Sc50&MQ_F=zMT2s!a
zln@bBiRsA678eW~@;nv>U?9s>(2mSa_O~BLsEg&~_Sv~v$R=tA!n9#UK{_$Xxv+6*
zh3pn|xkyhx`HkjMOx*KsjwZ1WU^Z;NHeB3>8^FdD7JW-G?#VL_)8a3l!Y%Jh`@^TY
zz3<OIg>oG#2FmcLEFtm0)G;_|{f%uw8V(8Mh95(?9}u~}D4l_qI9C%B-%!%0OPn<$
zMU9;hE{25lq^^8C0JJLrg)oc`6}ZR<0Jd-@g8cN9%5F9bP~QOMxWOUWdxrP#_kbQY
z9~_Q@VSt^1je$`E>~&pT!plC#g#2z?m(^-4Cv82JlrL9Tp8F^I9xl&j2il0pNPT3S
z`KEH6Pi9wYslQA34+@5j>Jxcil#xY`SKA#6XEf51P0+Z>39b15tb$iBu?X7XQQ=R|
z7tW@Dl-xNQ`$(g~`GqXdH0S8+?(OKeZ{$707DFQ&y-bXM_*6!n`A+fIo=Q)I$a(|%
zVDDjneNF$0kdx^BcQz#|9fuBC<jb6*{~?YfAR^k`(N<N|oHJh}_X0Ekz0QD~1>ZB&
zm=t)u0k3nD{czGwOec`eZ3puM$7Z5#5l6t|5zvLGxW;VJNO(t2{P5b>N9Lszb(+m+
zL1~XweZ_SVCIT^u&9l5)DY28$olCW}xmy@x5c&y1r0{~ye^h8rZTQV6lq0uklVsuM
z4i651s4WGIN6x;~Rw|&pf(nO-C@Uvt8SgjXj!F!+WWoCHNC%)obPWCf7eOH{DG~;%
zk&XKq>ZX{!g~Lo3*X7qTrU>{$k}MR`tG10`!au-7-d}?81@;llnr223{i+caxZ*z|
z3)6h2i&6ndLt})~b~`lGQk-MV%zUGHon2%gJhI~#fN{0i`j`9#Z+O!L^>U2hbV^eb
z6^O{a`1-#Nsc=(%#7y+?h;s@}p5meEZRmB0Hz2zCak_F^h8@{T>OBPLGr4h3-~N@r
za>n(}p&3K4JHj1cR#9p3FJyUdoL4)8X`!i$uSZJ@zzA(!Mc=L)fWqmop!^mhH_j3y
zVm7G`PGCSiY&TTT0b3h|H7caDGG)_ze|Vesdwtm4Z@Gt~p`pLV^?p83<>y=`B&8G%
zb9e|FI$$Yd1Qr%fn4s~SZaP8dbx9`Bau|s@od=HV;lL~YHiWc1eP3&M0z-cj_*&j>
z(dPwbC>*efw*3XT*6cu{2WcgPbJuRtv-IEa#wYUa<CUL+w;~J?ITuQf{B<X#<LIuM
zvyBN$rsVWFLMxTuEyUJKZG{iw{KAVd?Qnv|Dw=~9r~Mg~5VbmUJ4DziX<(=8f;x$&
zP{JCPINpX|F<$Wx{6PS~AC_N<4@V+`(7<{s*}(@AjWAhCTkOm64s#4Vt}<BCx4@e>
z=IADh+KSsY$!EbIH&6J$s!uWcX6wx$e5eeYiwS5*Y<2C*iz}VmIxkm>)9AaZAsz+n
zpGTF2pEbSa!%JQ=n1#iy1}QZ&PSD%9M^|gjx+zZnaR7!058{0|tOnF{AR!^2pPy~T
zyT-=kM=Nkl95{4fjnQ7ghg(+f_A>79V*y^;vuF}ge^Fxo+We+AviG!nWSd>)QaP}>
zp}(0t*mh1Sm5xultP@u`PEku!7pe3_y7KZaJKB{Rm5gfcEal00AL^m|I(aKWl5>P=
zK9_6L#pYMP!$+(vX**Za!;Z}JL$fW#{KSF%ACT%PDJtJjo>wUnGt?ld(bg5q%*L~o
z<f|~XJ$cVOR#i8eshcNgEYO}3Y&+C!Iqa>3d^PCfGUyKgVvtzwd&%?i26)W6S1Vqr
zy>5KBmN=)FSyDvOBoxd&Kk2P39<0NwuZ_7qMI|I)e|$DFru_@A0zJwd@IiMqJRxm<
z=+4q{clTqolQ>DG4d+?RCIK~N)o8m~^FcF>mkpnk5^OBD61y#xy2e{oFK`j;b%U$w
z^8Z-DI`XYd@bAW5S}d?>t3QyXbf6fj?`UaMm<59lg8L>Jwg*0a6-DUQF4}%ttODuw
zsv6VgXF<K$-XW}28eX_ViwL6()D2C#p$mhm>X^=QtmBK<Y%g_!#>86(+-9>tJ_IY(
z;RJUpguAn|1N-L98yJ{B@2D$oy|><>Sijkz_s{{accs1Z8@wb?ByYz`E9?%&V7~d+
z4%za1x3O!e?X&K$lOLgZ-T&T!!DzPXQ9Qz`Q`eaXJCO_A6s{_td?ZId8?$p96&kV5
zcJXDlg8>=M!S^S~hae-S{Z2gbuhxDyeUf?NkI-KMUyl;_F34V{IewAGmx0K;TxE1*
zWJGc!G`q60vak?-=kn72hZhqj{SYv}BE8~Kyz-q)4ETL<d0Qo2eT^nJ#(y$Qmvc>?
zm3IC-jGu8|PmCq**Wo)>M&8eGm7N*HSM}i@K5D93F{`L^Xv0^>Ly~vBY+kp<D~SZ9
z2mzA@_p2K9tLK~{AZfJVef@cVqG7q@{YmG`fbQi`pmRqZJqk+4S-brm0oqN{v%d(H
zU1lp4>1Xr_<{Ncv!)L@{MRw=>Cg?94*?|e*!fnD{ZYh6J+yscPxE>UODth)?hn<?N
zX?tlz-;oNT!A#pvSV|bu6=i2Qu4!VdN|+(Eu8|va(X3!Z87h^u4Z@S&Uv@f(6l=V%
zaEAU+(kq<N!3HM?tzTM*{_D-L=G7pZ&R*S@>xV1RzH$R>(n((Re6{O9?r^dWr)~ub
zHDth0L$7qFckK9oiD4UPf?W1X1Z%~iW@HTi7SHphqta1dPyD|s@A3glSvj$uW8~|z
z{Kr>^s25bi3FP0=4!GoBUtaP6XmcH;Ye@aS@fQGvL;CkS|9J_(A1{MCLhl}y`#aV+
zQE3?XR~IMIlE*2TBVU4DraG#aUKj0Gtk53najJ7KaN!@<dS$~+r<ZE*zf>0m+kVBt
zAmH6@!jGP0B~ao%_?K=Vz*K+deSJ@A2>aK9u5g>jVDf!zO;dB@`F8!{o69i1f4vtV
zF8uf>o4^^*yQ!%uB_*Yzq5|mihXH|{lkQf{nS9b~SLpZ@a$3IwN%TLBatQ2kbz=ce
zz%AUu1=Z9R1YYjO08QRYUVi>(Z&;#JZV=3|we62N^t--T@1VlHSEZDHnW9DpC~zK;
z>AkY|z+@G6J8}x`yN)I%Cc3(rR#)Kp)}uu>Iu3pX^LIz{m17yYy>;=k|I!x334!42
z=*2@;2jIXpM<_#<F%J(9OU@t|8YrPo(ip4O>cg*l3r&kXu^&7=J$jYQ|E<kxoDT6~
zZ=8-Q1ALNO4DZ83^IUI0L-@;=FK$H-L=y{gsT-BIY%}E&@36xDNthEs&48W%+%2RJ
zJo~ad$;XfPeFD!cSe^UxmHI%<b=eAqp&<bRtF23YoPmKsYEKi8P?E-dA#KJ%DgT$b
z%+c4th;<96NWc&+N9(vB10<EMXIAl>zy|r!%JeDZRNFg5C8b6Coc6w%40$&H<$ggZ
zaeyIVo->j0D)0zHGQPOj<Z`hM2>pq`L=bRC%jrOe4!l7}Isx0QXNd%4!`>)Bn0W(=
z1OIisPCCR6#L`Z8Gw?IN#9Dt8IiRe^ZMXeNL17|GECeWdyCZpf^DIx#7t}I-D9OH#
zHu*OwS@FuB;U@;9bY43p0kxJd?to@3fSjnre`-h-yjgXx<>;ZLGGR&tg2#VGiVr|4
zcyzJ;$`wi{kBp1UyAO5nkBNzyp+pCoPfH`jL)#e{Gi98=e{Clvzen2U@316B$NR@%
z7lcX^^|JHgGpRAA1MGwV_uaq%69eNAz+^srz_9b`?(Wtcr%4`{&u~>1c-&<gi~g6H
zC^CR~Plxde{6u;ML2y8(eRSB*k&0P+zPh*|$ACsNHaGWD5)$f!sR^U{_ee?vs%23U
z0d>G{8Ui4&e0txi&cim??Tj8*dX+Acj4v<OI2=ivdreO+;-x2ius>v<sI=i2WKI6}
zL>LCbtYq|ccHq7d=mmv^cYrh?Ahq3@2?!qo!ZxQiB>wvz9><x0Z$hLfse`XAmw-uo
zfM`G(_ODsU%nHfqW3V}q`C9z9B&h&8uNB&jAJ#g50_7Y_W*^x_lF!zgU3e=rUz{&1
z!hDARo5AS-gO>{G0<zhFC|yBu@suMmlI{`Z)G_7wdqyoYL3;xI=~`Z(`Tf6KWE=qT
z#+t{=8F++_Ik-!pP2Pc<jEszrPg9e1-4QC${T>#imC!O({6bQnEc!RD`a9=&13UZ#
z$a(vX|3Q5lC6A1Zv<5`)ju)z7Lv#>vm?6xBc*+@O-3mb;#YIOOb~0PKVaH}?zh4dq
zhlV#!<EaAG+<&Yd9r3TB>G^K;3GleH@b)G=C1CxsW_Zw>fXiK;juqt!_kWG22nxY5
ze+eY~uzx+kKSvr`!&hLVh?frC`rqp=Z#3Z8|BqiKm?5DqoBfZ^P9VMZUFkVI%b}pE
zffbyI`Cw_FnKg+{J{6NSX?<<~)(`Vd@;OH)HW0R^tz!S2PsfUhLrYD<i;2cdHAIPF
z9DCP>AKy1Js_4df*l~8Ip><)|;7;(~YlR>54~TF16U3yG(L}u^N7q48Uq0yZkba+;
z+2AlEwwSlx)6Qum^Vs3`6tXbLR4YIMH(SCW)Ykc_tT6J#pN-44uep-NYNNLWadd5C
z$l*sHK+8bQfjIuGriP1&nQO!hAkcU~iIJGNJij896<7oT$<bd>q@<)kU@V#b(V+;K
zP>yM)H_CEya%N_9!MQm(yN6Lv9|1;X4g~$>#YMGt!s|xD8}&a3U?~5K0LF{_KL}uC
zG@!dPF5F?KZkLm2>=t}D92R%*-ne%=C&5G7S~V2y<uVvQJlBS@_O1!S(%ATR^`;G*
z5a`#r+=V4_CZVDdH^#!mw3x5Z1!^$>02+Lf{(PDL^l+0s3`l!=00X?}QAYMvMg{2P
zisQXHA7U~xGI}|(^3-Uu-_wua;{aCEp+$Zm69AfBN!x*@KTkktjUGXAG{WOD8$jiA
z6b%3L1l0wTz7*!C(K0ZI{TbysN#S*=Dvjn`b=Fr>!aQF6aZoDHd*)lJ_o~}@`Wb5Q
zOlI#O6cwYKNjRgkaRl?R)W}bS4i@Rf*P-{oTOR(_`$UCngGn9vZNPT(dZ>!<%z%?f
zrcPI=muSeElb@U3X$ctL(B0-Fw;W+jHko6lh7bXp@o^p5lji5y1Ng<`cQ63v*^L49
zwBvC=SdP59rG=N3^<3It)<rotnmXOh7U)EkY`>h80UpSGJJHC;$EW5h9uWV(3kBi>
zW{YQoe1#=It@i8|IMU$q>lYQ3{Cu3hm31sgc-L#uu^d<%e+hSK<t8_?4qOv?79vme
z&aX0KISu*2v~O)xQg|)*P~V9(|1W+V15EY=F7Ar;=s)Oj=8^5jLinTC=@G8qw(z-i
z4_3TJ#GQexq~UC<5*XzZv`l7;mq8RfvTY(l@Z?7Zg!V#CZkiAw<8O9PPfwk|?ka&H
z#F!?_eh~hg4Rv)`M!%4$PcuaVaw<}q9S*Q?3b6C)D7rF%Ase=9a8~Q_bTtP6#$y66
zE$yB>2=>I>w%?DJ8;uD~aoe<gznC5A{tbc-(Y<g)AkUuE<3#`8h<JPVH9I+smw}-p
zp}}HXuS7ibU7rq+W9o{+SQDkUK<Ri{?!8i(K)q_N#n<Q2S+)R2kLSuem%NC6OMzJ2
z&s}Vj&9tr=-e*FP+UU%=*LCJ}-a17&sAzSoi1UV#uUUBWD!L0N3L9Cv!|?EDVu|J3
z^>=l;XWTf3Gs0{?Z3^2`8_&Ac(s$)rm!Q7ZwtvV$ICq7fcW~^h`pKW1ty1kmnE|k9
zJTFE#C)sZu1fFm8rMl1P;2WfniFj{!vm=rk1w9{@z)6sa0-itzY>PT%s9G~n!gU4Y
zSUk@{v@tLewq<rpb~XoM5U}V`*hn(p15Wad2Ud4SIKj}Mhq)pgjkt>-e1~#Yd=476
zlEp%4vNO|Btebr;gLlK9;}T5Pa`V_Lc}Y<4JoD3>HomE*6f)T9>oyLYg@}<ZDyMu-
zbu@y?`(w1-k$4)Mu;4AAg}u4ec*dl{<~mIo%k1Iti%+uAhov2_2tr`Zd;#?;V+kGL
z;Her6znX_m8|TV$&7jVFj^rSB;Ke{st2yiJPLn6}bO{>xIKv+*9#=bD%h<4bZNIs3
z^yR-fJt%M2($==(zQ)DHRh4+lsJ*<{V3S=!Z=g2J3VY$~bh2uZXcbot?9;z~-nAC1
zl=o6n;fp}%H@?61hzeS0EE?XTygpijl@j>gA8A(Bn5USJFrgf;f}j3MNuYu{J<j5R
z^We}pf7|7}_beYetEeVwYMQQQI2)X5{n!?*pCqPNqpvoh`^X!|&dWBriQ<2DY9ca;
zFMxs<!q%x1M6UGJfSo?7tyiIakoQ*5P`w9|zuqi>R;L5h<Dz`s=$T6TV?DV`dj|&D
zxaQu{t29a*xedR}<!+`~_xcTNmuhM54xY?qjo!`%98q6A8}##a#iRB1dqCeHG%#f7
zwhUsm+6eiwXsuUI1z0OT?^e!EX9)cih0u4jEZ1tKrKLSTKhJ@XR_~=Ak{&HqE>*7|
z#ZW4E>G-0t*aalArw3VAbf_IXPRHNc-0pyd6k!j^q1E~9kLUA6`l5149?%U;fn%wg
zXtwKFY>)u(-PQ;}B=)6_qSNJ>j{wPP-Vq#_Kb<R$qxfVx;%ak?(dbKzFQ?-$Q~{p|
zMu_*R`b>szV<NbRP<-0k#cqKG8`y7T(9VK>y5AwWHHm5z&LXR%tk#C#VDOiQiN|9^
zy}43hF7{y4b6)0Z2M|AlZeYH)zr`?jz1cUL&Xssv{XC0Dz1|F^I-A-hsRM6JpB&2F
zv8Vv(eUP}dZ}f(B+YUx%M@F^ZjaYro07gJV50&_MM*>l(W>k$lH%FMDS)l4Pyb?XT
zNOo6h$cH5V<V9sWfOIsq8co@J4se*7PxuE^ViL7owtfK%KXjt%Tm1c}o*;Bdu;Y?N
zgupTGfwgh-008QFc|f75n`5caSNkXgL5hVN+x8gB4<zLtZBK4AF3RZVp{6|<&sxt@
z5t(DoS$s0n#e9t9qT>t?Hvdr4dERTf0kPhpfNqIs#_{fFl&LH|B;zTfS@l9QBoE><
zP-L`TXr?&vSNm4kDG<JPRgvOs^=M@jIN|}M<Dn&h9jq5*3ff7*m>rRBfggG&6@h|;
zDJw%qZhn3QA&=w!bRi%l*Sh$4U0mLVmIs8m&PTO#-#cmH#MmH1_nH?iV$2btFWDTQ
zel=%iX2!*M0MWk<c8C~VZc$M*0gIpk7B;r$^W9FIpAsa+8Y0lk#`>#wmcQ%u!B0@U
z?tiIu_8wL}Vj}FpfotFT`rnI%R<a<@s{6g~44jG+G`48V&!McESeqTBMoXaeMA92E
z`iWmM{Ik%Ms$%dm!}siUq#yrC&G0x=8`LbVUn+a7hFS@a;M#X3o-RLYPbGB*fp2;5
zZ^WCkHx8lN=)5vDGj%G@*{(r8c}f}U8-9Yn{|rY%-<YVYCpqh#^#f@{jo*x7bcesV
zA-6J9<@SXLG9N{~W#bkWeU(9N!t<~MkxNgBwY4?#hths^%8il1-S(chy7TE$zXFWM
zhKIk#|06FMg44OKLhE2OyBx&tI-gFX^D1w7U@Q=Nj;qD=-GhQ=Y=)oO{zO#GIcsn;
znTmYAVomKXZ>-_Ybpg^JTiD$r9$gM!bb7-)-VGo6z5y1AU>phh^0a!4zu0zdLd?Eq
zSJ(XWWe>W%jtoU(NXBkK0Zq<2RvHj#{K#1m6&CiPRs8ZLYtk?X0GnI^&9eSSAeb>&
zDapynaXo3p<{sZPj0vb6lS}6(#3ye(?Lw#;h=J2_{*~@=Z?e}9C>795xtF(IFRpjX
zdb=cCw>TcDTTm{3Se)dT0|+Tjt1c26Ua#q+JhhIQa>c~`jNy)w9wxxGO>(I_WJxSq
zz#LF!(ci{j2+$8nICJN!qrYizi*SA2%MS@JVv)b7^BB}y$CEZ4`rob}R!t22<Y(|=
zdAKQSKJG#iU#ho)MJiD9<s)x$1|;v_(m5{py(ns$Vq5b&9wuz+cU90<SS)cQN)_AE
zqXRwpy>gO)*1e^ZlV66QqNm!A1o4_#q?%QS?|SjA+yK#Y7N`2Wyx!TL<2AcU>MiPV
zhr$whvdL5tuc2N6`d*v+!?S?v2_)g1P3}Q7C`gcu%}bOd0e+i+LLsL_RE$m`OO$eG
zA&$3dXVq!T<ziK%n%AuB%K4Z+q9m%1D1t$z%662Sb%#I*4L4Ns9fV}$iJ5toD({Yc
zHl#gg)5HUPiQ(4bRXWtX=h5ePyH*4YDj*E+TOpErLd7l3dE2BV|Ew4G-;o6q$c7N`
z*~{Luiney0K}Mxm{%;{y@H2&3Z*BD6*lCQa-noZja{mM~pjzV2fpAKKY{VdpNIQTC
z_GLicqY7B4068w(Gb?v@K17{}3O)K<=oXx%-rHX)T6chKB-Dqz{rdJN25FtljBh*m
z4VBGt&eKTOGT-U5#0Ad#$<wsjjuU2%S!zX5KZ7tJ#RUJ`H*d=b!4`C#8-!jQ9JHYs
zp_j+87y4Qt(Cj(DbfACku-065`t6YbgH~DuU4Ljh6N#derK=ma%ozRyh#Z(S>W1SU
zCnSg+Bqq^db&@hI>hPUNWWQFNc)mR3>3{hWEoCPB-|qHb_x4s5%BY^EQJ&p<Pkp}%
zoUN42E>``c8<BJT92h87cN9qVH!Du*xRCeMAe@^u-ERNHb4SWheC7|BR0N+6joF?7
zg<mXsRS4==5&ut_Ji2hqy<^9Vj=wq{xv`B^uq{g9XrO|<$TI%hH^CZGlsQmBhO*uc
zz117plJ7w3a(Ht&%r<5|U(p$xK%(mTa^uO=q}{N~<Z*^D@dr&%21<4!O;yo2T59}o
zD_)y}yhAdcQPZ?)`52!UvKMIjLLlv9<A#9jg`9WB1}M67!&`F9JR8flLk!2X3=03#
z){tTuJg=W&9vsp`H($00I2DkRKSYySTF(x{tuD1>-_YSYV#X(8GYrMGez-mof{EIG
zrXZ8sfM@}>T_8wLLM4C~{va|+*^i|pzI13T9;c)JrT?h!SpEO`ZnxSmSK5`H{>#rp
z?T-jd?9|i}$G0QH!;e5z*ma)-h&K)2?&`?i?@nYdEG$sTKoObQH;$Xbdx|BLL4Xoy
z(KC}!w?|XWU`l|($bND8VZ-bfgBX`7RrJ3Go`-uUg&&=+78w^CH(spb;C^-7-Hb2K
zxrj)?SM}0Qy4MJOkC;(cRhE^Lms3_bI$_?m2JimhjGu2_xN3VoEhX`AYQTmb!#FU&
zzQI|WQU;I~l~n8wFW)N`1nHniev(Xy<}vuZpV8x+14t$PA$OHAz2^A{Q_ab$$SQ%1
zbF@pdkQBr2iga=Yh$yUgY{mwuL5mxFzn0xqwE3gDS9$LcfSeL{V9@>1h7+&FseF|)
zyxC+fGnEJFh`Ijj{DF+TG%>f%cR5oz>GU?(2*QGr@@4I6@C0kowYY-#_334(A_D`l
zO57qsBWpd$`_7xA`==^*qocR7bWp*9(<FdHRST#%VFnI5zTzMqdaye!+rTPhe7a-u
zyc_Bj2RpS9zuflqDm7>-l<W?Lwatr(NJyQmw&G`-DWJY=2t1Pys)|$DVs3rw2Vpv0
zC<X8@^i#nf?}?@L^oSBTp{6y5)9jGtf?u9*@Hs6%U@hih`+5Q*lxT04FieF}cUR%8
zZ^hs~rp3l$cn~)pFSTlUuvjp`H$%35QB*vNwoKn1I=Fn?yJj_$pKWVc_k-?Z^sO2@
zPIjMaNPb%#plPhkeDHOsaE_zB?qVECvEONViF!r1Djej?9Sw5Uu?3%mr*1~BUna5*
zAuIDYTIf$DVoCfm<U^(DC-|`w%kw~~b<5Xee%s<y*V<a9ms*2tYc+nG#4?A4*kmnk
zE?@uDaovx;=6BcK#{NV2&+j~4>ou^sruOn0??PqnOiftFCTR@y&b^06^WlI<AM%1y
zjuCR|Q<#E^t-o!X8(GjF^50BWZiS7xcW%1&M`4N3c9!@YO__}gR2@zcG);ECV?9>g
zQ9n<99kE55b)kC?Zw~tmLm_>-n^IW$tf{492$uZb1hV52-k{-D8IjuKarcUltx4g&
z&=m_RAp^2Tvx@+!AHTf^leR<L7;?V}kOv8VL)YOP2efvtJfG$~xf%JY%I|U!(prVR
zm|8C<kwBeA#l>_C45=SX(1I5L&G86G_(DIdqz2_28ySzY-`F<X9*32E9`{q}w(l!N
z`T;o~&jSr`5^(s*`PLAjlB%|hAd_2k`{TKc>1%#ADZ^xQ#H>Of610MWz1nO%L3Zrp
z!yxeTco7cCUJPe11N!{_w7J8<fC_?Ws0W$&1uCGM*Au0p?i2*c6GB(sGFe@ufu*Hw
z-&&#FmVL-m#Ys+S=QiqG!xECe@|0XoEMRvXT9Q;=(dFSpyy(7r+X+bE1{ffo#Eiq5
zUZxLunzdbV)PCsvP9PYzD?nCQ&(ziO<UTh+RkHAtTK>?iVCWz|3CvXLRIU||JSu+@
za~pC+*Y(ll1}7!e`ewR0=7FL<#bm+7*l43LMx^>}CC0pialD#Nr0dUXRYa~!k5*U8
zP@-LOOoF@wNb;Bl&*@u@fH1wXxN4)D=^5a}1U+YUaUs*i@##x^|8QrwgZuu#2}Hw0
zc6*Luu5s&*M?&Thym_m&T79fP^vYn>h~NgJF|7oM9O`_1ChMu&WbKv5U=v&=*KSDz
zv<uiBgoiD+O_k)?1Y22WGG=zCeZ&pRPrDAI2iAX3z=eHzMY2|wE*s_%2u&9x$P!sQ
z-yA-P$8mqv^xRy_?2Rc2X~)m2*uSkz${uASkq@k4c7vmVZ1Xw-;t3BR^@#yj8HC({
zvEK&2g@ba*)O=8k)N*FW(<G97|1FjY9Ixq^h@#UgGDQc%amP?=35S;-xsq|*Ex~0o
z<h@<{IhC)S<6UXs0>m#{2(1$afL0ja&9dD);WcAM3$he;N_%fwI|t^u_crx0d_H-Y
z-p+zv7gPk0w^hF(QLv+xR8%gSwY9XK0g-6Cfkc}X*te#Y`PMpJCsc+Qb@lDpLiNLP
z1cy^m#{x|+3l3v&E2Z=;oBJ$t-zkhf5%5Np(^u`^)U_k1sHwDh+^pLT!;)Qggu)8C
z4rf#bT&F%T5zm|rC2QG2T=g3Wctga`#C<s^2>x^pt}k2Ca*b_d4t@q#?;uOcC8qE(
zm&)sP7b3hZ=$AyZs~#q<gt#8+b+))DUP4aeS=?R7&VORy=x^;@j6ZHiq4<)K!1_HH
zWldHIpB!G!qkTF#;NDV@%j13;Typ<*!zht3^|WF55PZT_e?<QNOX#Rl0{goqXJ2j2
zy1`Zu&DjIb>W~!v<JoaUl3e;!=nBshKhkfVuGSydtP<uE)tt-49c1@?8~LBL=9Vub
z@RifdxsNQfDPg?#T&AoDJkb}>N2sp}S6~r|W<0;1_^ztHwMIH$NR!VsI1M15uq#`v
zcOtGHwn=<KR*H`yOpda6t5^b)_Zb~kToB$GdEJ-eSk#tkzACmuC7xdGy!FKW1lSEZ
zdL}K+^Uvl=0fO2`N}?8P05V{xU6%ZA_UrEYU7<Mi@Re}Z1|`jh68w-YXxLF)bUnDR
zbmrw>OySo0UHnUy-S5magk*F~>xH&~vwTe8>9*;3f`HmZTETQdW5W@AwNVse5tI0Y
z|3yqBUF<UDq@O$&uTNqL6^1vCFvJ$a=(S?L+{n-ndL;lRolh&u2RZZtN|+<+%nfTS
zYH0SGI3YcNQqkf0ajJL}LaS~VopfBXRaWtkvNpdSf2@P^3#vavI+w#AKSZW^<Jj5Q
zHTaZC>Ng0g&C5}}o9x9_SblUed~L)$cmX^bOUpH9{h7t*{^u%|s;2kbc;Lny{$~^j
zN+h9z74_Dc3hgS62g;@ORv|FApWPj=^C5|Ltd!`Xi_Rrzd1d11IbGK5-Gjk3^5D${
zItxovrzp*ts@O(h?}$=cIpwjD>>Zv2X^{?`wcd&7C-`L{(5H>EMSO7xsdv)H5AAuw
z`%`q8jk#Ot93>dJ>Dgh17NA?r-n2mds-4-F+{^(Z;B>{n_NGS#djH;c1p08+|8(rl
z8_VBP3-Q8UZ0;|e1Nxj?+IcVHc-{z1?<d(LM%;>(x!bKWQLA#h-^A0XwLf2#S5g8{
z{_kT{9x0kXJL#U`Atc&?E^BeIFH-_fieAM*!wGJh9n-jA{RSFo>h~{8?N3W4Q+c?f
zYO1PmeA{_??@A|@liH{z+C4pEJRZ;b5((K16@{Vp!|zq3MMK`iv;*g25%yeJJ#Sl8
zT-5MnNo`lktXjDrqK(3Fp;pLzD23~J3q@mP)p91Tq3)3kgG>~PmH<tk46$TE!GJZ9
zqQvbp)2QK?kJhC&V0##;l0TM0^%*fOJ#k>Ci^iD|cNO6wx2UOYu-Y4A6n9^r%WY)E
zM#~c?!v<6oJ<8*zcaG=1N5&y0<|3vfHZ#oa!GyZ&MWOayO|PdRbJ9th#6J+e^@j@Q
z*TiZxPkoq1PJaXBF{vTl$Qe`tg7<@$sf*^^Kb%F}=IPq*29q1_8tJ)fctAX;G>F|*
zBDc*#WC_#)-8Un!S2_^aOMb51T2OA=FKHjC$ytKRtyO=Yl%3$=V`=2<%A=1T-_Us&
z4GrMp5<PF&_Uh6@AaXn-5%Lr471_<i&Y~DsefZE3-67aPuMA(|orQpYCg%lq-ay>I
zMeu%H81uLWI>65PRJGv6`+WfvfF-SIp5eh&$!Wy_TZviK6O>@BRuCE}!EU+CW#9P6
zRFVl4NyD?7!4DKjaXo?4;3~8yzd3DMiT`mx^_TcCa|_+9>2nmGpb<k^5vNIGa%SWh
zZx%#`A^>+<>ZdI@i@!F?Y<lN_Ui|hE^$#q8@*pRs8k5bpBflYUP1ER;h+i9|35Y+E
zmoJx##kFN;D)aPtkhI`@wv0c4Vl&m+lILe*OIZTE!Z}d;&z~@>cREYYWDJoBhC^Ks
z4v;t;iJ@8yw~}V)+#IFcMw56#L?xZ&UfOor)-lmw&CXNx=&hT!K3F}Dlv>rKSlF~Q
zJ02n4k6Q2%kTNE*e6W6plSdzS`lQZ)$@v@h!NAp;zYEz}IZma^SEPy$$3nT2emLQ7
zMoV#f$>V0s8RBJ?v#v!;%jvi|?g^%ljCpc%`TZZ%rrBIvAc>n<tuW{yIxeRk0Zvls
zYR5QHb*z{yJL1@*_I#o+TR#ymaP*^QwbmJgr|gI@f`0#Q+uAoy)1i#klQT(OolEj}
z7+I|oG1^m%;w>ggk)Exv)spzf4%S-Q61Z=d7E~o{VmoVHY*C0$$fya8Y1qa6?f1p)
zSs;TwWRFwmlBCQYrj}EmcAbhU#>yB9j$dk27}&@nx-FlzQ{ZKPNuj{uy`hhI9|cO%
zl?dXI$)Wqu^orOlD}_fZWQ%uh68a@60oj)jg!;n(b^2-07tT|^d62>mGStXNlqbf#
ziS1tUw(yLtjRz3vN3j5rPvnoTYVk(Hw5Gpz6|kQF^kVn)kDv!Mmco>!+?3O4A1sit
z`n}A3C#L=|<{i`bqAOA#?8Q!D6{wav;>&XvR_EDn2XcOv)TWVeIo<l%L2)JL=Fxqz
zGc@|NRMraFOvJ8(!8fN;f}rKHn^390u-sNSd1kDbO>s=XZ)o59hNribJpfGe{&;>(
zVSZ?psLOXNBPV9*r($&>kZ3WHrf$(7K52n_+6r!$NhogQJTA}ElWY%j1(=?fzY_*A
zF5}lxRHT|b!76mEn3NyiaQEA{2Xv#VVQ7%m^cis|Cx~FzJ*V5=-s;LfL^%?M+pjm8
zN*C7!wIeIuBa_{-`BUh9`TC=Uv{0pMtqo<(nOghW^`ywYr5&0+0KTzBzYmF#6Rln~
z>(dI*LKy3|!vkI~&0wdzoL+GPkEndFDVfJa&wmSTNVfIakAYGYyV>}xU(Ee-Tm-o@
zcfEC<d4pzY+qD&_RlTeeKSM5=^v3qieX|Se=AQzS4EwR-rm~T(x9yInkdUhDVT_)B
zmtQG=Cj*ouwGOP_dTv2ll3ve=4Pkm4i|8E8mL@p#mlI86OTYvWdowU=Ap^h423?hR
zM|4=uGEC8&!7aW^$K|uW)MmOR{-)@wP;<6d%A>ZU#jgGR>;~O{q}JEg{l`f9mOXeP
z;enwS`CN0RH(qn8XK{l5d?6*)!zqIPekEMisA<Td+~v+C>lX8xF4FNCpW*%^Zt$s?
zm6dA<#M&XEDr2)>zfuLEo72%8_Ty>>b^!Tf)0qWMx}9qzT+YK4ci*`BC@goMppN*#
z5fv+su4Xejq@k<ZMYxq7De>Zw&?j;mACxPmaj6QYF;2K{?o~J5T&G|+_pbVumbzgJ
zNILgsYb!3_J{f{E#c?KvdaL$9^ghDc6_O!RIB`fl!VcT-0jId?ey7tdg?}uouR4@D
zjgLMOWV&Lf6$ks&w>364w8aIEs|wwi<U%i*g@=xv6Ji&^%s+XMYoncjaC%<P7-?G!
zmaS@mkRHET%t7^#S))ng07s5*b0jYy2HJ=T($jFp2q!}yWE_SAsm-<xMjf4*S?SV@
z0zMs7WjF-3P4>hurLW4$daLH(+ap!N_RP-)&lo*Qw{*}@btQ#TPp1tVL&XgjnH89X
z;rRip_!`>zOq)iB8Ch@0v4AGeY*-HHBv5>IfBcG4E}g7yJjJu+QI$olgf)0jUe?w6
z64ci4Ek>n(MUr%G|FZ1(X-}iP#wjcW-Cer`>}FuZOgN%4qk}h<#|Ab|9@U<beyom8
zdJ65G8Mm@<jj2YPbis8&f+Bca_2QDn`x7D@z|QWiD<yhf$X$L*iPkXuAZ1{(a0WA}
z+ArUahmyw?X^zao8MdhhJ!W7P(ZR4%Yx{uO1YQYnU!3qwgWq1nchavLe7XCh%@R%h
zIAhSgy=AzmC2$NwpBognX}nzP+KuJ!>IJ4{&|)<u_|g8t?sBbP-1ZK<wf=k!6M$VO
zX_5DPs(HjP4{{cgZF@Mf<f+~-43!q|6OA{WgywII$Gmd-Gv-#4xpm38zh1oiG!&QA
z{V2f7PuHx14Aw??_QZ`kMo84<fk!C1$8`b4LTF>iscAv1$F89M>b|$URX%F4;3}Eg
zTLa275K!ZqL_YIJE6vzSr&R_+x3Veh2V^{|(9=om{P@f%giyvovKz<og7A;Si$*Z{
z564%sdojZ*Uq&~q5_j!p3;0e*4}pnebhn;761)7qyDEVD_;)5BM$!<oq;-A8gX8BL
zFI@(1_v?2_Df;>HM+JQMFQuCI(>@248p+Xo%$uMDC4v%qs}uFN>I}iOgJXC4_4Tfi
zM_c$7V+yUKd8y4yjU(X>rE|(QBxHvwi`jiK<Y>orX9SretwQCvcWhgcxiUx+NcF3$
zK{#qs163gNZ+E0C0`K2I(fiq44O~m^M=kTx&WCjR=OC`1A_U%&TQBu2Nueldpd@p;
zt?okVH{9@O5C;8I3!vZPFj(b{1d-B}QV%Ha?DTNm5(;peNSqG8_CmX>xgp0aq%+iu
z^<%8I)!D*ZvGYnP6XuJ$diOOJL`47ebRq)tNH*6`&zy}$i)imQ8e@ICmF0~B){rG|
z8qLO(#5#xgRFfl!+T7=NS$4X$ZAMl(ZQUmrze1b0Kb1+>TVyXOMenuzt(=KMK)U^4
z+1n{I-~RK~atv2SMy4_Ao#HSst6Uuq<@}aSyHzH)D2Mo0F5ahgR0rInnDMW)<o=LZ
zGYH-wF52)2dLm%R-<CsX+cR!>>W@2`PGplUopa99B+vv~PCZTPkw0Zicw+EAya6@V
z<K`tLIggse2}8ZSb>dsKA8qbKFN1LXSs?|I&%$mFf7)K)EAd<Q|IMNEHYgBlwoy;d
zdVxrG3hyVFsICf|_^n6p*6kyqGc$FfB3GYiLcH(;`V^YYA?qquUfs}*e^d{}v-{A;
z60!bK;uKHKXJ$nr0eEBUF@LSr@Y-bMHA;`U>ECG5YpF+8ux<OFkR*oL&k4dCP>;{;
zloU?Wc-@n#zuw{dM9xr$qsy-K>?!8Vz|KF-l4)n*t@Z1dvC+O3+eigd9KW+-+wg3n
zUoo9+Hna{aU<Rml@qjruJnpvN5{u6n33fQLFp+zLCtCA-MTNxq({btu%^Ynrxl8Hq
zcZ0H<kzI-T<~KxHWp(hmbNbp?HZQU$8V&Qna4*k!51n-UU(;LjJG7yjm(!&vl86Ih
z@-MUasKTFrERZ)(3G2Nl7I1zny5Pi2WXdzxA%CiKvigL_`<{KEub^4<iEikdONHs`
zT1#f(9uAaw=vR8<x;}EJr=Bo7kn}u}nM#>MG3?RN*;Tyu8z%TXGN7zA&;ymBuO~cN
ztM9HW(eO1zRid|wP|;=5v4B^aVo}(jm95P7!yzIpoND-^=|z%f0ynbNm{nL};Dr$v
zqsVzZ=W_WlX&U(uF{Fgl8a-0SWCvKZN<?e%L2u1wxwZoAnzuq;S>8tT{H^SZ9j9Gv
z|2o`Kw>y{c5Tk&~FPd><uS%a)O%-yF_9e3jlBF|6VJ|+i4({241#9vQ5Z5x?!7VUW
zQ5@jb?#+1a$cg>O-F|5O6rBOMr3EwdR`V=!L&^LMR(N%$5MR_4tK42}(azU?-K-5;
zA$}t4*KA8ad<Ll_>?8{4b@tEFwDoxLflrs)^<l9LuC9JhYXX_Q!VIO_p}O4{;2Z)3
z#i^j1rREuBbm}r|I5wI&Cz|oH{KL?(+d6#$C8|F|bl9yQscIX;vT6J2LC!m!srs;C
zTbdztSXU=0v;C_e<nodW&El!mRv~O$Z-kmUWh=xl(UF|4F5t2uTid&|r}<d5c5tQ3
z$U5}0F)L~D%ceQlMUB&Sm_hBj>0>)zowi%G6PVxK55jJvc;ae=KEYvS{vgo%<~jVv
zk!UgK%uUF!laqRxEE<E@@p&)Mzg0KeUT*Y$QQ&y-{3&a|dhLbVW%lLUomh9_IB|O8
zPHs-CC)VOpTVD#%a~<q)k2734{wdJ7DKEuDdpK1*wla0x$>TpM@8nr!|1ud;G-kBu
zz$KjjPv4*#+KsGVfaY%qH$=@cO})n20U%Tb-dZKA-0rpb?2FowhvcNK*KWs&!!l`b
zT~t)0RP07z-V=yw=`ve(wK4+D$w&hyeYZ`Ni64v7WH@k1>8I8$O8ql`7TdM`_6Jz3
ziNx)WV$^OT!{*T%ogOA~@_D>cL>r6eL?NCg)fZ{?b0sMr$^Al(oq|><^8qrkvqk&K
zVYVx8-D3VlPjBz$Q|bxgNravAV7(!qD0jO-ixa;#_&jMjdS<oN+udAF9ZAH7E$)Fz
z*LA-l58mbKPn%|lM5wIv?o&SqtjT|EH#=%yZf{&Kkv#t)?PJgq^}|k`RDHDt7w0-2
z!;h$5sfM<_tXm_6Do$SPE1|pRtkA<dk#l&Q=jx!T7mugl<4URJ!}<#z(6wvC$qNQp
z^GC6aiUm(a7_{<F+LvFa+RzKvMB(;#ji!3#TDH!M^ZTL~Heym@W}7Xt67EKYrcf4I
zHu2Q45Keb=pCJKojKmi1G_0tut}d}56`+d&u#d1=BV<EM3jsVp09avco3>o2@>91I
z2u_Ke;6$hRuCq^~Dl4K7E!U1u$JwB-eCF=g93E)F#^(ux%CkjBkJs|V{s3NjF53tu
z_eYCg3;Tu7XN4Ay19O$1G><7fop=e9*4anGw)!I66_n~81-JH&ZDG-5Vh}Vd4G$}7
ztJ~v!&i2icwMByBqyAi=LVO~drC(}~WvZRb)pY&IxbR-B0Mh2_(&<gOfRwP-^Pkn!
z2mJkGVm=Q^X@P1fIFu&`hu^MS55oMK*hn~SN4iYGpP`~_HK}i7gcFMKdx10dkdsxP
z?X7#n>1}xFm+xP87w{cM`2A;{d-HeM#;oeCHa+OGbZubi<1X;Y47ja8a1ve1sE8-6
zl3Pnb16=E9*F!ixCDF#~hP;elHMA?!%$t!UjKNzwMeke35;;R)aN5DSu#EGkAutKh
zwOVaUD@}c8fi5O2ai5_G^qD^W268p;QId`@p8C}vba-pO=u~W7Igqmf;%pc|kk;rV
zbe#D5TK6pFq@?^^5W)j&z&GwjOFXg+vJVk3_mgAwOXa{hlgR$zAa-wtIgZ&MWq6}^
z#6xLo{oo5*oiRpTT3+k(o-Fy*w^M5q93>H(w?6TH&kGL5JI5l;%pP(wa^>7M(?=(S
zkE?<W4wwfVN*05k25L;c?D`>D_9z7u-F2F>w92D-cOs|ouFg-QeVfBE!vt*U#pSZU
z3HH21h+&6+^nPjCe*Zj=bjVrZRL&1TNvH4Le0l(^Y4z)PtB+m?ZQ1*B3NxMitv(;Z
z$yT_rvJe@oS=9KC;hC~-)NA?p^y0b{Zjm**;k7eJM}3DDb~vo%1XW$5<r#G}At2C`
zKrv612GG<jXz#*Oc}2ykC~^s%cHZYrJbt%Zd5?2+O9)3heNW9Mv%66d9v^MInrqQg
zCMwglz8?9v%b(2jp&)4(cL<-ud56(_mhn%CC8PFcw&1^VX0`6wN;OqNq=e}5jBi6_
zTUgb+x8^iPvE7&P`Y@J_!l~Rz94^}3NV`6M{CsI~Lz}ZXv~TP2IAiKUfeQFgs>Xp4
zK$Qc@Kn+)%oSgNt-e_oOA8zfEX-uI1i8hmbf&;m5bsYk($x|60@wd3~(_ArsY9jdO
z8~y{8<`M#Gt|=|XntA_$;r;{BJq!0jTXP0OHhKJCuKfdor0lRc&vHoo8)W?_4BW#5
zCGEB04!e7g`JXWO>ra8`fQ|bGLS_wsSmQsjV_*wB0Wg5@8^VkO0OS9k*OJJg09K%8
zQjahEC*W)k^7a|_3AaC(<lkVeYO;UkO5)wF3pftrT1;*FD%ODve2^!I?B9QH)PoN7
zb1DEh`^$n`BG;hLcNh*=B&+vrPMYl~LrYIJZxVtP0|C*<9|!yedn?grrQX5yKnA0d
zl!%_-lqj%+&}adOOERM-@vp5`aJ^G%=1Ds0Qpl(D{UQ1y3yw9@;-lns$I_0Ib{TM!
z6LDL+9GC|5EM0e31Lt94TTv_bKJrEZf6zQaHLALsiE^3n7eoNQE}`}-bnlHLs3ZB~
zFtIUQPLXX+(!BI>m^Y8xl>^Pr!4?VimryV(>qqXdJx#!k(h_<Gug6>0@9w+QjhT@T
z=raj<XFZ8ULc}?VWZ|tjJsO)n{B@a+7{o}CDz-#*mX-8sOQB1AB4ya8p>X)AKYlLR
zWkZA}J>k#3IH0(>UqJ<TxNr3M@kU&s6;RO>#J00SOA?qF#3e;B6W>@b;VBMg?@v{7
zMlw*n8kccF>=1E*dEznuXDds+by;TsxNo<far>mVR3rd5k$nOZaIq7_hoh`lKM9(X
zlYF}o6e(;C^%J{^3=<YhzdQe4tsV8ao~3q;mc?c<f8rmUD{0)!B9Y%gHZvIgOPsfj
zWZP(4VtrLmxSH?KsxtQC4GT<LzdBfN$czqUsjm0Kt%OF`Dt<p!?UKliIE7RAgSGF%
zNkU8D7|r9<x|J2lk$z0RI9ff@ut7B#ladaHbP##;V@0pElL8chrLTkAUjt=fK(6c8
zS<i)C*sK}5ZVtr=ED!}*A{}ClIqHXV6o{n(<#kEmC~;g$W;NK>P?!N=qgjHsZ8Hu&
zajn~E%&iz#K;u*EzZ+wEPHWBj&izNMai(BrRq)VwiKvOQ$+VaUNdl$&!l}BrhwWm}
zlkWMu-J@la)<ooKECUtNXci<NxkwlIX$1`MXelWuF860-_@yp^lWX`*Bo^J0ER+6=
zND>GGdfp0=?zw$lPH}{fiHoh=IgQhobr6{h$fMFcjicaWw<7YqB^+FLL?k-zE%<bj
za4w=D=Nf#N6MJwje&(rU)2-0lGBlN7^wO@lO`awRl_PW0Ci6r6+2DB=O>i4r$}4%4
zeE|b9MlUM5+zbtF3cl~X_s{b`<K8e(eXD_(=?aXJ0Mo3<(4SxD!Zib(k0)R#@^9Z|
zx?V3Us2r3Xb)n_lA19FYu(4+JLaNTP@*DZQ5AE^=j4`^q3>br~(Qh(ls*Z5J7mSFM
za|jHWW&DCq?R*bBbtxRm6L<MQ6;6Akt>?M96L%|sM?mzvv3vVoBc!!#G$-Z<wL_k(
z??aje-}>5=$7qTtD=RCIkvo$Q#WM-~xHMK*SJ%_~<2Nan5A^9c9WO5cfWRn*4}m#A
zMg&;dV$qwMn<ULO3!#J+h9gOFad93`_ivbj-pQ0J6)R65L@lE$H0%8i2L3&|Y3Gc?
z3Dnls;&Ye-r&3DG%5H(EZx`y#7oeyzNF{jF2$2at);Js}<2f@fSBGG5aB%pjs;Q}I
zX=!<#L5F521q(*P*@r^ZqcIZ?@y&h{Fzuk|`&P=)#CNy(h#q}d5T=R+DUOr?((Jja
zACYn&?cj3_mmb^hzc#)Y;8+SMhm0P^OK@^umHg&;q!xGVip{JRf^XfN*lte&&&=B4
zn)%%=e(Qs8d9^t0<oOYYKy?N}BD1y@TQu8Ru-lPY3=5XQcPs<L^U_Khw&K741xuAb
zjL*9{+ogM9>yINT1yNhzi7neW#TYSK)86V`Gf}~3Z)HDIXF{pd2F?1gHVij)Z{#aL
z^~UYJ=~K6!DOr+^Yd<(_cB6$OZ(APrrS#M(+bAL}AQ^ATn6S?D*}fl)2)0@MJtoo2
z4>jCRkmA4wwfvw*vB9aLu6{qGqFw3X!A32gMnFr#W#$Z=e@GH=Fjwvgu*ZH9#Pz}=
z6Ac42So7BYb%38|W@(8u9=|BV)QS;Km?7)p!o4xB1CZE`42pjL{;lnCXP~S+>(q8Z
zxNSRr{z}CLNa*7mjdo*VsA~keTZ6v<iarx9?OT#BJH=i%Kwm;xNy+B$pC$0K<0&<^
z<SlTB?|B)q`=!Dj<qifQgdi&~&*@_UZX>i505q`xy5AB8OpF)APk08Sk))Z`4S${9
zIgVh#9n_9=EU0gq+QFnXOZC@o1Ac*usp%}s<SBNwVT0C+Uhk$!tcm8Wf1>)Fu^_p*
zYzzqxn?tKWElHNVZ)OHv_}RhzeZAzwn1T+&!||5jlXxXZz6dk8|0f~m@X_NDVqRF|
zQKl=oZ?a!IJf_3eq0y-QvM2E}C27jXPa>%gA*jFVK~U#+0)*H;&VKL#$DAc-Yj!7>
z7h?j{Z))+mZ7B{Z6F3q74_j9q7uC1z0g>+R?(XjH5Ri_cyQRCkyFo<+q@}w%1f*MF
zKw1Q(d}sXq?)}~S-t!+n1I*0X`|Q2XTI(Cj%|3mtH_WUjfzM20<n*hCRFQxiRh<IR
zMZEp#X6;4OO1%aAX9kfuML637{m6z4cb{$U84-_@Wln}B4v(2(95&;2oMVLdDE!dR
z-_q61dL{*chPg>7K8~qo2S6Lq<Bc_o^z+rv@mYW<IEuRwIs{090Qig>fywBLBcj%>
zf;M1cvale4G?sTelvCsfp$AemcD&7EfJv2s;<^b6JQ|Lx1@*ssyT#9&wjE*5R>yn7
zPoU#fad7%5z(L4B2&)&Quvf&i(DEbvI|AR&m#7R@D4;5T>S|(v@>@8Q-A}MSf+{(l
zD5uAD-Se|(&gUrvLITLF2!$k5;l!TqgL)@u${%ZL<lHOHvDHN|zhO}nTvS0Ng7m@Y
z@1be%+7~%DuAEvnzRu3}3J?&lIU*?^rKMqw?=<l_g=3fPcp^j*^3m2w(zt00Hl!FD
z%A#Zskmd7fm8(GXY81Wf-FH;0C+YO+Wr6QWc&h`Xk`*Z^J2Cf<0h*v9U%(8$X+UVD
z(J;I{*{u<U2cU{+pLl->gphji3;pgZa3SGj{y&cwB~%3;vt|Hw;@W}`5N)$0>ekuK
z)7{>cf9ty4<hBzI^)p4RLyal#fQ2St&p?4maL1x!xn_yd&M<~CxJX}J!1p-Q6ET;t
z7)T}n-)r}E|8~7b<b+waRC>3LkxYEB<LMGXXts4x-^xF^gTRwRUTRZc@sQa2aN3K*
z_tVNBj42Jzk-?@E5?GD(V6rVy`28d6HGGXGnIB(>Dx&zHdrlU>n)LxXIzC(<aRad4
z%ndY>tPS#<)Q+Ne3<F8#T*Q;PUBCou%W{87-4N?n4?vO#y8o_kg*1{(?t*RR*`~2x
zP*Bhp4!`9#LaHwQ#N*sDnKbv=)>Ktq7<rK#=neT1$q9zr5f%zW=ml_W(R4aL<_UU~
z``h1j7I>4m1itHQvYVH1-|7wopog_)C*oC$dCc!_Wa+d357EHwL7~5?k3Ls&R4tEZ
z%tH&6&^`4<&QS%TEJZ&;@A#dhEF$Vb^vXVWzq#l6k$`^8k;TjI&a#L7G%`--lTCJJ
z^QyfGW{;u!Tip%fon?;tZvKL3YB6?i(+H11sTe4FWWVZJLXk|U+g@%wIrx}6-_^ld
z?z%FC2pcR5#EHY9c>ICX=d0`<60rb+U^A5P!^z7Hj-8;v-W>O)>VW>@Na3e#cyWnR
zq{ygD$#CCME`b3Pw;^2M%%XQlj`B)vQ$b`MLLq*zS#D*#%?|m#s$>2eg}FRMLJMdj
z&+QP(z{Shfha)8q8lo93(;vzt;uCW*S(9`)(GOFXZUpt*z|5_Az=oK=hNH{@m@v!i
zVqHn8ls|Tnr{c=hx?C5DtKb;E4*9vXAJGx;j-VFcb0DxRamI{sAtaCG!3rxOTmUEY
z)W>MXr3fmFLIglN_zqutF*{b*)f0)(<JIS3tRI3;UN6?%n}qDg2|R>3xM03-#-L1d
z^2d`UMeJn`-R~#}a2ze?08p`}OWEa%4uE-6veWc42pa0=!jYo?^%#c)6;yhp7SIpf
zSZY#11fbvC#hbSx`x>^omil9y6bvosM{xzcOY1twbEumh0^^776yWr8=l1snF%~c1
zE3k`!Jf%WFv8Psd7*a9(;W$M-s;QXHtvhgHv6O6DC8spd7Ai_gRI@xs%4}`04XmFj
zA7L?Ct8!c$y%y@~R)F?jF;LbJ9mSm5zzjsK11hTUC<ULb><sIPQ8R704Spszo1Ny9
zC{CysvcVwH;Xpn_CQ+G9qcHTcNQX0|<JDJ;dC7ZZQylp9DU4tXoI*+pVT$3xq%^%Q
z!c*3)ZAW4*)cuQkTcQek?fOnNrb$xw4+VC6_`LH6+AKN|4+8!QKthH4K|~=d{&b`+
zYPjngpQKAbZNDsh-id91U={fRgq6Sz@Lam%V6c&*6<Kj?ufcOS0`YjPVFHrLLrT8@
z{(1D!Tz1Z@a>5r<E|E=pk?~x3T9)>u^ROgd`FmxgnRg~&sTYl=*Ts`(CHq)}`Ios%
zqajf5E|W8V!2FU?8<eA|1b!}tByBnpVx59UgK$kdAVopB)8E@x0tUJ)$>_x65gAt%
z5J3%vy+n4*o$?F`QDAs8gk&)OKH^5#_)TWU#aAd;2akpXLNnZ1JKsHPBw>&+dcJ#1
z`~OEjrizky#4=kKhtLRYi5(*tw0a&k&Y?()!n>2CDkwZh`{*gnn%r>4tE7<QuCRw{
zn<P!gb2O|}K$@CgqI^afWa}HEXv-oZ>Hs3W1ElA*8)2iRTV7_2mS^7(ekOaGf-7V0
z=u?~H3K!#G$r39u3f{Av;IT#)%Y-Mo6k-5+D5Rs@K)NO=aTdaewAm5D3=IYkxRm;H
z^lDFVkEN>RNAl;3=$lVcUVCWoK%E7Qu0XraFwH6{tJ04l=vOdeZ1V)U{tc#dvPHjs
z90uPXeTZo0;_596zJ5!d%W`Zgh`RF$@hu$5Y&x86vXfW>Vw126&pGJ^`zfbs3-JWP
z85Z|vy8oNS1|STwLq{d`m(M1dC!*ws?Sx$2cHfG&Vx;=>yKJh!kg`aAKv@b)?FMuO
zXg6Wc*nuodo4^dAA@)#}r5#!Ih};ML$ln?q#rypV0oN#-Q&ZQR+fhUom2;p0pUC=A
z8&fW--;tP=a~uS!RAAGcUd2`<x@U4r%Z0f?sKt&0J2TRv&<-zJat_NW%%@qc-ac`l
z*?U+>Ir?ysY|`zx%5qC7V6DGlSt6xonk`ix`M%7ev`Ni37I6hfzDfFe%9)TsJ`j}%
zoX)91PsE)9IRtSK8yg!rqwq-vTXNlJId=M1ILZjEVSSIz-pA?->_az=$Z&D9Z-|Bg
zVZi@N`Xxp&V@zRCGW5P|0{u^EO7a5w)rR<R?~!&Sixml&7#Kjs-&PGN4bZ;8AWOkB
z2OwI<%i$l8+=-UzMtJshA=*TSWh;BvMP}9Yg0-Fe4f?f+4-FL>P$m*E%;ZA8z6$GJ
zO^14GDW|CXqCzasQc(n;>T|{XlF^L?@rj@wCw*O2fp3Wzs>k~pZ^u6eP#@;Mzt1+2
zvc_^h<&eSYF{11p{gLPrFp$84I4J#Q^26Is<CX6<9cYR^j4CwfC|`}1RB(krWUc%u
zSkS}-f=1gQJOoxFW3o+w322N>#?KgL_KE{pLnj3{ok|TF=20)P@sNMW7po|zuE?zI
z4qd{U#FWmSS!aJ1J9GcP^zu-SKU8)zrt;1@Bh9rkC>m=BDxmRFx`_k)^nBZ+ZsF$j
z2E)v+uS6qjcb@ppz>J$T_S-j0g$;m?)~b*1Z|uRCwEmTub;r>sCGI6J?SVD*GQ0kD
zF%=??_Uc-(YcoK+A{$nq-0Z;+#HyYKJC1!xb#UC-(GYtbYM&RGFWK4?t(*X;Sqv^E
z<dTu#%kge(S&ENrYpBBpfTr<l%ZT%7Z8?~;7oYhCyjc1uT34R|@oZg3V*praT#sdp
z@}fF>_2H}oU4*iQ1C;Q7Znl5ZmqXYFaqy#8rx+ndt@S3U4K(b08SEf|Rt#I@a-s*<
zE?U@-A@{+q9EY`xb~<e+f9nU)W<QuU20MfQC3A>@g1J-<nIp#%QKXR5SAv<Ubo0n`
zx1|h#BQ425E|!sY2rz=syAUYZN}Sne%}mIU#?FIoJIZP8U&T7V)RBIOTgCH>9jY~w
zdf163&&#3-xSx8B`T-y%ArO?WvdA~|A8$-u<Yyv>mISYVrKVZou`sR}$=yKfv$9t#
z5tDUbnoS*YUn6i)Zj2@m%8}d-!s3}YTdQfZJ)o=!Nw~+yH?^fNj#%Xy!~#cn^&jiI
zd`Bi6V<CaXc#{wvj<PF=d`Q#8D`ULy%wf}Zh?r-e@IE*7gDU0Rw;#(>IkHV>DZyw0
z%Vrwh1rfQcJOd3-jZP=u1YtQN|5Y3KM{5#_KrwsM@`!*iN2}GVqB2W|38i#W;`$2h
z9QWAa8xQFa!E%N-7iC|)nYZohxhJWV)>Zht=%TFDwo>`w=r&Rz&lqcMO_+V`RhG}T
z!fh^yCh~Yp;E&{4S>|(zZS0tt?*}g#H=C2B#>$eKV>#(xMu~puZQhMiyeHoB_y!fJ
zXFK4dFI*cQj`#x)O!b`>gtKQ&g3|^&9u=3LrfcFmlw&!NGIW<~SYF4J%~!xepwmp#
zi`3%!(Mr|_Gk=bzkNE}0G!7Kt(87-P!J%nBXBImerHG~78&2|Y=A_d!V=+mRrwS-3
z^-;K1v|pX%a<7EL!Fy=nPKK<?{j)B1;Y06eduNp|&G)U|8p)ap0kU(RXbgpVq2aWz
z98@b9DTF6woB_ONt*x<9_O-nwtyDR4v)M#a@o@xYY+5<Qei-OjF=O?Y(0r$Mh;3mc
zQh|2K^-Tn71G^U+Z(^9r7a|e>%K7uR3WH9c`b*C@+KPCqDn6_k!xy3%y^}9J%lG$^
z#gkCzh$|z&{%#$(g`W=V%0k{~mxjm=IU()5k6{h!$FOKiP(tZ^k2=>WEAH4{M{=@5
ztBjuy<>4IG#=D@aeMS+^*+v3?5hj6XCFX(`rV6(6CC$m3A4YMe_X+G2ChO3c2M$sS
z1Rma^$Ge~S#K-nyH;O8q*T=+BI5<oK|9Qy5CPSXY+VHy#$oOflO09vrT1X!vcg-i1
z%xp$E2FL1*I0fklUR`u|_w^v=V8yAj9rbZ8(=}Pcp7_wR${@#^GIEZqe2g3|y^s-1
zNEx;_&`z>u5T;zU?uhWr&vRPHH*!G1wM0VTU@|ovI>s2|^r3I8lehFj>E{gXB)$8v
zHi7SA-yv$0!E)+5YrJ;|EU$1{NfFk!Pu6U^p^`s+*<U$$ZaAV(%b4wzDQ6of)Y|o~
z(M-rmUB-7CoFJI(MIbd=SSibk%~499gL+`|ya;sj`SM~=U`Tw;Qu{bD4ylXSnYqlt
zENHNCEiRZh%D+Ay9Gnt=Wq|gQc&GnQ`5GYsG85s*kE%`8SO?kaj#_g^n50PYwhD9y
z)mWrTO?gq9Ihayu65&ddHfKUtw@zzr#2i>xK5D9-AbG*9J;d+(3=vD0btZ<wO2jyy
z`10RebLo2oa?(bW-XzF45k+%AhkgS|m^(<~&#g)S+{scG`$ZE8OC#NazGG?UW1Bw^
z?}Zq$#Fp$yiGU}~Sw3scjpmqJVpLG10V66$V;+@jkiH#RW-$^^jA$1%2aS)PZy?;q
zI0@((_D`Uut6`Vn==<$V&LA492~G@te^G$_g^4He;YT#o@Ql}DX(f_ymEAuB)_`4=
zfzYZaV_(vB|GZKl8ltclGS>i!p!`mCFrK^9R3?(w!UE&ISVNr9kPIqo>w3Qbj(YBX
z%LN^ciS==|52+(OT(W-s^b~7h1I@$PUN$tLa^BeL_NU4K>b5^!66Xo2uZprdYV$`_
zMVOn1`|q{Xa4zGeDbb4V8Bj7Lge(S42r$?_awZJN-ffIbuF4&F&*~J+EXAPh^~K40
z1UrjbX9M@Vkk3D~)I}pj7R<fQlA+>5TRdgnCTW9&>^U3k`pIE@Hi)Sap2b{)KtT_W
zZ|1H>DN=+z^>mJcxOLUKZ{5=DN)Z2Z%p?Gaa7I~Ew=MO}5?&~6Xfks|yD!>zv~0>l
zgMGf-BDQxf4Ir0O4eY)^0ZH%M280CvtTKJ$IDB&x<~X4bb<gP-zT@5>3JPgP=g0=f
zHFtLH!LI}XIjGM!DNPP_Ubx9}_EiJVyE_pNvrB*)TXs*^-}sRi5hPGRT8FpLxZE`n
z3zhaGD6y~6?p$pfU^%N7J-4H%WjN{y0p+VrUwV;(iL6}6IWgR^{G-A4dY~YrZa&6y
z%BX0d-D)<?m14WDf7TllEk&5`pl(j~!OL0P4-B=D{%}Le|HgV`c+TXX9gfigjQ3`x
zwhRW>@GI0q2pkpxVz~^y!K(K$9C*2~QX>!<I_jzHDiV5JA4*02vBIie&L8jUGq>;~
zIZ&_b<V7iR8v2-vwj#hzLBv<|g}vvI%T9PWlZV^h!-vt{HH_QhR0X%c=f|{gPPWHj
zFEl*a5M5NGr%WocB-Sg-3e2#vO3wTb?43&jOxPE`KrW9ic1OYF;2FCfDnqP<@cnd_
zxxd|wJ_?HZ(+OuIm8uLDbU`m-1RXn$H2T?k+_w`UT`1Ul8aiYDhYj9nblxJ7)O6kL
zU*E|~I$ksWXS@iz?A?Wt-18|!y*yxq>T4>78IB*A;OTR+rC>pU#_$1LiCKBn2h1&H
z93zZIv-V}DZ%h<=<l{CXiImY&A&AZ_mx-stI|?3+Y%O<OS3r58rt?Y(uRqQ}b!ld$
zhFEU=61Kj2r+2~Kh5MFuEdy)6&PQXuC}$JHe`i3~$nB-|X>0J?p8Y=00yl<G;@_9a
z!4ZXFe3Mzoxinr)`qXec?onaxCP*tZO`+hp$hOh&Y<3|N%gr_qdX+oFt@|ve(nMh)
zlPS-Z#UpDZRT&g$G>xFgJ#uW=_!c|^=HwXGQh)Uf-V)TFsI#sB<HCPHIZrqMZVR0a
z|Kj=<ok(1uPUe0H%&)Y}?*7*Lo06eElr{%Jwx+<NLv5FJtv(xevog#(#3R_?ZovAL
zL~aPEa}MDzc}DEDb%9i!Y_KBahhLEfZz!hIjR~|m^y|{14t>^VJ6KsJ6Mwp%2fLG&
zmd3tAMSc&B)?NYHX~HmL5T%<!kri=W&jF1JoVgG7Qt#!fBgR=b&}i@~<Bh`}y~L=g
zbFcW|BM+$f_fA3vU`V0_z3NxkBZ~uX2-gz$rMUfFRprT`)kFm>V;?((Eb<XB?&9=j
zNmS7Yg&e^O=APewn>(48qyCdFZNtFaFYdtLo#7lymc0Ts$8plwB~ZpD>^tL?z;4R2
zzm-Fq{ZiBaEsd>zg+h~qXRS9UKj=b>){h%UnZ+M*b#kLw?w4KEE)m%>PBLRDyMByl
zBIwF<ByefLkB-7_G=wd~K=16f=XYQS;qX8V^v6a<&hWQfnQUHr(;xKbASszYNd+C;
zva7Phww0g+h4$hAy12@xjYuAN!X;yGQrj4G?wx815jr$HX~~~E0~MB~<F<j4C>XHt
zoAJV}P1liJZs~YaB=al!(~N_@%WO1>Q>-WWfz&(Y8!*B|4t&)J7wx{J%ffZcKKhlg
zXw0jpM4bm0ed?P5`t2Eb=R$L{9H6N4StauSJln!#O6X00&LUkElC}5KZ*}_K!Lb)7
zP;DKMc2bSbeTIOOu(41{eUC74U7jh%P5L<)+X_R=uP<J4M57INQmOPe37(XgR+moY
z$<M6FG_8o06IVYU&+j_rPhq{9=XP#CG^AVW!sZS>HT1c(u;{qudh_P*vqm#U!r+ww
zj?z9JqPa4qpUf|rNX0yLvTGHBimO;6mXykI(F#a{Cy|5E3({M0$*FTXuOpGmVS6ma
zISke+i)E7u`Q3W5lCE{Xst?h1{u}<Cr2~N4wFm`b$h!k5Lv(udIp{c=eR~*}WU?tZ
z%ujs$H=hNiPpZrR6H&Is26ly$)H}$kp#TWgyUfl~{da^mE@6p#*kq>PlXn;0f6kq}
z)V(F=X*D&tk2q=^QJ?n@d3)#d(e__oE}>0TB3V~<^|?X=_|fbe1Ptg<0y`OM>8Gk4
z^!77RpBa%dTNv@pHwKmeLY*NOX^2n(*UB2vWC8@9yXeqi46fW+Z5vF_P%+22#X^gd
z>e}%Y{r?<Z5=}tA=xy6TZl-MD4tZk2tpA?;Ip_YHyG3XVurxBJiBbD5Q}TZQI*(m^
zALbpm%?#QkA(zD_KUc$pFtHuvTmHQ@egj{<EY4@}7Pua_*j_-3AMw<1Z`|PpMDPr3
zpqOFVY`pW$76;*M!U9o`12dhWuWzc#G?g+H|M`?M0$}PiAKkSfNHG`*R;@_HPCZ^~
zdD^}m8Ixhne<zA*kYTIk19Ift$A6}r0uRDNh<8!7dJQ1f98?@`yE5E<_V!Hp<@wcg
z?RcTp&o7*yx$e>H8uNg^_&0zLl*Sg|TY=J8C@}aze3)=JRKM*|_-4nIFD))xz&V78
zEY$s#e5i_4(0MmW^}B&uF&^QFN&(SOf91b#6u=Hhgs=mKTgteAiIrHQ;%NPOWI*WY
z#SasxHSgT@yMxx>i?>L?M4+94m3n?dPWhiJkibL;0q6`++qRj1ovIR^l(Y1lb_;ik
zbF}G7kg5E8LDYwb<lPkd>%#gOw>XpX2jBa91Kup}`eL!^A9*iW!~^fI$1|C;Sq<g-
z8zn;k@7Z!7#<K)W+yRUQX|}pcr#dw<!b>F@1%(Vn1CSE0x44*&(t`9jTpS%e6>wFW
zTU+k{pbH2l3^@|1XQM=W4|X6vgRtfEjQ@GPzzq*QOAG<%XkA+k4GqcS&#iTJu9v$*
zMYREol{&ybL_|aYmAG`=*7pIbg#a!QR(Ul40k{&eCO|*m-u%-STpA6B*2!=ke`wT)
z^L1gN^J<(qMf&a$P(os>;CG;sLdSK}($Yc#lA1IxR>wql0UFe_w6u$|lcn0?jb1f=
z9v+CxLq-5laAIL%YN&#F*Y+Hti%|mYX%GcioH)9>yN6^I=>T4dAVfw+Mr!#aOT;24
zD*fg4^+%v-JNI6-e&Yf*Z`$a0qknC<zc&2_R_KjpgEOL}C)+V#wg|RMbpi%aYTh%e
z3+h2p&g(ES^9#)ez>Q&`yMRhqbcEe+zzl31u-^c%asZkT@VTHU<`M9}spbiZanC)b
z%{DS$6~+QOGL^hjFBSvpg|6DaCbF`#sl~M~0Ojw`rSkNB1QcjE!ki1MY-7AhTb6fC
zO*}bS<x?ThF9a|E5g&<X2}+AHjS~vIiT^3DI!r-fVc>qIZo9C3>|bl<-^W!6LMvvB
z1I*;lB7odq8Uk2)$-`W|n0FnJL2Ne?<CFt%9d^X!QJ}z1Dlu>*sBjTUARfQy0GKL1
zKRv9SC^Ys~YA!P>r|ZmO831-@Gi(M;4BXrrIJtnxxwfI<OA+Zbij}OSP{5t*WMgTc
z7psBRSwd*jd~cmYOx2`AO9WZ^OF2-#S0;5~QIQw`&>>~Bn<k|ZCNlJIxelPF*vL;%
zG+rzMl^roxi-mKMBBwJz3P&j&mBXaH3jo_3D`r?MBa$KdsVB_A8&9Xu9=qGMZ?pdM
zME=XuL6V{dk;6cVp`cF+>kO*{I;unD6_>>@igbu(qThW(8Byl2t&*s!J;)9G;*?Q=
zI-F7j@Id+a_AB?pD0Q-{RlE&uB+!1w7cjA?{}AbF?w+uE0aVw*GQ@sNas%c#qLz!M
z@{G}SbLGL`)3dS;Y$w}+<1B0b-sg**k^PgV48kd3?tV@%n;NNx4BdU&ytWy5YmC56
z_m#m8bgq|af#cM|-`$WQT&d>|6r=1&48DxIN%%W`A}!yG83c{<cVD9VQ>FpFC(A&s
z7ygU*^JTIqVzB?|@rIV||Guk${A`dHT29s%ki?8n$R)P~K6vHqOy+Wnnu^EC!w9S9
za8R<ds}liUo4HvGQuWY$`rf-k_@<utuhR1K{kH;dS9HK-vh0O9IbiF2FXb<KTyIC{
zcGRDc!}}3^0T8PxR1)+x{w58Si-U&ZGEzZ+1pg4WDFnyA;<h*JMqD{2gk@`cI8%Ji
z(A1dYnoPty&K8=IzJJ&I`u!^E2@jLinADAP_b=;ZI!_{2wwwXtVxL{aj(SC87ao1A
z9HcdN{7tl~3^)z*gp|?|0Uu%|#QCTh58|YzP=nw1OFhl-89eeYM9!|fGC3H@4u;A4
zu6YB<GC$XOYsu~c00TK-h+$mzU)kfI0|_AnBGhM?UHGW=k~9YnmcZIpiKN15vy%{}
zptzWv0s)U_SW*V`8f;8BZXD_VL0VRk8-cYGM=ib`3zdFeaM0Cqj^p={dT`n7EZ=;H
zFXbEN*VPz{JkpY$5N&>S>rNHe5y;2F3<xF+$#AAKO6G60clvb`Hw}m79Y{rfnp=`l
z6Wkk8_ST&NK6?3AW>_f_(<~C18Z*wK_S={V;-7e4faX4yMatE)<OR=J&xcHf{NhJU
z5($Y<1hv|3>kAo8SZ_D=&uuVN^^u2?el8LM$rDfgU;Y_nxz|bd(ags5N2+{PTlo5Q
zRe$ChfUgeCJflj=96brfYfQTGh`mqTw#C5~L&jdy1%j@c{M2QlMoTEP@6Zfvv0WxV
z?L-rhA^&`jgcN<%*xgM=Z$q|g{C2Z*Kg)1?8AH6fT2pu+%XfPWn_i8Eh5O!yn%K!l
zB@6Z&w-1b?cZAdKrV64x2xr1e=i&%3M1$+Fz3a5?IZ}{u=!2Cg0vv{v^z!D4vGG@L
zEQepO7sy|PZ3g^M<$#yI9*e5LMkjgC|ACBQMqjx7b){?5@U@Ui6E^p`JbB;(G)(6$
zpwoMYfqly{^*u+k(Jj6=H0lc~u2|3Q@%_!qH}Qspt44R**QJ7Xfa@Rr#ftSFgNufV
zZgYbrtyI=xmTX%^J(Y>1wWNt$P>{7rkep=oXtn#FX`B@WxOo9{{t+5ZD-HW)WeQd$
zC4e!9X+l|Mh`LBox`nI%2&uP1riM{IQQy8<NSUCF4FYAcus2)zM$^pb=yn=?nDT%R
zqDrJ4Pw6|ew1~#tG<wgWI{ESXA>3#aZeh969D8LvWf%EQbAi$i@$8KQ?@9fXwP*W}
z5g)Ga_LB1%*Ac<Yx8iLRj3AZeTH}|6crcD4_4*BS)@ygO@xu^@3Dj)@&3HEf$KPKK
zU2xSc2=USqym?liAuu7W^y(a<MF?utO(&&d&(E)h&$|l5s29P{hr#WtC5aW!AxN=4
zLJA@jP(L^HF5ie$^Q1X^V+buy#1$?7HkF@;udV${ArAl1h*{}%HN)leZ-zU`ruQ$P
zldu9lAkvB+;F)j%M7g)G8~=U^?np}@UdS#>B?4-6Z_T-1C~)=5^u;rg&!%_8CaoA|
zo;`K!nrOni2B7e%K|V}(Y_k}0<&Y_<%?ndpHRMmcSZ^OAa6Js!KV!uaeqsp#_L-7}
zXAwcDbcm`yRt_{V`8E&_3L<bsd_C=C+5j!l;qlPM)CWEJal4y|kXA2VBPqi0AwS?&
zS$_>$)X|NV=l5yA^E}A0p(ewFHu^bu1m(2{PAT>~{z(1=mY3t`_ZGz2J558yz3-1i
zKI(Vim03y%k>xp;Z3rvvNHlg30z6V|@nHZJ-zRn=Wgi264c%ts&<kF?L?L?QE9`h4
zJ)EAhpRyK$A6%0vnWaC21YVmlsNsE+w{xusS#<kz&io1I@g-q*A{vdgJ;h$Um*Mpj
z!@m!{6qBuuXJ<n)seYRaWgbOZD~hdh0`Oj1VpCjc){Js*DgrotqCQBjQa0Tnco9k4
z3O^K{2f&k?k#%t7@H7&eTCK+(!F<L$b|$tS2!e2kxVK-Ri%49vq<_YSrSacO<UdJE
z`7mdP9fo{a((Q%7e0^Ak4JQp|yD(=~TX)PDsO@<cii~=q!g3@$^^UgUmit+;Pa57^
zH8(RcF+}nN_+-gwPjd-~Z38V7n<}nJyMQuv6F&6YJDuY-6L6RvyMd_+;7+Q8`}oE&
zSDJXJ_SKe|iMRh+%vXGDTgM4O^ANZyK~I0qg_}Ri!xIGv&hdBP=r6q=syNlUE2I^;
zQ%Ld?UUD}xXi@^)MD4-;`Nve>`Q=%Qf(X&K67fkm<u*;9%RI6$-{C1+NH5ec3^ftp
zHVw!SMsgS6Aw@sus<#iMMA8t0RQl^lw4AXLLaewN1x~6|!}+l5ObG-Gyz|TEl}YL_
zLu5C64+~o@J!mfbk=fS+Z#Td}P8-6BmxRp&N?Ktr1aDafvMven2uI^|1zX^iV}E&)
z7-~$Dy<j*Q+rMG4#L#t3!oAo!xRd6iJR}0YpArCo3ZaCM9MO?7>xKd4qyTxIW90a#
zas3y?@2J_ON33xgZ5CC$P`W7mOEqVTjVNqTIY3_|y%wzh-YTSkF~o)JtmNh+=63w*
zuQ9WU<LxoJINZ%4zBiUo7Td=*btQ4KFBs2i&(Ms-zO@FAI)`)DVVD6>lhdjW9V=z^
z9Io)f&=-l<mdvsM`6Seemj<I5<+KwZMA0fN7XN;<3BJ}LXb=sfPNc#as~-#kBHs5%
z?g*dhobF$x<>fJb?tJYJn=;Z1^w0@<*)QTIexTDYJ~t)~Av8cWM$}u3j8nK;mxA@^
z;@uhujb2B<tOs_bcMM*0A;S2rF<B*9AZ$U<qPu-nL6}b~sDSSPY%-K(!f@Hco7;Y#
z_R8)A_4*_){uqf^*i`c}3R2tK1#(ug*Nq*|3U1P>u!BGNhen&K=Z>B}8t3@$gz;oi
zn8Em`OkDB@S&k1$;BVBfiQ;yEuU6yY+TA%5lM+PE^l4&n_MH(o61^7|Pb#X`^bI?@
zYM5__TNA45b8}<7zt4i2Q&=P~U~kN_EN&Np>=cp#N%#Z#T>z%JKv<qYFTTz-Sn`@q
zx&{yhDZ4U~0h{H_!S2*xhR0GRBf1<fTRS}~B4<vDg>>J^y8Z-LEj}x!Wc+y*C^jw$
zW)znRWUltY=1@a*I&rQIZxb4tV(02V<~~gkmympA+UYyV(IKc1Zuc49PvZl>ar$5@
zFW<2Jn7{Qn%qG7xNlmMv-y)=28DZzWESBpXnky>NSLNH-oZ@389Vj?$cG~lF>Y^#;
z&4Sd@#h^OE4U@vD`P(n89^Ff1DYA2^6W@}<+-Ka*Ank4{Nym7?KanE_MC0bVeH+MG
zZ{CYR6vupQS`akVPIEb4p52jkOXQ0&pn#Rb^L(yK+z!0V#T-!B-R_l`a$mq$HGBV8
zdAUCtNFn3vBK-vt3{-hR>HWtq9O<|aD=dIsQ*D<qH(0%6o;-+B{Fsg_mZuT1o3OmJ
zNSrzv^APJGXK4e^&Xx_Y{0~me7ox#glUz9VdN4|*jge0<wSqFe`#IGXLSycl^8g9t
zSYLJr$T90jqS8(Mj^3A}E@(E@f^)6xmd%K*leVf)1yq&o9NU$pSlU%fZHVokfNl_!
z^f1pR(S$3eVGd1oIA$L%H)Zh?b9uyiWhf>lCf?$MHK&JrDG9qo&nK$qwsH(=5PYaY
zyt3UBib*MJDTdEof~Omm@$r-}K7JqG*h_gWBX#*OsAjqzVe7wHyF4&6U}2M}bUU;o
z@8h|uaS!H?kn4-@B@kbutTh9CqdGB0DE(%mc&-|4$EgerFwuw3#a&i0M9YX2P1sjP
zW@hNsS;t4yq$1=$pu)eFwhd4Fix`1`4dbR70!rrPJ*+Nu{RwMcN?xQF@5E%B@SV<H
z$PiJHy$qXBTAvWsco(24N)w^KigsYe8@0_8Jxr6Tcx$6zKfWW*K^~KGSB=%V>OrzA
znETR?uf!F|1zznRy<kb0CfCYbS=07$FAp)<*l~(~6e)TY%h_myi+2Fztffe5F|l0d
z%6V?Z>AlDnzgvPI_>tyPzew1-?M7-V=c$wUsjjMFn4t{VF-q<w7CUixO<2RmFxySe
zafb3mO40%Dt_V+&wY8sqzJw2ZbD4!0GZfE}oG_*{!_y6r1QK3}j<x}U0Vo&@V|9{<
zC!i7M-iiLqeGQ9DGrW!XK^BG3N^L6k<+IaQ08|~3Lv*Yx;|mq6G2{dF%(d~S;9Uj@
z{kB1?j|AR1M}6PisQzm3VSay$gDW0u*^;;Puc`$G9qeu%lt*GBcm<{PLPs+?4@(~A
zYaeyw1&MS>+eI@_Hkd7uj3QGe9@wYwPh!%}$hh09@w90I46}q`DdJH%<T~Zv$9B(Q
zx{c3S0oQndXDXj*shO(;wvcCyd!0L!ZoVVO4EE)+8PNa?4^M$-@40#=QLj+mTIp;U
z*D8>E_fr%|VoV@8l13vZt+ego+dW-6*-a`!%VWI*h_sQ`#P2z84(|x^`N0J9sV^C-
z#~HuD4tD9uTQmUGlXrvbS;KYrg~HxKdG)V6MEYJ!&QHfv^qKpbO~@?o`d9%3;GNdO
zWy%EW4ni1ngOfUDyjru@M3E=DKKRWm$nj_OTSM@fLtcDB0K;AU6%X->Ot{lY`&%u8
zcUbf0Yc+aCVISlAyF#@aL^)=<Ev_P~uua%E)N$248%#_0fw%DaR*o_fIa(~SM&AD|
zF2Qhz%&Nuf<C~%(YXUhN4{jfX>tWSm$JZ;NYvJ21BBVZVQ^?PTB!9(bVZDNVkTr0O
z8c8IMHm%4Hq_i;$*34Kdg4LV+px<hf!itasn`)n(w@|IynXSr~18d+%nOl(|%Q)2^
zuGtc%w|yB~pOBS<KV>e+9>R(ZLiU3gPMSZT#(3@v;?&O%Qi$Xr=%_?65l3>vlU#MT
z+U0)SsdrQ`I|PR^f!We}fJa$HE#kar;JxSdT0xK5xvDanLki(f{}h}JEk{;uSQMB#
z(@P{iTFp$1&6jUvyq!==K|RX^@|gui{o7axh0O#~{(Lc4Qn8vOQ&QtMAwuRKSb4B+
z;uGDpC)Sxr*!q_3h^4`{czRY^kh)&U8pM!q8S@db{|8Xz0J$MmeLL2zKZ&&I28_^`
z@5@#OPMS+fdNI+M0u1}WJ{wvBdU&hK+L0pSfVKKlE^`OGU1J1zr0Md5F%1XTXA&w;
z$6<gZGGi*A5W3;#(^?!M6Ge3&ufK5+CqgX2UjH)W#Sd#2z(-aPdnaZGpsNiI6W}uE
zhZ1NP1-{4l=GH<t1&V0H5|r@g{1DwmY`sZT<Bv0#Pa4z16KEIi%Z>OT6P~g_u!HQ;
zebO+|4KUHlFp`#|Q0k~Yy@I8Rg4&#jf|7UqGOaG-bG%I3TWA_IDA()1a*9Y&zaq?s
zx$`j-${R)K^!=Zw<Ol{({9#Gy;|8?kAX2?9CB%#uOjLG0nEKjYU<Kbgez}$SKJLM{
z7BTSi$~-l;Fd#{%O7hg;)78%?$oW_AGB7%Om83jli(ZxPy<g{k#3j*D@gmh;_aK>(
z63O)ysS?R%d6#+vmO^#8J|PRBM2>b<nq{%2VOt;0At@A$nqN1b-024Z)0dJ%;MGsx
z>74O)%7?P^)5G$e+sDXBWeuGN@#fv8^-qSu1(!cFnE>Ycn?;?oNJwk)$(L6u<Iu36
z-sMC-X)o_NELjQ#*hk-&@GGL`QwIB;D&>2_Z)2v`#$quRlMpt>=BU;;=4l1`xnKng
zF*Avi!%n{JPX&|>PwvkeCuJf16*nM2W(4Iora}By-8z{$c&5}T=YM$t%=8T|a9|6d
zdvBI_g;QehBM1$iN~U0x3GJ{TMI-hpyP{Gi^(p*>xbY?@y0NTE=`x!_!=l8oUHNnA
ztWpRj+uTA$qA-W{k$}3uFxh+7)L0D4^&My&3Ku#B0unO%bjcbH@U`J<;s6$I^n2n+
z`eMMZ`I{5h%Xvi%_Ej_aK%kx@RQ-{%3y9ayYx8eD-TxHTFe-a>iIGcqSyH|37r6sP
z?Me|=-?a96J;j%2te~i_R-mq;y82x_tQTD<htVF*y_W*lP6q+`MQE78gSDNUguLo4
zy7(hTWdc)<Xl#RDZwPeLf;=V|1!nF%hpDP@pQi=&jrC6I5wUbxJ9I2%tu}RKo6~4l
zfh}_^rRG~yp-g#5F+Mbj5~Bx}U^vpLu?~3@g-CqC*_BwGq*Sf~zP5E2$@7y4hXmVR
zXnjm-rA_uU4j1WVajb&MwyE2olLt>bi(XxCBcWLDv*)KTWQRH+Q!j5sd6a#RS*g_$
zrf9NsikpV~tCeur;saSTcgGg*8RW5(klN3p<?l3$omZO_zqEpWYyxF#`y`Q*8;Oxi
zc$)MzZ_0M4moK8xr8VrLwrcB4)f8u^@_>R20@Nr@ijIMj#mC5Xu8;2su^$<Cv|qkw
zE6B|n6l@%+cdAQ`n>BSrUs&>_32VYKBWC_DfCsWno-rUqzoW?RpzAq#4bu~!a7uR$
zY#&C<oY|#PzahLO^6GMuH494mqQ`L_4|)nI8H=zdspitYGq`ftLdwUl+&J7w(pj;S
zbOxV~tmw@&WOSn{S0c^Aesec(d6mAqjEsWX%Mb>Nrt++`DWVqNzgN&APYo!)X1n_A
z07|aNBg}&Hv=JoTYu{!GX>|1u5T25R)5i05_HoSj7T~1NxF~sKXJeE5KH;C;=hE}!
zMJ0><X`GL+j-E=@yGBc@5IN_d2$UmIu+qsjObNw{WFuYr(OfSA7Ioo-0`BOud^w4{
z?X-iB<g=R7$<2QOAb+VYA>*IiEhT)ei9oFrEE(shfI>ZCx?2QXg`GNR?s&efoO%)k
zcpI=8c<xBWK#|rD(b8mgK=W;$NikBwq}$*|4HoT}V;l^B7Nv8b=Q#V^NUHq8AV1^>
z96r0r`sSse>h?+ai02@b7(qn6Su|z7$r)_U@_<q}5Q<E1e9_!B8%i?xf687jpj~EO
z$y5J7zxk6E)I)@zdcomLJ%42h|4{~q<O~`BD1(MX=k)HcXymWL@xT5O<2%COXLQ%<
z9+6Cl%uy%`ia$Cx|NSW@g6AP2S0TgxpzMetakTFY+zrJBS7C0NpkGJ}v;Wjso@n%K
zj!yE4I9G>D^H|<spGCBi{Y`!~O_WVCK^|{Y@YZv5l9nN0hp=mlG3HoXBx-|BB0@)9
z75r*Ex6x)Incwk~V8h!pTN<mFjW)lZC%j@d0VZ-LJ%bCY>AZ`mi^6DU0)Ss<SDDvo
zV$-`O%@=a}R^L3{80kCNU8e5tO^uw+QKgU-76~#@$4^~I{tDtIeXs;Qb2O~kCuNZQ
zFpeon{%epDj+B6hL-S^~5`>#ZDPcC1$Gc9wPZrbhktB3IrV&yez<^rkp`#JN50Q*g
zRTQDAA@p#Xqu4q%J+pZTJq21Yr3t?Q{Cdx<o7^zA^GAX`>^Ivcdfz==Jxz#jKBacJ
zz$%pp{kFK83>}-U+R!DfzMmn@x6jX~qL4mOOHD0s`<(#aaBmH`(N|RYy!pZWnchJa
zbm4EIu$tm;v!4BhUiMyXrg(F9`Qmz2oLq3H!&}sRrU_aQ@Cb0Sx2s2VJuedN5%$93
zdR$7HQVOBIVe_Q=13F8^0Jk0^?4vXUaATqDP1H}4_<rWI0Te{;H@o~1_eB8&P^?YH
z4}i1Qo!<bJl;JP0gjpS|j9<nH_~&ePVacJBNRNHY((-D1r-^(n-oC}Q73^7DSSW5D
zTDKKGf`&)VMwVqPKqGpa2FhOG`&z?j=+u%RL3HyFPnb>Hyjl2qX}ziIM&U;;H+CbO
zB|WV=F$cpZ^)jsOUKh~iLI<elB<0KMm+|)TQvH{<&U0|4rk(>H-+%9d*A6xn&I$vz
z5*`5KRF6072gg&6b%58+m$doq<>cU}b5<Kek{9-`{{@Ny<tqS#ewob&!8Xsrdt)%E
zVNC5_8yllOSoN*X$y#6m{dydhYBt*6FfTa>*G!*@wfcOrJbHegw96=6jsU%>{drDP
z77y?GrnzN(|5ZOCjF9M;=w$Ne`D1auLT92>QJ6$>TJ9e<ayd|MXCKBQj{1X4H+mjc
zMAu|T2Tc(9aZpAu+JR#+1N?y=rXtwmi+hEEY5g<c<)WM~n~tA2K`74RuV*f0?lB>&
zy8^#S>{-m=Lv@lp=r0Voi_|B{1X(|CH}$!0*M|=~3)iWZ&#M26I#6PPFqn;NI>PY<
zLL9;<MsVEh%#HNeYN*=+5KLCXW(1s9xW#p&m4`Ufw4u*lTSJu_W*mL^IOysIH7xqj
z543Ja7aqFt=qjW+`9;K&6s7juff8yaJ=$^)mF??*BjuEh0g&o79$bWKsN$gRX=mtG
z>$lN0rET}KzS#ZfAh+p1=<S{{%T4*wJB<;Ai<8$IiM8Gr@5V4i5a)(D@I%w<mx4)r
zf1*psX(@uKfm%n;Vo>oX;!2K-L((ANwa+jMJ;O&6v7Idey22^xtef+&__s1Vz0US)
zebs_E(Hj*0ZmMRWL!s9-$_Aak3+_EyWpypjiYq-E;kUgtSfTs#!b3Iweo+hEMD(A=
zUHvvD(}&e<jS7<m+>Jl_G0p*h)TaA3Lf`yKzOfMB++Q?m1wwAsM|%Dr2y%|s$U4x^
zvyzbI*f^*aGRJ_5=ii__7z$W9!cci$fERh_SxE2BKy=UDZv5)1L4iLYZxr#p`nK7{
zexL61*vfufog*Y22-uevrl)gT3?~3>cd`Y(Y(R%4)qu`4itlf~eN2zK5Rjun!>cce
zB~5&B7#elVeiNi`<+i#&Q#}0BbHWZJk1RJy|Ijy$UPBm&IyZFx`Ku5diYZ@<&QnKi
zY0dM3Y*zbDetnf3SsMSKiWB#a+7~lDXIW$4AnU&BF#Q(~s7AWoSwB)gwsl`vS1IWh
zp1P%e7l;hKg`=Af#JZoYK6uCe>?LUp9Zij@ib~APH%aW~YhUJaD08Q%q%iv3AGA3L
z%Uc+KK|Fi(7ed4dgCDqte7P)C@aIg_On`ds+TD#$SmwjtJ_a<GXKS}cBxW!d2+#-4
zG(^>gEof)~W3<^NM^wx@nw_m2aZzK;xAPo*_i=9kkIftY`4ms`4XP9uKll65=eGz^
zO}7;@ELrllD37_GL2`W;&(vo94iif(1oaecy6zE*YOl*?<Zcz-s^^?NecL~b-PK*L
zWy$h9#O-Hy^a-ugA$YlcJ&~O7xHFCZI;-Y7f@gM9Ao!7TE!@m5q0aGl1KB4Tp;BEK
z$_65Jem^wg?*8DO>+uWJ8tT6xQ5gtb0u#>Y1F$|rYve<|2YgV?hg%}$bJPPmA}T75
zeJBo!lez;8W%-sU3WeUVwYr&`msJD<K(#^+c%vgQD>uXQiK|^9tS!<*@a1;g(xS;u
z-YprU9PP4aW&Is^Q|m+i2nq>z@Hd$2cI5aPfA^K(n9(lmfZsnA9BDXRjhln*CUWr*
z18I<YV_1{Sbj3i^1+mKsT~+?U_g|S$3!UA{X2^D?biLr_F-^D3@^bkKwGj^Aq2hh&
zCQKPz?^h;a+wD6^6zd8&HYIa}7a$>=^AiYr{p)HcTUl_8`U<wSZC?s}w0UyyRf{84
zUi@#;hdCNBaL(ItZ8Hc@gazh8kBl4XmXepBKNxUUHgdB>;ONX|ZwH6AArbs^v9Q<!
z-~q}Y%OhKyA?p+Y#ge%~9!swH4L4W$K#MN_MPerY>+QowtwoK@ybQU?L+B^C-qgW^
zUot-sk4yW05&q&R0G_-{S+(zBUu{&`uzwU4mstKibS22jS#MhG(aC)B<FlG;T|;LV
zHf|Hq=Ie~5rWT8i)p)7a!wM6d`7lvTim=<XquZ-0O#`i~;{)A#P?4x78a{sMuO9FF
zz+j`NEh7XLF4)ifYQJva)Xz=2@Dr|AhS}Nmqe}aZezcIgb$&4*Z$m$WHo006wibJ4
z6Y<_xrK|dzUK*MsEn%#0ewO*M7jlaF!Cw6c<n%A;qgN|<@SDQ-1GWA9`P1jORN6?w
zrLjLU_Ccd*Pf#g76`ou{s<;+UQ`MthOFKR&?1jyHOXbr`>tgsffDckFf$z)M{f9sl
z`1#k%>?;;im|b2K%`3N3(eKND5FREkEBpq}k-wY?l1y03|7Asad7ri9_Epq<7hws%
ztMyV=iJ{n-gC45V#DA}KU0^Cvp87udo2#Yj3XvRmZR9X^)~6CvITY%J{om9VfaOF7
zQwi;iP2~g$);7qYQA({+ul5bU0A1Z+JMIBAjdIvFYTr;S>&wD0J#<tF7C2^KcTqQU
zF$+=2DTqiMByCJ&K>b4c-Q~0F7BfmTgAx}&FNbSkln#Ld!XuSYqLj=G5l)BRETXLm
z)LRcf0Lipwb3SJg_Zd2rd^!<5)IeG%W%|AXH4m<gW8(B_CY}u%E+7Q_zgRbpPQE&%
zBozr5Ea}<Udy}p*-akG+O&9v*FbVH$5?@P=tg+W`<%C+;wUt@6HT99?oz#DQi|r5l
zPrh*~3vizOG3Oy@$}B2oMNN&hPHt{4Un8X9{eIon$;nB*MWE?O=?K70pp?|%mnr>3
zt4buIXe9cgBDnEY!|ZBoaBYG-EDKhv=WBj#Ma1qB>q@{QPQCE5%`ka_aD<-5_xIdW
zIUh{ydw8aEk{$mx@qB@&`bAUH<}%O@SwU)!&nOdOrbxJZARhdw-}v-hLb33$rWMul
zd46r@QBD*0f^L+(Z6*CWKfbWVqvNJ9+@wr>*vQwSYF=)j>4L3Mz&juJs$9`%>Rp?n
z)B;Mk#yIqcpoi;!ce@Y@2O_iSk`IBvMy0sH5CEPrfM}k_ax{gxrZo&XMGuOflGV69
zBZ5FGpH?-G$L`nFz9p!q?Af^4kx&Q}5Kga>W0p6hZmw2(enZXEWLVV#c*fNDFD-P`
zg+p9_Xn7ynU~H_PCmGwcY!j#%#zl{GJQ~V@_7WUbDb+^FusgY2gG-J}rN)?ES1iJt
z7n-tTyuOjSietgTZ>EW9hYTIiu=gt%s2|Q!W$gm7$PIs54aJ_he#dP$?JJ&{{$awc
zeYs=q>@HWVUch}8Nq4bWR}E@~9tg5)JQT4)1=<@}Ne{tM_EuyFV)UH`%zYEy$Dciv
zt^Pag25zk&#AXCd{PYvBitD2wt#tvpvF54sR(GL);4gDyO-;$kLx6F^uD9LcF(kqe
z@j<;<4YnFEKKc@Wp<Bjqz(vzWJl2#D4V&HJK7-0kOXD)}D@G<M(&9XCmK$1jE0Fsv
z{H%=QaFb}2hlj7T5lGW6ZT!VLyzjf}=xSy-_rWMVs}JwT<XC_@mSNPp>--#1Gh6$6
zbvhM~Nnu8RiCc<Z_bnGIU#sX(g`}ejUV%gRm*Mm%N~D7uJ?>AncCXz%e>cBaqal9W
z+y+}7_K{k^<Cgw>TC4g^&P_B(;N{ftkIY9X3b^A*JLO%#BbVYeCPmgF0AhyNxBzVt
z@hR#P0L|B#bpOOsb8yzaap2EI+t@ZLz)!0H%jX>6U>!{VWR%)F9a9_YPax#q=H2fu
zktv#~{GtO-gl5Ejuv)M{a{W!z@5WYWL)*mg=6U+|67zEh#uJ$Rdr_C&<J8l`&krP(
z0pPn*z|A;ldl|Yz-||Z$D{GHl&tq1<<`O>2jG9uGqI#jAmRI$2+b-$%Bv0}$`+L2i
zVXxl6x;(o7Zn{tAPv~&-xpAGl=Rz7^D}?tBYWgny_69x3W%g-bm3>R#to$;3#NxGT
zmT^<P`vAPKI5;Mt5UjOy;<mPO)M%4jXs>pfuJ>JMEq0};>hI($0^$ioS@MPmcs|9D
z!NQ>uHCc|O0Tv$s6^(|52H=FkWfftS;T4Goi`Cbfd4?MLd7bk`erNjXRJj__LeJI>
zjTh<kBly#!Xq>5b*m5nL#!BYbtmlyi`Vy6uz(#a(@q~N+-nyL{dqMx3#itI_wH|*7
zcctI&GWI^G>l6vdfm#nw$@Zi*OxGTn9CnW1CVZQu9zpkCt%vX7FPQ=iQh%JDy11oD
z3H7oeF^7<6oF9&GzKlXe54!ArtMM;B0A~bna|!(PnJR&CMPNZ!u&W5<V3v-&fJZ|q
zx4Lzf7BR`O=WvL)$6^%9$(lXtO%TeFlv;%ARvxW#mFYstjL;NA)0Ot$M01J<?6rE?
zO4|GI3)TKj9j1st0E_lg!fHjo`VU^_zs;axOd!Tr=N+13f8x3SAe;W5H1NN(f5<Bt
zb|CzHd%IC#`8Q(w-~UlU6etLN3#I?>N0;FP0mj^evo_biQk8#S6r?_eK?UU25oX5_
zZtj0q79g+Y;(=KM2l6xh<;nEF{zd`;!d8{yc*F4Lqs?(c`;Me7q&y9$Q|<IQDY>PF
zQ!1Plkhzf8Bj@zZWk|Czx&5i5WD=*dYhL|f?#@DHr3IhUsrFA2!Y@NX&&r2T$9f39
zey+cwGgr{&f9Fg1>#QHl!daFyHJPA>xbX^TMCH8mR}ZLAJ;=~mx_LA8A*n(r1~mtb
zsC83-^**(hh1`UVWzrCkvYAZA8fT<pdT>=if(pp6QX#fnmabp*|IAp7J?w0C+#9!<
zqB-Wnj80#zA8g!LiApmNA1A=vhjkL-<J2Y-Bo~^4C;wv;YOyUcdy=()`2sM4iM4aX
zaj_|W*Mf)E^9Ib3s{gOJjtcVl7~QUJ{KI?2kVQaP5}nnspJ=KBlQr1PtXgTN@^wyF
z_fV}+%Qn818Vr#lxalZ0XGC@4KL~khuYLt~_BGB;-A)>dSAf_wF*S;!JmA)o=Zh@T
zH(HjR%+I>#Kh-ekhvp0?3XaRX{)^!O76WQUXJY5CbpLXO>cGGdv-WOtE=YbMzee3T
zQS6AGT!`xgvv$=w)VPsznl+bYqTlcZ&u$Kf96qUEzB&4XkGRWz?;L|il}gbrA^!mb
zj-l+I6<y*_Q3BiQ-zje#`DYGKB_y;zF8+LvM$55&(zlWfvRhB8@8817WPJ5&FOfj%
z_gZyi4q>!u%FR@WFJBmCk>`u!L|oJKq#*C_fa_CAV|DZ7YZwcJr}<yv1Cy<R3=uuN
zOj@wgBDdPWn~$zs%&bppj#sfJ8!=HX69^<A_D?H%*R6b2vk`wTfHPF$JSXK<r1oF?
z4S^CSMNy9}0EPCVpUURZ#=;K8CY&bPb<+#=<+-dHxJ>-mA=!E|!F!3E(Yd0&imD*$
z7VAeYlyTI398{SLJb=?<gK|mdCFv;JFE}%Lf2FfiWercZmer6%oq!3(SUT~o7(M6G
z?^n|Zxc3S_e_s3E?(Wj-ANxxsgf0I*t^)EIeAyQ4su0~EWR;Oh0ILjMVxH~K>p>Bi
zI-{Ky4DJD+smkeWqZk1z0E?s~S?1WONW)IqXV?*`)1)no=D;v6Z51dd`oerlqMtlH
zr|X&YLO9v4Ojbi8Yd%76kk3FuTky}iMIZupwxslX)IX^N*aSghc(e9)Wxqc{QNG8T
z3vUPBa3JXIRI><25rNde`0R^;2*oOEE)FBos-Y{wjdR}{;x`BTq=p$ce{L|vIAk~P
zvnve!sS!{ZA@uqTVG!-psOW+9t1B1=UMhiyKYwIDSm*Q}G(#yZwRw!Wt*vB`{w(Qu
z952{H#u<U6NBURQoe%h^bvl{VKSxcdb39aa0=aeuIFwc<J-}=2rT0)jU>GuI@e<4?
zP5>^0&%#i>TES)TS`!r1pS6hmAJ*P7Dvw~>0t5m<f=h4+PH=(;cb6o%TX1)GcM0wm
z+}&M*2M_M<?o1Qm-uK?D`8BLwtnRO^s`^ybseNRd-Pze{0gZ+j14wgN|8yqb@6iI0
z7d&0RE3u$}7Nv9<YIr^+H|oyq$^CNp6<64*$(lUd#p0f*eC50|=v=&>iCDmnAMxwl
z2yiIy&mw)0#My{kx9B2J1f)FV1RkJYOe8AXm;Edwi_I<;o!J(4oTZ3Lr|ideh}C{I
zJ0IpQ(X+F&pAEbB@Qt)E903IE)3N-i1XHqKjbp}NY1EI|AZ<O2o$QI}^tS*!?|Hre
z$G5UjkX_U>=Q}PmPd3~RBa>ir1rfZw>qk&3|4qE*@yO$#->l<2Kz<$gGG*Z~yJ+C*
z|G7y7fIuAkSd`QK?-LOo$^cP$q3yZ>%l|pm<^vGUOGBZ*`M=N0i+L{C|F5q)##x45
z(boFIicW@NkXMYyh(V~m+SGj0N=FtBkp$32|K>%XL|WEBD8T-JB>_gPX%EK9$?53m
z`1tq;EEIrTUUuf;aEij|rL|j~EE)#}#)6ii;UfuK8mMW>+6!4!f?xn+@1IQwpjJ<Y
zeBQUf@&xn_0887xa9S4<7B*jOx~ZCLvcU6PoyW;=)AA~5<-R)Rh0)v!1yYOrEruNO
zGM=W~AJ+CVd{01Yfw~AL#lpg(prkyQerueH2ukG^8)u%EAEog@@;|R#Lrw?5Lq~c8
ze4#pY&}gO+JUqO^Nq2}VX5J)<S{i0i%2wUq{L6os<a<bXKsjg#-vU*)palb>w4xa;
zBqSsNkiz*wqrF*jXfP}w4DIzT1o)t8nLvBb7~>1CJjrtjNy1=E0YY92LeJ6BQNYRw
z&07Wr1_q>IOE!Q`VkSsGIcZ)#4W$l+Yvx=i5B!mu>f&$A7x2t${AXK31d0oZXb#9g
z9RX;UyE>2p2HQ>*O$|OgNZvPvG3p=VJ&z|ixd$36Ib$HWNLvE<Ye>keqa}cdjlOSr
zV<2uEdVjE;&KTRX6!FchCS8~Dm+BqX?4T!f2AwY0e<k)Thd!3}FaLE64@kQT^7GQD
zM6FR^y4G~gZ)3EjrNvB?&oaf#u;^*~VA@A%qZ?uY7q=3f_DgaMW57!}+QI8Q#oE33
z$AJb+=1ngvlQELd9gm5N6OWT%jpO-b7B=q@<%M!8{{0Uz{c}5Ossh5WMyUP#ZLbI;
zl9Q=yF|=ZVES=fnq{-r%Jh{=>%Uk&G{y)A9zzxU>Et>Tc91=3k`LN#8)AP?qHSM9Q
zw~Z`6`QNXbfAycQ$_noAaC-qD)V_Dqot>S{A4~TaSGTji8V?I2QsH>}FnCsO(#X^_
zSB1S)((<{nS%{yj-L?ac2-Q$f0J8-mEGWpffPwXnEFzW@oBI^!ziQa#1k`Y<Qd<<L
zVePxo$;k`AOR%c8HmerMfd@nuSOl9D=0<;1;|`fLaGB8gKuz*j&XHwcKw&g<Lck9I
z5tM=Q1b9bbF5Wo9z`y{qo|%<}rk#|OlrfEfGygyj&+`EmUZ}T+R^3+0Kp;DbLF?+J
zjY$POc*{tAf_;HsRMU8*rNf(|EuaQy6YK~*Pggslyi}Xjxee$hre$%ttCj+L%AR>v
z|7=V^myut~`>6*UvLnYc=!eNV%g98?7sk*eSkQO|MH2}#c1HC_5pK<PPQAQPR@g&4
zU5-VUF&=267I1BCZD!NiZ_&}-?-Z@Kh6Sk%?rM5xi%AjjFxAxL3DFQjbpt*?zeahH
ze0ijFkQx}2H<5tkqj}b4gsa#pp`}Qsv5_5Z6FjtelrbB_hx2~!uKOwSx1=(NKubZu
zy_O{SUGOrVckjp@I_+CD<Yh<a7Gk0jaB;BoGU&{KC;lCuJ=lOdtVsv|+#o{^8X9ii
zQ&bPb6sGrb5qT=eRn2?10E2h`?)uN|)W8Tm=S8^puccm^3|WQ)cyc!a5*+cr@Az^}
z83b@jMMf9*rK&GGL1a9jMb`wGo-e<=?9{yD0X2COROJ0n27zw#XX80}7DjFX#)yBv
zyqs!#`#dL6lUKk$mrRDuvmxxXQ_gubaQ4zF#$NFKX0NY-j(7D5!H;YCAjztK&z?^O
zrk6QsP%z*o3umy17U2ReduLeY*B%Pc*KD7eOx;!sAOa~(RoM%P{#7p?6%=M!RBMg@
zxx~xJ;67^#4z4TZK2lkYWAd*kId&Z?-?@={n?l51{B8U;+2{Gq7ccF%sH34o;Iw{g
zxx^4$x#&hVu)wo|a39_ny<8sr_*bMf`M@#2jrr;n0f7Q!*xy6(5_V+0Vc&S?x_Z10
zjOrNd!!A0P7CTdy(Tflk5%3_CF@00?`+ZBO2ck~LmGL4ARcMJ}X<Mx#uBmz(C>vn_
zDprNnD^p8hYb{}MOK0m(!j-QEu?qu3mIKZspyt)mB4}cG(ZMA&Yb)5tDt|LA|CWK7
z2%w$dv??fmw=N`T0R74%u3X4LpYyN41_eSWY+?qX>Ms<5UD1w^$%W1&I+}jEfq}0V
z%|ZgZeMgZgNdJDpHfZoV@LA~5U&PNM#u^9G)JO-iXC*1m#gD;V`vfX#_i<Vz-!?!<
z5n?VI#}O=SX%1mOf-(0#)_R=1AV?Eq5JeA!$z@i=nxM+M*SGkO!cg}t+$?Dz`&__q
z&W?;BE@3v}ipk2s@vTo_M$haQiX-G8LrgRgi@7Ryjn&|HlE1RHTmZ<Enyv0H+UIIv
zM0*^cByQ9HU|?fq-Si%AAYf#h(o4c9Yi^h!7WRx&Or<VDezePBn?Vx^A^qEHJRY7q
zMmV+c@7a11pxj1l^olVoA6<_Kvsz-BppC_(9M`Ou18%1FiQQs&nV**(fMGIBfB5a6
zFGwoNv#*}I-Z|_HyON(W&H6I?BV!N%^KysR`{yEBsDN3G6hsm99drc>i!sZYB?U>u
zBn<&<-@m_79UjmQ)7W1wf6q~*5<Jw{UpDM0=uXcR=jC*F71cC>2Ksa5>*p&mgfG4R
zPfyas0b5*~x6hap{MtOnZ7%2!GvK6_r?L+Nttj}8p_^81&p#8r1io??^er&m1BLpx
z#StyP1ydB!*j0~9YTh3Ohthlub_bi|Hdbr>81lgZY+v!)f4!_t4yvvN#O<k4{=Pf>
zBr$c}{<0z>!>6<m7XOYHYzmn?f1k4WLy7CPu14cEIxn0FHGAw!7kq9CG%y+(50VS#
z;nN7~SpSCpymEYEIxVpAXqOWrJQOU}FMDy3+N!8S2!E^mx8l%1#*DU(alwl{(#nK|
zDnAbg6y1rowA#feWc?wc5{2*e^-87F;j^Ux<2M2VLbS@qloG)HnUm8!GD7?D<3~cm
zj%*Oxmu?5hwJdL23<TYLE5@q=4LJz`tQ`@s(Y749hZ*FMgA=oD@WX=x*Ubd|9x%5#
z)7qQc)Ee<jz~6FfI0g6{BLZfKXL|4)aTZaZ8($KCl3sse@LTXHy9xOkIoT@t_$ybt
z`F#*c4@WL5D<f+s8_rV|E_JRml+9l7?rVpenv0sZEGbmR?_<y{cs?=^QxP$$GBRq?
zF<xFWp4%zdg~HapGSU3cWCKsM+z&RRh4>2*Ixh_5vNKK=Yb~=e17&7>oPmL1T(?hI
zMFkrR%K~r-7I!Pm&R#FBUHpInYiVf-1aDe^#l^&Q_w@7+)bTs<c6bHrsqb&F!Rkxh
z<DB0b4E?ONUc^dfCPxZ@3u<;bL>tQy%`D21pz(<AtWp?ig|SkmsIj^&u$OMK&fAUn
zw&u~*kvC&JrWemBJHL4AB)Zb#hZXIj{=5eHz2&8NP`+7SwbJQJn-Dm(lD(tKc_7vl
z2jk-6dM5W24Si0Z2X0|!S5te{XD+y{e(iPw*M2`_?uK%TAq@u)pI92noIlh}gHA%z
z;4nq9Eo<*?FKP{~YayiTR~vWLbnST1e2|9fN_9~yy%eVsN2wMhpsbr%TKhA9vGgd;
z%=gCMRJH7<^ja><_8Io6vn}WB@i)z-WiLOl{174(zxH<iP+K?k#S>7^NVmrw0<G5M
z*7LNR-o-+4%WO=O;D7Sowg@itI8kXY9#*P>b4v*EXxRj65($nf&U4?0_#}jCoZSh#
zx4qprFu-pej7}TNqO7V4J3>c%B8aX=JVATdkaQ~;N8nVx`Aa9UcR-_c;^(v{4wY4l
z?S&~8t)#q7tSU(DWmSvad8?J5$Wp~A8Dbk+@kSlx!beI|xQSA&(Xxvf?D~t&L`=!P
zhaaD{Ac<{WcRmPT2Kx<%h}O|NtCxk3d>>R|qYm9j>7hB}|F?)(#sUw4hjV)#yxUTs
zaX#8WnJxPG_*`E*u=)4&2&w7;agO^iv2m9EHsaC)+?QMr=ZmdxE`n+7_Zot+f+N~4
z)%rBwAXey9biN8<H@S*I7!c1sLDrH=wnVx(nO%#z?ary3piPW*Z^<ilt9b{>h9zCP
zH>TfjPX97crrUv)?1ReR&5XJMLk%S2_R$fy)jAZ`2g@fy$o9+=IISjtm)*<D>-P5c
z_}HRYzR~Hz$j95x!&J-+3=3mZ3zWf)YNlSb5zKzhY3@|2-q8~C5TB+71;2zVM0_9T
z^7OpqAkUM3hEFc6sk*Snir>hOnOs-O;ajdh<XaK;3fr2OwVWn5Flb-u3?u^mUzX<`
z85yKyhPRiO-XLA5&&0%p5B&bG%G_LiRy%sD<Mv1q1r66~c4N&VIVosq(Bz&Hp*IC+
z1X<N9%Bbv$mWa-|IlmAw5#Nu!5AbF>qA2q1+3;|CSITvCux7pkN&Vg^AK96#>=YAh
zW@(OHU~PPMN&je5k^A3p=Ai@3JnVi9Du7BSLkOBzQQC3~6HBdHCo{W2i5V0>BEtW$
zdN`INP7qa2dF_qBl~-Kc{e@DY<eON7iZ<`6S6&<W`K`l(<r`OxNNt;^-SY<i7@@u~
zfJ{&kBrT>zs9!*q8a(du;?i;BnDX;?6qJi*A#@flUMx6>GM;wxzvI3IDA@d~eK2nW
zZ<_NxSbuAF+gHpg?lW`xz`$L&NVj@c?ir(_aB{LZb&$q1peB)7)J``uOHX%c-L!TH
z4&>8Lx3WC{d4F>@q-4O@vrx=>VGlULYH4W&_(9Opf1~?QSXekT&?pN3mM$&H67OR$
z;^<xfW!U5%;!=bXeWk^f;!yb_kmS>C$D7Dku)#e2=pw81;U?=Y?eX-;7tXhDFl4x+
zMLRzm1;veDpG)h+dIZGXpVbm)=HIM26A!}K#{9ZqY`4aJ>U5c#5=GnP@hmSVfL116
zy7_bE9nah<Tl>Hk1Z@)f{vJa=`#0&U+Q*Hh$qUH_B}`E1MenuG9E0UJLq|qNlL=c%
z>)WqiYfUB(Mn?1HfT?hsaD19@okoa8lG$3(r<`NIKre#5I*zwniv9}vsJ_%l$jl-8
zMP~NQyYbDI9>n9tBJ2(?sR$3D#ql!lvu8XSBI3KRVu2A65yQj7AtB?W(z@9{ode}Y
zKhxKWT|3^XH6AyBq=ERrby{tJcE+z-<l7}!6dchm>3iiJO*o1?vE8Rt#D1PH-Yc53
zTRmW(x`*BA8tu9rc8V6pao^#z*+pXpadr$jRT)0HEE9a0&Xa)kcn!4BhCEoVnf~++
z_AUoU2fq}yeVwR=V=1Vsff=@e!IYqI2<CWoixQ;L+*H2%UKZ*7^{oR{5_Xf3<#s|a
zUx!yS<hl1~&y!;-Xaj2X*PPoWH`mp?U37bmdHJXA>4Pbcv-9}NzS8lxBk;`co31P%
zjTBiKwlkTK#)_Mw7uZ`31R>3vKEfw-M0F|R=YyaSze8#h+XQ@lRB4nd1p2>`@$vJo
z>~s@|o(|U3Fsn9fz1B3BJ}N|4C3;KOnsf&rCL9$VnTv#ll?zFfo4upUA9pexd_T@?
zgNGa|^yY%n%=W^b01~0+HIS?4;{(c`xyzAXt=qvzfWhO|U=-wUYm{Mnj{8Im8GRKD
zBCw##J&Qv~e2lyu#Q&f#fq!D(+}c>5*>jDKH%0xl^hU0=mD-l-Oozzzu$ctnO;R|z
zo$I6AUGCi+*IfZF_h?=v!>e5^TbVwGw_I~as#w-5iBPoj7;Dy3W21S;^tl=uPs?E=
zp>wn+^^X-Zf|XtZ%8#z&wkH~RW=~f&PNE>#u;X}+HOODxYS`$B`xI|ZGHF~!;ty%v
zBMgxd!F}$~Kc!@4WeI-;0}XN6zf-H~%iHM6eWuOv@#BhFp?UJXZMIvfCcK<1S(O$9
z*((3o`c5kY%9MorL4*QGkLEW8cM83`e}sCI;g+!~kW<pKf|K90hEo0rTG<g=@>nr^
zss6BYgotYnr}DDoE5r4qM+-Pe)RY`1TRz&tMAJLpn_{`*SLx3zmnt;h?X~(k-*D65
zaP664sNveWvinAO`c)=bMD>{-xTN%HQX1~{?p>(Al#O=bQ8|$Bl%5MK9N#oVqnUNW
z>sF8xy)>{bJa2TJy*2v|!JWY<gvWiP(R{2#RTq_DGwmCAYj>r0zwvE$&IDSutF2^%
z_(-T?rHO<8%6pCTfLWGOfGkfG#BHIeiQ|0X{+tN956EAOxL;6Jg^I<>$%%WziXjTM
zoSjXaAJ0zAn3@>+rc^RiL{Oib=H5Vh2XCNRy+kbxY-nM~Hxy!%#ImfcFBy%+_$mL)
zGgnvwJps+MXIfF}Uh@|~<FIMq7t7=RSx1$q?M3nQ7y!DGT|!3HM5J6W-(fu)1c_N|
zD+ZTVKDkT%6}Q^YNgY;w$L*eA9b|1+_cMc?Xj*yWHCF{HsK_AEz@E1Ykxj!yH)_JC
z4N~$U0@Z<`W68}_MLCj?5A&tiO<Pa>KsTe|q&+>Y{uIgIp;FLp1@@*a&9T_-?of|>
zmjT`H{`|J<dV6JZKy9HXK)KyhJ<~7AO+i+9a_(o2zsTb-?O7zx<IokF)(9O?_=-}v
z!u0Z^+KLkV8|fC=gCplz8ZMjTu%SZ|O{!@7&PIQD+zuM~YX`}i>;6xg2y}d$&zWyk
zYR!BH(90{zF3`7LuSGhZZT=8%u*2HDniZUeUOMtTeIVPFdIujn@f8OuL{WZ>1eqbT
z5>N{u;AQvYw!{sgmhW%xG3gnG#Z<nGtAF{a40?5Rni27nRj#g~Sd3z)%%?O?AwJwZ
zz4o;*z8V`R1Jlg);(>$sc;f~cuHGx`m&J$$2(Y$+<dHW+dAgGzIk%9=-b7y#_lwb|
zhE}Vkz%dR#a?RW?z0%D#mR4cAk8@XOU!t@XT08LkI^u5~Y8-+-0@JXe(u0=4-K_r9
zp8D1VfhK?7^>OGnu7*kVDs&rP6^)kDw+oG%?dNEw^BQesW(U)Z+x~kM(&m#e)ouNv
z^cK@Egy3{Ao%u<qd){aPd+rh510(9mv;`fPIwGp&37Arvk<gg1Un$2j+84=!{8Pp{
z5U5VO?e$rv8T%dUbQ)R~G4!B~laK_4_@2r+F_PQ>O7YK1hBo5bd!<k?rfzyszG4$@
zl+3L1c^Wq08O6s$M?cxgYFyPWsyT#{-N5Bs>UPUGG*TB+pB~Tqb{?^wuw%`HxTbP6
z-yJ{b4NpCOA*fj2z>Rp^QrcTDmbJ0F-?%1#gs6yP8T>aZMtE=nc>P>-iPv5aexkc;
z{bsY;P(<3*Vo?l7Ve7ryXE`+uDXpt;cLg7if#W@~l<UP9OATCrZs4S=W6ihH3sJfL
zdj|fZ0&0ZaN@gl0O+bT->3W<$JK`qH*!ew!5Qku9K`Ivxl~=2Mu2w5Oh0D5vVN@K(
zF8bHhhc9nCScyI<&YpDwTy!W8crDfrrrCL*OW}{Rb$DoLrfH14J;97Eo&3%2j|;>c
zUX00e*M3b;;|KX7%hr4N!Hv$a?vF|ovC_dfZjIEQg(VFzh3UPaUm-Gr86u{Nl*VUg
zVdQ71O_b;w38c$26n0s!!EZ4-g>mz_w0Zkip>m3QYf93}xh9sjjk~`D+}{iC;MK+D
z6yQV~?BQE#?7{i<w4}}+9!eYabC(up-r5c#mZAMqh=>946CRTnQ;A4d%n8}(r-MrU
z>{HnhuB-YvnHJnax^(5RcYs-a9zeophVEA4sG+`9>*b$F%ejQ1*{nb|x<~eW*B};f
z+TJ{#j$%Xn0m_QJGyX6>7ImNPTEEIHKsQCFgUj@mVJ(l?!8=Ev2`ft&9;x2#P5?8O
zQ76}OG(TqKGiId2Ry1kyq7TnF6i+D5O3UM+8blIpc(aM=1etSaP)@!eWc}XO9`qC4
z1TFDLmw^d7QsRZP53DncRo99*E-o$rirLe!cX|_J8q>Pum=?3Z*rIy3Dq0lTGiERl
zj>@=>&Wx&gVqK;oB5q%a3O8{2g}Jpcs{)mqxil8-Wd%nb4d6x}db?ZX7akPfhkf9~
z&JS$Kk#nVOHFgpaZJ0tx(j)M0Wu0i*Nh(JSWxuKlvo%7RuTfDitu#5g(f3J!(hS(W
zJBoiS^cNRM-X%K}ML1?~a_xo`&vJjNwPKBk8-{Dxn1in4u+_hAwGDj;=TfNNl3|}X
z!Z(+GSo^ZU3W-5u+!gF*AWq^0z5$yOKIYU}H6OjeN}XTV1Q{0qC3#^C79B^dX$|%{
zo^pUmhg!tgoYIX7eNF8}6GARS13sxrr0f???mM%w*lA-xB~edWPI5NNDr$Ol+}m+<
zdtO+rP!x(>n8jimz?)8$FQMZ97>FKPo~1wy@2P@;<?!?qet$siqrFXBBI<xx0VuQv
zzO=zK{!>j}S<zN^?Vh{E#j*Sf3zvbB$>fU2${^~~otdPsEHhG@1-$ze3xrIQ7Qy1x
ze0B^=Q1{HSW^D}uM_qRv4c4&w_GQ+M8e*FP1Y6}8CXzB2l*Ioqqj_Kh@UmT2du#&?
z+ik~_Ua<I^MlJIev-RxpUzncPNa29m&ixQg|A8V?Zs9?P`f^WujxLrkYqrr`EK<3g
z6twi{!9M%Z*cew^<_X{&b`TKRTX$IUcaM3CO1JtpmZHmP^GE~De%pbJkc|lbZLGe&
zG=d@*w<0)0A`21XTzH0OhOPPBHxN)*YS#z98CT(tGMy4Int??B0VRGTsd@kyw_wut
zb)ndJ*I(@0*W_5AvXDR=E-w+cSJ?N6sxa6d%}w7IoW+9z<Vk4he%kPb9I=dqc0mh4
z;ZUdgYM}c;Tsu0Y*xCFvL|a3$46(2;eSAtSH8aG&Ug=?_au#A#N-?wObc|$`xE`}6
z`ot#d#A`Tml3C*2%U%X}KHH5NqMiINJgm(WSY$O0$t2mLnvE5+Ck<BkGaz<|1yxbS
z@D{yKM!sJ`?}2k>P2ARZr+Hi3^;Qksx8)eJH@kzdTvHG6@-|UdERJ>IYDdAi#%;zY
zeRNO3-~6cvqBgaO>_Gt`ZZq!ue!EsM{P80-^BAPPBp0j6PPjCtH-~uI(ZhEcu{G7z
zCytLO#<`Kt+M&Xt>Ggp|zb2i$WiZ;pXVHJ4>OT;C-XG{}Dj`fYtu2q9Cs0cbq$#5Q
zmKHR2U;_+D%xqWLmW@R}avNHX?4@JH^>?*<OHn0ZdhIjm<ll+2)%hq3k?(BQ(5DOn
zTDRls(j+;^r=Ybsi}fhPHbt?AX=etvn^rQdo?>_M$APEpH47pXo#pB7&-y9D?<7*9
zG2acN2xS+R;B_X4@MO51Ot1`xd4QCdGTPloRT4?;u8{m&xc)(RJnj(bCeaSZt!sDR
z^Ko)ts!ryqwV0T$$LwWp)Y=`GKcw{zth0$6T{mq+y34I%5EK!@L!TO%VAkEJK*y!v
zlLToY9QUxFu4cNZyPAAIU!ErWXn9y-V;JS}bW@EhB-vtOc3kQnPsRNjIzg*_F?=D$
zZ7wb7EZy@-@qQ-%i+hgP<`7iJis(qQ5+rDdhyud>{I+fn-}c_opg%~9_ClFf-vsG3
zLHcxL6V0|!S3s<h=KmIsg=gXD4v>~URcR&`*ewX0{dU?b#>lvbxA-~mi?4;rn7O&A
z<HdvDl^ymph4h9ugERMS#f9I14y^_@i5CY;ZOUd!&*7^7kwoLhRd>J*hY^1@+`~w#
zA%`3E;&O}ID{Zl-n;jT~W#3A$Ej_s2y$-c?+372ypW}tSQ>(|Lk+1xPi(?aBOecSK
zO2j<CX5@q~tK7aCJh)j*9ux5AE|eV-e&jp5OZ&dhIe(HBdNP_Y#mOl3KH!+;@x#E}
zT%F|At;R;DFg0EP?Aeq90t*r{IJbqe`;(^bH91PPw7w!UEru{?XEY%3)H5a_9wWz6
zOAl+2A`^;!t|MzXh{t(N)%@YdYEO5;RhCq1rvDi|f8)dGB%0XtYnc|R87iaEzYHIt
z{5ZOYsnXD`=DrK4<ZEb!$h3--s$s$}SqTL#^$QZP{t_`W638Q^ar&k?LGJx38Bu*N
zM!2HYQVP8509Z>!IQDoU+9(yQ(9+7{4)4Lh9N!;MD^o2#o?7&}*RqJ%CjhUFfa>x!
z$f=4#v0`WNlB+D#5d2Qzcy5UOR}v*s+5%+boz#kWJ;5tJzj{2mqk7{fH*t<TNRJmm
z=^8}o7fuvqMfz>VIUASkd^K`SaN)YgP$-Kl>|%u1vs3?G$j{IMzKne8XO6qQLgf!4
zD7&vwL~4YJ=L-BoD~hCDjy>vM&$rt(q^9>E@#jC^{A#x|rw!*`;Bp1Bg6_lhXmz{a
z*xTyYKKc!4Z=5t_&&C5LQxZh%qGD581-C1$TwPr!5rI$sJEd=SN-~k@<UU=FV*FDx
zQ~)T-jQzY5*Ih>+#mz({qjco>w2??%KADfvXhXV5k<+LpCIKR6p%K37V0KAf9x!5s
z(kZmI&|_}V@vai)U9=|;3#S&F>`m}LEM8>k=4pIuFK-)NKRPg4Jaxj=R$8*IWM+*x
zTM}EO+Pno{<&O#v!Fw-V?>Yhtzm%c6XMp*yM|&Uxsv^0iERNxL(YeRBuJN}b)6AFd
zu9*W~a9c%C;*#f`pZK$4mFme+vF$BkBE!S=t&&S`>Khd_Fec~p?aGewY*YFLzERcZ
z^$agAJ?1oJ)*uunS~?wnHO?A+^G!13;^E4hp}+8sc}dR0I|1=_?-1XZ;md=x90MF7
z8~xN)!qb$t8Y7s}7Z7n>pb;J9%NsDHG?Vr9+)iuwt_P)6tKV7X=t?+QfXBY2T!L<*
zq1SQcYtUu>&lDs@%mcbFa4ltq6&%g)-BhBA?n_-~_2m-(z`!IwC=i1|`84Q;;5w4q
ztGS(38l$`-A~2;nSRZoWC^6f-j%t`#e}2HzvwZ}iTD%(=7VFy`$r@>uQ9OB+K64>M
zrN@+9v|g?nQ2Do<B(ma%?ttw}E`>-+Uv_4+NA#XTCXj;G627Z4QxmRt5j+7beQ9$~
z9$=HD**`XR6+)(meu<lNr`xcUWxF9L9C-dZH61i#+M7}OD+@AUp5tBK$gr7k@I=R1
zq0ra#=I|LY8cyVM97}xgd>>m`+l8qn^xWQL&UO)Zx%7lPibkHT84K^k$zpIBy&nRH
zu44e*F1P(fq+;Z${Q#s7+-fOeB;||ltoZ~7q|Dp_3}`~lIX)8c`r3Z?Io?00|AW!b
zBzfe!4=x^*Kcln2mWzT|B1`4qhoWc(TlMQ=;IK<f$MO64xJ5!oLAedlTR!dv8{Ak-
z_5~@FS7jX7e(fBQ2or$SRTyioSW@it#ml2j3w#^Y4#S99;2De-BLJa?j(NkWcL?qm
zI3}iJz)a@n=XdCv5)rH;s=+2{m|$t?Txo3&!GA@#$pB^}I;Jr5ev125Bhx~pedvD-
z{MdkjzlK0U{x_mqKmZa$c~0$<knKRSC%q9OkQ`<9o|(SL6AjZ0CZfC0=Zhwqc%<Jy
zOJ6Vwphum6>Rmm<;hI!nh&pp~p?g*tK9S$`t*B(a{D4#ueV{Nky^+1`*8giD;>iJ&
z8o7@aj7iU?fbU`;K?+npe%8ohihT?X<hel?6K7UC!5i}~-4-ygPvU=Z_u*$*l(;qd
zeN(bHNC7Oj#V25i$j2CHzNNgOUA#5~ra@UZ6JNppXT;wHe0Pc#%d<9~4>hsDBJ=~8
z<i^zr>>%d8f37VROul+kqpEUvY3&K}TzC&~Q~?h#MP6^-FVBZ<O5pFt{A>~vGu7FG
z(dPc+k3kEX`s(Ge|NM0Ryb%R3(sO_+Qi=UD6}+5IR|f{BU0il$ssD3|4iq?r;?bS?
z=NT{mQ&iaB{>udb{P;g=^YYx^JO7`r<#;XHtRp<|-1Kdd(2NuE2w1R4^p=Z@_pR|s
z!=QG*n-i!osj!FpM~N`(GypQNu>9YCT{Md-7dE9YZe6}Vu<+9uMq0_a*aSH@$3Oq=
za_>ONp2gu5q|6cc1p?W?(C}Bq*I@Nhf772oe<rb*%cn;k8h*Ak3zKQxZu#fdb(IXg
z&-8Eh2?MzTk^WnXuVBJqI7qwbDJBL6Kvn^pjm3fjbH#hA+S-ioVs1ZP7Udw&ill&d
zL;}JQu*9k(`sdXp!W-!-HTu2(AV_kopB5NQUP?It$RG9D%JX8zo|w*jkwf%VZ&w#F
zDQN={gy1C`69YTpNBQ_obVNGqc4Was(X2o6@hl=@9?l-740H{k{9jF<&WX9_Wc7oU
zZ*SqMLm%El!+iMhc0n7Lco_;TBO`-l!3M=k69ODuS67!cQ?y147w|7Rf`~IWF*Mme
z*a?%AxIAAsR^4kWNBuWvv^~49U`zP8rL3@o$Kw4sa@s^ln03g38eV#;zSorM?X>?s
zGz?qCOQr+?U5EMCAuP#OnP~wIa0m-6W_+<G^N2oIGE_*qv?Z^pwj`gMyp5874<D_B
zo)%7cuN411n?;fJ#cG6)fkreKNlY^uldJe9IK(ykEk?{mVdoW&QR~A98UF3Yxg&#@
z1g!OH4oU)R`Lv0$+W&PfE6Q5|h@rc@m@!~aW@Sx3!so9(^`SCxG5+?ucy2aH4|kRj
zHV)e6FHctrMzG#Q5Qj6#4!>?b5lxSO$AtB^=aN00w9L9~KAMs>Hy;;av*%V<mS4EK
zy8ED?1KEdf!{ao$I=ZwJd&(Ui_qgvF)q5zGl#+qUU51jN=-phYl4f7QPW_9P@Vx2@
z_l9JF3u`35$m;0uC&D)5t5*QTDY+G>i!n8}m9l?wdD<s&(Odh?JgTfB{>PW5s?;_h
zqYq$UA?Y`ttAQKHaCMc`FjvyR7N3pa5!ZPTHg6@RprWPOKHQFPc1VER)0cbcq$QFb
zU=HUe3%6QpOX?-i$5$N2qT7S#9$``s?Q6J{oBr|N+_uK`@|J+bp|iOty+SLgFRnW@
z+`V_<YMN8dW(IZ4(>;Ie)=a~|NzMC8!7`_t6sHq_G89egYQ6|<w88lTXo;y=uHzn*
z$}$|y%$~Iq>e9&vd*@e1ZjYXrSp^1lIB5>$w?ha?x3)cTG%Z|sOSeLUn*(bSvlYLq
zmrU;2(ZRQalp>{|uAZ8Z@P31CMF32&p6zr>97ak8WWbZ|#jL2A063~{yV&6ybcO;b
z{MmuHe`lz=`!5SVr}RRVr|_pKKH0~S@ah&W7`QI0gYKWs@YT4K+ivCxXCzw!Vm%C6
zQp;zhv+DEmX^3mqlec*(8dYvpwYKs?ZIkF&wOCvyN4trBkHE^91^S}#PIGQ;L~fF0
zZ&2mi76-7{!DdhL0^^|NWI-O^IS5axX;NolWj$zANdE3wOhsCnup^2nA|=J;be`vc
z_}f2_^b<6GIix4(g5lG*`+MBxx*og~?Ua|V15cDL^J}y0F?>?SP>$BDSQYi7Jm@<2
zlRU1fS7DsbM>oexh(ZaocF!B{!nMd70IpE<GPa6~vjV#dw_83<49+Z7MSo}}_*MTD
zPp^NpatUB;I^SAd4MUpl>kO%6A16CWpdwyhI6q=)c|PhqT6c1t72`8II!ZM@h3(Xu
zirxS0arpTboGn&Y98O6|f?}jA8(LRie~p+pR0stJ$K|ko>-B4juaNE8&g&l#z7NHd
z9Es}|om^paztn+PlLXYsgW9vgrKN}LE<}Cxjl7>qLC3zj^Hy7>`NYnJH^cWk4VTLR
z@wan<)-a73)$l3XA+XbfKcMQg)livJ#L&JeT(#6>{TvurBU_S+pw*kge!Y?=;LD<l
zXIx<_$I<wXo$e#w_-GM-@-D;M_>$GwU3+b9DpI=q9LcMVl`vX_T9)eF51;R+i(%r-
z^->w5Ke5kEFniq3h^$R5#b=l^&i-UN-g1|{HsEkO%hG-0Y%g3avvv?D**fc>v5%+0
z!G0Z-mb|@7AEIn^clego8GQ&^nQk1T1XfxL$d;rC{{SqXu%!+-YAa^)B<ZaAz%8JT
zZ!h+yOVr+6mHPL_CzX@QlD(Pp0SV($uGw?}Z||TNVMSpzJ_JjW9T0mNoacQ2={0=y
z&;uEI=Qr<hkRnt&_uyU%1;<QydUkQYApLn=u={-@)R!u4-ZG9QtA;Fb_ue#V0B_Ko
zJN^!rTb%E9nzO60Wd04W7t4gI-Ss%maD|{#2OQ~c@o=-{vAr_RcX$LZaMy*g^-TvW
zRo7k39!gH{2K4<+i_s@2oRE!4SAFs$bHO(f1$%dH7WNq!Z_c6K)R)s;hhayRi747w
zj7hA!WHYLZg50$b;U3@X7_*$}OCUI`Ysg6!zp8a3<7LlBi8*Rk3jXnmgsS?35g7Ym
zByBP4%!v|%ylPtcJB(HQSP`(9e(fyg_Q62pHoLuo0*d5UIB2%Y+l_%!ou|xyoKOD;
z-dOhv@XZ?+sxN9l*WV%(2PdQ;KR{|pn;}md@0U!Hmz#!+QxnLmofkF!+_R2M8R7oe
zR(AW)x|BVDAlLC)El;D5tqv1?7`DK8?BOK;l*mzSq~+6_X0qLrt25<la@2zB@dr~Y
zP^ucrv__5zFZa(g8tOW#)0}}L_>c1HYD?yi@Aycb?i)Kd6PBt;d%;k^!)_-#b7Wev
zhl85{&A+b?fy>;{Kpc&^y(AtV2gML4GM|o~<tVd~u;$RDD+#Q~rKDg_I5<*kaimqL
z)j)nUW{>o}r`N0ETe7KnBO5NV9t?JftD`gX$xid9P-{X0j}_loiRy}Y+0;N$l<nPJ
zrxjoH*}1t-`~VBG9~?HR8XA5TBxuU;HMVFL{lkz+c#R_2zd6{05~*yr)LLP;Y@=n~
zjUU-fX0t*ijHL#a!`WTFAH$6s;6c|$(wYM6itONiT8btMYFxQv`qY}YWnMb5d^gQP
zs*^#5eDag4wV7lian5?>SO8;dxoxGa(^$ce7v$*U=xhIM#aL)EG@6sX8+~QvKsW;b
z562*D&d6yff(vNXSscNfg<ozI^(xlR-X>#kuuv}R=Q1+OhpZ{;)is`2kK1<g29geS
z&094^Ijk$}C_-2irN1#Q20&HE?X;Kxa5uoPe$WghpEtk!ZjFb3Yt6Qkwl!^?eyHyB
z?W6t=S;}D1jf8kcP=Pk&U34Z?R8&SrMgd{$&Ww{a8!)Gbw)O@5H4x&?WlbBC`&GFu
zAEA(a63Yfh#@|Zvb8q8W0WX>~hdJ_F8!|Rz>5sCEtAXjfy@hRc$pfc!5SDAbkbHpp
z?#nbNz7<yV-4CPlMBD;QVd|2AU{?u1Otdi?9SO3#<!9!jIqO1##|D2?p~A>9*zlAC
zdSlTsA;_WGS-7va(a@Wubwxd|4n^{?qv~Aqa`k3b)Lrxr#RAhYiEONOXdD^h9n-E-
zqrHiz-5%ZR5y;oC59|lgYTSdH+d<vbEuOfp^l){#)qP!3j8*+YNme`fD1(1AcAjTL
zpPysork#88$Ac+muFMNKT55^%mXu|*eBZs!c+gLE&#;!%-g_B?DF^|*{zto52op`S
zu?eP9s!>MfU0O+7tW@4;@6kuojY<ara?X_DWA5;neoCYd2nb?e7*5VZV=_2gA#$U9
zAV;%HLBhlAMDrEF$crYZouJ&Ox5d(PYY}7v5}GP*qAV@;E>ov+VV@v_q*eUOi8QS!
zI<Miit$=C@Nj9}MI*w#q#su>%e}BBBJ*6-TDJ8HVL^{9B+sKUyBo}um1<eS~`^kQV
zvCzsrm+S-Md>4XL$>%@cA)=^cLJ@nc6xf!`W(|+WK~4iW=2R&c+XO>zA?L9wk+Y;%
zWQ+X2sL~_x_SGkDb&y-ss&;E1`2b`t5XHN^^m@sBI*?@Q)X6u`8{s&(G!z?t1K&W8
z>MVMzh?4;a%whVmCdq#aBu)7Vhm=+)RfzGut`toO3ZBdT4Fyh{jym;}|I=}z!<mb*
z6%_+7oGGr*$ks`w*-A_7ZdZ<|%;FFFND4;j^vdlI-?mnN@rHA2z}Yrv^Y(e_;5zW1
z0KNrep+B1l-a{t+An+((!93K!;iA&533x<9(hCs-Qop`smrH(1;qZ))kC#kh-T>(9
zp{C~Rt&!e1o!Xv=CLu$Ghm_DzMi#(^Ca*ub<iGw8T09>FOdiDk*!~;K1~>-F2FpGe
z8UxjX1Mm%3vELf;DP48+zc}Pw!Nqm|7+ABxS6wYjM#t}u-3m`sr(;0Gc3J`R^+xT$
zE>HZ7;>u9fgGJ>c07c2Dl@a2r0u{osi?=*QmBnpmg+Cx6qwhC`P}u119Q^jtbU;!f
z?1!SQw#r2sAW(M!&noU=?hv_OpKid&{RAZwYmEI>dyTn<k;|3VoV0HI>&E`tCiP&@
zhn?>$28$N#S!m_%DvbJH>E~uQYpT29T<2@<f({&R2iY8j5q2Q`+;4P;KB*fxcUNR-
zy$JO9_fH_wR&O;qDelvJzj8Vw*sHp=Uw51qkz~xM-U8k}PdCbH4gs4<TcHA`yi{Ll
zOATlC-ZcC3jK;$8HEyLK`9=IxgrHW<itW_Ms2MhMmC`~-o>?}kKP^Axa#Fw=#$;~A
zUgpM08Mu#SVtX6EY>C6`gVCq4Wfw~6LDt^o<)~uMj61la>Z~{OYoH_5p&W~(ay;a&
z&{71sWdraWmi_QkWnc?(?OuN$c|_{WzgCIk@rFRhp>pF)ILxf3Vn#qk-w{~`$<rf!
z8E)yuP3aS_xxIpzo}I-u>z;<}1XJS68XQP2tvb!(*f*_i5(0B~uVTxJGLxum;dHP$
zp!4Yz@IK<koo%E{?cfy~*nExsI+yb}9A=*tEg`_c=OF!bsN^%s7J{QdIgFFT!x`q<
z{lis%BV5XY-!Dv1>q@X3G16}Vq351)bN6H>+Y#%~a$i3?P?3`RRfchJemA|VGkhBT
zF}TVL^6N3-C#CUe0y#=_Z;m)?!_%#mt!!PbVt(p}s!`lhHktIgc?`z^yuGwf2LOK)
zVfH17K0+&I`*xO~yT%CM%PY3|TY&^nDdN9j3f8ej>9@8&PQK>;)qvVc0CXsoWASVR
z*7?9&2nVU^qO&Iyy<71MQYQHdaZ)X}S<BIn(+Hj;!AkG0FZN5>4=c@rcVTuecj!0A
zr&=18Ql2O41pB<M`z1EfiAbT)1a)1B>j{RBf#tFHBQu)!yO*ygEcWt!t4XWb9;~QH
z0k0i*C;nBU5&4IG&uGmk)V<)!xRoRb92^u9ZfH!kc*N-Ph9VZ&$DRCBK!4(1Or;7-
z?Z6agMZusYwE#OCrd2N6cD-0da^F|H=sR0_sM=X;780i6x)|z-FhqE)>{y!KW^3JP
zxIX`4JWa&M1gvdf!=7AsV~l*Rdz>Ri;IUYI+>iQMef)&@T#Bgd3Rqw8qQAm!fd#0~
z(w+1fZ@RQQ9Ge{0f3fTe^l6{<HaCR`*Y|VVn@D*DjKRS^?nXwP?yju4c)e=IzwbUj
z8-d!x$C$qqJ-cfRZCR>}!&HzQNQ)WkSP2x5{^FGlM(Ek;{CF+vC|wGgJ3IW*Ha1EW
zvsXj;2e_Y_of|4t=jkh9cJ-%p%cID!K8qs_7h34qnRye+gm`Z94V=N9zW4h*yXPBc
zesYJmlSoUgABHvKFE@oHp@eKlBxkGEEo)T7s{_F=&-wU*@gu!$hgZkeWef0Cai10_
zwdwO0=O*uewA7^Y(4Ide21|^j0@_X>X48xB(Qnuh83Yu;=l(q{?X&^o;^N}<CD!e`
z_4kjIU}-_-<86&b9`<u-Vp^N7wWM>CGjWUgPjdrI1ib3f^C|Q@k~LAj7-3@tTmo!T
zL1)#7s#v|WYPKpgQr}$<P7*S7iuij7cb7Po9swstz%C1{$KODIF0aL(iytU(UfHWD
z+n&WDMcyh$9&J;kJfyX5$RvK9Q_YW$w+iK<4W=nw2gSe@n<D=fd(Se`edI~*-O06D
zer)hbNe6V-ygo<C&a$aBni<(p5}_waI6gmIxBYOuHm6JSU+-a3v3E1mms=iE6R(Z?
z*JyQ78QL6~&Woq_B70c4KBkyyYJx1W&PCyA8fz+3STB&!bKls3Nfp&UJgzqMd>V$S
zI4}Ff*<|1mBqe!XneMhS?Rs8MQ3T#{J|9p%K}*pirIV)tF6VU5vMb-ZEiU7MKFnE@
z?pCa;-809i^CMXk<sujv1GP6#<L6sakFOWTuJq%FC;t^V2z1H$BoCrwWg6-0-8We)
zA+GNB3^s{s?7>;u8HP)93n8JstPcj`ETII|J-0l9oe4L`DTbbQHAYmgaH6>h0E)=K
z;y(`GFaLl04Vd<904_~{t<UhtceTEI0l_rir<*kj(%Fx?&i&J7!NpI7lHiJ3(VBJ^
zUuDuRU6_O8PcOjNpPfknq^tRb_>sqGSmLUeS4@2CwTfeU<SU5^%$6VWjGsuOP5nn+
z0-*kSoj=C}CHf(@XIdIWBvRG10!`uGW8w**iVM)PHFEoubC57-#XZZ8_Yx^QR*F{I
z2A@AGYJbji<+qhukR4#MFjL%Q2yCQbU?Kf!&&3B821Ib|V+@=4{zhIU(@V1MEhh2e
z73b7T4EQH?R8<3*nH90|qe9Ft6gh)(oChussqd`5VGkyPfi{WJwMddD)evrkpuMO3
zE)&gwzcF71={g;cefh5QqiCBvfPI+?M*R*o0zz!}`<xRRrZ>GIv;RAMNxk(I1?n*8
z%7w3jkz>DAbt5G%$WTA&JKRsm=5M>gcXjEu{9;~l25K9nVMlL&z$XBOd`36vESQC#
zL0lL@klv%q`8Z$RV@1B)`~|gqoH|XFadpe=UF(yqkC;?!SLCh-^!Yy1=;G<+H8`ah
z@4V%za1yOM@xJgCe3`W7--SRSPS*v{Uokw~S)u1=+7Wv&jg0CUc#KWseLJB5<#xz@
z$NH+eA(lV*>qx<w#H<eafdU!FuIO2mZ>kTn(5##3uQI)1IP4CbLW-E-(DH^(7i1YA
z6iZVO4l?w2SX(a=;;y~yNcOS%D)tnsu`MGk|K3z^&uZ9aM_BCYr5=aegx0-XzrLFG
z>)9b#cxi+%#Mc2ABk6GZcYvM3CP)s&RF<m4=V;o+nPRF%zD8cIS}rK(Cra@z`3=GJ
zcN2PM8ICB9rqqrA#$Q}qZ%Vysj~mOtz~~~Rh><v#E(y41&_JcOnMvBOk9_1Z)iP_t
zAdx^AhU*=HsSyF&B?JO5SQ)xY%Zh5VE6kmuN*jcHr=mQXp_i8+65CploLRbV(ZqRt
zny};^#8S1kuxQWgW1J0Y70{3JD6C4_Gi|kc!VJgLeWuB>gCz_!n<U!`!A)w_<6Mi8
z_p3BtF@{*2XpNVOmQRPbY^p9${(8kgEKU{N0~v;AS8^C*;)fYULW+fv_Y-%6)~AM!
zWmMAlxpap8^t@oibQGW?pR5x^frz$QaIr$CpY1l(5M{>UXYtM67$~QoS;=y&`j#TE
zqUttQ2)?qjfjXxG7Agzjq$IH3BOvGtHPdZlvppM#*79&9{F3hX8n2M(R6ixj&l~-<
z=1C>TI@-4poksi^#$0RaZ?*70p*l5FIlg4CTsN;&N)rzms<$bzna9So(Z!Qtf=nE%
ztbWE}A=#j$rr(|Si0n_sOU4#U;;!-sN96;8ZH{l{dVGb_4$T#yj1z&v0}@K$u`E$0
zP(&Y_<ipfZeSpSy3lHCa#LDgJV9;1mk1M^7Yq9F3Z|y8$Ril6wjI$5fqi&q-d$f=p
zpGi}WGd-U=9oFP0vC;IFzFa0=Kk8;H%U{w8)z(luwZ2vD(-e%3PzrWk&iYP!eMVcL
zK(t6(J-Dh8h<^69mao3(*CVpK*<|sA;%JXdsAY{V0KB60qfs?=5$y`cMn;qpF)59?
zQbX1gi*BJqZg|tLS|RfRn=&n@>H`YmR#YVEqup05*g~Hqg_aUUle;czh+#NI5?!{b
zrT)kkC3T8cSv{<QN|H{WRy9v9yB~bSgIljZ#Bgx3vaEOZ0;U0vcYtJJaH2|S-WN;5
z4Pr`zd3j{JO@Dc4I7vpdEM6zW<3$dR8R^d^v_Yr(R*K)Vs|``&!VC#T)XirAI<Lgr
zJqTC%0rFJH1iGf8X)QQ#2h^05+Q;v<`-4ue%7>qC%Q;k95S=o^DKnZnav`_;kV&CU
z-+|^JSy+O?l9gRkY8YtV@6c*Lk(*)|AVAL~f#`9$rMhPE0^vAEUWXda3<?Sl+MlYT
zOy8#B)Tad86zO_z)a3Wc*8eIH55_In{eZoaKl!yxtaxKyW~c3^333@Es6rSRwL@U*
zX|4Md#p7WbbEt~f0ez%mt`U@`28g`S@<N0W)%OfyIsqOBD?g4lN;&^72iEcYfYAa5
zw<6OtnEe1<3Mr1y>5f^6x{Q-`EULx$f%P5i?|%KL&p3|EbR-6p<q}#CP$Vo2?jv`-
z`z0+)N7`W_D-b1SUa%m-cTyag=W-M2<oy^VrS5odzEMnZhktDfIz?-tl#}}WLC!NW
zZNsjAoZ^F=S<ScDcyYFV2@$&jsJb8txy|%(3S^964;3iQpN=%wIL63yY0pFd1Rswr
zwgH49NpHUV!05Qt-?^#`2uWLdWr8A9<nwpN|EuIa+p!>?T};~ERlNDD<NcR8Yz-Kq
z@zRjQUnb3$ow{caSab{lJ7CUwK{EdAXu1G{@EU_Q^#7VDfkX6n%R-;h)ikSSAb=xm
zWB^Pm$j@)LcW`i!kO)az+SVtkt*xD&p0>BQ&yujQsfvq>gEN&8mvdWmvtHW@Gdh@-
z(?Gy@y<W?~$)VppECwqHdk$@MV3>c9H&i&n0E@N$H9{&}A{;?9048J?ce~iEkiz)A
z@t!He`?dH18T=&%9TXwcJpu7AN@UXE_%We|-^1fZ?tO0PdFi>-TTGjayCum6l*J@r
zl-OAKT=>Vb#&o>3ADBQdQfwy=CUdBByjO`0qOlHK9Hm?;(yq4M-#2S~(%$M(%f6*+
zEn6?sz1KlFhwd`>?yrH_5g?4l69N|)3`;^;!Oy^-(3zKJPBGaxVtk*KTo2mWb)L6v
zGGb`>p&alI1Psumbho9pBq|bf&n>DM1b!TM4rFw6+8!lnR;MjEJwI2iHkt%TxH&mE
zvint(l>t7vPwMJ48xGFSr2x^=;r!2>blJfRWZo9uy-He~Y7IHl$;kt`v0|Cl(Icuw
zR6InQjd!0W<u7{5r&XLo{L9z8xvgmv97V+hc1I^i6;3~=sMlW1Ox^o6MM?<gl%%Fs
zb2;AT6?0nN8^bJr`Vp^7>Tg(@=#GXO_O125g6wpL=6P1W&VJp}O@71Xy4%hsg35x{
zYPa6{aQpZrA?(^bLdbex-&dzv0F>h`rsJcR4+Q#9)69T1Ffu1QtQp`Hv)$Sat9XyU
z-XIwfQ?ZtxRXSa2bMk)7>Oi=PIf@Q?uWtqwT_T!>bbwx#Rq+i>5sL^2UqJ)Z5;=N_
z=d2BFvEX(Gv$o4^paF{j`y?4DDc`ERtnB_`^PDDKvg2k#W)6^417IR-DJ?~KTsc3t
zL8YOh@*#G6dbs*z@_2t!!zjXOyD_!Vp+yPULkrd29EZF@Wm+A&Wfqmy7vziKq@`db
zy;!b0_Jh?QZ%IBOp9<wIb@=gd;GyHhVR5Og<#>AC-o;5X*)a7{+VIR;Zx;)vsk;~b
zs@jRh9kvu>PoHKsAspm3S@Q}7QWuiP-uvCFtA#Ujkj${urDyOg1~FL^eWbhfDzcT~
z1p)>k;BN5nQWHKU5V#R2(pvl|GGAs2YT|Rwg@pB^-7OHLv?j{*V&bB9ZLTjK>RT~J
zGG3+?Q?)rM5|^oHY;DZ02mioI^r3TZz*+sCBjkuo5MMlIFko0cy5)78+JoB7#SM7^
zTFOT0Nvmd0L(r7iNs#0xYyOJl=RW&i845gqpm;E|JDroKYSde8VCpA(f(smxrMZBK
z0-Sra(3<%8X@FrtK>^4l+l&>afyxf>NM^W&1F(rah`aKA;7z80A>Hz7FkDzS$&?@v
zEECq(YPA@{prfB7l--d_#^G?Z)v|T4W1Dxn*U_Wp3Eo^~ctYBjS`?27NAjIQwqU6w
zu;#JlE_}b%7^Os+&Bb1(RdJ)`ccfu`W)j{w$2tuc<<@I;casrkZf4fQ&W;q<SFV`_
z=G3=#%DPzJ=;URRN^@%QC)JxDS9Bl+AKcX&KC(_g(h6kb+*R*=VB$a59%9e~Q+KmH
zw@udoP4rMvSn{h?8?ChhO-76MZM@#NA6#^=y250^<vD!Z9>gc2C;BK3r71WBhtUIs
zUwAk{(?P{L^@ha)9<dUBJSr+G=A}RV6H-#BIk^Fj%4{Ie_4R9^no7d6Wb0w1U4?JS
zOvZ1KtE;Q8`6ZoVp#ynzd9p<ms=|t}dxf}kog5u*obG}e7a9(qa2~_6-6EA1Ka=7N
zDB@E0AFEJ<AJ1w7fsJZ=e*+s;A6Ccu>pi0&DG^o=0)eYvDbTgJHn}d#33=gHBO2@&
z0)e8rX^VIEK;{?b#{+bxw*;Qes}b#=g){x!Y?n)9TKoLx5BB#22zhEsQmy$3d%&S1
z{yUd|48CVX1fqsU7P7G!GtF02d=U*|Z5^ErtE-8j$R}ndOrn%`sIe|tvwfzu((Q9Z
z>Ttw9q+)c)oly}zX*H`OO7AsNJr29Agx4o(ru)tkYN$O6`U|}8{L~U_3fShkRrilM
zR9!J_39aP#L<m)@NiU?G%+gb{M|E9vFpDcYvJ=j`<!G1O9!w<=l130wRIlYcaEfAk
z!)*$`XT3EH&3!$vBS;zx8$i8bn_~N!{tSG}kL~|y?<=FKY@&YwLAs?=De-`Gry$)T
z-6$Y+4$>V8A}FB<NSAbX!w~}k2}#L=bW0=sAM_RReeb&8?uWbXWu0}_!!yr$X3xx?
zJ$v@-{oBNIV4Zrd1Ryh7W!|6ZZZ~C+>OJ~;dmWve5Wa`2<z2$IAZMbBi_2MNaN%0_
zjj7T)EF+yecQ*IuQ!?N!LH9m>pjdtw+XlE*OScWj<fgZXOjuC8+FA^U!iSV9E&FH%
zvo@uuSaY=LwD#gV3|S0Vcy-Oq-pwIO1aUc7;*Eikfm__&txQ+Ar)27JAek<xEpzaR
zOC?wcB^@>y^R`VUO@TX(t6B7TgAMs5q?9gr3+SA$V03=i-@IjriIb?@u?+kOCEbl%
zya|OC^A)L-_Hy^eqix{Z@I%6*RLz0t0Zau<{y19ZrzO<FOrmIUUlp#N4rr*SM3_)I
zY$9r=f<X);zl*>(H<SsU78mdI-5Ld^nwc?9s}^c7$(MmUok4df6Yyj)420LYEcXyU
zm;^ZpF}|hBuq}XGQA927{j}F8NxhqelknWSMZPzHaGNmw&otZ_kJDuYrujBDu5OHQ
zu5Ou#aeNmX<oEO1a4R7OaU>fIP@l+VY1($J8xaq5F_v!_HF?fR^xjcm?K2CJmpHZ3
zHlc^DrR)ot4C1#+zMRkJrAZ;@(7UPAqS-I>BH-QfL^matIb*zJDnpL82`ohiulX9E
za9V9ZR5jG#SaWgs9$%|C`^nw9`z>>*Gkwz6%{J2ShxWaD--Q-}?XXF~9Wj)|Y^%nf
z;>}~V{6r}B+iX1V3x_63ZFTI3(gxZtTp`>uC>iEkz}JAN=LZIu!*!VOB*-8qLoZ3X
z*t4#g+1abtD!`2UPKz~p-SoCEX&msJ2~d@N@W6v2R&8&=6Ynm0Qm}6Nb7{SARYnOe
z$nQBH2~B@O5WBE2qF|T=@<hE+dZGKmQP#&w?Ap}pnQ8oCW254AiYd~Tqb7%SkF91m
zmE^L%%-CSLn&K~BtUlfi%0nB9)%~yKl@+gqo22>5kVTRTqsK-?2|M(L=9Sp)B@vGj
z3{zo`Y}hdH2=nj=V;hKZZKuNn=Pnz1V_>X&UyWd*a;F}B4l#g~pxwRu0hT}v->%sX
zRkF>qu@e!SaW$_zs->8}ihecq+gvoF#n-fe^u;{=>gr-xNCktRNSAyRVrne1&lDJ4
zOo_n4$^y)yU=roL2H-aMqIDQS(Q$DeUu4L>rDnVf#{Z6JmSADY&dXamSS}8}5#xp*
zTRrB8J=QFEV{!8B<IK!Vj>hfYFoB7jFVAl~yohyc<9&l+zNKjN_)V_FHcW6~oz~3r
zc08kh-?iQ%gKhTv*K!7^S|{LG^A;ns&!R}D@wHJmeRkob)EI19kKP-!BHjz|_C9~T
z!e?z8>3{hNov!gmGwVc$t)AS-=JYR1H}B!lCipejHcCwJ1EXWn#^NI;SThs{oo`K!
z?LJNQ>${Q<Xww2&Zah9zP3pu(hv_M?F1^p{v}c)Uy4Tqq`4LlB3Q5fwI+-iyD)yW;
z@JBa9Q->*#*-&sRy}e3tg(>E<Ya41-D}wekA-#?{g*J*G2UcHX<Zk4zhGfiaZZFzU
zznNEL@PpmHh7>YiJ>MLm`KUajyt_*f9d?J5`6kXTuIK)8>}=4uEA-RVGZzs~5}+k(
zrnR2A@%76g>60yyy)C*~J45tTx5m4aSP%kP4k9y#b2SsZ>xc<sYmcrAe(7+;%)}(N
zKNDqSWE9yBaFTnC1e8q+xvvpjHOEywj;`~QU7~2IJhALbFz4Dj^!QF9Kw?rpNjbxz
zWZYD_ikn;VinD#O%hNr0j^%S}o^{l;(;M?$)did<4QUL<tK$Sq#l=M+IZT`M#6n(s
zOo+H(+GeEikBv|3)Ht-po1AOY_F{$CFVQ8bH>ZnEyrxHoin;s9bj{3N?&@qYo{Hb4
zOiX(0nI)&}=7G%Sz`8}{^v*5b#P8#J9>sE4AjjSk+R)R1O^gluGIB;%Ud$!3%Gv(e
zNmM?@63M#MQpudD=Q+yPzs;?^cpa2()P=jeUk)%_{4tSZ^$`}m0zVx>0mx8bgB0^j
z{#X!|!1k@C8rzdsp8^EPZ@p<{=O3KD8N=Z%xT#)5C~Xxtsix&oVVr2jkUoC<vcB*X
zhDIeET?9#HL5J*KX6V{ezFvu@)z-m$lkI#Lc_iuO%lpsSeB>}p9)408>QUgo&L3SH
zu*jJHOd2Ei(HkX7)+{+h%LJwheyab)=++7cp=;K<N>9R-iL2L9GIQG8O^L+sr1Cvv
zJ)Qe!LctYLwvh}lLq7n$-Y`&7QWD9tci6hFPOHEh4~uf2fz}Ge%frknC%E5<E%2kS
zso@lyk+qM8Nbmz$mvNwFv@mwCePFXjn5k9PtKlz0;pQL*S#<t-_fv2V_>BF1WF<(<
zLhME?9i<o_Hh)PeWk!A4TH!18*I}42?;VOEd7SsS1xAjYw+}bp4TaShHw?Pd_telm
zh}P&ZwXSGmR@1<lCF3v=9n{RwX0iwsAgckPr`V-UGUA4n*EGKHuPj$NLMK@Z;y?06
z21`qa|FC*`JfE&lcJgt%W_Bq>F!S+iT9ehocJJc`Z%^;0QF2bi0lq5#NX<G(!S{W-
zC1Us08ke6orEOq%EF#*tNTFGH%p3aY+y7z~G$BAbVvz8dl!PQRJ9`@67Gr$6H39&F
zr19LLe~^fC1jG%%1v5)2>G^!U%4uHpfhk+cNBsvoJKkla(#KH48bU80LUdcTwt0da
z_2$^lM#I}IH*DEsZ`_2ksp9pu>{Q?MItFo~x?dA1lSA#{Ex88$54Ptg8xYH}WBy3`
z9y_&kB)+I_T-)n<*0#MF+zw>RnVBQhi5R^PTD+g5-|mnoJoedCGRV9~#4PG}14kBr
ze}*@Yld9!1dSkrvts;A6sGbKVa-vC!1cT+}%Y?Sk5PitxiBWPHN`y50Zpz4xedidQ
zLFr{I2>xqwOC|H_0;nI~E-T|HH97AJ1aalOSIoD&gHzljrKW;eoE8-(%_rW=SlTyM
z5;7Z=b6c26>15?fHhTZ}%4bEyO(sWDk|jt-OOZ=*H6p00?<_o&YIQlA=^vU&>qwj3
zODm3rxvnU`M}r&vaDNdJm_GNUADi)-&+(iLxwL^2-AeW+mwsQYT#d7n+X8@>WhVxS
z0jC}gXedv8q7xIJKh=gcY{;6LngW<U3k#<E><9cnsU0IqdM|78-cKBW+MOi;^DAy{
zmf+<%`l#+hX6$~Iw**pBQiM-XVRrKEqe{bw#gAL5l+=z4w8v%JO7H7m=Dj^>)O%P?
z*nwqr8anNlX<*Trc}<%Xm}LdKhq-t*9*;DL29K}cCgIjUb5n>A6eOH1+@II`xK%on
zq7%AxVsMAPTLVVfWYYG76^kmD_J!nR`r?be4V&pFnF%i#(hH`k&`0I5kqhFe+^ckk
z9%t_4V8L|NFELiUwv+eMttoHpt~qHjOQ8>oXnXYu12@*O=ts}C{iAm{<!;hd@w9??
zDmf<P4R`BtBpf>kc??&6d@%b$N9N;vYfu<uV6ExsFy;2vEzz90ZUg-kW=KR6Oy_~u
z+bps@`^7Q?Iv)&NIs#C~7GQ#Cz1a#t`wVCC&(YBV$<JEp{BZC&QSB8%Htdp1N=k;y
ztx~||wD*yfV5k6W;^-|p-K*GGh8dD}Qz2(5sg^vge20z=OOaBUn(1VKH8F3IEFc2K
zdsKsUtM}`Gd&R-iwnwsp!KW^h!vH4dIY~*cwy~hY<kc~~^?<LKI4SsD!uotZ1L<iC
zJ?T|lO<lb)y?agwX#>@jT#r7klaFXyMH__QlJX(>ER7=`Y<Rk*4Le`8-J#OQ(i)df
zpH3c~raMPmp{0%+{EU00Be(O`Yl!kyHrEeR9?JNrxU#y7934%9#$F?BrS~YNUmx)w
zvf(;B-^i#kZ(iiGar*R%l%FB&!xoKC(vM04VseI<n8^WMBdb;PeG$m$69K*J4$z97
z9ht+h6G*y}z&CZXdjaNW@LHWfHyx#Bg#boW7e@X8;~+nfL}Iw+eE<HN6ofT8JQNQA
z6Pi5yK;j?<Qb4?up{Ak1#Vy!w8g3O&x>YUaC*tdns*z)&dr#+5)lT@xmF?BRdmq)i
z)9-8QWbD^A0Xu^PWFJQYIUWi1$?C%DgH=9RBG<wB?;dg+(*=Vx!$lf1Y}HDSF<i92
zs{4QFe(QUceY`URI#Xo{g$p(qc$`c+sek!OxU`y^`@Miih`aSB4S8WNo>4P)y+@~)
z-PU5jy?o#1E%B`<vYl;(A^~&_J5TXKxyZM7jCOvE+upe&<Rne*Iv)_S`jmeW?+oZE
zQ3ixl>CFt^1g+n~q@RfvT^h)_{0;x%^%)IVtr@eo&yUiq>A_cl{A<wFsx1B(4RPd#
zA^0;K+X)L@9szpaNm*^*V(T<}%t;HmPWQAfK>@pt#L5@`R78_p@=(Er74F{-S-*jg
zfM++BsT;M+Zrr~Ocw=WkY*cu{^#GIff-MkSugL>4Y2=c8E_i=~y#)9OoP`rSdE9mL
zueeZ97r;sbr#!71Rw<yFXLhag4;&W^bN#o}@{WJi!Z;ZY6wvX9{liwjUjFCXK^iDc
z=goOd^c4F`yd~?2FoU4f27le7fHt!>o5d&hmp=D6RDLbErYR?LgNtsb$dQ{#L<`jr
zgl1W#T4Q4BN`q!lDzg2;AWFqR*&^0qZ3)MuECn$;kJPT`xSKzC`KX}uLFoOZ=Ovua
z&`6v$WwOE*Rm{bgjArjE{$qpflI$ZQDtQ7r>l_m=QPQsD%cYfXX<5*$;GRn>Pd5~?
zl$>w#@Y^$p@b+izl$LQ}=0H6ipwES38g8LL&j_)95>Im$4*>u}-v^V&*5cuX8%a^P
z1tzt`d^R0mbJBW|J2#zpC7vxN;>OYOr_fhC+HVR7cCCV+<eTp=JbAT9RgpXQS?g6s
z=-J6ZI)#j;0vs81APrKS%9**=zYOCkO|uKl>`T3Mq-O&k6iJ0j)ZO!fh8N!w=IQF=
zFqqx2BZWsdkL!OL2S!V4PeZQnif^L#eQ(E?zC0kYL<qqG?l+qgJMPq1+i|SCs>-|3
zXSr32EJ7jzjt5=|J$pccDVPL$p)c6~^3MvLFsO@07+~(VrrK*F@1uoMFBa?SUKb!=
z+`(LI#}7hd2pZ;Fl~rIJT4x^D=$~yW^KtYlN`&>pv5uZnh~#-R->JGxJ0NPEpNFEM
z#2oh-cP66U<i_^`u(dD$RBlA1E(lmR2%n(yCs^AkF@a)PRioh=sw@xo6;g9Wd6Od&
zY>Ot}xyp=3x+#Ke9CD4zW6Dpr49a2^`KfacsIB*JKo?`ui8?f6-X(_)V$~9pLyY`9
z2Um3!^R8=};dsB~#F>kudJ@!gs_%mrLy>@RgyO|my#ohFamf8%9Zl~uTdMoRg$15l
zLL9+h$`e07vzrMa!}ihoelhc!B$BE;+xsA-C&cbXyPuHdKQ;RfCw;ndr*rXo;3afO
zN~cfrOM6|TqlI3V(fns_cS#iD6y;54%V!RQ#99#0vQPs|*Z5H+u1jgyVwdGidK>xz
zGb=vV<P{QO4Ik+R&q|KM^{{FM^R}ZCuCnuV!R$NjZC@Z99VqL_9{LalD%|u5!fnaM
zTA6ljeaoM~Yh?yaeIu0x4p!Q7HqH#Dz`3^sli-(1Z9t$K>$B=~NJl{V^|tX8k+EW_
z@sOUPuHCC3`e3HP0*WX7w^MUl@G=@6rW27aml7sZethcFY|gFl{fe?W#5M0$8%D^p
zu-un<goE*hH>$85-#y`5|CCR=uQH#Ftk<BTj%I-Ebm_X*7qtCIC+H_@p!q?i0PCw<
zjvxQ&W1)$nd$&Ps&*JJsl|TyK?8qeM{Vc8Pi<FNvAE?$M1{N=yzYyx@Fy@655n6s;
zWY)7rBCVH-ev6O8^t_@)EK1u|(fR{`v1&qSF6lh%=xA;EP|HP1K{c1}3<a=~`PYyS
z&+t#_3<iISv`}WG5Nw6Z0Ma<Js&_nZ!I<@<VC{C0hWof_7{q{Uj>^p?G^i)i>IY%H
zpVmA=6Hkp;X=d}XlIy@uXn@nZ`@HsExl6TX23HEgP*-ll?>RV>G&C4yd;xa&=~3H-
z>BYs6(<!RLP#8WdR(2AOS>-RDAZ8(OLfjH{UazVp_H&-Wv<_I4C)KQC@Sh#ibrAn>
z5F_e~!*>NCbT4#AdFmls56MOx^9CCoMJ&<;Th3l3%KXQgX_07@yksiPMZpv;`T$de
zDVn|olqis$8~5_#AA`#~^3zmwNvZ;zoc^#vZ6*8?A>lJiSfsxfVI==?i#03ha-GiU
zYM()A7=_)y><_+RWREAhn$d+?s`%a(&;(DX$(^8$CC8)qzBynh;@+VKJ^-5Ya7uZ&
zFOVp!tucIO^4;GC<0p7`-(y#;K4eN8H5A>=b}{%aYQa>UkicD0citq_v1p`jWY?h=
zR?YvB`<-X!O~d}>_5YFkMQ3u~WoGy{@YgT58}RMGb0+usCs)7%2?)6Gsezm=V>BMS
zzay{C7nrf<fW;GV1?zu@yq#CKb{4#BB$s^r-(`#eEMu0Jy4KFoCH|?)zn*B_btt?X
z@#`gdj6LcGVh=cPzkl!HwdH4)M}3R(ci4w2BfOb55hF$A*HWnLFKGhn4u&<2d>IV2
z;uRMM{;(R}j_s()R)0K6s#)MnJx~cWjI)Cu-m`Eq6Tf2@5MW|lOt&h&l_;4iC?J<(
zQc<}4y<5z?2UE60;e1i#BThxv?aYuH1s%O2otl|x(GkNgb?^)Ndsuw6WH5vfK4rCk
z371dn-@wh=ND<GTqJb_O3x~g8kYj9xNlQyxSY(b~RlgrhT#@ToZyr_g?;o9mOII^Y
z&dxG@FAok5K6+_wMJWFZzq|18Cw}*Py_k|e02k3jlSB`q@u)jNpO-KM09)cJqS-_+
z;GVfT5i#-VSMvO-c>j;BdyhH<s(AUgcb!|AnY}zWX^I9`bkCu9O#$*dCkx6M1H2}}
zz{PD`%t|0YhS1Z~Gcdf{<}XfCq!+z0lDk^|@Vs|OzzL@I#^e`gaOaS4eQ(bMV16Gj
zS#?G+_``LcqS<qjPgUlQY%6ncoS4`-((nI{9;;zRK3Sa1y3`E?<ETr|DJb}qsi!rZ
z<}r?OlebV3oK#n6Q~RHICjCG0ObocD2Iq`s!ve>>YeRQyL=A*YdZDnWC686w>Nq($
zX=x2q*^dG=K|91{+eE>D^fBsvX(lw5nb-@!8t@u09sV(3L*>q}zn98YvmqQDu>dLh
zS^#pA>O@_NpFimO^VSlP#{$3Gny0#ekKn5qj4UilKC(IA0s~POUt+Ql$tQ3rO?ck7
zYxv*%=05>7m+NRyWL(MR=-3UMeD5n8nmT-1k?F8xpAmwGQnOJ01}?;6hSTd}(Nf0)
z*PBU36o6j8JXCB_@5(;b3_#&k%N})xOVP7?@%zfwzGeGEaLFTpjHfMWP6%%8G5AaN
zJoO*w@1OBC((#ONsq;O$KCU?O(?RI0Q&Z)EAqC>7`v44*zb2-$i_00V>FVlg$u$VX
z_T3X)RleXbeBz#EbiB0_a&&r%%jg;RrpbzhS$MC#bUv31@&G>^7-W7~zsG{$Uozx^
z4rGF{f1-eoWzM&+S^aWh2eXfte91O1oNlDp&dZwSx8(7k0wN3om4840=;#CP@7tg3
z{iSt%+bYU2?j}+TC1dg5jkzM!K~!}vds6QJ33h`<Fdm2rQ#ll;xz8_b@UgIZZ7O@2
zh*cQ@a5p<ljF<cGKumCi;q`|D=$V-<`?6GogoKchk$<6nS4*dU!UMSqqujP5eN82G
zWBIHCu64fAIOo9jv#8y%(liTj2h<|4{V*NbZX{7sQhoi&ckkwcoYd-i2osNpAn)e}
z9H$FCgaX7WwuAdGcu`3`R9^8Wit@P|9nAXY$epRQz!f+<ximfVyt?xX&9m5DG<Waw
z0LpW<Us4Qk^#G4{#ea)Tu|QEaQbfeRr7y5UpW%*pehiKIZ;^5UVEHSP8-JwfId|;<
zP&Dms-7kM4YJV36u!5pw6jAYW$L8~$4rmq#E~bF!|F?(}4HRkmx61u{O#>!epvvot
z-IG!JZ&8*cIBCFI|8e~{`<yRd{+@u3@~sLUu>PkAegzb%A=A>Ghf1F>hU)lWY<8ZL
z{6e+oL4jyKezB)zkv&XfS%Zhn)zlGnY?Q6Eg8B2E{)!j?!8hmq9ox<~NL4XcI(~<m
zYhrk74TQPsyg?Ptbm9Nq)*=wJ{WV%P$_IG6If$T0NI;N%d_7@}qdQ|s!bjT^!fs19
z4}U$JdIbfnPfZg|ilrZAUBQkWgE9Z7kDL_&oan(3c>B(_xQ(e5j{ouK6$Y=-yc`1^
z*^y?xs^2}$fNH3AoDQRX{P^+g>?~#2$I($Lgt0W8nwr`X8RGiYCgA5FE6@2$z@(C+
zcqxk9^b$9D?KB<w^+O2qv#3W`?$O}JF(Q|KCj*C`<B}w2Uaj|Kyr2KG%VbuS{NdXu
z+Q590)0gaDA~SmV@h$J=9nUu#VG*j?ROICFYVG_?B-as)QnNG0D7lLK!1TJA#y3Rq
zYgJr3>8kKztfjr+;@GFIgojImS{jfF<Zyw<?7w)hh6;JX*qI{S#6`h`OIaJs6y`>C
zcQ^K|Zo`-GK@}d_F|Dv7AB{mm;)M*{<I~->?KT^8{7Vj)IFC6~=^q`2*K6y=SVW(k
z#+XzztQ|hdp+_leW1et3>a>@hOXPVL#q;8DMmn!=(b+B8+cVpVyLyzv721)_znT@E
z(x{Et>w-1pa~5WLqM%|B&`X+1qiFjJywBu9{`J2<(%HpxRnsI0T>KGV9gCIJ&*y&K
zC!psH^hXj6%oE21zx{nr($pCRWqpA*1e5T>O@BB6xJ!_C!1(7uf24pfm>BR3FGi3H
z;b%?%yha)W11_Dj6m{_)sw@jVQUoyT6Z}OR&Q*FO{Ioo^i}VtZCjqkR<jnsM5-aAU
z!i9uHcwOQ4t-F8f{=b0m|4-}%Uj2WUe=oAZ3T3*c57C9mYI=l1cGK|3W(NnI&-NGT
zV7x-VD&XZX4E%KRk4x{hl9G{)R`RG;@*8Nqp4T<to45boinU%PfdX(Z&L^^|7b-|r
zvpWiF9<O<LFXJ8JVJnSJk)e>!fwSj=k;wGj;#moa#ChFQ@2YzXZ?V?NlOG9P7@GBB
zLU#a1&piZAbG$b`kToiF3l7-scjFI945s*<#MPVtOE?=l`|;Mp(*ZFI_~}xs)#e}J
z1cd~EQ=ilAJ~fW!qs?S7uaPjLChz@s_!6QHlkokmc>&L*5SC;??;j4!Hs)84n@>*;
zV{aObfYvcYh&lqFE}ilM9G0nM5x1Mzg@=3J{g!gG>tG^kD>kmP-<wa9@i>edYJdi{
z<gm9kUe3{0e@2yu@qnuLc%|(SNZ*;_z1e06uyhl}fTFgC@Jli12pYZ<)q(Kd>KyA}
z&eC`{yLfc8)vdQ3E^SO1p>^;%H-yHr$8EwRJ6WIThcv#}E0zRXI<J*dbXxaR;l$Gk
zNY9plz_knFFA9w)=jCu26Zi3a@#<V>f>u<&P7rRA;zWYzo$Rxo@4UV@;RWlR6F_+P
zb$J8yQ?Pw7)YX-rIGl|&;ZDLC?}AoDUKKxB$e8I3{Q3r=nXTFgeqrmX>*ljJ?uGz4
zz1!v`PJZ08ESu}W{7mP)e#>zYZ1O;qd~$`~`df5_`*hd?J1FJiRmg;i&yLp3Zn`Td
z(auTDa&LU~gKH~Ai&5w5*Xkh4-3llB8M4fgzJrOU4!8wK_*VH=e|Qj;pSc8vXflj!
zc(vlZyE6PLYN{+Va_sd=#TU(iZz~Fn26HY`_si|{W<K9>C~9wk`A#Ju?Ssyn-z;uE
z5q`n3QMoy@g2$4q;?OzreL6xS83xU~<>&&n>ck`VH1S%kT;hZj!5Vk8xjmRgA3oLI
z2MMm3{QwSpAK&Qng#5BcNtY86WMiDRDoYr@0z7m+zc)D!2338+%4?kt_!37BF$Is~
z@{Iu_de=bOnme6N(2(6v=43CdW~OD57I};lyD_j911T6@Iaa(azo(5D2m8GJ#BGGL
z@pmID1)f>9bW4-`Sl0gcL>&S&{!R>wEX$vVb*>@{MlW)D>;TG(4yycSqji>8>J<|9
z4J4tWth~j_CXJqzm2uiR-JS!7ZPrmzIDKkRr;of@J23}_(H&ck?mKb5SZ`D<nh%<8
zAhFEP+nIYqW*n#lklm>^a8=Hyq(7V;1+z{eO~E#|ajQ#&xQ?jt<?-&?c)~(uh-S1M
zjN+aTdRv|KYcjX;O2~+xgbm*^$IQ*%n&X9PtY}N8Y`F;9RTnK>?y36kO$oM647Wa+
z9rj5U`|NS%&q^GvOB=6tr9Uj{tZ(1B>@xECwQO~;u~7b0ZmtBuwyJ&6J7X3nkt_c5
zvi9^BMt+d=Q?EI<)=T3-iE{D;q{LUR={o1yJCpRiJ}I!<ED9Fmvba`l5fht=h}5gw
zX6t<@lw$84yiReg7^2o7T5K%GKo{OF_r}po91=~-T(zQYsZ~oFv&^@-ox*5{YpI+u
zDqU>2mH6W{oqx!z__US=3+|M`e^H6B#b%tH^V`ZYx@OX1+?4*x=XlA*Dcj~#f!Q42
zG+WACY>qvJ>qonh<yMbdp0eehCZ6VxCvvfR_xbGDce5h%9p#9N?V~H3;=7qytSrSu
zuMAh07xqv==nT4wpFNI&nasA#>{byq%>k&YXj$L21iaByE#2~W#)qq7SNyAo5DS0A
z7RK1MNM&6}7^V?xzd<X>6#=(APc`@aJ@+l^{GB7J<f9qEFE{Cey6Ss8G6ds9UzCX>
zYtanC47V%_j=1@`_#QR}eGbWf>9wWmD9#j(n$U0nW^v}}f!P-Op5O8<Qb*$GK0zT-
zy0Z5Bn_eRg*CqzjS;C|Fhc|0;#~gcoxgEsE4JG=FoG6LY%1{z%rDB;Dwj+aIe%F{c
zxnp7B+ldEjOtTj!@~_@UCQtsOo&^+1vh!y#2PrnQ4slP<scOyd2UlR`gaolV2P+9h
zkH-ruKk#16jNMF$EJIE5GflAdLKt`5C-Nay+``OHRFSmrs3lfol5PT9@qHY}1LeaC
zkKJJ_9!0l>f!X&RsFQCxy}2N10w$5FGhI*ZnOvuI7x}Tr<6KW3MY3~9StSFbN{5!M
z>OIPSr*5&>xcOqFw)Hrxlk4iuvdM#Hjd@8TD$|iMHhB4#J4s#HbKyt(S4|G^)T_K-
zL-r!sqw;+^`3_f;X1&>-OI?^P_H2>YUmHffDNplKj_intBo>FX>=db_cpwC?I=EE#
zsb*I5s-7&l@J)02VSGw|D65e03R3Jcy7y60zl(sq)at{J)oMhS{=+7=@uGOHFbegy
z2)(sr_huepyT^DsIRfvNwboa*`fXCA-aE<-Z%V{z_jv8|2fG|QZ1wS65cH^XtR-om
zhnZs-^_IH}vkY{N<r9f4vXk<tM_2E6Iv(Sv*$lE*V|(4R_#y~m6kYUQsfu^!cUZ^4
zRH}DbKfnH1A=0k3=oJ6)IbQvAS6U)xz3{g|VD_w;D(Vpl4mQKMFd;E;ZbZVw=S}E*
zHrrV2Up1s9ap+gSJ57<|Sh|TmnHNv`;?(cK80$sqpqB!?6P9*{OuEU+H+Ny$C0i%E
zp5op<RAcVrQf2mT53AFm0|f<0*+$`B6z(pa_6$?9XWNb6UF|@HJ>%B0FFt7R{kRWW
zNafR)MfL=?Kc;6pf>oQ^J|1t)kjrxZ^v???Qe7H-1AqIV_+CY%qLDSM^@?~QM98;`
zua)$N^9DfQuQsh3u6pqulT5lkEFQ0T+ka6@0ecWGjP1dPPP%;d&<^AptxBotvU;|$
zo51?;o4lVF(}WMcxR{p|wnrl+J{E=sxl(CKtd<NwE;Iu?7f_4&xhs!-R6C851AQ{&
zRxR_my?&?ubnSR_z~7`vs-;qC)PJcQEpUX{<ZXaP3=Z6!1&Ca(wt3e13TdMm+!wnT
zgWz?x<cHpvJEMyB19#sP?%(Z1AiD!R7OiL>;J8m8WT-xLKP6_XLEzqB+b*O4B6)iI
zZxvYV=~?QtE2Hhu_K?O}R}ZurD*xEg6Ie&?6<hxs)$b<A3&T+Uu8>?lmD?Jv7f0h;
zW!M0b?SR{!ANu5n4<FV-C}t^BS4VT~MbR$u4cHDwO1iQ0f8opcj8QVK8PaIo(13E5
z^@I&~D29}^!j*54dKYW8WT<Ru^{*YHKU^ELVsf~}dS?u;KFG%Ktt->QL_^%y1f`fu
z>n$xUYvc8!A<*R;*(%FL(e-?V+-OvPllt{WK*(^pf!^$jt*vbx`wa6s^RA_MNAsnw
zs)`EdwXs@P;h+LGs}xPvH?cG#uJ;iW9!2f0KXmA-184F||HWDc*VWs254YodNNzN0
zzfn;k88JhFshE18362I_LN9}@p8T-QA7mZO9pP|8c&OAF#Fd5p5rt=j*`-Ma^{n(+
zMMr6QMGHkQjBwjQhO|iB`z$Tc1Z`{4@o7b!=9IB&nGZ)s-jt&x##8Su<=5XGTrX_=
z*BE>y3V_ZO5X3_bFjUggzc2Z`Tu+k@zVUhPC1AtevyAY@4QII$Lu(3U5}*S^oLXym
zhMn3b12=X4#lKWUIsL<BRz?Z$@^Yni*$=8J5m(A)hnns81%^&&{G*HjcDv)$`w-qG
z)tnuJXK?UDL4wpszZq^y$LKIrr~Ser1$f?6C7?ZxT}OMSpxw|QXvJ3PK;^1JmAM0!
z0CX(JG$C@7##X4_HKN$C)^T&D4W}Gv%17CgffIJDRw?aOvoHIdIh2L03{;9owTu6r
zXsDLhpH*Wq>uMW%VXK;bC=Qv3emXHv=k8>&@qhzl!TFm;b<PLdi_c@n48FJtp`McX
z+aki=j$6ANYBB%)Dg%hRQeopl!aM!LLh?k$#P~C})6wc;frCJ#MAAyUL@5Czw?0_=
zfCic=S550u<X^*BrJgE-SmM#E{xBKi3qi_$yHts&vvEY~sx6>Q5q4P`skCi_w^b`N
zRAw3)jJ#o%9yBAdQO(Vr_&0Miqw3e$nU!NH)Go5mj_4nBnhpAH4dfrK2{g|q2~PDR
z8H#}{qTfJL9#)pVUC`h$<H1fd*(AZ2ihs|q65oIU<nm2R8N`SVQqjSY6JkvuMF+pa
z)mTMtzB{GcPrlv8f!o2dr^-3j(PacHzg1oOFCm7?&#u1DAFFfqu!;%EYQW9fn)QoY
zr*54q5>)eZGX~foZ4Tt?Y`HpDQ5Iib!0T(b?kUpx7b7hbz9zo`F||x7AKrZFR0RY=
vqt_mYgek}#tr(U>GPa6{|Ca<J#5y9wqIN;3v$vokfj<Qq)!Ri<rjPyyPM~ZT

diff --git a/chapter_hashing/hash_collision.assets/hash_collision_linear_probing.png b/chapter_hashing/hash_collision.assets/hash_collision_linear_probing.png
deleted file mode 100644
index 31263aabe62aef1a3d70c0da7c7360618b0af13d..0000000000000000000000000000000000000000
GIT binary patch
literal 0
HcmV?d00001

literal 58163
zcmeEuWmr^g+wL$7Eup9=t*DfMlG39nC@tNfNS8?05DEwgDBa!NJ;Rttht$v^-7&<#
zz+OBL_&oZ)-*J5V$NsnVkQo;%?)$3yI?wC6SAe3t6e%$^F$e@Aee(FB5(tC`d<AzA
zf`JbxgES8Cfn%p6^#D}VLAwC_=Z%rZ6Jt3!5F7BF5QK+w0fc*U3h)<%L;csqCznX$
z(ER$Ygu`-r4scI@GZ5sj^Fbgj;Pd2<0r2nSn!i7BQ*i#dV+#1}Y&=j3?%8*67jQPn
z^WlAW;DhMpV@*2{i0sSBKb%N*G8$mqpeGOSt2pB<j}o~@^ri0FmaP#{TzCK`lKF%n
z@+nwlS1HUXEF6UQ?Nsfo7+b(sR$i^R74IN+s`{&{D^+Fk`|3v26bl@19=^nZpmyKC
ze^2op!L{c3>eFPi>;>E#Je@CKTg@gSc1b*)c1dgDTE~KOf(jbi+QW=`gp6Jw@V|bX
zv-kc!mTaJ`tZZdvB_SbUcOcWOSzJ<bXXRr<ye_J&Y6mt~@eqUqp@9DL0}9sllcu~Q
zN2vPx`;NM-tgO4cyNZem*XSp)J6U=6jf{*O92^V{4V|59LSE>1B;}Sx`)6GJ_hU~+
z0jDad?Yp>btzTGJ*xlV75D?JZ+{|!AMw}7Ej!6=6Q5x+DiGaBgBD0pvvtZjtyru!a
z4V}>o8VyF^{P-ys4^veH^|$ttU*&#yx29D$w#9lYFH0~wBEqy+;QIAXS^6fR{$2D_
z|86z7>_=Kv2Df`R;{QFNlc~*XBC}*@_~q`~s_Uzu8iuxPr0}iH%(_iqy1LfQN;%bT
z72&@0@W7TDHf`f&>UWl`<*K{&q8oBQEqA=o-5Q(0$@x=G6SR02ohk{oihQo3(Jjb4
z75x7G$<O{x-@ak!OM^f<fYi0L^4{ieFP%f)+Fcw)R0v0UI7yTKDJc(51H+O4gsZ@l
zK_1A+krJq125n|$rp3^jk2{8=Vc7Wf>(^UY^WMR8*tjc}cEv<+M~cDK?yG)s)yubt
z|E2A}l)tT%GH0KglaC!dXZgIO8SXlOZOB>{CL3V|<?B9smKu`rC4bw(-&0jF^Fr}h
zy9|NyM|)j7x=t8x_W*2pW}*As@74gqVVa0!m;1>ZX`bT48t=1NLQH%z0ON^*g4=Ug
zWa8?%{yg=eXddj)x#f6R;`xCnEALjnKXi!{B#ue32+L}ZzqM=LnU&(obIXz@=5<_V
zA`cIb6@xs1f#}9#3o$p+!#LKi*-`qQ)n3gzqh$w~zuPmT7jUCNT63ms;=JD0-a(%&
z=uk$t4xIfb+v1Q3lLN%Ss%s0DI1TTZ&&TXw-DXAd4R$TqR-PutThjc8s1ho@cwWVo
zp&~Ej?B_U{Q1?k~DdnlgsP@W9OLLP7flIhc9aGuD-TEGLY4gXo)$hlRRZ3~|`_Iw+
zAtG<Yr8^&gEdTIR#8Xl>49gvhe3sax8hpJlmbwrb9~PEYNQYBXSEnV+9Wc-^9LhEr
zjYug&<#G%f?)4AKUHsEl?~&ldJG48=tygR)<Apo4*AK<`1Xs5pi5qT#{4MO1mBVjI
z4!2_vdKgn;S9Kb|I5!d^v)Y9J!?3PT$fgfHBR{Vizg_mM-%kfm@2j520Hv3Og~bZK
ziAAKGlLtwaUVK|??|R4|3WJUlC$uCcc?#`XiVKk>NoGGU39bu-W715B?Ik2$n{{v1
z3%(o5F&N`3vm`dAT>B3*O!gv5<&SbTQqnH=8IUPehi|?EElobw8{Y2T9=yEWU2zvJ
z^e*=<gNxKZk>{^(DUEot5Ba=RnqFn8Y<1fsdxgg@xm7j`gW^#=dctK*cl<YqQL~^1
zraw$$f&k}{3XQzn$2V$pLvQqy?`-t<CXgX-bqO^Z496A?i^lO+WirUWllUV>GEUqy
z_?*ic)0M}M$%&>zRq|zdn?MFpy-wM)2UW3F%Y9*?f6i`C4*5oT%lcLR7(B$<LY7AX
z<jBuwH0QKTC7U@QWg^q^9~Vd=*%L4@UOra=E_5CfDE=t7-?2C9>SpDwKh;0NYLK2!
zTE3Xg5%0qc8jjABEi_-gS2ik*^M}>p3=qeNEXjW2pNtc8f*2G#4)yB>TPQ?^T>D)z
zZ{oaorZ6GXu6@p-Ae!5AoU$lQO7oNiuHWs&%L30`BA>LR%0S3d2xRe^j+KA7A+B!6
za^cGFCxXBi)&on4YdfeFK>W$@p5g&1mh=BwKTfpxve8RDhL1sRdBvW*gy(Agal!nx
zKkp(+81vpD-C7E?6a2mE5&6M$%0JI2x}X??maEC~PXaAhwyWx9^ZY5-gmkX}I2{vm
zu7(TorwMzt;t?V_8=>~(zY8wK211DRnEtN!hu`UNLP3uEcxi5bJj8<u3R<O++VT0_
zMJ8V1fJ<7rC`KiIH{f|19PrEWdu3F=Evg`#Xc7u9U6}Vg{qM7cjuTRN9en!$|HCY6
zbi6>zn<Ni+{}?4k(hD>q5VDN-`=pRFV2DAqK4YE#@1yJz07E7awlBE;m=q@!BdGom
z+%5Y1D7_Kq89}?jOm6popVZ4*5YFHX)!WrSY->9hgi~Wfiz4}bQvdg&r&!oL`e!hV
zH4rv7wh%gDV@yI+6#t9w?<W?IkxN!jo;-1JsqL_s?@ImbN4h2Sak?o~>d~W{%*_72
zzAjdao6|?wgUaxThzQPVB_N;pbC!hM-V**~g?jKId(2c2SCX)kwT=A5e0MsK(TG;d
zDkvyOOP5*k+l(E4qp^tz9nkm0<~&UYR@wdi{mp>T(8j4i_9TxTO|0sJTXmO7F5h<E
zoAfU)E6Y+yP6`iC@5(P^R!DmH_U*m3hAmF`c2CkmTzvfT(QcyvAD<kM^o%vQ<mTpz
zR-3Sc32Wp41y`{@@H|y8as}KXPR+ku6m4A6ZP_<y`1I*hCyq<WY3b?h{R4V#g()d1
z^-)=RsY?<JnD<uccht1CEySuSDh6GNr9x<3rUIDXeU4yN*3#B4Y>wj4&dbYltZcNd
zne<y;w#?MGx|H(G+p2t(*llOo%+j*Ae`UBj9~-HzXQm~#GiV6p7^5CCXdaV}ieNX>
zZ?}Mq$p)}vPm*%aQwzCb3I<X?&%<d3H#;@qA^p+H26VqR-$m4@+PJI9`>j#w;7eBo
zUu77x#)~VR{Hh9pK){yz3umWmY^OIjH+gkzs?EJdqw3i$hbo#ad%89f1nn$&e9g79
zfPiIv+2H(b0ew2mKdHmZZ(!+c$JttIl$C`APrV{W6<<y8?%j<zi=w9=1ugSws@%lF
z{O0+TM=QEbMVy>=+rFwnMp%)ACBnrd@CSceus058O1%8^)YS45bL(<rwc*f?PwAmz
zd8m#K>K0LwhRqgsQc}{a;9G)JmoLYaAtQtNY;<t;+6BhjzJGs-Zy=}U1mo3@y=VK}
z*}3WM2l%v>aICl|EZU<haqvf$98WxN;m{cAn2{mdc_{K2aKhtwyN9PDBecfB%dTIo
z%dfX{UW4yiE-zrOYiRk_)YGw9J5&c?IPu0jc6Egp-PR}W4}at2$x6wOmb67%R~PBj
z_C#6T|B)dF5*s<<M)MfAb@}wvwba(u#z|Yz<fmYAm9yihv5!6<-MTldC<*cg5mR{K
zzU@ps4aAHrct`u4o<fF^1A>F4QhiJKDsDe=)p<N<MV!~=1V&#h@@bheB>n8`F%~R#
z6-!Eo0v-UU*Tyj|e`~XqD?W;dh=@wpzPlq)7#&Rpza<y<Wl;@&H-i++2}FqcpAWi7
z&n8KYBbO^`JN3|}E+19piq6Ws+^<#o{E>}T&nzw;XXD{3Y#-FZ&y2Ie#xOXCORIwA
z)~&4i#(RUsrpp88juA(gr8;Pqp0IkR+6q6z?&_%9q%YM_@%*ddQAdI7QT`L-I0B;8
z!FU4G^|O_23_SZxWUSI%j2%a`TfICHjU3}_EVL{T>~Z~ByhWrMw^(3Qx}6=IoeUdt
zUjm%D*Sx1r)vY~_5Ae*8(Y~Qd3w`&EN5UP&w-dv{o>#MxFByp|0gG5Q5rx;N<D+@<
z(|`sE_OixTJGwjC*OeR=X52S4Huv*q4D*cXwdXTA-RV;Ca>T~`VyJI$TBWKLR(s}@
zg%($hZVY<K<HL%&eW|@uk=+}$XZQH|tFp4bRXxS@v6PCrt~9x1O1`@?>3$^)%ZUf9
zmW4oct&H|NTe-c4@usGyn?mUFZ^l(yqSC$?(U+#n=fgIpzG{(bOxMNvT3BC^2a?oh
zPeMCwi{LNhd#>h3aq8v`zxGfVt2M7!Q!{_(C27HDh%z_5WNIeB&z~pRDXG-bH_p0E
zfA#9ZIV7glH;KlQo~|H@x|eT3eTG#z%W|v%wc2%gTZ)vFy8K}*UaA*V5m=jEPjPoY
zIo0*cbm*f;zPG+u4_CF59kP+NCkSpGZgr|VwfAa{2AJ0!E#?=qU167VaJkjN+C_Ow
zR#9ZB>}n(f3*+Hvy;HpS-FX{|xW&Wu&*br-g0+r#0R>O5uG=$o!j8@>(yby(Pa3mc
z?X6Eb=KHyzUovs56%gPpJ$dZNx*)?@`(m)<Sye2nsjlhh4a*kdL7@tDT(Rq3Py@U@
zCkq3tpwOAdlD#BN+b2>bsnPc|=ZNNyl!7l~$gZ&2vr?NWRZtHX4@czNph~4UxC;cU
z^?q2lU*r9mlPWVe$#Os(<Bgh2a+AkVo%O^n>9;2{^JZ#>aw)lCJ??wfu9G6`9aqYj
zw&F&tcMHVL-Iom+en_<!R4u57D#r0yL|GY<)Vc2jsCAq-9`*u*2_b4;AX*L2kh8?(
zBlG*XICG&w)=D7E??Wz7QdZsy@27wrtW@tVqwKcY1%SbEv4x_pNsszrTJ?{5tY2N`
z^*Ws4@<eG$)XLzrKT?PGnYY!I?;^c%vw~Z0ZJW2$WeITU)F_tsGs`FBeAFw?C|5(4
zxwW>mlo=^^!M69<mHYYn9wTPqOJ!^u<|?TCy9_{}sssYnfF8BbS+KRH>cVEWJgC!G
zF?>f{syC{NT}GAjE#}Nyq(u)ME+}~RlzZ~!_oD{MM1<HqTB(P(3p2i{Gm4Ar+eN|`
zEAK^>a|;P+Es11jXIq5Sd1QUq5A=J<r?Y%mH>)Cke7HrOBM@0Pq9BTnU}a|$#w~eX
z<*`{FGCx9O1X%xT!1_tmy~R#5AgCg-X<FH*&{dor=|<_Vbq6W}A?6nfBs~(hqWJuG
z0+^FDsw`t;$*kn-qj5BtkoTK^w#Zv7tCPgU78w~E(~G+HIx43(bz~OuZtc%R>sM*R
ziHUnU;=;l%h~8+{l(>om(YXnvdVMn~XZa)rEm+uTwYU7mC7l&&^$wWD8^v9Gw^4da
z8kS2-&&sI@`axy6y}G%2hM%fRjUNtgXQHaAk{*zQsU!P*hN+zetRjs0E*9?sYw8lt
z<E)+$a==1AcK}(dV(b>oz^yAMhb5Ta0#hN^?MQjz@a4di+tvLMr|FcJ44!>!5f68w
z8J7diB2TA?-BMw-`Lkyp>I>ENpaRxP$2o|BOt;<rP@R6fG8~O6Dt-6TepJ71{cO;4
zCm-Qwk>PN9fy|9(?ZyL)jhB7;a}Yh1i2O3Uh(Q!X@Ns--9QTTQNl7^=Aa2445Y9ct
zO<Jnc1ky(X+DcLkq(m-Y*S6v;7K^I#sqoeNd`!W0@hYK{Pcv`HSZr?XZA|keSgaEC
zlcs6yqaX%zu!fe7CMML2nLfWz1lVy<Cw@DdSTy9Zr~RE)ZuS~Ihd$LEcCGJ=nbCS>
z43S#uMLM|~E+z<7H(hC8y<yqchg!Tc#ZSU-36@vjN3C=?)DX}+BVoRP+tl0#5+lES
zD8p%D#P}V;Yn+q4Y--STJ5@zfGq+65P3=pcl4_{<Q4JB2_;X-O+-<n^sL<DIav$OA
zpGf*N#_ML|EZn1C@2GZ(W>zV6DwP=#i<0PgV$n8mbX3x=MV#Pq$jgs-RHljpy-VB+
zf=~3w6NQ}DC;UihW;>H@$WyNw>2kL_4|p{+!*_~obe&8<Rr;yG>a%(gSpBx@y4cSm
zV!f9&dtZbW2V+6%BXng-3KYj|ed42@?c>zlK6QOQX1kx?&liFV(WSgh0~SeE(I)xb
z-#rd?P;wpTA8S8JmBEoyK}`D5*gv9oTfSS2Prcc<SLpX6(pcYl5|73xvAw@Ym)+gS
zAQ%@gELVfDqYKYCE6QVAW@cve_}l?XN&tWrqwWs#G^gRO<|*{Gw-!Vu^}AqE&VHv%
zG^Z-4KPAoX;Zs}n@^n6?-7f)@vo9*lE1s_yMeAnu`N8ECh&0K&yOqr=t4hEz4=S;0
z&dz%!&prbrS*b9NE_JzLtPL(H$x^=#$1@`vA~hO0<>SF7v8=fpW_{LMmq>?NkAaL-
z(P`I>oo1={iYrBhUr_r`bC0L$iVW@a38D9uE~>-79d2!IwyBMshcYq(h{UVJPVp>%
zP{Wz&83&SN{^+<LS9pxy5$~W%c1GG3rQ@InK;&_q{ubQQM%+1+ci@fI(In+y(?@+{
zW5Jkz8Pqgvb>%J`pmYK<borCaUhsItfS<L%JlDi3tl^4-dWqhSc3$oNY`lZ`PS{Nu
zUa^8`RK|{0i#E@&mCU8>xpTUTy0&nObDC5hKx$Cs4ZEAbU<C)4=xIp=fh^@%7%3=#
zBp5m<$a1#0<a?#{0x{)i#IDoKKyfbRE;5L-?(ydaYNB3vx}Hg9KuwmU06v#S33L~i
zeb;=2T~$(2a!B~;N;U88+!r(T418UQ`Bhha=^+t@OG`_Mq!EG+OO=xPeD{hQ@0+gH
zNxHTxy)e%Tn4zu{pd5&NBfj||RODc}oH&0dqalxLQQFKvKUy->x<4pjUS7L}5RwRZ
z^E~HOI?2;?7erz@zn0E`&AF`56Q)l5c-C6)5z{4Jq^VFgOJ>aypK}g{!?0DgS^KlX
z*AD1Db*I{#NP4p6OJ0#95vA>nc3zz#SICN=I@vDF>gkdNW8@Qs`o<y)%@#4!zVZ*&
zjCq|`M`}r^I90w>nq=XOg#v&;Yf5{1Ye3g2F=;nnPJizcl_jppeRcy@^7yA7CLT^k
z{Tr+Dey)(iTNGJlB3iln$HV={o9H5Og~iNx*|vI2YS|dNNxl&sfcpzweq>2`CIQ%7
zV=iyFX6^j)(bf~Ut_yN4DwsN@idu#m8PfJ%QOD&N{)NW=i(lJ4%N<bMy=<A;m2rHB
zW3L0iB^Nf=CqLJJ?jGlEOXjb$fQkZfMH>214SUz~eNVmhCxJD#c}|ZlMqaG%2heg}
zzNE=%v^m4Q9U3XoID<TOtt7t#ZICw(7ZgOl9vwsZ2O+!;Buo3Ee-I&rM1TQ3)-jg9
z@cV7NKy7QkBXuw6W8el7Q`~l8e_(Zp0gT{}(LHzoq!t&VW5fR#10!fl_$)_0y$i(!
zz~A22v?bg)wc#_O0Vihs_c4LI-%~Jx{J$8@-uQ#hAw(XMon3Z%mp5+!!@I%B!~6$r
z4+YISoyqVlfZqTJmut4Mf@f*unT)`98gc)a>$Pi85LrNL+mm0Z{@*76qNO{#>@0Bn
zf6+o2{|C`}1Ge;!xb7)?3y`T|?c1MvEX7k9bJ8Z-XX$6dWgzx+HqMs2)toIVo^ACq
zLXrX$^UQ#~ihnHAJ{2<5z<@YrKHtgCH96^rYek-sL6SLPf~ux&e#hp~fT(AyhG$Kn
zxXBwNA30k296&6$c6Npa1_r)+*X#E1fL%mH=eW1txy?;OLnBAo_UKI8(C;KMI1+ag
z#JM*@_L*d_{Z#d#pBS*YjCGYL6$~~Jzw3Pso6?we%>_(cCA8MB);Vs!J=W9nd`#8U
z+}zySy5G&wk$)HD|I>zmIrz+v5+c1~cifvA-i?nYWS=WYE*~P*e--U@6jeH7F}F~b
zr#*Y2KHqa2-y1;*kX(s3-A*Y290-1e*R7Vg*iPeRCup(-OHu-7{!v=0jOARle;RmB
zqzfPtak0d9uwTPZCXTWFBsO|e*e=Lx{|EkSq;)O*b~*!K=UA^6&NJ`v_GU4Nl77DD
z#Hgp;LFBCnAZP!U$XSuI-vjOk)TKsx+b_;1MGjK;0*;!3aJQ%b-7Qn9f#YM+-DJNX
zX3PObb>CxuUgUSbhS~tf;gM-{e;if>5{1{8&2E=7&7Lk8V*qpD#{Nk7kHaaK89@Z-
zne?r*IiE@yehHABTA<?}hwpO$e!JKzHTSQ%ofx1iJ3yWmUR?Q?HJ%*y(E{REZ**wK
zA1wa18o+L9vkv`Q2>yNyq!I`=Ia~~he-sPm0pMIytyJ*`1xsiS7_p+hm{91MY5X0$
zy0n4gHkqb>aHJIfU+{$g*Mf(>u%YSsmq~gfC|HU_8ggG2?x?8P)^P1Ki3t(Cd)(ao
zxaDbI!G|DWs|j2%;W_GupxNqw)&~Pc80_f7PV{ZbVCu@3lb>J@G%M}!YO9ki+pWJ^
z_%<W4((N6up9046PCZ!cm$7)Tu79CaFm-By101a4HDTd;uHDtafzLFne92MrdPNT;
z%S=+j)W?ZUy|AW6N3%YBvvcKJs|&-}a)JM1dviC|B@bk#;aGv676;Y2NS+l<O8aQp
z%?y1#?2Qz0_IWA8M&lCQHLqPtzIswgoXa1HzvW9NpP9P17)4iw$;`O6b?sO21$Er8
zMc!ux<V8Abj?Z%V=(G$!!4L2YDX#2+-+{;vE!wXBTH17pO=ru~Y>wrecSPr1n7FnJ
zc`cr!hSfZ1_8PwxF!g;VtvFz7RlBr0s;xPDjBs%J((to)<Y(_qO_vV*ICI3SCSnf3
zsyC=vd8(Fcw*d#74C>516%v$?1mM?r)@sKu*KekA6m6b+V0_D|u71$Bd%%9UfGJa~
zvqfv!A-#+wy?CL#rv}z5YGiQp8J8!(sd$|?Am(i(I&*O-3vmo+xtd1+w?Xfj5>t2{
zImwnbSH}c&F%n};Kk)M~?&_X{Q8YoWdJA$fb)^JHV6Q3+3{E{6(M*14?b(Rl63?&d
zdv>_5Drs6gkKG>b@1NNLspqNR!WFhjsazO{)TPhRi#=ChI|16Vb%u<v0U&)TGFAWA
zI2wuO0~%fDpEj-_)P?!O(?(-q?L;vMK>}~N5_=QO%Dmlyc*1KWyzUC`1I8C8Nrzpo
z;M23fhLi(;<mMVcDX15^_I>_(E(*5ulGyS=N-{(PlAmmV;y4SKFSSwt@;oJlQA9+9
zot+(EoVWctGWGbE4m02H@!qh0Y^kDS=J3SM!p?~~;YxT6ZFm~LT%nw96%jd!f`Y7#
zrJ2Z6x3pILqvCS{0?_KpO3d*f?RoF_0Ce>KX*8E{YBxxIaC>|E@j>Hpz2`B^4cQ#d
z%%xfO@Y!I0PFJgOM{$CTCcD9?!+`Ew8Nso;0Jq3yT!752EQNQ$fqmz-wX})ZiIYcn
zWQ`;;%W-3yV+CZj`FUYEY}(q|<O%oI+p4l@;%F@6OYT1#kk#V$__CezmPNInx4&Qv
zJGC>lQgt6nJRPRAT0e1}uC4&FO0slx{=L{sMaToWlpl>Q5-UFi_0J>+lw_0KRs}Q1
zb8>RFI)rTi1OT*j2s<u215|B8$Z)H%-ndYGC`|8oe_1Hk=8@DxPxFp!6XSN?1$Dmj
zljl(qW#WQ!%B3HYL@f0_U-08d_K5E(p0d?dPK@$yp^K__@847&7CqMCHd|Q!P#y{E
zlUxwECN$}n+xjhA?q$`6r_0#7tX)^{U`@l%Ye#D!sfUaZyel|lAA>qrPp!)<84?&2
zL{57z<+Uz=^9`FqR8uoEXGWdIM-d(eX^(=Gl$2z}T~P%JLWSG;>Wb%%7v1?LH9t7a
zbj*zlWAq+se8Cf>(us1~pQ!n0sNA%Auj;c`8y%m(EpEwacxVIGKWs6~f>}SiEg?3H
zkCV^I6D3ypB=Ct+FtIjq^`S@8_*B{y!eyiS)2C0DgEcF%?W<8wpks5Hp(Ra;;_hF@
zTEcgj0O|)wuq3?>h@wV+MS<5<R>QY^+uCHqVKmg#W1hzz)6e+@TNwtINA9DynKH+H
zNvM(ziVjN%MhgxGg+q^?k9J1F9BQJfqJsSe@|0#iu+qtBuwPPWj>(I2A{kS~^hKDF
z9>*ctzb8B+{vj#*W3-XDhigT%kXr5yKU$MjlUkJD=(ut2#x0X?Zmam?imz1GI_@kV
zcf5QEc_0PETA_hBo=2xa+LPqs<;#ojYisE~$Qm}bAQu)E@_6HA{asPZv~I=o2S6NV
z!Q#t+`uD4<D%JQ@P?YNUMK*Z@QuS@BuPn=A8R6CTp^GNL35A&@vTlV=4taNUe3@qU
zsc))1(7S`NKT;6x`&O|%SO278zc12Lc)3>G-C5^TOh(96oTFv@rU#6@fFq|me*I;R
z>&Z|#xnMHmEFpFb0=qN(*`NG`VgzzhU8{rcR^uv<H4^GgzH~$&!gXhjqk81R!-aue
zUVmmX^(j@4Cw+Iz`@W5aJ1{%=ulsb9R1o$r9q9j1t7p9{be}<?KXS>V|GQ@1xK54c
zim26)K<>nGG!fD!`tn-tJ<aZU&0-6Lp=8DJ!RPbm3D4uK;*fnHX*WC7rB@?f#24AJ
z;Gm!%r2<w%8RtYikK9K+@<NTniQ$%xm*Kl3%Lm_RW`hC|C=|-1lv3SeCU8SNN4$@;
z&uys5O;!Hw>Xo&=O?9nV>FR?;$??sdf_yg*zAa6|??fwxpU`p+D?~1-$N@SXVdMEL
za|2lSIL(a!R6x>=#?p!!tF9C$=}_IMNKr1)t<D3d{aR*PGH*pn1IWGJqI+{er^yiP
z0+2&<OZBvL8t(~kaBy&O6&K2VFnMp@*00Ae93*d1GH`A`FXg-ejbG<;b?d#BsZy$t
zCv^Eq4Rvdmgz<(PWi{39;^k^oHPPQtm$inpOpIJEZ1ztTN`Ig2q}W-4amGyQi(*YZ
zGfi|bg+15dCO2<{NI%}RQ@BS9PQ8UBe3_$b+i^xe9^Ob9$@j;yg)Lldq&_MvE^b`R
z%a5qvek%GlG*kdPZ&Y5sR3Yinjx6Rb0k3=Pj%NGlnN(MUU=~{6DuSAH3&>1&HlxzD
zEfsjFEnBu;&9aV|*WPZo;uow%)are19Lk%cUl0{zgME8@HBZyYpis;lU9cmU&78KB
zKCVZ-+*eAirB!rw;p*FvfOUIGu67@>SL@rNompW{fU`;f2_wVvvNN_1I#J<OR-{z4
ziY_cD=pAhYiqJITum*m1q9xI5AMFhD^x&4p)XA;&uhxLNG4I6!r|`f|Bb%ec)i)JH
z1M;=<QX-0u(9nmk=<BjdnLg_Au0B_&5uGQhmY5dl?5)f<QLV1-9&OAU(W+1-(hQXg
z4Ba`z`7~=1iQS>5rxNE!m5-?!KbV@kC2vQsu7D5QOfli(0=oXX6aa_-^D(METPl$$
zU%ouVn~2tj)s~iSw6GWR{;&>Z5a*<(@lstiDz_t0UG2-5M=uQ!JOw4ih}ohlXdDh!
zKbGMtSnmfV4qEcEEwWc|R%jBsx^3)GRx+z3N6+p{yiN*yF%+Q^dCuH(q6lH(=V_;G
z*UoD;4ES&70iIdXSTCPIqniB}`nw$btA`cmL}|<(x<7bYX!1Rd3QV}|584Io`m-JU
z;w(hKhToiT)v#g7=!EP)y&+;_e+@9`oz_Ypqr^*M&D=xQ0ujcvd$haL$;Aq?$@bF~
z@ewd|M0!)T$g0~?v82a17i`>KGQFOytsQ|B866N2)!-Wrtd6Vg%H+#5sx;D~U78w^
zQPEe_O9`E=KXOkNAK^LPPn`bRI1Fz;5~(qikvV9e+!{8KIw%*XCGmcL0q~U!P66g$
zzH%vs-)bn{29YblhK-xl4@Q{FYV6`G#BzUi%#3cgJg~cM%2{EJFV>W}H@Bp<qp2no
zh3~M2*skA6i5oi{x9~I;LwNiw%)P42N9ew_9bb9bUOK_V(e~M+kKWv!TMp<RkvR_E
zc=THX(W`sxL94w#=jPwe@9g(1$>Mq<$b$pgW#|i-5UNVcBG#(P(?y$QtP*}^9t9?3
zD-PCa??7M=764#L$U6F-K^^-GSAZICfo6FHxc^%)4f={6ho`E}a)7Aol`t3nFtgEC
z<3vXfYX)Ajf;rrJ&+8Ta#niNO0YR>@jf^p`j68f<=dsT18<*mboIm#(<r3v~f9Te7
zu=GS7nN*2d(d3l8nrrE=s=6A>(>8W7Kz$8nyS4!uvC7Y8Sa=wxrOhAdAks3pV`uoJ
z6kO8p6GBMBlm79qqQ^Wt;7s~Y${2p76(ruRT#X`ZZ04;|9C&zmLj@zkCLIYbTeB{F
zD@HuUHi>Adb{{oHCr{83R-1fxmNtkjh+gZs_09a7pMw!Si(#{BokGKU#Z-=kuC}`*
z3q%XS9Kl)ytrq#?V%DtewHq^y4lXs3Qe^Ylt#T?rtxzAR?jA^oVSjO1x+FUG-H)jB
zoKyP|J(hZ-=ay-k?P00W?Fss+%NM&|mby%RDDTniCmn3cgE#3WlCm&)A-#ZVH2I!P
z8_{Xlhfd&Kbp6rOBUZuyx7_hQNX0qHB!TwT0`TZflE^ckJXH`b(DxzIRm3v)`b=Y|
z;4~A!vND%}Hi9#Fgi$wmC@p_XpAx#Wx@@BN%A8@P($k6ZHg;JbZzlw*4)}bLO3pvn
zcizNXQ!~inO-Tt%tW9uvY@35=!Cp~6EOKsPOK`covC$k8MRVgmypeBE9E<=efcli?
z|KM_rE+dnm)a!gJE6#SLbmL;Y>phDM=A8IwpG<u9;gL9RAT1L>cR|p~@Y!TS#+Lws
zcOUY(aF#TCLB)w;0=|5W^iMn(U@U1yc1TA@2=~|=+^H;=X^8@Ie0E)>9l1vQk%{_@
zaC=;DB=P!{3?#<R{>&U0?eTaC8*T`iD1RK9%KQB2Qev5{!BY|3M$Mo;(Q#{2ioK4X
zy{f)$yQ)zug}1k?C~~NI)|dG9_f3runCXPCbUCZGIuM=f0BUIVO`$mxI}&<XF-b?$
z)_Er6QgWhG=zvRA=Up+;_Cbq$VR6^lE7jxV%N?sIJu6NP!&aaf4+@s`o*g*T0R=Q=
z9IuV8QK&61ksX6IpiR+5DkckTKA5v=8)T%I0(3xej5o3UOKajpw__`Gq<U25`~^mq
zVs}RNVFuz3*CAv~8dyS98yhp$56L%ou@maW+GXPPNcn8`AaA?#U56%*^xIp}hY77A
zd)8bKd*<@}bP2AZ9>{;;jsyq?ah_CjxX<7xh%LO<+^VgA)PVU(u?+E^04N%QwaWCl
zGZ6q4)r1!0{i=0UMXeuZz_NB5DT+)K-Fx%91>S+4@Lb!UUTK|Oc>4Q9;Q0T`)1A*L
znUIV9!})BNLv3d!<$Nt1-lqkA#=7Syj=+;}6Fx+w^N6Esaupv=B%Gg@2biM7bLfAD
z>cLfFK1ck@X1rWzheeNF7T*!6_z(#+@6GQ1qfMj&nB1mjfYxl`=M3A68*cb)F6crp
z{J~JQSsTCrU}C~+Nr+K#H;MnG*C=?w@x&rOlKAdBHQ!Lc%=9UMG37om-W?14VKkYu
z_|x)XgNp{|3k({}w}Be--=0OtjgzTQ`Z({$o4bv=f)a%bUDT92!}kR#fZj9%$nPz6
zxKa}hAE+=%?=&e}$Ep^Gk;i<-bh-4_DWmF|Re3Mh##*?KcMI#8W^ZQC-pb}|Zn5L<
zQrU_WRx@obz1ha^RHsPx3<$A=`tI_-I+WL=p|+7G6x=+5!!A%NN&O$9<slIm5q68x
zf#4R-cZjS`>1oW<-3af<H;Ek)KxY8)9lRkW#a}UqVx9|!2f1|V79V#mrljOZXuft?
z9j-LqHXWC6a2L0+XnB(nEqzr(w1SR*0)Jdh3Cb7&SWBuqS`f&e{=N;P0l1ERFk`%`
z$_t(9kDLEr06)EaupHr=GJxfaC>EPLYnUK}$RcF}9ZfKNELk=k_YEj-1BhQ3Gjc>e
z$M_P-d51s}83}|jb-l|%zm`8>%Y#8|^wM&6z8ZXSlIn&A2KAY>gvc9q0pKkuZ`YsU
z8o&!^yzeBdM<2+&d(tM`5l9@m_$r_6^XE@IVcdS-$XANI#}|SBwS|s{eD|h+0$pYQ
z=0t!>@TD4$Bf5ov1wHJrZrM`vZc;_$-!R-b4Cq%|@}?w6LhaZ~*uA!*;AdHmdm@t+
z8bg0+GN6esm@nU{u?Fs3Z#B{RDd$Z_a(m+!+S1I*%7RoxPSxyJpVu~#mk-KmfQ+Q;
zB9M{r77LsFV!0vy&<FND3#LXMnON3h_G&mo)E&$H<>3ezzzHnIEmoXUSuGivDUTY)
zX9Gf!{myrkbfbCtcD~2h9S7821yKk85tl$^l_~8#QBIho`B1e<8@7Ad7c+lseF6Zb
zz0Oa(uNz6YeHPg%BEX@DEz_gs&$^Btt2woIKis8W^Z2<U9-$JgBfMW1tI5NoT=p$<
zc9m;5yZFY}8@ZCc9KPB|h-n+!r?%q_d)jfTaMQLl(aie#k!(-4#_ez7>@+lzH*bxK
z7=OZBV9Gl81Uo-S6uLG(lbmjM5%NG87(!RWY69Qc5bjVwu7A3o^+L8Uwn2NnsK@4o
zbB3R1d%(XCF7<(jS*LlQ>Gg`-PU+^J`BGMbMR;xDih=5khxYiGD(r!W2EP#3-MnG9
z7~H-mAwfteU=idQ`OUSzvH@H*s9{x0wO)2KZ9FZ_rTi9nrrWld#ZOBPU!$QxVgDbL
z{`s?yT@aE1mHv3?RB`yO3P9K$wBEFP_7y=Vl$Hezm3_Rql`2RJzIJm0%k|;Ckc<4~
zvrqtKWPykYO{d4r6`a#~s=wiQG;Bk!XH#c2z1mzC4$vedl3ZQaH7v-BYE4JJIx0Uu
z(EY+ZY(ta8_bO^pfXbR))PDPY%{Ak28VH%XdYtu(ugr1X1_IlGVvKjzAy;tdod+U#
z{wZn1dHK04#V-vH4JkcW=49~P|D>E=L)1+-4c9u7Zq-?E94~yN-F`u{Za|$U8Sg`v
z*e#uLm4T%9RBYFZg=^H79=P!*VqB4M^Z0l<hOqQ>+_9@dUP#bo1Bf$7Uq_zwY+8h_
z-X>LIbm!?c)$AG?5IXq+<3bku>lu?l-)`%9ntBYU@VmLT)Wr>3ezNL#Pus`N5nq_q
z)zdG;-WvYCnszkpO~J<(2fEQ0<FvJzK7VE!mZ+DhdniD0#rcFUZLny$`fFhT0%TXS
zgjSp8f_ioa^A$ManD0^=Q@Zk$l1h$sPJg}LU+~YGeJrcCYjW~@UiVvD3+;SjOw`zP
z`V^maL7W3Y|6;mYr}=pAhC?LofplP?8b*~tdeIzrm@*^;i3DmM<jYH~sDGX)4JFZx
z-MZUJP-M3JxTJ1jfYO@W_0vjM%{A9z^BiuD{NdsG)$xqMjNPDd^#}bcUpBfohRnCh
z&8{MMiCB}wmQ)pgbX#qGI02I<)rWD{GJ&(W2=azqyb>;?<~C3;JI&Xm+7+jPmP5}v
z4+m8z=b%MoS-7kk#?UG^l=YSRo_1BYt=m|e7uAXmR^8>mMHhWdj-He6@21h#BDNUi
zW}#yt4GDra0>zwz$mqmhOgUi!96DCAF<!UFIl5tCjp`%TP##XkxD{Yxt`hg>6yrOz
z<5V0*65Ew?-BH-}Setjtf@yE4@le%OWK|SY$p#tfCb$LgUy7ibPdB5?aT?u-j~4kU
zRZjIzdRqkhm|P;y#*9eC<Q^wDl@WPeBlTsZpw!v?fF{(A*0@}BGFLPFMR&|2>Sa1w
z0S)p^D{Cv5!#Mkn`<U2flu~Kjs0h}$5YK9rl(T^4o?_K_Mfd-NiI(NTN_#6)?ApUa
zyoVMch}56+EldQsJ(OgD(D{?<`J9$r)>%dXeNQA(iO&6Mc)63_1wlWSZ>yWxpVo3c
za~zxfsjx%JE>+zUGfk=-op~$6-1asHq_D8l(rw5kkKL(Ar8nV&pu~ACbl{hhP`$fH
zZxZhn!N-1};bC=O4!yNcP?f|&`k3J!3*hMh&7IrY-u#Qu`*<V8y=E3kjWzW(!J3lU
zDa(Yf5wTnnuQ-a<y38)fpIK4&P~r>1N^h`o@#`p826Ki$6|Xtn?QwiqzMzt_!*r|X
z*6`##3NYb4U@4U+{nu_1>x*4s9geDVtC;L2x>#m<hXEwdh?Yk|ePJ(?7nFstgiwt|
z$Ef4{nREWV02@%?#OQ<1)be*S^uMh2L!c)Z1Qg;r>u<lq!zGArbE5FFfyjvCLO)-V
z&;!WA%|<ZjR|NH@h>5J!@E1i>j6k<1UWb@rqCVIQ<#08(Y;EtqMqELzWZBf-ztD?I
z_%&5R4Y;~2I*IaEQ4h@e{zF3g$G$55Xk&v+eYBit0$&ehZ@bJ#B><OLpTZJTA55;^
zmI8$09#C@>v${|8Yq9{9-}Z27s^xPB)`DX2g@H+?ObgvYwMWbl>ZXxQxOZYCC+k6$
zKCbn;ZqJiCZ=iM5ne64iT1Ocv>cG?xy|9GxTmviHzR9#edDOiUmL%`-g0G87HUhka
z?k2Am^MHB|TkDQm)IL9<O7PV^bljnP1-CxdwquG+Wf$;-KRcwM28<*u3PlC?8eTO8
zc6QV^Er|@zT}e(dUass*WDvD`H@rsRXtHZr%uiKNY6NUkW5mgVZdv@($I-P0o(<8b
zGw$oSgoWK9>*6%X>7;Q<-QqX4q#(2fqRQK2@Jq~@-2+T`l&n?}lUd#tP!L1Qx~;m4
zmm~|F2m7BdfW5IajtqxMOvKp*nlK_S&hsGCSkG2jFJvvD=}~!F@$8H%tiwpky_yPK
z7mhmYPNlLk^MU4^IM|G|UDB@y(Lk2HGKMcBUg63oZ+|S<9~r%_=kbcr(FeK?#G%)_
zL)~^~MhC<Kd7}wN?L9V@!UbM1q5b6v`iTyD_h0MP-?`$I6aY}+xIPo)IJ@xFT04N_
z|1VD$!OtxxNIp$ifoEbgQ))KXvp!V{J%0Li5+<g?vZ~jK)A6{aJ2u&MM1|%0%ML<&
zW`KG*>1;Z?%v<d8o$lz7;iiH_C*~6bvTFI68G?V_YafUaXI8o%j%=Z0x4%L9w4+6<
z;8&$`zWAIJ`<4Jz!Ci3~X0E1M8()<6f0XPQO(Fc3oU=qv0I1*119Tkg>Y~(lusVLf
z<<`x^)KvYiC>KQ{AP6YxatfVsScH&lFCxQ5;e`PkD#c!E%K>}SV4{PS6k0-HPtqOm
zZ<~y~y_r%b^~b|)CxbtpV2?5kqNVHva|70%B%flw8K!I(t{nYhMo>5<cb1)9L?+}e
z;qr@A+7>`RiU>@?uT6*(%-&OMos2JxUsY{6p8yRvV>(u}CQi>1zSap2G0C*W=D4*W
zr9a7=00GVbF9vMI%JM6a;85Iq_4B*74cuY#XETU)IMkna>4KZ@lVI6AvD<B-*m-nn
zFFU$jq^NoSW;N-d&_PxicZsVhJ88|w>d1=}ghoJ>MPh%^ZuQhyDGa;;mgm`UmDS=G
zi(<GV7CoR4bLSe8ZgYAP=o5U>Xk`TxF)t?1JSjjvGmjtEO@g&I$J!d;d%Jn$nqAQX
zk`e!Y^sMD6&_{}b(P;E=wM{h^Rb~{#;s4;{-$>=?FQg)Ohb&NLnifJ9NcQ6i(D?=h
z?a=TM{4#bSqBp+2zW)BJp6~El8+1&>`D%t1F4UnVO16I#!nQ3KN#3kB+7WE3&WxPe
z7ULDj^XJdAWMiMZxsJKap}6t5yi+$Mq;8l<`t8~u=slNxZv0A3#W`ZYX{BksWc^*n
zxs{fFNCribxVydGxSbOkXMvgEkpYx=dz<S6j?1Tni)U^>LGPVkRA&yz`O%|CE-o$-
ze&=iznsj=?0U}ani!(k}kcaIPrG@seRuFs8aTV56#zHz#6o5<(&xW|eE&r!_qkVaD
z+_$*Cdi@bSch{p@E7Z8J=I5TZSV0A;eRRj}(bK_&jfQH41lY{?ZvQ+sMCk_lXchlJ
zit)usWe+9O8E~4!c(Fr(?f^cgRh=H2XsT(-InU=EIfBxKGY&JVq^i`P+GU#$w?{h9
z1qfrCe4Y_~j_O3nEmUV#W)|gID-NcNJgaRr;c!}g*_@GCF4fTw>-|@85znBxl%q*z
zGoQV$I`my4#YzlF{JPj=nQSLd8h>QuJvVs($z#+2s-Ze*`B%z&57!&0FN*Gt*pZ8F
zcd-{YD5<ME;g6pS&a$D0Z9QBGVCJXph*UXy7l8Otkc0R!Dvls&WRoh<N%los#$@<y
z<j7My)%1<AajU}>1^s%@rS8I^h`&mU0~J7BF)o%*c?N({u+2_4&&s1~kq)>!X?KH8
zSmA0i>g^`Du>F_RyQKr~s13=n8@A!sKYa#3Rg$PZ=9;7<`$?hkPr7yD9iAG{=WWuN
zw79tF1Q-!e8x@^iBj4sSjoRcIcYe9H5h7btZ||fTY;rYk`^)5PFVkP3OLc$L$4Mqn
z#y-3R09{!C^DFyo=&c#GQ2*eXjGJ1%BxS0chnjShWT+e}d5wB{)bSIK?}1;p%f^Q!
znhQ-gGuspxQa>pZ?Dp~t9F+3_s8*2@D1{GQnsYz%CJwNioZO{Lm#PE~c2>%bh;@nQ
zqb3G(G^~Ww9NKsvhsg2sxykJ2825iiX%V+tN-M~UtFC9v{Hi0mrsfW~4dwDzeG~U>
z+F3QVu#gE1M2Iy}4n)t%^}n@$YK30(kvLiaN!<tR3up{*TM)E8joXAJ&=)UWSQapM
z#14G_z@%_#Kf4;pnHy?RRPH-IoeMjoi++o{LDjLB`B#$)gs+~bFE!W(bNHY!M*|go
z*3$3fyPCosW?Yj`ahjT&Li~;#+upuIO5XF8(g$?g5-3Biwkv`jrg1IoJ1ds9TZSL7
zmR}|*<{5ys`?#h|{cHu9cn#s5cLFvokTZzs_>PQ>2-?lMcL_YOueaWS&oqSU@=dbw
z7;5gTkvzW|^kzO}1K{>Ejf(8+*ZR{6weHGjPp3`sZfW|y*||H3$*S9V)1XM?GWxMn
zi)yHRp?9Et>~Q~R&O<m}OZz#~^+q9wsF3>XsV{zE*F7D*46jkdfs^XVoPU8ILdZh{
z*@OJrTFvy2I15lkS``5d!tN(s;Z}m^4Q;y^G?YoscnntXL*iY8179`j&2YjsK_Ra8
zyZk05#2i+I<z*s7F0I`h(%&)Z5(b^{3WRmvhu6l$6|S4}^qnml4FI{?2srzy&9j|f
zom$&BQZAK{F^Cl$c)OWj92z!{H`fR9WQBOOk>f=Ve|cJ!eqCP2(rexJrphtVJPMPJ
z+8g}sR%GO%ibfuG@Fbc7pCq@8-MySWU+M2wg-c`weNw)QJ92dT>Zs%5Z1UAYvmKq?
zYMCG>)r56Vf_vA&*I1C_)Dr7yc4v9^#AR=Rad*4XItS{scL4#Kz;2TyqUETh+A@ar
z!uGgH5!d;ciZ{F*Z~F#&G=2<zFyNwgDrFv_-+nWkx}rc-^&{giRH$#&GZ6WnFIz}V
zNRPn^M)rMy4I9<l7xF~9n*)$1h~UwGHZib6co*w!rzLsrSEr`lS9tL1QT0eK(P*xP
zpSe}GBx#3QZEoe0XBxhNm_SUHYq@HtY>&ii)eae&Vkgl{&Arho4i_I<{au$^`B)Wf
z)(ou2=bUlC>t2mt5*SY-evJyW`bfw`Y@pZKcyY4~99MC;P@7z9x1rudMwc&rb8^FM
zI{Ss})BUah31iptv6CvB`y-&rW?E`muGa4+HO_-Rsj_|hcag0kH>Cl}AV+i3;r|d4
z1E#x975C$;(l<c#<?C0ojXAj6Zd{Ta&{6K7d(PB9LWQ7-wBIh&IuYJbRm#tOUFk<s
z9~0?5!uDn2%FwXXSX|s)RRvsx3#MI*MCc~xqj;d@g)Cx4z>2riMP|}i^ty%u{!vSs
zFyFrBfmt$_hbyzA4Zz?V7yzw~1Uu-N<<rFz*$0-1x{a!}GkN;78`#Ox6oP(d2TYtg
z3ELjus3&B$FxYFWb*RaNZ0Bf~Vh=UHe|xTX27u)M07OYCNsDXqSfhhv)K0}{C^3K$
zEv+o#0gxD=#c=7g3?|yakHZ=*z&~GeX=Uwi4gcA^@bZIKKOzow^y+EyNbe<%iNl|6
z3VBk^rOmGDFZse_;TR1S&FwCXzInmDzkuSG5&Gpm$<qD5aiYb-?ZVeHm3)c}#~xdL
zP`bG3>wwcjekaQ)WWkZ>NQOb(OrxzY>8o1i=L-z`n(Bt7fgbobKA<22-%qNuw5O5x
zEG_*bN&PEb{onPjLqQP9jGvH+923}M6Y;Gu<xY13oIS~sZ5|LWE%(opV0+9CI;%9i
zNkRgZ@eo?U3xiup092$SBq6cnauupu(3b33NI~3SFV5zwG1j(z4{;dq>i$3hkaYfC
zUuRW*jhE?tVq#))@|prEPl%R|%OE{3P_~NvFIB4p0`)!#nqJZxJBowe+;s)W0~G*p
zrcovRINK{hL8XWfn+_HL2c_IM2=~Sv4(1FU`v4pE&jt2naEvB+CoZUuifJwE^Z46Q
z47+efoF}}GlY~p_LzSp}dJmv?c=S~(hl0q)n{NPzjzy*x)R#@200)^cg-(`!#u71W
zHVthZhnk$J?THcw%#W>WXC*CTY6yZy&_Q)_%p=msjlI>K29o#fp?-05XFN$iBu^aJ
zqU8kOs8JW)`AcWX8UO`PS|0HcOGWh<>|^RTmdWb{5&1Ps2`U8=)t(|iU5h+Xa96^4
z_DcN`%;4#g><Ln&+N(_#bAvKE16ej*!$3&VX=()m&)rBVJ!vo+a~k(JiY2j9gZISz
zJb{hxFhZ*YV%a|?S`+br_Bd5xb)c)G$Hs(S%(o82giJl6LGGX41<FFg0$R!h6<jIs
zVX1)Hi^~P}Gp?J=ji%4%8_ez#896m3)W?2biI%XXfcOCKFQDa(4h;E4mjEr6^A-&6
zDqvVw(QD0bCXenV(7m@G_GrY~mf@hXPbymgW!rO;EYQmhXa!oWy}S)M15<=CUXmUM
zW)lOu5hw7ner;g)Va|P!cM2r{FH`DY*k3t2^KSq)VF}#9B>kJyX=FGve;=TlL~9@Y
zj_j9U{>BXn!21pMEPMCJ&gB0$D2H|dh2+<(VcpNpR_?!V<XsN5cqa!_kN@%d1VSNT
zq3_b=76J<PXXyFl+e?1HdCQ+p3;+8d@QC{WvLvgMk@Wv%^?yI70}!4&zd7Jwzde_6
z9+(wSm72fv+ugm8C;+l|N(Qg}f>nP%2a*VV(S?rr_hcs&ynCiT_4oJpZom8foyC(r
z+VGkeG#Ln_2MG~$zjQ@-j>6jyQ`grirl$#0nxni#SH2gR8H+N+|6XfLP536`WK#&2
z@JUZToN~~q=IE=#jCuX;OOG|geRc?b2vkpgxn@}-v6C-|fIOjmN|xfDgg0EcDsDS}
zjgODta(t5?XYU-5S%_EtiK^@9xAB49n%51|xM~M(M!&X(JcKqL&w7HniZ~iwHw>P?
zgcgAbNNb>GPgBduZ%UCQFaZ64|JKgDlQ&g=)KcS~L(E+!L$0Lw5xutyyXmh$5S?2u
zOHw8kQ%zPs=hLvaA7B5D<g9;a-^2ip6*MH-A|GNhde`<B9YgUB(9&sD5Azh6H7>*X
z81d650w!{yUJ^M9HkAA}-?ZKRVxnPraD=uq!&Hy(O$ah(Bb;p6wXtA3MqZFp>{*M8
zoy6RTpfUs>kdZS~PfeZ}2hyR3d}sdw)~Wa2hU^~BRy3mmzMlHgOu{=HCs+anSd{3Y
zRFjU~k4?%ZnMDf=-a{Jt4xWc@Q_pF@t0(X8IHvBFfKaR_d--`f-03Mk{vxRKo{$BX
zfz7g)<71s@()|g>T2uRSE<8UnnYGr@QZ8WkX9CFc3vq&|)Zg)o(HYW)T{qU<o><@$
zeUw5Dkq#st+ndX)Ja#@puF`REw0o3DIeLS@-X~pTFL!7GI5fgsB0gUJvvdCT>MQ&4
z%2X-9sGy7x`3QQqh1$j#CWf)<`mDTHL;G9c?(-qQ_8<=?py%uFH=<m*0-jCfa-2-|
zwpB{N1AAOIIC6S+B+$bw{DPSf;_H=!ySzMiG&-F4rykGv6LBJ50Y1Udi!@YghmV25
z{1?aFdtxw>k=wzPY4q+TECcYk`^-SO`*-&MI5O_CvN`=%k+&WU^!2}^6L*=~)`SV&
z@dtv(5#YqTq3mw|lnSp<fTwTC_jP*RyCe?=LjGMmSLD%!ipol$Zz(4&?bGf#pmP&w
zKkY+0g}a%@DZq8c6n5WsQ$h~8O1K(V2RFWniLCCx`3OivNNf)#BRwmQzE(2t(C2N5
zs;SBWT~zrtqI`sm6lDMm3dRtje$0J2f93H>{Uama1*5YH-yH*bwb-#^u1kgbhf`Dv
zHl|!=KXwtj@cH@q<>h5Aj|CaKxem1X#9<EY(4h0T<8PsF-@Xk9uw8A6YQ(PCL`Ov}
zP6MrwuVy0Ehg^$4RSxKBtEy(U7_~-u06X1xhgtyEp0EaLCo}AHv@}sVEw?*zcX9En
zgxh>5_sXs(%yjU5PVJAd%N^1k9m`X!%FOI>F!aN25(|0BM}8j1`ene&R0f^=TQb)g
z^jEakw3W5TUH1<^-t8Xq{MpWxr@v7h#(w!+EDy)R%5J{rj_D+`xQK|2{mAO;%3X1t
zlEXTCyAcNQh{g?g-oYBRu#;=pT1PIRi}x40UV924j>_o0dWZVsl0FEUY#6=vCnI6S
zk-zMX0}v}@Kk?wlM+cX<I!g&!s$Ubh9Y?1*T6}{6JC65(S73;7m;LY^tFnqG%hRa0
z8AsIA)FcV71FyI^X}ospv~sUre9Hyj4&$y`%X&>f4(uLRK?7Uq*GCt%mDLBn?!B|&
z0h(k|$nh@n#m5WFT?hy!3JnT=Nk7#`IwRefhw>;{UHsa?F*Z|JZxQh*QWw3|HT?+1
z^!##ia)YyD%g>R$l9H12o1_Yj_J{ie^1c0)Y=9cAFg{yhaHsC0ebXn?fOu<K<q(n7
zqu8&Fv#xzh6fJ|pjsqf&<B+*5|6{F!@_X(TA5~Td)rW`pO?%%K9S6=GUI(^vUs(qS
zA_(L~G4q4nKD*<iHS>X)xJLzo_aXQt&}<!Eug)Kd*;VF!d08D6OUaMK#rK;PF!&R#
zob}5L$9w)eYI=GIpxX)nnfG=Z94wkBS9s-xVTaChSqQeJ#zbxHSm>a7!ZHDlCy6^&
zoNQUBYr#f=IP-YF{caTlX>g&Z^K8ui-m-WI7u?j;TE5y-uKuV@1sf45VC7uAh^}rK
zA5+6-H%2d-m`cBpS8Iz(<g2^JBx2bWNkZUhuK6wJowcEftNFG=^bT+D;nCO-u9OH*
zPGo80e(Z;;>Z&`omJO1A`mpjtbhW}beHqMdCSE&l^VL)YysvCsL*kKxjM9TIZ!0*D
z-k3N&0$z{x;Nisjk!S}`yLd_{#DE!ixxoJ+>&@e#Y~TO?5+#KeQWO;ulFF8Kl*$%D
zjGeOYvad5#B0~18lkCRW8S6}?$S#bXu`e?i+YDyR%=dD?@B8z3{2ssm&6w-D&g(pn
z<8{1_=kfMAaIV{Ml}2nBg25A83zL(vZ`fmg@XC4$h>Q0H-@kuf*Ojy}<*Wp-hU%I=
zc9N8@T)C2J=J}C2>h%hcA_N5m6_Kw1S`TBi@_2vI=!%E!RKi6q3%_|fsd$e6H!C;4
zLH5fFsAc;I+OleZu(~1@s)3s+a=yf#cJG#(hQ%TwTjbKuk5P8i%Q2eEth6<)D`~4!
z1(s4g30DsgeX%$_9pswQc6X)9`X0Np|A8gpPi!1s(!v#8yVm)t+~v0TZ8tTIm6dgQ
z0{Hju5A+$)vH0_^oC;<wTi`H~D3I*{ehXlG7gq@W&T>{;3(!u0edH5^BDG!PUbc=0
z@!(tZ-ICJMnvm%RufhhrL5_FZrz>?9;Q%>_?_vLzI2M4I6cz@35bo|0F#0{7ubB!U
zg)&Pv_6wI}>1a~w!4a)vWN2vAZgzIIk#7_)N`Cn2=lh|dm-?V;>f%H}S32L}%&GJT
zQ;W9%?-~$_Kp=hf@mKDre?JrljW4eq7OZ1*P%ldA_uq-z$92UHGM6l|)A4<5iXMCQ
zf7En7c%vkfP5egP#td?)E))9t23}-K{T=&TT9+@<$4wU_Sa>8w;IJ|M3!p{;*Xd6J
zS~0#Gc@b3!4Gima1>@4w105gFBca~EYE#cjS%O8%+#RB0S%790bY=0}v?br)GRc;M
z4z5@k=>WT81yt1&(~R`-jeVIuS;)a~x8i!&>-AAf3KUX>#n;2=YHdlAjO7|Y6AVxd
z{*$E;(jG*p$!xTDovYb7NjmWK{U@FFxGr8f_ibm>B(C$hwjs*E!N+YJ=$My5A86@&
z4Qk1R?6>myx=GpcIETo{I(M^vFR%l^Hhxn+sa|klXI8OrFH?Fuh_(fMAci{17Y+bW
zzU0>p3=C9NRgve<tz85}$0y37An0D$yY!l1irAHT)plo?AN1AGHPC2bBxMl95lr#o
z&l)puegeg9OkrvZ-6Jn6-4VHe_cfIAWRbqpafkK5X$Jgb{{Y;@5sIC%K=5f<(c;`=
z-}HtL4^w#W)^7~F)N*libv-lkepSC5KzWeyLQzSnQt~FNGP3up>dKx*TRHZK#heC_
z(1I`v=|c$_yP^iSuKvqaEP>+XPHqmnlM9ohc`dcJ1%BPWu^-tcQ032vjiyG5x<3xc
zYM9mCjnYEk{5@fG{l@*(Hl67=4umrDc>4W$A)$PK@#Y7ieOdY{fFuoM>kGE)q`Y0e
z0_Tykbzd(Tp5_82-@%eX+~HyH6x_vRbRwHCc=J&r+#PkW1hx#REh<uDb!*;gD-T(B
zR$PyE1s46o<61$qB`9xEu`?#Hm#?M3n)mC;Ff={irRS~1!T86Ei&|KUUR{>CLa@;;
zI#^+6wlLaWTO(6Z_RVn86TxXH<@YP58RJAnTQ8BpHldYelIb%A;@q1l-C)|#ulQE^
zDX8g4f5{&Nlxwy4sUOH=Geyu*#vJp;yQhCxTglUBJT=umy@k3=U>R;P-NNYDIOdHU
zm;^(jATRZer-GMTD57xrfzqG5wE$7+09O;aSur=zW`1fLv*aaX?{M8D9Evig?RV-;
zF;LTZB9^^tA+<Z_08<uli-17z6KufIX*yIvOPeL^91x<ge?Eg)EQRbfVOMR25vF^8
z_~VMsadHyjmekIGKszJ5kuvi-J^il+zGa5_(t!bpX$6<jds<O-SX|E6#jKt?ZspSC
zKEsTltc>Tj;_YQwmPf%7jcat%Vv(Is!R3QjMBWn`?oA&bV$In@Z=s{p4snav0G*-`
zEUzK#&s+nI?e2lQhLrh{f#Ql|HGxy=Q$<_jZJr^YqF5-c64~-$S>jq?+U8>GF6~cs
zHfLRm`TcG@>UGRy_HB0>p*_}Vfi%x27a|c!vLjV**FNZp9KK+fu7ya>&ytt1_1QMv
zyEY2LZq>}DUA(v*%?&vyyva00n9fEVj20M&sK5*C;iXD=^B@Vno+GlvKRMWSH9&EA
z6gb-ql*Hu#DivnjG@R2-E2g@bx7h}S+d|uYBLa&3HkAOy4jrM{kfL^DDVpP!By09?
zTKy@bGse!YVnO|*qoZ%;+s5L69rinj!Ne+{H7Gl+Pd4qo#;04C0<V!(xY$G9tgBB&
z!;OEjd^aH-?CJQGa;#(Y_=sQ4sr$q7&UZ6FqoT*~2Q7OL*Ihq4_Qr2_El-r^>^XbN
zdXO^>%O8Gz_8sI9lUX`@t+lHzjCKKuBVG(-OKgKk{V6qf6q2}gi?-RDNuch%n)=qf
zO}toM7vUAMNNvgf*dOTFiJTUS*?Ip8u>b#)l%88V%2Lp8r%33WoLL<xIniqez`^Yr
zS()z8C<Nyf1C@4PT?a&AzE6(p3H|=h+W-a)XD~LU+9X<jGA%6)PymouoFFq{r@Gfs
zsTP670ZNH%jdnfU<>jMs?se!j)x{mq;Vk<<ZA_bS--nv_C)XZonGd_zvogu}Kr|{=
zTbU#h${Re2+*UBR%bcFs|DN`0ziq!qYb4jFbPXIMfK%*oKYmiS@zEMQ?QyX@+1!gR
zc3s87=0kn3wBV8DXS4+w)eUI<ccuGAXWlp(lJ=l)jQCrzEg?f|!r5b87UEvW3Xxh*
zq95vBXDmCr)<^P~U%OHZxqgG?uCTKnlw-<oqZ|WtbgVdIX9ESD3<B3<{-byPlg24q
zNU^GV`}vn^DME)f-BT%B=?v?bg1S0iEGi^@qS;=j{lvygLtc`TA<(hDSllAgx0}0U
z?Hup4BPLdypEe+(ldW(t?p&@oX#N*y)MgOe43CSw7lCqt6utr5Lu*h&yQi<=1)O~r
z;ao6?OZlZ&(r50_yAWx&ZqWC0TAioMj1=U@#=0Aj8=X;O8ok`fVj_;g>j)O9!Fi~U
zX*rAEbV@P89J2MHOMe8VpJPxU-e6U6DR;WEe5vHAisYZtHr@DH84IbkM)AN~84ktE
zsUxY*krV{N;9Vj=MlX(88n5QpVEUhr{CXsiNFQ%9;yd`G`kZZdJuG{&$$#rLHc)?O
zkd!)={`qr7Akm4k^@)W?#%;*^HR8JqD*p+N;xombnKbm<C<?3zv|1Ecz%|Fm&F}1y
zZvyxz;5*Yz$4N+?(;H=dol(7l>8=urr&mw0FX7`L(RM=kUJFy`aJXr?*2qo-%*c3P
z0QJ*5*sOlob$Hr)&)ttQlo$rxYI%cu#~Yg0&@bMiTPAeUo;6OoPX(X?vZEi68&c!?
zGUCm2G2Z}HNx`Mao;h%1m!0Nk<##IozxMclAx;l7di`11CYbV*K!w^_CSY*ktLY6A
z1pt$%?46!ilXDypz^2I5po8%(PN>ar@h{gA!kvNR6(hr52lWnrZ>~>n{7~2%h2#Nm
z5sjm$%=IrfSn=vs4zvq6MJ!modDfB8z!zN_#gM6{<dI-VhU3?W-IA~NJG4FPa0|<W
zRdegYg#bc(UBEK61V%%B-88bs&8R7gsq0uZ&ThZ@xHXGD(5xgG8cvt`m$so2T~eUV
zNH^U&iZMld(H4eV`D8b+azzt#K)&pXA@}LVzjDSRBBQrTIqDa_xv4g<m)-tXzxj{H
zmi0&|*<Z_<b;60oTV1`Q%C_ryPnO^G!337(3!pKPSV)sG5jXSWoph<ly}mDh9Y50l
z1xTj0OS9kCn+L)SPEo^$==`fnUQ5sId#)t=+(h}^g8k)n0FD5Ap|83xdX6iZ49rk`
zSQi2f+{Seg_l?TCi_!h7C`*KtE#b<B!ejjD?~PYRWnVqf*}{Bv^D&Peq4lUD?oel<
za_N&Z#_)rmvci5Lz6*om*TBaNgUumRn>U1Y_o$>u-ZQ24Ojuv42ewJ2W~n-*ciiWz
z;e1Q$hbQUF_iAfuT(MwycHfuL^9{Az!%w~RcFpEKv|Z|1>E%5?VQc>%h#L_30H6C>
z!chV%E+$qR0T>&mt~x7e!<481BC;~$Wxs1<pAx0CxB+M>%M8#%j>wq~kN7D}@GDJM
z+c|o9RZo>%4+OxBB^J3TAom-_b&lI`8KGw0p4qMEpD<z~+5=HrZ~Al+&^krKThhnJ
zw(BO`ynII+)ZewGqeB1_fxIXnIE895c2`FR%jce>Kqpi+vNDtovZfl(j~IJ>`=+jG
zkd~iKG{e5Nj)@wC(lHzp&-RWv^KQ#1Wi2+J+7|^)7b-hXJUqj#Li>gE!xxxo`O|Q&
z#+rAxQ6qk<PgQdHTOo(=LwZ2f!<*ltf1lq#DK?c99L!@!F{4A<iRCf(o#pY4&w(?D
zYy98~)>&K~06zV#)v@OTdR6|B8<mfIBqw|imU=Rl73#b~>}++*F*(vMqgE$2Ya9og
z>*V&V38JylJEg|Bv)|+6;{$i&9fN;!f)$8E`n}?iqhJ=Yt8(z;6rZGOM{h5wb@m}6
z19N8acUExT`0<JA%S`55$P4+{&5B2`{mo71yH~gWmaoeVviaAJ7*&$0m#wB0{cPCz
zF6F<nm~s#PHn$5q7@|dmtKhgzYL#oAdAEGX?U|-6i~n9U5Q~~KnKhP@CygkL)4FGM
z%s`U?_17r!kNvl{2K5X6>A?BlRoy$%#yv3{Z(PC61ve+i(;SlUF-ab!$sIngr7)F(
zHd(`90B{7*=Gq|3eK0~T{f5eiyn=#p4WK)4abdw`x$Jp<TjKh9d#}4A{8@%pMxu~T
znR(OjCxr~|9mu8m?%r}h<_DbP`+qQw{1VNuf(eRs$m)DrqrDM-QQ+`KrBYP<c;SWG
zg6H_K7A*bXm6oTpu-_Atn)Oki)Pkj@Us}9e^b9n|n1*S83D{93S3^fKWGP#b>$#3x
zaE*mTnNQzlK;lJL9>ryK>px4mbCs8Vq>ocsJ4mKL*zr#|^PPHRa5v*ubXp;fSjw3H
zE$K2ZYn#l7b!r|tIWswF7V^6{($F}lPX6!3I3R&oySfIj5`XO-S2J-PuNwg}f&Dl-
z(C?`iQ=ms*5CZ-6ubL`(YtE<{RJX@Dancm&hFNb1UV-cYjtT_$(Uy_rSaU#ib;5%q
ze4*9c<vv9YU0w6;n;RkRlE27P6BK`l>iao&3jVNIJ-7O`B*Rrcp0bEtT*tHCSYfIh
zNUjTcM+?1*lT?JPhN+&BaYGE;THnU~E=+9@x$U+;`z|6GUf$&GU><@84X4sqQV-Dd
zj{RTzZX>C_8?XlqKSV#nVCB8#mS~Ic@bz+<d@5k)%U~ICqCe$~pb&1~Xj(omEPF*=
zR*q`S-xN}!_Givxj@i5Oo(H3bvfsqGO;Nm&y`Ez3-4=lQ71&sQ5S8to_m)~z)gU_R
zLfwJUT?WgYECBSU7JTCsqSzSN2Z*JBnWMOpR<1j?FONNl9W!vBCb|e<BjJ-lKrUzQ
zJ7z0~70UMiCPT>q;QjlmGd!>>W36Gk_XH5FYZztYzwm-RzKo0s$ll0JTWy3^zHA5i
zwb^qnM+v$^Yv+j0=#)t3_;$LVg3bw2U<(?F5Bk_8nt>fRG|*j4lSkOYkTqw?Yl=ZA
zQb#F!zy?L};5&afrWV1~twtsns!B`NZOFaw%d4M_g-!$!MxM#LUm(d{;ycgm8zwVu
z*(mJz<1G^)?P;R3dx0jUKP^;|JO7x^z)rrrN7D6o%UYlj^x$9_hNSNAw}afe>`h+8
zN?BHF%1x+VEuNm_EdA-#r?}Uz!Y=DqW{2HxlY#7HVDk!LG<FU96RceH5h!(p3%&oe
zTE)kxb?6B7RjtKt%gP<cEv3;X0}$b0!=cr~1%|flmahPccfFyq@t!k%PnpkG{K12@
z9x(%7Rz&x%11pZaVHs`hgH%d!x5lQYkEakbL@l9Bb3J0o8smY#{w}-q_G_5XcT#U6
z{F1Y|sV#J+-Eq_G>x!~6G*!PPhZ<QW>A48Yjsu(yiBD;K^MJ74LOGM${2@Ig?lCLF
zkK0zXvxrH2gn=yYv`6_36S;r}mMb0EVHy@8qF;}ba+42$%Gwtg;K3|(-|L$`_YWv0
zR2&Pu^^#emzK`L8I%%GPA77ecGv3|;m75}aYceJ5V?S1zB#sR^oRtPJu0UBnw<k_v
zJCeXAb^Qp<dC-KVy7`Gp$MGtXBS42am&&EF7)T&rD3KH4j2JD=uS>aO{2Is!`SrT{
zks;}oEK3%zvD_2(S<yQ=!gbjI@o-;Nx$jR)@S{TEcDXX%O*k>F2_JfCkUY@->{kuQ
z5ZNUSLP@Ch5itIxytaAATngnf+Ag-YWvEho52iLmkZYyG+r7T<Y&^V>5udxHjc@n?
z7UNFnSArY!x6nPE3oex!k}=*6il9~ft`8Z4RYMN}>D3*YxtB$k^DnA+bdYw;MN#<d
zWuRAy8gHVXP4#$|!7_}yoeq@H5`?JRIHBWI<3}KFiqyOHz*EhzqA}N_-S<QQ#v*Vv
zpF%)m%k+~!f8Jbohf>z$^7@NZua4Ok9T91*iWQypYQ}Otco-aI7HbdwmW<FR98Yco
z@tJj^bglXoBd;9vZoc^HY7<KF@67@3hLEK+`(1?mM!hwr#Na-eFt+J2#bahRS!wm$
z@9#_gi9p_jk>Mr+YT|>h*TZ!)@#P$;QdiYFEh;-?^Bui!I^#Roc<O*|b3=5DS@Zgh
z;{s~RhQ^2-k+L7d!-zVQT5I{iSi=cNeD@Icd1^8J?x3S{;Y7`N$?yE(#&<ym9<LG&
zm@hL62)vT8!6NC)o-?zv(;4R;Z?yDz5h$x6`OC6>0lf#=d+M4>dlW^i*Vb>YiHR2<
zjxoMfQ6}GWHR_I>RSA*Vqv3V-Zohn})Jw0M&HMGG&tmnO)dM*Rx5+R23r}=vyf#MP
zPgb^Qza}r(gan36cD-u{UoCORX<S=cwM=C*9Y>;Fr+1T#nS{2@(^R+K{PmlBXeh)B
zU0+&rR5~cDQf;SW_qO>=A^SVv0G%Jry*kYGsi6$8cg2v!&m5w^jQSz3-kaR@3s>n9
z`c$pxFnZ<BEaSQFH%!06s6aER1_2;?`~^KeA+Z81;pohcC3Bx|!Clc@;wh4~b(fqe
z8%PvUENFQd2BiV_^~7S8lcQri8<JNMKrI*>8w2}Iw1Ks_8V^9t?rbfc`ppuRqB%x;
zX^ZYOCR(Uhcbk%~np;pk&Kzfc_*ofOG0H{jqc4T?LA`#iav#RQuH^QuqA+xl3`fjB
z`!r2+WKS+rPlY~<zBR!!(RE=HX`W$Qo^v*A6EH&u?@jrg^155?b&0}e@A=yJ2#~{w
zZd-`QS)W)hBjY%e1qF%iy?>Zd;VAy4LOX4Zo;#hrNRVF9!S;Grl4oh8gO@y4=lSQy
zj$f_%4NkFheC(xN{@@-IkV=wmu2o0@y~k0a!>3hnxTF2QSD6gF){e!NKB5tb*z4m!
z?cmBB5K#V&e3o>CH4Vh0C>x0vh6e%i<H}No`$o@&-@2MqT(O>0#|)rNVc_{bLls~}
z<hjsejMt9=Hy|o>$lc>6tf!P+(*J@|oK{b*ipSSosiiapy{Z6h-<(v!P}so8=pCuD
zxbDQ0DHrOz3eFy9HUb{kr6?<|nlQsy!$rN6ghN2BD3|QAfBgf1^ZNAmuOqQ#$Cdzc
za}m6`S;0#n;qZH^xo_G7Q?+stW?3O2)ptNBJf$=VK;DaaIi4UCTLW>NMK11+;$3!{
z$DBC?<A<MN`+}DwNYWvxoLnKR`KhF-w!PKK2Cop&;;{eycmR38%s57MzS?Z@S}$82
zV`?7=OQD9j-GSRooc!$qTa))mpC5^SC%GAQLuEtZZYZnA2`pR?c`ouf1M|#_vZl;@
zIi1_`@}__~xZa=kOhd<ZT&<Yws$kds1=u)1K#5TSQ`r)wm(rMGZ`2fRP&^dN;xmlz
zY+ajp*S(J^hZumt_8_qiWLnEog67@$&xY=vXV`h9pHsrtbtw96=97FHHUIwDvvS9;
zk$B!`_Jw31GL2#l&{byk)mK<uu*!H3qH`z@=$`fr3QG0ot~`1bEXWW!Nb*mOjzk?t
zcr31VT&>^47T%AXN#c^>=Wlfi?tJTAuBQU4y25(&7?qDPob%v5o~8A0rknqr6xT%#
zv8>h6u2DOzGW?izyNR>R^T$)33=?=^m17Klft2l^hkx{`Q02|j^@4Xt+zK<{KTb)7
zo}YTXe5{~N6exZJ_eg^A5B|TU^3PubADm%hc(2@KomFuG`1Jq2=*feym7*2h)@QYT
zwS10BbH8smMJ|I-;5hUOZs`3`(*DpAsbD;1Jp0CtGw9gZsDuEER=A#gTvLesV^+rN
z_xyoNe%GFm{okbkUwbkmbZDKE>8V6p_hs(+j=8a+>D}$#)VgaAeXDYvHcSp{llD2V
zuPns_s8cNjBVxm9!&4?rRW=?+C!8rBh9#M;#_Pc!^#dRweMsfXPuy^dJeCsV3{JhW
zx1G6Vnf_p2*=ul}fZ~<Zyv)pSUM=+83bUE_(c=F1Ld{f^ONf)1Uipxw#-=<-;(P)q
zq!*K@n(eCf^_#DyseK03nm6XTQh|>T99fnT&@$xir{kxk83XC$T<h4r+9)b<<G%24
z-;b*~)sgWx&Yfr6Jf`~VfrR>h|KR$}GX~G~-p*{nE*S&2KnTU_qsm2ezz^iNZ{K=h
z9<+!Ezw|4L4U6iOp@EA7?jSl__;W(pv@J$l%qX2BRiK=pg6A!DMa0C#q$-pZ!7I35
z05|UD`(wN_%*GA{r~mItCRMG-Use;UwyCJ?*{&*!uzowXF~>3f1l9elzQakT!2F!r
zSCk*?1&<6hhR1RXib}uO7h7^J+<itR=c@`b{>(nc@Ng~l%jw5Q3+A6kj=XSL%BAKx
z7HoRAgPZ4C(DZ(svBVWwmn4Ha7SDC=xGi!NG0IDtc<WMQS-zW25AVm>x4KNNi62bM
z|M`(o$8PkWubq5;>Ax>zuK)PGqTVLWba3v?L~lo$#2v_JTW8FCL|mU*_r190TN3g?
zb&?+Te#;-C_7JK-H>(JIyX@yhfSs68lIpr&{q`He?uU3cUmB+WuUng<`|jur&-ci4
zk;=d_{{KGM$w${^Az#kAt~-4E7#mMPHZ@V!72&te!oGGcJnZAA<hT6TX%~CZbLy0m
z!-hj0uPrZYiu8l}O2qxUx9;AR)<(+owJahDhXwFuBVIdrNI#1P<!VhOu!_#z0~Yd;
zqyGP{>S0o-tSAy*7^F>V(1@%pc1r9eB=-}Y%U)*;UKreUa2?|gdY6~;amjF52q9((
zuQIWa-;ryGS1q(Lz<|ejPE|LPUl>emS%0od{Gg@L#k{ogi7D)lK<Kg9ZXf&M|6V}G
zcgld*J*0(xed5=zUjQFD<jb{d*C>00^5SB3H8o)N#lq%n*my}JP-O-vS>l(OdtJ_E
z1?90Ne7MzfRYE@~5PR1=f8tBgWvYvl`z|i%)$~nF5+>=Ii-H4msDH_^Vg5y>E?R_(
zPh>d7s(3MTckLX@%qd@pM;-$6rNk@r{CAQ;?%A+ofYN=6`Oeh;EtIeu?r18BLV%5a
zauRyrw=oGEOn)r&_4Kv@9KW=5cE8VHq0Z6hk~P<pa5D=FNGq$%Swr_QeBoA6CuYNv
zwbGV;>Dnw@3?<jEhGem;i_1t%$sOu1F*b!HP{2|?s>pMGd%L3(?QQ<Fv$1hn6<|Fe
z-1+~l*mDmUw&#|XmxEZ*L3?iNwnyfO7D!*V;*ki01IDBPLqHZ7?~01@D2^wd2<R_A
zGND`Z$;WF4^i%kLv9U{C<$lmM2z#9qL-EsF63Ft*OIL}BSUVxsZCYf?q()HiUJJIu
z7t4|zg4_IC9Q0K1%=rtstF@#N0x}(d1Tx+PoGK457^cbocW=&dGf2c*kSgP@%HGr|
zcPh}zu)}EXb?(7odR<_19|P|i)fx3|V%-=f@QoGIX)AC&RH_Mas?ID48vh<YThNN>
z!2lbE_!sXSoT!tix3d;V@y1l<Zj&3fG5dy4Kp>`|rm-d$t^%3=eUS^@K+(c<^T_ly
zo9Z_8aqI)T!xQG?j2`drNDjXL_c-`|p7HsUT>!$pP6=APScX8v#Kee+h&;f7>rQG@
zJE<8N8F=Qag%2LT>CF(4>Ftp98>-N?RHSQvG+Oi^xtyHdsiR^J8qNqLOf-$l7`j!A
zWO$l8PjwC?Yi_4<XqzcmuRT9)lPId0jL2%Qn<1l~0-OK26h;NCxaXsP&mwPcUqZ3R
zB%ei7r)gtTOP0`&h}Ot+%wPt926dzeto17HnNhBS$SeF)+Sv-SN=nlfpcUH#h);tc
zZR|NTU~8L58SV<t$o_JdD5`$AJ6x!tMDAy^_fHUlZl{!pxn{YN0^!Y#Yb`wn8H+D<
zG}RKxt`5#d4HN`2Ht-!nTKo1;Ed_}^UH9q)<Ii`%X1ZylYIpoNbNwgfAk{rZ5Vk46
zevk_K(|2t?iQ|sEMh5*Ls7Xl)v`!BZl({ud7v{fvBBtS-$K|k|3>iOP-_E@w-$IjP
zRP^xrXr(o{+=4nA!N)7-eVd<OMSJ|`&&T=i>W~VF+w*atvXQ9^hc2+yXnDitnw{Ue
z9k~nh2E2DD{Q8jK!Ff3Wb)68tG;Y}#*aT@!Q{H0euWHs*7HM;J+Tyes6;<%T*&?VH
zPEQpf;pPoG#DJ4^<>+LMO=7!oEKE)4g-;Q}+tOLpzOSe|NB`EX1Cfq8(gu`1mhEH8
zbEZ%0n*6}T#Ng0mt(T6bnc0x+LC2$KvP$x^nH}ooEv6F~%nl5>{JZVp(-RS&)jy|(
z&i>3$27^aFux1}KZ-BP^%z(ocCyW;}lA}kJU&P$K_R$+qAz?Wu4S(7bg^8l=<xRop
zli>%#%ZQQLXQV=ru425we2{4Pq@NI~{Kbjm%<lo$l*bpb+k-&N^jKYaU~dAr+f9d0
ztac(ljiRSzFl7RqR)^)FsU4bh9GObXnzy!YdAgJ?#)>__RxwHFLjw1HUDvsFLy0Ve
z&Gg^X(Zm|*j|}RQEd65GtB$v@ay`D)l4eux?y`}v6FgV{e%4V)kT}&)C<_#f-)Dw3
z5#*Wz(@h(9H4~C%WQjwBd?WI;d@=I1E<Tt8U2DfRxTrD2-FCvb;dI)n(AerkLi(}u
zz%z}AeW>@jT9KN3MN<}L@R^*Y7({9g*zs1X@MS^+Q+!UbUG2}FJq{nv-RdQLxv{YC
z(}ltw+bT3Y3IzZI<I>2{>i<4-ZUwiYd+6cgx}5a!W3*j<LE*2Iq}sgvU;d5>T+<3S
ziSlmG5B)a&>=>ZmS$AI9y~!F(7-@sjHnQBy5T*@fZd=VY5-WFZT2QCvDSSb*pT}fc
zY+jL})7d;Bl7Y<)wRq5mC>%iu#)0)C1c@S+6swxb`YkBUNY@bKJNs5L1UxsP$5v^n
zs7LH}#;jk<cAeOIqbmb>J;YVkyX|V+SpM|J9_OjJrx6-(`le-D+_lAPAv2VlQtvda
zsAMAUg<}pd&Zs$XI9?5y>M2Lu1ES*lalJ|um*Tl(QLv$bL4ec-9g(zC|7M=Fz9S&#
z+jOd)UR@vv#G_$KK(&w(+RA@)QwkqhnW|S0xodcKm(#5Ef-~tH?^qV8t(NR+e2$5(
z?ylO_f4)m<smD_Hpxk>se1rpHu0gb2;n^4>DE0f<jVcQ)1icZz%pP-%({E~#-y#G_
zB4TRwg#^u^ztyzn!CfUJJ~#TDkMW5Y=vvk+bU+R6cQQm;Zu~fPE~m550>PWYLG6fs
zK*aA(V&U|C<U2)0720fiqNGQF0X_>fYCbY5<*czixhibxC*6??X@{=Uru>9rI(JiE
zk!Zr~caQ(R!KdK=BEHXSse5Z(R!YjCcNQ2bF~$cB0>K&T_LDjX#k%m$vXI4d!}t><
zA=pNLp$q7im^;*bOgJOFIc%-Q<&RF!onp|N!vq6D&D%BaboJ2_$0N?o^l?YrVYCBo
zQ<=~U!^MxmN`B)NN=fUjeY{DU6&`NmL)8hH3bRZSdiI<G;A>8Fyk>THjakciqo&{0
z%bOBU`O8~e7F<<rm&Xy=>6i>03_2facu=4di(8+X#$l(7pz|_*YE-*|_H3w|lY0-F
zAreG2@p-=cnUB`>zR9hZw#{nYZFFIQrK1i_+>dJ2L$j37e=FKgZ5RIqk=qy@ms(Zj
zb{ku+EGl2Tw_&M1StAJw<1DDk`LRQ>HV5W8iNI!0TES&jrvb6V6nTp?#enbU&&;*Q
zF}#Z{=LOzh3Sf72>C%wB5gJ{!)50UW4Y|ND8jpXgt9?E6)aYq=C@YY-?4P?gTi(*6
z8stn|8Hfvr#Xm&gYxkV$)*J>zk->pAAt&s$%-e%9xThyxTAEMX7Z%^D+L0*Gl8cwq
zEJF)f(tv4CIJitqEl+`i>w!@6DsC9A8sutPTiUqL{7LJ#mV0S2buzh7Y_?RJ!Q}Gg
zi)p*5oDrhzbs=k$FIR(`!u1drVD>s{W`U2Oib5ElEZi&ar5Dtfy%N-+$C8phv=w&B
z+=pjVJBx2n!u@OfWU)flXh)~jMpD&z%VueOPi?I`+LC}A(-d`HSj+P2tuSV49a3%z
z=RAXW`!mNf2)U%s6?f0Qw$7(Z9I=gn@w$ErI9TV8>6t1Cc(Zt3w&;{q&T1O0@TszT
zw%_`AK6t4&3%~c2KeU!GvcV_a0Z-x{Cy1VaC!I|>X4scv>Tg9o+i7ZC9ME?9PF6A2
zzR<i)#Q335JO5CR;H%YOp^7`+(Jw%~$@CA(o6IxE*?93v&j5ecAy8g&s#_V&Pz3x|
zXh2sqs0P}AydHn078}rd+#z0c>Ygc*^b_ca%~!=?EmjQ-Gc4)kk*Kci5<(w>bZfQd
z1FhyIk1N;|6?^~?Mag53?>$M<JAP=&)EV*SemZZq|J+9q{h&`S{U<?`%m!KR&FY+9
z-7EG?G1_fx0vNOuEO6rILQM6pq%h|BCJkx8&@F3kQpzUAt=x!Sn83Kn+Pi{KrA^(Y
zI!5u#<ktqI!s|KPRLj&ZOBrA9OmnKp^01a4;c%9)=ZM}IX3u~@YRM!5LGNlQX8F&o
z3b<6^CTlZMCC<ODOiVuG<w4tcV@;9;`lM77v};d(_etk*iSvvdnm>Yf4_Yss)AwHp
zKf+7wM7BaK^tzlH?5f+H3lUS~01|-AQ8X&H@^7&5YG)ImVrmW-3Tb{NnT;JG8&@sR
zJrXPJOILRUQO&r>n`K<rsF(*SE5&7V14~OO8@oxDFM40kI^3*|;5d_YnNN(r3x2f`
z)wb_JE`DN|-V3y+)bNiGn(cbh^Ig9O?QJBVlxEFKi#gWY(XmD83>EE@Cp3S47^Zc7
zD~z1@I(w1Pu;m1%e6v#|j;x3)s2fbF^Y#p_OeITwXAP#@xvg^j_32%5q0X-hr#pUe
zUaGb4<IQ4OArfADd3iZI!)dZdMXFlol}xW*<7WRip4+GQVk-@sKCC6{IUlu`0-+*c
zSJ6-$Kz{|&jgW45OG^uoaCB<9=4lJoQ5;HD$*LwPMb}%s&2m@(S08wQtz!+CbyV(m
zG!>9`u&im+2{~;=<m2JNXHW<5h`|<vgy+RC(q3sNpF@(#fz&l92=}PSHisZOcQ9%l
zSKNAdcnJ7M1}#`Q%1D5u{U{kmnOp{H#zQKuh}h3t;>j)3i_!|re`f1wC*nBbO$|V`
zT_ckv!GC{xQ?4%h43&>=))?8ItQ*-ghY+W@)y-P`DKXY=x8-I(8N}v8DX<n|j5*9C
z;UEsyp|@QEo-R9B<rA$H_nz(Ms76ZMzp->E>*#q*<3?ZR+}6c(%`wEwdWT0QeA6Jo
zEj>L!$HF)#xo0;1!5M`<)EVSr)K^l-)74be0lPhU<S^}CygHY-27OTflnkeg6C6?C
z_^Gs*kQ8S=QQczL<Htfu|Mt5T1|jly*gaJO^SX=xg{gyCd$yi5x#xGyg1QDp_LfqR
zex7;5JK^S}+kLkzG>0K`Kc7Ek{By>&R>8AI!OkZ0^l|@#b#6o#8uDh6uB6uhFEtSB
z6Hu>}VhKl`Ua>4<SK3#0^(O1Oi`AYoLX83aggdK+u#_&DTeqH>LW%4(j|-9|;Yj33
zLvd{R)(QDpWh>dRXuTcjm!)$3FP4g^-=C2?6)gXFGGNov8@^T9fJ16?Nhf$#@tlWd
z29{;Qqq+4V_D@(DZ$<$r&u*6(lc123w|7mf;%3z|6J05C1TMwYEdY@8>fEME+T_^#
z;b|iXg^mGFi)3oE0liaN*t)yl!d-nzUDLGE=tAa&_ZOD+ekM#>w|x>871h)MZE>NW
z<Z{$ARtS7Ukx)Pdy;<&Rsi`foAG`!yO|?J~W;sVCV%Pq?5B#lmaz&N%IG%D_69WQ<
z)ue}`vg>yTG($`a^72;Lf!S!o3V>{koDPKdAJko$<POQb5hm8V&3V?XZ&&&rgJ%bd
z_I0^$a2Z=f>!5OS-BF`YgQ<r<@=j_j!(pw1I`edY&ahyDdshgioE)DprvFzi#B)F<
z7O&2<u_3beO98*r2a~@f5zx^-AQ*}@0sAd4x2L;D?t*NlN+P2By88Q+?rLehcEr-^
zjx*1!H>K}g+nhHa%Em}E_hx>)TAkP~1gS?py&EX}%sOtsc$Mc<!}3{t+<r~L^#>pd
zvN}8P_q;Xuu%T{^wi_0e_iM$SKKM{&!bx_8Dc4i~L%_BszKI<%G-cWSk$Z0Jx$sDt
zRHkqt+s@%|fcLh<Df`SU1^e-eg(rQ{q?BP%j+0rTC~FKs1!(Di^ym>^mZ+SGWrN#v
zbHlf9k9%r}BLd-UztDFseE-L=eec$}xCIS!3vgX9rE22R^gM?C_wxMXa*YUV;OkFQ
z6@32IzcnHfe<?6CrhRujymrZ^>!y7@E06RFLHFP#alL$`G=?R4{EA{=4XPkyy>{f~
zXGWrdQprmY(CpuN*^xHe4b=2;2s%<`+CO)wbh57PSelS~NoIEhJ0EQjMzbNPYU_sE
z36C1ZNIZBT5PDRuF@}<em%g|XZg|*^tu4maMepdximq*Umz&gTpx&(FoXZ;8HtdjS
z3&2J75l`Te8isKMazug*hY+Y2{e;l5r@laK)foF^G$v=whGF}DXERO6AVq*OUEbB$
z*b;)ai<RH2De~y(nD_`}O^M{>dvy=HVe#L74R!k0g!omD@tT>9f14;huhQ26dV2G&
zS7_q>30ws%97Oe~LPtj3u!wj}td@a~eZ8ma?#ZBe3|&ile{5qpl_5pY@DcAzynH0E
z5h-fO5Z&ny-F74Edwa9LU-QZz%*!xQcqK2#XH-SXv1h}<KYJDCuPg`{NK0lhKfZ74
z=!xOUIz&t;@a`AoI!15+Tw?Io)6c)$n+1HAB`8fIWwA=Ck+$BCtN}ds?VRd)8bLpQ
zs{O|T2!CNr&o*&AS^2em<X!W{(ebUOZ~n%*KeXOG<Z8slgucN4UCaDUa_w%BD&S=}
z4-g}+&V{F_>Hn#u^_bRs<j@?Gc=Y47FJvajdG4;NDUTJd{~&7^p^TF`AK$reS9e1F
zizA^-y)fstusVO%mD}R*^WQxeO1uId^_Y@ezmFg0LiLHAK()89(9Un`XzbR0ZmN^F
zumA-p-AycXBpxlflCMhn$Edfy4S~mxd_$jf*_WnH@ddv~h8=X<ce@rraH65#zTKp(
zMBT2&k_<1=0spdEPdeyPH`iv!A?7vBMpv>PH9o?199IWBL9`2XZ`ss{>H0h6C)q@Z
z9(ow1OmfhvDY+R%vBqp{U&^`(cOb*XJ8D#wObHv4^QX6=0R}x3K7Yx$1{}8nI&Az*
zVDryhBuGhID}r5=Wt@2iIUGo<v#7c~p9D39dP@cx+8-LV5YhdrB5O3iIgDq;m!b*5
z=mF@?D8w~4S!sxiQ6uBdCl%}5U!BhVG^~^9wmc6GBrQ~%UyCnrU;n(^JX0!=rItsy
zPR6Q(OhvMd?Yj13dpE$?t$HYWEBtB;JPAxLmNYR06{~i!41pt237_$%aShA<YqHY`
zpc8jqhKa3Una~}u5LL|iA5m%B2=+Mc)#+1)SojNjYLW;~Mmk=m?V-Xgo}b2FLeQRd
zJUlPZH_Xm_@V$PVws>aio7#X{<Xw{*wT(f*n&lAp*}FWrfuxmp0Y+Ya(FoS9Z{+ZD
z{*<CNTz7Lvs5CQin<}E4IQb6uh;^-@V9i!>z+*|Q*zBX?V217=@`mv@aI3nHrne)1
zWj4;<(XrSmPiQf+?(B;b^SGDp772ZB=vB}@Xi<m@Gk6V*GP7k$ln0A<S_cEgOde(k
zC1ATlXps}B_U&{_d?-wrL87S$19$P;{Vhn2uYg;(3Ux}?P)y>p*@lIiYmjCqo6u+Z
zw!{moFMOKJd<(tb$M$KfeYuP{`@I|u4(iG04;~c8NclGhPxwk{){P03na)pEizN3M
zGZ;<xPQ<l6<@58&9z|Hy)^O$J*B&>LYOtPLCsOZV_dN1@SGQa<Wu#|eN)l~I6iDjb
zpC>_i_S)*x&AF>ttUjq+Y~XEsF^$>Dq2rlj&UZ#^q-=$CvflY%TMhII&)DaS@Q>3e
zzo#kC&xEF6YMMLNwI<Ds!6@VVA`LU!`pgb*=+3GGss#PC(bAt5U$t4+qmdEqZ{Nit
z7y3d`_ak=n^RNBQE}mI_Yj{}gdnj^uWaqT~_t-BPz7OVI{C;Uzy-#G`6t}z$R>@KI
zq-*GOw%?u=A&M>v`v?^CD+(h-!$kH<58)80FIze$VT0B7eTET7gD?vO&WpNNupD`B
z0zU^C$G;qY*<;zxjgOVzxR*UKH}^W`+rHC*e?EM18*}&dQ(OFisa(P%QuE<<SLbZ$
zOPyy1oty`N=ljoK5I`^<lSe)~{rD9yk@)1>0VU^$i=&ddoo$6;oFy(dQFf7EsGm=l
zpG-*ALvQcloZlYoEC-zqDsST+@n34e`AnEnkJZ^b=X-bfT$h3j8{1RoxX}Hnw^00g
z^T7;qcT`p9|8NPhD)<fwzs&EwOWwE^U`c;fES(CWs^+69ZYVvuiRFjFGLPcBu`T?-
zatdm3Hx?p`NF+}F^yJp`*JO(6i-jfO)h#F61q;7r<9_GmW;~@htnS5M;HONTFq0pf
z&*dGJihOPp`t7S=sL#D*#)<<yWh}?p?t39S#9S;v|M@m_Dj9jG)d&78cTD{t4Z61v
z$?9zK44Kk`T~(7?LB+&ZVam2awDr(SyUsFviM5{ccripeu}qkNa0yyjeaCe1Vo!&T
zCp}$_kv|U6#&I2(`kA6K;P|optpxS@r`MiJ&Vy2Hr0e~5%p>O?Zn@{-pZhiaxbS%(
zEj>Ibfvxxcpl*Ww>MPNn<Z-nw<LQ@+PKIjLw1EeKqx&vmLWOzpk_m6~G0DE?(gFkA
zFz--UgP$T2@2Q0ga5pWh>Q245gvqGrlrCM%vl+p<+}dvgmb%lnrSbjzr`P(Rw4H&^
zETe|?<%jv>oTbhETxK3&Ez2`WBM4KlzP@$L;^In5f@PC0f;c2{Te6Y;c(YB%g%IM`
z(u`r5GsDp+CRcw_$x!4s0W;KC9fv-`%os&Mwghgra6$!n5>IaMpPkqfbGoXg{0hDe
z1@x}c=^+nde&M<ARhGKHK(wWOC~f*~aVqrS?}jCPSs=0V&vUKz_1joN+gyP@i&YFf
z5-VhJsHWTBW**$R3+8@JwCmfdKB0a7aK~L|NVc`@C8aN{!x0|w<MlT-akI~~=m^op
zJOk-ssSNzZi{JV(*0Umia3cwC*}j_4AI%Fc=Ud(bQNeL9i?@<KW>Yasp9Lr>Ybc5=
zqVSAefy?N0(R_Kq^XEy(v1SVCWFP4G8N2K+kv}UIW6KbPQUu@jyu0?jo}_9M%U_>(
z?@PL`6+_u|x<t5D00vyFvsJ1f3b(xGa1toKrvdS?4V?c*-dEd?k_|e7{I(IE+#S)*
zR|FOvC*wR_Ix)hlqQ^@M`Ja8d$6)l@AnT8-vqijI!bSpFFR3&?3NcMK{%n#$PCj9*
zdb?OfHlOp0n3z!O!n2g|p(UdLLqRsFUtFk7CiNFj-*h#jBuq(OyMwNPX)M(k^<p-`
z3!@eo{#NsBbV5>tJFJt*RYY(JAy!+!7cQCcbwlarC#gNrvihI9R@@U2{l%P(m~^tz
zgNb*iu7_e?=_M@3IhNhKzB!i9kEUmMy8bo`{IN+}OE}WxV9>1nMM9wD<`lhUnG36=
zd20PKn;c&4N(hV|M4W4I9KNgH5FkTvNYWgP#{7;30yj=3MeiaZ3zJ@*@{<<G&KN*y
z$=;;#q+~PmZaEF^t*>;4tzF${(%JE@__A_#Az(SLbb4}g=alHgc+g#WPzy+O&N=7m
z6gr^P>B+OT5qIL+&mNvckIh`Rke(aMxD8Jo=_=)4AoxVr83_nImD(BayU5gj!C3T<
zF+VO8dxk4>w4+o4nb!>qtTidK^3tfNyA9eOdPMvxk=fk3Xwb#<zj7+G^O1GnE&-T*
zBlM%d#el^;<*rGicQNf!yd}6w-xD0x|LnnPacL6FFxE`4?FGbcN`oLw29H&&J=UaX
zE(%>WqS*`EGwpT`7A+WX|2Z_Usq!%Xl=t4JARb7^$Yv!*+4k#tDeXq%qfS>c--awF
z9Kxga3|T4x9=+KZS|D_hJ(YjN=vz9_A1lmW7(D;jMx=JH!})EAZ2saiYl>@uzvq0)
z$b~<bWji=)T&N+Azv`qKvAjiRgBZAAsk8-AzSYRDg_e{*?oOhX4C4q9KnmFNb8I3&
zCy{#**e_NjV72Pd#t~y6ivFSu#7xBAs&~adOX3bFk5q;02UCjCIDI$e{Fw*$JEGq8
z@P@FUvAN<`4VBAx6Fz<+){4|fz5Dq@{{@@t=^5*cZ#u;MP^_?M^$>lp$#Zo%2(6?Y
zJDeL*(1j+?gVqL5cgvL<JtBlJXK%KX*MGtF0uZ$I!XPc%#Tz<mI|XwE?uSJ$!_@;$
zTOO<#?Wna&P3?cwWd{YV_{D*Re<N+yONhLMRM!zZVW}ENYshqkchb)aP|0fZ&Z(xI
zs*B#os$Lg*J!=mk&slelO@DdtKj*{s=F`_hRT@wUdY(Ak7vo~%#nc2H115FLtmC(<
z7aWs@lD;Oaw2*OdAJGsZFr)o4vcd)fMs0J33r+}qRRzwnK|6D}9?rz}W2KmB-Iq>a
z=)FnRi@zg!2$sZQ{`qhS5Unh_0F&)UU2Kx$z)A-Cxv(nzGBDn7THAcsRgJ~-LzmtC
zzq?fK>$k`#WlO=!fdw(z;7fY?G{6aZ=YHwCV688enXR7QqGc1WZGD{SZ9hsRnX;De
z<Rg+3NW&X$r>%ZSp5iYKJ3ql}CGHUK3&-kZwNn-eYh*xPu;)6ff4N%xI5yFfGvYAU
z{rNtb-H*=)Y#5BMd$WYlu~c|$zuru8TW=I&bq-YcILA2@xMPr;9~07)e9>qu;U&Sx
zGr_%!b%Gn_zg5v)Ki_6;(uLIe?9A}%Njpj8)fc_vA_17m)%NW(*~3G_(EiOw>N^IS
z4-oDw3y{=P`^8{@Ur)rnv7V!^l1o3%D`aSqp&h*H4naX#Pi&n`#ua4CO7WT_aevh{
zp&_feobK0jZ3CUwdcZM_8=eHZ$}rbWG&xQkOEnl<%F@d4l{{T=A=EJ<;Mur(Qzybr
z_}?1)&o96hniLJMFm*kV@+XPnN0@FIS1Mt)k-Z1JO<_F=?M@!pkiFtC$>g)iiTbns
zdL??c39kk`4JFH^SY0oZh`+|KWd#0?loNK%0^76{UAJEh9?*S;`is8c({{#{+w@iI
z(y&6-1KTJ}a=r*6J@isiH4d<=j+~R5R*!YSRxaquB<ihHnID^oW0HoLI0jw(R$As=
zUy1to5P-0)m+$+!mH$<L+Gs$&-+=ew#aPEF77*ALSfzO?w8)~26<J1Kl0k1?6(|*E
zCiUJVciOifk}9e6?OeT%3s|i>J{SyzJ5M;bc*R}_O`AE3?alYy{VS|wYk=6s7ZmQ2
z={Q*9L;cffd8v054_2(om5|AjtM?{id$XI|yH3AYD;tTVHn5(%7@)DpWZ=J<%*6(>
zwQxiGYV6Stu|nDz-UD1$0JVI#2gYqM(VrYYj`!SO?|CWW5P;#Apg34Tcf;Y;Zq!|e
zr+@HCGKqGRv>_3^-#j~A$`~!QNSR1t=;?auB9;5E3yC?1;lu$_b}fg|^{w2*Gm)3A
z>UvH*i1#U(E#q_WuF>n20?Q@ie}aU=OF1-3bdx;!wAIwbgY0hQKT09#uT&*7YT8rN
zd!?ePEPy%E>ORiQg25?Ry+RuIfrv2$==U|{wLADGMkpFtNl4{>nvo{vHn9Gz(o`yh
zOJKa#$1ojwjAHHMSyknG`s=OR7@Yj)=BjcOxdg|_S7ttpVm%yo(A)uv4x&O89HkEu
z4_xOBikTA7=FvrAyK0SKlx2whjY9H~p;${x&A?qRHlU@;HShfXWOA+mlICZeoY_d<
zYdQSO-|O8}%0{?ve@J?!7dr<7y)0f?fs6MHO^-~cuOnQj!%%{wD}hD=#q3O}O-`8h
zmVyK?rnT7G=dwlWC2bSI{y|z4kg!*288|4UQ2HJbkI{j;Nu>}*ZbK|N5{vD#@-S5C
z+<#40=h_$psS>w8Ew5!33!hGT{8jLgV7IqAo-D_cpPQ$>IGgk&Y5VY(kkSotTR#04
zJV7Vs-CxGE3^bRe9JSnZ4n#bQfZsXctqx3nPBy1@o}mtCiihCzVGpwPnvUP9H<3@&
zVsKhF9nL!pe7){I)-|3Lv^n$W=^6YdL0hXj5U#0|z{CMBt$(wwlG2XplEye&@8B?S
z%*V&MK((AOy{3ant|Q=9tXuAGx$9`#x!Wa6*=C*3H+6knH@UrC<Sbg%?<kKP9@%_y
z%(VYz^Y!0?_G{6iacB2u#vlwsx|L8%^QPB}=Uo+2@H)o_LYj-zX3k$x@p-ux%Fc+(
z^-@(FnAQ8aeaM5+_;4t0`DYknqM8<Q{~WO1PT{(wUzQC>?u`U&hkCN!J$~(7QgT9}
zQk?w+@8rfRE5pXEP+;00*&Of#Unoj(ktk$QcN=^9Rek#o5uP#tOW~LC@YR$NIcK6f
zI54eoTa2*rmg&rbYO>G)z@pfZn^HARTD)a&r;?-GCi@#S`J5)Nd1A4qdf_Mik<O__
z=eoSyp>o{fb&Q)0Wio^(2;*Ru_4p1N?)yR$X{yuX_}#N4gM0C9%Gf1)xG|O~C&g}f
zH|9hGJL{d-QK`dE1VRwk&^WVOjyrW`8&#@U;i52+7}pT?o<Zgt9z;QY4rov#I<4?b
zp}*gb4&5jR=`GL)g*rdx+pw(tThJc?k(BMfm9@da@RueNX9y@P!Dv0oxW=`}8!HzX
z&aK3JkD9YxnVz0GtI@J)^8WAlcW;xle*)-}he>c@M}c(#0=$kW5^9*P&uzrg8F{<o
z4<OIoJ~#5^Hnv<KjqPT_(#v|!(6tmDgBwj%PfWCx3=%0CP*zcu+FpvmYoTx%&F9?h
zRW6^y$&PD(XB!)VQqF0Nnwax5+>ez3Kx%uIe5<&Yg{1lR#WH8w6Ep59S`o;0{V&G0
zmZQ(S$=9*4ruh6Trh9ui<_NA9mTkK;ZwvSh#Kp@bEA9-DTr3YtYy$x>NX^^rB0LXE
z`A*aw#q#pgHW`z^c;+2aRm_CP&2x;!#vX=qTxGn9?tz`V9gqjs2S3lgRY$!$iGIdY
zSZ*|#pBt)$Tl$|L%!q-#6gAQvvO1LU@{b1bp-98Y)X=MI2E;`kQN#2;*E57GlQdw_
zl>M`4wuK!Gt2(13Q<h%dE+6_jzyuhm%vIMk&f(&8F`}>vn=jc;=(4wo1{ayZn?R@Y
z;yeZdNNB^_)-kXD##@@S^9$Ric7J9_wbnO{%)gNAp?T@Z_*#>+owQ-lTse)2wO#Ke
z@<_S*II|q-S#8NFDY>I~U6A|J=h~hPZ>5+nenfEDwuN(9tmLaveQ)oTdYAI9`VezJ
zSw@)-Bec^Jw!wLgb=ywWThu+Qc(FLN%IP_1+XMutBc6eH!yAJ~Harwau+YG9eS_rM
z?-zqQRq2_rD$gvH(l;hhYIrqlZH?lS{p`W<taJ+dh|SXn$I)JBhaA83`{<q`z#DWj
z_4@}FozZFr?`ReUT&k!t<8JL+rEMy=eG`O1LAhvkI0kT;<d{hXaOFcd#qQX`HUIW%
zaNH3t^0$`NT+|)<pm(iCR0s!Xj;gDC2I==qPQOI^b_JN4nYlo1ytCfJr{K9Zx;Vog
zfeJx{U`dZ?f|nk;bGcMMc0s;&FSn|ja<~klFC^-8s_nc~k6XlKDg;z5R9d{OsWAJs
z9e)>?Oj)K)yro!dUe6+sqMYnfomUL*+m7vY=^25Pm4kV(rmTqBJg`skDR@{7GOxV<
zz%8h5+@CYA#TG5XgjGmbHVmqcK^m3<g`@?>6pA^EWh&~-y^hu=Dr4vxWluKe7v*j}
zy5C>t_Y!}HWs8(d!nHu|#Guz=i2=X2Q=+{<@;O)j4J_X?<^eAEq~np5UlDI#bS;*7
zI2^oxQ+JA0{)BAi(OY*$03)#K5Lc3Hl#m@?qd!#UJ8km++WX6}D7dI?7=~da1wllR
zMiG<{l<omkIs|D6MLMM$M!-Z6=>{bvhwc=mq@=sMq&wa{N_pM)_Z`o__x<r)$Ms{5
zk=e2K+N<_j=PC*$vSsp%dFiZ|QTnD#g6{#{{BpdaZ2jeGD^t=cCak1`+)rc0yYg|_
zo4^<i^ky);GG4+-Q1|el;X;bMS-`YJw8U+f9eBb6TbHc6S{9DiSXPql6BchqEKXnE
zFt~b8YsoM#P$B4H=gd8=w#Vwbfrx%G5_iN*J>t%#QaAMp8Me+_0XbvEwvU5;)ua$V
zOb=YoFP$9I|J@pRb31)JMCpq+C5$zHR?^aD2TvHJZ6Vctr6yE=dYeb1YT|o#emd{d
zhjf0AsmKiNJ5>;0nQkW|>|W;8yxQ+*lt>PH(7R(7aK*UXW$#`BIpg)dfo5+jC?O2x
zwbe>OZ|SR$#I|xZo{Nj4wZ?3=bB|~5JQz(e{XwSjyE&4l9W%c@NP;(0EIH}sJ}v17
zt4)Q9cj-!3vIZ@ZYl<6NRkR!vUU6c@<XNb#Dn0AD9CNwzoqKTi<98}(w@p<!80Nib
zep(UbIxD|a<Fm!c%u*xO7_Dt93-{*8C|h$222ahYdGa+ZgpU`tn3+Gg3>K#)h5NTD
zn<!|#*W*ylHS`~;!(xeIDrMN3p2wQE1+^u}bUC=?b<5bQfMrKh;|x~?yuk7r{s1va
z&X)Q+>#I?`^1GxF2{jx3j%}3+-|U(LX;4rB<aLk8XyD7p%3_yvf06b{4Fu@}roD6_
zJv}PdaC;)qPSMZJXIBZ$ERSP)xQ|RKm`pE2Us=i-EeM!3YkBwcy4%Yw5}a)}1`~zk
zCR;Z@O&&N(nK`|Gz=fDM8phq_!EQRvpMDCf<aQ|g9?u_;;`ffUt$n=kb^}9iqG^m)
zxndHJTUn(98iM5BMDsYL2Zd|7Ox+3xWRzMu`G5AWf1`#G=<$8Jvcm$F{@MB@QyC%y
zD|tx);)M1_R$t(giTU!}PYy`=K2Y^!he4p!I`keW`R%bFb^1Ope7_V*)1&z7>MV7r
z5Yz=T^hh)G=)*RDJOqM9qx14J#mrtFovvv>L|@7yk1QoSD`Anr`l+X6P!VzPo*=S)
z5%;g3ZHWsn3rf%4NPE%}a{mcF$rXtC+n;&;x2NY~8wFaU3V$@itYh6Vw=cs`_U^@@
zL-5}`frP~T=Aqnd%G>aN?-2$P-SI7H;osxl>MGRwic=DB&^G*pb#9lHhKKcor1XW{
zNT2T)hu!w`FUcnyLj8Q-tsXeEFvF_bnW5K1Q6w_2JFJB9f^>IL9R;nI*ZHLy)Il<t
z{V3!J!+fvw{sri_7>`5Zl^W6(Vo{YVPUW;?FJY`$pkacx;N-h~|619t*_k=j3X8#E
z`-8HQr2fzs-D8M^@6LFJ>&05fS?fV3S?hekf;r`RhdX91L6o=iNTE5))sEf)ZTDQn
zTukj(0-WDyZC((?g`$4|>4?Ij5@I0x#Q~pHR_7ocQL$aE`>+uLF%Yj*s0jJu)`EW%
z5hDmM3@s#UDXafFT-;UM<=Yi^SCsgJki~2VV|p`#@m8K~ey`Bfueu3Bu?MuZH?_Ie
zoRYQcr^16t4+0r`0wx&lcl#EHC;H;KHf~c4YEI>s&4;F3^4GkG17D{1z~J8R4!s8Q
zSV86qSVPcJTZ;Pl@3xZh974K@ZJx-5+~S10&?jP*&&%3;Jp_oN2P<}mFDz+yGe09C
zi45`Q;x{U!TP<LgGZ!ip;AK$P8tCoKN%D!z=AXMT4t2Bo8L$}!;{AI&_FpHL<}{TL
z+Fm9|ypUMk70g|#>g(#;?s2Fee^-p1D*O@0eRmnnm3>Bz*u_OevQN?3Uf@wNTOB7W
zIrMq}khb@_qtpN=xDv3sPxiC3YP{V0_9G{gKGqfWolmR1=u;s@x)~Tm`FnN;qA_4h
zNf@FUJ?hotHRY?X9Wgz9=OaiBHDg75JxPp@Jx+|ri`(7E3nRsZ0n~f^N@39^7`}%`
z1g1FJ{2D-(AC@TjsgcLnBh#e|fCW80cvdiH`AC>%bw{9h9F%Q81q1}f+pM=bgHt1;
zc$I}Bc*FNow2SNv^jZ`=H;CpxxU1?B;%Ig&6eQ{Ueb2n71G2Ck;&<Lqz5q$G{s0`0
z+=#K+1!Q!#Q^P8!jX;+Kq&z~w?{R)^VeOprIm9B`c`YBUzqq(W-#6;Ez<zTyVQ>0E
zbpsC*?m+KgQQVkosvsMWqMp)_lEZaPWn0CKY+QF``P@!Wkx7k@1r>iugq7Mz4usZU
z0pP)iC7yTqViE10=A)+eTImpb6?#fn%Mnl8y{_G6F~2E4jaVm+%)Qra0b*Yj?y1&)
zChI5d=j(4;Y_hg^`}W<+;%g+Se6T=H(fAKN<CCm)Smhv8VO$Xr_Ts}-tY%4&Es^83
zaox|l@m@-6jTmyyP3bz1h1EY#Lre1XOcwk=u6lTXh<$l({=k>W&eguK?%P+LY$TPH
zTocOf>VXN6F`a5>*D#8|>Io?T?!qrP;?%_ZDqUGWFgc9X{b&>Jzske-C5S!qW#mu4
zCG7mf0#*zE20aeFzA+P}l-Aa+uQ7ahL}VMORx5GO%&>yhn<ZKvqV%ghdIjqtq=xeT
zw+<qdbC*1<d~I14R7`~TMMU@Pd#z_S)Lb%^VWMZI=L1R0CO<)BKP55aN5HSllB8PW
zG!avu+Dlicq@1kzh#K%Q-9bcgSzA{h^O)Qy&;fC3WAVphzh?9%%d;0$67XPcX5UsS
z_16ra4v7#MYZ%*8t_sR`le@AD>Xvd|j;H~p9Ccx7tB1P>iLYXSaPR^p+G2GgY%(Vj
zoO<LQL_pN3!Q|)j^^RYPwedcWglmtYxeiNb3|q7_ol~UJcYy4Q2yp9O)JQ5wb5gvO
zerIuJPM%>FB#%dgJC09<i9A>oMAQs`dp|1UAy7G5R^EtrTIf(1>S4FYuo9FzPfYBV
zobcrVL{%b_or>aF?szMn$+I<U;<}Rlq0aIwD^DdOqAP-B**24(_HTL<61R}>DMETD
z8Wi+Q3=Dl8j}D8d_!v6_5R6MRHW}Aq+?9sZiVsX?U$+D<W-}!Lo&=Rt{KrYnrxZhf
z4XYQs>1XON0jq{DEtz|ZN*(0e<zA&4$jI?uz@WgDYiM=QNXfsYmOBhr2`MWmGS0!n
zmpz~SZC5c{@B*JfgO~5}vu7J`ec!cNX8rm#m7i5@eV>pRTnuiAg9ln|aP;ZDK!G*~
z!ql3EgwhUOO>NRRmn4U~ayzy+x3?2(ZEFzxmF0fYGWK#?*8S10Mz!yGcf}2GRJc^O
zy6$mr2n{SulaG&FY`TU2#u8bga&$pw_v~U^fX1s&Vk}k5^Vse=7*k5nI7fZ7X;3i)
z+XqR~BC*w`!eMx)Z2q?<2Xh<f;msCr_0vN?zQCAlU;<VR`9zRneH=GCwiFJ*jXAK6
zJFCKhQO81S;wLZU9#zc^m>akmPwCi_wYm*FGl0>w@<8{I>h^~SGF|t0D3}gbWBr{D
z6fr+k>;)Lw(qK<;kd??+V!i20g#|k0-1Rp_1VW`ra3HTxAfdz1v-#op_;r#^0oHj*
zwQ;1Xpv0j58xId<ocSFrscAkHy*Lf8-4_}AT+o-G1rIrYmk;!G?bm}nuxJJ4we{(#
z=`(*-Zc4rm^h+N8Vs2a_(H1P*RjD=C4a}OwoY;%-H#aMJDhW!~rO8hj)hpB^vhqQ)
zBN>A-h2gD!ZTnB0c<FkSwH9`9jcXjDvLk$oY$}g~7g7*+k`bF`_$j0}T+3d@q|W`+
z^AmW-_ju~=9Vj`-eOUPDU3u|zJNV7ec>0j;Am-ung?#TVho&_{pOv?)x`?Fa(v9yV
zB~OKxYu*JlL*FRjV-kV$6MYc<;*^hIPy$vyH;z%FA3v`f_R&P82n+BTWVw=Ai!(p7
z#PmW|U#**XTsY+p>dTl{hz8<~7&>;~om)=dqUDAzkz+w$vWdYv#XibB=9%N-?z#4Z
z8Hx$F`ziU9{`9mg1yFwoN$n!viC-L;Mhc=XKIhct<sOt@@Py$5R`A4(h&wyk?}VA;
zpJb(6h&UN_tpvA%zcZR9*59XQ1xUUl@E7CEr<+HCqh99DfNKVC8++tTasbCb0@{PN
z5Z_sO_3Ur{9v>zEJ+`cDZM%EAreoga1`&xKiBvfA=`N8e@xao?M^5Jvm!SLKp)4<>
zLNf!D(KJq1d|bvttpjv2s;E@$e}@{Og^+tr{Ie{4R486Yh}qXC32&DWjPE^W(VgG%
zVsJCwl>0&{WX{lo&PoZ51jV@v6P;C@rz^lWhbmuT5#2(!dF0)F-3J}-mNBpW4X_+C
z72Jr^V+CrHKXX@0cdIR#EBRy4+>6J^;1o{}U?nc)H1-&fFU3}P&`t(@A_FFvo2+&?
zonV9%LdL-Vv<17BnPK^>b_NPTYd7|8-Iht@;x5)QN?f7_*JWy~;D4w4i79^2Ky&*G
zfv&IykEi-*>naw8nLPSSk7}TJ?Y1FLDNl)xNd-ZcEX&sX@!WPfG2K4Y-{`DG@6+7q
zWMq(%oJ;kz(6BgHu*@a@zZ5K2y>IC_-7PE=liYBbo2E8#st?2Fd<k*)Lp=;hZQY!X
zLcx1-q^goV&0*jbMu&hJ+9x86dU`Qo)bdat&u%H{2DaqguU}!fPIL#rZPE8N$=(`g
zuSE=U1|`7t;*^X$$hMVlUckJ653mv~LeTp4@wuZwXl}%6Ry{n}T=!~xC5RrZ^boC|
ztCjc3LHI0*kR_GkI05uJ^2zm+N=y;bJ^1U$eI#HN{?+`r0{vZ9(-KtK<3*iARCA>r
z{qk(7m<Fbo5SV2fahL6+ND2jlM>`T+_@pGtDuef9JVL@etG(OGm>S;@LR*E+{&e?j
zIr!X)kZW(RVTlr6;-Z{eSXu{lT7T<eg{G~HMT{j~jIEs&&7{m)KFZf<iS7084lK6l
z4<|nYa{3~8*l?(vaUeKHpG@epFS>|O1$MoTK(9C~(&W^V)a;Da*>t(if=&&z;k<2=
z+bg%b(v=*_CN}K1%5?{)5~r^cF;VcC#wRCRq`SNITPKJ~rlVIeUD4NbUyQVN6?<ZB
zcqEsfww9g*d?*qoP}+Oxs>JR|fi)l!i8SQJ-4_MTd*9L))E*wB%!kf|4)_dcObv$P
z&;P2PO8Gk2-PNmq6uRqQUz?j@4(enP|0#x*up*jEEld4*c#X7)YC2Bqa?K@spi8S=
zy~C(ZS<;dj^#cFT`I6FYZ%~+}`}x_`31-z#?k}94?S5~3+keTNtKA9d8SEs`#}B(5
zQv7=Kt0dK4Z9@ttnC{2T`uV-qVhj@vlX2bgn|_RQ3~A^zx7ls&2KJ}k(_9M|rol&+
zRsX9AxWi%2Dtp!QRG-%J<I;s+*=^XQ-_}s%ev!pr&0{pqgu1}-8dS5zyOF7rrJ<|c
zRx|Jm|E&McF?d%=cxmiosy0hbkv9r}R`9s>e#BD$%IWO|mN{Lls@@m3riix6bc%Ea
zdmH=hMX3x;Z|V78pfJ{{JNIr@t1Yvwv+<_*MPeTYl4$mU-}8@wW%X1J<&tF&%U!}V
zc6%zKv!3}Yx~xR>6}d6@jJ;$|j)4>!qotGRk3D72#tG>lB}bLfw>D~>G9WI$uO|FU
zIcJ3U^XvP#enMGcYDTFhef=*j&~J!Pe+C6MH;jwIm`;f9dm|IXGY|H*rl+S3o<HYq
z=6-$6rhY=|`6FG8@z<|~);U1=pYdVgg_NU_N{l9oCggks3}n~R?1_Xah{=-rBc_K|
z`|aIsAhJ8})p>vK=@Gi3WsIxdJ+yg=Q9J+7GaVe1o8v*1cF%TnaD92~J&XBZv62kP
zJ#GRWp5_*ET9&#^2ztd!-07doc61E)Y}i-Ow7xTwm6BHUM4JCzXXd|4dV{g!V&l9`
z{_;#<TFS1Z^SDm%<m$oK^dF>Iab<%Hir{8LK!Xo*>P#De@^EbP$O^~i<=KKZTgqQ#
zA~<P0m`Sy~XVuzSxaT2C=4k_kpg6Z%(Yge<1K7YFz#x;u{%CG!^7z14^atSkCoW%A
zHC`qJTeszi-tvej;jP%;G^ufL1BX^c1G}8|4+o6Mz-UT-MefbX{AfAoz0q>`Jy&i{
z*vK~7_x@`8v$~Iwxxh&_6;MAeVr7nQY#9^~*d*4~<#&s9=y&|KnFL}+aLb#3blpLE
zS|^%}I|}CFvJZf<m>5B?B(tE~s?bEAaH}RC6W}&&J`NGgnq|Qz%ctzc!CAXHm!F?t
zHyszX=_EJ#>x*BFflv2}_|&gA69l}P5|alTdu627fI41WNPF_U+vH1U2~tErFO(o!
z)iUO`z(*Ilr7Iq~t$wPeI<)<%T~d5NpC&0M&P9Ka(O-~Z@TNc{c)0LO>W$lXj8?w?
zuvl_a)NKNlrar2VN)QEc$v_}}`vk-;Q%I1+pE6G%uYrOa_tna{%T@S_VKL|J<rXTQ
zone;Ue2zjqjB<-kmb89w^Ckw(ej5*~7FDI>V%w(MGD@l3sn`C@uFh5i>~7AY?8m)*
zvph=Nk5#M|TE*@#t&$$#Sd?`Pxh_C;5n@O`#XuGX)n)49?3t3e__4Ce6Jyx<cUekG
z3V^3zQqR40cSW^)4AqX<4#APfl|Y{uVPy0(m!o30i#Ijx+cIqnmI81ba&32o#O!T*
zow1#x@9IBPe@QQsyS`TQ4%Z^6T<<q+=wx5Mt{olu;5$>?!Jc13y;42}ov(m9ZAk~@
zj)91u{i&j?yhh-FY@<ZZ9ebw>p-n|hY!50SVjkH)1(+$_f~_$;0_C$S0NudR!`WnD
zu>D{l-$1)><+HCKP$6mN8B6JUmU9JNE;dajEf)-!9s*gt09<yxB;jkPx&rD46B85D
z9K@2F0{B5Mx$JsA&?cE%ENPo$DAe)N+@6^0&VG$__FaH+HNs|a|KyHPkI>+gkwtv`
zsFPJ!U!T=*<&SYijSn^fkCg<j<*}|E>44@YZ-842K*@8l1L$PJxqhn}k11A2;QSei
z1Rr%1<q{?t%gKSGz^kZPM`t>Fdv9AT>#U1W{TZs27`Sq-zebOP=Rn<Hvcqd?YO=HM
zEn?uU!(`{(rPZU`rB_Y-2AlUgq$|uKm1nQ=Mb+RsgL>*=j)x$PP3&at<dQH0>av5)
zeh^<-Sy@3s@%lpTzQ&=ln#kIXt`^^mGMnhJcK0z;yG`%q^vLeeb%UmvdN3v-bmDT{
zP)t!PI>b{7<<j!VYCPA;nAEM>kk#D`wVa1@Dl7n0f0j1>u>9K9#cYMOi6@;4X48AT
zhR;A09{4Wa!D^R-o9#0iM6hgs>Vq(`M-(t=Wj&8GPLO+}L^V6e6BFd(;J9G15bO6G
z^7c|kNUvBhVUMAXbAo7t!W893gsaE_X>~kvR2saj1A%Hj!Utv2hf(JOV;+y${o#pq
zL2ZRaOGn4BV=W=^R@kzcXZk)V&bca${E8)7GjjDSe=0TDCO|V64(kVc^#GCPGQGFx
z|Bq6Q&%qJ(;MV*(nGq%kXu0>}#}5D^5X0}d3QB#V^af(pb?x@=9Q!!7F6=cu{lDfq
zYm5q_Np!iqu34n1&a&I|put-&gGfp4{xymdBkK)a?0`y+ep4|h^>5~#XNp26uVHHR
z)t0e*u#(Lho%khDU%sVT&2+eC;TFzabVwC&W$^^9AD$@<fAQF_BXlwvam~p0JHkzu
zRksmw+RLFlIB9|}O+Pn0s(@EXBg}8YFmp9j@Jddvo5wuntwXgol@~?Pe)DPe5mkNl
zrsX!45u-gga1`LqV&LD=JT(SUF&zm0Iz5wmNzN8B%?4)0n-SlCmaToW!n_E&Vl2n%
z#1oz}2k6Ie?D(Wqw0{9%rx6{<0;=8em=5WQiaoh87XdWr@<>)Z{n?NIDke)-;5T>@
zW3>O*jnP>K>KeoEroibHI@V+!o>(8DKdat*8l4OdqbA3i3GBlSN@ZuWmN(;;y&Gt)
zaCIgvkYCM`zgP9vho`2P+@SACj}hZbfwLb)Vx`^EdbNZ*1HnN&Ai*V<@32{V2*K3h
z${^)DBZ<mo2c3<wnxzCq3kA5RF<RC;t4x*75OCH;f(6W_^!Q&|>7h>~feX{-U2S^0
zJrHpE|Eddft25y0dmIRek*)Ea#4&(e!?%QBkn+pcWhEDF`jg*s{oqLF7ibzCpgEKG
zsP}&bLBfRR%gdjLMC1j(f;v93aXDZWbOL2ykoSz1sK}Pg4;v3(IN)wtF)5JIGtyBr
zR3aTgFISR4h4>>;pXyUv22Pn3R)=Y*lKH4YK!7GE&JV5^1i~A*xp*oS`n)xl25LJT
zpm1^UF6}$fX|Qy5j?bae^0{oC2>3J896mUa4*5N;B(}^!EEnG2zpg??<-jb5CXE+Q
zXYoKgh5W&zoi+KSv9O*ONs0*#2THotYnJL%jT{?J<iZ|It-h-0KIgVN69N0zgCX2|
z_2rer;kfh0_IseC2#34TR0szRx)A2>`WVe5POo6`031ZD?;V@=c^)}=0U<M5$T;;-
znie(RR|H><8RJXnmeO*!|IMfDIvl0i1krr+_MOwSdiq_GNegE|7n?0#LDFS_yTVNf
z9G4g@fgxazpWGu%Ciq0*#Js*1%SQiTyJow>mzdQtr_1bA6{im%^>q`vFVzZ?7A71F
z;*Nel6&)9`fL?`ByC5Ug!+Co8r!=lSfCgV>l6fcfse3EV_EJ}VS50k=RIhS}k}8`s
za7&ccyw|<f`&%k*@G>~rZ`?^e42)7`M$?>`n=Kms&7%5c-=?b8`jaB%pwj-69dpHG
z^e#o9A}V9S8|Woo1>Q3`hfhKdIrcTmudIO#m6!Zwb{q42jR2@ep#nD@7wHPgVYI%r
zDDYHm|21f~p>MaJQln)gkN|iY#72RPx{)AyN@JjSX>`7Y&a2ODb}ab&Hi<WK_c$zz
zulWx-g}6H?Z!!sJYG-LxwI%k>+O=s+cYurk6b3j3{e9hE<&RVdFo(-^(#;*;c}w_y
zGw}P*rW7YT^}Z5fywzvl{Kp+hJwU?pBqjB~-MD@MgyQ!xKSCMzy8^GB3NJV-&Bri)
z5jOvqO3~9b`8Au(cGk{o0~*ghKP#oXMnuHnJ^)d21CI*e?PY$}$o5&;17NmcN+BIZ
zE48pIXXlCmkq{+pV%HklY3p0fV*vhBq1}}2J8#OUPfAMKMltb}2{#jy^^wpz2Vfj`
zf1rW!-2nR1>*4Twf6xW~94kH@l(dhOBY@)dyAQicMceXO`Owsl0nv*b_1=!}A1f*=
zCc1vx6ie!Sd+?wES#A#4_kWBqr_LW1Ba`ynL^A7cG)c{N4>a|mH`2Oi_oLPNYuz9G
z{ys#5e4b!JK2Q92D^oLHR<4cPX8VV=0K>fgMLolB#IQxo=(keu;&ij*K}W-+vLQvs
z_5Jumo3V}S0J!acUx;L?6kjp#r?F30<(`-(vRe%BD}MbtXdrVBV8W0Sm;S+o5l}9>
zy`DpeC@2Ki1eoL!ncx1qoKrJff&0aZPZnE(nM^pNQodcjI$LB+3GB|;X2#}+AhI;c
z)YcZ+v`xSva8_iZ%)ie%8&KttvZT!EYr6XJHy!TrbLDcFru8f<&uVPGMMmNmPjOfV
zVr0{5s#pNx3K!pYFzfaIiQI#NN=!JjH0x&GpTn}~@JNix*3Mp;OJz@XYDLCxK32!k
z13;pLAKJ9_m!PH}?apzb^$A4*Ce{Kbs}>Bo(-VPUNsjtf15y2<R65Y0C$(m4Gcanq
z9Em@MuaA84(#L7AIr-BQL01W)Kbh`#I!>&j6Kw$tMKVM0%X<{3_YA<I>9(ytdHVH_
zp{mleaFtIJmGDM20IlY3yc#%r7I?SE4-L?~CHm!aq)B=fGvlO}JWB(x8;dx9(iPqR
z+Ap1m38x0bV_>mYpZy542kUvlRDDrj`?x$V(*|Sz^U+9hKY6YYuY|Rz)a+Jfkppg(
zLo!Ge09MAMG<o>)bl(J0mC(ynUs-YpKc3i`wH?17apeut8cETc=&&Hs=e9T1<X^$Q
zUmhWef1~L{hj;2Ui%7#{M?QCy;u59eu?H?9_$0_)cir<F=PHq(+6kwjUye!+0}(^J
zPL+_3J)Xdxt)P((l9Ni{UyF|hs_wpeL_MMk%!=AOxUbH{!7>fCKv8Li>CUDeup(+r
zl*M#?<h-sq3)oJj)7SLi?!iHj)P@e0_NTi$go0t!=ggJA{>GzsB^3*COY5p|JKpSL
z+__$!_ly0ZqQ(TCqSWi)=;O4}m`+X+yqd!P7>|no7?0HWkv!NZ#$#1g^DT24r17YX
z&3C3L=dsR=M}zToEJOO7owlmkSI?-RFOdlg_j@iL7Y2aIu19-JezZ{^OU+cf7O+-S
zK&$nXO@<BvhlA6+<U?k0x_Ka{KUTiLUC92ff)>e)0N=}AucXwWPe;!`cjA9O!YY9k
zi1sSj_jFCi2Mc2C_?5EixTfb~b$>Pt_dqhwMP`aK6YejQdIW%>qH;-lAg8B$%<rg3
zrXf-11;|<d-T-=n5fa*emIVi$0b|QeMJE|#Y}_@~pwe7DiXA+aYPTIpH@06WR&jc)
zP>(zZr%jK*%Rk*P-10`|XNPOWT(R#NO0Pa;w}d@vFCqi-aInz0=N#mo#0YrMAT0@z
zEtBw0d+hh+lZho(U6q!Sc6rvbgq?x><>;!#m?7#BV=#dV3sue87Q69#<VUfbl|9TK
z!Nm@&F1+z5S8f$6*B&?Rmh-^C<QOdW2l8&<-{~I0=2Y+`u6-cE>1(*wf&DsIj@!`l
z9zK*@7UfcAH8JMeDK!AtNN7|}kNrJ5`rtgX&H~|O6KTq1LC)5t6ol3zH3bE23YUH-
zvb#bY)(Xb@kL=3J;37>S7TSq{x)1J0^cTtd>Htq0Q_Cgs>}tJyFaq<e#p2=Q=oXAc
zOF-OhnehMAWSxyu#>v3<zh)58v|hyqR>SEj!LRF_U|)(oxM1AMHmjms&uRT6po|LS
z`7GuqGvPAfq)Va=R2DGYhEab41i#_95yp3V%9z(s7qL0#3X<rbbFSabOuI+gQx5MM
zo$Hpa-G=XllKN5O*8?{5FWqfCapge3$j1Zgon7KChrExO9epOmN3>?%20fn-E;lXE
zCqliCRCDeh!e~xsv7|;V_&(XU7--!Ir*)OFdLLCDtcV7O5mI9*$6~b$o&KRmWhK`A
zo&M_sy4K`kxGVd$TiFF!(TQ~NiQkhr3%EM-J2o$3$t>j6q9#aetlMblQ!wA(OXV-Z
zvInMA7;xrdZVL~cc*sb593RfpYaJ|G)>g3gD*x4R*<OEFv$8<3$x64vn4(L6sn+Ul
ziSuyQoOQePd+cCea?ZAnj)E?sip8R~8wtvuu|!KzD%?EGU*f(T_}Xh(EG)2&NAo>f
zFEC&RDrsl4Sn1|Qo-o@hI5oZz@Xvj7i44k5kEfCYTI^KZ$J@U^rCWT(;#(_JF#~91
zi`eXBsxTMn`8iIWJ3GZ;-BJg3TQ=Rf9WzN!swlZkZ)Mcl|8C8^EjpeN<B)$%h>l^d
zYu|`Lg@bF!=qrx*BOffdI1Na_QBV$dJX1^E1U*mk)Tl~&V?uZ9)p~OTjd#WGHYOg{
zGt2dnfrtJ7qlkGGlc^v`{znU%Hqg_KW;>jGR~FRtLB%J6mD4fQbo;=UIVyi<Nk{#M
zD*hXMV3*x^9v4P;dU)V*k;kg#nze6YR)&k2ML-y^7v>6%ktJpRMV7pY7qrVkcQ9Lh
zDV&e*+2=17QT$Eg*wG^|E>x)HS!jIV`(zrXwoC{y2SA5*<0((sPG@;@A7WkG^!|e{
zfNvZuJ)$kh{2`K|x%1k#r2JXgSfotZTki~$<bK5*v1f%kkE@pBN4pqlZg=Dt2sp9h
zJ2k)gB^0e4%5P(+E4C+kvtQ)dMNed093MjQ=x5XOQyJ@_fd%SZ8k@ox=ed;37G`*Z
z`5H{_{jqfI?d;9JIt)7nhD9c4Ga#+uJE^DEu<_N2Z$I}opRnr>eD7HQ^|qeWsW)S6
z*LRb;ztR$kMG1&z`3w2{b!<skQo(_dWJra;<5E{CZ$@nJvKoPSyVH6V9FQhFoinWd
z#^d0N%5!N*lUdfUx#KveCM*0x5%tzO&YtgNtn%t~cWQ&DDN404^*!La`~wXMtJH&D
zowyVDgNky<Xme#(9nmwD`<=ZL!K|U{9?s7GYoNSzEg?^g>ymX!A2kZfby|u0!jDrY
z^VkqS#T!Zf+SC^0jjLm6<ZO|$DCM+#a#&d}d3bgI*U4m{%?**yeU~-cop)1#9nGGQ
z9iHv^0b|kH#L%Q;@q8>@sZOFLzu=<2<4|3iTG$u%X9fiZh*g7@@Ow;lhOD?cOqloS
zz~kHV48EK*#bkaxleLAg-z9TYN3BV#!frZ#@_CYD$3ov~z(7SxGM|&qr*A%sEHyO_
z5SnpaKMFci_bXnjtur$$(wpS_C6jfdh;+9vsU;dku|j<H0V&}i4uE+JOaohK<2gMR
zq%;8lrybuLb2{E53iFD!LZ`7lc8yl@U0Td#kg4*L_G=+QjQdMBA*1P!j-%-q)0-)!
z5)H05We!_k_iu7>l_{ttzF=vh6mnBFw!Elw1@k@=nCbf+0m3sOwM4CBcLao+g+OK}
z;>Rr3>{R?P$gA48$Wz~*x|z_K&_J3FRew)^hZE5Pg6da*^SZOh8XI)u@?`|2kc4Py
zk^At_LpjnpdP(~^Rh>oX;aK1-Dn)oRVCGLcE9V0oBTpb!ozZMl<h@A&A3%24J}Iw|
zJ-oDJQFD=uk!zdtt4X?sTCtVH;iqqJ-y8Tu-G-Z5=_P09<#ZOf#+sPd$6Tc%?C<K_
znaOy@7K{gTa{8S?Mo)Al-r%af9)cG?yYvY>n(siAdIITdxnQv#hZ2#j9;*TYIZBdS
zcJ}rNgzB)ymr;ppPPqxjQW^#k!<?x<hx&o|61$afGhX6=GnXT6;Gj#RWO%)wJ2t4n
zCQqk>1b4->cPV_6u&Z3Yyrekq!G<ITg*@5}IfMY{YD=#p2&?OvDQ*a9aN20+I^q+!
ztC^C=B}z5CUf8@Hgi%<4J}5BQV&=S=K*2IM^QC#Id2VWMNFBYnJS%5>w>xHwBB88g
zk80ShvmhFztm#++U4{`tUv_H90L$$jYJK;OCb8Y6+)Iw8Ww*Q+Y(+k8yg>%jX^=YL
zqqlzesSfx{f$Ja;%-!aW1`=XV?)_g&4U-1Ma{iBgKp?I&Q21hR(;Hyf^3B~fS`xQ6
zEnpMkXcxRt8$9?dNf-5*DhV>5dS&b$NWeIzJUDP*PUt;(9B9qVp0Ae>i9ZJtv70%%
z^?PYUFl{61uh8Jr0=tA7u1|9IBXUSlQ4uJ<ip!&C<dAFbjHY~Ttdp$WONTQ(;owzV
zM9UQQ`$>?uIl)|Q(dsZVstvVVR%N?<x;aZcRHG39ph|DJ844Ri+tAx2n1phY_Grz1
zT)n&D+#zGeCDGSbPue4OfDDDXUJXP(&vIjMKMRR|dt%bz|AICHG^<)F_a_nX1TWDG
zBLBk=X`p4xs9lNBytU@i^pSA8xuX%lt(VNDO3kIZl6j@nh-)K8rc<2!VumSyP%x~K
z5JT_)!R_iqbkI-NiphXFJLKoOp!>Ug&)gE4xjwO4oITkeGMK+iiEyO+a95B(e_^8|
z>`#Py0b@utt1S#A3mX!59foQ1wT|u1*+_R$v2@h%BVmR)<0{qZz%>~&5^G#W-}nof
zLcr!shmCp!tf|8y`E#BOyb_mdAl8WCDlaBa);nzTHdSm}HxO`*&YTX|LKA~5jx;{f
z*&ujMsN}ngi)Z)n1rB(w8_ZVdIm35`h``(cL{kF%gJ{qG#X51(S0_%3oJUP;|2Q-^
zpx0&Avh?K<kfX1tJ$Ase;>oi8WnrIHLY^;|yY9KI2E>H+qX=jH&H9PmL9fvG>&8?S
zye6O-xdn`FF=mXK6Yc^Xa0xyx;Wqcwa%BFztbG9k?+f@R)SH!*BOYT3r^(|dEN=<I
z=b4Ji5WbTyP8LBO3y6aHLu&dz*M@rJ3Yak|4Qh8f<FVrcgMoXA_AUe|<4*Y&`LXgg
z(kW8IS~wZ|L<GS-kfHu7EXc^fKht<9BAue_%RK<$_1|ew0hRD>Y4M(k>f;|Kfxt1J
z-px$3e@6mO&XUxev1RS&)CfrBlpR@yH!LkJH9k_y$`TzEBwlz8^8z<jY?}q8{oL3y
zK`;%IpFib<l(jX!TooN3!(mb5<+K+;q&tG0aYv)jwEAjazj!WCh)Dqdw5Z{;+qq4#
zXx7h}j^j^r5ir(8JmgD*WjyiOe&EYDEFIhvToqoYFf0@xs}Z_^k62<}&q{K(2WoL>
z&6G^8UtmyxK}7;^$_jnKi-E1wtEzJZ6TZ&+)Jk}&?w5Y%_xK5;oM{XromapEg@}64
zs=`Ml5$FDPi5{Pr*!@Qy7sbwuyooi?&%b^-_zhHiZKTcy=Xb;TAWYzd4T1fhjCqmj
z?%ZP;2jC$UdV;Ab=DmW>4M#&`Y3S~4B|J|)vM})0F@Uc2`|_5xco$rlhLsz-P4&O*
zd1ARrC3@$5m`ZO(lnm}h`}CcQ6-FQgcpncn|L*-}bvDIwG-|&=J&ZW;9^@<NwLrq;
zX8@<zZt&An*0VLjK4RL~+4P7>ic4n?BXOpmfaJu5;+xev=f<HX;7%PO-xI%)Q`2)i
z5b*80nXjRr<2~qGn6ll{XB-wqY8xr*_V4wINsXa|@$hRP3kUNe5U4tZZH(t8R>kKw
zY2exQ`tdjv3SfP`@D1It&flX}Vz{rbo$Ib~6&tt(H-Q2!c^=0K>i<qI0%(3)T+G{D
zx)F{Cn_HTt4C1iU8vV3BdgG<}1vKDCcs>L#pRsZAXYo-G*}FkKt5Iwn@!V3*eyb|w
z-K8OILVd#Ly!da}fzlAycrkS*$B+-DdL=@+T+A#2vt5U8fQdVTjr7u)2p^ugDVSa!
zmCFQQ7QQ4J_~!oqp<pPx?L+B>xA8oRi7j|-l@~!m6!cZ)+am#tM0cliAw3UZsMB7O
zDw+yr`OVz>t8ak)>1sz{u1!HR6ubb!zW`~lfBpQm26o7c7b^itO$!@$F98CoAhXbv
zetKt}66#n!u*!oi!at1*oSp1n0bxl5#8_%Dj_!YDj}B6dq1~)?{_jvD3`jaK6W5%h
z!=E)(BE=Ynr0>@Gll&vbl)z9K>UVt3Zxt!B;cy_vE(MbRK4*~p8OkFSh%wE)CnV=i
z<gaW*17eKw7SE99smMQGp9)e07#FdgOaA@4cXaTU$1iVHit%5Gm;s=Q?K-WVp5_mo
z?DS$FNLGuTaJY2FZ-0k+0{YZ1q)dKO{Vx?sfXTfKt6w=wNjzrMLVy|A^M4QIpTqh;
zJ&=(ji{DxyX<v8wP>5O4>Li4reh%Mrl$mtZ5|rwdCh)AV>Xm4fc6QzBC?*&_rH}~S
z*X577bPMy1N8|+e1lN9jc5jY>Tnp<$Ty4^Px*I?$FYB61I#|`+SfYV>prAsam}!q;
zC|b#p^O*S5$KQYtI`R<6ax7&?{pI5?yJSZe>FxBFj}B)C`edr=pqTiD%&4f_`P)yV
z|Bi$F)gb2nWQALE+5Y&jV5#|1-3NRU0(=iK82QOCm_EeYuPee@9t8Q<6v*>g!YfLh
zZAR>McA>%e_#PoBR^flv1jdSmu43C9hN#5qjo9wQ+!yHLf5uojzq(VLd>P;4AmntZ
zttul^*OyDgj^?xv#V#(T+SwQUtT3E#cR#Yw?p(DH7%OpZ&==F0gpg%uSGa+GmA$>a
zVPRnlT!THFpgYo0iy%d}TlFhkMyl^YU{im$JO5xrs6uG3<>&?NUU8iJL5ZjP!Hn;Q
zm9=~E-q#t8f~dUV_~C^k8*Fn2O-$OJDZ#0!DP#A=zP!Mk7Q4xYpi~uvzWYceJk0h*
zj`_=zE$K)?u*5BdRtAI)_WXT94i2_VT^yzpZ+|cg?Yvqyp8B0}H-j_%a7h7`vC@9l
z^DZ+uo#O?84>Px0tuORgcsM&5KRl&4@&f>`^>}@--xz%|&!2yF!p5u=h-1HTN+|FF
z{uBqZvf9l}U+$j)1TH{FqUFO0&YizUWhVIYsgO_({XYYM{$ZAKx0=o^3!Hin;FZjn
zm|nv31Hj}^Q48q<_0MmCn$;8))uE@QWdZAKU*M>dJWvJ*CE5PjE=j%z3je~i!R9{$
zv?{_-mar18AsP2{h>IF96w1vtHs|wS0(w!SY<ac${6m#j%+x5C_IAPq{uyBX3ciQ4
zh|&Kg>pxWazhwP?pIcek7G@*<VOC`Z%gu#eM8)CmN-fne5bj5U<=bQL8C5bK?}4te
z=DpbontY>=O>)$|jePUet+m$N(ohgPH(1Y~ZP&w*)ybcrjZ1%Ls!9mo{wrLvJ6fd<
zW8dGdvsx{BDc)eVII;}a9XvGs{faUTWf)hkiu~-p;gk4O0!+`4B1%D*?NmfLY1sPT
zpJX1Xb|bXqo>bT^_W4rqnY#}N14HQ2?n)T{>FjXZo6Ddr#^L^23jlGM0{{#CA2bUs
zN5OYPc_!UqYzD#3bID23eI@o5^Twt$2kzUWuR%lAVbEUyj)p<$G!thW95i}=0Cbr#
zh_eN?-YxuV(pzTJS(-8#`v5SZeYD7Wn$xWBF$I9QbzHsa*u4vIwi;9W-Xhr8*h=hw
zyY0><S?^4wT5SRV(${zt4e68LOq1&;L0cQUCA|ynUq@GMd?^LOAN=N?NLW!#Xo)24
ze~Ru3pcChkZ^DtF<&N1!n{PpnPO!4n>e=6A5CK=~8>cD`pPE&R8qN^LtZ}{lXs8FM
zh7`JF1oltfpi(Zkc-h6RVfUCvlnx{C_$Cmc$cWkjr0}EQ<K*LuDBS`}ea?HWI7-u;
zM$`qsV%8^MWl2=j`cWN?cwP!#$Xwb5?cki3t1tpuK$n?MVN5(WkTo$X*T5&pMnK3G
zXNy#h6aE1Fn30q*;-ORByDfm99Po4P5;k12xVb_s-YpBy+Qd-{t8r_{*`g~ZV1Lbz
zGz_+@W_4(v0Vf*aGe|W!Cr5+nGhIRS`(tU~g3Vk<a$vw%cEZPj(1qLq#m><Q30jRQ
z+p*_4rfL(73YHlS-z?n5B2acf66w?`ASb6k%Sztr!~|Y#w2Wm_-|ql9!7vN+1Ys*%
zbAx(3LZ@Me@egyXj2XX6*JSTG((&7YmId>O3OaW|0PD=r?-P-l{W1z2Y$MouEiaR{
zr(4@y;7I(@Xuc`&JZlkGwZLYNu39#peufjszFiy5pgrPjnI(pf%tny;pNW0=3M44`
zlS98oIhF-h8BZgFVTRgLvLFldwAs-8VH>UAng$YVlT4rWwNpcGcYMG6Q-$2a`o=8%
zd}FT)4JvogEUV*2yPQz^ZoWH!GoGU_k%-tS@ECAVFw_bwx0zKi$x)3HoLBlypCp5Q
zS6Zm339DT-t)OE%<w<l%b!yAHBDF2Up7)j#DmRai0pYj?&1;iFtV)wN7KZ2OY)&BF
zDuXSfF10AIH4xAmG!wK?VAh|1A3+qE^4$3+$pPLc+jdr#C4Cc>+zPi2<6UAaVxs}K
zbq#OHoT7G+@9$@$gnMrcFhGon^$p>=r+Z0o|INYbwBV!lb~(p9zV|gnoWB{m$vTYK
zo{|nyK5S4Ul9M?=tEx*5vgK~8@4&k-lKhD5%{j6qT*%H1l@5vz*=S*^p+lj+IVF};
zWTlrBOlkGxy*h8RN%h;P#r+;=PqXZujy@yh7pd~^b2%hm)y+5Pvb3aj|EhcaWtAZL
zNob2?!s{&Nk{~su4DU&&5Bvx8SSp@a?K7LK3K@>R2hNWe=Pl!pk}0q&6~A!epGpc;
zh!hU(<dnr)qULq&Z(8M_16>d1Z1s|i>(ZW1af~y?Ooe<kyJq*zv~RxFQP@c&$4T4C
z)YD&)D1ObPM}0wtMrG2sMysE}#FZmPMz*=p$>CPEg@MM?=V>mcJQa8F)XQCia02@K
zCAUAdli(<k?i5+@ntCcft;ZAVLoCLjl;$5kJZJrkT!laXrfwuXBN;cun-N=>t=Q@O
zO{1(fLQZ32hmC)y{>5iaLF_2|xV48b?m1r9bA_bvrVSTP{Z!r2Gks<}=7bZbD|d5i
zDr&+-k^zg;apN_WoA}X2^_0faQI{vv1RX=t3o8e~=Rx%oTe*%8O4A?sQ81ciPg*M$
zO~xNQA8{!za!V|kV6PF;yTC2rbw{domgdsU;V;cG@eK|8pD2c$L`__1Q2@L<>zTAg
zg=oUnO{Hb9gWMD|^lE~lQkvH=j0oikaTI6pLaZ1{IBY{(w;LD{6D%}(SiJ6)oZY@I
z&O8AU>oT{R=+mq?QS+FmeFcIp?f`J9Nw&IKw#D`-klNmIYcP&Dn2?3gBY<=5N1E4=
zi!iT0-;Mkr&^jlfpUK9cZ->~+)RBO9jo)EeCqvze^u2J|@;96?$3r6OYl3TyLf9P$
zf8zN}t<L7C#24aH9IusfmSvL^b7+qCKeD)D+|m$i405guuJ0_L3P0#;w&K0|@Wf*Q
zhMx`v4lOoaH|;FbJSE}8>WvAnmUosnx)WPUEh6y?Gy8wYCKRyC9+J))e|vgJL;b$y
z+D$WsjM6SMp?k`0R<8`-3NY3n!^2(g*7RoWI=zgfJtW;4t+smhqFSGltv3_RH7z?4
z@$d2H^(EnF4Lr)<mr0D6xv|6f+V&tSA}0F0{mLo>*VAj}%%ZJV2WVe|-}Xhuu0OKN
zQVh~9iDFXAsGxb=R6J=nTBoYU-mGBuO!I0&K+D>kmHL!Md%7z&VPaMf#bnBQQD}`9
zUdgy@TqJ7=>u6UY7n<b{%{Y7POV#-2OkMoKFOZ!n>%;Y51~IN(59`VLc0Swk?XO*V
z_<6|%B_rj>_0^cyHBsku5g--jME_%p@*Vy1(4YeMoR?8s1$!>rP80(UgCf~x_Ad%P
zn|BU8L6t2b_j^9#%`yM*`-fB0`Y)*`?7!^@cJY>1{V-1_b8XkBy*RvDl+%?<WF;I_
z!twq?{J*XTrnH*QQ$sV<d?I5>u#HYT6%XRnu+=CM-!tigyyZ-Etse>p3!+jF#G7WY
zElV8Y2cLN+pSyBMFU8)ovX0jrFEz2rOc13YMR`WqF2uWE5Boe(s9_^Z1ctwCO*7LQ
zB2c+8YzMFxIaA!Ss+AGvy%#WNA{{GFYQCw4w=qAJM=knfxJ`i(hslQ|I~DZn|NiL>
z$l#m44;h2{LC%VbA1u&Ej5QY(qCvZ~uE*`l0U`xrdgr7!u#Es0yh~tC$PemENfy^w
zOAZ%;EH^evE9nWfWoUjBx%1T|TkfaPP(;=_I|}$qFf7`S`IhS5S05>Uwc0e(<C^?F
z^n|YhGJspTW_INMGx>^%2SY)%|6O&m3;#}N`5MX)piJF_Po&ka%ABR_YJVh#GL)?+
zwe{W03b%FBtb;Qea!!~6f)$EF2J?FEcl+F<skD>3xtX}KkG%}Kw`8+F(NK?X?dy!U
z=2kF#eS<l5=szc#77W9QW{y;DS<KY<T0>-Nfj(GN1Xg;F%EQ3GfXiZNK-NY>g~v?Y
zK7AnFDCl<2zq_n7#`0;39&BJR(ALmsH>2T#b7gU@g&k2?<^wSINI}=)C|MfDpS{zM
zv1j$hYd-WA*hi;kQw+_F2Y-CR@vjRA(;>RR5T+j^n1c{W=zf=*oGij8J(7;qh(Iyu
z&ofckOdrf6)5w#}lI?UW-)lB$8*B(P`<GjgBY1%kQX|uN6~YwXW-wRhTWKo6xy;Nn
zPz;#ux0VL!<)Wo&x}R%nMA#^MC<avf@6O!`;&3tfFGDFmh$Z7;^h)f%Dx&yxro=La
zwiJ|cVdoT0=%dIQ0qYd}Ut%>W`Cy>yvrNI9NhpIoMut8P!Z?KS{3QdvxgOTzIn&;p
zjHaiZk7@R<y7u>3VE3-h59jYkm>gkN)@ST(F7ml-Tawz+ckHG=7`f`I(IrD;HkbLT
zWpdH9fbl>4m>Cb7Yz<~)v{Kf~NEg}6yLpiKkyhg_w>OAQC}+ylE&6iAXqMCxvuN?#
zEvUZg%{5XyRIn7W$Pdhs)9bgAFfJxejLb>bkMI8<mxvBWS~di$xTv(vVo|XjVwo`9
z@q4(!eZDJw5dIL&vN=k~{SXwFTw^IJ`25=ivz)-gWcWkXpposK65YR-ER|7SD*eVU
zuGe{+U}+NE9H0TtAb7W`o6&_>s(0{OVh^GW$W+``5hL>WF+!mH`k!;md<S9PRgS4I
zW=1bq*FfdQy_#{*r8Ev!px3#*y)qucqAiOqTP`z}&OF)IM#ph28!uJfT2f}i{NMNo
zRGGT9O%EqRNxVVE;&yjen+0CZW&}cO(!OFx;CBxJF>Yn&I5Lg~%IB=^EsCRL1oC~d
zwGMq$>l^>+Uy-&>tV+VlXra8G?s{P)rG;v1(QVCf6ecy@X=4Kbxc9x|)6nVB4A9M_
z>~E_irDs}R<oIVxFr6QeAPZ|pqHGHdh$Xnw3qAfbCC`~Oc~J^(Psu^Gfv41#Amzx%
ztMNev&E~byB)efZ!+$tQ5TYxpccF2?no~o|syQE^3Ij{B33T0<<unT>@NnMz`fvOM
ezYyob;U(tb?r{T2(Hs=;pTq;%`xzoSFaICmrmAQF

diff --git a/chapter_hashing/hash_collision.assets/hash_table_chaining.png b/chapter_hashing/hash_collision.assets/hash_table_chaining.png
new file mode 100644
index 0000000000000000000000000000000000000000..4b0cdf46eebfd76b0f57e518e9ba027d5d795378
GIT binary patch
literal 91610
zcmeEug;yNg^XD)?aCd?R2np^1f=h6Bm*5^OxVyW12r{_4ySqC<g1g%e@B4kf-F<og
zz@D>7bGqkL_noe~Ri9f`w`ziArA3h7@!<gg0Fs!fkURhY4ZZ}9!veu4K4NhQ@Cm|B
zUPJ&;I!dqy{@`b*DrO`l1)u_7!vdfo&;gLIw}AfxAn^Zs`1KKSh`0Z9Ef4YGzxRO0
z3^WBm{dGS8pbkF2{?i5jy*~4wGh`OT{~j?5`1jq=fGo(ruYu#>y8)g;{BGbAoQ<fO
z9RPsb{rU$HPmTN*{N4aDA$~<Ch{JR^C#9K&=K%ty*eJhYKHN^s9l1AhP*9kPAYr))
zb?c(qnbq3bmKMvGmX;EilM>~k*=&c>SszFeA12sAt}#8>C^#UTfpq_)rwos(#b}(M
zZ9vPI^G&RA)Agcx*;UEfVt4by!>qbTNlA&8QxpL1pNCf+2CRLvZ+LikO-;?!)s>Vb
zOdK;ZFE8&jiE*L$&u?>QgK9BQqF(<z_}W1QnBE`XVL}6!BBG+A%FD~MvPfVW?rNwN
z<gzL&D;padv$H$a)`)2f1<mo82rXiI{v1WL{ToocP8?|LP+eUO1p^}@BqSs(Tth9f
zgw`I_YG`Q4fPlsSw20QO&l%Ez+}G3*L(T{M=b;<#^|KwbrEr=a9krdEyiKFdDyl=d
zC`K~X1xs&qcQoC1?h^?KU!hJ3p!cF)h`Byg5Pg!0?ucbT<DWx;2iMK?l1~)35C_`g
zpuD3MNqug~^-fJq-9VBS73FiQo*67bSP#Xa&){~&M&Wx(S#C{?WGgi1Bozc<lu#QN
zAu+`MQ&eEKImH0BIIR76aA)@^rn&|KkiV?-_4Q3m3JgP)p=_k2q{PJF$myoblmVf~
zJ!*sn$fiT$$%21y$_JFD%rYn!)kzbEOVw<*gn?o}-s<b?`|3`^3^@$V;MUgD)05+|
z!HPXs*01~1Rrr#MvK%Bw9neGL5DJG*0`bqoCd$j*0j@CACGHJ29!(>T@$hbZ^-tnk
zDu^&!VPRntxDcFul?KmfzW12)qqbR$<lXk<;~9;Zdqs4FheV;#|DsQ*3{&y%I4Cfn
zqoS(GvjU^Nek)1q{`6Lmm#@C?E=$1+Q!0~9RDPmDvMBVZL09>y<kR)#Ul>g%ClOGI
z%bQHiah0ngkD}+%Q{uyq|Ct^e8yk<L0>$9S)tNG86rls>ols>auLP0`QUhtf{}&C*
ziiL_pR*J!ZGuVtGh#zP3(>UGPM2to#EV};ENbdCw^5MzssYQJ+^s)9{ig8S|z=cAg
z2GsI%kb(bSUW@R3R(x7a0w{}b8{N1Bzvm}`Yz=BvRAY2>wETJuAmIHMtbX*BPyu#D
zb*lk2qAomEP&LaK^B-mhfMZYef|V&$2$qGFA3!q<VP+|=)!O2l6gOdkvbMKpIo3vR
zpP88{5XCG@o1sA8Z-*3>_(_$$SUxOQm-OdEl6WJd%BrhmU~Lp`QKIKKY=<$$$ev^4
z<NByTmGfGCVq<&9puW<3!EW;rE=}&ssPfX3k$8&nKlK4Tunjy!3BItuBRQ4ThOEAF
zuqLc_zc!aSdOH{&_5*5JCiP1V1-5@B5X5x-J6r9BE2j5lwMGtwQc3Vy2_5450@s`T
z3b6L>?k#cUo(V>>Z{Rq(s%YREdj4&I`UtNeSqg~}mcl`i&O@(5f2H>*3~VAyO@R^>
zsuVUK4atc|L?blMCI4l1O5c;9D?xo+oCGO0U_z4XxCR{d(Aq)JOiUVK6|&{xF-OxP
zo&MW{RwRI6P<J7@P<4(eT1yP7Gc^ZTZm{Y{kf5}rQnNTFQ0`mK-hWfC_AoE>{20`U
z5T^R>Y_29M5%?so_Qjlp_`wTM5|xE=Oya*_%sLzJo%A+MBbIU1tWpFfGn}raoS1p0
z9Exb(!p~arsegNf2xzo9eJ*cnlK`o#h2E}DY#X0VC6!pF-wE}Hc6sr@eb@ta(;O<A
ziX}mnb4F1#^vih|I3)fX28`1}OjM~;6l0doyNLl(<GZ*uI2w<rkjVZ(i&Ivhda(Ik
zAL|g~4FG}05-VnQ=N4b~I`I$0<Ew+B5iUY6ry}juL2Iwi=IXH>D=x5dmFW5x3k5(8
z8_)=qvh|UBZ7)hbrD&m3{J{|b?sukFa#FlRbc@Oe#4Od<r<)M$n16vELf|{w_~{mM
zFItL9D!qKV)pvieK?0$L=9N^VSg)TA=67W(evc*K4-Q^2o6q2c0>y^%VDs0%Oh}d;
z5VM_=m?TBy4@F!j0Fy>H`qlqr)?V5RsJaU&bnz!CP0$NC&q1Ju@CWl=qj0i-12-=d
zqCZJ?u(E*9fn?^Sf3P{u0RgX@j)FS!=S12dgGswK2DE?j#YxErQG5ZB<NPOSl#~zR
zkRYPi{|{mD?LvL<a^T@(iTs1q&H*N+cSYCy)A0b$Xc_>zd=w^V=g(z?JrGQ?W3R;i
z6QI&DvH-JpfC;WYNxP_707qnzS%E)h<o|)m^5#ol68TFl+CM@`r?F2=Py2x$pPn8r
z_kP83s)_Z%>XI-JoYV9I$#P2aTU%S3o4MY<e@{*>lxj__rJ$gosA!-TS#my1`L`yV
z8iLiZmFxcSGu$nzcRaO<vWm)&E`EM~8Ll%wUv6IadwVUd^rucZI5_a~1sXnHY5HWf
z{2|e9cT`G3LZQx$10w9<`slOU?I~^DvhB`rG8VNmEK*p{_0iJJ$r`Uge^iGrOkiN(
z?#>RKPAkFpXzh9%J$w6VcPl5yt^g#|;jg`6{1gxn5Z6N&ba3_Ie9o3?mV%bHlHyIY
zIa?i5Fs_a#@tEmbC*Nl%vmG<zfv)h5pIBH)2#L@cKR8GE%2eRKD*P=8SX+q+>>ZP#
znq%Aj5pdSIs%PqUc8nTk=I3D{jEYokY-}_&(;6RURCKVgu|X0=!QPNCqsh!7D?YAO
zwYAE0N<a2X$KLZiT~0kdy4iakE!L>1sf9oWKmu{QXUlX@oSRK1ayB>h8$ySJf?$;<
zl{eeHA?u;@&k}V!l9Q7^5|c#`^FB|A5HGk0ofErX%9&U^7&;|FaSH05l~U*ssK=uw
z+X&8v*P*m&fv8GpR^#g~G?fN&;6fF*n-Cn^nx73d-@v@#by!j;Tq(Wl!Xu(Dq7_6+
zK1=p&KKiJ{jPW09GXmSnh}S9D-)=8}nk~_Q+07=KZMzu#TpMzAxBxz%R6ER>c}Pfv
z&bS$w!66d!XhNM1#8TE|;tD<G<Ys2BUG7aq%Vtu_7HfT{GwTXOF@@E67e}q#{G<+<
z^d909hKZ@^s;xdVKDUa)v719-bt{>5A9GPg!sReOvx^X=7-!wqWG<kM&VxJ0MKo{Q
z*>mFgf_0bnB3fb1e(yqOrUz6O;bB;V$RuJI76NPf(iBtDmn`#YZ`yod_(FISt@W34
z(t`1Ou8i0xnVO19_rr44;IidXt(ePXuGql9z-@}n@iNCiaAc%Pj|Ii_uko>8eUWua
zVRz)~9zd8e0#LK+$D<w0-N(J57s1Ag1~jx$+LF97qg2~ZD=aqm+021aJofilafjHm
zmd4L?VnZBkT(#B$I%2#v=aB{cu5(OCEl-mw^y)hjqs-qQWhkL-^wc_td0&3Tc_>&B
ze-p`SyUUC|6|iP+Tpb&Gna!?CSvcLxkcnch7|X2>qLyPbGA!24DB^0m>)sj98prcB
zQm0)PeNW|`%FPJsE3ejzh)ZOGktSx>@^BHl4?0F$IpT82A-|cvQxKG|{6)5OSK@Dt
z@q~V_{-vjk=h4vI{Gfe{|06Qg@KS}4t9g$%mIG2v?7j3CM4zosH7xGc<^%UX4m`hI
z&~u_1W|gFwqBF2ST&!sZ93zH<tr={`QGDqqt!l%x`l)C?%xf0wR$U~NXDVG1lhuLw
z(&;{SM4qdp7!n!~Oz#qY^0~OUXloNqo-UNCRpnW)wZgNb2O=j|dtd)vZTb9OO9FYe
zHOBZG+>Nz`MR9GexJ(9@8WMF*@dk_Xt7kcfcKg^4ujI_H2H|0YM?}EG?tI#s<1T9b
zxuzt$;q1qXgd!t3D#??l&T|=?v1Zvf-qyV}3Xx|t)00LHq?>aE>P)IaI&W$XXa{r4
z4<&T&)=RFacSb<m1TtcZ2a4-9WeB&%O~j0ze26}1hQ|#ZqI+ANjaB01)2@EmDSRYn
zob#93GwUcHPc_|(1Fu@Lm}i?l-m|mKQn~LdjQTvbbZoP%tf|-veldOw0ow8U8ZuT-
zPGfz%4SST=&<s3|{dK{+Cob9?FLIFU%@un{Zi`M9`zUE2yb_O}E(J!Q0V+UTTD^4!
zH(a6a0R+4~;28P30@(1}&FUA_&`*tkb!#4`A?Y*Ht(TJ$gsM<r6&^IR?6(hDtyOAB
z+$IA#gG0*6kHb^5(nZSfj&pRea|jY~g{@t3#aCDoJj#voK-{SS3T6g|)5e2R>JK0K
z2L`+;IapW}m3*LPXXSzQ)zxu8RfIrO9JG0bav1S0vu#)bYzViUODN@*O7&i4qq5@`
zl9u9CZZ(&^A!H-8B{aDXhz@1q?+h1X=9#{M98@g(#>^hrxHj85MZS?uC8|>HBb!<;
zo$v;p>QA0+8BcGo4%8_KDz+@P)e3at2<9H-?Fa14GnRgyjmaGG)|ktxV6xj@!;YFq
z7GrsONUGL3ckQULK?sKody7G4i=vU1!N<)cgnn%^)(l`HhF+Iwd!MS5u8e`pgt$D$
zd(ZI(P4KQr?ZvbPmsza+0PLN(KA~3mlCNVxjb`#j8YUb{_VpNX0D&Gob2^?Y$Z>@V
z`TDdJAH9@{M>Dw1Ys&ky7?n$yT;3<FIF=*WAXAefU4_bEsb0a~U;m!?!IU`P;i4J_
zl_m|qzZw~_7OjCr&tNrR6AIH5@I)5HFHq;w(uR^Ms;2gdrPT_8lM4ntdX7B^$~nsk
zr<+oFFPydMJjyt@voZ++1&@i_`VUJruY*q@oh_~s$dZ?2EZ0;_&b4?MkNQ@~=z8v3
zpGVC74gL4e8ox|c-UXdKA62duNLp@&OL?LoAS-Zi|8k*AIrVC+j{Q(Z`!c$OqE3s7
zLlih}bwt}8-jy1%H>;}QdiQKtXRx-oi0xQPJ7tBR-6_B0Uo$4LDR2a>_Cv#G{vZ{9
zmQXE!Uv80|n{7oNKxVHApWA2T_HboglwTd3N%I_hjlLI1$<1ZiE+xu0yo*W9))YDv
zkk?x<-v7*934A0}2M|LBZajDnd4^_pdqo^`ELKYIM0w4D9ir=dQX?3#c1l>1T<p!h
zj#7|eY;l6M34<lYI~e<`rju6JyO5V75^wDmmw~)i8)#xKr}0Yc!_Cm`zVfYj+kN$f
zXaaWE=ypy0;yW4+8`wx9ZkMqP?sMR}1kAhAnv1~bG9FJ|KFgV5H*_0p@BPr3T`GDh
z!%SAE+0F`t8dky2{J--YB?zbN4!e0U&;ssHo7RL)7zZzpS2e^V`f-C{YGev8W3)os
zIG)2Bt0l9jG&V2%tzRhQ$nt43YhodlUXGQg&b@5{&Fa*Ah#zhnekGuU&`&cF+Zom*
zk2@?%eBPU-D-jr|9Pa52O-MeimLX<;3Ki68ZaaFK!25w_8NmeMfm|pQ=eMfNfB5^y
z^h;)yCpWnvY~yJa1#eF~xBbfZV*+PND_S<B!8sIZCx*`szsGp)3o+R~)2}okauhNa
z&fT<mbX8m}$`qW>04DK?>4!7qtBU7#irrm@G>pE_P;4ew+}AZ$XSSc}p;idIePi!*
zZ!_cfln-_UnuEa(>!<Md4`APO-2iB4m}e>MWFNy9SqphKAQF)Tgr-ID;}m?-AKMDW
zDSIS!U30(D`@Yr_iW92APC>C9@%fl9jD^Rs`Q`b+Y>1jB<!X?+tiUi6?I=vFE$N_0
z{qD32MJWXi-3HP-sXS>9(zuxY6mPN9ZAhifLkZuX827^HYu7LBmK)ZeoTwjZ8<9cv
z-`!4R7L`K;oHc;+NY@&cz|~G>EMwhk?ytua*iI&!-#7Y{IVi=YY1Y~Z%++4j1BeSG
z$+K>>Rd0ak7b3$l5n{@91Uk_OqZj!nPG7hSq%>{I%&QhB*N9pGjKfJnge$Ch6$_V!
z%na=lZLVv}mtUj=k@Vw<Q}1!#MgKg$RGqq3G`E{w=W00F;`Vo?c-K;!{e~l-S~~E}
zcj$NZn-%jjNf|%7eCRE!9kX}1FqsC22U?*sIaW38<Kx`-iV|Bn8?8p8I1u_)LYb5!
z3rgiq6H-??cOjve$uO2gQdcTHgZY;y*s^eE&k`Y<k9a$q$k(Ny2%d!3rQD5lz!6q+
zYJ2#n)%g;QPkX;AzV=-ouM{1fG&^6c3wIM$1!a$nj`sGp)rUG~o5g@?%iVP<z_GU@
zEZ+}(5kqz(+9AI2L6FLLuThgK=`BHLLuI9WhPb$R%s`8i(12Ehl9J(h#(?*&@fn-W
z=(?v^J0#Q&aw;_tcL>Kk)!NK-wv>{K$~|`&K^RZ+1Jb3nr!sA>bX&K_A}2+<M$FPO
zTL}vb0}D6ZN+rOkNdLIhu+^7Cbr+68#3+pAf>dzyV;?KLZn9x4;QFG=Y-}+l9?&a4
z02%Yf#F`@s83nG6xlT>V$FM->ai4x4otVsabZ33nt>)wXk9C2L6P3rrM)QQ<iQ^}u
za^FeqtT$GrDA`E8PY;WURMZfxF9N>4%{sNlXLwS{d=B(Wm*A#GDUE}&|A^fbVs3{c
zF`AmX>Zcg7htJ$_LO~-kMij5XPHdSffcUL+M5xs<E4%LO2T?SXK17DjgK@WO+2=}Z
zbIsJ1l49nkb2q~-9ao_nuY<P--i2dGxI%~&y_me1?MBN^dkC-VtX|xL2>K~4a9#>V
zA1(*sta=eEvK(V9?xR9E9!jTS+w;A7Jt`U=LVixM{Y)tUoM~kvh)MX+<alJ3JU}1}
zxG1PW)^KvEIIqG_bUkUoiLFCR4ih!1fr#Nk=tzr?|5;tC{y@dWMQ}C=dNYHHu8M#^
zF}+BTC)Q2|Rc^qTi#dzRX0DYMNQIH8%BDt_c%%`K?m-@|RM~oS+(sI{SDAFP#9B|i
zrSPo>Z;P)~Rf(oe>sn*M0Z!n|HMWiNDk*(zE-qj?P+gjtjoQdLm?Fh-J9W0=?UY^E
zww9&z+>q9|kvM)!6@F1M?ZUWXrYEURs&BPZ66r}~=4T^EghbPdy~X~GfV?-!1r}=P
z96>*7?QrV0gAjwg$Z&?UMdLpp!NaC~wx_$M_GwKYcLhGqM@l*i)f)Cn>iUVTB{`6#
zRa;wmU=ZW4@5@BAZv77EU$(VHFq7U(ct;($VF&2G_}NSMvioC&cw_fm2}elC^Hl5N
zMr0-4?=ZvP=H91LK;y|LRJFNVwNo8Vmn$OMPY+ia(JCrpj+yy@iCzpGfP!OopXhjS
z@bx<g(A=8JW;xl2@oRIloSi|DG0)fI@vM(Y4HG*tF3#<=0|tfnv7GjxhIIVt;U*ET
zpcbBajSAw!YN~bXU91dGhnC5lhII?pe7sxFO_1wx1I*H$`mvKAbj}QuiWBy#uF^{u
zzi;`vnwc5Z^i=|FUK`D~^^5Lm(<$;2ZhFmn*%Dxj^Mz4W5WrFlJcq$hRz&v9ml?LF
zM)?L`Epul$ifZ1;7A=ogUt`Z|2q2GMN#T%s(JN-YoV9rz202F=IEo7>lL8*pwK|-4
zWjffn5bCmjBFQR`(B`Fwf3rsjb>BNqWE{ggV33I5<o&*zN&1o0cN<$MaXUma%B<~i
zD{&vq5_rD4Ut(<K`K2kz(ZHnJ{nzmn&j(YBkWg!+Cya;4Bi7k-x?B=vTjlG^h_T0s
z@W`*cAen2oVp^`OKEOo5CxaDLbuAyfw)aw&@b>infZjJMstRTU#}r9K#f}yNk=jiJ
zkYy#}lb=vp7nrI_vysuJ6Yio$Y%Y*x-j>e#Cj`$HGMXkGrNz&$9Y!b4w)v%LR9X8A
ze0ledTwVhp7!1)<u5a_8xoV=W;bn?`st=C*wYlmK@xhTlgbAr6o^ap>L$_JG5qF@k
z98?k;v8N#4)S%B;k`7hm4=>w`%`zm4`0V9%#@_4_{z+6PqlaVFgtIe(+f`CE2#ATj
z+q`m@E3;fQw}>+I+dQwR9l0N0OpTA=>4sre8y$*r<s_R%=($?hW!KZcugXEAE?YT}
ztZ%3QlO`s7LXAJ6dQoBz>FDiHUh50n{bKH0OJXgl-r-tK8a(*?b1e>~){{g6eu)W=
zs%N$YdFu!5!oYP(Mm(Kvg&}L9(!=cu@59rCoeI#UrtUCzH}ZBi{f8vAs2UM0gJZW8
zZG==+pC0MXLW<!g`orZWqPN+Vm7X&iRQY-P4|02^*=Qce>)#;3B2<PjFJq_tm-87N
z@*TC!f{N^D$C5JMvZt!*qE`C#DS&bg_E_^W(`R0Wj={#+8JwbG`1QoOwy?s^xtrAc
zmXB*)8gkki0cw2(476-m$0kR^W~SS|gv7e*0eMJWomxgmo9I~#SxG<We9hIoILOy~
zz-H9qWV67Eeo6{NWg8TPm7!ODTf62g%7odqTBVu{hvA;xJ^gE+pN6$q+3!pFWhi}X
zft4wSo}OMLcYu<-(>$4%+QMy?7rR}}8U4Hum)n&Sq7L?Z$t150K1`NYp>|sOHT*aj
zT)m^`XO#i3yuA0_($qNI<Sf{IK1;;JpWjQTnT%nsl0nR2coku|z#XmEB+ix_A}5I7
zuWorB;A1+zyuHz~U@E!6#=>`>D`;Y{#tx<Jc&c|>v;9D@^_6MAD^`khoV{AFDCXDm
zh5sTG%OdUL<RZM$n|6N7gsA}u#oI*aS<f|43dD8kT=9Xi(iaL;ZaV64J+co5o77$l
z#?WUisT^C3yR|w3I<UHuORWwc*yPQGO*jR9Futp#W7+wwKcu7Rlx4!JNVh!n4Q=Jy
z0ymd*N^guV`UE$V`_^bJuI+%zZl?O7tDi<KPmnzV^GHX>+sWz4+xe@=k4Ne0KoJ&T
zk4#r{vab<na7jv+PYPIXX|qH-40gq&UZ=p6WdR4AEyREb(zt!IQKfV)_6@D<B#H6s
z`i}e6jEdoio?nl^n*JF%bFh-8W-(E9tQXAusMabvaLw%^oFZhU>AN{|Mfyqow_oTO
z7>qs-Hz#weK5Z(l!QQ_2O6vG^iX<$PzAz}W*gQ7t03LbKhy|9fmW+RaRXHbG0{^6P
zkdptIZ<-2DYu-qk<?YeFd`Tp<3i;+wB_8y7q<M=kA7<@bwh!9O>PQ5(N)|tu>|~|l
zNU4&ul3Xmzcy{hjp-8#GvZk8yT2j|e=Ais&`l3O5x)nxAdQwxzv-&hK=`OKB^0arE
zX?j5sKE4T=kD|KML<bY9o^4BmGE2s}*Dy17%-izPX7$uEYY4AG3(gEPd}dqsB%bI0
z#KlgKN%g!NYFzHY#D)<A-Oe-r%p>r_dZ5*Cc;;*dG8V=#-{|Xs7TAs4PZ+&*(Vq!}
z{(6iIkJ#I7+pLvTk02q7SQW8BTUK0jd)AiWWgEcWx2mp8TsIsC5#LeMJVfw+0n$4N
zx7@%w)Cm5esKwP5S3&#^6+{(MKUBrpR`&-#G;{|CholUUQWY}1E=8#uTAjiJmq9<O
zS`?zWjwv+58|aRG&_~2G^RkwJGkFdpIJE^0L#z36{-4ROd3|<==dE8akI_tGJ%gR`
z`RBU^W65mm@8je;u@1Q0t6c~3U3udTGq=ADzwcRP<9%EYWOBY8>e6Y)gAG?vRSx>F
zyeU4l+q@j}OJ@1j&#|}IY|%p?rS@lBd3kK{Q7#o6JPWOHcs?pjDU;H>_O%jXq_ekz
zv&Oy8by4*;tDB+i3e+#R(?>FeK~@V9?22Sw6|8dGJt6mOpFCFYxZ(nzaA7~l40mF+
z9cNDkKD+juMAP?ZKkoOaw0b}%{$4+^e&TLbBYE;I<n0zWa)rMpv2@nusWp5rkVWja
z1l}7I*T?uM>%ZEYYv^pF*lR+b)A&Va?c}~jWVW^LO3R`R)1o4?+>p9I8bawLeuin7
z9HNXIoVAbd8kCOqqDODH;>`4X=4fs;ThV2Pr(8s?l5`0ES+%a1_W671WIL)BY^*YL
zHJnqJ;X7)k4YS!*{Y5J8i60_lbXs>?jC=TN9~lf(qcsL^_Gcuf>FJo6n96HwW9n7s
z)jog6@xXNorv0Skqe6Vgj%p<(Q#K=~o7V?N;-%cQNtatJ`Ky{mayyfTyYRSEF9^xH
zmHpB`ML0|Yl_9j3K4qacZL*lOYIWtFjww5QZQ=YnN&D+FI1ywbY}WpzRfp*LyeZa#
z?jawaNus+Jnm2JKE_u7@H@d{~5q%@oo9;@|e)S>AA`VxC8_b#`MXu5tb|{sX+dR*g
z8Oj%LdZ6dZ>0o5Omb!{0l+E0_tWuZv)B~2m@WV=c8$#W>b)QJciPZD+!eG@Y<W~({
zr}$|4i0@&=@HwUC&DB2}XzLnSs_jqYXL7_vPn#QABy`>PQtr))@#yY;xJ1Ns*NJ$#
zDjdJ3@ebH--9c&^Is90Z$dtuYuZ#dL2WXB5$A)zgG!Mc+9udF+`GQ<q#5%jj<1I+3
z$Y>;m!av)?5>EGs;48eY$h<xz2%LY?h)?5kwpCZh=TR+4%N7g-v7nz8Q9~3bl*>b-
zq9H+q%~X}&;vpkq<k@IwK_Enu=+Lf(7xq*hm4iaSF(S10x0YT#Dc$MEp-4|TZIuWp
zx9_T)xS#=$LbcXgh7F9y?@I$E31<~mfy3BWq2lW~nw92aS{i)x@6*k8(>w3(+WlZk
zPk3uqYH1L3EsYHlX5-XHGiqp-?+7HLp3BBO=I&f_-=HO*p`BH-GU^AM5PQCuuQk_h
zcN@{jy-&{3?eZm4{2|+bG=gNviX)4js;+f!Hoka2j5GFVz8m;qmbw&2+1umHYD#<v
z9r$#b8#p46rDR!)eqz;99hO-FRKCE8Xu)wsleoP+e$+w_2w&(A0=BE`ILYiFrw5|=
zD`zSt<BB7Gpfj{l;=v$a|33l?IN<FIx2FH#k02hw>-Iu$0vx%Yh}96&&THeVP?m+9
z92!BSsx({?T`*l|<=DKM2#2?&w}Lr+w%1Rts;fBq-LLOTXQ>g^QA?qrp*x`__JTxJ
z+}5@F)Rp(qL%(j&K~)WQ@O>RIE?zJB0{`PZk&z@yZ;TO$936${HVgkpS?fK#2A$~%
zlN7L&#H+BjGPhh^jfCzUU7oqU-NDZzAF#6|_S7*=`~ebmuJI^t?@96?fz5iJYd|JM
zIzZyIfpsilF2%2Un-ocmC&#jl^<2Z+y5YP+>>QkOcR6i@VZ@s`|0ZH9uP-l)h*l*M
z5{W2^zur$qNR5GsnueCTaa(m;Lu^Dls6JD!|6<Iv=5$={Om&H$2}eRwad_dXu{H(2
z4lAXU)D$XiaAGJF14%-6b_L;Qc(TSn;G1};P7^8siE#W5cxQ8_XUh4J)AYU_FQ(S+
z*|Sb{;?5zwMyAAVa8%)KM2Sjl;7h}=%)JUc)fN2h3N%J227<ZYl{4{~H4dFd;KGcK
znN|H1sOAi?`p=;-eijAt2$6jL+~m6C4c9(@j0MESH=Qrn3kn_?8w2NLClNYvN41^8
zD&QHhwSDHk_k>`n`oV?574fPbc}<ydC|c!{Tf;$g#|ow#&sPWnr_ovqrs=t=nT<yk
zvq)rXbQq%|JBJczHL6XbQ>?;8NP^LVkS9XRaPws{zW|AuWN|wtjex2%!%%SGLa3e1
z=f_`}k$W7<O*bglL&?+MD=YUUg)3ln>j`S^KAeUow>^$b>I^MT1UUyFV(k6QPzruq
zX~jpu(ZfLnqmCRZS95@_xJ`?}sK=;!cKdtb$C9+ALm{9yK(H<CiuiZyPoxA6*drc?
zXH4wz+GYxl`EUE_Y&g`QbkH|<$R0tAwuk3yPdD>iQ$o{v&z>@(8P-8%rI<)q$NICx
zI)7qcUrB&+q-avLX6MUE5I{PlwX&rFl%JQa{F4>~_vU+T(qr#@H*DKm#_b3C1MS<X
zx{Mwi>|xFTS&?xE^`+jngfTNahPZkQjegEAsbef~w?ObNnhvhvbu^TlzgKsMz~G>!
z!iUnMr8*U5WqqSEY=~!*+qt%9e>VetW+IvxOhQ6#<Iyzmnrs%jApYwcltfX};*+V;
zdkiC}EQt*#Vh&sK=B8V=>=uNz&pa|DAUt?%YTIAqtMM!b7Y`?GC}q}~X{MfNzx94=
z<MCH@!rJ!Mry8EeKye9!_m^__#;!dBp!~2ko6IubT4a81STpDcIgT96w9I{f?*W71
zvau~VY`1#%n6IMs4ZXISg_xcrq9)=7>-e+d@w{c1br<<e<<Qa+$puR0%gs$b7y4VP
z5QF1+Z})GcUY~ZYv>EQLplo#%C{9^gD>uscHcp5EK%17$ZzWAiGXY|?;J6M4wf*H}
zc8%i8`_{UnmchosroLq)=m_!E#mD!UC$Y>P5fb*NyTsgTQ?eJg;gK@^&C)Yj=&IuT
z3o~Q-boMrUr)_JO7)R6QaRWg^w|B!jqI#0y2||)8sq(1iI_{ObU)|#Sr3bJfmKPV#
z4>;PQVZb{Om_wQ?9Ot9OL&s-9wG=7arRf)4C)yWohn^PhGT0Ii;Lx!v|LNf8OK{K)
zIJLKp^XUa0>B*uu)-gq)?(_&8>Pa9L4I21Bxdrk)wAr}_Lc5BCi`Gnls!Mo_d+Qy(
zs(iu@2IE=$N$&8%xmtJ#nJ>gn>kt;hzVqsL7nmB)udzF7`#j=+tu(z`yy|;=bY!`y
z4=4`dNEScg>O(hdl}8x$LIK^hMn}N<?M<a1ZS7V!j+{Y8M_eH#NF(U3pD&S~kC4z&
z!C5B5?=l#_zR5jbs4^}A>C^|Ao10fq#ISuKB<4qjq@U?jDc<kP>&BIZf}Ky{Di&wr
z2NIG2vU3y*roBegaax?)Zr?^%u^A&Z$Jqsr60X>VvBfNy*(uy>@fMDen}{wy?f-UB
zdUK%8uQkLZ9RoLU`^)qt!ap<{g#u>rHW-CCbJ7|<$8&^DRsL#TMl+EEZKC${lZS^c
zbZ77p4qFpKN0@NQH2$3JchQiKz4M1r92KbT+&PlqM51@sMI+A~|Czq~M@hc`RV@dT
zZLJ@zNcnU*ZgpwP=Ys(%>%A<Y$GspG)d&34<s5X$k)CFqs(|W5Xv4euZsQ;)1Y_H;
zRUb>CRv##N@9{=QXlX^3rav>iTyAH2us-lkuuRUw-~w@V4L3j85^$B<R~d>S{)7Um
zu6ClE6xk`05g%_C6RC-=yTTi}e^oN;9{5~;%bd|kqW|H{6wqb10B<MyfA6ehrLW&A
zjbdNoQIm%g^AfFUEi(xMf)Q9<e}#Y2Un4B;f?}nBE=OhQK02yfi(n0@iOecDq>u+p
zOdF*hn-CkQ!_sIqV)EF*$tg>&bM!Tis3yPVz%34c`w65W%D27w6^ch`y?A!erwrG0
zc&%4{Y|$DOmwtG=H##cnbk+4FdF0$5Fgsg3S?R!l{X<$tMkQG?$_oSTaB#^~EmgkF
z7GZMR-+`WQ<?3XDxME~pU&Jk*-s1{q_@Y}z!ES1*j+gcUG5FpeR?}`i*JrCd?JXiD
z1GeRTm!+rQ8|7oETeyn1s2=wemk&p@ZLCZ6zikcKUJy<guN(YlJ87m0)jp9pEg8v$
zzWt5UT#p)6&O6QvSR%X;`<;sIYN*`CRdLsCB&wNPu~D+6drrGNI)CP5vM>9{mc(e&
zo0_`T{Z8gPVjJYO;6i6|m<-~4<!@f&7kucg!j-$Gm*#7ZyLSNVyDbj|^0is#zCyx!
zf3+sFm~yIMLf_~FZ$1c`Q2)J}ybkfh$P$o8)#2PHq$D2CZo&i<5dI-0QNy#`5b#t>
z1FL=LnpUY}Z2nxFsM-CN@D}7_SV5rDc8l)K-~Fo&vE?T-KSV+Tb0Ach0C>Cn1DWt=
zF)ye?wDvIB{<$9_k>aE@F;MQI?MA=pN~Tc0Gcw|yi-qvh(`we2)9yP~1sT`dk&%&&
zs0%O#6~$7@q-_7PJyh+DRFh{M<6pLw9*xHfz6CJqbwaT_ZSaclET5=CA*^bhU2f_P
zceg&@A8e1Qx#fBtYgHK`y@BNjGV1%KdW{Ff6~~2X<>%u~{WM^Xe#+u~F|(UJ8;7L|
z`mQ_KzWtCWf&AX)I^qOrZ)ULvlPo;k0Ii@H-W&tGWn!d%bpe?<#3{L`AJgkMkG4lv
z@qk80I{(aY5;<1-jFFpCyVbtsZG>fZvMAQ2(6V!iPh<Afxwz}ec!87CdlWaf+BvOu
z^wSW(iM!=;CbXY8ffLbI1-=~x5yGw2vO<4LbM3{&;@t0J({Hp!JT&~f^k9^y6Py=F
zxyFy*e>u2Ij!G80T+Qy(@nL};R=?eh5;2K@CNs{k06ZEreMmST+<Gd-6SkLkCii1x
z98>+?MeIT5-yCP$Eq*F{=RP*?U+;Ewpfa~rtmb@rL62M_9wALM{<VF=t}m;XG~jFq
z-WT4pX%VZi1bGV1uIi=r%zFRaSi%D|Nkxiw&OWrFv-&7eeERrY>ltJgjuiS7sn*u%
zAuUgoDUng%oQz>B%ge@ze0ou4Z5HKUDNq`rB2vv2fT9C~dJ+zy6b=SN9$~N^<Oigt
zQ$Una0O0HoO6p2A8_+ifr}CtRhKJ)yJEIG*+EvTp(IyrROUuJfyMr+*I!|$Q+`LUx
zMd`P{jCcCPj!Oarr?aVGUy}|c=w8&?ovEbCFo?Kb_4eCrV}ne>XB%GR;OQ?rgV@|j
zwPss#H|q{U>koX3mx7ncCX3tU_v47;0%OOU41SSo?z(1?bifg9mDD=|l~0tpI^>p=
z@!L(uK`W#h5QXv*&g#i%)VdssWqM^Pb*)oU_cM}cZc%M}vz{GTj=jZ-1D6MzbDt_s
z3c@DHrbJR2l(NrA63W@9`kHuSlu_Bj#F`fu31kA_I6Q42@jgC<tdV8m3tYCI-F$v7
zeu{BGa<EbUMGZ*nid?ZVR67hpo!adWX%u(nqG2as!kU=Ykhbs#eA!9L_}UHwvOX*A
zdFLf{UnN0}4d+XvD6m-UAi2hBSD_zSpyq3wiq$2gRzK3^+eO^+JTX0AP3(RuIL(!P
z1I3<m))wrU`q*;tAoXOk%Zrl1qpGSMWITgDE=rc=B5-n+0K~P6VGLJe&6O&WjE`!9
z#q+{lRj7x#gMADrTN-WDfsrBR%WVWf=s*m=TV=Gt<=OiBfiVk24h}~YpdL@-;fo^I
ztwkQuyqKS{yS>|xw-K?=6LV(TVBJG7KTCiYZ6RRNQz$GrGiCuH+eVmi6kJou5Q<wB
zdNzc*DYXNs0qs)=LRSda$vBlT@2Q<R=ZS%%xz$0$UaOtaffD^%M1JeasH!}q>p(rt
zm!Z7DppXfLx*F!6f*qm7Zr)Gv%>i^tKI`**oO`mG#45FbxJ$X?_%7-STmx~dlI=*6
zNwP(fx&B*ly~1MV#~_(EU=K;;6QVeg-(5vitLm+a>zo-rr{zqx5<=gyZ;ek0whaRY
z^4MIPGvV=ezO`rXZ1eU^po*u1ftHcL4kQMVeXjZ=ZOB41HHupVp^Iyu&b?bOOa=XP
z^k$m(fUg10yDeRirJS>#<De|Xm7RobUFKrIQ@G(G!yri<zUxO)w?*YCn{c|Nrt0j5
zioyo8v<i>&+f|G#TH2wL{w0W$QpKzD`$Pu1Qw~9HGYNeMI>{{_6(yfY!Yipn<@K&y
z!z0w)^f6bxl?(UH2RG}%8wrqj_fc6%w={kSkO7^oYxi-yJ8&JTRsr|hjw&X;mENOn
z*y)Z5_YwnEY%&^Fqzi#s?xM6{voP?Ud>q?jLU`7v125Xp_6u;r;8p_CxSr*M*A<6b
zb;#dUj_s#VsIW-xKaajhpKTNqK~{4Rijr~S95C~5*sm{)@&Y5x+x%MRFo7#~U(|dR
zVENEU6qlHa+dsxvp`)L&gB|in6bPh0tGR7pAYh<RmE;JH%R?>yES!w;q6Alcy83V~
zk^f!m_djFUd<KtNM`rB%XZ>ad2{;o3w{P)hgF^ceI8C||k%shVMXi$$IC`TjsFM1#
z+_DZ_c;NWimQD1Ja?5o%@cu(a)+ifzar;N1>oT|icK)b;f#lCp*8k7c-@PsWf2RJf
z>~`|u%c8_LO#P2Gk5ZPODbBoDv4^{OGI88BW<-x#d$Bf#dLeH6Ax@Dz+lyB=r5Jwx
zuj;Qqy(a%X!xjX=x?4s`;sR&9x7R}URyuCR#l5Vh-q#p(z?j06HFGty_O@>fPn&BI
zykYjb=b6YSsw*nXhk6)_c$V>kaaU7YyR*9s1I`D%d9z6{?s)s~@T-meN1g5U#l_S~
z|2WgDahzHL;o6oU0A%u=ZJ*gz*Tzubo+sJv-&RzWyBNzI6={r$i>zuyvC(l4|4z?&
z`p--Dz8hbjTwY#W9-l@<L(ld^LexWOrlqB|wX(AMf^SR!?#lvq2eIep=i4EdS7-~U
zgVzl{;11NYam&ZUyX=ZH&z2u^zpMMB3(*wYcES*y!oRsWS#(AaBRM;1z8m&@PL+pr
z^m!lqmppM(`Mf;&Z1@<atp)A6{1*{=kB1EpK6=r|g3A}cmfG$GmE|D};N@aNYt@0g
z_Ih6@2w-wD5Wk)EX{5bFG`9}Kvi{FV^+5mw8}r0j(7i-#iRN^OE9fV{5yiOnugYsW
za=;D!Oc}zROXGfEA4NM9r#Ck@vPI@A6u6}TSZuTe2|KgHrM-dkzsW=&z~Aha(w@gP
zRW~nJh{hx3o&G-+%r@NK>+S3N0cLY`zZS7ScxeqK*1W!emjqnDKnHBJgDG|KaupN<
zG42}@_{A!ta)<w-)G6?F1C$}?5D31x3}YRn()#?S{N-=OZ~>}f6txzvULDofLc{CM
zof{tgm-M#<f<JPC%iW7(y|eKCB$ZNtkyO34IQ^gKCdx+%);R|zR2JVqNbNOX(%&5X
zt>6Cv_uqbCkd=PpWArE1*C&8U=698jf8uXCxZHhqfNvb}PtqJZ7@BEyW~Kjt<}3`b
zWH|9)Q~vC3T2}{?O1Fm=|3qzj0dU&_B_u!dKhPZfQBwj8=rwL?pZ^4OY49p_U_fH>
z=1-D298_bi%YWZb7Yb-xbbf<r>G!iI{_acp9DwaQNL(gNQYJ*aYXPvc$XZdJqiepZ
zjQQ~ceYr-|CqjxS?AQeK^c4Kq82t2|-^`6Pec!wGx;9x)0;UGa1;90G;8oB#+JO6Y
z?sOG_QLV0_t&E^6mzuYk=%-b61w-R;!CmsDQ$@)~OEm^-`unTbj9OpeNLb}Y4w&e^
zKGuhQo4c*n4!Kyd=@E76YubQkDvpIpdv(^;$kk9@8N!Y9V)y7dK!~KUPr<3Dc3?u>
zl<P}`zGKWm46w64TkYw@&@QaN`x<^+Iz7+?!Q5V3-fSYVYIMh#hPczT(fEDf_esD(
zf4R{=-j)G4cqXxT5E6}1MlX=n(J+Gb7+%qtUAJZF%?61luA|aSbQ|YIeCy%QEc^BY
zLCQ%0wKkkme)byD48nU+zA><tU2$<%hrcSIrYK)$M)>b!ds0ke6{N`fuwwhWSuf_v
zQL7H6tKj>ZOG&Wl7UZBJxiYZe2Xp{nguhA)t4Ry@M4#Jo+1BR_EA=lHeb@d%k2w$$
zF&c85Hz@wdY|^#xe7i-d*qVV+yNWbl960BD5|E)owD<++0(LQq1Ld-iUgf@S1w{R7
zBJb9gU`fVuFKGxdicV;$){ewc8H9;%YXh{jn(_atWY`do6QQDI<Lg|T@*4v$6%Q-4
zi8+>83D2Hi7ue*xA~)tj4uM0wSfkiBc(sdGR2?4j#?Aowi1IF<XW(<8`>cYg;hVVA
z=F5yhL=#;%+4eao$-)*g*Ve%~<IdS82y=&Xm(!K;-BiIMQ9j;R;V@%Y`@IThSqPvn
zx!k7QGY?9;;Vy8+0?ua*mz(8N1$T#XEO8gP#xpVqs_Ex>tE9|!Gx3qIq&X#Oxv5|q
zn++|?t6JGU-rqTxS}Jj0+W_-6ji1Nw5-wslZl74_$9(B@G)%Jm&Mqzv^#-xR?q(`4
z(bzQ{yOp_*$Lj8_+7aDbiQGOdzXX&EqccE3979?J>E%TKB{NCj>2VGx6mKf6Gqm30
zY;Au0p}kRTdI3TXnsNtQkwg30L-)0kxScxfujpYV;XXaw;n-Pkd>+f(o||K|SON>o
zQ0DC1?r4w*Y8Jv3!d|E#@4iYhrInb&$Kd?yqlxT$r7r?$MJz(}JL<pWYg6U#TqIQ8
zKk4RX=%BQ|b#V<fL4k96ZOrKl^m_9OM_x^E^XReEC~YVTLR<AqdDn{=OEeNs6vj;h
zMniA!`_V4C6C9uB?-{_o6DK{F>V}aqsGM=F4CvN0-3?6g!(X<lDs?j9g6vA7ZGZ<;
z(j`g>CvT3a&N<z<Z>>xMBTd2R1xDK8Pu{O{;uhg`>ojtibS}AnQKpKBu3t40V79%d
zIWQr`cdYa#ghs@vb}OV!%NqH*h{mcZ>Su`}Noj~n4NYMzf%8|i6L^Ilawy&+xH?Y8
zNe~_bdfp%{#Bqm1PqDg5g6Xx@dg<sZn?_{)65y`|<L8d~e-K|cWGG&(<KBSOvqyl_
z%zaL_4VHN}ze7L1-`3B#h|h#u!+eM>*rmonh4K!)HcPT6WsH-tSc@6a05sG3VMqC7
zpEUL)far@iTa;JnE9{xEn;`xLdtTf?Cf5aRIIY#L^XbOwA=j`N8FKV2^J49R9m(Fx
z1=ZQ}6^2=-33YI3Cm6Io@frQq43hO7s6GbDu$);8CXBqa0L`*NCWBZtCShr7ho_w*
zNH;SbM#uRt5O2WBZDV7g76#Rv1fDe<6uPFr+G!)u$6vY?_kw4o2}>U>5bC@oYi6JY
zw+`HZB}xG<+WCv1jyEG)O?u<rKNiT>;a`zIYmoC_kY5Ch{NDuye8H3Rk3*9mjD}c>
zYLtJ%`|+y?tVB&v|0Gd^NliXf2Y-ex<AmOPD{4aj{iaJ1lJ_j{Y2VX+q~hRWZ>|T`
zm*=#Pf<P_$uKC|3A`wEV3qKA}4-L@|RV|XjgsQpE?j@5xLww53m8dC#m#$@RfjB8)
zV5VbcqnWMr+yyb-=MSF~5?uC2_4BMe<O=22*4ARj?e1obm6#SV77ZdLdT2E+N2L)F
zpz79?j3G#?j~M4A@F|Ka8r=+c2X&Y7>+OQZGD^AJL5G+DN*Z4#k&zpHduR^63rh>>
zj_2koR;7GTNaOxqF-sHs+Vpw<>OW*wWKn>xttiHqmo+st-JT!sZf|e9yM;VGQ-cll
z<Np3F05nD=B_)4<{|`|yG3aP$8_LvI6Z7R;dR1?Rkx$#mA>U9U1!z5t9%{I(PtDTp
zc=oR{ozCig?5Ym1=BaVMs-Umo5dEw=eE4xrE8;NYR`!Kd-jm;9#=BB}u4dbi6-A1O
zt)P!&NSctI+v>d+SPZ%SxvpR64)Ldz_6ednbN2OTK7U^0(Q#d^#7f**FL5$hSE8>n
zD{XB^2C7b!$K%HG7=brxd?0=3aTuQV+jqlyTwi9!mu)zvE_GmFRyy<-Q?ycuR=N3~
zR%Ma=VcyX3I7@1Q^IPOupTN51@)m6o+|Is^45XCFc-)GW!GHVqX9f6Y1MV(%1=mt)
zR;H&f_wqA$c6LCIudQ1ttV0p%$`mc{8Q&RpA9~x3r!NL9#^Oi|ytxTJz`#XKN{`cW
zuCQG>t69vDKIRslK55vuYxvo~{grv0g=o#r?XKsX5PC^T3?{Vj+)6Y|LQ=jYOhz;Z
zpv*!b88;K3-e@DPaXal_M39S&>|&z(yEFPG;EjK6b@d_r>e~D=JClQffyq`2*@^2$
z>Taq=YK>Gq=g|oaarqv*oSH}Wb58EIrn*jki@{<HpPSR;r3drl<Kt=QrpW*rFYin1
z%EK4`FQf*#qwN|zi)}*Oo9kJhRV9@U0)*6_dI%|cK-p+37-yrm4h@%!1#Yi>#r9y=
zLRF=U|10=<nICYx9LaMJOSHbVwFRz!-DCm}+J(Z~yqn>Qj*ec9%}1We{_Wj|4<@JU
z9qcCyRlDQag0~k&*M|#>`m5;yzlDdHpL1P3Z+JobMdJ(QS>?pi_j0m)vTe5>>JW%b
zHnZ7$rc!&UOKSzzpcBHSx20TLVd8{8p~`)Gmc>}-*F1$ZbIiV32uvP`T&FhG&RD)L
zMq}6d=5m*9ID4FQPC$Ig&;3U5X)}7vPWg~((O<|+(k!x{XuSOi<DQt)wO=uPDe`5d
z?Ux0iuX<VdXCuDi;X5wIN*EyD=@K7Nt8sVd>bI6`zo(~14Rv}cRvVjfLK;U)WyjJ>
z@5+l?IR`hJE(=fI1BeR{;wu^wQR*^pjr~fP0KB@oHfY`@8g&9sd3kwss^z+y-N6?-
zBZ7jbZ%)A5!b|Ufx!E4k%-@ffQ>_~Jz&TH1rf$r4u3$lhguq*hok(|8-7F@k=&YQF
z6zJI3)>dFol!%fGk@LMNI_|3Q-E*#APN@@qUQHiA;B0tHjFw3dPh$#JBeRt#T<pYg
z*6~Z>TOG=X&1G8hYR|BEu@bBDZjDqMxA8y<6lkb!uF!j_P_e*!EE>TjD`)C=WruSS
zorIZ$+NIO<_pmAqqaEHI=S>1GN3R+&Of6Qa0On8nwMIuMsTiDCY6n1pii(71!Tp9j
zS(cWmT1}GL?+HXA2uw}tnP@Fvo}c>t66?R8tcp(0%@MQPv@4cM;51N}u5k%M{`fUQ
zJ8~-rwb?~~Hx`+YVnCiNQ8ur=Pd8neOGuMPWG|?%>GScqp}yA0^!Y3gJ5~i=ZrsXb
zZbS+b3;Sr^Wk!Xl4sZQ7tFNwwvQL~|DmyKPLm2O4-82QpD8+il92qMolF?Tl;hrAq
zOf*6QdzerT90YT4d+{j`5YhX(mC-N~ti6Y5>~=ed*d)SSb}lZQgZ#5rYppG=H^-_-
z2-54|-qH?cnlT(KEYgX58RCZJ20Kc4vM>0CTM1ha>v$XEcq>ff-~2d>NWN%(@e^8K
zo?cee(h2X5TaEpu?O-q?<!;?symwmL6oDfsc0=Ip;qhZril?`P!q_Y|1vw!eIb4Dd
z^YX0-N@E}3rW&}{<Q{5@&o=s_FZ_%C^t_z31^$7q9_{a>QpThj*IJO%Q!tV-l}yn+
zq1&f&^_XtVxEZbXDpe<fHCa@b@;Z~T?$y|LK2r3!C@QEnSKxZ~HdQg6&&~xj*>zQ?
zgMqkzAz!Ii*XzRB90p#06OleNfq`xu**gV)%7_ZwSG)O)r55T?0`BHi(blH>{u5qI
zL`3A5ygd_kC=rM4RtOgL`WLHwyt3AC!_vmU?;<!T87<=PLU;<zS!j`=cxB4!S7keI
zCBBQFe9V5%7H?r!9kzrG?CuSONdY$0)zKPNmE__A*?CxsWfX_c25sw-H}(T!<V$a>
zYsBY+nb<!LPD3eMTWS0*KzSdYS+AQS<ki)|kCPsDevYlTLX-O`eR2AyWyLp|_5i~u
zIyS8u-1tJrIpRn}T;(!2M-vmP-eTRkPY12on)fcc(;h5)-)54ZjITZ8AL1MBU+p#z
zWa#ti8d#uZ0cwQ<?!fxID#llBZc<<xPuQ<M{NS%p2kt_A`^icu0=-?;TX|BeDdk$9
zKZymN%naZB&Loud$XukZbj9ko9hpmbycXk}%91+`Qn<vziqJb1@cRYfnyO8Sj$k{M
zC)FAy=Jin~y{A-Rncj^{ZI1XXKITzZ!rd+G8VisXlS1n&E70K&vEL=^q#WISN8Z|c
zrhn{@5iW(Kif?JVgL(UCY%t>HJS8z1<?BndWqptC4QXZICfH#nb{kMxWV4&A9ZODZ
z9W4TNx~@8fL+qgVNjsT3n+Yks{KduooEnZNNcZh-skfHl(_;ts8=M3jU6*oHyH`0F
z{g%r*12caNUiS})MlHZ?@_h7ASzq<UZOTn`#QPV)zZx@|#(`n_K|5`m4&5w}JWl9+
zXKsZSgZ+8M*Sx}D5bh+8LwjtM?(K?RhhBTl<$Aspt<>W2S8ZZCQV01T3Zz=6lqaK|
z>HT2YDZ9lt)!V-cWbS8$@jz1T?JgmOvEjn*WT*or6}5|qupn-m>tp#;Dl!eSW|PH0
zjk2ps`A1v5y%@3xuAqUm2uuY-&OOvsI~N(8M@^nl#q?m<;BJ?7SPZW@>CFwWc_(W`
zqyV2F^9@o2et+7v>@=UXcfKK0TDLW~x<Bd5k1$p7=224G%LzDhX@1;I)KYZr1I>6)
z?5QHnV;;#Iyr3`+-`3b@jRg-(417XKQc{%*+TNDS##eaoJ=U#=Q0vbJYmHk7*lJ{u
zKD};;j8o9iAYzuoSA(_Y*}piRAgyOD6w01H4J*od9$wY{JPa=niS}D?lRO+ckHh-d
z)aSqzEN~~D_E$p{i%5gnr<6Ae2JCENjXW1F<ZPKtVmKy71v;9_pOR{2J2!M0KOXL1
zWF^)2*Orlf%FB(Es;^$O5sKP-5REK94GSu0Hrtg*x64N;tI;vFG*`yPO3*s+om14#
zjnE-}nH8P7$wK~L+`R=?9znJ>3=af%cbA0V?hrg^fZ*;BJh*Fccb9}faCdiicXxM(
zx5?a@duQhR1>ah|7EX0l_c>K(?_Ily-)-MlkSf=fl#>CAD0_F-b_|av;m!#0=1peX
z`d@8Z)Clm*@ANe-n*M0n7kBPBthF<QUQ~hVAlPu8QST+uCMc`Qt)ZJ&gAn_<676y?
z5ZL7*5Qk2%z>ogU2YzX&gcPlZyrvMTRKP^%52oVd=#MrC)M3uZK4)h(_D~V4fEsy|
z7od29zlq`9f5(P33>hdcDvDF8c(^{KM*apw6FKzMsqZ?x;c?-0y-sqPCziO<;(`i{
zLidr5^OHzJPEQh+M>nYu3@mhLHQ(07WL?)s7K3cJZSiWF@$rL+MszgD$7f=X*4P8=
zxUZ((6NN}f+`jL+#%CE?1P<n7YSjv2e)|<Jwv;*FzTc~Nau&|=)F9)&wuKB8*u;l!
z2&SCOsr<V*=7lM9GoAIW;bN|q2`6IplL5fHDk*QGHAmF)x6)Dt6(v|hK>=ihkBvRs
z+PZ&gA&pQ{$U?V_fr^^#8p?X1QmP%^9GxqdNzYwhRfX{`PFDFxGmp=_(<)I*mWhR&
zz1?v+8@`-n)q>8@JEi;7OLmT$q!&1XC{8dFm~2IC*?ukP(9e2_8SCY^_||A`ZX=nG
zB)0{78^p-C$zyC5?)nqZ)Zf$0g%u-nQ^l4YiXC1SW6+(qn%^b1P|bM}2z7r0_ZQ3j
zz)fDlYY84l%;lI<oL5CzoXbQ<u)>x6NcWC;^MS<2rKwxVgrfKS(<onNYI<CF-Wj5i
zn~&N2!QPmun)b(9%UiSjF^y4YKBC4;Xrle}CZarexzrzH<~otP?7VI=HNQpjbj!i2
ze{g1qMm*8;6{}G!wSRIdn`2Yk>*`R9p?|)-I@blKCNol^SR(`0)AXRhZ@`peFA3I2
z0ASK&F}S2-k~2gCo&-A`+oA8u<CdFUuW9J%10DbX88aQB_eWe8ozl=D`j=LCu_d~e
z)#Lj`q;x*W_Ft}uURoZC&6)|*@!Rp+pFhuope2n>C%!E4sek_}vu;<G^sU1oxF~7P
ziZpk7j6LlGud<7h{dr9ci`@i^Vkfy`2U*Cs^rk&0p^M+eH3X;XpF;bakj%gG!YftU
z_bXIlRWI}$CHN(dH8>$PqQmW03TJM|r++)1;HGhy8Z(^C!dAj)H>bYl<ll1(xd{Rb
zC`4J6Da*ZjI<gKntiW?x%Sxv;&IBm!NO`kgCO4VEqJzpi?w&bYFhC~ODb#=-#+3Rl
zRqD?0j~v{ZH`4Gpc_d#>swFVY)6#fFaF7-g=PE8YX^}Dz@bHW+z53Y&2&cU_Sk)>p
zAOP?lsq+_<kbs#w0?aJR5fzM$sTTee6f9Jkp`$@SBgHjG=d6<o2Ux5$;hM!IwzkS6
z@aqjB60w>_#hw4K(>MHSs&4OS|A6yk>el=;R<SJFs5H{Bd3b_ri~KVSJEBR&NM9<o
zRL<f{q6DX^^kdM+iOq!>FDomv_JL93Yim9g1n@9vP9N+{)?#<#D~J}I=^rD9+Db~A
z&KBM}U@gJ41obH2v5AAr)KE{9wTe1KY?TmTp`i(B9{TFjUSQSE9$tE@bn@{?Jj)Vd
z8Voz?A*)KEzxDX8&*9{=5Nm$v@9yCiDceNvu@tuI4fPqtt-#@&D2((_Q}Z%%Z1w|E
zG1G2Lxw^(_pXvSa`J}~U!otGl^Af>vgxZ3JG!U@=7o4t(Yy&ny0PZ9{NxK}Y?kqGk
zaO-0d1}1B7`+>rPf`f6H^dXho78)GPKYapE>#>3P1;#F{U~XhK_-NeFbW)K1z5HQZ
zz_FRbWR0#u8S7<&F8{;*RU5TQVW~nA5|$mCLXqtcDx~<#((<IrL`Bb*f^6_Z10xZU
z#s!4iDF&W-lD2A=@sWgFtHD*rnu8;m=Ui$riWK(x^F!YtFpKY%7kvZp)w!0xr`GSX
z7*=YXZ@jr6+z`4N+MNk7PxzWmrlXY#XgH|x%0H<8N*q0~?>@B6x&uq7Phrz#@5m?*
z0-It;!0ajo6&-n$-4)PvF=hSDWSY+bX@3gtPM0-W(v#m&(q@XEHzGxkS`+dFg?DK!
za~}en#U2GX+?p(C>&-2whuk~A6&{OLwZ;9u-fnkbQ09T|!-xGD4eK8`?1w|Z<~Cnn
zU!Yu5R8<Yq7;6TkKLMWXA9t1$=Zd#lTb|N4J%$)Yz04*<*W1@sw{oj;F-~*}N4Zsp
z4k||mo{s5bcUKR5`j$oUmDQV#mZW3*a1Y%tQEy)!W@gv!WP&8T6GtO5XWBmnQoGD&
z{~knU@cSdSAp2wFbZDAQXlSW?f!FHkfNaHXJ7gB36?|po9E(EV-Pt|MYpnjD@|zDU
zi_PC|579VvZ<k!|o}q6LM-dPa?d|HQDr(JIERcIc1Nr;q&6mh4%#;-P{1R68_LpcV
zmfrR*JT|=`GCBQ%GQMK2bTY3C^Gu7c6MU@Cwn1xg#}HtwMT6!!^}E>LuiJue#Qhn?
z`>Gp>BVulIEvxf4)#4VX0`=ftGFZSwdnwM}yI5+293P?9s`*fbe`ErvD^dXz*TZgU
z-W;d~(S63o#(*l>Q7vf+`~3VE%i!NA@pSYx{{O$YG_A!$PUue{%$9<WFC&;#enMnl
zI&639%(BKCrUIvaV|>V@l||neA2G@?a++n7T=U~2bX;?oRJ|M@X*M{8LdS?f9BVe6
z(d0{J*Zq0k((>@rfLR1e9wAUVVEeS>5>WIPghh}eVVb}JshXP@$LT?q0nnj)yy8#A
z=>1(27x7lEX9N8!^E4+l<GMHC->KRA2ocsEV6be&|D5B#73gQopwIF>@OH=e{fsJ3
zO#%5#A53$rrwJ_`DiE14;|)c{ohoQ*`K(A3i<y}Q-uiHG#uN+b9t-4T>j)k<nYTWu
zpn97q{S3W6+QUy_wpAT)7&sZ~Q-!6Qski<vCYhPspFCjkOl_!aq9^K;l!BK|wf@W1
zlS7v#%s*e>PT8JA*dMD?B8i3_-X>ixpUsU!x1LlRfPOC`&H)2B65tKGr}_(TkD{U!
zyVcO>EMDTO!Q12ui)T(~sb7Cg5J+KLFs!V>Z}|LCtz_yn<7ar8EKj%^M~^y_AwWgN
z^Uxb;ev>XhT18a-qm7J{k07S6?JD=o-~>q?Km21`R6<Imd|=8%=+UZ8X!#B9zq)@J
zqxlcj$0!O4U#_Lw4p=PI%pz&SV1i|2wV7`7Jc64@f<{VSdQXvXrQXC`SUD$l9QJ!^
zM*88c-$b<7E`GBR8}4t61J&?wU)j*qXQZzC(aJ!xaA0+Yn@FRe;wB|vR(J|EG`R>2
zudu)=0v#zhA@GXKtY?i;`~^|yz-@nHsqCb3`D72D5MNS|g=;N7vCSYQekiK=jgJcR
ze6)uP!_v~DuBA<|KF^4-^I1x;xpogf=UQMH?^7|_eu2Xk>E(I9+}^hjTKCML*c}ru
zsdobAy_n<O*0L!DovNluSB5u?m`@0)0C&}{hM!+}9OOBnyo#8VSNrznc&^~83xT*P
zQ2q#~nxg#!ESG{6lor|+ifo7FB_DKuHo-JQ7>0^IQjj|OinI*RLyB$rS?9QtW{9))
zqT{>(enG=ZR`^zb*o1cMcTOn|$%~_|Qx1<+&3r{YPsOf4?YbJL59v_VNOO(uEC%ch
zX5{bfN~=Cpj|fw}JE>wxonk~7mL4HRE=<h6CyLXYn*^Row8(JEAiXf<hYlz~tR(fR
zld9vCg^FvdEHu6*;3<}vv8p8jud25WAa?fj^!)PWi>@xo2)JcnYpcLZC`(q~yqrwV
znT+fa+gp$JVgx%*9otF>1@I=o50$r@kUh+6D!xJ=tdk$3c|Ty@GHA{pW7VkZPG#Pb
z3*7d<D4#Zvp`VY2-qMQ=+eqOFCDns`3lAX;>*mk1+f~!<t?C}S1)rfjIF<whWSr9k
z9XuQqzQ*(pmwf~Cr@PQlSKnG%S_)$w;RF!Y)RYt(K&P7rJx9Z5{3h-3zD4)Wb29q<
zfgU?UI|p$+nRV%pH{Dbz=fpLZh7~atZ(&r+ne;&92ku#Lr^07$7Zud80enM!B)i5E
zi|e9ZbaxI-ZpZ*n4o%5`_*m~s0LteHr8xZSJ?Dq&y%8^H+Q;%<FWQ9WWnMRZJhL9K
z)wHo9_tf{^#1;TJkC5@<Nn)c-4gV-DNKE_^Vt@l<H2j~wL<v#@vxyTL3GrY09|GN*
zrZW<9Pcp0|4RML`Ioaxp#7=_n&Xei1_Rr5Rz7E&DbIw@(UzKPJEJ%7wDUDk26QsE_
zHwjP0cDc%+&};|+GG(^hXc$N(6uJnYu{Krn18E~46P0FWDB8f{xM$Dsy}RloGLe*Q
zhZLj8q)l3oJ4c#m%r)@T>cW9cwD_fx^es}x7{L97Ylp#GWLv2w{wh6yZvxjID?r>W
znfVv}7cnBy1_R`ma7M|h=>OzQB(f%fAMu1oVZJ4wf4^{ifL2k(g4zFDg=L=tq}M#u
z3ea1_|9+99tkH~#;ZQF8Lxz<_`bELLq53x^d$zbP$ty$ddI!Zn8xnMbyvq}I^LPF$
z#gGu>fIMKBDSp}NEC~6oih)7EtG7^;Q-!dsDlQCE=Kr{^WW7npT!~2+{$X>N1+zuO
zPjZ0G6^@7)czg8a|9X-7IKqxWEYXu;0XKNY1p@YQa&d8K0k#c`wbp`y-lNw#y@X<C
zl`{=7ETRiix&O;GwebVb>d_srQITldg^7!ge||povIYb&qnn$XZ@U*Vg|jx1sPk@l
zW4$DClaf+OCZzv&>;xMjaX`!e(<~hbKpHWxL#+U70t_sy2j$o6<;4t-O8rgr?w+x-
zGVo5Z{Y7o{e{=?TGqM;!S73+cyrzgibo9a|b@M*n-@7bP;AO!;z6+FYeO@&BO^JQ@
z4P9~K>G>X4rCjeX*7Y_vSstLL$!rfXT7cvL1fLa^mGMx3N3g`_&*%9k_&+O`8+r}S
zO$u~`5wODlNp@+WW<mcG<>!?n;pTpb7AI;aQw27Bdpum7H+`yF`vy|IgERkBTUABz
z`&N3ii^k}Qcz)X3`R~O3_hn86d$lSX4sd!yPvXI5yomVS>q>95XP@am^3@ve>oYM4
z+?rY{O=m?L*jqA%|I7Yy3>_F|zHlf@AYRA7eP(8608_T()mCC==cBoDd(fe-bV-uU
z)0xjlY^{bgUe_SNq{{z|p8d!52-ze8#=*v>)#NPSP>^6<y=u2Y36Ay!l5v~u{d<_*
zHbI8_^sI&%A3&i@4VdaNAk%BqAgqs(l9Ces35=}s6;w3%RkJWwqW7N<zmviD-M)sr
zyu6|!#PY|$XC%NaFv^<}{AsbBn&OG4qc!*8!F3SCA8&Uw$27g#)6)aE_&N0Z_rhMC
z2z)UY*3^%=iTU3fMJtnQYXkO^)iyNXc~vZ)lAZzqrHKyyUawF0>9HX<uPNU~T|MOh
zX$DtTR#rJt8sNKY`0-eb)HQ`7&-(s+BJV*U81eAt<ELW%XBdQuwEbC+uu;fQG9f?D
zEvC>#0o_$$;NcylX14-Xf`BqC5SbVXd<Yx~8JVLm>pmp8xe{u<SH*SE^Iy@-8ShQ{
zj&ZtFaTQ!y3^W6~h97G^0w-1q?6Pv1l;LQ9KHS|kNk_8dlguhF2R{bnW^Pk(?EjMR
z=<<RBFxsx3@lHj5b@xzsdzqu6qV`lZD=Hh1?*05pb_B5m!0fV0U4iK`S@rd1y#dv8
zVEMnR+4z~vwz~4i%WX%j{ICDzwdqU;z6q;aGPYUGK+cmZ08%A@f8B7WL%~~LJ#D&_
zH8P@v%F$`{1gMqC)xNtD(fj&dSt35#X91_&y|ofc^xWm6M$S3Af4&|*<`lYRqGdQw
z?%|t*8x&(|AREx*g0CuIAc=kr?<gKg^j81SitwNEg5FV=6pe?g!^;slX)hNA|1(Fn
zJ;LHhgR$JrKk9tG`QioXZdrWY(7=66a;JV<?J=v@prP3`Q?SR`^T*tU@$VY(EgZ&>
z!2Mv?99=sXfv-wP*A!)eO;FGuLy|!085t$?$!DBCL*RZ8pi=3TeGccOUYVcZZ-4gp
zf+Dlo9))?vAD(Z0ASPFr089)?NJ-aQ9#43Hjr>^cc+7?{Grl*zvMw^%9b{y?%a31H
z&VON>n=?Nci;DF+%goN9{&N7pIZzm5z#Jiv*nxbY8xN-32{%=@T$FI0J49p|$Z_45
z`hbQ(Fk!NWVts)6W)t;~n*gkU#V#yZ+1VSy;qd{l+A*}XR(?9f|C1fPArU0oBtSU)
z@BI{V=P7jUK~J+LSExDvqaggp{~^((0A9X-h5A2Z77g%)22{EyjNJVHt<u${0FWdx
zJh}y71KB@E<bOUH(*u4)DAo)8ze)OkBLQIjC4Px&{P&NzrM*FQoqKmA|D16CHNSaB
z!$9KotNu?*Yk2>o_YzqK^j;-q?YrNOQR6dkk~1*k11iUPbX4Wb*sMRg%74+;y=vL(
zdZ|jPirbr-N{XA>V@*$*Vq&?ovJXp5&%3jl^V!_2ZQ5BryW>;<b909={oAB-5*VO)
z|7p!@;Xlh3DF=HuuQ6q0I?$!}VHUU6OX`L$_r&4h3_L&hn|7it?q;u1n4RnMNq!U{
zrQ&q!Z7ip>9!zK&E?L_gba3r$%nn4&0XtDpQo_W=-S5-g+T9KO@x$SCWjVUTaRBhG
z2Z%T+pS86$Z*Q<1z^?`cAK!d8-w}WY9E+-}F}q`8VhE0+pSb}O`QJjSdq9l0GQMRb
zoaq11kD>gRek>#KKlEcTaGyL8sQrLd;EC3SuM-3~dG0BXR>RqCfZZy(yRzVqp6BLu
zO}zB{;n{aK1_qmc$ox2%m~5_Bd+*?}M8w76hk@O)K(aU3>Wc=PI73b=NBP~Z_T({I
zj%yZAfUuAEDh>whe9izHm*~8gyIuh#0?xB;Y#mKt8W%?9vmd0ZRh_v3sQR}}D))SD
zH|`hx)O7F?BXXV>v4H(Zj=b^3R)0+h>8n%gqn4T32eiGuseDDt_@>8`#=^ovTPFbY
zh~&KpD%O89s%3l+zJ2%m%Ap%3WEPurY;9==?xja{eQdy|Q$SDa+;vS6<hk~UIdT^|
zBe*^WtUk{r|8U=1y~mJFLX9#-eJY8PL+E*E)|<f|)qZFI3m7Q2<l%pPx&#`NgW3dc
zbEQlVVq*1SrWT7%og#TGfm$|Au%V)YnU`0Sna44}M2Qau`_S6!aS=e($#+Y=o)6bM
z12dgBf`P*fl)!?4-{j1U-dm_HWN+=<Z)$1+JYspZwY5(qC<k<oCG--2sgw~89M+Bf
zr^&>7e?4m61D1-3Z4HPK3H)y7C$o2obbPTJ88ij&yR>XCoO8q(5stav<Jr*+e5av_
zsCs5NwGmAgM-cl36y)n^n1tz=%QEvMUgN&(X~&Uro<iG)TzZGg-oviWfLO};Y`gr@
z%6W{2!F=H=n1V;9Mfeje`LPk9y|9zJ7MR!b^{fzX`7p8jnNQ9-Rs!US5LhR^riw~n
z<(-Nxe1tw~rvk!mSQtXEp)!{v+CmIUThx4zHkQsIKpbTE0$ta6e5|b$<PbTkFd7_#
zo4SBN=Jo#ajfd_6>n)&@P`z=4Bknwht=7@9$4zM9Z4&lO2SHYS(V{tHQGV#Ac7^l=
zg*1c3O*TyjzW76x(;}IDb3^YZ-4lRfy#S$sgwbcY{p61cUrbx3vgxeCGtF$Kc+mtq
zjh6`zbKp(vlVavp`V{|Reibu>q%%-V8$q!$^1oj*2jxz!MDyuvAF{j+Mm4v~+h80F
zM>|0<kzc6w4k29IcKH#H=;C8#`spdtv9jPK9xNt93#1_ioy-VOLG_q=nMq)8-9nY|
z%n=SEJy=A@!RtylE?0D4y*d+|9nz~+h)jIRiSbTl<>0_Z?M7*fAvfuwGiQkQd_1lN
zY_EoxEw!MawA+!uc`fG301*b#&s)H0*SV`bx$W=y66z^Q0$wef#fudoZ~SMA@V_ey
zr{A|h83icuD1D~T9-2Q<TP_Uq!5u(jL2R0+qDlY<WuH487;%imcPB3}*J323611vf
z{Iu+boi>xB(xvg-K~6_54N4}w+q|A^;zfSh{$?E6;E&cb3Y7dGR2X+ugfZ8k)9849
z5?wiW95jL#UfsW`!gk?*tspiHB^)0ZHnZNVQ0-KI#LHZ%6-RF6)AeKSl!h2QMQqwd
z>giC82p!$gl-K7ES_ACz%J7y_6A}U(a@H>1#isK(=?~LDuNSFRLNN^;WAWSXMbY@(
zH{)}pJTZRw@ByXG2C4HlRC;Jc$%s3F^ZOPIg@>c#P0r`osimC=rS3dnkqQvwO~Cd&
z-^}5JCSOKvmphMU2W7126fRw#<Z69tf>y8o`4Wy)z0rc7n|Cg>=Jv)p{iFz+>yrUF
zvtA^uSSG&hXyOHJ1K(81Jg$Fv#=D&P4AllfxPMzEQW6Y=4Z18kk}4lVX+D!#FSSdD
zW>xp#Xj2|7g<eIxZF)LbW_<L8&?}mmu#2ROsM6ovgdys!Wg&dIDSNUpj$6f#2n$Lb
zyek14>F;lEQ1o@1`Xk@$nryt&=Tn^vg-k>Xa-J>G0z9BqKQv^uUEPvJ0G>4(^ue^U
z%YeO^@nVgo!chC=&9Tb!a=?E3+2POY5tucAHz0{~J)9}FVG!2xI`76F6?k=Tyb)yN
zU}eq1NvIEav99HX2Vx2*5zN0tX;bw1V4yYc$lvld(nUe5z@LA*bf(Efd^Aexu6!L*
zxz;{4>b}|L!+Utj3e-eETv-NZO{+O+Z0jB5u6%RI0$z#~_LZK{c4u$$t5N)RqmPEG
zClDfk%IzG4RuBi3tBA#EPhHueYt+)6ONFls1>0*lsI}BuXHZ%>;?5sF1HBKZh}UZ?
z7y&lv6X+iQLBL~$X<0qr?Ctd62E2Fr`UIZVk>8I2f{j0lcj4=K&45cKPd#2jjp!gN
zsF+enqdqHJ9teccn55*ily51Wy4QC{m7`VnzzVgFmX_B2YFwOBN5<F_NKt^Ll8oU`
z^*^_jCZl9;4g;rNua62bZ%0v-QjlbK8{2j>f5ds7&hA5%iI_VAK)EXNiVORa8-+|W
ze-i+e!>b8~*64OPoK#nRCqOYW5dMn{-@&}BseFM`kke+$Ut>81u~Rok9bL*B-hFw&
z;>M~?Hof&tZ+k=E->8SBQgj(f?#xF^y>j@vh^t?jIYdN7ZXUFXZ{-F{Xx-=Zj*)_x
zEWG^ctF-hGpw7Txh8eWo>{)i+3<tJkDrT%W9L{|9QL8k5D^e5R6_Q{KLo!lre5;jF
za7dxd${fuUU`PgPo`gv!U}p7cjLMhHFTkS^NBEMQgxqAmuQ1qA0ETu3r9nrMyznEx
zT8;@=%C3<EJ1>ls%lIEZz6nq}oQgr&*`BBdMRI=C%6gKF8&#Aj>Z#UoRU+&MOX~L`
zAjR#`Peu1dc7E|Lj7r0h%E?fYd#~4PjqCZdum{+gzj>!!8;=KGm9rMlQN=w@{T`-Y
zYgr&8*YGp5y{xNvxJ&5Q8bLS<n1E-4fI%RsG?a4I`sNS8ADVFl7@bF&{^*-%`yUi@
z1;GkCjDvfL+=gg-4=88c-^>HHu`Jrex|Bn?GJ*-chv5w5P2X$S5`M(BR_-|;1T<D6
zVTBjj+1bF_;A`UFGTnO-M)#%y@E$U+x<u4-`L+qSHsZ93$kz8-W%*98q1_vaLvJCi
zpV7_0p)N7Q9ax1?@8f4%Uat?q^k`R%?-7siMl1l2Wvml6%)>j9xOKn>jPGfPW%Q4a
zk2v=D_)iM+Z{Nz4S!zDSG{S_4-LXyp)YRovzDmdWbY%@%l3}4$d|ce0Dm753d?YRl
zRI;kZAy6YoP*72=ILvBEw9%+qDQj!VX7Ur_lQ%zI3|6F;Z*>+TOw$pz)6E~ig0BEZ
z>f+!Qn^i8A!=?5~e~Quz!_>wYn$CQ`MZf~@Edz<JxpLV`!;JB+gFdDs??kFg%@I>_
z!8~TaGLy&7;e4P$Xwr)ZXALcfX3P2;3T@@q8+P$Y(md}7>x5l|&?<;{ggZ=@=*kQn
z;oh~E(23;51yFjmq2l5O_nC-bmufew>vhvN&XIoB3PFjNs-~R*{OOf^fO?ONL`_Rw
zMt7KwHifdh_xJDL%7Y{<g~x)RLEF!bK{Idu44Pv}jgPPMZpdd1C5I!46cQL{>5!j(
zmffy={*3V%Gv?r@YvmTFV~nkS<Yux<`DIMgmL2ouiu<PYM%QNow-(^OKPHF-AH+;|
zueebI2_424G5j4E_}Mc(R(-w8NImu~sLo><d3Brr@u=eF)xvwX_0_!8(z&jYJ1rp_
z7gZyI(3nIjkv_howCMtlnl~CCs(BF`G{y)-1yLo~A@#is3V2Z$W$hNe90?S0GPB*Z
zBk1adS!Z2WEfLskxTvtW!GWja^ZhV9JMMztsYyS-c*J3Fgc8so(`3$vWmIKQuY&P>
z519nv>~(tUS^D#*K9I8so}{)+;MN2XK6>77CqnSzfb^3afzo!Q!QpV|x5-AJz!NE1
z*_Sae$hk`TWYa06n?{>;p`T*t1A}&nrIs13>})!yUm!8Sft&o_4?h0lB=fLkkKmgK
zLkYSONDt$Yo)k{D)>L0Hztf^Iajia|IBnNuwcdrcMwu$XRGv73c5y(`th7rp!W(}q
z@M{QT_V;eRUT>G9tE4qQ%6mgBqTkWWw`X|0xF|xgN~@!Xc#~zpya)Z?4_)w}&obVv
zug|B6iHU<&szf;S!*T-8tgtswi|#QbsusO$a&dPGLf-R1JQk|h<SI#)ZDU_^)^zp7
z@ga;yGdzG@<!HeJX$BTn^RV+LQb;4Cj-J>P1UWhKr48Px%JTo!%OoKZU|>HLca5qM
z!G_7x2ZJmHa#VCY8~|5ns@^){*W=ZfV$;_5KW)t9ZC|(KUb+}ZGoQAo-}isbNh0LI
z6KgP=q?%j<tgC#f+khQxXWB4a(a8`fy6j;1y9dA`bTW~reZHegn1JDyZur022NxxY
zMv?diIy(J?mOap-q^!Jy`+XjX*m5b!vVQuGs4{wPot@Y9%5?G_hJAkw<qor;?`5ow
zXn;?tYPo(-n7O!a<KXMVY->PT>T{czrDGyRQi5SZLPEpow}}55-uIwj|27$EhG;0P
zAyv;aKjJnt(prI+^T-bZ&S$z@U>~TdcP~c;kaK^~C*lHCT|PWG`~Jeh0&oI{-DeQ|
zJT)!Xn8kP|?4%L8Ztv$-5g&Hcf_#ZFvq_Q$re4Bx%kLE6)s9<xzyCIj1Q}qANY_s{
zEIBB-Ke_w0Gr!XWnWLJWYruxfb!{(uUepf?VdJF#p&(=-<bi5;HLYKm3NRd8)k;j`
z%e&ER`96QC%*kx0IBE5PmYI&Dwt9w*gSeoydCaxj@EaKpq=KSC9<~f|8W$%UWpPV>
z$<fky$ijE=ZrvR*E3p&6@9!nFO5;znrrXw$3^n$GQ)eQ*#As3shpDuz)oYxmQX)M;
z>sZ;bg-js<1AdD(df|49$HR)ixsR|35)r3eTbhC%VCF>Uc9k{$Bl!pJ^FwCK7rTme
zLl?{XUxw1d;jmoy<dt?MRn;Eu7j=A5JfV`43hvgk#A%$4(=FL%Kr{v6LdK+k!B59k
zy1S6o!C_-y)DaH@r7EY_i+k)SYTX9;uv(*Wp^b!mk!c9J$9ZT;VIjE(P^PkDR#qon
zt-e050`Tq_GY#uKa25yZ*CqbI&qHMn#@`8Eg>7URZoUMBH;N2x6p;@cE!Lg_)oWMc
zqO+-#qPy@N=@uH?qTx3oR0#{nxu;QfaQ>$aWI}HHHgE8g^NZAzm*ZIdDShjvMoG}_
z*#&o@VFF)U!=OXy(Vfij54_mqRe@KZU}S_*V!iLK@gvO>j@#kO)&#tEZH5;Sk9$+S
zL%+$v^&%+1=_O8I!_O57*{f=5O9ebGbZ(9<tgP*pCZyybCG7(Fn4W{d^Eo^tt?=v5
zmOV}_3Kyuh{nGF;w7IS3{oB!b-R5;F1uh_+UHXGoae27dD7)EVk)Af27YFguKk_)@
z$}GZ2<8xc8N1yIeAHHl4b+g>iO<V>HHyRA37iDXXW(xg0(wsNv(Xli$ug}2MurrYT
zv`$Xm!(LN02YI(IkDh_UhUDjz#`F9VY|!&v#+fWCHA5psW5D-=7q={1MnRE)UZ#X$
z0c0ho&^nHq3f<72fcY2Fo2u&C*O~$$vFM4$+lm;}m=)mB*KFrDC&ZMlMvDMBqYQr!
z5ud#YI6C2r=Htv(L}b67Nh!*j%jJ#(DGb)>WPE%)0bv;9M`)x=vIsaC&5sSb8W(^O
z-rCRAmz&zxr_t9m;b588n5+$!QC=4F8Cr1?(~}P8?qgi1L%<j>l|cJs)%B2$ogKXu
zPcqEv$kcKui3yqS3dQ7;{O$Fuj?>b#lqd-)s&2a}06prspZ|dM?qyVS);Ia|`odur
zV?I+f4>;CR!#usLxa_89)S>}X9qcXK<2K>;T>URD-1=BJ>g*m~w#$9u()-?<!ei!d
z+Il~piTLgAhPo$(D+0p$@aGwR6Ho2w%)WLtU9;D+bs7=~hU0P46qhn|G(EQ*zDJ)K
zoJ?dOG%sQxic(`HDYVYyuSNdQf0Fp%cZ}b$V5ZMHBJJ$jGr9jfvAD2^l)*J;zkN~G
zwC)T?z-`xuz}Q#+$)yR3ps>N?F(-`fEE*0=QQ9y1Gp~U0L<p+EUg7b<H2HNkTOvdF
z(7=b`A-sfSkJU2y*E%OR!yyT8ZNP@S_dOu39a;rv`Qr=zZm@^0H?cT7A3PWkj`P=n
z8RnU6GMu&LK<lhFPsD}g*XtEA2a5_z`af6jUvz3|NVib&q9)0+Zngy9=3UhT=37R8
ztfviBu1jifnp~=95s!KMx})dRR0tDeO|X<|GkH96`*+8>RuN;>JkEuVU3T%Js6|q6
z`61)LR@)NLy<Z<nUsDbNcj(ktkL)ZV66-j4zIXeg9-`yh5FdVoc1W#{3VE9$|5kx1
zbLOc$Ogfut(pDV0Vh2tr^8G58%09fsiPn18&EOA~ns`@GPyn1|)N;R*+Eip`ioRad
zpN(~K0eBvHzCPc|0S70I2WiuQU?af}H49ZrcZ}e7Vbb_vIz0jIAmR5N<#P{5i(bu%
zAB5BKGMq0$Yet<sXA>hDQPl@wcRaKE`-{YyXUV;j{`J}=J}Wa>*O53<MQ0;a$d%Ps
zB26QW?VC=MQYPY{G5AUyuwz@l-b^mX<5u^a%~{9h1F&O_S`U1X`_B_jC&F4XyL)7}
z+T&6lIUP>X*HM>HsNW{igA9EKi3`r#0brQ8QX3_SqQ9^@J(F>)k32nI_sym7o87K!
zR`r2Y5awZduMQ2G43xzNH5Iz%Z7QoWNI@C$b6Q|%X<9U2<fSTaKG7~`!^#Z}zs`g2
zrhHco4?gS(+zoHz$RM@gw<QPt!9|U`^Mg3WHb%U^I};x+o{cNtHTL)+%9Lc2x#BT|
zrg1ccXwdX|4fQ!NHrGyVb>d0D(V}T-=9`sSM|fM&hT5&1tM`)>U1CJK02Cq-i;eVZ
zT#GYY8PdgkwA^pWvrzK#%94dvYXO#(;ChJBw1Tbg?y@cYLuGJD(lR1A;FN96{^$#J
zmFP*jgE0^~&wc`T5JGZv+D&sPQjKNl2`u5xvBvQ9#9yiErCz+AdcBfjn)rkZxQ1b{
zCC8m%;XKybz#~Zb?RFO6$>j5U!ttTOce+unq~}a}L+c2Y4lj&WFJcx0(Q8dE^tzi?
zW9tCi4*)NPLHrDW)m5!YIdlPo?0CRsY!r*X4AMIa@q#nNz+OhXd{|ME2oznuy{G%j
zqn{?9C5DXGgRjYNdWZ!)-2rISn6`+6D<SRAd;Fbqc&2VNexE4#X1yeQnweCN@nLHA
zRsL_NaSmH;@&RBv4d3@UcsvatzBkqQrnlifGoN`^UlN*WYF|F=M%SO$^*)yWvZ-S@
zR8Mir;IUIVXM7n5?;Bdta${fO>v4F@>LP;?o^$(Fs@JNyaFjSmKZ<xTLfqngI*BcN
z`BR!qKNGu0*0_;p;q-N-y1Pur^|h=bEi))N8jO&1gDE8UqfBF=lN*wW)HaqlzXBs9
zXSFp=3FHY0DA%THCxA&1&2RGYwg0OA`5~vOs`?plCJ5Qveg7+w9rQ%MDc8k3Ke*_%
zJh#+G_fzO;cd^y4cdX9WHUJE|l@pEUu;95^qM<0x;{zn;>@9Jc`w?jN@@f_E$APSy
zt+AYSe2;r1m&tEALE%hCB{?JK^`N+tI{z`qao|RPbA6%OoJ%msqsjfG;gJ4fz8!zf
zlx&i!6uyqT^7am(SlqVbRVZGqUv{jWr`glc1Eu$vTrq^oU1T`uqRI@6P=}IN2xBm&
zmYvxuKPJ&c^4;KwEPT@3$Nn^Ab-x@DnckU2u(?r1tqgg@oT3c5@ebTm(Z;K+*ofsd
zid0y&p`fIs2DVH~Y+?g-nBl9ZCkgj%3C=8+e<j-Eag<8&aWQ0p-mZz&L-jQ4C{u@<
zUh5L~^p|5bLFQfLOC|zsJ7mpSWC)Ciw&JQoe12P(a6u>3!=D8e1q}tRBTx9zsEw-*
z+F}`;OedW6els>A()*LQUk$3&KAz8tM%fvNy!3Sx3E|BXoOegV*0<<f^6ieENFaH2
z*DALteO2g+a&rt=qXzxXRx^h2;*fy6{Lp_+DC@(E<NYjVYc(hAJ^HlDva_3$dkz<<
z^0XeXcULw?)$N($?I^H#rno3O(>J#+P;Nsu0vgk;T+JQ~B_CH;8Qz2Op%NAbPk=-M
z8J9_VBVx!)Q}BSl<wcn@YVFY0`(f)A;9Ou}4_=(OFFG@6iYOVC>@-jhJ@FL;5_=|T
zDCWsJpol7Fa9BLi-De&C+!o5N7o|gp>I@8i9m*B?Aa_O+Tzc6@9+`wi0Gq~QCQ_wy
z1JPIuxwuUklz6;oc7j*DxMd2guGk@+&7+s0{e6)c9X*$~M&F&_gNIPA(5-wm{L*Dx
zElv&Zm~5uzn41G@>}RDIr)57o*Vtb_=DyyxkN>HRU_02GnbsO78Sr{y3iXa)My=a=
z#;n~XB|Mkf!9>XJ{e^g)mx>k$W<6hL1gv_(LQm`AcVhNXGg!)At2vt1yV_H3{5j#P
zYN{`~Ru>+P7nMvf%A<Cm#OU`_2}tQvY*|TIK*YT3(Du$WCz41vgIBs9{={W`YA$G0
zOXQP&Gdl?*-QmeP$8^;0lc)Fd3}vmi!+eD_haZ<mqctGKQj}S>9Q~~vK6E<9n+_u`
zLOrd&3{G)bz*Aq&8bQybx7>it5<h!iwLb0X;JowVaQ&w2tPg^w%KQR)a>j}p(!~;g
zk6Y}Zbl*6>G}9wQv-qC*@rIm<k<U*D{3lIr-c_|n4g`Xt^$$#+)D`271w{*XtBtyg
z4XLpY5xb(B&yxbribWm(_0sw<UAiHFKuN_IKlat@7YRFNZIFx+T$?Ou!<ZKTnf7R>
zGc4qD`l&lK;>=VG<UkpDuSar5M#Rs@LY?OUkHKiapYdPET?sm8fmIVDXly}_|K8tP
zWVuc6*zshkpBOTvTm-Xj7_xCNSiC7B>*AdMQ;_VqO^{jFi?-MSZe>X0#?|{TO%<0M
z8(TZUL%vARDl?C@N><mjD9J;w<|&crDRRTxp|2jjGAm3w%4t*qSjcP%i_&$e)>RPD
zn&fSvVyiar`V7R7RK?Z@UPpE1&*HAgW>#$_y$E>1-N#CczSzjajE%AH4>CVYk8*H)
z-UyD~?Acj5Gg#7ayBQ9tII%}nbU5B8l~%=)Y~bQkWlNRkjg3Z|P)nE?yM4&J5#O*w
z7HGD9aI$(eh>dK$+BM2dl@cclvFogXtYNXsvfhrXoYZCzuvnE$Vhtr{#>y2LrO%v4
zSx4e)+I)?x#2$5hi1e@GMC*2#4nx8=ec_iT=1f`}<%|iE8b1#WH}g;kxC#WL=DDxP
zbgP=^e?d4S5SsvYcJ=AJZ0iivs6Is{GU$x3w*s_5M4nL7dm%Z#hrM4qp7)eAA3eJ*
zK!%(2-)L%4!buxA<pv@&RZjp;4n8s9e4}$nY+g3=5IB4B!o=&w<W6=IgYHKnty+b}
ze1+^s1#g=%f7=%TW<@Do+pUP7{n{n;RiC!qS?*Xxvg7Ce_!JzoUZxO%AtqfeOc&mp
zE~fif=w@BmW1fg1FWP0HpWS($-skCXPJB&`Kbjf!9A*I_6IX-rrj_=klt9s6v1)!&
z!>fLUPgUD+{*+pu#0hr$VIx6j;GpFf<F1A@-jRmjmeH(Zxg$pClaXGJcb>T1-M)|3
zaq#ygbKB45Fn|-@yNQ$5@t?Dw75y1pO;#5n!Az{$z9-X(l=vQ(In8>yw~r!zE9dMe
z#kcM};;O|D7IYPCHAg5uc8#(lfHZbWvm$FopJ9uJVVvB|?j`CFZZXM&W(qe%_wQ>J
zq;6l~%OpYA)gSB*Yr(yE=vuiLXh63@R?Wxnu3u-&(Aqdln*di6eTGhJvOm@uk*6wQ
zP=jp$AlL+f6EuX<;--v}A<rvZvv^cIe;DvFryI3E+*V5oawQ-kp(22rOlb4na;YEE
zQ7IqChtXQiKX7G__hS6i^RSFTZ(La*cZggCFWC3B*fWhwUSI<B#UPH|WFW1YU)36Q
z*Vim>#2Jt&Gu78=PvZ-9F&;U-b6$aCo>VUOEBe`u;nOAP?E#I(nZ90j?o(X`9BTQ1
zkEeH#H9+e?sdV?z52~do*$iUNws)}5Vpq5f6S3DWa3$4EMIQTt#q-R+`xjQMH^eW9
zR45tWPWde(r^)khDi)gH)`bQuon@{X>v%(B4~HW|ZOsHM<Xwv#A{B>+jDyGh#gD>-
zn~M1@*oU>sL<qS*U6c@W8I2k)#TMP4lax0ym8KFV@x+B&n@{OxBqgwSF?e8X&g>vI
zSRMYHu0b^A!y-tL#bhoVb}&S@{a%%mB@(bLk7gyhh`ofmMv7#UMz-ZZl)Kb2o6aE0
zo=KdH9P>oZyw3mip;>XLoZ}=niRSe&w6*(l#+gcOxT<QLqWx*t<5?V)ddx2y``rLb
zgk7*!kEWw}CiL;=7sG|7Q_BZt_rSo%RD4?PIVy*gg!GkkES7g?NJ)HNHJS@v8c8^O
zqJFTHHoHlUd%mkz;h01v9Hev+B2I75G2y0$uiE6^%TPhvGgG^z73=AhnPw52xpRer
z_RoRS7HVDlIoYaH*p+FZB33L+-ciIK0%dd3x&C`)Lgla3wto|%7XO{S4L_~|W9rkr
zd0R@12_4cQ6)|!&7)`lJcUPYX<jeGo4r2dJ`eEugL%NE>%qDS0h41*Z)+*@{(TCE?
zr!!-gX48kDC)5Z#+xN&nb{G-R(&&!(38$8IRqfPEYkqBMnl^t&w~4I%rx!rh$<u44
z!!ZNaYUt|1)srs~bz9iRRsX=3UWJ8q`L9YYmI97{ru}FctgD)Puj*4AjxBa&Kh8K2
zXmtAqmFawljG&gHNVD9W7s|8qQ?HcT=_8Z+iX}ecn6?s(>teRg4C$_UPs+zg2LYl@
z{(L=rC2<(P!b~;i*A5_4M(6NBcjRY%apIp*lr&H@IKQvYecI%_?K?giD1l4hEx<1b
zhLv8Az9(OX<ZQ4L4$y5;NgyW5OpSB`<MDZ&%-I)M*hDD)CK>QSFLpw=0jAo0jU5p&
zAhQ+;mc1`|nd&u_m*rB8U^Ducs>Suv5z5mB44wGf^U@w^U+{Q2`bFLo(Ma?XVsLZv
z{zA0z%ey(xhjB@#lVA9BgH<|zu~;&1FgI7*_9#KyKqSJ8qv*}(Z{NPzbW0mY!pc^!
z$J={!H^@c056G?oryBYxNtq93D7x`}Vo9zzN8Wc9JOGRR5R5Cz(k;V{B`Z*2**LMX
zvSb@(qI|%1J=&7`$Lu`%Wyh%nm-q1<99J!FZc4JN<s@w~<O}ABYx%tpSRH5xv4aYg
zH@IPldq=}ttiwKZvMdRTl^%7xV@isE?c?Mx7h}b<$xbY{dExfaE}>OVX#Tp`A!7bj
zk)%ZFNBmhd*kBV!jig5TO#B|S*t<Z!#WSq+@8eN1Zjxe2Pg|b_{oFWi_U%Xw)!XUM
zsZDq(vmsZOUuD;RjTqW?5s;5=1mUm$DJ=|XbE~h8ul{<E?;D**uSJp4_Iu`IjstSp
zW4<WAIObZPK?xrXC`53Gltk}9w>~2w_-Qb~&Ca{Vq@1FkqUln_Sb)L0<V>%MpT))<
zJJe1RsPevjmx$ZBt8rMHbIk7U|FPp#ws)C0Ld<{Ie5G59-p}e|X&6oP+Cy}T9c{Ru
zmM3I+gRK1U#bZBtLYL;jE?DH=*5V>==6z)7uU2&*Hw-kX<j=xXmJOZ?(JoAUwtN%T
zf9wnnqVki?_{9h@?^Obt&h4)|NV_|kD{Ud?aPw8iq$92Q?vLA&0{7`B4Gw#Xtz5=3
zh|F6w3EfZYLYitWmC)h6L-IeE4fZ_#OtbmJSsoE)!c%gQbNt0+OQPyWEFv`_Ur)!9
zO_Kj^AF`A6{iz*R#p0z?kBr`>2`7^91qa7c<d9y*W{dzRBCRda0xSXa!X1NqaWJj|
zs@-gXfAlckVL^L52(1|1e$VE_BpyK<!N|81N*)*X&`==aBL?0B|6t=$eDt`i<Ak(G
zuZ;>iLIodT5^F}_07-gxhL_cp0_Z(cAee^NvCPX{AUW%5MlXqND5uMk==+HJXptF`
zCma*3(G)dabR9NVer=8N7WZZ*A1xQ1^h=(1$?wv(AN$wkvZ`$|0Bj)gBxpklK~+%!
zZ4;hq>-x5PYS~>sc2oH){kb`S$swN-W+clrt+o)hq*!dg1v2@Cx`%>DJ!GpM)2thN
z<bRWEYjf>QkLM3t64d%O`GXPjde}Uzo%5Q@n@4-?I*Hs+Ip6iWu9kCWk02IEz!PLu
z-%hQN(Cwe=mlE>WYv`e#&abBO-<m)>T61Z122%lvUUrapYSTls`IDVwg5~Giyxx~o
zxto*K(pD5*S$8(|)wGHF+pyL^9A{zz=hwAlKhDv_odkZ?d%g0UqoPYWaoQn7{NLt|
z>{HKAV;QTNjEG22tGUC^*7&WaO%s=cCMTZ#u-BtPf41F*Pq(dI%hHnwJ7)2k%(f>d
zCsLUoulH}ShD_!Ng-`MV1=KWJZgLlA8HCgcvK6Lgl_=p@;TU_4O8DH;!5&wb=p76T
zK<>};VwXCUZQ~+3kIIl3J}~6oa)gT>PDgW}%5DLvs^sbP^mHowJ?GpX`Cm&n7Rv`b
zsnAx^VcfUN6#b<3!<Cg8gc%${thkQfJZ!H**?O%eeCGzKZ8NA5GWw9I+c&^IY>#Sk
zUK-6~BNb6dQfK=)eLc2W3K`gT%F_<L(05(+tl0_wzPcc;?`|=l_t@3bv*qV^8cEQ%
za~8Im{K$53Pq$fr+5Bx3|GT8}A3KQGIiPe**)XKN{oLU=t0#kgaS(41n1RQ}Pxt$@
zmg;fjqFg}bIJ8Uh_ULL4BQ^J9;`~kjlZ)ZOFKPT48BVcK^_+Q%r7?HKr%Ie;{0zT`
zvI=)0*_WT$l#mFoCvj?C%^t$~(r6ry$1eyz&-|N@0^LptD?6L1H`7N3KGRtPUX)L>
zZAO1W$>nuaWR54rvE)*@*~i^AmE@;UxvXbhR@Dm{1XINcuKm&0{s@5B-uN*xpcwlK
zNWSU1j@=(EN7(&lzJqK45h)gm_i}T0Vx!y5(K>w|vFOOa+#xKQLKGK{^5oo9U+!u;
zwNsse@_9>#ns`@DvJ!J@Q2GU2sIQ8)#>>mgErB?}c$@|7ip%%B-OnAUomuOWER{k*
z-03wnwX-#>O4?0lqSwLKY}6X)+Xxf^RL~6@!*fQ~CSJ(zcBeTUTYZ8OW21#}+bHyh
z8!oDwrX=HmDp2Wy<su4v{$T$UhQKS~%K7D^IC28VjDUdS#8?=(aSRHH>u`R-?Z?P#
zXD4|JM)%21B8+Uvt%()x_DqZp&1H^r&nkX*{rkywH2m_edA;?SR|6BPsoFanb;U-x
zJ(kSOqt*U<RgumO1XW%j$Oi0Ia8M%rxybQW++w#D!$(xt(Qc&hyNY5=*K_%hzAkE4
zrw>K}B_Z)OP-C>rE~Scs8?T-&q~P;E{RFGbn(1|F(9oxiObWy@fu(G-y=j}$1SY~g
zBv4virG7UY#u{MaKI7zWO84=j`PJUI(~3)8Cqs$`a5VHraiYOQnC4RY%4Wk!<Kv2@
zl{vit@!s#u+QsQ!<x9U`<ey}82OVS_GJXZvy<9eU>G!W*+USnb=nWLryYHXNtsp6G
zmd_MLZr%ANUO(-QCHn=A5_H^iedKGrnQ*!FJYCy`>ai?bs3~++u@WnhiFIAsTT@@M
z-@y=YrZc{kB4>04>OUDv%XX#kN`>`QBB-E275dj}aRJ6es&>yc9jp6yUKa3B7+1%W
zr&mAlM!&ShMW)xE-<<z?N+Ol;Wr=!m?lg%Qa&Gm%{VvA(iv%^fT*8#^0nW_U{~jF}
zubLZ2kj^^PD3LCQGB%H|ZhLqz=FCY;F&C<cAgm2!`%DSI;F7STB#ob&Sy}M|r@$U1
zMhY~FMG)K{TYIIVdoM4|>BNf+3pnoxo(cQSXct^|iy%HRoyUT(CmU^jz%UZ8k-Vgc
zjA1^FAl@P8^i74hg7(FxQvYbgv_X~82b>D#L4;M;kLS0;e#z?1X8@nzO%z&EeFq?D
z@P`Hd!fp?fPD{U{(ir5FE;dg~cEr&DTr^rl<52-fMmR#=ie8~1A>3^5DJez$1e`)*
zu>M6hclZlNg_2*D92V%gLc-2i^g%mP&fPh1{$FbNUqta|UvIQE3YRf%>3`#^|G{3z
z5CU!X^F!D_{eS!|1uQUe#cq8%WW@Y;uKVpP2}c0Lr+!2jJOB7^l=R<rqbOkBgUiN1
z7k7UBPX-wn^Lf-SptK_v!QQtC@ju!Xj3LQ_<orxjg{1gTa(xdD^t=AIRzB7=H@e-$
z&jl|u2O_6Q;axGbVOhcgvNdR+3!dKN7Js`J1M5RN-?^b*SCei~ak1H992Q2dxcN>&
zjt3i|wVOpCfkg#@7<X`oGR%^jgY5PFrjcz|4U6`S_(u0g-)IAg+gA_)#TRwyx5j-$
z#IhJa^23x_?(QAck+#_y7Puu~@5V*VH`YGN9_@sU4u@-Pq77Emr4j-Ej2+y_N~EZf
z-pOzgmtm4z`{?LG7}iOYvTa>Vby4MQ97vE*a8d}ptV#?jr-s?k6bmV8ldMX#!$owK
zkA$UvN5gV)EnCp&PjB{pm6P5ua@|`xb9dJpW=#sLPRy|6UGXAz!wQGAl7Y1W31||g
z{H2ZC$-FCQR=Ue+uVfgsIe*=;v*e7c-P^9KH#IpA@rnKlpD)iu32Ym9K-d5FSvJ2e
zvgcx{?Q2-q*K!vjS#8ZaECY(%kYP~WarlROrt9M*{5dS_x552tjA|!LB~AOfuWLn%
z)6%xqd1`RvhJEQ|&|QYwV=QA24h*{%m`vf{M~Jct12bD}#%qOaaPMzY7xpQ8w262A
zNQL(G7p&beX_xUr*(#xudHL8%4?!was1p81cDzgHPqh7X!R_@vKa5@Htjo79eQ}@}
zDrPh+jI=O~7gv&?UR9;$>>w8P9f6Su+8VNDh!}e`m?YZefqJ#SOT|}xY&K&d3)aAX
zsF*(u2tlku*@QRI!ZD~Td=HMq(Xr6-cYv5eyw8{x>)fawIBkkNwzm5-EmuP<k&f6$
zfqOCk63TZOI7)5%^TZ$3r`~>SP_;}`TQ8X?>asWQaix+lGcXX@X{&35a_i}lqt(Rv
zk7}d~(+S%F7Y8HHOm5&vxT%ao?*@#q^NW?(An#=9Q|-nmd+%v(J|;Y@+~S7*IxW^1
z3wzGfw9d1VhldAnOmHT@$5yJy=}Pl<>i3-C+I*~d5j#7(uMg9*K$L+&PE1Z>2I7dU
zd3o5P6?%Go(vzq$`n^rS)wnBU_dIr_mu$x2C>4_--xMYAgk;N^)8p2}7_)CM`5J4P
zw=C+Z-ow{zaMxN;bl#Lse9d|?@5SVSx)V$(*l@GwmSd8zv|~*RZt=3;Gr9CU((ws=
z;A*P)=qjz?p&%ePpl7G&^N-jZHD(@yY&Vq|m7A~Pd=p5@boi|VmrKQnlA~u_LboR#
zSuG<T93fn)*WtG4jH7ejVGw0uMhfeOvABM)qxC-N<y?IBRwCcwjPgv53+H=R5wUWP
zR(t2t@Fj9vc}@>&(%F^E@ALeWDv3uLyI&gH@wTmzU$6$T!&KL-X>aOWX_hBuV&W5~
z6^noTN-re*NZ`Jhd2^VVmX_ACzQ-oJxKv}QAtu%ngi3yQ(oU*bXOmq~@f~1$JszP#
zZ(g1s0gi{&@o4Vo=qRJYAGZtuxIXzoVPaubOrR=MT3T8Hl64vynx7?&WKO_huRWxH
zD4Av1sWW|YZ0w7&GP})M8z4`)Ih<v<J3%7im7wFV=-N~}2OOz*8v(-yXQZXd5W@;p
zK&D7Ep$lRLmpq^oC82>K5vs^^G?~T|S=&ZWJI@TyV@f;z+9_i-5nY9~5}Gcu3n#|R
zX4PYaxEm=F58LS$d@t=yU-N#^CU^zus2!oV1Sg&~BGl`3dzBO<JY->8+BsjXn&u!{
z9v0%VaT>Viqy6pX`Joch=@V#?;7@5@TS17yOUMr%ou~5P<q#(0)lz%7K2R>AL*4QI
z_s5qVD8!zQtFij=ZR$k;4aHAO4ujET9>!G~A3830kbD6So++hQF>!^wck-hT%R6sx
zXn4M^);g(5#k`+f2fk@6YHgC8H!0w^Tt#~R|JZu#uqe0o{hJu+?(URs5KuZKq`SLY
zy1P^9E-59YW9SAc>F(|h-&^<I&$FN3_x(?f!x@-0Ypwf=^ZZ<8urh-f_FJ*&S-|)?
z!1`k%5(W$#U29z2mibBW_T_FfJv|)|oxQ!8GZwBFH7vm`lz}?~<l~iq8z9$CMrQbE
zzV`A0>Xq2nZ{LcE2|V`l!qy@owVYSq0ORh8<uX`zO21@xCDzq(wjhDrfni<Tkbt%$
z2qPsqIhKTYrI7{v2#EHfSf+0WX>*XWAvUki?ss!8D>`nzS4uPeq>m*Ld;?TgD=G-B
zwG<8kV`29bAa@t`8ptXp2OEe~TTT_zL!MwUGofLF44S&^$<0E~31q(QE`{@&+V$FO
z5WvO`Iw<=y%D~SC#AssK<Apk}0U`-!OpcYhEz{xFiIoz}a(cKg4)T{0gp|n?Yi9@y
z-u?}9c-3Xf98aUjultsNul4>WN;`xfX7K78oUy_X-iIi|Q14@wQ0LEcOL1mU@s+>!
z8_|0h(qVd4SKs?r3VuT-^v)Q_bL|dAMx2}_*qEko2zVttZo$XOk1Sx0Li*PG{$d+!
zs->-c+O(SuVY=qD1laQ4d7AkfWjCP746-mY>wUMH0fxns`rfUBC$9jQSR4@_R1p#n
zq+Wwv78qdYIMr_&FQRftj^BO)*utOc#Eoen(5g=y05M^zga!_|;L<PVnyD`zD1|dF
zXaf9MEZ<ykLbw^(aBp+v!HK<s9GHVe?w<%S>?+(8NsC5MSl-97L4Fi}IhI#O{|2xd
z5{3P@`)S!h<P8#Y19!(`#qH5h@9BpT9N8$c2n~H?9R+#js8`ncYDj2g-^7}I)X1?M
z=e8S<=hfmp)I@8ZPscDI^=Hii>?iU55AAmwQNl*e-uF&-s{UR5vBaY9K0(E61owQi
z90oQ;kn1E$^q85l`+IfO`#^~<%io4HWB5$8kSU$_B6OrP)jf{Gju9X$nI4BzOj_@;
z*O;{OfNql|&-D~&EEdGQMNliL+@kCr;<-u%MM0H}hL<-iVXX8X0dX?L=P63k+#O2G
zM?!2LV8)zlY+(`WdoJSyBAmCWFhD^m9gs}EtO&`qk3?QvI1PNa1fhCxaFTQaT*?t9
zH>j-nENPTbddM3w2@c8#h-h`9Jak&aE|KvKsr+avHQl}8;`T=8{!I+%NaS}Lxra%C
z49yThYWpBaZ+2=WJKAldqx!KJIDvTgOhPk95Wz^?k6QO>U&=G@mLDN<K4~P)JwIL{
z6-5H;Ro>Hq%WGiA-FAdEH9b8IVQQe<g^Dgi4<Gcf5ydhGGh(&|@m;_^!VGajtHqUR
zhCIJc+Pcg4oKvsarS$k2F$yr==9nu32%sFFo3ve~q`?*A42Xhl5yyD}9R&r4)3)38
z^FBh0Y}R!^&m8e!^?D&i!KZ#UU0W~%jGVC^RK*#!S|b|C({Lu_>J}r}z^XkUKuXW*
zabXf4d{FC_LS9gk5qaj3lpIVBX0+mMPKMH;Lqy)}kGsuO0p{Vl)|IA23aOy^e?AWq
zi$EDc<sNWTiI$$0*VGI@G<~I~H{m;fOSnAh1<x($?qMo+{_;}hOi47wzOozY>{zJI
zGB1seQju6Mr-tLAnFq)y;2l`J^?ReP17Jz2BJ|x1LINqC(cNAHaLkv-(=e#E>z~@Y
z<2k<ozNiC|gz=S)4pDRybwzX+2G8NVd5*Y3h)DNLUZ;0sp<{a1JHHoT;(TKrp_pzV
z3;!-)QqtM@MKt$Ovy3;K!I)g%ou7$}ivuToBk&dCoa->t07*qED21-vrYJOKJd5yK
zH(%a-)#}0m;RM`|d`&1;wn%t08j$<JbZLP^Ormg_{XpwcNa*f|bQdOIR1rQ`JUesW
zFkS%GFRP!37NBJ7GJXusuKt8UYL54CXSNN?W|eY{GJrS{4G~UgJe*5)*+InhRezu~
zyg^XrEn+?Vns#hi!MA95R@!bhP!{335EtaabZ>%#K##jV5j-r7t~CeHn$XG-I}F(+
z8;aPp{-WS%<*5{fW8ly4cCv*rgLT8ua|9fZAfB!$hoz7#X05sbVl0Ap=6luqZKb7y
zh0=^Vjq&kayw66gnMp*c*ku(#&x!B8Z5kic1gXQFExWA}zwQo0i@dEopDlXjI!N(8
z!$2{3EuSS=!Bqj%BAs)?VO(M|xq2-c*$vxhaL&H%T5awqoy&Tz^bz22*1qxtRCYQS
zvh;D8h~g=cH#|#t<K~<mDmq~aN7tqVxwIS-9ynOWJ^>-{@86#HV7l_tAlK7f?kHiH
zQM3VapA%TIN4(RLd|*$xp!*koJgak$^u*TfsdM`);|YL(+uM+WaJW))K?k&>I*N+q
zFW?ftGYWG1thcBov!^d7r=B=Ln&gWJ#$utphInO2rXgR}8%E5g0m~a2Bqjo^bs!X9
zJ(}n`T|_;-8hL)##sGO@GP&ZJY^zmBU3dJtdXHZp-kYxF+0hY2N$Pf7EenI2s26x!
z=O0cH(Q=RV1uReLL>uqmM=|XUk9us#k6Ha33C-j>Z4+r-I!z`MI2ovP@Z8PJb|guC
zf>ojrV$O{q6mnx0xifC^POwC$u~{qzQ;3EL^&(OE{0Fja!`=K9&wgx2WH29r6u%$I
zNQ+J{r==JCpL}Xvg3JS+wE|`XWZV5U#X*gw<B44Z@fq_q9Px(nI|xJ1Y#lgkte27b
zcS@oDgLUw#5*Ol0h3GoriogKZJ}!b9WWyk&ZhOasZC<l|aqqbKyw@o<=i(P3Chr~S
z7cuzd227iJ@@8!bk#OXt-a64`&#=q3G)r?>A<?WQuMhG<6DGs;KduF#7P9ujfsj4x
z^+uUuM?OQ*)L@M*O3-l=f8-NZhTE?o2Fr{_Lj0_0gt#MPS*yMBPioqnPm{L{{`~5b
ziHLTZtj3k|xS%;R<a;&IaHCOy1n(q+JN6G$Ikbl;m~v?BKWXS7pj-`0f#AETeD(jy
zDg7zXXh4Z65TcTX%DhyYF-VO+-nHlWK3Gok@xHd}rrH_JfPKZTgDCMZ#(&Cthg66d
zgL}ZRKzS6dC8omu{fJgl_bJ}7rq>cjBqZpZp|X`7(4U1fV;2>Yo4MbJbdS7Mtu4oS
ziN@sG(hM{<Y$D>bcB8V~EANq(Ko7a=JPf92mPsda{I-KZYOq+F5*hEI94)ig>`2Zn
zkR~|J4UbAhJ5q<^9XM6EB}6YVy6K-^dpL)LFfu4<O#6xF?c&i`NP4p^8EFtcnP&}=
zWbo`&$ID?yBz{v<6K^siN=-wWcgYKj-@ObyI5@y53Fd>xUZTBUlr}G)fN6hlg3;BO
zug$o&D?gxy0g}-F5v`Mm{oWsB8?cXnb|XH1Q_s+@q*F&kf1P$O?T$lK_!N-nL=aPp
z4GU`-2wPNjr5M!HHD|qP6e-Iycc;M|Lx4{gbvp}5t^(6_*S}+0FGWw<_Nc8^!<d7C
zq#@mrjlGi^W_rvhMzb6=R6w)AIGe%MbMIspCD4khLre$?DA39{Sp#N(^@+UIYyU9@
zOX?keQPOfHB@#;<>X2WI02ykQaW+tli}35Fq2u#w8jk6njozs0;DD(FZwGK+i}u1g
zPBfM#o+-A}xn5{xO(QrA3ht=UM0EC^43~q*VJ$7cPSn3iCVd8kNt7WuI2C{~JXcM`
zmy%50H<=Yt-z#sQt-Dr@hj7fyZ9YcisPDEq`P+Q(pHj=81%reAEwe|?br7Gd(n+vI
zhk(}$!H}sl49EF&nr5Dz=T8e+jFZo7M87Dx{H>}OQ8Lh7G5$^Az)ZRNW~DVsZ#8Od
zNL6)^ia<%JojgGC7}(2k;Je7njqPg+t|eECiehi^E21jkNdKy`g{SS#`{{#3Cs<DT
zOd5qv;uy;VKS<m&L|&%$Q(-<|EF8+XP;?Hf8+qhaI3kbNSGihU8GnHS38sefS`0|t
zum`7LmS=XolbQ(v4zdP|yEE-@L4`A6Zb<|h`R_u84Wj9~qXPUtq2P*psTr{9=*3cG
zpZf5>^TXkMkP~xn;qo+T1CMo5Ywvu{lGakwCQ9=x{lB-0=<i+gu-;GV$2fohDKRWw
zURNE8(`7E!O{E`Bitu%QbI5~F;r##xX^T<3CDq=SY|kOAV#)}+SE`~u;`JeVBK*{$
z94hmls0^{>`IRRf#OKJm6J$Qz^fFD$M8v&%rtGN;!e?jRa`e32)sL}>t!xyMw64HC
zOCZ@M{GKN9L!R0q*@vN!Qw;Z8xQBoA6XLGeK!|GoVftvD5bYrpBP^@l93!b`zyl!i
zdJRLm!AE(J2=9VsriLb!By>mvnZY$Sc?Wey&T$5tJ<`uC%97tKnytA84uUusV~2hF
zsu(Z(6{GVS?Ra|N;B@f+F$Rc11Z+`*>5^zHk|2<&>tAUEy=_%5sT^d(rben6JT=?c
zn<zMwo+CcOJ;n_T&R{EJe8a@#ED~3T>fHS*-H27lDc4&hW1IO?+-36Gv5v?q!D~Z$
z`atfL4kBwRzF7MNZ{jqk!JkH$-cdwq2uNOAlQ$co(ht_Fwc8MB?iStd!Z7+4Fc#TR
zswS;e5dG@~D7d{|OUc@f_o1vZl5njXPa_x*+2e^3{x->|VpA{-ndRHe$C!8TCwB<h
zGCxBR?LZPO!9k1_TdTN`Ap0JLpXIj|$oK(vn5!{5v~szRazIr_=nO8C@8gA)m)DDd
zzS!-WwWajGPlgbg$0|u~3fk*5P<S~S2_8)i`Ahl6$7tHGhGI%co<Te;N_jS=A$pPd
zbCewLFs4@;q816^A;ps+e0i|e<lt1R8;FbxtRS7vt?HQN0W8dZON~s$uQA^#(kSA8
ztI=qbF~rJoU=1YOn}WH!1IXLX1f^QKpC55M?m`R;i{Ia3=HF82M427V=fYLRYFl*V
z8nU0K<J2Yut`{9G?cl7p$U<`84%Is(bvr0*ZYRFxhJ>+gWOIhrl821%q}EG@b{AS3
zcY>+@Nj7JboZR1;4`V93=^EJIU%P2+ZlwiW0-%7M;$hNC&!Xy;hT&X&tAnp@t2}kn
zyN7wC|6Yo~Key;mAyGFXE{48^fX%!z!k3VZjp6qO<^!y)y;VAVx#3mPN^DZ$L5wgt
z!NQIts3f)Ad0aDwWr;X)7>iW>;b~5|_voFNj(C(Yvz+g_5(_Mc<ii(icH>>^_8W((
z6Ip;~=4)Lc{{(N_i0@MeCon<d0fIFeYjor60l}?-e$C?KuF8ws9>qEroTXhtb{)^I
zO;PU5@OU+f9i3s$8IEA?*d>X>Vu4m%#aTurg)Aw9Vu%k(GBg;b@x{Gy5Zq%4D%s3G
zEe3vg&9P`#5|7OorTR)DLHZ7B%o<b&txArEVYA89Q4$8!JbMK{CwdeWnf{7pdhc)R
z&H44eH$)aid@E>92-*+xgBkqgFwb<XoBovs_xG;gUevUUe5+8)Lz+nD_L|I(Tc@^*
zjs&bY7i<Mpn8CR9EYg=GA2e7bX<AX}vEQ-;|5y^YC~9rGO3BS{dgZ)n%-o&sFLaTI
zh{veJgoL@bmdw(2g^?EQvI8m1i%-B`H@YD%MMHi@5Q9r<>7OqL`@U**^=XHvBKrq>
zbc$|!50dk37qn?spo5Nv6k8^W!u4|RfUtD&D@}fX4hA4=qi0X!m3&(4c+PmzH0a#6
z)_>G8d6?0ABMz}^-ZGMAwJPuX{O@u#ngCE8_gbfAbQiX~lOiyT$MiY#?BybO2||);
zU!rC@Px^rk{Rj{H3y&^htI=c-V~fV`yDZp{4qvUhce;u{B5}Kt;y&IgjGrfsf^4et
zQO&=23ug(U-b_WGj_xK^D;uG{X^|3s?i5g9!s%{FPqZx4$YP`zV+q8PZIqZVHq0}d
zO$sP%xj9<%q-D{p{Q}j9RD}dMt8r}MaLpwL7QIr#T-#z$|JFlt(pB+<Zs2&9tVMSa
zO(848l!YRPSXD)Fgi9CR(r0(c{1i(Uy)Kk%F&BQYxm~>7mH17Jlye5C0Q~0@ONRq(
z1VWI;*o5N;sBmP`q`10)Fq!Gr?CTJ2`TAlO{`0eL)M0A9ej93WCr&Saznj{edFt*I
ziL+1NA>^sLQ1O{*sfcn6GeVrg?RbHs?^sPG3}H3Laz_Yj=8U@{^<;G;P-}1wj3Mm`
zfXBBzNe{O8S^>q1lR19wm4Xe)_~jXb0loN@Ys4j-!0n+(j)KoTTWks!%vr!UN~qel
z%o)t_?)>u_vsb}sFq`>^8K@Z~T<G{9B0aq9I9~Q-3l<cRM0A$J(b~(Ux%Z>+<l}7)
zZ}<N323=*!zvD$-GzF+7#EpPf%JvErmm?VjDFdoh4An;L=$xu$5vW3Pdl7%b4ykrl
zp+<^Lk+{#^_yxcuBJY8{d<Q8wZl=p=IO=U_tm>HSK)`rF*n9nayGm<&b48F8ZG-Z-
z&D@!m@UtoE9Ed*Y6B-=rLT4^3&L!$|xL)n4NG0S+An8lQEDC(vKhuMTYpIN=z1}N`
z!^lNclPz={iWhwhzTm!z_x}jZ2*UF+iJf=jB4z_AT+hdmp?+F*6M+`1us)_^g?d(+
zN)~)@IiBZ`OJTvrN%4GnfVC4o1tcGTI|zjm0j2hwTPqr=-z7wr!b<g=+G`LV7mI|q
z^7>YIBnIYi&U37{27XJr_*!C>Mraq`dr!TgZ^mU{v^h)JMtX8E-K4ib`IQX~?cw_>
zhSpek!BL^y9yImM7Q5!48jN9rSE(%)kAM@gPL3X)+^kPzgw<O|{DoQo+wR!rS7_-)
zp3ee#n1r6swW@dOL|Eq!rk71LW@|ck<tSuX43HIy5XOTTzfJc_y)EI(dL1}Hopt@U
z*%;+Vud7R@eW~5>zL{8hI3Cnp!>@JH7jg~|tzRvnfKi*ZBya)ol;lpaYyD3U_W@{D
zd38B4VZQH<c>9Bdx60<UXP-x6j)g|#RRT}18Y5?C7&H<*N*v2KT`-M-YrA>6ZslGQ
zD8-2vTl8`+%DQZ=pWz^FaK99^o-pxozH%77Ws-(bJT`6vBhoqu!prbGAo92P8vEmi
zO@3&I5(Kg)ie4xLV2adk9g2WOkrM}*IR;R}yao0E$c$fk>=OlSepE9e8RudAm)xnI
zp2XS&f4Fj+Gfm;OOsZo1n3nF;c^}I+P;h5NqRTiWkmYrVXk=&D)w!DKL~m?*swR5&
ze*Wrp(fiN&j1+={+bb6(tBQX!;dk~KyHb4*0l_dA;hUENyOnUED27&EiVFG|Ohn-O
zJm>U!zWp$neAT45N=By3nlWY_H(a7_=!^~HgAMMHqB-a!S|Kc@vZlkdTqN#r3#4J6
zoiy_!BO{o=D!GVi(4b1$Tu4ifnHUOmZo18P>{1+DBUm^o4}fOSx`=_pzBWll@0AKv
zT;fKo;ZWVXRMxwtYIvmz9s=>m;7|l`M;xNX4{F#5+fs~TTW+Yabh%L%(+Vei4LdA4
zf-_tRkLW5=48{HXV-Pu`utq>Tp^;!iasI+S>+$TDt*_R*$)qg&E~V9u7e^lC-*ZF$
z+nppEMBf`NCn4lrw`~1+Ihw&k>M@aW>wfQg7Fm+J<LVp}iN8=vfrbK_!y7p@V3Z`R
zM{P%dg{q!1)6~QdXz3++dA)%`%<oHT_X*|~*bQnv`SfnNfBhRq2VaJ|pH}^;gjCna
zQ6_BmebybZyj1e|eS-a(=_(<q5))I!KX>I7BNT2r3({yieWcuY{c6@vvU-&isRnOK
z!yz8{jUzIy^O!H@WTj>N%htL;6afbh$&J*{{)lYJc&?}6T0cy8Cpw5>*cwM?c(nVD
z*^6->|M^%(?%!S3AN0VZhd)FL@pqKwMDB0jiqFc-`Vwo$ZOVzx29k*B0Ax_$E<D|U
zSUj?Yg#U)G!I8ivu7Eyu0o(-fYj9{rF}BCN@0_!7$X87Y+ymqI<U{)>BrkDR1s%@f
zAvNcd%ttdgmB%4tlW4z~{pbE*3-X8Qj7*cv3;q53ZODX(g1t_f%=agY20E(IUdXr=
zBCr`G<WfgIRA>~q{%eP}lIJ2gv<k9)R|jINt~dx`EWoq1RdIB7TPzqH3jWN%^c1Wn
zDf2%cHNgKh_zn7>G^`OGa;)7Gpl0w5MJ)m7g|8ab8^w#B=z^ey1+50}dwN*1@A_?8
z3cM~iUHncLuoB}$$D035<u*_uRsA<l(@J}RPmiVsay?$4K1$I;0bHItBWYExUt(b6
zz~?pH{V2z~tU=|+$6w0JZ|oMaymguWodQ7st?i$df1KE0IXInm@A-BKw0agUVsVf>
zk)X}3p2tzRPw8(v>wl8SH{yWe;0v1NpT0RW2w)!@!DObT4F>G*C}B>Bli3>t*b0q-
zg>Q<A|GSp~9S0WVGV~I?*q^H`5itP3mvx+VAp(k-{nd_NKw&cCRhG_X-1<apHt#n0
zo2~8FuST1V^c+TW8eDS!{q08RK&Q6)PGy<~_?yC+p+w)jo%k;7<wp7A9fx)A<!TA9
zQ_22h@47Lq$@W(Bu*LuQpdo?BArS;oThU*;8%-PTN=A;5!_vxTzVPS2zS<|U+;2X!
z*)zc0rrVQcuY+lNzwr|w3&L^`>pxeY+iIw<KLPMk0Qw}Di7QQ*MoUZUugNF!l)`H8
z#dyXhWa{5^;ENq*hYTE8g@884F8~)PXa_$U=mE4xaic3sN;EorpVzy2UM=j4@C&Mj
z@PW71r&d;0lx?l}|9P_g^MISA$VE8&E~&4p+h#VJzOk_ZOX3c8<~~|#x&-(<M=+VZ
zj``-0<0B6b4?yYPDXQuXz^utOeKHmCa&_}2@q0QCfcDy{kU6>sYFA`orlzKVl{CKN
z+w-<Edaec{z=3ZDItoN;oj(V{M3u;xn2skTNk<0;&Ss|p$#(nGh0Mu{&+RgR@4itV
zNf>`4Vt|)7HF*RG$*MXP+oojB%;5I-_W^vw2RXUpI`2kAi2Y<H?LAX~F5isFwPa!a
z_`jbBJ`Omzcs@Pfzklyp>uf})l;CwYOJNFaZwD&e6fqaToGj23;*yrG?lM3XXYKQr
zy$7DYE<hWDD8cjQA*>4+nD7}Y986bTYc|ThO$;x^&gb)ZgZ#FKd5Q1_1v^vFtG?iS
zc5{yb9P0o$IOr&(C^(7sL#T<6o?bSwd1|vu7~Y9p4=>6SP=`5QZfR(NkXv>dW;*fy
z|MBSa{H~S&P1xWAhFnfg&UpVPFy|6$0(8qJp{iOqg3VU_q8+7Fh57o4`Nk8YUZrRl
z3NWbRs7^TYRkB1i=}kD4tg=N!qj#m&cLZ!6etv$T%^ZM&ASV~23o)jnr4=bO#B(zL
z!{Cv*%u-Piy)X+ZRCm*bX>Xnym53Kioh(Fl?CqBBYymXe2UgpCTIlleI!p!=eV-qi
z5Mh&`^?d+%6LgB08}|N;?h(M*B!6Eu7?ymx*f6dGlVre)0yPpY0AFRvl*(s-U@h|B
zgY<XtOyGABIr_Z^;2VWyJ|SuW1N}ES$T3Ma05`hXq>Ov7QdaQEvw6B}1MU2XSxS@<
zdEHQ^Z1dYL^_P0k8BZV6ebR@woq~8>9<#b`6Pqok?TGlkn=w2mjhnIZTpDnMrX{`R
zKt&t{8gF)MFbVdfx4=H9w$-zu7~C<gzW2Jt4@dYc9H>^Cd3HFyVEk*m1e_a`T^@qc
zX?8EuLANENBZ_>2w1o-9S!PW*xS81nrv2K~4f-wiRXvYwY$UIj`(4H1WgHm2YloEC
z|F_shmWF=jUL;S#8&78sq>%V5Wn?3-0r-{HVFZLHSwL1_Eb;I;of4SF3uqnT$AYu5
zsWH3uJsPU2&?Jo>)r^e`j*LPGTjq;(6FET`#2KKYF-I9@Lj@a=<Pv$-5<cghAC#jM
z#zq*iqrBpx>vljZpzmZJD$Ter8vmVdYex%R9nfCBbV~uorg?)5TOfinW$;><iWXiS
zaVFO27`;0pu7}Us@gRQ-5cSSdI-ZJj=L$o3(q%BBCwv>vZYsUE8Hyp~2YwiHyA!^L
zAKgLkJ}g42yWf5HtBKwo18J1)jWfd?NK{l>ug&v&LFD?S)K5FyJ>by967fwcinILt
z0{(M>gGqmH=RBb#8aWJ$Tpl!o)Vx7QA=k4tVK~<8KFB}=VPhh(PiE9ZY;{Ad43_gu
ziizVtmu^?Q;$kg!SG-P(_`~pHWw3T;^}J$an_ZXk^`(gIx+&zQu*BQ|aFDxWxB7$)
z(7!e0-2%W$j_p3zGwOq#EVE|U#lm;5*~&+#;dyP(rlXSYQxDK&$ib{iCEo{8X&~WE
zMxj*Z4UT>)LN~0%?+I&UmS~CzY2X;@Puna2HY2z+Dvb+(KK2%~+hGFS=5o(`88Cw&
z`BCCE-`Z)a)>aE?b3rp;i2mP;CelB~KZ$GpHjy=kA~N}q&tabG$Ya=q8L;Md?jZ^H
zhRm$f$!P2YR{qpxs<n4EQ=gA(ILt-{1_#kU&H{B^3fpuHC0M4qd9IV6XQC?lO~Xuh
zEE}{`k#b|+KfmcBB2quG6A`*u-w;yrcPHQH+Ed<OB+suHBJyGRS}+E9!+h|UW5TGC
z^Q46gL3w*uy9{L+tpAjMKExfygg!xVGQ?y-<-1IUmp(DBsCJw+LibBSQaBp+>b##c
zh!1Zg%qINJIk+=G71aPlQKx2C9S%kiPqm=6ThV`9m?fgzPG|!N1ST6BcJI(7+1gY<
z&2d6<o9D!;?W?28$o(y=>Gcp$qBUXIX2^u;x<hWQ&`O$qM#dqhVnLW6N!A}Wd|VW(
zJ2)Hac)t`<H8fIv;d~8a@#W7FQZWHRnZ4%~+8A)3Eq}r;MWoxyuy42I1ltmmj*mGu
zwgE=3tz-qAjKsk)Jw=oWB=RjW?ob)!w+swXqS?G4yuPSzrf(B~@|?K7%CXL9juNt*
z_gI?yDt*OKq|Z@{`TWW?*g6o?)9$?J76^a%Tx8y0tBrr#*MHi;Ek<;MdU)u;{Lpwg
zm?ziYZn{^;h!DOak1x<1lWx1&%{2Eo+wt-dLJ|UZ*J0ptvPj1COZ8Q_7q?@*!XtcA
zU%W69EF@7?rvk#&8V}NvK9OYsL<i71fAQ>5@e{f)&%clKhlVUU9V_FCm2EqsfnuaS
ztF0}Yz1j%jh_pX6vsSEV&ok-{jm*tg6q^`mJWMYFty+nQSH9}D*JSk;UYf6j`4iWn
zbpY{G`~G}q!H);Kp=RFzQAXL*2i5Ukh_IABSRlM(+z6!}Lrf{n2g-}20%LM;JvZE}
zX#tB3j{ZqtAQS@l<9%u*T~3veK+e1$LtZLAt~W*qCU^Lbw0P~gs#T})D2YL#0W4&n
z+3k*MDO^i^7(`2bsgr@gu`vFo*Xw{V4y6uvE)LhsYSS2qmk|yB@OYKfFi8mhy5CwL
zClJBK&}W8uZks*M^%k_S78?wVhkWs<k}+d0vDvy%+mdZ3_|Oxm;=-7!--Tf`DkzGl
z$b%>&_zyA=P3!~JVJ)e22NjG19|R^1(0#?P#j7*ldAARJ7UZ(kP|KxP!`YIwboc;S
ze*7nP`V+|82g0!-kGU%Uyhen>nB2QA&;ErAiK&~iHV)UiSM379)*Ux{GI-3zL^Ron
z4RFy04V%t5rTBw?+I7ljQ07uy{+7<jrN`;gIB03$w`H^qomrI$wF)N&H{#1s#yb$T
z$^`*KBk3k;M~bp?w}1|#$?laq0jfELdjXZG&oP?X-flj85V;F3LgZOgCGQ3+O*OY6
zkQ!GvuIVMht*C6O#4(<hys9*NB?iYDy8(AiChb;o%P2%92OF-jWAUB^8|bj&t*e*X
zLwsuXmQm5y0j5)nBIsf2pZt)xQ$1MR=0nTPFKKTS+SDGyfacU#&VvRQHT-#;?g{^9
zL4as7gYgu3Om#b0#|CFPJYV#sV&(b*_l4l9Z2Y*k=f_?Pe4Vmw4kf9To=Z}WkU+Rj
zjNR+H!%IqTaVH?me>v3uMKEhbWf2y|-jfQQ>{#8$s#U<;Toi9&TrbTVYJ4FV==#HQ
z;(+*Nrda3;d~+z!Ka!g$r6#NzG*=+11sR)5ZvbS|fP%NTOU@A14I|lx{hp8vDB*oo
zrkj#r>a=N!qk7$xI<M3bwyq%Z#NmC-If(5Y!a-sc&6jxT@CyJ>ENKmNN&r=)qgSk?
zX$@jfj2br9^)_bcpceFMVS%Z1$#djl?dznx4ICv8tm{O}qMDx&m^8#nAOFc5f4us$
z6a<_>o3VC72-|_FvMAX$%=34zd&cX`iFD-TaWV3R(o;2JadM|1@wlAw(F|OhDcs*2
z3>E#*tuqSKVRR$Ury_c&Z6V&YM>-bUP9{_J=D#Z}r5jC`aWevn5gI65K1bF4Tg+Pu
zB^9MIv3x~o{Z>3sX}AX`zMw9Fgkq0RtRE`2pU7_@ID&!EJ<^m_c929U<NbD;62TBB
zZ&wDhjMYDJLblmTr)}f$p$&gBNeHCfhO09>0nj->COd$)E&ljXy@#v0c^$O6L43@N
z7C;0~AucIwmn%5w(0(LxydLUo8uJ~UbzC2}p!TBA40Y?|B7dS7NfeDWKyY9^wOLU*
zJcxOr(#z|$@5JYis;bwYHwcKaFZWaer4k&p_qg|ke2xPi9)do8d^{}R<DuEviaF(V
zbO2<j^$AGAXP_H{P~+K|y1%ksp_1R%4LlofTm-cDRE%C5xBbeIK~*f24#w+<IQ|@>
z+v>XP-Xqz8R7xsfMRon_6!`s=$_lD{BFrltv~=3x%WPI_rbPVnyisai+bF{o9%I|g
ze&!s>(NN}<>3%(-C}(1Z37*%bc0jrMOg#3f+E`6GR(E2>#%4E3V%C(WhH|Q%N+@O1
zeLWW2pGyhm^<lE}cCrA<yu1w$o=LiSK!%`W{n`w#@uEZx1L4826HH4&!aRBo|L5DF
zBb6v>TBvxo1V6#SxiDD0Sc+4w4<N#5{A}0sL@Hlz17#PFN;VjdXlfLcrvMfjH6mUS
zQAhC?)2T}Q6e_h7Pp0P9*|{M6zC>{0x!=hGy6%d#O&^kRL=ZGISGS_1MbKxOKc^6m
z^!Kx?3+JTsWIm(jn?4w?yBYS*^BvENxZnvV6&EduVkhZlR~8|&TY)%(X+Dpz+`IcN
z%o8Dnh$j>5bLtQX7X9|6^-0Fw;8Q*o1xdt#DqzNue{7fUeitK!!2MQ|&KrbbYVw5R
z<*rzEsTKzVUcQO1qf8|QjiMYxeAN-6aWR~7DEGyz)J0W;3BdzhG*h)mZqM7b2ILO+
zUPQ&Fe(<pqMs5CSq3ujsoT3J(tmp&0*^yd%i(4FQXS9+HyB=w557x?;*pMGU3T}h_
z_w(o%2u4qxz8&QKf*FxQ#h`>{^9>FZ>muvmRlhfld{Ab=3%#(al6Ut7=g$2myUMtm
z6Loo4)u(VV;HXaCcZ=ke2ECQX-b^ZJ6bdAh1LK=hqzzv``=a~)>d@t<Fc2-#ttjK|
z8^8TBni`)(`;m=Aju53H_D5b|>Gq!(5)M0{kOo{O>B1c#OF=05&cXE>r0A_&YD5Ry
zGmb-E`YOON(-!fU&UY*9hB@H_2bI3K-|=9!k2KBngbnrgs07qs!fw4<^R+`wZ(Sji
zLf>Ub$<RzC7)+IJp#?3FLUPx9E%<hI(&RD6JeUsE+-%&ybVEpW+*L?Seca;k4uydR
zRz6(E-o&I!Y!E2?m!KJ#*dj>ja-TarR9o(L!jf`Y@(VA~&wby@b*~-g#_KSh3LGKI
zW@r9E!!ZCdV#({6qqi+@7wUmj5ilK#HPZ2pU%F4`<~vC1vQfEdh($A*)nepB_uunG
z(V1guS^i2*IUcAu&{JPI_L$wWIcL(*CqMGo(loq{K}?7~w-h-KI%%|941NY&`e0!E
z=cf4T$5f`Hlr>}?H6dc^e9s7vU%rpTeIWFJ(W1ZhB~T>_7E;1A2!xLqGXwYbYiubb
zZAyXP+)2?0^rIP|AW&4X`j(+6nJ)zaiI0eKNUbnGv2Lo2RtBqKU=t_21{zdp0_Oyw
zBLAqao6*D7{tlM@t*(<okYJHnu-blal2HVK^fiPi>v9txQ{i;ZCo7AurFIyHvz3yf
z#rXprRdPm}kQMy7pGrlH=4(tf4#BI;Lg__l$y8E8vx@bG6QD|?xavhGN%1BS-6!oy
z8*G%~p-SIt1}F=;G<I=>?t?fI!2^r5g!FCr=>CZ;Sn?p#R>pZ&T|WMYyf6}k{{0>l
z<16+~G_+ZxF#YNy1hYc60pAd}^^7*}E{>bpyR*X6TjsuZjplyVT>{ZquNLn<_E*er
zXxThs4<{QS#RB4aRdzv#abKH-O_&+g{$Xn3j3admz7xQm$1QsF=LH!70C?k1DwAve
zCw0{>jYu*v2*K#yv$2Cg4OnU1Pa1tqJmD{A4T&*O|MF=O;(Oz(`=-k=esmaV(MYmM
z4Mb`hZj48f<s(FXfEpyebVCKMc>@vVW-)6-0+PLfa1%Z&43RIg-0yv%Irtne%UkB)
z1VbWw8nDl%3w9^piZ_9gSu@2DVHxas=C6ut&<Jm6;thty%!|B9s6o%vT#Mi3ay`;$
zmZ;eY*x&+Vc6O(+8Syc&56lMdhcZ$Aa&ox@)ZPZIRr*ja)lcib8{8Ivm?cmQ;)bCm
zFo=<K-KeW2H`Zdd51rs9D$X&OX<x+62EOluHc?)Sg5ZHFm4xH;D4c=6ENTg*?}7-W
zVaFXFYzfA-w#e{2Ms!ZSV{mM<s?}e`qe1`QJ5KV9mdNv5I#feMg!e&Jz)O*G)#p}s
zOPH6+B?Q`@cs;j^M<%-O@T9A=h849mejH#kECw0nq8a!h4|z0IS^K?OGF#+hP^&mo
zPY?v#5tE$Ik|%h)c`;I3Jci8))!RUHSnqn3eFOyJmO0ILD#p-n`^3s=FuC3e1(C6Q
zF|Womj1@ys&|BI!JPl3jw!9aLj`%L&Vs}8%vFi8hnaai&akCd*KlKt2R`WHd;ZSgs
zLq|*5(?g+)`Y#WMLP%Cjow$j)AKX!cmq~qlv<z-*yl5SIJWsVGgTJUjEphGDCI5Ls
z>Wcn`vkAeB2RnAYF*&76Q$Q&RUlRYhiGhyS-VfV}Odg9|Vkg{ajS8+!mWn<5kgD|M
zg7PNnlv!sWNr@tJfof>EphHO0M!KkKSNOe+26l>Wp^RHl=T>f8%eGtT9-j$$4AyT7
z_IgaG3sx=?beO|?0alBxL~0q?3YK#dvr4Y_*Fek-3HinPHrZgq41HDR#tHiEQ0u!l
zky>^mJ37=AMyalboaQ$VL;27br(YXZ4(gx2wVdR$#D7sXqa>Q+Rct}D1{9JQP%o~p
z!ltD_2ySy887@5$lIVNYlFeWhehQbkI{a!0fd-Id#cli>_F|_EMJen8jX86xB_b4J
z@yt5wKLuM)q~Dh|Z^Fg{Vgi^{7437k8JZU|M*@d^{IbD-7@vqWFt>(@D!4?RcOz13
z&iKQor|A8Cdwib71WWrJg$Sp~;+%8az;{2OMVMmLL91LuWD*fqVDu%0)i0H!cjUgI
z7(pjCDW);F^G%(FGR-uI0R>GlG=ll{bb9bI+|@+{Z8jJ(_4wy+45xrxb1pyphB)G#
z;wk_fM|tEFFZ_oEU~hG1;>8q~aq-rpEgy<7{C%&PeO|wU+6@&)ltqAfaBbb9`ck~d
zClj>~cw}+1T@f+{<_AVd{k-rDp;VixLXUfs7e74O&7$l4iFB2fYdx>6O4yZHoiTnA
zk8s;eg#-8Rhd=z)RNF;MdBO`KMOo9ngi^bu4GZ-$wwX-sEfV>P?Vg0vYM88rKe|Jq
zSu`m<D5OnKKs_9+OBOHUnXsJ8lg%p<6A#Nb2K)81yErQtn0)}&=#ieOeecG;ZwE|0
z7NhDroy`$Aw8(jFgZa^9h+1#xrB00=Vix<xR6WI^N8v3jQz25YoC7o_&vq>#{9EL(
zUw4~v#}_BQ<Y~Hd*0v4wmdVg$lZj@8+~Yozh0@tFNJ9My9X0}e-T3uL3PcJZ(qwT+
z_K@eA_krBjf%1!jP-MD7YNccSOMxp>r8<)|cS+r42yZwt)69UA<)fS$d>j;`8vJ79
zNv5xyKwAWw>w7=-{}xH!{m~P8@`(V|WiAE%C-)$7Css^%dLpDY6ykBx^}6a}+yrOA
z`_H<Q34JY}_eQJq2e>)s9B13bID%I_mB^-zMHmcgBh+lwIW6(9v?x?Yx8fl%sVp`T
z>{g9fIK8pUmnOap1{~q*>$fBq=6M_?ng*4Nu7wD8y<VSz5dRn&<XqX}`Grpf7fgJ-
zh^;x`KV$@BuJ+M06cah$=`tbaXUT?un<KsC1+@~VMU~I&>Lqo~^4K(#>`ruQr)U62
zhNJ}l9WEI!A;KtAdasm3XSX;*=+%NKSx(H4irF*&r>_fh+g$%rcKp2rWPrW{cms|n
zVt7IWC!x=V3XlkM4QuMWCkuR?UqWbJ>96Qs0A;U_=FQG)>hYXzZ;_U===si^$F+Ge
zymm5VQwe>0cP8c6maO$%nUF2ApvEx0*8*TgY)Nm8GgpA*o)-)o#7ff{F9(R~WtWDy
z&EL1kym2C`m~&MB|EbOefaMk$iEpoz{!g9uPh=~F_uHm8QZOCx-)6<XIJzJapff|}
za+Uqx9@&5YpHLTB{Ir)p<_`UV5b$PXR3Nwp*ZT`oH|(2_=4NKim+(>&R2;6>&Tz@*
zkZzwr!-Jy(#QXz~KTa2hze|phux%0xI=J}ytqR-4j_)IyzqT4CPNTe(L>?yOuKES$
zz-`iYY_0E7Buh;3@x0AeXEo80Ujf%e-;}E}uyCJz6?Dse@usp3Uu}Q5I^igFP;!(%
z_n#hV9{&D?-~%zQPwul-i(r2Ij)a=l&s1UKNay!(r0)4A?(<DGQB1QajCG4h)}A)5
zC#jhNG~HpJw~Hxv1}_rPbxz6!)gALXxBjVZlj;3#^00h(e+;-a14u*-0INmj&as^x
zP?H7zS$nCit^J$M9^1v9mZ>ie;W1D(C>`1}={QV-l)c6``ONib3nkEI(YHmOv`kIE
zNd`uh_q32WM{3!6xVR=IeHj>w&>$$g)c-O{FLipl=Qy>0;3rsB{;g;}p%MVj@$K`C
zkNc8W`ekQns_I`qoP7S6Vo&r7=V=Kqo$IP;UVm^eg&cY8b=u6_^xei!{p=Q(u@j1=
z{j?y290IQPrmv$kU>~pBm%h7FmuEkeBQ+?Z6Up4;zsgN0!1o^pt!n$*PPzdBDX+f6
z$+)N>|Eq>Y8t5-X237I}r8_s>?Lat;CG5DAvt~h_><PLufB31M=G@v-*6yR!hZ9Zd
zQ#87n$!)TJak*XpyuBMYpAsd(gmdHd(6wJvYf5<$hC0gJY}&&F7^VR<S-p$|8S>+E
z=g}g-+}$g0FY@qPZc4tnq4x;7n3^<4A;_FzQH6I{`*JoN{l&0jB!2T_|A(JBM9J!r
zPEiEjr@@bUD=*fP%ksMto~u`tBff9j^gX@29#528(hO>4%*>0-JF9;=j=rnYwRPq!
z`Hy}@ND4@HQQ(>XR1_kDAS6GqXx31H-FYbpZ)5^~gWS5Pc-=jKCS2xXE5Njt??X`F
z>9qUGq<@Gvag{d}0&!ZlvftQC&A6B4W8ZQ~9fl3!6r40?$$q{aeP?fHOY-?0LT_9q
zAGI@utUvlyyP!vM)#~gpYKMzS2VU9&?RNWQ0<TC;;~X8|!*K+}g}q_&Y3>C8>snp@
z75mA<dtnn3kv3+4G$B24Ve+SuI+6en9iPVl)*MU3Eoy7SS1ZDZ#HB=XP0=;*CT!fQ
zdhNKK+<)#~AeE;|!PPI>v+w|()lz04*VC2JGr%Jq{LIb6b2?uu36Y>Zh&1-J-oE)`
z!ai=9@faou-b;9XU3xGEo6w+x%8uA0LxpjGk#2|?p*SJ?HHWo=;W@-=-|5Vk*T|3C
zHAQW<s=WzJ=GLBN1sWD#%4)0tLaLxOymn)eu<Jp3a$NT1SE8aTdFjIpGxi|a5xNUv
z;kfbIs@2IQ!z%q!{<clE_+tyUe_Fp_OrYT`XgKkg@!C^WRW+b1mCYE0Sf|f>27u-P
zL?Tl|B2EGNJ*D{7qW6+9!^baGSV(w`roaepF{n@ucE7?>E?(!e!O)}~_N54In8!Qr
zfY_JgweK@A4!3w;Z}QqRc<z>l@3UJBm?QWucU@NTHgwmYqRaF@DFbZK6i$syZIO-1
z&oY1@A$UPtxY*v4=&hH=Yi5$RxjM3jk^iJwSOLs{@468&*An~p+JZo1*@BM%AbEOb
zrn<>(Af6n^Ob-`ti{C}yvOMIEMV50+y8(TgkdP3-2I&ht@xv*z;Luz?A|Zy}Z><7G
ze!{LziwItgo<JH`PC{O5f)4;9W7sNc%B=VvYxZZonxSNrB-6%4cMvHvam%MYBj`6L
zZwQc9O%=nQyeg{O*N5b?o7WH7w3twt+N(F0&AOHgJFAw;9)=Q^CYy?!0WN?|`O?tC
zKs1HEd#zkQkM8lu8MYO$Gjz(nFa2|glGi-0Ukhi$r``m>)S9Krj}zN0$T34H)l%?G
z(jhA&O@HE7usV(PG3(GV`n&L-Z;T=mENAb9e$00@rlh1a=a1_t`1Q8{Zdu%awf%$}
z-RpXOl|kE^4SCfJN=NYdYU=q>KMGnFf`lBL86y?|%*^Wyuy5MN`NYh;t#%YckAbs(
zF?7#)Ro7;vZS7Uw!5n7xxQ7$qT{~4PiAp5OT3E2_V^{4R+y~B)PTBetOT>#n)B4?M
zctbI2>akEVb!)5W!P{k=%Y!ItyOt~9Z7+2%#S_Bg=Y)ilcCx1o;tp~fY<WnVhiyr%
zm*Y-U9+K6)2>sk9N1uDqV%W|}3q#%eW<6rDH$@*1$ZOKIG6XV^^>^Mad79r5%qIWc
z=Awue5<oXlA)p4MXOk{uQINr%Ev85*IAopzp4jzfN{MJG8JY5ulDn&^59q<O6`IDe
z!p%<GS`M4j(<%vmhzJO9m_Bz^;~YtuVo+3t)qqpnUlk(OefbFc+x=b>J5}cngPiGZ
zoSvmEzB;Sj#9r@S^DynwCClN9=9`0zjmJt!Bg%-NLx90ydu)sGAO!-)%O1!Z2I}5N
zTiTz>Q<BdddzGDjv9ClbMF`1xe|=Bc`u)Oy6?^`WP?k-(I3v)(@F$w$wOkMt4&d*v
z78giuny4KA{*LPorHYrm%-9j6dViD9AhRhOH-Nc@V}0JnQrl#VJwj6PkJMrVF2J1v
z3|}hTJE5bfj2#dx3_&v7j}&$p4`>wBD)mOuB|{;)y*wtwVRz^ZwpNRai?@eUM4uW9
z^U)*aD5VpHCbHhR5CjQ2JP3&@2YF5N%b)D^j$eQHX#CMk3x_QS78wsDiIKAl;Bp&L
zk(meS1J-qHni{`5G4RD7yls0NSUyA!e%2SrsZ~;j6?2W){f+d3Ra;nh*H+aewCar?
ziXvO`lFcdC?ED6Y*7-QEIeuOa1P&Y5%axnm0`_y>D9j@Fes(|AecSI>dC@d%;H>O)
z&PS2o`aE9g3M}jrcC;H2$HIJ_{qWAnqiEB2tDP72Zhm})>-pSmeVd<@H6{ITsY*CM
z$b~^>NsygO13erHYM@YYk1J3&`O}@zjZhHK(ZBH=MQp2D3JryE{UwsvA9G3Ug^0Q1
z1vIPC>zG5E({<S;u@>ZfTeX+#)7QWr`1ek?Mp5>#AAk8ir$p<C82L2Ct*<QrOzjI1
z8L>FxGV61}ALwcG-n93U-i00aS@tmFzQWN{8TY2-)mG!LxetLyee7nG-uyiR-_|%o
z7Ab^kWs{?#eCAG1fg-eIEpN?s502K}>UaZY-u`>cY$!;AY3+Yvb)heCJxNeU;UA{<
z=j#57`GhG9@Y-9wWxkG#$Oh{A07FaAj6WHA4EHOiw+u@Alb3+r7~Rbv&(I#ogCf4p
z)7q5C7)zQMgmbp|O?ZW@qlrrs9EmKgkujY!)>qyvZM6ym*fiw}nB&rG!6gSjt*|=g
ztV@-Wwx`bbt0)I4*-fEJYX=IN<4}zf>guXd-L<;@7qz?NH|oR8`|`VPL_sbullKqB
zp3b)bKP7(`mB_(%rhBOd^Q1|biE{<A6uJ*P`pZ^m<h2rvn*}qA3uD$Clf`dg`d?LB
z?B6>#IwobzBvugfU~1+fQYelrK0AAb^0>!|5}>?vwJt5`WXuDt?L_Z6dtcv|yYu#0
z$G!6eN=YdPhU73zn#E$2wAb2#&;uPF_#P#$H67|BWKcNp^)A^~70E<5fdq)N>J=T6
zCyRE109AH1ehY|zcI-eH*4FZG*@kW%I`~b0-f~yIwHEI-@^X;3I>2Z6^5qC$XX}y|
zZr?e7dG~3FEA};Ur|+uPeR9FniGsdmS#?u@!z$5H^kuEb2`?*VF9M0SThrJT-pEp}
z0}#7f65HJ{#tyu_%)BCs$WV3tdAkVkf&P|L<?_Sz;6qA)c64=g&{{ZbzLo<wv@iwO
zK2uRLr~+fNms!94>7cywx2g-6|A4U+l@t&3oulSA;B1d_-h4a&OzBO*&yi0pcFS)#
z4R2sRWDCq=$z=BcQNvW6g2iq2!Xckk<4F=nb`R<eK;T!KPId;3WhU}XMHMTj#^i>3
zDV5(i*^1ltp0%#)44q4%W$%mn^rB?(VXez$(=v1Ws;E}ixx3qGJ>-n0{xTDvUs<RX
z<4ccE`gOGjulcOh(Xc;UCKKUsfW1(;Htu%oQE6FrWP?x3SFnq@8||D2@6APF4_X97
z#-I3{vT9)XcuHyttisR?s7!Ih=3HOy>S(uce>6mCy!+2azeNk@fEqFIz@>dt9vXDA
z;yk+$DO3eVh4*MW2Mo63^?Bf&JORK6e6uOIhh=52U&@e(cpc7-R?`@Eg2)5_m_CJp
z?NVccR&WPKUTSyzmJO9MJ3a={$q*k;^r!e%+gVBsKA6}J>-VQv!R?hJF9<HUote(o
zbO5R8?&QVos4Iu~{-{ZFyfdBmZU0sQ{<pUeMNQEf8>^_t_~~p0?_Y8a)8<#R1*RrW
zr=Nr)0LwT4<^D|Da&&woB*EOEZkxkta<Mkjnfc7n|0~@Hdw2MD<|t_xKnTgu!hRsd
zd*=>ScAB&Nyj#o_&UUn*12midJ_CCMQ0J2V__T?i-iWvzdsqV~1}YH7<b9fk8Zd_k
zir)*EEyxD}FN8<4OI|%Zd*g?bd(!@Br(zTf_pPFW3U&qXz%IQ)^cJzG@d4;h4#sAL
zXUXsN6)48Xi#Ia>R(^7<wpyxYxco}FTjkEr9e^ZCO7!F}nD2_6Px|b+D1$2N>9FP>
zuqFC=Tu0z?CtH;Z*Xqb9L7M0L_h*C0hp@1?rUn-i-vzF)Ukt~`w9K5XI<5wbO+Dng
zZ&8To=v39u%=Aw>>|gGEFi%O--YKc*YYDdsx<9N*hWT2X`~sF>Mt|{o;Te-OmD2>n
zZbpYa$~AlGe7zI3#Yms$V7kFQ)Agt4^+5;&Q`)oAVe5%&0ngX6ztwu=pp8U`a!QwA
zvoP1BB{-^V;K*eI25jG(d2>f9K7e_&TVCC(PQ)k&$sfSjYB50pU`h9&QtGU!^*ps_
z>UC#Y=8gw(Rv`+y8}5JEJmGh-B$B<9LsGQ>8Otw^<#)nq7mvF+ZSFYtJVLeW?K7^|
z2Z!5Xt90)K=md=owEB8~GSIT<l5s3O(?~p`O#|SqF%8}aI$FWorQX_X-y?wYYH_*v
zxZ-L4Yq6p*9)&fk3t<gNRiAj9!PV>K`rc~;(=vaZ{QzDOGG=(zyN%>Q>+%DzBj?QY
zG_Q!iKJ%P?SHG@#D(kvIHsVzyFrP6sF+w-gy_I#wpbzevTFHf#I&Uff|08S6l?whH
zGkIkf`gPeC#^`fbUV?>77mLLsV3B<xzYzFL>|g!ILVHC9b^hKzz`x-V;EwF<n8ifQ
z1YwF~D1jWH<=qd;Km1Er`nxv3haPSW#fXYTpNiUPd1f}frZLDD@o{=t41!!mOA2PD
zAw$FR<3E?!pSvueQG)CQzA87)pcj^gXckp8<_{z2U$W7^E_qTYpRU=u`v1s_|68B<
z{Y>jY0XlcayP74`|J(-us&3Fh8UAKn;dRdZ6YTtX%fF9~0?6n$I;r}SaT?=){<6P4
zq5-TF0E#Jk&FViH*#EqBbr2v)ob$l3iuhAIQ4}?hx~VF;CVt;vp9M5_MM?=qYXD*r
zVe#aWlAD>$4xTdYPS5C4IHj`jWnQ`JpFj8CdgNR<Dl(`L&2wRYTmF7C)aVpibjjjo
za;7nQNAo_jShkPec6K&ed-bnlWj_*D^8I;z4<+#FH_uB;NB{hI#R?@_yD72FK}nj0
z&+|H`nvVpNx~bRE{3bXPAfjm^|80N`M*?0(8B}|d|NEQ>$x{A7D7AU@f6JPR!X2Y)
zAD!c&;eW@h6Lm^YQrl`#$HsqxLCsgRp+z+846Oo?q)a={UO}A(X9_qn#jfuk)w=Ya
zB`}1>pk-WZ|8+Bwu>+}iEYjFQ)SuO13-)(dPVd{Smm8)P=-!?wch!?EL_V#Vuhh8t
z3V&(T)#ERLchgc}#q{dfb_DWJ{J8kXGQe!=3+yizlz#)W3!|2{Z#Y+(`V1hCyt#+P
zqkRaq>}pq$u?bnHY>Z>sl4kx=@?re`N+T{AKT`d*z`+3gsAWhH(}#%n=i9E9r}-Pn
z&E3BA&U!(+%Ol$n*Fg;#`-(Y>jH^2rQrOteI9b#Wm+h;a0mc)+un>V!j>S~tA2wXl
zzdsa!CI&W>k$@y|$e+(dPDZA5P#U_4f{tf*Gvl$^J;fVb-=&W=h*kb{E<u#{%kIQ!
zDZ1Mppt7xH#~7y4&iH!*e4NSZj%Cl6v->#@fVsp3wF&p!AJra};b=h@+`*YhA8MH0
z!T`MZ`G((t!*w;%4&`JXFVv$CDR)JoI(yiC$<bCK5B|@7-GB;ccQh;__*<R*BM452
z2GGW^{foeZoVXP996F8Fip!rD^-@x~obJf+cFEyeMfJ~i>~+r8l+<z19{aR95?UKE
z&?uJ=wsm#+|7d&bsH&p%3zROUOG+A)?o>cp5s>asTDrTWQ$o5+K)R6@=|<`9?rz>X
z*1h-l#{2V)aR!4kIGnv#eS59>&2LV`1mBI;P7H6U&$FToVM*3X?$i$_<yfQQ4z%0k
zH!^8Ys~A}=IuN(F&c-EdEn0pH`6OKh=V#Wyy5@c_3;6tp{QW;?YJfgHhE^>G<+urN
z8w?f4Z7oET*=pW#krPj_EXJ2(M;JU^<SS)0NC{xY(8{Pad(D}x(!<O2oUT)Qj1z4~
zb1Mi}1X@iQdkJ$|6<Tih*BT}>2H+MVY7E{ll{K<546ji4p@rjKKji3ecLTP^i-;QE
zJ@oo(p0NNJ{(H|5M8!oZ;o(D-@x7(X&@<PR+m2*c=W&Fbs$X#-&>DPQ=LM|%@$blk
z55uBu?JJ(_i~Qhu2!0ToX8MU{J=bY_3jbd0qfknYlTgyh+X5^DS!s-<tEGV=sfW+u
z3#)%819HLi-@~C`{Kb<OYNddpUq%eVB2g9Q=yq&H;~|9AGa#3V!%eThSx65-V<1ml
z;U|1TW0qFPuu(4DDxgIY4+(BmV4dn6mF3C(n#`gY&>IA0pT7{vbQLckoh5f^bvrlf
z674sw4za(JRvJ?hdw!rqA&t+wui`f^>hhTn4@{Fld`P2uqviR3XXPnjA}Y~R@nq#n
zT9E>{+}UAjMYbO=B#{r(|Biv)PGUl!;9;CL*WthG5dJx@`TBye7qRf8_17)^Z!mrW
za|kK0aB{bKU-N5;{GZSK4?g#Q{su}CfE?cce;3~1Z6W`b^S4$eGqfc^fwtuCekTRd
zO{+cT-a1m#;A^*ZtZQT#eFs;&Zk;r8{JRzmB#c%Va;mq{5sa5c(Pl5XlKP{llVq^S
z>{w>G+U+!1IvQ2FZK7REj_$ABc7`vSa&u`nU)IU)p9@?)TN_A8a9wjP3H3Nn=2ejY
zQKuE)k9yi%s@{ZO*MJo01$ku?L*Jf8*wnm62=PKv<o5<vKmf7?F0nK~P0C^@{Y90I
zEWTuD%Qx8TdFRWov;2-j&nVfClckC`;>S75ir-ViP>}t3VZvawxS)v&!HF*5zyO6C
zPr!5nx=^poWn=~bxy!l7gk<EgcT5O={8hW}_W(4;RCXzt+Os|XVunB8@bsmSsh7f0
zb+<7lhW8dFi{qZALbGOOZLQO6o&BgIW0)p644mNgZU{HdWdI$x<KK-46#5EB<<%>e
zjR5XtQ;ZDbSQ8jCo+Nq(8cpX*anIMCrPN>ie}7&VG*bq)#&n#Co143FjdW?!VLN4>
zFSn6kqSoZ6hseOgvNASlI7q|5i!2nb5`ibwQH(3d3u%PH8>pOJ?>DDWsY)kt?E=98
zM)gc7L?nHEuDYGNq#Dbo0;Qfh*E0=Qr>AJ#LXrXhdTSLU0*VPSLI$)Vn;iN`5SX2D
zpwgydDOikh(Ngbxiv0IUaw;-t;?^XJXmI)W(Jf_qorWNB2Q1n254s{LSK*5LlQ8Yg
zv2-FI)MaO9>&01Uxs<<*xnss_m&E<|B?j0-X=nx&!vvsbE2&D~kA6WHxM=x&H)UFa
zi8c%BA}Xmc>t0&UmtW4R=&)3vC^JphxSnr*7xx`_MF2>azXuuP9gMmV?otxvPsqLa
zv>dJW&KjVT3INff1vI5REf{({<^xpKMzcuIyz;-J<AwA|N(iP_Q}jLfk_c_Mqobo4
z-<K7jeumaDPk0xL$L6BcQfQe*`c@=H>~|-FpXr)lI;~R3!-5+=p@>LJ8<deGARtgv
zQ^VJ?lLJ*0KTPk)Q_Vj%-MVj2Rqk()e)&6#z`d?w4G}KbVCH)x1q!)f>S8Z|PSbYT
z%&GO<9xaH|jz&K>o4hh^+mMp{(9R{fgFIuj5Meb<zx`*7h2VrGgkX5=YD5trgUknw
z^#UIkw+!71xC)!jJ|bAa-iY+%6Z8n{`PaV`5j@by3vFuoIpC7&7!&o5``EJ2%D|*D
zoX(X^19ah>_DTh#r~q`*)``&2z7bZn*x<ht*w@bs&PsL9cLxI+kodfTCtJc*d#XWi
zEG|C&`pSxLTQvvw^2RV_g+Ou-f+Tfk_-f@okJ*UdWYKgsFSfMK-?^DC4EG7HK)7~9
z74+X8_C&L1v*1hO*1L?JD#>)+)uYi~JksYbC#o;I*HFbC7!4MR>DifJf{Q|4-ilzJ
zB?mi7b3sA@r8hJzLhW!8x8+=p6#lPqdZMXRC&nIIsL`0|usb~ZZ>Z$My@b;h_F}tr
zA*+^ps939h+OpaG+Xr~6Z-hKnWM9(@&RqzfzlAB9S}D}2pW+;}$igu|^GEsDdB~U%
zP%=o-grKvtalO$x1x+|tKgF93dcel^CApt;VOCTRLYez~!aA20|I=wgfk={20UL&0
zIKOY62QHCokkD~@)>MUoztqxleC|?hl5v@1?CIb3L1PBefQ8gA%K7`c<kS(7lX)ul
z-sGGzhTzJ-V~KC7*I2dR9bUK4fBx@p2kC<)D}x{wM*ep>{Ed7R7%pJ4W;Bbjz4<#7
z|K>3n0f<e}FXZ(8#Hzm+0&l^!;H)+*BOl`Y9)bV*DTx4Plm45LNB{ch-!B=opcPjd
zRIvXB;NPr`dLeWTMeCE<@oPMBXiH5Tza?kN#<z87!9Nv<DUF}c5Q{rg)8eb{TIOfq
z>PGw1MoCw2`zH5DNZ{s#rm%&s1{kk+c3G(iph~bV5;W|l7G~r`YzC!|HV9?@HZWZt
zw2R(PIt6m|bQuhm&Jt($L)FZmE5)zJ!Z<(jS>o+Tu<@wra)$ruT1Ch#SK7!gfxORV
zfnL9eIVlRSH`dk>PG5AJ!M!PK%_#7x==jqc-YA%FunJKY<@F$Una2;uutPAo5`Tki
zbEEvz9iG9-yYFHRyZG}16V<;%<t>WT1)GdSU4;pm&voK0ZSj{LS?l7)C;nP~ZW?xW
zc0Po8WmNK-Prkud(mPseG`U{)XiY2c%qhdJ#n=aFs};Fc8~0C^rMT2_z5b^A;rX}C
z+9tYxBS#epT7dQT{S(LqB~f7lS#9q-aP$;npJ|2EjbpYU7>U2;*OEeM);?0(-O@IC
zXviZ4L+E5fMH>r~K|+W7XQ0yYke<NR;iYd!K?e0rJ>0?GJ1Fa~-d#q%hdM@gecc07
zoIkWkh69x**52R1gwI=ga<!Yt+$-+J=He8!u=KIB3x&xhmBVD1o;Pi5{hk>nG9Y60
zlR`nF0T~JMCu$m6W)DJQ08B&%P2!nPW=RQz6hD*=v(*0Tv2zg5DE0Sdim@V~iVGZ-
zkFg+~#)cgKkvqLJ+30AZjE#S64Eg6un<3)E_y!MybQ<3PU!x?YHB0m)pXa`9`cZ!e
zmK03ZExm$B$c!X2KuY&8SF++^<dP1zJ8>V+(`gO;Zc=KAyEw^&F;$|X_HPEQAxlE3
zgkAzKZ!U`&)iMEV4QAC+-P5g6>m;gO{TDC3f$A$@(ewEE5(p_kjgeTZgb>p6NVw1%
zjl^`(SgighBS9PrME}Nrizc062$u|E6$i4dP9SLpF|K?D#7KFb4_69ad_%XfvGE5F
ztoI{%Oj;B{vM^~ttMVRVTnhF)Y;0^E7vD*>t-ir~BM@gw8TBXPYLRMHc;4ShF@4Pj
zd~9!pz&YAfr==fK%p|Pu+CYxxe%<qKJ)D1UW48VraLMkE1@DhRd0oZ!-3qN>0;^t!
z=k2)XFayg6G|)LeyuJ3-P><a{PCFN?b%jg3<r=MFeD|e>KFafz!M{c%f;jB<flK}v
zly3@L0dqZWlOJs*34Hc+TXBRVdT!9qz`m$*!>Cg*PZRFIxl=GV&BLY9<#en>=f3p;
zbHm-$HgMP!xt(*_E?Q5v4fiBh`Mi36?Rh^)(!snidkbl;5D}AiM=B^zVw(^=?G(I=
zR4de~AEU!(R9BRjkBW<1ugSN&1lGEM>UK`VWp>eT=~3~+Coc=c2Wc$H7{C0c6!N|s
z%`rwPa)sW+4_kj?QMv^PkpkAFq%Ip7)Kak*+_-YVA4f)spE(^2dfru#G=btD6-{e+
z4@F0=H;)`|Du8GE=FeP8c+6H${yP(}%LD$<>wO8fI}>F9DAsY9Gyoe%BjU-)CiiR8
z;;;T4-iNc~m?H(sMN1fA5c{mo(RyJI4}sK0@VRwhRcjRkq#ZUZO@5Y=?n)cT$qf&r
z@K=<V^EvEnOeyBHxB)nJ0=Q3pc_<(4ez*&2*dh?U>e=l!hP)_mfj;FF*eJv`o#fCZ
zwz;ohH5hrjEns;^2B9sGpjc|SoNRoPiUw+_2!s~_xbJry75~lUU*Y~om>1l^Q^(|V
z1L9`mSy26ssJ~8ncM#CpD%?i5*an>PCIo>)m|S#9iu<d31$0nsY6~QP&UdFBK?a9o
zZKZmd)YN`h4B!2<K&QXI|9REVrxHc#RabkC&91LTyJ2H@D7runP^2AbugWSqsIhGV
z`MyrautQ1BZE01`fnCzu4GA8T{1?}UVJQw=vrUfsbM7EH%xB~jg2(7_e?1St)=3^<
zQ?&}21SUW86>{Hx_g5lBlRFf=zZ_iePwGU1OV)8(^kWTJ%D--B_BaIUo%I!{gdAiC
zsrXFA9k_HO6Q}Yo{;uKQ?T&@CyCxOm-6wRqRiOBIF53sv*AQh#CJI7OE`13^V=)9n
z5e#1znMgLX?uin+I~`nLxQ05|7!3+so7vF_y!EBmRueG(0xGsH3o8aFIHov5bcD{x
zj6Kim=P}8`)I}N=lPmY~mS7Rl^bHLYeGZpD3f|RtUUQ36He3RAR(`t;j8&j>6<kqy
zQ{Q~ekJfw`X32t&BKkr?f?*zr*Ex~#Y6J*wXpAsl;nh6%u+c_z10CWCyxPor1aCKG
zzxot@Dz3a*b??!+JHjume{|hakDJE$0<om=jF3~r|KT^eKA$#9Uq8FAM?Lhnv7hKi
zc!pH|v!REC;Rt`oL8N(8-{UU8^8yhENxlM*4D2pCJ#QpNC?osy!&>>*O;v0}qYd7J
zau5s6)_AbPYO*oVujsM#yq-oX0@bKQN<ITGpei(D(V_bUuO|m@RE-BHEQ_12-al*U
zQd!EG^@3A?$g!<vic07q5XSp8xlL7@hsa)l8a&!U!g;pcG6GUI_$I(y43ZN^U?()3
z@Ctl;48;x;tD197!!Z@Jt?ylfyMmzizTrq{HL7eUR>NZPw9Oxt2nlJO38M|IF@AA1
z2&!!4U8wjnP*=5?Up`qPUkv7GF&WGf_U7;U*-C_>90jzegRRFKg~PO%|32A%O$Sl3
z6cE_sY|n#;@2;Egufa(&>hb00B#ZJf9`Eky(1$dUxDVW4UWB4lDS#}|1#knu%N4v0
z%E>k&zQ<U3O+mkcA|d0D>35Ny2dO(&#))Q_YM+_n;jzIKbepI`3Rv+)#<r+kMBq2z
zJL@2_Y;!i{bb4xiw$z-{I66^dFqio{xCA0)XIUWejIyZnBdM$tV=xIf<td~H5f}`-
zTm+h#?pK?+YB27g1{egP{yM5vqWCs1b{zS%)gf<IwctK}_z!~_Z6W@9v-OCC5yOe6
z#kDh8DL<+M<IWxt3o<=tp}`#Jh-R^uIi&fpU?u;4`ay`!?Ust-QFs>ExqF8rKL(n>
z0eL!99J25sWsK_%YVPw+%cwGk3}5*}qSMZq6_02>XzU=$sN`9zsVFx7d6@p*Y-Hnt
zN2*f|(f)k%O>c8NKR&7t{(xoJ6XB1M(kP@PksWY_nV<W70xV-=iJO4BDqIuRaUXeP
zH&a+FQ9zGrNn@;Krha|{aQK9|3X>uu465p|4YB>PZ)_mSgE?Hd|NOX*{b@ZyaSIX;
zi?oE?OEbn-N1%ef{r)vh&7}DAsH9LeoYDkK3Xk0g8+ifWNIis#7V3dfSiQTWxMnI#
zye12kLG|r@_kC9n3X3SY+coayjBg>#O<iQg)bO8<Yno0OQD(A$?Du8vQry>~2Ka@?
zW#ahwd`Cp5Quv}g-kqP++<-vh9hvn2mdHR6`Q)Q{Cb+u7Gx1avbf)6F63<)uMyngF
z^1HKX%WIfg;jrGicT;1>{7PfH3#<ovd=D{ioFl)LVDZ9q;b7ce(U`w{zw~d1Oc9|D
zS%wWdRI1`o%L>%&EWy@2pPmj&m(*?1agnx4OW>3t>$)`$_ZRvPUwpD3+XCF-B`>Is
z<4`P01R|5pw6(TxSCqOdp7-aTl#6$#I`^D>X?PvWwAqwRIxDOqa^g_;7oCDMCU{aQ
zyw`wiIqCJ#0N!l?=jwcaUneivpx7^w^R!oZTd2;YwR*Tx6J|GfA0Ib(Ol*Hqi<`7i
zi-d>9OD#VHc80rK|Jj#E&2>6D770jJH{J1_^~fv`3uU_(xY1o#phtCEHtdI2!#BAX
zESA>KO?&7ltC1Df8MwQq7O>Xymm@TXe31|0zczvAkxRZVoYVMsE?tA+h45p=3!}@h
z1(TC;&V%^K`2ovlwAI)!jkT)2?TJi<iatXkM@!9`ic%|yw<m3~`&KSLLq89njxbEr
z>fSGQJ)k-7HjCh`{kh=KKW)HeTzT9Q9;2aBG~3jXQj{RPkH_e0AQ2mUz$-6bzS?rP
z1baQUJFCZeh4=Rilc)D<2r}B*$|KP;N=5l8H8CxRrC)0M1w{CztjI1g$kiiB38E$3
zdZ@Jo`NSdV-+eLUxREq&0J0!rAH`9Fva+^crueytB2>^#>^^!;!32|wT-?F(p-k_y
zartQLL&*b1tf_{d#7oUCE0GeVVH-MUQ{NtE)4VLTvR!m-Qwhb%W}AxY89i|DVzE&~
zbiq2^UTQJt(A<cnNUGJr*O#ef_MYbnQxh@up5&luAodGY72CUldDP7MApzmZit)VG
zSFUA*PTAhl8A?JCs5k+)C$QB(j(Iga;uFFQ3{j__Muk1Q_A8iS^T=vbA$Ap+Y-{<x
z0x6$Tgw$~*Z-T?KjN00Gg=aT+PlaJ2mH(-%j|J!a7U5_N)XAW}S?Z|titwR+&76-x
z-AeOfPuJ7$ZfQV0*48@cDf{_KMZ3~+?yk;zJP!Wt?pak6)PU)v0WgT_G8w;{*~^+!
zJ-OP+oGku~fFd$o-JCDMf_T@X#jmZ|=q7Hhf7&GQZ!y>hfip`(y@_*_iFY|&0m+;&
zzHLYw;DHyK1_f(Wn-K({KRfVxs;^n%#EhI@ly{Ak5N6Xs-&^C%KY2F}M}$@o@48~8
z1@lGDKkrqwCPfS@mLt&m=fcl?ucm0`I!$qp6wnb9Hl@#3Df$>LS=T}ym$9_v(P>C0
z+vh8TN`NFD_CWc|+{z<U2tbLt@<6|S{_1f~4-q0xx~rO(0LKf-5j(N|tmmn=H)on5
zZ`Ee|w-K~C4%DFqSas+Xm#~8DtP{r^3R>qM5R{hM%~ZRHXJiCOrz+)HQ>e%ma8>V-
zu^7anlX)RuJ07lc2%RrouO`hSjd7|n@jV`Y)nJ6I$y9|l*!6t5=T7DAag)fkvZY4Y
z!@beZD&G-M5$%a9w_A$Om0#Qc<aIh(SdtEz&A@f3+#Jq(+m`RKVZ3SD7Avhj_iSaY
zgCOi<EU}h)!%55Ht(Lld|NBo>g*-==hW(ze!by@E4HT9UQ2Dvc$39y}r!uO0SRNb*
zGN#-cE^Z}qi>v%Q;pYiJV69T>`lwYAFdCi&(`oJA2s|EYf_?KnKu*GV!HgQM`DT?F
z`?Hh_oko3Ear26~A@NTsR>W-70`oFxUI{Da0`W=KM~y~vW=)tYg$?Z=rNgP=SlHrE
z!yc}h4#ZQ^s=nNLG8q~~!YFmi7H-}Om(vp8W=8pHyhvkxyaEYto&nD3<3ipP5p;v?
zu*LIc%Vf5J=POL4Q>8l&hfD3*n-Fak9=k+#ne*)A^7`&K)oJW+7c~<@mn^LIDEBeD
zp2$f15!PcWJ_&(hc4xrVT!=wzzHV?7!a5G`zD>+cx`HRnjEi4)$sKjQ3dwaKosmX;
zF@T<W-XDrU;BIqu0prwpN5b6aD$sK2ZQJY(#WW+=qUN}D^EgYcnY!~8&48!L;Tm>g
zg4D&G{&+0{N`Ta>J3R|3@@HwbQ}%VVo^O;5*LEAPnJ1cZbY=B>uKpd+M^GWXJ0sDS
zWd2l9nO`|ayo8@RI6mFrgU6;{u&u@00&=}rv570a@~kLoiZgnx1nPVaUAZR~vXun9
zX%U{H>*Yi&1)hh9QHDVs##H0&C?nUV5-(qca!<${IzCg&zgrf(^AX`-5qLY(9&7i7
zA<jnk;39xwRqU36(W+KVLO?_3fbD5db}G%-2<cGYS=c%Q+IwHt)c2w#*e!u?WfqCg
z>Q#zE-$AhP2tHLAZ6@J)HGzJ2@(0|hi#=fpy393aN%+_om)7^?JP8KVb`s}DVf*9l
zdSH|A0U_I#{ll*HF;+6EYKqKb{?bxnGBs$-rzp<Xce|ePcdqjn?g8gT6XlsY*B%V>
zVhE%HE)#;=amUlEHSY=4-tuQH_%>ws2@1gSiGIk#x6s@eVGgLu@%UPKe`$Ao6?%0_
zN^B)Aev43ZvUC13x^==b>mP_K6bxVjfz^&hcmp{DAv?7YV|;2)j^)4y#xiJ=lSoQ^
zF6!Hlb~C6W3-?9eVYs>PRN4hUrA5EMCO!=m$bJXRuQuL~?NN9UEP~Uq9w##qk}a=z
z?d{q0?OSsw`6rQl5BBlOgFh5C=diy09=~<ONS^nI7@eiy19H6qcY5@A$&KgmmS%WW
zk7lBx2F)<+_cEBt_Xn^^^gKf?XHSmkG3$_YkxB`%pTA~yu*rO}x|DVs`PD%1vRl^6
zC*NtxdD9EaP=UgNgP^tc!SFQm<!phfLy%u&{o0*@pb=4Y91@Q4!k(ocp~`S6-+aot
z?cU7S*X#>-IUNqWORQ^3NWBD3x!)-}EfI-A4>dH`yW7&p2;&jpSdOuCSG$;utR2?9
zQ>0|-oO#Vgvtt-(Q!6~s0t$&O-ZU?E%o154brO7`k##S%o~^ZLtmCj`O;?(}I^Dt~
z(~4FZulk4IefbDENST>4XDWONCnb9~Y0CZP<3eS7LUF2K+)E{c{M5<uxC5<~%4SYX
z^3FE$3Ysw;*gllEE6GG{%nPjItC^liAqGil#+^GcD%wHoc#~(>^Y?Q)^&1G}Vb}t%
z&t#WM+>#q_uTGb7GDeVeZHzIwcGSz+SzzKt<TdJhzTh0FvgyP=$$A{Q@g%_bIzyD5
z!$^%uS>tFc$@>jBAbJki9jNG4eDzeTBbbn!+>g>th-sO5!<L2#Epx}>a`-IWp^L+R
z{RX0lV4t?|CdPP;gV80)$$k&V!kH+bDj!D^wmDgH`PHLnWi2OxOEJpo2FrO}8Y&Ib
zeko$xRv$k?f!d9i-(v>|<5gFSizx10%qHup!{1XI*u^PF)|gbF7+vn8Ommp)4XUaf
z>7o+KGH?V)gg;g*ckV8Dpu_9JkeXQ?&Uqlc0uqZazxy+?u{jd+sluv^Q2*=Y_g;`*
zjtKf<k2d|v=|!5`(aRBL3z14ztntAuyB-59fdyu>j&G-;HYTydSUKGbYcV!@rL0(<
zDOt$8+xJ16gy~^woq;&qey`~meqKtNj{ASeA^hAzdhX$_)B_hD^(MHzl4@WT6=rV4
zi!ucv&`O^czWh104dWbq1WFQyu>g{8)25RBIWrwnQ13L{3e#i54k~iIYjnAm*#Ia9
zx4istbnhj&8hkvwr8@(+^}E&TrI61Et~2)Zki$25B2+UQI2iGs0-=-DIQk*4C$R4?
zZkHICLovDwQPxQCULc<E0U-t0-Jk1Ll6w)={Znl7eo1&838!jWl+4yh5vh$#Fq7_6
z9Q@>7gZsQwN>NH7D?h>r4F%ZO2~^ZV{Q40om@EYP+1aSPQ2m<zf;(ssaA%cfX*55W
z@(>*JJ2gTO?E#S<FV3}RBZd!hkQ<m^ZEM03yYV5t@%oUj=~+f`Y0`Z!8g3j5C!yn8
zsFGdX8WQ-qwI&F!efiZZMjfln>EZ6NIEFVIAr)l2S6J5XF&cLi`?PBxc~$GbWwg3E
ztDVJYx#+frspl;A@Y!Iq!Jh>_nwIPu9N(#A68ARthB<kl)Lw;+Q0;SP#-$_}FDDNw
zFPPbNu8bX&f8PTIOdcv`5`EVXm~al#KoGUrEtJYC(<F`QWkh=x%O#;5h~Ya(;d$=w
zry=619oVM%L@utYE#U!lAO2}DRR=BnNodv2-uIK4av^uS6w^V2^DOr*k&?o2=WnIn
z(vv>3IXD$7VPw{xt25bt;HovkpX<1vEKo>4*I-m(s;S}E(RuE+RJC+RDe=A+K}+Q?
zZbG&R_u=u!Y#lNs1S<bnbkBX|c3sUvGdiMU=FL~=y=iOJN6{;?JM4XkCN8(9<I(7o
zq}Zq1q*n&M)V)!jCt0M6a2+*4Y!Y(y4Vslyiqlxi%WqcE-9J4Jdnvn$E+50zv<*?E
zaT*NNfSf{M)vBB~h1M8j`Ic7=!*a9&3o3Y7!t{D%j^xN=A`kPFr>6PVzo<(3a$yYd
zmcAp_*p?Dza1D8jw#egKU}MtEoH&*ofuZM+3=`NNS@X!^TeW@u8@+ovx@$O4fY(mW
zJsxFwo%`hY%HJ|`39#}!>4Utn?iLoAxh*D~T8A_e4Y^hwqpemcsSSd^FKUTT96zfd
z!;)Y0L`$7P-<;$fWSXknu<BlvcI9fU-cT})PD<J4E-te9zKjXo;BNLt_CBkyC@FpW
zZ}R5|xeM0q!_&)%<sk!hs%w!+%jH=3s~F^10u1i}W_)SM*KCapw>Ihgd;Q#VPT!U0
z+>ZN;L(zL;w7hw=Rn8vNVjyQ3lu**ijRY3d@70BfcJ9FT)#*H|M3PZXF6SZe#3!gg
zYHP>uaWV9aEEUuh>#bFKIcA_i@%&^+1W87!vz_OnIC6ge{_ecY>gM856O$*~p9{W=
zgSmF$L(3`>l%XK)5tRml$$H8I4yl6({%hb1gJm8LQ`0=|+%81J!bRL6JJ6%y<}M_X
zN6V8w|FG)5s>Hp&BqNk|rh5uN%&jTya_GcA+}Ta%tSe2&!*O)1gpw9-9QzC3WOR5p
z@o~U3EG)?7_D$!+zm`PnoUNhKFZRBDoU;zI;D1Uq$FoB7K-WX>aNF$TN+}#lw!h)I
zE}e>{mQn+EdEo5*&a);`tc+pPniA_%SM=Q+|M1-kzS<sjhDysHp#{e!C&k~@p)^Cz
zU&Q@6(0Nl~LsE24)Z>U1kvXLcF`M2knQ5Uhj*w{-i8@mADyv<VWfDn@N2n#<JkJhV
zQh#F3aRxvZ={W|9oZ-e=f=IV&f4nqW<bnuiV@4E^dnSwg!9f$C+%ih+9#j7QQNN&{
z9&tu5Za2AaALUS@ee;-C)hEH5MRaFMuXIito<{2~2#8mW9w8VWgV~6r+Y=G0+%>$r
zJhJe3ogrh*Nv()LFN!5ptk+oY1YO&4OzIkQ*;@QTvap<pz?<$2rMg`=Egz7ECExFs
z_xHgp;UTsXTtcqdF(^&|m?i|t!zis$FFdQ+Ey+rla8PJyKiC&2$uZuXTM#|}Qoxxv
zk1Rr~x>ta%++>NI+?%))AtS<A71MkjX=+9UlVzV|#5HfbAzJ#<VcG1xamD#U5aD>!
z+JoIBj@@~>@;A=AsalBP0eT}1sCAitp&lW7NJcS`E@OCjy0843WeexZN3jDcsSnGw
zK?l&8R&RnX9$o73k>N*r){@>rV?V9X9vK`JP1Qf<pjgC^@_jx{q4BH{Y&LUQxA6VM
zdy4t@YGFr>;##P$0j7@`$3S!p!0_A{jF!TSRcvz>i|P1qQ}qvVsKIjXW}&{30B^TF
z;&CB<kI^B@P=WC1m_dfqutJosJENaTK@{gYOisX9mrHyJ?|L)tmMiEJ`Jio-q|~^7
zRg;@4o3tX=`G+BEN4h#NBZp^ye)Z><Dusp1bQH8vMdCNgzXS#|LoKnsp*VIlUIkGM
zEn#WGexX+c+~_GoMfTigsdYEAvSV&o^B0j?;y-k!o6LJ_7(y(%J6e?|n?>#uXwMP%
z=IZK|@b)zEXLD#wkzAV!2BE59)-w0a1KW@`DF0?*-xz^ZaGWjuaDXv6u_(hHDn~nW
zXIiVlCWmIenE=klho3R8n`ulA_z#getOD}*1@>6JwXzRB`~F#Ctvd5TF#dz#VDHte
z<klTaw`HPQ?n5()_4-!);JEn0F5_i5X021h^tC!SECQ6x@T(jHvN(GRcUbd-T7;1j
z)0U8rU-ERgWvEe}*|=ftsAhB^hpVk8mHFTls9qW%GaR1M4%FkeVmnRH$RrzE<~vFF
zoToCubzd`XI}n`mFNSLLonNbcd#$`1h1e^dfa=|Cu!{Edq`%v8l;g)jMQegbBR!>8
zoQ3vOjn@3JYv^35smNlu@Juu1$J|gumBmy35Y1jfdXD!)=>~>bhN$clR~!C&jr9fw
zwwr#_HBEA*UpmZ&{QhU}W5pYB`CvlFZ@b1&uD~;1GQqFP4a-FBD;ERS**G#gl3bes
zs^9z8pBiIoaL>qx3{r~PU2q_tOpo19<jjO>r)0#cj6X7^WWq5l6PESI>K7NPl|G9X
zYqnh<XeXB?ddKI)E(RyCZ`!jZf4((sRK<PTJ0fY`{!vik2al)RiJy*MJ!wYpI!^oC
zVsb}xoXpnTXV>UZ8pnst(IT-^Hk210&fnTZXchD?^~QuQW!FC*mdMu{o!>JhyZ4pI
z|I4|ModTFS_wM=YT!M(AEtTf0nAJ|g=Pn#F7j}t_Yl*L6^ff6__y#E8>mLc@f9?Hl
zm?U>N^`uEx=5x?fwphju`;OLJHA5=*k(pE5Wl6Q_H;Fu+OA}3c6-lCQMJMmJvt-BJ
zKDbVzDzW>e1iYFZmymi@O+3?VJ>PWBg)>yfBJ)=Zz^$Q7a;wJB!n>H_&z$6Z2?#GV
zCfn*t)Iujb0u&T=m{dT2ut=jubJTiNkP%rQI56{AF0H)mNzq-d8#kLBuorZ`?nE94
znIF2pJ{fP5#3m$Z?k!)+=?#g)yh$FdZ9j9L*5oR@XpHi3=&9qpp>kJ6ee!n+V90=T
z?_vXUIUScbkPX=%RnajJS)RyMqK5%$%P>s+N^Z8{DGp|x-Xu3|mY*yBp+giA4B$Vz
zDe|q~e}JNoz8q<bu|xfviTsV_dGkq-g&oz7e09x5{zsGecj8tAn`tX}-TeH&G3_6}
zL1+t{7-eQ%X?y?dAActYe*L5q0{sJ1I->Y@KlJZ!WcH9j-D`|q{m(uArCH#TkwI%h
ztG=iE+w8x8popjgXrsdUT(`~t-a90tjRIn9F%$zQF62$!t8|eNrl+i&^8+B+uK?_6
zUy~~+z~}G$B^~qtDoQai_vx=>IG<R$yYhP^-T8r3MtO0l+=zVpt+FxwKdXr>7&ILR
zO9|2!LRXj@6BNv=G_(8#N<EVdKL6VMJ`Q|p_h|eVUxo|^?x0ZJ&brYhqm=eDrjM-z
zYWMT;l&yqOK5F5R&XqI5>HJ)F4fwyU@Ky)8V9k&N`(G@bJQA4C_T0Nn2h4&ro-hHO
z;g|LqPxz(x3Un%VwlBYnynUxhnS7O^aDt3_YtUzXy_x-YP=t;^uhORFi$j{}{fSK1
zrH|X*tT_+?ZMu`gS*`jxh6O6Id1`YguUVeK$3Ooy;tZyS{T-g^2gp!hQ0W$rgw><K
z$mmv1s)#=Wiuk1>MUR)++P{?BQF;$G6ASpWEUQ<scC;f8cChqS*rumyoUpDcYFd!!
zxqN~2C*;~AR6{JB{jsCJM>mGnD_(Rpv(pOZV>kMmr$c0iF_);#DzidW>W21?C{rx8
z`|YAu{NZns##-8!MYg)Q<Uy(pn;+v3Sv>hCuoGlZrwe=k%uAsw$XKs5&ed4X19f9i
zTB12vBvY^=x#|d*Tho9=0Jvv_9L5Xkwx>B#ae#Gj5z0Pb6=RJ8m;(HOC2+9#ot=$s
ziKC!Q0hHDfaa-&RWxyVzXr6pW2U44#r2(ywkn=qbPmTy^iaw^$YGRXEJa79pf}om0
zqIFLSius~10-8bHQ?ls--)LPCDIhKKdqD`10NRe`9jbuMN>}Q0SBK;qG6`<;sY<}I
zbOBbU`#tm}g*weHl-={r>nWV3V|E~O3pSPmn(ra*o;1>l4++?)FkuC*HYl%vDe46B
z0w^Pi{q(68I_p6~LV}D<mP!^8mHf}rx8K7__{D29OLf29TpojFyMheYrO{h{;F<M4
zFAnOgJC6b8C9T(^qy~DdxDc$*41@YVklD%1Qm#-n%$)7}RP_Gtvb!K@yt#Cc$S%>S
zK^tdE1DU+KR^ZM0ipZI|Z5?C=gF_%zhL)oWxiXAT^4w~5fvxV~bM6hx$<nv5>T!p|
z#SXaFdp~mrL0YpO&?u@*$1}rj6_8^g`AhT3a%!37?c#bgZU)q$ZirrTa_ph(^NR%^
zr!TPPfX*N*?cw2(?g5maMk<YmVa$nnl)j4C-Dy}hR)J>?5MhQYvhm4_LmGJr^F;fB
zZwGG>7MC*(zCrn36|+0?`WU^xzV|54pFr{k7fk1z6Fg?^XF%-shhB*<eK~;h0ih6t
zWsA`-N<eC1y2>;_@;Fg6IFCWmE}iXAgb8yte#n6CE7Q@0U<hj)I<{DY&1z2%vaV+(
zT(2evre#H#cpGQrG^<31rwkHzu2lviA%jj+a$@T9=xQSxG`Bqly-Z)&@gEsTflyyU
zNi{!Rcr%JcyNA5SLOw8jQGy%Qr6BTmiYS474B{ra1>(a;UU>FtfM|f#No0n<?F8s7
zfa6i;iSY6UB%8<yOF%BTK*C=-kt676HBRR-(&1{bhfYt|CN9158=mdL3P6?#)tR#N
zBF=#hi2#dXZ;Lg?#ZlE_(Vxg7aBR@?W|{Psb(Rbyy5m4Om8s|LwoZK$4j}7Z0s9Ym
zvh10yprvYIP{0Us!X0A$Ps4s*1Ij^-!d?;r;15~_KqygEAy7x5nhHb?xKm#i^ih-6
zmM1)#OO?!=69thIn|{R*h+;tYwy=S<J(0*&j_m+%u8qozc6h!-kw;-$A1qS>+p~yB
z9uaTc0dHA(pMtMohCEq})A8UP^7=mb(evhN-))_LEw?=>*z8OeQ`hXvH2fnyBGP8m
z)eXXNsAeVsB}Y}|Z$%tuL>RBk2UJxy(Rlruw16LRiZJrAb${W)BZMt`@Q{3C4-;6q
z%*R-ZlC?!?3img<0wxhUNV6WygrrjgMoBq**^0CH&{AM{mXuG*N7Cr$y;1gGD}W4h
zb&U1X`W_TqN%>QteG@mm3X;x!-Q7<M2ok=}JRQ>-OyQ3c8B+%t{UjLe6Cosyf)r=#
z1vZ<n|HU2q^TZTd0#7QRLRI<er1={fRig7pZynBO9g}`Sj7rXrbrWD?hjeHOwU$<m
z(%i@JD<uU4Vey{UGRP;=Q@URo_U7z+oYxx=d=O|$BaR5%VbMo3VpGKqm7WKMrVrK)
zsVh*cKouE&#16v83QfFmrn3b^hcJ4%1K4(g9`Ni@tB|DYz+nQXR3Q$Y*7%^d6FQZp
ztugpkz=`?%Faoe_5IPna=1kZ;6b4-^CCeX9Tl(ZbqjTU=-^$v84zHLk54<E%`j_Q{
zgml2oV+1RUwF|M~Gpo9&67LJi1*V|<%z-pKtsweQ%e4|jajIrOO8TsI%k^opAE`T7
z^r10VW>z<Tn6JR~PK8!nL2+GAk7dK5Kk@=ZSJ(U!P)Dp|^YrkYcKAA;Vo=<*z@oRA
zEXcH1&ZnT_EEpD~AfghkFxZ(hZ18=HnJ89ChMBBzhJJxyIfdau;uW+^a_5oFZOP5l
za3HK+$Lj3N3Y<~3%}W^)>_>{{P#Emja$wbZsJvkH?fz|{e(fcyB*DG}r|Htrx-u0I
zigK!gV)|~kr=rArxh~#*q_Cq|I+N15ib|pG#@2q<Gp^&==<J2*VY}96?fx{q&}^Hs
z`A5%+l6X(1J!~Q>bkOZiAI>a1b7hY58csjVQIxbx_ciW@pJhd1e;N#9w7v0UL#gLT
zo?Ks}>3DII>kRQ`_Yu@`gZtjs_2jEY;Kh5Zri;A);7zlck6A*E_2#jRFN@iG1T<pf
zu&=p1yOBMrA>U^_J-;F4=_HD+*PbzF|HJG5JatgPv7HG%ocp5>Fj>UjS6A1_$673p
zEqPSb4y7;Suo=SmiXdk__G_Z5&G?IXCe>0e5gP&Po*%|vD|UE8zjH0fihE&}OA*yj
zmYK>zd+(0y09SzSm7S$D-jIdR1o){;&s*yow#}5?V2>PnL4b~U>zX<Cp!iSqoXtT$
z7j(O@+G!JB3UEeTtS|4s%SO^wjntW%*>|#o-NMhg1w6V#>7_DcY#MzdBfV^7!*~cE
zN1xJGL1do7tBkbO<4sM`%xAq5rcN#c_x}+7f3<D|1uS0qozFc{kBoYUXefs*op8+c
z-AYGn8I|WKs->7c%Y8Qp0rd>xgI&8649G!S`lmtn<&R^q-i4-{u2WVO`S65lhrZGi
z{ya<Odq;6U)KXnMF{)CjyVzg*JOwqhCA&{aW6!wxqMbQ&S{2QFgqgHjq7`?4PIRJ_
zM>oq=DbJti5OD4m1anm?uX3<Ts~uUP2S0n{>sxcOt`9ytewd5$;6c6pwm3DZ_FG*n
zJtnQX5&RZn8@y%gdA6+!r>j5vqTjnCu#~hR4=K0)921KU;C)(}mzQ^<IZ3S<Nb^dM
ztLz1a4DfEn`w+{e>;n#HPQ8pZZ6nj`X`TY_*gnrym=2SW@BUy@<6thZ&5~IDk?kV9
zH?<S!*-_A!187xi@dzq;5NW7W5l`!4fuk<UpwNZsAjFuD+wG4PABBn=;O=QT&KfMU
z>kziVE%C)_2#Ga=N!TF>61i~453{yXJm>ty`mt8SQ>s5r(IvpM{@__*ee|IJnYOdp
zY+Ve(MQ~991TBt|Nq1Vl(xav>nzlc<XMK64#F74QD>_RFHbO44jOVyzC5jnu4^CrJ
z>Ff1h46qJT23xI6J<UuUR@|UghSxwH5Ffj$d!}@U#2R;`4%-l^8dxay1s=|-@4_h4
zA=121GX*$8Q)&Xib|<g0U>71QU?XC|u5Bc8b73@I_yhi3ww6v;1X~YDCc7H*El{9O
znEu8kV;1jg#p$Oh2Hj`ufNLR2b~LG#k|a#9&-Y0)2bW<`jZB*)CIo8D9KPVQd3#B_
zAp3(|bz-P^n*d)a2DNfu9dQqHtr^#z{>(iBw}X~DM{N&_^MNk5>(IVFTc)p>dfMZ4
z+|vD$e@`~)i4b(+11Izjj1KP$6dl3Js>;p7AHc;FD-W5NVi&`*dM54&oUX0DV_k;!
zE=5T(y|~3n-pO=>bzdgNS`UTd;?Ck^Z#JleqTxu~{$U8jU}(IC`+&6tME51as5;~$
z_KJ0}>i1m99x*;sdA|(C$UTd88(esn-cY&R4OMM(AqGPHpLYDhF{fAG9hHBk>T9iO
z8R_dlRTT0KXoM23<@YLmfWpKB1jR=sTpPWXGoV~YE$GEa4j)pXW<$#evk$3&o$+C^
z8dl5bH?@EJLoI4RR9zaNkT%yUVD_5qpouW!JzVz^OqraBJ=6E48UAFBb_4be3g6?+
z&O{vOt81uhShhG0-<p_w7(&*iN}%p3=d84NvUOOPd0v|=n9n}I<KrB8GpTMPxl;*@
zsBgaGv61AJl!*v`f|wamCVmuqv3zwlPNdR`bri99?T4J|Ox#d2=TZ<oX2J1hB884#
zbOr`a)Ad>7!Yx2tm5bEdd(qtd*F==>i~^pBJ=l>p-@?CEd)HEDhnJJPp}7@53F?X1
z>E<Ga)Nz|b{!`Ae`C16(qHUIY(kC@Y*(b(T0I8N*6R%%foPG?q0xDitPai7_m4xq;
z<qw8Mcd^by8JQb8nrVgvyhf|zsJ9^){a#YhimwA%ncM-L^U_C8-om1|;03n0k+*mr
zErploank%n=Ew)%*)FB0EF_s#1kmeA&R+`Rt9nBh4d4W{@toNC9fXBp5sxAc-?ykQ
z(V-{PnevIgp!AY!E`;k~mt~JPy`C?(%6a8Zwl?WGpkRPvKRO_zRcHQ0b=h#d$rfKl
z`M*e-J=AZSXYfpZv`}~-hA6WRj9GzAJvus;LG^K2OdSI**J-bz;M$i}<{iL)#X<|C
zE5OjV6|QT~iycK?#k+_m382LaPnI8z3wfkM7gRD6@Et{(%0n-knRH5ZE+1~y_=c6&
zbxh4@QM>x>A*^1*e0!s4JePT*4ry-RY$bmy5uyfEAHQGrGcjwXFAAg5UXM`EABe5-
z-lxdf>!>ex(he0ldTb}30rJGp&$s@`1kH^D|EgmGy<~+RFCd{xy%YVmYqiY&MU=pi
zdO%2=h}S0D-bn08Cek?@LF%m6jnXZ^(9JK8R;%U5M?0Cxj0u8AbDcD;Ut=b}yk^q+
zV1Ypq0LYwEJOp2sb*LjNAohf}3`0S7Wn5-w+l2M17An|JRJ|O@&Ul7C3kTG;Av@AG
zV`dalwLJ#b7*bRrD;>_gO-(%Z)+^=stk|Md(X=~1Wd&D<8qV)lYvJLZRkTg5Vkz7i
zrO5`zs&QHY?(}iQK|O<~N1nwyal@?M;(F)nSiqG!uNn-?HbReaW)uG#CdgL6zL1g|
z$+E~mu+?;Ho~4|6`ioXGTO^w&>+-djTV2=7D6Lti<*-`T6pikVmqX7(bSoOe3&(4%
zm!HIsPyOI5TXF<ihz@wGhG_IPL*rX|9?ihSb9lJDupw-6LW!dJsmhhCEJrgDorm|(
zJKKUpZXS<ixIr5QNhWC=4(t6PpBBz>O+DL19OthPbLMh=%<_Rw(&(IFh6#uBkrXy)
zvjC*EjR>1@c|RPA7O8@bbCRd}p0iw4O4E`~f&XC~QM{1@53yYGGKRSrDsJd@$)WOg
zMim_TU1^Fdl3OaJ!U1Z~eW8ivtDOVLn~v57GYyB)GRxj8%Tu2FuJg957x3>YF54`z
z-Om7NG`P5u@UwsKC+Dw9J;Qti-v~DLnvrxV3a`ap{)j~N?r-?wy6D8bz=YyFvy7xQ
z)0=1AP)|iyQQ<URQoqL+6)m@~%&G8Fz-p;GYm~Xs>F0~J_YYpt(kd^I1k~rDJQelQ
z7~Do@D<k&_TF$##juW;;Z_cM`qQK{{yybJ)9Lu3iQrz^^Uu-rh|6AMBDlFv5o$Rk$
zaWi;f23rIF_B-vHO*DF(njIIlx1chw5c`bY-FatRBLPa6D)y(|FzQWWJVn3dLR=7H
zcoWCFX)eDb4H{LC?V=i?EkZrstzi;*p|MP?+eD!R-$A_b-L02OBq?Q+DPcOsV})vc
z<IqSu0NAHA)EVIsaPZ|$jJ0IyXIN68=5qmho1x+Z74dps*s72Y*0uowo+T*=lZ-eK
zk*4bN8wg*|;JCh|Nw<Pt^{d(Z-fS*9k(>%`f%88gk17Qu!%g65qpjlGJ?>%~MB%fX
z4{q8f2mO_re21?*#4ONX4Cprsx3)Jc)nX4jNxl$x!lCcb*B_zE9=i8VNb@I1G|S$w
zE~imT;eEbR$00&GF*vlU?4pImP_QM)D9r%6T$0}|D25*DQvA%7HPY5ZyS^opZ<wLd
zX2O>N)O{I6d5z`8w-`($2YsDsCglU~a-~p6JYQ?$VUS1@DZ7sc=O6a}oP33GkadEL
zMgBSqklJG&NoYmM=(aC)&8_WKxJ*(Y>q?0H2Q{-n9{HZ%HSf^%unl=030)u$|N66_
zK@+x|z^e9ZRMGTsOtOh2WAihmC3B=^Hf);LfeyLjWlwXv?eLg1FTmk$LjRKcpy_&V
zSxkv%eQvKa^0vds-By>UU#d>&=VuwUdbc2=YV+&xxX}7xlCj0sgpYkj4)mnq_yP(6
zxh46(d)L>uCDq53uX^JVmL80uY9#{`$JQmyV41r@OPaT1m}Ro(5fozW<{LOHYA>l9
zz`m`TXB}Y<3C{7rHo(7f@FkBR3+tPMgTX+?Qa>efiRk7om6*S4g0lE2kbRFXbJxfD
zpF|QH*knKoza*t#Bq_)ID15pjINr4(nd552rNYb^mr9@K#Ayd#s~j?C)K!?dbG$pD
zruz1di0TY(kKIZ#uP>VQ4@yD?Lk_7gJ0hYw7M5NB#PGMHH9si*u4t6TcruNHgM%dz
zTj)-D!ZSQZh0`VOHg6PrhY0_{xaq~<yivUEsCrx=1EYWWWnhuhp$L<V{RY%Re*0m;
zu<<kZ<8FhN>DWfA92@{CL`j@)GY9g7|3*O}xFvwUhD%7S1B~@YG*tbkge!w90L;)c
zF%5Kgzm&y!n{+yyC1L2!6N4H7cz3-f^VSo24=OaapDRx6MeRTezaTK<0al>C)0o7s
z?`@$i^}P4EAF4(<H&rZVgn_4zE77iww+rul^@_{#i8_y~p}AV--`p}NO``zk3dIJ~
za*%0AcR_ymh^0l#%V18w&oO{*gvq;Asn;ELtVnzDe=1H7k)Ocv36Q1$lvz>&W_PNp
z9&nrR8B~R^3IR?w<*>1dMB!#@F-l`}J2g5`yu<ZMZcR7uAAtQv09^BkAm0x_$%I%N
zRyWc9*yxv^T+fI~_2+i7B*NoU+!2h4vLohM6KMay--{Grpo*`_O@HIjOBlve&rD~`
z9ZR&zc3PSmwOrSY3~EAus^<R7{)mzR+?@wX^iR=32F;%e$P6yIj(-usH^wVU*Y9+o
zi|Ic&$?tPMhIcju(x;O_rTKp$@EFP<=C95tfO0Bk^~#N|?qvE^$H38d%N=2WVAI{|
z_h7Q=M~bYztz5B&y!=ufF~5Tuh?T&)2x&)Qi%>DM)N;NFnAh#ke65&i(wwbnE<CGu
z*i960zXJW&^B$ww1479vwV4Grb(i1}W8J)@BW&~!X8+yB9}!+-AQku%{qZw!aACHX
zt}YS_!2@1Umb^ucKL?+mYXTQ31oX#d{DBmG7%iaGY#ZEfQA8x<cmxEoAw?Dihjpp)
zZtE$I5w?IRRS!IPc)g!Pj$MAhv5NKXsWiRo0i^yWiK__k+kq_|23{;@-{SWG9dHnV
zAh+N?B|biWH1tKOKuB-p3g9>$#yEz9skfsg9#x=-%!7z#!0!eG`-0aAY<{mwIV@&)
ztg2_e12D2ks~(T-x$D_O&AOQ;NV)WXzuwdUJhrpGxmH^Tu!%>Q!^+Fc4?H`D1MY-C
ziI&h4`RKGX%TrKK@_DGve%l|FvTsuPWGF-A;RPu2HZU{<a-Fk@@J(_)f%<J!Ns$OL
z)HZ=}PMzT-9#T6-J_?=+3Vo1HGxp(_tu(>rZ@$>QW%JOgq$kCpAtf#XVI26*alfk7
z>kO}rJe*-00WkK)C;%xzksBP<2DqeC5{ui#0f6~BNqK`-fg(H6bUe?iiy7NN>7_2h
zSN~b$kijAwg`msMh=)~~9@3pZz(IEdK$&+x;+phPs{1TDWf?T8L+`J8#^6|%e)3U>
z9^OK*BH#>QG@)VfH3yjI4ePO?!NgnvT`h?;#u`H~m?h13F6onD+;bB}8r&*DHDmBZ
z%NmgKh{)Q#LLH%>;Y8fwaWESbKtE7#I(C^<Tqw<_H#5swfyHJ;QgeQIc__+|)bqyL
z+WHVzMKdxoa`9uD)7SL$g#@G2p!vt1{Auy#7WKPaIIevPU;a^g|A1iMA-Vu({RS^~
z=I_q96`GBbtvf)_eZ{Xh52By<M#${CJ|mwMD2pb>tTB5}Flt0^W@}?3Q_Y8Z>9|`p
zj-?isbPl$Y_NN}-I$k(~tr9}er>_`gJ#Lw}PgA!N*p1k_fCzsew_yew=J;V}o9k<&
z6EA33s}*3WGDEn02PzK8f7F0_qv7!-oMX<o3s8?}4Zl43IV$|FlhNsnz9{tj4AVM_
zL!RaTUD=YpUe8)spG1Dy0-O!b<|hMvAjtmA12fW>e!0#K==9|i@Y&^&O7498kX^Z>
z42rNSUkoLTrGrYBf!SB6beIxP>aIZDR_5a>vk#Mm*fy^@m{$R=ez%D3S^6p$9njS-
z<0-J`*OXMW48nH#nVI(i6rCQrDyiv+qIL%!xnwlfNbHnL32L#gAF=y^s<f|$%0h)d
z@aHYxz9k>9I+mJ#3diO02(?d?1s##OScQWH<ts=#-0}3G;q$#pdZz7U{q>4EPV)$O
z5lvYx_jq3YOw*i10b&8eVDvV@sRd%yxErBX8b#2|cQnmP<wCr`lt(oE*m(tWT<iDd
z!5a>_a9WK=Z}%Y~{@#<<r6Gy!v=QTM%-r?103=JPI9{rGc&YZB=w<T@`?X0)J_3+}
z?FM1k4dvxcr7tu#?`y`RBd~@Zv*`y`2@PXDel5x>^&zqoN$ez^RLZRXO&6*ANn{L!
za!6lm8729(Tt}$E+6g!UX8CG0?&Hy5R~6L29Pzx-3mBj$IxZ{_9a6Vp&WtN*IC_;$
zNfDd31`z(&DSWui93ie+dMK&`PgQ&_Buuh=^Sk@|Inj9u;~fzLH4581djmw3$2D!k
zw#B?3Xn``y4JD{LFRSJk$>q+WTCirNWbZ#c`$2Nq|5TB6pXLdJc7qexOXA3Y983#V
z{O%k{Ev6!v*H&;`yG-#4IBJ}w)+*iwiWzipe3ctN1PY`&@toaM43gFN`Q3L<HcfL!
z>j>=optPw)=V%I_?-mvtrHxjdc;4o7N<SwWwQk<(sE{Mk=lBe=24KI59F=WB;m*pN
z{Muk~-yn>s>5XSi1`yInvZzBoHSN{uKAx#ERY}gFA{HN?6sjdwyV~ZL#BNq<l1kwG
z4rFh$n6LT`ek?^qT8k<GDEk3YSoq`QH|rZcLZ~msAAaDEbI}}nJw~{|M{_`gDrmjb
z2BL1{o1Xp<;*kyK6>0^V63)!H(O!&nO7f*K62`D`d|F2JPv#L3-$a$C^INz-5O_<|
znbcs8fI2gVb@rPe_T1;%riumjRLmT4wmw$mGYxA{h&W5hHCXY%f|Dc6jAhv9&!+h^
zy35uZjt7=;2COXdx(&G#Arc3mI-GGf>7)}X`=*bP&)jM+kNoS?gy_L!*R|7jdd~9g
zE=5Nbnp-9n7oluQcjpRS!Kbu7r)G**V{y~0qiJC_w0Q^=Z??hlP*%jc5zJv8DmCMt
zTOnmRp?HW2uC)caca<-kL^*khmTBvwO)1wlTy@OVj!xe(P`Y-1vo2^GZ2Vrpy2Gxl
z9!as)$E2IgSPZ9XdzB(jZk83k)KpCwdYtvRDqFMi1;vqdSPBnS6hZ&XHnz<15e6ww
z6aS>Rp?3mncRBv!&};7YK5uk~*;Ee@jx%-wm~8R#KVG3$azppc6s3kv`hOBJib;7V
z<Y3mSg-(6K7(+(!B5prIg36XMFc3H>)O1_)n?7)BeT`UPh5><dg`hh3SK4XsioWXw
z$w=8d8aP?dn{n^ZC2O3N-DW30bQpO4a(>GxuWwrliKA?_;hhjd?i-%U)UYils+stw
zw`R3!U=Q^cqU(UEw}Y#{h3`mTEUX{nEYVwMyHN&YC`cA1D%l^{scmlceraiH!kg=R
zqi@3%rZQGqocda^_AM`!`h-ez@e3ssV7FSm_sA!i<_#|k;fs+x2^_Znr@goStFrmR
zMgb87q!pyQ8|fC15DDo971(rlql8Fzhkzi0#HJfT>Fx$Wy1U_>txx!T&-n+==e+)e
zu=mW|Gi%m8v(~k)YrWA`&=*d>!d#7*JU*X^{hdz-ts*@9R>l`y0`6`r=qHnMuCE&_
z7gD0Q-#{P@)LutUa@<82*NT%D;&+Etv26koTKvf2xW{4*l9?D-<SPVLZIaYp1xwZk
zjDBQu438j6dFp)S0m6By5U7B)@o`wNbi-k$&~Oa>%dSzEFVx|M5UODIZbHVV8DY@e
zY<F1kJIca4xHb*|>m-BD;Ez*Q1=-F>TH_SF310esE?fQu?IDJvQE9<bP8AzD<vZv~
ziT4y<x!AeZs?ZDI%`EnR>)m9GQ4?dr+3JOA(uP=YxoeKFeQ0qF4z{XXGgTM7tSKJ6
zdTb&I{lIRgPk<E{h9u>%XdOlxmW-G{)4rvnPV;hNqU~u?xMHxT=^;v4GGR^kfnn;X
zWZ9jV?c7hX7c6M`8^e*l`SXeCvWNNy=<!qU!`s-4(yL8%Ydoe8W~ViF-fzt`zH<3l
zr!Ml^-otKoPV0-iN!ppl>|(};u(E3=D$=5d1&r=5&|1Eo5;X|LO^iDUzJKprR5q~o
zK0LMXB%c1=U=~Yg<G1Lv>4dGB8prnV?}BepxU+~f4CI@()V(5*L&7$PdYe#H*waCU
zh=BKeGF!VF4?FGsh@kYaWFJPyr`R&EtX0%yK+NzEpW4yN2al+)cJ4nuQ6o+fo)IKo
zvzm4{C%^RUxF_TzTQcAH-WVYdgj@BAz9IVbz<ZH@^EfOuK@6I{sqN6#C(evd!e_O(
z>dYB@&#&r81I_3#iYL%;5C3G4x~Ka9eJdgYZY7fF+1b(A{*vs`cYXD(Du77kT>>yL
z;Q-M$U6hfuh|J4s&yP2SS}Q_Yj@;f@n9>y+@PGWo^}>Kf+uGzg|29|b-h=|3{;MoM
zx0L1r#CV;EPQ^763l;@<^w+E+c-Kfhu6A>16$Kt?!ihhagV_jucx)74EEJD_u~0l3
zc}{obH(-~Jo=XtjF3}(8@e}6Z-vOl386sYMjk<swd-_mfX>W)2)u(VlhFk>qh}0q7
z2cn;25{m4=u^Fq)=e*lMH|(J;gAV))`~mL~kXTOtSmMXZfjODf$#A%a<d54v(uVk`
z2~_!4=5gp-+;9GFUf>)|kw^Tf>*HtCkr>O+fOezln=XyUS9$N0D`^HyUu!JswmU!N
zy@$VO|7miKX==)3OrcDj0NoS7p3CBiq)&nRqpqodNp|F{DI@H1Bo>-f&$XIEC3c;f
z6~Vj1m=ieSO?TU1w`!5+n|~F$%}cRzVMN>%6QVwr1rUYw^e??hJIJhy43!i`((%wb
zIOvqe__z%s-U9H$)mC1;_<241X+Sb>?hF$p;d#x=J@m$kF|_tw#noO07yo3Ny@RRI
zD^H(+$g3?}Hzp3!CYmmmpMC=z8R&3<hx-F%FAn=Fi|7#;p1>l;RxJf)-M&nA(_Pv#
z-L)#wa&_=gMmNfu;tulmF_x1R`)CumSl%~UK1NL<Upbj#2K|k>r6QLM&{K_NL5cFR
z<uQO=qDOumtlNUB4OvyquJC4uny2wt5#DWyo@LM%tA;-8NPqarF6hi@sZchTU>5_1
z${SBdz<`LT;|?=6m3C1ot)fJx2J>r&mWpc0y)z!-rQR4%3gRS-@d*)h43JLnT<M}<
zChu!XCkqacI)aW7(y?QlaGZabdlYOtV;Y_7-Fm1^ZAh`=wRvTO%-EXmofegNnsCVK
z7_@@u9Q1?vn<o!DcMohQ*^0<PpCOt9T9iGMGjLl%bM@`K^8dNS#nI}j-d!tu#xlzz
z?oISy3M8ICQ6wgPo$Lsz?*d#E(4Mw;%`lDLvUePWXC!(Ayv%j1H4;pTnDLy`_&-+f
zr-s!uKa}giCfPnP_HQ2Pz~07@ynKuQ;6bK$+J?!PXCeFyv;VZq+w3_G?kNd5{4vZs
zc#t#x)zl@{ujb|s5s#CXV@)W^Q!vikQa4jr%gft}>K-Dvu$vHVlCFJ{z?R`f;G;<5
z?6$ZL)=}c(ei_r4=)cp#78U@Xz#Y|p^FUm)jXNv~56wzp0gI4;y;D5oy84yQiEJ5`
z2$7~SH1%wH6M1%F<-q<cp$3MP-`-XbGCId$&s(cK2@Bh!GQa$n-a<!~{wG?|FDaEm
zU@z}xX~l~wc+tF%(o&RA&k<@?osPv?BW&id?AD0uot$7w)knfW&Lpbe{{U)+m6Y{P
zr*S!62kSkIM%VrUx-5C={2*J*ZPJ=)Qy|pL9+iF-vFeF<8jd0Hqjn5go#g^0M%l^b
zAxRw~6F)~@OqS^A=GWg?8f55=(KYW}0o=mld{7fVV16d`4VqLU=y=z}YWMC$PJ#=(
zHJM?gwk9X^JfZ1|W}D(Q8ybCU*mmv=`3yF|%CC9ys%%l;K90RYf>EwLg73CiMqaGV
zT(hO*oPA1Oo`D;(uo_u-8HR~Y#X=VkU;HKK)qYs01D=}%y;&+!g?ASzW;uahH7(VP
zrf-kNYhNxCHb)ySmg|u_)@(~mkpF}k5|+qgPFX~A5R9}9)$z^1-4E=M$kcb4b?W;X
zg7kPl@O8|`%D%gVkKXL`i{92VjDqyp5FRvI1@(iB=?=j1N-WY(OD2?YXAbO9udc2N
zQl))%<laZiiKDdOvRacFV~VvsDr(x7-s@jHHHl*@#$?`0!AJb2y|f<IM2|l;gRzQr
zg6y~qq8Bg_M=Q9^;|hcipY`(28->|vRdqV4f@}&L0^S1>lLsrEUlsDEJI{$t-g-^5
zkJ1F3Y^o`+!mEFhDn?Y;p@|kDT+dh0hNB~q;YR-i$xd!I*Tj~23SKr}>jJBdgBd9C
z@G1LrM8zKw1mD3$k#^)lC9opiMs9Pu0w6FfnVxDY>2T`saaLbfiSMNxm;zy#ah8%l
zhdA$s$!u^SB=&|e2^#@i*AFq)Wi-}m^2X;Zr#Sapx**A=c(owf@xYcrnhq|6G;d}T
zh{|vb5%vKU0Wp@CmuR9_06`DCYEqVEx2uMMP?I?}yJFw|!nT7-w|!xlWuGG_m17ry
z!5Fk3OW|8mSGY6<7hA3@w#sWZ|M!zZj&b2`Ys`Y9<dD4dFqN-sGKfP_VgR(|IO))4
z6>>P{-2PpdsNp+y7rNJXxHYEuV<f2-(W|PaYjlo4SCictaHp(8l03mt>8&bwlD_?E
z<yNAsiv3_{{^f*TgZN$l3n0$XrS{<_@g`cY0J0->KcW^b<D^ctHWZSs+8=nGY*F;m
zbA-DJ)2a7jl`g}RbH%wmt}#{My;vHxq3j103v&kS+f;3t*V;q}YWa=5eX3Q{kv=@B
z%MUoYX~o)wRwnmU1q4;@xuPZ!rV{}MBywzo1GofbN)dupmfG0QfGURSlkEv~2VbqH
z%8OpmtUX!3{Nu1afC7S>=0~=Imr*aR&snWyXVPKUxaG`O#%xapzdeMp$mqS%3JCes
zCaYuKZkG4q;jG$~dzXT^%DpYpEp5ss7HvKgPRMvDLRaMWyQ}20$++uyj_&8?-`{tr
zr&g|W#5ncBnHuZPKO7pe_FqG&x?h49-CM}kbY;J4zq)*v)y10r#+i6Ghm2~i773v*
zJM7o$;h^NqAZVv}+;cH|wkSWS^jEYfQXIG&IUBqJhspeo@IgPj9P$I4nt&TgFA7I_
z_2uPdJ;3imFXo8fZH)cNHF*D`NVjGvmQfE0olx?E9)w%YK^kGfe(PN~GJL50l7y6L
z%jeQ>+dQh~^Z7If3TfIe+$9%_E_dpRkE*wDh6YDoPs%eo2Zn0J3-#2VvpUv80d$7W
z9i~d~kcjIu_eOGoA^$G+7Pay%w3`)8QiaN$?s?)KfGH1<YW2|x3KF$=zB7ryFo>uP
zXZ$x-`3n-f@c^85ho*yXBopkPM>BFUMwLI<N_lfjQH&GfPv)`3K@1MAvRjtfk>0@(
zadt(uY4(HKlGqs@J2id7au`P6C>TN}LlZ*fT^S}56YlrONPa8Z<zuNRCVaLX?sMf=
z`VGhNJkFcoJUJyLBxt7C5foU7<L6^i(h_NUcGm;=+X|sZZ8P5266j739NR@Cg+#UK
zk#CxS(<`c1LfbjJZB>{659<C%Fq^30pJd)|G;^jk41CkjbY>ESL6RI36C*Qc_<%Dw
z%}#vrn1!T;i2{576z8Oew%O92h~!8Py(a&RJWf`tN9mo!2-|C2pX+1e0A3Fb`m#qV
zs7Tt`PhaFo8X#Ylx~d1ORo++gV|DJ(ML2%$uVjn6eb%P8<&vrOCg_pk6boVd{y=m%
z8be4o35m`QDg<fE=jv@`J5hvA`lBtrw{)g?$^Qg<f1}a>3n-Xnoxn4$Yc1`ERsPUr
z+`P_-($`C=PI)q1y~s3M=1L2}?`+2#aqc1no=duXQ|YCv6;VJ>p98>7L4~)dX|EQ6
zv(~s`Erd3%=cX)H1&f5F-SZY1%v1fRPUCkhGZF|w-4!6&fv)@)dId9H+hn0;_j|wu
zhGLuN8az6A+Ia`znQ7^u<h1v2T5RU(lVY99Uj|FMxAnsc%M9E7IL<v^9DR?9rn<=o
z^|Yrp^P;?hRaz#8B$rh-GYxi~D>R^<{E8>mqjG(+^l2Wbge2v&H@xo4s+b<%5h{5+
zkZXcb_LwMbxKX9Yf@P}FX*<26apxjdj=b#2%7Vh%X>OZ@$;`pNJA&%gdKJ!>$zsKb
z8DV%~+DDetWnPCT@|?-mb7f}NMaLGE#S9h>{>?Pe9<DFj>)X&@-+tuEw{@~FR@0ES
zn5;I|?-uf&OflwJGI;AGh&CH8>BmrIJ#}$}aYvii%<E|4#m?pDF9nrbvpA->>5x0E
zTl@4gWfosgI*=$~1@1YheiOHadGC**DzHE*;}hSe9H5tXJy`|;oQ@;4Wfn((#S@U*
zth0T9%<`pZfU{Dy99CBUqEGZhO)?h)m(7T$<;^k&olZFjZ0kMUQFUJ0nhu<u`@GJe
zQ}=M2+1>0WMDS#{#N;Z;L#?TxwsL31JuRO1YHzR=cU4hWyFRBJn){5`dG|3-u}4pV
zaP1x%%0i+MLYx~*T_~9lX~5D(|F+0R*wf;E*5qw-95)_Qp{(wApeoWoRb-L_YS-NL
zg~=fC^6Eo&kb?TyH=h)Uk&x}h0JMl2UKfv`$y+9mLgT0o`s5l(oj>#SPwT#E_TACD
z#l(W!iSq}59H4*KuJM*_Z!kK0m(>R%_4WQZvrvCvlA}t0BY#+mf>xCj!o)1qLrHQP
zkPXZGW)%(NQ0=5{rZvj&Iw8mce5N}_+|rBCh*Llg*CC=$-CD*J^)9@(4FIa&`BX#t
z)46C>NTOkpFfOW7S5EY2X{C5J+M%suRaLILCbxUJ6ujBqZr_zkvVjR5>uE19o4B+Q
zdAi*^RP@=8t&p5cywKCHPu(Gb3OHJf3THn-Lfvo~_SUJdnjkAd>N<{CjTCh~TD!9P
zDpx$EC#bManCOJVHVBpNP6?Ws;mhWDZ)~<dbSLQ4#cY(j;Kdkp(fCFU%%gqsvhEn<
zKBMWlpI-O-gs}pRCYR|s7Q!lW{e{mr28-P9MGc)2B4T4bYt0(;j14y{wFr`?F-bM+
zsi4>C`XST^x1lqSi?)0ovYe7kRk=@_8`&1~G!XKb@_kw&-`VwG%B_8JvGOxwhd;Ts
zA?Sp4wmvo<5H)ahn%Zm4a|8&EO)^y~2^00%!-$@gVJwJ@bKH}Fa8=0-!SwO8R7hH9
zAK>vq5<h}w5JV?3uPMOAOr#1qgK$0FlQf!-RM&hP32EhLIbYzseU?22p9JriEG$}N
zjHXL0X3c9})sD`yuLXK<U%FV#qGzPL?a{J$m%Y43DjWAI_3TFR^VhHSn%M407umkR
zE5`V&#Oqyw=S(VaM&<xf-=x{tSUB5JYLcu`OuZdi><zI>K2|7Ltvkc<<Z->`aO=!D
z(IT1Cx;gnug>3anr~k}8f=5`XMN&z+eMp0B^p14I&8r(`qT9UI{_d{6p8@X*@*6kD
zlA^F1z6l*t?;Tj2ex2<pFq0Za?!Tn9sT-(jgxeV|!i1c+pGOSemTVdt4Z_=>&N=L4
z5Afzipe%ridXx)_C_n)WAg~;1aDnQAL?S2RghU8Q{rb8MvQ=k)NJvNoF@s*;Gn&iP
zbB4*u7a`%6G`(czaW&3*yTiF=L@BR+gb!8Q;T^n~%+!A?g-$d%3Ai1E1y{B5yz`kS
z8pnvcC8c$Uyz)@t^>yyAVFg?0Roi_~X(GPZNN7dOK-ccm<_)Q$1H3D5nG$z<0+U?h
z7}jDK5i57+Z-UmFZm*B#0mrPR_o;@Z))T*q#STN>sLJ-+^@YNGgN>*<4~(4;10x{?
z<7GeI<pa<B3p}s(A+HhasC;Q(t0F6d9jj@|51}VdE|d)=I1P5vg|sf_zvxgUDaZsY
zv#Bx(r=8H$3!j*0syG+Djhco&HohsZ5QXS97>J$X?8x-C=@DJI$HmBHn(7S}642=;
zcM{g9#i&=dIP_ichsv&eR$#HW8%1g>J}Udl2O{rhw4s%iLpgU>lr=C7y!O>V^|UAj
zyzZ5X82aGBRW-n&+vKFa5PfUwUO;Ws93N{lRo2NJ!n!v3&Lj)4M*7)<1a0ka4q~Oe
zdnL(LAV(L1&*ptRssXMPSAgx-a;khCPyoJ)ZVg0dviQ7K3)q}}K<b0*kwAG*J)f~t
z@#ACO`-F<rj~jJ81(_<DZ*50|yk!`Drtr3P$7_t|fFO+|d!PQPTh-WX=bP3e2wu<q
zYQ%gadQbN>ZO7W`QySu|$WDAch-QEl<-L^tT%SNSPfSq@zJSNlv@Z=DSEsh0krqB#
z3Jx&&NhKX&%VeN;hPv(<Ch;@_-M#cE0kP$+0D5JQY(}vh)RDLK$O_R_$W^ojGiY=C
z%kD^xiZW>goPNuPy2_1bG)xRvJ_7Mp`dy-geCNCTo4Y23X^l?v>NoNW!c;{|Pl@o6
zkbWrjOL5_j!m#`>@=!Z<a|W=|()U6M9tS36`oRR3ho0!Lt`S*R!@neU2sCPKIrTW(
zd)cS&x&Qqw68if|W)en+<kbl-K@-QViLBQN@p`1US9U&&-*|l7Caek(O$OOSoj1OG
zRJl?uDiWS7k=fk9$Vj;?M2mBb<5o8vuI?o3uj^@=$%to7tUQ;*pl%X*+D+mhDA4Ui
zqx&>%ICnC*`t&e@jsq$expr@K>eI`W#}4Us_+JLfzV_+N3+?I@?OvfD&KsOJ3aV19
zBVM()#+EeD=Pxc{mpI7mU^$Cq+yBT_G1~rYRiLlWZa3p=;a0OkN`0b1^=3+_?S{{t
z$CD6tt5tmid>Tz=ehBPRgxj2E!O>$>OF3O8ZvsS&jQl}h)W@C6kjao!RA+gn#$m8C
zC-7u?<ow{K^-`26ln)c-g^7y#Ol87J&3%sNoRG>Zy>hcCDzOX7ljrt9>U;&8lPRZ`
zv{VY2>7quM#3F_w5(-f(r@>kg(zgvnYijaA=o_OJqx6dnju|~jU-|T17$2h5q&f8N
zTWpNyicLCV1jWS&@R?cBt8X_pu5ojE;12W^gw63cc&r}1%%`iGBUD|RZ2m4SzCeqf
zf(3oz5>HS({h|X$iRjt9EM4=G-SM%84gFN)OnYlpjOlrZyWVqjhD^J|i#$!t=jHDV
zBx+t>2MWok#4DIYaNWkHqh|!dz>smUiaQk34N%t@*@AeoJ0BsPpsESVfEpLyGfk|S
z!ZP@fK2U4)1TbxCG#)%uEfp2UAah-SpJ}p;<FXhl1PO7W;}I1YNJvV`3<<x<D~*}z
zX-Ds7ZeY%&(4{P~W4-j+Tx}3;v#|DQ^>V0AK6U=6+@S$wi<@LZRI32y5~e!N`OSG*
z`vlemy7-T{0Jg(0sf}q?AIFHn2LsJ#e%CzQ>Lx)cw*pBA<E*vbHq^+9L!#)sJgFDj
z0ab@J3=VAZ^%t+GNmOgd(2Q8Bk}M39+hc8?8t;9L@i<&u(5v%8e+@M~taw^1!gaCB
zP<AICW#PRD(b2^&ruSDW$(vP&y0DGd+4Tc&jl$`g@QQDJTLM}O`)9pWO(>%ySMAwD
zf%}yfe~}y*Q<m<#x?F#-CUCb%P}h5xno;kFQ-`>^`qN-wQ+zJxelJP#=%@2x1EFnR
zg=t7@P$od^i@^$iGy>8u0OT=;6uz8wBf&^RL(l0UC0+s>li%gh`r$WR#gbmOSFYdQ
z4Q1-`3TrQ(ZO_yk!V(N%F(~5z!hEGK_obhvF(*z`X`r6Z>{0)Yb7jq#f&L!!?qfym
zgB5W0vLUp`J*GO4QkXf9w%9_&=5K&Jp8N1M4GEW<WJ08!yI`l~M|3nzdzI^#9W;)c
zmE%oD_qh6{xwR~(X{M=C@$D#qtC3B$Tg|cH$RPW=-I=DhJZEdqueCkq5|!TSU=|mT
zs_sl0&NGkU*i2OTH8?!V^Vr;R(uX4|vh_Z+<P!L@|3RNF%LIoP$6zN+!WwGortFFQ
z=7|8rMe3S!>Ww_w#FH=t_@VAf=ErI?1y(k(dzD@v`O&s(-Fa|Ui{pVo!Xr2_HZrmE
zlEBcRVqEab`Y(b#kM*ia!hJqfl?^r&BH6IZ=5$-BtDg#}+lUa0##wAGc_i)Sea`rj
zAZ*DzEuUhtU&%*Vfaj?RZ<-HuR|{ej!@tYSpY~qjXf*X$wA;alj#;H^5nd>u8chE*
z+1*dGG*yp-ylwA<hEVw{zcEVV8X}E&D}kxHwhwoA!=+^aCH`{bZQQO-r7c-h-Isz0
zn<SGwS3l@03!_$Q5!S(El8gDj-3+x1K(Zn}$xi}<C!rW9H&ZczLKN9+M=3K>c-gM0
z(uMtqxD1U=g?SwiK4@X~P!Q49bUD(Ogs}DLE0@)FE|yr$QfEnNCap8Nkj*@OtbPx-
z=Dknb#`$3a&9@G1m1nB<JiK*>8&*-*ezSCJf>0ftkUOWusB?tlxz-QD9r^6nlX%q}
zS$$4lA&$?}O7b8wp1xHNo(vpVYo=7Rkh*+H6%;qhw4zirG^cAj(Inwx@1-MLq|NkT
zN9f0<!ro*i{)=HDByRyO^R4m7<5eC@lAD!%*M&BlkuF3xA(4!IH^-~`TUXDkm((x4
z7s;G?YTeclyMuV0&g(J?&#7yR>&A1!Py1^VEOs)&xqNs$`F?rdf0@C>Hn5vd>r4l;
z0PS&+W@#2UlwZ9J8vsRJKc*@yl0xMWd;6LJUE?bd0n?(hOinTZ^;tZGiF;<RKB(BN
z#8o^x_Bb3!(b|+FEmTzZ2^D*KtuMGI(5+DJEbT|+x*QL?tt?y+#fYAiy-7mkaj_T;
zGj3iP(JQ4{?0?xbU!3ZOj8YzNseiR|;9`fL9n`<eQ45*YPo>eH3R7<lSRo)_c}#Sd
zwRUOXtC+kp#<bJty+ajEoc%}*h3w?sdqh0$=o7mZDb4wanApv7ylmUkMQprLn#(OD
z0o6Xz&cY!(_Y#lkG`#2zEC-f*>VLex3>UWj31`ulfXDV7J#n0KcVoDi<MkuzCk4?%
zp&AC0bY#Iu?JhiheI1UNvfKcBP+E`kwptH*)u`qvq|}7lSN+|y>FTW*6z*o-b}42j
z{F@muo+Vp}?>R+{M93)~+dQ=X#apTK?aL^9-?B5;{2Z*$kk;Ne;we&L$Q9u^mCj^i
zD$GUs#}9V0e%1B;aTdV87kSCZ#ugE(&em|G3`7^e8dL${J|h+f7;q}jGMf2_=JpUE
zoxCrn=NEUahH_An37R-Q?;dosN#7a2ix=Dr|702}ThKu{$4YfZ@d7<%MswWEA~$Nc
z3%&KC;f6$kF5#ia?bJ!r&d8LN1+xa;kAe7A{w6(9??+#rT;p1wEDC=oE4pfS%Ksrg
z97q6U7oei?w{9lO(W@G4hZf3Jp}XS*22WouwUr_ShtyWBgZH9f;Jj>@G2mecv(hCO
zqwGiW!X%zkG!>TE4-CML95^X?;SD*TuEUU8WHa9y27)GgGDlt3%jQKsbZ0yt+U^(Z
zpwVpZ8wzr%G(8fk@4n~l+1*KC&E!4F?7s2dg>Cb3AmYJ{OA|U~t6=wBWpb0DCM6sk
zb(yT>6IF2dZ;XPhI4-mof4It?9A2>sS#$ORw<d8J^01pgGzzaIpr)a8h}hxI?R|9y
z2$&b)r3Q-hNhVYB0GI}pd0xPh7zpWh4`7wR0C%ST<Ow`Ov8e=~BdEue3M2fUpUhi_
zSNu+J=XBWH#cnr5ahKhfx`<W=gbp}uu4lx=sQP|1d7i8?UFgXo7V30`+(E|tG2J}}
zjcY#hoY*u~J$(To?#Hmo-sZ1{^qz3X;5BttnA_zJCRmSC<FFg>ip0;kUDqDRg*&r`
z+`;Y!m;Y}LDYMimJXbhBu5KNB=~#vN;(~>UxO7VF;LVC${qH%`xTd$i&H0)WmtJ`?
z96+Qv$zRF*+C0}Aa_o;Z61vY(tn3vb-P8SI9U+AQSE%W7f%Hbpbi6PvAb!u>ayUKA
zhQ-TcwhuRiS^Ug$OURWy&u+_y@`SX=_HzkTEMFhM#nwSkGbUX14siVbX>d2w-Qhl1
z%|`y#pelQ*Ezc6p0=J{9s}__Q+6e=w8alq6f&vC1-<CrG=_N)2aeBQYr>LcA>}>UN
ze8YF<%`i8HqwR0!QL6o8_M3AogO?Yig4+|)1)__2W>P9Rtvezm9_@ZIv_GaUuB<zS
zyv;W^xZP&obr5K=;8TxI9xNIoibA-pOTFeR6VYmLL25bNg(;%{f{8Kt;Rp0hh~-=v
zLy56M#dGqp%sNc6&#l&TYXo%H`-an>GwQFG*3iBeYSo)zi`E}^n9UXC{9IdUNI9?K
z9pD534T6(B$U_}$lEiQrXS_K8%-C8*jXS}9&VXYmzADt<KwrePdtl$AVx}2f9FZYO
zn=T_)zTZf4i9;Z7)uQNoN?6|^^HWa>SpFh1ul*T>1uaI-H-UtxOU@}5LRHhloeUG5
z0g4)dym~7CQ_YFx=Lkp#Qo~*J9R44F;e!3;{|n#oBlp8#sRddnJ~K=OPHR?$Xh?wh
zRxZwrPvz3M>e<5-m5z}_8Ir?9NUO^F)^myl1|xG<>vCpnARz&e)Z(&MV9UaG?Gr-)
z*io8z@r0`F=gDWo2rTaY-W_5}i^b%{=iAdz<C#DTfh6(Vww#s3b|IqlXAlS~yds54
zt3$SN@I7jAaIM0AX8tP#>Xa&WS@;gQTE9Ux*`y!u0B-!-^~MZm6)kJbh{aC`gw9C_
zU7gl1)&t}XW8K)C#1V%A!O~C7n9KjdS9j44ls={IIi4tm>i92(PMTF7^*u{s9|y^e
z3lW#TzOuc+$R;v=aMge~33qSx_glx|{K#IabtW7CsKa&m;InKnNc&5n3cuh~LxgeQ
z*`kY${bI!<*G07azMDIHw~tw<8BdScB<gLzN<L4She?G(@W89kZ>p9&3qK63t?XT9
z`@~OObw$^Zx_)?yE~abddH2FHpLQofl?w&)00;IuPv<kCLP~Z9`qusJr4JCQRK=)5
z96xOs`@v?F7!oYtEVhl6sB#qS^Mj&h)!8%(Up#8*=KXi^dBd*Pg2(rL7@0%4%6PZl
z%RDn^Mb5?j+)7{pIXjtQ=gabwI4h;&$#t8@tU?MmO9wrPkM!j<mp$=%epBRS_3+4Y
z1kVkStck;3VLy3gR$y^%z<rSzJyTuK?1JEsL_s0PVLX)3^y<aR>r44}D6cGcP}~R(
zEw|Mv`^Y-Tb}SPCXN9ro`{^`PwU<WYQ4=cF*#j;Jxa${R4x8lZ%|1Q<{>U>L=-~|p
zV&A(4IdSS9z6;guF)WzC-f9or@lnMv-~IFGsl<M%Z(B+tr0zU3cXHo=;zz~I4?eKN
zK5Rq+Sj{N1<g5sf==Kt?hR`EF-FCeT%IC^g-=y#HllbXSzB@iC<+#rl6p>W#y&RkM
zu!!^iUCNBKU3`z8dD3@_7;n=CdB{z$YS%c3z0#1=D4F#V?FRdt=zp#?a;v|s{Hpa{
zH<ZE4>#=U){t$^E-tNrKZ|aQtM(URbAB!gqMbt_X1k(sB`E6_X`jJ>94qVqJ@6B+-
zj@5`@10egZ{i=2udeaO9SA5dW9}hRfyLD3NKMNWE!a`$-W{mw)Gg_vHT{%WlrQ1dN
zr#uVe%aC?jVeYnxS_6;78NmR!jR6sJdV-j0=I2hI+X~T%1D#PDU(#{et{0Hr8f_=|
zS=!(#zp+Y%+=*r2xO*GFIk{&Bm?_L)TSnfxJQsu_$Pu0(AU;&ozbcoV@nx5ANZz_X
zf*f>jnB&bbSKhA67pFTYoYL0^S@3eqy_#QAVl&|p>$1A`?qvHj1kF57TF7Y`3+;e-
zHqnjRthID^w|s<TGjqxoDh>ij6(U#cJ=Oo{mW&`qR?BcAmRu_-49pU4Xa%(K8C<-2
zP)vklXB^aa)$v&Y&0i{g|8;?nN?#K`X*#@|r<+8FwRyv<fimpsluqI2>%g_rb0yzX
z#r1OsuxciH`i_nc(}@y_dGv6fjq&1spYxT^Cwl$HKMH9jxC(#U!grMN%Y9~n-iwvy
z_bx2kKM)+{3RItw!nf3*@D(q*LPP+$rn<;X)%zvYEJ66%_>6oUuhEaX2=!Vrv*W1l
zJY5Y<YG#o`{ZeYQMU516C94bR;Vc4y!!rIXfpM`{w<kM4tBN*D?$|O!6Vi7<O?04Z
zFDfm&rF7{^Um~**Qa>Gto3^ga_k(*HViIM2VQ@r75ADdBe8{5BHC^e8_RThIYM)&3
zfLV@|S}U4cj(8-)F?O?{U0USXgP`_9VMN|l1;|;r@6UFJc`p@XL4N)u`^xjshzP~!
z&y56mcuelPx+!GnW0Q*+?jt6%U7HL-g$nCjt%_&jyT%h=PaB{$4bxHYGw&t~I3Dap
zH=UWg&tII%sCx~c-)Ntu6>ZPAImVomX%XD=tn6kYA)wKb!?C4)Nk+jUAK*nmG1G9+
zUd7x#>4kH2q_}&~QLqcgMr}(rzCABRrkGxY`$?^N7j9hOuua|<4juvV9u~QnFPvW&
zBH}_9?TjsG1pN2+@0ALC;dD29h<N|`82Et^7t5C^#kQ5^pO1<8ihV&qu>JDbX6CQf
zetrJab1}Fg%NF#6e|v#Ps6f5fT+vr=hx>0YVws%q@YPThUfsV31N-_2BfIKmb65)O
z%NNQEYY7<!>B&>|*Wn*1ZgIyF9)BAC)t4d4-K(Y`ns4J=urJN{Hh)K3y*-@2JwM{5
zbLijO8127WQ{0*HIz^w^RsP+6raOFun8vLl9B6tLu`fgPb{e450mwToHFe8*u9ODr
zY%lGa<~nzKUoK(JZTmJp6E~Uq_tRczHKW>!_NO=El9#X}0O6FgWi}tJtX;sQ;|;*o
ztj`6_8#w%gu4Wp4tl<Yu*LD3pz3B+*z8*L=V4^n=^+6ib<i{zHvH?lZ&*6qz7_O@m
z!rR{4)fR;f1<(JQ{WS)1xKnC-czA?Sl=~PMmF+_8>;rRZ`iy=+J!H1tO4`h8yQ8CZ
z{(MLIShDVSKVliEu86gYbP81{Sejyf?EttB3J6$3ngJutJRq7u;K|+KN4sCFf7tGG
zf=?Gt(qMZt6RuaM@#TPbhJU&y^7m3zGm^ty2EnXC!4KRyZ?+(!-9#l)Qc|R@3x0jW
zCkd*C!(&!*Q;luEt;J6S56kz`^}sO=&MyF06WoSiI&Zee1?MY>2a5&uXzu3b8-1l7
zZ9DUi`PO{CTVo9A{TgtlGW_lMhoN9zO9Vs{>}t<*ds07d00P8)o8i8}5Yk+x$+D7<
z+a7*3?sFw)w!aXB+?OVDy%sZX(1T$b@_VprF7O7K8>a*#J_v}`4b9R3h5*<Hh(*1x
z0CQ2(&2cds0CI0mD=megdG7VyoXC@rxz_!^Pjfv$689#yx3_~@nTah%<`2!^&Rpw`
zD>kL3{#;1}TSZEIEOMo^W&kEm;aF8`1*}Sz&JW|278-*{&8ixW+tar7jQ_G`F@TP(
zri((mhxJJT#szdvlk?-p4|F1)tGysm-6n4@C&X_1=JWOJ-P<1#m6lDfuLGw^udjDS
z5B%rh_2Un7RDK&e0h%ky7-u@M9+jA3Fd`B%vd=+G#uboU=sVbLZf?do7BAC7+?l>K
zy%}Eim-yT6`0r`Lr{9T|1HCJfv%TpfDrp4wfs4S#8EGLAZ-!f~orV$7-y=2DLe&Hv
z4rhT5ne&@L64eK2?trvDV}tA7S7aD|fMz?qtr+DwsO+A<y>jt}Gut>=wi4X&JV5p-
zw>!iW_`BB{G|+2Z91{xGr>6^`_Jn?&_l}6|LNh?SSP+~akgk5koWDJ576br*guL8v
zPrI`(8V34v*Q0`e4P_GLUURqgGskyuel+-eK-aMjQwz&_mys>58A9fDd8oSH`XNG8
z^K-iCU*2U+1<dk4h7T%XxGN&U!^6YExa&~m=u6DHE1frqsw}N`8UOY??x<%N|19Lm
z_B5;<14w;FgoX;8OuTl(cl@<3r=s<{v%LCgsfqLr9=7u?@y5JP?|&PfW+MW^-a#6X
zFjx?jyF1kvS}ho+?zPPwYk{jb2gM@S3(Wxzklnd5m)5rFJcFfszq}%F`grj0u6V?G
zFvn}?h63A-%~TOA#UktIzdtb`ijcm!nNc&O@|Owy?k_RO7fuLMs0!x~*Xb(;6zZC<
zA8WWj``c;%a#V*{SiY-%tLp!0V2upSk<ZFA#Xo(#m?0^6457W5|2A+<1-wtc?mEL?
zgZ|xmkAxUpI&!+se;Ua20k4jmBqrfM-w1GiZeU=C%??ceY2YZr7j8z>;bY!kmh$_L
z?3iFiNL{V}+rSMra4L|ZquAe%|JPHmP>{p*-|7GIp9a8;A=uvb#HE9|F-&eQJGJa6
z)xbzga&GgBqf%Nq&7a*=?~4rehqZK}WN2@0-#d^jvUTR9hv!?oR3h=~>EctGnS%O1
z$|=q_c-J^R_kpcXCZk_xcTDTs)@u<X`09Cx(k(D)?S<W2LrB|gNJ6;kmy#i5@I#~a
zx&)U9Y_`|#_{rfWTx2FR)Y8M9;@GEyKD#x^Bg9rki-|=pLvG{z68439vn`BGZg-G%
zd~UYl-Bg!;FBChQpIl6W)Oe`1ro(cbhSxR0#^&6n5Nwi+u+Mli>Jy%}T&)&o%<cay
zilW;k{64gcu<X&KHQjH(%ZayMHBYAs#z#Idjv(7~r-`=&VaUeh<pK~SMaCp0CM6{$
zB<ynD+kgOGuk&3?ho_Sm_wOGar>?^~P_JyxxEc0nI{)cN0QmgR8|LHuF5Mbqyl+<w
zL|Lgi>WaN@-hNSx2s=9TJxcpEkILjW4bPeme;(G3ZpQmu$d}05<mKjeIosQFE?XWF
zkdb91CU!VmTK1sY8r<lNn1QEoymvKyh<V+Lma)1Jl98@2>S^Y>;M#uI`BKKvbYanD
zxAq{px5>-Bb+lz9DMbHhRvPzH0hm-x3WVjf{;J|Suj7G@hn&<*%}geg=)acp_wfb1
zBvE_p?oP;+e7?qiweY8Le3Apl5R1mJ_&?2P6dXfF6&n2hb_T!JniXu1qH`YYKR1mk
z6FHoQ;4zZIAKS~X78rc(%Cza9+d%0HI4f<B5b^ys>EFkN4IC`r&19SGKMh-~0@!MW
zip~EWBsgFE-<kZ^*#3WElYtwAMT397!4_N)fEMu0!duK8KrR3%SZ;STcW+@dK5gyo
z-A>@F3o0(<9r~H`k}a&&UUE#=s(I-jxEI2)oj+Lnb4$xn*{%=4IGs#hy;_t?A$#-)
z<VRWncZ;$_dqY|3Mz#G-UC89vl}8=1c?m*2vB?v%zkLVHZ4>zgk-F1+34>}~pj|yb
zxUQw(q|1LhTT|r(*i*h8cXoCT4i27IO^<WmYxWZM5>WidBN#qK@jRJ?7ytwS5a4SB
zVofH7t9@zHO+L4vTETf^B%esw2_OfoW@{_*KU+{7H|@6(fh3Mzh56{j!~~33h_$=R
zmU5>vhOTU&7Swqnle%VJmphDqHW78bxjI*M1uRZqzkXHzu`yZzX`<=ZCIcG65$1G_
z80hGLFmoLU5A<)B&Bv7iT{ltJJ;T6wqQlOpnVYS$eiLTi!LT7+lhtmvrk*Sp;)4O#
zLS=}8(--!zMxfbeJQm%&Tf14*W4Y6?n(pDeGo!_*d-X*+6MtSe<PSIMh%b}*%%qzx
zYW=t%BR@aio;ttyf%Tf|f&OW{wzTN^&zN#3h%x8%0tLcq{==QRT^Nd_wY9a=1At28
zU4|STPNdMx7Qa-@J!6%BCx0OfNI!ul+gMo(=LV=ry9RopG9tHEhyBAb>GE{!O+fFf
z^CRrq0yUN^g56yJq8&FZWmC$$<2?+kmN<Qg93V!cx4MhXFQO7apuNK6=LRb4wR{u~
z`pLM5{6>b$ZqZ!)9xeowsXhL~Df7~ncwb-4MApY{IWB$+j*VG7kfo^Mm|T}qj6;R&
zN<xiE=@fXn=|WPqQ2X?>&U!UGammTteuC))d=xYXG>!2>{2l>%{j}94+n`)yw^y*r
z{)xR);BZ-s{~S#I?PE(}H4sk=>HN8FJ5HPY*1+f5=>R6gsp+2L?4Y4u;_$WCiK@HC
zO-B=FD@IWyNmM!3R>u<ZnZ1U$cYCfuP;TsNj~>t~?GCAnzDn_C^?m}U@9Dtu$F>>J
z%QX5-J-5Oz?_cFVw`KB>>vU!<zecD$HO~##OU2D?M?fx_0fNmv4RucvU)OwfE|0u$
zpZeG+jelBM2Cna`YGVBb(2+}6>OBdjOQ$!Ol%MLEN8sGc84%+10)j^?$w{co75dBP
zKXqfo@2e;V^2_m>d}e8P(6H`r{qeDHL`AGC-!d<v0CC~xRjPcb4eF#`O9WiK|5-Ba
z?{^<;b1ew?A<pIu<WvyrRaxtaYh-Ca=Q}!Nvc~0889PsEc~&Z83RBPy7l5t?NpCS3
zxAcmB2fe-B;m3JpdNUrX+0xh2(rU|Z%Fi|midW|DQ{S7ky5SnI^YY*=SO$0JuIyPY
zuD%90^%|ikX%;5yQgwmh_Uhjqa<2R`mqvQkCSG)AZKF1aNPVIB*UcijqZyfTBr(de
zZDweN%EKu<>q#(iSnW;Qm^G?m>Kd{mB~sY3>~oR#?VX%NGv4MZsQ##gXC}vFMj656
z(jXk6FHOZ3-X)h~|5~3Zj<8mLQY2Ar8Cs%CN~L%$+p_#dt9G#HL$>b4<nd{ibx}+B
z1-_LAoIaO1Itcju?K1{+$QgK>dQ&!W&T&o-@IG30SLxgAsG4zFB)awRb?2SanwQ-d
zl(R{0j{xT_=7hM_k9GP3cApW~J&7urPjVycIJ1gQd62s=%=J@JQ<IMOl#HfRtx!p<
zmW{j5o$Uq=b_!+^XXXn1Pq(BrK4nD}U*@*t4l1u{y=*_0t7C#=`_eS_$ML0Ffjp_C
zkc-ywqf)v6>y!Nzg}5o)xh{u#w~A3+??5^OeueUGxetfTj_LFYw2C>*#lDOW<9Dl9
zdNt2YEMJ)~y5n-zr9a#0ecb65r;1~FumQ4m$rs)DDaAy$$AVfN@~VB`JAb%EsR_jF
z4zFPEo3PYc=+w|=)LS!3C`>6L^%bOak2`ueXEUj)`>IH+K@rmkIT_r@oV=qMnGS`S
z>b=F}>gnLv_7P2CC+fdElV7EnmSs=WgJ&1=HO!CaX7ZKYyd!zwxl7ptoE;ce4KHOT
z<xM?-uGE2?jMkez%!!q`a2K|`$H9##AKe1f`e-wGx@+_lX(RxLaJCz|{YKAmjS0A;
zn|+);I<j9hMz9?+nM;ftNa2;Cv(Ni(LQ`p>lh1=TyY77RCQ^~qUqSSAYci(J-T5``
zC*YI#g!>KPqkjzdU%klmBy!6|?arPeFk{6qd(msn&*_yD;$TGX<K2<ccqdj-zbB64
zXG~w5)w)Hc+;sQ%(gD<e9t$3UNt65qdkwAZYG7L;c>)^+ooD>LaXXuhp2Id2zu|(k
zbyf53@0|uDYQ4}DQADFbzArzMW99TM4CV*bhwPJ0aXi#R4cym17Cv0<9qQF9b9{~W
z>1R8$iwnsvU^WY5)%_qupig?YpQlW{l0lN0s*A3v(-FOaYTl%3rpfkN<xhu+h^Mj;
z$O#!PrS62@%n+O57co=!VHraN)a)(mqSKcTh{Ttn&NVfq*<Y9mA^AL|tRX|4t8R|`
z8Y_Cky~hkaLt#l$v31I;&k4&^C#+qtyHLu8ajnfxwc%LpG}iR|I|mT|cyvTORq|cW
zK1H$yz}ha)<R&g?Q*Q0N$>1nC%LHFdoXkKuF7Z0&k5?0xCOm>0@2HBRa2&76^7?$C
z;p+KzP5qhs-TU?TDJCl$s&%rg`R%Rl@{JoeQQc7#g}#!!|DU@9nC*GozRObeJva!V
zw&2A|ayYx^>}FrGT#C3g{qjjvlD2*7zg7nuEHkwEXkZF)B3G%_kp(Uxd;8%+QaJO0
z443rZTm1K4H^DKLo;exrTfPXVN@Hs7?IjuS9Z6jJbNJxO%74$XaLJ^K*zCfY297r<
zS^Uz_L#w(*-tT`pCG(@Lbw;mTUZ{XeO@q!qNPZc+^mv=6{ox-c8Q^4^vru}{)lw{V
zP?s0MoLMNbrdb<kvs$p~m%lK3_un=h@0C-T3)WV$G1c%&cYPm6u&t@pO*j}CQN5I@
zDd&$Cuao*alJ(aYOA--i;&~V<wDMV`pXIPzGe|e0H%mxJEGt!#jC1qmL=trgPp))*
zCr+vS@36$MWyq~s%ow<^xdW8@Dzzr%`Ad0E^|j!wkr$Z8Z+2o-7~+wh)l6=iX4gpl
z@1sYGb>`4S<_6>Fr&K0?(+;nynnzjyNV;;x9%WW^uIb#-T;aQa`-R`;R3e73T`?g!
zUd}1!YnAbAtM|Kxy05g96qHL>q=qtJrFLk2%lSd_Y&cW5oz8#1YFmJqyfEoMtn5%W
z%^DjbSJHszn3s#=;m{oiCnO|P?|!_oB6+!?+{Z2NBwyo|!=LyD^G_SThgGeHpjQUD
zG-QD2i1a2~<J#l8;(82cFwNiTgE%@K0U7t+^#@RBs+GdWNNqsM7-x0Z<G??$rT=BA
zHc~fy;*Xa-up~bndZlQy%KXRE%Jl0Ml2gPC0VceDRgMc?sJ0^DjHy%E>lC9Qy1enA
zJ0IGh?6t|Ue)2We>%a5g%<_Pqf@^w2tE=-f39<v@U`1z%e9ep+f=y9PB|>V&jC=|Y
ziKw?wz)XzQIagXAs%^MY)skyIE3({S?=k9sZFV6Z7!CyGLw+U72Zq=+L9Z0*dbh(B
z9219bV4OpsN(cso6cN#<w03wpJZoRirP8$>*lj$#Yi_Oa?~Cx)F5#tCQicF(>4r&Q
zQ54g(7d#eC3_oLRZh5+!YEGx&QnzYBM6Wdnb2ZC3DA~Q6(iYb%r7%Ujh@tM|`OI9Z
zmBz=vqvn6L?2Z~sJoU2+hrj#lj1KB#yyB1zsw|WSDUY3l<HZ{*aqGG-Op_H2K0jIl
z0C6~DF9@)&B)q|OKa}O4Cbkr*p^={A%}p)qjS4qUS^A$RH+1%!95#MqZOyh`W$BQE
z(oA!`as~+I$BOi(tv@}6Tb%)+(+Cp5_>*W4xuXW0H^oQ`P^<O@=c=jWf1;1SSH@3=
zNhw}iFw4fdd&(yGt85ED6bLULZ;rc^&(XlGzK3F@iVMP34cl~m%);^gzJQ_rSD^o|
zt!RsOH+fBG<N27?E87@vIk>*N!{grFdb4+I`;14=I-;l&SoNMEDKyG2vSh?|(~bX>
zNoKD5sB{ra_0jo%Egly^zSgqEgn@cFw=%XnPqt~YcgkkYJ#P1U<+5H+CzS&(fe;Ys
zc>Ovvn+YP=%GQu*@z$ADSjb`gkFnOEJ;zL>v58;Psic8RSUR_xKM~Bx;~fz!&dmZ<
zgUk5QP{P#vsia&PstNY_<qXelTCx9U{|zJ1%&(j%cT}EJ!$C$}938m^t02tVB)%!E
zD|BxFxws2BqzaLwDVh~?4Or(gtiD;%|DWy8j_+6W0gBjT>A;gA^fR>|Xzzd&Mqp6T
ss<Ks4jUSv)JE5M`f4z15hvwTmiq>kfxYi41aNwWpQw7N)al<$N2e0u#@&Et;

literal 0
HcmV?d00001

diff --git a/chapter_hashing/hash_collision.assets/hash_table_linear_probing.png b/chapter_hashing/hash_collision.assets/hash_table_linear_probing.png
new file mode 100644
index 0000000000000000000000000000000000000000..80f78dec1a8ae7cb232afb056a28df470ec25f0b
GIT binary patch
literal 68495
zcmeFZWmr{R7dA>sh=PQmG?Ge*bV*8=lpraMba!m&22tq_LApDX66u!QgmibqH@A=Y
zypMk8=Q+QQUS4|(YtA*-m}8E($30e{ysX&mn*=xE;NWgch>Iw|!QB8~5&BROz=r^-
zBs}<lw^a}mf-C4DS^@v@F;JB-l#zjZ1iquf-GIl2Lxf!d{=&f%{2UA$A_-6U`?~@>
z?XPRVoc<<oNI$QKgL?@+VSjYMKiHUmJ`q#k|D7=f;ri+ua4Cq_-x2!2)o`97f^Ogg
z%}QL&77h-h1@;gAJsk!iST~%6h@g@a{CYjwJB`-ZtbF$uCQzv}Kc72f5J58p`Xa1*
zgz??T^X6?IqgnU{-Lv@k+F7pbYL~8R!;P{wEGqfxV=4&8S<Q>!OK<A2Ly(Mbc>6fK
zKdjGq#6Xopc_F6~&_`AJN$JzKPjxwNn>n_DgjgJNwQ?D6-L~*|o}DRvlr7(j@Is;_
zgGUn=K*0X>HDL>ho9zNVoRr_=czZToEPP~ynARxlaARUnh|@nyH*O${!$RhNNBkTN
zhqQY4y`T;<mZYz&z1V1hrtAK4f3@urwT-E#O01;sr%#`}Q7}n(9P)(yG4^r8GYs_E
zi=}cU{=M<9HN?r1t&T*@5QRt4$T_SGWWFfWGB7YOdY@^8)g%u6_D!-YjeN+G0)aC|
zmTlemR8Lj$_tLMQLY@ht0lB|#sMJV#r-_KXQM=LO>x@hM&Dh(k%2`}n<K^gumhEB0
z>8CO`bvBpYTF@?_2KLcKhuWD${wWRd6l;X%nxe(`vA=3sP!fl6U%0+ROy;yku-u;c
z>>W$0X*qv@J`)!gm&oI2gSg5ue|WK+9aR&Hb3e5@#lE?E8l&soUm`AxfU}9l`w}a%
zeQIc;^Q6D&9mf498S0f5)qEoqUYNw(Wv)jSl#Ht!552rM7l<(9C=w^Kxvn?p`YFjE
zbvOY}IK{Pl1ksE%n(R>!V!Y1<y^*m<={mj4;6t_?!7~b8%&}n<K*_w*H*cqLa6|Nh
zC76l2f}T<TvFl(`8Opw@8j;lj*`X#uWR$7S*n>Lq#5I)57`UwIk$m+PwASF$&`oV@
z{WK>ofA1b~q(O;3?Ydh799rx<J9*UqQ6ktHQISgQ3?dT9qi#|PaZ~m+Q{JiXM<Zg}
z4#1*#y9VK}coLKSqU^m=<8#ENPtc5((3Kdg?|-j~f%1-zg?!v|OXMl3PI5tyZM62A
zse^aMoq=-p`>`Oz5QhhxBrF`?R!nK;a=1?@L;XgrSQF=OVc}s1aI;FvV(Z)ZB*ch2
zh+s`?^aN;RSWFVGl)+_rU3f%YPG{^>H5OcSB^Y5BPet5!mBDM}{=W#Sn>ylM0y%M<
z5X4WaM}qB}0jGR<fLeyd)^xqF?;yfG8EG8-8&gtLVKErbW{E83rGuG?YmVsu63|yB
z2pO+%{BxfN;=;1>Sqc3`9UdKm1AaOEsMAl~Pvu=+!jbYiMfkm$yS?Nj@qlDffSZ*7
zr#O5vK~-PqFQxChh46gM&((W7WH(BruVz*{F(P0W?{>({ZG<Ys*7k5xBV9ZCMGp){
z;WsSyU#h1s-^P+}sQoof1U`ZUo1}NBxKa>jT1@Bz{LjJb3)3NRPu-5K=*35<iMzUG
zTHJ!ZVA=3W{dIPCrDiCmVoxkf7Mx<G^&h!YdZ!OPJG9X=yt&_>E+!n>)|*PW8i8uW
z+ewZU^nV%uGF;$J>hlkVCIc~Y57q<@b(Px?yB5XO3^b5~_1<*K)BG5e`HB{uMD<^j
z1+*<+hD>~jOnikdN1@r^G1(8A-mh9gB{!^M7!rr&*D36xs7i!U{x9Rq1>gb+T1~`}
z`XxsN_x(g7D#@2Z;4t2>I}7LGONTS~aTgmB^2TWXK6Jl#u>@7bngCm{Ou=6&Y<Vn{
zD^;isF(EH*!nlfGCHQ^mYnO+=FTK`kV-^I#1V7up{De}MaIVysqHr|1es;S_PQqWi
zYNSV48U7wYh@dvddi3On6$Xk*B3{$yr#9)S%=w)hPngO7ym*E3PNpet>G%7C<dIlS
zJ7jb}-r`(*Egtgu%chZ)BfUwIc{H1C<=y@9hLsB6H-c{x8|klO{=D)X0VJcP`(WO1
zLEqI2F;5?dJhAH`TgubIKQGMqAW&c&ioj0&X2%HW@r`~(qHiUivJOqyr2kSdI0*gy
z;IA@^`bbt)JqnF#(P@7h$c$ux4>7l+1rI&UZd)nb|9F*CCjZw&eW(yJoAe<*1}|GG
zo4kH;b-cfwiNZ5D=J;GIZ{Pdy3CbTH4YG;;J&h28;9=4sTxAi1W%OUBIwQdgfpY;d
z!}(8x5<!Y^bLQNt?CzhQP@D_?hSfI|@xAL^zjm=?{7AS>C$q+Me@$frrh11NvH0iu
z1w2q`z4n^>RsNc40ZjFfl&m}Ij|D@{@5sX~`KRaqsjmXx&}h9Bp9;j${HZo4<SB4H
zm}2UYe@^udM;`8@n-{CxpCa287JyG64Xb$Y=Tr}AQs87y;7pSKRF5D2K#KfC=Fk3|
zN<kJ(wF^JM`==DYVgf08aE=H4Io1EaA^$ILNQ&aOjltjh5tP_;da!0{YU&(>LCh^3
z^EmZ8sn}U5>iT%O>DA?h{^1tXbEXNRmg#!9zA{;DtEQ%QcDPX*v|6uGX+a#izcTo7
zT7d;-ugfC55UPCP>NS7q0HpMe)2uH(1_`e?l}{h(<t%AZri12AB!yUo`NW8m%u7PH
z*GeTl(5nk52t^YTUN!r<&!TIK<HhzcL1g0D8PqHC#KK89rtAiB<an)Tn&8K;T4<hH
z4=camJD%~T5Dkd|PIS3H9jpGGii(QE`uCjyDW>|JHbO!UZ+t2_{tH%bPW#m%y23h}
zCNKEV(Mlz-vZiWmdAMXc=Cy0*79pbpZEy!S>h8H%K5YraArCAXYj8gk8ymaY7|4{u
z<>kEVxf86dKl-)$^62UkdbBpmWJnPoPR!G0AR{Bw#Tw~|5YJ)hvEMHyT#B#dG}{qH
zqle!a%~V)Wa9OljH6O;~Bn&yteAf%dM6X-!hn@SP5QF0QGYYBv)ndFQ1{<l%aw;*8
z1FIeWNwkKIMBb!0TQJNZ(0X0mx<2N83J8UDyEj>0#1DLH#^j%rFK5<kn{+>#y8V76
zKKY&2fy(1jHq>{~(JWH2)!nR@Jv>`2j80qI)2>^-ojddGatWN)^KGHUb|9){o|4xE
zad#@}=*~j4Hc2k|C%ti)4}pBR^B7e{YT5Z;>rcytkgaIQ<KMp6+Mc8MQHbDx&~2;U
z<)CKagZfwL8grD}1VfxTV5eG~x1=Gmr-y`%{R*(7E<=-oQniwockLquE|B8xL9;L8
z`M*75bAM;X;dZ=j={8Te^Cb3o!_qT;pPM>Zy7D$8THAxG$I0mJ9tcQ<8>ea=m!hnW
zw_o|$%zp6&c?F2)4I62gni=pltl(4og-*LUptsNnV%bbp#ElZg!ib#vpW*vTXDRo_
zb1>z;iH2EX0${W(62ddDt#U$Q(-QyHiRhz?Wifv4Q8LxMtB^HF=}YQu1(mR9b7`H9
zw^aRWwLl%e^OzP16Qp)R@S|<%-4Dl%^th>GsELuRo=suxGBq6QB1lqL1m5paT2+lj
zIvLE8LFb}>_yUe*Hs*sDQk;+g{3NdA$hFx`5kzo3+H_yd`ADD^=DOUMYQ++?(9VBp
z?R~r4)Uo+ChsfvV9`0joTe=s@$_s{ZQ9=lH2gY+cvz_iMnbBV;_SeU357)=&UKF@h
zZpJ(@2<p#Q;H-+Hgv?Q;z%fo258C`=Vg(+drYH&XW@M=f*DZ^F@<nY*MSzr#<f#pc
z8wB5crqh$a<>ckO@L6M7gD|Gat($GsZe!ejsVA{IvxCU3@$<#mxM|@I0TpgPXKZ1^
z>FcT=ELKzYqph`0G}!SA?vh;`u)riG5I86qBm=f<yFUI-U|ykGMy9wl97jh?+mNU9
z)mD3{oOWtxEJgQ+#tw$Um{n<2dKL8csr>KRvBm@InCGW!g-lv?oa}6#mu~D~VWuJd
z1Ma8$ftky%!kkQC0q|dkwT}!U=dl~b?8GGGE0NdnDfw)2iQ9hF2gkBC=<eW0Iiq=P
zNi~rmElCxM(10(+3GY`72v8qu#&!qc(W~BJdtIP>i#gXeisWUBRi(w$oW7F<$e*aF
zBZp;oTic6XHNTA~UvSV5gB=E2Al9cZbVsg32C#o3mZD|AE(S~FcWjGCQOoGQqA93b
z=!~A96W&Yl-G=}0{(Zkn0i59mtq`4^aKfx<VSU9kWAnxVUhJ48()P%cs$y$VfAJTu
zHo09XQf+pYZ5Cz36yQopVw`uaKk+8}q<EMteL-i^s4!DAdrWPGG0)l~<+bxY3k@da
zn>zf6*E;+o6i!Rq&3pYep*m#@%kEv}kYne$K$<k9@p{*z^zf&r-Ig9KBhu7wEd)dk
zVEI^P7P|OMNhhOv`D<m=t*$T;X?u_D&nWYA8^AoieF*1v%WBu?zC?_X!|Cl<VZU2}
znQrXgCj+*7%y7G8#hKr+V)Y|q5Z%l5MY2v+qa+$YHLL0QG?NJvR2wi<giCrk*N)tX
zyh&pOg~Z8A(&@zGq*L2)n7XPzO73aw`#^Qe-5(v~Gc0rLld_4x#`?v5op(a7?WF$L
z)8>ZlM6iQHZ7W^L4w;EDkjBdX+TTv<$-8dd+U~Uxyqp-xXEh^G0C&0Fj5%K*ZiYp)
z@uPXWmB}Mg%1}k@pc7A$#jq>DUiZzt{{D^R{m1P$e`a>9AOM-<B$c|(C^*sK7fVF>
zyg8WepJq?<#A3*>4PgYK$}wHeI=SX0<2LztF9tm8Xp!NV5)sJK4_jd;lUG#q7N8<v
z(X02kIPIfYA#(xl@<d$2{b0E3M%Bz4bgM(Zh#rxqpo)c>eUl}Q#uJ(BzT6i~i_cip
zlPYOwwd%g@i2h7iUy6gp2zgC2{tB#`?jr=K4`HQI$vT7@d|vB(@_e%HY8&%PfGr4*
zQ6s=HI#jFKfwS1g?rvLx3r>yaTI;}gY&^TUZh?&oQ{I@YA@*zt+cbb(3@bCLK0dFy
zfzP-(_hX|g$73<pD8LQxiS<MN!|!_Jp-Qqhb@UHix9ahO<{s_nD`vsO@uz5vAHgHt
zTC=C412#q@*1osOdOk}g-cK*$dymgoAsVs!!fyf#E1@2)N~QF)p|xKO%cJba0DhE5
z#H1($2W9dm37J(aHlL_4zBfIuZ%ns{P`5uIRm@6<CFI*K{gl`2EiRJ`%%O3<0P(Ob
zm7)8!@hCwnBG@}wN^V~x{NQbfUuoKo^dfBXJVLlD<71M`YH9L?Szl8&#lUT4YJEF9
zruo+v*>NZNVsM4@wKxnf%V_OBJ9Q^;MeU)Gx-}t-le6TZV3@R6DZsJRbD5}bA~{L&
zIBtd<#jFfIe@0`;49mh&#(@3m7F`OxK2ZtOO-US~+0ZPVm$eQIJncP+Jkj3*ND&^g
z*}bqMRuqJvypyTYP0C_;OY4-@OReAi;$U?C#Aw)JIohd5UzG4|vyUwGCpG#95YHIR
z$bk4~WX4|v(+jGjS=pk7b>r@SA@2_H_Df4|{q|EW^|9pPjNo?^u45%zYA+RXGOHo}
z$#6=;92y0G#H+{ZGd`kfh`cWQ#*5|H*e2`Wi;<*tSu*bQL=(SN9llQ^#G#KAm96(&
zL9JC9$6SDn%jEtR;{+D-yH`XfkKI-klY`hF$6vJKYllQ<j~FGpAA+DjdR2XO&qQ#)
z?X@)349*v3gKzILKC~4R5q_-Qa^G^@!TYJFfBLQ&dZaA5<eq|jB6>KFqbWzMrga;;
z4yx!PI(p`)G&t&0ECm!JCKA0gBpfJe;g)SLpIDy`drbFD-}e(#VPd?Y<fN6eYQr`b
z=!-vm;cSPX&P&9L1^y#*DOS#{cVEm5-9G6GFig$>%0$gG1?;f8Wj&keNM1~!RII9+
z$Ww|o<-U4OAK{1T3AjzyYZL=#iPvJ9>iR6TqZYl5(sYh2c?Dq<Op1M=uB`mNJPsd)
z4Bn$-$#7_Wt*|ldOZ7&@1hs6!aq%KSl}?r&z2M9CvOsp~CXof6%__u>(>`HL1N+cU
z{3`~W_s>i7ZiOqbtC?S(pSWT7H626Lh<bAGq^Zve%Z{L}WHj?v4iUjrcu7(K-mRb|
zkLlM^1lZw~ZW0n;A)@hX(Nm1{uaA{J|I+bQ6*Z~QeZ$nUZU?#8Gg3fFl#Fku1qW4!
zUHDt#K-YB9D{Zxe`Z65Nut`<R?TqiWfhtsYblq_x=qvHt0y3+8iX>$NmlnR_Hy%Gb
zlz3V1VqfLk3%4cdboALZLO&qyI~nQS#a<RiI7jOk4VnJM?)d6k_HQT1$Xh!|AL|I<
z00>S?8mu-`Q~+M%HO1zh<UjDvt~A_K@H|KMSRd>2Jgd#wsZ82j7D~o=a`)Y+<htdw
zU@Oec$!ZoQ0XA~~r&lMv^Dm{R6*M)8sT7|ivq}Y&+SHjLA`o&|=)-RVlm6D7Tm|hw
z8jI&;aTB3nCl+0V?Wm?B*8Sj>&0~KqA*=&uOB)c+w8c@n9Bp=o7$ZlsJk?)B-xdtI
zyUgKye-EpPsHIN<PK+8H6Nn3NEo-g1S=X*bhN>y6;p-@^VxXUIgMlu~;QOdY0gI~l
zy4u)NHF<rGpq~7v{uBX5BbXE(B`yYnCT3h}Esqq3WS_L#P23S^pBt7t^j)mmtXbP`
zD4C1y=rRlR`RE8jhg6Kze2e;nk)kksDmS3u^V?#13g1v|D3XJ~GwnK)aTAC=!Br{2
zAB5S9T@czO;D@mP%8zL^5sqCg8!rw)@DEwZv0dyUKUCIX2B}8|oM8teOIp;cf|y}g
zq?Pg}09(3>{*BJ8c-LHjPSyn{;s*s0+#vMOMCHNG3UV*ZWa}2!-gEuB1`tgK3x0Ch
zU;c~&$HIwX`B<<K&C;(Wv|=Z0UP}8E`+1-0X=l6N=gj4J=(%BDg!DGS4Zehg7s>S9
zGVR1~ZGyXCf#)66vZX}2;`=9uv$cUNS9EhTp0cyjncMuICa=gP{)Jpvh2Z$fSrXPf
z)a*nqN^X`#ehbCLVn&DWV*0SHe&hXcU+-JxToqsYRHuhr1SW%NAMOZ5V&}$otagmv
zSG)bd>-pFI*<|H!R8g5Z5%HEk<EKR|)TqEObSypRTVx3m+x(G5$`jeo(}C4(Uemm`
zx-f45gHIyx5M*$hhzE2F9j<@$F9P^73M7_nE8`W{YH&R|!w;YiY{IGJ*FU%(+ZP9{
zd%nbI#kJS}4biZHU*z1sdHXslzeYGABa|RZkg2Ko3!=*b@QG}<ym7#vcQ2y`2!`oE
zx%sshy9RN@Z-ZaF_7f7m{=xO#Q`mq$t49@>U+13J&nWO3;6REjxCDP8F8LC`%Ej54
ztN(HozbuRwk^&5)iA(Lf^XJ`-Wq@-X$uOPxQz#Jx;1@%;eEqJa^!x6nASJG()|>!Y
z%YT*(83JI_M?+dxkw5SL|IwE8<**S}{*QbiW(bxRd0O(3C+RbRDAY#yu9^f$$eu<!
zq`f3PrGB<1yk&9^AzuKlh3|2z?DyUdkZ(6?O|)sdO`8wX=#GozV4)@>^%(0ISmlH^
z^s3VWxd=s8YF|rIGE6|JG5Y<{X`))Q<mQR{3=(9)(`g0DFe%#xtuLpbeZ^*l5H5jM
zh6huC$a2l=fs_%HcZRpZx8efeWbtAdWe|3#0tl*D`Qe`03!>gb$|d{00fQi5Qii;x
zxKroWXuBXkY}pa&o{kxEYcUa3`PirEX<dH}9x%-eApfv<D7bZ<e+VELQQaA~v^z~a
zz@vMI0Y4q+Gx~s>_2mk0mE0pp1uV&RT|A`ytsvkY;aI4aqPR_@-gCZ4FCpL%-Ax(K
z_`Su)oRC2h9Yk$+qTm;>MUBURD?%X?iNCJ^KP*A>dDvF~-?KPZj<hQSRL(N3;xB|T
z2b>+*g(Bm3|2q<<Nk8Jj0fmZ~|AjCr0JTo|_Nt%ux9EN;<5vzK(}uwDzYxZZw_vLG
z&1uj7Qfo`FeQr4Ae1A?QP6eiV<o_)FKRONMLk0y#;Dq|M>t9nzf~k}+f<^zrX&b=7
z-IEzQ{A;TBFndCT7y9<kqvHmYa49}}<FBb6fvFU^=n1almfr(Ur~yvP@qFSh$X5w_
z`JH4gtK`3j5agm#m0i&1nu0rrh_R(&si+z+J%}}XX&Wo#k-r1@#;O3UYe}-}^!gFs
zG5&<qRExZpXsqq0`rGIol$3dE=d{PG6l+Zbno1Z76<h98<=wIfczc2^eiw-Dlb^8O
z_4A59gwVPd)~r5~t~;7`otTy<Y814-y~g6w77#LOZ9KMI!O=`Y0Wa#q>W$s@>^4zH
zOoYH|*n{%05?mJ!0Wd+CxdmLnO#?-x#!A_G?J4!_=U-Pj9!;k}{G&r{j7#n~KZKNF
z0T60jRK)f7z40Mpr0#Y<zD8ELp=W!LW4nb&mn-XLuI)XqM2@M%R$W-%FS{LjC{7mb
zMKYs7z4+U{K?afJ8*iws#k0Y^`ea^@E~9q0&d${EfkhmmF0+xV@m7B*kNBv{ma9eQ
zYZ85#;px0~x#5MD5_lY!qvRnYvL)ktmQ+rneqND57PG3a0U{v|L#<ufgrxpwaU4)L
z94He4r=}rQUf^CDj<bn$+N~4ykpj(n0+Qg!hF(j}DA7S%Goj=?|MJR^7|u#J1$rap
z!%~z-t7*1`xZDcN<d7jOtDAPKej?t#Cq{(-aQVPXG0kHwv{;FLm4hpeSA5%$h9y}1
zg1TE25hdFG$zU1qoPX99<nO`INZG*C{G*fD6Cx$+`b?9a7PF9WyeE6rs&0+_i!n_$
z>zL86%pKxr(!@$-#8cjZosx3icXzlxLIjjvaE6z*-mSij-&M+U`lwkOuZoPhCL2$i
zk`_7Mz2UJ(_^5M-RS;oG07SkRMR|{|Bj1%fIydcJH9zGDtFg#8nO6=<XLXSeZq~>L
zHJ~6+YN`5)BENU-m1!jqp79N{o49?`dzyUEth|1hd;p(M2H6YodY;l-3V&ezOByCL
zR&y<Z0A@6ssK^II150Q_vp*&i6BGF2{$WZc?}Pn|21dor%kELV@t@I$0tEoY%CU}|
zf8EQM(hB5HG|6r@00otx$dZnI;<z~(1~A+%YL(!Fy(IAygc)0xX^ah?kX4@7s$<)q
z>rqJgv`SB!7K7aHqJ$IYRYn$Hw1=*8ycP(Duf^Ob$j<w&<V^iixx{0upq}Pd!s9f#
z6M&JjZ$Zl}wrYgiF{tP=$fwGM+X=-&Zhq*RsGHR%FdIMyxo00ZoW3ORXTMDQJ8TF|
zl2cmR19ioGjcRP<<dZI=2Z8@Ai_;Rxs+W;(tLAt!(!Ez?ucmH_=5^TUx!Fo@g|d0~
z++l1^rS_A#xB81;LeaHf?yc!#th}oCpW@iN+)S+XKfk}g^2ziQsn%}abhB&eYrI37
z#U}DAi`{3R{kl<dp@sCD#_GPlCR^B?mZ(+8$94B5Nq;%}2nU3TO3Uz7$1gr;j!^fb
zp&Ui;e&d;ovm<{yoZRy1!IBH6o#eqf6a}2*#J~k;)g1K3L9M~nqJet!2G=_*$P~9@
zEq|(xu<2-MJn_(0fp=|R{X}j>B)@4_UZ<#5(t3e9&F00E)uSIBQCk+SjysF3oDf&X
zwTp#VOgl5rHvi<hO!*Z$|69SDy##L5#4IrEfC?Ze8gINeDSm}eH-&Xhb{A6T3p8t|
z9VX26+Co-_R=V`dz=}EEu@}Fj<3n7Hp68Ws+!l;uoUU7L>A=}j=|1a7OXe+|Te+&8
z5kqHZOvyI=SfF<r8h9)68>daR2>F#=zufj|L*3$nyo=h2K`}ufy1%S2f0WZ@^ODEG
zXT=0ZlF1G#0;k=Xj*d8A8ON2rS8ZP8{eE=Fn4MY%B%MFgED^9$$@GoVUuo7&Nw20C
zsh(+C_5gdYsX4tkf`;RnPr0~=THxfi67I#29o}69#&xS(FW%SuX7w39)0O9znF~)`
zvD;cn1WCV<NEZ>m4sWMRwOj36etNl>ga+H;syui0Xv(ZXvtGB9pSE-ySFcnhBNcPW
zR(5K=zu!RcT99t{7iz})kE>j#*50>|6t=zf(5#i&oM<ef9;*fB0~xqH){r;szl^5j
z8@M12UZbna`wvTu`yXWWx6$xBZQH440d?e9q}y3e4`);@f;)&`-0+OwDLRHkISvnv
z_;l*ggteXv@}c<eukzim4#*>(@HC?*o?Nqg$mP8{V0xH`mRZ`~8#XNTypG;%?pqC4
zFAoOk>2OwgxjiY1ks!W<$hs!NLs+QYAz<wHPaHABOJj9@Y^}@V@85Fa3g{q@mz<aT
z1}~e*yy8_E!i%;~AGkN3O>LEI9-S*TR;Q$uOsUn=eK=el54PI~9QPJuDI_-xuMK0t
z`PfVtlw_az!*1n!rfqu<<)iTR`L0#nm$^@0UbLN_XdJG-HKDvM_VI9oiSXTtMt!~O
z+3ff@=IR%1W_0e`6(-(Dl=7+wMtIY>BN(pN0olwswbj0{p{_Y6x8r7=eg}3LW1KB0
zmGL;NlQmZ0iA{A-tE}~<W-{%>u1aSc4KZoX?=sw2>5M9&8aSA@B(pyLK70FYBnnlm
zuRtt}bhf0f_iHg?TdGgAnHsO_<hliM%`*c+yC?QSGINHJ1?ox()=wPQ`y%hC^*2k)
zriKNdVy=!oq!_~A=y5BX9;=_9gZD<UUt><q+Zz8gSUhsmApQdAo-bA3z?C!Zh|BMV
zr>LR=>J~-ZOGU*}I}^hjD|u?Ax`qG`k0_VP!`pi8@aFN07n=5WjWF~d>sF1)-0csw
zrS4f7O(#Wethg-yfx9eA%pw~Zfn&(V^!=E+zf`C$cjh2dXbI!Ka)<SKi?!Wu6?bBt
zUFX}RL|4CaRTd4rRbJC=tD2`)>&yOUEJ>@au1{XoaDJ&<jyMFYnRl>6$|S5-?pN+*
zY>E&tk;Et0nNd0If-biO@E}yAZjEIf$wIAIv@&4r@z<=+k>SttE!~5WV{e42b22e}
zEXA7R(q=xDG*fSMB%Yqih~)IC7D0|adMGwR!tG$(@qy|`0`GgZ3}Q)^!1<3Txr+X>
zrR_#p5=?oj@~$NnheK!sM8!f?^k1um&kmEb<FD$Rj(Unto#nbC50p_JQ=`tmQ8oC8
z9U&lz%6WsE3NiKmKd}{LFIfN(g8-=uHyH<oeg)L5{D~y>(jE@$@;FN%QH8)6@@=2s
z-r)Wc%WAy)k@1){+HCLadu_PEvo>x!`qKSMu_cnx@W!N;FQNC<I^7Jjq-~wIzppGC
zpz2xZ_fk6W5^(77Mz14kIO;j}u(g|75k%3hTfc(B*Vo#8_LB>{XWu$ANY~|R-}B?v
zM!&6HVM&m;vTu3cG!+>H0lN=TL*Urqmt<)f5O8Q@Loj)rwr4<5kY&dS+R#O*9HvTu
zqtC98znR6G9Pyc6>gm;aQxvjHjqPb-_Sl8k;niA+*xRUN#LufW-(N`U7#=WPPLr8-
zo`v1YB!7ZuLiFWxdvL<yZhnyOvOc!7|Ds!w>@(OJ7a~|b7xdN7GR0-!aHc&bhYV1H
zsvv9o)W=_$Cazc0Gki^-idzt0P@sgBZ-E1R@?B7488}iun41|uOo3P<=+OkKtfqy=
zC-NHa;%7l6d_KARAMw@wNc|M&a-J+56sE$Er|NY6!<zBqt=KR3KW?_U6Y8zh)URb>
z#`jQhJNGX>qdc`+W67gW=NjEmBh0<~sJ}t8mJZn<M6JPbG<{8ls{1%S*brlLT5lxc
zRd~VG<5<g=2-vg_5nQ~aURSxR{u3DqkfRlS;}ESMuXSXyE(#;+@F8A|;d5mt;LHFP
zNy#FV#kLfyiCn<Wv<&*eT$aR6P`+{bySDqbQu`tCnf(_2<(-25x8Eq<-+g~~*2Z<1
z9Xoq6*k4mx_h56l<9&T+B_rlA#t>0TH}Kt1t_w!$XHnH|6Dw)*sbov&r-xgk<%F7z
z4ep(BpT7No^3+yFX-}6P1(2AG737cwtScc<$qHav1$x4{x&2yiJa$ulP@nsJD93li
zhjv{H30$@S(*IDF9yt8A@&~hw6@3^lyJ}MwBOw=vVUevaR~NLUUMgrRUR<0&gSiUx
z+!q?|A2Fk!UdC#N#hN*?dS0yUycK!2(577bG=cXRp{@a%v<KD2`VuqTx>F(_NVhh}
zpUmm}MARefLtVXTyLoz>Z6MC^&TUiO22jOH$pApd{|a;#O~d14fyJnY^6+l1=NM89
z#W7|ny{T?_UhS@ZAdb`LH#e3bx1Kt!OAi&(bDo(#isFhtvUJg3>9vSIjfLk!iI6MG
zo$`0!Ke&wI!AzPKrd9DcuWz?Zw3!%6Rjjq^;@k)yA#rz{*mcfbY`u9y`p$gN^ow<<
zYxdzj;RoX`|Fa_%QXWyay#D&0ss_Cr*cwG(Yt&D1m;NQhAk?DK{)n1%>-ad;{2kG_
z7eV_5R91VNGQ*m*s+V!b16ddG9%VEBe6{=Q(DbV$VOOiG5m4YOO48cNHBx!Xmoa*0
zz{KiYl;_HB<xNbFWKrti3vEwwx<M&$w;|Zw%v;>Gu7hvNzI*WO9CL-m1oj410gg&r
zoThAaF!v0yGH;#C*PN_>ahzTTgUGu4>v+MR33x^j$eNX#Q<<;x!0X(o?<I&q^Pi14
zT*u-O0&7_JMvUy%*rvxBXhM@!KcI1I)`=BQXxIHH*Ffk7@w5dA$JYPkxyICx)cRo6
zdLzC)pXmz#1A`EMKpN!ri~arVzaK`PA9A0fAipu?o(;(Hf(&~Yl5q!HV`7GkbeQAv
zyRm82KmhWV*o9Q%8W~9=zq5F2EBjLb9wq~!yUB_DPDucEOz2L(4sSL{pYAaQ(?J$o
zyn;=?mZ|)wC@P*pi`E5F;APgw$a)TV770zQ*^pwcl?JUEgQva9b`)>f@U$dn>S+2_
z>O6%=|3yD>dEoK7E%@b&?bgn#(V!18ePi^wcPc)~@O+}nju>yhMPim^PUGGvVfy@S
z7nPQ~PVe}tyXmJx>fnJ77|#nIt3oZu{X|_U`*6XtWXYGnGLU}~B3ep#pG}ZkQ&`8|
zNX#U!&g<-O$i*9&G&~4RqSulLJd1{(tG2zE=zcRR16+$KEDQWEq9ld@GUeovB+VTr
zki(LwSLEPf&*Y29H}-g1kV{xb3lQGvL!3m8*!Y()TJ{dkLTmr75S=kY+~C-Eg)D|z
z{uW9-EteQKt*za~4+k?-;9i$7NTYWM?_UKly@MLW@p>lPM?IZsf|my2c&RiiD|v83
z1z79x5TIe*@)Q5^r;Q)Nvp)8Gg;$19mC35^;2E&~%<YNh4g=!K6t=M<5CnUxxzTU6
zOIbjAGpFEKo{+%+R4`MtiA*(<eeO@5Ap{%7W$1?-75`q<Kk&#q0{D*t(c=MUbw;Q|
zBO^A?6&0IL09VK8rnE$gKC0dN_ei4+z)k|Rbg9Kuclm4elZ*z-wrg*AmrS%0ys5nZ
zVb`e12ovc`BSO!4@bXALVeF$<{Djx5OlXIpCOb2y#s@f@PTMI1l^(2%AJ`#}2@#NA
z&kS6W9q(WJ{8%qjuimBpgRv6SnPcS(LuOFQQ$vdQjDkUgijGtg1Un4Bl%N$<pf%Ph
zvM-hdX8KZvPd$1e(aKUWa965BO;o&>PiuZfyLB+afu;WlO6LPB5TAjnDsbSUs4e&V
zLx+mRe}g}``0%4}_@hoH<}7F_9v5s-X@_Z*Pe?J0pZSSK5u;a+&n8W1itIYiiHGm1
zR$mA#u0N+mi2k50Hp=p?kl`KtAsswg0v-H~?P}~&kLTF(7kCRrCU&W4+nE0DZ@KMv
zuW)@y(9WU--ZX`M3Nm_eF7=>UpB#;TVwZc$RuqlS8=VXLkO4xCvuz|3^<1sk7>)C!
z+Sp&V8C?$U_9UP-eVItT0o02a{tt-AcnmiJjzVbbmgGHrHY@n{F9lS6B0x>3-;}(>
z!s)wEZ}I-P;!CYFStS(ibs;r#3zF?&nds73b95{EO;+06Z2~8!F<Squ6hz%6Y)&3v
z3KJ6}*@EJ{BF%zbj#;1HMmiUJ=l8r18BKuf_+ISm+!o1+CHVVY>S%d34lX~>XM_}R
zkBm6BJ#+}Cg*~~m`>$>adU=X4A~GU5oxN*nNA=06IACNoP~INMj}5Fc!3bzg*hsAx
z<JctAR4+fO&Np?6U{iMGKiqy;8>7muBQ)kEQGaF|mbIhu#z-IaUd}RJSSGA)wGYG1
zjp)l@sk8tA8WF$8q-viD(LM9G0>ltbChi4ZdB1Z8)6oL0+u=Ln(51>e*%L*iy}qS$
zK4`%d!$Q<zSj;_h!~Z9YXjiJ~M$^fHiRn*ml)r;;(5Ctb?;xJC%^S(m;Yn%0kmZ0G
zuB(+A4T}uOlmC~s2|>WIA{K<8G;LD#!ND6oMNys<aCRwWCY(=q?{Z_rgIbnxQ5O-N
zH5;hLCoTpq_nYBh(;9$nQXp|p{>|*ur7FsQtymm4U7)F2MzpT2SzqWxiqvV3fPb)U
z;)Vvw3DGktXJ4<+6)qp7rabG}6)vy9eo7K1<~$3q0XZ-(>BSwBl<RYX{gqsPNYOm1
z?IZ7^EynSBh;AkSnRDHTrW4sF+P<YT)HAnVr*9ui$NU6fH;0>3JjQ(~<idV-%YEMo
zPu$NApEm+X2()U*Lep^}&*o7=wxH>r1*x?dn+4gEG4J^+uBx72h~8di);S`Vq+?f3
zQp=0a8>=<lLPMkpSyuE|9m?rG<H(<=-RvtC?f~(E9Q_(ks$8Rvz(z-u>+7)f0<OA+
zzRw78`lDcLU4ZW%WWjrRT?j-&AY?al+U=kjdqu~~aAr2;yp#xdieKH20caJi<zlii
zUXDBEd36EMtKNLQ9yK%#-t)KU{#r5W<{L@nY6!<Hik6M~EmR$G=p2l0Cf$WmTp9ic
zBo5H7vs%YZl3k;Bz1amh9!?#?u9zQnucoC?Fsh9vf6&K|DsNo1`mtGVO((tI0<;|Y
z*GL4evoBxMyJ?|i_`q2Xa+r^|^fqX?hLP~qn2s_&`hk~8gCZtlJ{4)hGbk)AMJca<
zRADx@+o^qteGnX1zxpXxG?bu~W1`pd(zappEs<;z?+G9f@B-?k-~}M-afAyjM1BKc
z57m`N?M1!5;(uYD=iI+wp1hHK#mX}ykNXFm_v&jmrds3i_spTS>RU{`ZYg?aVK4wC
znb-dH&L;8J)<kLLBI<__rnR&DV5Vdq8?#sWC5|9SnnBu!!*@ev6+j@R*nZ)8@FEzG
zLFi%*^JILq;jp;GVT1NGxbZlcQL_e6AVG|(-3XW`rH?3?u+l(}jMO44Rkw&p9rMA+
zd5>d5sZlRU5R8{eXi=3q&8_dTBBjmk^q6IEeMH^zq8@ry@AoMd)big^Ljc<)-jb%F
zWwUxI2`F5N`Wf`R8=B&e&!oi*@WUn~iSw@%;p@}&@tuJ<GzDs<S*&UcM>&<m-w(Tj
zJ`%nz1uDsD^Ki=6xK|GU;)n4@zx74?>>|}t$!;f}r53Jboz-%gMPjY>$+>?o!&J>X
z5ohQwKyK0?G?+<sx=TT-rA2}BG;)`%wOdGp1q8h3@%YkPQ<<HJI3F9dtBnRfuYMUf
z+ybfyql==WLJNXpnxK~((7AcDS;Q2}v;CE*VbpG9=vE<+3XGJc?cZ^ePDS5CmCSUs
zP#YQ{9eSYcexUrruFgz14Rnl!^ItmEqi;NV^hmW-jOXlV%Tm(x+{av!Z4KtPg}o~E
z+}wBSN)5YjLM^4D4RLYXKPl%fcEvWMKOIQmI`*S9IzQflUR@r=?{F6uD9eG8J@=~*
z2MT8!L6!22lm!H?_EpaEg@VnUewMkms8O~Z+reBcOI+E|NO!SR58>`$f9(Vkcp~YW
zOE+pO>^J*nF|)dtCsXI6+vH9<!+oqv!c6`rM(^Uq5lF1ifP(^VQ#FDUAV?P09}+B*
za9YjOA5C}e?jXZUKlFI%fxCE;vl=&FZPhbG=cS&`GXeawWKa`mdW&W3<haF>>};hK
z#awIv@EeilFKAu##=Olx=0o+f&<J8)*if~8^upxHUYhAUTjk4@ATw=0<Y!TLvMT)i
z91e5!eNMGuuSw<k`c7&3SSqbn)}x*AFotA8mRCxJB_<ch4#v<Vw1J!_a-f_7VW*h6
zdNF>hoLB-Bar`legKS*ZzYp?r9xqhduZ;kXuJ44)!D?$^Gx(oxCm{JI3?stQb<=|C
ztj}8fTHCY!q<$;iq`il*dXT_Vv~7DaTR{55*o0C^eMo`Co}7Q9D|}o|`OfbWum>W0
z!_0FvdFFJm&}%G@8rtQEplbE=<p+iS$_)^i!h(A7p`>g+C)QFwgTtyd&R%u4t*k(f
zop0qvnh&`&xgAy}nQ?+^cfUUEp*RZ@p?N`?@8P(%Yuctckt>xIIYiRsCJN`cHI$QQ
z8-3B9kp6BQGVmC!j1d4jYrEwKd+(cuUubJ;x*Oi;UmebE{`5j*#TVa$et_EIwjl-z
z28CFdeslO&q(CVG$2AzQrH7fHGG^<@b1ls3WYqIw)E|?SdQQCR#}ex7s}hS@8-PV$
zoFz}M&85{)fVh|oda>!~y;S{+f&Rl+;P}(}2t(-`+?CE6ZLQ(rZ%2S2OiA<5Yi}Si
zR3Gb}3VR6A+>7`2bcFmmUm6)*^)DK_LhQm)G{cE{TY?{LvDmD8S<}u^spIvMaMY^%
zTRa~_PLxiRkE&A3z&F$AE6{999WNFZ6VeB$XN2r*aqgm3(We(nJvV1?F(RlXQp|xz
znD8sDPq0L4ILNo8A`R@se0uDa0FQ`#ev*9UToRD%cs1{N9v)$Pwo%!Bhp8B&6yA2&
zl3s>-?%e1JTJWin=b=%@K*Z%?WuuJJaEzSJu;=BHXION8q|TU@YJ59o+pFd${Q11F
z=#o{0%m*2@@JjVU3Mo&{^K?)N!}3VTMEEEUYKE|ORKVkQzTH31wsx4$ujOhskRmY}
zn%o^cB&WIk6Z%da13+FQT6p4DAK6=_arkC#djKCNpH|*JRT!#nUdfNKrbv%!A71&9
zss2HO=Wx6agH4gntJeOj&#=z!UL>B_4l3pvXfdM|1rdTS5t}*VGlaYV*R}l0@ym{}
zq8~?|S4YB))=7uqp6Bz)m-`>}Jq}BgVQ_@Q=A^`F#e~J#6!c<Bey|h-0f6n}6WCpM
zAiU-`+*swAbAKAqVavlsd(35vt#l0OgQfa(SYvqD#_)uz{f11}5`+(BuK%`e5+-S<
zlUU^E1@~`}<^EyBFG~#2xM<`O*ZUfTX&10T8{f)M>friLtjPd69o|q<UOu0_3yEUh
zollvolR3hMXL5LOj%Hg=Q*sFIheis-!?+L+EqI~?7~%20V9mU9t3ZaS;tOmf_Y>&V
znJ0~Dnn$&?1=5#zSDU#I<AI^suQ#=Z3$^*FpV7p>rj>D8dd$Y0i-573?Hcuryfm<3
z?MEn}TS645`$~=ENJ!haN(?$Vp>BKKZq~j;J*j2yPRhngEvFkFnz;-Wx?Yii{?JbP
zi;e#3_JjFCnqn(G(UB*~z<Vxy*8BM4f-L0Z3L(8MOl%%GWa+KD*P2CFU0pVpmiJ(c
z2zNO76bmW;dLj2F!i*h8q>4le156*^l(>thU?H4`pkhRX5_0&x7N3iVstXQ{o?8gH
z&+<iN?PPE1YC-$b;Hwcu_dRC1k-D7Cfap-lmwLA!L-GRi@A4Q7lNQ&`Wx~)ABs8SJ
zPUOb*qqew6(CL5(sk8*A_(Kx*Mj=ux?vF^U%2a6fi`+F`ZDvU9aO1J7cOJtQ&l4r|
z2eGUeuiWYYN|L}z%i>_EOn*y;nK-V~+x`*v<lBn9h)uq%Lqad*yC}J@ZRRX8x?gSp
zmd?v?kii{%A1^_Qlkkd#thdD1#X<wj>TqpU3N!-O?j{m>3*oq#f`qA9NPI>C)`d~}
zgs|ookL}_I(9p8afAR4OSEIY-#{+CO`-1wz@gjblL`IFO$43Pb&F7+FszFb$K4W^^
z`N>SB68F*!i}~>d7rS9O?JPP4IYq~T6~0(9LV}Rjrg8JaYS{0fK9%QzPNWX;R@mwW
zxxf9F{<pq&(ZiFw+$QAiKk;RG;5^>|+AOA~?Fap3mar4+jBOXC8ssXUlGlyY@WrM|
z&wegjDwK<BQ)&8s`0cR!VVQi?PqzT@6_z0fJ1s071ZCmgL2;}~{r7&=p4BoJKWO+n
zx<k0CB-zcrH%%^PzZ}E4$45lx(*pWvP~{TeI~PQE<+KG8Z9d4rW66}D_{x8fBbR8Z
z_>;QcG{M~<5J2$th06D?gn(0YygR~GQ=pb-+t^MyVuN5jRm)TzpBM!21v7x^DQ?JW
zs(6gGHZx@{<fBx8^QEaol9QL6cW;VmkCDwR+~-@plWNxZ>QrtNoolqECJE9uBo5J7
zPgfG)l?B_4rCqx7LqwXO1~QRp+AEtlcDmeCjMKiq>1{%)wCV0JxY9J5Q>-Kmdt?~F
zMRC%>!Q;+x8%G0{ozCWb3RmEb_wl4Q9;%Kl3X{a)e21!aydRPJ6~~xkP`hRsJ>(as
zWfO+8x@bbAJk?$h%?+|rcG}iH76ZNzGz(Piexq}CZV%?wU3vfhJy0%I9z<=2F@ugQ
z`Bv-O&rsQ}x>$N=__8nx^mscuzGV@TKTa{a3fthBLu&9`y!fg)-CUxEb&zZNDOvMG
zdbjPxNP`VD<Sgcf`&AcHyITcMT;t_|lLW%u`q!iWQ7GD8qem0Am+JIF_qMpJ=(MuP
zcV_HKU0>9m=p0}^RUMx}UuRW)vdv(6{VssK+rVY70cJ?$Q$5!R0Ys#dy3fpMcTe};
zpfi&3-m;iRwlF_h%`GgE<$OIV5k<W)QdhqDwY&G*Njm>&I$1_+T9-w$S|&sF52MZK
zMz_TmxJk($$`<Rv!=DIxWj305gvCvjn~q*yoH^4v$m>OOwpi`LKW_!STM~;t-+mN5
zba?``n@5@++wbXFP2`ZNaTYHmkA(}`m>|yQs{zGZe3km5t?h;%^&)Nmf~+j21}Diw
zo5HopE>|6iD2~**k^cc%*S}ERZm2assZ-u7`E+-6x2c$gxj;67w|Z$glGq=!vBZ6l
zkf-942Ra+=A>HrfIAaJc#R(B%vO)y17!7^Vu=_q@540`pfdFT7qLPV=d{z0`vm0Eg
zxS!oX8yWRZ{mEkdaat5tXht)&s8V)bUe~U8dNWhaa+>I-d0hYs^Q!WE0R4Lb6KtJ{
z?Lv=(T(^~tiAqd9jjf4dxe?;b4w@~w?#V^c#*1)H50oQ<u8alI^RoCu%hUchq}cPH
zJi{+tF*ZJ5s24Ijy-ofHx(&^yo)Y&yn4TVw-K#MBQCRL;3`pxK;vm=#wwqzCjX?Uo
z;Q*>X{RmmYrJU><C4T0hzos|<$@)_gXc&sH1+GpOw6cBht9ILYa&x8#$Ixbv+-JG6
z@xnZfc7A1J@FQmb`)ax#&m=Be>P9j>9?Bvbr1uhrNo?K1zEkdc-L+c{wdC;9TTG4T
zy9||+*mUtQ{+N|4(y=TdXxZkP(p~s)N8r?=aD4h5UO-GMRLykm!SwS)v|F=3`*Z?;
z0|+)QVr64MD#80iHP4d%tTauS0kqxRoO!62rT?Cq^kD&A&)p{Rg**1Kryw`F94_>D
zUst@LybSZ&I!#|AW8Im4h8x%5u{<uo$(}Jw6U4qo5T7*G9#Q%c1AW&5Dhop8;Qa)V
zsDv24L_*B%crkZlaGQ=jU~5+;z;+4*=>#cDtp2?LpI8a@yH9p#N^=y%X|^8FFm|M4
zOc3AbwavcY19;yOT5<o&MHGkw@*d>n9#=s^s<4ETux~f1lu_Bfk2hk)Nm3gj+@z{w
z3FM^UE+dLJIHC}-Oz;M+884PBh;|dV+-OFO(w?N|fAM+Ub+&bN(P%UrE(o|R9H=8f
zcj;8k&M(il+V5!=gSS;csyxmnplw9|dAEQ#3#7|$h6J43QnaFR_D90J#nqR?)D?B0
zIxdvt_l?|2NdeAZqCa&X7QZSr{z$P*w<)MB1bvaPMnT;EPFOlNqMn~BE#%h#>iawQ
zh1oKmlz?FHB$;q*FDDhb`?{hGBP<G}f(=7|Hto@if&fyP@nEKgd&xi0wU33QlT8tb
z2`$JoY*F7S1O7E3xstRv|IwuF)xO*n?w&*u4z}!6UboQOy8#tJ!kiYUA)lG*wuMTB
z=1mgX01AO>uNveA`poX65{NOg6vyWu5^nv|tcPuU6Y|Pklq2&c_ZlUD{tt^e!&X?U
zuyTW@E=5VYAD|^f!+_C+qEmTuL9c~ESbC=?mpx+G>uGqfHDTFE9QWY+-M8=U?Dpoo
zpTUvxIE3VU<v*Xr)C*@8?7rI7zLcU+j1&tcIH2*|r789ZQ6sh`kh?SL0=nR|&&Eed
zKm+8}dGZxYYF)P6wwwxvZOc@Mt?f3UKlct19mjO~KfQZa9ys^LYXgQ|NBX2`ZQzp+
zIDew~GXyhx9s%x6D&*V1bY9M&@C&^28v$=8*+KE#M(JKdvp$9)1_{j@pp_J-Ch~)x
z8H39C6Z?~`%grs_7~|Jk)~$C(wOlu@PWZ2A#3h3ws(fNDPe&U`66+;g`-VXgnr<h%
zuy&KX0_p~+>ouT=Q)Xzs4Jao<G6}sM>beBIhnkL4@0Cyaua>UdK=i9ijLq5;+4VV}
zm~VpoN*#KN_dGAkUiv3zMPLuL>z?&SDT*vgxUm-cjXG1OvFz_>lUO)cHLG2VZ<rfZ
zv7=m)1G&}c*-bwpNydWs=baeT$dVdD3OW|mB*SkMTPJN-v!Ax$$hD|`V-?C+=yh9U
z5g)8tcR1Rd@;v?M8E19~lECxAtAoZT<gxZ&I@s#>7P|>S9to1-_&lOP<9W4G!&Dzk
z(x+V%M0_r+c)lXNNqnU?Ukp_G@*-k2(loX-4Sy0>1W3>x8#$dpf{2yx3U|t$$w~mK
z;S?xoEEPvrnA|L#SL~x88B+g7!`EnFKe3+#)hg1!wDO1?k3)JH@1>Zc9$&PP?2ptI
zO6Y%l3)4^GA`yB*>|;=xYztb!d=wWQ;!fxJFZFoKBo3sWVyLgS90u~-9b)2IhdU<)
ziBbri&kh<CG?Ww@s=RsqisjY$@Bu*=b(>nH(?6}HCe)A9&tJCa$1!x3-}Ywap(CYv
zEct|v<s$lf$U=Wlrut$OV+~f|VSI!@AgGjRJV4ygTa0S@$bYc{aKrPl<cs^CWBb#5
z)GQ>{@HOrFj~b5n7Lf<(Yj5@|IXgRl$GJ!428{T$bvyC$FvwM)t^8dgYoI($U0Vwr
zk}!H6lISfX870{f>8#>dwMlY+Ezxii8F@Nx$q^IY?z&~rcG9rJU7ZPQ?X}4I=Or&z
zDhTv(t%!B7dK0O$S2II^L>7)^?s!>x&6}G><{#zn3JuZyQ*zRihn1W(>n+WPr`cAL
zu!z&NUKKS!f1t*F5GcN5+>0RO@fxT5ZaALNBDc-9H)n$Lt$~F2<J=lm5_KLae>j#P
z^_5p+M8@BXUU?(meqHB2$HJsuK|dtuke0BPuMOI{RaDv<c_hcwV;CakN1gn3M*L1$
zg%a}p5SUoBYyKhI9k3_GcOV&lxEy#1DlBR&T`n_|+>7F5*r-vsu&m%6DrC#!sJ1S#
zYqS~TvPU=W<)wc#d+lcw=&5J*(MZk_M+SNPR0&5#0^BC_G4TcA3y<2de9hhZE=)ho
zt6qa{i_e5q^52kz^b?ALB3Q5-zQncwegc|Xb8KG`sKB2H&y`jN2;dMm`q)ty46C^Y
zsUIldXeO%jcWL!>V{+AHzpgo5z{?We+iFZ5>H29;A-LEAr%wUH^*GlN&-&(VM&c+{
zz(XtCOO`U~b07GlYZjnE0RkZ|cM-K07_%72i5@yB*)gd+X5y26deka%vrPnt(#ioO
zxuq;6zt~Bzf-E8=#R;oP5K)XO0eM1l68U3R^f5|PJJSPj<pTnGnfJenKq(;9ft;Yj
z``>Nyy<qkEs?|a>cvt&7q{tC10SA;~xMoXAe#79jypWWtAx&RWGzQ@6gF?N|;P58`
zO#W@kh6Mny<R4b_Rr_8i0ldbq`@kH?&mjm^-$kWe|0tq~r>Frl-u-0}lp6mtfKuKJ
z{GydzcO2A)uATfp70m7jAV|k!xBQ>F@6WLiT^PZ#0&DQ!vh_a$u#NHHkKq41#FwHd
z{gdv>$jN@=g}}4fJlcaK|AYH{Wk<%eRphogp15w8Y2ZGLpJoSs5iP)W#0x|;tWLAK
z-Mr`f_)cd<od>7{f16>w6~rz+lLwY-^i2Q8@5M&kgb|{}Okdq>Xb0tHD&{i!dB{F3
zD!i7cS?;*V=s!g#LF6y8R3LN$zRaid+ixMHJVr`89UfDSf&aSlz7liihDcvibEjx)
zLc*#ctWZIwb0<&fmbd6{$$*wuB+~TNN^8j*4_kLStNQF!V>Is&0s;oM@dE&T;Rve9
z{N5DY5V%e4Q<V!mGq|1+W`Y>!6?!y7t^Kjpm!Jz2_bo7y=n~L|-&-Ysj)wb8WH}2-
zTI-*ZQ%Z5xYfJRlvegZoPGo6XLIHeRF==UsmQU+OnEGk9z4osh-UgeXWq<-LrvYNx
zzi*Ku^KS}U4bhII%2K1Uer2WNG0v#hq<<@yLjiZ-=!7A6(9og&Fr_zLq<5g{V1xs_
zWeX4tJ_>yN55Ztan9Qs)>aI?X>X7BGvuX!XmhCkKxfoE8zurp65q+fA4I?5y0!puR
z+rRB!F;QdDiXIS>+`65hL93pz%E60H5EDBgL-3dmu;N$9K>eqk)7bZ4#lMfRq*(SN
z1E)$Kxew*N02Zu|V`s+XSAi6eKc&d>Za&2%(Z*bLejM=h4N_15I06C4Qi{LD*JOh5
ztbT;m#O)TXa)z+_`XT;9hwcv`cDr|@W^B3c`LAt(7-Dl;&$awfLz3?$JOM8y+Z-!3
z0%mTi#-5N_R|L4!__5f^a#IeErsG!z%_xUNs*38R8%-lY-+~a?P*!iS{7+FSbxLVM
zN$skjqQ3Sp>9N(9fTs%|WfRBiJO=?A34@qN$<o_Afvd!5%j5zjiPwI$m4Q%hVc&f)
zpg)n@?z{Vs?KwUk+ne3sj7h!$&qnDt=KrgboZ;W(cbhQDZMS2-Jsc&f#$m%{DbewP
zbrc@s%d+KzQEf4r_AX#Fp&n-&pa2%eMI9%U0&<#4nQC*pD`uld;dST7f%9_bhk?qq
z{Jc?W(WhNQ6HNE5C7#&Mw)ryUpV&X~-!GbO-i&wlJnH$VEzw1r{2VZWw%__6k}$e)
zW~+;aT_~O03(3pLcQ<eUkg<?_k9FTMOGCPciKE~-98E{e2LTDJ>?L1Q3BE?mYf~bi
zj{O}VUQC`RQbSwYv(2E3;M4PTQDQ!qeefCvuB2(>wmRoME$4;1LtEfw9!4O4vRjr9
z0`Gq~3f4Y<Fv8p~g1{kN#heXg`#-dOWmJ`0yEd^<P#Og34wdebkd_wd?vU;dX{5VB
z8U#rJY3T-0y1QGtzPa|+z29@*^Y<Hr9}HPOYd&+%yRZAY8z$%`FV?S`c5F(W_a`qu
ze>lMZX)j+Hz0);_y6rsiO>1+0PiclWo!xlch=Ng0d1t(6=9aZ3>?$waxwfgn<wQTN
zwW;Cs?s(uKPt8G6iCWYzgB=y3mkLr7=V6(%MV{BD@B*#}sZ0U=+XmeklXcYV&}i#*
zIOr>QLtvY!^7rkLmw*G^ejI%@jg2=M?)zJl6$Uagga4y2q>DGd2pZ<*K$Z_MRS5N{
z0jCjglT@4i$nWdx18w9_j$uPf4>nZzCyIo-L3Xuts)}clzj$Hup)vmmXgQShqdAx_
z=QXqop-B7%5Jg_~n>6C@A|rMLP&pa76XSJiTu!p(!%qT)3mkW5!#hq$_-h?@-e9hI
z_Jh+3eUQQDavYleLVxf*0J{=-y8XD~?UuzKZQ78b=;CWJ5@uQnT*~QlKcl{#3{(nw
z$NFeW7^HD!pl~<)Sx@u76{{dDA|aoP&F$5x1K+!Gx}S_lahB!qo$dfhAC<vjIqiLc
zc28EU!veyLwsKh);9`D^*r3Mb0$Jx4`uo~Kudg4Bno1zl-*z`A5kL5=jrXt3JhA@h
z^<Thc6Jw13C;@GCI*L{pf5hZ+K_l$vYfCqvaoUTzOoG;eGHhcdcey-F=M%yyK}hNw
z1I3F>eLVm6TLD<g=mK^c=|m$UM%K)&)ZXEeQz9-K(tYu?)?T%dRmyOKbelv5t)3!I
zP36k`ttw2x^T4$R-r}0>K0h~9)U7ec2z|r7$vXpstwrqusb0LdiP}{gzvz~yR!q9h
zL2U=;xq|(2$M8g1_Bj9$&T*I%hJ2;yM%_$MtGKE9^5UJ`T36TexI8Gx0^0`&FwDr_
z?;daY6bLF&ALP+K0EpV$GpJQUP(1d&Oq^}~2)dD1XG{jbdRDa*@@%mQjc)^0n46;&
zk1Ns{@!h_|v$nii^Akt&s@rLIQGu3hCNc`CGCOu{Cu}on&50j-O8zQ&K_x^{LPD+J
zYDlsH3TfG~pCXl8D!lj;o9YemCEJg7N}tT2nh>v68Bil{&96i-V@a0r%YW5XG1jXJ
z0_Ea9U=;KCfWP#&HqMekVnRr{n;Z{j9Zhs>0Sp5fT(<g$`yAvxAagBawYAXF0#`Q$
zFUD4~&~SAw;QXD4ZagnKv*p?vabi;aFF-R{K_eRKkH4!aB)rkdiNx`iBfYEsDIJ64
zO}Z=Zg}YhHICz{kC4%WN5d>t@cupDLDeH@Yq@lONY1(``>yL-T>L)_qP=3JtRRP9s
zMIeDg`R%#HJ%SZsjKp7M_~dQ7jft3&wrGr;_mwW#^Yq(8ye&J>oX?BElPHH}AC=GE
z&8q#&W|rfW^(D{w#b&WqK}2$Eq0oMy+Ms_JzwNO|u=A6~=C_-(OTReYTIBl65~~!%
zCR(YDR@o1aye+}gV0gQ{H#Z|Nn`x^Uw34nhqe9If(0A4XV)b6o#h*AEb=~^6FX8(N
z1K_H2>Vo0I$5Ft-?gI&j<{C2RRXEJ%flN=bB@vPv$Rsh5sTp3SA@ZGmi@o0&JGi@T
zYjJm+`&80ltj37XRbz88sW;lQc+9`nGYz^(=%*_E(_#x)6tjfQsBQTa!*l)%xx7V`
zY7kJbj=(RPcn}gxL!#Y~-8w$m1Z*-YoRwc(gzZRZHdVRvfj0RUrWcGmNapX}frbt(
zFFj3=8%?Xq{%WX{PkjpPl=?xWfH88Vr7`#&|9(yU<|!ZLg&1i4&lvOi!D!}BTk_I9
z!z+5BgCO!J(X41(3ibTxu{k7c?ID|V+rbt!M-Tl>jS-Gd#aGkj8wn*PCI3A77cU67
z?F_L7%Tpk)69g~Zz8y7KOtB1EIAAvuw_nZAGG+oWguva!O5CyanPTSE+g`i=6~C%(
zM(^ADa|->Fq&tJ@+IQZ?TGX^ZKN=)YZC&`6k$Arh2_Rst#3`^1I>R&R1(gvRDT=W6
z`=66Xrn5drnw4labK%K}xGqVy_^}eb72ASqf!pu~?&q#8b_X@>$&%9`qvHeayw?ND
z5puYbjo}4AWl9BNG(bl{Nl^Uxv#}+Cz%BzwE&}3&gv`e(+OAZ*8q_--zW_CXC@9%h
zD8S^<emC2745=0~XgQmH2UwAKKEW6}%Q)Dfw+_(o0kV?a>}Uua3!+Nc4ajTyO|IK=
znLbh*igsrlWggH)7By9<rw&8G=dZPUv39tV{IH|PejB^uYWV}B{^$fqGzUVMATaz^
zvvnW`#HFHj5}~`+7yt7sAh>Gh5t~(n@(2idHvh_F{4&};T>=>*fD>BY2T%m>F!%?^
zNqpQ@tSDud7o!y4aJ7yl6<Po*4DC{xD$UK;VNZsR!Pm-6a~5#%;?KX<g6<bkmElvR
z@%&$98~3Xw?clIZdM^K?BfE)Qq2vnpPx@p$$&eo(xr6d0ayJS~A1^CuY;?;;DnUUo
z*iZ^EpToWSO{7Bt)YE>0@*wf?c7GCciPv6Zw(}sl$U4l|UPA&H0kl4UpxDu7P&+&W
zNt^64ko}b|88RjWm?+P+c$E}8idPKMLLJ?0a&PjfF%umJQ`k$s2yaFASQ>&z7Qixi
zXOa&c>Wu7Ota3h#brJVDHZ0YB<FZkkI5G`f2OXCs1UHefs)uHuVY-A-Nru37mRUFK
z)ojj0hK!f@aZuUJqth}nqA^Y+MPSUec<3DY+}I0mcF|Cgj<?*-v>dJV;tqkN&R7DL
zbT-O{`1`s+imN#5$y)wPE{f|odo?A+CsaGY710m)tNg<^v=&FE$hGowuFl$kPOH{=
z?w4M2k=W*{Xew^>=8w|h@=86*@x5N;JfLk!ec6C(Tj1(YO}__$<{b6O8=M#E2P)a!
zp4%XM-JN8L%g}4qp{sq^U~=KB+&0n5rtih$aWGW|QW$OXR*WHVP;|Qq<7>b5Na5_E
zfH$B`b2(@_Kh#q6*C$~yMC3#z;ZKv{6@JX+A012<j!Jpk3Xk@4#)X(wA@!i;o*%{d
z>s0SI_+gf|l4hG4P6WGgElrjzTFbNzn}*YIjic6$@uk~N6wX;D>v=xSU*&C51CJwS
z%}e9jHDLHffA#dojeFsaypGhZqLPIn>KBk3e|Jd5?RDc~%A{iqAlsBlgBUH`3N062
z$@lMd*WD#gXLch|u5Z28D$7u}**Dv@UU*lnb6%q!2%}-uyWX@SRfoid)30EGraEY)
zN!H$7$+!sd`T4RQZmepPyQ7`a!EtH79}K^|J&dI^uCr{*i<>gT%bK+cp}(@VqtJfh
zA=~f8<fN^$jgC7k0z?c=zeWqma^~u|Ug5KM%JFy|R){$Oss{zht`z19;DUil=ui@~
zUs}TB#gW|rT<wbxIS+Dwm2g(C%da7H1#SI|Eop0uoo|VQil*y0lWoJ1^YQIdfqOxK
zZ<xP43@X`Cvc24NMAG;_kVX5-EWO^dLaN&-r4#Vi-A)Z~K`Yu)B2Nw!GZlq;fNv)N
zU*Xk^>A^RNM7>Mi{`UPdMV1UaG$d>ySZ#$P>+nkokdczR)Hi&NV%8iNoP?ek5XrNh
zD8<(b@B_L7G`_+Y5xn~n>q%Drf=Lz90goTZEk#;-O%>64=<M;=U7tFZQ5|?1?Y%f3
ztcz3|IUl~U8!&0ex!lo-Or(7Nob&Va>C);q+{M$|v$T7h59nPb3=xTcQPJcAdIhfZ
zm24$ZK_B))L@BQ(GVIIKKt^n9u?wYdMi*OM23eFCX|%mruU-ID&<;Vd?c;Y=e#?2(
zs7ga|%R7jDv0{fF%F4#d=Aw+WTQ*GRT$`$C2@V*BPfgr%UunupU*#ogXETmJ7zP|Y
zuHOMh)R=+!L#!NU+zE*>**r+@1?yQM2TTTPB;mD$U&Pv{n0-L@V&14<819v5WzcCR
zT(DN%3u|x(p@F2^DgT4ACxGlvXyPX_r`WJk)2T*M$fhV7sgK5FM6DDl3Pknl8cGYr
zP2J$Mr|-!~9ia5YBVFud`EkQ6r)GGgSXgapFeCzW1-KjuPlPoYi(L*>S{dn;QQ-Wt
zDw(~w>Dw?jAKne^p#R-zfQa%kYXgSCHM#D3WWQkE+iv6AfPUuc(S>{D0?%4ak#NDX
z9CfDl{9KL4e6edU52*ITBK@<gW;B8qRD?dNuAn55<AENexr}bC{QNnB%o7ryi&nD1
zNRFFAQ`TQ^E?~PE1#;~iRLD)EyEo1AZvr%IhQ-k6Ey;cLt0-;Wf_^7Z8Doj%#{RBu
zV~~xEWGJes|4Q0=vfTHLmxCRuZR(-ZC~1t#NS4rPJx|U<UN(Xup)D%=M;T(?<Gc!A
zp9LOO`Y1f+jee6^0gumra?#KG38S%tZXhDLL`4MN9+F7+u{_ubN2&_5QL*mkxW9@e
z)umSoT|W%rg4X}gE;r;{T?TH8vUOrerR7SggZ|#;!n`kiX~3N}!U12$K^bG!^)B%8
z24e}&NJC4psfGGv{^PvCk2@Iw^+REO&C`SL-oqbX)_L!g1{z#$J!x?>Ui%^JhC-HZ
z+<lNqm!fk(kpxn@adaSo(u>-JHtzu!ES-I~{N3p4g%tB8tav$XO1o?DFpge`AFdg`
z|D$&z3LhmFW+zoXzCy2<9l}YZI}mApkjVIkTY{J2`%KSniI$VT2leb%Q|@ZEPkI>E
z6PorYr3!cfVff;_wjtx4>X-n=mi^3-BRl<}&~Y>#D$etjsBcn)8h3@cO!sTuwj&9A
z>g6y$kAmzDT_|2Blc|+?O5BzNSE`L2rUm77uCj`!BXouHdTm8h&8me{G7>xsFXN6m
zO-&Lr$nkQunH`cwciH?Hl;V;z2JO?np;&vzx+az(w_Xu(et7qz;ez8%)55AlXT_0r
zE!9%|G@?qm>OIsvyaj$GG!K){g}BI%^5$Xb^{o9cncF3X&j&Pw54yrf%lX2F{Kq{M
z1Jcw{O2Q2!WE(Dvv_8@47hXqCABu{jucJdA*D~3Ld^bkf^W`=hrJUB20d9$&87=kF
z3^HtXuu*_hsEuUK8scI{hcP92MZ~kV;|U#aBBf!7SpqCY(vBlsx7akPkk6;Z!3a-g
z6PA48_a>`7eaMM)Ka5W8nncNB1A@7hqNf^J5SN<qi=;6y<23Acva&ylKQ8<+`)2mQ
z|B*G4^t{^Pl&<^*@~Z5^!M*Q)ktO|hl><SUi-6pq8G=vQ>NYJeMz|Q&x+W!`y?7B`
zOQw$Ay7^|Eh9ZVrzJ`#Fu(LlDLN)rNp0+D-SuFS2kTzd?VNrs=PyVynR0&N?E>-y<
zL_6}q5sJa=F$_CXj#Vo1*fD39RE4&;!ZQXimB~dDnYX(pD^=K(uxU(s4fFGU*oO0V
z!mJ57yts_Esy;HjVG^d{-37N<QFwJpnKQVX@1+P~2WG-&AJLIfV?A_l$}_cq*hneU
zvpB=hcw4pn%Q5gTn7$dp^1~>)xko~kDLRSulV$rOjnO)71;w7Zat2(<kRItbkL^Ex
z&o<RfYv25&+LyLLx?$7WHDF8`HB}d&78@32oVqZAV4D&3#nggM{J0_!O&!;ja07`o
zoxt7Zan7cE2Eu~T!^g415iug|Rd4Xy(W~z-BJU-(Kv_7(L(yk^O|Q!E1o(<QKlcq4
zbG?BZVY0^NAbB0$_}E7;YI*6Tb+esg3Y!4eb_x^Crjq?HE~DQ~3iP1$)(Yw60lfko
z*A-V(ncT}$Y((^AJu3R_#4q2{{ML~i3dP`XUkK@-_oi|8kdfdTjbCwg%*;7247O>_
zhAf@gzpPTlHtVij0*>^&<Aj!JC*4aN0+ARf2KtDFk_jdttViSt=c?LZeV!$QP~Uii
zsqQ?6PvN|*P+yqC%?4!LxXq>nD-oqTjgPv`&_$P}gKV0^oO^2wjU@1Wi%ic7#S9=A
ziNb_yzY3f8$|9%gO8bQOl*Bq2An|3Cj3+*kzbtQ&pr5e#x1lusA)KieVGI|6b^TU;
z))Q{5vf%vaXb@>{#C$EII}!~J#4Fdt^bEZXvZ*F#0iKZ;VW3)mmde-Lt%A&m%WvO$
z-frvMZmTfIo(Y$~u(M&W8e!}DfXZB*1V>cu+=!q<WwtJgwfo#SM$p29-codw2DJR&
z0{+a8UcT*bPXc%K)}2(9)1O!)Guo!X4Mqh_;D}_QXiou%2Ifq10$%<q16@U8;5@0k
z@6uzv>ZkI7NnLm)8=26vyZ3lIM~7WtER`=PE(L8UhqmY=?|F*B;9d*MfXwJMy191<
zGyt9Sxvq01Z>7}ZAjxKqLo;h^CZzjm*vvf2HehH>e9Y)|^msfakRQot0JUl0yJ(^v
zZZgVO)$jGvQA3s3NQnbsp%Hxo*HgpGROTr6G_lp~Jo6=Dbs`^aDNhW-){=T5);GzL
zcz83Bj?*mPN-Xm2e^6wct@>}|qO|I@)7T+;6J@{ee3Nu2OQzWcITUsSR1N;$+pLi*
zQmvc0=f~n882wReKMl1w`L(UQ0ZXN6sEvLj4iY`BPwJ~t9uP*e{#_9j-GP<mKlrN<
zn)I@@*91z`mzxQklUsw_fFg?4u2*FH7zqe^I5HwKoouh4l2F*k*dkZXF}zSvXz^Ek
zMcK`BN*#=lj(jn&M>b;1g5`_9pC=UeoE*of$3as>D=BhN+IZb8h(}~kz0O9jvJA>H
z*A@H-BSZh0w#;m4u;F&c08?Zwo|SYQ>s2fThodZ#mC5-^`5KEgN(@$N?B3zo5@2^k
z;Z~gt{=nrbC7t6RA_=XuE{d8EJjZ#}on1x!e$}}C!XF8%Z~)s``@R3-7}sih5Lu&D
zFzQlOjTxv|kiLXmyyBWD3#ei90>mj&{bd?8Yo|54Y>b|IXJN;z3Rg#2^KbaKK!*Ng
z)P;ca{Tkv0$NtZKU=|WUTS={d#(4s*Z(Rp2O0R`pHi<2%ZPmDIc1ceMYwrOKHD!)L
z?>EV(@g~9-=x+%t*b2q%@YSD&F&SsGzrF_kLxl6#muNExF5Agx11|~E#pI`ib02%(
zAa?~x%8m{#Qt_)i5%*^@)-({vb^t)`UhR}5<2lA(g<)4~%sWp;8~t=qStEy629jB6
zLOzEyk?KTON@p5l9PHID5aXC-o@&1j4PaXI7c?*w_B_kdCwaDBf07^q>!BQ|4B~At
z`lIAxPC?0cKinAsPfZh_OX@bz1PQ-#lg%dK%E-YbZS{Da>&<_*(BzsTlG>@#^^wnS
z23qzwtlFlfeBewnt0=8#<bY&}!LFx#b9lF|wc>B6%n_YzW0yUydKxPCl#@{}!Jf(}
zX?k#8!q!heW$jsENR2cAx-@Z`!MupYnAh89b8B#gdz$KZjo_fyYgPGpbaSA5KV=jO
zqt&x=RZg$cCf8AzXt`NqtVm{37pdUc>A_S^NyM)npdqu!C3N#e(s<EyGQ{f=-|Oo^
z8ucXUs)Sli2wD|{U3Wn5y-%YKtZth69$%kRPd><8@t)3b+UZRzjjgD__H=R6v&fJq
zpp<JfzP(_nl+0PP@#A=X6(%{M)fEtXdCVi{p^Z90(9?wM0~wHbI%f?~*ZFh+PT@N$
zwwb2(hdVMlR#d%J`Cm9)DW!3(inqu8j1*%wG8BiZl2YQi0++pVm~tPu>s6sFin$S@
zu$A0QW2&M9cuzPTx8J@cjIB-9AB;U-1b7r{rlickRm00BVT_GcgG$1bgyAt?X^NzW
z)fEQa#@wI2FBRIR%?RBdlk({b_xt5YhEtAI=nCDk7?!Mvc5q}*!nVCb2*mtkvt=^%
zfV^?%V;Q<jn8P^Vi5MNUYYi~w<T6U#ss-Bu{}*?*xO~|e6awwBh!=Io#PKf%a+lw0
z%<#d>zSA|q=0wYM29+ThXs;<g%{$4(6$rXNmqIe^hkYudN5XX!qjWjI7a(8~Yi-jC
zi^@Taq{^ckDV@l?Jd#y+=&S@as^HMDYN>iQj8G_%^g44$;-d>+gT_zsFI2MWE5Zw9
z9U^nZ*8?_xh|G|Cu`rBtIpdeHhzl!M5}pGx;)2KPUWznDK?L=A^Ec&<95@x-EWU}h
zisI8;x~>N!e7G+v2{$-adivi_IX-;h(rd`z01#@&yxeGflRoPv`c6;P@||dO0z@bb
z$PYKBV)uWkPIo{kFiCJ`+O#O!cAnr{cclhUJ6QtOWSFgMz@?Ed1i!+CQk9ixm3$w)
z?C9}E#K#uN{yR}Rc6eyML>50Nsa+K&(fEoXffW1W!W>nEhom!?%d~=P<Wf=15X(n>
z52-?qMLtwA#LY#bOKozlljTf}Bvb?#lFO!qCkvgBrbcHm$3ik@G+l9?A8PFRq46)`
z<YGK$bG{?~o?9MX<k@r4P3#^PP&Vl|@+kERU6i|{Asa!TqAEMSsOP7iAIbL0jfE+<
z)hOR6-Fs10a-Z+LgNRvAH2h$^EKqNn8f}9w8x<F8x3~wNNAkO7zdzE{OEP6@gwxez
zinlS!>JlE>*4Kt;0w(zHwF4d&*_H_0eLltksS$ylA{S|gc&0UX1<!V+tv)=#-;jCq
z&@ApAiUgd@0Z?Po14z=|`v>_`@2`FRuvFvY&&jM@{S<C1+rF-qP60=Gq!?uIN<$~Q
zhUMVCEp_FNle*c4X73-yE!)o3*;25u@NsMdX5Zr^9a)Jw!2J_Lt4vGl|8A5d)zF{M
zYc*OthMPG&lN)a()MFiH0Z_(J(zem}V!SXQn2vXByzt6#=1d5LT%pub+M#asLv&f9
z_rImSw47#R!0?46>R*vO$jQc-x$v@uqu7@3<ilUa`6?@8%w;bto3|e0*NtQw<I0Y1
zH?$R&irW;vk0SJSxk<Xdi++I8Qa`eDAfFQbvmP;5{E=gj##7#TopRSVbt1BW8a4gG
z*H!LYQk%b@rzggYOO>mUAbUn!dTfDQCb5-dhO3{?pvNnhmeyc@S~X;m%Av3MX2sDO
zOqJ1Z0ByW)0@mWEJ1FFc5$BR+qaoXeg)7iALZK`$G2Gl#(z2gq7H8-+sYsK)wwtP_
zmbFJ&6^A}BOIhJaY-bI{;W8DxNH_Pp=?^`Wy5sN7vZdg@N27PL888j{pm6LX%<}Gs
zq%XTDIyHsF(%<h=Ys6ZN_vTx2gv4^~&rSNgsQLCFbsjnC^DAajN)e10^qZFD$(18d
zxyS;q1^1R(k9okW%X&WGY$)0S!g)z-I6_8$5lWSE#!H(cvOM_~4+>9Pg8D<<H&`pY
zMp8^~Lb<aaz&D7^b>vW2+Bv^_?g8-Kv~L<dd`f^r)qccBTeE^86j9wCV2arvQ7t;0
zx(2X@ESRXtgI{IVjYQ#R6lx7?^*_-4u<aH)l2`mbBr&__qLz%2wQET2{9*{MemeL&
z@lVwN8XV@3sS0*InH5&Vl-Ygqj7#AJtO8mH?G)Qo^9Q$X$6+zk$2zsfJ=Qosk=9$Q
zTn<{L&|6|MAI`I1uz#U9SOOvO*!0;OcMNpjKq{YoQTUSzy-O-|Jk1~Fa$!6v0Tbjt
zGVl)-Z^ZX<`nqTY9o)ihw8QT`UJ5}(vTz{k#~b(z&+bH4&|WuRHl(3>Z%lDgOf7ia
zkz9Rwsx2d$^%bd(PDDl*aXS(DO%Lmx;v>EYc@0!Z+takq7OE&NM!og^@**0`c<Tba
zf(uU*&q%1-$=NThagbi4Tg&Vlz0aOH2tB}l{0<-MDDZ|A<P9JEqVYaKs7YcGCv2hY
zCa+1}IDP>q6U?xd=X3vI`KX(u+x`Qh!1ZpG!guzU%wjK>`VN|}8Lsf$qq3sk8vH8V
z!l@+eX0MpCHO^~u9Jb$^AT_|mmLY6tG77#zv=HMsiERzirem{y1XuPT+X>m#NJii-
z8K=g2h@b&F6N<D0atq}pN-xb&!LOSoO!dzfsTH<0k#k{58u<QvC-%F~D8J3c=GT1Q
zBkbl=y_GdMKOZi%6#s$?i{ayQ`^55_t;b1slBeS0u)y8qda83GX6u!iq#c~hGoM&O
zBl?1%g!M1@4CCr&iYH8%Q81`0#Xb2V6eHzuT;Giu-B-v-VF_`m*)e_b5j&pwJb}}K
z7f|}(gZML25Lv+f_JOiB20HA&KZO*&%8t7QR^+5`|NAFO9zyAZW&YK$1Tom>fBpyp
zR!EqM__V8#|MdqSL`rN}q(y&q2D}&l^+0)0Vs3S$D)9Q>-$V+BBq|8U^)W%JEA+n}
z_!HoaY_xidGXLiiz~=;CVMM{m7Ourq{PzPLL7GZa#cn&16rx^hl}?(_C;jhBLpQ*;
z3w&a>&V#)k`dmsLU(hW_bA@f#^6%F?g+<c6rKIHct*)-7%>0;7^FQARodmq;1y_+$
z8>T#>LmNXnGTLL<TXF1!_$Z=(7IaEIl0Q#j3WI^j?#p5MOPF{YA;xxzChI=9twpR-
z9)cMsD0&$UsG*Og@-2BSzetR*$4!w(xj=GJFs%m-Z7q=&TL4V0*pl(@`@sRT(=7<Z
ziW!j*v?1Kq>dYK}4+7kAd|o#f&)UUhdCr%WOR<wDpO&-dBL=r_Aa3FgZrE&+KSSDN
zyvWs5mMJzvtOj)mGveHWU>FFf*C#OQG<)5;HGPr3$_#RRk(lL`Oue0WFt{^OqSHjT
zWm1X+&cxr>hp$yn6=7<m4ia4Y3Z8`9F4vYM=esEB7UJfb!YI92A<bJ&%^Sclo&0O>
zdrmjN3wO$=zF657*EJE+)`c+_3*)DdFOq^Df~gJMF$^cy8<eMFa4r>bJv3pDDN<ia
z!<@c2w+^15L6Xt<YL{n!1CS~O<>gFBG)2!mUoT!98D!!JT;6v_BD{k`ad-wj3zS!a
zaCJgV=1~w*QXPOgjFCphf-PELDiwP@iRmKKJ3bPZ<WwwM>0Z|CTjYE&MkAl|_X3c?
zMGO~GG6;-@@f}I$aeS0xR4EC0B?d#3eXshehWeS_5QvfY*=(S=(W)v%{pli}-slzT
z%h1GQvlZ(6=g5N^;1DE{Ownv&m&e;v5@GPUSXrwY8#S+eQ=Q3v{bIrr^mW*u<sQK4
zt1+Z%J=nP3Z-_)zCE|60f(|NW6;D{;%q(ZL-S+6+o%XmKbiE6Hg%LMZt({B^2ZF2p
z13e13i9>F$gAwamWqTLVOGBlRV1c*Ei{K)M4X0uFDijj{jN1V`L($>5h|?0=dYFHT
z{-PifdVkr-U~fPE@Gn0t903YxfOCEkOdi~|OICShkb{ijn@_5XQBWhSJzD!Lcn6Oi
zYmqBW^aD<*b`w4xA4sQh`@R#4r*u}e<!e<Ef1y!pMuBD%Lsy(n1{Wd-#1unWl7j;u
z@MC0(5op5$)dIe-LrS+lf&QTJB;tz~KoKJbjUQ~dOi}4J<iy8YH{a}LXw3{dK@I~{
zG#9Ap>0t}VV?_lam|;FKx>S?zdo_QHro?L~)waV4IR}k^z=BqBlm}#-?z*)|$5{Nb
zeeFYxbxKM!*c(Kke1dEg3}b$aYA&HKsCazkt~DP6<cW*S-20y&NeZ^Av~Z-qBsq|H
z?`rl4T$UvopcwDiV*-B5X4DNN5RGI=Qo_v4Y-?)^AX$8emS68vSx*%^>b|Gf*p3{9
z!PEkGpY0Ls9;_913I1D%2oOD}^eICmdO>wLQOo0~v(DR*T()$CN`IyK_QCG+ffM?I
zu9mlI&=2B=_-NO#W2&P3qYLGE;c^i`x!herL1C}H$Po_nsn=EAw}J?}Kt*DX*EG7^
z#LuDUM-J=iLxAx)5a*Ao4vua8C>(TmoY)eVkTB{6jvgd@WzvYo=rE8LHv~=^rMl7`
z_dojOrSq6nkA)zI)P+{6K`>*1*oJ(ys#O2I^q3E=prcv(mZcPhfCDhM(|lbom=YoL
z+25Nk4f<(~%~p&F<dY35pZMx1bbk~cI;U@CB})rE>Jsrww+r^?G<d#!eW5pl1fPl{
zDsOq6M@Fh^EMqO+r$m6`;esBIy_RA8pX0&t1!Iu_CZuB>keF=D&d&Z!@eUn4JN)QZ
z#(#hD5q=Egz(bi{&1K55)@gIHm*JEi`n}=eK)8=4%?<zPZC@88FeV1Xqz9T+#xkJu
z9boP|iNCwJ7X#`B)v8~f1zyaV$0>Ov(p($wA!(t~VDluHfTSbU=(4E%*?@S#1FTHL
z^z`*LtjSu=y6%QLTGf?WmA}s`)JMCF16wkj;?Ii%tB8*4>$ErXaQfL3Wtd<FaBab<
zLTo5}$I5?Sq`xfZccfKRe9Sr_;u67d=!c*hnif*eTxkBEcE=YVDUHR$aB4|-N11_M
z;LZ4F&mcwdND?*+k?>MS;lJ)o1bBLT#ZQU<eEJc_Q*JBF`v_&_8cC@SWkKptyDJEf
z4(txR;7|1b{HP-->8Zv;(`|A%a(NQ)@~0mQn*a0ffB%jo3<Oy(;dS8uVQ+)L0z5a1
z%6=aoxQ@Sn1lxd8l1<8s`S{-tJS7A6mc(uQpPT-VKM}<Qbt8<63=97}=idi<A_6xe
zDC6qCS3!vkbtBZC<30b6qxk!o{~un<G?po$PyWwE0}@~bcX@gF7>BO)(IZ7!kCe`A
zqkt1<qMnuSyyq(3J3llbUF*_o-&gF0%oyN*0rllO4Lq^W^vqBr{kMB1AqppZ#c~On
zNQaY{bJS>epAV*fIg2)SttQ5o)OB6rdwwZ~B=tc2SRowIA7qbg5OGDR|8b}MKeW2j
z@CVNWVKJ^o?k;=wnLqiq+epQo$lc_ZwV3-aQ)LJuU1;eCwsJ2@5z-s5#qEFj6Mr-m
zHxjAW<42E(T^4=U*|J3+7kDv}*fuy=pL`B*uUBl$_q{e=H8&$9d?G@c28n~bNZTR*
z^!xt`LS6~AUV5d@;h!*Ln!gAc+kJ<@1Ow%odHy7wm=u^$L^7bBgzIQoB!5el2q_%|
zy>+$T-02<NPmXOdMJEKt8Ev9qf^~n@4vTZy1Ckk``l4#nv$Jq%LjyB~D)>mf)~GNm
zKh}B_nc?Lb_LWkIy&;n7vke?4XC<(Kh-l#W4@&~*F#hZ(A}*|AiynF_yREJ5cXoC}
z$(Mam-u)WY!Np6=m|MIBHo_7m;g%1s(!A}}tCJE~9o){)Cz7<Ls?IjjdxlDLM<PNW
zk)!j#J@Q4Ji|HZ#bJo65=!hZLxcCb8bX1{Nrz)`_Nt`of(xj(5sp0yZiC=VzDuJZ+
zKvkNDuVKcYD=c_|ju?3r&f`s<Df2|UiD3QpK$nXNS@dwo^0gyJ16+bZi`Mk~F4Mzo
z-YO+@-?!AHfD!yt+1J0VC6Fh|=e|UFmm%gnc%^a{>Kxacgp-MNSl{fpeX-mw4Lu%#
z>m>V4bRrI_O8)whmG#Mq1jFo{kDUg8E_Z1EFm`kD;~#gGCvbR+LJbv??_iPQ8`<jr
zyc#x5RAy#oYAS&`A`+4L4gtw=+Az&6tc1h09FGt?x-TUKSe4=9;;ny0{Eujg&}11z
zW!o#1{&``rVk}=@H9xzCb*G(4OHk`{?R35D%*^{(X_hg5T^(UYlq2gp_?g`(-pE(u
zwtf|LpTABjh~bHNKc4+qgpzm!F;cZzLO&Uv)&mo#mrgeqp8{smU`y3&8re)>65oCJ
zaEzKz@Ad?|?3-{P4aKE(>wk2~pxEL{qyTh;t4!npz`uxz1$v(Y#|O~SWU2f;vJW&w
zF<VTQb6BP<mnBAZ3tY!7Khxn}E@qxGxJh_iOYdQ@vhz7#WkY)+ynbHm!6QUt9hh2+
z@5kHG6Jgt|ebyXCty5@2*VZlhU;7Li&g)%A%8!emgU^^v9ZR(rqukwIjbXM9eqnR_
z418fh#Tz+^r|ZuM{*joJ^wyiplUj?ZH?er28?A0R^u_EP04g_wQgdf#=jXt->w^~W
z;g{zZ?BQ=wT_2RF54vq<*~{F5U2;E}AB3;GI`7?dANQ$x9T7+OOw~d-UM0Tl+C@uu
zQfThMmv=uR`a+8z-H%hXGq9gFoR7?xUe`F8WljmaYu!%&bj$G^da?f7^0N5?Jf^_u
zPsO#hHP}ZW%0T_eHcAx)164`U53Kw20O>S0g9)LWNXebq5lMe!0$Lxw!_37@5jVvK
zGL4T^-|GyuQ-{{_GP%nKaCKRfnGO5O6R29lo6Zjs5vUL%89Z~3Rr4D1-b3$+e<nD%
ziwOyw-|Ad22A#BsC3@h_@GR{@6<F*{3&EElP60!?mVX|A1C-<4s|NKd>zNwM**bIj
ziAj>52XW67+tT28yx<BPc&VDSc=iN(+(}NQ^p0DfjW+=@QBT&ZecCw;$Lgh*LC$-V
zU+N9+$XmYk%u{H5DH+P<Icdku^YUbY?gu3VYC=@0@&1YxfPnN0>VoQxuNmLvYV2p@
zfh0MOA}fG{2WWU@0lU>6P+Uy11C-mKI{0>??&#6(ohXdJVJm$2d2l}ASMh?3vpN)a
zPI*%MvDOmbAs;~hI!@_Bvz8%Q1z1GO7H+?eY+9w)D`x7XwSXpLR5KzshkZ4>y1Hsj
zvpmAL(3|~A23Xyn{S+&|?+s}PQh7fo<3X%uM?sq1Yh~pG8K>@uVUHLve(m|QXJq6l
zH>v=6N1jz%;Y$aIiO;PK1oC>j4rV{I4)drx{?fe^dbEL>(s%xeq{;0l>I0a6Hn!C<
zCt)y2Dcxtforq2MjqHGPbH0cm@nIj@Eb9?*%2X(J;*()*-go`Y_?#}+6l^kIwRXm*
zh(2vtW!98Bo^2G+{kj(={Q`7J!P(Wjv)`6}!~@b}x<<^e*9K9crkjoj6ZJj_Pcra2
zY%*C+SAX++*wBEY-FiM#rqhy(*=qSoG;7UfsCSpMe1<gcaI}qT1C^)N^V3<n96)os
z7~h+pTN^2@Rkr2%HmDJOLSQnXzC5)+Zgw3A>rN1O-E7*@?Am|Ndij2xT~H2KRA6tK
zkRLB)_fY;Zu3m7WqM{&HsCHeRKINPRu;Yorg(4kuE@U%6*VF7h$^OaPw`T(|kH5E#
zk-TL|=P3QuM3m5VIjcC7*Qh(=uGC#TU7%#$CHpSD%Xu;OJA;A9Fvi=MNp72JM&{uJ
z+?0lQ0@~LtkG)PZ?eF~tTg4-Z)`YOG5QJypDL9XeM3v&NyDM5{ZX909LZBve6&7`)
zzUTR$_1VESU!RAu7FRu*DX6R*6}T#tN@Pg8Z2*i(ZEdgcL06)~_iRz%!VeY<5-i?R
zcp|wQX8~W~nx_#q5cL~+&<j)pgl#q&)*yp$R3$=nx3(hp-3w+rwW&FuWGp)xOd^@J
z>>D(=+UF6<=om7SC*#@l!=+y1**Plvs>$ietQq(H14z}@T~b4^fT~4p$fu@M{iWBp
zC;M*@fVUC{avy1xQe`2(?U7&=25H_27>c@g1e6vrzegQwUU6|>Jg?)n1AsGviZ1HM
z)0u_4n(AtvADFyBT7Fm9!A|Q26gJBW$C5g!(;q{(OEF;|YX9K^Xd(K+li}Rwij8BX
z;Zs}VnR=Gcd#T$A`)<AY2r07vv+S4fjye0yDpiMf@{Wz$x}8F!udNxTmk&@F_!}c1
zfYxza42`-k1oB|D;QXHeNtUM%3j6I1_{Nd?;7;_?$a0v^)qhFl*r3eI%UgPw|3Hpn
zd*TsLd7Q8wi><KwAE(fE>wlIC7P8KG0%vGb_K-EvW1Hh`k~<Ms^z|dP{(YUBCdw~u
z(`gL11IGPfYcm4*2dW<;P}96tr*|1&2*H@7bCLBb#XL@7DXQ7crBW&TThWF4oWTTH
ziW>eEY(uR%w=bCAS*re}k2+-Bv4G^OSwVqHrbd5I!jmUYl=)rCr(=7A81h5+D)|>&
zJY~+OKZ*<79Yv<g)$z9n79S*J4-RDnxIW%nomX^MBBAY+U9`Ne`P!hI6vrC^Cr)U|
zXKV3hks-0uh{^+PhkJIo=OyVonE13p5kqzaPpC2>1wBeW!VPRJ(tqNd*wz>-Da|z2
z?wjRflmRGpx3XU%=wdLxbz1GgNW@Qp_q7Z%&r*5GsL%#^m5KP_j*_8113oa9_aXMz
zfdO8rPs52kO~YF`*J1hPdc%S3@ngLHb0(^hOImVuPPn*qcJaP#4=)d@7}BSm>g_s|
zEY+2|G41qijIX61Ay8fVcGY7;(`@A!AV`^17CHOvWC*fg3HAZl+w9<oocG#uq)_ep
zU$H-&wY_gowHll-3U^=SKSX}IsLo*l8^na4WMld&C)P~rP$PA|-g4GbL}-Ek4plrX
zz5b+jz&=sA{6{3Bfp&$b=wd>{tXjRj<Trgxqwsy+6z|Vo*LQ7~8XFB#P|f>)h^Q=F
zp$_gCpJ7iF=yetwihYgAqVe**>(O$jscr)yk3*rizK!96+qkNHHC4dp4f&<52!pc<
zqevX0=Pa=<@#WWx`{D_AYb$;v*J7BXVLFNUl{_;Ql6P7ye9k{KWhLy&DA5OY__fa`
zE4#TkC#}ad*KVJzMMv_x-CTU@+qSuiF?FVx`6LF`riRo5hOfW)<oetH7kr9jXk@h1
zwzm4wpgW>7suIAofngwm;@TnQGJYj0i0i;w)iEz;dcNs+wF05W;YqgBUrSuQcl%a0
zQmaN(bw)f*z^=ghK7m7v*8!zN^xCE*jL%DN@Wg(6cxXFnEZgXV)<Y+5X2Pkut#{h=
zvt2E%_S_FIK09k8z1@BT)&#01Fa?X*@B02&01F7$&qO&_S8nm^_0<j@js(F?P(uY|
z7LlvNX+b}8#L)zH-sH%_+*hpySp6(uyImxN8)%svHX63seX!3Ev5@`{e_i4^XFfC;
zLq0MIE-XQ6dDlMy6Cx&Q_(_(K-}^5Z6SVVIH2fIO__gl^P5JAJF0E#1%pCsGt-kqG
zSua~<`ZeUR{zL{65I8R1SPL2(a{0vYzn;AbeKt`A@jo%>Kfj<q03k6nkNNMvFu>u!
z5iz9lTgzk)++~(Y<i1$AAj6x(?EQtPfi-s*j8yar5|aizn;6FO|4aevQH=1u^c{1D
zSzm<U9{O%=zJbJKfRBwbR#4Oa30kB4Azen9v2|73sYhx~6<brnn9k&?{A@2@eB4Vs
zB9Af$D^;}YWY_s^IM97ND0G?I8(yEJZ8fo8MGhu!Ghh|^Og%k7?(*ZIHz{n8E`dwv
zhfh<LqJ9T*=Bfhlzt0D}P*fD8Yb`C-2LCB&755<k8)B|&aW*&6|7e4?%wHqARsHWZ
z4#CP^QH?|X2`w-)U{Z~p_lGrVJntNao%>4AWBsuXXa^S@Nh2S8OfPUPN18eFY-#>N
zE2$p>0+m`2$r+eMd%v(S>URtHc6=LXX$Dkb2Q;TZ{M!6Kk|%?bFdrKlZHO@wX*YcW
zSC2(xMoOpC*2lM|Hhaw_lan;w+um0S4)Bh)Xwf{~rUchQ6@m>nr)tRl`QN~Ujnuba
ze0IpRYMfvHV+{&dWneK4?ELGbE2SIzmy*Q|h-|PR98HC(BqsZ_?WAz0R6eP=o&h5)
zrJXi*9OH>*w^tgnEX$+x7kt}i>sK#@nxL5+=y|oXjs^d_ha*oR(nmZfyKy!Kd{PGE
zp)hxsf~Ibz^`9z$e;o_z4OT2a-J<?o+)t4CP4dP;poi7eNjcrIPHyUvqgL^_6)dhr
zWCMuLMe5Gdpnt;pV8L6Yq~)0XVgbo;=z*C-L+>$V&66j8F7w~X19V?(sD;jcTxRx9
z#P~;l7DJ03U!F{O{BwSPyh%~0$Zod1oBsE8{=Vk_ea-%SodoC^ZGBdMm{RlaEB*aN
zx%jX|esSh6K41QmoT23N)yi}2uNgMM=RMz`x-rCbf=h!RAZtx3J1N9;LNRiA4h>s7
zl_t{uSsP}YkEG7lJQE$sC*8*tjW+X>X+<&L^i;8d1cG)1SO5wz|3?-{;Xaa<m)P*D
zKUO?^8PU%l^y(nY94(iB@Rd&@2Jh<=SGEuOJLD*{bdNs<g$kBJlShvd@&DZ+5S80(
zs|<CmtN8>M9G`t_@?k=m<)oMx6Jb*c0Ov=GNQ<OQn;;}ci2@xM1^7xo!4?3RY)Yv{
zEytn{b70@_us3MX;INu~I+YKqJ|O8?sm=cPcFKsgdW5}ck$J#(_i*XLNXyikplaoy
zFai8kMoy4;G2i4f4K=+l2(kcKz{2gtO62_!$^8)+OZ<UZj&1M$+WWo?3}VNkmgWML
zM|*pF3IbeQ+<QR9k-=&rtFAsRaQj0b-Fe<M+HxdMDuFJfB(mh$ix&-GMkR2}aO(m#
zZvlO&-BBklblf@c9-*kV=EDF+WIUEt=v3sRNN<mBBIikaDBIZ@z(QP<-Cr@LAc&3R
z{dKs4Sm>>{{ffC>sW6Un#J&&a9kbk|m~6k>!A*pJbPM^n<j{sCXs)cJbos*+L_>hZ
z@g@bNZL__KgkE;xw1V-uA|Dv|kA&99eTKP@xc91msMlD01$N3L!*v~uTnBMF)Al)F
zzf0wFt-L2y$zMBfx%YI&Yw&SChqB0Ip+pKAltF6^y9-yh2j0VU$H)AV44~zA8a(85
zXJXh|af5{tk3{7X^!-8uGoHwth`-MOT_QMa<cLyw{;fKjySpRyXxC^qQ`zp{nIyfX
zU%O<@>AQUyUs`y0&mAlW&b}7X!I6P12Vo^bG`Aj=&He2;h*0KhQ58ZXe~tk*)qAjM
z)%_b8?p9a7wk{Or<^-2gurjl=v%$2@djR_qLlkgZj*X8WYw^B+@<JJK9XEo`SI|k-
z3oURxt*lZh(^k>(WDkd5X^<i>1POpPDtyrMa#!=oIbf+hXa&y;%C7+?!m51L{q{cK
zF|NMAbZQ@<ZaP?K5qSBsNiLKBvyA5>MBN`V02%4!*=5$(3?`{}3P;3xgFY<ZCuCeV
z0F^fgCN}?Ua6WKL=}>fGjEauNV5e<GiNJ%*lxfsPoKqBJdb#a(`C}fo1*otBDvV_m
zDc~>6aY2g-l<2UHA5{Bse)tSp8Q5g;TO=~*u>^_^Vh8+6SF9tmFc$yv&~u;CO%Pt(
zvg|c*+2nzSK^?Q}Nh-%8HO1>@RCfk#;;>Vf;8uUm%7QTy;W`pVd-)3u40HZzXl&e-
z^ahMq0sKgS!Huagi!Fbx8H;4c?i&Iwz;(Zznwnx3+noNg<J^3bUWg)Zgm?^wDBC&%
zE@Ba*iChnx_T`2y7s}5lqN?medn7lD4=tzP-iKa*LD-jFvJI*47eE6p+|q*8GUu#K
zyUzWoPD4MGeFuu+JrK89Z|IxG8L38YlN$m>2Iv%To1W_&GSB;U>$?YPJI`G|0KV4S
zg&t!S0|YM-fPTx=Z~SCESI@3+)tGL}{@4CIg5|ZMLDxv7-JS>{WY@5RE7I|1$e&Dq
zP%~B$f1Fwb${^^^fu8)Rj*5rn1m};wvASBK{$;!QdjG^y3-Ahq`QIU$B5WCUea}Fn
z67f;Hscy~Bl)zsE6prXpTx%ET?$B_=`MjiR=#|MbmRQ|#{2D7rgy69nr@5{t`-?Rg
zS3K?^hU{5;Uu(eSVu(T~CB>^~o6RY7Zhitpc+<v<&?!|=vZbfthsHlu05WS0ifn4A
zzS&l3>09G$K0;Z4<x9J1?YX0YeKQPTMo-d0y=0E#llhNhT(!U$ibh+PtE~bgc@lQ>
zpP(T~f{NcMn2gR-Qd0vF8O*}HF$5jX<IIOvoh0EL3peYWNIeImd5;C?ZyYMdZ@3h|
ztn<4{`;8$l19EI_w=F93t}r}5flT9@#@p+bd)^gR+?G73uNWdhiZNDZD+Yf(6@&Hm
zc3N|!Rrp609XSt%cc@_%VlL<&S;W?KkooG1v>1Ke&~nWyg7C&3)U(3wpoE%*;^fJ;
z1j{xjUtYj|HcaLLMD?uinT#DigplyLgXsBoG_l!VUZ|ebCo$s!edQ{L<hCcWagE`4
zz4+7THux|PD(z_$38vHgyMy~<`Rp8Kc$5J#9exlKcGKK|JB6hjZk>EK8J3;X>MSXV
zlwsM|qbt^qOn}a8L98p*iu1`~0UU>2B~H&Bg5GkFn$db4cxf;NFLu%q!eotgcdBzA
z-*8x+S4Qs-LcS$VFQAaOf+y0Wd?(d9Y%y}Yj>fPYECtXM^QAB60VgdQS!$Q7$};jI
zP2W#OVlS`Hg(hDwzrPwj5y{>`%5(~cX1mdSsi~u+35+lf7x*fu>O%0gZNW}DQXEc^
z3_9+VX_H4SLxKtKW?F7F43W2@t(z~6b9}Lq8V4oh*?Qs8_<Zzj<0h%EphQrn3gmg;
zyDq}PKx{RzS%7ffR@P}*S44Ehj1tWrbiPX9gl|ltyn@{d$XIGG66KtCp`f4B`cYva
zDN3NBx(lUawF~LXZh9x?+o9pYcuATB`1Q7|^teY;Xf>^t7CY^GN&($Lzv1U)`+oXb
zn_e8#zR6v;u@;}1DZ&+(R0{ES`=Oy#ka>XuZD=G2)_pk)tMeOrPh07)rh6Rach9Wa
zxa*-wwg<JZ-<s;_k+IV$E{51@A6E%svf#&BrgGv!*~G&l{9mqA7r-9K&(1`-o~)}S
z0#>I>&%GED7>^5OIT0A1WEOM_!j>lJtwR!TbwZ#?n~HuAd;Prf&0i*aL;_@GtSHOz
zIj9g9AKYws-<jBNEQ_F6z*0#(>3nb8z9*K;%v_ku#Zo}ntOjFy383xK7@<if3?b4^
zX4QoJ&jCf5dh`9S0s#frImZcvvnMBr9H?0D!Z*$Um-Z>IIv$2>936i<>kyY;<-5g4
zVS-+Cv0`sA89u~NX5iejD$E)aoJv@orMzi1ZVnl&k?KP^7RsqqNZzy+6J88|%G^fc
z)E<b^h;i7Ivq%MB<4yMiB#{+ze=VoOc{#T5&bvHTFb?m*Ut8cYo6>$cX=RSD;rm*I
z3r*jQiI-*MHn&|J{y20gqf_0Roc+{@p6&^^HA4x?Wv@2iyv{&<IW(@1@eqyJqShkW
zMQ+LB8o=(Qoe5hSO<h0-ITkIvnvCFEM!09Pq#w^yuDTlh-yqdzg;;sN*H4@xmp1_l
z&rz%(qDa=qGZj(SqxiyFA#5{Bf?P$@79j|2$+ex{3@*uEGJ3Ei@cYG2hly>Z1{6eH
zf2;<ckRj3OB~|L`F%npcsg^!eC2~iK6Ei(NuU9<FK_bMg*hY{;H17*x5h9KBuh(EJ
zr+ko&5Ilyk;o!!+O^Nz8IX%{8Z;$(0Ngx4oaf~6|QAd=&^m&5i3YXo%h;Hxw#*tQL
zSZT3$eDimR)GObU>&9=dT>8Qy9Xg(c&r(?@U&^WtLc2$@cx?~XTO&;h3oR!<5`E#X
zjCrOQQZ_I82z?|Xe=W{9B7PkQMH<F_mz8<%XL$-ogrpHe$QrfOR}`b#U!Vvb^$4Q=
z#ezM1B6xRTSJsj@G49C$Px-ss{nPFUl9LTD^@ATg`J!^zEyfcmm3=HN%xhj+b`PCN
zX7hv-Lvz*u;iB3XgE4^afwN56Ilke)ozCo8d1}_0_P#Vaz8EC4B#6K+7gdd?n89O_
zI<o5f$*aZ@w2iSyAY=#~KWEvm{FrDEStshG<DW+oB)!Sv&T>Q^(-AyZ6V`>J=oEVe
z+k2OU$aFv2M=4A`f{!=wS=U*gNk695%p><{-~o1!rJ?u?z4S{OGO~|@yn|E)%w%*G
z;il#h!{3NyEndMcb9bZ%r(z(f*V30obIAMo3un%7OJ8__se(i`T-gdOo6;q(R(}Mb
z^h)EkFnn#km@M~CT$vNCrEvCy9YEv?GV^<Nc5a|i7VG5~@m&J*Y|#%*-5?<zD~7B+
zTB0K})4@N`T(Ad5c<HJJ7Neq38xOFtHEW*i9Ot)MRcI^Qgd>>-oq#SIOS0w9zU)70
zfsby7)nk$A+I_*>;8Y@ewa7nnZtZP#T190v#@K)HYkPL5USUFm`<S<kYZ$kcUZc9v
zZIwOe%40u%IS$rDfUAthNVm$Hry$Sswz`5nnG9AF3vcX$U?{Y59UU;vMiAh$CTVOM
zrzC?$$~N6OOK!{9u*))msY4#!r0E5?^*IB=cAgNqoK2b7^ToWwk%LVRx9fV*U+c=t
zeTS<cqw|Jy!eJK$c8pfIhQWRnv$rt1Zdd5bSJFbR-R`v5TsLY${8CXK+I(TDo6G?!
z;&$2T2acgH;*ZSmioA*p6WOiNY0;lsY$vja^Dr}3x{__&)ak_W!6ls`@|{=uaO9s)
zI?F8Zc&L)jQ!{xkw;siwJo2k0p7dcU^UMD12Rq*RtCY92Z?;8nk)go;$gK^VB~f-k
z-5{5RH~f;jBh_-_)e4Ci+6j5iP*-6N*iSf&I@bZ@pNuUH$5O}6y9?1XUv!*|QRf%U
z+6x4lZ<tdhT$L{CBPS53*$Zc~oGgpIXH?!QUDPt*ITaNxGzFbm&DDO9x*oVwgI7K%
zxzi#F9R6<5jpLz7#L{l^R{8u_bxr4*_;~!=7V-h!3pM2ktn*VUAUbx?%!XAj`%)m4
z;O^%&;bJq@>g>$yDfafG{yV)pLZN+f5iQU3$IxzfjbKUifO0+bRXnRVk7OA|Bcut=
zuJqxxmjPE%)w?(t1M<AV)IrYoH<ufk-Aj_wln^GC_}C~slhIts=$x^S4^BT!q(pBK
zDBZq6qiybuBDB$mPbm7>B`Lhd(Y*Y)QwkY&o`S3RObq5Bi`KR-rIxDD?5+nb1rY!&
z$v$e-Y2BEOV;Md6sxaqE=Oi*!C$A6D+8E`pS&q~ChM)R2@Q`Lt*3h3?n#aZ>rs30j
zM7HO!+G~?#MLh+FG5t+%L#xzQNsEy{bT#v$iHE-Jc(322^qLZ@1EpZW#=HyzzVbn}
z<=l7&{pUp!<(EX8*Qd`G1YvOFR(ZvlQR<yG-Nah97x?}urx|6bROt{G6<=*_QyF)8
z%W~1YtlCR}zt)neN~M7Z!F~#$fU`L{p7?>40fSe*EAcVKxb5@L9?t?U`jExWbP2|r
z)**TecEf>Jod^$BMX26?hL7L31Bp#G-Ao!Qxnp=Ng0LG3Pqw9RBDgDPje9jSreWib
zS|x%_Ekto~Z7zO$INpIVg#AwS*}g|eD-2@6cD2-rcDjeL+IRcTEffh!#)b%wMfe+<
z6a4VmWy5MeRlmPQ*_(;<!xswvg!6p|QjVaqLWt^6HnRpAP89DLHV(;tQXn<iGPV<1
zh9y4bw3zD(t4i!-o!LQJxRr9g?zO#c*YfS6j_=jCbgda_s_s7Tj}%WER$|346@<Gf
zi4knhhYi^+-;Ci(9b=2w_Jo_`ajKGXDEYMTrWyfuw%+L7FU!`3ooVC)?%C{ofgYXJ
z=g-1+U&au1VjFv1=p&AmSr`A6$wUV&7+f(S<|0{Qa2L-p$eNe!WNcUKE1x9LYXnj-
zWO0A>0A8{}C!|EZN&=0Zrw^om+DU1fdKA4&cooV((8tJ?oX`&f8(giyc`XPNg$)N<
zgDbaSQa3Z4mz1~aj;u1JCPT1v9412lXAuJjqWpU7*ND#_bi)JfOm4=VI9We&LLkR-
z941b&c$;P9ty(i}7b5AT3D69EPP?(6#5c)($ON6<{bE8j>?hLNxG>>lK|qXpf{YId
z#X<;Iy5TDqxC9RTqHW{5V9H(RGLz&nLkKn<Yny>wM}wI<;$&njdsg_15iZjBqht-g
z|3}zc0A<;&VWV_PcQ;6Pr_v%NDAFL^-L0S?4N8}!bax{X(%s$NA$iuT-`?N;&wpml
z%sY$&uTMW~-Rr(ehPOJ6`}Gwqy@ZIgF$+Qf9;oM5;!yh{D>bn{ShnRyAAMfhx?@=4
z=k}Tye9h<R8c&Myi5Y`}Mf~kpCH+QPZ}I;hy!q`XZ-9C;7;EZ4N9L22sIg)X^0cN@
zv<&q-K`VZh$mOd0xDxUqD%+O|7yW`lorl!vcUd7wg7oN#>s=4z20EcVg8aeyZSwDb
zNsnUg{Nfakj+g-k1*Ai)n(rTv9v_CtKCMN9;_8)zlP@+Cu30IWqry{Om;~KYUtc37
zgqqZb?3zp2@5)30is%g3A5N44G;t!yh`w0yL7@n!rsMV4hO0dGD*JXgA8Qy@*82&T
zGulTvj(>Znaasa>#cpFC=JcIwm!LfSq_YhNzU_lRa4>0KIb!~h?%YIJx_E|#Dmq`$
z+~q!402oI7Vqq5ZwlWF_7}#`H3$+R&jBAy422Cr%@80!RwJR&8LDK*SXQHoAOl|;y
z0LT*kdGc_UTBJ#k0-`Y*>6qJ-aDokXp+#y!BI6I|z1zui)i=6ZG4JUD`0E#hUpIci
z_(D-<wkpa~S!?mr<Y(p7;B19msLK?X909}*oP+Jn<7GYuMMJ4p4;pGCvTxHwioC!1
zSsB15vl`=5kQUpi(Jx>;`uw9q7lyVa5ozK9Mqj&J9rQ@xJlY+W(ZFz5oxV!KWgbI*
z*~=}O;(LdvPS=p3$<k6YqUO)%biT=D#}K<q(pg-&Qj?urtlv^GG@Hsd0*mlbD9M=S
zVn_xpJEN3``il+*2$GO~6+Y2moKXhg6NasMx5H%0;I;7yl$<7Vo1Lo6#rE$XyOZEw
zId{TFAFpFbGCB2Oo2V|EL752$sVNEmY}nR@OG<@$)SOZJ)F$@mZ|J~>dOn(i<?i@1
zwl=c$Lu#A#%|`m`mdlYsigmx!IU4No#QVafq}Oj=QzyW>RVsC=JDJAl4|N&5vJtJh
zQ$3Zwz4*(8n1(!y0HRa=j%-h=<U<;AwctkK_haSR&jSmG`ipedITfttCVvK=_#Xz0
z3BROc>f2`w75b^LDi1p;-9ll=)n93^_&%e@itW$U@lMVjcih?=MOcVXs?j6;tWZfv
z5_8|a#uy7tvc**31*~g2@hahGgPx6&<zX%*baFOvoAw8rN$@Z=xPe6E><^p4rU{*L
zV`M}ARV!gnDVN{T5%C71Rh+#^Y$qhzGIz0(`OL+4sKwDVR`rC}?NFyhFg7Gx$JTf;
zY&wSO>%z+0zIgU66GR*85AZs&cv2Z5$e4L;g+!P7*R9pmHo=ve#<CL<85*8Pg9k#0
zDk(FMMGJ^-u|EV=hD>A{!>~kURVd4ymd*9wrLnT}xJ~&sxh`(H0j`OC$MLxuyWLpB
zK%g%Uoj;970R)gzhbwR*+y;$&`&TeM9AYQ#ltxd2^j4Qi$L+%Ss+)t(D~`Ei#2p4X
zD6)4zlP=O}lmg{qPyc2^+qOQ)rdRyB9m5`GO+hL#>$|QVn-+F~4RWEw_e|E`YG1pI
zA5RhU%@UuybzR41Y`1>{x;4A@@6;r_STa2pSRaUG?vlmFUTZ;5J$;TP_$yb((mLHK
zL$R3c<nUqW@eV^*fK`x&23G8j!(RRi?@}l2hhUhH+-ut=j24IZUwxwvXGNdLJ%b4l
zabdpgAQ|jurwv1?ZSKG3qij00Z)_wP(h6sRIl(ljeSZ(t?fTd?!;;33Ymod*^Mfsk
zn|5AJ>S^eiFW*tSe(M!;sO6w}y2D)EoZu72nBKtokV{l!)xglYRr8=`=y|QGAfv!5
z(pdnjZbW>&GfGM6-!1-m18JX2BmhK@baNuwhKjnaW{7aoo^UjVE<L4gIZ3lY*G;n!
z1~&8Rn&yM}E%3%I&Cy4H^4`m7vPiRJ)GaDzXlA0ZBZ=2aXNG+lPfFf#66@<z%kxoC
zCWjZ|sQzlv?}&+Rw5FzeljyAg$BeDrN7S=#cFB)?3p@GkiQ%anmH!M{Fm5a8AuUk$
zC>aYP-knNedpg8(7}T(h`NJ9DZ|o7PQ9==#G0Im)<?2jwKP0|ht}mjGaITGwt3|Nx
z?^1UbFg?Sqc{#;ea(%n>C|1dLtC(*)S2M7&Y8qRE(_Hl%@Q`0-@UE;LZyhrTOsDD1
zUJsauJa2h?xD8?5VhA9h7WKNMr663xp;pTF7gbuK9^Qw$&H-U`e2+K<m_HH(l7A9X
zeYH#FU1sr8zUfFJn65+pEVyR|H~`*f3Ca2C({`h0x9MlUv#XUz;zc8fY1wWjTczuF
z-6z^Vf7m$~<tMP=q_al*jG=MVB5#)-5n5LS;MXQGNS_!}39PDCbO<!R8o;T@u4h<E
zWS!u#>(mWz3{wjX*K{C&=Jy)T_prwpgIREuBKH+VP;<h&x^NU0SwQ!s*&TgG%i7EQ
z#3tqgicOezW*b(W)Qd4f4}5#x?nh@Wt@SdOZ(&A6VV$g%n#AlmzXR(-*HT46p4-e&
z@P)KZ(sF0F0<3Th|LM12y*^?z`I>zhzTj4b_Q+44>DpHIJ+aj9nvZ-U)#9-V?bon$
zl74hnhg2Gr3c`eIq8B>AH%i^Dg_<H`F4ow@DDJrTXkt<1^3vC&xIt(0{P>_4CFr-4
znK)x^lRpTfJf4HZBMR+%JyX!;guEPilCGRGkhJ(9<&kMKLubVOJ0*31<kH(2P)C%w
zcPAP9UTYb?Tq-{pn^l8w9Fh+Ha2#CrcP*brp(Y(=y_N+Ou>WfWeU2^h4gSvVC2TFZ
zu&-4TMs$@ma)g5;%Lqs@RYybiQq_m{kVImebG9OG%Jr=AZ_s&DMfHB_-8<wI85XR|
zu!3xIW%m5Mnb6RijnY?An*=S#@U=@{4?0QLLKbOuPTs?#?o#@znhb93B)<q|N7rlZ
z`YPxVe9%rP(_;R;0*A!s@K6R{fFd|s)7+vT*2Vb4wN+H8b*{81^~1eh6C+r4;?I$S
zM8*^oN9XRD(Iif?yM`1msZ;JMeydM5yy0zn`eN=O$fKq!)Uno6<Ej_b!*FoHCd)qf
zt@H2fo`h6t;t-}}L<*?r&E`lF&|1w++AKu3+Gtg`D=X+Y%WJymK|OLax?#s7ZH9aC
zUtg5y=)8HZv|}jxX-H3ePB4JAb~0j=Y};}QLazBkS3+LKWc&Q`1ue|B<T=JluJs|>
zba-Jn=7xll(G&vj&lSnTQIuezn5(20RDI52Qe)qR#R3i)n!SO6Krm^SfmO)r&*xR|
z)+1E<A3%CYz-%WSN#YU86^q^~==v7XBks$y=4-?DNL>WVMtpRZy?;f~V?s8=l}0>w
zLQ<V0?D2GWp{sB`RpCxM;`i_MG50QWW32Ba&~t*%KfZ69%V{(JJI~UTc^qwmo&~aX
zi}STf=ovxuwWY)qG>#L)H(!fNizE7}n2s{?AB}1D2W)I_*QahbFiw{!X1r(@N=Y3i
z_FXC?$c2A}v?m@EKE~%{&@S1{=$PoCnAX^sDcdbn;05(p)#!>9Gv-G{Hq^h78Nv%t
z0qbz|pIkk`opk=fgG)hs%ImV?H_?7X%8B8r-m4axwS3mtmsiN#JrJR6(#PjqD?7zI
zY<^|fFuG$4rbV(Vtv9=cq>N!`wC^1mV0p9TJ*&WQOAF0+8LQ~;iG3}-=)&v3=XCHo
zn6}LO_7tmGd2gnk!R&GNq_sqGvBkz1)VH|%=QJG&8rG!_eglJ}sR}6gu}`g>mqzZK
z76fhFA0~Il{RbX)QYJ4k)YvZu2vcSzCUhRVUOvV_RuK6zU;*(5vJEh%Z&Q`Gj;>aJ
zmBJB*BbI1ZSRW!mjl<E(=D=3|183Dbu7{R*!PW82J>XUf=9(K!N}S!C%3Z?xRo!My
z@i%SCvQ(yb5J!#9z$?gB+a2cCAB+htBi67IB5krtYwPLVViSGKs=-j+@U8dzQAt=K
z1(yWT9&iUt89~tN04UB;YdM-sk_#{3wK-{KWlQrmj|%)njH*q^w{I2y_B=}<8F^10
znNlTPUpI9(F)Na5&W%y1>dJm&rAP1X;qKzSzRSTd@2+mE=;?J3?@+9wP@&|T&^T6C
zvgr*z*xP}mLhp=<=eCQR?@PBnOI!nl`IBF`@i%bIo8Sfow^Bfv7sDjDh;9kQal@o=
zaz=w8tLrqB+#X?D-7_p*NDX+DDxTS2`~rTpnK)=(jM$!d4^IeV?1$y$%>J1v-63_F
z8LM#!*rX3~8F!+xkF2U6Xo<_vmw8>;rf~p^KtjQO3rw?08NN3^{(`-<5JFhCmXabU
zR{pS~JCv8ZNbG2v1iJ+7`GN$JgZx^6xb6?}M+7t?epKRvi}&}duYx2zJw1WdWTmEv
zWPbQRxVJ>cjWy37D%GFufv;kRN&rGgh)J1UvE3a&7$1rQnHd`Hkr8zeLM24Og_y$0
zX!sX<1`5jviKBD4H%9^a=t}m`6bTV*Kph9Z$8e8r^&T=W{rSkt8R%RJ_Hq^iE=Y_K
zbrJ-Zeh%qQ1)Ib~|My$e$AU0_`5!m+1#tCk`woKX`EDZL#~eS>2Om7+F4ut(Lz14N
z#<Yb@b$S$<|D#Q0)tb(o0YJUj6Jz5Ji)H_t>YWTK993Av@zUam*5(;~mapI$dH!5N
zGefchlk1P_<nN`iRBWq%1!N9$^^Z=cb(2QCriigYfi`P(5jUh;vJ2{3RpnJrEt8|v
zwI-RLpzl8{s3t`Q^;R_t(zcm=MB-rqH|66-{>a~rL4IbeAXAc=9sFUIoFhU1&PRA)
z`Chj|u|!Mbn;B3|S0``2M@1b~0Z1RI|3gOvnB@~_(mVmxlM^=PlynZ6yqIrAeWx8B
z{nukxSou621Fzw*KZ7^nIct2_f2k94uVLaYiN4aIk=9T^=lSB;D!5L|{UXOQhXJI2
zTbLftz<)Uo<MIAEz-%TtFM8$1bbYcar=|r%?NI>f?IiQ+sLhqj_?@1^lPr30KNLYw
zM4i0Dp5edu2K2`9_4as<PlYhDBhX&>Z=VzXZYDlgB?jcXj27^??J20-|Ca$FmC=g?
z{PE3HhpC3{=8az_?LA`v$)q|Tck00=Il<%K?VqLn@76J8VA4&sUR?JN83r;ZgR2;m
z1d+*IoLV{#$SwnqX?S?}?nnwd7#yHjtp!+WK>^dFCZNLtxysub>qLE`tS0-F=d&6h
z`oMhbOKnE2`^mc&8VVu1#U>1K;QY`eavEp(?>&N$;}8IW#;9$C6)QNjZ3Hm6$VJ|s
z?jQ=@00f6Zz}|l_FU@loK>LdYuh&{EJOQGO*#?V<-UQ4#Q-6*(0cj(dkTW5-=}QrW
z{&anxk}hC%JvKUOjfuMnC}Q*e(Ln&itg&5~-OXZ}=wXZI1)O0JA){=356av(rFsh>
z;t@mv&9$P=0o*;Ecz3SaYHR7$A5GSO5A+>Q6ja23tef;QHw-|+*;rUQtNXS<=5&dQ
zs_Ka*O=;k@2p|ijiF$#ENs|eH+6@d1T_uf|2mp#72m^w<*`Ke+DORAHooM9+k-7lW
zt1K#F0XCU7`%9lI?|@+ipb_)S0HHvm?eTIuj|2n6xRq0@tK|YXoI=7*1NeaEHpBG#
zcqQNltanvnqoV`((B})z=pNPqM|O0<?}N(L$hhi1BMs!x|4YndafXAqezzl1Nb#a-
z7y~43bZo4$q5{Hu$We#~hfO^S6Ml8H6!{rlz00qchMEMY;U(RWH2JL?XRh1PBJlg0
zZSrthfGZQ%N--fPj;x)Lp%H7Us^Z!0xgJ7Z*~Di%m-qmDA745BV$6fv-E*o3hYXl4
zG9?;5UF!d3m_gu1Ou*AY2Yl*m6&#8A2vR|8)?G0mO{I<CC(mL~Omd#J$otJ2-D%f+
zfuDH-fYl05n8>aEL`jd?DvJP2{j}|?oUoL|Dhr$-V0jvQ(0HA5kI<t^TxC5|QCBxT
zVZ?NCc$ysq5@@MjiGw(u)~jyk5A(pf{RAVT8h8nm>gc0b8-Y{igMa?3IPIw|^ZCJ?
z8*t<i8BZA%XioRNv1r_AvEVQtrgY2y!?=Y^6@NZ(NSzlNUKx>KZ2gMtyf<kBf>vB;
z{6C{Q^8mW&*I<*z4Jj7#g`T!$3AfQVsvq_oJA<*Ft`O+CQw{s~<uHi(-b3Q4&c;?1
z(Ttm^+osiPQ8~K!#C+X;Me~+G`|9#ZH})l=*yfcl`KwsY@B4-~uH)aty)|hJ#ok=2
z&E6+O*me1jpy2OI3krg_;>grd-ysph??~QtgEW|opIBs)@iM8jGnFiw@r}2@e?^-p
zzM`<`bpY*a@D?7+H_khcDFU1L@A*WDKjv94bxU>XV-zm6v|m{@Z3keQy9%GJwwbIu
z`uqWi|HIe9ga#UmGG$2<ECE62n(>EC{#HQ`;ZpdHeFgoS7(rd&j}NftI6(vCdzZ`+
zIz3+y*X;8wbp4FmAo_hDb&d!6X#7!1O3IP<mhhsHxP}zPsxrD<Cy>u3{z!Z>31>7$
zB`iGG0Sr{F?|acVU}6@6IU^`LszXIDL>_xFaLu0Lv;l4sRX(Ab0BD}Wj4UG=(PK{(
z?pv2g2HY9)xt*$4_6c#o7*4N)jxD+SX$scU!?mC4zUtc@w#Rb$kp+kXgRXtl_=KAA
zkgEs!3xMkwXHz=3*y`lBC{I%Oj0S5vcBa+M(+}bC{OzWUXT(P^!kYuLoi;RiHKQD)
z0RJhTG)>`Wa?5NX`P7Y4Z&qJiB>%n*!0H9=7!?*8t!O4n+|Mhhu|A=ZY%Wm?C3%m?
zZC4Ho^-Vx5hTf#{TE!tl0%yA{6e3nO*i^gOj;CG1R4JwI_Vgb;!w?SNsNVt}5VUR0
z-0$--WjFi=K741gEhXzIW>@Hmdtm50iXiF-pzrH&k9qL;ueJ6pvoUsOY;jqfoUQ`a
z#>xc3T+EE@fm>ex8#6tjVQClv2^q-QGSC@}YBXGBXC!4n|1TR(u}vouGvEe{ZzbZA
z;ZaO*{rsU>7b#AI`3ETj_j{hvGJWXR?cKqHQu825;Hzsqt+IOvqds6vZ$isl7r!m<
zxXAIZsK|=Ed%+y5LBtq334mBQ+Dj)cHDiLN;W({CZ64Gfg_QL5dzABzTFtQ)<$yRe
z7mJyuvd8_(A=5*k!MR#k+my4Dz~IQkyxk>ueWV<yo$DL$!Hs}{V`aOk!yPP4QVP>~
ze_8;;kI7Yzt0jF7f^l|Ona#S(^h_X;^GA}xe)~p%qF7qArQ2a<;?ZbaIBOO*U%3)<
z*`zaKbaxC*6IYwSV%by^NmL!q5^z`R-qei?<RC8(7(D>d0li~g8f9=^wf9fBUtG9}
zvAQ?!P_v|W>TOEs<K}TjYJ0fZdVhDaDr9XOVuyzQ;9FLf@yFs)BypoIw^D`<I2hkQ
z8xmKhHzRoL*M&11XBh@wwr7aQU*wOhm7k2yZQNfi9m%4~)^Lu$u{$CgJ_9_wHYFBX
z-vl?z7UsEqyQk1$s0%T`L6|?oH=bSJmd#;)$Gcz7@;I}SwD3(aF}G>h>r6YWwrLDQ
z@$Yl4wqx|CUySy?|8dg@egQP<f+Sg|7B?>z#p(z!|HvyFl5%Thl>rGp7^0{Z`7$m8
zSAd+rWHl|I9UHyPpJ{1h>|J)ra`!p-K<+#-F%d8a7r}ISzB5MQwO=j)>zeZF0~G!C
z>~Fb)ZAvy8{;W~L<}Cz330!lh;wd{|cD<-(ee2F`t84~K1H}>L+>mPs;Wx=FR*=qq
z*B2v=3}jwx4k<GP>MD|%!Wv!*pL48NaeAr~>=!)CBr(2R_UEjl@vQAn4H^7Bf&%1O
z*mS+2t!WIr?_^~rT=6a00gCqpuD|=~1xd$G-fni(&aVBP)80?^K|p!$4$2%+LZ;6W
zFJU%EdHB~r$^|66uJShnKO~n8Cr6cJj<S;#;vJ5pHTxE=U<ZVZL+qEcb`L<l6g7R;
zuBaFO0@f&--58h%2#J(U*Ud#d_a=*jMU%-+hUz#y&Ov-@Cb3T8FOYscg>nBA>mCpo
zMAERlg-<e09h#$3315csH)a6q7F&|^-=maFm{Xi-FyEHho6oV2&@ErJ&Q~<g1Z(Th
zaSN!<AQ{ZPuo-%XpJEb3+hxGQbLPIGs;({tt5ov2o3{Fou7t+_Hvav%ow*<Ra9bm~
zx*ak-o0ih@Fk37zl>k*5#CKzr&Hz{|_F)ktRO2WsqdG>+VygzyOxa>hgylYGFK3>%
zJYKDsn%c-el?`tAIz=3{ON1I-y<O!G6+!%X2S{C1?2w>1Py}#vyw=bSLL@BwUJFgY
zs<n>3=EBz*;paNAt3xR>dl3`{PpggAm_NgQ-!1+Sy|GNlfc~=M-U_8Y4TjL1z2!O+
z&E;%>ACWr!V5f<!?8)?cDtZ%iIR(bu<zS*RfjS#ZLM`5YQVm%v{$oFjvt_yVJBSQo
zSDuoJ>v?x9hliTQ$o>JzxAO9;8)-vxaY?QQw88I#Xq=*6!FIHb6=nyegM+LLWs%Y*
zSV$zGt}iPN-bZGKRuhn-6vmNX+51$};K`hk3&R_rkWIEaP;>i=z8c&1EiP`_k5IM-
zqzeW6iqKQE^Kb`wXEv?D`LN0Ul(=Y^gkkeE1(HlxMX0PqAcmX=>2s(arg_%_&&bz8
z6um>Ub*x+HUK7q@?;N_aOsPSw-OHS7xiTAzqyP4gjJK!|;?vaA8$U<rywX_1=Q|Q=
zm?CJiE{r(A&kFJQ!<j;U26aU3S^<#G;yFUn?-+AA3JGC`s@&34K3ll9NXav*2hY-l
zL%<zYohyXM9Mr*cELly;Mc)J$m0MFfLC{8Ogd<l&`UrQ7;#kId(2Jy)$vCD9)LS_p
zIR*DW?Z2rbf`mlW=J5=+D`E;khmluGY1Vw2M0+lp_WGTtM~Zkp$T{a^KPAytV59N*
zcKwOfcs6{pGYF*DKv=J`JQShtyDrG`HLOhVJnA8#z1<Xkq&jj|fqMYnrXXzpW-xIL
zcQ~7q9*U~W?%ta$on)@(TK04HG?wwvN!_^sGNL?di<m?1oTLYm<t@DbKgyyW486(-
zw-U_6*qaWwkUZ(i=n<6Oz*ekM8m<sSKojlb-$gxQ7MgT+yo=<9w(hOk4oZ&C&>7cl
zgMG<F-$@wRviu(PuAP$+lm-)+31o@z#NWsxp&me0ycYVZvxcN54L(=0itoenA)hj@
zXLXv<C>iTOVl%{(U)w`4?K3B+Dc3O+&=L!S;oJP@=QAj}>~?-hJ)`kgZQY0K;#L;z
zceyKF%L1jIL@F|E=1p~PX2895FLHse4V(G$w;fG<EZwafby-ll<^p3hMv7ds5Q$an
zGC700%!{x}UKryidi9QUCJ|@lsSVb6d>4I&;+qB1?{tAlN1)`?x<wIk?!hY=U2WL8
zg3oI4(D!VlO;T|djxTui*xs!M&T#ID>D(ZUSB9N${Gg0;W3uep7ZQ2zVB2&e6RPYB
zl8BDE5fK7td8P7hf0w}6+$p>ndlSfyUIRT{A$e<~4sq!SP^W2=naNJ9IM7x~+A*i5
zjyebQvp+%$5`TX>&UYCgC7q|uo*`noov6oruswM7xz?H<{f|m7xU^{qqb{2s0GTCX
zuF%i=RQAPwu6>4$ll)*#u~X7HC*Nro_GF?w9eZd2Lh!^-Csj6TMf-H$pg_=fU<m_{
zddwG1RQI}8K~H`e(HG3s_Hz|D$vG!vH8>1PRqm!0K_?$Onl{#F^y=)X;^u*YZGZ+X
z3pDhQb-8PO=a<KN+r3OZP@zD>)G!OEBnHQ?x4e+5G^qsl<2{7ZKO7W0qxb^KuGmDp
z!)jMN!MeA`YN|9WFD#?uD)ibJtAn-?c+e)>izD1sIW(Bfq+6Sj&5V`SZxW+yR@dk#
z?q4s|*d#B|!A%(_&uv>>sJ05?KjmsjNUc>RX?(HHZ$jOrt5}R;{va@yr8-b-xwtIg
zm0Cq)T+(v03$#yh@krcegT@vDuG5|YwqOlH+5rbQXox^>gTz(a*i>LJ<!s=M)Apv9
zB%mkiRKg45+7c`w0*CEcns3*n@Dy*TNOGEf<N$-}RU$1+IAleydSZEOOzGd*QQ!SC
zN&@<4Fhi8`0=)(H$k84{{yR4|teRj$+zK1<%gC+^FHItTyZ!7jcgo*&5f~!J{><HM
zn8^bSuE{-(q%^pi7Q8RRGt4(PTp49|jXTXU8Xu|sL&}Z_=;US5;rPzH8Ei7_QsSXI
zn)W5OV;G(|gknDc((a2iRuU8fwyzMEiSVJwPp>oE<W0Mty@`%oQ$$QGWPO^N@;1PY
zH2UE6A3+V8LdNU9H}$%Xx5noOiHns@r*iEN@0)x)5Shi~t&Y-M{*uv#^2+{_(WXXG
z{tp#C0IDi2y9;P!t?pY10ys%_xhicMdz)`$$ZTvJR2SQK!=6B(t898O*pKVD4K(1x
zVOqyM5~bT@kaT=h&KT95WU`&PsOSK}veOLv8aJoYrL|npZE`F+(b2WkRw;9Wr*DkW
z7%QkL!l!E_zfsSnS8Y~L>A~h(ecT90Ff?Xm8sQCQp_F1RnOo@C*+rLh{CYybCU_EJ
z?MFT4bgn*>y|c;2&N$qL-$<SyZBPYDb}QhCuO4&8Vz2OLu`v7{PN@38d2KuS#${(K
zjqBUbPMWW><hqyJ5u*ns75}RHfi*!3l<iFB#sp0%(S+HTCF@`Ql@uvgOTLQSadyN4
z=M}!NS;WVE81V{FvUFK5u;j47@`ABqILUMY88hW&#|n@k+{&I}<ApgIA=-tVSx3oa
zzo3_z^y7OrXwB);BJ~)jzv*tsL;flXV{44MGK>6UXPV(S3+!sr!!M1N)ku{&uKHAt
z2@QwoHs}s(@(A4DJ>t2Wqc4mk0hRuwvx}xUu?IK;3^lovUTXics>G+*x2auleI)?m
zV!A^<W5m_jBCL!+4|&^c>D6Aogq|RaJl-^cMwC6lb@ky7&38%8@C2$NT4-or)+O#8
z1<-+4E@Nk5oOUv2e^KX^cL*RJpp?ASZ@Lv%nvDC$OW@as1~kj5T(YltuhaY9x%ZYS
z00RQiD!09sV%=G@%OT=2PcsfH1B0sEChLg`x=7~I0<C5{<>h*9^nHwRARd#V%mI~9
z-ngSxg$u3!>gt+X%lW9nec$&DKxLPj)CYD*(O;u^gAdq!b`+v70+N8#pG!q;t55i-
ziF<g8ZX0FXNzmjMZflHq*&(RgTIpqoPWl-vVY|u)dR31aUc67YN+z1Suvvv^UzD;M
zO6HHOr3!X^mz_Kf1%%em<^1o@jPb)P36Cmajz*B$4D(=@nygn%=H>OHq{;ZcGKW0T
zdR2Daq&Dbhv_=woDn5hcv=S9ckC6~oK{o8t*07Ksyckmv1EFCVTmTwYhUPPQF}H={
z60(N0k)tPUs4q~+b#LT0%9UN;*CDJh?w3A&jQkqfVH62*B0+)$F9%1_dussl$UTRt
z>ja~={%WqN?RR}gTUmryhLtK_I;>!M|3^08$J?c;@lIv3NJp>RgW7mj?ags6LxLvh
z)dd|1+9{r--SD>eHmLZUtmjufMbj<7kbPml-<rXn#sTd}u*s^sWZW<6Q4meA;!2JW
zPfZ;78vH2or7_DUh9FG-pb6mn1kzv1P(@lU=+GQUzop$?J<fJdnG1jS2>~yF152V)
zX7e+RG^xja{YGB!8s*{7Py#jiRp*B@Dl$sJgOI%C9BjmdPZmnZ2BD?CoKrakC~$m;
zrd*6yFD)-AW?CQA*vomhC-a4a?pE)7K3%!U?G0x+4aNNUnX~bN8E-icSg8d>K^jRr
z9X%}I-?WtWARV}3kAx@%&S?Z!D&rYal)1loaGOdB^G7Jtyby)12!l!~f9pERPoxJ}
z&5-U=%r#Ih#XzA$6&-A}6)9Ip`gj|-Df-A0rOxrjH!7gS!JRu@DJ^^#SMgm=3%MHZ
zCq4ZSC#E!lfo9zJ<1VDpn$ZsW><~w}Kf=p&Ov=9aw_q^qq?d>jsCY7J3R+7gbc~ZB
zY0INStrEWOa2&4^N!^v08rhgS<^8u!YT(AM?SHNm^X^S>-)c1aF&8q$<FTQIrA(CH
z@RR(1xf3kRx?SH3#$WT@tz_|{x*Z)`L8<^bUNDa2*Q_S}$2=)87^=}b#M1OrQ#ws5
z&uySmluSgJCfk(IC_!VdIQxZm`bDF8k91AtRVwSzIOu}^H6joR>KtU#n<anI55%;a
zjtAXVTQ<IV>vFxpdNjG|o*v1QHh@(`$OK`&^_3im33e>(+s!q2UR6K<@cfqmqWY?#
z@AQwhHeiz$v`EVxH(szDFSP1ZT)2T44Y1Nm7IfMi&sUSb8_c%`AyJXmGbxh{%aubt
zf<~jrQ-?s6u7Dap&hr7e9!C@Au%UCL#N_7)3Uwy3*P>R{M*YN)mh<^9GUiHdr>--<
zM8OghLKHv+eXzRN%GC&8mHUquK>gZqI|m^>#4IH#8UkN+OlAGk9jDAeF4C<0sA5+0
z3uloO$}n%>TL7fG9(|_Gwhh{c(1xVu`F#S&PYyWuM_1xU+^^afluNyZ$||SOVkU)b
zbS?$hqU*fS;W0*vh4fs?Rt-EG&j+Nn@31~&9AznZ-a6}a9$Fjnn>yivpg?W?S2hWM
z7y`>kPtiNSsQ`ac@bEyMpB*I1^f<QSMSUUH{kLcQH$$5xCK}Xsal*(U3mrf`J)j;D
z+cr!tX(w=xzz5}&d9>C?QOJ0mIMQ`aHYZjrWG!HS6YVwpfMW*pU(0~gk%FuZ*=h-h
z@en19AuT0_J)wp)-+wgTqd3!57HSR-oU#<*<f1|xGZhsTpD272)ZeBg^7!01OC5ok
z7N1osu-hH9GTati2nqy-rQ<n~p6qe%-;CLrFBI@165N~Y{K%1gN2bXG@M*~r$F)T?
z)ovCx=H8uAySGCtl~Y5mO3Toiu;xu!&fVo}6Q9!e{*)8n=)mDXh-Cjc94?%<71^Fn
zo55H#;2IDnFlZ56C{z?Om(;zte!JfJj^P-{;Ubg?2f_%^tENnz!2Ixh!hfOdQe?UL
ziM_^lCMj&-lD*Q$G=nCbReEyuy>x)~;pvCFtC8k^{Q(+Z32;t-WO~}`HqfE6of0>h
zW7F8y`tP$L(l&sk9|@_ZAq6!qT^TT{eE%MX-mi<uOp2Ov1Me%y{*qHraB}lXzXsj>
zu|wb(^bSWLYsuZawQA)S6{lsJU(9~JZD><`dun<|HjuM)T5nDJV``2tFhikNo!oB8
z`n}a)x1=xNXXTPvaqKNrBY*p2Tmkk{q}=0vOgl@s7M2y#-vylyTK`x_O<u--l-WqU
z&`yt=o12#)1aDO344FcN@a42s^bqa9=l#s2BqY)z0rj!s7@D6Ctfc$bF8Nf2PGO22
zJPC~!wzpO2G+vQaKC}OYb+-_1VLw*RS4wiMQl_~60=6LmGQhWWUe18`zh<iv&M=7R
zq?D<6S1`a(V)EJ-_|$~PC-`&#s~8lfJpi##_+A_8>5<!fL7ENtoOisML~u=@tN@ej
z*SxGDB}-8vLfZHj)g96l7ye&ZxBGC~*v+re7w<7?-vOd#1}t$<<!Ahi$)}=g`^fYB
z^dm@fbgdRj?pg9k=C?Z>&FKTclRUD~8pIeuEpIpegj4KJRqj$fUgE3xGXeG3Ku(AR
z5r{?KIfp$?0_9^lnyjL!seSER1I#qv{b^1!zvYrf7FN~`<vC8Ht|~kIRP(AD3i_UU
zM&p5eNjLhK^z@}d4fYzc$;*03>uFd84p4Htj!=Aao{)<O>?W+Y>`s+ZaE^k$0ck4&
zAhBw`efw5Z^FVjKjn-EBAm<kXl?p&sYwg209qtZA%D81<7l4@|1nl^JyR=7@67~{1
zAeX^^+#7KFuMXy9BjP|~iQg9%U|WoEOibv8^6Y^#;8&mGf1v+Z?~erJ^EIma-GV~u
z$nNv>Q-Cj1(gWGjIEXn_jT8miAY%B3BI~En{epC;1Z+~1i++#y_y?OL%fIeygq$|}
z0pzu@zP_B^?hgzm8XDh7l(6eHC5${hCO8JI4@pmwRy3T*;&cz-3)b?2pltjZ6pl*>
zA~M(Y7nsP)0TqCLWvC+WgUGuRfGB8;mEt~}K@c~H^$uc!#5O>7M$<F`^HN=B*L!2F
zb|=2`S=s-6bJi(=c${?ayCx3?v<M;S7E$lUcjx8htv!aF4RMKdAxV3#9Bm{=-U}vt
z{c2)sEYbjMN}gPgDzKMt*#M`INtWYqVkuf0dK#zi2wF1D>lx88G1!mzmunUd55~5J
zU8fs;jFgJ<B9iFDt<CyfrJ=4HA3E00fRxAOXpxK`{Y4$nwbn(S%yWIQ*#$Gr9LUHb
zj>>R%cTeU37D5kg7qYf(r<!J|K{hW*=|oI^eL*1AlmtUjr!tg-0<QDE+uJ*?ruEKG
z`ozY8oAEOHmnY)7tbZqsSBYQ_VJdCe)MJOa)>3WFH6jYmVg#9ZL6BlIO=263q~J{X
z=GP<~$Lg5%^WfE69{_^5?N7Itfp!zKYGd>!7dp(>n+EvvRdtWw8}YC|76BBq-{SPu
z-718?M!~xeRN^GqQwtZUcOIStyi>=opvW2>)?}>byjFi8Z9CaheX|%!elH(Ozj6~n
z`YDdb3vf%X_Gf<dru$xMJU(M!#aX}W#8K|F{n(nSJkIAf?|}GObeHutSeEkOLi^%%
z3gR-Bez{;$dSm&=xeWq?2q9i)2aij@Wn#9God7H{>4xs}5lBnS#VR-g-2v20_7{ky
zC}ee}1H??h+I-bvyG9b0ch=u~TCGZ(<9aOTo4`Wy7~#6ed@V!dJ|cY~qO|iv@as*S
ze7O^KCt`*lFH;1tmQYE)hSWufGA$ZC&ybBE4WXI3ANYJbHO}r6-LfAa;f-ILP+H$9
zezQ%Z)9zlApPlvi%pe)sH|MKE!W^qcnSu|5@F4LD8$dMT4qF=};<Q=Xt4eTvz$hc|
zBm0_k20CbZl)&=1$h*K8Q~Q7x<pBF<?lT|+4nhLdbd4^T-#~<^#tmj!@u+FpkJ+@1
zc)VFM;T6w@6DR%2YzG%!pfO>|K5e+^=N`%?ueN?aLyY72l81c*XtI~?58dAEoUe>2
zi<7-JUY%<KE^9^QKCw!hA4zO8!Zze|+)y>eK$dSOExMtplnD1+46;!!W?~&)`3rsT
zR@&lrB3oYz5|n^&av4}|to|SEp?i2}Vb6hwNvRhpyy+)YvYh63KT(?MMD8;~*#J)I
zyHV?~0Z|*5SO=l9)wPMMe7W8QaQBccC#oygnue^e@JFdg*m-ytqq!lFYtxqS$Mgo^
zRZn1=$8g>@Bl<u2zquf2@=)TehHY^X@E#s3K?E_srpf&?X+#o&-_^j;L}Gp3<`j>c
zPWl$LHI#0*AxrK-Yd|WW4a4gi;-19;0xrIkSuHmP^-3M=7W<2!k5A{E{gP?kW5TM6
zn-AUIfbiybf`jP_5(9a%bK2PlHua_wVB(zmCMX|NXP+8cR#a9FNJb!RE<ms1Tb-Po
zQbkWpXy_k!sxCjXzL6}28HNwMMSJ&Uz-XV?-~+sB)_U||kDcwe&mR2G41rr37}&l^
zD3P^chwm(s)nTdsnW{N(2;+SQi|!{%pW)ndi+c48DTHGC;8*B_6{9LxF*5vm(K~2L
zFM*FgN)Y>_R~`RB?{a$;l`b`=GK@yl7U)^WOKtq<hMXQB?j7Q0sp2M|#M5Z|`5@-+
z`HsFndSyCvT=05=fi!bThn|&<h)9+v2>8H84sZ8xBD+KsJsHPz9-ypq%I}6hh<MlG
z@^YD<_yIIiAr|lQPlNQTTh=pVhG^Imxjc%on)mfSLb)Mh)$*BxFd+epkxWQvBv(R@
zWh36T3<ph_Je^I6<Kd!XA8Xtr!b4}G+J~vx11ef}o=B$;$CUF;n^1_jt0}eE37^Gh
z#@SiRaWL+7CkjW_r=0*H${y8B0M)W$COr4AQ&g<PQP_i#Q!X2O3W3tuySG6zz%<kW
z?KnfJk4Px5Oh{O!!>5cCI^Ev1&j3r#1hRZ+x=HfVfm6|e#Big_^CgW!Yf3{KUIIgj
z?rmiQR;u=inW(eVmxMGv7Lj$&nKS3F6Nahrb}1gOWo@w(2N=2%*jxz$Ubu6x62TP*
zXSz1)!0{Fc7eKkPS}`pPnYP4z3FVWM5-Tak`6R`aB^dHn<~%9MWRHEo{tR2Izk9xQ
z{8*^1sniw|#aasib<sfV%l)v)AvI{)1zghmCpJ#Ra?V9L?i5vMKj{fktlRq**ph=S
zMZ0}Ub{cGq|2}vdM6IRnPd3%GG4wl^{X!V|t6cc}*JNhyb<(Fpmyd~IFImt?Ra*H7
z#-fn(0)XOh!cgep(zNy!M3Nr}LCoAIpT`A$fqEBK`Tphos_oC$!9`q0=8E`P-G@N7
z6-Y5MXgzF_SIAxnvvs58&Mg_;JHw-=_@lv-OLgVrMvS?k{(S?&1!L3cFXl-yqo^@B
zCPW#UVB(A5=kyB%c8Hj5!2B=-x|7QV9^r&taGjCT|Gv?MIm=X&KGaf10jJ2e#O|E?
z*?!YcfycYEL^3r>`&8YT&e*K2$Ga_YzXL0M)SjINq6|pilzNy4E``};DnJC+aZIEN
zU71r;Zn}nj`Q9Og!UaGrUG}n4+W+ND4TZ&6cvZGaFojBtLYQAkIpb2qp-?b{-OB(*
zn?4M+itfgYAQ}2GjrWq2eNZ{mM)$jY22HXqYfPf&Tnw?fe}|Mkc4O#|v4!U&<tzAp
z^tO5$Gb->^)a{Gbp(Yh|GBls0@3EP};uEG#LnBOUE7Na@2Oa_HG#njr_RIgfH4jG;
zj+@oG`FLkNtDxml5)<-|E<W;K&fYINpC>CPER6T))*!AG(I=55kn&6CjN2*7y@u3e
zO>oxTM->NWd0ylO+&gM$cbX~=XGvOHd48Dzc&a*P?{~oh91{_ANdzeK<$vL{^;%e@
zSSr9Qgg%KFL6xPW8lG$$YTI{vrj2m<WKB|L`M37_`^yU!904C-oG?pCf1QQC4NJ9{
z9LY-~Fh4jYJ$bqcRo&lYueqj7AO2?i8#QzEy%c@rK;58|)ctDU);DtlKW{jWc$TLt
zV-P8ONQ*$<=d(Do{)B*|+T1JL2c*AhkV?!p2TRpq;DqE?;GX;wQ<O&tNGacqR11wj
z=f8n_4zVucQJ|9SQ1rJcaT&x8%j2=M1`*8S1<Cx3xiFrQDWf8|;svqsB@Up*#q5Fr
ztvca&_Ke!lsszKn<5#;Ap~YnZY^v;niM@<xJqUp~vJ+i!gyL88POiC}dR9-`ep)uV
zhEU~^68-|6mho8Yu<&l<xfVb++Q(P@RRd3Kvu~NQH=VYPu<}d<otNad)ZASEqQxas
zRzPX%gXg8=+O}S!YcZ-~w>54BiQ-?PF*39hjDks!v7k41%8kjVO8ruZTkU`R(O(fF
zFHcn2w7GDU<PJ3N3)9tCkzmSi+6B?^Owsc9#_5u@`inxZY%N{LUhb{2RB{t3zEv}V
z6MUFx)2$iLoL)%mlES@3i)xR~+jmqSC3Bl!;m-=Q)CCv<yto-2J0;9OPa58Lhxlt3
zqkZ{Yq9b%)&<|_4#I+YVD^L3V=6Cq(KgftF)$*uVW08grx1-hUt2q|@+*wK1Jv@h<
znp+`D-%@p>%-{b~OAVhQrFib<Lt}6xrbl@b%Jy@lO(Yd{+U-POoz7(p$FXQWM{DnY
zGWbkv{WZCWdzlHJ3|tGqmFK0yM%s?Hf7KZZy7cO5wR@L+5o|#cH(RzHM=N>zE@E3Q
zo}C6RS0=(do^qB#L|mNWVo#mFa?=QH*_3L&g@p7XB0rj3tD($~uuR|wgL2wFdAqHp
zQzUm15Q@`OC8PiDO4&<htE%cMX~ctJCaey3!Egrjd&p=N=>InYg&iYAlhF=gWQX(A
zD@TMJ8Z*EiVx=<W*^@MkEunl<v$9on-XkYf6PeVxfuyMuZ~Z>U!T7p-DV0Yx5GAWS
z*qHt_QAH0Ojam)Yp$}56K0iq`OM4cPNrg;%DSTscDvm>TFr~t$s06)1y2UB?T@5A-
zc5Rx@qR<=f1s!9fPLjFR50<FI&2Q4Lu-(JzatM%filDvxAuC0C2#amZ@>-_TF`=x{
z8Q#?92wosN-VOSY)F4XhEmy^FFhFFB8t<Dxo76eXe<2CPb1-T3A9UmXsdOqX*=v{a
zhvpHO4l%syoPTH8!!7=a!c>%1#KLmVGothmjDz9N0JH);&--Z^{L?`iOTT1>9_U;Q
zwud5cpL{fmEv^}aCvJOo1=fnQUm%P^TN2G)#vm11o~sasG)jjrWSM;n^eX1=F`qCf
z4#S)aMkhMiqTYNi8man5qgkrb5uNwYMc&>Tx|FQj(j->aW~YaVX%(Kwf0?UeUP(Gg
zwU4p=3;6AVEP^%1jzHwVh&3Jv&CDyzN{fC<^&fVAfHF5Lo%iMzX2n-|aL~OFSJwI|
zjY=zbm|*Ri1nPGVRI5!FG=b640vyryQnFc5BVEzH20Go4l~h3ITRxDHu<AY_)k(q>
z@xf!*!u$I=C3SpU{z~3Tcretay-{hV>rcQX{1Kq@3t)$O)`^~@4n%>eLp(<8&N4Cx
z@H)Suk=v-d1$UgFBjO1y(6&Nw7&7B}%YrB#^7GOf0B0h4CfW$1#QNKw0zWB#BUQa<
zVYHB;9(ISbpIdFJ9&>OQk|B2pbd=OLgu3}`(+sU}i~%b5tYFSgZZlwMbXZ>k9o^ii
zes*9PWkyFwcUZxRlENC+bgoQTGN*>Q3rse4<X?XmuWL1#+D&Z4`jK_mk$2DL!nT&k
zFi~j;A=(pBxD1?rE17w`>!FF15<RRNj8p?4?B50rWNkf+9fc@Rr9kuJxvc-SaZ2s>
zE0(_A-e)Q+`zA~51qpVyDz2juqRr+Cc^fDwD4T<+3i_@;sDI2~>dwd1i9!lo!SB;E
z3MxDfKfyCfl?PXeN}w7ZJJ}uZ###Afk5L#|k;>k)%qrxr#(d>_Z;CEA%2UY*np3NH
zW*V2;GOXPBz;?)?4_(x>qJ#*lIBc)+jn-^9rlvtJloi!XzbC*72R8=$P<0Mjo<6ve
z9%WO|Y&Rgo4AO+F|A+YvUf_S7-Bdbo4BXfl@Md_1130rOPqFKR9;AGzoE6^yMCj=5
zY)BS5vvHa&RN|*X*pwS^%*j>XaRh?lSTPjnFn0)2>`uzCdio41YyLV4E2+$q#UT%E
zBJgXI8t($N!_-vEWp&cw&4rw-TBNUu&oATtigiQ2;G^f=%#c)PtY%TbV7(D}-}2om
z?fpiRY}vP{8(=miPnkqK;sq#YkoA9+Y}{FIe}5ncMdl36kEuP2um1-NoktkVzNY#x
zM8J1{IDPw7Kb<@t@mD!5luO0-$0&^u#SUQIgo$q0)Jf}FBOl`%68Y7kq#@REL`w=w
zIg#t9hi7j<m;kK_=ckjHa%6To#Iu+HqL5(sOR~K1&!t--k&j3$<#4*bIr=g!re>f+
za>cAmWEe6mz55}!7lChys}v9&8oONB?4>x0iiEk_Ld8t`3CW2C4S<=LU@)Pw@J{2&
z!3Sda2=cDMo-T+B#($qDIcHG+hP1q|Xx%|tP6mWj>qv6Z)n1aY=k(>=N^(sts)|z7
zt4DPEiIV<;>wH|>@x+d5C(oE-D-yn8e)_I2)A(?+XN6)HaZ@B=qRvQY{sCV)72AjG
zxO-KT?#&FBI()-4ofGmnH`eoZ#i}(DxALU`QwP0wA{Mpgq(3ATgxIoK*xa1=<=q6h
zmxFOAszevv=TAEgx(P*;geU%EtqOT5DFflODq=ar#nW3~{7z1@d)Qx-v?aXldiTq_
z`;5Q|DUTuc-*-2|7S8u>jRN8&?Xm}`SX&tJD)p;&T{4RWl4x5{PDmVNZikQixaUG)
zS!@@y9DHU>G~S*}uSF59I5*ojo|NC-nvJ_rUJwL)p*3K1oVM@Y|Ghbmahuz=C^>p~
zJfOty;jea@CmH)s=M>-&FCnx_(_$Z5P8;Rth4BP~MsK{c0!dyVFi_De%ENU?fg$f@
zA(i(39Hc3XfUly%Men{iTjLGV)gsZom2HV|xRO8K3elgW0sAbRDOjnDMF_z?Tm=^L
z-u(SYtl`-2UY%mqDqQi29o3~R<Ca=1w-D89CDj3WIT8;=!0vtXA6?{s{!3tr|8GL%
z>aU$Bb1$eqcrXXN{;Y&CH`+sv6%1*U)8b70&(`aZ-hQ_k56|64(W_||!sPEqE)SkL
zOkEVO`QZGQ#+29teBkUy9-Dao@R+vwctk_(+&<M}_eawi<fLd%FT4h=e#-y15(J#Q
zrEJ?z>8TR!*jgE)(@4^8RbG)zN(fcR+_7=@RN`FlakI*tlhthde18c2(MaR6=-z{&
z!b!t!Xi^qzF$D-0$Oc`aUqjXae?P}W0pA7Vu%+*P`NDC2XZ9x_XwXO9TnxyRC-=>k
zLULg!*CCvv76~rpf5-PsOv=+4b%!rrD<vJ)VQzfbzf+#JEIlqQrixBEkhzjGT#`{r
zU_(7)!Ih4}M1DnGt%7gEIP!(x1KVodQ8V_1pz4<wIU>D3M6OLNAN(2fn0#N*dpIbD
z+ej1rjI+^<iDmMlc3@G!m3Kgtv&V9cqIC724*0E0x?46=XRfmhJU&`$-}2`*DyMIZ
z6@2j%SnxSWuz5x^bv=;l!8bR=pE+l!CPCQ`1Gmhf@3R>J1%pKC4+ZlKZ=2)@Wp}vN
zniGRH`9wdJ5dBb!#}PjO*5@~&HxfKj8&%WxOCo4EObIAxI2iV_(;|yyvv0`Lc;hb<
zo;ZPDE}>%j`}l<rQvTf_5@p#7%Hi5sA;hCIH?h+9ZbwKr*9&KcBmpl8mRW}reS;Dy
z{(ci0D<Lh-*3OQdiOJH|cCfb>x#v49cmG|=o$MZYF<bHA5F=qSQL~tHmeac0);7i@
zIm;lk>tXpuC@ewVR^CA_BagMse523NWM;7wYUKyD4_mi`LoEGuyV<@@ZWh03zFzsI
zKHY^HL|-^;6~?>36vmRETmxrB<QJ0o&(T6-5)u*pZpZK~tE>B7emGse2H3yIZ5bc9
zrGh5x#BK&+?y!Z|*D!n@4*FU}#=N@r^BIdhc82-)RW-gjWsed0SJoK&G++Fb6vhxN
zBwM=w4LT9EgQ6CU6h-q7X1ChSjSm!CO4$C*Ap)Nz5WuD4zFy_x{pV`Z*n@bfSYO`N
z_V)I)w6vR>o3^mUCD;k-gTBaSodgYFJnwFD{Hy=Y*~mmq^V!Tq`)zBZaHGJSYvBNI
zr0Cow?mE8t*8FP9*>L=&-%R$Bu$r4K`qI4C+Y$BZ+vkt)W~t6!hcGZ|!qH9adbwcD
znV8x8L+*wan6s|*t0(w*6H8V`*kO>eb^W1IE*09K{@i3t34_qRw5_5dFKC3MYxuN<
zvy{=J(bLgn0^eEJTfJWsOoyj&CUe)@=i99*em`uJI`qjNt>BjrN7%@!KQV<erJK7y
zPhQAc5Er}8`kmw9)q@dqm>=@!yIbo@>vuNp<n@dBVM*fXiao7H7%bT(65!pD-z1cZ
zImv=Y3{#?w9R`$+HAHm{4W0ln@g>r1>;5KAS2ZbPi`>Fv-<zv%BQ$0=&RC;ftB$X+
zJ1ncqkcv01<@#pbPvT*9bm%_LH+3yL3_Rdccn0tSOsL?#|Jg8Q4h(3LFZ~{LJI5|s
zU0nr|mE5YMu)~+AHG(tI{GU?~gbVFN_mX2%g*iq_;SG;GD6G7-@VZR9X2rF6_%3R{
zT5Ei>%C@>bv{%&|0fgw0Mw+$CwZ&owTyWgSAyClM3<U2DA+Hq@C8jHM^W*QHXc|Ke
zx%0bPyd^I>$JoUWF4xHo1X`jjENoRvwo}-LtB&i%Mup<SeS5^rB-M}VSNR(ow{9=2
zhAv~|KHya1l!{#x6eK23$mYr}*56%*uaFcbzrz6AUuK4eDJx||{P67Wxn;w=&;&~!
zpc{Js?ig^8-@+-4`ytM~IW5rgx?I_^POcZMFBaBDbv)A-zin99VG&ut)qF_RPZ1wm
z^L4JVq*LAFk4?F#9=t2=*7H4xrP%Ws8NB}jxpb|_nEv;!(u9!Rf^##(tpoH(fU=mG
zJ^;92$94Pt`<~lRzdISrs_hFc3|$Q`<Kvfh3HQG<mE7Dn5Ah$F+b)(Xi=%pboz@hF
zp1wbYoj|NoV|R7EuPQzC;5!PM9O<iNYxTQt9!VU5<wewUU$;V;Q05bnhH^Em2!Vp}
z#aX6%>)S{jhWKY33gAF-c6Oe&7#bRKb8(qbL^(m~_q{}wdGx+a$J4x+EdX=DV#6Kk
z*k;M+r|cwN6({-o`#q0RA~P4!g?sfuf=;sM1K&u*n~!7L^Pd%Cr|${p`4wpDx3g>1
zw@pidAq||ckDELp=HC;h!ZkNHFROfWQ&3n~nT)%NMX3E7p62KHV6?K0u$q(FY}P<h
zg;wJj?y2Kx#Gz0@1$D`3@!t0|qO_FIyWqo%ZzO|eA7l?@d`)VL%3dmTmZ(8?0_RO9
z0d+aCVZia{sv-rdXXNBaw*~@BQ=t301chq+moI_1)FWej;wy!3wUhKM=SrRy4U^j_
z4akfZot?d1z&guh0f5?!5WT8K@!j*7g?zVXg+*>wJ2F;{u`rN_L=rj;`f^3uQ0||7
zC`pLJ+<h(e-U!vd%Z&3I2n~{yjY>h@yYJ6kfvrYV^1Tdg!FVld?CKhMQP&_k>HgB|
z97mSSt)u}&mPYT4+!UkT7HThA_;s_v9F@!#XZfu8>^(HR8t0n<_X#Qcr9a;C7u7MW
zzZVY49r>x^#pNYB8k)!J)oBEHT>sMfmdsc%r0D#Z?D5&udJwHSjoJE{^RuN~&&=!A
ztxCOw<-m8|XS9Av^WpoRq;7u9U5vQE@u&Kk=p5YpcV)Bc-@K~&G-J8`p4}UNA9qzk
z?7zGFhLez#bhCotCm<$Pl6V9RT7MGgKOuWIN`F_#d?Z$NKqZ=bo2T58sf4Rv-Bogw
zuIue|SgB#0I5<#BvBS4n*=#mNtn}#qn12{~ky!+0p$T#AVz;8L&H)_Pzt>Y4`i=j+
zhb|%B-#xBi3-~=W$+sq5P84b&A}*BbqY%hGHxm})e%K7+@6PRhS@@#$W+y9M|0Yon
z<zQd-wz{NH)HA1&nNYYe|1R08b%dRk@p<w+O219*te)^$l1F)5VFd-B?3O#%48~Ld
zC*?9K*rksH5h2{)T~ZN%S<@B8{FytT{SJzLS;MLma?de3F0fT+V`iBmNghZ}(M4k#
zez-^U)6i7+aC<1(i?UKXd0W_hRMV>VTD_Xis;{lnAMHm;lEu>9VXv1sTk2&r2h^Vt
zjJZv$9`gz8-`7k9wW_9O_IG?-93LOwtRf0B*4xDj5h3n^Zs)9A{kfntqKFg4!GcNg
zky7DIpJd;I?5B|N;f+6@fx<KBKihzY8>Ls#)xC$<qOSf71?zgydmC-c7~{hgl7S3d
zJvz`Z_M3XzrXL}LroTi6oTY|X05R7GX~<uZ5}^F_(5B&y>i#~ze}~rpr?>YGYU=so
zhC>X}Z3u`3Q2e2QG-=Y2BB1mTLMKY^D1=@T6j7-bq=}$3A)!d`1hF6rA`n2T3L+gu
ziUb4ChN^yN-g#%9nTJ1^Omgqpv!{N}*}Z$g7)i`r5Vw}dqRoW09s<EXD32m!&!3lL
zU|xn|)Lr#bzeeU<>XUC>;F$kGb2z1*yMT@gI?K~~j(U?#ko0~+OKhmLXYw3on0zqa
zT47qSvlbvP{)mgGJFy<pF^aqCkM=Kwes0Oh`@Q<Xtfl}bRnGjeaVZu-?f09J16u&%
zMuXR@1dvkKIfdyE`b1@g2OPpIOb0yESB<OKQ$ud%*7s65Q7_;YRwiu==nqTr6Y49i
zBUq`R!fQ<16T}`oXR;Pbut6~yHF#Zh+JEjAyOEWbpk>OK)DvIo={x0l)Je3~)sVVf
ze=+!(dcM_p&FFi=0JG4!PHl1iP>p`=KFI-b;g8w$waHn=^_?!gEhU!U?PE`(g?<ok
ze{mX8J~pJ>q8!AZRA%8oz>`T+ZNeO|EBm=1Z=R|g+dwM&6uFY2^pz>|)%mw@RjKCe
z`bqr$eeZI{j!tKi3?E0RG@;}V;J;a#b2a-fkQOtA&(TrA?){G-(E9dXhWR!PEYwnF
z_KoAz)H{W<Wj#CvHi>uOiovnMV{t1fLl1^MVftJIdUyJmG3b_7ZXp%lRW~8&O?aHL
zrC5&)iAT-^{M0_%ALr^SA5HS{2#|A^fYP3%=*b6eLW!#D7IE)5>Og)oL4xj7nov()
z45stDd0D30s3#vcMzIM-OW;k*<lg4Wg31O(7WF>Qj2R+E0P?m%H7OApzkYE^9l<`J
z--m%WY1wU=pW<&Q&(*tCU*poLfpsQ9gzD*gS?p@Je%`QQbqZ>(nbkb9HH&rl0j{Px
z=Zt)`ylG79*FvDjS-2o!^DjhQw)k0}1D7+v=>_IjN5GoGAH;7MU?4}^7(NtlBASi)
z{>Sb%tZ1J;RS?a&bhgJ1+?(d>PQClJ%!m2Mt-n^@NMDx;PmK<+Q-!-2-?y#bdzOZ*
ze|A+DSg<m>BH_%I1)CC7EU)Er<~_{|sn`ef9}KMcN&%-Jy_F)$9Jo-WiopiB0;~ia
zchCHOqwwL)rzLOFs%le}Tzsvm@9CJp=HJ|^{UM0X4Zo7dz<y4EEkt{NcMOEeN7>9^
zJqS=Jv~i=_g~B7pDj+yNq9x}fCzs~#Jbt%ge?x>F4V3m5I6oe>{PnCb?UtMfrUbmm
zy`Y-dwrd6qb(MnSJ+kr14@Fvep|megD?+07-*McMoMI2G_&2Urqt2lUGJ(c3;#b-h
z)C;D=E%F85fSMo~+6PV64kT^!^7SC?%Og*$d@s+H{CMK+CzJkBME+owhQ5xQ;9zN4
zKvJd8Wn@tiw_GfF(P((8PiPiZ+8%lqDi4Cv%4CS}(JdBHu>^vOwYgq&d}UNO&2{q?
za;bx5JRYkW2!HT&rb-S;mY94tq$gjtzdsh6)@gSN%=03~G&K+{b%=3G@B35<zx$#l
zs4tz@sB2js)v)!DDf6(ywB>trU!1gk+cPPKd}GFIC*JfQObDcU<pAv!k~lMbx0n3s
zBdzmJBTpIeGG$hkC<7%3RWL2UbytraqTU|rFjmvgw9sS!IWe}F+b8y+Ky1bcaVT%#
za`2vA`uMC6Q4|TEYD-YHrl*Ce19MCbf2F%+j#z&vHmI{h%4bC>8)MOv8m*8z$#?{-
z#W2e{s?~n=#P&cC?DZ0w@Sk_m_RN1Jyc%0}@HqY2u{8N+Zlr(NOutDn+V!%RyW?!Y
z;BrDJyT4dusGZZqrMWr3EFMtKNQeFSwU{{m^j1UNLO^AC^`xu{C{SN;gV_I}#5QwN
z>-(g!iEW8-djhR;9lWDF6Cp>f#M{9}YJ7fKt&jcp<90=Fyn|O)X4Y~&bWEE5SK%8x
za7}%%oq=KP+jYz6=H|r99S2#0mu8uLKS`P2AF3O#O?deHBe1St=P{7UFdX5~R`S87
z)4msMDeZUk5U;W8eH_vUoqA;YNHpvU-j*-eVJ%LJR3nQ1J~G>!8_J@Es1lmDbYHml
zusJ()nbXo~CH!H7YDGoxy!*Q~XBoSjKTb8%#0JHIbM2p#Wy9+nD#SeRV01vt+DXhH
ztf*HLHp?&K^iK694u;HZidBu(5tDtQv}C^&t+Qqy<S;<=>5)W-{rriJ^nX`2zS2LP
zl%gF~X6PzoSOed+g0@7ijJo%zHG=YwD-v1_<B$C18MzgA(oIq`Dl-bp^=pDU&~0fm
zB{?OXrM7met2Dzxg5<uiG32gx=!`;XvZ;whOG^`}h@5+Pf`7%NBsjozF|13_Uo$}&
zR71OgDILl?>#-f8r|FJ@;ws~L!t=%6Y16di3r>h$!$Nan<%P<dGke&+v4|T=#Iik*
z(V16Xe*LmL-|xg;5(lWM2cu+bs_;tR*7~pdUK{Y9AO?ND!bp3A;x>N<t{WyOJ704v
zn>1Q&bV}Q<=T62x2E7)AT6S9RwW~=TxSWTvu^9l--t`u&3$*(6+Jq@HXw9jsM*(S$
zG}iU8HZAe1lRY~hyix^MVDtlA*U=R~C(HO>_-t$4nr^3r^5{w18|{dAbr*sk)Xc$k
z+qC6NETCq~IQ%QJ3*V+SALLB5F!LE2LG+I8&9f-Bp$8(d1;DN$U?D+f(<^SMD=zVI
zK9f(Sn}}@YsQWabr?n)T)TM^I`=9Cv)N-Ia${0k<?X?fQntd!H2=;5_Wqf}+2=q@V
zMQ?H3<J((NzZ~}1Ie<?_X0DE`?G-pI;t}oW!Qe6SdMrs<GRW`CDbP4E(UkA<)?VvC
z1*+Dl74gb<7?~`7yBX%3B{VfqRa4ODs;@}#evljd#}dwM^UEc4YGyPqEwP{w7cyZY
zx|CO1UVTnVGTS46Z@;^|lI%6fxn3okP#cpI7PxN*XM)j#Pafg%39mwDl2?q(*@lP5
zvoLVk-IdA^Do#NB4=7K|6@$XQ8IL+R!jhvmW2s<L*3;djLj$Uun0v>*MzuADXR@-g
z*|OPAwTQ7k&dzhny;Ge_YSzgQ6zg8AG7aQYfWxymVcJ8_Mh{cLesh6Js{w&x+)fDB
zsH4O=;54MEr%^IXmP{p;@6fnNJnS=>D6q(6<Y?_pbPZgJToMov%5@ce<v&;Cv1)B;
z{oLE$mc*9ah4}Tcq%<_6kzmmutgf)<(bpfX$JRqPWD@tT9<^;DFBv8WKk8Q$+OAw(
z(unS~%3jp#3aebMI9WHmchB$3u3p3F9MY@LcV0B^o$`wI@)dhrs4O()DiOW1+P<(@
zk)gUEBP_R&FPD<jYGkrXB=z&no~P&mMAKFaKc1}~-sSzm3Qp-O_dhH?UWoTNLnOUf
z(Lo2}*=*!YmY%JC>hyc#r`;!eS+X7RjF)fKuf1X1d?sMk`_109)s!S;P=4N%lae#0
zd&?dj8a<Yha;b}Uj1A;tegMV%$YaO0K#Y1GW*X5Ml1pl>O8m~+#TX=F2$!j=SUf_G
zxfe+H@EW=|x3sIJI#W{VlsAt^@v5^+V32kc-)cTC?%}b8Q{TS_`xPn6Jismp7Yxy=
z0`wFI;U|2l9C**VIl>E`)O6Ak=WlZxy>I=?RU97C&l62_@2q}$B{}F4oR#y;@lxkQ
z>}{$eH|2VCnx9CzS`h1=1(NYU6IWH`UTOo1(Ewq|b|ofk!F3<%3z=$H5&|NK9S>N8
zR!)(u9PUd48^8p^%Bg!4x<c-5<LwR0IH?DKq>5SMHWJuS<t!lF{r~6kdnXHup7Lr4
zWThH^|D5!$EF<;JFna&|k5f7~AMT&c0#s7ELiLVs!m&i^!$*!(RaUmi-eR1pEj>dR
z>ql!X?v^D~Wj63Y*@YA#Ex#_khixWTu3gko(<CL^_v4}F%?Tp=ZLtt2b{`jn=IdDz
z^-aW~UP1uJ8T_QI0#|m$uiymSr1jUF-xC83^cv(%f)#2u>W%=h+DJxK?o$LeSVSdl
zx+R$OsuO{B({2eV(A5g+9$7IN;eoLm`Vov~yS*|jMUUAua@nGgByr@MWuKy-SM-38
zQfP-s)<-w%MWDvnSj=N8dGK0{39#W|?w!zzBdVpoJEH@8yJht`&DZBeCOz+XSjS6U
z1kBWqMVPDANXT~pXjKxW<CRFMKJv1HS6*}LMA)?rHOo`k9ilyH2zWEnF#!>RGDYnB
z{lZj669oE(vE<mNL%mkXc78h51$>G@53w_Y29E}wxK=Ltv&XB2ND4IG1~K+Jq)hP*
zMulZlKD0QD&SO~Ti)>cClGpy3-&Kr+Li4}pPRwb1SULRFE;xF2!Jhpn^fD{J<jdot
z-kY}>sVO?uF)=Y!?)OXfd#m7Vv4Ve~x?5X*@wH#Un528OwVU(fjtgAez^bIV1-b8U
zB4TVh-ROnU!PUjG!Igm}gVs|HWPE#p?^F@Az}UfHs&eji2}ibhmcX7<N`&f#i%S_v
zS@~(TgZ%r+t-C={qYtL8uGIs8+WOQZ4(d)5rQN-~%Wl{6Wqr#=dHClx6H=_x(U4Oa
zRqb*EGb{u;5o_34V{qSFWL(9TnLUL)@L3QMF{;~(PkM^%ybiD70uVTOM9@B^Zdpoi
zuGYn_A8EScHO$C}6$TyZKXa0^CgJ7h$mIJsdQxf}cxT;$v_qJ*DDGteaKgJwVOCoa
zbrUYI0}$2{f9b8trY&voP6ew50LDW4=%yMs9e!WqA%F^An_c7y*+Lr|{`i^F8EgA;
zXbUcG`pav8S4Btk&+gw;%U0nb1UjK{d*1vr<k<^A4kB^)ZvW%sKA^;@@jSQDZ`d9;
zMg$aG5fu+KVOz{?P$yghU@xOV<nJM|5uiM_d!J!_;-C3jKr1Y0r2e3-cnvmUYsbpU
zdd<V*Cj<Tc_FcIY@woz)O>gYfeAsk)u(3Yy*UXyNP*VmTj|Xr24Kp=~mRou?={&8e
znIjzuN>>%knp#6J&CZy-EcP<q7srt1eB|*Jzm->u40ig`P-$fdwgBYQ2ET6!l3Oy2
z;lZv>Ya>74mdg1GD80IqDnLH_E*#$IA5#={3xV?WeTzW*zO8wKz-oaha~%g#xgp#}
zyF~?~h==w%jhi9Lx+XoRE;EC>)Ng{Q%brtAp}8UIf=tDUk5(-&adY))I=RM4yTJE~
zUtvBBo?p*6fX2Y4qPTWrtAGC%TFY9KJ=ZEJE@G%}Sexb*XF+qU!PkJo)mKm&zu|9O
z-kI+a7TvG80~Jo;t3N0g=z}^>`?!SprlkW0@U){eF~!j8a^aNwN$==|*Yv>9|5p4E
z>@C8J-@o&Nm+#kOEgGIcesiu4NnZOo*GeIJPk?Z#;GTfy%FeKRY0YGR-qos;PMyop
z(U#Y}&P0)o6p+nuc^lu>v@wLk(3W|p9L9lh(=@><5Vo-@Knu*-8m2p>Cg`ngzL$?%
z+x$?tXnxZ91V&LG_G?XC<8p@HmRum%64>}*uc|${14B6k9zZ^3AMg{ULk>H($z_Or
z*r2u~f3308(0A<#_eOg%MwV&-nk;K-vXj4Vorp<JCeP0Vj*WhQoRoM}h*#i)(CJ(H
zx6LU^IRM;JLoq{RXXpjk1OJ~4UU+2q5aogspp|jEBVAzU0wdVS_wSW?-e&{_hlhv7
zra#5SrEtD829G`fg&hP6qiY0DVr_UV1bT$ITt<93-)*(M<7K(j)bH%Uz;77}e0+kR
zjQBe!TuKN6X-l}iX5YEzDv&n$iB_HCg>T_m3U|`vv?;y7D->hkQ<dA{<OVI{AiHOY
z=-J`_PdSCWP(mUsU{g?vwca}kEat$OW{MAPjHtq9-`74Vow|goSlsXnWzcE(pK`3k
zR#8g@>pbXFo`EJ!8}wGR7m2o0hpI-)l72lV({$pSDdx;|6_~<H<F?H{G(~XE&|J0X
zvB4L=16(aEob7ZOD4v1=+2|DHF3(P+k~pqN>W3Z90(Zy)8b0&q0QB1V8ITqRUlYvu
zcHh}zctf`PC|HL>u4TPVx)lfk1d0G(3&-8T?o4p~`j;RsN2x`7?96F>5GbW)exGqA
zbw~Q^pMHQyJM?kL>@QXzSO5_)yF9WFo!&P2b*BE`vW|_1Ma>ApYv6MCMTnW}A_qa1
zmhkp!2I3EXudx0K8(hFmd#B*Sml^p^U<kJ0q9nbco$ib>^n;kHAx5k5Q|s-GMwEIg
z5Fa*PEOblQDr^96lqq_!d3vV0&k!vytbS>rVlRLmonG4)AIJwNX6t6|-5i#-0-zs>
zPa_`&M^VSl4X=rmXXe-4jtMg7aXt|vi|rd0*Lt@jXhQ<*bDeMghxB7pYwtcx6|3>y
z&?59Pq}JVx4_W<*T9$NPV-g-LrnMFj5(3LyAR&Ak85x(c`*uG$Id=``7Wp>7&c-Ig
zCctysG_3DoparX+*ptcmYR(Bt&tM!YtEaqb(=9<e9yDQ2caQgFWc=@E4Or_gtX)V*
zNwG9CYW23V;^rqLv5u&0Ne|Tk<r$A>#LrX~K4Oxrr(-{k3Sz&sH*6w>*Y0I;JPaDd
zhNAACLEieY6L{CH%!lD+IrROdf@*fDZJsvFHHMN%7%O5lH<lK*ZJb~V((6>iPV8I%
z1<OcDuZ^MBhj+xa{%HUTL%DHA{bStLw}94^1y8o`_`&+8SpehwSKKL!vw!@;r3|#j
ze(iVyz*rm1ZNvgh8Gz@#VQGJT34yYo0Ei}r;jP%8G(bG629a?<{^&pc*GP%fH_g;D
z0XYAY&}RXFXcoWx>o_+lh-O&nEG3@+n%n=}06Zw$tM-q#o~2~$<81dF{$v}B;{!lj
zP2jozTah<5$M_2W%?au{l$n_sEW$fEI_Bi$+#z>>cSpYe@F9uR+}sQfv0OBZRxZ_k
zN}oN+uV<z0FN23<kq=Ool6GdJ9!==$>+A0Be(~bPg{lutO^FE!;9ZnaCho}-R~r$c
ztIY<BENk}URwzFqsGL4xYu#v_1eCiVcr7Thq^ztgEv-S^K3X|1@rT>%fv&l^!mp&S
zU#~bgIQ%B>uB3*#rwVai-|SOT1j&^KtE{S8Sy|c3DQ{+EWPi#FoZ1l1CiE~aE;>5e
zZN3%kDFvrpxhCB)(Om(X7*i4xn_602ot^tCJhHMgV=t@ref+2=Pz>5cQ{c_?zGWUA
znbqFfIy$)ew{PD*dUUiM6%<sv#9P@#0#A-qB20gXOG=g%7S4SM<Ln$8up1klopnbd
z<1#au7d~<%gOccKvkh~DaR1miBO{~zN7Fr(4rYdq@UW*6&$Pjlb}o5|2YdnpYx3|d
z;3!RRbMs^e;e|oam-h3Zbf2~*iXDa08#FnSPM=LST?UXbLGEH;X2BEXCjXEA*Cxr}
zv^(OvsADn@B*0Oj4$;MBWrLMyejy<pUpIGm-3Gm`#nB54<6qk{E;VJ)KfhR4<~Aq~
zp2MtUN;C#<R4geiHC(RF&)4BLE_0$D0gptUjx$6e-Fi#47QCl=7Qh2t>Q){Nx(p^i
zYJ<p?+FhInVHuveb!zr&CQOcwl@|2x!3GPHV8gjCPH{0vNzwGL`$#Oy=iyInl=a%}
zoa?Nanx3w5>a-BAOk_mFGyK7<X!@qeCha3~)`#agZWLy?o-&kZR||h+Lf>g@@{7n_
zOCJLsq-`CObnVj}h6jlIwpG<XQ)4kJSzKvV-aD3Tnv-glJBIH~Rhj`Wa&$P{ac6>t
zGaywnk4kOo#q`m`hxJ$c%G^@eb4f&FlX}C@W+vr#6@I4i2PTK274j7H<K3N{yBu{Z
zkp1FfV)k!M;-zsVB?zHu{kgIs%|I;V(SNnT1LytGQx(86aL}(L8=;$A^ilbFUopPQ
zmnD!`UNK{GDUr`<KVr~!L7!Sw_|=>i4N6O8%0Ah6Ff$c`Pj=MxT>wvD+SZZfuMOYw
zwMII?gBe<1#wwxT%}-9^bBhe?t2^KIrQoIc8g-}a6FC};aN<*4#?t1JVM!9iC@PV#
z`5He99ti*UiDy@;1?)v5Iic={e~f`{*N*dX?9**U&?8LR2cAAX5h|!EWK#!xMm1mS
z=-Ic6Sotfxx}6Bs{&HNjT*E5qZa=gC`66ALmDYUTcrjc;XGceQ;#roCA#gr)*g~)%
z1VZnrp>p29Gmqy4%%w+xseD{UvczPdy*<ses>B}efzB_ixNd@$z4^tt9?_Xoz8J5t
zuY8Y7-gzW9Z|_M+Rzzad4r^e&HIPa`fDg_)=0JvrKc^>LyzOUiXy-cJN;1EIyZkT;
z-CJ-aOO8XFswZuLy2vXBVFnitFV18`Kk1E4dz@#QpYeoEZR~&g(t7!^`V4wb(%z1U
zPiM{~^)?b~?-gW!7Gbnw$SY*G>lh60F}t3(2rt!uXtRqS`!i<|NYINFBo_-Jd>G!{
zZu(%}<*{FX-|_a0PGNM?^M^VMCv(hiE*y%iAsb1m`x}TZT~f>aENvZ9{P?DLcn#m^
zndZ~u6<%4!mPDufv7#j$g7ksCX{DdXFA14;w!czpugdp)dacTw&eHpk-jj%%97~An
zrEs`W*?A;+-t_>ceL`pE54Yf&#bC}p0j+^i{rWz%bI8|`JqevG1MdT?{YnsL6dKah
zqFAQp_3ir^a%JwszGdNU=1<kUKEjTyVZWsFnlF<tuQ!H$A?8~Cv_>Z`{Q)W#DI+68
zto1Ee#x5(AKM6HcwLuu}=?ce-9g@?*nZBGd@$9HIP~)s|y$Cn#LGJFvB{f@BPVC|4
zdtitmhKv@&a#=m~=H(s9Cu0pqx?E=K=`wu7A&*8F6qo*F`}0BJ@W`ID5RE#%B%9aG
z$IeDh&^WN@vM?ary|N0uq?h8gLSKV7ZH~po0Fs;q#ELv`At&KGwe%T&p|MeXsXgEN
zo`pR)4$dro*2RU>A|jI?K4e|^I_ZZt{-IB0<N$YjuRlsWlFm{=Of$b7*%OyYR4Tif
zTgNq;cI1h8%gBgra>=xCXNceMT{W?5WEMqsi=hrq>i6x9PU7~i#7<3wary;BlI@4_
zgiKqVhpWF+B?B4MIcwrCd9<os7ag?4leA|}!>!H>{W-0edgz^yCh?2XM-tOQ9&soc
z{u0~Yg3jydAit)^;*!iKVocyR--M8GjwF&YhBcBHKK{&kF0rT<CzN4>zRX-@7y(X+
zRnBFZXl`3P6Mfl7kypX7LS{Tb?r?E3Pd;jzQL-##!W7vYfa4NrR_7%1w99!SYl)ds
z3cf>WHh=grNN2IoBTbLIP#5pnl0QvfWj(=g+ezh9$)1Fx6VBHCh09FG;myXSrz%Np
zPoF<@WSJ;Fog0v68i#<-B$h59W)HnK5p6Se^blZ*-knU&OvMXVNq<QUnxRH9d(+kM
zmLKx`8?T&1D9!|Q>Ts5nlzg)A3@aV5cady>yQ}uALnNv??=*gSa(Qc+Z6l~F?xr2>
zHvl_Q+K&`@F6A2*px3<42-UV=ZYS}c?v-Zq*6I-VpU#Eg9+#T4`z$<;*nj!NpRxv9
zD;P$lF4u7KUq4me+41Nj5^Z+*7q%<;Q%-3rv*xD?yWGd!(SKtqjN%<?!!W}mD3^N1
zF$;)<e=<M8X-eaV=IEY3gCK}GprC%VALQ_&?3tb+3#!snRpYrt_LYC&)xO#57^h>%
zBwKLI$Vo`AdFkiAF*DZEEWI5tv+;?b0F|h`z*K7cy#|73Dso})I&8aUlH{cT_5}QW
ztv=7^WQ0qpI5k}A048m>ji|jH0^V$>{Ruxx`wx#)aTw93(rLJ&#J4p)R(yjDgv`?H
zthu(fdmho*j!VxzJKy~)hf=a>_Cew29hnAI`c8}S>Q1k%7W?)RDk>^$<7&+pCh7P_
zVIEPn2+>%NG@*YPi@-p$nX)ob+&T1_c(<xTT;Y}cmPkBAW|w>Vv>oR${g0lgCa-p4
zSg!J4fQ%x{lXUT#j?nB%;V;BR8)n?6ncuaX7zTR!M>MicnY&h8{7cCH5gC^Tw57yI
z6}j+rKPoxwpg%&Y5Nc*-hR?YCQ;&(oSx(g6rIOyO9nn7d{qJ29lqL#YH+a)ww!<e^
zX@<-~y3(bP>9%`U^0jZnK37+R4pM+W!MOJU;*EseyB0aGEc$?dl(0|zfnvwxSf4`^
zNrJN~(@8lGntvt#HM8#?qm;I`HURVdji__aOqhll=<<ViU6V?|vRks3M@A%#QsJkD
z?GD-&e4#ri{MKO55k8oSYQx<w?y;ixf@8ZFxeB3p9beyyT9=wvvC-MNPo=DDxtnEN
z?|V%fBy4V-+%b7T<TxPG{vZ}%E`wJ8NVGLFm9R@7;G~xfF(nU8jg6&bW$_^`AIp}z
z&pS~Y`4^A%xFxo0x7XzA{6`}<XwPwH(LHhOys68gId4wRJ!ytO*u21NSFm9aeEj@L
z;JE0N6v_QvodpfzD_WA7lat*BrhyOTk|~=6x8}9}>Bs@$>~>onk35NH4tQ%>WUbc}
zk~(mHKHq$mSh2LLpwJ18M!UJ?^GVTI_lk!TBuG7YT*!F5R(p+hnOd?IWmVuWV*|TH
z?kl_GiQR3V?5N00b^EDDLY&v=e2HQKO;ODPL?e2U<!xTe6gWNCw9GXduzHlNU!asP
z&o^NzGo_YgAN^A$7Tqy@RorO_{<n95t-_`R8FRkTanJif&1H+-5a+i1#jcKygRHF5
zGS_HO$C45gD?zP6f=`QolspiEgcdA&y+(a6cmz(8{D)7j=TO^hB1>S2LuZf{qv3(h
z$KYswumiK)FZuum(SYBD`^-pana346G{R6<3c_Qx{+cEP3#0EIb?PzbED`C>v}DF0
zE-&=tOY!?bIz@61gXd=aU0t==jg}2>cLf+oa1uXqpdBQ%>LWD#H75c#S8BJz8`zwd
zB<RvDMx9|+l3BRiJ&)7MC6DJK{icy0eqNZm+6-|vc@!THwyx_L1B8IlYC_wXyX15|
zlY36-$o?rMY&W$bjpltxt$Fc59!L_Ibk*{^ObXJwILHE_JTx>!3O$*-n}3%RY%y)b
zKq9i|#khR;^=(ErOoNa~tyxPP1Ik;`gLLM&IXGlLovD28NrpIwJxigbyzCxe*6FCu
zH}iJV?p{{!a!?;K{<11yT8d|&ddeAe@uW_@K+pR{@}PPIy8(TDeV>crq>s=NL`u~+
hx5e-9A8>khjVk7hEffC<6=?|g(@@n`$x}jw{2#5@j9&l%

literal 0
HcmV?d00001

diff --git a/chapter_hashing/hash_collision/index.html b/chapter_hashing/hash_collision/index.html
index 1c5ed031d..928e9081d 100644
--- a/chapter_hashing/hash_collision/index.html
+++ b/chapter_hashing/hash_collision/index.html
@@ -2140,18 +2140,17 @@
 
 <h1 id="62">6.2. &nbsp; 哈希冲突<a class="headerlink" href="#62" title="Permanent link">&para;</a></h1>
 <p>在理想情况下，哈希函数为每个输入生成唯一的输出，实现 key 和数组索引的一一对应。但实际上，<strong>哈希函数的输入空间通常远大于输出空间</strong>，因此多个输入产生相同输出的情况是不可避免的。例如，输入空间为全体整数，输出空间为数组容量大小，则必然有多个整数映射至同一数组索引。</p>
-<p>这种多个输入对应同一输出索引的现象被称为「哈希冲突 Hash Collision」。哈希冲突会导致查询结果错误，严重影响哈希表的可用性。哈希冲突的解决方法主要有两种：</p>
+<p>这种多个输入对应同一输出索引的现象被称为「哈希冲突 Hash Collision」。哈希冲突会导致查询结果错误，严重影响哈希表的可用性。哈希冲突的处理方法主要有两种：</p>
 <ul>
 <li><strong>扩大哈希表容量</strong>：哈希表容量越大，键值对聚集的概率就越低。极端情况下，当输入空间和输出空间大小相等时，哈希表等同于数组，每个 key 都对应唯一的数组索引。</li>
-<li><strong>优化哈希表结构</strong>：常用方法包括链式地址和开放寻址。</li>
+<li><strong>优化哈希表结构</strong>：常用方法包括链式地址和开放寻址。这类方法的思路是通过改良数据结构，使得哈希表可以在发生哈希冲突时仍然可以正常工作。当然，这些优化往往是以牺牲时间效率为代价的。</li>
 </ul>
 <h2 id="621">6.2.1. &nbsp; 哈希表扩容<a class="headerlink" href="#621" title="Permanent link">&para;</a></h2>
-<p>哈希函数的最后一步通常是对桶数量 <span class="arithmatex">\(n\)</span> 取余，作用是将哈希值映射到桶索引范围，从而将 key 放入对应的桶中。当哈希表容量越大（即 <span class="arithmatex">\(n\)</span> 越大）时，多个 key 被分配到同一个桶中的概率就越低，冲突就越少。</p>
-<p>因此，<strong>当哈希表内的冲突总体较为严重时，编程语言通常通过扩容哈希表来缓解冲突</strong>。类似于数组扩容，哈希表扩容需将所有键值对从原哈希表迁移至新哈希表，开销较大。</p>
+<p>哈希函数的最后一步通常是对桶数量 <span class="arithmatex">\(n\)</span> 取余，作用是将哈希值映射到桶索引范围，从而将 key 放入对应的桶中。当哈希表容量越大（即 <span class="arithmatex">\(n\)</span> 越大）时，多个 key 被分配到同一个桶中的概率就越低，冲突就越少。因此，<strong>当哈希表内的冲突总体较为严重时，编程语言通常通过扩容哈希表来缓解冲突</strong>。类似于数组扩容，哈希表扩容需将所有键值对从原哈希表迁移至新哈希表，开销较大。</p>
 <p>编程语言通常使用「负载因子 Load Factor」来衡量哈希冲突的严重程度，<strong>定义为哈希表中元素数量除以桶数量</strong>，常作为哈希表扩容的触发条件。在 Java 中，当负载因子超过 <span class="arithmatex">\(0.75\)</span> 时，系统会将 HashMap 容量扩展为原先的 <span class="arithmatex">\(2\)</span> 倍。</p>
 <h2 id="622">6.2.2. &nbsp; 链式地址<a class="headerlink" href="#622" title="Permanent link">&para;</a></h2>
 <p>在原始哈希表中，每个桶仅能存储一个键值对。「链式地址 Separate Chaining」将单个元素转换为链表，将键值对作为链表节点，将所有发生冲突的键值对都存储在同一链表中。</p>
-<p><img alt="链式地址哈希表" src="../hash_collision.assets/hash_collision_chaining.png" /></p>
+<p><img alt="链式地址哈希表" src="../hash_collision.assets/hash_table_chaining.png" /></p>
 <p align="center"> Fig. 链式地址哈希表 </p>
 
 <p>链式地址下，哈希表的操作方法包括：</p>
@@ -2160,7 +2159,7 @@
 <li><strong>添加元素</strong>：先通过哈希函数访问链表头节点，然后将节点（即键值对）添加到链表中。</li>
 <li><strong>删除元素</strong>：根据哈希函数的结果访问链表头部，接着遍历链表以查找目标节点，并将其删除。</li>
 </ul>
-<p>尽管链式地址法解决了哈希冲突问题，但仍存在一些局限性，包括：</p>
+<p>该方法存在一些局限性，包括：</p>
 <ul>
 <li><strong>占用空间增大</strong>，由于链表或二叉树包含节点指针，相比数组更加耗费内存空间；</li>
 <li><strong>查询效率降低</strong>，因为需要线性遍历链表来查找对应元素；</li>
@@ -2551,14 +2550,14 @@
 <p>为了提高效率，<strong>我们可以将链表转换为「AVL 树」或「红黑树」</strong>，从而将查询操作的时间复杂度优化至 <span class="arithmatex">\(O(\log n)\)</span> 。</p>
 </div>
 <h2 id="623">6.2.3. &nbsp; 开放寻址<a class="headerlink" href="#623" title="Permanent link">&para;</a></h2>
-<p>「开放寻址 Open Addressing」不引入额外的数据结构，而是通过“多次探测”来解决哈希冲突，探测方式主要包括线性探测、平方探测、多次哈希。</p>
+<p>「开放寻址 Open Addressing」不引入额外的数据结构，而是通过“多次探测”来处理哈希冲突，探测方式主要包括线性探测、平方探测、多次哈希。</p>
 <h3 id="_1">线性探测<a class="headerlink" href="#_1" title="Permanent link">&para;</a></h3>
-<p>线性探测采用固定步长的线性查找来解决哈希冲突。</p>
+<p>线性探测采用固定步长的线性查找来进行探测，对应的哈希表操作方法为：</p>
 <ul>
 <li><strong>插入元素</strong>：通过哈希函数计算数组索引，若发现桶内已有元素，则从冲突位置向后线性遍历（步长通常为 <span class="arithmatex">\(1\)</span> ），直至找到空位，将元素插入其中。</li>
 <li><strong>查找元素</strong>：若发现哈希冲突，则使用相同步长向后线性遍历，直到找到对应元素，返回 value 即可；或者若遇到空位，说明目标键值对不在哈希表中，返回 <span class="arithmatex">\(\text{None}\)</span> 。</li>
 </ul>
-<p><img alt="线性探测" src="../hash_collision.assets/hash_collision_linear_probing.png" /></p>
+<p><img alt="线性探测" src="../hash_collision.assets/hash_table_linear_probing.png" /></p>
 <p align="center"> Fig. 线性探测 </p>
 
 <p>然而，线性探测存在以下缺陷：</p>
diff --git a/chapter_hashing/hash_map.assets/hash_collision.png b/chapter_hashing/hash_map.assets/hash_collision.png
index 2d5d91e1db375a25c0c6476a85fe15176f9ad719..ac2aa60c95367862bff3711255bbecb0b8c8c85f 100644
GIT binary patch
literal 91972
zcmb4rbzB=+_jeMcL5sUXkwS|XiWhe+?kUCHo!}0|Deh2QN^zIsT8ew2SaH`kba$WU
z`R(pMZ<u^$hM7t3Irqr-$W5rCyaXCD5i$S(K$DUbRR#bMV27YFFbK92B9{ijc0dPZ
z31L9_2+20=B;dV<l(C!~;5qCV3_t*40pK2Qf&Br1M86+?d_)>Z{GVfGApM{Bz&<nB
z3;_T8egHrVwtsvXz}}C~{IQ420{-_Cvp|2{jR44k`|B7q2D=;JBl^Y@wnMU&)N}v<
z(7PYszywBgV%WF=Qlf9(x&rsopLmk=EZ#e*wrHr;J-b-4J?J%P4@3_V5~ldjEOn2x
z?Hh0kqO{o|)&lv`;P`J7RI>IUqQVnjETz(L_3!+0JbOqJCyP9n|2et6@3=7=?U|7d
zdtL1>?(?183`dM?*gvzS24YeCZS&QjGdOMYdzD(&(9lp@JGJ!X&FgoQ+m3y2Ji|(j
z2qf-C(-@?n@REPq0PxLW(v&QLU@_3U`NZVp<k(mU+sE4<1-uoqVt&`x*S)>sB~!)I
zyLQhSK0Oo3%S<w2`^R?!u?{n#-^!?<3JtH*<!ffs5)%_+V(j!Z-N}Hc+uABB{t!y)
zB7Jg@1`cVzBKku~M?8%X=<nM~0<^Fl$6cjZAD#kQ6?!S)buEPGF)S_W{7HRvQ%6Y&
zSW?kp@L@+Cx1F23sU9^7f(^7&-Mg-*c^U&i`tY|6Y6DW%m9Am{eQ4swG_0!KUUo*?
zv*k8G8yOt*_xU_M)PiCV-ebQxM3@FR+kJJDF+Z1AeglU|#hdNaQ#g&n68jHcLE+sc
z0rvQ>LlocxrqpwNF_F+Ba<8tgq@<)W)K96PsVOPX85t?<vb|M-OpeR~8$o**=R@(V
ze<u`1I))=i84+bWTp>GPk#^+^8i;^+&B4KeRWPvtpan#oKiHlu47?7U(n$6WL``f|
z579G&Pkdbr(ZG=*gZym@f1lpctZ3^B?@*C{@(o1AYsAka7-j6ta9)uI5p2t+ar-j9
zITF5;K4Auh1g!NG&e*cTi;iQqpZzHR&}u(Dy2DEN4+a8|z#t-B2AaYUQ4qYS27Fd9
zCUh%7+~AY%&Dm~Y)RTP<Hi8;GN@mqNX|%mh-m0ODU2N_1;{TXdArL<eML@Y?in0yz
zVtASu;HZ<92|FY_>{EJpSeOwZ4?K$+UuW7VQCEenFJ9(xESm}^McA{G_y0zwyQI*L
zBExG;A(~g1)Nnh2w&3qNp29zbcLr)><`7uW4O;Z4mP(}cyX!U%&fUa?HW{flRHsDP
z(BS@U5?Fw$_F<KM$jEQ^)>Kq;XK;z%zUXGkvvzlHlpK2r%?^!0$O+gNqq1aULJw82
zBNB+oMGYT3iTfAH@RJb&E5sDyWMkw}iPNii3U?Jxi=on#*+vGf3=a);k2?bwW@bVn
z0@iRd?eT#PtMCD01#A=*tAx}~S^udELLeZ<2QBq9#(={3Ofa~NQ6NSfKCd|tF=z!B
zq!HcqDitki{Fr6rYmhExJKaQxLdCQSwODfIzfp+;Dkc&O5}<jGZWsqq3)2DX_35SU
z;<XPC4<AEQhzyl<Mxha3DXT&Wykq~SM6gpKTcotf^!<maw2g8iTRI*(|NL)(dp)7n
z_*>t<tHpF)6xO3oP*4aMYT^OyLjH9CJRso!Y0cvCJT@}mFyd^ua>I*u4H78_)TW$n
zHmGilc=tLRmH6KAzwuRAPDt`CrKH^p)%-ABB>-lHxA6Je2Q>hSjhUSIG0_?uQOt{%
z?F#>5lE834$+ryhVnQKmI$9xmm>9=u-Hu=bO4BK9BOWEkkGYc6DnZ$hX83=Rd{eNb
z-E)xeXDT%3DyhNp2u!2}JOj>8CIxGrA7yF3=lyv3FAoJoLNN;0RJPPS&C6fD6J@Id
zsKtd<x<~Q75jA(7ibsw67v{QxO}jt+EDz}@oKY-x1~Lr<YiKGG7WAvL8U9oJDcF!C
zx1aYg4KQ?3t>CrWi^PYBMSP|n%tigX@q3)NZY&IUHPue#)iAa?6azUPlHKRDkdgtv
zf7;4!Vxa1p`<xvos}@QnG~bxA(_FS0_}=TE?t&^2T4<U8QbQD7<%MTKmz1gEE|4Os
zs(s(_cfSG~Jpi7A4UbAa(hkL-szRwPMK_1$Z$1ll>f1+`g;@hp?^}|82UUGfa#agK
z`sepbwm$(<+UI|>!f(&O(kwWP!T&dtFC>ZyO+I^DpA#T{TlgAJNh~_CbLN+GaF=1t
ztfB#YPW}uN9hm0Xv(-rh7J|tAOgOIpicJU}$kZ>VC<k|d*7Wm2ZAKC{ntEJ+fF~9<
zwnv8c?GFkgX6;-4mi5TUNY8~+97simO_j!vGs>VVk{Awx|2X3i4NzHGnK>~nWU${a
z&=2q}7=vPsw;j*2jzR_Cf}&p7y=8A<ZoY%llTJ?u4F<mw5Y4%LRekxV-eL^G(|f(U
z+DClL^~InmFcMU+UC)Cxc{txewJGcxk|oc9@O2^bec+$mrr1GJyc55BfvSlx<9CK_
z^_8dHJEPr*0xA)G$U_mS@eE1_zUGG1I+x=AC9gspSVHTfA!(*ee1jy2Aj^(xxR0P2
za_RJm%JnkrsF}q#<WKgU_P$4R{s&`((1JMHMJE?`TB@rNJoL_S+JB0DV*pOs(2-QN
z`s;D9Hb6?%<InzkzbVMlPyF;(Xk}+Mf(&C+w1+To4-Wllj1Y)4^77e#c(vsOvixv*
z{UW3sbcnLP?yUs4fv#_0w8`pabvxoLNSeY&ZSxKd{3)+OdDvN;%o7KSqKVP^spZxv
z2)61*&D|#!KM;^}|5y5irJ#t(iW8Bu%~!SCJKvQ7E@Hhh&BMkgSc63xbnRayN|z14
zNB?QUsgeL_EHNH7RINsi?@ryr>7gwULz=&s^_RkmvI4d2nwR*H4JtI6CG3CcALu~%
z6EFC`AF%97{ORywWT0druusyc-l7o#lB8cm=F|R<xQD=j_ClilQ-_`hB>)g?HSA6x
zf49{bh@d_GBV^cgFye{-(-L<R0pFFX($DRvC@ICjfLdarF$;lbd`our>fve^wRnW2
zy!?60&<TbyItNi?EBggs_@BtbuRVrZqMIqjy~TTLEV~<v9sckhCZ%Fd)ipH^_VyfS
zJRawz{YC?QePi2>DI$6<Fd*}Y8En9<bb8n@AmpAdR5YKK<EN^sdUke3wNPiHe;eZ7
zvc?2JG6gFFET91%7r*M3t*xzlZ=43=8RBT=j@{itW>ibmR{2}ZCTUGqUOQ}FUI_%v
zckNcRq5HPjt_pj)52wZa!2<zssa{KCRTU-@MR4my%fXf8Co&$lV<Q=vaH4fW7+{l8
zP)It`uCu=T5vS0-Kc%j(tE0p8lof*sl%Jo!k`^0lzn!1ddc9NP<mA-nHuu@A#(3C$
zEtKy1Y?sUX_7Vt(xbiGKmy?roOCW>WZmkDj-*XAHx6t6Q*yyCGso7_>P;a;ABEZZ_
z3l{YK@a6S;r}NKN5SR14*>_)~5`qaRe8H4Lz=c$<&TYpqyx74FX=&+WEu12KzDiMM
zPWTsl?XD@83{Wo18AV;)NK1W>U$xI<5{q8EsF>a{qzMatX$zC|B22kw{6G39Vdkw<
z1TZQ^K4>`re489{_U)63E^fc&tFG^q(cXt0Pc}9-?58aZPPfL@b?gH9;Cb1}G9c=D
zZ^_<g{e&MF7)WH+e|b#EZj7qe!8U3&|D|KnTz}sASM79Se7w-z8of0<kAM*yxvy@M
z^D4dG_k-4({STBP-6$7h*&-Fq$6?Vmwp*#ox5nn?#RnXG(jb01jIdXQX&FROPwySC
z`%X>2b_!PgOn{)%U=RSkuR!bHCu`(01tNo@rpyBsaopZ;b&jJOp336m;Dksz%6DB-
ze5(j~!)UcJkdUNf-|yy?J(~8~AKlCj&mM}{x|w1jT<oh}s-dK*$xt3L>I?Vec$?OY
z<q-u}!7uqdc%8nuR%tHG^lmIMa$Q?=U60fyJtL|>W~o3TAk+cf-CP8huzRM){4&Y(
zqGkWe^O4ti52I<UyekL|c9hJAEYgDNg3IlGTC`;?4m!2yQ!hIt-P&R5jT3SO2NVsv
zt+WIA_{4Bm(n92)El<7nzU7{Sd3Nvj_uOiiBP@;*<6fb?U#4$wPPZo)C0eFE31*w%
z>7gFMf;_256p9rs?+5X!Q0lleEXG;pnp_TgBZ>KcVI7uwTx}$+wkBj|R%~V=nHU@6
z;o(VpAe_F+;2mrCb~d)KU;hgwh;jl6(pNGgD8-5p8u^R_tKYUIN54B->)}T3ps+|u
zO=axTMaWC*eP%q8Hmk}88+Zi<SSb~oU!t1l-jz1P<!#7N*)$xBqLV73S^ds);Cikf
z%!tq|(V{AAwRyK3wqb2_;gI6%xvol(d(kwO8@>z@!zZ1Jqf-#qkDumgFT6e;WPZ3@
zk6xX4hLz>x{%fu_N!R(K;3z|d8{6+d2NEr$NESLK|D5phm5hlXC)p}prl;~yaenAe
z>msBTH2RzP)gKYBOS*Bh1CB_AxLB>%U^9kH$D|6#CD&ZUEsP*}tt{^x=xG%FYN*Xs
z-=nOr+3n;<5<KYw3z3IhuOt?j-8bv=>n<H*y(m~51qIay1N?n>5E%?rPI^4tJNys`
z44kJ_)eUW9_`=XFE&UPEgneop>y;I{T~YgtyCu<3>&h3KTpWZ!30Pe)yJ084(zsiG
z@@6GQf(*$3i-{aN6H(0OhMwiAlbFHD=J14j?v8?4vfo$_B4)V4$53?zNp4$d;O%NK
zd002WnZFdzVN@@#%l<+`$|wHA%>)pE*Q`14M=ea*S+H&Exc$FvqB``8xWAU&%4)RF
z(r3y`dbhbs2ea+ooBNC}wLXJ0NBJ+(k{QUZ)no|+m6{&z4tzM@`;DHkkMdDdZ47D`
zbSN!P<{KCw_F~ECo4T4CmZo^34SN1Y3%=YmP+VRXAK&QJ`onrm4TEv7+oP{u6pdRs
z;Va41SSwW#p#;se=bjNT=JhR6LGRHULI&Lip;y)$mL`gATbJ#n>SJ{TWJo?GCmAE~
zG%)Y6YUvP^&0|;(FOCTjc6FmfHVCCM2H~`~I5UoKFzHumBmkL}B1U?)s5!oTu~{z1
z8?37#N#yQqL@{@lBXBnO+@A*!Cq^&-21$;ieZS?*swhgz2=ZZf(xm0!U-k7jrcWWQ
zj5H9CMYZX*$0<&S_qM2xBin#y9RB<f%8**Qm3(37jik%@ksSs<zhSnM_(DuW1)n8h
zle)>3q7!$)$vNw|%MJA%Vz=MMY<ab(f?CHi)V~rxx$AM|a+-3WROnztBz7KeK&@lK
zjBcndkWUZmNVLzx(kcIT)D@DH&T#48x9~VW7+~#Gc2uWv4)FNEl<S*oQ;eMS&~p|6
z)*ryDb_=*+v0GQx!#B4@a4!Y5rjMUQ$+G0W;Nudrc2(^2R^T)Iu?Kgob<g4d9)jp6
z3<Yu16TtP0MhSF|DsU8cD<G&iu9zV0`X=KvmXxk)2j=@9d34FD>*mKC5k24)$ypwj
zCL#$F2~ipvDE+KfGeLoWQi|^v98-Y0<=tgup!^jQkdS7H!Ep4sQyTXe=QD3reV}Kn
z5ZSW#&97qbL<Yh~1O%f&k<Jd>wc(2712z!T?}KtJxprAVn%}HYM}9PW@536~F+~Vt
zjDq35l->8UY5nNgyz$Lm88mAhdqq1jv7X#$f#=KbZEHHS^drs^rrlQq@r{y!k7}k^
z_xk8A$)QyEpnuNL?t}l6r(wEI_D&xupa9R8OCAUOZd7w!b&Jla3u37!S3fh8@G!w6
z%wF3v++m#khj8liImbBg22!0*zh~mrx+fC#I;@w~Eyc3B&Smj4J69Fedn#sWdYlY%
z4H|(jXHnG@4C{YB8q5)vc9I`ygtn5sqsp6pFX`)*I`qO?jR+Y)TMDr#D66ljQ2Q=F
z4F*Tiw#)<qH3cq>K=lqQxJzC8FF&Rpw8IQej({D@FsHais7lst)c|Yp%11b|ESuJ=
zO_<An!PLTy;-@C9<CtH98%$o$7f>n+8Ra7sc?4hrU;~b@G&PLKSCQ=K#^YbH2}t8@
zXMA1KwyL`&<vEJ^PEM^D&t*rG6|sft*wnP!DX3?$&YG#L%Qq7O#9yRL7aKmQkYDWx
z;HrpkqGBwiVLAzTsF9?72a`5E8jPJ+KkvT`*Z2{jK!@2|=~ye5vz|yt-HZ4Wl13em
zM*?q^@7A7A%=oM2%;8Pp0D>#u4xn)@V3cC|nG=4qFiYdPvq3ER$g<!7(?)(10!j2r
zje!gnM{X%#glmZMDW#iJN9TmZR!eU*a-3|Zh1R8Jw$EH0An1DPc1aO(`;Ap57$?W~
zTSuFNA}1g2do5E})Hv)fnjD;pDynxm4N#E@O`=GoQgz=?Z5U6ZF}aKSqTGapT&NfF
z#6~dMkFmgghOXu`k5-drB~?gC36reP^^1WPwNq5iYFF?(;Wzd9?H#xxl37_<AqGe|
zFQ5O!ZBPENyeovOAi=%dvp$}IG4t6hF0BmtDoZmWsQOSVI2-Y~3k*G7ijoIktNC^J
zl&CdZ+2OUqDSyv#z`L8?xe&#BdZ5Ny5gY-FWZh$gxaZRhi)e{jF7Jv3`8gc(0pF87
z5ucJVg$3xBJWu5xM3UC<MSy$8_cV~cKzn!vBZ1PoCLge$t{puUnny3@AdLfRYw>xw
zS=P{b<8@QK;ZKK@q8~!YX&z5>z{`~Ig_aPHu$Nd1U1^L2ZQvzNX=!>N1|r_<W*24c
zjpz00HolH6Fm@G4gT}l?EV8^>Z?}#SeN~<h=zZC#3@91p<<K_(;w7!qJ!1b$1%R5q
z2AH*}l@Gze7s8`o1d*huuacq+C}a)N^*k%lPhj8#P9eB=hhR>)NyJ4o8B#;vh-^jT
zPV%m&gVcZ0Ww;814dM-ZBM41})=>Z_tp$=S>HTKqEP{dVjzh_;Takfs1ikdl4c(NE
z&aPG>%l3mWChFnon66S(*o~6mh2K!5S;-3yK7FxcB3;o>VWA2{Wem|-7QNT9qe`i-
zegmG3=w%<0H06O1kh(V=5`3N1OUe2`#;V7RpVPPh%3tJd#N|*TsNQA2iNpT7m2Xau
z<)iSnRP7#b%TJ|bh96rfBt6OS&5MC>1OoscmgY15QDkY<6a<1i%2fP5>=L}Lb}BXr
zLKbvQJuoNk4n8Y3t*oLpqAMQ~Fk*?<Da?`~=!jdT1#O&pYo6vM^T6*=NvLJPeYb1{
zde1$yTmtm#53Ag2q{WJQKK8kD65fizj%PxWo!RqO-rJybjA&lV6xqsfS_&e=jH3u7
z1mIY&sosK|D`ob{MShYV7Jua>XeHmDaV-O~6<G)fs*BgbMT(L%pEcO-2};_YR1kcz
zHa-bdcdMwwy$2}+WZ0`yh`VSos6dqF4xMo0yIGp`^wLgYnYh=Xe7guH$fJ@E?+{T5
zpvx(i#JO)m3d?ON-<l+gu&J88gJ!!U@ueM|d}Vrld=-%$xHY7#pfve}D<a&vj*w&l
z)a_;s^P(pRP?2<F$n%Pg_AUgK`8Oi&XCdeAVYFDSZuZIW-V+3MK^NtFMZLu`TTgda
z-$^=%HK6#gyJ8LKO6r3R8p1^s`|R;`4~jcPy~_JpiG^a~;;2&-`rhyrzCB@P%X_HF
zd*ouf8`4S)y($`!L$yg+3HH&cINK?iFn;zf+PR@yBOd~f^!Z&j{xJ;2BnE#2Tyq^X
zpU86tt$x6QqC)k0Zg5;Q<=I0kF<MMz*9W1rZ0=gCVF>S-X-!4lzNtqz^2Tm-YbI|f
zwYC|U^zx$IeK8Gu*C_EZ0*JLG2Ff;dfCQwF5I;?Nvh5pTE-fJ#Fm9>xQ&?gW|D+R)
za~Yb=^_+#N6GiJj>}axglAr)*7|Ol<z*OOvNH@_gh#44s1z%0524R54pdxirL*Yyj
z2enwn{%iD<g%{RT!@k0&NOx8uO$D2=k5She4->_FdRy$PlWP@-$T9w-Ve3S^j-zoc
z%cJKVN}EIT3TvMl>Oca6KUTZyH%}Hn`IazG>o5-6H%cvv->{DiVoB`}{SrY0!{`A=
z099=|1NueXZ?XiBvA6FDmJmB88UtT|DjknqV&yfYl76T;n*ThxvZy@<H=2#FjuRVM
z+CTe%F{tq4MiZ)?6V5r_>}4YE*Bh}&Q450Hrd3LYrD!%n5X)+(US98t1>lUa5Wkc1
ztn7ssTMt8%^Dp6~U~oxGmw6CsoDe-YAZIvKp8R!~9Ff+Dwkzt9NUl0fSKN8?wigYw
zRs`9A#=kTWphmt}{J@U2g5LrQE@6mv5OUMUhZ+pBKn%_{u(L-(URi1wztn^PV(Y(r
z-p@fo=<+jFN66P8*a#na@iF00*jKdsb|U8;aqyU;zq0D|P2#o(0dz)f7sT+=BtT+h
zf^Th9HOom%1`|Y(5L=k_Q;!-7o2Avqh->Tx$W^OT389R~X`3hpZU~IQ&hoUg{>e5d
zJt8QcI{+{Q-V%R1RhkLX7|6Cxhzk{w27J*s<Ltb6!%5%aUh2HQhH^6MbC2!PR&u-|
zRzcQDqrLMIrgpDDt7Z;CWjt%bmCi*=ewUvh^=amqN_Uw@7Co_xy2GK^o3Y`82;Win
z6LNZgh%rDtuD;~3%QjxFeLbx3xsxGP1e!cQ{m_x5F{$)JA)D1Do+kkXbz}ksp^WSE
zVcy~WUd`xAXE3^rPxYA~8cBa11F?yr26N-?m>`|~Aqmw6A$3KdNgBB8D<b-Q^$kXu
z>}8cf90QDQrAN9~=zx5|tknFnPjodA4NMf}&{8Z}M?phSjT$*~15^){%pd0Nd_x<^
ziToVUqFJ`Rr$ATT><9Jp9N}Sz0lI)8PN!oj)e}}SjR49ZRbVOMKnV6Y-0o~%P&8nz
zYBf+yrb6%{(5zFO!qIA^QuU1<Sa0k@eRVcUI9U7;5{G1@fCpir)jUz@nFL@FStk=z
zG0m?YFR;M#5w~QpRufbcGQA_%q68wZkbzJS9qWa&s}NNDueHVWwsMur3S7@}meFGt
zTTt25r#+ynkj<fwY}n0TvgJ1%nGbc}tUo<*hIe6M*(~ks5<_<iIzhT_v%}RPeKwvf
zu%aH6AZ&!>1#bY4r(#Hr246WhAN&OVF4HS(of4M+tbjk<I?VQN$;b)q2BVjfHyQO~
zVLm;ZPXLHB%4Ns^nUn(PpmkV0DKJ;bpCafZpx1qz?q>}->;1$9wt4AfluOTI*=eep
zOBtn3@G32Q=|{O%RY+2q2I?<g93+J@H(V^RQ)*2exNDOVfyG;8r;nE-V+t`_{H`-s
zLOvug(YXS=0!{5`5##MGmjN#Da^bXbIeq(}1-=c+Ru_wyyC^L<BJEuuh8a3^_(Itr
z+#n7c>*h_?yM)tI{~bKW{o(@;H+NWwuMZ1<5j3$*1J@at3LM1`xKlufR(KypzUJr_
zec>CEeM9r3d~>H5@SX2q>!H-JM;AuD4_Ij4APoMKpDl8RJi%e;SK3!#+^hOtZuA+F
zvCmivbbK9^1hI;2$+1EsYAfqGAGD8)(y%ppSuo5&6Sq+)t7zc~A8fIENV}&ERyzZ$
z0c&#4UB<Cn>^BDTWs;~qMs!ajwltas%B%~v!nr183nJL4%6_0#p|br->e9y>r6hUS
zq8!a83(BU(n0RHf73Q^+Mrk*GM{^T9))`+|bUzyM?NVugp=s>fHzu!uC!pi_s}MkU
zu_Ko6Dl#1Tq4`+e_@1;<WD-Jo&g-y67#}k<S!n?<m<bd@>0~(MN_6NR+&e^UIh~Lh
z_qn~^tr+avM_idfJ!2$)!cA&TcDQ~#^aO=smH&lL&ZSfrZN#VBx41iQYIP6;<=!>%
z<d>=$f$9R+E3BF98O-3m(2B7yP|#O6lo$dOv`?sZQ4)wm7+a8}LTbP^dcw=h_d6iT
zQy;ZAtg<kj69f+VLuaL{R{Q;rh%nk+GggiQow1DNV?hLJ0^oN99@(}mZj>20mDg*t
zfg=JD8soBo8)rMk3Z<3-ZgTy7iWtyB9z79zC!tzF5Py$-wg887l|0t9#uVF1S>)^T
zw=T~KoLKX~2h`27<3oW%LPCyvIn>(J(5X@aT3=f%ux=`QTJ2#o9@#fju7Sk76rnR8
z@#fw}IBnLE9&F+`?xJDIynr%-b4pIefN^tJ20)yY@8swu6t%a({xH1v4DKnsQIrW-
zpoPaCaRK#vd}Na^W)=WFLR(?9vkNSU>-ZqFFMJWEnT6TTtT}uQOGgZjjPy!sWhce}
z1chnFZil)VT(>)GP}(>+pM3twBJyeO-HYhXkSf!0st~<d&cMtIVw+}PT3w8v-JJtn
z1d&V<-?KkxTxxS8=hXTp<~Q@8cO;0p*M!*nq0;xqbcKlOQpB<v$*76KA2O*d>T*al
z$ovugfJaq1EV3+PP&aw`<i}rx^hUbl&9O4KUgi)q`kCMdIc23DgfW)4)1a7Fmv?gO
zT9vFGEvZWP28RIL11eh1wNNwNc0LtyBtiS}E1naWQ9@XmB;{Xa({|mUaA6W@G^-x<
zin6PFl7BM-=dPBZn@*5yyhI9s`MkL_^Q&c85^u`9_?~KvUX|Sa&4W@_q4KbPy!84*
zgyf98Q60Xs;mw<mQ_uTYHUomkB_}P#Pn1Ve{o@ZWI%wrP7)3Z1Idj3|1wCv)Hth=E
z_LL628i<h#k|Mw*NyBy`H}&evyfwDlC&A}(`-;soKMpVi4G0KDiJY!1yH}jhlb#Qw
z5GNu_%JG3YW(Ra{b?})qpj<5x9VMg=)`rDTb=1YrX#l#&^I%k3HtY!G-bv()ccv!o
zE2zO7pM2jF5ehw!Y}PBos>dBDb1Hzz2TkF3u<})wHvAZYund9%?rS}`!gbb=p7}AI
zxI34S?#avZd7Izav>Cs`XOP2hUT0J4l+Ye3=ak(wyWn&32wzupYW@`Ii8*L6F%LcG
zb_20Fh~=uYug&emcoZeu3sw7Np5G2?^!{e5O)H@l<n%|FitU9R`S>odLbADa>Pzd8
z3b$;hPN`P%cs|u4?bMMRJ!&hNE!W{(?TZs5C_IQ3<MdTw0nKq$LFiZOdC`1Q_5^p@
zEyIXj6s;eKV#Q|Nokigrt@)$5?n-=NM{w~2B&9|r+O%CW{Fmy39I!$xA6EdN*MW=~
zq-s29)Th|YY!m^8hY9(Qu0;SWr~d@-!n4p|NvYW)e~`pm7^5U-UW(^kh+Z8m9qUo7
zFU$B$zfKpIs1Y-g@6>!Sk$e+zjE}pKM;&`PVIrslPl5h5G2X~rr6C+V3n)awgpXum
z#gHC_qPm9~DH<!HesTyKnrl1J>o2~ZCjMa35&2j+UZesnqI6Zv@pOpb(h6v}@bk{C
zNCXEzy+#`+>zveZ*3TJ-Q-aSVB_Nn8p{_Ear2_J8HM$!Yzh)s}0v%e4`jiypN7X$q
z<>!XC5nn*xQnow}3u#ylA|5-7C^wo3t_l^Aj3&eOL|e(CVejTeaUs8}naRpYdZArF
zxWP!b9D5ZG)!-o*wr-B%46c^}t<tRcz${4qvDb^w>f?Ri`s5=Y*zKXL#<0w-YjM|m
zkzovnFYlC;xz)?{TD15^k8V`4Ls-ZVG<MPNlaDDW*6f^WmyyZhw^#yELWh9S2%>AR
zb6>uC8BK+u!LBjvyW0N9=-wByCaZ<{_a6?i1C`Wk?}SOhXmLcDw2Z6OiOp@7n%&mM
z+y=v@1^JFDg^9fDE)&9}ibp&WO+cq19^zpHt0#MB^cez`X<0|UZs4&Sbj@%ch$%_w
zq^qqfKf;mz?HWF-kc{)DuYa${!ft59?;0!`Fk)47U25)PjO&S^|Ieo+s&8Ke)QkoA
ztzZ_4tS-QUQN=ei0j@!>)lrp{P9)ek3i(Vtg^0M@J~0rYa{{+CB7sl5N?ny;R*-an
zz}o*=%$Q{0N6C2j3Nc5ja4FV9ww9w_V#A%_8r-Oy;V^8>b|tVuvsY!dgvc2P&B-ZQ
z5D7jV`d}rmLln*XnV?A<(P?pDKVx3ionFIImo(wXR6FM*GBMUI+hN?-m)<wkc*(=^
zrs}ti8w}=vU&;iQhaUKaxwA+&FUW4pWr$<c_1vBXaKsu4@bNi(05GHffSZp^NhLzh
zA}q}qu{D4tr{LD{Vr%%$$n=VGPzV*CG0BHyl6!xIr10MUfJLXVLDlq!QQ{If5hb>-
z&v|weWVZ>0)TZ@)_{BxrQ9bl>tA1|tM|X(b9oz=V_fjdq(mgu_pHW5mnGqde*}M=g
z5XOtGIf)Cw=C>^LBG<77*Ziu0^`mfa@iT@<laaL74u`V6&Hjh_J=ilA4j2lrA_3wh
zD4K4y?A^q-w%_r+y4%s4`1QD4#d7$cn|O-W;MS1^b`(}3c3pvOl*jFH14TuyPBI_(
zf==3{gP0@68tb=bn!kf`2l8_hr{Pm1&$LoR7M}SkVkl-BQ$1MMzCL0EXT5bLSo0-p
z5AEPV2*XL8UZ5}?XV^UZ5Yo*~o`RPe&Ebl&QWrfeK~xdkIE8wi0!Q5>*8VF2J)DYc
z!}W3v+XbK48+Q%cEmS{b`og`g90x9xQ=qq_7*o6*na-p+W4u@ROJyMBly4vGZM-Gk
z+0wqN*=%js)}39xA0oJG>!@mP6xG>oQc(imLL9wjxIoIYQU&y5Laq1OcgV!{G%~V<
zOKCv!OMUGCs~v|3fhzHGsF&}=IS3Ao)b17<Rkiru8fpkFQ<2SW)px_G)e;nGb~MOe
zuB_IgG<`NXc`G+$3xK!9UjZOVyeGG$gpOk+6nKx8T-JcXeriTg`etB&Avf&xRwMgr
z$X0Jd&^dnEQhA$JV;47Fv3S*iyH%;xJe#^Jr9Iae=>#y_v0i_8dMWyq1HqQ7RT$Rj
z=d@ldTa1BW@#;AylBpadMQz+JtM>^PiTY^NO3pj$$7I^?ji0jp+(cpPXrbP``<emT
z5?%GfB@mt}4l2F{S%DYFx1ge~`N4$ye~ZdO71%2TD|&4ROhQ~>p`%Vg5;gsZiuPuo
zQ>;BiUfO5>Q#z*bt$(aKT<H52fuOZgEKbi6@5EI<X=?npd*OFRIfMds7iOJr;9(q~
zK=zRRS=`@SJ)l8=udr&ZZPGs)m?&PsyzSRbulHsDTT1`qm;<IhoI)^r_#cY@JithW
zU3quXTCMi?D?%V57z8DvSolA5{H7^H4tAx=O<$Ao{|^80A{r3c01adRUuxg9u*hhp
zxuW!MT!iIIU^F3AB7$B1*)#%)gVo3^m(;(9{exT~5hzFlE}-e3<F1l|)dOA~Fj|QH
zgWN1w3Ahy4`4~3*-_3XCvErY4kx)zZw<|!bF^nw0cfjgjmB9Zt>Ihk4WdWjwZw9pf
zK1+WU)&IYzDI&$|e|RS(iS$`Ro9t$5d?09`<Ym44T)P=%i`uENcX8|f?2AmZfrl%p
zNo005&X_-^=`a(<%7@bA|8zc5fZ?@%m1UCL!xM7Wy+WXDA{fpo{&ciKs?Cw0%?;r|
zs0>2-&3G7AqK7sGhKK%l7AQ#IgElt3JobCg3$gL%we8%0b$G4TKd*T6$k-}*7@PmM
zeS!uf5FRVCAeB}g7hzdTPZ~%Pc=16Dmc@Z}AEv=GVjUn4ivD9pU|p1-0Z&L7*#Fa5
z1P%~t$@lh{eU)a$mTZig@u?poaTV24c=47?^=H8b`T!wc_JeC~M_$3KgSmq0x@Nk(
zpve{qCz+vaQ|<PpIJ`Js#DLuB6v?lCYh9Va>vf3_T_MeWzO!DOn!os*){Jzms{8qD
z`dHlh_H8M=r?=w>Hs(#Oex;_o;^sBEA6sR)8sGrJze*sL2on3KxsH7Esj#iaCwg!r
zMTd`qj#DlYe>F1y>z8!;5=(P>$x)JwB*7M=5B&x(|3L64RUw2h^<Z^i)WrN##zG*V
z$i$%K=BwR_9p!I^{WH&s0bgEQwt4KfF4DP_OcAH>p57#R3(}Q|3|lkKpU-_!k13$Y
zH85RL<UHzKCnk4)c+-9BI?msL+s>1|-+G}on?4dA6jg82&$%Op*?O^<@V=I_%l<eI
z(3`x(nBiKq1R2k}{p!QMuWNsn>_;Wn{LnONsrR6{UDbalL)N@+e8z+`x@qhA{yL4f
zU{r0r%=zX*-^Wg-fw+D_d;>oR4`G{-E$Fu<gs_4feWR*~2X_7xe4$fJQ**29U&YJP
zXE*tpbtO)&j*Gd%cf#NG`0P9KVx_p<i;l-^mTn`vwm&fBue#igpRp;!zxv#h_pBiD
zKv2)2D7cAGN~#7C{S9p<3IBp+ZE*uBk2dfuJXwtTYoDvXo*-=-{kUlws{zY*j?U7N
zP8N@Xs(btreVZz$fj1erVeJRg<#;<Tj^3*Y?|Q?v_V^ukv@7_Y@RNrzvi<HO41tG9
zl|-km0pVY5R^CV)+NlQ~yGywy(IB8@8`0U#NJiZ>=`BXEb(-h;L_Zf;mYh`QV&&#(
zM!8^%^Ky!eggz~mOtnnd4NlTj{G0tHwmUq`P=)Z}>K030P~~&tvksdpq2+R3`>~x$
zAJ5aV_tfHpyX9u7b($5EpJKSL2LsjH8MMwgyiX^c6s&J?P#*Sqob1i}g+7XGfhzW9
z8r?JJbIP@XmY3>orVpCka>~z#7w0PoxmX?5O-3H=+E_TeDR5uxvYF#g&(qBd3@_Wb
zuk&^(TEh@>E!Gz;7hHSw6TOejb}?`FS!qMpX5>ppnc--3FB)o04Dl8AGn1&=elt5$
z?OC;wE-TG+_Pn^KmF^IQ&dT%xI$EkH!=l3w7xN>bh-1~0QAugFDQ0wC{&P^wiiT4{
z3Y+8V#nT3SRic!*n|!mHAF6m!Bo1%dAbaIYbrRxizg;J*ILr+6TGN;OF5<yPtt65)
zwRC+m)wb+oEGWIFdIvc#pf*`lk(DE3(X810W=c41L$a3bG&MIOKxa2izDTjo^*OLc
zrADIG%$Sh86gq3#>^dX)<9z#wTCS{&YTiFV?>2La5yE2o{vDi76jvfCubPt@i65b+
z9Ci*%(SC)kLn^;1J?gg|Rf_2<kLp&nNLcv=Ht~>9p+iz%NGSTQ@LzTZg9oJGc^uG3
z(&f&XF-mnW+eOGNN!{#zvEx;^C@#}r$YUB{kz&CjhG!g!cjQKR)pZg?Uc_B_zg5U3
z*Mbzo-I(u)0;&lb>J3n((i{`Sk0PjnOgj&8BIs}R<n~fMa6Y+MW1lr@wC%GU-Wag3
z$XGm{oxgFZo3Tt0S)C1xV>iz1t<{@regC!J{wxPK5^aWm{#yt`HO1bP$nW-2Axn&v
z+!wF*sV#n6Sr|jdB@8xKKC+DR=#I1$o_CtL8H`ZKkp>Ki(HOC)y`CV!Z9*^9MK<Uj
zBI6+jT^jxBKTfH>_X=~#m>GvyyzvaV%@iY~#X0*r)L%%v!@92yUa5VuXlzxqOruiR
z6Ip3F!KLqp{zadJbb-r7L*6<w{%zslS?3oysuC7YwO5>BB^;XCbs6+0?qWm!@6X+#
zzdOD#Hel`|_ZIPY-($<0_V-p!ufEh$@G4x-5x-yM<Oe4YyVrOK6}&8)Y?q04jM(x5
zVTaSnGkrYmd-7Bycj@B0S6j=qUa3JIUWrfUJ;dey@CqM2vw|#kRrFmfDm9D4VJV%U
z7gi3De{hogOT7Ehz>k6c4vP+)!KVIJgm9*;F;gb_62w|Bl1GZ0NBAF3)?%zJDjV+(
z=B9-2?r$ds1K;*4B}a8JK%b;*SGe{URmq4q@b~j`&6M*~|50&f6@rN_qBT_sOpq}I
zK))uE8o50CntYy>Ofgu0sGYJc&tAUMaTQMn3(bCiH7#&6Tiux0=%IdpzEpBBEWJ%#
zkscEt6PM`l<*0PrfJo(ARq_Yf6~aF0ej;rS=dYop8mQZIq0?4;Uog##pMG5b$X3sK
z=obVCT0QORdb08(VyLQh{KpzFrNkhO1!BOOxT7AI72NbvaAZ_kzF%Rmy;FwP-%j}f
zOK`*h>$hhi1*LDsg`}HT(LS073?k6T&JKL>@>nIBcez^0`YFSyCcL1@Cc#_Kw2m#B
zal3FLE*kDdS!2cQT%NHYw+V}L)jnoa@sU91p<l03>GNje<&<8vx|-g!F9hU;r?+G6
zd#%(b3!A%~PtHRTK2%=E7>6+o32d0F6rtgTyZ20JUAP*Pr;@bjSlBf=cq~S^!>v_a
zvXB(N_j`)|E7(nQf1o|2*)st4EfG^}v41#_Cop$-WSgWZ0W0UMVAuv&1jer5BsF}-
zG<8v<i|nJdogZQzCfd`B{^@#lB-niSq-3$hJZ7ex#0MAepvQCk(NB66UI@SGY`M~y
zs%mS#NU~vmz*AG=Nvd3b*!C|7Kl3JkxXcV8jb|^SFVX+H`XO)yA+nh(o~(yS1?)QK
zn*A<2&TdQcZ1&8mz#xDX`C=p~Qv@(SzEeY$b+woD@fk#K;Y&lS9N)W)Vrta{^XkqB
z*}b)`rke{PxM^*z6}7vQI<+D*qsx=H0z(Gc@Wt~xTxLr_%_Z@vz>g(9Uv_GVGd)W`
zE_%k|JT6jTm4Ln+V|9_yq=ZpChGA<s#!MWTZAd()Q>I4X>tvPdC*nc5xdaDN406$P
zG=ZU=>3-ehy&W5ihl3|cw?fOt6C_G3Ys4pQN9}V@SSqHN^&Z4xS&={*rMuxM-nJ`U
zV(;+G%F`h7J)b8sNpEDkgF7BHb+#r}bIEQ^%UIgc2m6U9xYSix_Ph;`KkJu!!}%Um
zxMG$(>9W+GT+7(x;b%qi4_5!R$l34!P}oRIO^m{IuS=)zN|6dDztJ|fx3`iR%-TzP
zU+1Z*x3-o|t+%wAac~WDQdd8pE?IriREou^Av}5A#i~t<?RzA4=i}ZVtKV|hdz7;C
za52Faap}aZYmZ5b^KLspDn;dwxTER~6mMmwKDrd)w=)w;f;WZV$C9%lXCYpkObA8G
z_4IL_)rGr3?|zB6-}-rD;~dWV$!3Fo=7kd~qIg7)HRg_s&^ff}Wz)RMU0BT~>Mw#*
zM*Js<ghBKl(qnnb^1P^a#jL&?jH2lBc%EKt>c&Fs6{;4-=8(_Avpd@~9jDm!>qU~?
zZu0V6GXj(KnVaq1wKorKg096-c|a_YHL`qFKK<zqFWHC}qQ)Qzxpskf8J7!XDszeF
z3H?R@vbhT;je!0VOn-!r0oSB3mv}Q+k$asG|JV!`!Vlu%Zi!D!Op&F{9S>0unJ<ti
zEa`wMyw&g==%A|#Zhs(}nzBoac=!x?{@%D?z9K?94cqoca1un4uMevESYs%*U8WNL
z%aMl#_0m!WH=;e6l&Alj*|7=dvrfs|Uq9O-PgxKiU?4Chx1|-O#8T5r&Pir+WiPGu
z)33>dT&XWVhdyDtA@qJhOr922<M@^|Jw*j1$uPt_mxYtk(NeLhnwR*o*>$`7Q3!k8
zmWLJfQdY#PdNyJ<J8nL{ffmihBMC5{*)k|NS3#y8slg{^*Oq1_z<lY*eHh^21F4y{
zJPhhEk&;5v&C0#g9zKRGg$M`-Oxe^+K6&72cIhygLwTL!&`ME*;d8HZQ)^WbDpgaS
z>Y6UN-IdmB$${SA(I}hlnP+H8prZJriN<Z4@bV;vb}Ehg`7*O86?QW3waHmWW;CB$
z$RDm77WgqO%6$*~Gw@qWZy&FbnBMa^NasHQbbs?z3H})!;zCs__*<Hw!mw!2w}axZ
z2wjK++tvL}#b(b|fi=)d_yK9T;j)Qp=&wa47%=B`CHFhzmZULQY!pjMF(wjN80~D(
z(sJzY|0%auJ<n9K{3?>zgoI_KIkZXIfcb?}eBxTsONMd2_vY&TBg6;XUUOeO>ej#Y
zf75PtUFwz<0^MWu$&F4v+Y0*mH1n0|T<3WBQ18i8zcV`R0?I#Z;s1mNzB807=2m4b
zyD!zP$^--juZ{;NTaV<HooY%oRW1hgw^Wp6<LE?UXh%}s(|<z;bq`^b9kk3}9(F|?
z9|z>+o!WTuUiA{grLI)&7YbG#EQV8UqafQa>ufh!>P17eHjDG8c}Kr6yP1>lFxmB@
zRxl7s!Sb^#HZu!^{>Dc6pDR-4%N#!bMoN+tWUxHu*DhUSQdszx69IjHW?rO^Gv~G$
z;WSCRoNseI>O(~CK9)WMG4s06z2&5#AwWczP2->E^N4a=6E*Q_*@)!QQfuC%XS5g{
zfS6sblN&(g9!6Zg4e6>`tiOw<)px3`$`g&84&wigGeyh2+$!(_?O8mi{;K~$5s(>8
z7=0rKU<4G7ZSCSehoyyKmXrG#EF>@F%9w(Mkg%TaO?5r9%Sm$n3JVhM%7dEGe%GYo
z@2B75?5Dpt6k1KoPtMq}iDR>%6Q(&%seV@wbW&3r5Q%#CHRY(zQWNz3P1SrAEtD?+
z+G?{L&+Nspah-3TH@|n=MNW~Kn4~w*{BYm>vF2MYFyMtv+v4S=U=z={-A+88(PI74
z9$Gpw_0wltj)a0Y4Q{uWQ3OH%&9P7@!u*?W?7G{dOCHk&p*Kw@1Q@!gI+(j33r4Mf
z<%Q^!Uwa%3dml6CLLd@(Skh^{PkllvNqJ_DcS>H23RaNF9yUXE)Z0>Eoi~j%zo4sg
z<agj5{GW|P#1?HQ>7Nfgxz14Zx8hZ~T++^*qH-nf`1&QJzs67_;k0|(|IcF1Oqf`E
zt*yR!#0p?$;7!##IR(D#hJw4X?Ca%w+LNUljw6EayWC3F%XQ1GK5bSH0-ii2#T;gQ
zE~%Mry_!lf&8LWyeK9*qC#PoLqXo^Q?RbbEu9M(XIk&3=hnZW7Xhmj}lqex-g$i7J
zhg`!->xZlT;dmBQe-yDEIUodzd4yG1`=G%`h++aSTX1^dU9mCD)%{kv`gkM=k(-ik
z#*&KG?%q>Y1K})OHv;)pe0-kQnFSjwh~Rqu)+o5<v%6$aq+)|}Q=h14V@j&Fo(Gzb
zZHfF{FBev!9QM&CE+4(+LWR2u?+xdV*7GpQ1Z&l81mbs>PmgXEW=wR`>A8O@1jx6p
zio3c~=MNeNM-s((JkxCk><=I7peprRPs9#7iC={GH@d0p&ea~%Kf3KdHw+xmb=Hqg
z**|9ZmJSe^blfm%=>Gf+2lX!Sx@Sfg^V8_?@MRA(`+f^ohY=R5Tr~gp!xgw4hOw>!
zB<yblqqfHr`CdtanJs&>KT@qH-aDlbO?&SZp;HGWpmlQYR`~Rgj8lz_Rb-mox*e;J
zoa4$i9}2r96v|eWx)0i|1y~IxCaN-45n)pu1@p{3C4nL|T{W0sNA&*KtzdTwT4%H%
z`_EDx3Sb*7?{^a!_Iu40g%Nxulj5(Ztv2(`ntGJ$No^A*M#(|wGB=y)Y*^<@jhT0-
zp<<}w2qt$&3fE~Qdqme43XQkNrykz1S2xRpr$~tY$-1)~5YgVJ2LrliYQ4-pW+bmr
zktix_$bC9JI}k`i=Y^ARp6^EcbcbGdb_zrbnA6jb(QNgWLskO0oF?NG)E18sZUio_
zrDjOz6dLDbhrf7v5br;vhdAE6U4CdP&X>`iF2!WM{ZGb+!j}Ro3&jz`knMLu5gY)x
zO)F`0O#OTp#<X%0A?PwQWd<@C+^H+ot~0v7<_gNmDR{Ug{<``DHLhBKm)P*;-s{WV
z&7w)@u#x%oblb?Uv~XhHkqz6G(@p%j!a?b)wX)td$j6~F--lb1^%cq>KjE+2>}&#O
zyARBE_klBIH%HN8X4x$@WbR<r5q8|#<*P5U3?Qj+yxmw89l6LC70t>wEeD?@B6G#x
zG@>|Jk+8Cz+%I$8-(kK!!-uXs73N<r6l6yyjWw{W^DTMJ0xO;WB~L(D_7ELFr10nf
ze6z4B=Q(%q8?=`^b4x4?><mzcr=C4~qv4!Tz`q39eje#zzTu!fvDSkW1`u~#OKbRv
z?tE)Q-xn-KbVGWgL>x)g8<Q~}v#$dVzuUnYM)UE6pOnrFcX-Hj+(;n2xD|ER-(@+y
zh?T)&ZY<h3!;O3@$b=^(&UVw`Kc#<V{~hk>fYN|D?f<M}6av6(1{}0k<x$)zX5d-y
z>P{e%0xv(@cahUFYeMF02PIO#uYY9t$=C%1WjfE*wWfbI0ESK9-k!)kSl7v$-0rAf
zx4!<aaBs1vZ<)+LUu~}HHyFs#ODQt6-lzk3ExgkQ`A^PN6cd&Orf<|_dJgL^x5Q#W
zB}qO%dr)^7jjj^5@tZPUY?!p*kHgb5Uaot(ZmeS6NQmU9`7zn1fjYk{TRt`7s(eVL
z@Qe4MZ?cNka$SYlL|#;Px=8YEgM%nY?HwBq{w^w_oTrNmr78Qt4QX?()5niy`d67h
z@~3x4uGr^gqIpL%a0#`hZA`s4%`n9gSTWW4#o2h%H6JdxbgP|P*7gVCdKUlsEr3Md
z?f+&&g<#3vMEXBE|MjQ=<OY+MszJ?s4>AC&k4`=}p6VJH_4m_lJKXAp{(G`%0xib_
zjA@1PluI1e&9VzIrQsiHJ|VS!Eimk2J7{YQr&$b<Pva~ZeHTp_j20~M**&GET6v#V
z--Q&9!`kb?tJ@&4baP|y=B3B?_q9a!4)2K&|Lb#Li-;bZwLiRmWULSdxSlDoSAtC5
z*5lr}Vf*AnIdN&lt$y{XPi6B}L4<-%CBQ*vc5ncT1RZm``g6St|0@y0Yz-H6{)y&2
zLe%bB>je#`!55!gJT=KWu{zK+XpkoDr=~(BW#@FNRv<2y3xT4|m!E&lu9w;<n9b*N
zT6Fa>Vb4dCNVV=f-@QI7Ps9_YGH|oNMO{Dd+UNXmrm0yFlWPR|p8-=Cz?>v7cRln`
zFEA*81eWPjQzO^zXP)y>zcScgl^|jC{^%zHqV~)j{uHchJ}*wGK5Mx+EbJ9hR@3!}
zB%<#0($_ZJTh@<s`TqSCvo<Xx%O;(Zb4Q86>wTU{1mCyAcDOHc#2e+&LW@s*vR=;}
z77F$guv_*$<)e4`-LC%|fKm8DVb=0VL=@d)g+eF`o+)u)Fn+b^*X&kfYP!?Bn#TJo
zh@y+aX-w<3;Da3}XDEEZ(fV*4UERSYcW`h{W;@+iqI-{pyWrwmTfOl;-|caIy6;&@
zNGmc<zf^7x8Y{sY$($7F`o(&!<js7rUeMPt!hcF0`aJsNt@j|(rO{+4@}ye-+RPWL
zI73V*TEo%9{oL(d4djc_@Ho_k)MSLC?b45r|7=h{#t<IWACb`B9;5Qt(l2vsXL7dG
zVQktJ9~0g5yLO<9EcjJ}fin2mIMEv9b9+d0PZK_0$fNM;Gw<l2B%)+i6MV7Of<^LR
z1zvn5M%UtS@NaRZsD}xU|6p9hW7PsCJVy7c(aHYO#&20|teaNil@zmK{Q;_NEc3?q
z<zC0dJG|B|YHwF)CK2$BmOL`KiC-<j@X}lR9q_B$Uk_MX+C8myKZ?3%YkuYDH%6ec
zCOGbpy3jD|`Q@tWUpAAff8AQx+Y|74cmj&5F|la9=d{Z)J2l1ZYkcsYZdeeFxcqFr
zsQhq}S;7h?{u<GLz5LMg<9mwh-p+(FEK!4v1F9UqGh3AMq^e`Mn`{-RQH1x4ea#-~
z0J;>nx>@S>@pMNfxv#qCh-cA3-O|VSxs0rq2~XwwxVUNoA<-9R)keTHw8ai=yUNOq
z+CJ&>NoPrI!VYs6dmYFkgo4+0UHT6b0u|M>mh|+dqlXJT;@71DY}JhXW{b@YXX!3R
zQp#;>uO5hGq>sNh(wUsMbg-qJObn)QWRx&c0&$$yyPjGoH?F%JSbHD!eCBNnEOsM%
zFB<{|pE2e!3y3)48WWGg&v~eZO=btoH)_d`ka1IG_*U-2G@(UaXnFUU0r0o&T>@{N
zUU$P5TxGfq!~?)E_+Nd0`tt{|_1;ZqxKxrZo)G#D!^_mN`}^g7g7ujysgs|Biv|cx
z<erLNyZEeiY92vbVAqv5pB_>(J+We!?AAmpUw-xU#D<EY`@uI}91#a8-CY~^<idW-
zq0RVmK&o(yZ1eY0Mo9{m$0AH`q{(lIs6#RsraVb|%`KOdymezFVfJYUWzW7bc*4zE
zgNu7zLhv}^f(S0jY(8U=C$7KI+g}#I@UpYaVwxw4H125I#akxGgUt3d3G6={FSL!9
zYh{LC+-WcOKJOqDywhA%@S$3>O65{tJZ;E(CKH>e^HLnYWSbD33iwGR!1rayYj#Gg
ztuR2VrM}w{1w6~o?j2;zb(k6Me1w&#AKZ{0HOUrRGL0SI=f1M&W_<CUW>+l*23M`G
zZ>ZDdS&7cv+^A@ess|^EOCF)&JJ^B`6GY?q{rK0-DbZxL)^nzdpOHqUG&Jfbm0ASu
z%A1s}>oH@bQ1BrQ227jr26gZ7QFv>cZ`tlq@2)@6%Cex7K}dMIIaWblJU^f92UG_0
zLOOp|jM8WQstcxZYkYt|eBZTPa4hb5$IbBhVd1g*_J5Tu086sre6GOfRyUms#X)B~
z;+G9DqFJux>Lirig!6XQhZTd1-l^!W<6^PEGFnbwBiU|L!QduAA}fH>(Za{Et~hQL
zWpN+fio^Kfr_^0v3>*I=VpWnBBJdS^kcn6G?Rl)TIm2wtxc3uH?>|^%TY+oD)&M7d
zQTQ{6Ff|VE<^QAWEyJn`x3*DOEESOMmPWceq@=sM8|m)uP(V7Rk#6ZO>F$t{?#?s8
zz2Emc=ey1yuEl~m=M&?($31e|r}33Cr|R9XMrD5U+=@>z>h*)V=Q(qcHfnE5io_xD
zMn!wJ64Sj_no!l*RTrb-NIT!NOv-3<yR|n}j&~ogvGH0IzAQ$85mAfm%6)cVP-8-T
zc@&|a88Kk1NxMWC1JUA8RFJxlM|&Ynfa6u8B`OWZs?(_YX=6FqikaGU#iP8OrGxM7
zbPB*&640sP0^U)KWIzQls~E<znT{5B3~*jvaVxaiMi?LB?Dt01(Q4uu8wV2!DOfiS
zFf$qgM<qMP*S5hX6@d#UVw4GRLv(`xPNDWIq67+nGdLuM(WIECxJ+0~<H@<oyCEs{
zqR7lArO2<-rp5zeJ|JwD<-;%5A`+8Hj8D1O%+d?&$Br|zB$afW^VgKStGCt*&z{O<
z?VH?{9I%ScXW2bBU33YU!I0`M){GQBGNw4M6Mj`DCj!2pxp#O3uh!}bGQ;L(zLrb+
z>^>R2&N}N;bBvn#ZnHT^EDK@v(yNh=gap#Z&st4~V@%PF;J<zf2pCtQb|>E!etoq6
z{p!DgwgVtjF}lU$H_rbZUUmfn*$4lhs`-EPz~C!@d<V;lGp~M>|D_B7y=#9D1n24H
zu>SA3IFbjT5)6+sszm;WxBkxu9l$f-;n(@`f9L(O<1d>&M*?iR$MttsU;&`vA*(rA
zZkcAsP}f@C^BU>^zzaMQ*sYf`SEVI#jDI0%LR*l#gTWfbxzvB}=ZEzoJ3{Pn$^b=%
zCWG|S(D+zwx&l0ZTp;W0B8-`0@W5Hq5iK$ApTV#r)jsEz=<#oSD=<5Hp93jMr}rKi
z3`r7v=SvL#e(qjLFQif{&f7Xv%`7f26)2M4?ruob(NSXh_|u}j^IvWP=@@8;9`a?;
zZzO$1^nAoWD{u)puZmG245IXa5sv1Grs((ds_Twc>KMbRyRu(efABZI1pEQ7iaYR|
zV<tpoJ77uF<0ok<Au*(0&d>j$F_)AaoGI13K3x23%hBnktwYTNrjkvUqgS%4(ponD
zkF$jedh87sl{M;naexd7fc4}ZS=qArWh|+Avq^S(`?G5<<=VB5uQU)hR1_7@Uvlfk
zR+pBR7H!&iBQgKxbqZvewXdP(iEhQi-XVU|{}0c~4gyxXW{ENZXu?A14;{*w7aTa3
zjIkdl%STB^M@LB+M)-SN<@@1cy=0e-v9Yn6o7?l#V@@dwO*uU%Aowd+m5r+M7B;Db
zj5t2CT}t^B&%aJUNHKtLket<3$i1vNk~3&9k-qKzsHw|)ey$;_Lr;!6XL5H+JJ`_I
zcRuZx>n`oIDK*WoG{f`WC7vh-luNuaAT6QXAW!GMWm?mq7e?J4*M3k3k280UWcWbJ
z;QioQ<ad5{29)~${Tn8Qp$)EbIAgeFp0;sZW=%+Vks?w^4PP?Y*NGCA!SI8+ka2K9
zcJRbwzk#Z4?+x75b~rUkN=l&+1b7zQ49sybl}x-Loms);e7Vty?~g9{w{<zhcixq@
zFH=|(_eHdpC69bH$vDU$cHfgQu-dlQf8ykHTkj5o%p5@_N#l3gN_Nrl&_O%9`SB<X
zf4PxA6ner`?fOsdaDbrre{({*S^ZM28;geF9>ld2p$pIG5-owc_OG9wZmNt25%9Ut
z<Op~uvtin=iW81co|a!~Enba7c>q2*{v!qapg$ypEVkz6<~MZMsH$A{oBbglyw$X|
zy?_A$Wu-Z_wXEbndn6o@Di*)sbHl)h4^aO9-pIG-Tb3Uuk%~*$2Od|s48V6g7eHv<
zEv46ASZSec{~mT)JNTbn^Z!1aoe~f@YLV{{_LXxU4AjKbXCM^8nCR#O+HVa4_yyWx
zlQC(B2I!@vN3q!5dgsI^4Rdt<IrF>GA!Yp0RqIpZUz3G=U~Co4e8kfw*@0<PRaLck
zT$7WLNoVr$va((-AwPZK1_wvtMYPQoAzHphW=}<dm3TVhw0yOjpODvb$DZsgWP?8Y
zV$y0j0(~JmABrb;8=dG-MUf#>hr=gQq_#g&F-J(en%RT^qnAYcPXiq@n9z=PEiCcD
zya+ETa1?e$1%j=Nj0~nY7Jd&H58*x-akUF1CX>iqo@KVT^hSNYd0gI8NZk>DGoXVD
zBwprqdM%(zfwBUap%m8ls0RAJ)NkM3d&p?z15IDt?{*9J_xI)Rfs#vIhhbK`Frox%
z_+5|9r3q0}nS|qoX8n=8#6J5V_1C^Mp`Tw8UoeiT_FofUI!M~Ze>@sB81^Cj@Q!(E
z_k)U$kN3{#HyRgQyZHlUArAyf7nBiS67OFQTII{JyPB!cd;N_P3~-B2F4=i`pQYah
zR5T9S!XfpK3@BR0Oaol%f00EFLbS)qfaqm^0kcF;kj7QOkinKdk;I?=lk=Cp&2~V>
zF0j6?d7$f!2S*dwFgQoz<8oRX_+p>3{DbuslCe{~;})iq-~W+Qe&0C3`&MxPFX~s^
z_sg`K7+_|A;!6h1n&S%|94D~C<V1Pf;eH>&Q8f!YJPschFEjPt&vwuYWI_O&bI$!L
z@1$$=kTS4`sY(Ki+uZP9MOXoiVRw@RBd`4iBje?euctxW7i>JdZ{K?b+iPe&1v3u8
z#DoOrW0w5aP5C!K=$9-xNOr%^uUcq_2w2sezdDt<|Aq_v)Bt#p2JsTbKP@f&GW_kX
zod5YVvLqmG1~%~TU-1p-`VuE7deovn@K0d@KO4z`P9dzg1pl1&J1Gz>w(9EGm?C>A
zNMHY>oFQO@@c`Np+C)Z!^fF7~_mEPs((rh+>=9f4<Jf`#^sP7izuST+fMG(J_A&oE
zdBB&QF9}o!{cZv;vkD~wrJ->JTay?6H&>xj7WnhkF{7o}i#QOG0hbGfCno<}RN#r=
z7+=OvH^zTCc!2Qw!c;QgVz7bN<M`8N?;IabX({+Xfr?Ij8+e}&0CUcPU*OI+J2KWk
z60%a2`-L75BEXD+@Iu(rm0uRuZw(bVcO9lUWSrKN&t_X0ri5Na-Z`7mPUT6zN;L;(
z|6pv0xExEp?u1_`DgS$0;S~&waIn8{R@u0`_W~7Dv1P?ON>vk7FEG<&6n4=O!RUHt
z_gFkZoFKh!Ynt=g7;<z?TF@WW9i2HCipx|<68+reoQy=#9UU{hQ})W|X7R_rS3H{A
zuj1138E7z3-+$gniX;dUyjD03MzX6hj-nUR4rm%PE+`d*3lW1cR4_AJTVFSTgNtSp
zqp`V$=EoF3{(~p6dgK>THzjz~`36Vls1rxZWyh>3goYka;S_*uq}$qtfV0zmMeg!R
zckfM-h4W(LI5vqEY;4xHY$`cYX=T!Ml`Z28u$lxCJM0y9nvPq!Pu9<d%m@jm=nwtI
zZOi@TMCPs%jo^@42;@4U-w`RAyk={(0FeHRz3@EcB{pwdprOBt>Lzr3HN1|<!;+Q5
zpz7!oN`T}^{nO&`TgO>33M_o&X?q1!7YP@vd}Y5kGLm(r^<sGlJIzD3>`Y>Yb?6;Y
zhrt=e+DVC_Y9s=y(uYFsh|z#cW$nDMhZ}utuaJDxoHWTh#M$o{AG_0gFx!1-Ql$Px
zTU#W34>wk}MvLS4$DqY7C3kUI@)=W*St>-{zSD+sP}sqGJgQNBkD{97!?>fWIH~Nh
zT&-_Toa2az9^-T>dca%Z;-$2&<CZG-ULBbp=hx~|yw#+^II;%HOJN0JBlH*<Q{xe)
zq$FqsXkg|3w{xxxre;8|-h)S~<L1dRouQoskY|3|aa$a?=8xoQnbVZzS>c&#KAB39
z<8p{TgV42KfBx{-PKSs)u4gOxo?TgNB#-$#6Bba2X;F}X$BtiT*Bu&EKJ}lh7$v}s
z8XdmaEg0)d4^nu<z$6u%zLEHCNScMzUjJqlTR2b*s_RW-NeNt>AoZ*f0|s<E%uF?o
z8u_~zuJpe#SYgQM7aGZJhqqIfo?nFBXGSK^KH#z%(*oykJrLkcX-j4*%qB2mm+wbS
zWgO6}>p6|kyIe%1;@-kXVo&*d<4eK9LuzU4v0>RqV1qh`irwEt5Oox04WcvG9w;Fb
z9sF5armV9vRlbEB?Z=AnbE(%L(ZBsFZrP?G{i19QURp+#tf<dWw?f-4*?2A=XU(YG
z2@aCw1SGWpD;4U-R4hh9X!16?M&V68kKmlpnK|B%AKrf`@Rlq;>sg;1&2R{c>Jh1v
zzMut=9{i>vGb<?)OdR8D@Rax0fpjIyj56*d&4vCe8i<5}r6LK9OT(-pjdU%*7wh?e
zM4*JA^I)b@gLNhX*uIsQXx}2fsh43mzgL`xvFe{r97S|P<4zfV&j>+%u!u6DZ$v}{
zCl<$n3#%071s5rY)GWfiF-v^ZhbFU!DVBp(N}X@Ojg|l%)g_%aO9Hs?eFqR4?AD73
ziK7-va*;WN0fprl+AbnkXUB@6q&Pp9dfQNJqx3LULk)@qp!t8&Bx8P&5GIuUxMe@G
z_Uxxhi{11l2?Q#X(URi?Lk?yb4PQb3pGpP-9g^X@FMvu|2NO8;UL$KGcdYUe-Qe&a
z$cho30s2Pti5KWV*Uk;e2%)BS*j%7T10#$Ds2+TM_Q0Nhm<}XlzZfqr^=atQ*dPN4
zhS{g6WLz8y^gp>{cJ?{y(*JpAs1yJfF>bnQR4-pZvqO$26LYBux?2HvQ)nJa1B3k>
z<K|0DnZN43d-;zsl(jf{$-w)6y5<M@3usFx-Col{Y72HAcJ(ds8089t=m|bg)s#o!
zePS-(Y0hgjX&(zQrTt~RQ+S?#kq)8yxID!vJFMGW_}pHmfKia|qrX!qc@NL94=={d
zTYplgZ`gY^uuH}J;uR4iWP`>s%)$9@R)r&Sd+r!O(EHZgk-Eke?3<Ro0R{<loJvW-
zY0=5d%+!^W`xXbZwBfG;nu^TK%w+pxV`Brn`7(w>gAlATf~NR;=V2U3Gqs)mv$t&_
zP41rFN?M%Dkn@qAw|v@!vY47%$E$gKp-?<nJ6D+Rk?B4!Wzs^^LWVtUMYVEt*S<Wo
z%o;lkTgX0mvtWxNRe=g;G_B;5Tgi6P;FiK<zpb6hz*yQ3^#OGi4@+akt>`#z8s`We
z95p==opE$BA={(9svOpt8Qix~Ns43Tx)yf@=oDV2NhVC_xw!}uqZjEzxwDvgxkct*
zWcmiS$+4Mf>*YwXGSizHACe*yA+bVynB7!@IguIFx4U!Tom^y-!cXGK0@^Nj7ZfE_
z&d~lD5o|9fpx4Xj1pved?_Q|Je-+8Y1VA}n%7F^iYiktqrILY)*^3Gsm{Oq7J*8B$
z{%5u&&^1F<+iAK#hGhEtDN@Fi%|uTZ25D-n{Jg4ja|v>L(e@NB`I1_iGL5{HbdpJ>
zdV-a@bJbH|q%a{f<#|M$&0*YxXcUjU%X)k|{cPPY5A1HXQlo{>LiB97Lw|{Ti6Q<x
zPF!J@BJ4MaT|YO1m!}QOu~j)_qSAP6M|5W&KS#k3dM>yB;3&?{!``cB;B-=HUA*$h
zk|}<G>Q_$#+1)2%pHEN9va+w-uGSL2J;Tb^M$X7kh0ZxDOR2Un2!!YI3LhsW4lyxO
zuB{7Y;G(RMge>WJsi*Z*BOcog!k0uh)c$v-h|~Ddq+z`_`;pC@WG~-$rm|VNKR;fx
z7On!}YFf>@!aYowiHQlI5lD$R_F|Kpxm&$#%j4O&D)i+((3h>0UiLX$u5GK<SX1^3
z@8V{Hg?N6hCi!YM=e`5x68Q4{&pyj&ANPYvRHrR57|WCO7)hg%hN6Z<cwOjAO`D=s
zr8+x@TNALYqu45uYGkVdka099LW8!4iMgy+cdEAq`EfJ7z}X_!$puqnwgX$8W1n9e
zp06CALuz#!n%21~HTCNSLczJCgJOK1cGK_g?C=Eh^sK{2j^RR|@Yu;daegL1_rnNz
zG;(N)dX)1zJW8QThM3XAHUR_!!0oRPwC$BHvg#x+$2$}UWUpZ6DlBUM;~hK>i^WtS
zVB6#u6v(D=AU_TDef_Z7P_0b~SlGww5%j?csLC9kHzxpL7RK5IDjFenBUqr`A+V(8
zsWZhE<EB-i=VE%gEvN=s;kEvryBxx_z+iHE`WCUmeY0Ykhb!#=ri(6_)m9~&(M~VZ
z&x86ZTrA1weDWMQSWKtkS{k{*@nJ&#Hs_rQBG8g{M*D`LeC1lj+r7i%-Kte>eYlZs
zlH=f7Ye2{rf9PIbn`7oCpJI3cp@6#8eAV#iTpC-<ufLh9-)mePlr&QQOz@OfwDqID
z{R6?ozIQPoVi-^wcc`(cXl{PH?K2A}F?ut3am(~K0yd%?XYH!h`{<+<Q6`?3;e6e(
z`Zfb*@_7CRS-4y(m_KFU(W-_E?>LP^$5w{uxTK86#sag~!r;~9Bs6(BcSEH{pI^@%
z6^tGng9u3UMo%wvage^Pxv<deV6HMO>_|T@NAzp2-r8h=EXmT;)YQ^a8qk{A8e)$a
zH0F(T<#qQ<+u5!xG%{1xY+OT<*73mO-3qUq+ge$~(Ur#aGr|3FLEk6k(yc|AFF_C@
z25K%qBbw9+)ifOyO{#NF1t&0QE{l1MYNEwW@s>Q9AB>=M6avA9JG>jV>y+SpzCGt(
zIo2h1a(9F-pw!lH>nhR|cNIEx(6Os-D~8d76%+4OGHw-}ps6phr)#POmOLQwsOx~E
z-Z0j4_8wOijka;(SX=qx#AW2E>POZSaD>H&p*xE|9bb<BDbVP7uIcf9gB-IU@7Z%b
z^3%bbnx)k-TEC1`=LeJ$US$natCor^?YuV63q93j=2zPYu)yzyIN7MWH2xVN!X$o$
zNoY70&S#qgf{!33u%@JB(>~=vBPHb_T|PocPIk87QV=qU2tRsaVxl1xO)>|Ljhvpb
zGY7t`_1$P!CQr@A6oRV%HB6!K$j`gak!b-E78=5x!8Ebx##eD$yNO!~R>O7My(+pQ
zgHOpvkiEk*CPm(ri|nlLGV@sTu;So!_hb2>7@RN++*{MlcatJvRdl5fryl5cQs24p
z5Yl!P`(aY1eqoz4zb7XXn*T}R4o{EIaxh5J3nLpC6<=VwiM~FXyvDVX-$>N<%<|Yd
zu0FrM^e5Rm{>ZjL1&=$@caB$0wR+O9refBT@zr~nod_JpagSp)``5#W4<brIyX!yV
zEl7BDo0|2GUEW5+LDRuP^aQ#-0xE5Kx^@x8bSQ~P>D^g*S(!7}A_bX9l_-H*w}q99
z4nC7nKhTrPiluivb+(@FaL*a;w>74RDb7L@$~P1$%mD9uQ*>F{jBvkJ&EM>ZLj;Zj
z<8L@F)OSsF-Z+aWh^Q#c++@QTzF$7qvpV{MJtFRu`W;sTx0UB`Fv(YAsUsyJMcG4z
zpoq_32-4>3!E$uN_aC&YA9+0+^L9IyHBGlMJKFD`1`rl&`yc!dw7|bpaYh{f;J1`E
z+WT0s)=(#iYG`{;t?x`gYbC`xpMQ()iOUM)9bBbg+zr_%SgAa+!s8mB`qlCil=rjZ
z7k>2*4@K$x+31F--lf;GRR_~OZpl$+Lu&cj-*jAt5G_tn)9Ol|J7KZycD*mB4Cn6C
zCt9qPA4s6ypoT15+{MGFibsQs<D1hBW9yTMD;yEh-nVVH+o@yi3bcdY;lx0;k{O>i
zi4QvUJZh?uyu26B>!qHEML>pQ^iSQC#|J(hT@4*wOsL@4Nb%L=du{B1qEbGN2fwAy
zgiXT*?ou6CtSC?cjMFpKnu+=uw5+X~`f6Gq7OJH)&i?G$KMZJNGweAURxhjUNXMHR
z<(lf<#yqyAv7m0ameXLLt&c-xz!*v83@?~fcU(mTeK*R5R>QkWpEkAmz;`vuz4+KQ
zn1bV7?bIT5<$TKs-0q*M4+bb<-^sA?^y{*uK=+IP(1%Bu=@cW6gM^NRi5~aRb@KG-
zY5WoK&hwT6s<&Y{*v|@RuBz}z{4RCa8NegJ_uAPh81sY57n#{)2rG0GX!-J<`vho%
z`Sa(`b!S#RpCnzT1C+|K@eolyCG9Lby8Jo`NvTOACd2lj@ZRv8X;IcwhG#bQ)Yzy2
z0}Q&zn;x1;dsha}48|{NX;puRGMqv_b=w-3Ff<!YZHWZfS)A5nK<i11H!k2WQ&0@7
zSqEG3?Mp%!vK+50{FGPsD#v3mQl1|tZ@M06tbm&+uk&2^QqQ`0sI6@m6#~;({QZSs
z6Z&BRehj=W_C)2EY#~1#av<N(Ze9cR3kK$PMQv?eQ0b8@wE@y9hV@sM55u*!I;mEp
z?thO>HEHTp9`p%xBXVk|&1*SIOX-I6BiwwoMjSGsIh^L4I2{im54arZ5=Z8*lGj+c
zxTgGxIykS!BxZT3KjGP$cN~7gW;E7-aMWw=(P&LNgKfmb(1ttiz8HaCvg^Z7PEPJ0
zE9?L2cD~)gjS~ZO-><-p7)<AKqJn_*yb5PA^<N1Sk6iY7n<x`9>Y(2uIeS$g+T0OD
znaEI&+UYLj&mB2h=i5=pPO&#U&`Wx)E7&<JParz)?SjLL5riJL{HHFdt{+$u7pK1y
zp%#JL4ie9llka|o;TLh0oT?F|@dA0=tq@OntbMxkx3KwM87fR(_Rj-IjY*rgtGLfW
zZ~UeO1<;?jx;~L$=eKoEw0=(h93e_eSx()jW<XlKQ2NWI|Iln2nTCWWc-Q(<LyNA7
z&*uE6YA=zGtX)|l^ftIN5#w$5BlUbI=ONe67H1_&IlEO)P&$VTlD8#!#$qBEy^rp+
z7FNZ^#>sW5?UoWEuh|G+PyrkF@P2UNH4M83&Jxq6jiQrO^v@fZp4hBnY5b&#Z2cv|
z+_9D|0&K-Nd<gSxXdQtBK0kc#Xp4~!^)1cN81%VTQ&3rx`i)e1*Ml+}M_?V|<Yn^A
zpg@v?Xf$3J6wudKqtc+~>G2*p7$0j=OFEh9jedy-scamxVTUjc3DEYH**Y!pG?~fI
zwEf6-4^`_99P0DnMu7OyBt;W~Teg9Me{UpT(u`SS9qm3tc3D4Qv6tYxmFrPx5D6v`
zwb?9YeOqBNx5ajQ@>ns)-9p(cgDs|C{Z%QKmeY*`rYFMbWOzZF#&x(Uqn;38F&ryB
z7TJtGB19WFRwA_{B<74Sgo^(_RK=I4SDMs{GTIg2Wk9Z<tJ&Xo-~M1LWoL1>iFf@|
z<~W_>h-Y;a4CN?^yDvGxgn<@+gVf${r6bTrEwN-t=w{uAv-i=Lw~`?k;P(hG5b#IZ
zG#;>+)?*=3ZY#1niD5A%LYB9lY8niYD(c_Z_8$-+syi%>f$Nv7>~S?b>eMexiV=MB
zRlpbIE^0PayGZ;}2AYxL-A$;3D_&Cv3`vgLq(TO<9cg9~QY;i?$+590af(AGIXZ~%
zlv_IVSg<bM8ZH)ev@`@9W+oZ^_UaD|d@CfmRn*beCahv$x)OPz>BHyq<cU353V{R*
zPd?K5TSO4Tu)eNNMffM^SAM>T@K2pdHB>d>yJvHj9cC34Js#%ob;FP5^$Y3FU_EQ+
zKF$M#ko!seKV}h5eQQ`x>F*mhXlaLM5-=X-X$~ijY!$*f-Z&jjHGR^y$~<By*<vW&
zn8YVRslopoc~3o6*MPHV`Pb*OXD(g_H(tb@0feoU<e`IR<}}Br4PizjOdv0ZnbXjV
z1SmVGzRRzZwLZ8+;rP7Nbnrde$ceTVsePXEP!b~y)nW1s34*mDxMCL00}BTKxmJGT
zRJ)2hom%oS#n$q0V1ge0Lqu{JgZ8;!qw^Woe$&G`^(K>Km6C1pihZ5oQ^n~#=f;A`
zVl2$R^eWdE+!}Ssbb4_UxPz?mEkj%?m7y2dC>MX&{Q0_=Zy)p4k52Thvz#sa6RMVS
z!Gd9=iME1;pu*4PGz;cDwMg;d;P2$x3N3U+Bk^imQe69DC61(ZJII+!xw5?l(Cqt)
zNY*nH9jvptv&N*@OepZXR+-SIRDU9c4Rx{wNc*KMWaG@>7ErvDiw@NfkGRKe&qwLC
zYASN7mf-;UZ2Wk4`O?@KD-+JG!E}@$`CVGtXDm^oo=Pkf=RY{SE=O9C0<_fBag_Jh
zh}|t1ICEwU6r{<<e7tZxC%D%}VkEs$wcOfl51eUiA<(}xM&B%~+x2hBK&4V%`1lV(
zQ#%f;q&0C`rFCpEG#<c29W7^kA+Z<L`s7V{$C71}x$>aYk~eA4K>Rm&=B{LuMoh((
zRnqOt6s~@OG;4t%+aO5qQg4&6q?;IpG5hbj(W7{BNq!!NgT&W<+y;wPDswP~gC!BR
zW33eSMLXH!TRkcIDs6S=-0h{#=GOA6ql>V`;3xrF^2^~w5LSWM<zn{D%7>C-udO+O
z<UhOH<gj|;0WTgIARM~w@@gj$$NDbnSq4-EwK^eY#b;XCs~$Ob^<k+{1i<hWbCK{Z
z`+;-BLwteKh=L9?Cv2331bVNBD@2)^l;0ZC1*zJmI9Bkbtq1My+JZ9SjP%RjGfn8k
znYWsttbBI!n^_dCe^Sn)v9RK{d-)@~n$B?SPk7KZ-ce1vE-sg_eVID}n(3{VYz-#<
z-P#J9_R{x=ztsyPLGC5G5i^{jJ}|(}P1JFx<mUF+pK%TgH4c0a3%jY_Lf|V~Igr)$
zA#lp=J(R3=#IkWE=hr%HLS_ehq`LOxW-o~^^w|6*f-~z7+eR26!y?Sh5y*9VMy{!!
zu0xk%X1}%(3{+U3>^G@mIlh(Zp+OM}lJGeGQymgfEg|(5bt#uU!TT-yuAkRi11yFq
zdXx`b9%5-sd9Hie$PpE>CwpEthviE)4s+qv;pI3EwH)D6!VsCb60?RTG-=*jJH;x8
z+Ayhi7qQsM;>jFJfaMYwL~Q%3^-9dkDt7$W!wKJ~^YZFC0;@vYw3vAFqaAPuahHpg
ztq*NwN2xBD=TpEI>v1ykOU{HCA<m0qY(v{H8Gyj-Oo+5^%MJqi+Y}K>)rW$rVp@f|
zJ`1H|mE_eUW-_+V0%Oko8iiUvY?dMGcdUHY>KC+W*+e6T=f60tPvTc_Aj9NCEvC%)
zEWnpOJkNU|-f;YMc=Rzfy|<Y5NGw^`vFq^dU<r_B)Psf;A|z^nVduA>ywOz{_$rBl
zA_4j%Xiw=Eh|{=>^(DZgoT|?KSR?+B`PtMtcif^@qcm6B%HuC{=4Em+bAjimJL_ok
zu^S>men>`vG7X8DMnP75cPaA^|D&KgV<LYcC+1w^lDj^-o*GT84<EkHw;7QBt*b-+
zt8jtac$XbP7n^^-KE(Mq4JxjD{9_U$GWC00l)1Guprw8OiS|3S5e6=@E21JE3gxlN
zIT-{GxX_TY%!+*sGR%gI27{ycIlJxj4Vw?<eE!|)oP)wKk)w+Vt4Apfqf6I2(W2eV
zAvlP`(wT`kapAQ-JzG9`X|>v{p_?=WDOTiS>ShO)7+TcL!s~b^L49PopGqIP&9EzJ
z4Gm77?z{#aRB3)|1!_~l7sDSHt`OnBC6=F_y^m{I)NihZr^h~&q#aex@Evr#t$1d(
z?w}6yzVVf+2|9Wn4bzaB4TC@?1o;v2gE)|silm77!J!ZYGWgBYG=Y2=%4H|Jks)wj
zMMHH8B1+h$T+NhWt5lHc{kwyTRC+>9(=wTYG&mfC-<+u-5JXF}5m32|fg3ED=V`Ln
zom}k?0|lqx-lyv7q#aT@Zq({OB!Z6mP&L_j*Kxh7YHH9D7Qgb{75?}EIWoHbS!^{o
zm$U>bEi>~t1>XXobi*%A-k2o++Hv~}ni?C6n`RUF1%>wR=l7bw>z#f&J-<k5%3DOP
z-fQq0HAp4~SD}=){sQ0Ix@q20pns4g80^!GCK*Dn>Nvzkn2>A3>#M!0Kl-`smi?Jw
zu*q6e*5)&_-aCvID2C(upVfOUamSt32Pw4t=3n;`W1^^4WgT54Xp4^7SMGY=Wy5H5
zQIgG=Y_}WG;BWVIOPEU_LB1>%Kh~$2u{GqE&;C*nD5@IceMR;^oYEzqp!1hu01%{C
zdh@0@p@=2>(fRwYp!Fb!vzzsq(v75SPCa~}+*;FxmTk1sxRQx3(p7`({a+(f!7{}G
z#zTzJWpq}-FS*C%2t*&W>oeY-A{FB;+jharDXR5jwhmWTR-Oc@P{k9Z28yY&FFT@Q
zz>5r-&Ji#QspVjwL0%<&QjqP;!*04>Y4LiXJy<ypRV9*J<slDr@0}2}OSu{Gixya1
zo5SUP%k@<G>}Ixr<`phj_GRBDNZR!aTUv+KdVO?TnAt?wf-tn~M^m_jzBEW)7{5lo
zf_Baxjk+mp931mw)^*w$*Y}_ekpKlJ$y2RkvN7e?HJJkN9IsYL7M}tn+^z}|^rS3?
zkzDv)@v}6kovBVGjzM5{@a-f?H!W$ILR3=ki0nrlBBHbp&SF;z?XHP>3qebV^;~zf
zT5WHN8`|6V|JY%lsTU*RsiX_eQo1M$y5BvuZ?MwfjC5s3vPNkovYt&?4&9)Wn79oH
zCFb)(FqZMW{cTSRtAKGHs685)7+hw3gu5E$F=Q3JO$81yWZ@Di#dWZwqNuuLgpSy9
zH;u2Hy|k^`o$Sp(UB;i#R<ohh{8Yu2=$L^b><f+L2fV@q#KF~<?k)`uZN~z+>I7#w
z?P&@uan&A;{dGP1{p}Z0eRdW)-y5&N!YtQxdrX<Zr#V6^X_YeBZ%qh0I)S<V6xFF-
z&@-AX5)7Lb=p(WPPMGGI()~|nAL9kU*#Qu$$CjH^AKVViEpH2dyrsjk4JW8sw7m1U
zu8|h})-<CqX}YvLQ`6RRdA=RfzM)&oRyz3mxSN`1A@t?!3PTWaLW5pD5H3JNdk=04
ztS~|3l<Ca|?erLFhw6+3;4AwE^bc5+O63_(;ruN~kT*BBC?)iQsvs&U(_3(&(itDx
zpP}p5=wHUF<q_$DZAuABPOPzp2=)&r1rb2^Po7muu-Ooxd9ze}oT_2x9_7_`c3kLz
ze#3v=D4|;^1x|k|KCRIGT_E^6AY^`Duq_yl*vSuAJv-?3!Uzf_fqjH^bM$aka#BLa
zJ~xvfPSx+f{AZlxo4u>H+`o_|s0NwOny)#9>lAnK<vZb!k-#ov#V=)<{O}e(b`KP%
z2y2H!(mM|>nC(P0Jicd^BT*IrfC`wjH?TW%Um1!%z8pbuerSHOB;&i!8*qF?F1++{
z5lD(j%>}(^d;&WN$qxEcm$L0^FocB7QR4^gE7S*9m6I-&2V>uyRN<lMX<BH87t(zx
zwaGyOMEu^E0v$5(C@&{FU(^?Ta&a@h42T0b2%-;$Y8G5d-LIVtGcp84fPvAO%T@bU
zBT;_ecqEin$j&k!+1CPgIVj$&or~0k$o;-F$K-@+^Tae5w_0xjeYhE^U9m98nh5kF
zU9Tttft&>R;?`i0<=?){Lb_f5Lu^y_I_o6~Tl~98x`Rd>Xl+wRl|PDe#*w-ze(5Zb
zLmP*zobI$07Yq6awM{fF?{i`VXunQ=TxX$iZb`W~$~~Qc|37b!1BueE2n5{$q(Wi<
zCH;E8f28-pW)Jn#n}+>50b#*a3&TKdw8k5_O)2gAyFLN~GM#~9Y!jUbFC`w@(%2ZZ
za)GX@O-{}P!u0=R-27`m!U6)1;ZI<rf!?96P4ORg&})wLGU2jkmyQXdu!%DD2GMKE
z6i+Pz%opMtL478|Wu2rt9TS!q7$0Nlh<+Fu%QaWZ;L@XPP9MOAO#B~1hQ<Jf+(9gR
ziQ>0IMo7cQVup4F81=uAntxk$d1{yXjbjJO7DTCHFp(?LbS<))^{rS{HF2>SlIcjT
zM@_=&4BJ_}N!WDSN5x0+6C?YEoH)CriCfg-u&<iU*Y{<E<@b;0wVq1x_+FWM9%Q%B
z3=yNYLPcNz!a!WFU7llS%9xm85?t|{?$cP;^)(l5i%9Y^+s`*@#+VwanB2LpPH&Ub
z@Z*W*-l^pm4jLT?AF<9`(OIGiZ1q~I6(p<rnYYxi$XC1z-$O+3a}+{@(c@06EL{k#
z*QRtguF{b=5{pEEjLdlZcmH$ktCT%R`+_Ul!W7(qG4vbpkRI{Vzw0w8IEtSaS#(7%
zmH5_F8A*_77dnLJKlHW~Z?nv7*C~B0V!k;{<Fmg^Os--faz`>7G14WN$<P7uGd#GY
zGs<{i4aUFar{v72c~1WRlsq6^q5OeB)dU_9l=w0sNPvP+xNL8K`>yHs$+|?6<tHyJ
zS<Y8OgY_WU9i4cSsp)T=4D;Y|YBl$FhbD<1RV?1b6)N&yuPbsN++i`5<_9DB5u%EH
z9Y$@*VpN25*dTG$jBPP7zj9OSE9u)b!>w?-STtf2s$weZn!)X85t*eMrP9gNMw$1@
zU3n2jUf{)GqN8exvSGe$Foas?{D`v@A9Y&WL`|xrl^|U7pta>s*A?-@*>oyvG48+R
zVP?-7;kvns&QbL*gYi>yl_vsMVq)^pkiQKGH!K>I1YMxJm1I`mK0ALxD%w*;xdPse
zK~K&NZPV=ts~+w=);oNp`_vaMOLFh=C*K>9?SS9slr{7~NAVcIl29cOsV|9>QIW1N
zAp;mZzBq`@ecMVm=V6>S7^#+*!bsY0h;jmRiOZ#5-0N?9!n0}J=iA~ihM;On2_?u*
z!7<#-aMfEVWJyppB_@I7heTvsVb^!34;e{rmDJ=mIDjdXYxQIm{PAGCqq1l3`&l#i
zlGkC>`(U%IQk7%_&i!vCNz(n{DNj1-3p50B0CGsg$3MkGjD!M4s!ZNL#6oF7XqqA?
z5@z0{bKY4&Vml9q4=&Az(usib4`F8ivfsm^6RKk;LoZBEavAlay&{G5%xBy*-7S%C
z=cl3JEKllHmftO|{RlqXSi&qT(BBITTa?^KCfuW^W^Z1VI~6d@OZ=km0uz&YoKgL|
zbRNsmE|l?l@el?7RYp7g0hp@5BDWw#h6X``tJb6NwPd+h7a6I-<3;GdN*fu(VF?lE
zD82h(99M)=ec33DAb%|(c`3MMP)RIo+d~im)0*o}5%B#C1=37=C^!h#o*5JnxkDN$
zESZ`0tt$oHkv=l*n_Fx_{q>QUcW1$UV<#7jBXSqonP;V-a>=+u%b`7uZ+9g4p(`r@
zsuhCI;1nUM>~(A=8Nk?*O=Vb7{JxR5BVO4pmwMW8Z(sio9?oTo4-S*;HT;(4A*6HR
zUq0MHA}sCE2H&e=UaRBEL9rVcFBy9&A$1DBtDn`2>^DXZ@q=1IE6I~=oSMz;MlOjC
z*D5vFZ<#Av4T{#QZkx}t9H300;qe8y-{=1LttW6Mh474CUZ3z<X{kmGF}2su4leBD
zm&A&T#ZwsnHjG1L^QLT_#Uj|!V@ud0f7xBBDE^O+2QsDa95DeUHc8=|-15k)<??=Z
zlAIY4AwGm(<-{slwnGR}WhdR6j9Jcqex&wtv7&2_x@V&UwneUatmPDk>1w2%P!4@u
zkl!&7@WDx7nOD7Y$9APj4le4PV?@sBF|#_VzSP8b;>9??3F7I>`W>olV5Lt_HZ(>S
z9D|Eu6bxo7n7U=E`7GC&&)1q$S(I}ST2dOsoK42?JR;{&i1P{<5YPb1Lnu+jLI)y3
zO6_lPrRtsGhy5v08bnn{zESEplqLWn8u7Jv=j0Z8L~Z{FRXMScnV?oML@RP9E1lVg
z68tR)CYR>74-6JZQuO~UFB~jzjEBrp%pe|sKM2i^`zDn^XHnTDwX&~J4J(k@K)HXT
z<y&$?_;m)&Rmu8xw0-lo8C(62702F+P;p5i2;tB0acMmtzcWu_{S121p=&^3!uJt6
zE}R&oFU0R!i@3ZvPg<Q4f>Sy^urawAW**7M_Z^C(iMSV)v>8_O-YTFgCJlL<O1wPq
zNP3(a-QM2bIq$PM@tP0thS<5Dc2xsC($mRj*3Y70#<WDsqhv+Y7z4}=W#n^#_)ZkY
z@LN&_<f#b}Z&rjFm!~*h7OC9~7=h?{76~!ZI5_Z^N_v!*2Nd{3PIOvB-$d0w<QE5L
z&V0qS;I%=bBR%;=KJ=9iSxKu}Hgk60H!e}IU^D~^1Mz28?0sUw6XpI6c)zz{`;QVj
zM_*R(%9^4qi-o=mx8|&@$kR{uRbvO81=iTQx#581ieLa)0t1<RYkCs}jbZJP$nEPb
z2t4JEY>1^x#d3ldf_DZ9$C0)ADd_q~TE)!aQf<clqu8gZlLp`CHfmWKTv8l&orxJ}
zLAD{zBaqR(?W&U?_H7eznazGZJ5Fgj6dNNf5l?pYhLXA+RrfGX94{6HRs#<sKDP}4
z&>9(6d7l64#)UwL$f(IsEQM)fa3q4reWA?jl7InpmxTzWL-n(z@V#x(I>&BpQ#}Yp
z8scPCCCJ2~E8pwcDWVm;m?Bz^&>La6BK`uGT@c&AzSNdE<qh0H3#L8fb0mUQogKW0
zrC~Yx@e>u-Pysh>k^7tP3?^>Bwh;|d{MLulyG#;o52K<Jn3>LfbM6XrD*cD4Vkk_5
z1~ZcgLAgHx1NZ+R6A-BF78u&YT9eo-Q}k2dI2(JmT>6~xH@^&?(Y_LnsC5^Po9*LN
zM3^8A9S0rt<mksDG$uZzJ$5Ba0L+Jw1;*_ASvKi#2`PL6qs>n3`gKK5!+!kP64=S4
zgi5IsuV39wql}03od6l$uyW^xUjNz*4x0;`3KFz*-4qottL!vjw?00D<gQ8LAWB-J
z@2Y;hiJHP;Ymv){C5a0OzF!jV_mH|G&p}u8?78$n{w*=plC&jx?m^)%`eLkyegwHr
zhkWy%`|}>EZRd_)-#3bT+T`Z}Ll-3%yAD1vQI7s`&@^TfVZi>Nae#>Eybc{-{BY)I
zAqz4q=@d3Fg3e4}1ScPa_8^gMi6A`a{T<F)(mOe$MmR~Rd9=nWFrXc6;_OIkl+%KT
zBNg-e3cu6LduaD2#R9S>`~i~YuS!xOrP!F>K>Y%NWc`57qE*p;onFj&^9|Bj1V%O$
zd2SbIh&6rNW8t9Bxx&ri%~t>{U${Dv5MUVe!@Xe*gqDhf80E&H=5)<E<-yBfq?fF?
z3vMoEz=`<V5UeBlH%kcYJEn4SG#IJ8r~Ic9_LQYB${H{yeW7o}Ali1!-;z1gfZjna
zEty(=Kyof2O3N%90h+CLN{i58`U_H+a{Y`xZ?TI0Nunj2nr*B9i-zWSLrsqDW%7wH
zlgH<_;6%nEYS$c&W)8V+weCQKXDq9d#QIzamcTaO+Ch_QO_~cvqR044s@u&Tl=>m<
z4u!GD#ZiWf_+=1CkgA}!tlXcpRbz=C!aM14BD(Nxuz8k=MrGwl<S=kS#aYY}QP~$X
z-J#A?8JkThRv2;FM%Xz@O;`S}B-bzNg@mCUC{ZGxP(Ze}_360rn^gZ+vgj%4i6k1&
z%)4)*5w1ZoXuMG44$jf+DGd6|C-^ZxqOD143)wG}V$7g~ckUO|@|UC1sGE^s`**VS
zw{1>p?>Lsfh2&+VQ)^3?dAdokp`zN*uZHBs9#FVYZKp{q`csI0vquGp7X*M-P!REe
zdB-f~`+;SF`fA|7nVc>tz4n`Yp-IKrfU>dEiLF!c!0e{h3JN)FpkwewkA+Aab?EEm
z65y3jm&Cg(ayUqz>fZ!JJbsg^BlQ@bI1s1595ORRJ6Bnxz8ZY%ep;r&X&RroDBAPt
zA|V&|&ETehiL65PLn6_mU!*Qv?RK2=7IN;j`IKLLsg@GOHqwwCBg1NRrY!GRjC9W>
z?-1Ia3*COww6z(rPFsOWH_T-NE7B=GEtX6{>U*O$t&JfCCn6&S(<|BADa>kMChfZ6
zip}s_y0=jXezC_3mI*6kG<*X63RM>d=hxkwEBd$_AOxZ9L%{m;FsBt^yx2p|xTu*Z
zRePA;Bi~xnp`0&1FncH(qH&&D&}`x|;3+WxqRTA2rq_k=kyuG&!X-HLUIpIM0;LKq
zH1-Yl(u8U0KJtUL{krm-FbgS!tI|mMh7$!S?k{cYp@w4xYY0&lXyLKdS$?-8<etVN
z%KYzMB*-tBjQ{Ho=D}185|B4VJJp>3n;$0kTdo9GI$+Afdixzlg2pNX<pvm{YNNbW
zQ9oExpnV&^Qk&tSUv@`Do@^2v-b~r}4o)KjWu?o)ocj1|knED$?gL!>@#jP-l`Tt6
zx=}iT85AJ{`7g2iyxGspz4#{2Hl>ZDm$CHbH-dwcXARrTtw#AgucK*42IP^WPKgOQ
z2?lg_@$fCY*!-{Sj*c){Po(aJZjPS)#`OFt)n{m7vh=XiEUr*~M<icHBz*j0Z?bAz
zupSb6>#>9Gs!hp5)(>J37v0r5R5F}|tCvcp<<~5~QwykLR)$lL$F$+HL{ITSW>_(Z
zdr<fp5+I6lFQOQp2ulHiq#*q87|geJ8Knz}R<3xbao|6$icyS=u_+cIAM~Kmz2Op8
z23)ch2Jxjio5K-4EHLgJZXG-BzU{lGS;Mg7(D^a-1Ke$E0-IoFsaCnRAI4{w@4P<h
zA6yTqZ&|?hN*&XVRH$K{p87_rHX!B8m*O5%rN5%e5S(Ap(A(tX1bJFuIc|jcEl(&l
z37PeYR>Peqqb*4C(*z#LchLu{FN^Krci$?s`EAM=qxumd^NW#A(YQlPO8aWkOqJhs
zQpZk}PYLvUP#z|@9!wqeE4C?o_;Hv=<D}&b0l^O;E-awLf`ZhNbQu-+>m+`kOn1UI
z@QMs~>(#0TM+4Z@UYQpg#t#8w%PUmOOI#%eQJh?8R-I05iJEI8T|eD1pl}f$-*9KF
zeg}qiU`6I?lmRf!m!l0c&M=QIlwh1AQfxQETVPITMRNH&S9D-1pJNLewz-){Jzpm@
z&sNzuSG%H!C_BKJ*XTi;phNmtB?ROod5{)0XlN*7oJv&nZOGrBG7duJ%3AXuhqFFP
zO<_$P>}WX(1GXa=1xZL#{HQ!u)Di6L^h+|kB7~$yQ;LS;lW1@A>Yr%$CrmHLs4y~w
z$0_18Mw}L@nT-Y<F3A^HO%gJ&(WYQ#WkK+Rbo;mhZ3KKY1V)#Zej|NzdS#WoNJ$l;
z0KU+~?5fZU#@P}Px(kO$S{5wH*cmW$QB(S$1tpCt(lIn!3(IPof@B*`r34#4`nnY-
zmvkuhioHyT0UwwUFTT4YJu);7<l>)E(^hL5>p(KHwvr?6Ny@_2?^r$aZjA3IoN~QQ
zy=e+X04Oj?@-+ivEVr5d+LJ4k(ONXWqt&0%s6;yVc;<ebC<MQv1scGBGe9hjLD1l2
z2pfWmqnm3fHqfb7YSc`*#oh0PAzN>mu_|i&3rVI+QZG|`v_d*!q!e&>=-7|>I{tbp
zoQF)P?y-kGAuTc5c)Tocg-Srm0to;E?*}{i6frRaGNiy`$~*GkTlM=bCig3it%kJZ
zaZz982NR9<68?5~TbhG{R-qLIUM_p@S0wETpSa>?Ua;Dwb^gc;h3FIVb*jQ#M{a@)
z7_L9yNU*IC_1&WY#Zl<p?lcUnvcz-i9q^8G{VK4|njJDn8+vd&oOcWUo}|~Co*}`$
zL+~<7fF?150OeEnEOcJ%16}D1fG<EdJb`T^@rf)7K^AGho7TLl;*I2^%X;jTbklFN
ziK?ueB{wyC6Sn7Y2A^C>CESu7^&h8JI}6Ot^S=3aJ@-G}=l4FDCi0Hl0FVmnDZJ1^
zpr{sbvjKJ*&by2|WSk$5y^nsD67>VEO)^PGmM;CVm*LZH!Rtow@A0K@UoLx5x;{v9
zv~60~Eu!)hYr4mbJ~xq{!gHBksRbW^Uk9k<zlFhqf$eJ!ZJSLRXw|Ae>7P{yQv%7N
zWonbJrV%gHIZ9*I(~2}x@@9*6LWq$n{slbvIgmLfczoNCy}wkNbk*0cx+A?o;Pakc
zJ8#RrZTB{k{0ykCwIGO~%2QAX9bg|4>v2EjZ3VOqss$aD^<mS9?;e+0jzwd)g*uYm
z@pK)k6ZmR8EL%{0eOU`6d+-UAm*xOZb=Rqdaznu1>Ptpkd)TkeP6rm2XDc&NZl4p4
zwulxZ3S`|zIj?^D$K+&J{>@`XDtB!Odvn;$%<0~h5_!NjxmLIRmin(+ax5b^-zmT7
z{^=3IF2*ciIhT$u)qhm9Ia%#IUa&keaSZODIAUzO5)~B+dOD)m3>Kc1pah)P5XdLo
zfXI1^O1wew^F^{{$vE;^+h@v{{c;yWY*Xg5-!A$18^OWrD|%0_#pd~hqqk@4sf}V0
z3m_exF}^ZIsi|z3Hb*0l8M`<K_WPYBx$0qDh*brpZ7p?8y{y$LMZ-~}gVCc212+Qu
zdS0?#LN)=GZyE86qtoMgsA<Wii>GQY>)EhVEgCJC;37{KZq_%~E3en3>Wl6j`^>*4
zdh#?-v7U!7srNtVdpXrl+j|M@HtedayLSbGI7Eu1W_RDip$fan{oYD$l-Iz7Rp}jk
zs@Ve_(|Z0m+tjQToK>>FeH>Kj`#B}nS3EWC)$&QZ25*<z;r;PKZLQl_mmt(l)0nB<
zLD7C@99vC7`E{db^G|gb?$ngU=QWeXG8cE*!|~O}Ulu*?ACB|ByvUp%<qJ`GW9IlC
zImsNPWh1&;&UWUd{d+6X(x!2=ZMq4^`+eNh8yK9b`@2Mjcnopy7dFihhe?ZCAQ>Kb
z$M%<F8jOf>GdvFhQ(IN3p^wY!jGBSzS}C;`o$C=<+T-Qy(N7*F5IWx*Ty^f6D_eqL
zozUBNgD+AOR!UT(3|fm#W&r|qhUC+=7`}vV89}F1`STCzd5rIg_hY}MO2|oy>=GSi
zgQN4_!Ji!Y=L`#8R%u92D{o|pKs)q3cA;Y3^n|dka2=PePd{e{@c1A3cr^BBuCE`T
z`gOkRS1lsC)Wvs`k($?R@oMLtcBTfkSPj2NQLKRt+MMlTvQIbonCm0|#j~J?bmnU!
z8pp*)U)Akyy=bYNarb6pTc)UVj&l2f&y_watS9|02NbP)ZO`u0Wc7P(j~*hJ+^6Z^
z173~*gBt)M6r+(x0FjdPtxvi;TJ5e?s{Sl#;C;o@RrU1qgSTw~_b|Zb(4f1HA6T>_
zpYawSrp2g2paY>H=MWL`xoWHy+068c#OLSdaoMe>b{!|MNn0Pz27xr_Ul}nIrs+;I
zL6|xp@kKm|S;?Kc(%|P$Ia@E#oM%(YaAwn3wWlYDq`K>Anv`><I5_&ow{ujQ@>rbM
zN`9IC&0J=kbE`PbN@D(;X>UHjRmhPuuQskT!eF1|X2@E}z@*D~{hK}dQIo2osD6By
zyyRPT4<%W@o<k&D<@eR=?#}M-opY|6<vWMHe_3yPvJcP@z3BTA(`W;rPAzJK@!iq_
zzCUhMK0ep#&2y%d^vU2oTpa{S#wx`8a+^uJYzR_FCJ$*bulU3+f|Ohk#Y@r1ohMoG
zR?>VHEJ!pWJ4?2MR-h3wRW;pFr1lIB)0;epZ@ce5yV^*C`|`N?;i^mX@{_AX!wzWn
ztz62>a<5^6NZOLTDWhQlTG8GH&hq|)wf%9GLUx$-VQ)3k<om86my`Oz()f0VbsW^y
zin`HFI)X$aI~Vl9N{dHdG`^e)@G5nn3YwOdc6xdm9v+^)`J@xyWvQdFIk|Is-N0pa
zf!TD#7Oy}_WSnV%Vb0sK2j9Md@SDb+hV9N{>crII#maz7-=Jcw0_ZZLm>&O5wN?=e
zh)vt|{kGv|J+Tmns7I{vQM(dIA$pwrElcD4=a8T-HPM<*iYgE#f!RL#Z+D#Tv?m#P
z?&xRi2w_Oin%huEd)P4QU?-C%Hzc~@BvWb(P{0YAMAwjxn)Uq`k~+(xZ@qp`O)gf$
zW4j-8y<!|Eu7x8N7-BW?qrc)>PSy(1+eJIovcp|?P?A!spck81rn_SwjSW^AJfMF>
zer{mFJyxJ=s(FsF;if{kSgsdv`XjxN>NAqR<z|kk{c83}B>?<v043)^SZ^EJws+*|
zo_&7siYZvQ%Vy;}Mec3!(TKo(<+ea^fGTxT5OyP&_7UyoJ#9Q{C0MWdaBoke+0{-(
zC1Gx0WMt%TrcY~qeSKM3SymSR-mTzYa(rSxTxx3Sm?ZYmfShv65itp&h^r)zDcH*b
z^h~81)d!<P*@8)KsmGqf;a+n2M`Ek0WCV7C#w;`1$S#-#FxI!8vupMPmtyFAJ!rjn
zL1Q^w_u-7;)L+KND^#9!m-XVxzv4GG^u@pUCsni1RgMAgJZ%&TISpfd%<<g#q5VO<
z79(M<ErSP+`C#sBRDAGZ<RAzmWaFN@9=6)kYp&`tI5lE>lT*4$^)I^dUf^tgJ=!pB
zG_FOwnn<=r0RC?2uv3f5;O(vu)#K`PC+74$`I|7T8oQ?b`vjxC#~abWVah149f$LM
zAC{JjET{dpl0{ubUGI=9%TMur1@1QJ+GPJM{Ps`L)O;!;^Di1J-8ZLp<|Zy8%X^EG
zv(o40`|v4`>hLwFC(VD+A>@|73u20X=7yJhbgl1Q;s9Il8LA%xF~r7UFgz~lWkdo6
z8ChPzdzInsZIfesWZvxe@86@M@&>w}dE4CR1eKqi-)DNP7x(?CJm3;_vEW6at^YWA
z=}ZYyN$b^|Dm>umc!w)c-CVf((CyC>a1v{$o6ZpD%%xduPU??V(rO(&Q$|KFBN4<C
ztafR(_IU&{72a86Xj?mz`7F4n7W{SB@;rhlz|LIT**irAsXcKEZOGo;Sn`%p9Lrp|
z(7S0H4rN{6*yg&@PLN-cy^&nuLLxO_b(O&vV!Z5cL2|Fuhr?NKjO!`n>4ow^Jm<kC
z*{dZ+pOc=|vw$3(4^q__jp=}nDkS4K$vnYzcN0o(uEfhUYrMhs_DU-3xl+cB2^yr@
zs(Q@1Bmc>;S+-al{r~Xvj)9f5P1k5Rv2EKnCbn(cw#|u?i8V<kwr$(CZJ#~&^M2=d
zI=vfL*HyJ@tyK@7XIfqDp>!IAD}E>}A9Eri-eK#`!vVT3-t;o4df)S6fa-VwQgEdQ
zGR9k3xpVc84EcPm@$j#IWHse-N}ubqW)J5-uICtg2EC~;X=XCLwwKncYK?eLdQ|aI
zXdT0wAq}ViGOR9DNpjD^wukIT--PHrO9-b1#E?c<ah62I7}`X44YhDpdrq#<TXjhs
zVJdUOVY{ojmJFyrm*dGrgAAsJfc;-*8e2yr=qXm%hsL;lJl~dbU09RQ!vubt(xEmf
zJF*shH|<FTyv=YH8fBIxPP(>IKu(mI4Dk@>?ivy9kjp=}8m88m0X}SVqSvYPsy2CG
zq|Y!qm)4wN<xM+97Ua6>sI<dWHdRKk^NM?4*u7r;o_`vuzy8!=@AvASN+)k!^$o}d
z-7y;l`W56mBVCR$K^|hbe?VnJ0&GtLgdJ5n8YF9vZ3nNKJ4_;Cqycqa$R$m6T#Vf7
z7R>nYGy?A<NycE2hD+dXSK0>}6iO1H;ROGniC7<^3D#_m_xb$nD?>?v<Uj$W`MzqN
zyNe>Wxv`=1JWf9h;Mdl!Uyh^#s4z~y6Y(KU2A~<<5gFF7n*Ku0`<A!;9q@_mjIB?M
zHW;6j9>EY6?!SCJ^Az?c)amDmer1E6<U9Tp{JXDlU&}D%Lxk5xmgpiWIx5QPS$dn7
zUEi*oePL+ZeS4b}UfkZ)$ZC)VUmOwyU~rM|JNSE-yExhG9sa%3r{i1CQ_{`gId43R
zs>Lc|`8C|W{+r1h6MlM6lJ;gCZg^O2RC7Y|su>}}s+REPGu%!3*>6E1SeN^ODey4P
zyu^wP+S4-}YJ6m${@cm`wR9xc{AJL(N!eRw`g_jrLwcU&I~FZ?@!U?`{slgh`Jn02
z*qTZ^4{C<RDi2Ee^@~_gzUPY=>&EFu39b&YX**yURSGR{e5G>vlU7QmcSG=cN59Md
z^9~L+=&WG!?fN^^@ds7LSGvLNkZ>%h8Be?gnRNXFH<_$|I=>1vkrY%Grz1#h-upZF
zI(gCcVVXXGePaFM#EA=m01X^v_$3;XODW2(*j&y%4ZHS(j{QEPiaK*M%0u1SEIa;0
z^W04T>0qim$~~<yB|E!YYn0la?|jM3m_??s^|m!?_hi`EH<KtIq5@PaR4t~DO~BVr
zSpIY6wAX02{7%i#WyiF$TCXN=YJ#1ENHb>3C$B#fh<|O-?{A5-oX=c}XZ==nH9n?V
z%|6@R-wsU;NsW%TbJKF&`d;(hs%-5{UET)WYB{d#+|nWS_6psZ9!BQl0Vr#jcX#C}
z&9aY8@g-1#%&*sgLZj~2M}drO4-wBN)!#JNDpLZ(-L8t3%7lW`rOE+f&0qjd_zq!T
zuFm3L|8GAh4iN>rpP=?_96{U%tu!9}d^a<;I@;MXIECH!Opj|ge8-s|njszBbF2o(
zCQw>#j(_w<=agR#i01G_4AKSN-8pF6_7s(sQ8qHC`JOj+qp!YGQ&N6XmoJ``Li-=e
z85ZpK%Z8h-gf|~`9bq;aT0YI0_&UXKi#-(DUE2G8o}BAzKd?b+%_{I_>Ao}%FYJ3o
zuo`LdbzI78z+vuIPmKz2u+ZP%ah(I!-fiioQ{PSpp)rx1kg@SCX>)lX&&E#HQuJ!K
zDM}^6$5@7wgl4CZr={Cgre0^Vda>CCr*t|u*s$env!>0rr(FDrlyUs_Vzq{!UJ$mw
zx?E$XoKYyLUMkA9KU_?d$~gU?9mBS{-*L5vvd#M$-G$9A@ucdua<)HcA*@8P5ya^{
z53rZm<5YN67&dSnNa$LGhaEzP6t8|nTz!qVI6Lr`8P>-!sINdf*jXB#9`^IGuAfSG
zr7yb&zwqZDoaFI3$xpH2Z>%#@LMXwjE#K!&jW<Y|x4xn#=i@2g_aQc%D}aeLshEZZ
zgW8@TJG;(!)iu^{`pi5$C>*!8!n=e^1mPdo6|1j?tKssOZ~BUpMy(|En-{g^4zXbs
zfTwA_w-_`KRJ)pLnhV~~Jat{U&hlgxFm-SOH=Y=puAR%i<OC^q;@S_k$!-2}63yJn
zwQl^mOE957#5@ss1<$GbU3hm;IE-K<u)xI%_Yyjmq<5aNGzgGaW}(tWaju$Kv3qGW
zSZWowZ&Xm~;@>Bk@8{CZZ+I}Er0tb*GvA!Jdv_@^zicpEGy-4bNuyA5MG2Y+<j0=<
zEeVeB7kgYdtq~9hxUYpNxX?lchyAFF40>;7xl$*jfs$KY0?mE+I(E93{wCSS{eA9-
z`97n@UO1yKYkA&`XZsUY2}@_8W+Nesm+@0Hbu7{gBz-<QG(oLO2MQStEyvu<$g^l^
zN$q8cUbl_)EKn9cfE8((?t+E4SiUjmqvCGf_tCq4uWq0*6oD1@Mvoh}Xi#ASvhFYy
zg$9&iS~D)mp}gw4%)K2uPZ(4B+jvUIhv@>hx!BGkvHrQOi5t|y^u%buVbbV`)^}nY
zL+|$FZ{yxB!ZCxW%qg`of{>NrZPD<Q9!#)9otU@yDTqlx;o~Sik(u@myT#6`9Gp+b
z;)3n(D;2BjOA#B1%_IE*0rjfy-T8}(!H(MgkGKAzZ=Egg<<&nN`1{-xkP}y(4sB=u
zmK%6EBw%*jXC|T^*C;qQ>=4b`(Ptb7=?<bHOCa7QT(JLpnJr*Eqq+0($(4@^m%onq
z*lmpm*EYX_@Pv8kc94jxBQv<qQ&1EDx}ZXqkV6l`{CVirq0jn_j)pck=&4;ayx*zl
zio9FFsK3niYq6q;7*UY(B$a<!%1m`@H7!{uh&LVf!}JkeT?cXK#^kF0L6X8zEGuC1
z09j3|qm9rPxT7K=NAmu9P}39eN~D?>)Lpgdlz2Kxo0?hu3O#aen8~Or3!1gZsOXq&
zoL0WwE-2BzeD@9v8?z>3Bk7`IzeoEHXI7wFam9`><flViQM+cyal%_>!ZUxU9}R(V
zZ-H&(EMjcN;5kQB<aSzo-pPtTDxy4@Un|q{5_GBjUBto44u{-D7L)=smiP*zfJm;f
zTz~7wAa-YiIYb~Jve}0O7y!p5N6d6gTKT;@&PyYV(FQZe>Uq!mTUUMYv*1pe7ERAf
z7*-aN$OhxubVE@qb<YDyHX{cjfuz5cE5y9DuP!czj^n5O>?;OHN%yH?2T4RlG@+Fp
zG`XVXNXY9~TvLQXxtb+1ZOt5INh~&T(6@m)+YS%VL)?c(>+7bql3O7?5nnZRzSKJ~
zav4{q<gz<St*OkO_7I_8Kb5t2K<G?4Y0O_ui_>~Z-umkh#@5FZh$#4v|Lz*hnsbM+
z+3Pl^c=nx%r<?f{9EO~~2K<@E^foA2q(o)NrMj;z&?_%)t8Qjw=bs|m(@Gos=-17S
zCKCiQ-YrJi6lULgf4U6dVNKN!dK-MDkjJk&C-5ZMF)mgfSNmOn*Wl;@8okOf(<8+N
zy9K-*LaFJjcJ{R|-}FhK$?ref^bGo*z)*wm@d)uZ1xE#Aqg2O<sIUN|7nmTTw309}
zN3qZlQT&rAJ`6tGm|#~EDQ@x)yEkdix^1ewK4bTtcU31amddeSVf#M9-GNMeMu|_|
zu!+D1E6`(RW*)U8cadx>Wm^KEc0~*Tr6U#~;P>$WDC3=vCXg~%IXJF2+c8f2gb?P@
z;c+<wq-Tb>xVVhIC_g&vcF7$*iOR0kCpwXN;J3NHo)V5oBuGzDG{ZuXJnrizf3*wJ
zSsn2^Z>K6>OL7ngN=&7tR?U}(3E>)p+++@KonT^Wt*A{{Hf8Ma!^Qee23aej@|F%t
z%u4ucy++P5QxB>78U6hIGd;q)W;Y=CxoM!vn&nR}fHU<ux^>C8wZ=L1JeO0>3+!yy
z8vTlqsG+qqQkf+xSysOf?r*<wH*yQAfj>$oyaUg)_=CmnY3bScF|bfJID!wUrENoM
zs153Gef2;b8JdlLr{(L1>3c2S65jU^y|Q&mG(!lc8hy7+4k0YJtsfC!_x9_R2%TUA
zAb2dWS${LR108ZfCwOp|D!*AfKX|Gd(NR}EUfX!^2e$XiP_T~W>a%&~XjlB4_f+>>
zDjb>TECDc{4;j$w!u-5(qt-TH?*Yimg_n%Lcfx+`vZ=YbJ*`l6wRnBJIO+_ZiFYj_
zMZWH=@ai?Q%JDE(T~)5HuPu8?juu-oS@tE0#=xTM(rP{!zJ}`t2L<Y`IlwG1h&Z{b
zKh_=<QfSM?sa68m*TR_9x%I$y)6lITXKDMKBEPm&+np<7ITSO2P?##l_UYnDRq-N1
z#2?4=zV~esT``u=-(#EoZh<ShjPL(gxp1JSR=9?Z*Ky+dbGBXII3QNkW`Meg5t*l&
zow+YQy2GwnwbR{1!z+mHqtPr6moaq0@%+KoZ0;m(5zFN_S+57@u``rTD_5&fui6L@
z4I8EjoI(kdM1p)aUyyWV2LX6K#s&N=q7UH){`qF-j|M-jleFVYF`WUIYrfdJ9OXRs
zvF@cIU$d7mI7M-)q163lDqSqf0t{Ini^I_e(qTTGqj&rR`$w?hQiWy&_~j8stTX^J
zc|oXJv?6nMbeZ!$9#~(YxbU`hzubQQfD7ARNLN|0sSQdP)<*n_+Q)UUc`7J(B(drH
zUis#IDLGL_bu!iVFGp1xuUrX^g@|V-h+Q7?W|+C8?<N4y&a0-W0t%TMu9eI!EQ&gp
zLHcXggL<IDG!qg7R|jEGk_H9nBfvkO?~GZFUN4pmVwLy>bYU1yqTrni<O~&Ha&B0<
zYpGV(WCi--YBZL730B<fYw=z;6uYKFK0~)hl%0u!RcV%Kj<R9SZznk7tpGeULP`Ky
z4*|}jicJUB@&(}3Pir^vl4<!KW{3to=sNR((uf<dSM;t}A2mps8HVKu@k4|$rC@i0
zq4RJ=56-QwLOn*?@}h%-gS&6KVyFS(m&XpbhfWE<5u?^)!2c@yRiVe+q8Bvl$4hki
z8*Xi7GIH(lY@!GNkt0@BxvFA$>mv9{Vqot1H8@x_adpJ&S5j}UE**@=2975c0HDaS
zb8os~tsm-#LtyS$Af8HLM|Ji_$CJTL{o0k@Tg{j6K+*_WTfWHcGR2A$x|KRDVgQ`1
z$s*EU*a<9-F-7LTVi(Zd!RBa-hLjQPQPejZ%3YlPA`58^TI6s}eG1F{yX2Q`2>OEF
zQ8heg(m-`kH<;0|bqxk8k`~#M3{|>#HZc)-d|6K`-J4qi%k|f8V}9vQQ5bHb`~RnL
z%lM7i71thD{+_R;Mngw;%cj89Ni3%NUG)=(926j@3zrat7AsV)Yy;uZOW>q_ik4bY
z^quhYpm9U-uryA-pHdZsWzgwIr-$BvIp2YYTa*JU$N*&V7Wlqr?cY#6>#J@z#`iq(
zYY4vNsZ|<2`A26wDdxK5Z$+=&W4p*muJv{OF@>I%Z3bMKaLu7#|G_MX!1_=to>!-J
zg<VJZ0^2Ywbu+UskKQePV;SIBZ+x!4jeJWN9<F)nqIWYvxAMF3bp<Y5ZmX5udtU2E
z^y6*^Fzd6II>yDe-{C7nVHxQjgF*MnFw^Q20%?<(;zk}mSw#M!3FAh4roM%J&>=pB
zWr2aj04BYHN!f-4i9t2D)#nG<I7ao|CY{jsBKKpc{<4lMMJ9{4nF2t0$Hl2BR>3@(
zmz9AH=+XbzogxGnL=9N3RB);aS2q@Hf?bndX9T;d;->}m;I7O9O`td7ZH8_7x#0X^
zSas`+*0o3%tESW=w=xqw)w~;sF=%ARJvW8MsC8E3io4u74|yzIUBodB6B))}h}Lt`
z^9sqjn3KjUapUIqo|SHbVi-NnE$=vj@R84aWN;tzn4VqENY;4`VjJnl`xG*39y6~t
zaXNBHfq40CjFKvk)fWwTBRAL#)s-nU=^I=QjiyTXCP%<kT`}c+MCaE}KJi47dJQ5u
zx>5STRadC)N55<gCSnR#NM9?+?izeDrh1x}oMcO0fA8b_vH47pHwhP~Fla^BplJLG
zxVAk03lC!&b|2QAoXVirWam2yyfy`g;=7pUtL%Hqap1AcsjQteyT)apUdK$^!>R15
z#P?sz4Djg4$rX}|EZNtz-fcAs81!(?<a5&LD)hWb+*~GR)xrlu4AGl%H=vko1e);L
zR}4L!QjMOVn?!1eXc%oZWc__QeNj-;w&;1^nVh^gCCRxmJ5SIxc3ST`Q3SxOjME2P
zJiT_o#*=HM$SoHpP`jEpRdrz!amYVkRFa3>y?*0YD^PVi3KT|*vU|(mZYvdb?3zp5
zmsd6L-THQoYkPp$^OaZ=NfIvjhY2BTNw7;1gnySpGSITc>DK0OAgp|O3T$goWuv0V
zh~+!oS7Tl(yr8?ClKJSTT@rM=yowq)@ObY|l9Ufk3m`l@nZvK^c}tj~9gT2u5Y)pR
zPh}T&e3iuT+nr#3XL(m%c77ki`|&!F%P1M~N}i|L@5qy=L5h}R2^UyRl0SxWKz*sO
zw6Eg&h_>&1z&@564eJUSo8gEy{>NVd;E{-srD%5_B99qz&Yta_rgk!zKMj?gSEcP#
z^_^(eXj>%HuItk->(wuuRd9E>v1{8BVR_iOqKo0s$i^AX(<gJo7gI#=(8T!QER+w)
z%%RROV9&>IMsvLJ78s_vUWVqs{;E5!a;%!3>qysk-cq{zyx4-vFfbl-atywG*L1$%
zAROUx!EEy}AtY%|;P8acSy-DPK^Y{74frGi#YN<s9Q@_MH`+^_#j5Jcy0$QIk~$n+
zjS;Kf_^>|D?WSRQjD0|%uz!W4-z^F6kCw?4?Xtle$h=#656zkq1<y#vb=%|!&80A=
z*qR=#0g||7CTG{=x31kA<GK9)O49fpzZ&*8PF{KIWm~8d9!I@P-t5erF?;COi0TE7
zrS?e4g{pW>6rqusfoO03&|b>!*yC9v2i0_2vLe{<bIYG~BiEZqZg!SbHAl$TYecqR
z|8+=x!R}BN9{HB=>pRyE3@`U;c8FRet2N^BDn)_ls`59=!k^d1pZmcl6kWmE7m!Z)
znhf|ey9J4Sroyc?Sf>fhrjdNcYj5EW>t0kmNMKHzxHDuu+^=(GDKOPNI9d86P?CBm
zbyIWLNvW57m0O@QYlsx}YJeEna0vvC^{N-aco6qd&wP}NcSN{4Zs`{LCEqxN06qV>
zh`^B4&1c~DC$ZrY2F|Ar3b)A47q!8&*qhOW<LP6$%fvUTTz`BOO8Cp`Z&}t(>U!yn
z2M`NI&r_+Z1ND}H=H*p^mv&yh?XS`Met6Otr+bFO(CC9fX;Y`r7?iJo*L2wmEypjo
zg0rUm?5qX+0a8qJ@-Po|N}oHmde?3GiZp}uci^oTcs9vORr)T4MyFt>$3>RYGhXzF
z?ETsiuqg}*>mj{jmjCy$2gwN%nLF*Nn72**>iuay@qhya0}SG0psw!&Bh^1A^)w%T
zW458^JE7>j5tsp(wYXyIy+!a>y4cY9xCR^s_4R(0cS4OOwZx?G*J(59gR}v&ndDcb
zk2{X{>?EvBWdUxs*12Y=OfjD68W#QV*RAtLt!-5G=6GrqCU<!HmVUds#}})cR_+&4
z`y2Kk*D|G=?qD;ALpVQPm;H&p7)=Ysja&JC&oF?z;gMR-58a=rEyoS(4nS1<eZj)l
zu2)|F7%#6^86^s%8aeg}tJTUNXWj5>HlRQE9BZm{_ciQ3fYhQ+Ore1@!nb}B#K0r<
z81H&O8vGF84g<s5D&PWq_J&L0FMaVmw~G;PqEPvN{XEC>3R|PBc`q$04%W_Fv#X;&
zO%s__#u>s#)mtqtBm7%D=p=GuJJs5SQ}aysSs%8!B#Z?Y|D%;h^oW2VLYMy?kICpk
zF@^0u*U*yW`o_I5ny<wNTUN2G=GragzbfSlljoHX#5X2T{FY+N<brY3UYQ_fFNY*I
z+GRurwPso+n~Q*+&WhmQ-#E}DITmLoHKXi)rre%2@qdQuI&E;#lNzZNT70|i@t%Eq
z@h6r`aoKVvCI@EuGKdZD-FjLwzTtDR@fOvqL0nOUq~$7Pts#Q?Lzvu;w-r^xc?W(R
zZMxR|(R|!@YQu?=M{(qU&)3`(kDk=g>VMManj9W^vKg4?wx>Gys-F~vWNsl5ZU^NV
zcau4Y@FaP*Oc(5N!i1CbYp5p3yJnve9l|KRfj2{FltVo_)g=CK;zJVtYwHDN(d9>5
z+PMv?`4jZyuW_Ukq1pqZ#j!^KfRX<+*3=}<_-*91IDt}#{hy|k@c%S7*_2VnNz~!T
z&|(z8+uoI`V@VHVae<JiJ$8tgv>;av2;)=javcM358Qd-hPYvoEnT?s*cyy|ir&cY
zl(^WRlzdr<pu$WAwyh}yX5pKaRdDEPV~C(jkn)u^fiQ|HMX?!xPD`|h6lxATpRGp=
z+C{?}X2@U13!ic2)O=?dpQy7Y2*f++VIOrEkZnfiDKTuMoKTP23L($K?6@qY_tX+o
zctga4)j=V-DMNR3nlrbG$U${wNQ;2ThFCC%qS(>}f{s1pd7sR2=SV4<spuYi;3{UW
z`UJQogW=uEsC)KNBb`2FN$^2(5)1r`p$ZoGRO9dPxfDgH>eZqdpSulD+C2j<-<n;M
zzLd+_?oSNIz1z|`5dVOaWgmB%<yk^Zk6ozw*&gkp9laMKl^QJ1J{--CG+BlSSpaMl
z{YN8sb!fQsfXZw46U6p^Upjy`CtbG;*6{I*?!yU#XDb;e1Ft0N2QY7Hybb|HZnGAb
zeWOccI9uIm!+o|l89%r?OQ{iWd~A+1?NPIi3yvD886&_5`llTtzawRMs}crJ5@2Rv
z3WVW#&c$9FE^ohpUtF(C2aCqbemdT6GF>opC9w1J#sUL(v<Az|fO1BKd9n>U*G`gv
zGiI-yfps8D{f!9s+7OAUu#n^K<Xk>4m9pQbe339!FMXFpjVJC4r1?vnSOX$W&WP8V
z!^k48IV;ms_7tJ{99(h)>OYQ=De2}Lkvip)AKvlHPZD)km9_|d8Ky~|ext}E{av)*
zn8TQ2TCy=R%y=Z_<YJ$}CB^G_!%aM09+KR+k}}D$lGtAUkr_R6x-mjz5mqTnUw6UA
z{$Ry6ev**5UOb530q2*f{Iw%EenFRgJOY-+E<Z%zjpy$}N4ZX4d!sDK8i$`nehhZq
z;h`S_3ZI^BusOIOaLjwGY=6lQT`!9?brJNPQCNj2eCI&JheFvOEPp@(MYFx+`+6VU
zVVtW8V{oP&Ce6e2X588Oaj7*#*3XKwgrQ!FeroN{!drt|!cr=4I8qKv5$xrE_c;^8
zMqTy{+o;t#EvDFr1$r9~@g3o{ZzmXHa2P`rOn6Muh_~FlwhX9VJ!kcLE_Gd+qNOs=
zVy&pEb2oLf>&dM+F|Dq29rGEoU#D-AtMt;hAwHR0?NAs&`FQiG$t6hbKlw-Kau<n&
z{9|?+f^sk5J?&`^oW4KVR<~4WktRtR-rAt|erUHuTwnL<_@f``I|~260G=2izXRp-
zP^1u}6$GO5^yNDGY*Wl+#IYIKqf6Je_J5ZAxMGaN(lCpp(;G_7I+U113Idk17asM<
z<?eVk`~wj#fceSSQ42bUF)uoVK5YQLpKQZUCa#ePze}mJY>u7D6EaPDdMe-qiGaWs
z3n{`KII*G=GDvVAf|ao;X0FSlW+dVA9ev`(6*PBp`rr-vh*N?DLO6Sr5P<tbuY#J_
zi%FET;<1VKW@gBD)8p^%TiY*me0v8A<Q!+*Pd<EU9PTm&I2hxfMB^$}B8-NpR#^PE
zBjNH{idH64iz8U(zo-#Ro%*yo7}a>bJ{g6y%hhZHR(ph-%5scqe3GRgk56@h?p4KG
z+LWEZ(6n7s0D4n^uwWSa@|w4oL!C&ce7IbQu7A$G1J;E<2x`XJ84SMaqhcJbyh>yk
zOh4{3NI$%x7m+(zjS|fo%(%kfOB5CO_yb}$F}XJbp>5%<#J*30hCwI7b$ti9Lg(Ao
zT9|8F>9B+Ufyt2F&*Ri!ou(TFgYQ_|`euFL>jVq6*CgeIGGOwWkL*R7=R!kT^2mWx
z;F9scXwW$0-hH)EwaQYgvY%N|qu=0!g&#bhoY;8Pi}nMj{LeAe^6Vd00DCTwj8N{)
zmTBqF@KHXwPao5ZLjO|)2S{P2Q5soS4NyPFOK=$Usf-BujQE4f8Fm=Hr4L*YOBV%l
z!^6QT4;>LjR@QBhUd_Xw!}d)ml9Id-2(N7W@9gR?*-u6wSRBw0u$<c+&DhOLJ^OGc
zaFtqEy+Ef{XLE2GNRnd+@8WjG+*K849mS4?_;dLh8umP&pNq>Wl4zbXkYWbMQ8^cN
z(s=r@`^7OCc6e|XtLptx`?ZJz(P4|r`()f$w_qpclyhMk9_}6)H5*vVYS!MDM9+-l
zFDVC}EfWTVBr**>@kcXRddJnlgd}8S7tljieI~k9tx~?z%AB!e3%G^gHws&~^|w<{
zXdRQpf4B2LK>0X>F@D`}9O;zf2*eU>I5JSPc{EZjL**l3+Fs1O%YF1lNQa$-0^vUo
zF?I_cZ8H)GTJa-6s)In_xL3GC8@Lz%RE~5*zs>erhEg3ai|RKMYs5K*-AsJdZY_<?
zO~U(x2y}V24sb16y4rIdm}1#rd?qAU$w`59q4n7_#@i!nn+>SMiKwYJ_C#!9!#T5R
zwLB_%qf3}4@*6d?bEjDLJg25Ikw`pEaL`Jv4jN$VgLLEmq?jPymV01DIpBUQe6G66
z^g_yns{RQXOik0_tpXa-rH<W8w2x`^J_)HTO9Z>|a3KETh1!Y0Hu4;G8vH}B4}lak
z|5Obj#w8Gq7n*^}uIGz;?o#7;;Ux}B%s@Z;qXgTY6HwlZ<F8?DjVDb4>{)tO$;p3`
zFM@bi%#&qa6L^-KRGMVSbnXfu>L?CThosLzgCh%D#^M8ic5LI6sgHi(l#xh(5`z#)
z|DW=Z=~|r`q_9l7e%XfW)o7&2(+Uoyn4zPc#mITK_ZB*k--lMn_$SFkW9Az;n8y3<
z=@A@1K5p|p6E$*=odk$CB`0rxH7C2~l`|i&&Lv^Yu5Ea@*ahVBgrU2}vu_Bdt`bw9
z$xc0eO6RTj=>#isj8VV4Vb0IRIKJywC3yE2me=Cu{Ycc^->-%ku!D=+X}Yc@Ef*2i
zM1VlphV7xVZ`^8D=<<LVp)`q@07}cCOH`__*6Yru{e4T5QQL3Kv5PTD&r6VosL+cQ
zBu^fUIGG;G60tzBN!&uVKkcbsa*kE1Pn0=6X2WkL++kXa>vm-|yhUe(ood3=%O<mP
zPHfg+QXm)+CzweC+}QUlU{&?3_#aJ+Q53`h6umP~H@1iKwNmvN&t`?_Zy^;ro>6lo
zO6KnC#q1Le8~RnRzh>+1=g=7BeQ4P6y~blSk=XFCSFki|2ZahWbkJe8!c8?aI`{;7
z*z@B_lf;yZ%@(hOK6|0V!($o2XqsLSS7(d90$}LEfVC&&_?Vtk=FXf(!vqs;KsK;-
z*me!9d>2a8=3}aLhegG0G$Ny3bV)Rl9DqX{0$bzrBsJ(NfV@!MZ`R)@#F#{01osGc
zed)Dc>}N!_MFbp^<lwP{oxJ=F)=fAPuxx3>4j4X*mbMw#0`i3LHI#Clv^o)yUfl6!
zcT4SVCPDF@E(_3}Z>C(EN~_l#`@;poy}mJ*+KDjqpmkjC<IoHyo;pK=F+zAiyU+e(
z;v)v0B5DYj-+y2F0f`xm5UD#xu)+oxMB8Z47&->gbok8THG6jNI|i$X6qQ0Bn~dM6
z_A$N|1pj(Ci9YYpuU(#lfnWYffDkc!uY`KSAKfnqOv}p*y_wWeU;$NB?Qg7~-|lm7
z$%{+87qcIo=6lI^^w6l%>$i{HyU=t<bv2+a1XZJDTwCl|(j9v|e`$S~%&_rK^!|*5
zYbDTblYKJ;Uwy7oeD?J1c!@?#ph3_o%pI)R5?9xGae;OhBlI{e-Zw0a881@64A;Yk
zJ#Ue+{DtTomY-B>f+Qulb~}2{JUTl*Y%|q{^oVZ_Uno=Sxu;_CqO!j2Gx6A%wIC<;
zA|WViKkrK_`X3#NCJ@e<qaRQSwN^PnIw`8eR8f3tIiH~a7^I9Estuc;v2C!Y3vTCu
z{qi^rykPu(b4zO0$qsfy?%4tg-C|q(ExR|t*3AL8``gz4JrdDv+?e#Y<5~Y*Ur?@_
z@au@Hhh00ZDYMfSpJ*zmJMpZW3<#%?818Px(0Sy6AFXLk_t&qBsOz!g9FnliVGyCX
zer-GgJ{r@VIQ!;C6)MJE_Hq#oc=dc_Vz{OyPPeYf>=&oH)v!C`!)6YGK*Nkk>0Ydr
zETkTwe3+J`DR)<;{N!{}U^Hp^nIsXhRY2Kr0|8vB14#sF;3&T4Zd@jCR>Eu+5m5dh
zn&NT0TPV5V{q7~>rWv&6jo*f?1O`&%C;oP#_{mMN9edy?dD}=)MDng3zq;)!WY#EQ
zu7h%MX06k|#|W7&rR{?9Pxijg@G<Rw&ZN)N&s77KaIr~&6|xXshqkoi`uyYPg~$4R
zx8Q>Jk9pE$tFA^h*tA2n(D>DX_8nQ<N=`yynWGibuJXZQOME-FxqJ!1nh73`&@4TZ
zxwIg_O5H&Wh{b3>L8lqn*=Y!}0vIJYz=WT-cT)$$G;~K5I1$GH<;bm~o!73BnGqRB
zF?dmg?B8_}wXr=pvJd_~A8r*YDNF`nh?IC9`RlyLO<C0t=p!T}`;qJf_4$|+V<(m<
z!9wyXl)BGidE49#F3HYsP0d*@|MBes<-knOUdMJSKM|{o;CVrxc}@T)9(I2Br_oEw
z+O|B1hSAT+S+Mj2n+p2_FL?gBs_-P)btG+={K{|+0G#m;@Q?zm>$thV61#97;6l%W
z=KS3)VJiVZ_OL4qG&fQfHwBYRt}GoalV|_JX7_9T=VCZMaFtE7@i(CEyK~E&FzQ3)
zy;`^`V?~Lk=CXJ3dD^4o5NnTRBE91y0X8a8;@m`;0yGoC?@tuh3)2O!PejiO)4^N;
z1UBG*1oL>o=bZ>q`VTF6I(SOp@XfC;Wxvv1yT<OP@Y+MpE)UBKNp2KXFiIae6*vx8
zb|=VR;G9lFiC#kgi0u*lAm-eYv&)ueOn?g}`U!|$60o3bL69=3f()&K^5|HH|LJ@X
z1Ah@INP=*h3<Y5effdC51JQ9D&+J1GPl|7dkeCw};QoQlf~?4#n?KQaEO6b=SdbvW
z|M9&HQA^=O4CcTro)(G{X5s#?3}XfZz^Z*pJq`Z>gl7M=omk>>XvhGqLg@+PYau4}
ze+1}%=X8L)_<IQ>H>g4bxWw6iA`O>#fk%EDs4NRIVBDr)ak&3oB5=mVI5u+610Nxv
z{Q~)~{Q~@EQhrcpF8_o+Mz9LTnZsaB0*t#FEYnE>I6?%fp_#RbeQ~{3h{|@JL=eQo
z>qBVI&Pxm~(lAd<CK0F-lvmOqna>04qMZFl_1(<h)<5IS7W+cwvJ3yycNd}5q{|X?
zz9!a|;NYqLT{zaQBVuVLoa4bO{Q_u3%Gj0P1L#DnVO8){=#kQ?{;}Yci$0YRGy^{S
znevKf)*A!%;D-A~zqxS5W7lxuzyOTFeBp3_RXi@dIO_w)+M9;wU1_P`tYhY))80*&
z1<B6vSB^Gf^xPI7RflXIozFkc*Grr(YjYNDk0Ilmj+!NA1M`h6DLnE%N@cLp?|)VX
zA&`MrS6Ajao?^*e0BUmcwx4$dYs~Lm29V3i*ecORHntXgB`+ngs?6LMOVewd;r6ap
zURNa!rK4ZOg41Su4v68u-n8UaFzbNiBPd_6ZroydX#@kdn5DJ{lURWP9|#mNA~RSV
zE*CMD-}?GG4z>hd=)}rP8BvC3Xcbwp`El!i=clKMU8XwpK7T*=qD^W`U=BwGP&5V|
z0CynaOW|t?3uT~B2`&)td$_3hWd{WoBmhe^AA~|@0t}zgn+Gt=Fa)6;ho=bj#|m@g
zD{=utq@>J9N=_tq6Dgmc)~*9+=g=zXPgH4H8Lj;HHPma?1Rvi*0hES0mcRO45-ggK
z0F#3vzRI?OB}mvq`_3!#c_R!>j^$^KGw(_!>bGee&3&m(D1Q(b4EkhN2P-QpH8r)D
z=SVNcr~s+rE}!|M$K`FO-7xFw)<d3CO|C-v`Cd|}jT%NMcV7Rz&8gd@j+DA^bigga
zRo><;$%q6T0m+L{npE|V4){#hNAcOyxOJm3$3lAu-y}(0FK$r!>#RnzSep;FW|s&9
zzMUXxLVEhEDV}Q)FxqT6brluVjUk20K$2hSGR|tB!tR$9D|;rgrs1#INxI8Z7z2#9
zhEf4Jiv2D-1x>2}5YXmCQ~<@(m}?EMOiCl`JX(ImZ_p(jPAMSsT~ZXms-=NcP7H<!
z9Fq-A9*kUCuzZnTv(BW>UGa;NcxGuMKw}1X*z^$n2rZ?CmQP&P_kmG%$Gd#)>%4P~
z!mTM0D2IFaS8Gy^qOcidDG>@{9>En9Q0R{7Pb{-(vHlTO?4UxF6LL5WJpH8yL$h5`
zQAaeiBSCfXLx5;@hX*+4`1xwn`(lM@WG972JrQZe-DNkizP$5szgZ7STid(MCvUoC
zr$Tji?q$a2_z@=Q%iMauHnq3fD(3hA28Lu7eF^LYi>)G@!3$e{9<tE9qO2rA(7-!o
z_G~B3^gQWtOyUILF%VJ&F%aMfY`fm%>gvkI&fW!>k%kU4*c6*L>*@yHq`yp`O(n4F
zC2>lHs6cbzUV*4H=Km}@k7`$<4Tyz=AONl(hzIn{2|(P+3PPX?i4wp-hfZuh2cY%}
zN+6Y1R3xt%*RP(PofQd7iTnU=pFCPaid8!XoUjb(<!P*eG}}mC_Zz}=Q<*04>VM4l
zC_rG7+%1?8AxsC`F?c<-ECCt<Gx#U#28hPExJUq$PbW_^GqVV`U%y#&LF$ht-06tP
z`1&7z%_)-@DAWsRk^K6&G>?UchTvn1_|Nnri3o6&%ng(Pu^x3G$z-tYXH$j7;sz@-
z511=ysS`lv*>ka4UyGcmRK|)4i=pR{uUGw?96c4v6!=iFQNLUzEjK=cV}wDg&E|hP
z#&{(|$@Ymet^|#|0FaU};9DUSyD9#A9{(n9fYC4yr+A?yfNgQlhWb^K+}n%9(YsQA
zKp7zIjMKMYBudi<zGCd!_IC>}fFgjIP3FXJ_Jeb?!GTDr`E848x_9V3_L#?}r3{o{
zsmxQx*!|Z+l@Sb}?Lh%57zadQ$n?t%>2RKz^lCaO_ylrA7Qin%kOX)_M+7XcuAaK(
zz>`D<OqvbiOY%X7cImKjAeG}hq~kqzD5F4M=CcF#K*V0K5fI$oU}@cGN)Y?plQVWM
zbkmbmlLUQJkyu(+awAAsSXh7#14gV6iI19!YPH4Dc)%r=n;6-F^TNByHwye0XO6V&
zw2t4F=xyYK*qr@#oOtz^{{6virFqQsm3{jsEfFj0e*j{jAR-}*17WFBhDgshSk5NH
zL`<767az(?E?tTQ*oV;0$!uZ4o2Vrk8rtP0YvwG2j&LcW#P;7ilwZBP!;S20xB@j4
zA=nsSvXaq?{0&41pD&NYaH`o2GrlkJl#hUDP5n>Y$j!V!PrM_vqjA5}I~2$X=RMgW
zk~W|Gk5>=^nJz=VywpQ@0a$jBgbLn&`Wi7@RSV&D85F&&z;+;gKZ8V)vfJ+~t)d|L
z*uwr>GAICNIbI^-F+iA+-^uv2wHSzvPHdEV6Ttb{%|k~7jt4uMCWwqhML|i*%sgkp
z$%fSji5xBTao9^z>T6~oTEBx}n4XML-OIi%)MpR3At^Kbx3jPTd!@sl?-mY;g9qx>
zf5sXMeH^b(7lc=qVmh9gq$5kn%62|3X{XWadR?_1Z#j+AMS$b|!OJ&`7tgb}5>jJA
z<~4l^BHKSKx>qJgELZ$EJOkPID!H5#|2-0GG)8#(PiQ(s#(2lWZ-?IYFBedN>ToJT
z`7$`h7(yqv3|d3{n+3=qp&*NRnxU9y4{ONs;+b@wW3QJ~QZpbRprwwm_xAdmXoxm%
z?xBsk>zN-<`D`6RzAkv2*`U4BQ0MkVV@W^^#RL45`|L(aduK&^j&{D9O3-|}Y_T%@
z3$0Jen*ZG>A#jS6F0=h?-(k7r=MNVbKR-n`$+|yv{XWm@iyFGLd9I4Pfa64P055Nr
zeQ#l#k>qACKW+`*+Oh7aPKlW<WOYT+`9E}D#J~#7;L-Q3tq(KhqY`Da`>V*%Ds)B{
z@bCZLg9MQGfDlEbpaddj0~aF{wCwBml3A@2Iq8~6EFiD>cMvh62Z-~$%k-u~(JvPH
zD?8t{Qz*0-?y`R#Xa)a_hDtHb{yqJd^_-?Azx70!Pc&!bz6O{D8^8hoi*qD3e;A*p
z)sOeL^nFymrzD9mN&mOJPXWn3uWy(N2ofY@Ab!#(gMMS)$vgc7v;_E1I+tg|{Y``{
zzpF{~^4R-gBJVhCgq(|Kvim9FA#Fdkr(+CkS@c|~r(!n-Pp!2|^l}A7-{`}&cDap*
zePvt<8FlOHCcJ9QNPVqM1HT7?SbN{K-D1i%fIj+P@U;VDr;~Ua6xDoD?Yy5n+idi;
zQ$PK$&B+K3f(q{SUtDHH0f@3<(T9J7fa(QKi}<o=4-0Ht^Ei6lxKy4lmCut`ydFNU
z=lH35VB{$=OCJqowX;554Aw?EN;Tu0|DO1Mm%6_q=|fS{HeU`x{#;ARp^)o-GJIDL
zkFjfxcjvTl%4(;zyH6>*W70eE_wPK^zi!-g5k14poXhw2e#5Qf567%L{MNI7eJQ_+
zo{H<f76=(Mc*Z;THn%pn3-j6^9NkwHIsU&lO&i!gHEO}U_GPcXPFJ1fcm1?lOtn_)
zc>)W#Uy+`F%{yOnQLf0I2_%cl`Y+pR#1E_lM)Rtr(?yedXPzf-g%lbLtOu>7#*6(F
zP=#(z<EA?T-$mb7&&VqE;XmrMj4PMC$(Ln+d-=rQYFK3UH#FOvQ-^W@DkTct&TEhD
zZh^BEZ<`U$8W+0>1iQ&GIrVrtDPHHZiJjRyr27kx)uQ{xN%RIow|qHn5^^=#h(MsQ
ztggKvMcq<MR{yqo98Y>a^AUGEx?w{{e!k{bqN0DPN<_~97=8<FN%3@BamDeFznb4o
z<?88=#eru9`2YUQ30TJQpkZ<-fqBR;`%h-|+1*ZZeS0##3OLM>V-S-Y-|yRPwHzO>
zU7GjN;$FKuFBD&kq^90)i$|)_Mkq#|pXg{u7Pa<W)RoQCUFS89>s?!*6#V(WF8`kw
zz#CD1Z9j9x@+icQ@Q&<bv{SoQYTH4fV3n@n0n=kLdP+RYxfNbs3h&GPrzLnC`eHIF
ze`j?)$*%Ud!Q#+jrgC(wyov444&}KvX1%A8``DY{E+5&xyH{a4E>AJU9x_kTfZ@JB
z|Fwq!;bjEtXw({pqf?=_xr+e%C3{`Um~HFJN=5+}V0tJ**akH-E&g9oLJEaziS4m#
z!1G~?^ua}n!}+t&Akj2?7u@PMt#N(Vou9X7Bh>Ntc@u5Ayf(K@_lNXkzW|L2H95Q_
zqPaqa4r=*)okUNs2Ca@#w-uW6>+b<@GW_Jf+ALYno;nE|bB3Rv+vlQ>F!AU5TNyYQ
zELZY}Db`6(xR>WR4ic&^SeL$^ZXP__uJ<!Hu1_m#?O=4eLg)riC}hOZg3+~42K(?2
zWv$KZbzWkf38n*w#W;5W)4O@&`=AI=7?Ms0<JmCtF}bD;c7FY@yGgP#rYjV~pcUS~
z0N4$n4r9Dh*2R1b{4E7W4A_!;KX*2<R}i|JsVgZpQQ~yHU$**+Ja$`6`rYF*Cklxb
z4d<@!?V+kR5mVK5ekCUqyp0MkQcy#DKiKSdZckxV*DDm=Xz;5sIW!pMb$KS2h85{(
z{N46$sIFQys=f2~`LlbAfy1DeU1O>1WH(fF`iQ{!)mVHPE6-iQu2-J0-NXcN^G_Pq
z4mjhGU%;n7cjq+WWmtF2dyekxG<xs;yoV+=K=^)(mnW({ojcf=$WP^c7b}-rzgn6c
ztT(o6;T^mr1$Z1X5<Aow4g;Ls3>OTn&Wa#+ihn!_zidwF)w8~LNN%2QPe5r6T4zeL
zcWU@`EV>NVn^xP=kIG}Z|Bd!9|1<Y5Q6dF=$Rw7mWef>|JJb4&Sr%-&@o$~GmS2y|
zKOob6uKO3+d8!r1{XNPJ@O0UyYy4#Q-q+g=rY5IVwp)l6FP}EWV;m^ZCrjqYG`#X%
z2m80TveObv+wRYqLv;M?wU?WG`O?)twlH*8cC$V<t4$^LP+pNrU$+EQX*7;*^(UB5
zHvK=_VxQK(x}9cIqjywW)RS)`>_TtU(?fhV`6w>ozj_Id`tPxd;b6JFkRHccC82P!
z!Yh0CBq1pJlZ}~hz&g?$K3y^iFTEn?L<k3<BEs}%&tQ0V=PK@ltVv-Vbqv>dJ9Y%e
zZ{vhFf@y;5_f#T+A0Pcy@$IlX_A-=fK&Rz%SI#M9MwROU!4I%YJ&X4MsR|GNv&(=9
zymOoHU(ZaqPoTMP7>m>m@}*)CxqHC86!<h&Rj<xAG<o*r5RX!DeWuHBojlr436}3(
zniDu_`D}AhkES`A>C49k(I_)GnwX=@K&dy0>*CaZj`berX|t_|X;A1kf;dh)soj2k
zjA`b-^x2<>H|_>?Gw!!oHjP+0a-+G+q|;Ha#tQs>y_Q9lVo>W)@b>xme7}^1Mu83^
z`ne*2-R&oO1{gOvP`*(kiL=U>t2yyw{z^O7HOkUQuZH(3?tC83i|8RuuHWxHEl3vg
zKFd%Z{r-Yy4T32Pv!vxH@nBEqHzuu8{xl;AA(o%yTiEJ|Y+Y-?A_o1;jT44UFWh?Y
zIed1Ja+jm^scm)EmfoiO<Ne`xN3DhGR*SM0`KtPu93Z<<`Dbo~)-RI{3j=~Xy?rki
z8@q3>``by*PlV1_W!>cK)tD`|GU#Q)LlN2NXQMlmrDMCd^AaCIPGJ2*cT+=}YNp?9
zr;g0+AX&v5j5E_8X!XU+WAxL7zxf;>+V1YcpTzxW)=58PNRsRw!%Q>Im&i!S@6Elv
zrZkbGO_P2B?`g6f+4kAvR}Z2dj%m#k_-m!7u#ZL33s|4jG|s;bo8vGJV;WWw1`IC2
zOX^Xs@6IfJ`?x2+#V*$CU!3zP@dMfVf8D*@o%Q|}>$P3q-Lda78X4GJumbEWIcZZ7
zq4N|-kR%`l>&_0BfrcS88=27SUvDeCx0MjdjB`IP6l0=3mt_YvuwJs0HkZ3KZkuK6
z>1iH2PIM7*Bvt<zFxCA-!Y*bM`U~QE=DoE5%0Ls$<nA_7n^gWg(_b}v^r<~5<e=TJ
zmK0C5972DDuJCzRzc=;O`M=whB$mv#ZA1quYPpJ8(r=@6xm~1rUlR?aho2^`=MjHu
z$w=ouZ)bn^Z)aOxHhjM1|E2KLOFqeJpw$%xxqEN+uMB>hlv4hD6L2<cL2usm4<$*j
z`2Nzm=gD;^^6ib{bi}?<e#ZEoR(?#c{m7&^>uTB}b;Yfkt#OTJNt#~BbR54Bs{4e-
zw1g1{DbTJkc*kR*LiL*kcrK;#8}3<fy2)DAV}3w|8^2Q?I!b4;yQw|6?$*zp?5a=E
zIgj9@50j$}LRWt*nWMF{AyW<{0LG2F)7pi;94ZWs<#tsuDr!G(1U{|n@qON;ymHX}
zQC<2BN(D&S6XXdCd}vAhTS~(dr1So)-|eUwI_3%JCYUS4Yq4=`@c8a{5Qq?tLmTEE
z?tdTfzUYHT#Dq?5Ik~QB1Yf!k8q8g<tnUVY-gMR*8Ec4me_e}P%cL4koAs*DnE0P$
z{HV|kVN1ntq42*5F*JGcu}3(9jXryRvYzj%b(AosprAxrcpGbsJh4%%Ix1uU_oTJk
zI~#V$s<J}`XOz{&5flCnLj#u3nf-{C?6!mR|6YjJmg|Zr->veSWtiQ>@I_ke(v}~_
z|9V}x8kW2K0yrgAEHb=>J{4lD0GyL>*JT}N0>SlzYt_x~V3)++`olU1Do1-vk_kGL
z?_Z`;Gb*wHL(4=6eV_o)r_XSl7CskPUc{AO`<lryAm{98;hg(u+1c%Qx7fY|XNs0G
zrq|47+^Xr-^;ER%?b`R%K-ZYKue6>=3SVUtPy_nf+&*(O+iZn;-XIQ{_43zN*L(z6
z!s`1xwUE)I;Da$<4PF@0-n{P%s4TK&;Aqo&ZO(W@0MsmfgSnSyv!&?}{u(>jV&jcW
zHFCyMEU0&Une~Y7*mhfUsvbt)H#n=yI$0mn&ufU)G*o)ER~sS~uP#M4J9qcU*4UHm
zI3U)e7Eje8G03~3KtJ?YF{h@hh^h(034Qy^N%))4jS$|$S~GP4C>w)J*RQTBb7B&@
zu^sQD3S_uGqY@zCCdUpu$TpIOm7HANUnv#pU(XP(&;Dx)+s3b#ZMc}>B*6lY|4?}#
zq`d72pul3I$R1Ki-kL^7cU}L#dbi(8hjM#O4x?iuS1ZZzkI_#?_}3mh{fslQiEpB2
zp+Sz5I*SH=FI>I5Ts*RXc&-Ua7W?^f8Yu7nsIrhgARM1trP#QUp06s<PI4?SkO|K9
zwoVaVfu*4c6<D@=56fXmY1ph?)UW?(jvu7UcP~h_z;N`;|7mr9Hdq_Kp-rg@vDt3i
zUBf;{r(RsCM>}BgdS<}DTi(rWAkxODU5K5tNSh)FKqS$@cEEU=vJ2i)$YEk85wFZU
zM&2V-y5~G%FE=&DzrUxqJbQ)}b***Q{-n66ce;;Kr_#D_@C>2i2(fi0g@l9%N<d1E
zNE0zUDhd(80qSQEFc5YF8Mc+7&N0>0iY;%=l$53u-@*j3Le*O-wbeVg_oVBMR_Eib
zZ`wH@=P5pMD_*itZ}gDw$KNKgbMJ$}jp`j9KbSqF!g`|t!-iU*fwcm359J)Q?4)--
z=VKi<g3_+Gt25Crj+?%v-P~5EQe9$vFboqP2{4;At>RIo;`vo09y)H!zeYLseSL>6
z5Ai_wyFctE&j}VHa;9610)9rqij7=pE6x*?Nn=N<M8K*>w??<O*=QVh9G4;)zh7lD
zt%%~Z9C&(r3ViNc`ui3lm*sSz>2d3eYKOy7MK?c}8nrH@y_p1p=>!FwY|-k2P;)`;
z`{Oom5MD5`ae7oww=CKP3BN(DH#$D*dbs;j7}v7G%pzZ@=v}FsgHwRNZ`_-GB}6qf
zPG`T(t4f~FZA@lM?M;I~{p#^Vc33aDyg%rhmo#vKJXmzy=x#+^ej6NgyviN{{uxi;
zsgr&RnaTV8t3y-PcR4<X+U88MEn21n;alHdz{si~zRM=Wz2O73HimP;8Ux`RJC<Es
zzPazO&Js$F*Qw6;ra0L8g*}0k*ViO<$o^Y@_n0-#<g*SA)wQNq2SepW$NjL7ABkoE
z3Om1t)>^3QYwx;o&f6|)t=TB9KW6!NYgt>3j6-UdjcLt7A~>>xC5S@z4WipARhIJ&
zz^>~cxTJXl2^(N`*LTdjxrk$+%DB;S7&jxwS;#fpHr<u;dN~<NaLm4a_qGa=D*ELh
z8*`Aj9|C&x3o!iSPZSXNjY`6?t7K1k<G9zc|J{0<jrt_y+gkx}w65-Ncp<*tcMRp4
z$Kufxd5BT_!*(OAXiEt7D7KM-_krlch-O+gMA7PoXplbfOuA3FB4G_Hnv_duxXGjL
zE<GsGC@<L4gzCXT(U%C274`C$N#V$D&ni^KY<=JAKb`$=m)Zrz^Tm$?{QS@r^h3C0
z^GqPVk(nC7F}?FiZ~Z#98hA0|k+-=ClbqBQ9Kp2<EHD6f_$hgy^V~y_l~)K}JrWTY
zYYL2>bj!TzvqK!E9hJv(+e7*5ziawSZySyC#1Ch;K|OweJKYHGL6k4JVq%&K0?Wz;
zDo{IG%=i;-ncGG@`zn6^0_p#Cfp`u&IB$sRdwx36t6SN5zG5&fDPrdLw0Kv^gFUOa
zOUH?3{5}My2xA6yZaH`f$c^H&?1FLb@zfDKf^Q~sk9+mos#89@+u@r(_PbRbB!&Xf
zFkS>)%xwbnz!|K|vbBm|MmhFeyAHLRI3Oi6J36mA`K7q2(TRmv3HSu&jZVMT<ej5w
zxRIW)0;>mvM`A;=hBV9ksGvS0<7&1z>Bk`4j2rS_m*L6Xb$|E#k`B`K5+i}_GOzor
ztv1BK%dh3ZLpI~4q)9}PL)<03(noJ3RQq21M!%r4(|vDF@^5GN)HJfU5v9Oo3>N_*
zWqbu2vc=mxK*&}n1x_QsDcMxL&ao01Dom@ApS66G38&{P?&>A+sN=<4T;ZKr<F0uA
zVpUh^-t9dr@neMx)6^lN70E^|OyLLqu}g<vhb75o^z)bpd2R>D_5Y*l9iS@<nziAW
z6WgBHwylY+iJeR`u|2VE`^1^pwrx#p>p%0(d%t`Cwf5TUoVCv0r@FhkySnPBdfG-p
z#9K7`UnA@(McyBxIzA18d-2>e81xw2zI8QM2{XjJ;<>wb+&j|GGv2i%LY1|*-cH1v
zP9LWKe2}It=<}@VJZ2fIY3EFq?#6)STF{>U1!cjhr7`8U&&9BmPMwVI?PGs<BPJ@J
zaj=@=^jTA1=XoWoK14Z{4AhVdal^17fyZ=Wb5XEKDML@;F-Ae!zTxZ+7G`d-(@0Ui
z80L<**JBd@qthQykZoQ*-N3b~S{wPQgV*@JH4ft30y=|v;<3%OpDxwX4}-I-!Fb5u
z3?jF>`m_<m`Za*HFaD~d%~(FGDG45oH1tMOqMeqUr+2|9OM<5;gEMF<Bkyx2A=sfq
zpJk}VW5*AfE<><lEyWf+^yLZOGz<$Nihnh(o*x*Wg^l$igXncWX||Jn-N3?7Jg<Da
zKRWP~iB#0j#zyOIq>S!1#zS>*0&-2;`2=$FQ<6LUZoi-8oD^Z<|IK$&cT5&+@uRm#
z@i4ZtiTQ_q@kc<VPw0_j`^!OvX#eImbrjXK@|01}$yMwJC3z~q_oWH~U;Kr%EJ{^~
zkgQPH!&T?~)nFbg$@Sx<Mfv)hMJ(=0QlS|YKJVPiSr_d$q0Q|km$mD44l46P$@pfY
zw7<l+Qik}jRP7zU4PVWSGCw+9;RL4awLVhNKI=Iis^NRDemLO+daHpy)Qtww%hkI`
zcI>W}-<Go-lK-5vW?kc${PHoA{xL06&0mo{^ID40tcwyo<#s^T%Q~960GKecZ;mwS
z!dnd0bCv!hkJr0>`*!wO7<r-}1X+gi^(Bgu<!}lal^`NR=2%U8Atwygv@$}%q%!Q=
zy`XPG=l9MUT!fumq?|K$n8&Ok-@ioIeh`Cc-K&Xy1Y6^+d}PQZl)k?k_rp^r_ZM9v
zZ`qd#fP)~5k_)+9WQPTPx(gwb&coRmzqV}DK~BGYOq;NNM!~lDzH0gf*Q<?KmeZT2
zGNy42Ke@u?2w~a#HGyY;FIcCxY%D~qlM8dXUc^nPAUn&~wi>5$cBffac}7cFiT5|Z
z)%c>3sMP_6>)SzNcmcPq1*XL}(k6AatY_Y?(a@s@Q`$ge(bH#6THdzSd!NxQ{=}ez
zA*3yW6rD^RJ@bzqwBWGgpBofLqWW=3Kn(|8dm<qIxdzLrH^K^gWJHN)jJA5W%_>M$
zkuQ^VQjPI0xsIUY3R2wzKw90lWrRHky%Zt&3irLS7Bz|6S%|*dC3zM1{TD@;4Z%)Q
zH!#J1O!QoyALVK%I4C7%g%9Q=@h3_`Hs;S4%cB$+#aW^0u7p-2^r(@r4rOg7TGP#T
zzpCxo1V6rOS!b|Q2)|BW!qs^OF@xE?-}nbTSr~P2F0y`}bp{df>4&W=`1(}csQSG2
zJ@zAD?i=G_Op$`3UQvOSefSsIN+cvkRoUPC^7t&SR`7bEc>*lG91Ful+(#&m=?mzF
zHuhvFau7rIy)FA35wQGy5E(cd2!9lCPf&lIwy9gcva&NWKB}bZ(y)`8Dd&5vy4_t7
ztvudX!y>Q>dUbweN2xje`d~3kl0lzw`gsbChB6746Nb#*tG)u6%kd{sN}X-L<*2fM
z?*N(?YWVQev-ZqHpI0Gh!S%g7c1#0WG6XIn6s7a@m`E{j<T0abSk%vAp7@k88DcC2
zQ&I8Zb!<wR@Lg0%+LRLgNBzw1>0H;<Q)ZwMIM6twr1WDib}gRpV|Z8W!LfFAtyJhD
zVR+UQ-N;UNY6oqnAu-jH155At@o>j|<R)y<A9F}ow`}w1^ZZNqRO0F7-EK!FN#xph
z2=T0{48J;uE6d1K)ka?O^<lJ*A>*f#=KNjvw&>3VO5D(^Ih<;=rSiw6^6cMy*Q=GW
zmz@TQD%RScB9j_eA)imZ*qmbn+uEGL1r+`xltQ3<&*SdmF=W$rO`A8XD+vn()Fi8%
zcG3&4k>*0iOZmU}y1PE?X1AGv{GROPabO9$p4T<iy(igd>{bK2++-A<Vm36?YM0y0
zk-CAzn)x8=_XsyY)8*ssGW@<GATAi&J@BBUuSM^4@4efWIfhT`Y2lO<(8lFl)8;7`
zG?n9%e$yXeI-E>SWA2Vb$4luCq@0hACQ(Ovd3iax7hR5vlrYxPN)yQo`}GT_&fiJF
ziB#gC<Y6pwxc?L8`TiN<9DI{PI%STEy}rOa^t6v%CdW)g#m8IN(KyZ-Js2mBbvmY9
zf+nYwXU6EFgIznx#cW>gIJVuP@GWe>EN%(g>kD-rH8W_fRD#N?YQRq8PuMY>NhckA
zLT~psHs>27OCw{Aqrt+vgE(epo<45K8vUy1yEzIRut{zZF}GHFcC-m%XZuVJz0FOH
zG7$=^<RHl@SlASzRTaIs4Pv^xX)5%X34;^BwJ`U$JrxU^kDfC~Dg%@pug`4Tr1L!x
zVIRE`8b*0Go6o_>p=J$YqMh4U>!xf=4=>T)VCo~Y3)T8<!@rA{oFACm_#Zb?ST3>d
zWy_B9`+7}h^gV#EObBw<?F7>Pv|1KmX8rgj#V3nn{r9HN*SU%{S-BHl-3*e`E?*5g
z=i;18kaupAvD?a^Rv+lVyNCFAD8-0d?_HD~P}kqK3LzhYil$QM(42u)PbH7AB*iT)
zaQ=bNNEcgOzE>7U<7rOU16X6H^q6CZ6B)O+w?(7l<Ky?IOQK(7*|Swru~;vA=Nmh%
z4CJ2AjXw#LL53g)?K3-+N@k=rlPT!8ew@7b9fS^~!+7_zvjUQ$S24ozA}ByBA7>1B
z-dWn9cJ17q#KmP>oT)~Ue~!KB4EX2$&_ClV7<szM^Id3OlC>RF|NWI2lCt+V+&$hw
zg$^!B5Z|~hq4smkIcl@qSlGfn&wRH9p9$r+4VQZi+bW<kde8!i5Pf5m-@s3KJq?Jq
zDIi@obU*@O-)em7I37lEdbYd)e>6>Bqdq4^Z4l=RLt(d+?f#k$@_t~;9hZ#eoC6Rw
z7mtI!N7<z(KoaoMEeqeNpH9I$s=A=O`}8=%6o@PO<#)GPd`>Uech9Lu6!Ni<l;p^`
zxVRV?6hxX<R^?t;2l5#l80hH0l;X-tx;H+LyFX<rCB*bVRzkz2*$!8u$&J`r5)KC;
z^_m_P#5;s`$H^$|#zm|8>@t317T11gif)b!oeWy`iw2kM>ZV6H1w`owC0LGe25Wml
z`!aqw3;Vj%efCCM_F0B61I?3N2w06PHbWKB8C8eRwYLb`eYUsuzK3Ii+HJu?9>!~C
zkf9W>@Rr?98F<&XC;h6L)<qk&_m-}hXAK(n7H5j15$_A>;yb-qH=L4>J;0M>=C-L*
zQ_*o_eMwh*EDNvLRo3%ZS;5b*!n?`Mk5DpyYP4xqb@uK9mcHQT*qklB)j$=@qBW((
z`4DX+TrYJj)Ij+ruDwa?-^x3Q5NQz*SYE9QE@nGyaZ959qlf$&E~I39bPw3yHUCjF
zmC;;0012mP`In_yH%sWpkDHT)3dvM)H8qTRMqFL@gCvW{fCVdl=ReaU36v>}2877l
z)Y-{#A;X@SK5A?p8aNd-y!Z`CBNY%Nt3al}r?nDm54Gy%6jx3@(U+#;=;G$+j+N%6
z*URRV4J6PnOQ!gZyg?g`H-Z3bJQwcM$YDBNbRe_27x8MEF}N|al*RVl)t$;h36$#}
z!-<3IUil$)YpYOM*2R_ZHYS*eV5N6ecUmtsngVyf-md(it`|*FTlb9G#-S)2Zw8o%
zep3C~+q0K+i!1>^krH}$MgFdjqgzaor;vbChjy&Hp8Dy~!9ZMRN9Vy1p4HguO95=O
zRcZAyb{=VGBOCC%Ml#(E6McUY*V-Jz>E-SC<eDsw!{^o!PrE4-od$tVx&5nCGkVTQ
z78RS-e^2ckPoE3no|kvjer#i|%x6e0o-*EV428?*jcX8}fPlVy3s|NQjZz`39vP`+
zJ#vs^d$noxs|s53yq!Sp@j>7xZZ#VAU_EKQ!=1^3wDkLTjcT7zK39*YJK`>4{8bH>
zAcL3Kl405-v8h1@uWVqnhsZ`c-<Z0t{lH?(@}sx3rU)8>5)W*_+voDw`$Uy5JV(i=
zb&0Y4ZDgQg=O>-oDEt^{{%7sYE+uBwEESYn8(+g?#L|sZHjmGr$p$*j)BzQSaOv30
ze1N=68>RQ*Pif2Dyz$&v_8IWAs~!PuF9&BGQ)wp+$`G2SH+!RO&8yNJBcA)qMM^LC
ztw>sy03N!glCDbatD(KA%ZiISL^soIB{?oFR0m_Q29UPR34Wz5@BF-1v5qTQ9Mh!?
zKX9^6X89-C9E`Ip3>IZoa%hkA^sjB<+BFx=jblwTE1v_WCCBXGgu2CMa_uxgXMqU{
z6(g2<T5%yvg-~tJ13UsgA)&sC3K=2l>Ba};TiU1l6~%8%S8X0~$pexS{C&K_GbL9^
z+UR`H#TOckavEcbFTJ8oDKuCEj1ny?^O<wzY{`h+$}n^AGkG^B9`~E&mKBBd{i3rM
z7VrxMwovi_B>Kuu7yx9Ppb6!bW(c3c^y?aqThXAc8S7btN8{4V??U+j^P(5^i07(a
zT~mW*KsNuzGI#fij@2(P6DBZg>8JrwOV9ur$)J-7@m`sqj+}s&>))>-ewdU3y;J*!
z=YkvxysC@gs?wga+C=ZAcP-uvf}Knc<v7B98$Bo<x8tH-68Gb;7eDHYL0oEe9z3$o
z@7HS?<$ffs$T$U|b}}yvyrFLjZahUb!?#v$JS9AzsYy!>?9nW9D*z23NtpSC1>3F8
zj<Pb?2v0IHGV_V_B4vap<JHBlV$&FUStQ;__*}>+D9pYeZ%6`9AdZCuEkSDymgjtr
zUZQUz{m);C5f>|?@^$J4tVYU4+#mN3cNTXgo+XE%2ln~{i=gwELdjh=Dx<>a5Y9K2
zXWW_?>?L~;rBw^`tI$P+*j-@!%XY!`;sX*Qvj)#@3dRyN{;-So-x1!RimHD+J98}l
z5z*<?h&Nc6c^DrdlO@fsoqV_rM{Rp>3J8X5HMJc)F={V};h4|1wDLQ~K8_Qhqs7m>
z)Hu6JPW;lAJ=LNUZJ~M3j;$6Y?Jyp4u~4><5&pvd!0qX<1U3BS?ILSVaMJeWz}(c_
zO8&7^@2Z5~N3e~`MLfPnKYa}b;wh2`44?1^4H)=`8Sla{7d9`LTiJtl_I+VSy4U$v
z+H(=uz1yw`H3lQNLDA*<wu+C(`X77|-amz(01Q!kyvE1sbwXfvq9CW90~DR9C|(&T
z+b4r~_IJ0ZdLqBVWb#2I?8w=;yq=iYuHq?V`?sKWNt%U$l;E&4_i)=uEO?bNWuxJv
zH%gZJf-f(z8d{meslG-)yW7QL7^?Kk9Q+NcP9hJ@s3461(}zK*2Y)RJwKgC5VDuoV
z$=L<ND!rS&r+W`+6tb2JXhZ))^c$U>t@}fw;RI&$xti(I-TD1zMZl%21Jwi4qWa?!
zB29<B!=d?Ya(7|m&n|n+2T8~TPOlOw#cXIz9~jd@V#G_GU0MPfTUG%V6F|eOk`{`<
zECW1N31qcAtQ%R|N3%g9ncQ6?;}L^Alb5F@1kH1b_tjG1RB2#Z&0rdk$(Hwa1Ba<8
z=Zqk>)uEf&b<6+eQ!T9CS0h6{`IQsP+f4$d|7MS!8L1i@nS61>9_2_9j8GWl*b7)$
z0KO_CHTBQlo{Fw+JFq%2c2L*bjVv`n{E7{xmIWK`%o`piW(d=ayL&(dy%k@;yv0|X
z(sR8JIK|^f#f}t>46HM(_OA!Ms)q2gqWH(@iyzYy--kW~KGJs5sE7c30-D7lbA(j<
zeg$guNf`7PVP88K&cBE41Z|7$lVTR=lwkxsW8slI+X&(3OZRCa(07np25Ta{UTtR&
zi0<99vQnv5pno(Fl;cT*kj*X}7r#Vy$I_w}dw<hjHamU~7zwQvV9-juxREKVB>e58
zS#EA*0u~nY^LBl@qCViW3GlL_r`8q`^;8&YiNbceT4~6>(Pr}W6iE}<lMj#V;G(nx
z2198Yc14qxc*=DwZukfVYW@%`pughtm|-4~(F)cuDrk_@z)<z*J}K@0LlbB&8Iyt#
zM9A}CJjb@Swz^!b|3a6H2MM_lUpHR%kAuTLG)Ne69-&C-HVM+pq{0a=QqcT!HfDG?
zIKv4v0YM5|8(%t9E(ID+JgJ5t`oCay!|!5+_Y^&*oZ)>zHfk0aU!hspyG!o_@YU=J
zuLl=yn<#-aXLy3MRG^ou&8g>KXYX!ct~Yd^Nh*Vv<v23h{29>*TIk|F8bx}O_(;o{
zGALImV~mz}GpAxS<zjVR4bdZPBxP|~hrZ+{cqzv~Vu%UQSn5Jt`mnWU&&=<tZ~3#d
zHrmxmwHy6x6p0>X50;~p^@g+H^kM(gt5`Sd4_5`XHS7?orTkeU!uN8<FJRkD3kBFO
zF97^%z0Y3D(k(3|pB!)ggcDZ_xk?I9S8`-LS}FM9?S}__VaOzk^7Z6o%*u~oDFs<H
z(re(<E>S3PlKgVSUUHcIMWUuZ{6ymno)nXvO7e?LHqdR{p6bq}s%hXSG#9Ol7vTw{
zD5f7MouSJ0bv$5VA*2YE>tk3%E!b3~=c>*a|0;GRVzk=?JR<s7K)if5v@dgv<C-0x
zXy)q7t_Ey0&h*wD^<*eiT`N(AzBVAr<*_|EFJ>nAZA!Xt#SaH=r9F=){leMl1o{Vz
zbCM@~XkM{$64jf&41fDMS-oBfnxo_>n)QscFwtqh$4;Q_Hx#iC@er6gg|^&w>WqLm
z*@XJL&*rr!d6zSKA#nHnwzuZblH@>&O!aNju9Wn4J8U<K_L(SQs5D@SY<Zz1#|O^n
z%UI3t@5tG+7Sf=6*e$8OSaq0rCE9Hsfo6~v;QhpEwt>AC6Th-)p+<4l9>_FZ9WA97
zNpUf4+IgZF=;;XVJtH2&5P*a%dY0IMlDrJ;FtFbCgLFNN-DYdb%G**oYcw*k*Hoj5
zF%A<g6H&X=Vf9IK^T;Kf<al7QwAco{E)`7jj)4Q%kfo=H6_C+$W*L%g@%KvH0N<Sl
zufDTyUIM&pk+DQ=;gP<pD(}tS>`N10Lin-?8QS@;8=|I4cL`j3%~cg&X`-z<(Yp(J
z2L@H7g@)hu<xujRta&>>wgObx2|8&8_EIQqG8gcMOlfegSAo+eK{mI%91aVJ|4gJ^
z1JWeVi@rlaLzk4mzrc;|13|J>+td4q(~#96$P>F%tYoZ@kEVCxa%Q!44K3q#h!MM3
zdBu4hBmlcVVc%rzO>^xHz1yy=l-FY|sh2f|opcseS2d233~~f%tuS5I+ExeH`@U_2
zB?YIy@$8t%uZIM6XwF4^G$&%Rxo|hoc}c206O^&$rX2-~Nr7SW^Lbp!zGWT~J-r6g
z#^D`Lo)gLR>EjZ<cW7a$HZ%*=966Q62RoAZeban0(P$8c>T+$pzCZKu`gYqGyi-x~
zO#3pc5;fMi{7V+up~+k|#g8L6un;6$<SAM|{bMRRKE2Y#tl~VTtvq{G>zA(NoQRkH
zdg^Z4r8i{+CqNWTK{&UdU~htRD>6J>yTgMWmDosbIH<vTi2+?q(!w$kSg3rx-W<s#
z&qw_B@?xXS2yL)#0f*I0YJxA%&qnlnv;l+~=23-`rPu3vWSgf5gD6N&88^6wNznId
zn=(3EnqXwTd9-~TsI~CJAKayPHOKjQxBj#5Hy&kQ?mhR`@oE>b(p@xmQfdxF-u3x!
zaUCZd994eJ-&i~=DS`Cy;$rod#&Srv8+@1eUUu*s>qaLXPCLDUX5sXi8_{KReL>5@
zM&SYJ%byV@K3cA`iw3%5U815`+s)j?H=}FZvRMEnuSO6+LEpWm`Xs5oq=<tq6Ul#N
zru7Jrp}xNS3_Le|3MfO@GYQOmSfz&9XA;DtufJvq=E!n=ws=YW{P65YLHr8z-=xA?
zXD0e3RDud<F1~C$h9g6Pr`o0Ay^KZd)vygq$2tC8p!Xzm8yXsli=m1)fK?930E~&s
z?(W>*1ww;@DzzJBd<d|EjwUifVKjl|1pBmLd?|3l<Gx6bN0Hl~Z5~*g>!qNkljiIl
zq-ksirn@TIOjeI$B6+)+Su0DSlK;tqzYszAa@ZY_lcCT)w}3?|YeQ`&DAH~*tWi67
zL5W`i?j7jx()$$rM4ZFKLi5Y^0sWlXk}i4Gc;q@QJ@fABxaLK`V@9#i<BpH(EZNyv
z7Y=gpF!b^A8!dXl4_P1TOLE=fsk<k^DMZA;BOvDZOLf26eo{&L3&LKYqWJ_i3^~N}
z+hN^PsD?P1%%ZjA2^=2pwGVy{1?)@4QILKd&VI?EXfO8f)@5pio5+*z^Tl?*(YsZK
zvNc@T!K(BY4Sdx<V!+uo6SDBnZubv<$)bh2eK<5)I<^D54iQC&u42u;i-6YiZy9$G
z*dvQZ?S0W+8iSV4`sF2YEIkNXW@U(!q@+BkR@a^Y$OtS(mp?Lg^DsR{AsJCkLx^;Q
zw#<#~PH$PVbBqXA2to+^wB&y-^7X#=o0UP&8!s@p)YI0T2i49)wM1mE-8MItS(}TQ
zJzE0n5$P<cyH=8VYQz~<r`X#Qcv_1N9yoM_6ye@aFRWll3i8~>wNLaXg{pRK>TmYx
zU7Hwpxp)^4ADxqu)T$@uT<mDUi!}D0%n4@m(J4~5Q}NyCq&c0+5g?tvi=5PZm(t11
zDq#-F5ictS8_qnPQFHX-e(CzdKT!4b=3qUd#u|_pgw=mvoK1L30dzdYcDteEf)Fys
zpAAjGdd08ZT|p0E(3=%CFEyu#``DW{BwtsrzhyglkQ*uz^YOhMX4p4rSKZ&=%M_u?
zdXbEr;oYD2(Y60Lkm>IXxIG`Hf1Pyb^WEZa!6B0Tnylmb6~KWtIR#baYwXz<YgB58
z_Hlb5*i+=bk1uYP@!ZEsw7UnmN1BFOY+N8^y^1v!qN3Z^@%X&+M0tTpq+Gq?-N*ix
zmiuTxloAxC{=_nI3X2eR;}A9AfuD_q+eyy%5>O*$I+b#jmEV4z)Vqdh$*L73v{;-C
zqp3^*k0x&@9RNzS9K@Mp<%cTpZSmnGj>k(`q=9n+w#CQAB1m6Ts3!^-_J9MLmx?4_
z`m5|P^UXS)pVA+PDk7=L+%rCkdU0H2y;JNVlS;r4x*Q0olmV5IBu@w*B0RiPA;p>>
zNHPRxTKW}ES_nFu^}ZPwTpx?Tkqwldo+)}jn*0K0#T*%3^4kd{y~u1aN)t%b6ep|M
z>z$h`ndoeVxgt?z1z{dPk~|A&WmK!F9kzh^sT_cyO0+4g{=V42NByJ1_8=_jK50BR
zVh$|O>ls;Kq&YZ+%wHeu%{RsX5*0gHC}QLW=!fZ?U7T>&^RXI;S?u?+RpKh(MI4KO
z2D)2-mxQ9Bf&7A`sW{VTFLmq2cWNu!O$`<9ADj+0KD$pOLA|RgD*kd(q8tLc1|4O8
z=)AK-gIFz-sPk4oTc{p}um){-*WNA*ei9vU?6rUq1vfA4y7j#r`==B`4?@4lt-A3&
zh=34Qs?Gmo!bu(SfrOIF1akvHyomLa%B>n}J+~RF&c}>EsF-QDOU1YuPXDtE^6_gI
zE9hUyDHB$+)pqItAJ4WV^rZY6XNN9f;pJvUg^X=GPns-O)eRsE-(S+X(f(|*x5z3#
zOw!(_`SiA5FgxzBHC7C*pG?R_E2Fu4k-YXMbwA2AVJ@CEWEHHsz-jgr@<gN0v$<&|
z5ZWxLt)HF0p}+e4HuG>x;$##sRUnI?X1l1fY1@F{G|>-o&?=Tw&apNWT&z&B6s{?+
zp6X#Qz7%J5`>dOO#6toKXGqyjeZ*TRM0B}uEf8z_O4~LXCE9)(K2Lqs<?K;IBUQn*
zX2GpwE}&(NbJHvwDO}6ZLphimgh*#mhhNH;(g0%}zOR#-^IbTRhvM78Wr0veCe+xB
z)vZI9?wjgn3i&HJWcjyJyZZdT0`|#!>j9G{Z>8zFf|{ZV=#ff`F4;LS6=RVD6|;Y#
zx_=`pOWd#M{TSfjwf+5JWhEKu2W}kqv8p_@fZ|!H7+lfVY@i{UetND3Ek?oldfJ+=
zbvELZ&s83;`da!n;Ozxpuo8JiZSm)1s8C=GXSRq+;3SFWJRE@Q6LhAjV$J5qPXrPK
zfjA!1NPR7<2H(U1lBn5JBx`W62CxU>s>c<HQ)Ak9rA;n9&)3%|Q&E0}Jt|Ht3Ww;+
zgow$}gwUu*lc&b-(=ealf=v}g>&vE+#@=;Pf$&!mjhqf+t71Ln&(e9v&7L~vs;303
z?{-r+NuF=%RU1<Tww|Yvv7j(`t-rtOc~0460m=cKjCsxANqT}?mNrC%W#%DeggQG!
z%eP}iCE$Pzb2t8$uKSMq4ubF`m3uUG0|@(deZw;*czc9m$*0|)Hj!P(xQTfGiOT{*
zvmmgMSfIXDCnuGLUagfJnt{!SY~HDBK|&eBZ2mD_F*o`1e()+_$^EB$x?92?(veUn
zSbr4e;W%P+%$`KvwQV=J5%$c$o*%q6G?XEK(b{&c+P*cEs;qaAkC<!c1btkHY&<qM
zF7sdKr^&#uY`wDa@{8%MZCVTUewzziFdf{iF8t5}0zS~Y8N6Siz6ekYJ$D4Z;24pK
zW3`itzfOygAp1I%oPSHgVR1KVkSMs*PbsXjY<}l&+v+fJuRNSg6Dci`NU(L)!qOLG
zh??mhe64zZN%)yOcOL*PE8>R=xVx&zYuX53a?>>M-*Pna8HH3zzhs;hY#O5?GDy_F
zK2`hhhytVW&~Q(wt?+dDO*5}iTVZqJTY^5H;eypn7-}vz1!%L()0W!mC+6WBvnL({
z?wtRwJvpHQ)ygzXzp2Z`A)+daP}jRqb6h7YdHWoTZfLB&h$q0rj6D2<G~!H1n;FD0
zuvBExaTyPMCh|^Hq&o(Oj(l(Z{*#S^rI@7r*UJ3ML2U!u93!YCxA`DG3DD?Js;Q`H
zFXQTqsnB!QhMoRd%nGV`r;~{lmQOJ*+2|>%m54dyTo9LZ9Y-H<X;|ft`*<Nb7GcgO
zBK9I6rJ^1nw7k^;J<8`vJOUe*xO?a|iZ;+&b#uD;2WUH;dX3j=Yun{}jkFg+ND&I7
z9gGNtb~xDY(v_E?K-=Go2GI?_e7^c}O+WZzy-dZ-(?u^5OC#f#6rDfN36>hPU%hT^
z3=$M|xL8KIUdeJDC;nn+$gm9^4Px_Vuj=KM;)*htc&e7VQ3TfhyenD}{9l!mf-qD_
z#VhE8MyZFxlLG>Ge6{B50ELb1MW<3NOL0GhYj(J4sQW3oHQ|}@ZNKfIA3K-O7eZFl
zoGIYzn`Ycs)W7$KstwQ7M&WEuc3NE~Pm&~G2rv35&p&t3B8+|aw8j3wwLc5MlVdm7
zT6H!qzLZb%!7F*iWY-ZGZszR9_Mq$5TeNfgDsk#bP>!VW69Y;6owF(KmhOl|2=t8a
zakpJUdEI89+*`2m(IBSboZ-^rvNe{Zt-_+w+twP*$3UiwBb~SHQO%_)5^eFoN=<)u
z?KfB8m9Idwi~@0N8v;R-p+WF^sJqH0$fc<>yb2QplMiRG1;&CmA~|xarfejlAmef3
zJflmA*gNT-xTDI_=J&ms(WY#=U;0p0Ka?_k9NPtAxnV=zHf!Slvpf97B-Fu>Lt0<z
zMJhsMYZ@XjR8}%tFk!Gc<H|4YB@sLs5(`*~D<hBh1`rPJ8fnH;T00lCDVSMwEvDiW
zXQQmrhOml+TxmwKQ|W6G1+lk&HUrp8hE}F8zFVWRZRzE5YPH&X0#F>wB{l;ZH)9O2
z{f=}}oqRgl8jC9MjG7O{t&kz0v$l=gBILmPxbROX`CjZMIN8%%mna?(FBcL-%~6P+
zXZcR{Azr!?6$HK^+M9rBHokP1Ogu$_$W|(NM{@?mzhJxu4Z*-+>NIOTRFF5%fZ1DB
z&Ei#$B~^(8!eoIdfqomd#~r~Cds~3QvX*||MRz8x=Gjc&`o$0ro^;hVY27d^-*3T@
zr&BVJtYgiiH|N;e1nw)+Z(S5@nbMDECWfea!k5?QP%;TWCU2^ib<2A1(+N(h_<IhY
z8w=>G{d=X-fYn@^1-(kVVkcAJGKI8qu$nL}+6p6aHt0B6@m!${Vdkrd<IKlF$tQO4
zjOM~Fz@n5CTP@$5syB@iGIX@lXjkP6V^8H{=WL)+FHY|`GIM_m9+GmWRBmYmc9q>1
zTtLN~mw_OEJX<i}o@fb@)DLsAifQ%DyB#G2_aFvd?zqQe8psv`PN<c`GrfxTG$4z9
z;-HG&hT*EXl!n9#(IB=J1&7{!;lz46l(_z-X@z^ISBGIawyJJRRP!;yfPrcM<Grq%
z(@D-$q5``PN#nVFdD9Z2B=nW~s_ih|qzYT@bi+T{XeK+-tiE@lOOxa&Klck|LROJp
z*P1oD?|rTrY11ml?ePiXAN{vR<dmmf8qm&B_nFoK*brpF4@M@JlP<TW--UIzih}YZ
zQkcmRylacAcKj;K+2|Drh}c)@+|8wW1?uF3ksC7|9eq}{E~jsa`9w>xXq-AW=5V~K
zGMDoZ2Brq%Ej{!EHXKi4i?M#U$YF3&r8W#M+1GM^q?okaKg&Ky-0AOca9!z*i!XTC
zvC=h46{4nke`gyqe2t(AiNNKp(3!Zm#RL{mxVI8n4kWt^K#e||>5GH9e}4T<KxJ)v
z-cTjQBE-*wXzLsN%ow_MC{~I>g7F+Q8l|3U^~N49-$GDVGP(Id?59Ly*A!Nq(xV~#
z5S!3wrfIP~-p)NW&rG#h?hGf=AakJUd%&m;Ly~pgG*)aG*Cys=BA%QOn54(V+n0wr
z!KB(T_<FBGW@*#5`TJA^;_2>Egwt9i#KW>q(aZ0O-Os7+4Gg+syld0;?OHi7N88_F
zdY43M5nyW@WYEw~F{;UaJ*d{Bd{81@j1_%9G$-QS?t958e*%}p1SU$~XZt#HPXE9!
z;~mxMXE+&FplNzmZgJeZ1@*>{{Mwx{-ET<LE{&mI%+hrGr>AuhXR1r<c@VlWKjuAM
z95iMV5Af$XaKotX<85X4Yr#D**!{;dGfRS<G4o@WcfsCQH#FPeNo_Tj2A9y<*S+e;
z?a}>V_Faeo?q$Ye=$4OK&_*!6jhQQ^t8_OktQanz6o_%%jZW+?GZ;2&l49loH6?Pc
z+C<c#WUPCQ&SHbs)xOHgtePo0p}!%~U_G*c{y_)XLODik4@oD@GRRxwC<u{SE`UX-
zV*YhouUa&qX~0Ch;Y3fI9%w61#Gu?@bAy2*xqXftcT3tt##X=(vF`s0BLL5e6!jcE
zXH6Ym>vC%+h@JoyfFq}RS^8xJNt0^$-TuHCNbw~2`-U(`RyCDT{zh16@$nTk&M<GQ
zFQ-{*BDeZF&PB_C^)HmnMO2bA%c5iV)G5dyD-7YvZ0quCEqo<(HWqg`Fk4Vcy<N%k
z;af$6s-{h3Fd7VIloWWr@Ru>~I8Dt?KI}oGTGNb`hyG6WH><wO0>I=Vee?{m16!{(
z33l#s_jQiu3}}jdA)VD_-R_3DX+%rikw%we?pkDyL>%E^#2@u1SmsN&Pn+Xb2p0lN
zA6r>l)zrh)2vNbcwY%re!^r*CQwG?+$d5N|;3D;WVNE)i>(j+I|2AHM(Rd`Yb~R3m
zks(mA^h{l?NdR{L`hkVOXj?wGwaE)*WeA<oa-p|9%pWS$;QNL$m3H2pR*VzSj99rt
z2rDN5%pvXh#352bG6vCnprF~2A<K>)SEJXn)oaQRnIr{(E+RGrMY2D^$Z#Q-YgXKZ
z(mW^`X_TN~0`9#$;Na{{u7zHU5l>GgPhHSUIZYsTMy&8Dd3kl|ix<{)nBzetP!skV
z&FFx&_9~j4<bn0Ve|+iMT1sCt^sgkip`xKU=G6sXY-0u<6F56tj#6>Qo4WMq+eP|h
zS;#>zaGz**A1lDkLMn`I-uHSIW8isHhAc1AiUO@RnB?JGB8X>iHc1Qs?rlAa2mFG{
zQFnI7Bqz|A#5(cZfZApiYRW6cCcJ^dqi6ZWtxMKU@2D#Y9C&(s^zNyPYL+xx<PHK%
zoh2q8M%<()bC5AZwp!5iC!wf7M(P9B?<+;H_*|Re*9N|pf0C?4_wv06-P^CWf2qT4
zdk<+h+1RIMpLxz5>=dLE<0tuE+l*Wk^e%n$iu?a5u}#H*X1~|VXkMTN@{PR;?VdUJ
z$WG*{2t4MLFEz~zMah=0^_UgllH(<GtD=P6DI#~|UX$|=PqU~6rpKO6M(J@gx&*gd
zFN^c{z`xWjH{3Iq-TbOQ+lTN{4G$tF@+x%1<*kbCmnXo4h_vL;dKJKQWAAH-P%N8w
zP7PS!g<k`*zF8^v)ufhgfjXq#;#YNY=*7;_XEp6Lk`1H_XQV_o3f6LfoF2z++%_7u
zC+?I&0uJ$5yo|DOen5m_@dxk`-k__uA^?Y_xh1I}BP?e2G==tk?=5&4MDfg?UzeR2
z>pAip5QKneOM8JXy6>&O4q0DS8jdAyja&>Ew;;*^p>Z|W!pb-A@F}`lLw0<)!S&Qr
z>4(I~O14va4>uN%<xh2ptEi&nZF#4au8rDIY;R9o>dt{?g!g8Lqx&T+079it=L&nH
zrhGk0EpOIRv~UBMVAmwdNdD92bKoZ!9z~z*y+ZF<A9X)*nCP|@kpg8ZcWS_`t8D4<
zn&45H+HqM-HKU=0&#^iA_S^_pv2gl8+jpLP6U_t|G~0Q_CnTk#fJ4IU9Qj>ZJ8=U<
zq2e|^B6VR>w$emS2X2rw%J@qQ%L+Q^jJM0ZBOqlFDuDPlRG@%?`1gq2M+Dzr+Mz8%
zyQH->pWD8S26qSqA#&8?K>^o8X_&Ad&E-Ydvl{rbFOfQ*wT~JX<vtWf_9Z?8EkGRp
z_4{iR*GN@buF-PYR-Y-aBT3uAG@7%e3$H$e;o*R}gZ&fl+AQ^nk*rf_BaZ1Co0g%a
z-w0L+^4l}3j%}DW&y(*}yLJNdh!r0P7dS&S=7+xh2xk_nI1HEy28R~%CXRaA4g^zc
zFBz%w2O=kr$z34`A!78}k_t%MJ3Zm|fG5bOjD-&e_MTdx8raff=h7(Qtf8?XK|ZBP
z9rc~#z$S<pMM4Ea)-2bxPCy-*R8pdlUH(c^<7Wnmv&AMk#*^!qq=BKOH=_XtO`MbB
z;2-IuuGFZ#7T}}|h=h-#=Pozm0HX!bC>FN$AKTZx>-o{Yfq{okmhOISt+jg~EWGiK
z;+;2b>Ei?I9yuWeaDfqI)RPX(8u)W|qVMkiSxMMe<~D)WVteVOOl0wG)7QGexByvO
z*yoaOzV0&BaRmRfuLQ!H$?D_jhq!mb!5XLJkYp6a+d{!s*xU<MZjdBlh+7MVlV_l<
z(4XEtj~Sc3P8%{rX|UxUGctn+NohkXSbT=9mQF<wV{$we`;8wbNo54H5PEuE7ef%C
zr=R|j1ByADyz5FDfT6RH%z%v_e@ND9W}jiVqa0!Za6~5RxJC_{60aUE?|F5b2W@U2
z={N_?Uspaq^vE*z|B&#F^EZ5p3FR>%f4;;CRo}FuXWHOYjFFUgL&+{bZNwI=)BL<5
z?MQVI^Evk=wC5aCWl!E7iK#pDhnT!(I`S7=_ZihLTC&%8or*$^G@c@|eLebi4Q}<i
z&Wq+D*N=)utr%}HBknB`21huf3|=b{S?o~UX~0Kz(y?qNugGCo%LkyG2OZU9qFc<o
zrHtR`8IO<((I#mZT)5=+m)8e}kO1OmA@g6nZ$d{%{CiI^97VTFB|pEx+`lHV_hft~
zKF@5`clx?kHm7i6_AGMTRo`CUE76^!MDZfR*$vJ%?R{e%t-ykc9yRkEx!Il;!jJ<r
ze-J}!%viOHg3W7w;o}r_y>De6bY%XcdZgNgZ6#WNWg3l$_3;_-{J8LFWma^`U_gQ0
zXB0fB=;&0VW#IH73pOcks2{lv6*)Y`1SU%s$o`Z)5YsEIS?-ttCYP0(ZUW2@WaJVN
zthWGv3xX#4ag6KcYOL?F18|s&Nj&dvuX$K2G9T)R2?rr;HKZM+hJmi<o4M*^XKtQ?
zkATOQX64=dJfPODJQjcb%szHtDj6ve&-!jrF)-6hr0dvM5K!o|=DGVV{N6tELWsxU
zIFM@2+x*G^i9!gz=5^i8%_EFC8@X986T_-M390JP?s_66*JlYLtZB=2(%DOC_7|5X
zDp-)KgpJ1;A%Hnza^$qca)&6u0wQc7^3BrqAt<ogvOZjaOryxMi`5`>GDl##siGb2
z>ux2}0umN{*-6bg;LLX&V9|I^bE=DZ8b~#5j!Q>rMUUbGvqeew(7h($mUoxgLsTu3
zTQK)9oDj?n8F0R&@cvzf=+cgc<}x$x<Z+vzcK6E;L6*TP=p4g(_GJf&Or>rc7tBn#
z3%<?A;)K%f8p50H+Dbtvqb@!d4O^b@$(CSd`|(^Wn)^8xBZ4ju=k|zi^0Os|;FHz5
zSQn?I1#0KR2hWbiDP<d;(aXoCUhQsMx`Y;(Ep$ed)uN3YSb_wIGO`F3&F~~lB&d`^
zuiD^ujj1Sz4R|t2lTDb{FUDm5Qwv~LV^a49O<+y=a<(Nd*OSBpWot~~B|Kq3UJ}#*
z1iE$@rS@zVqNe(3_Rg>9*T){AGP+_2jArmR78h<YiSA%iXBf5w%u2ZV2f-oIGC*oM
z8d8T_?m}5;Q{o*DY4kKNQVTC|%X)0-6Ev{Xr1C@v`NiKpe04=?6wtL{{8swy%4yI_
zN9jG^>t`#YK<`fH`L(x%;{YS-?FWC`xz4R~PiJ@z-6=-HciKv*=dn0_Xl$`f(LZ!1
z<dPW|cKnmQp2BQ_cF(7A533KL(Gy`FF={;)Z{s||<GBchFquVhHkLtbcHW|UU6Zo8
z^>Yt<C2%_ne1$IqzvEo71R1qa$#eQ{+(D7M#Sh-I72wTIP{_)wXTFfoGayY;pLN@b
zm3m0Xd|DZ~Q<5dd<x0)22|kM|$yVI&cz!1nVZ)SdmSMj$=tuEzx<YRM9BAz6)P@}I
z0<`OZuf(wTt#Ak6HPv=3A@%l{A?hbiNEyn&2>l61#TpZ)n4yg>w09M%DW%5Q-#2K`
z0B^Hzr&_nW?vU8h%k~;<-%UhW=CY1tP(8wDp1<rM;^+wvq?8_N79_F@L^&|Y`D9f%
zV{#>{pW*gQEe-W^(oaRm3;}_xnOhIPC6wyBqP2YY#(&A_sH1#r=0dLQDLt*(;OS$e
z7NYh55};<=HV|h#|LWXgzY-j=uJLlsBaEJo?ZhpL{e`%bwZ*m3S+y(>#Lv?8Zk2NV
z0q=~$Ljnap&j^N1?A&ui@jyS70l}N93fA>0NuAtMuC^H?$kKhQg$wbPuk>M}vA3fl
zQC7D?RVs`vRfNlh4QMCc4kSQWLt^^{hP`NrFFt>8%e?m8k~yD~F>7zjsBYuAfE8#)
z&n3KH{O0*Cyy(ZtJIgd#;&-JteN}a?USIS&#~+2!sE4$U5{PI-GNkD1ZGVRXosl&q
z<;DOj2L{R|VsDArZj=|KRLt*ynyR=%vHkpI4N&T{F+1Z8w{kN}>QAy@-{tO#Tzr=9
zqbRDWqAEjvjIaH^nRrb5820dpleZ+CVie2^#C*Esw7s--R6RxV5w%n5++McEtw~8X
zr#SC`Yh|G4_VRL=(8P-)|FKnD|L%P?XBOOyr4CP)ujZ35z>pO`j|bN_+V-I89Q;b%
z`-XlXQGt#iyBT7dLguirI_=x8XUgH)_24t%YKL~0z46s*L*@A#dE`cPxlw1R!$q1H
zg30-k(=JkCEGr*`u;{b?4Rx5~?yLgiTQ*Z)zF(wRm}GFGl%Qwv6F^WAM~98h{WEZ^
z2b2cJ(758@z}1>~Pdv@`?AHfH%=dG{`kwdt5QxlBzkL`4B?t<-a8g{TtRtwXC8_;c
zEV~`A6=r?Il_>{^Vn~{ud@2Fwa9OXaqq;8{SIQlf^4GE6o5}1}f^{UXMn!9XeUuqG
z+)BWrBm=9Fah{<}E=+NZ+N6HT=%Uv9cJA{OFynGd?^B$+z8^N%#ZxEX?`q8kI7Xaj
zme<;DET2=HdrNdYL&}>g$E~qK7-u6_=@K%9;px@=7CDxV;Q06FJVZuVb`L;>!tsjt
z{iq76;>DZ3i31Fh%rD;Bt9LdPJ&cLca~cRFJ4}=5qJ%Pi#E(v5ajF?#DeqgQW(A9a
zzIWLJ-4r*CZix`ZnIQWN0uB+u1e#wW$v-l0{2f8igh4L3o&t<XyXzEr!LC7N_BrD<
z4%xH!gjF})9B^tI4Ts}S?1ys+lMUT0@;?2?ML`|@q9Bgs4WHlqpfAJRZ;EbGHp>ui
zH1ulCx>-mHiA7Lz3%IL}(7Ue?^y`_fs$x!E@GUSkPNF&9lDueu*;JBEB$`PY3@}e)
zrx;vp{L<62Ww5=9&o{=;T1Q&?OmhzVz?%4CC6vz$=?fWOEFV!w8twzM-W8S*Ie4df
zuAEU*@xhSA!_d`cly{;00bfH?t@XsmA7%Rh)*I|8gy$(mdY6Z=5hdH`2ur4wU29sa
zU52CAWx{tCR2cd~g02nn7dc@+!T|ZLjO+z_1a<#2jw8QfyH!zzBn(Ve-j9k;1m7z7
zga84Di4ye|#XAeG)=geBAX#)(?N#OHJjrV=*L9$AwGMFT0AfERjtbB3=>VLHPu9q4
z-&aM7coKexitQu<tOFH2djXyA+SsKGbZDgZ1CmjSH&B-8-$7YlUUk$sGO$SXBG@&*
zWExnBAnq)%d<EL(r<rZ!+YJ!gh#U1#%V^*R+~@K;-BR7+utJXlKXW-ZPoCxS=1%VG
zv)+3o3#;*C*y*!+12TXyUYB~j(c{?eM3moq<zX*hZ(j}A-cIZ(puA_-zjSaVj-zk9
zHxKZ=18yV<8FjhlkkRt|J+JZ-sxYlxO-en~J?vR)nMqYie%Wa?UR7g3t)*Vo4y)4P
zzie#D0yCS4+5{E0(41}0<B93sz2AbBe+!Y3)M%e~*ywkOxkBJzQu@|*N!w_x5kqXc
z?G~{VGD_^=af(qqK3f{+T>_KA;yxZ*IBA{WR#Dtf$NGTQRkby#S6pzV{r^~1|1bJL
z&LjXq<u?>c=1BsIM4o##;z5z~1l~Nv)}-k|VD~&SC+_>K<(pVW%lM_1l<8)3Fpx6x
zH3r^XEU47Jh15$TT*0SRQ@;%eO)dNu@_4gd5Iv7Cu;OuJ^NL{|uwzNr)McWD4EEh9
z>834*lUQ$#e@Xo70HUUW^Q0ZgDoNhK#P$*01&2O|q3taHl0<pZ=I48%-RYzR8w?wj
zeFy1odW7h~QT~}BYg_$q+5bjN{tE9P0MU*@SzK5sR;6B{O7o`rU;`Hn_PI;his`#5
zY0aNw-FntCF(IOyJhD~2I!koqeFL~q)mU#3=BL<$g~85hboc?)@*1|i9Ej1B;MC&S
z0!K=oqVCc=h-ZlXaE?c6w(<6kpEP^gNXfb_&);-PC}24*HS-HoyA1lRRaDAK>?Gdm
zYqg&>hKBPl0qETWjD};)3JibbB?+_n!fea?Skh3l@53P<L@yC<SP%aDh3*j!s^l&S
z#3A2L2-d3SV@N`lt=pVKReoO{mLCEIGKs|}IBK}v4v<G)VFY#!M_MsMG<Sx5$_?2$
z>J=EKZ~bN*8T6R&K7&I;ii3gM?vp_!3BWvb1kl0}45v3lPO^xi*EEgM9fGJc8DsUX
zKVF-WB;@$|`|{B*10W7n{i#kst_&Lve1=8fV}DaB|Ap@UrZ$&4)G`CX3u1o{XFi=>
z$9;@=ibu_4uQT)pusNl)wFdw7djH4wtw;fkZ<M)a-+l$9By(u3c`x%#HvZ;t@-ZPQ
zePsOcvo6h%>wnb?n1?I^Ocl|(=!e-GhPxI}+REwj3`*t`1FMz=Va~DdVtEUo6IDM!
zj;qym)yL-sCK+a+lvdFU<=4etN%bo@)|WZ*kTYq6c}Wn^GdH<H0sV554p>}Jp)l*I
zi#g(hd1%YSMKIXT<-CAs=Q0wf8sL9ti|5YGU(fIY8rfh$Hy3boFittdhA7=J!6uV|
zF%YW1FAER9U4(VaZsF$kuSDMbO4%ijPx!Y_U?6ySc!1SV;}a4B{SwG`eIRZW2+$T7
zi_I=h_}uUOUMJ#MN&S^jwpmYr-Bz1`49tj>w(FPb8-{xzJgynSCxeb@S;(Y<{Y~ya
zI5-Hb-zc2eX=G#s<N-{PRR|0u%oegOLM{<nwW1j<WPvB&PJ?)|`MT-)!=dU@P(Fge
zp{u4dARB`i1d+j^nM(}V^NJL)Sy}WrKGxROW22?f>*p27S+R6E$|g1eUMZ%iS3<z%
z49Fj`mXCSgQv2!cC2ypbr|zuWAVKKvsXHeA?GG8DGJNC`5b13Gq@cA)UTS(WaypUB
zY(S3P;CiqfubM(61pe1<b5(%?o;Op+<Pc|nmt<bYNyqiX@;B*@gUpF_0BEA%;f2rb
zZX^%`u^!o7sa5}Qxy6X<-`Ce?{Qdj7O+aR}#Gcd2&t{JKh1AtG!w)s8C$nS&I8<bq
zE1aY)@Fh~9+ORyrD}2r1C^eX>@5nwCu2tJs>wUChxFt9clJ2gDg@Axqcir+1^E)^?
zN{Nr(U13^xf9T2Ex!~iUi~=Gr{H96^%m-PE<Nv1P&l2@D=0Vj?euxFeVlL|?)%;$>
za)e}7spW(E#uxlI;Po}f4*>XE)PeG|wSBh`rL>Grl+I!wH2RmKf|Rrh%`-l`<(WH)
zIVG^==3S!r21KAAyBB0TJf9+H;dQaaN=q%4_|!m+d`0_naS;N4cfB`65{N~wEk;)J
zx^WY-dJ@CgK{8qKbe6_pJT?xG*|x>TO$N*|0Tn2S#vxG5lmpZ4WJzmqr~fy9nkl}0
z`&Q%q`VbNla&vR@xakR~ub;CmIVnR6Jl7Doe`BRQXruc#JAXp}&nzjw<?+e?Gg1BO
z(T2yy5<)CEGGt|B3iUA81N{bUk`={HPbs%d|A82~DgNfL_S^0f|I6mh%o5Vo&14hn
zhmMYpP6qn4k-+9y>h{rKBO>E3>*W5km~Nv2SAV@-4#(JkQ+86p@a67!IH*v)0s*Qo
z7)!r&?l{xCAAgGqR&21JQOil%LM(A|ThQrax6(aAVg)qgpSW`Tpin*OFP_~f|CW{C
zprA#{?#D$b)jG|HhX(fc_ME9GB}}Q^4aZtfU#iU!{<W&&@9a^#Kp&F+C(RiIG7K(C
z&B^I$mUk}xmOC<2M%xv445Aw_s|2`Q0ZoQnNH?0}+rMTJ@Uj!lt*SZ)Qrg>DTJ}WF
z&dyf1p3pR>;Zl;K)@akeHu;7_NHy8%xS8AqU|53(io%BeCl1=(2r~_Kru`UEK=Geo
zo`W*jQ1st9KA4h`p`)X7S_pnnGbjTx+q^w4J-ls~0W3Rw)}QBXeE#bQh;IW*B8LMC
zw@ocN1^?f{Li3M~MtpWQL{7e}JA;A<zjZpOr=rHLp%v_B`Pb69zh?caPM`n37yL%`
zudMu7mh$Kj5D?f*l9;OH5hCVd)7_+DBA4qN`|m@t$lJL8e<c8t$8^0vtSM%4?HnC(
zIvvXO2e>?-IC&M2$HsG?sy+x;43K7XdLOPUxpW`?>m(ILU|!_OC8*>-z`-^l1gR&-
zV=BBkbE=<${qKipd-Q_?;Eau*WkCS-4_vDW`PWG!f3pOh5q7Ws;huo^%wRu>y#x;9
zruxW`y?=2~Y<^H4i>PdzsefPp@7+Q8FCfEhj?3i#?jHa7>_3ABgvs%<W()tH9sR%J
z1^iXWt76CDf71Wod%@pyTn{t8!2gM6{|C17SG;aWps>Jl^?R}ZRR8~p4Ez9GHo)BO
z#@(R)GZ6o?@BLLLKls0c(vvYr@_%>4e+nF#?PqmYa`okZW&cC@Z9&=Vw-@CDZAQea
zwbl=KV5k{3E+oj}^GWIxqB#|r64;#WW1#%}?|9wM|9xloGcuQM)2-A>^zE_#5f3Y9
z`+WCNSjy7+a?<U04X)d7+#G-Z!yyQGawbb${@3|`o0RQm@q|&;S%Wqip(RX~$4|Dj
zH3W|+2X@KTk7QbNx}`kn2f>#Ge5%A3oXhvWa$<vnj$Fwe^FnzrIEP!@2g9?quS2Rh
ztRS|EwoRY!eFJt66q+IMFfOMl`agZ|fC#MU#d_v{%4%1%^N3%g`^jX-Y{zEDSxj2}
z=<?3(2n8GjLK#0yL!^%DOpgC{V`Q2iu;%}=4>Ubouz|C<taOr+CKu1)N7jxQ^Anl`
zi(7Ob!ljL@cXchO;H~yasP*34Jup;D{Xv3#^pdLDHUk#yW_}InfFGepx&C(^`j-I>
z3%<rT_n-f5ivu%Q?C<<%tO%d;kdK~Y4PCuQ8P;C0!j}J!xWA5y`g{Js@dZIjLP7+j
zMCp=7Qjm~Tx<R_Tdr3(}r5mNY8&)Zi?(Xhx7JkoN^!0kZKfm++?|aVI!`ZX$KKI_a
z_s-0ndCc6oJWo$=T-}SMw{*-F;{rLNC^>AqLzx@{V)RM@CYtv{T1VXR<BkxehD$fl
zFcs(?3p19DTJ0LU(t*(Fjg&&TB6r<EGuyCWRuCH27^h6r+1}LCkoJXyS}o{knN~MO
z`InDRxJj$*hWj6CL<SlGBoV?kFcI!B(L1F9G)n`b8UNuwZof&O<nDnjxJb>ph!mXE
zJ(PWhrM^cN?Qg<8ez-@*zQPD_AwO(=gQrd9zWia{_F!Mr)o2goFloO550|rZt)CO_
z4+90BG@xK_`yV#^h_+U_w`YA3{<^DKQ{!r7$PiHS5N#NnZzZoZ{9$lCHdM)rPt;5L
zijJ7?#zhY&ctu2^KjmFR?{m7v2D(%yQynjBC#nL~04Tr*uw>}j*AwJ_<-j))7iUbU
zeq&iY;ZcU>N5{AhSgQ~x*e=rB2%JT@6EDaG>Vw*6;}=1^f>dRR1#3Y3$s}v(NbEfe
zz!q}Aq3iJw8?0dQKiniI5BWCgHz_*`eG1%5>U5M8k0s%I0z7Fg3Os3L{hUVRFW=n>
zJn+hj3ux1*_5H_xDf>rAegC-qfV=q5XMf*>zXs&`*-QSvJp+9dNmBeAV`-P)3#D3%
zgORT%0!)}Zt&X$Y-%jW4kQy2rcBK;ShAK9sZ15ZPoi07H`!sOLyyS3HpMSqL+nCf;
zWb2(^6QEcRjE<d-dfB2|NHop!YVWptuu>?o+HjvTms-xG=J|62Z5coD^w%pHCA7ye
z1o-rvdSKY%PJj0O&1BN{=1$Xpg4E!dnwpkq6pA{N5EF0CP&qA2^cXuB85tQEd;_*w
z3=9k`tQhi>oU+tO7WSuj9}c&UNG5}S(eg1FYJBx^%wZlje4)${OUV6*J27DghpvI(
z0DNHj$QpHzBT*_*I*cS#vtDB-0r~QNR#4WYa%g=7X@tpE?<8p`Mz}nh><@MAnBK{%
zNdtlo*8BBb-)6M$j_xO&{GX%yDG8xb^@I5%QQmdWL?OR=Z1JHerk+ioS$95<2QXy@
z+B{lzp15pIdfS$9N>)T3A#yN&oq0n{&Vf37j!&HE!|H+XTeX#DuGvJ>$YaWurYr?E
z8(J_Gl|T0?G8NAF0LRA3WHsMH_gb_!z$j$<2M;R(Dppojybe2Q3Jal!maE<IvD(h@
z!w?7bBmGtFxVll*oiMs)ukB`MM4oY$^TY5iJU_fEa4Qq5X3yRepEVh)NTuANb*|nf
zL1tFDJoWj?enYNC_w$j^82en@KqoUodF)i?;;7%*`SM-JCDpNK(dw!_;R$q{!td1=
z53`;5>57R&fm*HjNy<Y5SbvVr12@Pg2EV;ASl8lT*}w~y;~1U!l!Qg(DXVW@GrE_H
z7yM*TcB61#F}LlM?go64OsY@BLRTV<u+8(P>KUNVd11SsOBatGT$_REDAL~2Dk$#k
zgv!dwR#sN>d{;u3`#z|mrdH#2WSrRZh=?fu(<cy>t(~3S>(>Fp5K;7n%Y95D5`CjQ
zr~THk?^?8Za}ARXlT`_lqK5i!KWpU9@^~!Gon8}At0y5UJNIQ2-#10BH&s_Ov(hB}
z%G%wgQF%IgQ7w41LeAISc!`OrCk$L95u+=a`8F#k6UfEa(DAXme4cSxXpzrgN&8^<
zzTUGAhL2rS;pxDE48{o|9GX=w?!~o{klawRJ&>Kt15zxv(9HU)Z)F+D%0@2PMum}~
zSKk}fKaaPrH;FZ;YcTbq4_wYh$2?E=Zb(1X)2^(UdS3~gg=yb{mU;jO<P8lPhaZgU
z<#q!F#Q@Kh9EQr*XD2;`i#_BVuiunIRoAOhyLqqqRuF0bcw<O8@1{Aszp(_mNP~0~
zt*V3O7G6%#dH+gs>SWcp{!`f*<8>Ynl-_{AIXG#4bckFyjf|P^vuZ2@*9UB=8n2rj
zNc5u=9ZgzPy?#D5cfFGe&eT<}x@N=FaZ9UBF=@Qm%N$Q!e_Z*oq?ng;$`#V|VSy9x
z%Eb^o3)nPY;xCgpzM4iJXR@OAI_YOHo&s4ha*~KH9G)8<6lf^&X(gzNx4}-he@y3&
zuKuZ-$(B$b#9uw5?{+#opxT!blnd}w#RTPh=brCB(q=8or4S$2U#7IR{5{a_y%>Vi
zX=DYp#&B-5i-oHWU*TJFOYXP_*?*Pe7jcLw$LcbwVBOJLU#u>NkPvyyd&xzhszlf!
zwuFEzRR1^YELVI2#ap2s=(B3Bvjt9}Pl}&^@2sA3M>bLJWV{_z3s<hOjSq6EP-?C>
zJxf^>upinTIHbaXnBw5!P!U1~=@j0-`>FrcLc>CDHJTnc*<O<KxPC8Xnm=-rkTmN8
zB}DZNHmV#KQl7`GZyL1#YfVn282_`I@WUa2N>@zAQXfGld}Fl>%F+hLr<YqpCQcfK
zbF+=IO|66su0x1^dQ}8WGjE$sZ_RHu%9;Fnh%{@8=R$vtV}-5w4<eS{7n1MnZh)Oz
ze_LBv_PsXWLD{fa>J~V-KAeIK6CPV>K$NWAG<oUnL<x<?_I&?+oZC0xUq;3<VSavo
zi?xPE!c3l?8;Lxvrq!qqnJ1b~M{<nZFTIZJ2Qv)JkBiK6zotG{ZO(}mQFc-fu8Is@
zqrOig_84jH=-%_ImBv8eQdiAEH9yYI8m&0NhTO)|Ob1`#=xUb+t(gJi{$p|Dpb;0O
zrQ4)Ww!aKsTaxucri{5-<nmQL3O`CuDov9&VMO*2c2LJu63x+fL(B5CzW%sil0E;h
zlthG&jxcTg;+C)3hqTfYy}xg~(%Hp^`M1QY=^hJf{#ja2k6PGP;Y$J-#m-BKUAcdJ
z4191=QPH;LkJQoL>o8)Zuy%RWrACjl)z#I};bA0X<hG8EVzpAlg)|y-VYvw#i#6IL
zGft_9A00S5<d}2D-S^j4haWJ_w$@T3(}V<?8}y)->po$L^C^`)S6g}ER{mBS)j1-$
z-Q&@$|F6M}5VH3fLOhk3Y3Xz3^g?Yv4pZe#sAAYERy>|xD3e<CCGnR%1JL`~J_f06
z_c%O8S4Pne73?KauZr|j8O3`t9g-i9->awRvY_%>{!~e1QZaF5wGe!&M|rLMCV!yl
zD9WX4N~3(sf;Er$%X}Q>Ouk}1H^GU;c9i_uJNPPV1FKx*vBzWoM`2RgF1Dhz299o>
zY;0^e`{xuBE~4#BR_1^E#?6LjUPAeN@MKJP&y08+s~5HYLr^8Fclz+W(1eX}vQ)h@
zvMY<h8&-PYP#;F{SU#mUrKDYevBYm|P0L4aG(WukKq(J-MRh^~e{gr#9?VJTh>=md
zL34h$6*8&CG9;HZ<~<-cQ>D*oXe{?bW;p&aISWx5q;y+2@ne@<!}xMYa4<B>xUEeM
zRhaE8GzzTFHhwyXi>Ur%U{WF-edtn(rhN;OmI`%r5ZoDj6d{{2&U|-LdzkE?VjoB^
zgZoL`fI+t1&K;{r1-Db<a1d>Qq8*ZwyzDN!T4vG3j?Y^?#fdfvB?uYSKvCh!KgfNq
z?SLX5y+EE(JW%717okuptU?@hn^8q4#jULi<u;Ju=OLHEMaFQL-!&4=><;pjge_Pn
zspN5%wr2H?@CL$$7XJJZqnlA`o?s=F4_^!emEyr=I3|6j`K#%lM-L%~7!hxKAE1xW
z2X>T*dPT(tTY46xpE@df0hiDbpbZJqGFg@%-{10!gf<(X5C%*1U}0TllpWWrA4QqF
z+G5WoI)NJwYm*G{>+C6DK!z&?pyRO{Hj?ffT8P_29*<K-C1wTko)iHOTM6^Zy7F>7
zb)T_9O&YSm=*K%Q+vD%vy?aq3VDTC;QQlevA^yu?OLno8P9P!&>o&yyLJP+O{CF%c
zP4M>Z#E&1Ct;9Lg@$bst1~E8=nL!q3nWbZEII2sU=69BE2~-J9R1JXx)4d%&2#pWZ
zgSOnXHo05Tn5WgCi4H~A5S!)Hi;L^bm(iDt;{h)B-RbrUbEj1mbB|A%ZP=x9!xtUh
zeIiQMi5Dt~`2x??21m!uKL2KfdyXc6=XlzE)vJEz<%K6he)#*X1NDA@f&#K+RC`@>
zbIp~NoX?+&=@8*Q<(dA8p`p`xsD}td{js&8OeFf`9>^V^9`2qJe;VdyVuXI)h+TZm
z;lX|-`>q~q7lrf4fJIpFJ^uIZHwx?))s>a`1k#a5TNuj%990-w)tDOhTFd#XOB@$n
z2^JlLF49Fzi{!h)tnQUR!frx(v>sDY1sQR(a%@Nji5n~v=@5R|@1pX!8Cs)&LgNYb
zMqZ4f-EQ~q-lw1aA*>Ggf%6kc0Z1TNJ(;_|C(l6gtAm3I98L3n2)&tu8wdypv{Y|C
zEBT8!IIw%$Ba|d{q8cH6`}xk5Zj0lkTX{uE#g?&lFfv4zRJNG(;taL7&$OJv8lkt)
zGWT_st{aVhZLKJ3+>_}g2_{l8M$@lMDi}{yrK6X0_D>J%xD6h8mNRip#oz`bT3c<Q
zr4g)T6Si<liyo?46v@fF8vLgG&Q9MbW0u@|fYyeN$@j92c;3dScYr>6knV0hf&txm
zy3Yd2mWLbqtS=D($MIcq%g+FuCV%dCAcL9W>$h)0a1b7+r>{ga`h)z0Xpm{9(m!n3
zi3H8DZC4DYAD0|&8CxmQf0fh<K$3RW=}}-WWo5U|nw9u?sCQI6o>nRWYMIdpzhzYU
zxf(7aCXF0}8ODisaFh{;1f-Aj_2=lL&pGHAq1cn2JPut8M0GYWs~6;*k<Z*M)5wf&
ztp0AOC%#|colT3)8?)P$<nZ2+-&-oX1isUg$pPL`OEV}*@Xi>bMTHb4exX`kB}#%y
zZW{F_@v7a|Qc`+mruR%77unWw+mMktTAXbK`Ge*;?$T2B?g_zIj=RPDRQSR|{|v@n
zt<y~*iHXhYOWoo5uVD&fvRh~~NxE~lxRe5xmzCv3{+D9z3oi23Kmn))Y9?>Q3ct=7
zYdk_Us@TEKyf4ndtutQFJt*nkzi)ba#6TZd^3?L(wSH;-AoYS(TdUQtQO*9r0OY!2
z>@VM4_A?XfUt&b~;k^>p4SN6e8`P1o<5`;Tyjn*7kzdI#H-VIq;^k!XYPD{zsjym_
zem(Wq-DRjvo(O2LLQ>D>+c+WDxPRO`-)~4*<bsyv6M9RPK!FP(atq&wn-^g$O|EOn
zE_#Pz1&oYPv01$&Hj5aXFP#otk}5ASqBx9ND}SN@2FrMoc08tN{^K<_ch~!Z`vO6&
z1hQq7g_WqijLELArahnhWcHq|ooCJ^Lk5aw1t-gQTHyMBdHTRF^VoKRlJP8>{PS<y
z2tmM5e043t$ki^9$6~`grCy^rnfyTnTzatp<<m<E6n1Lx`7Y?!bsTT}gI8<1iOVZS
zAzfI@^s&dgdoJr9*%-R4NRc-c8A#NT!sJYc_Yw;p1td1nco{p3TIJVre{i%RyoTeD
z{2u|&Xl=%!H}1|eDnJ6REwkNha64M|F8AkaIn-mk?CI@gW?*P}#|S0x7s2k0=Q!7L
z$urwBC$WC1QTeIjk+fCRmZ{s|p<C$@wDLysRe)5SRTyztRmu&-a06R?`lY9;Y?iky
ztq$`z_b*FM1ET#O3kI*htyGmyv4$7?Vmz?cXGK0i-b;1IUJHfFtoKol6q`OKKde*u
zWOA^c_iJ4JhacXJCUR}zqjH@>Z^zyY3UbO2{HK;stBX2{2<+w3VP)U;wN*1BN&jaf
zcf6eP2H<7(Jw6lJJ6U{$NWyI$KzPh+p#Ez8Dav4;a(+TWfTXk<6MvZ=S=U>wg(v6q
zOYDb|50{A^sd~;+lV)Imc?s#<P*Te-TB$wnk727j)LieE{x$$NfvIS1lRiAw08Ubu
zbFTU8&FQ%s0tKy>AEpOyyFI1HJHFXk`dlzGV~b8m8uyOuLd2VXWM)I%RB_VWvsnrC
zTi~-dbO<8)hL#x*#M4{!b2%%=94lH7lL($n;=O)ZJUTou6e<MMf)G&vI`CMJSgW|h
zLE6P3daOLI8RFm2un9BJ9UKBcp6OGGlcZ)Fk|be03S%m3lG2a886p(pQ|MK)CDa%%
z-ePD3tTa(ss%W~HB|eO*xba?%ixbPO`zBD|)IK;9f!w}gRS4KtIj?9LOYvTVy{#|W
zURDx^fw>7%Nz+ZpV6Y8BH2`{UpH|1=0Z!!|ylSh1cx9f4(?YbW%Ogf*ul&y9s42k#
z^-wPH(~^t$+g~B=?q>QQNhe?xhN<&UF4#MiW<!B0GtR+x5!4iMV10&mdDi}kr_KYH
z*3DGCVC)G@JTAQ-EHk~R<f0PIH;}}O59>4TB_ed-VV3oShP!S2F9LHXv@$#ZdV?m>
zjqyi@|MM-+Jz)Dcslj-153bez^UWtn0HCo`Y+D=t`{CVtUv^loM^HWF#s7bc|1Wh`
z^8%dXi^QFhJTtsaow!M^KL*iu0bs3NcNAV0V8|hWWCr-by${%&gWutO;Bfr}s!FsB
z?LgJ*i{Hq(MVUu~Ax^Nl9NB%`@pmqJUsFs9&Bh0@=Ni0WN0Q$>aeV<_Ht-Q(?Rn0k
zP9Xf53RhMzfEo|H7@wNzq3ga&?)Lm#66Wq_vu{*twq>BOf@cB`>}bUT)NIZ2MJD~(
zp0j*?X<hO)LNhIZirxe(yVkis3(-H9R4X<wK5PC`I$mhZH*B~)yth!6Y-&{f#69Oo
zO#&v0y^;X2M0@BRKviS-t|KQmZ(Ez@_uWb~D-Aqjj~56<#q)#|a_-xfmuq6}#8jtz
z0eJBL_+J1&&>|k`BXQ6FUe&LC_&BovjL{ok?kAqpNbVM4mYfVG-V<w7+W>Flf&1rZ
z*kcf}t%aEgw~4^!pRz&<RrlBrmn-L(-9>pVfr*Lo4W;<U?2v@mA%611seAj16|tC{
z7UMb10=>Zt{IVslm+z(5bsqCl9*KWyI(#qf{nJEq69AQ0g0=D=%wP<Jo$ELcswM@R
zUUU#bUNIJNx<mqTUI-q5WP1G6UVZWh$<*UV`#1MZCk>wacF<6TcQ%p_p5fNPx2`_d
z`L@T*chEE64<kzNG2oK4_`c`-%e|0&;DWZsO!fVsKwR<oQ^>-*+Lni|f-R>EdAik(
zjxNE8t-Juw^1ztlg`B0>pJ{$ZK}7)ov-q#j!ZJPty&|IIru&`AGX3+StVMR0A^Q~~
z84N}Bw-L<#3sbJW0@)Li*R=h_V!SVo>ysi8%Rl0VHcyJ8Ys<5@v+xU`?g`9$V5R5!
zM=d;l4az``%AnVfnx@zvN$V`l;GSc_Y`&%kC<3ws;7R*QsDFkcgNaZhdRBmN+6qxs
z6irgS!?YhWAgm&gG4Q6q+2xK${=CjBz~VBS&UUc)`v3VefC2X^_WZ#0XMZioKW`wJ
zFfe&|XHoCZ68z`;b}0bAEm(GiN8SHN(qUzWLC(2TZ9jl20sr$2aMU;&G(-^*{iN^C
zX#%8kUlOrWc?HOgc*d`gso?PpB$oiALn{uD8jLx9tYkP<kO@>rN5|#m<@3wStgI~h
zXekpCvJQt7q?fX!<c&uf(u!1<?<_o33Z`&KQyo*h4ju2rw(}V<wtqvoF4X<w<L5sy
zSkwwtWY`!Pw~Oj`?bjyUm#6Qt1dMIqSpq=U65bDa%z!ossUe&YX3ry@y9N=mpTeT~
zdAi|wRaI351>Lzp9Y2zUz>~l2-Do%o8rtm1;1OV7444uGC$>`F%>fV(=1VmJ;;6BY
zxllHE!0Q2qZcD$$kuI43oFwiA!d&AQdk-Zf;mb2m4BY0J@Z4;Ee}6wN?(x`TZix+6
z@b`-FPbH|OwReGktkmB@x4>OR_t%_e&PZuay(pa#ktF>nY80Q+h2TC{C^IxqH<Sq3
zsZh+<p(g4$G2D>(()7k;@D0t7+|>7>EI9%7=~k(onj*`IvW$_>w7j@)-euI_A))E(
zhIq|gdD!N(bfI9Afv`*Y&t~`VdcQdI37kzk2%=<Mbnu>OA>jyvz&SYcM8J)A_ldzE
zL{y4-1RyM0VB@u=If=x;$yu3^@$;TQ2F5GIkdQa>UI(>BBs)~1{s}h`5k^lbB|nG)
zO;AiCqxydH3NR%He(&oWhE#ETG~4K*J*<~N3>KEtd4;5EhX(sfm;)6DB+)|Ke;?K{
z0t>2)ynHIZ+aZu2fbI_z*MmGOA-wOTLO!WUTuE3ldrwP2r71mwjXBass)z0AJp?42
z5Bdl<qmhe0(#?S8K!`=SIk~yK&f9Tjhte#K-&gwIym?c!i4c)2k(U2$=Y-J56n#Xy
zka&A<%Bv50q}5^uAFwIz{6w@VG3KNne89%w%}w*E>w|-X%S(3;$)6;M30F?e%Nird
zYm|3CSSO?aMc%x~2!waKi$lxAREarqD%sZ7cKRuR8;QETBboG#+#4sd&*C5$mEH)5
z^XueP8Xw>tV1a@AR5xTL(a_L{h=@K4UYY_>8Q-KV10iFH+ZD6P#C3*KujnAW@c|YH
zJ7hpeyaESkM;Jni=#IAkMPATt`PW0)+xFJhnr{OY_Ad~{o*Q9%uA(sokdYBH7EhO2
z^)<C=$*RMLHv&+r1AUQ(3~w;yVZV4k0C>A&+v@0~m;m)2lMoZDcLvE#u;7D3AVk9f
z)ti=>(!*Cs3F844mf-F6k(Za3IS?RODen^`8R^Nii$V|o_;F(}AfQ!}Vg4n&BV|0G
zBTjegaQG-+fXhw#64q6rbwKeH2?+^r@1~B+^`l)GIk_aB(<~id4o(5(w@RLS=^bSb
zahqos*vK;yAcR=76114E`{Aokf%QavT?pCVFDbW5z;Pz~eCq2fGMA8tf$pE3oi&+2
z(&yv&^ImcW1~4w)VkA^wFV1PlN3dzqBSLoGsXH+>b$54HSD#>;4bM{*P1~I$ShL!)
zu;z12c^UyD5hodu5ggfTm#%!bj(D`RwCBH7o9u6{-K_j7J<hCmkawB{`xi?PdEJm@
zoj9u`otdSlneL<AEd>%}_c4t|2z<2Y;Eec>3<*+HR5&@~rE9<iUSII=Rwu3M&&1!N
z#lm<KwIBn8uus3}U;&#ffK1yj!W!=FgiV({lbc<D3?<UL7#bSY=bls$zz5MojHu_0
ze)lXOmVxNcsHv5A8!XZ@>4M?p8zJ(i;2Yf&arpZT>}NpBF%rHYS2wL(cr&n`;N1yR
z{08Reo29TR7Hnl<E!@384go1-`N&WSpYeacc^wZzu>FdO+Vkq)Hem16$N+9$vCCBX
z+wk4jU|KvtD#{SjdH**2r;9Esh=*@%N3_O6I34>D!WOzS9kP45^-PUUO&b-uFYA~s
zMBlXsEq0e>bYpsNutQ&i5acm%KpyU{8&B@&>|)%vTk^;znbTfPd<)G(TaP8aba3xU
zXxzfy)ATVNnfws}G!K4`3$Wl*$-Fy~Ats2%i(}oF<|($ios`sQjb~J8y0$rrm!!cL
zqK~&5DYGO{&t-i<<2F=sK6liqAtLY{NUzr;CA`xLj6WH{H7&HqmO<uj>at&_C1Xwq
z0wEq@l%S1Xi+{bFRS=j0p?q8Y2rN-8)X{2#6M2Tk*-C7RSzTwGa(1dizVQ$d_58Ij
zkzVQpju~KFz@+JQB6XLIL#Fo%f<-Es>uQUeDuwpv*FVqLaMH6S3T^b3U-76q6rDQh
zZ0rrXIO(ow8D$9hNE=&=85d2uRTxUYwGewRt|A1&FhR=;fN5MkCqUz>j-}R9!IyNN
z4I!|`_)--cdY=<Y&H`<mTGE-Ka%w#_qWm#?TjMxAVpqIV<Nlrx_vw9R-eWe5bf!lD
zPur%0q|>x{OgV_)JOduV>qjcKE*dH6jqVE#y<I&|9sgi=qEUV9q5@ngnCtJLTu3)J
z$9qtQNxVkCT6e8VT%4o3nOwd??AQ~*5FFSq_Xtp8^G^{F^$0N^$%@?#{sg%K)!CU!
zr|JCccX&v=S34DNmOmxm(HsjYcKlvM_e5i&z|mer${+?3&VC38p+x?Eg7qD1mT({%
zCydq7kMrXeOlD`tu09%22}9eigm^f&+?3|JJ7;y+SJX{SP_ZBFbxwGjaKEAQ^;HF?
zrtxLjF~;4XqH#+0L^VPZ3kL;c^ol>Rm{L|`=oaGXWQrF~TUFNanNlAAo=N1R1SV3N
zNf^{HoG}cSHsJqc1gw2R9u*D?b(u4TEy=4e)|>}~LGLV_faz{@6qiUMg1Aq-dbAQA
zAv=u<9cA2XYz$tfy~O}@St%e-_}EyoqVS2J*hKa`VKjYf(pY_Tq$OkxJg9}Z3=nJr
zh^YYkS4Si`!T-EaBmqC?A?>Ba=|NN{IxwHz|E0vi{kaN8=^u&15kN$O46r|{fc;cW
z7U8H1|0pba#1iEUz74?`HU?mK*9p_y$G{V|(UAUbbH8qm8<!u-E#d}u5+JPi0`XeZ
z<b}ppF^UAFQNrhWyvYJf1H-g;+anGWVyB&5JR0~mbKW1;vmP>HAI>2laNOvInH{+k
z#-qIvJJ~%0)Oz0W3U$nMlf;j#c8H!lu{1LqIGe1rz(7X_5;;YyN{Wk%8yme$O(l&E
zkB*iW5pRDS9)t*YCvfWKPxG?zUiet#QD<k5WoHU$Yj{^}wWI9xEFh=MytVso=pPD&
zjz}*^GcOmIUnyLSV)JR-4#j^d?~2VbdZJU^<mI}qCcQL1ybQi}nksV;tQ&A{x@zD4
zxeU{8DGw<Cp!n_JLm~8ayPnybklvJ#Y0DeU(<N*O?y0(vSY8B*Z_5`sdHLp}UOoWf
zKUiM=PDeySa@8-2P0C|SK`l<%*CX%Za%NH7sG_TTYu27{etu3R5xG6vIJJ7t6qWF)
z?wf7!*CHpKE#gh|38*aZijhT^y`lr(eZI}Qt<Cx^zfh~*nWQfXcwci{P7$JuF@LLe
zCX3bEE7((K(@ddEn!mKLesI6TDgI4-;t>~N7Gc)2?|Cu~x(-$@h2p$9d8k->EVSNP
zmgUTzl?(1?<Lj|pR$e(d-=8rV%z}6XDAQ><trW#o&J$xYO+2l-dOsP-IaZKam`O%r
zTz~vI+aTh_jdf~5bKkpkL`X2pbXqI=G09cO6}EBj^49jr&8&~dSmVo++OosBi}}Ks
z^jC`EHh`LecpzSXoA5A@`sn#AO}U>PVV?(~<fFKkTb+59j~j@mVYk$vL-2ZE6uB{x
z%L=#{{N0DC{{H>l`aL;WSyF!2el0#OuG7XnFB?ZkrK6TaZX1;az}5<EEp9jr4V`fs
z(_XMy=q$gIIu)o}Dg7FNf3n+QqKird^0Dq%+heYsnt)=P3%QnGVw&`7x4G;wqCY&*
zZnWd11qo{1>@OU)^v+4i$jRPhT=w9d&{zhZMbDhYhf3frZKE$}zsx+pzD>Ru7+;QK
zdZfNM#-*|@B3nd%sU7>-xuirbSk+xr;^yJ>QvpGsBAnkRLaql`p5CHuLJV`}eK(u!
zOqbtUbgQ_a)koy<*EMnD!{<m}ihgzPJ|X2YOW*he8aLesjEWR|fVY-Q2I-nnO$j)@
zK)i{zSGKd`Z<v^*451E>jb$GIK^7HcGSB@VC}gg}XvmE=&Cn{5#k@Rv5)chFwcy3_
zm!6)UU@X$X*5Xis!(UXP-hDlu*N;Gi-wF8}p&KU?neX+Sqz>{zya6^To~fyNVbW69
zy@<jk*v~%bkhjp1W>FtpZ&7ca9ABwDmK>~kR4veO@qXn&B&JHGYFk^o@~SHRwYTRM
z9;QG<kC*Jr=+u~7*A+bU(@XKoB1fgR)>iAzsn79Axo=iYoPmS3YdW?nHRH!AN!N$n
zmfB94)tYnYf(9m!P~%$KMjvHeXQuQv*V`}5ZP(HW@t*YcCezEjxw3C_Hn~_$2XhWx
zHgks9mC_rmf@Q%AooLBS(tX1VBTXq7Gs&kSJ@=<L;Kq~(ptxp96y29u5ctpvtl6=*
zi%WGgX6Y}D7%BtRPESuG!^3lytE{FhFA6oQ=|Q{e>v3^$tP4eQbc*Df;vuAb&a^jH
zR#wXRJ4rE)F$X$zwBOdbcdul7!1)%1(88AwCM3Yyn$7ar6|XOBgs$hl;eA`-UD2Jr
zO|sur_vzaP)znsBtP$#>t4DVhFy<(U4EuOp7hj5BeO0Ns>hZso3MssZrUs4DZ>h30
zE5yC~{>FG_K<j+Pt1o&jh5<J+A|yE>@|s|)?`w1-I-ht@#dr0-i3Cwu)Wp_|rX>S?
z#l@vccehhzs}|7_FM*kFROr?gS671CGoI!1@>@llrL#flH$nm~d5la;LgcQlj+?84
zUW!k>jC~49J3Ge`H$xQ^WLIm8BHMp}C(fRt0P1@`98@ptVNAR6K^~a{tssQYN#{kl
z+sAx)%5~@0h?nuTwPyrF%|{5v#>Ujok;%SqZ`M_QQcf?nN5{ahIwmPg=<S6ZCsh4B
zlt0eDq5n0EUzGLU$Ni>lP2P*;dpH~CMncrr^wyBNCF(~4H5;!Kd4vR-dDu%_UEifP
z3~NP`6O*$I6c3trLQE-gq-ABwm6Of+PYyFvr`A<363|Co^gT1oJ~GvgzcyOcaOfN@
zNIDGP4v5!9pf#~@-oMwqr7(1}Fko`CeIrq^$+N6Y#>jY+*z)mq100NJAZnQrgG;FU
zDJg-~A&>Prr^PB*$3(!c^u^gKA+)}Jk2@QGYqFg8O(!6g)f$@~9pWQO4x52nBUKOJ
z{PYE}8{}cHw(+$YFttX4MoWW62d1}?R>4rtYnOgazO$~ywLn^P>hgw$>%mNEp{t2L
zAj;8TF;)aX06-SF{21&8ks@LaY&YoT32=3DEPaW~-fV5C8=LOOnVXs1X42Frs-NQV
z$<JqA{gU^d>@iU<p03G2%$zVvwC9@mtns?AF?V}G1eXa~sNtB5llUq5^9=j+H|es^
z<%7l|b5-CfR?dPxbjA@fVv<eL+Haf?s}_Hv5N>j&(E^(|v)g(H416*h$-W1?Kl0lj
zM1HhL;SzY?GcYL2GOCSfehv0>x-?+BwcUfhGP!DRzghowcH44;;<B>bQ{b<|&SSS#
z=@zXHrq%Y)hgO^>;I5X`RbM^P6h`5-2b|Cpz*Ik-{xnFbi$4B%ynFTGy{p4)J-cM;
zOYNjFnGKp0SCL!Y7yB&U2N+f;R;PY9i-gTN5FSITNla;n=A|WY&QfUy*;KiS{4ag7
zUXG)p1-`hHuSJM>U+}W_fg4kt&NW6XB&wbau#gTK_rA2~7gU>EQ2$XVvQ>36YQVWy
zHBCmTYgSxWeXJw9?7eg|H&|f5_IAxcQ!u~w>}KF5tdKBCIlh7n+9TIHtLQma<OKFA
z5j5xLtnbdSzgZk4+Q}>!Kg_(eC~Wcf@m@H-7ue?Bd%ClFndZLR+o>AqY&NRDnx?qA
z|D`B0FNIl_bSqH2m`i8OBib)CSEJG3jfdbE_OV%v8lNN|M$V+r#d51jSl2LghWElN
z(rH-M|DMUqDJQop$@$Sxk0D%KodV3r(&Wl0m>JbTDGb_<u=`GkT42`>LHCbGUp3KZ
zMj*M&135H1&;@o^E4oc?NYx7@vH=%;j7IhwJ5?Of6ZGf%Rvwji@;j`CFB)25?l6jK
zAZ~<!L9VX+B^afvdfY338d1T&w7qEQEbUyi#2K#ZhE!yqRwhhT<t?IQH|q{58+6e^
z7cWxz>$g-ncRXE<xfzoa;u6mDmwa-a2CCxTJnNvjolW<#V(+U=@>rYXJ7q0<JtI7K
z+i)Jzc&cXc?PgpQC=n7eFkOHp?-Y<2dlQ_HCp3BHoAp&lwdz7*?B18<(<3=)|BS6$
z*FDi_b>7>PZMvRk7NU$Eqt8-i)a+{3S4Dqe-h-Z6w&>lGrwUqQ>sl0ykb6iX!t_xI
zV5|qD#1>u1L97?@SNcQ2vX2=9hnL5{8j_u#&Gh;2lz8!I3E_%TaWB2tAul2wK7LTk
zB>uDk=HnYXRuYWHFlk1T3FHxy!cq@u<Wu;4Zaftghg6#{mBre6i5<_UnxRt(HzWC<
z<&s}2YieFW_k3<i=FY`Me)hQZ@nBr>k_sKQYaFdomU|psRo;GI8R|p>(<tFBTHB2{
z>L?=dy%e-B%s2Mbm+|0ZXc}QWz?(|B*4?`e<Q#rZLK>DM>+NaTpyPh5F_NFaUG+Tr
zEox!*SH(reZe#8GP-o6lj`agQlXxSkJ+(xW+0m<k2wQ~xi6X3>(*^;)GY1l`TZ0y-
zHMZ42j%|B+RTYuXF~YjryGdtEtr)qV*Z?ctcM9-EW(55z$iY)cmJg=6d5m-(77SI-
zTH9%=V|mgGuaitb7)F(k^LvU?+*XN@OA`)9zCfa*qx*zz8+4BH_0F5Fb`!PBrOX#y
z0L?Uab6Smpf<i!VGhJin{6c7LJzmpE_x=85!O3KR`og+I1Ua3=6{`ievBT)O=iqfG
zG4$eiXmIXx%GY$#??;1&6_Jz7)i;D5&01AeG8TEdh3+esUF~Q4U=WC!^v&y6N)uKW
zQ)Id4;VQCwOcRMwUvK<}gw8AcAh%;-u{Yb}shd`ix)XmAa{69+Z}Y2x_E~W&%^k+7
zCmY$)_ddSd+L-G)Y9v1o9?QFd-uRmxpnWW!+sEsmUy&tJzisfeuvQ4&yf`^5v}0${
zER!8s`hm>u!Dm5K#pduuu}P)&Xe3CZ2Rh0242EHlqvL?CZ2LFL&X6r1Pxs@xHU^^w
zHO^VN^91`o)o}=-o8t|5^tF(wSV?Xn-vPbabaiNOP`|fVIm+0-GNd8}MdbzJJVoY@
z(s*b*o&x#A^#?hxw^vOu3>HRZ8M>rc;elbJ#O|9t3|~jHmg7Kb?*PwG+qG%udLwH{
zO3So9ZKqO3Nh_*aEXsDQztF2eS(v;BC}7Y$Jveq)AM7n3JQ-+FdvAWQA{^=#ST~j^
z>!kQ<j|IJAz3L-b{|Hr+yUCtGn^7-F%_8Nb10OKgm#Zv{Pb=9pHF=Lt)>#lr@B%mh
zu;48KNCf-K#d<x{qk2z%5?}PRgdZ_C7fhIm^#Cb@bFHJmQ%)Y6|ChO-JB_VYlJSzh
zV2|3jz<zf!wP5%6pL?FYN4hl8dHda|%l%UIs4<%uvFl@HL^-d;nv<wKof6lD2AdUb
zsEzER`&wbPU*-0N`I<7`<F%~SUM%09=abhH{Hs<BFD|5S3RA=9CYvOLDDe~(S;pqf
zP2xxzN3?D$e`^DKH^Gq3#tzr>j%?~?pOeFZG5}C4nZ3-XTkMOm?9W}=>FFt-UGV^1
zH8NhZ<Vv7yTcSNWOi6qPlmtz1v>e=RWi0hIwr0_37@wSUKiM4VN#sV!hz$wBAY=ya
zUfGayrZR0LItPwC0SB#y9DY(8tCVujx{AIiiIKNpI>zPhf{tu->P&@TZwfw6Md$xk
z-)LLkL@+w)JTh5sp*U&|u5i;BH?;08d@FKbW#JRnIiS)<9hLfMTyMhLGQd(N{QLFi
zg3nD+f||3-ak`p}r)|=w%osAXG9&Db^w;*HvS(^~$-ND!E}Dr=bw=3<)hyL-5p4U$
zfARHT7IOi&f;b7it&v06XGz#h47xApQneM`94t6<@>?ap`h`<O<hrfl;cD@NZ8}_-
z=+6OuJ(O$lm=Kr-VG3M?9WP}KjXcsq@9QP<?95Eyx-AYaF8TsxATi8(gibM+?0Dp+
zkCT&g?xNR)V=nRY=ZrY@qxMOIjoj=Mg$GYM8?`+mQVJu&FfA*xp7&(ox${Li+o-r3
zdbTzsRe99Z7u8$0OhSe;-O>kAoIG|lTw<|`9koiYxEMyEC-pws2b*1lx<y+>Bb8?b
z&1*%A!lhZWKq_fLfZ)l@NoX)<s;5imY~+u~O_Gr}c5kN8t1aZsl1H8tvqjfrAJ5WM
z3-YqPINV%O&3l>W_{Pk6W6kA8DlL@LqG+au;7ejsCbVgEOmS%J%M<cj>@jARlGWML
zfh}m`O8kU6yGJ1>Hs;Mm+faG2!0hZ{yi;a#m7R1yU8B4jpBbG)9Ej&b5CClLr}{SE
z#E$zcNq>Zc6EWh#^*UY~(z@<jh1DGQ3Vcs5Pqy;7`S?75OHhEg1_yia?}66`W6d`}
zBBD=YQ<ILS4xL0-dRSN(x%)b0@?d(gpziolTWAC1Ss|3ae8~Z@A5)WWH{xU1sc(1k
zZG7D3VhJh*t8aBDKfAve^x)i^Y?-b|s)^%~MHH&O<qfRY$hQ>Px{11pWr0pVN=!=e
z+}dOzEA|wb(uZ#D>Xu(fnKm9Ls?M_VQZ2Q-RH7|n%ab~4F=jW<oGbADX2VgU<8>j(
z32pSTJ)8*`A3u<v`&{|S18Q}G%oJaA=?DZRVxL%;^>6tt8Q2s;RNu_3t8yXT&+uW~
zXCM)TaZxI;fk62$k4a%%r1uapq1nrG^&3cyPh@R%m6~QQY20!2b5ztpAdBa#bR|{Q
z*sKr0y>|rn_%P0C3JJO#oVeVK$;OjLbX4YU&u?j2du1^gA3RE4HG`S{RbWWF!Ky>q
zjiIK`RMhVdj3JDB#f+iq>@Q#BsXl7dI5F=BBqMh%lzj5|?JEtiTWyqcfHjG!SL0?x
z`|N$isf*F0$<@vE)9gwd4I4>?<9u$eEobuKMxXSPpV?<xv$y1Iml5weR?oH8b^0T3
z640?P>b}iQ*J%=*MX;E*ojj4HAc1KKKR`<mibn~;(ddHjzEutOyY2*sqX~E_0Z$IU
z`mp&pFJxbqf4Uhx8@_G3nv;{38M?2;ec#6P(&bcHgAO`Ib0dY<jJ$!IP(DHuZXEl9
zH+GVF^W)R0>tjE<=qHw{Z%LKZTrOsFn}=98%ofha15UwQ^_ePfJ68mU<$5Kgxn<?#
z8BS-o%Q-6srJaVl16~UdXvKZ5<Dzr3H_vl;hP16P6Xp)vmQ(@wyk0-f^w}K@H%r(b
zZWs5)V8|!1$z69qgb}|#Avm-JUq$Z;^(QQc1>6*k)EH}Ln<}T#<CDo_QfhCXzDB;W
z*=w<Gz%35R#3<Y=c@JDb3j_>efPjH{r-LrA(s$TtPsr)$7_kK>G+%5$6c4ZRUL(yU
zA^rkMy&|a<=DmCVc<JQ3UiGy)n&SC}x8vh|gr~os2f@I={VHHWt2<(6|Dc7!N*FRS
z^3au)@`v09fs>o8V@)%IX+rPOZQ)8fQMh34rOY2l{H||+fNMIy^6j(B9{U3~-T{xk
zdw^c^;$C)yL5lx8i?g2%^eEJktaArR{{<<V@Bq(a=F`yo|2``WNd^4>n<p;r@VLz1
zXHn1PfUVF)R4(`rHZKBpQYVQisiG~W&neerbNJTqLwbb&_SiAEH3#sBGgN#*Jm$ec
zL3e|kM+9d)AV-G0N-o@&1#PFM)XfX=CIH@#3$-xF)5Kfrt~1|e<WTl5PmH(mQA<-z
zLv{dRkW7FaW>TJnyC;N|Q1OkdSuy+#^fNL9y2d`-1s#5=H?N98OSsN+PogEHt9bb2
zh=CcfEe6Kz(GeMQH|`R2MCxg)o&54M!8#~!W_Gq!P&O`C33jNrERB!L6*OhjDyJ7o
zteKp<DO=&yN73NANPd6<3SvOazu767;@vUTJLY{mMGEw?)NB_deLZ<^89nkW|K_!g
z$F4=Q$O2e9o$1+%02uuS0Hfux7?MTq*rgWfG#V)eq561~mj+ykbIHAXE6RkcQ&eB1
z)0nWSG&cOBHX$vr-^Y92tPn3H-&gvmvQ86<K6xYM?_GDGee$cX&%54H*o+Gi^)c9$
z;_vE$12JgvmD2KQCBHx<Y_KtQo-T~uycGL|QOu4mO}{(xEc<5zYkG0{gmd!#NK@}-
zliV7eOD4e?{rbp_&a3p|jllSeF>DB;`t*p4Mi>au8wcQt7TO_+JD!M95C#{a*`4s@
zV7m8U3JNq>mFHwOxZsaDvEM)4^?pZeedG}#FTop%;-3XuX$L_5`Vd3`BH`Min+X^a
z%h`RE7J6KjgbPS*ZiB5jLn`N)MTV|Cv*X!MiUAY=9ghQK>t_;e;2-cD3!xsUTo?89
zJs$px7wb5Ol7mE-=IT7n+xx$21~HL583EQ``jNeL*T*#2_op^=piHgjUSdR4_Zg{D
zXXXGy+ML}!M&vpvnFbIg!gvHkqF4!#|AOi<zJ5=4@JFUq_rMXw#!ivpiF;Q@i?QU$
zfN+KbEMpS%ITB7kMafG<4J?792PFVcXpq|NhQdh1$p!5pL@GsY{au7V!lv~cAS`bo
zqx64d5`-89*vb<09Zvt}<04!Nkn@P`fZG3v9|$Z7up3qM5<HIkA2C*i#e&UiOd0>o
z?Hz%>!ruY;i27|u`oACh<^!5Qn^TJe9)yLnApC_w0emjWviwiu5En$!LRm#c#ad*s
zg9EgtEq+p%V?E6R4CUs<ca%Rgms}%$qiQLJE~5Z|S)H<o{$M(lJYlSr#?6#Hu!2Ce
zFB4x6?O4HFfe=QAZy$0{aIk!;px4FWN@wSrR7Ka~s}Vw22wIzjoTPETGkA83N&qGr
z{49_MC2PTPSn#k?!6#t=%XewM(#E@7U0d^kZt3c#lQ<+2JX|+5v!BgwtQ~NZgo(B=
zgaCk*{!#V57)U@8umO!X-^-W8K<RxgR&xv+{evKTlZA{ElBD48@TJ#+!3Cl3Gos+5
zV#fIp7UodJMor!BCONr-m`Go}wn~_w^Zk3)&a_ABl*j8U*ssXZOOPgEJ^;Ll7%{!R
z6al~;1^{JbWaQ`1pLf}l&}%;jx3+%IZaUW*i#Ux+e+8riw6lekNKyT;0)7SN1B9yS
z9zXM4Tna+@DLVS3(8f!ePcJhoOGQbEr}xuwB#?{&c6li(4`ZrZV6Crgx;I|HCKFPI
z_Wk?!?U{O)iM;GZ<wvGAX2UxDK+eD$^^2g;-!(ipq?Ny^e(u0}YD3>AJkxKZ{RkH&
zVN>wNh8YuB&}BF2=lnesELOB937wU-+N4&+&F7*+*LC^I{!p*_z1q3T#`Fc)!pS4M
zdbVZXldrxTtyWrA*6Mhvfws0bkf*@Xcs#hizW#a64_)=0utRfiy>5QpJpVJeYMw_2
z6rSn>ya;$;)fO!5<Wy<3a(?dW<<%(gYyklra$sk|@>x+K`Tt=xV3`|*!;gO4Wp1D#
zaoNnRY>Rmhy!?~u@xPlpu;Ks&oyAT0{Mj=@Lqq<{^>1coX3VA>vRWm=@7_$@OLco%
zY^$vyzPbxN+naRJ`w^=E&)cBTKpID4&=B`?hD%V5HU%^DZYNDDzy0!uEFW00j#<)4
zAx*ubD(y>lzSJjh>8wU&y|*0`m6801bAY^!NrZf$JO#2<X2?S{So($h>sWgrz6`9_
zCI;)hhD!rs47h%1pk(FYIln&YJ3Bea<%6LIf>#CHmtrj8kmcpp5CfY{WJ$##MP#wI
zGctGJ25aoQ9$nCY9*Yh#D&aj2FxZ}MtK&iQLR5>iHrCfa%vKGSwPDa67v|QbvAVjO
z=M~l-TuabA(nV2)538UImf(O5ss_?HU|J2Hy1@cZ-EgiKo~dN$WgZ@zc3$TfgG&>I
zIc$$}HZ^?=7vC-<AZMdeKmne!5#RMv*r5e|d6|Hx&tz?t4;zT&0_;^I;%nlo{X&KV
z7cP#-h=4fgUi?<=O%+N_NT|EZ*zgk{YDLCS+8%c}=+5m7L33!Un(-j?q`Ona8DfBu
z@Xt!P3a6Q_E`cNa11Av8Hi&f3H@PkHSw23%w9cE3ii#Gfe{h%0@Qzs+^kn7U>!UyF
z7g$hSyf5@Fvjj|q>7?-K3M15W8eQzEfk9#annA*lK$tD@gd+i-74wg2Ls8-iWKpyw
z+9AUR|7Q~d-uYqxlk#s2{-3t=4uEFDxR=oXr*RMhA)x2$ZTn5x{<j&(BG3$>O*_GV
z8ZY<&6d#!moeoZ<m?s3}ra7DgmT2*BgSV*rQ(rzA$bz1He(p#uB$}?>kkVD-;T5m}
zPvn9TIsXbA5P*bzx*1vj8sym#p!6Tofjp9DG&C&oZNs5}NCVx!*uMs1{fyWIE3qbI
z#4>g8^eSK9E~Le!CGAoD1QJd}AV2HfPz<d(Di9gRye}Ifhj6p|;h&5gSmFfl<J1So
zgU(;b6Kna=eAhmsMHSCM4tPva3FS==T!OQMV|yv*b-^gy#yLmX#3<L&!hH{IKZ2UW
zT>8|+-br7S##^wW!hV-5&x1c12v2c?jag3+yyw}U@ziJE_P`UFmz)tI^vYk12a5rM
zE%TTRxE+y)QqBxFE;Sp6nXG3}?Wl|WV<gjz2xJctg&WD(SC(VZ1>^FgFA35yHtr4D
zW)L_ul<SaXe7^-?lv$cqbtrPH$T|*lO4s5ZRv#uEsR#(Hi3kLca7|TS&52M}b|YTC
zzv?|unQ6T~XF8hUR};8JI+;&n7LCQvX7$0FjRwN0^6TZmLAz^QW{wC|`-}P(2C6qg
zfNfaen}WdA^)?;}3-k3Z8|wH;-|E9-qZ<FS{N>cNS@I>mt@Nk(&`;Cqq_fQlAfBHu
zj47o8Y^`e;nV2G)`KDRlRy;&N+LaVWC|Sgj{S96Hm=}-IL?y+XA`iKVo0x0pc0pcS
z!=F!0a~M3oLCPm2Jg0($wLL;5$cVc^95exvHVqA*wVIV_(WZsyis%wXlE{jKz^KUH
zw<V`f&2O?Nz1tvj4b763o=0G(hofyqsNJ}%&1wU!#cyaYlP{tYl_SH&(D&v0#r)iw
zdD8bX+IfuK-Rqi~1Su(BP4R7LBKQiHmX@w+I?)yG0bxF|k*(^VczAeUzI@r_{83UL
zq$9LuUUJd7CU&$-%m=d|rJwKXMsjX_EZiw>u2@MqDM%|Pd-fEcwY=$6zmP}o$RxkC
z0!_9(=jXwJ-I2{eW?|A~hNAGTALp&7^3geA0Vx%7m6W`!Y`hJWFukJbWWa|abnIAL
zMWy{g2|@k00Pn+Y>{M?W7YPD8`1S}wWMD`ud7X&cs5@3XMUUGn8^Y9!dTsv+8`0%y
z8u_!Mf@1Hw<Bsop-$ja&r6Jc#Uwr&}S40I7UjYUL3fLB&2l%h(%(H=!dqL$u-dlV0
zUEbTjD&aLXz)<lds(&1}znY>(25^mx?uk3V_soA4&Qm-f39CCI|KCsG@3eqcw#yK{
z)&55x!1{;+HhqcJcIE%`F*DGL^MvofKhkoiCcwV{1CPpKiT+=m0e=?@GZQT#rp*7V
zgoF)YW@4=!!T){?C;&jkap`fufv|rS5Ct2c5r0kBz&z0ZDo`Vs0wrNh0M_}xWa7Zm
z(+sV({#x*Vz5{Zf5cOg)ANSlDKL0fT0hllzHtwQ3*XW;*ZGl!w{z*6d|9sj%xTt%W
z{qHoEyhemVp{m6?GbQgu<>Y#Q<`?AU5tEa1uT)!3eE#~?uo%<fcZ_;otJJJT?qtK}
z31A3piVENR?;PqmApwQY+&w&i6oW?|SAa}KMMVKefO3M;ELxJ#>D|_X8QhBbY^*qj
zArEXh!V#_hvj8B3F;q*y0JpL-H_t07!ZLS^Q+)M&@7i|ZEFmRDrACmKH$ElBd+p50
z2@?rYL?%dlX9>cW%QqW|n3z~YL*sON;!9GJB_9_DhvUulMR#|1Q&Ur03Ox%;UsqST
za-dAk4UjL2g@pwW8WSB2MEQI1hq_Bdrc+YLWGjpf4V3_!Rh2KefZlTz2p7>mdHfhK
zrP&Fnsi}jSUt1IwYt?3CPNM5BEiH`|Y1ac49JI-9=#zIgH}i^%RmU9D1%D5$0M~S<
zUE;oC@802fSy)(@a2(_RD56WsX;bMJy3-JliTf)&;pskblHbD6X{SAc1i%et0~v06
zaMz=`*CPLi`!s|RqV>7F@Y#~%FJu7C@kGpvx->^I^h{)~GYY6!m0!QSw#G2o;0>)4
zZ~#0KAg&DToNXSYq@?DN)>eJYz->2LHMXzpa{biAns;_~Qaukl8we6~OiWA&2?*!}
zZLF<Tq*og&5mz17dg+*%XlZ}-^eA6^{`}b=1zU=$%sA(MkE?FIvux}ZA-bP}W8s_x
ztxpm92xmkr;%Y$wV~-HS;TQ|&FldC`<|?)r#182)k?#5L7)p4+6%`!XX|8Wd6<u7a
z2SXQ+--+0L)6Z^8VIv5#3DB2jqEWHT`bf>oNl=i_agZ<JNg%vCUMd<pHatwbtaxs|
z*tt&-#GemQc4!6?eg;!C>C<X7X5y<wkQ-s8)N<dl7XgJMn)K~Cd6t<hjZI9l7yEwy
zmKxHSQB^g&uZjHBA}GtDQZw%9IP~glD;A%+hO^2+Ij2Uont_RF<ZC6X(+IGZ6?U;t
zeWrS&<#9m84ZJS@wOPRZh}2mMtrn^m^sb8i`Jz33n+a_x8ox4(3Rjia^MCi$S;(5v
z7rs&QN}P~>F4KY^Bk=^3Pn9Qe)P2c?h79?w6d0-s1RzWgcg}zm^&YDFP_C1DkdxNC
zoEVvpk&%;Z4$r%*bd0^qe$!Hlj(oEYGHchWq|;U1uxG;JcFH5Wr!TkR;oK|(D&WyI
zA!wfpz*0RB1vP}8Ps458zk0?R?=66rC=DdoD=H}9JJKC1Y{w=f<n=T7DN>g;?vP>d
zy)DT1)2PY+*!Z&v`fHVuKV2uM#A|)*nG8pM%A-e*?kgLiuSWvOXr)EU5&>zVSNY(y
z!(P#z7;Y{ubF*sd2&ckP`b2_Zdb}*6UShw&1OnB_3*=Y*xxeTi<QcYMq4}zYCy@Mi
z6M<YKCTJ+hWJ<~(r6z<cg9>QhVfSqQ{w3Gr)Ajaw_i$+pCc}2cny9$%spWY<Jl_ao
z(VMt88V-arB3;p<Iz^ddgZ=IACSOYtnrqUH;FNu5S1kW+tUtj>r3wuVkOi~$*pA|S
z<=T00(Ub!t!sq{ih*0|zYn^DtU)g%{^|TvP{3pZ{bPm!z@6F>&v*b^n<s}DU4iVR1
zt6_X^!Drvf6n%vH(g@K^0MmlnBf4LC^W85CtE_n4k*dy6c206;bg!v$u7{2+R#gSr
zVS!nV#g6HV&U|=+HtZrIM3@4*`RF^cvih^={=bWNDG~NJFCAR|yW7;r3cpB?H&g1*
z3{ZEnL~Q#d7e7hR5bxA5IcZK=yf8r3fxc5gS1~GLAy%qyANbW6gH|!!tz8+o&AwAD
zFc*Ey>J!o7*F~MeH=`;Fp?U<xqa!1^-bZ>zR?udsFkUTsv@#Gy=PFY$IOZ>m`7l+x
z{^?AC$g5)JYh8h<?u(KtYp#zQy}-@QZxawyFf)emE6n@TOohxFKTEM69jUl_1gl(p
z0J%n^_)h&7SM^nd$Z*k1py5I3t+I%y_>AbsFw6+j=oyuMy76U3Z*;#1MkfaHR|>f)
z&CoSiN=7PQd9dWaK=&f}YL3B>tn6!^?H~#Sm1-T<<gEM)UMlMt!5rOs9vcC^!hHpV
zk__3MxXd(FK1qh<QPLe5%U>S38nTZ06PK8Nf*PoW&ejuUVyZn;;k9X1HgiQWTh*Y@
zg%LTZ0)#(;Up3G;x5_>5=TpwSmmIw19(8QIFD_61e`Q^HSW;OOe+p_)+G-P{B`x@+
zm7}SsX{KhS2Bx8arbdH7fTW4$m|`wCwpuexhN3evrDiN?f|ipFnVPv^3NE2#<4i;@
z`I)xSHc$Iza(REfKkj|++~u5m?(hE2xfw@w%g?*3dAr#UcAd5FFBa<}9^oZt3=(Fr
z%@<B0jbWF3sDbPtWJ%U})8xEGHrmk6(pL>|eJa7V+p4p;_SB#0SK+KH`=N(AhzWs+
zBJ3^AMvJ)bb~IOKp6ziYCx3W*q}7x`r6mRPD4evtAFe!qasHz*PEhmwC90(<reaxG
z|F@3gVosfEEqlVhn6LF56PvWYYVLNY|IeG9T21kLNr86YtubqS?LSAc@=waW2h0V-
zVI>&zAyMRGX=2uSD-EW1e#VO;Uoy7STBN)z9bjz=$NP>rGMhInE=I6k`4CDKHyvt&
zw6{j#mrYv~*)gr`XhXSWA4(gZcIV0R>Gl~!Vc>__s5Lq*NKtxi6Dkm|6psjwFYy!{
zMgr&%R%YWTfuLkYjZ`D3)TuKKVk9N!;6Kw1_YGBjbA3!^wB>MhVNaLKO@>!Em&Gz9
zK8-V925D1_otd|CMt?)yHWohP$hPHVxjGZN^99$MpayrVm<g2AYL1O9jj9MsSYt8M
zKLgTCm-ALi)j*dehI<%nO1BHdji7+P;q*>7H<R9g?Zs64x_HS^^wW&kbZY8Iz2{R+
zHR9cj7J%ivGdv!+NldWW%za3pG6elsOPv4w-e#Y#-r1KoknW6*Ge-2}wea=IOj^pZ
zJ%@Q8ZkjONCn;e6S>7)Lhe0Nb=;VD|+f0aFOrys`2X%;QSw$v6MChA0yE#Zb>WRSx
z;RW@WKA}18Ed_}3<Ht_!4qRB6K>j68#m+CGIn%@jPpDwKnZMAfbZj<^hE2jK#DFuH
zMKbca>y`W(4_G)!(q82!iR`~I1yxRWWOsV#l^XkFYk$1r$CKV3X_0imlj4~q!yW`+
z)RdxYw?efVW7Mk*AKlGaJr$7kb=#0C-wfmNRM5-SnXm{j6LlT^WkG+H{uA(8_Gc$;
zX)MTl<|uu1*DOE+NISSBMp17a*BM?5EmPp&Nx{yxkbH18Dm^eB2t!4=C=abPL=7JZ
z@a48S&2YKFU++edAbZTf(jx-<18~0lHKowiv8ar25vu=$0|o=tc_-C|s4oXM;HgT5
zIlmNYF?%d>{E(5u&s!X5Z2q|drOZ>JACXx@-}A(U#O_ckla3u5rlA}vM9~F%y<~L_
z4THUsM0D=!nBwf-^hoaAxdN>xt--N{{%k(yWCYenXwEImg8zVp=-bP6krc{cZw^2I
z9k0VL52tYrs3GS{?QyipgVgC`FmIzE73TFyyagLtP7f&dw~CY5iLiVjMlRg!L``+P
z_{Y%^wM1friaUF|^&UFZUf$GxAmDbXf3D_rrQ4j@mg6l)#O5J`I@QP^*ixP16MkJj
zmrG6$36Hf0@YZYBl1U^|a&jN%MkR+Sx$jhEM|*Y_TmF#nu-SK(V92uddQ0QgJ<2fQ
zb}o5|u2OKV;C--{#nz9ElH>6sVt`oA@bvV=;ka-Yv&bPwt{gofE0-*>CY!X5#NXUH
zBsv9BN@jj^9L{rAHC(X#$04`6YuyCX{Zz_@fOU*o5(@OCF(e_fJMo&w@Sxi&1cJt3
zD47ET0~5t0gBsm>ar8m;Ih(-jaj&BIE)6u8F+NA$MG?s4xKa<oMZUH>dBZ)>9O!~m
zz+B6*vDe3U-q9;l7@L?pzHwyx8(bg5tKVah+fslZO<ge@l~WNhN3AxBQ*-IYaCZD5
zO$v5}$cN~Xn3xD6uAT`C7Xw00t`WW#0k~e;UxeLZ30N*L`Tpq?+WJ-XNic&bEn_f9
z#JEc``<Mq14Jd6N^MqbT@+~DHe}lB*@^ZU+`Kf5rvAlB~noFCT+BdZde0gZAdn(18
znYMUdkG8{*Zz)($kXbR^(Yj87CPg-M;n(+_<F{6iI#Yot`ta!J=!+NlP&;M-5cPXs
zA(4<(&1iJ}X(~u;+MJWu8c>XQmX93-*WRJ^%I<eJvkQ{k+itgi7`ti>=Gs-7{p?^S
zT0z`YW)WN>Emc`k`ZK;@wA0jS&2rl@v5gaq-Fr@-)T%2kDcLYl0CEDi0hL(QhIH^C
zbmy*JvMr$&tZgjFGiFq%!LV%IEX%lvc*3Kxumj4|b%n5{jUm5*u)j*B0#!LPNVxel
jh~g2~*3Yg3rr!9xFe7|SYa=*`0Kmt0hrhSPi<JH^8&TKj

literal 81300
zcmc$`Wn7e7_dm>xAfbe$G)PG+DUBdqQbU)3bVzpy$U*7uW{~bdx&)-VQ>0s9==fit
z=f2PF`Mr5wJ^Jx8qh9;kYp=a}eHTHm<t5P3h|mxa5YVM0UnwCVAOT;&gD7C&Lzr9|
z1bl$(l_W$Eiu*}6fWP<~t4qC=lS5ztzM~)@fv^$o-97^RMgS4rExuhM4I=)}cO}r%
z-_HQ=3^YSPyn7x2K@<4A{iP55xn1+?^IkgWzi&(j|NS%)Li)YGzk>&XrxCngz4QP+
zP;DhO>=6(!zTW-;#V}$J19T%uy?UwQ0@`js_8@JqX|i$Dm@|(x?rGrGw#`YfPNWBc
z{jnvjt*u4AvBKvs?Uh-4wTGjU{8b`_!SREiS{y9jl$O2Qn~R;Lp4n`;YLcJ|n{W>`
z(%_AhcRl_wz{UssI^2F)x8S<qN|#wvQ-ev2NPz%C5k>%G`5^rIN->K1%DLVT4u`9%
zs#aB1p))5%SHS-I3uR3I7|M_|J{77aFZDkwZWsHYoZ`la>k~c72M;l8X=`hXh=|C_
z$|Bc@B}1V3!WtSHVq#)CIyy#1*}F#ECOy$pEm}$s|GVpN0tVlKA=Qcg$4(aJ<{v{s
z<fNsgrKEU@m;^!)Vvm?vSRfTD5u-MI;7Jah_R-K#XTQk*(EXnyq#@QLL5GqcR}7S(
z!oKB`tqBFTNfTAt3b_Ub?zPrd5e?6*%*?`bM>Kt%645zvld1&&ngWcO8k*ccd4T}l
z!71Gw{wNm}K06j5om3=t12bRj=n&WNtEi}0A>XO6TL6E7LRY^<P}K@=P8c2wlvPRU
z49F8gd9xh*=GV}_`Tu6?f5<~|i11l1Hh<<$6FfGN;~PVdURZH;aS|35cG8%I3DO2w
zrJ_O|#0cNQZ5BT<x8YXJt#r;={^u3_de^0VbGJT~XBD^fq#@XPirS}&UWk!V=4Y8U
zy6pq~DKAWNLCevS!j6t33!~Dp2Js_Js?wq%`VVpy+w|D~Vw*1pwyB<u^kzO;fp5q|
zu39zszBNuW8@_#du=)xH$%}M8sh`qUnujIW-O)>9^Om&<*w78>b+6+=Nj>+;mR-ev
zU#33F7l)jPWLjmU=x1h8;bahz%n2gjqWfeoY}4%p_vzXF@Zi#pJYywe&GVZR^zW>u
zX<aP;O&AOIGm(j>as}KWyQ+P(86Ji>Fr;2NIn%Y-S?!q*QDAjOGWykuo_!1L^uGD|
zVaTRz{M#uvsed!9R<e2XH6u^VYbaNgAx=N>Ms#7#w9K;f=5$qrCQ_-qX@g#F!vwu&
z%z{!==b8qpR!LW-vtw$xvE;ws#VglL&m%XjLW5+EQRSSkNSY{@4|xMo;^yI*!ZpQf
z9{!pyq9J~gAI_D;mD@Y74Q(*5G_!X<{@3w9H`vcwM@G%WJ|pIJJ?~a=H&b8pjG>aU
z(9WW9QC3!VgsCE^si=H@lI7AjPsU)tt&?7vH%hxLP;dW#UZXr#spf>Xg@0~Ln)Kr$
zi(>{uY{<OyJ(+zX5J}z$pw)K4uw2ImE>b|t7z~dE_tttj%>ECuny_s16;&rgUyadQ
zL3%YK7+V;p3M>S`U-I+2Q*C1*(;O3g28WK_mb8Ha|FR*?O^EXA@&n!}oHL>(t;*~E
z4`E7b<!S_O+UXV+7IHzyC#zfxS^iT!<(Am1xbFY5Cc-C=o;?}uR*IvoI+Omw)umh2
zZ3r4)k}S68<zR-Pk|wgz>Qz7ISq=a9*6DSqkAut+^LAHM@>T~qnwR-bA{%&D@S8id
zrd1;v0&7BKjFN~;1OKI#M+hJ(6-Ifv*1sTg(|_qkJv$g*P6kwPke9V|MRvq01RBgd
zb&vE1{=ct~0Q75J%uoiG#Z(m!)Ta}?&9teLS2K@a5uiiE^KT<?^cX}X-#5Pw+0k*X
z=7GjbAn<)ktUM%g_w8~Z<&}y2@NfDag5qAl1vz-8ljMrb@tUEY-BsvSX0na3sHlH3
z5JeUYsnvX5;51z+<$_o`7j0}8W4QC}nCV|n`Up2;KXV(;^Dk=Uw6ex)F1F*HfXFvH
z#e8`AUyF4o{=#1#*-C5M@D($5T7kGqlU3s@+399|hV}lnxjJ}0a|}&A=~;*ny^mw7
z=EpuBwIQD!W^})Q9qKP1nGWe?UVDD<BuU+9$re`hzqsq$Ot*+#u{!u|UU?OPFXr9i
z$wz#VKWIZhoTk)&RUA`W1fJA-GK0M{+D`u`Sw6zTkHX{OkT1{xGSD_J!E3qP=l|Xe
zFgE4YW8m5L+Ak#k@=jQbh*-^_YadgxKPCP&5CJ?XM3RT}=NfP_0{BHUIac4l&VGX>
zjBpW1RrRNB5%$3mMnFEjm+AT^b&KR+6#X09Z2UiuhGGjwSw!#_=D_@O`%6&-&^CGK
zDENPUJOUUbj{qWB#QbaZ&ujMaMxpSzYKzeP(-%@Sqf+?Xy95pK|GE7>CJ3?A`-Rej
zKe>YV0)%MmBSevi{O9)9ls*W@m=fl`e@KKc0-X;6#y;|^!#}rg76N#G{aupzPp$x$
zl6kM*lY`YCm4w&fsi2@B4Gj$gLw<^NY;3IcT&?49wiGHV>JILqpsKPm4i3(U*UG$F
z#JxL`G9>g*cIVL1(KpqMjFtf}E?VMeFq75V+8P;&?I<K5Ai&N((*AvYDC-=1Fi!l{
zEB~$Nfwu1M?t91>>jaq#K?7hTKo}{70d9gZpR3pHUmgws=6XHFVYg<jKY_i|gq!+J
zn%DWpkIpbwEtuuf*Pu9EH#6h~gY!YxgDyIn(vqfYw;fN2JnbF#{84?|KM`z&Wc5p9
zc&;$&ZRnR^lJTqS=*)S2-`?I{UN+Kt+n31cW{}WkQPRN0$~utx<U1?);$)A&1pU)i
zf$#!0(NncPc9Z^OKIdJkFn%`M#pbRkI!r>gSL6?Qfyk^dV?R$hSJz=kEZ3^}13Gam
zi%w!}EOeUVp#Sl?S&$+ExJ42;O|Swp?)2>FX!bh@JR67<Z5A2@>r}L~3e@68OZue;
zyD>bvXyP1RBWxi-R8+Dbkb7VLOtP+(%4!m{`CcN+sgMSFt31&WM!r{)n1_5Pm%Jjv
ztPdJErx~UuCr#zYCMJ4rJ{P?yD=Q-;Bs|`B-)m5N{aPQ>llBPtX0xCKmV3neIX|B*
z@ECf`6jY4!ZD2s}i)}`pNvl7q+uAhmM6r&Ru5NJ&k`>W48NW*@K-K0;)5SJ?3%as*
zKg3gFq|W-d7f7DJ@h6;~tg&CS9}t-6SLKDbvwA&${=DppEja)I5$q4Br!d*8$DE@5
zVv&t(JJRQg)?1EMo)=Cz@PonTqOMVyttpc<&drJC^+@mQ!?XwZOfQO9D?7H;iZqRj
zd7ZW=7jCXkW^9@SI623b9XhXr=u%&JoR${3j(%1o^_ZBJk^E&o)llj$cI)b#b~Yu^
z-RLV-E!PJ#xEDO^wM;x$`H<oPK{}6XPJijQyveliR`p^?f_$nQ9#QIb<!1kMC!gTw
ze1rRr2H~bvZPC|M0rzdSzz)tr1HG&nD;*I*L<+26#Q5)6z@>eesrNWLAkcMrId2Lh
zCigncu&eakZ$a)J?ey19I`Vz9APUQ_PrW{_ZjxG<CP@qOx;o!LGE<PUvDk(c7x%A*
z|0fZ6jQZ`7>~$A(h3KHvZ$qhRxVc+FTDo@WBV)8JhOCLPaSE&gBEN-i)z`~wMS}~h
z1E(S2FE)FNe;*TRryqLS*b9TrxS92(3EhNn&%dx+{)>$h>mtni(s1_6J2xKJz`AE@
zUAgB`X_wiTaohT(vl#@;nhtZ06OMy^)AK2acN&3+1Zui;jdQYdf;9HoB{;249%Y3I
zGT4~7OJ;VW)F1ZqjZf&v_uDbDSC1FyHG$63wkXZ@1?cEH>3vpCcKJEtf=T(t@7E~_
zTpaJPpRwIAWXBGWrFdVT9ZQrO_uvzTc;ZvxfU!`F03#~w#hWn&b81vPdh)J8<^v|V
zS0CrZ*Y@@~x2+=9hNH;kGT+SVP}oqGgr3Xy071_rye}f<8UaQ3=gSNOANGtu<sQft
z9-#r^F6@Hy<@*QXY0&<D8z!;DI6K<=G5O2CoaT*pIQ*1#==Ohhl4})|9457VV2m0Z
zqkUA+(2#P!1&D!{X|0g<BWYx0y&N2lc-E4$5;_tkJ?354YL-kH$a3+T?b@8Unjtb^
zfac$ZpK_A_Fyx?9=z6G7i^7x9zW6*(Z5oitoz2pD;iikZJz3}pKcnlbYVtR)eo}JA
zsmH_<;S$PN5LX_){87sncxO|wa1ocekCr~Mx;4>S{*ap#Bkj(-SQEOLT6L%6D9$I$
zrqwHX{KI2er`P=1p7Jsx7!=|h9TVeNN|VHG0~_kk_JXIRCnyhBqrJA9GLCaB#r_C5
zmlhGgm@p|YWKZW|KFabMW0XUUHGueX+tmLQ7i%kLx0MZ?IS^ns$;p|qQ({9hLXP!|
z!fQ^v&(yT8;IV|WYB{jYNoz&*elry9XoW<6d@T|BtV>jD&uj_@*N%#tdxB|RKPgvA
z?s!Blp*(QryNR;+vmIfd+Cn(-b`|xl7xBLbx+3IIjNl#C*h9eSFGvPaWfyR6bhySk
zl;8}yVG(%_&L}qy&W8*osaP;>icO7w3ut%+(=)stV~{@QdUp0PhSRX)p;#1`5M6@@
zo>UKyxBA&}$aZqEaRChogn}ptc)3NPEG)|mrfR5~of!KkybYZk61k$G@S@6DnAObm
z25j|g9S*g@HOVf3b=S>CWpk}aFb{0Px-Yo(LPmLI`@@(CbE=3kYCb`U8;++f=0!)*
zmU42E3PZ=h4@(-)^Q|U*K=*dP{J?PkocG%Md?c-qSws|7@A@F_XJ3WKorziJ09E`Y
zpUb+|x=WGn{8>C!&+E)MEoRH=X&@W(*_QUUba6l0ryPw&O`TTloD5q}5z}w#qI3#^
zXW1z#+Un}3fkKxpE<FX=ACln4ne=MMx|$)a(Azxfr8IDd*_bR}l9<Izcqsyn*4)Jm
z%Z3BX<IKlH3If@Zrvm~wk|rL9)3D~8Xw#$wvQhA<y?mC7Yb5hPC;pwD$@g8!p1hen
zuRwHSF5_-od#aEp7BPmoc`aPRY1#?`@X=gBIKAOUjCNdl6}DQ|^k!TR<poS2hsfc<
zXbFwft)z>B3G_V5K0K1^gg2^JTc_Z>&!jYu%+=*Ma7*ELEq4tv{j8GTrO}(6;@#XZ
z5IJ&)$nmPt4Q^gUXh2ioOnhXk=Y8dvi=6Pa)T5+u1rjHDl^EgNAX_xcsoF)@H%@<J
zqTG9D`$T*Imw-t2CfxBQE3;=ry!hJ6iUz3ABWTzp)wM(1!NF;J+M)!IV;e!&CtViP
zU%2SMid}%!X(4-0Qw}tgjF=c-r8xhz(bSnKHSjA^Hb2fUC}!JKDKUVL=6S)b$LWdN
zM9DOW-p1Y^FHqYe+fub6tywwA2}lPN-yEjM*q5Q*xI=oEzXGRDlzgH<m~enQ{%r#>
z`%4gkwyp0HZFdX&>SSR;M#B4}F)D{Ir97h#9C?;^^+jGceV40btrlvbW>vR%!EgvJ
zl4eA4Z;y%v)rMTYKKZmoa2vf3%{$KZ!oEtmCJ>_qXMOSWcWZlJVR{RXiJ;YifXeuW
zQvyL)f&?K4sq0ozb>Y*oC2{E7Io8=&iC0dGOD?U0la$RDJVwaVwZe*iyVdG681$`L
znfKL}-p6|51@GbtFP`Z4V<?ps49vNd^cHrb?{e2F8oPkNB}aL$;UqN$sYtEr=n(L$
zMIN5j0CPp#H}~m%I3wo_=jWhQ+mwLTA`*c@%DP29qq4#bfcU_UDUxA)LA7RHoidx}
z#RCGC%h@$S6Pa3Ud4l!lh8>cS8Z_I<HpC<OQEGaec~>Cjvvc%Xj*!@nYulcxFut6?
z6khdIYvWM2Y}1DCEiAY?0bvA@#<+0B{VC2?Yk9L$(WsD=cG>ge8JlW@7nPHdJx$GZ
z{5*gmN5EcGa77S|#<GcgSVOvz0ai5ChLkX_QCLf`R2nb0FMA+uHhfm}Mv7JfRlVFR
zay?v~YQ2_QSIrko+Gf;<Va(6IpWmmGeZ1o)->s++a;~a*ZxVvA_1fauV^HClOh48X
z<YAA8LDRB|?&d_T_*OXjt^bI}3U{jkyxW+@)H!a`#Fz!ob^U(pgJM~pImwYkp8+5O
z<%lZ?<~%fa3c9*ia1wFtU}3MCDcVOB(>27Gmb^<rF`d{~kejDJ$2QO%*Ztzz7P5Xv
zCtQ{jVaMYl>Fv6wxtiE8c1u63Yq&rz4cYtVVnMD^oOhXF@35>}uNiI8npE5w7S4f4
zv8Z>OcpPNIMsNm++yp&CwAIXCK}rZct-j4oIOh8WmLsSuSLnX|xb-<MLAG$!&b4mC
z*laDxv9uopKPq5~&`WgKd3UzvSQ9SU)_eR6h^Yysl+eb_z4)$VpK`phGSo~YIwI9?
z3rd*Y_lBw5%D#b^u+rCjA`Q0`Z(mQlaIKJ!W?Xp=5!b`rf|jh+D>+%)FQDSY-WM|q
z)5`t++U~mzC%PsW8`d-wISdW?1evMjq;e1-k8e1E8xE#dG=c!pC>W_fNvSB{nE!5`
zQ9R71IlfquVG=+Tf#W;hk5;?E&`SvfQrkeD(Q=LGS8`RZBt0vQvzhghmAE3<S0znc
zs|qDNWb5;5Rh^9_^YK@DT7L8I6QP_|(;RZ-Y+3D*=^vXt0EKaq`1W){yZr2Mjc@M_
zk^T(S8Rlv=Ly|OTp=)FO!y$KolhG$8uX449hYsP#jb%*)5IMCb_*`plhUNaGw0rjq
zqIWj^t+!xhT~!uo8H?Jpz*eGo@vm|H_581npUWiGFaqbKg{hi)VwvsdMD`p^pi6$H
zPSqrZ%i+ezjeRskuVZT_U2DAVD>e0><T?67o`+2HJ+PVmGSvTenBRVlei#t1QXu_A
z?ukN6aWXfBWW18~E_75&BXy%puzA$vpbC;tE{mY?R4t0m9%nC=LF;PLlpZ^Me6a$B
zVK<Pbq|Qe!)s_gji_eY9%%SN!c0-=9n#Lh?+)TAn0v^$y8FaNWu^=AeJB{)QKj2zY
zx_6zF`bTQ^Cx>!UI#rS9C<ILEiz*eQxXloZDdLEAM=%k5{0CRx;9iTD<x`1q!?o~A
zuV<RlgW~B&)-{ad(D#<Eag;z7fx-d=X^U>Ulw+DTu^JP4HM}<maZM_(O=m=TNX-&M
zJc4wNm9)}R{O_BtjJ<vEZPC(mCVE^}|AJ*SNw)a4oqt8ZRpj6klJV#wG|nQm=he7P
z(<-~9Y@>XgTy3BANE!Z;adWG6{21#t@j#c%4VH~zm3SM5`r1;ZcTpW|4J~xQ=85d$
zs>mwlZE<;|-U=7J(B~|D8wG<qg}1ANNabkQINc}2<xd_BYH8UgLW;G`tSLG9JkK3=
zxUHs*0#j3dvcc^tSv_?!2M|nV95QCJ8`NZ@!+Z{^%<^$#b?KfDW1)b6Lt?r7^>Q4k
zuVy$&JVLBjvk?X-3K%Qs3GM0bl=^XWY}tvE@9}e~9ag`3#h~&*K;`P=*6E~SSOUoz
zHlzQC_q^xMY^6`^O}D4K%({?d<c4)*_be|Tj@)N%wmt0Qp23Gjy?)AsgQjK7k<ztM
z5^!VBH~RwVE?7b*fMt2{i3mSHe(H7;qo!+yCUXU&@ky}{e$-5Au+_=tW@e56+`0f&
zKxK3vkb$hS5Lr73zF50AtTpNWRfEgGlV_ciL4m`n7UH)mNTr|WwKC&t7BV*zPwKTz
zp$Y_rb8-lv**X8b1v%kvSkYL}GO^`?EW>JJ`MpjesH&|bs=OA2@nOy7$kCgT$x@wK
z;ZOwyp{paS>bce79N33`8Y9G5;i{J6qbj4hqLt8`iQLNSJdO6FA!uB2L&SVuceHzI
z-*eOzbr2JzKcVAPs80PI3UD}LkQp($peA1S?iOnit;c3nrkqGS29Y^NDI_w=qCgxQ
z2vDF+9hwijo)V(>Z|=c3!PV`r?RruV_UhUoGMS{{@ylYi@?CQpYJpdWh;a5Vmj^vN
zRdyT|4_FwKMRz{oGuQs?AntRiq=%-3WQIQ_`{KEKj=o-0q*kF@g%<wSLU}3GeYZ?u
zw#F`_;-MLe@ZVLH0R2M_SS^rts&yVEJn3W)YNktdX?4v15$N_n`f55orS^5&3r(%b
zy89vc78pg2bg|6mK#ItTzRxmSLy`~;56PKiIJWCsjCnsc5#LyA)KhghawHfFo+waD
zNPJKfSNyexqx4C+Yyw-mZn1xM-F)46odTo!bj7KV7VfRnFQrKrI{jEsBIm6S4^*+i
zzcL#mSGsyRo}Q1_>^8BkP!`;v^x`94q1b^DT-60700W|eqV|+2?OBRo*|j6Zfh!-I
z4&qVc`0Nwcq9l(s7ynqi(Wez%aasw<^+$q^y2Xx9aetWiC-ZPAi|aI`tc(|*lytm0
zV$Sd<%#Ni?ltGv&xD8`lWPn(+et<<?iv?8J;?nnh2wH+uQD5{y2cEFB9T{shD$&bW
zQvYVO94#9P&G#vG#Ai2a_)N`OBpTf{I!YR{!7Jgq6X2FJXWNFZ`E#I=0KV!D6k1l8
zb~@wL&p!`GXP1|=+3TUpTaakp8{mxwPn@Gc3bvwYnfcb33xdC)M5OQ(lEB5DxB_(+
zs7PJs%~U4Etx;nK{itD}XEbKSU|ZN|NEd1ymXT+AJ2`auZhXN2$#3vt1*lq#ldGGQ
z!G>#RH#)P|A6mswHzlF0uee;nCm5v@QU;A|sG~|g1aYb}Ju2Y&-Y-cA3r3BiN4IRm
z!mSXkooFnydQNi`k**iP9tikdEHL1UDEG1a3Lj`9Y{=-HN19c#vjh|n4|hx#dW@Nb
z=zJRJFXD__Z^(&D=3GmZ4JZj8wKTym6VxcKStSZVpSjpf5`SI|l}|BGN#D-vr^%LC
zLAe4-R5Lwec114P8{(S#QshQxU*2$*G8^KUe~=xK2Nfz4<s9QT19D;dw_L>A)ee<r
z+2aR4Av1dt%n=Mvc|_izvD<iIebu5Si*~i57HSlE4Us|Ufp_p2k2XhlhPS@j3V3ou
z8WUFwvmr_N#0epW^|}}QpzW@<CkwX<>TM+&8V5_to48E5RBdLAOO<1ox}Cd)62S+l
z>6sbVm9G+!NR3#WG~+q5-ykogEIcz0_9C<6Hnlh?wW35t5l)`~%8~9@j|LGI5P=kn
z);&)rK!ltSyP#vM*Q;~gIO`L)<)nU-n5>Rc6B^^n)uSJ^Q4U#<^)a38iAaddX7ag}
zjM<jGG*0ibt+5TWvL9k8Mhq+C36OXjp~29fwU6G98S0jr*Lj_8*`Td+Zy4Z5{VhNC
zsVU|d+e#EGKKOi~FkTu-(@wE_K9mNz8X8Af$(D-Z@G_56k8_HA8tEPWFt}evWwH)i
zS$KYQRc@I{q4omhsb&l<LY?k8(a@m#>s;JX(J;|kl_V=aJL}pF+7Q~FA)R9btJUak
zi?6SQ?wx&_LW7rO<dzUra^<ael6z}6j>8yev>V?ZM{Dq^&rcAoR43e0)l3b9?7eFu
z1?Q58o1$OehkGX)6^$G-BGXav(Y!H!J@&1bz7Q#p!+#<6NflnAKW*?v&QqB}ac}tj
zoywa-I-xTuwZ7xmdpb!@G)4ijIB^~M@H16iT^5Z3!S48ULSrjA5#?)wrqlMOYk0}A
z6*C6Q-n$8%7q^`atOLYlQmQla9d|SfYJ)6-K#!OdO-YhvE$S9SAIa}e1)EgDxu{a%
z1nR7~1T1(_Bz73a)8NE+<|EW@K0dlr#gzK!92WKJj7a7kC2t)pq^LbHzfE;>i0@4m
z6xVhm2E<~IFMg4|dTXh3ue<hjy91;|1qpo!`Uo98<w#iK3lbv5;3q&+8c@=-(x?}U
zPAdC-#dlRjq}7MAkF29wAiL(>LwvG+h5cV}KWaaTqt;Na`WhjAq%c0?8$IvgJm(lE
zi~R9?{UgDgZ^6~;S1=UEB0oGSItwwH0x!pyS9OhRye>TLceMm+P*5z=1N`-Ytl1d&
zlhU^L2hewD`sl3PRMTf2LyY2w7TE#I=+rl=S7KGlHp%Hm<Mycf4KXS){$&-9H+E^$
zxuK;!)+KR`g^f6L@*GQ$lQClLFkRH05KeV+%yWL*#wVP$8DiwPH?luA&RZTA6$BRd
zne=d8br&;lSNJfFxUx>rV^9JYPKlL4sSqGOnuc(tP|z@sIDKUO%$;+zp3b8Y6P!z2
zNiB)`wBEl}<?~NA!$dO`qBzx8Pp@#{<3o11=cJp_u3{V2`TA<-88EoT_P1#~D_^A*
zbJ=G3ImJVc(xR#U>0W6}DAoJJsR1tt71#>?$>X-{|6NviT%=~wrO`4oGaHEBC3Jrh
zaa@Rxs2+ib)3kXAtKflZWU!80%`}B_8NPO>7eXjP$2tlxOGJ1Ws@ou7b+oC(^M*YZ
z6EnV;i3_IN^eP;C5V=Cr8j5euYNmfIy?!xO7zYK(A=-uu>LrpoA$tA%r1v7H<h+EH
zC&UQHn`YY!&EYYSApPzfG=CCCMzYPG2rvT3^OY3db?Se+@w(!ZVv{^=_H7~w{PW$z
zgMuI^25ca(0t*EftW<x188@az$%}g^YT;h_;|lL-2$b|cF9nvMP~VmV-H0lYz*ac%
z+%~C8s&0XFRu^dff4}h8yK{j!I_<sRJrqPH&>pAnJy;&c|8&BArF?jreb2N_@epqX
z=pTzu6M&x4fN&nhe-HDERB#kffq0hopy>S{-4T!w&>FfRd^+}L(?(by8;Ist?K4#W
zd4yXQEt&wSo6x-+-hb|VO9ap&L|JV1V5z(<R{qaEm$E?5$Ru6mUrifdDZn+y4+KE|
z+}<Y*u*Fvoqc{IJp)kd>+n&*3%^<^{+wZdjJ)<;VCDK2+f=CNg)AR)iG=X6BAIt*2
zdeH(sBlg$%e|FOTYy1A(zIgz!3SRf69sf8X1y(%pAOBx3Mc6@~>(f8aj>zV_S-UCJ
zcoUd;kcp&RoWkSqmV&#AV8-cl;Ze{Sc@2^6Ol877B_*8%5}-*W0QBN!*^_Jj+a^Py
z2LmnK9w%nyxO{U)(R@R%o!+wUk0ui(PO7eF@jp@Y32-nd2MqyY1wJGa|AX!R1ip$I
zQzt3TiiXNjwGBD@`+R(`4{A3X%!uGHKzjC5QJMcCJt(N)cSFysWm61l%c1&0;1|@X
z3@IqqV8j-*-8G4=f2zr?jHUz55WyJ>_s-<~z65!N^g^hm&b4ODr=X7s0v@4T@8L*W
z)g<#C^#?8xrSa0<?<VMpB&2vhm@3W&R}JwbsGd9-AayNf*E0*4)2y<|!8Ww-Fs3o7
z>33Qwt*muBYn;nBkag-GJbI|6N{m7JLS1v1oA&tfQPy_ehYs--8-9=16&{S6=Iq!}
zA979liFq_>^|YWkL8@mLDhAf()7hYVDRE6@R`&Mxhe!342|-f*9#OhA-h0#c&ctF?
zc)IekDlP_y_?c)Ky6YYTrp5>8Y@QMRL#R#zg~jB~u1YQku76yp&c)!AIG`<_cbt<q
z9xp=ul9HW?5;zYE;=DN7H?k9TlA4YKss;*V<)!<-ZAbLCGM*G&_SH2(`n~&ZV!e@U
zU%mS3XVWk}IO_2I+jC4^*OWu3w9x))=4IrPV!{*z!9sp-EbJ0m2<=ckI3dsGw_T~i
zv9r@TBNe*r?CcSmZgM_PZ)s}$4p~z**Yz~~VPcZvK2T_%eCCLbuIIV2F@{98=tMl>
z?c){^mHftD5;#aK0?Qyi5)cjjws8o){WzZsi!NIVgi1G0M(p>T#^HfE-p@AG%8xV4
z2o#9<<xHIMcj|9qE{KzetfVYXbs9}-`Z$8{n0ch$Nkt*cIi+ka8Ay9v&Sp@lbd?L#
z<!^2#SMBg?K7|(~pBd6kUVi@e4fV?YM`o4@CSfsW2=3U_<F{cd(VosfWyavSqxvPA
zp<hM!n7B5bJ#Ih~vhkK~Wh>t@SOre9k35`bBX}u+0!t|Z@&!)z)qk`y{RCBIOjY1?
z`ks5}uA;Khg=5|VH&;`mLnn4ht?PLow|r9<$H^6`jQ7=U31%Frm&w*lTxe6T5r#Z@
z@&qeu(+fSjlVgqQB-tH{O^flB5@iv{%DUu@cZ>7_%UnZNaoKl0cPCx0xAhHsGtBRj
zsHmPKC-7c0^pwOZSB{LFVv@6XI;;e0o;v@?@MFJ^S;gs~w^ReSz_)>`kEX<apQyGz
zPvh3*d98WS4RxH5OPuy}&V7r5NDpFaetEuV%Jm;32DlbZ_}I<GG^R8Du8Lp%SP5I)
z-f_HrU^Zrr!8Dy^)&Q~N^(lxf@9et&#0rYtf#Q+9{cRqf$4b7aPfvMby{s^mZwZ%N
ze=R^qs>dmjgdmql+c&ZAdvJY5;>uQ`5KUu=^3~>O6;5tE*gcHgK6bnDsE$wI6GKRE
z@A*-0%`r<{SjsbF{ZtGBn>kDN+e%t2;AZYJn7^gOwgb_e*qmJRau7x}<B+2OFIbnW
z3v&~Z1*%vAY)jE$15)?s==C%wTqo@1C1+RMA(NMQ%o|5vkKQpSPOV-rJ|ZUd9Qs_A
zztiSf#|Yqgs`x&7oC@*neeP-&!&|ZA(M@P_-Yd&mjqd%{&o&p0KV}s`X1(^1nEqbX
zAxq>IFTXlush1iZgz^}C?M&gz^dI*52%loP7)?<@D-y@I4m`NdB)Y@Cz0}-jPr|nm
z*nX}#E%!Y=hNYMR@)wg>2-n#Z{gs4C*u3r+&$Coan}m0t*c_eU*JIMXr0+t(kc2m0
z3wnZYTR#y`(2qxZWRyJSR)jY-7=AkTG<?JI`1!PB-TTNTI*9ktIZSR04lh;~uzyNt
zB9=DZkg8GbcGUu2lY79}?dVcjE<#yOy`7RPDT)BTWNoqeTib3;<sstg!!)WxOJ)0!
zSW&IzN`4Oe_yU$JyBK=HLe)@hlRg7OWk0;;ZXT0m9_(gh84P^fHO$Sp>hI0xo9E^$
z&QUiNW^EcZez-hmwyp`QS45!8evB{;txayh)#&z+O3Pt_G<PMKUJ7Yy1SbP~fu6`4
zW&1;+iDEWYcyr_D^48g$@?xhxUyn3r6_P^rG`es8!jFM4A@FBg?$&=btOpUgDwo3R
zGTpX!1tEgBOpsl+RAHJTQJEC^oujh_9*Pgt=^yd0(I<s|3avJy0S<Ms9vCLAVsWq^
zGIAJvbLcY)YOCNcORO`CveLjY#rw9Ib>-e|VS(G9pFWCnbM~=}%%ar(Vu<fk$oW-&
zjv8TJVFerMNj3tR)0>7R#!k6<yX4NOS@)=&X}%~D6n`GT&&S^&tOL#K-*M481BiYm
zGCz_|(5=3*_Q+RE$YpUFc^LbAN?LhInJtPf3_=nT`Y|Eg-R?Q1Rx@8jY&h3*=cV&|
zTUC#T;mS7ZHO@KR$?Qwody&_D5d@Wpr4MsuoUG!aDi|it#YYZ5eA&%(ZS9U|pUl@&
z^JO99a$Y>IY(%|^QmWinl2tjXeCfw$izEh+0{~i{HQl>2t0>0cm6a6$2kV&2vQ5}c
zigD1`-qF#~-cCbDhwLiUT6Q)eS5uswe>xUYf*(sDc)IC#Q?clc{RW5mukQ(MG(J_k
z5g(1|OlB^fun*qHB8=y^+Sqv3Wsd*Yb>IDF9dxs8**16-TsFm{^#HS}!L#7`jX9i3
z?Js(<G;?dk&nujq{T3&2F01U-6;o3^G@NA4)@fP}M$rdVr==wMJDv+OHFB%Qdk2Q)
z7cvMIb6I=?sR9%<V|56(4v*Vc8T`{VjrJG*f&!}^G25#u!^>|Sb<-dr7yp$NG%vPU
z$6ipt`HP7_s%PiP)hV2Og3|@U%r?UrMPT|<xBb)gcMD8wfqF4CrQJUFu$`+jEukix
z?{SqMhlAeJ-SAmVGF8m)rQN{kRxo-<Vw1S`mp80sx*ljcmP|HDC_<z6VLzoirRlat
zcYjF4RmZ=N8E2YxPxDklwQ>)w{@}+I=p^)vvoAYM_u`$#Cl^R^{#@rrOAt+P=-3o@
zwN>nWmV&%kEx5C;`;bNl)Fz2bS?2i|$EY{F-Mg4ieNd!IBckBuVvNAr>nKe1;iZNW
zHN_$YR>qC$@!kSCfc7CJE%H<Wy8MKBH|8agZ*2k#NhTtH<M9w#Kn^O4f=L*avf}#N
z&7_N?Nn*=~mo?s(Nt*is4;r7@^aeob(L>-u9y@`=nAW4;gEQD0ow_ED6wTzXEY>b=
zPWo>W96TKA5lb~D)Ob#k4-?LCR+E(buM`$eyCmF&*m$Z3Y7JX79weL8(R<eC+qF<N
z#hj{KWwBL|H|$vN5jWI$9-iPgSsqlmmG;8g$5Nk7biMnT$Y1DhZ(VwLz{-E|bvo8Z
z^^xZ}&_B{r(h*=1IQ%&yWY|+kKUuP`x%!Nrt2n<=o>}Uz5LJE?p10mk<25I}yzLLK
zJ79ea-VIeWi9cs1M=c2q&Nq?b=3T})wAfKm{P{sYl7;|qPpbLC<Y&ijes?PX8G7z5
zdC}sBYzV?Q(*u*<W%f|S<uekf0A`T&;pzMJ=N;mmQ{(2bdlRe|9fQFc-9umJOdvuQ
z3MqUC^#f@)u5$Mw@^YdficO-!fgV4~ZO&Di7@T&$MMZh-EH%Sgt);W+sQXFydsPIR
z+KIM3vt%T~Zo1FnsK2_1Fj>R~jFv#r7KFT8gajSKo*y2|NbWaE^W4~<aaL$D#MQ^1
ztA^eO<91Bpr}CQaH>~MCCSD=rd{#grNAzqzLSf$3sb{zm7BBZr^g@eZKyBZA#q=d@
zmY2law*n4h=%4juf)Ejtf!Kr3Ec^~#={rbiyT8~nxFM^4OwG;B&2&M!loBf-9_1ef
zA&YvXK9uppP#*Pqd$S&G;bhd4p#<;4jm34fwu$@IYseH3)%_TYX&Ye&!c$pyBfn{n
z<-z#v<aK;C>9i0gCRWC$%!(i$eiIrXj%SgoZ#s366K#txyk@&OFZ`N7&lmRwLQc=R
zMNC|<KIo|xT~mQz1|SuDF*JQp-{WBj-9HEF)xRA!_`MH*ro9sKx}JpQVe2$OwwLO`
zhdgeFY!A%1ppa0qh&;!H^5m1T$`(|fT*A68dHErsHPvE=H<q(su1Q6VSVq6Lzcjl#
z8c@XqkRCqVK<34bWB0e!1(H9vsOHox_xbtrapI(f*Hj#FE)F-(8>WbM0T=C$1=wj6
z0omIBLI~fdH7~>o9Uq*JH_Mx#^KSJJTs1B3;Rpb40tW!e$LmzYoqwd1SiXhJ+kXi@
z%DM<k<*{5{`LWh1p5}$kG<!>dLpTEXi(mTF`~NvD#UKu1Ke^-lwn4=Rwx(L&PLP%z
zCQvB1L@9l!G|6wyi+1<uoRsh<bbMS~hfdP`{CuaK>9O`iJe(OzPR>*@X}$(k6_rAr
zx?=#ims0HefYMeIj9M1-d0|8;6UcQ3dBEyEe4QZ$zj=_0rCwvVGT?Pw(c9a*F_NnX
zl!Snub8fOAT-f{!0P5TT7@p2Bav_6Of2k<ijaKDPE}=w3M7rKr@U>L;;`;i_@*bAD
zAEA6pOY$sVHgy_{lC5T7o@;yy&rNRYWdq4P6-ALd%QstkH*TAGxuGOHnQXwyUC)!b
z33&tg-<jS2CjPz@RHddvPpZ_Ric;f@#a}X0#(VBx^yppN!8gYkDk_bYpRlspnD=nK
z?TuewHyt~a?{T_3eWyG|Y*P;);5x{!)+JcbJx=!xf`%*lc?(kbq;0D0VSc&yG0A|z
zfNpO96;?g(W&s(eFKBWoCA&rI+y)G85x|uYe7Cpw<^LSOm;y(y4Khp!l_rkQ2E4tF
z)`z(40W6hPwRKgXP2<_Bj`N%`rVi?qqw#4`LBR-(bW+6`^Nb8@11>qa5CA`%t8)g_
zi;wjdkqAKYww0O=%o}g6FK8ldYF1*2t@qnR^6nrl%TDui*;UPXW-+)`*)CdO^*7hB
z8SBHwWRhR1AY1|jHYev)>7cv72I~tVMwR9Kj(vZ&m8Iq75AvIJrb7Um(Iw^b^{+?$
zvPtsN(wc+idDw)G3*I-LXCgBd-41=H09@oC#d)6oULms~c6p~4(D!Dgryu&>8t?$X
zf?fdlz@eOQow(%V*E@<~3R<#A$JLgCGWd9Sls=x3lmJrfmPaW7k0!`L=y!7NyGXl#
z(8DV8koSV(Uf$}xo4uQB8*}q~_J!=8?(XAC%gDm=qwc_|x?pyR4@&?x@B6R}D=D{i
zGP@8Z<xBR!5Cq8e!AcKa#%9y?R+Gy7IYZJxzm~`4&(55joPM|H#>Mv!-WY0_b%+Is
z{<@Txw;e){&km?})LhC7<LjL9->k5DzZ<Iu@CUa*MOx+go<zcniKc7Sz{IZ?0LX5+
zZsDp}S$%wB;%3eJ+T@}oGb$=dB7}(MQNiK>RFg-B5g~?)&=(I)Mq0i28*ffzzMix@
z0HB3tZ&w3_U)DEo-cWy#3q84>i|vaM0w7T)e2z|o=`U;J=%HBJwe0}Vf|F-T_cMeU
z0J;K=p3SN*Tx5D%EuUXNK4A(3R6vCh1aT7)?^GBhA?%yDHjqY6=-TbBtZbWOx5KZ?
z!@zhswi2gjtyvP(g2}({Ggj6e&CviTOETMVU7Au;`BHbTra`Qua+agq^Qi=54yRQ~
z4{1f2<QX@pY{Hun9VsIdlY*vcjv+PW#IZO4P21x-V<hb_li3qoB-OLIc(#^S;-QgU
zXD3k%AV6<Tz!8G4vhK2gt&la)=eaeyDCppinlzqT8X9J`Sz}==HOtsJRqBe?*2P`X
z($Nv)8@~MSmR@ZbrNlVJG&TSozox4l8ySJbgK5V1(Z}VT(&OeknR-{7YS?2P-EJdt
z+@8DkX%#ebB6jEV?t3w)YJtuRp4Bl6#cxtxM3;M>eh<Xk?sm~&d>n67nkQlLqDZq!
z+AP6?^GY4v1wN*>BP>j}+fMT<n)gkmv>lGiGuiFb`E9-^g@xJ8R;0Hd2GGcCun+JX
z)<U24vtcAv_QEvX)Lv#}8&+FRl^b?qtPB81y=EU!M=DcR@wiC2EH#y$$4@c$&#!={
zckx`cO`1v>4~?%CZV5fq&4?v7uH3>`5AR}Attp=^(Ts`S0_|2!V^P#Ji{Qu6*VWz^
z++x15OFCt5+6fx>kt`ZxcQkWHEtP}tc_A-MnNN*gl^E?W08mo^V|oi_PT;ai91*wb
zuJ}EDfrtY579W0;#9wT0c_sWVRi`f|u#~Zr%)GV`zdy$6xTt!5SVcE!kKJG#=h(HI
ziL_8TF%%e$>Q>x0i91(?B31;ETJ?=~tIRS*ZP-7eGBfP6_qy1r=G4&$=!42+e-8ve
zoKLa<;OfV5*V@hef>f6!)S0ZMr8j-Tv7B1g^Dye)^%Gz|04So4{z(5d7Jx;9i0dPr
zks&_=k$RoCkRck_J;1}juvxisFT;oSToYcv#fTfLT@sTAyE@7hQbn<#q5fbj6>CxL
zMpwgVV6&v(gYP-6VS*&WYI^Tij?+vBxLyUOTg3S7T~1S_Yn0GlkKBUaiWHYCKGW{b
zdmQ$mnZN->z6D$}WW5;Hr0l|nWSjC8KoTND4;W#MBW)khqkfbzZ_5Ug@C>_tu4IYE
z-&uOn43+QF5vz_2tA4`I_}NijKD0}%hjVYDQcrg(F}d*RAaBm#2-;Vgtx6wBJPVde
z`T?>#A}FwYfbt^f^tCDW9g&E<pak)zvpyShR^q+ouBaKaT}<y&QTK8G*Ia>`!6)tu
z7pVe{$5SQ+BJ{oFH>aJnhu0T-aeHOVgI*#Pt^gLgsg5LOrYXCqBC+Knht*Sx5mm;Q
zujkvb#hAOMW@0RcZpGUWT2zZD<I@&oaurk4_E0BX5u)G3nBEp<k6)Q${vrk$MCh1<
z!1=T4YPI`GVq)SZL)K?Sq0<)3!ZNk{V>hQ^H{p0{Nfp^!gUJUN&uMhdN0k-2QVTy1
zp{W{MglipCH^P}oc^j(miZ%hYS6eMJ?6j1Mdi{z~_08~R3cE`cTS^Z>K{lGlDtp=)
zyu`amIsc|+Ewv6n?rzgW?(UQv8|}8vHzCIEFyH8>t)=B(ouAdLJ(N4Pxf;d)fOwQu
zdtGL=@TD1N%4;{=$V<iGlo+Lfg~~^CFJYMK&XlZEf;B;s^Q}7zvLX{SJ~V9J#}#P_
zQWdM3NV>7{4r5sqy~QM?x~?lRcI-|otQzHCP0jk|V$i2pAWR1J785LL26H+|j3Xpu
zybkLYdKZZU%Ei6hnp`HU?#xMj5q_1e+B2fq0>X=QG8mg_4MTJ6i5Rim)1uf|>m<I0
zW2qX%$GJ2#mS1hx%zrST0H9q&TMB-p>0c?gul%Bd_jyz+l@|G;JU38Io_9SOk|-!B
z;M4Kj5+O7M1{chdT!H3w9YnD_SJIyWG_~$kdz5~>xj5w)DJay*ew6;|^KqOPoEmf$
zKJI0_xhKS*opkMWW<YOH^LSBjFe=Q){S0uHlY5eRSa)|U67J&wg~51Z<KyGw;!Fn4
zE6ckz&QF?d8tS1|&zq=?K2_n*(JMoPA3tw}6g<_Y)sBU3nA7V=m2iev{uME->8+kR
z2`j}G6evzX;!TA?)<g9~y5w=5ZB9t)IoRYrw=>{F)Ra&?h|KZV`k;xC%I+Y`x59(u
zD-84xFqU&gXYR}<#S0WubX~cnDk~rcbM`)|TbL4!ddk2sU1=5taQphi`^MS2*yQ8f
zIed#IQVyDF0u+&?7(**{62C3SH-MFS`kE303OqKnr1WS$JS04r+w)Qj0zBWOj~1G&
z733jg@NGhtBP7aE?$osE`}aU{NazVPp^e=0D1u!N)Qk%S!0KK=kh1G?%Hob1)c+`4
zO#c0=+LHn9kWFoLZ6shI^O;b^fMA2D5YN^Ae!wmT_eUfm;QG=99!>w6Uh$P&{K!}w
z&tVp6l@NPewShrfc|S6fL+EHw^dL*{=JF7TS#7F{{fiZYJGd+uDie5*Fg%RAO|k8a
zjdP?F;-498PnJo0!;IMzcD4yBE&IVrt%3msBC^0JR<XIIWwgQ<hpI<2{ce&ck3m_Y
z4t$2`TV)q^S+=z4<VhT*h|ivvwVs(^je1HTAj5xT{k(HfgQAGpE>%j31U9q;E8aIJ
z-hk;%d~Wzb#hAcigs9b~0UlfQ%HnvsvI*PnV{E`#f=Ox_o;0Tn9ph?+9j<{)q;5+s
z^{N#JTR^HA(c}7Zn}k2j9os#AK}Lw{N=x;1MjH9cjJC^8tn4{p+YP_0sbAaTAR0k9
zhl1JJ*rsdJdNY8E4NRD?B7n7iUqoxWGAM+Y+nlZF?dCLE3UrY!&0~0+LX7!Ag}}C3
zW^u9g#&8aR-Ql%e^eM6eBASErScG{XkQy)2iqQj*(N}xkdiSm1GHjDm{O)*wzo7Vv
z@|dcW&>OX^cqqk|0uZdgTv_tFK1zBNqTor*fa9{XnV1zR{nSr3?6F&WS}78F7`eS|
z>FxqRV9lXrP;?pUi=NAZ01r+@jhX2x3mwYxWxcBq8xJZjE(m(~_Y(knUt?5i7QE3o
zn_IPB_TG}7ES?MLeuW&(kR0Ojhy28!-n+E*Di44pjT(>(NkItjucp~c1z|;~5yTU)
z(pCx_Gfu$J(eZ2X4I2P03B>DAl>*BOuBH)Gvkhc2m*xvQ)NL6c!YQuX{TLMV+=Nr@
zjBnvAblhIE-ldGWM1K?*P^#srKVAB?vTdbsi&Yc}@_AQdgNjTlJ(tP){TAQPqLAoy
z=hSXz?DC^o%gmItQrqk-=K%z?QEv8LsX^Onf65kiZS6jgC>^Rb(JG`ebroTa!$dgk
z07j#+>{Rk6RSd74%-V+~r&Vp2iWu?4y;h<Uy4p~fk(T^B5eBC0Uf8B0G2e}i`Rdc8
z2Lxo_x7rdqUG(cDbMGZPmtBv%#Z3WaOdgL@+ca7Yt>!({8l{4t*wxr=z;uT4C`%n~
z)PTEL%J&k_9g9E=QYBedW>_VVt!-|a=jl}xM-IsRJ+poE1mG%b>)QC8fMLxd;y&u`
z9U^^Us}F=rJHbn0jH4Ai9M3Da^Nw+p>H#Z~Mjw@&JnQv6G)?u;vWiMP*mO;#YYqs!
z>42f`;pQD&`xGVe5}T>Y))Ao2qVv{V%>ZcS--VnFz|7U`r~MjE!0&yDMBn-QX8`~}
zXl_uu$HA0ua%|sP-Z6Vl=77M->~W97QXzEPsa~_H0jK&|+&5z)_>7sG_OGIWfG|Zl
z@@@<B@A&YJ{NLLEV}G+-VLtc&?gjk%XP^zQ0Q9j>5RG?#N5FS^%`eLSe_!&~Zcvgf
zPy+aG*&XqrZ)O`Z5D&1G+h=AOf}x5Wh+wRBR3Ix#P45->$GO42!d7zdtpOnoh*Dw4
z*RLHZ&Ks&Vet}3LZMRX`AUmS1?=E5g?61L1w?tt}OG|}?$cwWugs=f`ro0VYFdtV5
z_oiA6+_5TYyqJH50~z4f=i3VVIS$nOmba}j!oUwa_~Imhdp`FmtfaQq4M2_o*)fom
zK17N>`mO>N3&eQAj)sZ<0#gcTAy6tH5UhuLe|5NZh{EyMlJfG9fu5e8w#u89St|j)
z!&A3Loc8v1@3S7g;G@3o?pk1Q%)JqPwoD6k8H3PE|Ax%{Q}Rnu%UftF76wq#3T#t`
zhTV}8?K7nKV&wkNkBK%mg`(=|dh0n}i&JI>28O52{F7Q?nRUB-mPcQL3$LNaji^C5
z(EjaWK1EjGJ>j=)xn;u)#XE6Xqysk;Krcs87si;hU`#-v0VtI<Dn!lDgB2AO`?sDv
zd6FEME$RdCYZi}t-s{rTKu$HMw<#h*-A`mOZx{(B83ejc6S}94`#Z@(#Ptn$KyY8h
zT_pW^6rBQ$=mj62`(m>%<sg0Sq8x<)yH-n@V$;0QH(%jzIL%;^gRppvUpB=Q`^8$a
z{pfSEMJ?+Z8V>hK;s$9sxvN%!#&i^QV6>A;B6K^1)^@;}?zPKj;j;89jQ!@8w!mPZ
z8Qp$jTg|?99}9&9e2Gc^V&Hx3Zz<{z_TeZc$*3ZH?(vpDxfUJld2yV=>u63)*M;E*
z?)(&5|FcyYN_^pDUBJYe<Z!&5zK2H&+%>N(aCaD4nH0YwdWwA%$@A5<HJN+Jx+Cw)
z#rpdC7$JqHhiNyLr$55>W^34=UI=H+&``{j99|Y%B>_AGush+mL#}5MvdDMJPw^G?
z8&Yli!{GbJZGOO%-z@|!lw8OQ;7y#KR}Bm{jv1pQM)An>bBQw-U8BwW!&^)~0J;LO
zfj56`{G!BP5R~P60+hVZb#_+Cb|=f)<}(@_$+Ba`zfp?^C#`SGK>88ZD9r%ZwG3b~
zM6Vx>y!@5wdV)0{N)g4U59)XiYie{uGO=2KanIxMSEg9s2w%AL2gI2ilZVGAvzeW5
z2aUW95N}$)1zf!Zzyq5UPya3&ffE6KuHM7Jt^I^)21FH!$_>Unv8Sh}8WnG8Xlb3w
zL|8C|!BidcqfH2wkL3Vtf}0OeLP4gmfACAO0Ru$w)M0|&;?W`ioY!;P$YHwy=4~As
zM9cxG3LNfet}ZKUsm~R5i@*RpKWNs|GLP_A)-X7N82l(cAfmQa$2T1hB(sHJ^7gG$
z4p}j}EI1?toiVmP2Pr%;F{#|%&Lr9SohC0P@3S<#qW8kpSo#>Y)%rO~ziF^}G-#xc
zFTTlf35@s(U4F+rpuPbLZU?OoSRHD~SRSf_BOB|gts);<TbuLRmFoZKWCZ^L{H$XD
zwr4k8I^|A#5PavUpE>Vp6Z!_}&jy(QL!9TgpwsWiJ2Rg?e&kg|jRUYFo^>$3q-yUI
z`oMnWJE^#Z@O5=c|N1E;6osf*xV0l;O|`Ytu0;=9`$dN-g#j&@nfg>2%=CZWqy(7j
zslyAW#s{9MFMb-?E@o#_8*GahYZLv2C?1+dg6GMG(myGse6K8~5~v%kbAjn@ZuVeW
zub=;tWdv}8uuuA6ice}visxF2v-Rv3#h0bDa*5gMgDIc=Wxxr-Z<G$`cF!;8NwqBU
z83IGd(vlPLzZK<J0afLNTL@5SG}>=}<|}ghDi>@XW-U6F<w$)>EMj7Aw^ogoVa;h&
z5XxyB!jHu36)9llZ3)J=`HArB^=3D+%KLXW>J|gYhT2bi```C+f&<9L3HvI>-Qz%J
z4vc90Og5$YMR@uMA`04^nZs}IM=1_OByTXIcYmw82OwCLm`{!F%A3NcK$0K0z@FRr
z>s7IcxLAyUb(<<THkfkf1q$A`tM&nBc*u808W3DP0GTabUV3oYe&M${2Z#rr&;=;a
zmHhVi6D*+jB7wUVIVN{6wRHnzVT3*N@3L1k3KlMJbSkaquds#vi4TGxl{W70AMt=F
z04zqnqRPH^w|GzkJe1N9zV){cLxBLdTFIa3SA|(Qvw(;Zx1;5`=sD*0*&(fI3)-kl
z`;5X-QvM)(HoAp}Uev9IewGZ}a0{=WQSi9{oQ<zUdSzzWqHT(qnwhKUB4;>$0F&>i
z(SSP-&Crju7;cJUt&2P#^^YHN<btdl9>pLd`Hms&mC&mb;mYMiq)?>4M8DD+$sHJd
zxu!tupi5`Ih>ha^5D1LE@k{dpJpqRppP`1Q^Tl?{=PX#ygqnu!6!6Xhx3U9iKGZ3o
z%AB)kf5AeZ4WPqEiz8|)DLe0$e_^%g`WRL8drj&zGP><kQA3hda<)?yev$wJ;I%FS
zHf}&fdrG|++4!?8!i>Jio9xGrzhV}n2ovT+(xEUZ`1q*nF^w_$a2s};QmZRZ*&Mas
z3OMBcZmbC*b&O^k>oB)usybbgSz)7{Z){v$C$4rWuJgKl=5qPst>L{kk;DW<js?qB
zS})68v0kUSD@TV$-^=T5S}cjq@RBbp4HJ5yH;y<>Hm#T=oJ@Cu@o6Q8t*&k=?S1zY
zYO1fOkE>0#eJQWw6&w^`SB%OZ;uSIJ4RREczc*o_Pyu)U%x%&E4~%8|=$nuVqhf|^
zcFCuQfgllKqRGlvMCw6ueEGF)xR!n*-iJvG55q%8f>SB=XWt0G^h%^M4n7I0!)|PA
zOqNUsIG{<pZ{7>#+3g9!96M81I;-Qz#=In^%3$4yUe}+agCn{&%-3T4#OpK}aaX%G
zkq6%~6-&SH7v8^x1MXF1tpM>w9Ev)e(Z+<4y;g;aKs4PQW&Py;G4&Qebu4YyC?P;_
z5AN=SV8IFQ?j8v4?iL^fm*DR1?hpv>?(S|IXTu%NIq!G>swt|V=$@XIN7u93yzEaO
zW?Aa}Dq%|2#On0{WQ&@l4p8ozr>`!ozj_sAFyG!Fe)Q{9TKw<YtF<Q4Ov}8BPJ0#M
zWw!r^j7C^-GlVdaBs2pX?Ib?C7GSaJPzAwP!m!+sM7S%T*;luby^H3~Pt^q(+`rP3
zB&=H&bazpZysyNg+BY>FpfBDMPY^KsXk^gP=2#xPq&`3Mr-3PP@J^Z@OLKBTtvYMi
z_p}T7M!MaxK?g;*!G1R>s4@+}Ui`m`t4kK*=9sG6J{tAl9a36mW)uu^Y^Jb!DlN6f
zIUSbuOYmoMvbOO+iO9pO@v&!%>tOzCVe;u#*R_P#i38epzb<n?T*-(1dNaTz&=h9q
zS<kV@_oF>3zD?s6!puc20w@UuGq$SrVi=R4zL8@PJcsg+*`>X`E-MFhZR5apg0^;g
zk9vbvSCe161Fg%8<VFuDl9rvdsd=Ou!09^~4Fqx)Byn&w;n6L@k4U?w1V`SrcuiT9
zfvM}QrCAf7A<x&(FQbeRh#{#y+nL?X!+J{cCz99AR6Yj^x1JxRx3%g<PLQq}bHl#N
z1cVKLbu=J(0;%5dI4Yr&v3W{Vb_e+RbiwPMX;L=fhj#&z->oVyaZ{pe#22|IgTBQX
z=Qf2&xJwim3uO0OUE2^;*|j5$Yivi*hj$pLrK$hdh6s|s5Gt4sPu;Yqp9znj4{0`&
z34DbBgevtvDZv3Pp`gMau=n>#+*H`A-$QL}leLb+mOTNg{yhq5UTEN~j)J<WF!Pn8
zw!rAcp}98HK=A(|?KXw7%4%qJTBHPe0t6fJ{DTzmlKeC_FO_o=-=tmlFTkM-C*sfz
z5=_FF2$V!KxV24sMHDK2`V3jhvlqN73nrs+;`Gng`bR7uFan2bjcnW-u%U=34ZxY6
zpo$el$W<9Zy@?iK*TC)?Bx;&E(XT+gFwpsbg}h|C|43>7Pm~j@dK2AJ3J0IS)|1w6
z9g@D)HRqrt*Z``b5d9N|UqtiC3@gFgZ=`@enuge7gKCKobda&KqR2d6?Mn>piG_F-
z585><oc>2xL-@14{Ud9(=prg9>SW>gYA*E(x1p6vV5~O`B^CH-VbHP0QGU7o_-FX@
z=}MR_G1plg<uY?t>x*4qbJS?7;Y(Jwb^M65%*)JxeIhaeIzDdx=h_;W6?Tj6zdp&<
z@zlhSsJ~#|z3E6h5(7x+<gBlo6Z(%hR8Sry$O)9RNNskT-GHS<`;9e#WpZKyNVoat
z<m7B^Z4C?zynvtf0mcxM23i~ytNutrfEeY-N=j-7;5k{QB?uSfUfT;y3cLjOi;IYy
za5o&g&Dzfg#h}FmOv9i^435f;Rg_l_GLNpidg+Vm29+iut18_f$`B^uq^c<CdNn;?
z%ypN`j-CmEY3*srKZ}FpkJdS<va7ZR{?r6`hTU;+a(b#4rM1=lA!ijYxREWjEMhES
z(DJqO1~3BSv4rDk>FJ&~8)$T$Uwq~5bx&n``qENa?F<aBf`dLRS5nYYQBjlHYdBau
z^%|0qJ7UD986TzMp{S`Yr6p^=m+>Dw)C@zoUGhqew!eQlbW}Fnj{A*;-&oiNN;Mr-
zcue`z(+S$-2_{fol$HQi8`i+*Ulj}ZyiULT0Hxasv)1YRy44#Nk>Y&&a8f&-0pPqr
zRjkTd$ES_!Z*gj6Cq~^Cr$0ZSjrt><6A*(zb^g;#c+U3gNgYQgj>nnKa2tOY{-%z#
za4|EE=Oj&<n#g*OZkG}ZXt;El(8b_odh~;Mo+v?%CPXxR7b`zarAzp75lvFL-1dUV
znL{H&`C?cU;o#0q=lFEzHC)N2uh)T0`Mg}4&6J<y*ofoLjHj@C0oOezGVh*=n3j^N
z7O5jw!S%n*V7`X+(|nuV^^lZNO7up7OuljVhwPG2PXV|79SNf0I?Jirnhyg-t=0EM
zwN+D!Xfbe;EL4u)rIxCfEPl_C1R<k!G3gKpb)kOQMd4HUpS9s9$OH9*n+9~Y+Df_6
zK3n<NYB5^^<f`UpFX#0DkjT-j+)XK@q@-j|Fp6tD;%U!G-bt(Jiude&X~g5rS=r8<
zsfqVo(fW_rXZ8<s1mz%!`un8&<-+x|mZRUwHZhMMXT5u$_*b4b{ih(~<Jj**tJRlM
zYSC+%@V%R7Y&B&UOP=G2vAxOy$07%C>~HQZtyq3HS&i(9fsYF4uhq|JmY9OtHYZ@z
zt6BNtCY{}+QYx18w93FY!s4P0UxZS7Sj)@PuOeh+gG=e6X6r1}wXYI3jXqFOv9qx!
zE9+-Exx9A3-IhtJaB>ioS=3jbGte)pc#U91voHKZbsz^I1Jc>vfPVj4V?^)pF&|Uc
zpG`b>A+J_|I96W-ej{++c6N3E7M-C?_w^2Me2zN0{BrHaH%^@?hk{dp<7KJIK3B5z
zxfffX;jr|xa4>R2M7_zN-$|i9e*A9$C6t`W-eCVgcRbPRQLH&Q<4(@xW!bMye5(Hq
zUWfN6wpn<;PqZKDl+#Ii6YDqawe9Q9i<C44^U_u5V4M9_#P(wpaSFdmD6nOAd)nNN
zEy2GX*Oo3#tcA;IZ;Q<vQO0rj>6C@orXHp5j+f6*+G<rvIw@W+qh1x)Rczs1y?t*s
z=DtPdq|i09WeONX7c0YT%Bc_$qAhZAx3s-rF4q?q78N{(5x4O%aP1b>?k%P;6GS%}
z{OW&t9Msib=ZSmub!3u?i~!GR)^^lid57p}%Y@|Nj8|4yR9{BCe{ztc*+J?LgQwFD
zs;>P6c%6cP4tqxY-!}X5{$HbZe4_?}hR)t|R#km>Z%;1m3k%a2tF^=P{bdT`8*m|?
zo}Rw6qy!xULspu7d66OyJTvVB=4EPanfv~8Tu-YmuRw(Rw*1uAhI#2F0>K-_%d6@x
z0Oij6pe~`3uSyJ3BkTKWJ>(a1(w?kg=0#iFGyVo`$S-tcQm)l!qowd_i;z^+?PjS^
zc2-VS4mu9zvZd~hhGQa!-#)sTPlx%abe7mTNtOP-O_~914w^eiaE#*oPUvXtHi~Rm
z_6z*0KhmL)un^2y8IL=+xBQn2>?pwL;$Ur*yOMgGf@kfc9YTNobCuO2$EV^r3cJ0^
zwlEazGu%=smy(ef_ncl_>)YmIEU9~(CFr5k_EOx%6MUOEH>(#tT{4xqTAN!wGzer$
zwO&nO{&OXOU3oy_PlOELe(<2a?sLLCI_pzqCOImX$-i2p@2vKtyrpIKM#W_{Fi;J9
z8h|MRY?s1DBS|buz0lCm@Il51uBa-on3h%+UQV;?KCLI5$0+5tXWKjw@rMP<V7mUk
zteO<H<Qmdc!{*}mjA{PnM2l*w`l^b{Yve?6N67{{s_MqGmB_5<to7^qZTgO}yOw-S
z>!?9vN^<j!<g?TPii1bTN9naMw7840{lc+IUU+V*H8mZ2E=%F}9ZC&j2;K#@1RO`K
zMpU@+f$^fjrlu$podx`(Pg*LCJ9qM?x}W$NS9N%}XLG0UQ&aU<TBYF}n{w;i0_Ls0
zW!{ltKyFGxAlSL_yL$ZRsvV&FXCT72-?;TeA<Jagz2>~)=sANK=ldx<ff#`OwAV(i
zcoe`rP+M0woAAZ+)+(1<<@$2FKQ%=w0KIgf2Sq?feg3G8+wkwNH$p9L?(mMRrTKho
zzF*%C%MH&Z+>aH0NJ;HlOr2-dwc)z6vQ4@=|LGT=4wfBE&rv2meH|$5k_(ZS43key
z^PKzpF5`;^ai#_Cm<%W>ZrE~Ifc2UcUeG$jz~1??G!^@lzeBr_yPdDiINgv|TDzmo
zcYgC|NZ(eAwa~W$vF)6Q*SwV@US4usDJQGuSpt7;(lQF$nx2d4v}8913;U$l+-e$@
zmxT0i4viXHJ{JAf#<#QSzEVEJetc@)`AE>Xx5X&PLiJljKZ|w?CkxeHP&-jB3qbNZ
zf#v_{@p=^t^6Eba9rXapp9le-@LY4fZoHs_{ETmAKbshQT+7ve)^szpgBW#m04mU!
z`1rB>R&3FS{mJ!eXRv|eLG($6UfD4~-+lL^xj|`ywIq6i-%9L$M3X}B=Y=ya)nEMe
zx5a?K&ra@20hRjh#d0>ZcWnLL`KBF$emQxm&wu{9ND$QEVLR`6s}KUh$~=PO!bnR_
z!6{SFmM?SHv2RFwFpW#-z2Qs+xU&)nm?i`~%`hg>&@iU?)DBcd#jOfl4L8rM*Hbyf
zuiYwfdAAPvmfH~)(n23wLLWUAed?oQfr5sVzMn|_QEPl2TjLyckHP!u3G1CE&5XAm
zfAqk$ZzL!Gk5vuW2B>~rhj1gwe8<JU{CqU*-xS0w9Cc+gTT)CI|0-2_%Q||?W-cAg
zjkNp@;dibdb)KDNzY)hXjGXCDU>BPQg_KxFmYJ)OwKQ;*Xg%>~ILT%vEy0fa*gC!P
zXShdZl#_7mKlMBMT$V<-f_N^@IrV3J4NR$a=jP@B90B+7@iBlrN{x?aH|X+9NCg2E
zg}X9IpT3g011XC><TfBS3D_S&rxsl>ice3{V!DP{+*&oBA=A)W>Hw3Nl1}XL)uQko
zrW)oMS4V$5^R=z9uJQUo2Nisx$ur$hT{;m%rl~AGN1_#fjr(B*WlBZa$Dfr1uBuKd
zpzyY2U9_%>ggWOh9r`9-ar=&s+qtK32BUkcN)A>!T7B%oVr?m%g*AU%tC$!AK;T(o
zHTD^GcD6d_{>FBh382IoFi|gn(y$W@gyjFM;tR5gm4yi%)j1v2H66{PMfJwK(`-4_
zL{E4Xy4SzOM>RW3N2N-^yt9Sls>d%JSs+YHZEq13MH#VgGA7@wOtR54y!T=jcpWu}
z(pSXoCA4~nadVlXq-e^b%+0KBl=!EQjoW6mI^f+YSLwql3S8;hYSDq*kvsspvaqxp
zh`JsZ&|jMzI$7`RJn7rh1M)mV5RF0Lldq=Zcw3|mPYX<m{Z|*D%|_X$xchVFwY!y{
z`<S=xdmEb5A7m3JRHOGhE1tu!pj_1GRiCdZ1(aEWI;W;Onv0v&!&_^z>I5A_RLd%|
z<;LaePq`YjhhbCATaJ+{@RPVDoROuhBVc#SCe9B_wF+)5ZqMhY%Tb<ZDy-Kt`8ip*
z_iDZhXV@-FKbXnh{EA~6eY#nkiCsz&eK`9DnMpYaz;2g-0Fg}?;=_NFsX#KJqr9l%
zQr5hiDajU3Xv@S?LNNaA;gTwUILx^1RK%7(7b7%x+7ZP@JH=UXvTKBV5;tfP3{O5C
zDN;aiKHVsv`K#e5Ji=@&(st-@nVOM_jGvB-f9bli(v%pN7~^o|E+Ry$-Q?OfGHvEP
zw)pw$7?N^-RQjyiZsBMmmn#s?rQ@((ssjj^?3Wv?rG}BqKB=2#dN)jI-3_Q2k{b<*
zSg}SCaD6t9je1CK5L}=VGmU8WI`MMWU%EMTmTxr_AI0Ss_fR#}U%3B4bw+o&G^g%L
zxO_86o2l|L(xy3{$iE*U$FWl$q>U0!*mB;+d|YONjsI?CVMRkxJv(cnHS*MDt*Gg!
zDU`CGdRRn9cO7qMq;;uce}|GvejHSG1e){rmK{A6g;mCtomkaZ<oH6nyS4J?6xJY~
zSHN^*Hh|BP#NF0&SQ@QsO=G~n3m1q2W}-2{|7YhxhIED4p0)V$&8v9j6{`p}iY_Kd
zZ%M5aSu^p?6=t)0Oq(we;(m;YCWwiix*Dfg30AE(=fPKQn5VL-3|-YDsxEJ;&MK1?
zA1(UDuPMpGHTa0l(^VUFm`RZ8NJh=KiP#}X2HyZOw`b;~zZ$r!AaFmc!<U;*bdkqT
z&1TGrj|hiQlarJT8FYo;0H8^~4?!t&DP0XP=m}j1Ws_Pn>KJ~~CDIu>*MY+in!O`&
zx}sJtVh(eUVp{X+>c$ieFq{n^xiMP)^0tBkfA>n2N>lhvV`wEZeBP~%t%)}?v#PR$
z<vG4o*W!Lz@0U%mu{E>Ms_PVf*SN;j^g5kOO*a+a&2GzV4c0ZUIPVUtXc%T#+#59Z
zxS9NY*+W%mDrXVWV2ltAc+%YB8;E)W>8<b7|B0sp(c1}k$k-;?h|y4qm6Zi?Pe!t(
z8e1D1Nl&P%{prrFY@VeyQJwXH9ni11kzaA)1DKR`;}--}h2jNtfUB9dNsGGP0vTOi
zSW{u&KbcZ4I=c*C+K4r4wXU45Z&B}LNyb5EC?e)%BV`pf5rIn*;wf}&LMbNRu<&RV
zlrA^$nYT{<^3`?I?|7`WWI8?xLA_G19biB#t?bY$#ibXo7<*%<a~>L8%yZ_Tqmv3F
zJyfWe1j5@Hds#r@W;r$h<|fdyyj@p;qVIde!`~hJT(aCe+t-&%BV%^swNa)@M(N{J
zszJI+6Z)uJ@?7IW*>Kr7tA<3g8-rPcvcFWyTzwv1RVP`DYC5_(NmE8O{T(egs+Le3
z)%7YeElUX?&#hR0VYWi`S*D?NT`$9LYq#e$pbP(2F<AxX0%K4kq(-8~jrQq9`?{jm
z)ymrM;Rm9M5)p{TsKi>p+5<wOAHM#NTzkSA3Y5G?6Hjk%`QrY!TpV;%wHmKp9%Vn0
z1|4(A6;rI#Tu7&VxcsG=EYqj7#CAn-hRk)eV}jOIn>lfXFd0pNs`Px}<bE=F>5g!T
znTf7OR$za6z21n@M8{*XrZmSeht0f6dO7qXeFB4K4jmSgPEvZhwc1_$er>smG(mEm
z+@QFYVx?1&add|JUNQ&-Vz-=2s?`$v0`M*BeY}DTQ61EBR%S_-H8sjL+SM&{ih#_h
ze-`Qg9s&NlBVUv>hvWko){1C~@V!>>(m`6D=M}lFS5q+kBE18$9=k75J5+pi>k6{(
z0kr>Sy0~kK^w?M`i|>e6ImMfwvmDwm%Q?57zss0pSI$)`B_s6o@hOr1a{^PR$@35O
zMg|KrizIe87YnZvx!uI3dHNdl2g>TwvhS{%l3q@rZe492jc?|<rx{mMo3!S|)z!D?
zjGvz)K4xU*bM(4%z@3B53Ch};Nq~YGvj89mf%NJ7e<A{4TPL^Frl^n!V}u*e?jKng
z>$eukl;8>$GhY{f`jyZ=I=T67d}VdVR=~X=!rIDW%_+}9)TcKT{LvCc?Top4ZgnmN
z2xEwuNS*aXjUMr6<#3jsSAjC3Th|CDRpib`<aYA%^UZH7Lw0mD+@_jUR0nBXFMF|<
z4?Bh?h5A1~B*eRqB!$N3%feY}y}R$jw?!;<_A{O*Oy-($T0f~I@{M?*1yA*1&l74D
z{#|sRj*yspnPxq6!D6bUecgTP{KRF6T!x#;O3Fj4ZTXtA>uWs-RQ%Az)^e2<S0=>8
z_jUM8A=Mm9snD0y%F%-7A~}aG<d+iIS=>}#hHwK+GvYlHUKW??mM)$=*BXOYV-|Gv
z9wVX>hTOC(t4ok=eV3~xnWmTJ?gfsyWr-@x$Z6_o=WK{g9oE9xpoCI@NM9Z?bNWBk
z+x~i_6BN1X0pg3m=Vu6yt2^KesaJHT{5V!@p7j2{AFd!2Jk=uQI(u>mrJ%UnRFbtt
z9<ufvItv{ie?u*>Lg_00{cpX7>yriZDi4Ehb&=3fsVCs()U0&8JRSqC4#!w+o~@YJ
z&$)L1Y_8~c{LB>)(0Kt+*Tq$%^Skiye0CdxsTjy`j3P5?oZH$bUEJD}F3GVehMvua
zYGCVK{d$=gNKM?*O1VM)wsO1W)aCUmqG5a#Ta_gGkH42|3G(uNQd3eQRR|vJ)<2{o
zdyZU<ou;Rs7va{t$NykH`n2k8bw{77pRl^1S(ZA*KWi(pyt&Ttk+_y|u#%?rx_v$z
zZq;PzZ&0&)4bE~8sU$6jED*IkfCrAd`hh*;KZ&hCzIWU04E?=Wy`{Z@ydfCX#Vbx)
zCyi)|MBbJ!^#$M(2VG7+1ug2{W3=|CVNPr{PA;}4hL+l^Sd%@<(E;fxl{M7gtxU*!
z3Z(?A0I*a^S!+POW0aPb_9`ec<kI?^T3+e0O{;7e3;?~dib^3RAYMOue^Ps;Fd8Ra
z`%=H&ip|-P<$IdQVoIryxxN8+Q<fj4v^^cEN>pA_dDU@YwmaFc#z!Zc8lUu$5La2l
zUWDV@x#7^H&K5QYf2G;fq4zW;Z+_b8cZ1B`R$67qo1wOE5n2h7lfBwP!t|>z?QAbI
zb3eLTK5<dqMk;PESNhii@px*WOq=Ijg!Dhb0ulze14p&6-3Hjz-*B0VE)-_D-@7Aj
zi&n6jmkn3r-#g0VsO%~>KS(%-ZQUHKy*H-zPNlRj+@Zpm<Z-l9Qp>U3#J-YOM=P%@
zh;h`+b!jQX?W8hP<1zj+3kMl$zsstSP)jGNIf~)3R~Mg9!LQ;|R9?#$EkMH}`K>yQ
zb4ge2h?jR7G*%NU+be#ms%2}gur)Z_Y{d_Nz&2!nB*J(c&hEcyd|p^KPWO@K$HJzv
zh?|T$+j9EzU9%`sbw^C=93I9N{=<284)414?FEM3*3X?eIcIscjuu`s0FaWx!xTv_
zB{p?|voDi>mLFf33aUH0E3~_(68mHpH8Cxx6c6uKEv|y*B#&fWTd$$*VxuI7{G5mz
z*Uf7&CLj@oz@w}IKam}|r%)`h=Z!srH<PFR-y$bvIGp1O#Wt}si^mGjFthq&spAHk
zH7tBv+apO_Pg(r_=kM0}!XRYHuy~_dt2Wl_*nX4V)aID8H9JHg4HxB?Cj8Rm+^&E0
z`^;HNU%BvyoPbWl9P^Db98~ukxA}-KgcINZ_z5<lN3+(7pUruuB^z(wu(T^Us28jr
z@K3Uo!#%Km=u=yt(OI5QS)R~YU!e2L_n`)zdyY+fKh(qZe4@_O`A+#MMTY*r_|Utr
zKwKU*%3tgs&rGlp;{tZ|k^hnUedX=iyX1(K2yRkWO7HjPzsuEq#?aeiJE*^(4|4Td
zcJR6z(B*JO6X96@n`-r=K-I9l^Ai!t{dY5cfn(#~;GA>Ev<)!1m}@0xwM-|CqIL{h
ziMW+n=PRaqU)%~$VJTvpu0(A(Bqj<935yI5i~JQ4x}tt$KPv`?nG(+Zmw+6oJpq8q
zPgZ8Q{~Xmc+;^H{=^T3MBXm()5tsL@;{76K>)ZAvV@1qY);7)#E)3e37#~R|@v%P^
z|HYjZ`v&{Zw?RMwsnk!MQ2+b}YXVtw#xXFWJ+Gs`A2~&Uc8Jz8SxwYSe~7=BI$6T~
zOCzVTpm%U_NRKfMbAPg($kX<FR9Vi<pMwA0qyn%&1DWyr88g<mguy2&67dbJ-sQrM
zF~0bDV9{AC#UEj0MoOmn%YPQ^9X(QkYg;(!YI+B`=*ZNh?=o&Z;Qt#H$pj0KYKgSZ
z!Tjg*KxF>PBDSlvNRv~oEQ}m_njY^NtY&FXLC#sC;U&kZmPe@o5kOj0<Ov2b1}-sS
z$jJ?Kc$*CckeeRJp7LIG3lJ>PN_XZkRgvn8tT7r(Q;;n!%wA%Dg!YdFkW{W|A1VJi
zLs_P91MSTn4f5XQ%TxFtr^!5w$SFJm{!}lD%2t<I;Pc(;i8g*N{Js-^aEjlvqlZn0
z>=`L2=YRue;5;Yk^4-BB3D)3dX3-uX(US*0;KJ(+^oA@K%tDXGu0m^H;>p#}oW#e#
zPTEZ2fmDe}%lEY0xm?Nd+FdS7ZvXsX5z6c{M)*!5`HVa|^|PDo-7L`pdz9R$*J)Q|
zmkoJ2puC;|bioN{oXWo?Ea}u)q8`T<Ao(y*Mwy6xDy6H@7Vqs^7xI!<&1i>`Nob{$
zt&#Gvd60cVySkcwU?sD`&JCo0S{!K~f>!q2$q()JiO93g-G8&|8Q1(ZVLt<~K_B0X
z>vEaZ)o$mJqGmw-AfYgE<Hz|Y;zdFLJFu{<qdBLdw4kCjqocc);{!|)Il2;=axK|(
z4LQ0px#4zz3V3KtTXo*4tYp*7SlBpS983qq39P=W89IpxISC;iaT54!`!9>LqTJdo
z4!U=$N4DyYBB|b38WjQ9Uw5Iqh*ZL+s3Cbq$KrJW4p3@1?_?&h8frm;IsxpkcVIU&
zg0~$OO_B9!Y!om_dc{+Qqd4c)Zp|&?{zm+g{v~mQy;$ih;@~0TWjG;P=fF=}zNM|S
zs-QBdptf98*U@HtE-U|QOe$P5G%U3H<Ty~YMIEk;e?#%BORGhj`1{};lR$4C!sn}d
zF49H&>EZ^D{S;*IYppAhor9|JYo?xysdU5LC{^kjh7dYMpdNa3NfzeEi^?KDLw9|B
z%#X{ZZJ~aI_@dBXVfkoCB>ke-j%_%WJ#A~JUpskBZ}-klPQG(2es<h<6}V1L^90EH
zGxj~H2A}ub#~f8;{0d_HWc)}cKEq>4_(1_rUou3j7S}0%FnDK6Z^w>9lY*Gpg;A;3
z|BLAtPg0K{c8x8B!(qyfk|gbV+-f%88%tf)foDYOPg|Km?lddaS3dVJuJblZ$$#ve
z;j!-|Tu4zLt3Mv=Rq_?o+;sgqBRX5}%L}9JTRM;NtIB|yk@ADoC})*!eS15J1uRKr
z{6zcJqaMQ<yJo#f7>ws_$yOJKm`mb^cjH12-Mt8_sb)gatiQF34S&p<LDey-^$0=#
zfopS7fItx5CE4sFk|gb~yP0UWa}e4aBok=ka!9jtm-mz@{Q2`NC{Ns{GCDakXrGwa
z54JimxUZA~RU3-N&&aalixxV`JM>?ako<|ttP}f=NKi10y<FO)-m2T@LAnxl(5sfj
zGAH3qV{laIAAJ=b`liI$<@({X=_#0WI%*C+GQh|OQ-p<L$kf27m9{6@T(<UYFqF<J
zEQvy9!zn-n?{)w40uuje>WynjrgeY*h<--ym{=~OkjlZb$s%!VL-}0(Lh-d>?8&hK
z%OJD;>HR()NrP^<UxH@${@H<w1p;>6rUpX9zXnY2eS#i?o?L}8M}uPoXHc^sB2$Vt
z1mC7m5E{x$??7)|(AOZIS*IgG<a^`P!3;S<b&G2kB_k+k8k?1hvgz}|#?7u;2i^U1
zUpAZr37ZI70u+LxNPpHNKb+KISe4z&LUspjfoKc{&~@5J?N|u7Xb8A)84?ojC&<(y
zobXtXs0;naX0P4`F)&k^dBPWiY-Y6wtq7ST-mAhN>W2OhJ4||Hm+=ze6l+G`P6)P(
z;5ImsU%FT<EZV;60y93#o>}+vZNE`vKtN^?f~S}|UaZCP%uGvVEkDUV3-+Cd*xh#T
zBJ@}4KUjo&&@L?+?zo6;2dDALv%UL8_C2)Zyh82kR%wU{Ho`c@6L{(pAHlJgC6ebI
z{D!^w$OmA!(SD(D_d3Y>`i*_`<u|IOpi^fzm=&Q13kHn?%c)e*k>+6877Dd2KI6MU
z;iq|sext3@$r?jXbQ1psO2Kyot&aUMzkzPL^3VlG9Q6~&563Ucf|+CzpsGTVqvq$s
zKx0hIR^3ASO<tFVO|_vWNd<3jg@F4@4h+IA&3Q=%l0p#DRHEzr{&dQXFZ!pJC3?bB
z#<yTaXP&voTW*R&ghpna_JzrLlfB3eMRrjF#JA?alST#fFb&ne{LiVdfs=60cxwH|
zkM(F_U5uBm$4*1y{**?P*L=lndMmAu(cV##tcNG`_BP<bgE#PjeQW3kCHA#zetjGN
zpchH&drJ*f#Man>4SetN{uRk|d~}D#u_fzqbFHG2Jf67te~ojg1mE#md~frAYrd7>
zH@=3i&>2#!RjW!!kma^{6|}9M=f)xYm;xHOE<-*xgZ^*C(SETI&{eT8!~c$f99^)3
z-n^3h-p5+`8UHzQ;j<c(K?pO}BiUeWbjQFcVkI*xZ~qX;KFvrjtGd-febvNic|w(a
zFTJ*BkkZdO+95WydOBWU@@^+GNS@kX@@-gy7+w8u3nFNR+GWz|t&39<cQy1qB!VTF
zFrUIZohT}9TXSiC-ef8nsin&Gf())GxvOGnwAGTcc(MDw0ZG7Oqh32#Q^}6#)+^E$
zr;dLOIGFuU)PA@B^hyEc73mW(PH)^^vqWZ2JZharq<`nvf9m>V7|;BfSDVH=*S-5o
zgFO`qL1*_dg23j~^Q;qkB<q#r0TEFATYMiO+(r{X{SEnkpokRMKkUkX{NI*S5EDai
z&(z$BrNSp>v!uVX6HR9Fm`&q2j4?7Ni91*fa$8Q&<yq-5lIK{`+wbC$3<^*2ESA2>
z1*0dM+F9uSVvqv(_+-$7)jtvn3331<h|#xtzjBfQ|2;Ch)L-7a`@|=*cGVos#DU(9
zY?^AOHP~NOrjPHpzprgB>!<24_}uuRi*d;z7A8|<0iBiQ{rUXQx(U)i5;dxnM$LkK
z&`wv_H|*V`K~ez}<AWycdi@mR*;Fac_F{s8y;2?P-@=5@uyxmUR~N_`2_nqt$R03c
zaBQ|ET;g3D36IVDJvCjIC9HEgeZ(9*%pJJ<nmK&MCd~YWMi}@ZVvOL90t+cnTi-;j
z>)98Fw+~4of#mOmm^(5$??h~>h&hCBefojPW?LgVzT1HT%HA}}$$+4!uzNL}w4E@}
z7kG9mJJwqy!vXF*3R&<3T?Dg~dm8tA3$l`cMM~>@WQP$NuG09$3aRsiX^J7|C<*NU
z4K~;&f+<;#ZSxiGkVeF&_Hr;&whx9(%ZLd1>^X(p2Vz2NsEv)@Xw>I28Fy&a=YAAl
z8u~sn{OjcK4;I7)f4XA0{fF<)0BA^#eVz%6`m5L}%L4Rq9C?3U4`(D^^=14O`Y=V7
z2P9@!Nv0v5#6QPftZVy{>-0d#vLQoL9K)59<My<wmFIMdNqk|8hVPGGl__Ix2DJ^$
zeI5>pAIZXIuGi_rbdk!XKGwGlyB@{sflU<Qxzb#RCg&c$*Q2U9wdgKdV4r59qv8Lv
zn+Py29@@MKtMo19CJqb@kUk|m+;Z`igKdJBgPAXXx&M3&f{EOw%{!z(P4Tn4rpx`&
z8*5P4xAabxNN9n)%d^S3ay}lZQbiLfr!^i6ZoHGO9W2GFN#(x@tWGfNH>7`ehM!+$
zr}nnX*GG$T$w?Gw{O5+7=ITkbjt=ecU+x?fc8R$MnH-UyxM6>dbWO4(T;c_x-bQ<U
z^`B7a{DnbOStusk`RfcBJ}@#R+n$8tQ#Q~!H6|yq*xMXc3wP}wpMtm^H^H-u1!hi)
z;8*C5d9raw&rW=}OeAhutskVbKV-(8p8Ll7BgiTJ;V4Mv1mri~=k6*F*bp)bZ+?+5
zxPleA!A=?M>8AeY^m<`jczCZ8PEF~TtEIAu8vQx~soOo1Eq-ix2wJO8c0LRdv$@1y
zC)U^U<%SYsg5yt*G~CP}G1~5D#uG^B>+X*>N@IhpZY=E0%iaoj+dd@xuz>ow_hIK}
z*6D1?t20yU)F@gwhCOiz4C<i8YWK%~?&~j%Q;X#CZ_+}*`(F0=Ss)5@`HNUuoUF?O
z9pW7zhY|mk!!U4NmzL+3!F-l=Fu&&#@J2%_QBT9GOcTYW=8aent@dyRCfQ+AeE-$6
zz%t7q0}5bpbFA>~FM@Sw7f7IollItcZ2NIINiAu^x(EfX44=Zr5831V5qgD^)i^lU
zWr02ao@$^;mjp21;$%G@|A-81Nd92m*bY5T#5ugtrNHkI{2s5af}y5ge5!}h#4Op5
zn*P|fdC8bl|0m4Dq5TiQp{!VQ)hKW6N&M}g;-=JdS<Nthllt|nep;MIy;$MexOHRK
zI11zQVH~(033$^N|2|}ZtR`Tg<DdXqzMDn8aHl-vnJB#Uph(TL_OaG-6pCA>4&vj<
zqwIurldC?uS=pr-q7LsNfBSdfT?gbqb8p9Pw3xT=xJSEa%CGN0ZWSXBLY3CjmweRf
zKleA9s`X6;gtNd2*JPfwVMi&;pCLKm?cL~IV-}eiT((`?58}Owc?2{Pb>;MF4VCTA
z(vIE>Pi*s;iF&d6;U@Bl#K`Lo_o@ME!5@$+6D==nU1jxAumXOibpOq}c0fou1>@se
zr0b1`j;t&eoAYR=B0JR$HC6!%_Wu>2MR5>19b@lk+iRC88RCS}8AB9_E*O4>T8*c>
zG~%~@Hjg<E{WeYq{xwymK@x2sla$Jb-5Nk_%d@t&PQ<ozcsM<cKJ|mneraV{X;!hg
ztP!tVw73_#82X;FVtrA6T2pyhwbY7aXmD@m5O=!PdQr_t$kA5W+tu4xJl|H~K7^xq
zZUz^Z_2+t63bLoTyQTYpG@4q)$WUvI88@D75!d9VlULdIxn{11hY-m^%r1^x7HZOJ
z3R=qNfN*YIy>8TU1n4kgYTt&d=L=4LRTnew`0pu_g`RecT!U2Rhf*bjUO9!w_+bgT
zUaFIIt&MHd6YJO=#Cnwe_kbQD$h?*-1&+#A5Cq4~EXmR$7pmRER%z)Vov~Zw7MuD|
zGp?Oy%oY5)TLiZ?U3W(FXk{$&aG`Y9u0#DJO6hD$YHDf{4%vQl&*s6|8S(?vig7K{
zBqM2RahZep%M^mC4%8`ptKP!h_$H*A;@Xxw*Y!_rq>m+-U0jk}nK~YhIp(m}jPcrQ
zOrFEkWXjLFX}V6g(D~RYpn^Zh`?(OC;ODjdG@^Zj{Jq%Z#Idmy#!Nbd;8f(yY={mU
z3tH|#$B##x^C@m}E<|!s&d~I}yTanCKOeyl3gz0<%h$i#mnYzSK+Dr}ysXAjExjIf
zwcctapyBR@y`RwL$!hO!d4e6axItRFKmO1R<qsBHD>+3uZRmTXDM29Mc~Se50E*$O
zpqtd2%(EaNIn-<N%J$5+j>r>sxD|R#VTdJX7mL&jE}W;0&>y<Bn(QBGGJ>-8LdJOM
z0hmO9YYfovG^i956zqVjnJ6d_HDO)>PKDEzW@VdPhBW6nO@Ln`yGCqvmqB~3h3gnz
z34xpi!)JczR?2vI=oaIOR_AXcQ|qW<om*RmH_}s@O@CS0;>A`)N=r$5r?vVj)8uDX
zmg}kH#IL>1C{DzdTqUzd8+)=16g`7pyDO!73$OCcJ&zSFB$-uT3o~Q5FpzXIek(IH
zMzvLaVszAUpj#q7KI(d^S2l%Rq?IE-r;bgC0DBjk)QVoVQskYyp03-k|1c)5-Vt!H
zn>RIO)``ss>K>imFJnxhx--9PI)3sDvl=X-JwM}Jn55GG!KuMi`~M#>hj6qDHKGeO
zLXaw<2x;HX3Y-d?BQNV}(C_ANqY<GNSds=Hs0;RqQ^cwE3y>6(e%aORq4@fC-fFfE
zC@dlpU1sE#*W59?=7TT5Isv4{e%7S0TdJ9um>3ythhR`!SXyQR3^hFGZOWAb5A#s!
zrX#SC<$ONRP4ma>c<=c+<Nv^!BNH^Zrg<02QG*GsPR#$B512R@d#i&>gY{zM1K?R%
zO@+WY0Av2EOE+^kXXb*}e(3lk`vq4Ggw3JlqTNo!NnTpx(95YEj|ep<bGxzDBOA@P
zbhUlLXY+IL&|LsgHH~WwYS$CqEsQSS>|uNWcdc<2G3ls=DZNdwu$v0_SD(fr!nk$R
zao)MsSzbluT?XU%4i&}ARa)52&;SBQ?hb{k2k&c1=}<L{&)>!MHKpZwe0ORqNl1H9
zKgcf?1=^~8Eg4=U1<sYcxUnAtAT#hZ0H_oVti-V=A>O>-&P}{}KWS_HBIF@HefF4?
zXUs}|&)J_y@e9>LEs)8Xb6#H0RWh32bwhi*H*g8V!^1;PVM9X$P<omJ6wkM`wB+T9
zocUzGM$0R9MHm|!(~P8IlTD~ED#;p~O^*4?)&6;&tM&!<*6j^KhdtHYw?k$d+k*=1
zBW&Z=;f_L^yN7)2E-v0)ZfNB1ldq9WgkMp9(BnWZeE&q5{JRB4%*nQbMlS?E)iZTh
z9O?#R^KfK`HfOgiuFhPtSfdjEi>z$v2_ZT@%IV|95W+?X_$Hgrt_S)2m3-0t)%I2>
zxc@pIWi3YSLCg-5f@)QVyKv!rslBC%jrnURPG`N-S$JGmkqEK534$I?=d{A=u2b0{
zToK4OBbvX67f>id=vffRAwltqvJjzYN1P?WZdw7?R$f@l+tw)E)LvSI7X@F)H(Vq`
z=XayqI<B%gEo4m?2^a!OyLafTm7-l9>szZAWAqA>xAc#(=*joL82x}qYdoGSS4L(B
zu3Q9&_2f2w{)EYgP-{RlMnmHRum^Q@sKpsS8`Z^;4C6BwF0lhKdN2@hy?%<pjWa%~
z+>)DiNmb_!Kx!-s#vv%>;aE|O!sq%F7Q}z2HqKqVwJ@hVO(u}N?VwOLfd1Up@vG|V
zhTs4)cA@E4BH^;1P8VAV{D}xYTB(Y)4OJo(mGF!53cJqAK$U&sN12a_Ow7Cw?<0!-
zkbT39rrOLO+NSw6T~iSWmU+hrahVP!ga%B9Xpr-ytYG|+x)}2D2ud4CW{n`EFsvIN
zzsST_kkr^(*OngJ#FjR#6Z70%pGw*_>hv=;a%1Ck<`p~-xIioBz}O9AF1iZ`!>`I8
z11H_Y*f{8L$)@pqy^|Ozfl(W)AeoN&hFc6xCX83(VwWrrH>J6_(B7z*>fY0sfvO#o
zuR_LUR{%*T*izkw7P|_>IUC#Z$#(Kt=Wu>Ay@$8QK^jvHOY%(LExx)-L(>;;SD$z-
zOlN2!p;Cp|w(gG4#qO@;g!hZvtFk`f%<@*9%*@Q~4O;{%VS8b_C`C>8tpvV>yn%jx
z7ExRw;h2B$t+n`QXxYm3Gm$Q@y{TpG3JeIjt}#?OQ2yN7vacxRLtdBF!J0^}z4tEe
zZbt&~Ur4y3c)%IfGF7X0Y3AfF)mnx@3V``Z>~<0E+sF5=QvK=@UcR#58$DQ#dAI&^
z_qyej+52jD>dHQY!LwL&exnT;_m2U!*rmch%e(=CmrLYA8=w>whxPVs_1L9#(&}iY
z_*=>)I_wVB{ubdw4%oa@s(Pg{r(Gzz__!oBLlIuz<}$9BjGe7JqcX#_zNtj!oWX(t
zX1KkylVQkheZA^+b^Cm%@M{n#5HuC8q;giVyn9RcQjchXy=bm#d&i7&8nbL;Rn{xb
zACCZ2?&6~bBj;MjHW=T7Fs?!X9-C6Nqt#bs12<#z|KyCeB#9ERvgu0s2E`jDWp!~(
zI1*(&by!W+>}n^>V+H%XafY(%xn5TOSDN1#2rH0K0H$rUh6ZjvRF)4K1wnoQe(N{V
zK73{vp(w&hoD;YVJ+DrCF7JVt9L)BC4a8>p5Isi*rZXf~3~xExC}E{ej^AS@{K>y)
zMi|>fAWelfHvR+*K(8*-KX8zGS2k_IPaCuyU)b;wjaTR@{V;6u6%P#{^igk{RjDI9
zcfH}!dEdWGuVX`frJK&_jZ|Z*%kgxz?sZ}Lbz9;(Mpb#7<tU;t-C0}M^}SBLXtC(e
zKPUY?MyaIPPifw20jl3OQ!-gQ8){ANuM8$1hPL992t_n)D`R+zFdRqHV@Yc`&#jQC
z{qE`;3C^rif2a7UUV`Q=<v>Vu3o$SclUs)ik{UYTvl_>^QPf(yyAS7V3(ftNvGBtb
zpWp#=A=j_Bfa23PsOZ%cNVje?@!<eo8``!-q{-tML`{-?>~@&n6y8Yw(B_k$_gL^g
z<S|2i;x_8uXCWK1k(15J&3#X#J6Qpg!)}hgk*-NJ5^^~}DJ@!Y^s7FW#+ZexbQbzV
z!Bqaq%`W_7BB!NQ#YWE3W6}`v<)~n-VE>NKcRL54)GR31t*RMhTFCb$0MkJe?6o~!
zh5u<v-~0PfvpcQ3`iN#2d(VJ)c^jJXmo)4hCXsh|_^H&;x`dt6&M(f*8eq>Im8bUt
zp3gLSRylv%%)efSeanqgH`!fd^XBLa?=nYQX6Wl&B1Y4lTa~=w@xd6%*!G7|_!_|c
zKP~`hJKm8R539eC;zul0Wt5jj<{F3=oir<L7w<{Z<NMt|`?H?>#D1@Z&73PqpI@tV
zt)&sjM}CisRiFXF%EdEmo_+bF8sZ(@`XzdyIVT6QVgrT$9^%pE;cAz3bh%o1NFuy$
z;#=EaQrqzBp_DNTSOdW%L)qWh=!uO9d~JvOz2?f-vDaBDXt3Tl&z4oK=&@EvO&^5N
zh0WN$GxGM`m33evNli)pMA$HfHvLl_Ub<Y;`19mDFC7BL?*wBBuEw>JQlZDki>NNh
z)uT0=lSNNOJw=>%;o#s-Uf*QBQoe=BM;~SIZ9<<*aG<fQjX!Fad^{oiD~TTEJ9Joi
zKy&jF>qRg@PDOsbwEr8Gf60;=pa$Q2d`S<)c15x1i=pR0kD`@3hlGf*1Z~RczFW(N
ziK~1YdoJQfY3oT<@RlC-h=_=S5X3w#40#ZJw-U0lviGVMhf0#em%q~d+E6)ZPFczF
zQ8)>^5p)>`^~r9r)-+pLy~bgqv5J#ozS9>`y1?k^(SY6F#pq0HVmLXc$z9g2?(Z@D
z{m^rI)1gMFu|x2pc|N1=>#_H|0);=tPJ9e+bsv{$=DF8RznjU``PrA&K}y}pl`J2N
zL%t>7X{_?Om421W@*TH$)=jn?ttmd>T>4J~&Z5`SfgAao>zNh`ai#vSTd}h(YTy{X
zHG4#H&ZM`{3VY6y(e<FhAfyAB4aFHT7r5q`!gU58;bdU_!x3pi&{S*&3gPZ-&CSiF
zq@)I5$}pj#$Ka2h<3q{{3KO@`r@nIDvIXYV)ws=4vNHdnWPtHG|7&8L`W)wVAM8oM
z=Rj$Z#bK{iDM8Oz!8D-hM`IaBJq7l(_hFd>ZDm)^syG?2-oi%8MmT4tu*g5MQ1WSG
zbv4PaeP1}U7wGUM=6DG@U_S=gVJA`*`gm_Tm{|qLeW1Rc-gSBvgGiB;AYlL`UX`0$
z%$tKuM(uacS-Bjn8YH2;`&FgZ^FT=t>hse_<{uzL`x3W!hU!ITuTF(dWpqTbGuJ$k
zo~thyT~qo2-v;i8p@g=RNgKa*=U-hp=<pqv)%LmTOfK^!Y#f0*CrGJlaq<TZx>K~{
zKIptRlqWY^jbeWJ0y?q`))Q7?r5mUFVyU=BR`+$!v>IG#MM}_6TWi8Rs2>{NUKA+g
z1HQ0?^-sW0Qw1)1(o7^L^XQ4;jBFqf4d|ZfjzXpi<6omYbuZ;r!<23%CLMY-*#65H
z&%L$^Cs5vN;I?;<wrkKG*P0fI!KXVNtE`NPJCC~g9MAZQ=K2-FXgfcE@E!3vc$t%&
z0B@Q3D>&zcGx%2JF5_90WF){X1W*cy{-m$(0?qrS|BWC2fr@UBnraDfzz*7YFYONI
z*Q3!pSi6U{LN-A?A~^N|$ZIj_XKiT&%kY7#!n1lE*7-bdbzByW9rs4iP|VHD78<Pa
zho%c84H*s=nw3L`gE*KN7!X@91q$bx+rC;cQ>4DRI2YZA!yojPmaDLXK!4fV)ljG}
z7>8~ASD-DjlRaTP^mv|2yvX4PcDxSDhS6pHG5a+}pSE7GwVojHmqQcYGx2m6W>;70
z+7Y%0LDdgnMqFtdzn-}u4%)M`ms9XaYW-?0bt&wpru?0mlneOL$IBdl+>fuMxSq*)
zUzA)>&sK5+F2|b?Vl~$0Xo`M|9%|Mq=eyaiTwVC5FA&idy^{x=Yq<aj=nHefZAM^b
z>?I-S-N0Jv+e9<%0r;#Lf3rEwvK{iVF)KUmuJEMaLHd`eYsuoxFq3CKG$#o{M$4zC
zr^^*y19zJ()|q2`XLNz6C@=3tg@=d#$$Z&6`~E}T3dRE13^EwkIZDXjTEeL29^BQ`
zQtqLxEI$n#meB@dX>BZX_KO3<;T$A!&bm8kWS567Mukq)LFy&>6WayXqRR=pS&yts
zh``Gwu4B|&s|nmJpLRXw&l0x9j|NRqoTJ>(Oondp;!8x5J|H(tp%VSmfn)^Zb0!$&
z>1FTbR@<&)9xnsUgup2IRQIoXXiQwZ8JTCx9fjrYZme@}VgUv?Khu7F+Q9Ldk%O>w
zZSSr>j>$>kBYHJy>-p?OW*x78EOcpsrdZ5M;#s>inO5vw^BC{dsnTg0`ui>_5+ZPs
zeO~81$_2o3)cXA4?2V_1-}^BLTMq{lJ3=}lB0{6Wyk5)L_3|L2Fkz0F*bA;wSxb3V
z@g}%Ds^>D*c=*RS77tEP8+3DJn;r^eYR`ei3T)=ZZ=MW@*O9+60b>g*%M^t(@JBA{
zs}+E&tyEsT$%EKpIU*lsJ!pv_jan4`3X|}tESyX5LTg9x!5Y?T!eV@Er1xkm$Q-wd
zu#p@aL>zf$y5r~;+a?8>O9lk|>2$1s{81J+q=d}wWvdHiFOLT7Lpe0PThL0-Ts&{P
z*wE^v4_?)JW!*N~9QgC`tl45UcmYl0M1TNUTw5D|hB-3kk%^YJ8K6|Det%(S%{#?d
z77P-l+xtX7qD-pU!=|A3W7>y;wA>2DngCOzyp5Y>_lF36VCj|S$5q{-X^A09Nm_kf
z91UwdAQ%!AnoG<!FYZ9T46KNV9H62c)U0rOp`2i>Ckb@doUGNVO|r(d9sh<A26(>5
zM}&&vq19Dy5mEnyK<nN<8{FRSYWesRj2)j=k=h}W$fx={ddITlYA*4q>b<f8ygms3
z8!HRsZ`H;FNL{s<KC2t&1~>X!3Gb^U4Im{eEF}|!U00!h`7=okQL=RU;6}^M>1|4~
zT<=DxO4koh9i^VYO5hA!i8VeBsH$UIJ-s#Br>Wx`nHMi9DJuv_?Nt0X8&tp^HuTK3
zmEN<pA<}2iM$>iwap>y%Z#aAe`gyqDpMZ!X4&d?;2`8Oc#KKY(;0V0vw{$OFZQqzy
z-XMXRUmmk6D`YA#p{>u@wi(wawcdB$9VhB-9h<xIJ@{41z67a;E#F|Tm9axR=vwSm
z_O-8Vd+Lny<=HQN;0dqN%;EwyUmC4XP|-C^e7WPEFYUZJdz?22es;8iy+3Ks*t4hv
zm0ULb5@NSt(_akuV9*jk{9ZGRSOMfAc{~ISYd~Zq)wOx+!jredHi)(JJAUiY4Oow8
zzZBRe@3nQ}Mb|wnzTSw)F#<AA68|b72;8%^*?T~pHJg0qC6OBIALC&e`KV=CA5`mv
z3#}!cbD40?O$=`9t62C15#Q*8lIW!u<@!n$F`TXKlFUIn>b4x9B<+g@Z*7wOQnOrr
z(Ko-k$JZho@X?4h!TdL?(=;}I#p92sOaTlDGApc&#1!kcL*Kl851qB#W%gS=>q}nV
zc~2`((EG?Sv_}FLTk+h+_R0CR1M70WVz<;%Z*un+aDo{Um3gb~fbQWc$%9)=Sy2BM
z3_EwP^!KrkK;T}D+&_xd#zp?W1SQ3%&ww<DS-g;vLG?>mefjzFBbC>dZ+G#r1gGX@
zYZ-B0CzoB@S$W?R#Wv=2VpJdLW2o}oaTLOQX|+KDM<JA!3a4ez-NaMVj%Be+=j8|8
zF_pW{%!x0L;5&<mM&7K{1_@51;<#N{`&u;4>-7qjvWF&x)iZ1#dk5YN7UZa6EY1tU
zz|;1L#<g1*$=%2L3YswG^@}2B+?2tbVFr<+X8uyx^DAj(`uYi~!eJ!MBpgVh%F3Rz
zz7h)w{ZvT-7L;9OK$89U{GU4{4aG~`cCdIAt0d#$+F8!EkGGIDnwhN#YXHtcPzWK>
z$o9!M?%|^BRw*0%2#Hg;Mrez;Iyt`2)j|lVVOe7lTVU3r^_LNiqsKyN_1Q7s2BpJS
z3B1J{Im;YN_vEomN$lC^W*a}0&M1`~R=@JY@xV1el9N(9F{3m+HdlIFd0<sY*Fx<;
z+u~z2M7DO7%L$yDH(rr`TPo5LCc^Cb0)|P{zsec-`9BFoP!9DoRB~O=)*x%_-R`e?
z0DnNL)u60`H@8BgAM_)3xCf!7TeApsb2o70>V`iPXjPCN%b1TaXU6Nf_LE}X1ltl(
zOuq+iQxbVm{zUDkLIdAv2NUcnhrWEO{^eFXpI4kim)DmIQk&_#L=HxEx_kNeyLojB
z`IzeD=XiFl?RdFzsTP~Qoc8S3YzhC(X-*tOXN<_<Upoy`Awl&Tg_SeQ3hu?I!4mcq
z`%u+fw|T5FF;=$#KF>9lvW~At%6Wyc=aOR+1tx!N%kK97T%9bC=;JEEF3Y464SX)4
zPbm~9V(>+57(WFOEgtzCvQ%HVN!U)>|3F;i_e5dqtnBo>AcR)LioZG>gwa?dn7pX&
zTjGG89BA2bvUW(R`->M8CqwE=>Qo=yIu!T~&3Q;nQ9Nt>(7wr=yPRsa#1#ItD3u8L
z*MFnm0ut$VI&!To5p%eR*j|uSLgnuCa(hNIOG-hj6V5cSca{4AH+Zj+m9f9)45tSw
zjOwZuM)Y6Wo1o7#z^T0FFS`7EnqO2|tvx!-!sENHbR~KzLM(pIf=8lQl$w3=AUT9U
zwrkrTweJl!9SxX?&3TB=qm`Lm?k>&Jkcr#Y<#^UUARr&kd`rB2*WKzgs87x=j9;9u
z(nTqrxpN$;Fa#6vC9fuELN->Vf<qK@it=W7M)~W3it7>R-h*Ju5K@HynDmGHn^^ky
z5yX5$sQi%JK<$h3d)d;iX2R5M0pcPH^%A+4t-kr<%>=Peu1jS4wuPqqogll{(Dz7~
zkT@BV`uc@^DS4tT27#R8`sJluq0XKDeF45{HMm{_IpyP%=RUifYc+(hTfH38kGR7i
z*72+FA0Mm!KgRwtDvofA8V0ch3!dPv!AWo@!6A5XY1|!xYk-j8?gV#t_u#?Z-QB%=
zs&nuC=6z@8$E;O<Saf$)J#wBSd+#GUHV*ID;JdfvJ!ht0vFJBWvZ()kRNoU$Z_q7R
z825~@<f}wD%Lm1%`!^O*2*?7TdbW(Rll<oPj%sBOHmzyX7dmUllmt|X36bAm56IEm
z?kfk%q0N?DD&UvYS^@QKP1n?Fi82$7VznuAy#M!M2#?@wrfZ<#{_b^%jb|JG>emQ-
z^o`D<E^{6Q$3B@;P=m^r!>hxc*I=i8<-IZ6;8-<on=J71(Kq+JzPgNWv!pkiY6y#x
zvu{RKCsuEcA&(3gna5Ve&K=K;FY1uMYA)Yhdsrq5DK`g_%ild<^!1NHZ|^#&<ybn_
zbz+AvRdbM~D?hlE4KnSVe$>ph3C~mU?Fuuu51qB1kUH}(ab!oZc&cN`D^22Vk4%C2
zOvrcg^Gg&qXyNY{FHTE80P;Z_BqFa&jI57e5~xGS4Tqn=fM%AAuo(+1NUzZrzOva7
zE!)Otm-$_ra!0{CMf;SUb{03aEas{$EUuegAwGZ3wpr@sP0>*UO=QLko)eAIBb!3D
zwI}|sM>4o>KTy_1mZDQ1_)_!0y69Ox@F!1vN&%dM^LElG*d#90Of3V?BW7?*Gl!Kv
zF}5=XVH#Lv2p%M)e}s>|DW5ylMnrE>0?{#TRH9BTe<O?Ds2OeEtA5ws(1Y4ogw1Fe
zs;NzfSyhV~+g-;VG*AHR+wW614P@xZKDe)Y3J&is4$YV)gUp79W1iGyRs@L73I=4C
zXEv|sQY5ac_nEFe3r#=6$UZb!tH`g$#}Et*%q)GYR#uukMAMRmTa<cL40=U?o0H}@
zymjOhlGpK?M7UW=NSl}x`90D$HC||^{tTp7SJ{4b^7{<R6z6$ppQ!cuyI1UUhMrQS
z)R=d`QM?7F%0z)_)-)p$y8T97eObrN1G!|DbG4GH!Ng-ejNTrsS%Fxw2AZEbfAttv
z0H23f8p};a;Zsa^Ix%sUuqJv&R3=yCNH1q+ct&`!3Jhi+mkCm;1L@Z)d6=#-U3gNB
zX!FVB>o?jzZyvVqRpmtnR{Bn3k9_7vn_h7}sfZSjyJ*fM7J&>71)bE2$9J=6UlpzC
z)}=ZKn)6<d^SepF9YWC|qwe91CC)YKQthC&u04mQ%Bm>6isTp)w>)D8rF+-Scm^+B
zX64Qr&OxMwV+iX6qs=5EN%M|6z8$3M;0lB4=v~4<_G^NgusNRvUo6>Bcs|~4(@9;D
z@ZUL0=LJ3^;rlYh(u08h%X{#(`*M5p$D$vI$c5iwzGtlHkqLC@JeGt!<YGB|(pOK<
z{l0Cqq9YAoa*5e36y|?dtOXxwtUK;#t|~7WP6-s)bl`~*0t>1nMLLc@7J|ZvNcE@8
zd~!KpmY(^@+EvQC7<9&>Z5|iQjvNb;J8sf+Fbupt;>5RMWKC$5jJU0+=Z*vmuvlvb
zCcO6qzXVE*ViOp!L)e$?o?$)Fa}+)ZRJ|qmFmsAW)-@`6$)-W>pG2F9<dc8Joo^Ns
z5QzsT3n+Zfss{ZXvxlPsYbJ$vlQ5nI+u6IG(8l}wm8di}N>-!#k4Khi+<E9O5Y_cd
zSmK1<{GT954UP~aTBx=PtQYOIo84DT5x$b>K8j$nVYKBjVF2NE)!alDT}>%E%l8Nz
zSQo7iW=;NgowVvkK?W;(xs_%CN=9r3+Pd2|w_fKlck7-xHn`?%D~CQ820c5jmM^3h
z_i1e-Gr#XZ*Q6ex)2LV2KP}+ys|u||7VnU{#v~5cl77pg3)v!x92s&leZ@@cv_gDU
zS*eGPZF?O3*6|CK|7lPx&PN5@hmDcwt-#@yB|{H8>U}*akL^2@<OfYR@CEEoOj$Q`
zAZ)3EmYnK$LvzqRb+&=AT0iR`Y3|(Uqf(AAc1)Nm^s0&a^s~+~qw{)|)s@q=mrWej
zCcl~&oS*wjGiicmfp9^r$?lMNx9_r7m7Ws!#>TO^qD^UP32T~2L7F@t`ML?f=@^_l
zeNmu9Bnw6$cMkd!G^~!>_PuBQAj(+D;rshc|Cv-)lqqJPIsCL8o@9*_X*gIQr~3T<
z4-ISvw>keB=G*c7CO$E5Mb*F&d%R02SFX_9@lW38aR`Pfe*Jg@&uP|K|D9V&I7&=H
zAN}_RaR(S*?}A~X$If3+Zcy(kn#1$HQL|w~ozMXQzzTKa$SL94&{;ocGQVbK7nb}J
z8ZJeif;8Yijw!Bz%_N3J5-<S(QrL0xuEjNYe2?*oN{?x{pwP43R)=Y*ONB{-5cM>4
zdTBVELtP`pC-FxKI61>2{tpbL<Q%GYKN9S7Ul$pVp>a9S-wSAnsAs&u3O!{1!26R1
z*Iw9tmoAud*jjT-vR^FJg2NOac&oamTlW2rdU1L#JKLAzJK6p-0`l#$Ltwd;{%*>p
zf!>_03*q&$UO_+NjurdF3xC(~0}nR7Cmd4nZ3S#Z{~vWDg;+rVg(AiXt6Pg61~tJ@
zoU99+#!Dy#<-MltnO*JJyZ-;-2dT+{64CD7f85)3XC$6wy@t8q)-hZv2qQ0vUu*FH
z{9gS{<a6!eKkR!rP^^sz8p2~*%oDeNQN|2ga_v9#AuzH4u;7(_>tBu&D3-+k1GQgX
zhvAJK+)9Vh&v;!ZKIGpO#tuw|!|T7N{c(P_htD5QSUvbd$z*d}(Rr#Xf#3Dt9@BXt
zO2A?Lf8aG@c)&OIQ!pZE1z>G1TF=qGI&u0isgA_;##3lK9@#&Ud*g(C0TZjUD;Pl^
z4?4%Y&>4Gv+ZPYp+=$ibz*)w@wTm>bJ9!8y`P5(LYh-)MqyG=V0*sCmu<9JZus=Us
zVc`>FRCPUaaswVQzL8VUMjwv9AI$FInp=wVq6{1Z)%c{w+*i<+OUqYNyb%gmY#tie
z9(wIcSY)wxut1TKkF=Gg_y@;sK-MFPQ|__-8)W@EstN_8af`5d*k6eMW}gtY-|uAv
z53;(l;O|c)w>y(qI?TxMi<62+51L`66Tvt?sM$)76^9{ot0onM9aC-ih6587iEjtz
z(tr_JIr+lBnz;bk#;RO8X>mOha@_vePetRomGu$MB={Ej2DL>;zQ0RwN!64b`h-A!
zniSw0xN#C9lcOv?ccPw#k9lwj5ruE@uYBlYDPEfj>VKmB={Hv3kBE;^)A<Sj2Te->
zwTUgL0((?@GN1|b@YihG+(c(-dQ!2Vwxg+C&3y>KF8Lh-V_f1BqH2{%Om|$uw_hfJ
z+2Zo~j&hIv(zCbca(6zRHbMszUj)uPqc3;vFc}h(fgF!L-{M+vd~ai6QB+pO{QkXS
zQJI6Kn%+fi^C3?41@Eg~$K+SQIJl7mfEA3IQY|7Av{Efp3w&fT0@wn{5a0YK?xFmk
z9s*f7kC&*Cw%X-G52gbNaS#pr-dAGY@!8412@M?VJ!W2hh9AA3fF<|kEwFliQI70E
zm!HTn4(7!eE&LRy7pyb+9Sey`r_mnZj&~!c#mC2IWC(v2RqJPfjUDvrMQf;S;KI1R
z>v}1fa`+@!Do@id2Uj5J2X}wnc){{-Tk*po`AUGz{s<A_Lx^2t$s}JF<mP&9pn^nR
zmj(s~PEJnpR11uLksBTeVGp%n0dDUH^NLLv<v)QL7MA_vm2he@n1NEu`fU$FsoD{s
zuxdCDgZ}arA%(~?8g=pLW*1M6ktMxo?&|5hDC&X_x$q|pq`SoYqXi0dF@@2=21^b>
z!ro|XJz(C-!Nq>*+`FPc@PL3{qPhUV*GwF@m^~w6(zVse>xvtHUFzbY$lDudRvxPz
z9svMk1{ex@SQgKplfO19|81K^q@QmzbYO^WuDUP6nEgXSLI8d8`i6$NnVGiBAx89I
zBkLzKyI6UccF+!f1esu=fJri74{iW|NmaO)BMQ3t`ut$(g}Yx%X*`#hDKCHM9AwE(
z6w%a77T`%7R@K#I&Zy2rhqFzTwfNbalKKDh`+!otujymS2Xf%6X(9#&SpuK85l4rI
zV-++N5&aLGb{WwI{|>7Du7;-E{x3YIkx1vs8f?--Mn4Qq%THUl8ndxJc`1pU5A^g0
zfLQ96FJHn=FC3k7Xrp35wTIt_0i9-?*cdz}ZC>Al5GB_xBH;NAlVM`@doPb2j{g~4
zC4@>uY*KMp0j1W5G-;~Lxg*w&=Sx7D9N`qi3=gKWA?>^Cnlc;fxAMy9S_SM+c07z=
z=L8=+F&=b^#Bg9K{BE8Vs8VQyj0ou9G|nR4XxP};Y)uQdgujMkNyMoz$4Bn}k7?hB
z{jI<5Mf}fBP{U#<>rcQF$Ex&yii{8ef!0(M1ZP%O!k0`()7$}!QP`<ZeS`-bX{6^-
zUqdBq%-r6{(4cnvWA=1ySRolFA^>n@Gex*J0w-k|OF~~I(-6+*rNlt2Fr*+U9~lm4
zm4tJMR{-d*Sy@<65X58oU6=8AV1At6yWyIdBb{$jHF-Tr4D7{oXkzMWL-jxQ@|T}4
za%C+VHU_pLH*CvFIR_@X!4CZ}1G(b2=cLJy!w`ysAz3B><yi>Dm@^c_OZ<ZdYGC6#
zLn2HvjzbZ$V>_Q8=$xn)tm^?uxP4+e$#07YlOL<&?(*}^7!)*VVX+kjVas9FUfxcL
zKyS*U0w)w+3zM|E#=bM~WaKZRrZ#KSu;Kz}$^qL9XnRhM=gbtAVnqDPf3gV`<78#S
zp`}-_29JrLcf=aNb74LKZ(!t$ZUOsm)3C$#2}iQ)yO8N3I6g}{hyThU;D`HFpL-;H
z^DtCR1^?m=7!%sO+z8#ZV`#PGH4<=^bW%I~{I?#O5MGOB9>D)zc3+<YX1ni)-=Hyo
zVVs!1?$v{?o^Tj=PeYqNs5J**)An%6FdU+pbj18*z<dCc0G;Sv;Boqi>G}U*F6*$)
zA9Xvwz?Rj!=L!Dz6PUihC${WHEk68v;20RuOiARhk^dfUz!HlCPTDy6H^Ji2A2gC(
zUyA%HblsogE$K;h;PM3iEg0;X&Qf76@ZL{!`Eg_Qbm>g^v7}=Lg9k2Ll!LH^p<zjV
z?HKdrW%Jh}(HZ~sCBMz4bHD%ZRiDV`!j87Z=Rc2qA&V5A%|q&%P?+a`ya)xjFW=w&
z4@4N+SuQHLgmK-uyD2c-tyzEGC)|*=6A7^vBZ^gOajUnPiP?VTgpIblj<lch!@obn
zZn<9Jus*NN8yptMIV?)2^0L>VCA7@Q8M?jS;5n+9^8Bk#vw0oSQj1>)^yt$xeDbn|
zVU|Zr@QB!|EBHIY7Oy#o!DqcnCRXXrcP&Xx%lO8_d#q#O`)ide<|&lYXn{l<s15sf
zZTbTPB=Gm64KT!tbpF*0p1LZXBn;X~@uq3oDep5vx}Au$#0`2pPv-PuY&il^A-q;T
zF-uzk)q;-MzDr=z)>^HRYr`Yn(AY8U1m!5BRrkuh-UcmKVkDl}#J^SE2fMA$)=uN1
zJAg>V@l)i@U_k-XS8krslthjaYKlUWzPDS`URS@VycNprn)hbCc4p{6mX{u!Qz+!F
z%!L&e&LS__Y&l7X>Vv;b{x`m^fFE)JM$UWz=Cn$79dzc}dYK^tQ)&Hbdq47wF<L=s
zzPiBkZo^Nb%+5vV%44{UY($L<i6QZ=#`)u)=F)P~yIF6+R9EK{zGW3Xi+<E0_KD)7
z8pQ1My)O!l4?|2yyP2fl<yl__-rffXFvJ(ko89;NHgMHRx9cF?+xcd>QEzzkqcyog
zGM~$sNg6;IRCh2(t1Gi6Toz|f&i>~_WJUY^GYBOt+*8!tM*nmBfDwNW^sk04690Kx
zecADX0vSkB!?))6Q2iiPLGR!Fzsp6N-p{qV$SvAsSafb`3=GGI#wb|0$i!?MzmkrM
zHZ8erJ6XwYEA^q^VHI{AYMrznQd{0sAD{}^&ga@21Ak?lKHFUQ1-WX<HeUJ(;WpUL
z>z$2YQ8y}4A%$F6woGKcY|>q=r{l&;%1g=m%A%HO@l-%_T4ECa<*U@%>=%a|qt}NJ
zz%|kL@=Eu*4~p{+_I_YDM~_433-0_0`q;PUa2)?{{pg1Qlt0EDJzoK~ghe56TCIz^
zyU0tuYm<`G9rJ^IPkTenk%%S)BBXb9?yC@-3IOO>M58GUA4CZBUh2X{KbK|+<Nf_2
z7Q*xgpFgcVIHU0CX6=Yoi+5*H_9F^nZ^7~yJ!;g^So_4~<WiY@;+W;^%H>3<70c*2
zhV~=lBd<p`#9xw8>GbfX6V)5iLnjt>wFa`1t~#hvnj*`v`-6%GzV&sAAWjtMM8fLt
z)_?mQeO*R@^R?<_9KvSWe`z$mya?}7Bgr_=7t1D?=y~icx-8#m%S=hF#{u)D@arcU
zbgPi7AwNF^^~v!!vpq77$_ChrZ>%n%v|qn`G`0qh8pTJhf>Kfhwtf9=o?6Jfi%FaE
z<6cv}!$l}AbYDm9O}6NR++8dO?0DN*TduX%pnkl+kvnlqZ(}>C;og3``}^$-=GdA?
z?quei!1Kstu2@^OLL7g~imT64lD#IVlJaJh$T9G}IG7>u1J%-%97yo^;-0kCtQfzk
z|0v-4UHX8YxdX#tZ_B5OI{sGG8~Db+?*kJwDT8M?v6Wgr#HiGmI|zYW>Tcc}bUG;=
zDe~R#GpeWXNdb*|-Tx4L6apyhl+gSsK;B=C-k|~hFtAKDATEs0CF_3i&8{nPjDDR8
zPa_cZ>o$-oXG6>B)8K{Onri7aJZoxd;A_mzpYMMQG8;^k{t>USd2rul^=T;085VRZ
zes`#T&0fKQRWY`b6sr4E&!eEMWo~Nv@QV!br7y}yi(eupNb=j3;Neg?;4XA`Z0px3
zH&10PA)~q}lmI$;3j{7Z?PIK-EtAGk-&lN?XeuY?c8cdDPO##0wMQogKix?YcE7iS
znwx3crdM;M&x-qQ%debeH1>P;L_f|^s$!$LiKRh#@+s&SItKPRP83N;T>Bwd45<Q$
zZLxM(n!a0ce<0RcVV6JZ#>Brgq4~nE_up{v9h^`GhGsMtQ5dXI-YK3?bnwY{jugKq
zXOFC##ZY#=dsjwmL+^+Fou7#9_B(HD|CD#IG+->mD@-qDC0FG|Ro;y-pD1>`7md4J
zfKUG^Yd=G2PH<|novBsFvtT}*4g06YtHS)p9T~X3xp-Ac&jhkok+5xoHi#FVo-9_g
z%eBY)yEMqvb*bG}fYIJg1oC;oGKi=tZ{;RnO>OWH@AYOv2Dr*)<T9>BC>jwfVp)H4
zb%AEKgmp*+_z*q9IbFqHl-M%9b20EIxC=3nK*1?8d^#ueHSprL;YA5z9NUnCA<qak
zEDgZwpg~K3o|`~Kc#YxK{xr;BY=@gbE=FJxD_M=APC-(YbUSo4mEloz(8LYjLK9>i
z`L4q)s5NkC4U+Ro=W&{IVSt=u`c2go$hQ#A*38Y847__?8@Eo=7_}x0_D0LK)=M}5
zkKtwf)#U^l)^l<AY!C7o{~eO&rj(qkl6m@;Xl$IH>~nSZ7{1hUOMLn=ni%4G?<&v-
zgHCeR@knVw{*F^wjH5az%jqBu2oe1<{E$L{a(EAJ5G6}<drNbbq!th1RIS)0T@u@J
zU-U7<nJxe9RK#8N={m;~)e3gd4SUR#Z0yvB%DM;k?>`XV8kz!G9%5NVIsuyhn;R*D
z1ZN+`RVNebW)`nuCNGEIt`O5`HnW+_IjrIfPF#FuVn?Ci<6B{9v<zND={Qp8;6nQ}
zH(rh*pmyU6%AjrN`V5MrD8o>{rb>G71Tp+5!1K_sB}YNZ2Cvkh*>i4j@b}!0&*i^t
zJV+qvr<Dt`+IVEWa#%sy1CPzJU_rt>kn|nw#LKAtu)0Tb$KjCHqye2KhoC3CP@e$5
zR-gL=jk&gJaW=7f8tkgO{S6Ewt-GNgJtzxNn1nn4clk|Vf<YCg8Pqqj?uN!wev8QD
z+4!<f+}5`J@=XJUVcW_S%(Dj^5&`I*R9&nLpF@Se$&E6L-XTgvlt7+Tm~BBdlsk+K
zxS5q3ZMQ~r$5&>wdX0u+BVi)@Q3`)Z#WftC*MutyE$|Di9I3V7Evhg{!rS7&HFY>$
zf7d$9ia&-YRFes)7p}cSjctD}dZr%~^%|&=!6toDqo1YlJ;_2@{?>oPtI#nSxCU3L
z#Y5K<=saE+2&3jQ@DceBFD#GSCm{Db6sNA(TS4NX6>ltdS@6xtPHC~E_ASerB)V^5
zsgmSF_@a^93cp#NJrZgT3~al@Ge@V0`M19x%kbX;v8>XDp%K)K{e*=BJfDmXdWAO}
zxx#Ao23i}^a^`I2XeqIa@0QR7ALHJhr=?qnT{47fYGHd7wvt)ojhK?8l{?Z!<3)`<
zSY^=v9pNyzIFBStZ1>vgjF54o*nQv!G5ywN$SX#7FV%?inp*s_?77f1nX~p#39n7;
zYpA=6mS`GsD`is$KH;iR4-n8+2gSATNu7-bw58U&X0={rzQsh3CayM9ixKg{7QsBW
z?+JSBUF+|<cIrv}<AV04)oAC1!bUOgF`hZ-8<1<I%gBZq6He<KB217bmxsFAgJM%(
z0AHe!%1`%a^Hc7&DisNCtUSG6{Kz^_FM9L*3zBsFSu>}wJ0R#b)R)8HYix13rf1`G
zI)Xc<&&Pbc8A=j%ZbKy9l<;~|Ao%ohwxkA&l{q^HQk9igJ^F!j?M-k^;ivM0rSj2g
z3^&aCa3&quy+v|ANKF|#>r!Ces68udiePp#`isD9j9)SG&rW@luaz3uZ*pdeeS#__
z{q7cd8xTfLj=q_E;ymORcfJD>^g}Ml3XQ~MEOP)UqL>cI*gewc`vZ=ggUq^_Z+UO=
zB3qxRAo#Y0J(yc$bQ_Vh?3ylORwQ5Oddc!6(@bMq&*vxr{aBsjS>jkcFg^Ik+%TtS
z<ZX9}&fK;b8ZL$10u`@mhws_6aL0J<ll>Vhgu&+1^MO@xpEZW5zr-*|K<Vxb1CHRg
zcm`|x%#XzPTO{BOVK3i&dk-qco2@a<--RUiM~owlwH}%>-)Y=f4Id<+8UkXb`rn)|
zyGdg(qF0AR%nLyX$R$fI8o@MONLOmFKbNc;14Ky*Akh>2r(5RVsw03y8;KC@e`3?w
zP9zjEx0az!xMyHpKx}o9v`?U)fEl`tE;!tl`=PinN4AXJLesPyfUYCnQK+7VMo$?u
zvjs8tGP9zyoKk)R0)Xn1hBgaMZwu5y!CjsqWRFJ7-%B#w+g{NZ?dXQ)vB<wRvC^?+
z6_~t73FR>(=G%9qXVK;h6eft#Lx1Qql|?n9IpqhsHH5vUv|n6Humi^XLLTNQBOZ>&
z$DX`}^OgPc7j9;fUjQac%2?wcD52_;{#bOoAcWDx2gO}~Z)qbH`{iaPzd$eMIeQ46
z;!lTrK6vDg8jrCyZy?WWN;TOkA#aHCE!r*V0l%x}C9}E-<5}BY@XpUfwb}Q>+PBUS
z6K|sq-Iy{Y|Gv?lK`!|0(j6|T{+qQ7<}a0pT-K*<59wS2rxA)xE#Rjbamb4%+N8<L
zHU=l=t?zx;-(zPB?VM54yAz1h+o6XXJed~o5F##vD9qN|7BYi}DxEPn0Oev2N0Eqt
zVV564*il921nOZeMsJa~2r@pX)Qy&R$0LgJ8v-^?iS=g-bRfyJjOC~D7EYOqC{%aH
zaXUz;1(8w>fsX3ewC{@MeVHT!#jh+j*-K_eVS26u-|$>9_)F`-`1j<^^9O_uZ69>n
z&v`}Hd^T|0@hVcXTa{R-m~jI?5H}$?`q&sf#qR~nR|h#jo#Ku2ost5io6t*;o_XLS
z^C&xOvQaF*7_56i?}4*;Ijadg^x!pybEw1R7|?KUAy59Hg?eFBq-7T65{?WQvJYJY
zP#U0={v?vlV>E|UKf9Lz7Y(18^bio7RjS>tE?rh}$Lx<A^N{e8aNy^H+V>KkO|Gmp
z5As8_o;>-RZ(fJbm*O)s2ZWHMUK{#S1y6aNR>vK`8LZ=fb~{<Qy=9TM=%^}!w|p>4
zG_zfrYuji;KR&$PSwe|B!Rmd<S$l;oXCzEV{aufXReHhie}NdeKM#~H7aS`e`_FSg
z@L#GJ*8523aG)bi!zbwPW(xm3tADf6(0++JarmxbPF@0J_T__Ve)@FteB-^ZkUBM5
z=MHF>|9FC1CqXIB%;(^Qi+aSvTjhx;bxB+;bxbFf-OS_r^77Hm%k~9fZoGutcX31r
z8y5$7#MLa9_QF??02>up%+L!n65(EzoYX9x3z}02=+wNj{-s9Z@<M>)wC?xr5U=fq
zS9H4(<?1cyPfLC$(R0=CM*+R?PZi>myE~{7d-3AA*F)liZYO-xPr?`(QDjRid;UlB
z)-j*EvV0)tUR$^D${`0!6=RwL{1@$zvi*G*;p=`vYtAr|m~Q;;{~|nr2RQ_=zon-S
zKsg1V$I(_ADt*-3U=~oGh^$rqWOGZLpe!2h+}I}6Kk$&Y)1v3m@@}DwJT*(8Dw_3B
zCFb)PdtjQjnp5Sm*wFsr57^di^!QhInW$Qt^h5UO6}}}W$=q<Z#`jTG?%3ZO*4Acj
zmd-}akDMXLW1NUXxi1-joBVXYll*?!!F%)!JmF{KfA%EZ+i=DZgNK1}md5$t!TP@+
z^Fm(#sGYP`LOhH6<DH#lH7s)B&hL%UbbdkSe3NaLgw%8w*pHq--s8^oo88LX%AUge
zaARGK=T_r#n-}deh4yLZ6&eC5gO}hvB4T-ZAEKh-j`Kl*i$*Kf!S^NAMmYJG3{QAu
zOp<*EHM^0cS6+)fyW!9$v6q2kk5RFD^mzTp$2MeE#bz*F9#JoZ4;NTZqd@NFJQ;f%
z8s$@Cjv$~^%egQ38xLIa9HkQ1$<et|#2hJ|yLrR2kl}(?UB0O)WEAk&N!6Q~46BC5
zcDTBJP&=Va;$>X<S*!Y<kw_n6aIYWF8J#FdN~Ww$zeL6aZSoB#T^4mhV3DoPB9E)k
z3ZDFO>{k0CQZe8WBru=R@&SW$XsN@&j3VZ<C><3q?yW>Nj9Rw=kjVw`P0yjX2gz5N
zvJfSQ>8-1G)Qhw4<d^1FoAa84j6It!Q#L1MFGDAe4=#Hgccg-9K2~=$xdkm9y)1h|
z)GSx5t-2LPg~l?c1Z(Y{f=85ZpQ0oU3@6>2UX9#>!_n&GE6l`APmiZ-)63)#`Lsmq
z&1irW7myT(hYm-kDI8u|%Ew8e&Y_W5V+3z``lq<w!j@BPdN-bJe?d2;$lh8;+#jf&
z@(P@*-oqC81rljBn4J>dB41h4tpd{e7(lIi7_rxCp*}a&+u}7i>GErHXYU7wQD&d<
z+3Lku=qp<rN>EV)L>GI9cqqn~maH0<f{Co^v~21r_$_{M0W2?|K__22i?Fb;alnRd
zQ5|hp5*xQC3$76He|W%?Ut(8l-`goAFc0T)yP`Rh+LaU@7JjWyOJv7*d2h9S>E8$M
zqOK1m@O)o>bxC7l;JRYl;5yK5CB2(F88-PG2e(aCcu?AR{+LF$r4n}+QQZ2G@oXsj
zpwUEh<QICumJv<O=*Zxh!WX_gn0kV6UgTc@va`S|O}?b<Tb~X`z<8U*qqT`=$*P~s
zbm`ELcG~Z}*4n%xA3IM}%P)K@0mGxxT+)!uyp+Fm9?k7l=Db7d@8nuMhxyT7j9@-J
z=p;yskN__9%!kO@@6dF|cVw@l@@$_LI-0MmTSP1)t&VcdQUrOeXeGWU;OpUEU~A<e
z+3YZzkoNmQf#ZGt=gIk55nbV@D_*TK+J%m*%6);>w7$ekAZ)g-+y72HG34K66`olA
zV~2;j63~YRdRU@ydjWLBL_Lq9>eUmMj_XNTpaX0o<KAdG(33#xr$G~~4~pznq8`r{
zWyu6eEC}EbN5M6+)$JRF3MH8HH4$!7(d@Om?9b?aYe6Wq*1r9QT26+nr79WE<Y!~L
zv{O@ov`}4M(%#-8-yWA5=Xq7F{ijp0saD@&Ok_-jKg0S6L*AEs4clO&xhT&Zd5>Y*
zuAK8C&Duh>x2k-6NVr=lAZ10sTmF-wzWD33zEA4C^j}>Sy}dydn4KPFEM59<)n#K<
zmWcf`FwV~?09Q1i@gfcZ0je2*4L!j`(h=7EdKq(VqS||ASha3>a+g(*C03+b$Y?aK
zQ?QJ(MTHKp8AWC8&Q}JP@Ph3CB_kL(0s;b{p`FZIcGJI#zq4C`UTh&DC^-{6zF@D`
zvxS<y@hs6OT!4ItYFTuu(&#idqNyIGg}?gutJR@gs9iNaGik-1`S1j6Vw<_l2d|ob
zt%yNxK7oiHxh|!ysmX$5v>1%31LP_W_!Gos(dwPL>sOBJ8@N0ncA74Xq=z>icigA0
z?mELL2{f89wz@7$MrVSD7vU^fZ36Odaq~^&W#z>;G!koxw-$@o*URD+lz6V-eHN{r
z37^)!sSZj^g)kk!KWqtVZ=AJdS0e0Oo{n}Tl7Y<~4ziu;srLZNKrOlyc0+jw-Wks^
zDbU)%E?VwU7b6_QC2jio{Pk1nc{pHil7Kud8`kgth(ci7H?~QE!&u$w4G2=VaFEK>
zxcx1r^3#364+cR0OY6W#@c=+SmoOZ#j{^Lzrvh&0>wrL3YK-II{w!O1|9D<nZW{k+
zy9!Smktd-8-{ksOYP|$@w$NGV6NqP-Sg}bfe6|4jm@$Hg|0I3v%#)=snALmR7D+#l
zWy^A$CavA`S-8xbip4BFk(~@fyoNiXmF4*_!0^YX<~T1c)eKHSM>}KdPGJnqmF}PT
zI35{gT3Yk2z#b{IyKogvD}6?P-vLeOUj1RK1fY~n-`re3_9RX0UH&Cz+I*J|5D-UY
zYvaGUBEh!OHk<>X=0<PPdg%s&yt3(Z(y@-iV#iYd`OB9R<~ncKXn|sf>JLz`fLqwc
zuVDAQe+LVj7MvjZfo!~-jLAC<7yd=kc|ep)OdqKCvC*-zDinf(dmPp~VGS}Hb7_rw
z<|ilTCV9ty(bTb$Xh5bT=p-$X`|qFA9vVF=FEUGg9E!hoP@JWwb9%~jztvgPBB5jv
z+-4pc>U9sb4@ol1^1%vVmUU(lSF0zsaW}2zU?8qhp3JAoBShR<HA5>_ad>yug#2qv
z$8Bd!{dZ)cQIoRfy_Cx;*;vc98RKk{v*>L|%UO>r#OHaS=gHN_W7o?qsh1gV4{!L>
z#9ZRvR-@VPL^7r!vQ7oLpeXJ?7#XJZ>p>-F9A8~|N$`u!AI5M@vO8UYP;dibAC`19
z@ZTwq>5A~EtH%Vxwa<Y}RSFL0r{v%{MV_9S@&9B|REzQ!(W_&;6X<ITw7lGmDO7*q
z-%S2T%*EwjM#m~7p4_INrT6G)UQ+2mM5~-tuVCl6<>;g!u5Qz5$~LDN(uLQRe4XBR
znJ0w;AgcMlYFde$l_j@Jw9D$mC`f9XSKrYjQ|~dLyLm_Jp;Cg<Ubj&h5?nUUClGJ1
z$EV&j>6}k3hNaX6(HxZw?L6u=96jLlUk9v!>z?g{jif3Yma$(A=u^+e5QWOJt5C;B
zyqRHDm0_Iewa`@W_sRFe^}Cmc%L1JF;OuU`fAJO_oL)x797S1NO){brOMmP`EvFE2
zZGAn^2C=H91}D_h$<YzeLpEo7^PoIEM`tqrE^9QZeW}52Y;;tw-g@Dvq9a0J(&1Iv
zoP(w36wc(USi|iut@{sH3CFjMksM_159_j2WxXSEql_uafkdv;$9~;!q;Gx%k%^jG
zn4kR<s#wSmk*hA0Xj5V};oGm2{Z)jbf+{;H<3TLwd32k`Z&Nq&ma@QgKr*oO`DUX{
zBL~&yLFVQ{!gI|C(Y0b|w1;mAGOdnS2TG%59xppNvLK}3^HA^{o)~p$jHnWv{IQ7B
zbNBR)WL1Zcu5eG~_bdgGnl`({i~#v7Q_(wG!tf(T1<PZV+s@b2n864?p0&w>Z>Nl*
zqeJe03VRGL`9M^Q+vw*WCE|tI`KVX*2XB|Mo&dSrw)r4GFt8I_#`r5X9KI)2R#&-h
zOQyeinHG(g-=?yceaQ6C^&g<?p~6N0=RVq%(_SiCzS*q+PIXRvZ_E?k>5gt4zbKc8
zNxoc6B9CKuQ`2A*z%f-geIsT_rBd5S?I>x4^-*59@L43Jb=G`6S|X%06G1E6oBB+(
zZKXqi+P$W?s;UaNqN^s>mk{$QJ;DEqgjtTxDmeak5zk|KUdg(0U-R0YeA-`>eCvBd
zlVnFS{T-UPs#gxP>)4<NWjWATK#Opk!v8lPR~i}{TzuB=JRv#XYnS1|&`iT+y`37p
zr}8`TN@UW6E93um__bz1M^*J^l>e-g;u#R57+fN6(qVz^GyVwh?@Uc;C&d!urL*b_
ze+gR`RPxMVYk)(f4%9K)lxLL_5~5r_9R#uaF+0&-N^#%){<6aKD8ofJHj)y03I6fY
zW5U33a+`9}xH!L}xTYIvJqhgRw}y>8HVn6vxC>=re1k8c@Yv1dd6)~i8>K%I^mMDW
zrh9}1TFo3RN>}&f2P^mUDyI0gdyw^woB5U(xac@viZ>4`=F;|^5QX%I3`&{PXmeYt
zm05^_%gGXspmj)mW*};uz%~Lz-+;0n1}uVb&kL$&%-=`0rM=>QeXY-MglNu8=*bAT
zqK<s&fQUpNu4FaLk5lngqkI3VcWlcY@bK`7x-JCE9X!3^)j1lcfv@`4(Iv)C-Rp~U
zuticlQuTPRFTJhWLmYi%!1l1Mt^3x|Iv(0Lvl}qcE>-}^Zrfvdwe{%0Q{9)KMlps<
z4r$#-ot&cPlbHtlivY)}@{K=HELY=G^s>mQ*<aM7=cjiDH)qi*Cm7Gi7ddOXF7p4S
z*k)zNVf{Tmmw}K63#jcOOezMq4gvWU{{dvSMP`7j^KX7FsmKw9jm|)I3lg4E<c4ss
zUd7b<y*WL@Kw>Cl%5rRJX{ma|qjcZ>LXX25$F_=tgF|)7uSe+e;L7%$POT7Rz$M0H
zsW?hn?~d(N1Nc{)lfUXws8b>kaB%M^)p4~#N+;fD`c^sO^OMTSW<;oz(nxrJS3=Pt
zvp4wG|I-5-ZS?v5moHig(cwM-MYj9w*9QNee-zo;ruPb3w*t>n94UYKUZg5kv$Wr%
zb)-Y>GZuCxBF|?<>wnTwmQ-x(hUYblyK%Q^q_7B|Ly6+uldQRjVszVXX0<W<&fkR2
zbo`8ykVRSFNbALIkE)XroH=?!Jpza({G?X(?wK@a9@VDAHVL=9qjGb-FxQ-=B*OJ-
z{gwYGIk`p=Vlaa{0kbjA6CeD+tJX+4AZ|P(wMH=n_1ptgQvNe{%=NIOYD>xXJK8}?
z<hO4>wWG|Aq|7|Cm@TxFQEpNCf-BdklIhXi!j$})>pho|(p=oz0@Uy6fQ*X;z$+4x
zvu_1_6riS`0yC-i?TKC3=zujK!^ney_nw_@e186?yt0Z){7`*vF2aps2S8}8F_nHq
z8Om*KC4QyDcNJV*ikNGTi#sxs++t%d3EDQsjpx*@`*d6WUdun_7JOShJ5G>wt>s<J
zSy$E}*N(-{oTr)RZEMAEwLP?D(~q~y^2eg122@J$<4~fUX`0wBp4RFa-FiNhvuz(z
zmlA?*CN|v7%{l9B*(YGWn|H8K4I_bZcjkt1HWjPl>v8KoPjoOv#68d>M8|kmf;v`w
zcGl)P?7J-k&HRl9LgUc!t+s!0Xe<I|;haU{M`7(ZT8zLuI->LLPf_bPEM)*1q|3|8
zK;sfJBJwP}<G^e1(^(EVT-J^c9+O6;$uMr(=NFW_Gej~km<+arGN7%2f-Nq_t79(e
z+k0_k6N8FD{c7|d1W(WOi4=a3Tx8<!KPrFVcIKXTo)!67eop89qo=;TL>}2vZPyyB
zueHrIwOWrw^kubno3`{ODBm0M$MbyW^NU`~I$xD(V{wg^ZBv15Bv6=(=nG(Duui4k
zl|7bXY9Iy>OQ)kDr}Cj)=YKD#uv}JmoYVFXQWDZqHrEW?477Gn*!PC-Hs_?`V#D%5
zrL7|6U(U})<89==s-2qKcr`y)F8_cc&y)a2B<VXAE&zo>4$FxNuz3^bf(0X$nVvx+
zXgD%Nlyr(JDpSkLZ{|)ndV;GeSmTs+bx9nB3JMA;G;1UlFo?Tl6IsMxmja#FHd%5z
zup<nue^B2_D08W~K0F3-$C<`4*t9yHs=8(E?!dF2*vvDs*zi0`NP8et?-wNczUH(~
zf@fWwBXgVJO`?>o1@eFtAdc;lLSzrgb?4%5D7L~a`_`?M8Eh_Jv2E(V+7_J_#w-~P
zUQFy#)l{4I9C<=|*J6$)uFh+<FK0f`f4z40_FkgRk>@V1-0p}Y5gWKx@_oL_uKgk=
zghBTATt+}#)4lL2*U0Psr1U?4L6CR%f8jogM6fNxp^0iG(shRLvUQr0fE^Nm-L7sv
zsb8wBZpg}l1r|lJ#ni$7v;eAl4ZD1#G<HhDd~wrtye@jrv5i947Z<grMebNY?Or=F
z7DtPXd{H`<)Sk>f!j+ASg5xg$NtZR_n|lc7E6%8js7$i2?W`ZUh6OW8OI#e98+`1d
z*b<iX&$8F-9#+KJSyB?&g}dU&r|qmjN9~VoXX-Mi9y=G$?R#@0P1sp;=U;P3n?3Aa
zesf2*7g@9W>_i=^mk?a6%?6Or)g9HmlhiAW<C-0klX`ya-XXxHcb&^Ybfs^2s}~)A
z)!QVig?N1DeP3=Z?pvrEw_U;nfCvJCbUyKKj0z|q)vp+-QNZ6jvhsQ^ljwpmrPw<E
z12tP56p=(H{2(3KKQ%j>KX(MUATieFv9V_Ms2Q%S?gQRI>r3a%3adHIlf#IhZbs~y
zh&p0sE8ZXLd(^UylD?h;9AD3oA&&tdid^1jQgN0FtDXroHyZ626{eyxZ{~Rdo^AXn
z6x1i?Hjn#wYi+Kft&@8+-q&Aomty9Ca%Rpup)ay8MOjLuMOB6UJ9z|}CDoUsLw_fp
zgacXC5^Suad~Bj4VH@HGJUTOAWy_5L@W%QVz|G7+7F?Bu`Vv)QFz#afh|BjwL2{9e
z*W3xF5k@44a8d1w-O<i(+|!bi38ZD~VPTn&Pl@;cFbbgYTBzNdHlp-@)GM%l4HcTC
zVNWg1A)okBt1(od?kt<i6~wFjWw&LQsk<WDJb)wytmWe-X{C~M3+RAQv(W-6h<*er
zerQSF-<%F+Wy#>qt(7oGFV#3&x$GS3+W`kY<A0f;flqj!CSGh^P3-1ocYmCxQ&m2g
zJ-Jf8n@!mDI1YSUeNkSYe-pnG=8ldW98YcU0Yx}O5}iTo-TwGg<0h^E-oIk%OVy#|
zo4c?NsXRK+U;l{<XPa?%CwUw0!U1T;oufF-`So9YeaK=%gR<Q9YZ07t+Wb$TIbh%n
zh!BbF379u4eMmR#9RdMJ{8SP2B<O#jm%cSHmXT<ZxBp~am1Hxa99NGlkLcUvUlrLd
zDLib@8$vICWB}PJ02}py1pPCK0}kHSu0d3WGR1Hr75_=V;;Iu78Vvut#9jgZPGQn(
zbRbVdZi}2&*o(qSUC5V{lRbNS^JD)HKrLOMxk)vi)eL(^goKe_nf~uCu<tO}?<n4V
zp_GHZrz#vj#_jS`&Lx030DpPIqqg9Ch7k$5j^zBEML2)ZWl9}WFVA*>E%)Wgi#E*t
zA4(ni1b#9|Y^b#|v@xboD9t;6*x-ijzSZT^YMOmn6sCiszKx!x=87l8jv}DuikFuD
z@!4{lQ@kmGcM1nU4eeZ*0~L=T58pKQX}jQ+lPhU$Fl}m)4^{tQ0`$!JcUeNS%DW4B
zHo%{;pVynvn0<Y+lnx?ZCP&=We`k~v{{>)XYmjesdKC{~K^45wYI@f2dg~8Iq^+KZ
z@R6#vs|!0*_w6?ihSsjs(-i<JLtGntd*d0QwkV78S0yI+Ia5*1gqxtQ*F9k(J9dc*
zrOmg~XxyrdYRj>y%_QFCxm{7q_+7`xfd)oYEH0JR?vKb~@czqjn?K5n&G82j!eILt
zGCorAww1QXY39s+WKu1$s0{^#Apo1e%UJ&p>aK$0cC%7146gammCbJ^eOVe4_*-b~
zcTbzyh=TI!fwMb+oLN1&Sn-wx6BL6cm^sdY#5H)?HKMJd#&as7T(bse{VC{Ce3Nm<
z$*B3cz?Vx1Vj6m{X#gM~Ak8(3!8Yj}gin5Zh#h5zhZoN`1vNN0^8Kp-+K<e$xjlcP
z%0qMLC4-evesJ&V1x$uk(Y|!*2!NnQXixfC$66nXk24dnxKNuz0aaHT1jm?7DVQD&
zn%hYL8DII;f@hc-GXq*vcUraJ1Y93CEH__u?&fv}o854A<6mZ8mqQ|-e6}AO774Y}
z8F6WKU2Icy+<ye+ioJMeu-wm5#rwLoZ%9HoM@&`YA6Kdip2&!_96x@U(@O(q*rXFR
zxQ?($H{Qm)5qVk>CQQ-N&1j~5;+VEmk0fdYzkD)tyYB#d_Ao*$WNQzBG(S7Rw+cH;
z-@_f#=RfwtlELQdNU1@-xD_#-##jTgEQ^AgW5190M!(2-0xgX?_khjv1s|5SD}`;^
z3lk`Q>0lPx;`>3LGt$^bvf=2gf^+N8tbCZDXyjmqH7T9P)8n&K>QVX~zcO?2qc_e%
zcjxw_EPHwT`z^JO<7IcL;)V7Ov!2}uO`6$AP&BWWxkiBZUPI)km;5|@HD=PyY;~8J
z$<sh}GTFM0r@SJd{(g3Q<Yap-jQX9JV!;t;xi)yB379mhs8}5)xPUrk^PrSSnpb<w
z%o=62m_8G3KhfH=^>-Ja31oTz9oPR;nXxa?&u80L$CY#+Ks(VqBosYRm2389&w{{p
z=&Xe%?wKdLEJ_R0yK#&=aJNq<wVrA$@qu>{Z81D)*IN}8Tn3$X?Q`YCgFi-23Ijz|
zHQk3CB@>BkswZ>vI+DS6w=CS<!(=|$xFx<FE}mJdWa!>QK5=L<IA|Joo+IK1k-omW
zL*i6meb}HkW&qx<{uMip1HT$-N3#-P>(ovFtJW!7x2dBiE>N*UMrvA`_jX)414`lg
zU++6hE~A3HqaNS&t+JctF_fthzRUG-ow4nk$=n$qx@C&>(?Sk=CXp+{o%#oz$47)?
z?U?$(@zw3yos3>r1|&~D4ZQC<^GTt^#xc`$CI;&rUioKIGQQPF@q!M|`cLgI4P#Qn
ziX}wEpAm;{-e0#+--Ozgl_W~9%yP*@CSB*S^?!#IestC~N#B0g@Bb3w5HgglQ&afs
zysdUVBw-0ds+-iR_(CXW9*Tqg^ty*eJBht{^^a&Y-_t?H=noa{2}0YQO1I@9aag<y
zZEZeG2k%?B1LrX;3+m0El?(b#U}?CC&;S3B+=@e@QLDoXp!N+a4fR=CiaeUGsCAL0
z6|JY2LCf&#!hz@|K4SQk{<zOpM0bm?V#G)|3vYqhLTj$gQ{J%}vf9d=9qaf|#2biB
zo4i6rPpDyxW=4{+SV%q?)=s;CaeGzv69x+3if8TJ;Emj;_|0pGw*Ve*+h;w(qRZAA
zWuf_WI2=;%;!`sSC)%12nS1r<(TqOHS@uGXte5wJWIj1M!I1l2*Xj>kI%~1zO8{G_
z$-#edh&m-n*hzmBP%Ry7y|&8Co8iPx6OMMrN{XTm)Ox4tPtGjP;#huBb(;o^JkTM3
z5%SM_C;=T6f8I6Y@yCKNy$<|;7<KuBWSdD5Fy-<ao1{hR2%m-P4OalXgxxeLQIQ<e
zELF2-qc2e`OFq6;htb6Qh~)o|aD@E4S7CP}C^ogjr?G76<p@y*)k##62lehaE>7k7
zDir2GyJA%05CGBDf$`STz{3Sc6TGC+$)?Jm&q&WZUqT6~y(AXR-jW|i8KC;?PGNQ`
zIwKB0#lH;iz!qG`O^||~jlp0e?{ib5JQg299*=IlG&7;_-m%IZNf5n%>WiW~M7%^<
zomu7w9YIlj$K%0z2D}7+w@SU_Ht!;NKmO_(xDv;@!%MsU9yz<GB3v8;i;I6}YaWou
z4}<wX`y7N841ekl7mWG*yOJWjKOoa{V>|F~thmp8!GJ^e&Wg>4Hg0TZR%*dZ&!E50
zOahR57_px;0vv#5>pZ1>h@F0w$s5Uk4%&o5=2S&W*bkKok*1Bwurkk<EUB|cJpx1T
zG2H~Oi6Q!GfBQlg^hOd}GVIx0jhlon^bJ7?qKmgp4uL^e2?eEE#C%*t{LJF>zp4qG
zx73AbcJlkUKI>&*JdyU)go_OgabYD?jj+0eV~2M<$<j|hw=3+K<)tp$X0Y*g`$)_j
z16?l2&K-2`lJ8*uzVV>)Kt%qoe`XjhR-D2RXDnO4ZEU2OK-qu6_ba`%D%Klh#_gUi
zx4;v@?Sk!zBk4k^U0zK+d{|8_qejt7>4HuE$=MHPf<IqBqw5tbD`F7LPoV1scek1I
zX}Z&y;GQRWG=z6#kLdL1P7>@;r9`#TF;bGyXQz=|m>%n_92*thBKKjbmQ>CZVfT}W
ze>v7>@$lRmkMKP`fmZ9PLihK|YyyTHuj|h|lq_wxJi|lFh~FH>!TLYoBn_^8-mP#J
zK!!!YtV|cNP3S;vsC$__RKrnKdRn%0r%Pm4o~XE8e|YXaS9oY^-<TEhy)LQCnA}V^
zy)KDd<a>4<9ceAiam$uONSjkuMse<cK_1|}5k2wu>W>iDy0fx3zvn(3(9+t@81dw+
zP+zt1J+p71-MPiM_u1=6^u2fL2k+aB5)O-jMr``q)a0Ugsv9bsD?m$2Src;^jr|=(
z@e^df(|GvY-9i@nyb<WIG&Eq*0@YxrF`l0X&$RLWXw55MT=QZp;*?~Cca0r_({l>!
zwGqDS09-F}JMxfV7&sT4_X82UstXm-wJJp#PDfE6iZrG?>Yis(Ou!He4EJFEN5S?D
zB(tyE**wADV7JRjBOMtOy256I_#Eo*%vg2t8}u<&V^x)TV&}iPxiw~))K(Xa-W;&$
zqhB>frtasu5IxRD625gWCc4!Yw*2bcY+^Ing(K+uP?ll`);##D)|0ZY+4mqmIQm<t
zg3mMK-sCDIhG(RI);;G;{VHn2svv3PuL7JuITjn@=Mq^(mG9x1KO?%xEz&iaetZU@
zd2;dja5CwDyx8vDaow9#&5?B;d-!XI<Sc+5nf{pX-V<xWG&!KaR&JJ82&olV+Ug{`
z?HiA+39H?e3A2XVi&?H#;Ce+kNLbda4bSz2DB|T^GO~q6rdykA{o1c>zu*sU?t8gD
zO*L(togM=<*>5{n%+}c+IWj8Gd{(<#7U<EYcbmOjB#eDF%V736m^)$E!}Dzs;m5bg
zuXWk+-c#JOTRu4ZoxY;3RjhK9APD~JzTk7(!Ng^&w`R-((i*f5Suky|UPklR#8PZ5
zAv4-w%&{AH%ZN{Piq*#%cO~}f!m<wk?7pk%2jlj;%bgewDX>LkVqjAvSmEYPlXvXc
zj~SmPyu}r68@Y!~s-O;tFk|r{BIF<#Eu&Rf@;mZ`lGc?w(+)T~{5yxP%dw;iZ;nIn
z+RM?-*6!aF=Y>ND)`>x<Z}4lLhpkgs4+R}68Y^t)+z_p&^bAg0t@xx2!PxN7-`;I<
zAcW;s=5PJGZ{-+fUxsm?`18W$Vv3LUjIRo;)aXcrc0m2IW6E|lN>i>FPaU+4rXzWE
zrNHzxrnw?~R}}datrlXrUtHDIt^R4CWnKK^?Ni<sz@_>QhY$b*YtL2-X9CO^8}>ME
zHDOVSeDB_xb<5ps*e^@)<0`rhd2UrZ<c9mIc3^5xI2qCpDY;ZXb1v16ck9W2Yt*&p
zXT`~KH>my$pCs(E6xe{)NWIP`FDpG(c*L_V)R#s1-0>t|_QT$4wG_8*cC2FcWc>6K
z$h-8`%C~u%&(U*v7+!uhgY5Z^j%Z3Hz0Y##P|D8MNqrVQH?Ohy@cHQtk?s+!y6($H
zaJlTusfyfU+rceK4r5f2#oKwS{Oi#X`rViRt<<;UN%PSLRU3`xs+e4e;-6vsd9lf1
zep6}KhQh!hg|V*Ni-Aw=wk-{|$pq&d`y*-{)YWIdsDFbTdWd(>OUuhWjtoSA$0Nim
zT4%s3863JTd=|?v_hzhh=5Cd6)@A&h;F`U=(np`M84UBaoVDe23xS6_;pn?$;fnFM
z`x&j{m!Q*>K6?}9$D6ygvZ;?+ke3cz{1WArR!&t<INulHLk@(;8*dUV2J7sb61w8r
zrLCt>U&58OysQP`Tupv1?+4!umF!&d+leQqaMZf8>Hf2U=ZPz3Lh~}4wAZh_``%v!
z3&q&HRO^Q<&@#N)1GXAqB}Mdo5HwzS_@ud`z#);_ON+o3ON_ZVd$wP=we8mFJ+2!b
zl95%Mo!r@I#^!Fc3yQAR3qfMkJ8m{g|8gYWazEZiKIizt>k+DyEz~P1VRc+xObjrS
z_Xv>v7Fa5{G!Ln+|Mc<BYqDG%V=b{P#tX7=RTmDnU7~MCPv4(FJ8S+h5_Tf&yh0h2
zd6?vFtDvn_ts+`F(<9K^La=~Pfw_49VOPFHJgmoWB#Nw^buX4|baGLbwPOXm3my%;
zFB}7#o=UpDa;Z@OP7D-jQ{auDua%_hFZHrglAqtV<H(yX-^MSY2MD)5Hmu&TZM|6H
zo}{f{J8?tb{x#eg@!_oMRCu)Mc_zJH_F$XuW8Ki>l_<*L-xC}7a@FxA-s-7}QMx`c
z8i`2ugSkert_{f3jZ=VVJFC}6NJP2?>|IrVmMNs1=@-U6+Z>rey5Q<`?gReFHe{>X
zL6NF~4rJg7n2Rc<;=>mZjZVXd_suV6ReH;o3~-vDg$ir3=ZU@|V_FQjn)j6(N5Rew
zyAX#Frqx(&3j6;TU2h#0<@Wu7!U)nW(jZa-5`us<N`rtj3@wsFN`sV$NGsCaHNena
zf`lO5-Q6+t4EN<6J>UDg&vXCd8D{T!-?dk-&ssYMbj6_KcDOZj^vw-60j->ezi*hM
zjg&o*mX<z6G0NeMWAH-(@e+0GtX?&6#ai-|3URlbYm7|lSx!1Z(q<;Nw7qDQh!Nw@
z@o&!UHCV3@D?vEBl!zW#MH39E7NG(ziw%}5zSNwt4(3Royi_GY4|-rj;5Nk88yrHE
zffhj(DS(_epsj)um`}kw`Ik1W+e%kw<z9p0yHh)%UtFbfSzeeXe@C<k3H~U^$w00S
zy$Z*cd3eWJ|FRdc|0Ov;|F4xxOyDz23;)q~8!b1HYCF^<N@si2hxG_5gbbsMEK@|y
zgsNY>-SJ+Fj(L;3#C`lf{0Z!WiwZLKApth@4}4I1zr<Uz*$&T}Ho`$lI{T;47(%!s
zO4pvJL$Uia@Z_H=Box(~m@#rK)-3Uo9bD7*F+XJhnu?rXNK*#IKb_>z>RBEt%>1VC
z-SqMk!Ojf$_kUmccYW)k#I2$Vq7<5C;N~jbwL9ygZ8#LA>x(TQ1uP_uw=vWme3<z0
zjzF%&n{L;fr=DT(615d-)-tIUS8Ky<VowkPfdDT47IN8+eu$6PG_1bNj-`?O;;mFm
z&n7LU2=d3ZcKyczB8gTl&?(AHp<n?n@Wiox<~Oc*?tI(29e_z=I}Oj=5U5Q2Iy|kM
z-qeIB>!Rg-web7*Z&_N8pRSs?=h#)x$MvuhskV!PvVon>?sjSpE_ejOM9cDHzOpXZ
z7&nZ}T*#N}yKs3L;zW$NZ>p}E%T4m)!$s-T(ai9$nzpR-yP5^R#${qi%zNyR;y?SK
zwN~4|W&45xddb4Qd1SEZbdG;HdO~#&(j(_!HE%x{69u9tj0NEbwS(=o;w!8t8Je<f
z%skDjRpV+eK8;b;OlKL6f>6<NpR^KgvcCF;cPEGFs2oSLqKh=-y1PAVUq;_*d!_|m
zzsCXo!{qO>Grl)dGq8!)-_z4GFp!o*<&<Ph^d%yq?gWW3!}*-x6kd2Oz!q{q7m#E1
z1Os%!Ab}zx-Y<d<Z2aX-oc%yIr)=Uz(u2J(k?ZybH(HMfok74&qiNT(8<ilf4<9}N
zWt+j6NKjvt1XyPL>0I#4BR`2RScE7+IsvNs05?jb)=aca#>|MX3O*jENcjC$J7Y2=
zTF?e<d3l-NZkC*X46iE$xV+Jd!*cIlvXO?GK6u^X@O;VPhA+L}guT`G&}8ORgBlfW
zT~gwi{Xlxnz}`qZwJH(i3H3_$iksM~$9)hl2{|q8IN@fNY$O}*JTMG1rIptdcO5zn
z?r*s{jSMH&N)w!$nX3W{u0QmRdjKA;U~gS$H=p?4aK~wJXfpg4F6>uh&li4f=7+hH
z4IMDis9~bzNSK+erHXn@Pfu^}?4)_0P5t=sBmF6JU}Bx$l}|BQnyB}zryM0Jnhlo(
zip@21?nlf=r6?fEliBf&E$YKUj2F{H38{;(!yHRH4nUP?ky6HqAW~A&byB;U20(3!
zFq#mcM$Xt4%h~8R!oNNTVNM$Qp-i4By+$XJFg8RNX<mx(QGqPv;Q5R!r%W%o8RGnC
z2lQz!C@?T^JqJwpf{Sb5ZWI3;_6Z&KsD$qjQO0l-P&Jt`e(7FPJoaP1RuQcHni`Al
zJd**>R3WdbANH>*1G?Q(Pd#u!6^x~CJ3@e$`_7`$+1Y80@9^qX+ta!D8MIIdWuKuc
zfrS$PL4<b`lNnU2Xy(CFrYvgAN8DT>wAPch-;#t9t>d8Sxf-`Yiz4TolKI-rCw&*;
zZ+})4Q>FAwX|^so%sO__0QfYub9=^H(wWMHxDuT#x+JX#YkI#{QZ!6I7|PGCJ1xiv
z5({jWY;Ml@h8OYRs{ST}Yp(hGmm?z353cmU^eRy78ESubHzsmett|noc22T>a4jTt
zYE3^71(d-qfkItxEBgze7d`re<1;)Duc{iDuhYU89qo5&l>vip^huvA7`UlGO-)Ua
z;z)OG?KnFvEiKoBrt|(zgF0D4Ecd3=CNIOW`*O`DMq0}Au_-mVxkpN}gnWe3FO5sk
zb<iLsfpy}**(ga6*&lp8e+ARy^@#zrh&kg6b<-3;EkUfdNn$~=5!BBzjmDZA8yj<S
zn4VJX>RSai$K*w_<I<j8_6v;C2$xRuSLN6NG?W26R$MHWJ8g@FHaY<v>gQ<M-+#HV
ziIh3&mv(%5EaFd=M}+y(ABpsV6pYc^h%(yV^WUym8wZbS7`j>_zTEMO8o(>DeF`}M
zN5rB(xU%-JfM2=dUDceq2tKZ=`{olJzsBMyj7F&Q#-9(uSsWf6AFrdKQJLPcv{b?M
zHTIiXla;k+?q9wW{HvL?nbKAJ!SlK_EuBKz(?bHR%xs;%YJ#+LdO9%Citj2lk_4j8
zyOYm2K2`zf!(w!rO6eS9UXmvURr^1e5QdRmwI4dB!+9GBwCMp=fDNbu%XU>8KpQ!s
zMh>*Jo%qGpQF=tPv+>X~v&9a&^)Gp#fN-9E<vj*3zB;@RB$1PQeKnaUrl;v>oep!8
zpDN6b9u@R@AOM&a;|GsW@H@3KUIT(w3JRdT&20{#WjKa&ImHm}eKD^*X{*Lokp;||
zx%?v`p<EmIm2N#n%}XHOApsVa-Os88sP6^>57!xG9DJQvIT2^%8E%2ue+>2Z-iSyR
zzO(cIOQL{I*Z?&Mn-u}Bas8;?3Jq?S6ytC*!*z3&lK$C19paOvv&{B_DopK<B?tV2
zJ5QE~ij3aR&j4+9e#x-LtyNTLS{EwBBE>s2!C9;*`o~(M`1hh?`f;5v0>-*c#<+E5
zgi;&ZFPyTg{xOL@el;I<(pg^SKM#TVh%f?>wx!AK>VgxDjXApK4Fm!WF_?1-w%xA9
z1MdrN2w>p^bKp;JepQ9T0JBtC;r1>Qc3%*Z@ASbrT2kHTucraL)g%~Tm+?NxP7h)T
zCL}4e&qvio*J*^i80@bUE2vNj_xQ}|dTA}5bzv!+%zwsooWfxDk6(UA4otKJl$iz$
z-GDdAte8*q8!v-#%m-ftvcF>J^`+jcFl&0KW#o0)tTunNm6pO6lCe3VGvlF}%)s!2
z6xQS&>_b)^=q~gxWq|{T1kC9G1Ak;96Dk~-ub=Yqh`(@drzM6cj0vZThsJ6bakMm^
z7g1%fd6K`|()3*MfVC__r~ZRvF)J(Af4k@bq^V%~<-IPy=p}o-z9o-yPTtXK)WT=B
zlu9?PVz)_oH8nJzMs3H@!fia7{gmO%-(^b%JmM|c;28~|DG1|v{c}sU1K{>sXW=Ph
zPG^L6jokmIyBS9vlo}#2h)IZop``xiEAZx5V=tCi-{I~(?JP3ph#;LFi(eQ%$Mr}P
zo<e?SC~gs(uzk9dOmxs_uQc5?kpml0e4{%rI4au0v}^^OsKgU25#QtMpG_H~#v@Om
zl-lA!k00|toGmRd-gpjU76w%VOjNDuq((7=Y3Tw1Ef!Sf+Ph!$^>B7H4Ww;vI$g)P
zL^w*#H;ZUG9&qHaQtpbxBz?vB$LB+Jxe;?)zW(fYg(a|dko|qor-i_J?Q=<@q>DYJ
z_@^Idkhj*)T~L8N^}abRp;xX9wUNCwR3H@NOQEnhPd|rOq;SQ#A-7*!>~udcnzPVT
z&0L<3ECNSU_ufvKulHyI%;*Zj*qK+8%C;uCnr_&G=X~}VJ%?1*Ql=~op4mBC3k0M1
zDkY-@MSfIn^<fuRk)j4RmouI{iLt#0i*{?)A3CygiHvpQKaS4sunajsKt@8zI>Nk2
zS^jZDnTfeG7s?R+GC?NlHNHF!as=U8V;X^0=w24}U|<y2X$cOy%sk65&iaYl!{`Ec
zGkL3=Us+IN@*KWSap>IG-tFcY7lsq*6Dp7sBOtx9rL%yGY%VL|zdxU7=W@ojFFGS+
zIXg;3QP%Y2sJeV~CN?M9th2BGdo2#YRD|ZBZCs7;E}0hdno>NGFihWVC!;hN%sr!I
z_CBeA_0cP-Pmh=8E_;jk)NqSn{HINynSBlnFVo=+!<e7$0`(V_JT6j?PSK{XMJeZR
z-g|UGEb8m;H_4!@nbIUqdFko)a44#)tz0Z<Z}PD-0orVl=nWl=h#DLxHT)~U#h%}F
zEI)ag+1uSYU+FN~bDc@m4DK{hh{2M$RK#f{-I6i0CQKCm*aY#xWX%<#U25(rE>Qk7
z7X0Dy*I>JD542YXel0IQd*Z11pxH1v6xJDuHc@We_!tayJnJXw<#{_c;^n2g9or^_
zu>+ne{Bh?OKaKZ`l^U)HCu%dN4;w2D8=O!cg6X~tJa5qU9u}!&MjowtjY}rwkk0td
z^E?E<gqeFoNpz@;_RLKgllb_@>Y`9k4`V)E+_`5u=~)XEu<DKQ3Il9!h|uS-yt>TC
zZk+OJvklOvF3-MuZPa4biUPiPhTpRm?eC_2^;8U*E|$H6+Hf^vSii02$n=)2hS5>R
zmT~VV&uUHC9UaRolF8VZ95u|>oWOzB5u^bQO){oN6@j%mY}pWzY)8SJmeJ?s7LL{=
z5W~pQ`QrBp<3C!~T)S0gx`!HR9q}b~E)Q*NF09q?UdFxgpTmn5UcawX^z~dSOM=aw
zd&|Kb_&vNYANU6Y4hc)tk_ZU%cdp-fxzO}vO^qw#X7QHQK0MxSqQ8min52YDS#7g{
zRh(YUXz1kCUFa2WglZ~vdL!n9nra@luVvQPZ4@||IDqpeI?z4a+ByZRkx+Uu0rP1i
zK&G}DRHk@o|IzsFq>#6#T{F#{8CP}-lfoN}QpLZVIaHiDL&Akd_61#kcsF+N?o-lT
z%B$8q>{?|J6lwm_gFkQ`zMoh!loS7Z#=KM3_LoacuF!YW%;*h`B-t6V1YYev8=1%R
z6dqpkzoRtrh&Q~N>X$HF7shKLttUPPu%SM$(vljZXfmVit+7w@#eu=ojcx{ZA1WEP
zmsxJ8fOi3$kvd{-A%EG=z6Z%r3$!C|gqN^E^J8a1ve-;|Zf!u_Ix+QnZx}7^4^Ix*
zd{GHG3sN)kXn;0*IrA6jM$Iuj^Q~nX%HeR9F|6S{v!}Z5sq=5~J{a~??37IdQ{4_G
z);>|x&Ylszfzh2JcTYEs4d#}!dQIsJ(g-&i-D@y!=jQFHuR?3;uRDK^LU>b*rV^4V
zy;y%=7mpF$mcllsc;jSlDI@XW=hG1{r5n8<H>OD{{O5Wt`Z|fU6~)|E5Y^@Cwx2m$
zWf_L*J&|`tPrg-$Xj+*s(bJ&K<mP0QuRGXp53s(r3qMU%e=xB|h|ee13XSl|+a9on
zBYdlw*(5j84<x?pnH-NdZd%H&mN1p|c{d+W@AJauR0$D>)9y6Y1Q+uKRB8*WE|){w
zD~P7P;4UtA<?5@h{fBukeC)sbmf9(%o$uAt7r*{s>*H+RXsT#;N>;<<v$kh<VyCdm
zEQ5fD{|X*b4ar<6q1&dVG)!Cj{Uy}1!OmG*53)X}a9-C$%5g6be8m^3ebAM7l~_M#
zPWrP!Ou#2QNkIO<>ga}`tCHUT&QmEh2AK#Sjrk;ra7-Q$65yMmBE=|sie;x{(G<u8
zo4vgX%Y-9j_~JMzZ)>h3M!t$^y6yRTW$nCb@qKEi@Om{;JnG>}n8pVPo*#_s%XnV%
z($a!=Sys+Knv-M5N`o7R+AG0ul-k0P>u^Mq=Xec1{Hz`^mwbDTn1{_rH43tLdKp&o
zvbFI{3oK{w9fkM+>HgbG<@2PfEW~g~0t@BS;s*2$#ijiO9BgL{Wr1_{Sq}RxSaYpq
zh3=xXBfhCk#pC&K53Fb9i-0%($LaBtaKH?sV?&djdV&s8C(hqL<%eG_8+=<38@*OW
z3|5@yMSAH<Mjp5sZoWaW!SC6lrk<a9;VhZqYiL)*`*v};@O7X(vLgsyK!ji`cBm;{
zh<iw8M$>-d++mg#=b{JPeTNd^B%RwOlR_7q>{1Le=ws4ah9|z{y&5w)lx;!SEy&eE
z=M8*oq3POQ4-z~JKN?OK$=yqev*;}D4q@;8q8CG>9hECMnbqDFF4Fj)(+C(5MnFnl
z4ii2wT?g42{UkF4vM;z$7XBYDfrIRie0InW-43n&-`1FULyuh}Wz@Tb9`iZZm35`j
z3)5Sx7Txw+2y@E(T8VLU`3%fp{;ZQU1jBbBF&#g`vA}Q%jnW9Ze_y-OtH|Kz${a9W
z1do8A=FH={^W}${h60QHLfb*|Vf{HV^47KI?Q_3hpf~mMnko*Py1YmB^nCy8eFBnR
ziw*bz(AJgVbRtU{ieZtt<tGj^U)Kn9$AWgNK6xgddl~5_3%ze~ve;Hp!5ek)s;Z9l
z<by{~K)VvEl1S-tI&$o}g88(@t~%C4+hu&qQ_DGf;kO5`hjlD-f*RZH$M6xb^Lo;z
zfdRz@!so7aN%cXAo~L5OJ8Z>Yw6|z$nnC1xxYE_z{hAXcL_6CC?Ak>85rNBqLArA`
zofyB;<TWv5ZeM$@Zz5+O`g7lT{p~V&Jy{^P=${XAE^bK%7vHh>AeqmNT1F7J25}D#
zLWbWDcFJPw`fdcehKE+KYY4Fl9e17QCa@S4Q@ZbV=fEqSo1b``w(y*22^A<COZQS%
zBi2L>{N0`(@HxI339iZ+Oz#p{q@_K)c&?>;aF5{tVRtLb!Jt|~w10K&(hxK%DRzW-
z{M=DMfK`a)S4_$(o7~XXb)CS55FdkG<>$eabpHeclVFK^$+Vn$qKj~3_Hm_~d+j6o
zqms5L23xXuTf6wi`SXWy`#oG*)dy*Uf*$>Atf5F}#JFg<i;AYEbKN~R*c0W~$n9z>
z;rke3Cp+5A^(rQ>hVg*@KZJMvudf3Q9K3GQ*3<qt8<AB;@tef`420_d&zT@`2%E<S
z6vM85e?}WK>V0v0s?kFF>cn4Q4UO|j@mI|xTEvJyty5vCWAH<#@wY?2hQ4*O=_l?(
z!vl*)0>%VwR(D;lo2zR!=C0`XIBvG!STiSCRSuQ06G9VK6h5L+nx;`Z{WTw!gZ9YU
z!M@R6&zd!hghlLvimR|qN47osDX<)!zU#}pD%-bwJk+74Y1;8307&AIT0$Tvp7(CM
zAR7D(45qtm_kr980P1gQ66NRT=jG+)*c*;Zb!AG-H#{o2(42xwIakAN^o(XEZ4^i1
z)|ofV7~kQ#-=`GXfzCjMF@)}wOH0d;<~(H8(^4Bx_e!s>sID)rw|G(-#LLI&qT5;S
z2MKQnu)(}!{b(OF;=vk;s)f+cA^{vt9I})V`M9Vaxn8xR><9aqIrZBe(@uMm0R&HV
zn;BTd#p$;~P#rRRV@T3U8ClmtR7Mf%nWkd;ji+ZHmp7~j5S8WnFN-`h%N2dE<84w^
zoi#?a`HkYJ_l&F=`GnT>-8RyS7BWvorI~yW_aWilP3y&SkNo^tfz*)NS4;*}ml@=q
z5-aO7WK2R8*5P1|IOGP?*G;`=`e|JKhnBLIjWwqLVeBkAgShm3cu7tfwp$g@qN=d8
zBkMb#dnBLaq@SikQzJ4559FBU_+>C8=Be(avM4??f_Pcs8=780Gv6{ZgE)!2BHIDS
zEKyUT>>NBa5cP&>=%hL6f&*&!9!}k^gp7J6_sYpyN$=EtYd>|@wku!O(^g)#Y_WS)
z>1)Pico(I_;{dlQeb^9QNWcVUF<!iS9VQ;jZ3N`4V2#HLDg!x(Hha@m04g&tf&K$=
z(y_o?`R@1&?c~Cn69$$0XsuR9R&KDyh8MO+OkdkL>|oagSt==Zf@Z0&zbLyKBf4<Z
zar$`m9#`YnV)!^5V&ECT*X5a9W9F(KLjvJp31S||Y(A8TurD{=iCz=yC49V391+Vj
zM!qL>MHc2?k(<kE208tj(k*q4SQBO&TcwRo$=$y91q3)RyG$`gHLt0ddP(p5Iv<r6
zO<ut0gt_4jf{(M7Q?iVvfE$ad@gsaPU@dZ+Us2q*qgHX*0ZmwHZO67l_Qg@^W)1IG
z;4h@#A>`T<pWk4*M$1CW;sq&!?FbBCbh1E5W*Na~)oO}~NbP$=IpsnMckq+zpij<=
z0b8F6&x*Y8y3fBRrCk|`q|YWTbTJ>~wUKI3*clT`SDstau~=2R%~guSYvt#8u>KC&
zr^LD)uSv_>+(f=3!^1Q6W|`*Bp)8Tm&=@T@0}wbgG&CF>99P{-wYv>%P8<EAC%<{c
z(zsYy@@i{!Qd-Bx#-^sGM!YTaHwF}b*F)9}&|~vmY{Kn0n>xPuu!Gsao=Hwo?;mo3
zm*3aY>fE;8dYsQ}M~yLs^w7?oZAI(&wpbd-+A1EPOSf%vM!0l{)n5LvM_y4O_7(4y
zkNOuKy&1<4%%bk)>2;QItb*Uz_Sy?%F5ong^;e}RhAXMcNAS~DttY(nGyt2+zc1u`
zdSEkg?Hw8?9q!yo8N^$=R2%31ImoCG>Ip5_ujw71jn=zR@E+Sk4?S5X3I9z|R;G~M
z)hVi0-Pw3!sn?6d*$8j<f#qeu@}4}?4YH^gim0hcoEoLF$(0AhNE66j6uz8Bf<k<5
z*K=3l4D|cw5vR>>D9ArN4BPc*{Bke0Ri{0*$|Q=2oV|S#WztW0VP|Cj$JITxxejJC
z^~e@>9q$UOvTwHcvV3D9x>nNFLa?O~b7jb5!Dma=Jhy2LjsJ!YszB!Gs`+{!r*?_U
z_fiqP6&M8SAjE}el5>Pz`M^v3E*a=9zqFYe<a~Xts^7YHCZ_S^dUITbYRrDyZg{B{
z?!B~ng8hbIoTjk$jorH^V2zu>^`M`cu~m(0$>J!n^T_FQd$8vTloYlPor1h;aG44!
z(feQ!#%q3**};;ek|^NYux-n0%Q(JKA^=)s2oLIueAvNJpL<A2GwwQyTx>m`Ywmq(
z$~%Kg>_!$tu3d$DY9&{(K1CU{O_=&)uJWs9^2n5^c`VEkDi*nsru^YBfR|-#>}IIL
zY-fb`9<9kknT<Iy7zN4>_Yi6EIX&!r?P@!@b|_Hs0pkSRkg}T4K>(i!)5%})HjBUs
zvycuSRK_rL@Y&{;j`a5I<pBu`r}v1BR?FJ*$KehJgP-djPHBu;vf3Nkxx!Vdhk>D&
z;k=y_?Rk1!2-I0_Vw9bcq)^jT5m6yJEA_KYKPDw|e!7=H5d%nEBGKy`8dOq_BZuZ1
zJu2W^76Yl81EsH)fg6FTmeR!VYBseswKi<KB!WPr+Py}s_N=$VeZFrsc}BeVo9TQH
zO;6qgC!SgNwT*qX3Xk9)Xi<mvH;f&C8(hWn#j{a#D2~;Si&0BGf)ggS8V$DAQ_WpY
z5?Llzi-xk_(jb>Fcq_;e+n>#Tg@)xlRgq_xS8xgca4(a$SAC?=lQRi7hAQn4z9#@>
zIWtoJkZz~5!nSh_pYll4EwdZkK_J`=E0mAMaOcaTrMIj3nrXC8p->-(v(*Gn-?R!t
zUB@F~C+sWH)C~xGIIpL;$=143Xz*C1a`U*(h~RT~(|*fn<Z2x@uQ(P^Cm{rU9F!$)
zM)c+6ZzbPya*4BKTjD1uI9})UoYn?~bND<!Aou!MWfl(9^R5^2DMp2K%x$Y0E2@dc
zmxj!1p1trmAD%2!KJdbm1Vb-Bw`~T=#s=8!!?&}`=ky+4U-n_uUy3&`T)QID>%UCA
z6S|!_V_f-sO$kuvV6Xni4$j+3?9(m&fwG4xt{+D4vEMl5SH_P0(gGQ`hq>Jyl?fU?
ztw_GzJdod>oz;h6aq1s(W$I~ZJ>+JeOk|-RHcUGgKl4?|iog&Jzz)bWH0x;U{Irx?
zBD148zNx*@ms9w;(I4_i4+c)IW)%J<esP0H^d3Li!lDo=vVsjIzZ2!;eFn{fH9-!`
zQN|K|x3^9ZP4YuX``>Ui*a2h8E!A+v16oMOda#hY*PI=Egt`8)D;cLp{Z*KwN)yER
z#1=ht$FsrLwd7_(2`)qap&BYFE|Xdn%JTr_++$WH8SX2~dzN#d%To0U&Z}t=!;Q}_
zG!t2lcB=EV|B-{LAIe20+AY4Bf6L^zN<RBj71k_Tqv_bw99!h-Lh}q_SnyW6FwqtQ
zsPu&z5oK{?Bv&)i$G+y-iZ<1W&xXUnfvtjEXy{eNj_f@!LtJdf)p*7bI;q#^&sEM^
zYL(&xhYpz~!>_`7a>XCDc;~B#wv*ZK-kuAbom*>_^7uN%`D#=g1?AsYgjD1p<=t4y
z=RW~iexN>5goBHRM<cdNr$RM|fbxQ$f)B967Q7Ccj*pMm*Vm;(9|E@d?xO78mjj;i
zA1^<P28@uurrP_W93tPN*grC9uBkAQYE3Kd&Rf{XXdC?P#loBjR@>QQ-*Xr<7M+#I
z+rHRui$<#DUZvMV#gW!#R#~Bjy;9=7%XK}~icPuWin;N~xbHz#vE^@jEg=2;@N=J&
ziwsD`$>@)3Pf4X#8vg7{*{AFgqT)X`HwmV}!1bvGJ32EAO*(GM*K8DSZ_-L9HrVCl
zuG;yMfO1Z3OX1cQe(mLI5WGn=NH0mVa2@rw)uy8fi*sT`Gw$u~FRl%Bv^I4=louj1
zb9PmBNyf~@+X>XX(<~w$DO9qtg*?ZW>E-wN#cPFp<U`sgXXP>u5?lvr@Xu%)xTj67
zt;dX|lQtr&nXMmHzB1w{D?-nyYCMTlIcw6Qxu9`%N;`nf?;`^s#N{M6P66<)lREqX
z0+rJiLy~x><5$P5|4@Awn_AfQ_0B66W@e!AMr5(SxEKllH1Bi0heQrt@(5+cRZCr6
zbcxg2J##?mXAA=4K_Ej~yzMIZw>m=w9^_vKH_eo=#(y<uG&_-WLAQ>!rkCZW@W<#*
zFF2_LV;&w5_-StxRnO~^1o)b^+lx7FVoV49^7H|3ZKrbf_408|jcDZ2oeaKy!N4$)
zed(2PUXv`K5}|aHe|(x|U$14*bN+w>u~qk;q5YgKqUDX-euf#eav|zr`LM)J{1XfF
z-5jpXP-2A9PY6-bPWf@sIY3Mkw3(`=IU~W-)XQ(<Bg2s%a)27{Bz=TJ8yEPUp82q4
zerIR^7<uIL!|8-XeeQveO5azX2jiUbKq;o&m5rxURgX?}ZVl0{EnLO$%^U|J4XvO_
z_1lXsN&s>ho;4;<*u~g*#R{8eASIv8`XqtcD4;pS(4W(8wEExkT<#2~>eFpDN3C41
z7!L7)Zvi(TKVXDt9rkjy%#My`LrYqap1dqrP>CX5tr<!y6N{DAIq1H}hg)Ck&!v2k
z3CO{60*;V#g5^2&I*TY^07+=gPJ`(}=>cN;yblsH7;oXEaTa{SGB45~I}%f+ezYG0
z^uqUZ1nR+<QL4o(qfQH@Da!C~jq(We^%Fd1f6D^g>RMUyTB#+^ee0xZ!&5X%J?BA}
z54;<>r(3r(!n0smgvbKecI<Fc_~xh{Qp9o#A0+}Auwz=G<uU<TNe)h)pg2DexNkb8
zu^&6E%WhS8pQ)z+z4A9-WoKWz{6C2`50V#7>tUJtw%(P%oQg66mpc7`fPiVZ+eC>$
zXWllG7E)m0Lq$f0iH%P`IcR{|7mT%+Tqy$S2xk&t%OKZ5w3>RCu-10!Oca*Gcm3-T
zro7}957tWh4Du>JtGVIn^Vhj`^S=AdCNu%QJjqgFE4B%u!r#byU^6bxicT`;^l)H7
zvsTJ&WOqSbdz$W|%R=S0V||A>xnu@AB(45K^s!f8xK|Pt&9`sxrnz-3nLw=IUqeXw
z39up5`><SzeHsJ9ybOC5+uwl%uv0Y;^P2w&)iEC}l1;WO&^Z@_tJuVRoKMK1itpdQ
zS5Z*`=F`L9dDi>37R$WUQ;DKwPp?XZXJvHnoQ!iR>rqn>2~wLB9X(I1dFphz$G$)4
zUye9ER0*GS+4XidclyCMt)heFw86-m<Tg3OJDSDXWueDj>}GjzGO(Z=qNH|cGp9G%
z=uk}@h$WxId!y*o1U4$p5oK;EX5Jh>b+*bsDfW;?MJ?qV6>D!e4!u1dY!I(|A#oK7
zfejUz_K_e@?j2MT9Vtij=3%~;T^wes9jOax{PRwJ5|}uaj83+;#cU3Jd~tZ3e9-8q
zsLV=!d7gnMLsL@)Zp<ipO3d<*XKdbusy$dkSmQQk31;W81|t$b;VWSu_swAW`{L{a
zv27gn)n!msVFcLzZMN_=0*5&-JS>Y}d<;CO;MGW5tZ$o|43~N*_4A-aKd)?xHtnD;
zk(HwsKHUuh*Bu3SzV9>t7G*GW&cQjBD=V=6kdlRrg&Cq>IXp0?#dbADy||!PML)h|
zB>#yFgsGncWSKQV?*;!P(mtj74I!YKDZIQ0#fu1U3e?hd1X#SV;0T6Nl#@}+BCjYB
zD$XU(j+Op|n&MNDWAAnzpEx+R?gr^X@FJ6Xx>k<rDSDVSe+5Nwl^}$~lsJZV1_60z
zNr&afHw*U9_b9$fj<MUc9;`GuSuJ7_i#93}Y^pDQt6_?>z%I6|wCD1CShbOLZo%HB
zS<J9pWPXeC*t0L8DeZ|t0j1SDxVk3kwCR=;lz%o#JKODqm>4Jxnga0{#fT&Q-&e@?
zyK({C!-GCv*K>vnF)DtW!RL#Gg>1a{$2;X@Q1st$(|uR$i+bw*>PK-W@ea#8pOBWw
zw4kSqX_BUh_vwrtowvhD06~$j#LVq>80Y0+xq+f=tex15=a%B9wFGvt>U|&SmTAKa
zvaU2oDWT`Dr!VA#;cj&pjbZX_(~4W}BS(IbVeL(P2dvo|1Sg_UvE8uaf!!Ic%DGxi
z+o0Q-kUB4`n)#j*e5FCe5L(h{gtzm?;9{NK?W2#;p~ATADP(C5dOl^uVCr7-?M5bE
zi;?c`?E~%P%@g-ou?4r@NY-}v)a8W5$yz9*JH3M@=r?LJn;56eKfo>&|F0x3+z-<S
zHq`0tTOSxfq@QExD2lcmbyBH_!lUayRB6TLBCQvU4a)6Oe3fz!Jy_rIxzh7Mi(HCN
zv)YZQz1AI8Ok64{cSK;_-~zgEQLQf!=U>&Qm6nd?Cv6aHfgJ{#ZNw5sWc)_VChaD2
z!QOk$)7)`7YM0ShW$Q=%y~KS8qWd+(@)QVKY982*y)#9`Z|n%~%nO~zdb}VD?%D6>
z+VfJMtH6Gf=i_VZolQTICyWSa51%+F(%JYDGF(5ny*oyM7lfQ6MH+E)P$R4*!|Myx
zOy5?CANoyXt>w}gG@m)>DMorZ6KxIY9dZFNa0I}|&XwJFpwPQ~U<TLV>}-*O&2;52
zAv;%_s^_9Q-+c(^#Pqeb^HliY6FLt(cT?p}VO1ju^BMEOg(N%2_F!m1_4JNqR}@VW
zHa|-jGX&>xibjpCrq>t_OB&swKDfNrVp-1xS3d+Ryep@J<Gt5h;{8V7WxmXqlPX?V
z0XgLTIC*hFn?|)3^7v;({dny_a&sgVf|6!sMQlQUb?V}@Gx?*774qeUIP~ekQ7wr<
z377q3^^?w);ApMMD{*00j*tjdcbj=OCZYA3*pg9xxpj&=4mSWed@JM|-JN9w4*8Yd
zqCW=h;FC@E60;l$ZLddj?knLmG{~6P=X&nPeu9;%%$!Y~Y&#aq1Bf)sZx-;{ZQ1s0
zU=GPx3Y5d6%kcPjSstAC?55TNf1FNa*qsr`f<<BKlUd^x=S7Ob+X^;DmWQ7|ZYXH@
zRsZ<3)-5&kdq?oE2Anwepdh{{v*fKsr>g`ZZbH6Zmy~M-ds|4eVqXdl+b9j7?VDVe
zivd?Fb794bViU4|piXd@SQ++BI-4DQ|4R1#5dfnac?h5$_$kQ#!3Y4UqkJ4jCMKma
z?4h9{U0tMRpofyQglWdL&{b}f6Pt&K*g)Vsj{2{Hh=tDmz}eKoNA#+_Z*@b#Q)_Aa
z!oPZVs7m(s#udN|g5EzTrMEu#E-a0k4;+><lTVzVJ%^ufhsCz>*kx*_-@0_!VsXYX
z-xD|RHjffMAp&8(ehk=REPOijl-AES6BrvCrcxsxC-nIY4td_7{7Y)W_{`S%b>`xw
zqJ1O0kntW(P0<vuBpBgWf~y;^n-arlpQ5I*4?WuWO%}QLi0>I5w4{hFhlNd#XpkKe
z1p!C*zw-IGMW7-|Q6i^^0N?`rbCUiASni*_dE*nICd0DRxuYGn(aXiTR|TX&`oPMJ
z)*M|piTTn!w2v~z_e@L%E78$k{=4vQ^`ljw`Y2iQtF6A3lAIdfG(fzHAGuVO<;C&Y
z#Y^4e&*R_yk~xqEan};8o0`S>fEbUi^X&$S`)|7WQ~7oMuM9D%0VGRu@gO_aQ^NPF
z-S%t{q4I10%m05g06gnSy)Vb%qyXPd__9l`eCqOfFl-U#8Q4yK@YRkP`>uBO@0k+T
zgNi^j^|oaDOafh4bat*mr}J_l?p5m*<L8f0@y-{lw*U8K?ykEcA@1+J4Yk%V|BYk%
z*?$X*sMk2Fxeo+fwPspUSH>K4-+M|=<fOQF^|lEDJtUF9^$dF>v7=~zM1oLaF$6?~
zV^{l@R?ob)BK>zPJQFAZD*|s0)_?a$GXkKyCtts76oI8>rc150i`1;%Uy+`CMFl<w
z5R5iSx!I5ZTJu(1^y8>d=e5H_TrPs*-msoTGfqVX-jOrqPbx}#a}lHaY(Pm6M*Ow+
zFC5l?kYq61h_t={;yiD!{J!iN_vBehYhf-M#FiV564X9vJT^2vVf(!42x2_;DEx0p
zQG@XB8;~0<8YA@9F_N%d*O|$tsz@ercQutNdd%OtA$d3g&1k22GK9c8V}qJmlBSyt
za1pCN7{V{l^M0bBh<M0Lz0~*zPk0Bu0R$_(HTQ!rb$(1*pRzHHUHQuP8<|aLtKkyD
z07{Gdsn(sEkj_xVHprK~`nIiS50y_)<2<(?E$lu)cRM|(8mOOCn^mZ>{$(U%9#p)0
z{GVIE!u~GDLwiQmQ;&biq*b$3d5y8$yDzTi|6JrEX=cBCLC11z^Mt)d4?`R}j<Iti
zdTS~hp!ZUa!B`vh47D24s|Kj+e+9sp$A69;XcIU`Dx|bx2Nm55h|%gwe<n4)$&$Rw
z`SK=#XbBPxE98~mgcSQ<`B$lFc(^4gH^0%gLp=F3-05J4-c+b4u?Yp|*M*x`@q1#9
zMPxn(u-Ry>+F0Fde~(fkAKOyy(21p4oS#~))>10Wgq(r(?emW^*MLAfxVZo$dI=EC
z(?x0G8n-yvvpDn;D2;^MA|!v$1rvlSU5EYY0ScA4f=W}xbIcGGqFgp(Ja3oq=8O2Z
zaTgkN5@KktWB~zjo(_q6{4ezZxF|=um?46^{Vl@e&}Jd+8a>AEb0B2X>kVme+avA)
z;3-dV`&a&o7=VC&gKP8q+IG8y|8w_!10vQzO-%BUjH*)snilPh?i_w1;6UUh)$smO
zZ_yg<0cE(9?265IFTR>JF!1@Ke6-2?toexnZGV*OUy=MB1DHqsU+<0nF8-r{(gE-g
ze&KpL_g`ZDS>SXRrD&JWlKmyZzXt~FkLedsDEQ=0)$Q-9R($}xI}r2qT>5|d>FzH~
zHo$PDTjOH`Rh_@zz55FQ2JGJZzxzM3L<c8sdy5%)YDJ7}VNbtO;|8qyo%YmaS^NBF
zG2!$bkULK~B_uRdui7S|eF<}~=grkKP{2I|mngiwB*N8uIV57LZl|O%lgaeGBM_<X
z-W5{@TywPk?7_|Je|C1(MeFr@2fls$FMj)-`T0^|I%)n3$Ddz(G+&($E*=rgv!LKl
zcV-%6{;o%H^0P>ZruuWTfTK?>_F)qEVo+>sY<+z_VF|7@ol1I6*}P|coj-H6=U185
zyZRcxy>TJX752~Xju2y#pHNd!2p0GLqP_unbTEy-T7U3Bk3gQm&#wtkC3|ztqxgTQ
zoy$^cHz&k<{}23n9=?k2>Ca@wKEhiO{<gD&rD(pEZ!`2YDga;|M~lBF0*Riz1M%OT
zk<Fv8QBlWr1K!G^#vNT<aj~(}=`tGh5<q@>z5kldreRQIa00r&kpD#J6X??msn&kr
zL0#<(w(l_dcTB@eICwQcC198QBT%3C708N0mtF%L5(2RE9ZTp%&E7%B?tW?a5x0m)
zqy0kj{|i9vYB~DM#nP^51Uxv6@uDR^ySDQ8(jx4qY1j*YKPB`F*jz52V$~m(H<keb
z_kVev?LOlKP|_BB)I!Y6<}z-}nU8?_pWyBBh&VsCw)eWTz1zezq#DCYm-Qh4w5djM
zqBYlxzWxKElz4)pp`j7q;npz6$H%u$kL87#e=q_5R*@I^|3}+5Iy#ny>1*GBOxSNp
z;xod-+PU$NpPe25f8PfH&)9pPR^Qh}MMc@wt;GV@A8i?^?5C6I)V~j}3QG{I8<!l$
zd}M5ox(?tSy$fjmu=;Bii6oST|M1N3-mRW;GP?nHp{|k{c%AG~V$Lm0=&4m(choCo
zys_>9@ck8cIC|lT**hHlKZnVX9+<wfvr|RjAS3hHmQ7l^2&AZ8G!zNPwE~2T1P~5x
zE6c**KS!rdyt%jMeRI^+P+uS2P*k)Fj2}xGHhYK7hg#z$C+%97DOtQ24TyA!0+6>X
zyr?Dr`#a1ItKCElSDH;dy}f#1Fb^-UtyUK|EMj73s$oOZ)^C;S%xrDdcFF@{O=*BI
zK`Oq4x6AoSm$v1X6|ntzU47N`mX?J?S(-M09Q=fDHuXHNYTFh~(hfdI&XwKsvVFr^
z2=JFWU{_KfKbZQ%1dpDgjThBD=X?I_Sy_Jmlc$9=$}vS^dUnNjN^538<B@WJcp%Wo
zLAEXYIWm7G*vY@Bs3?fmb91uH6pRJ|DvMwo&-L@=p7aNDz1@YdlINkZiT#9bBmrok
zGcrJJ`ckP&{?UB#u@e2=5OCaA!B1!k+Qq_-?ky85&w3i)?sXEfiAYPM_(OpwY*vuq
zyn_V)`;?eW{-1tkM|y8pXp-jLzw(TWE>=*G$IBU3*8+eMLclRVPgbn|d>Md5y&(a5
zC0O;E#6}gAJOCkmh!#K2gY#wfpYp|jyGlH|0OUTPCH%?X$n}rXZhZ=%M+ZQUYyMTb
z|1H4u0e)%Go<RX%l|Q8T$JTJ;05V+R*Uj;VrhgZFGy+W0#mpDt|4h=qtA2k3jKR}K
zcg-IE?_cm=Br~S_zx)5LlTg=&|G26-jqmK=7W5@2h&Q^M(~+FL+_;*Vyt;hp&7&gu
zX!Fi0l*m6J{QFpdbpueJLK^4mBI40qeMx@Jqk{t(U%rH+3)rwt3fd2>y~ISj>;56+
z#|B#Z{?K_{zIF40&(nKMrIyu~CFRqJlz3$15E->+V)F{O4`#r|P^v6?3b1OB4-5T&
zt7KbuFPKhK=nextLxy&s^n;XZ`v=%1Uf-7namF5sxc#_;<NrwV1N~<caTttoy|jE6
z_hSf#j~cjbxg%9Hfv(=MS<l>O3tqHz{aJ*V4^ch+0&<vu?v}q?mj>!A)$v_8h?mcx
zB%2%592wn9dm)r2od~y}2o>L|Hr;tKRMGET73)^B)szW!$rSnF>jSv0R`2V3>V$oD
zC9I@PDvNwjbNh)MNPtq=T~Ie@E36Rl_cVXMk)SUDvM=&2s5S1$)pJSFeLhHbNW4pe
zLg{(<_k%#^S%{W?6*oJNGH!CqiQxTLNji*eul?u;O~w~B{xj8IzP!PJkw2##7dqBe
zJ!)w=*EauY$-*Li4fKq^P|X=#yT<TJ;|=HxE)Sf&B-`%M<QnS-zvrvJ>U8<+KdAL^
z*aQfRsG0GU`2KTk6+x6}URyxRVI9eWHV@D7a@iizR>NV|8nN>0yi?RZ^1CTSpn7A0
zmM`ZaroJkmT|%VZ{l{Co%*M_qU|Do3^^ckZOC}AP<N1+9lMui2$!$?1qi1K?ef^fs
zHB~Y)11%h00B(;lyj2IFO&N3Yf8kD>V(Toyug)=kkXPUb)O#7E2<zn1aCSQlrL2Z~
z_g~F4_h=CMI|Aa=Wwyi!K=_m%G5u;;UuaDqup`Y9TjDUjQJ`v>U*dSVM->0r@7b*f
zCD|ksRI8?1Q8OO{#0%(%)H)jN|K#M1klan7RJ4%4`XOozUYgI)VZqj<%mywf7X`Ic
z{@*g>U4H;M`7wdDobsZ|2_dBR(NjB}K6JeNB7~Mt>L%IK57t88P&SCZqWHc$h5&+U
zLjUF~NwKG^vqxKIwFdED<sxA$0=(>z#tXnzs3wt<cg|OqaZA`^lMQUsZoN>>;}&54
zfR+CzKQ{t6fvFJ>0j2UN8eIp2Jz6iaJd$B>Xpe5F6<cRz&;k3OZGjFE0GaBybl35r
z?58?d4N+rTB{K$bw_yCs&98xQ&V5^J6=<Lvd^q^T5*}mq;CT{#psS?X6%ne-Ee|qb
z0UfRF<)iT>IoHd$vOA<*#pA^V^6x;-@DU+1Xd7*x8jI>Z&t<Pvd}W<2RFD!8QM7M9
zqtI{G;pyc?MMVW~wj9a?^z`K9q+{ARfII*u+D%O4i2#?I;s^Qip&FVzCZr%ba+umi
zg`Km+<TbUoqhkfTk;YP6H5}SGwXcHyFX*Y@Lt%sHoAMh(Y;KEaqrDBX?Nc_@dz{4U
z>$B(Mc$bYcJWkr#xiqy7NS*7zvIIfE<piAD^$9?`w8^z@qMdcM&ZUkrA~DEil<X@C
zDJy(6Sz}ugU-se?5ZoolFbHT*J)1h$fOb@2*WJl#TfKMLuTqD!y}Yg!xtcW8)t!!{
zK8<Y6RzW7Fs~~;6OR-<vI$%A9OgR<B7Bg4VoyEwg%BW0fX`pHY0Efo*#`yNeP^V&Z
zxs*axa9$L&uhXu<uwTHEp-$u39XTFBO?{#p?0W26r}sNuem(o8$Qx_UV%}A^9Fvy;
z%_wYAD5iFRQc&9s^fWYB7I1zjJJY`&T)d|kd(aIGDwnH&i;}$ge(fjAQ+b7in+)k-
zc>*pyQM=S84ka&2h$#(HJdfY}-A+?UjWFMI%d7$50SwhTYW@KriM%&VOWoPO`3~1R
z9r_>oNQQqN=v-uLUAQfxyz5~^g3MV;3l(r}ZqKSs@%nxYK;t@Q%6yy*^F+PQ8gG%;
z*q*@L)2OsG7-3Cy^;w_5!s+FQ2?Mv3ql=7;jN6-mTWV@*joZWF9L1Qr%*<ExM>t%K
z={7qPu(T7k`wRE@*X--frivX)UXbo>$fi;Ypfp>I1qrO$m&PLI3f+u~-8($Zz2`rV
z39d+aTW}_0VfxuWsXO`{MOCz*;O;$dq}f<sV-E9ZFP7G`=WJq{Ho@Q4&5C@GcDsA1
z64WSZUY)=sR$r?@R_LTTWN)Y6<}&3W^z?vQ{5b6g198gG&PYXPQz-yoYwyTuQ7xan
zIc@Ify-R`$jQJuaQCAunc-ZE*c!qO+6%+>`WWbg}j41ri-DMw10G1Wy6W~*n*7*tf
z<2YqPl0JtKW&Z?xe)}2CfiNF9#KvadtbwiHHgNQrJK$Z3u3Q0AfzPHPF>eO1fj`+9
z#k{X7DNtl(W$%1MJUl#LxVA<YtbERSL@C54GNQ4K1Ev2DNT(q1drkPVCc~BOzLl8Q
z((ZEQ^6Y9Ogv@B>*<e}A8Nv@Tb3Fr{E-Ye!PWS5)#95ToI&J~LaN$v}`pZg&9@SXg
z+{5eYwVDanQ9kFfovh!Ve$VvSX_rp$4QkH67vkZu22gOTlkZ%37MiwG)9Ad1J=?c(
zCvwbU8S}OakNaJl*e}8;DIOV9E1%naUlpGkx}sa_x^<u9ODH?Kb#V4|)o)`_&<39f
zoWiAWchbIC%0?fPBU)uX`@m$=9x^fS9KP1>Iy%!jc?G|pWCi3jje!DUwe?q^qoI_L
zTPB?NUXZlu3^ZzdGw#O#FJz{_zu(^<)t~|Jy-)Ca<G8d@W`~EDkKDr?wCT384b5qp
zw2Hww7c~V1@~V|pdc%obK3l*ba@iUmu=ipiSl#VAephjp1V5?Guq<WfP1AXc@FvAm
zdG^bn>liNUi60@I_gnE&@LEKUc57>Rlw-|eSn0P98qe(w0t^(`XA!$Dx0=Cg31%`V
zMXKXmsh;%0tg<P;Ju@AbSolSCq6{<TUa;}>2<-AI_b(#$Gl^FUWBtYOtj0z3R^HIG
z@zy5s^04)9jc%@$O{5+iKsUE7>8Rg0=#9;}I69wLc3Kn;Sc2_sjm{?`_PG?~t{Q9w
z@ULWo_NfGkWyiaKl7~?VtUs8FhV*@9aZX8%#cstNFp}7q)Y1nJ2=l4YABg1NQ{vMW
zFBMGTp{CDw+QcM8^egBwv9NUgykJqQt}>wPE*#XhD6gpK+jN_?sH(ndn5cZ9bs^PK
z2>bZjWeFG|l3=PL-h3<G6*DC7QqSDM$XZr&CCc!y$?g|iX8rfi-;M8X7niJ>c$P<E
zS_bAU01N|^Q8WOV&M7AJ0~n@Ij~Ga~$)P}OH`afI)9!`w_n59H+hsoW_~!WQIJz<_
zTVtYI8%3x>gwFxwWcQ&h(ys2Bu6iL`wQEIe?P|Btw`HjsX4~*g$U0eibeX!pXwrS6
zTXxFvh?RlFv-sRmO4{z%@5>6jnefO5JBewz9Y42agJ68)&iHtR`JJ*VsZj2duYk9W
z0(ffoBwhff%z>!%>>fL=vXUzgwUGX_*ywgac*7}sAx)!(gSVsP!ok?{bWa{d1qJ0)
zk;_n{o8`|`b~+X2eU~R23!Xb1b51AgeI#?bh_ApU3D<C#Z!zv&Ap9hWV*oO}=ev8G
zI<uqom15=8*NuCho!7*f6LJ~&-t5V14scZU&))?vN5M%wBFPGwWexHHB?hV`qqU<E
zNPL4R;-n~U;;YmHLGfQS*lIVDRo9=dgfL31aStz%^Vyq21s&V)l<XN_Nzd4}mF1tS
zj>7Jm@rE^eh|1uSFLQy4sU>10Z!T<g>#m+D`*^IJ`KdH~{*1h7751&WyyCN>U|30K
z@D#P<RnZL*SC~lD8PG`4Y<p3(X(Qf4JeW&_h1LlK6p{2xXh0)PxF0BZm2u+;`_`S`
zRH2mk(+`soB>fvz$R^aFsOl4dN`W;`*|i{C=cJw;!hGQD92mAm=-#)8b9Qdp^K~$u
zqIZj3jrevgFid!&SWm!?pDOM7l>rOP`0eXV9`{CCh7+Lvym^>2!nFskRx}b~4Etc+
z6fpi{7<&NQjuf1BU^lIPX}+>X^xorS3n;RWe!EWCYk?ZBjW>_$#d*tlAIt^Ju_Q+5
z*_&na!3FsET@2>0`09`@rTC+JbV(Lq3*_3WNpVim<ndHug%YA^LBwZsdRL^c!n-Mh
zc~OjNn8!s1`W(XT)GFJ#gkj5(Cp<msQiK<7SR|b19Rn)gs-8BLhlov_Iv2$0u*>Q3
zZdUukf6NoCkrrG*MtB;YuH^4{dEwXa?;HadlPuD6=30FfZS>B`@rG|eA{iKYfB}eL
z5&8pVU}Qu=wc}tivCZjy947v0ad}4m&f9(*|4X7bKOrLByT@bn83((|Nd_L^Ed{73
zm4G-ffI#aLzl^LNT^{Z<whp^E6$?<6Dte)-D5-byHCEznr8vsI+qE{m7Ts>tDY0~0
z$SeD&b<g<O#xI_uun9~p>=n2a%fuG5A(k>&*k;)JL=?omcMH5GX7lVesARO-hh=Hg
zHWucuwZlX2im*BsyJW7&43A^Wl_7!tW)s@}r>b)!a1|CYZrI%az#?M;&~^mJcevv1
z|3!)j`m)qrdS;br4Z#;|rc`62&VbRKP!?UBw+U&K!Cqu>^Iv&|u<EMwW^O90Yp&UY
z=6MMK^ydEuBm#Jhh9D&CkGf~r0S%tsNP~|JB1@XS)>K8HPt6tcJU~uwduU8er#F^k
zrpc>@U+8KvfZ%Lz#%*`9?CR=D#d}*lB&3*NYzeq#=Ky-Gt;e*t(9%*^xE;)rdhy#r
zY~_9UzNl#*b-&d{cSKcZzhvij-+@L`@zO{c=Pj;g+zPR_*^aJsX~4dJg>8)8z}InC
ztq)Mc<r(eSqhdE?$MaF9P>z87@RR;0dHkZDTc@Gh0{l*F8HC`9=#^y0&bJ0YWpC7F
z)Y`L@Z-6>So1=%@bw|{}q#Wf!PA^o;%P=9)N9AaE12Ui+^h_nkI8SI=P5&7s$UCzM
z9@0Rlvi5oP<)dUEI%%(i7XTO7>oXfG7i%yU5j?=%F*rIjOL!q+%!&Tsh_c3_@`U;s
z`?%&Qw4-Fd`PvS>Z2NfZ^<sH>c^93p{>%*<`Fy?0&ZI1Ro{$d?Ha7Ay?Y6F_Mmytp
zxg)g89A|?!(FwZEj>{>>I{5fEwk*LY%^*c_d(l{YxC&kx0j1cN!GR8KQ#aGMucNfS
z_RDn-zOZ(xh1=WSNDXB^4lnRII>nKtj4bNbcU0f%qvUIP=4-0<dYOO#akz|kb35Lt
zcw4#wna0zJZ1y>dXpC+Y*4{7KDH<ss8@F-#)(jmKAJeVyRWY#gU8GABMUW-I6dmgA
z*q`|H@F;l5tM%B&K2?bf9`Ob$`?Jr=r=oN<lnDAMb!T+jOI>(G`S+K~$GFC|3JxZI
zO9Hu)zfc(lKM5Vo_-_t6qp=E)36(+MV}&uz3+uhMJ_-*$etya{<<*RNV~)qgm#sZA
zDAehr!q3aaD%g>^IRaZ*ZqWH52ea_kTBp$V)Qn%5RnrlarZ_p$j#hwae*zwYaf-Mi
zCo`@j6{y91^?M-{s*YBjJko8p-f`ncTKAhqZ$A`XYM5%TY`FQn3<3v2O71NJkw+iJ
zl;=1UKGy7q2)$vd-_60QPh5tIdfE4}m)~!tJSn1M*ojEK=`Eqqo#+AD3Ox<geX;zC
zA7vB8#{$`x%G&O*KVd)pQ$o6fg(p>cU3A5|MxEUoKc#M^v{rIN{b}&wozjLPL>c~r
zi3CNGw(;*$8BH*qBW>PfJN70bpvZYd6>_Ny+&OhIx;sG=r<hUhXegN*{%Ki{!LbBB
zTx5*rB{t&Oi5WJsGSYRwwUY^aGZnvXJOA^A_|Cyq-^E<a&MDRM(Pb*M?*A$6D#N0D
zzV@<!qJ$uwQVJ5%odVJ!A)V5&gp_nB3O`voRk}N*K|)bfB&AtO0R;pE>5_MrQuP1r
z<pUSjvd=R!XU;iu=A3)((dd+;TGN&6Xfd~Sn!+dSjk{k(E-)tg1K(14@dmhE!N2l*
zNnNlQfNO-0+uB=^l*j)l-n*+LKt)jwAE3W9LwAZsJ*j8Gm{XGx_zcS2JUmGP&K7f@
zvVP6Jof7cfb9Z&EoQK^&D@qDT@&5S%4#(=i=e=uT?llvuMSyC%RnaPeAhOCP>}@w(
z{dB)z!gY7g*+t8uq_6(<NPZR5YVWOkA>86439PV0{bz>xfnN~WOVU&DI8WZoPcQsJ
zkL!phr6DJ$oAdUS_Z<|Ee>%Z$>TSm{78>84qsWoQe#hA}cDr_@ZG-0E%~R&aaajIA
z--~{x@$5AidNZXYssndlqqf$ao_=3Dw_@m|QU74y<~oIq-9TKE5L>aQ`M731M<q7S
ztYh=XQ3~}(X#do+gD+Yw7QB8fQDn8gnsOjaLqo&NTu@xBY*Lh8?!E2gW7emD?^F59
z8SsQuH|^W4Z??XDd)-2_scb;IZnaa05H-kZ-BJ_QQRFHm;8OIMoBV$Fl9X<P&K%07
zf0=-tm!Frbm+K0x-(Xf*T2I}m>v!kD@1-xZM)j+8%9h^odF!vtJ2NB~*q3~&93;>$
z7wt+ZYAiRze;nIgkli4?Qo0ijHdwGZyS$p)cvHbTkqv6L^550hSLQP>4-(kdnr>5~
zCI=9!G&t7HRNT0($hx;YAHL;)hj(w|bymVCKUe(^%X&ekdcnI%omY}Xc-{)#$H4}B
zNfyAhMXF<4lvc9&oB=1aVWZ(|>vLyJu{w91W*LCYVz!<$6GL%?U<U#46!ptrmqaN^
ze;#LC{KwEL=KE1E2``V>mgJq+Mp>+N{-)8=*Vorypk;J_%vHK8tur@cD-v++Y|q5o
z+SpV~$97uryBHddhfxZxMdGx~ua~)Q##?L&S$7Nq_+L*rj^Dk7r!ApDp{pe+9{c#u
zMbmQEUv;E#JKLCMRx?d-Ujldtibxz+s94SR%}4cQ1+c(@G1M_+O#8G$Xu)T(y~Lim
z-r(civFeSCuO3&q4R`u~YQecsmwYLi2(+li<o8=z@Ak<z>8{8Rrux0y8Es&y7iy~b
zp`@h|v-{<Sj=IMH09o3;Uz-b=N@1uoQ!y>7!gP~1APXo-^z4>-vX9*(GJVkY7-Ur1
z6+t@2!XC*^a+sf?xt{t9fsi)5=wC_e;_2xLTd;bUT`4LjCwFCc=pBJPxGya)grAE`
zouiaTax0VPu19)XYuFkpd5R5d0Rzr2@ql}t5B!WvXZuuk0oJ2ybBmaY%W&6bBk6}|
zQ^7*j!W-B@+^tBwhsihXbk@Gi5u<)xW6JqT_(S^z9W%{G0FGsrNcmyyxxL2hnpD|3
z7RE!_%c)hbHJ%mFJwhYbQ{o02m>Mtg{RW^;Azg_GKY((P&cBQQGOT*H-mzp$O>3(L
zLFwbUt!sdoN&Xc4omun|7DiwW$lbbE2~{4I<Ecl{!7RG=7u*x*V<^P%7!7~@ZJI4i
zEF&eauR1&9tI_!Ox4>C6R&m#~%?EXU?+mjdKTQnpI?Qi%$hWJd6uGgJJ%7jV{B!TZ
zKI4lH#rB`qEgi}q%=@={w)rg`T;hqgz!b{R2T7KWtCdiv&h<1+r*VUtH$uXNL-%{%
zf9jU+8jy@O=y^t%NJ-qpcx~YOY9$UFRY<Svi|C)6I!D=Qz+rhie1$%#RayYBrZlDJ
z#mJ!)apbv2wO@oYT*zdobtDpFl9lDwbm0A=Gu&^TUBbEY)>TiFjclLxtD;tr<%Y!f
z0v3{ZI@~89S)Vp!6GM8M0Hh8^+u-GE(9p_4Voa7+-Sa&KH+faAzvi1SZJP16Q&B0g
z-22c_!q;c@!D?oKifm`5uS)+SE!mR?;t`<milo?}IL+mQ>ccYD?yvQ}NYeP75BX2z
zihUZ&G{vILCV`Jms1xt&D~~#@Z6D`o1G>R(9A~U5WBNGReOOljzk0z5gXD8WIwzUn
z<33AhA&cFJu&Ceok;CM=q9o8`GHtWJ%fSDnx{p%v?ARdlX>A-ycp{3@EOC4JGS=@r
z_E}J-dKLknQP_qMsVGmS5kfUX2U$6~rD%U*Bp892;>v0y=*=jxtk};X{N6TXQ3rTx
zv)dr;m&|6Jd|GoxD-btyQY|I2>-=~pE{6A8*CYyvNV&m0-0USFI7N_XQwJnY-!(OM
zG@FLT8aGnamrXuaLKiAhQE#&1hhsOEr@{ab!}hHl9d0ss_Ve&k-yu{PnPAjy#<>5y
zE??;pz%yugx(^AP6a<nEotJ8ozADz_R9|ExWM~dep8$jn*R`5mW><=*C;(e1$bjgD
zs9iakI^!pxYO=2yv0Y~yD|W7G<|D=eL*67Yj1pBvquzh6y9(yX^ay00fD^?4(4wO`
z^4~}2o!JdS0YDi&p#UD-9RST3pf=g<H!?^%O!)V6<L&@l#wY&I|8WM+dW0@%HbCQ=
z)H1H*d#UqW{8l?bGm=WMJCB~I<%hX+GVee>y3mX0gtJT+)fkqSKDJ0WM>wkAucV#s
z&esyRCfv-ARyP@^Pb*o!?3}p#w0Pi2vF3M~v{=niaQykZ7kXf$G%GyWZy%}{d9`9*
z*%~iFA83Zt712}8Sh$`lK8SIT2VC>+8Jd4cAj{~*1kdZY!h%h#r}vGvZjuq}d0?S1
z;FeZ`tb5V(__kBx9DGbG>NV%2Up=Ky0%Nnq9Pcs-d8bEq&F}K08|mS=R7=vS2Gt^y
z`d+5Vr$a)^@)y9>y%|YsLdTeH%Fc+G&%bDn?Zd;8$R<=Q9~~kIy2$^AJmSl#Qftwq
zI%<iL5f%6vo0`y1?K9bb$a=+``h$P#0iFBvps0=z5X!w|U&TF{LF!<10s`x-+{eXa
z<SgEVZ`v_6xlNml1bvAMQQRHbk+!OCdz<Lw>&5|S+!UT>IF9@`yeq}0g#q;lk+{E)
zKQSap=Cl@ZG|}x%psBs*t5PS=9=j!UV4#K&7pjvQ@UdF39{>$qb?C(Z%W%Q#A?_&M
z9-u~YtUre<&KXj{KZ=6dV7ohsF8(d@%(ns45#TNpKKLq(cVf6le#96BEfI5B@z2gQ
zzrIkx-M{PIxK>D!(_877HTmI??+mRO)4!AMckhU#j2%-CvT}Tf`g@9V>eEf#mg<;G
ztUf%52@In3Z+?Kmj^=rD$b<2?-)JS`etrjOl0nKzf-~!$536Hh!0ktb3}GZaCB<%+
zu&E9v_esYdhk%W`2Kp=tPJdj+=!s~Ep^J-);UXIecsmvr7NS4j(>bpYEY;qIvWBh?
z$nf#?=^TPG7Qu5>KKSZ4k0qY)xEb6%(-Ag-1bqlXGp%RQ{RWU!eKgMhgR1Yav0hw9
zeu{z7$jC@g5>LBPdd$ifa>UB_*fW$7P=o=D8clca7h104p$+L9kJY*EZY**M29&>e
z@pE<6&hRsPfuV~_d(x)ZkXxEZYKhiZld9_4xktkekbZ10Fh`{agpebRKtW^qn`<v`
z20v;84^+lqsF>$o04)NjlDnYp^sy}lu;T`Ygdl3}nUZL5D;5lmYUfm@0?2`{s@y&6
zr!B80f?C%20&IeEAP294EbG;6j|D<vWbE#)EtwilC6dqXj;OM8frfVxys$(Z6X<=>
zIwjDf(IdYI%ACDK#v?5iA8Jl|3S+sgqf-lx?^RV*fqlMZijSM4V|QyTc1u3k1L}T1
z1#ukHZ=7P~vO&U1)#R(&3Fw0y!+q4=mi6w`mwz}Dk0*kWg@xPM_P@!OFNIel0<qEJ
ziuFy4ZdoW7pHP{dQ0N`@&6o@d4sdoW%if4*zJ7f!PS0LWRyLvatr@mwK;mAytwW;-
zoe&?*b&tibi?+OWm^-xU;$U%ALLqwfOi5|!WQ9t*G3m&^R5KN3Q16zv%g4#d*;gRB
z{q7=*L7B9eX_xakuyWk=r<!!MGM_)G>G$GxOLXg^6jWBak_|@iWTK5O(d-9mL|$hB
zVPY6Wq`7?Ry}_}GHdFn<P?xWM#88JMdwh+%>?z{4`7$3n!n>uhF!3d;kb{!aM+m^~
zyp{nCE?e8$07%cFY_y2@ou-2U>xHd{hlhf~$Ji1YnOO|RwIX33eUs(VuKSH?OG5z-
zY3gqBNE8q?u>3!u3^2Oxi3x|I5Wzqoc}auR9awGUMV{DrN?kEpB&#4;v;Ra9CZsh#
z<B5-xkylh?VPbmrIkbj_5&aYAi^3UsrLGF9C=eMUFxk%^(;1%31-M!AlE_+jnd!SP
zQ&ZsdOF?C7&OHvDhlZ&x{dM?3n_ePR8JWxj_E@L$0G%A}n?@c?M-I{$H6SrE9-B#m
zu=OH6{WYHj^^~G~exB~Z`b^jzHTn4=VPv719Pp|FBgi8=wnHR<QryKwad>_`z)}Fz
zDVA}KHB{UyxGIs%tG}J(Ye2uqzu<=sIgX`{|Mwb%Lj1xbPj$~aaueV=DK?s*kU!lo
z1o|0(4k@S>6<L3KM9@M&DOkgBc8yRVznepTyo@~e8Sa)HcRawOB~E+@j38*g1Ohqx
zu{%iq2FVDiEBw)E;1?H=`KVu75Xjk&g+b-GB_k>C>ZurzBE;PQ>xsz$Gvrulj$6Q`
zLIy%ToqZ?OY#4*%{ulawYd?eVMH}fy$j;Ux!!c%^r4wX6coZOd8u#rpnAWq%R~NK+
zYzT0Wujy{<J6TU)jE)9nP3MP#rD574`GKI(c97;@rbu-<9fa``IvfJL4=K9HCJ47Q
z#G7Cfz9n+!TT8Cozz9qPLDG93QuL#p2AHos=rdFpmSh%wf>E#sKKnZ{a`o<Si?zZS
z0mI1tvC1u-hKudh{!rt$H1jdLYbwmM=aU`w*}amtZ7qCPFIzw~2CqStpZ7hqIh{X~
z>&tJ!RhX(Rh&y9X0>tV?WX`2D@ba--&0R~xATcV;of?#7+@ai#eI9LjPaP2FQ#%1_
z_kRhH??9(SI60lD<Xh-|&$b2ia=!@n4hP#_C+f%I>$2RJ<fz%XP%;JwUux3fXzva8
zQRBg&7h!kkQ@Si)dNmkktry257B}35J=vI;($Dh`k%j#{?P@R4ZSC}1|BdG@4a7bP
z?43&g8AZ|Ch)GQCSnKZ_39oJ3S^N|p*(i)DgAtejTn){DF~KRU<Vd}##f_hcG_yP)
zoNWCIwd5}X6l!s}xbFypaB3pIYo%ul#0zjdBFYW&2+!!5zqtR|@b*~WHjsYAvR;k(
zjIttYKhQ}C?jMxIhobu%@_7;hq5w5Rp{6)%kr+eZ(CAR|qI}VBu^;{g1(tAFS2`UE
z((X&aCbm=r5vzL|j2_tn8j|tP-|@ta9~+3V3aA%&RWVnd!j+C1IX=04k}ErIxf!{y
z*nnx-oGc(GW(J%t1?2VrSK$1MI;?-aT3;@;zJ9m;Dc9S#ZviQ<R-4z{YHyB8{h0lf
z`|t~M4i1j5meJm3U!NAe@fNkMYI`}knRed&2u#&{VE04OFO#W`pCZnL^jyp>$M6T3
zHCJ0n@b?cwjkp_&rJywdFeoiGHC(jAVcfK15i!Qqp?E2*YyY-DWs>^(T8>dlo$FO<
zlnb)r(9042XuOY`8@x8bY1!)C%^xMad*Gz!(rB&oOdFxF%h#~EdARr5Jd3Hwj?I<x
zmn{6R1R1^JIewD<=p_ea(2}NKg0>>}mqzo{a|A=EdizPYXZvH{A&c)3-!D-KYinz}
zuhksbT)H^vx8C*b%OB0tm*!#Yt@Wxj?fv{H^y6i@?O^f95FkQs+L<r#+1(fe5mKdr
z3<!5zW^dQd^DG~{B{mwZbF~Hcg|jtoec|d7jy5rS99c71V#Lr>cmKz@mZ3+M$l~aC
z8}F$retQ8e;C57dL=`IzsB3WeUbHM~+FcR~v!OGp1}Iv;gJ0m@b`GCC7S9sHhMlQ!
zu@^koes;fJ3m4r9Zcr?P2Tl#vI(~-AIq*ALQD|;u77Wtd6x(0x-Lqj_{+8mGY!p|^
z*0A=eyi1fksGLm%D&qB3I>sOESTacQ?p&bG?S=`<W*>-n6A=^lK9~<F%fGQ^=$Dzj
zzWbwzp-o*y<k5(**9L4oQP=}nQgC*5o^1ft_i_petsgen65jjkgR^Q<Ec2TH(UAhK
z2$u>PUXNB0-3C(207TJZUGmo+OSAid9Np}vmY_>lgxw=nx<ocdgRb~ugwDkUoaY?R
zQAx27^kalvbnQ66s|a^`Kd{w++pZ$Kg0^iLBj#sQ3fWWCKiI)$M}6rFTW2{{4&*=z
z!<qrLa)Q61gb)a+u*nJEJq)my5-O@<#(BpEwfk`IZUyNjIc2q1?X)W&nHw?Q^NqVd
zoU`mqy!n&HD1+gh(8A)any6hL(7#&e5R_S)Dy|-y^v(UviEv5IVlYP>&l1r$ALq6j
z`Rx<#Z-Zo{dF2~(B2w5n#cHfiwWCCjANT+g;H_xdFT5}r0jbT)OOJ>Rsm-w!Es&S1
z>W@D9S>oC`ejC!2T#NUoW>E+DLVGkA#|39X+$Go4u41+&_PZ5LcXQ@=L^kqw)!M2(
z8=_ae9^LTf{p*MsbxdR42UmW!$8g{_bAQ2Y*a5(r%!ao66Fz(;3+cSuZ2qAc5(1n)
zn@eM4Ty5_w4Fyu#Nw7%11lfh@v@$wWaD~iK;DoE}p~==U25l0ez&mq@NsZ3+V|x=c
zlVePDBbDJ)FPb@_7zP@QHlYK6KZC9=!qBQ|d)p&(kibB->f_zQ!UqH9)aUPe*hu^A
z=jv+Omtvk9RA}Nzw-}y_q>~XW=JXE+B-f<Q!x*@^14gJxD|WH4?Jlu{_8$AF*7lh~
zC*|8*7VVt6mnfeX^0RI~Ozq`KY6**edWW!?OVW<|#Pkol1CE%eg;+7gP;IM3m0=ib
z(6V)KI@c9{pxKqCcWo~-F|%CXWNMzLbfCX4PsAr3Rq>w$Mi}#^^0!$Y?i&6l3YiJ-
zE7ja*DTjHZ?kL|Cc=vuK{Boy1$44tbJzQA6>808$u&|Y)a|cD3tM6RYA2I+p2;qy*
z{IoM{rP;>y8cmmaT5Xu~U0&8Hfr9IrPuug{*vFLR&jfwjQRX;WoDA#ki{~&)JgYW|
zUU+LvBs8C-7y6;Z$&OPn+MAz|v7j2R%yL8T>*C$idz*y#J&UmyQflCax6@vIZ{#mb
z<+vue0G}Ajhq{|?lN%iRy_31nmWC)LDAJ{4(&dEF5#)S-a{rB9=ZaHhzr1Km3-dc!
zp&O6BvT!pz>6w;o(?=l;@^}~fyv&`8=;;%Ew#Z?`qoo-|PA$1K<DLSsy=By2t9Msl
z?6Z|byuZc7MMBwmOOxgCrnLaAVeRa=HvIGFy6aW&5gAlxS7*cCBxDE8{8u1?YTfRW
zGM`0lMCEQ-_@=kakdI70gStQTgS03dIqBohvIfwTTfYk4d8_>FUR^Q&w}%xN8fG-o
z<T%e;tFGRWnnE}<b;L)=-dsh|`|7r2Xu%<CBz0X&yC+1v$i?1)nCvIe>1i@EZ_Z?n
zci~qU<jFmUqz!5PRiBS0Jer+3XHCzC$Bd64$E>EW)8Rd!UUtNN=Gq7xar?6xxN53$
zBLAzlZDI&^m*BQKwF6zaQ$ohbLd+{_>^u3^q~mii-KynHR6ZZn;GmG&A=FDD3QsH5
z>=&3UTV6As)&6VO{0XE6Q(ZJGWdbSKXy`=gJ_|apeDE-pnk+@A8n~OX?-WegD8`CG
zWy$a#aSZj?E^aBa^l{S2mql~@nvPa^Pv~6k(m_@Z=Sb}i&#d>_6lyg=HxQ#^XmKV;
zj51=qdhX2--lYjM-3Q}6)f!xW`vW<aXS7}%Nvh7&p@S(YckMu*wTMHOJ}lxzMqRq8
z9s~ZOw<KeWZv8d4yOG@2?t~Q5T@MxgHp@v@Yg^Z93fF1PrR2a&$*_Xo8){7o2u+~W
ztog5=-k<J1VFT9|2Num4?<s3+aKZ5#SBmJ)2Eu{)B11)OPhI{2Wd@z=c__b92K`UJ
z^PxhqXUu}W^a6$>Uq85LxH(iO@z+&w2ian*zIVd~-elHPJH)horoC<)XEQuwyr;Q^
z_4(sq^2ooQ|L?+bGW({f-52bz5nW~<(q6olkHta-Y3A%SZU|1MsKqnWfqXcC6rY5s
z=&JF@_fc_Zj=Bh}<=i;ZA8#E0{h}(G?th46x6UnP1wK^$XrU=-^zyS7g>-bw{J68z
z_wur{26%Cs`!%EyL)njPpFRHV0grn;xk7XMQ>E5W_B}a>x?BT%M0!N#PJw~s852dm
zkev%URcT|5AR!gTZElbd2(b^c(8f+4F2<riD{o*hv$$4QZI}%ZCOr)mX3J5K&RKYi
zp}sy$kF!FTT{nE>-$ChI4rXDE)qOfrA@#{Z#Clr>0-^&ErI@69JSYz@JeB<LUT3L8
z``_nq#UtYQLsc&m((#&`yOl*Yv{Rb->!Apf>>dQ&Xh#b+=vRi5W&EWPpoiKF(4I`Z
z%)nsxBJC{g-to8tjL9US`&E>t3uw77(lv##|I*gW5zT^lR?cOzTIq1SQaj=o@vk0Y
zE${6K=Y1B2H|O5d;qDJp?eBbFp(lUFV<5Xc@I?GV*X5iQ{r-XXlNgArY4tV13+8R&
zkgkr7#i6nc!I7RaQuU=ad%b+T7MXt}U#f}bS!szNdCsXa<DxK4>mJ!qXt_+q-u3$R
z>-F!01>_IgIj<U!xDVI4GMguPD4X87vZH-1s`u{oe<ns-5~`XVvy}<QTPKrKP=M#t
zx|jRkJeOcO(dZMyv-GNkA%mkg)@ia);My4P-QBZs=HXBx#HARoikfEJ5ejvoF;HlU
zOVYu63D;?ZM1LG>@;d;POO6D|r#VDQ=MsqWlQwEHI6m9H{8#Oal`txzxM&HguS#&x
z`UEM&EC-;Tr?q(cg5JMuV`<C_VA8}6_P8!rOZPeTCbO3znn`(u3$kth?UCj!>iqHw
z%dcum3RrDXjj_9LCqFMv$RBWSUO|DoiFj`<gQ_Y?-;Lb8YZvrCRae|NXR4;;o~`BZ
zU0&}WQL{&iyI9S&$#!yc@|`oM>SH@6&&x?N^=p3@uPS(ycR;+pY8@a}^<TP2vV+{;
zl)|fELn@d&*>{tRtcy}G&w{L}su7-(l?`b&M<M#u1-Mo`hC#N>es*RSnqwc^BDe!#
zxYAaOJeS#jt{z-H63eU=9JCa=Mj1RA1m!npeuyxy^sPJ-O&!jrtpau4K-gN=vrz{#
zcKL)j$snA?;qn~(1{nw!t%osO6H+}-EEGoTANz{3Q1kESjj=Dptc9vn*ngN*Yr<>B
zBI(=*HF!vNc;QNxLj2NLeb71SiFEf><8LNdtbvL=(gRWoFaL)|XH(yvfAPiwOXJ3P
z>1xbQmi$t@UWxmU_)QNlx-f#~l`Rli8zEy=B?MlxYAt1vLTqkBB<yTtj+9MdVsmLT
zd>p=}M2eE=Cc1<e-xj8@dSUpsCzPCTOXBjdF*iGN?)m#e_jFqwvGo3xtU7*hqq!$m
zn<s9wnGZ1$QA8uY`J5SwzQQ#AE94HtYx71<hR0<#lo57wuGFtK|3iT!QnfUsjnzJV
zY@xAC22P-}s|y%r(HmA%O&Wi#*&dUB-Ojs+<_Y-T<*F#W^=lCDBX>(#s#wDK!T$l`
C`Uj-|

diff --git a/chapter_hashing/hash_map.assets/hash_function.png b/chapter_hashing/hash_map.assets/hash_function.png
index 18e0f0110772b2d1a7ad4a901d5d9b6542efea97..dbe54a25d92f9d949350369ae9cb81933470b632 100644
GIT binary patch
literal 100007
zcmd?Rby$>b6F0oO)Y9FxG)OHS(%s!krwG#BjWp6oBTBb)ERE7AAkrX6NeBoi@h-;w
zJkNdK$M?tg*LxiAa=~@&?iF*+%sDf^nK^l?p(c-sMur9e05BC5WV8SPB={j{5)6Xx
zB&d~u@Ey=iOI`|4Jx;L$e-mzPplGA23b+S91_O|QcmRaEQ{X=UAlc80?=DdSlK*wA
z1!Vqx4*Z@`j{t~2&j$dE;QPCm8T|L|nqPZ_0^on{SOEHSHWHu!;m<K>5`H!yNJi2h
zzC(3ZFmwX|u=?+QfoZH*<Z!wHiZYTq-oX7_6n}~#pKmoq0!8?U62XW)%lBo=wO^Dj
zvp;BJSjgY_5JP$2vn}OAU5@{y1yddVkZO~)VY-81L=m%As!Vb!OWirLCkO%t$sD$P
z6O9F;gms1@ID55x-N)|k+lRkKgAP4EXPxJg7LROlJJSL2Ab;CJ?3m1syF>Y(S2Z*=
zym~dX+$<?%$wL-DEa@LpX+<J`J(0tr7>ua!w+(<O5~D-|jR4DnlvjwTsq<4)tzH{l
zf3l&_dPyt!`0-;uKR+j@nm1OxX`f!EV<ZQfJbUx^d%$lA3j%31#{k4Ox7>v{*4MSP
zw5F%0BU4MH!Db38FJCeepp!~of5(9pZ7W2&UYKIOr2iZFcW)CB7m;30KG(XY1pwnz
z`xD6pu(&^1>d{VDm_$5xGd8BI?6PSvEH~8!Z20f5a|_0(BKGUn?QJ|0kpa<5{C(>}
zRq$XLcnOv`SeFSOn0*!WgRi!4EtpSGK!EsWii+o)Ex5hCy~d<72EQPXui@~lN`2R!
zIvQslwTe|t)Fe3hpSPrkDuI&P;T)xfRCWnt#wpmDQH+g@C@Uy9cNd`m7pJB)O--?%
zqMucunHBmSvj|v4)%v}Rqxt7pLxS;>xD6Cc{m~dIvx0x{gUuYGC*Hj2xiV-2Z6iS)
zx?jJ3Ep^>%&!*BXg{-{9DpSJ?8llkTVvAwG=K9A_;gkmA9aVAAcqAvjhe;u$FU6|I
zeI_*bx_<-##<^#3nhvHFcozniToMCiq>k6M9a>00Mcd$2Usrtv)7CxPv&^`EXhtw1
zA~3g_;F-1zEf7S@2Ab>xOPngv)xL+}Gpc9|Az+h{#u?TmWt0b&AbaX}m-nZcldd}c
zn`Ua_;YjH-tCk5w9LSE-278<1r=#}E4!j>nLPDy?Kmd`jQkjq2=C0|tNW`l9C}x$B
z;S4;x<o>r|7SlsKN>g*d5WMHn$-pxyLBz)#Vl=Ka9-AK(u0bRywaYd3hq@)4>p#BE
z`RCy#UB)Q*=$<91^Z`(l{;|bn2Hz8sHLyZLy61UZR<5}pgIP{wL8K+X$EQobO$?jt
z9|mbkozvp-lM+SszY@gEAJ&W<*t}HyyQ;zYAHo0$e>JQfqXE{!rAuWID>R?kqeXtE
z*CHo<^zzlK4ZCi@6DKEmIjQ3q_14(nMQ2bitu|@WoO5Dw6v^M`GF)FmaB-51^mACl
zU!~@Q!ElXCmP35e5rG`JN(lN8-pBtOGhym0bbKh%7#GGg9j%@?r%flDng1_3i-Q9y
zCzFj7qrZn`o?@XF^AKz@Y?4!fx;j3t<|CmRU&~zWCo#B@^g#wg{9g<Nq!zJyPwh*0
zcEh4Bf>F^Pw}Fx|{QA;XiSyIbXo4>B0qZ1W;4$h*JvdtW>R+aH$SN)lt<GDmT*kCx
z@HYRjNvcu<z|w_&iEBRwZv@~eONN^`5=~M!qW%w?2E+sN18FoPAOo*;((ZZ60%bbB
zqt3@l`vTcIN<2v4JdPgOmT77M{43pvh!D*ZK|&ynk;@|*Us;La2e>?t;D`cU^`sq{
zDeDB<coovnm}9(uVOaqkWS|TTo{Hi9Fu=&(&Mikj$p*96I#(IE<jzv5RDNUpZ={j}
zY19T@O;%mJH#Q!Ow#o+RrNq?wCWuJN?0U|mVx;^-|B@u^z}x+0KdPg9UVYFg4+OHk
zjWRIQAbt5ppWFOzb{hT`B7&;0b8mp{ElVG50jgOmjZ#0Y+{ffiP2_(u$PfoquxQ0S
z^D<}ItRG0V9Fz$@v8W5>^=AJZZk?P&TFZgwL*uw*5Sv+<VRS7S{$mM4(|?RHq?Tco
z!>A-U4XAkm1jZpuYq2HlJd1R6G=%=+T)4Xi=Eg+~>ss;x*}i$~>NhK={`1lFI5&vy
z7JB<=^Y`sAYRlvLy7ky-{$-|KKp-;JscqMw55}}31Y%#;Y5wJbU{(-L!vUIp>SSn8
zo29w#sRB#f(i1O13ixC}l7nc)jJbwNNJ)Xj#%vk}imoYIlK+y3#0wk=d;(d*Dh+-~
zy3OkNt{l4-qbj{m_|(+m-xn>IP-y(-*QviyIypIg-mq!J89Kc>IC$a{5N$3dPmlQ@
z{`aO!sH-P_j6_{<tvBm|0M2L-qc5;(k?yk%6Ttd<`Ix!d7KMd{k!4+&dQn$tLgTTM
z!QJs}V!wwh!vj=WvFmE5D<^+Y+t(`x6k&Ua@bu9Ir5UaVjfji}Q+8<a!C<}AZ${!A
zBbElz-4G#HfgF0iKlL=DG!s`h<Hms%%X?EM$u;7^@DT$jri|{-#{RMH5IocZ7g`xL
zdZIjQEFiGS>^ejRxQ|^T`RKzjKUn_spdb<9T-bMSDElww$lw9V%xHI>#2XvVhf+Qh
zMLJ4~MrJ7ZP8m-3(Q7i6kx@VHTTFf6U&1w44OX43?GiQD6KphlG;r*q&Kw*7Tcg2)
zPEJLeg8m3Dgo_D={3dfHbod^i8!C1{j8uy)NQHGg@(HM<Bi|DrF1K3R)mKUJn>FG0
zfkr32*H{tOmlv;(Js&U!cP1a>Ow=T!FvrpUmwyE_!l?~a6tF+pnj2iGDgk_x8<g%C
zvpK;TDYavQ4aqmIn9nBuW=C%Z028|A=hWL}<!*WE9m^anYGF?Qcm0!r0*zcmmPOFa
z5)DM;UB8%4JS-ATKNtOY2;Gza?F!bEgQ=q7cQU9Srk4OxWSz&CF#Z=+(Lm6CbYjT!
z(R-1p03>GxmlKP>`1MDaAke<(F*pnKfsRP-*<YIZ=Rk%WsNAT_JiV)}uTKmQ)1E!E
z;C~*F+F4cgWwF&w`<0riippv7=rxWFR-*x17mt^CEZ46)hr%vTJ`b>EGp3YPR>m0=
zMFN()$HvA=)og5RJUyGLP3EeN8;q(RJ$fWptm!qp@kCyJXmcdv7_;ZR-x4JE43>!x
z_I$3bQ(IVA`1-YOctd^t5gpk{Oap+vfKCEfiGa7e)Vvbd-q3)5I42uR#BNXv+t{SB
zSn=Is?|60oWdQ}V!*x?hd}YYl&wC?Y08%?wX&9!Sn8ow#rx;);A!E-4nwy*HfS)Gy
zyT9vFv&=~I@$nfO8{5bE!K1Z1cRWZf;_du-JlEp9>&F4>y?f81NWcUkZ{I38t0^fN
zb^4w?uIZeeo(|2)U^A?@7>KdW5Af^_M|Im8%@TB>HK`Z;`2KzP!3LZYaI&hTiB`9#
zitl^w4-XGZJZZ3<u<1TY>d%CnB8Gn4N}Um!YJR#z{-nixw$kt`4gx(6BO-I~&{sLZ
zT(v1F*Vc!qsHjx2ptD$%^zD+!f(S|yb$oH8ql2Y(a&q$IFMBoJT~C&TUzcni8x_aN
z98V%8U_PVbD=M=}74Z>9y)*i&LOYgOszSkN_;n_&t^*H}*Vot0_LAhA9T)VBjoH0K
zk!?mZUCx)hMx<+bHr7}?H)Y{gUQWHBynMGL!vybgG)D-(#w_b|p>)*hBad<?zts?w
znAq6DKo<f55G6HtRwAs<a>$v0bI)tp$M)-|H|r68-}dMAO#^0z3<Xb1I0IOOgyy}-
zs2D<~@WFD=wbj%yhfsoq1FU=-E!Xk|zbkQ};E|95125$U9UE<DW@n2E-z_Yl7czeh
zeG*<w*}I)JJ~2U@yqyzyELm!b8>aVhFrM70`}!MAK;d0TjrGWd$Tb+b>-OeHSb4}?
zjVb)aSsgv`>=~Ze(l3kIn-2SN*qzuV8x(VXbu!_n9Lcm?oG7;YrF6(!H`qr7HVngK
zW@8Jl;PHQ+{3TD+&uYtn>0~&W&Vu-($J<mEVosA(dGpc?bEgn=Vvgto8+wWENdFnM
z6`+$XS0192G(^F1{M{>cIRDB4pJm+dT~?2mC}&K*Bz$zldNNek>lN8^KjuK0w@GwM
z{K;a=n%J)BR^M<Pg9K27|7vPJ4kg6*3jzvOv~f#kk5O#o)SDEh^Mj?mCmF%EORO~=
zp!2GZ4iP>SV?j~TfUAq+X%k>){AVoQ+Wg%4w#63Z-<APa6(GlS!DOj`YahaaJ)g)n
z!@0H5ax#A3g&<UNmY0c1KC%<(Mb02YI;ZIYJL!g^nF<)OZ0u<sogrnA2!0d=A*~zv
z2>?T9`7H!fe;E%dMhn&eL~S_sLQ0I=JyCC2HN{k>T;8b)1RV9C6z!31Ss1uaX?8lV
zNuA32R3iA7AGYmPi{Bh4I`812PKtMW?9JXkXz9!UoH`^z`ZJWBl7~PNW$c*JF#MmF
zG~|;d9=T13GTF>b54Z_@Ks-WD4S4J9I+&xo9;4BFfmQIFMBo@Ms8Ia$d%;tQl?O4}
zFIAs2GPO&I)ytD_nRe8O>U|m{cS<$Ib9e5u+vg&sQ-t&*f~L1HT(W$G@JJYdXsena
zjH?}z7vZX7#D_ZzPuejNMh`mAO)xl~$xnsES2Z>gT#rq!DT(54a6z8q((yqT+Y+e7
z$5Byrl<oqle!&nFYX3=;5bEn~dAdx*k)i%qz^Mf>v{C70@cv4-sgaY;H4COTPTL2F
z#W4%d@ir<diW*CBv(pL(p5=RN#vRywvcpB)3ca0|-(b)6(acV*E0B`rEP@fGR3sj|
zAeWAju0KOLbIqKT^w^Z>HqhW48kJTL1__>yzGkg9ZYRp;?7Aq*WTE=5r$QQ`*-jmJ
zQCO{V<a0CT6i7$AIr89TkLJp|5;HU8K|EzsJ8ygQ%4~nk5&xf|eh3MDFyVb@P)Ooh
z%TWuif!Wmc<wVc{!W4V+B4~&r8IWkL(!a`8_rr40l3Ol;5P0e}Ec-B$4PmQ2tsz(P
zx@ZHT!9;S!!khl8DpDjDRRMyCC^f%@A?YFIj2cJVAAa;ziU5Wu`~J>s?duhd7<O6I
z-9s=bBFT-NlDBi96!SM=Pj|8vVsi=iAbx+^2Hl6*r6>a9_$eNi4M3TU->!bKD2Nu;
zL%gxstyi)0?L|Nt)8M^tM&9F}NwOTb$*gl9^=j6NN%SqMUfUxcpf<nx6xU(j6<&uu
zw=EpIMAHQefd(e=f|NLzguiAQQ1VBjWbe0}W@aWAG6i4KP5lTKK=LnKs!0&Q`W}1y
z<m;>(jd~9&GP&neD@HRLZenXa5vNI9PrB<1yoc5AkNcuCa#=2XhZjj8Avic-!{<DR
z9#eeaskbvelHcucigKTRgNku|0$#!%BaF#jd2<~}UX{u}3~a34#HPqHlY8L(Bxdob
zAn7{KyLWgV<<sk{N5~`n7>MC;Un~JlpvM>b4i*=mD#a5gRGA9NXQ)K6(6Vzf>}y6-
zM%g%z%&P7vNj?_7B`Q^QII2uX4JDJHF*novT(4(~j)+o892%8ejj<irXJw`}WD%a0
z<AB3*+}Nu`_?4jXeqBq1f0qQ6_}P2y^1yT!(mSXJAA<&y3%F;~8#M@QCTltzj7iS#
ztr8~y_J6^}Q?<`2$K4`a+)Z-GGAhb4?z>$W1%1x@anZZ1CtexrUUfyqk2mUpv@6!m
z4ZQ`Xac60B->(mYIQuY?B%)Cf+sB?BcIQ|U`l`=j#fIewxykL9r&Np}(t%;0*O$Cj
z(wK@wuXfafj1G#%F56eG)r@2yg8BYm6)6U?tu8_;95sE=K(+L1D0}L$Mxx4?8?AMZ
z-Z7Gfy~6x>VnG}mGlGJY{W?+nrbQ((IDgFSj381TJ}<maG2}DDa(EE1-dq^IeK?7P
zByjJ8@>B*Joh;y5(bb$rL_QoyD(-PPIaNa34uy=M<f{O@usV9>=a(4VPAEULy1n||
z-@`jcV$Prz@^$FmP-&<imUnR1<<@h!AIz^kU1tLuvA9g7RqIg%u71U-$9uYTVuf)R
zt6e~Xr<h%hBzZr&j|*nXQmdP}YxJ6<EV~qq;L!<9mAX#6Yp(hrDry<33Rrq;;0O$h
zvr>M49n;d<rjJMV+RmgRlCncM0tJ7$L+c=>vi4c+DE`d^ZB`r{gAFE0)Gp)@20Zse
z;vxb(_q(#QFzc4YPNlexLgo>s*eoVTxG4EPp!=c@rAp>CdpRor%e*XAp2~+_gAQ?q
zyL4_^$m9D8h8~Z(_bGff%1=1c3&AW{{CX$X=#il7G)hxZpQez|m8lEQ$;9ueaHG~d
zTC<I~d9(r|+0{SylYV-vJ;X+-6`k+`>n1m>e65W6om8J?W=`!`QCUcK`7ZGo62-Ie
zX*(6OPBfM42ygE=n53-dC<3UBe2tOaH4>1XAt8a)r%gxtGaOw(L_<S6k{E12dPi2~
zMv#_~VJRiqQUdEClvXGxD2O&gCE&Oxjb^4YeCSdT(@vLjxPH8C2i{+3Rv*`k@SkLp
zlQ#6O>eE0-YquQ2@-Ir14q%mBU)N<_ZW2Ua0kS-v5{kWfeC9_R8|77zIVU{`l>k{P
zKvEsYadhzGO|AlG@~Oz$v;cc5VkwNOc(T1Ux@ltvn}`gRu+R{^gQ!pfo=O|%q_;Q?
z^ICw!v8th68LiYJAqKRNm1WMLOJ%m|g06s>uRSS<W1Rge`C`WL=alJ64>B-fF*Y#S
zqnNi7kgbT(^k&tpzzDGpCu>O`1G?OIrhQJfXh^9frjJ6qxK1g@^F+yyGY^f>%=T&7
zkZQkoNS`1PnYjoB-bLNPw}@tE5fL~Idn4LVV&<185%(eyL&={LNO_Z4ei-;He(RH^
zMXX_5@JcQBUapt>n-+3z5D9PivH@2o&oYa%N8q=4+X#RhX*&CZNMznF0Q7J#2Ju~1
z&KBB<cB#DWc+S&hgAd{6alOx#DWq(phWJnM)kSFHm7RN^)d=xPM=C-{?u_|q!_{O_
z;LFoYjCwsnSZ(O=nd+w+LZ+gptmNTIV|F5aap5oNBBu(Q(Gy)nzLcP%?ci=4yGq7T
zJmC>k7>FKoU<n@D>QbhAbvRP|1u2CkHBV=x>s>o_M3z)S7fdrw5w>6~7+i>Pgwpq5
z<+?JszrZk9lC0h*M5NB13xkc;Efu(tv>BnHT^NYV<8|=xwRP}N3Jz?$Q~T9$x&=uh
z&&&eOb!eCB`qv_ipP9AyBd^5HSezw-D7Fq~fIU{S2JXhhsPcq%Mr)5kn^FZSAHB#T
z?()>S*QXXeM9FW=_(2vQCmwq4J%|_vu(RalJYeidn!NlGC4MD&3R_1H&cLdU_KPVL
zH~^6>Yq{#u3(}TZhm{bMo4lM5zwL;YS4VlcDY~q8fvx~#8ymKNf{`MTbQd|HV#_3k
z*{l^Y&#(mQZ8N#n5a+Ng(p@Ls0fE5B^^S4KG<j{k5gNJXSZ{Pn;(?L73`fp`6Vwf#
zhClN}5*6_%i^{4}e}HlbFWNYpq2p|{YQj~K7=Y!`_OwhS9RZtI#SsN_XNvCQ21}d5
z#nu~hybDFkMY84g`eL#QjzV#V)I^#k!cC5=u~kK8FPZ?F;7txJNtzL3_s$Ar{IgcZ
zAqRjg9C<nD(V`sZXpMCbC*4duyN3XWYtncyI?Zx2-Yu(%>}LGqQ#tNaDk<W^J<M<B
zK5ZgM!b;z+3yHr5-Fy!EM8g++GxjP!&?w$quoMx3P@sP-Hej6oPKB0DhLh~w1$V*I
zxIDcUi=Gd$sAQT{XM}W1306WbL^eLDhnyd>j>o0C*^SmR4>TDqf0{Yy#~hME#-YK!
zO-Wx!arX2SwmI*@`_{>+(}4~s2r1BFJD!Y`Xbp)yXyD?}#v=^vm?siBr$OoZk|X$!
zR`a8K`}{%k7_4;!Foj6OLR=V~9rB0~6zU5ifEC*cKBF)z32zywAV@^zO$#^2FUNjo
zQy{<FdA^LFrBovP?D1*UWH4j42ywvjcDkHCg?o*+!<ttDu?X^fjASdfwFIaoCL3FB
zvP?gDLNytggSnhI#+Q~#rCu7#WKs)IJRbt3DzM)}#3*Tx%|`9JL%vXYATRz@Qm?du
zM-jd)Y6T~9Z13ogclkFu20E+5G4iB&3vH-KB|VepgwpRuzZyqo3ZwbOI{1&oY+M(~
z74gMQEgdBh9Li^505hG<Ikha0_=3Nuy+dD1`aYX3mbIR0Ih0U1A{{=nZ2o)NhE8qC
zyh@}PV8mpXCZdwQn%pLQbM%6eyE757)>8o(XO;9C2ew=M;4DZEbXAl{A>?{>;bQ1O
zofWk@Ih@@?!)y@uFcjqN@Ps!oog|pPn!T#sPO7IC@=+JaLL_%t<fd%H(4hgr<?3$S
z{xC?x`@TSD=B&&5yCyQEX{JpgW`uMtxq&zF!i~_*cuFfAAXoB<WxI6_)$F^tvf$k;
z#fSyur910LR;U@b$$bLwfch~;!=ML}Z4ykyGz?fY@K4%sb@}#Q0n%OV3^uLS3-E%!
z=o`f!1!!O@)lyX~wOsUG?c0j?EuHI8b!^W_XId#QS!W_j$w7D>$CGsBAA)DGW**>(
z>tbYRv(uK}@&r~H)GsXL2-0x0wk*QOXsPwSw1XMxh-5|2JyMa_^ok_#IM%cj;ohoB
z1QquM-kxyG6$|fHg4Qe7kRC(d!h*9%qCA3SICu>~rxxzGelvT^>r9{W(jh0pymPx+
z`Zi~{Cm=f2FRp_q&xIC)nq1If<UqQSdu=FG_2rA(2AQ5ao1Tw&L@^k53Z?XJz<`Yx
zWRtniTjU{S0_$v^zlV{0dnxv2=F~fLgpf`C5kRxS`U5rSs7>m&W?wcUdjLk^-^(1n
zV<3xVAyNyL#;5=p2&CdN6`{;_Dq>Ot`z`y>W7AE74$$9)$4MN0%%Q0W?ZD|MpmDL5
zCMLp-TODA;AI@XzH&dxUcop*sNYA?n<+3nr>f3Ck0k;VFE?HV}S@9SQLgA$)_)I|*
z?0vU}7BNVqg1PHN=u?=e^g4TeCN}WC4AwdK@I&K6U}P*jIWwYi^f6L6?Oi9#3n^ZF
zbOHB64=l3*4Vzf#J?S{p_U)jqvq!3o?e}0)Qa!X}hEv>NTmzMecwQWsy%RMR&S}uM
zkc23B)>s4&R@@i${meUt1CLIyHgLbqV^2opeT@JxPA^*|17uJHRs}dQxbrFl<NVxD
z#soHG*;ZJ#8TFiUe8Y~mwB-3?Kz)pHdVFN--Vx?~t=p>KW@BVK90n}xuwN+H*^gEH
zjGruJN%*l@f{&kT$uAckSMq~Bc8RG(U8UF>8;4{7i7liedX2^VZ3Hk&H|b+PZF$VH
z2$&OzuWo;7z=S>7iuq_~o%IM2SS<^K6=P?4(R<ADJL}F4$_%^SqVCH1*Hc`SBmc|0
z7+5*9%UL91Aa#73QeGR-HAd^UZP185la7+j5*@xcV{A+aYx_)jo$pb3htF5Bfp+97
z$q-!}wVrpV2x7+{`jHE1spm+BfX@-K_11U7nMjDF@syCY@rLKo{2vmyDpRGofksG>
zLsccRS6pa1%<J&*o)oo&U6558Hpmf4bSQ3e_!bE~S-d#v!=}rM>z_mJY_p3{-VpCX
z@Xja{M{?3tNn+HdJ<6K!ms@s;lL|dd^G!9!15<?*Gzo?2@6)(N_RF59>?=#5Yv&bx
z7pK$uEYI?4UrJlM`4pE5JgmJ%2g0eCRz!?s#qft!NM^`2v&!<B5Vgb{Fnh``Vt7u(
zaM3~F84QpeP!Q>6&^5t3i*mW3Lcd1t_L$tMgN81OJlK-weT_fGs(XtMEOA7Xnk_i|
zyz%PkIuqt|=*zF#x}`r1`(i>ANn^>)+jM-0OfI*>hWy99yC4vzE~y0&8U;3+j0GF-
z3+{d)DpEU%f>`6c1i*{?I&J>xW$2KpTSKG)=+8h3iVd=19f)MY9(*hT*zgG*BL1kD
zDWr&IW^f6KGvANs?fDep9n-rTYfCKr18N~FK$t#MQ6W}WkGsXiKo=$n$lLYCd@}=_
zxdERNj6{5&{4gM_xNWIB65Pzc)uOdjX7+v{iMAv0h+CG2m>U5&RTrD!kPFajuz;H+
zMTocKxW;VnwUM_*@e=ccXZE0(The3UJuHU-L1J|WmGuICx@5d2iw{xnD{<s1bkWR6
zJdQ?(+5y}opWpUy3eRDS;3Ns<(OjHv4-2i^)K)tzQj)?`7s)Q<UktrT)?S4kP!Ah#
zn{c7?f-V>;48<>2!?LonNEBJ$bK|YbM<cf7X9*&48hd-LWxU)9{zhTLtm{{~sY${$
zTWyR!#oGSz=w!Lp93k5sn1hebifzeTPhl7(WwGY8#vDD1Y?S_WR}fL3XlIP}Eh={b
zy*w5jo=1qnU=q6_E-tJ=#lvfga+Bj1{(*?-PgRE0%W`KP9tp}eL&yYn4ef?HuD*^~
zY@_8Flgx%Z>1sdhB2Qr}ebW))()LlWZ)53!(jdxHfNwap_bL!0|MILRsHz=NrOR8l
zM*$r-)?CuH9+i)D*|g>9By7DZMu0K9b^S*HqcjPosfR?$0kfAPBoz_v@pMMuIljXR
zJ?%5%5V^ANljs+TAkj4Yn<5?ITU(i4Pulj*TJ#0%x0QO5kz7n7adK@oJlPqp%M>rd
zyRrFQ&`d~+cB;u`qxsp>QIqC<G2$vo_qkZ*urdHhN6t@?7)9H%#IJYMV>{kcr*U{O
zn>c*+il&CfVbI36`SV*G2}dcX9YkO%BfVgxLTq!`<Or;8Uh*VgKIKNP@f>Z9C=+uw
zCKbvCxU)FWK{JO{p!Z1BS-leqbAe$z6w@z|(;ry@uH7;>ln7yhh@5s_K$Tlt)c8A)
zZjLKq31%l0(f#C&nUgRCA###-Q~kC=gQvdnD$jQ}G3bhp;=xg)3`SmCP3Jc<#9D)X
zH7{e4gUOpPE}RMT7xLPQM&w7%(kLYyqF!OD07g@i%k#sP!$6wGMDvjd9gW<zsimun
zjl^QrxV(ohXa`~kbiSgigiq(1Kh9?OphYQW#_FQ;wCTK9cp=<{8qqU{aDYtJ-ejGJ
zkpzPS{f@CR)~EiJJL`1|0-8H8m68KgInv^jP@-1J<Xy5l=&nVp)6Pk$2|=R86`+J0
zg>`;6{SDL;`(}naK29Dmfk_j5oHG<Fkv7jw%1v;HPD%%&dxE_8b?pEQPcS9|jJDN!
zI*PsLlrn^_!XbLH%_;7KIGs-j2?-B&iQg%`nX77+k`^dRjxuqa|Jt_*XhVr=cJnx1
zPUXjF@|JotU+X*zPl?k6<4TAKZ>%LDV@n$XlG&*gy;IHlbD!h^C?Zn$sd$Ay^L`gc
ze{xqiCLscDn~(&~%%W12Lyvpf_LirR#f3%uC!M0d;p7e0|G<l<il)8ThrvosD4#Cz
z;G(Wde*ThGwgq!80K*z^udCY9g_p}~zpdhQkh<J2P_BE!O1qUTPbE3W)Ar1qdXN!|
zM$}gY9>#?|8^t+fTMRgzun3C@T#F!fFZSR3^ng1E7e^VTcs_ov?f~bfeqTAcMb_(d
z)kJ)|N0uc#Uv?5ChXoy6^!c3YUEXIcJ%;1fWT~kosQ+ZS!%$@6_=hfjG?WU-U=Qmi
z^D7Nx-Nobe3K~`FHZ%hL=_oJ}NoHNBn1i1qkrrBSQ=5&@M+dK;h;Tol5k?nhKZ^>_
zXO3$t|3bX3!CMHinBq?9{HPHou<Ttd$ZKVI{5^_^N>8Ehkf>XWOK~R2wv|aDvBmF2
zG_KeLRpR;%!U!rEb!HTx^DyakDP81Xk8nIn)Q~pLEj(3(htOzcOC`A7F(jHdtZ-L=
zo5Y2YsPX2#2*3_-!{PV7foaOlNC~2=GJ~mHgbBvsh!jW|t{QEd={A5v$QMK}?e;cc
z5amV4$@A=IYi9Vt2{WY5lS47Y3?gxpg>h^A26(9PI+;&p6pxH#nCdeL5IEn-QwI>d
z3>18@#{98T5En=h0T^6BA@}9g;hZ$nkGf2efT3QjZ1tBMw@Amjv{-A*RZ$$YE>BDM
zSe$t33>G^+wYle@a5Mr_r)t0WGGb)Lf4|W9crX1`DX>x5yte1iI48k|X}{Tfzk=OS
zW*MHa#+g=#ygWJ@l>~JNCSf}$+dr}QMuaD*+#}`X;0Y?L#ZcGu_T@fwU3Z#|vhV@a
z<C8v4Z56kue2Q#6gJ}&Sq~)pY=uj6zjv*@B&Sxx32*bODQB=Lr;7s!<Ub6OlvF{`g
z-`|cqZCkN@rJv!fPLLdt;Qej^MS<H213JJ|Xmx=5ZJ#ny821ZK)R!yTNKmToZCjoE
zY45Gdhpl)MR-^a9x4I%BqWmbwR_{>F8rzc6<nK#Y_F!8FOvz*H*Dh>$gz3|NEOs4~
z=Y8O^r%B?E_86Lzc*ID^uCJ-Un|hbSw-m&#w7Td8SH(V07_(%DmOm7>_faW`)u}1D
z-*1cuMh2ceV*E<2_Z+`F6gL$OTUrDv?`%<^7D79)#U%hXa*y#5p{G3_je0q-MTfZz
zy7*#wl03LkXwDZVx&<3H$DQn$HrMPgrocA!Uq7(utC8}j<vd0|zA&MlO)G-bjSmTG
z@b!WX);`6}@q9EGCTh}%%NwHXnZQ_5Xd(6%jh$mZ$PoPWCE=n0E2{Y!of`qNnBOv9
zoTErgl#ADP@DMV%9=iJNgJmMB7&mt<aA^@aWGtr@UThAh0UDrBCD(M~j@gK0>54a-
zrx9W6k`PTcM@R7sa~ucjvLoB;IalM0d3%59<@mBJqKnTX0s^(5I|qjs*JC%~!0etX
zX?Oq7y)pz2T(b=(!R)|@wb!H{_&+<dM)2R0LCJO##1-eAN99}e&kQs`v?#}A?J~A7
zU=TY_!_NnsJ*5~%@h`H>26>a176QbABVBYEb-~em<Y{08qm;~-y6zOE$03+Q?;Gf9
zw=>EAl!@Vwsl65=^A!<zNmdt#W;S8Tc4<r#aztN%-$o)BGBwaPe8eWCEc?42^s6XK
z58Xl(MD`wa0-{4PKpGuK*ikdY8?4Yn>Q2O{o&?4JX~cnSp=tnzuJj>A05eBCmE0J~
zZd_e^qVzvS{a>vj5VpIz(14>E%@utx3;vbL8>`>X`m2$ufDXn56NW4@{8wrESMO1@
z8XSF0`Is8A{;ALZ=M+jHni(a|!N1g`nc(5jc1KMm;U8Z7sa7WiCjgLYvA|ycGmf8h
z7Nx+G?(WO_voZfmKKx4w`CyO%N_hL<$(8_3DZ)!H!iTJn|Hei5$bQwJd;i&y6S93*
ziO)Sxd;Q=20l$VjiCX}e1+M)JpZ=#WOu`+n0FW^L<E_zO{SSYAzYXW_Ua)h<Kj?-C
z!{sCYIl#K=pN%-~@T{+g#9!6G{|pT$7yeE0Nmsqze?I#oC}FrT{(p!m_DTMK@eW4^
zWZY>ie!a?c=6H5K-tMIM=2?LWt1D0U^vACY2!8IHw-=!d8}Ft)l7B12Q9fK~x0RW{
z>hf@bKmdro`=a+JzR1Ysic$iHIg}dgw(Wv8hk?eMvnsigz)H(sjEB2!v{myp3yc3~
z4;U$gMX1%(#G|5br++|gcIJtw+dTsPO};xGK|bDb><6XI^<NyLO_Jys_+EDzE8Byu
zr>_N&Ulp}VhO19+GJvTEZK%DM`=1g)%mJ{&fbwrK{!%kJse;$-XU;P;Igj`rWT+Zd
zkE|=4C8xY*BD+uKrsb;Cz%<65W6AYkhL@>2$Ih<XhBsR;y-H^Tcd+rn4~{RgW=1!s
zIqxZ!rl$6r+&#Xuxl;+LjE!-=8J)KFIDNaBoxUaWcriZZ)v&Z@6vFY4{bT6c=FVm&
zRv~LGn{Q**o6yU*yma9GineeJ^l2WO#QcK1u9Efekxe55UatE>vhl=gooU3_#?|GA
zb|dPloD*XYj2_zaJzq-UioDY+cy|Vp^ZP|5z3|^!Mw=<&=e5wha;0Z&$*^1dWL8)g
zut3pt_{4Y1d(7pvueFf1>4WRn`>8-aztY{wy(kmu?5oDB`bBQO<7H*P+aK4|v|BZE
zH>zexwNrNfTT9LRYM<Gywet<Vx_vdnyHCak%eP*#%(rR*EL9GdCT_eQdo^=xCW@>4
z7;pPwvqikUe!X%%c4O>!kCTIq?Pe`3vBI{{n?Gv9O<6zCW(U*Wzh>#?wSbA3Minq)
z;k4tpR5s8)`>u9!H=H<taY6BZWWDfjCCBkW6!sOqxvUCG-#vdrs9xrA@g^Z3e1>l5
zx7WBpM8FA~YB;m)zTRr4REtt!!R&75*ngHxTiedb$RK8|wnnj3sCn>`fxePCD^A7J
zL~w3?p<>JPn-S%EPK#N!=PVmzjPFJ}LcL?H=lc~6-hms0(fjsizRd=GxRT3o)WG^$
zX@+>?v1d~lX!|L?+jfgWGd4xP=4!rzQ)&WbBW5(^j_TeJxLU0_6B{7^R_ADAP;O`L
zgv0moh{wdifF{%2?@O-hUnp&xHYSVFsRO*%=s@pKY(1}zuBm66W}k?jE$@<gMGvo!
zt{1t;>Z<A{wX3rQNXe`>EX)S9>_S1c_a3N(I9*Dt90&%zoHM`Oh-mOq$)&0JVY1RO
z##pQw-#-=f&`ltxNLPI$-@kFAwUgR>ZN*aGo`^VOm?D(e`)s&p>=kcpn>}gZkN3w;
zjy@-@$|ui<uvf(W0*|W4bM7XD83yVkNF?&e=h2^Gcz~9gs)OcFml`~5fxX7pw61eL
zV>$P^+}6X;sh-v9skXWddaK$8I)6hTeHsh}nL2j*)~Tz-N=KDreG}##*?s#a%s+Sr
zUmid53ooA-mC!b$JyCmXtP=FC{+KvBjizq5p!-Ut4{guDATpozQSV{?43X}=k#Qf_
zH)uX-eD7?=pKF9KjlEJER`}U82YCy(sq*uf)*ip@0K@`(`oZtU<D^^fVU@&F(Q?z#
zW%rwG{(<+sPtjEeCF9fQ@ong+jP$F%V9qfdRHL_BUmbKg+qiC>ijA>tAP`137(B`4
z#%v96-|?4MPaOWH(us0wdlo~2@o;4sIb)+!mzb0PA%2vZoZdS`7L0O253*)*r4h3N
zy&6z!!cz9E4c{~KJAOqof<n9yV;F@i(f@cii6gK``-x$)P~_RJNWSdVOjCt(lAQO+
z@z^VSzT%QaC?#*NYOZP~Eqa4o?8RbZ$JfQL?>t_48DDH$#)?NOP>5>y073{;oM7R)
zw1zP8IhEYjn-Aurd`PC-_g_s&-5ll$J)MxLID7eKvu#9IK;ZftEU%e0!E4^3O}cPC
zB8A5$fAIB<^93w9+y1P`<BQ{m&e^F1mU_tkjP%d`QVDmQ)nazx1G>kOzr&4Wd9%wG
zo6rei<M9-Iwcbaq^zAzOD21-LsHAba3GVU()qRgLKqOoOsY?Lh!*>t0mvnRmtGBl|
z>5Q8=`cdB88m5{*k)*Lvt9E=m&|*px+?+Qx`cb1BbygCdADVx`+4-H;p<7Uxh1FKc
zbG+q+)vJ-SAJRW$^k^<B5ABHccecL>dAGjZAmqZ<%Nat5yK4{*0W-lp^O``?0MoB1
zBP5yu+HH4pwT>kI@tgQ$>4bytR{r4+EIp{!V{O4|js4|^fhVe)0u@nKg3He!ePFiy
z#`V_3ys*;2)wL*MBGlW@$2%KLn|5w|D38J%NfGS0l4tVXqC1K%WsaA($v(fm9DkI}
zXRvg0I6EeF9q4vuEOl>#S!Jk@09G<L$7&)FFx$41&D8n>dEvDmz2%)ULeTD1vq#m6
z@Q-S0p-Rm2d-30TPN1_Jv#-owOsupX-X~Suu(F=Uo37WcuX%0SkXglpj!cCA40REK
zRFSj+&4#koA2F6j6nfj!NqkN_hMA(@_6oxR1D+ucHWyq9JmAgANfw$FfcpncFTyx{
zISjTzt?OO9IM=z&p-a-Iiasol47}giH?c9ZecQlbyjx2UvP}cE6MMQ{M)X+fPgIFR
zgLshdC2j+gGT-~So9DBaHNK4XdNrk<$((qPYOR#)kPd^>j$)v^_b}JDrc>VS+<2aN
zV<UBn`rez-?DUGPnw9$jO7K+ROrpECiupGd{d_6My#u`(gZavM+i!Jmrbfn=vhOz!
zjahKhQN?2S6&f*q@N5EYS+}wxXuF-@47SNb^+tYAYa%%BhI)-{D1SR<NF}Pj?_~-r
z<D<RfhxQ$(PENNEYK$MeR&Y2UZ6%I9x9Hlw^JqF>6qyxT1WX-TF0Q@0Z#Oe;Fe;dh
z)di1&9_?t=Egw$YUhwp%+hh<~sgMX#G{V#D$>#@e(KD^lfL`RB?riSdSh-FeO%)Ra
zaZtH6vFo?7V6*ng58{-KAJX#ir+H*9Hl=?&_|ea^RVKWm!HExnim_9|yWP|VQ0-P{
z4>($MgWTTv^2K8W`S;+l4ZL@34sg6a#GcbR*Yq&o+U*Y7JCo1<@yPZN5afe)SFfYT
zp+wvUQBs~Kzy1|i!gZSwV104QuHNj~OjRKi`KJ2j@m|o)z?UHNU7km3WBK0)o_Ak_
zRf)qo^lpy^#pw<3Ai)D|U8P4&?-u69A68WOXg%b9nYQfak{FF0a@)`{x%+iT{K~8X
z3R8PCo|}_a%u3=ZUg!Kq{K;}KY;LwYZYIpU$#Hl3Wvg1eI&5{VS&iy}f#8&}(B~H~
zEFzYrGb(CrrgO!wYfk(7x2mhBNB4>IE-E|vtE{z6g^I?!uB+Ic0-YA_=Qf$7(z9@2
zoe1@DJz&HS5kiUx^7_#h<m=a0@^Vo8x(}V?c+a`*6RisKV4oZDw%V`oSq24Y6kNO^
zR!{UF7r)MSTt7*&`Qz+<m*z9wP!f#A>%I{EPlajL6<y97#846vuBC5J3ImyJ)UF08
zgLbL|2Mk$9kdd$74un`oN}^dYGH|jS<PZBg=JS2HmZ})B^*<Y2NU8itFybgGs?kky
z@9N9z^P4UFd|aDl7e&PbTbiv0j}Ht#!c$ex;RWlk1c1s08~y|*TcGbIyNk^ju2H2c
zuisU;E%lH0MO`HU*4(7QQQuY;n}|~M>5$R6QO_Qv=bqGfi7K42vfQn&!3jW&bM}Qd
z%r+WT5yc|qZ*`4@tLZn8=9ku9q=u;%!6n0I|7cB+^!Aag?%PxMv6{GFfDlH4=PXP~
zg6v;a43sk)#mY6K<h^XDHdDCTTnQlEF-N=EdmU7KUwEs%_N^YD0H3Fa%G=R#B{kel
z$&~&68CLjIVh_NCCPq{~eq8nBksL@+q>pVs5BXV3eOcYYll<%yl#?1ikZ~M5s)nvs
zI95G%aml0<u2aw2n|AhcK!romrYpMZU9Oqv0d0cwk@?Rjq3Tfx>VjYJpO4vu31EoD
z#>Vb|D0f!u)AN7Fm=>V`;m;@UhBhYhKXwIfdvHCP4LhMeWeSLX*Kf#{(oo0o4nqBi
zgd83XUT`Qru_wFnf1#KVo1gcYm^K-8lrn;J<LEP;I@KM{3bCVw+jdp26p!Dlo<a<m
zoYy`^oU3)VZ}t-f8$7IU5plAw#5ceGWg7_KSO*OQ`L76`HVbyr9@x1S%|AfU)EeQ|
z?YfsA3;nagLjtD&uq6=kn{Wk)68O`LEi%l(uN_|*N|a|u4ajXteQ_L8-{;Kynvh3{
za7+`Flld3ggzTd(3R=(9Pg|2JURP{I2KX3C{EUx6H1G=mSbQ!ff4ajJAPR`JAZNVz
zF3HdlhdTlx_rT7StEDaRm56_0g1-<iOaqSRqG<a!{t4$aCE@7x-V-|3KTi2Sr$7nd
zz^M>?EclQ6N$9|bnh>)vtn?QE{p$cj7M{>zmJ(6>WBvaCM|vE>J5;&OU;i)5TBPBi
zmnsG)@t+G(WRT!g{NFGv7`G0H>UU5855ZhP_c@yaycK^)i*^TE_FyuUX_}bpab6%E
zmH4jC5w5h90WyrZxYA6^SLr_A`ROaT^6e8dGX6&VA$AN$w@q`a>az!B1LN8JQH$2W
zh;niTg(FY#H}%n#45HVPHwPPjy8AovA;><v{LN&EaNOYdgB7p$tN5EHI+<T1HaBD;
zz2!aYkqkipVypm<n?&)p(CKS$efCu7LyT=xob>aU2-=Vjck2J({Q2uYITl5UQd63M
zW0nn4NQeaP_Mt9|QUu<?o_$$sp_P3Bx2@QnGC)C~9K^?nlip~*^*}}hXz&T5P~aDI
zGfYsv65XA<W(>UK>(f^gmW}dCHWY@>v{HDdGR5oWbizMt?wk-`VBsPQJG~)M2Lb6J
zT@FQ`8G`4zf2MT)j?kl#K^DEAIoU>DeGwpgVjKP*Xv%*afN$CjX5ov4cLn1(-YL?T
zg!-TK{n9U-Jj8I^Ot?il#Db@@xTN4(E%$`C;?Ht81jK$pmG9!%IOfqm=O={!E(#b7
zuwnmeax0isqJoLHyLJkO+L$}w%U&cZ@A54(_a}V+u9XsTaCJ?nBOl-Wd*bQ;scUNc
z4FU}RE4f7?6!QJ!h}tV2R)H0Zx&#s8ykG2x%E9F|1Qy}^(|1mfqlxI-*1jD0WngxT
zG4&%Eaku@MG15Q@t}epw)FDiQ*e($DcX)dT80|o|Y81G;#EOocqC?nUD8Ey@{AESK
zJfKEE)I6rS%dfL((<Suv=gPES;o;-IQptiZMWJh=Vr#Jlo#}H_pzPY0&lpGk5;|=t
zJfR`8$Vl`nsRUU><>lkMUMKE$7NlUdQ&St)Ru?5aV6eH2R4g!Ce=(9q{7LaL0^d6G
zH!@J5ks#hyXw_z8`Z+Ts4Dbd0FKRWqnXLl?0zCM}!psA@<uqERzwQ_c`K<T%zxb4O
zk`V{N&-)b_Lz@uofK(4|I^YX0;HFw46=(8Nggkzbxs0U3C0F9%!>e3u@hR`B>h=bN
zEz^{zdf|I^7eD<XZ4@AXDcP;YK<k%xfHFdD$0^D}+}zxlR5Eb}Bdn+7)F3?fiBrV2
zuM=`06F-p+7lQ=)QRe#RfnTF9ijeU2{Z8C{A*&LamYS-gr$@v-V<C!+TiUJ_-&#<I
zbrim?h(Gdn%%-Ur`FIWMj>vFvpjb=aEmd9kFE^1a2{;j-$QKvqe*0DnD__F$dWOB`
zRxQVC$3a&9!QQ^?NMt_d#4kCKD8s#}rDFcvuf<2vWFU@=#}j#?@`+Rt7$$A*Eb%Z+
zH(P62vma^Zh~v5xuK;=>P?b9`f-4zp8BDj%UzhajscUMhSC=OX%}!1Z4julNUn4Qe
zeSLj<JNwyIpr{`l`Oo6Q`{_M0%zrT_8s2h1f!q8v;@A35uonp4=$I_qIPZ{_mgbrf
zvJHXyd}n)2D|ET>|DhQKgoJNsEn-$fLqV-0a40*RuhDUp&NuI~k)r+1hVvo+<DTj5
zQsQ6OmP-~+u;s32L;Wv;duXAK9~;Zd%Tt)t8R_ZGFq~aoU2CiR{f81@pB^<F33$$Z
zPWvSlIc2!}Y((_=v+OPyKm;^t_x!RuQ(=C?M;32|SB2=%WTG=>A0Io5R&R3m0Gy>e
zd-&s~-t*Vv3h9EM7H}aD%>u{AZ}zjF|M_14<5)|&J|!Bs&Vu{x&E2s`NjV(0PXc?^
zb(^iNzRE?#h}B5nu^V{jCLl?pKa+k6kS0`jcXyH7tCOm#Dwu|eN#O1E`4E31bEW8u
z!^@bBA`AV;<%wTbI$h6<H4W7Dp5EElqHK6#G-h{U<n6D-Xm|`PnNB|Z`v8(UyfN0)
zl)9YtM3{!wd1vv_nNr$klrQB`B)`-G`~a>c=6;V2el6P!QJ|finJFP6MmG1zSYw7H
zW#v}P($cZY-?euA^o@5bPUQO?Eogr6uQwM~X^4=5@an}20%GDQzo&*>=6KA{xrQ7_
zN$&GIe!DWafqnYLCQEg*RUxr&*5-fA48#KU)7Dntu6Dk#=ROHzPqwHZ|5j+ihw|Fh
zJXHEuFT_rFI3J3*mA5w(H~P!j`$m3tkNf3H!IpPa`@0$N{?<9#q?Kk_on*rgYq-&|
zv7GrrUf!Rfe81+oAg<Z1yWkRLdc>bl5pLgpZ4f)SB*P-pN&oI~;8PDD9tSzMk+c1k
z^7$*glbD3_00ons=NAiqqrIO-3d{s2Y|UN3faoV-zYN!J^Hl(MVpwEGHb3XsFP8lN
zi=zf7qi^R)E!+Qm{L|A)!t25myp5y3*#8&h@B>H=oQ$Y<OJ;_@NAq7_hRVV48gsI^
zesbW>*s0)@I(E9RenlzWO-oni(p)nr|8#Ns^s)>eeLCjk9pj)@r=kA81QPJ|34$8e
zJw3aWG%YxsT#Sg5Wg*>R$bDD6<irHkWGUQ7MRzpgNWjMp3@0tBRGE3DlEK<Iv8zqf
zW;M*Y!Il##{&2SIv@6LphZqARB;8Zq!?9+#qGXIJQzc6o5l=z=^$Ui_eU34ML-J<F
zhE}GC;cNN^0p?5(q2`3~;a%RcTU_qW1*_W|I6<jB$v)(U_Ha6Z@aG}0(b5u}zrBsO
zSYmYwxp!C=!jK*f1}`ZOkmCxl@<#M$6qcyA>*zYx;PmPA7Sd4fS19yxmN?aFCOY2q
z?xGXhdAB}(xw=c~9!0fqzqbOe1aZ&cttQOC$OCsfsnV56V@{E3tNAnG8(-@0tmZga
ziBfe0d8pejoU}q&So`ihV`Oyh5}lZ|plPaDn4kY5qe`CbsD)vf!7Vs_*yZf^QWQFU
zSe(BZ<rrlAQD$ln$PibX&%{mo)3lS{=~p|Q$q0Vfu7175QhWDTWw@y$!7FW>M);A(
zOycgOhn&xD?wv9CQepcBM-+0Q$IH7w6Sk=zK?ZLORfJUETeRR?s97k`xR9M|)SGR3
zgdmULQpPnRt#T7S(mpr!AZxsdFYiff<OEL@=JIrS&{b+<W&L}VR5xSu*6KzHngg~j
zz>VdUb?*{0qjP1CN9B}9WzSQIMm;yZbQit!*{a(*mi@)V_s>V=?5!4sMh?!BH75(w
z@W@C!R|~8s;^bu|%1xD4G+p9CQVK&nxHHKF@tp3{S3_?tCTps%oN}*JU+kF}(&@;|
z4p7&fho!XB8lAt5DJH6?rQ$sb*CpQpvzv1j;9UGL{>D7pSznYr?BpD6Y;X3Ip&qo~
z79IQp=?q<970hf0jV(<;!`kx5Jg-I7xW*zk9L=9(3gbKX&I~=ie(FP&i~>M5As`!{
z*iF^f7??QlmAf}MT#<H;C;g?^zO<m39(s8*e-N+5>#I!Ua{QblU$Rr<{_9UIJGJq2
za%}!3R2G6Zs1o?g-BU#9yZW62oVlL;W>vbNWb&7QghfAMH-@3bIWGOrwKcUm-LjX*
z8hqxaCPdJO;MIlDLkuNpObU)>E5XfR{7S#C@l1hX3dK{`3aS0kXug%BLAe*hmj3QC
zZFA#GU#Thitl8yM08J~n`Q$rHgRV<-=gXP^d01y`#H0M{R?JVU*d-b-lXr>pCUUm!
zrG6^jFuE9zel%SW!WCxZu5(Y$o@TV8T)&nCFK)NJ$bB&%=bQ79XZL`UZoX$?Ts?`m
zR|Owl`fX|Bw~86759%P!+^LsBahvgEg6jujNY03h+-Tx1DZ?}(-IWyQ<ay@|v`P#C
zg`3Z&a5Wu>wB#j5F)Cx@>WyjkX)fIpCN;W`@Du9aw&|lRFA2-ro%6;$RRzI6L`)cK
z8!<YMM@yI<7dL#fjRyA$bJtdm3J@Jcf)h^Bd}$<6vKl&(&#yO=?GO_Ne~<@w;BDj=
z*O*Apf*T%SXGOx7s@b5L9qeUR`O)j;fCTXl$wpK_mg)tsrQLk+I4Uho$<iUuP@|o2
z<6+5u*rHgd35&ZI9Ie&$b(X~Ox!K=uKu4ts06mfEf&MKHA(`2LSAc}d9|P0RBwBES
z-(bnE_3N*>iqp1IOoJ)jq($%454|_gFt#ps+Ol;r-TY8iCIE^%SAfjg1bzbplRvG-
zt9TD;1EM|$n3pNQla$dVkL_+S_ns4IMkp&yn#i4oCX_xO?EQ^EBxLTu%J9OV)Sc^)
z;KeN<cIRDEo&Doudb8lMuHXt~dOTupYA^|at<uxnNQUUI#rHpL^&;5$yPg2OCQfqd
zlkB=)Gv2mwN_Re!V~xT_ws)T{Uv}V0YnAWqGT4q8&J9>1XDsj{leWGrdNdfyZRy%p
z@h!ArH?^W1R3U=(7D_k4YrR%L()vzkPsC5+;0$FQPu0zdYm<n49p8BDZ2TmuQQ0k)
z7i0l|&fUZ}{uuoFA1ozN2~T$<G&u!7>aibj%;#l%Szytm-*w0s9KXe|H`*N7OOi2Z
zdSY0C<D7Tj%J1@))VG};>s`kJn^(ZHT~qlR3i+mmxm%62x9Ruuc-0@=o6tf?NNINm
zeJ~JN`aWzbrG`!a;IiP$81;Q@2h!*}ObGb~jvgnNs>AbpZ5yu$VMf%dauLPyt9e)D
zb)Q+^@+CdaETW2>v`y%a5pfWfdBAfiJwde9q(ZFk5pk^p>Fqb~b$Dln(&B_<xA^k8
zdIc9hu2z1qgl3s_^S!iw&N$Jqcq03Qbp`)(HqoMa=MQvnyYNB|F&6o#p7y+dF~hjX
zXGZ-!zM)y-PYe$;CIlabIriGbw)!Wh!)Do29)-k-><!(_W+v^se#jy8!!-Uf_>?EU
zENlFo9}2_9&(Itmoy!OUi+hf&E=Qk4ZJd8*JxXU&QERQRn@%2lOg%GmQ9XZ+Kcc6e
z8Ew@q<Tvf5v?8w=e8^#vm6CK(@oq>!-}E%Ig<0rq@HoQ5ICr5&=UkXl*=<mLWOy;?
z%WfSb$K@U_37x!}nR(aQU{T9C$2W?yx%8xq52yW=GVf{<JUu@kH`6Rt2d8>vFgVog
zUd|V)HHY;@w|H1wtyC#geR1|*k7s<9@i_g(bN!6|InV#Y)LRC{)iu$=KnU(`!6gI@
z?hxDw5Zv9}g1b8ecMtCF?(XgkKDZCu$@6{pty}z?DrU~vt$TI%YOZGO<4XrTRqUb3
zvD(YB6aL?e98q-NEhztiOF``i68O>2MN8A5j9FuGO|y&7%08vTiQ4x`4|0N>hbb%D
z?o%@q#8l#Em>>G-Y|CsW{=LTExf)?HMVVOqF&i(Mr}5SZ8Y&Xz_PTB`3)r`Qb*W?b
z#AH>UGD4%8k@<ZIZ7vO^=j1Od)hp?LKlSBN@LBL3F;}`61t)g@a!FDo_!a9WD{n1B
z!@Z~L{lvsXZ!C=PYVFp!g@r$HadF@e($Y>S9Gpp{>!>G3GW;)>osa<pyo4@E?D%qn
z_=EfN2#(55p4OWx3@RxEOpT9CX9)(lwDHqHckrVQw39k=jW&%Xr}EsJAy<WiC2~{Q
znJEb==5l3L-J0{7PPHfbGRr!i{Ezujdv)h^Q3FxBo(kR)p!jr(&4=DEEz8O;AHEv4
zy_<uH@jgzA!NptI64E7A6FJOe+%A%knTCx=G*l_Y->Q_dt1Q{m5E9tbm|9meW74Nk
zTH7hjIwYBCSceNBVp!9<I_<?YwfW>n!y>z9mTpp<a4EbLt_uZU&Cjr@=+bCDQ8F7s
z>1oDkryG37kCr%HrzuVo6l8)|2+UgS3_T5*NiMw}f-gOy-48*dS53_ODrfa+{K7I+
zS!Ee*j_Xg3b#|O#m8H{&F$<a*#~Z-r<iuMBBT9xj+s4uBb%>3~+gP)&WXrnDw%|lP
zKO&?DZM($$uc7rquZo_Hd6nBB&C2#OyLH*M?{i192k)Z|!5f7u_qPXO2*P~~<kEd4
zhWoW}IW-$W5Mm%C|H!iED34Z_8ESe7(|ia}6Z39K=g{!T<WYZGL+zx^-k5aFoMlq8
zbdY45JJ+WcxMYdX6-@RoI|k><aSE`g#2a1SyvCLEY6b?opvP@6=@_Mv@y<jVE3o5M
z-t*NjB7@)aA<J!x7IQ#ezc=V}vwSPVY#F<d9{){*JOs@!l_1OGY<?6uym768RCDEP
z@F%8)2HoU%xI&sjU&q~&A*yI)3Z`alpZjCFNu5a+N2%)stufnZ)?uC4v|xy!M-r6o
zjkDuU;!+SNLDb`9oA1NZs^tMP72Su?@Z(}CdJqXcZNCO{l`tqqK~^_j&2Mv_!Q)Uc
zAajrwt$AC|wcg_;Y3iXwaO0aHX{?|khfYw+QA`dy<ND@bD~|L8dQd^;*c=Oi$IGzL
zk7RxDAce{J)mM1>95mSbNZFW0E7WO)3E6?=iCyO`OQPS&F*g_rOtM{W5f4G}>#QVA
zou0K4=T)@PIbJ%#zAjQX%gs$~g#HZTMvg>loogHn<C@#6+v?(qC8nC?>o4^f@K5+B
z&|HYlh1<Pnhi)q#zV~jOAE1WY5sttV`O7n@`;XvdwvMdVMPSeM*{RxqbJI@uxB(|u
zhd@nKQGH`;BNEJTcJv<QwFOZMO$a70N@pl_==bUYE`tbD`y=uH00LosFi{Aw>$Pgr
zHiyUMbS#N(d~9sO)XBx={&rdrXn%YGkISg7-tEJ`VCUoWK360&K0dy`zkhpkLta<~
zNoQ&+eW@Io(`GfaDGX`@L=GLArTEDI-99}k3rs=PJ)3#6!>oW;p!X7XTQa&8fVq#%
z4wI2f5omjwJxsPN3}SzpvN$uI;vVI8`%~@zVsl};sn+P`d+!5n@9emA&~9c9sy}rd
zUSJmn?d5xxKV+8*A_sfjjVZEE!u2t?$xDy-gqLWgUp)(rV&QciT*9&3xkmJ#R9u{!
zA73t4v8)bL%Vor68oKce=2cJY{z>@@EI4sovEq64G@EMTAhA2WeK;M5TGCI$1{<pf
z6iLo3lbnKfJ%A=-CpwCcse!AFy`;a#djEyKd2(|q-PM@)?{j*Vc>v##NtG*CZW{nF
z=xxviJDnxpUS8JtA>~un>#F`;F2@Ez`^P6`og)@as9&T7RCwZmW-F#O18a-bp(t%u
zzU0@VUdQwG^E2%NcoEn59+%3sodwSOgK)6DSz5HMWlA)SOF~C!XaYDnl&@u3k9wtN
zi1`^OCLJuBIm&TF**X6+JUb{bHH)RSbtb3XRuDX<s1zXqLAK{*YjSe(*x1<IoRWrD
z$vpfzlK>dcbKLfRG^qPb6kr{=l4xN_7MGL$u}YPLxfoi_;<{;tOdnUusnB(}$qKwI
z-C)4j;5d8$JFz{6YpQ)|`K2tZc;=6zB1?Wav{6EZE?RPu?Axom4t%OKs-GQwZHOdC
zlO-I7MMvG9M_I(4-LprSh}o%s*e#?vg8oXq$i&JJHUBk7zbUn>@-X<YvzD*+Zr{^<
z_ubOrlcKBwUIxjq4y{J$;01xEMT;Bo<ic@eGHl{5UOe7)^j@wy=N1}#^*rijeaD~j
zJ!vermYK478!x06QIogR32+}dol@Q>w@^tvOjw|mD$?USmUmYipOxNSg1s7QyV?r$
z@XEvSsr}>8zfL#kQ&w_4N`pI{oDwHe<H{6bV(3MF^U`QWSMmq`sv0?!faTe0UAfI7
zRJQxNz{b(kz(wJzyeE5~6*FyT`Mwf0Fl<K2&%$tR7zwI$@+h#i%=z51yt`)K)J|Ho
zo%bSS11vi0Q$HA;{z@u@XpglqfUZJDM)f}JOYnH$HgRj${~S}mOSG<g7awo2RatC(
zfsI09YBw6CfhlW(*sy`pVO4|bp|T&xB@+dWV_>6NsZmZJ`&M)mG8Fv}?C8tzTeR#v
zt7<QN5i<a@_UP}3L45LFtjpnbt7>gsHLR`BYL*`nB#LIgkNhSQ$>GN7cIR3l`0#T3
z>QhOs)K8-OcBR+kqgJLz#N+&&D+zH{C7YJ?hpJCyGKuBJtKU6nQk-?6E^0%q6BPkW
z%Q%ozRo!EjNyW%6phBIIB#7vN*KS9oM<R3|i8Ma{lGRXBY$h)~=_gXxa=d^9BE7nn
z8fDt_;LJ?hb)iQrhOr%?`~5J)+tqwm+|tD@upmO*e-<I#&1RI%F;`dnelKH|;pyq)
zb;Im|AEBhw&Fzan^fFe@vX6Ncx>>3AP0Pdc=P!rjBt$b~0vJjCJ7`m5RJ?UlfV!FK
zW906M1_<&VBe=AfA=ZSyozX~hsYk;yK#O{)^G5$@8aNRKTrN5N;myU``;^mMqA*#<
zqf-U+S=m}U>ub=$j@IOyQNu0SV0YgE_~GG2)F(E`a%P>`p1O`YcG+tK4f48?9x3Ad
z0M%;HszGAJ#E?ds#pMO7ajD;qCc%-=q^zvxN`JaFYP^3=nyXL_vePOMz-Asm-ww;b
zC+l>$Qa%k^Z0e9)UNYac>zifvfX_N?#7=$tCph){c)Zp@8KL>i@9}OUAWnZ`5loau
z-=6Ff5!?WN&AGB;$ah-goYd-Zzog`vj7(F>NtOdF{5dDXnv)Y`ihXdF1tkX21|_b4
zkespp5r)Zalt2$1wC<E!g&qFPl^Fwg0F52h{D>@rTI^&bEfpW*{<}cdUPDHKPki+G
z1T#jPn|w}TWX8jk*Cy+Nzbh&^_(V*zZfh#}5)!agabPW~%AsN?%i>iDZm-PX&CvAJ
z6q_n|?pRxdEGQp=RMk_oj>VrE9}DKoPE9zP?TJ+8vF2E@P_BUass*PRn>I2MDpSHI
z(CT{(+<I9vY29}iv9Q;%v}2Hx3w?WkEaLS3IPSunT>E)&<1ANX6moixJ3YF|${;7f
z{h7_)9+AkO?jmplW;dT6sqbmB|K<B}iXAgOF^L&FA&rT;rU%Tlno}p=MQ7Clm$GH%
zuK&$Iiu_AL@m1q{?<taOZm_b|TBgOdxU5L@Rr2koGOIE($?|eavGC#h@RqCAc2UsJ
z(Ab6%)${BQQ{Eoh-0J?=;tz1Av@>U@A}-w27SMYLEyX;YZMfrxO!-He%jU;PWtBbH
z>`nrkg0RkpyDem;gX<bAKkTwB+(=Cf%PgkkR)W>)^Hi+fN;A%05c-?8LFH$A--#S`
zI?a9eeJ6ac5rd*J$3n4sG;iU2n}{!_$BR9qP|h{?kyph+HpmMeG^{6Rmwq|OqvIId
zBw!YRC7d7BbMjJU1JDxuF35|o>;>a|c6#ao?0mcmZ_NVN`xiTQX`?s6usRZ<fcJ~D
zj?QL_!+xCUVwp-Ril!X?y}@?dg4VqZtIS|txs3}8@-Idh5RNGp1EXe?e-~`oV~TO|
z6kTd4wCA_S9b_`)F(FN1O>yC&%z)PVA*);ci|Q>JRI<3NinKrL9%};a2lc6bns<pD
zF6^ByhWpRr&1!ibM?ZH-viPD}|Ku@n{>m=DIDOi^4jjKlV4iva5qPTsJ0^&XRX1l{
z7bD&7@`hd_j>OH?=wlmNU!ay$Zd|XgrD(ylu#;vbQ?3f!i~_r7PB^}%!|Pnmtpy-^
zkuTCJ%az=wB9GKsmDPGg!ba_Y(bN^PtEn{8;~{KJ<$VT_Jo5X3w?g!VFRJszc>QH(
zekF}_>!kl^+Wekub<U;Z$E+{}#k35=1KovuY#OlBkXP3(Bh4t7_4b8zQztO=wXDR;
z^|D83yN~U*S+%HCLhNa36uyMu!Y*^x)Vtc+<-C2)v#dA9B(5ehzjy#&k7rlLsNHNN
z6<olAB%*cu#&vjp5uod$%T4l;l(Pd>JhzIH1<^F1LGntcybY)On(@JFZV2e5Vqww@
z6iYw@tbmSoDAuyeHLM0&toemO4>ZT-;!#ZvN<QHLfVMBs1xY%!R3z~DeJ>W-H3M?~
z_u7RwWX1!$+gTOIC&x2$cIO6C{bSMG)nEl#OC3EEb1OD&?nuGwzh8du4AJ~RC3GYW
zf4!?g8*0UjuAy-P*O0>ypf+6r+ub_%z;!EucFIR58OQnrJ}`>joIe~(GORsg=wUXZ
zDSJ-jwz)x5hhe&##p@<aJdP*Yr~EQ2K@!c5%%|O9FVp3I!@z|IvyK=Td<;YZU4{qe
z41k+aUj}nV++_yW+pAHDRjZTqrJlyh1XI4Ju34_P+Bo9+PYC3kraiCS;W+m9=*u?V
zuLm;eXEWe)Z$QvjeR%K1@mYD=u)iNvA?YuzYNVxOd+32w@K1<;pLh)lGOD8_-tZ45
z>UG(#@%u+vG~YL^Ti1XL$*AyYp*B%oXNRm5lBQp_X5V%F%D|up$p%$or;azeuVV@%
zhCR*9?Ec&SVAJDt;}#3|q%VGy_%cwzWmmyiefi|Aw+rQQ0{xQ)a#mE2L<%f&!93Ob
z;p~)eH#<N7R?z1NAMc5Bp<o8wz~~SAGDLCxtk`hZaDw%<xu+)G<qR`$aJ?{$+$RL0
za`_4A>?;uMnce-XY<GF`yb&}mv}?;#6t|8oY!tz8{M{b@m|Ea`O!8irnG(^0ML7|s
zj&#4y3Ukus29)s>@rLP;`LPFQvP_ZEoCTOU=9s!RqCOS2=Fl1C`bRs!!@Rk#M(OV9
z9B)-s59A;k;^nxggjlJ-aOsF}6f~%m-1Tu)FL1ec8Qf@JIPKA2<Zpnp1oA|oOpW?q
zY;NGdyFV5y(1D<QmBTnqH-^V{XVt>q-`16isF|svtn74mtSF06X&L~%68w@S==;7m
z7^$qJ#Qg2|crpW+uK4v4*u5J<xG;cp2Dc$_=vq57`*6Fif@@CMzo1Hc{em)Pf|;`1
zxU6H|kvk51q=zIZ-#{5*u!46TsZso$Pn|Mwy8doVz~O!%#%cY#Ha;Cvb%syMptXi}
zgE1SFx*CREJL`}MO=_d*%DYt;G_&|^wzX|)cD&2<z^I*y&aqH)bqVq~DQMn5mgk~r
z>P%1m@fWZ)Eq8OCIRx4Z^Z4AwmT#5bqy{+9&%?vHoNhjw?$~bW1-}DoY$~|tK%yDa
zR;|vy3{h?vE`M9Ue3*}R9np-HK&LILZibGEH3SzQ6uq4I)#PqDZEctvkm-N>;r-Ps
zbY1$|rLgo{4wO70+yUy`=5p;i<!<j%pFdX-|Ee|l#%q30;T}<5`f*{KT`OD_2OU^1
zxl{3wn|9b*fQpBifFw45RiZqy_SIZ+ukD*!4za5RIevQzk{VM>l`gZ_Q`v*;U<ZZR
zJZ~{m?H{ZDq)D;)=pzVTrI@aO34dtA2%(b6*%<@7^9Ig4P&fpAXQ!)KZ2#hiJO506
zMg6Ra+q;+DCe!00KQrC!3HCGV%^hO@Q#iUKF5z1yxTuV(d=*OK6Gjz7>U?;T%2-}f
z0$cuGrQ4|~YIsQbcMnWjF2p=;+>dbJ)2`Qwd{#k*+3nrtKEehb={nN3b7%af-Qc{(
zLd3sqFAu2Yqjj1a#`S{wl9wcxqRapCt=L;vsl(Y|R~Sx5_U3K8v%4pt$Fk|?;P&=A
zKV|>hwE9{zY3I(=$yu3J+4p3;QICsGL-WhvkXv<eb-XZ?Wuojj-7r4HdBnvE=UpL{
zx2k-lgQ(f=k`PUjCpW;icZ=N!<H-A%zVK@IN2RW%O?GYu5hT!J5`Oz6|0ZGi-6r(q
zsMkP?+6Mp7@JXA<j~D5)DvU4fk8+nJO2h(-@hmI)BdEVhiPO`=Dl|PaCC*+w@j4IR
z$|<t8+Znz%@op<8U*+R6nN-{%Rv!%)(-@MQ$3E+KnUmbC?9)a?5&TmLC%W&wCINZX
zOsg}^BXO$V2jJ{<Q-yTWQ)(@)vyvNgSe@NgI6)H{wafZv95{0ITaP9`dflsh_vAh;
z0Ea(xSA4#BZaHSISm345%$et?e{Yc>WTE7g^$o5m?_70%i)C^AnOnM~SUb$;68>B~
z{8Bk^!VR*b=02|)H(~`8qO+RrRvS0Hm@nY)gvdR;k@dHVFhZ18F>CWI1$Iw%&sbvR
z7}I8$on*AjBn~`l-Ufpk6@_x)gf?_-Pdb;#1}ZD{4uvmWSJ79St>!DQxi(~YwL^GX
zBKEeAIgmhuOPia>kl-|+3_@N;CNPi<2SK&kkG7z;JcCJ7uE*YeYJq)zDd1DX*?6el
zk~;$<lLpFtWI;8F=a)}z=qt{rm0-Y*IO7p-F9nOiyK+!Og28$O49MwNblx1Q==IX#
z>Ci*h^dFi7ZH5bH00dLzxR$5ZqIC;Fzf!~6t#v!;;!Xc(DLS6^SzipkTpr4#<}bO~
z;^k_sZfRyFxN7~VMTLx#wVlYZce^%@ZPl^1!UuD{rZRvz2T7r&=O)Jy*ggQ!fVMmx
zZ@bjgQ{nnfwtmND<7y~8?w;&(hf%%w=TR8F2ZQa;JF}Ai+R{(l>~r6iLc1AN$r2Qo
zJiE+$a(eZ(K12Y!kBv`NC{d|{cxq>XdW*WxD1=Mo!fbspZrQ9oEE~=Ex6<I^d$#*1
z&s+HKYm4<O3P7)$NmQ+K6Kyqgdkjd+tK!&d`_4)Egh-p`vJ^=Ey()|vQM>x08kCaP
ztaZe31WCbzE^Uf$@X~b;Uzr*Af*U)eCveDBzwP6ZQ~!_;dJ28QJRD#HGXsbvTSQhO
zsv3z~?cX;t4t3zrgNxVPkZg7y=khCP`bigc7QWZs<9SJM<M*~)Ky1kxJk~_|r*ZkZ
zJ=Ss{)2wAged^xi(EIe6zkJ4Rc*@k+#8H&O%aKhmr<`=+_W~qiGb<ymYTYjfed*cR
zC^B|h8PszJA%_9z#MclzZNBQ1^$3zeE89zd%%Vt}&D<<#Mx6#P;cgTaXs2n1^SkgM
zHZ~UD_IkHZGjrmVkX8qyCQoIj)VJZzUiK;~jP();_OPz!Mr8>km*y6cAT!enTbV|Y
zoqkYQyR9s${5eoWkHa3m%xHIk1+4|gd?cPYU12ovW)ad&zdB7VrH|2!n;8_-O>B9!
ziQU!?htzhdi%Buog9lsTQ%*iDH<WS?aL}-Nx^7!*EmMd;=~cE|@-kNteUweB(eLP;
z7$lL^VMLY;r=~pL8%5)NqK}BjGQ*(oC-Gb_kFEXqJjAqTC8PA>gI=Zf?adO?mS-C@
z_?Z@OJMtu5LHn#3?_;s<j~%^SFW+37jG!A<bpWIah}*=6UPt<J2o7A~J#L+4ocK5}
zNv!ALj=iW^%x>Per%7M0Z%X({bmTe|G!cWk?8&~>c1R0zH)g)ya-BLprq9CtV3QnA
z3{|;&UJZghpB}m+A{sQB0^_MG&*_*)hs;}1sb8&5=LV?U!dQ5;2+z$Pc;!WqfD#a2
ztzVmWs?UPWqAXUIg3Bu-m(+2$Y)_rwQ1>ls%_-4%pg2NhB(=Trk;$>Er;b(TIAech
zu5yv_Gjgt`Cs~imo?|w{QECK_4bor%YmS_f8E1;pu6;engFMZm`uoiWl7?sWDlW^j
z8L7RN7y_XoquB5s+x2^)(pu`2G9dAkMZk<Gl>VjM$|UKxHLJ!UUEV$))mrVa#rg3T
zYaW`c7_6ikyNmRPwS&g~SsdJq_;nh^1E;+sKh(p;C=Ca^t1T+yN7LKVzn9!CY*^T3
zdB~ihU#<^qXiCE9Fet<D*}n#b<IP7}bE;<9o!+-K_<L-AX-pC1H=(wyC8bk9(5H+$
zZI;1*@hmQSUX1)yrP7%71roi-(j6~G14`*dHwTdi0_y3q4m#@O^PJkZHiEXdmlH6=
z3Qz#h?Bmu}kjf+IPk2yCl)9|JU;%;huBEqP)r{desRGAR#Px2hrgT&5B>c@=UGJe!
zgmnT{R*Ox5E{mQ&YTUv0F0MMA2VHgX<!$+ZbySqJB*`7Vnxe-M4kPgx4p7}Rvix#q
z$s^%heYAx})zF&%YK>PmwkoWgg@ywnka?%t&S^n~TOL^d<+Y~?XoDB(x$TSYdyH5k
zt5rt3D`rKXcod}atbzBB2%jD_x3zD6=J4Rnv*z)|m8r7ecO<&$I%PS0&Xbkh!kh}|
zB48Ho*W;Q2M#To!8K*75NBA?hdQU&Uf6jL_NxVzX<C#2mtEGRud6}PmkH8Q+DWAn0
zC3_B-AJ3q!JQ9~l_>)3*#dCo$4I-qry87SZs2ApeZ^jH|;oNCrCj0abSB&B<>q`tv
zjOppD7kS*MWcW+SKKoA|^|Mi>sbYqIe_8<f-7d5h#cLO>gEQ{7#`x_M8S&Ku40?Wc
zOL{$Mc4zr2&h9lTFB?+rf<Zu)1vP!_z5J+rPqQr=7Ex+)zv<1Sc4k%_`EIkJPP?oP
zbGNk=93~ls86Kvx^v11-9UFjV#&k0WjXFJ37VjZIMbpERv7u2`dR$Vim}r>1e|x1<
z=fKZByVHa{_ftoaJ|Fzk4^r+e=jA)34}k9j#rQiVcC@RkdXn+?_q~x^bXNgK^HbL>
z3&%fZnk*O%8rB0LV&2=`h4){3HzEg<6DqTFp5Mf@VR70&X#I@tx7ssB7(029*iz*V
z)^b-RI<g}L?vHq~kXNntY6SJC82a=!#$bOcNvMbcyPETYE{5IK6ug4EtMon+zgu~2
z<Ts|{WxGW-^oM#kstaM@!9cFKuve~^hi^3zOQ==vnJuLtt2UuwsCh{bS`k=>^Kbr*
zZbqtj5evCW*}65WPpFvt#vD~vDn;g(kpV`-JUOjb{8}sYZw4u+7Z(>LKgpGAdY}h>
z?@2v%UvIMc$4ep$-kE~0gby(Mb(P6oyGRSuZmZ#%CVg{>|G0zt-Hu4h_i4-k8V8#J
ziyS{kfzd}=ZewZlA&2BGG>rTA^G?)TS}Sd<`l}lK2c5F6Wk*<A=AdmevOJ8d`8lkq
zU|2hhVzfq<1Kh6LbjSP}tG?Dy&yKf>CoV2inieyzFAHY{$6IeO>VYjY6kuJmtJVxQ
zs+priZ-`MbL@$dQCFLaI?0q_HU}x8rDN(q5@PQs`0ShV7j|5s(0e>_MUXX=D2=qRB
zWLiF|PdJ3ycUAD|i)+c*lgo#h_TTZNzA<qT-T3Y>GITL-C~ymV_h5xSn6M$Tn0gQB
z&jc?2T8D0hVq9*1G?nj4Pp@|m<n$UgPIQpj)>4N|1|O1r!(<YH@~37l^v5mZV4wPf
zVJCm_DihAyKSy}1ghV0u^>nsePa9R{WW)CZR09Fr>LlF19*FB$Sonqa+phCoHA|0e
zj!Clt&H{x*fL@d(<UK+vZ!m$c|F2LG&7iR8mSx<G8SK!kE6^gnJ>%dcwf<Di(>L5C
zf;m2^=4B7<ydT>I8<@F8&Yv8+NZik+CJEDQ#w95N;>nsSzfcowyW729+h^fKU-59I
zi-6><Id<=D*}g>vZ1dGZx*F+>>7RT2>K^Lqy&`6E>nQcjMj@)Sv;!?P$@K+YW<Mnd
zkgG?Tybb*EL-t5<2QO5Cq}fpfp`^NPR=Ks<?zp{dqOQ{)x!NgH3J6dr-iOIYKE{`?
zo8X~G|7&)<uBwwalI}_UL(sgZ`_{`a?ekt^W0#}RVi*g$;&{XNd0#GmOK2e^4(kTN
zv*MWTi9;DEKyYjw*?Kyq6qJr{%@%N832$3EKDHeXwqZdw?}ea}J#iTIV@Mz)BmeAP
z=}1Br#<e2dbe@;1A*7I#mzT#fx(4qOv9}n?iG}8Bc>kz(BffI@wfw%l<<_Wqzhxqm
zoMCMbIWOBtwjgw4E=77sMFxE%sSCvvETPL2gdusO00k{ffF><#*VNmoWqaD$eBu50
zK^V<PP^mh(mgMR>?e##h-RcCGYTc%*erN`4I9ciTTAgy7tH3Sze(}aPvG)E`$bz!+
z`eln5G7<FfE(r9*>6vc`^GtbM^Vq>eSr=Tw=vKOAGEU?ul|#$^Ic1L(YJ<Nh4YwfY
zF81UKzm2UDTNonleoE7)z_A+A)1t_vwxOxY?Skr@1UEqMk5O>9CT96DqDM%79h~)k
z!q?AOk(b8T{86crp8ACzzljuD5`qcN)x$g=Ee@M$SjKz4`P0%5p#LM@cds3t3LMwY
zJ2>6BI?KZ$Ei8bqW<Dns0y;qn8r)8O^JM>sj_O^Tw^7cZ(PVEsDOc?o5Xnh{7Aqp|
zO&!tD{*51tyQ+_RY%dl|3Fj>6nLRNnue`lNCs8LW^hLW8#iI5J)v_V=xul+9St}$K
z`QFLRpu0%>qEK(ie)6vnv|*5tPXg8};dOK=A;QNOobE|1lY=GU8n)$~VuZPVq9|yF
zI0*Tf@DhV*R!B+h!)MMtY$Rwe8aGdY-@Wx0V!oS@u)4laF>mK`Kl^SLQ&=*XXMaHB
z1VD6Iakjr*-Jx)UOb-$dy*Fd->%|-CHK<t2ieRwotQn0ZZ-r~}%rN|qF;+I$L9U*x
z?|Nik*LH8&*C*ONr+>zAYB98ftJe4TUMq`3_#i0-fC+c-r^~OlRulY@2%`Fz&;qu%
z9je1`ZRB4G^2YB)x-M+8S&wn@-LwenadsX<&xv(;#Q!KSBoOmfpCWmbXa&jo3D_XI
zKa99SV)W?t-i*2Yw&=P;oUZcq+yeg{djn(CuKQpVBM@zsY&+5%B@pcmKU=VHd?j#x
z67S3K#u?y<^%i986UP-#`ZL>Uc~a5z1%ncfB^{3bE2JLt)oY>zxgnG@lio|6H~Gn3
zVzLPONe&Mg)U6Oi+hcrZVlirJE2M4rG3@&A#qiV?@2&Pct1nI?77qAv`qG)|IDFv3
zu)iI;bM9c{ojdwIaZbPbUN>jkcfUaE&gB=y^`iA-7<s%QrHW&)Lenz}Cd)spdVRG|
z$F<c7luoD^O2)Xl8^hsnQklpl7YTzvCxsIAgG2NGO(6uuwPpHeh=L0WLpk~7#q;WB
z@r!-;M~B&&AV^N)i|>=&aL%Q~Pc}>f?+5DIOev@zu;^SyQ1%ZfTwWkoyY5W@H-l#_
zLzUEIo4bkBH`;)V=@#F%csMk0%QN(UKNLVJ1f`BPFDgzA4XL5QuA9#5bGrGO{0ahe
zyl!1zx??icGHSS=T$Cwz%O#{|p^=)$#Z%}zylTuw-gjyT)oU`!FODg*vm}a(=W{yN
zl+yg)FBTPo02>dYegaf$B-I7YXMOWOa?qh)1<9z}LhDmD#c1^}Z@unNIfV-dQQLLj
z8_yPLuyDP^T{buCpw>3XsZGC`MhmUQLbg{=Uj~n-$m}2iZ0p1kHZzKoX4AJ)vv^se
z{`VST9AH7rQWN>VOF`75VTwXHb$?GNWLsR+>qpF+MeE5{ct8B%clSCyuBKPqcA0Tw
z0&rj`6@nIm@Sp7DP-tF^WSh#YSNm*MEe^AZXjUCXo_T^B{J*c4{0&9v_xXwrZA60-
zf^Kx+FS?L+!zHipgVE!T8nILNs~I@IxK2o}`n7Fe?X|gRSjuLpP#p7F2;zN9Hv_i~
z_gz=@kvuEOVqg{Vq+EHfIuwFBUY7DdA^#J^QM8}&R<<ZAj}g?B7j^or6FJ@Xnw6JT
zRknH#7yI0V@P!&Nhk&=V_wA<@=21Q0nTL6;Nj=@8mq%a#qr{$lZhRf|&Oz`o|ANKG
z-(IEp3sFnDg%V2>m9$et8KiP2m*7!prS7|R7D4E`1cW2NkJ_t0alOg-N`}2<?loi%
z;ykF#`zPosw14>H(-ihdE4D4cdY#HNeZP$!lBZbD(!0nstYRps==;z<RH9(n^^i*0
zPC2uA{&dmVpQCs1`<<);|0rFNOc!3idP^YV(Y)EnD)3M;rC@pJxA!iva^k1nPwT%^
zv!;YtSf@nQ^(6KCV+%BK5GeT8rCV6_w-_4z7-og>hd7U&Dn)UB^r_Rh;Lg;te5^jR
z>V;SMW4fOk`2MI3tvQY0P4MxQeC)(6jGRKygw^qV9lZkJuIF^DZ?B>~;FMvpLH^Yi
z<svzAu(oL+I(K%~=;-o;BgAEpSIbhX2<_(Nlp;%+TfPd&Hijh3u^GXwxp!ji<fC=5
z{W7yDDzpM!CVN*RvBH{~x|9fkGtohTu;%hO9|nyRH5kwQ=L@@-U#JOfvLx17wfxJX
z#7j;monF1vfkW%|Q{eOXxQ$@<=JqDmzvm!=EaCjQ3|w0>Ufs3@GJAIV#Ou=1%Ba|U
zovR*QJ|s+%#_x<qv{l`o+>sT5B*crl2V8qsOz>CpxP9`Cx{9P0w!XsVHpy@tfBsa$
zg02rwdY6*#E2zu}lEnux;LLr%O9xODt_D<UQ!;aiN9=dT=l)Jpn<7u>VtxLc#H10M
z(tYvg_E3VK<b4tB?5AVYk}|q0-Y48B;W4v0F@Hi?eoA3_0NSv6*5oPL57<@;CzPh_
zi)G-!n-lLZ{u<e2bdqT<`aGBNWxqH=>%HY{*qWf}iI6>rpSJ<+emv%m5Zem4)=Bj)
zK1re&_QF5Y^+io2S>$$InL7`TuR+yy630#$ncKLg&_~2?;GGtJXC<fLC!z$qy`fnU
zLa;D^Jf6)i{_>LM6X!PY_oYNOsxH`D1_3$&zc{x_UKZ2_9jVYU5FneGW(=+yGWZ#p
z3cPAv6q9wc&3;jq9$#pFbxQr}N_@Q1b<zMal**~LRd@Jw>%je66=dj_7=3v;<`PT1
z&AqCUw`}BW5Q<hu#A8iZCW{6&(}Q|$==hy_$G?_l=Wnop@y#-#H_WIHIdhC3CA);%
zG!QxVGOlt1uOTB#K~VpF&hatS7jdZE%5>v6*qi0}>dU30wN>5HV|$(tJHlu_+v4+J
zNSQ2hsh)v?&4z|vR(}v=y}Z7y{T0l1?Sl_Ayc4^FvR^r-$o|GA=5Vmk@$j;>c;?lB
zOhDBSXU-w)gm;AOkHCv{<|<L$SB7JY=#cBM03VZjqWGTKV?NVYV+lF*o$tIql<~y%
zG-V+}8POs0Fu=J8>l@H&>l2VW+oxySdEvdBSG$_8>bWoWaGVM4G;VL%wpwt7d+(;v
z6AF(ifPwX{u7k2jN(4B4&3gt#f?r4)#Q5uH7$#o-UO-TLCBx5=0OGICOqrQ+?#hyS
z?+~qAyB=ryStfqIQtBqhx?#Epj|lNy=U<smzV6`aho}d!yVkifLbpinr27j^LbQ9C
zF@gq<JAZbJJV%}DQF<FWhnVW)c=x13Qd$Z_2T2L(de<5Ziou17|7_^qjk|xJ1ZNzj
zf*)}exk{;@A~?$#7=6!b+J}$sS;y206T+RMBZvY6ZZrqiWrz2FlR9gJM;_*89-F{=
zyf|yu{rzo>W-6NrgW|-%SjN10{zy<_#?2@$78pk4uZS#*pGO}0$0GvfUrflA_Qvp6
zC-ak?9gDP6v~JnDKgFE#eIIKF+5r9Cl5n?+yAC14Y3WoeWcheQGP{a@xOICw5B@4s
z4e^eeYq)7q$j|t#{AHR#ob(Qd6%!eeDvIU#)4qG17`doG|KoVsb_<eoEbydY79Enj
zheil0RUvRplvDsdEXndd`jM9Dwd1y0(4qSo_K|nGrTJaQ<zn;n42WLta?O3D{sp_~
z)`rL#nfr|yjS%n0;}Jm;0e6v6*djbdJ2g$uXJHYnAMo}0VMKw6pD<6cyY9r)xx81&
z7Q!jp!y(YQ<ouwoEHLhv(8JuI5(<A^sQCmJ&cv9#54Z2DEN}aq`kX1GGl7KNw~(&|
z?o#peawgZgjyc-#PUuo1YJ!<`9W6TSG6^uxN5jm~{Wb;>4Qj7G)rZHg<ji^y-?!&N
zUwwh~?yb#b6+)$f5+!8;hjWP#ihHm;g@w{}@;|l^w=mnYeBY{o2ez-%c8}Je&<Cqn
zB~j-;rf3#I9+h!jjO7^`C*^SwhzUt6OOheTF~_7(4nH9B;nMPX7%Cm&p1v_sQ}zYw
zKfY28+XdAsxq;IjdLppg5Qnp~Wub9m{5lMy-%?0gwq6o%6&^j^?7lC1RkZHYjLF#P
zaYgQ3jjp(tji2^v>Tz_|D^WAD&^jfM`b)hG?K;yu#i60_*THb1W9m^oEzDnm4~!Hl
zfI<jy8k*C@m>E3`4|4HPPtwD&`|X^r#;68VTdhglGPX@|ZX-h;Vru*4$4gTNKMALn
zWn0$IZp+pd7Lmq0$=FmgrEVt?88^)TWl*B}^5B!1h9}vSg$|MzN=UE#c#mBBcu8D|
z+vC0Sf3`Af)%E=b2PrX}h9P7N_`<NX&o5uX`Bz1<jAapkL*SVB2gC6#n^vhU_J0`%
zDO5Z;IQLVcEF~c))rT5Gw3YU-6m*rrXg!bF2BqAu<G!w2edf#l%<^Sw3w#Oh_&M{H
za=ec14Do&y<}>Z~=X5j=`u{(T{P&>3;DHwuDq(;q>34X^ggNK!=lV<k?nt?`F3k1`
zw@R1y+ms(4$Ks9QqsB)C51#`{UNY_9`apDv5o7be09eN?_l}z9yiOqt3IER{-hx-_
zUhxSPOQ1paqW!Gs#3&EIPT8QoY0H{^?{Ne^cMVYl)cTMii8cJrSOqyGHkyo3AQ<ZD
zaYJPzCMFp=zA_Ft&#?X{mw)LlBsnuXSoF%bdF7&{yKs`u;+vZaCnO#^3E4n9F5_0S
z!2MR(KwX7C|I}VTSfZ}1$|X#G##lk~Imu<5<8Q2NBR713TBY#+&ufSEK%wQ@#Nj~j
z@F&0x2tYnZL?&c!0Dd36UNUq$fk0+k{C1~ZkGK}94(D0|f;c=KkOO>=tEp%Xl<vBJ
zishF_0f5;%EON9!=r#rhSe~Z-8b(%=gxKEav_z>DST1EfzshV0*S2(JHD}g;ze|b(
z7Y7j&tU*c`CPa^cR^G5y{U+_Oh5R7VbzsM1_<Yp5=J}pucyXlO;6iL8JmIvTi`f1O
z6F{CO`pZ}eo09Hp|1IAX1pl`qxDJOs_qopRoOJQ5aEX!2KjO_zF5MSf8y1}oMwAr(
z84B7zLxIjFmVt&A7Se5HJegInj`dn?2VcZQILmBX)V$A7KO1@;Op1B{(rw#Uv4xho
zrEcc18kNK$r{e*#{0PAiMBQ33g43Faf(9;AFpd}qCYPqRG^VZda~?I`gs<fId``~)
zWbVHLo-yO%00dW%Lwy$&s`!2k{3r*f7g^J9v1fy!-X#wawr^%gtDJhp4JhqrFFNlK
zn7192B1UsFuK=&S62JhZ|EG)fyfA$NsqNIvoG|=gCibfUU`m#QEKjhA1QMf*D0Enl
zFj_9EJ>rk7Y$<3k0iieeDsZ#dl(Tun+ot1O00GMko2b*(Q)@fy*B>iThkP@5Vwo01
z)a?Wz-8}ReQWYeB2U~~IZ%bE?r#_Q6i$@T`OjoOBhyS+`Wsk<Tg7BGkptOs;naDKd
zOs*&ds|#fP#(MO{_Jen6Yr0$11Z*Z@etuy2;mjDvmx}89!;h3tNqJa@UI3cwU7y-B
z3e&_8t(EUcwoR@xkDXrL$P3-7CUT9{W@+RV(4Zi>J{cT|-jBBi2Q!CRSQ}%%Pb_zJ
z%_=^cdS0+)A?&j7MsSLef8CYiHt_<FYF#hFbS?Mv0p+lpub33m{;5AH7E}Xr!cWtP
zb4sZ1KZFu8^L)(_t)z4B3#;FAN2ZO1W5)Z>P>C<=NG?nl?Aqj;x_&B@X74-ZTl}o2
zf*@g{LwTl+|M@(04On^MT8AMFeA%xeG4f0F4;X)}#cbab0o@FTp>H;NBA(40oz~6~
znwam<`q@W=FGAp}U>KMW!_UZGX@rs-Z610+>Ey4sl7@ZFx~H|oj6t+T<n&03K)ahn
zWaIFuNEv`C?G$@eb8Y7_N@z~bK@x&Cp7|Sxa4I2jpJ6+FWyPIX-Q5!}N)-KX6y7Qc
zg>wws9;X%bYr5UlqZ~tiW>xQkkj<wE-|(^j4F3ljDI|TE1vy1H*l6NZvM830#TeUx
zPg6p^67=c6#W{BCJ#BJs^+WqF5YyS_Tt2@L1@1+8<Y$Bld12@;KN>pFbMkSJ6O=g6
zdVgnx^BnQCP2K2Ggqsb0letz5X+p)PID?Lfot^y(eosm8u%sWR{hY<fzmPT{9bMs=
z#l@h8b@fUZ`;=j|x6{wmmyPPYmJ!PL)Y1M`u8~KrBzgYT*w_cW-mZnLr?_d)m2Zzc
zf8W#(6Sfb*b3izB07TBm^-i8cgF<3-04rRt%yf)ohB++B4t_gI6v!9-6fP$@3Mwc?
zQquUbh-B%=GEoev+~!HOW)ed#gxIta#!B0dD%CT;&CpG6HGm~JT;AU4dmy2su|RT=
zYmQK)#$Q-FyN&3_-@1!)B6ch8Mg4km5~Bb+9DM@t+mt|xrhwgOYO)_CgMw<UDy159
z=&KjaBeeIHg<W_r48JNcn<HbMP*zE5>EJA3@eidSj9IuWITWI}p9@s|?lz+7Kp%f9
z5K@<m?s)W{Nc`czA|ZkdTlft2YKAr#1^!8=xi%}lhH5kW7&wVb29NQKp@Kcux1Orm
z^1%~o&S3RrW`(jo0;DxYH>-xDeGu6>iSLtvJ>o9>OlU{Y2R12$D5)^?z_-c@!z}em
zL>?OfbNv*4;V%-M8Ernxqq?|rOUXrLWi0F%9CP1KV~b$_Sp**xeESu9%)B-tusM#N
z8vMSt|6*-4$)+4wXJh@;^Zuw-V4p>iHz&^axUvEb>2c8K)#oqF37kc4RZYqwWgCt;
zaZ19i$^UoR4ihT;=cBQtPD8;)7viT*ox&iXWi5;8&fk^T9+>=|dWeApgX*%%%b+{J
zTRpL4I<G77oma&e4}28=sVmq~kc;|3+Xo3Lae_avhmIp?vrgh-mpFKQwS4>x)80x~
ztL*o}zj1h6|9qf?{=g%>s5Dl-l15Y)^#6p<*?$pU)3{WRJZ=Vhz)<6wManeqE7~0=
z5z<}L5Eini0Lh8#UAAgBOcGo11clN6aG`$zJzvx>lUNZ-W)lN^N(o15`gVmvT9w_;
z>N98YM}LN(u>NirY{n3mD^O!sjxC-f75W$%XpX>;qp3j;kk10fQd-{Lec7^aU;|q<
zH;+2@C;~yep1dW*0QS#CDF;}&tGD+w#kSnnWwP|Wfz(S*?2`A(rp+)b$XTNKe3kDV
z6&t!GMpkO=G&_2U$&D-KYunq(tXS<bYAv-t!O8<kZa)MTRL*yve_)gU3A|*z^Z?6e
zX#3m(`2#1JTRJhsETiXNIrZzOCJS~kQ$nY1FWiMVqNGsJY>sj!;zjE8ws_`v&PXA5
z>Iq7QbE(4L9M-JPtne+5mdg)My^MZTeOIGI;NgpD+HG=m;_Zgi;`j<?q@luZLu%BX
zw>mp%aOOZ|XEx+~{=ZxRM!TQ7ixh3>Wf=CC?GMQSKfQhV-8^7|8&6i%j#74pn%B}p
z_%0Q28F)BZX(Y;XR3Xj|Ze*jIBy-sAMGi5fnoKj7f&;KWi*;*y_AYP=sJXo*;h35u
zgdg;(oFOAn-{vUhS=Xg^cfQg8sUBnMvI4;Bp!61A=Xi90!RCMV0cHl+377pF0zME)
zjJU$X@LYdFl+PZT*Uz$=EtCnJ({)VekLx_=@nK?%t80`IUfERqmMBoV)y=*KKg$<2
zG&D3TUCD8p*KKOmsh0|1+)kYLon=-`9aJ^4l)V*K!A+V`XNMF_a#%g%^=kB^NViiE
z*kiaoX)hBWf4elw@rJ$3Zl@m4wh;Fw5APgY-&b*ybqnLZ$*cX!gV+V_?fQDWWzQ$&
z%ZxGUWOk+U9^%U1Wu_KDbXCQ{|MqvnKIN3D)X9mD29Ij}y#WY1tD5}X4js1I<jA-;
z3w_MRESYvQ&u!+T<rXUvVCQQY8S$#GDQUJUrIlkybXf0@8pMc}of2qR&?mCzU1jMi
z?4gC%Plf@3aWK+<+`lp77DYeM!JIv$Qd4Lt)utGR2H$J6$tK}}F5ykH-mbt>UEJ(|
zFR@XU9*>b6z~5&i@BM+WsJ5GJ*aWGBTDG>A?918(v*s-XSOV`)`=HmyTdS5EFpUIL
z+cEhi+a=;j+ubB~hEudVD?aU8)nwr0Tk>R}+y<@oKyy`_9F^Mhr*{e+2|j_x{JX)c
zy(&6w&SN~T83#X`v|_pThBubKT#@5S>u%EY$vu-+Kk;{ryXtPrQewLXTvjYD;lNAR
zDd*}M9NDg3hKp0J1aJFTlr?L6!yX!s$lf}dYNC>|&QB&@)1=02LpT5aDl0UyGmoq5
z=4%6P6_rmZ9`bpd_kas^T4@O}eUnt!88?xw0$D!bQN849*4*MP7B6dazjkOlX0>9d
ze~yUs9WJWVXlQ%ITomks22dbt$-tf9eR{skGm1>fbW|tLx7Hbp(WsLsTwo&Zq%@By
zcD8BNnSE&4f0ILCDv{7S%?5KtO-)TVH#cQvWlzsnFm1aVAj?g<$S88up|OJgPAfYk
zBt(dmG$r<B0~*P2sJP$2b9mKFno_oH($<PozND*he&ZRqU#+lI%vVWtimUeFaTQ#Q
zZqU(b@tS4T#g*^B>;%;^z4f>>%E@|{23+hsduUzVvaRYW;wr+ERwqw}4uEXBNjy>z
z&Tizh;->S9b^e0V%2qy4r*JkQkn)LaQr&EP3nlcb;>Cc_$b^ZnSrwQHOg}5^w|yO&
zLak$4qgk>$_-3X%Gn(cm9J~D?FCkOxaVL{m5a@m3x<0|1m;9g0?nMV@7%j9Ef#H5X
z;d@Z&ziIE;m0dRziTrFBV4E!2g^QUdffEM3e9E^D>{uD_3MmeRn@EPpYz_<z1Y-ju
zqoW4EFL-#r!RzEEO`WW)tP~Z|mv`&p19`<DIhPg}^J<KxQib$<#(#rnH&EI`l2{Hs
z8-Ys?i(78H%>Wi2deGp7PO`izDF6J92i1kBBlk|2D>QL&)Sk2+1hm@5y&-K0AoIg!
z3Dzy;Y^QdytD;qpB=ofD+@KJCN!zt(B}=nu{W|)qg43|`^0;(%!I}`45cT3^WDRjQ
z-23K<ti^!l!B<}V0bHPWdIjliUqjZ9xxq+Osrouui1mh9J)Q>4StDb9_p!1t(U|+I
zVogF_guwJi@Ys^wa|2)&Q+Ah<o~rkY=f5E1APbIeL<)?^(QpGqkQK1vJjX(wmEG4h
z>eQiHzkOu+Rsjv3P&`G2EP)!qlHiKNCn)<Z@YaPiUn6O0X;V|`%pUN*XfMbKyZ+?W
zu;aZw!$exyvXbzN{Q{WUvFS@snB9S^0b!VFho2Py9PgXgT^4<+(gZH>KlCI!C8pw8
zQ%<G}gK*L#Snlx6o0^j}q<B*bhAo!q#QSA;?!|K1p<w%5Tga)t+~66qR|MiVuXO4@
zS-3dP7I%<yxT~!A2!E@lBSIExp>K}sbavlb!DX{X#(^*JLt3on;LPpGUP=p%Q9>}s
zLHp19`26!e+pR_M=>Dmcq?3&3?wkJEIC`6q8iNG2AsYTTi=Vi2cqepAMH}dq`>FiG
zPcchxp~)Z&KG874WMpRx48~>217-^(X7#~c{K{;R<1!qN^Z^#}u!vpSL2M$dkLvBs
z9JYboDgF6zEa3KLV>ODB0`TzBp{C<!dJubA)OcNrn#p(fng@j|Bqs(%^?zlWU6mmy
zBOeg{pBz31ynn6wdUiI)u4^QMuJ$_O97G)?u1z6#O?`ht(p}pd%@U4}MFPF8$?2?P
z?^Hc8A5;)d{C#;296);`x(gLj(>!(q1(7tDK;Yq;pYEi-pl8I@N&lzLnzH3VXmGE-
z<>8H5I^fT1x+fa;e>zb6PY39yQC7vF_Y(aYa#@aVp<&y+N*+ePEk`8nW59tITiWXF
z{ARknwpC1*mdGF$!?87dgwc2fFQD0{$!vRmR<5)V1k*!J14Qck`uYY;IY7ttNE+rr
zUb7Sy<<hkq%?>s3ot6C?iV2zsdbU3t$ubBC45q;|yXl={3c!h_zs6<loL-3x`+(W1
z0upwwfvgZLB{tfk(xSh7D-J!lSHap@7Z#C|Hv`uq8#-F;>(_hotpT$1RV+n&&U$*N
zYTUI~%|pt9e|2F~Zd9JBKCH{KR{YBS`L-6<gW3Dxew)(O_S)?@`&b8yMzD`^<fL>4
zA^Vf?wM4c*UObp~v?zZAhixI~y;N}E=E~M4AV3FmPuJ}o3gmE_Up{87(Uq%5HmEDs
z-T%rN2jCW+8MjK!dWim^FR?XB{<rcw4sp%Y$SWhROHJD$c+a`xOf&=J^WpzVHo&mO
zmnJeW>$h6|A{z=DR|iV-@*?xf@x6N-@U$c0HlF{iZZJi#abGHVXml&_3}Jb^=w@AY
zd&%S^pqyhnm5DbC^xM#ym9k;eNNs$<8mFpkqU>R}DSSL|b!r)>V(^@F%)^dw|3_9%
z0SkB1<W@(w?>9&<V{p6ml~C~a!?J(`&b9RO66|whai6kWXkPewHQyFX{%(9joXfTA
zA1R3sPlw8REZ{%`F9FtrJ~?jWRJZ|X$Xa#PwmCOPg&Et2epKyRap#vnYv@Tr=O?s}
zs2#xINy8myfHr1ld0rmbZ)XjJtgI|JJAuayCz?RVn*%9HlOm<GpC{GS1>ZG5c~c_f
z9r7ePON?1cdRbaoWpazOF4jaYv6X;93Z|`wH)=S|B}K0`?pt6DD_bCzqXvJ+z1j*g
z-bwWoEgvT@?Q2AYoH}ci*TNg2Vo1Nc#S#lvZf&i*(#Ya*mMyVHO5|cUP02dR6A-zC
z)TEK+xv2H?M>>nNyN$<^nKVwnDYSfj?PLXrP@FvfjK06nr+_nW;U9=2Oa`uqeq|MN
z#qe*TAWf3Ot$g^hjqR-N<??D0IfW4};Z!7U{P)Tw^V}t$uFzX`lzi1mbfQ2$NCv_Y
z7Z!t;lY^rVy92zD^?1F0iihqz?BT+Q1%ra&4oi2hhLifY$+|rqG&3n>x!i{E-phNN
zL=(TZ{<jGZW06vFw3pK|tD1I<1nX9>s+s{b0%Q%u*lSLXjc6FL;{0%^-zt}uT*(eD
z3TKx!S)v6j3gvo9V+R`^)df^&128tqU(|EgE$j8Cx1v{{mErWy1>YviRFrC;R(^ia
z@Mn3xw!v;9CEwONYCyheZ(f%Yi!A?V?BPHB1hA-w_~yTc3&~=jjblY!s(cMh{-M`z
zFzcKHWyT)HQ9pbHZ;q7^V7zwkrh4%AItor-j)_BDv)&Y0b9pI5FD?8c9?VIGrlqAb
zY0k}KD(|NiMwsw`A3sOq5!0>rxV6>9&n?A$zSZ}-{;06Y3RQR=jkiWRswydSj^w3E
ze0%s=)N$QjYh>|j7CF^j3SIIpZa*%ZwZ#{m1HSuu0X(VPq@vl{ll0XgZq3bY#<rVf
zD<)$FU}>4S{E7HDvy!F3ZK1@n4qT{xnY1?`zsTHA=xo1Vc8cTwi)rxkU_B1_fSS1q
z?}5TZqg$-IsTXDW2XJho*MexSHJVLEqHB{%%D&#-LQOkp3kt9&Nf|;X5xV}Vcx`TI
zV56m_wf<CQ3{RScZJ6}TCaomx5aB$txy0zhucoV2b2&CvZXYq&L&9kTI92pxMv+2@
zCUAvxrD3XM^BkX>C<?0+cNf^~#sy%3501F4sM2Aize8Eh)B5aEpWVv^VW0B|<*V-M
zh(N!5H!wxw@yDTnv-zVSp;i2r21Vj_^LfQ~#da7}=EU@J;%iF3_-C+Z!bpesKUBSC
zSY1ueHVhOk?ohN83dM^%6eun&?(XjHR@~j)-5rX%Ymtq+yYnsD>ps5c{ReE;+LM_~
zW^(3C;?GBZbv3;PASWm&rdQQdCP03G9ZR6SP|#QR69s!^ZYj$jC6T$h?<6?_`TStD
z_A4Y<PEJ2VWKB9Qm`7R_wWlx2L5FX^a%(!R@Xd*l$t;AWj+9=%Pl7PD`03!Rev~dW
z(ac)jIC)TS!QKw_bF@$`t;NOp#-{e$j-kV&=8eXaU$=wx!$utYtkPnLEX5Y9l-V~}
zrg<&<RpkV_W_;91%QUx3InWoT0mdEo1H0<I01tz4)t9P#uf=EBpL6}q5$A_FDi)Op
z-O?q|gD-PdHUY>CuFH}NwpG6qdxjeWV0T>|JO*ySz(d0l!V$wBoK8V41nUzE9&i^p
z*U|*MGbS}-XUa2w=>RAo$iC-~5vN&Gdw^yKDnsZ91d}#!O*jmJoRnI(QkyJ8XSg<A
zXqbNP>?Wq!dgDUx;>AA_a@g%v57U+u7HXB99vu9sF+?8f?G43&XTLcGMSL*YY;A3g
z6c4g>d9KD=IQDP+*lj-SVxd{$d~G$aJyT#LDN}_ZwWg}D0?`CNQ)*D(T&gPdl+uC<
zrDxM_H>t1EYZR<oy7N3gnecd=gSS*oqpm^TRghIxq3%M^%n!+&^5w(!?ZIkYWB+y|
zB@?Fp9`3IL@0;hBH96Izi_t{arb&}_%W)Pq%Qo-M5m(pz6CD10>7-wcs>DG}=3$Lu
z^_5&??p0Aiw|z7bGe`Y5A|Da=V&8nu$V$KqCqJ5*?hN8HLya`RgfZ{_oka+6f0Va5
zCIjd9MkE9;3{yBWqeE)0w_dmz{p=Jezy}J}*R>=1FCPvoESKsLtFbu28X6jM)BzW(
zhpfF(MON0gWZ{{jwnC7jUq~<pQIUBArf-(J%+;loJ0VsxIcr#}o*FG=ZL&B1J3t^d
zo%qeR(Dbf>@0p*J6_JJDn8T*^@lJ47Wm^56c59IiV^_L98t#lGF$y2_ei{wu=LaXr
z1HHz;b@_BNSJD#zw)2zk&<XX7_PspWa7h`pSrWGFI^?V}Zx*xFwZ8XX99f;Q=y=@~
zz9Iaum$ndU^4F%piN76OQrw8CZ<kmAT{*2H`1WgdUhWf>HU#nb(O$iam2UmF-{lXS
zHBx)DK=2Ms+hLS>zVltH>#fD*fOm;YTYGNqR(1&O`=F4%ypt1)r-!0hlQH#?QyS}`
z3IbQm3giAIhM9|BE3e4mAUkyqxB7+O6h|~7o|v$As0&>F<$YmiaIemwnzf94$r#bC
zwt7O^JOz;k7!D--eGVNtyn++@t@6MOtUZL3i(r&Ogkx3i=no&Zi!vbktp@@+8LIA%
zYN<<UH4Mb`K@XAe56A`KGFz83r2CX_Co_;QW(6U|ftUo_LkV6ap`dWg+5U-b0(XL3
zd<qx2&kWhk;;8PcMwEogGpDM<j0Xn<(8;f1iJP7t>^elZnlm^!_@w!e_6UsYC!Vwe
z{H(wO3FajRKC$da<pQJ54#<LMJ^o}6!XGx$z+_K*kD(?N0zax(<uEM9SG&*KB<@oU
z@nPjGmNm++lTIeWmb(%bxh!wqmbc&=Z)wsXwND&UC)rD>EC!3_dY<T_AsyvVk}a*Q
z$yX|)pJ?U_DF<1M%P%An6l;iuYgSH9*FP3{GGE9%)8o;Y!Ms=6RxBG>yPrccjed>K
zn=ziIKS!@{44+YrUPJps;K5(c!=Y;fHV{~BSm4BFgM>{3u&~NbNYeaLJ`>H#j&6{X
zpE3e<y4`m*C4t9djTys<15l-1;ooq^r!{zJ56_E%<zts{7LH_2!2<xb@`fbldjuoz
zB%MYH@|u7hcu)CV%znax$2ZM;l=gF6$xlhp37q-dpvJ$iC58Z`70duGhkK0q<iKvD
zSA|eQP;12>{P9jb?Ay{pI?=R)FI1-j>nATnj8`riYLmai{ren>chB1_o$sUy0bxTv
zzEDynWwLCoiFqeM42zP8O5aN7rxz~~8tmb`8u(PCB|LdRy8r+29$X;!W6hGqginIP
z3z^HVuM_rd%jRxLYSc;&iH-#Zb${@gQ$XXNQT*>QIH9*AP?8NX0TwpUONp9BIe=8j
zyL~Rx-05?`<I~7a($-5F9F>W{+noM4NXWOi4>);RfCMC@0AJ~xcy;jiZ&4lhI9*u<
zbxXtVwcvVrr9*;00Mh?&aKxy9J0;blT<{eg92~GY3G}#G1o3>*!?gyk?@D13R~PfY
ze@6`D>w(oH!xSu~%d(d<5J62I)T4X*QsPOtiT)nJSH#S7bf8)}ag-Q*e5Z(~u=&Jh
z@*fpC8Lh7$CuAG4O9bB(jghpH;kK2rRd%gGJxZ1K3^nrp@85p{p!mMx+lm5j_?jOi
znMBe70@=8ks0!O?1#O|Z7^WnntCK-Qkwz97a&>O_sX6};BU}@Cq5P@&_XYRFd_?HG
zz6{*Hz&qH{B6k!6bF0^WNKY`(e^)Hv?u5G+b$d^17X&L9!&m>2Xk}b0%7ZB^v7&wP
zw~aK_d`hE@8#cgbI_HjH;s7QF2$a%4zs(Ub7=(_0@L&MI1NqV*s1u_#XoRi>F7YLa
zLJQ(38)PxOSN-&t4}^a!rG<d*yFHH2)ft3>7y9+WedTC|{Nj)0%PCkK0QRH2g~@$V
z7#I>^Nh!dM4YEYC5dMsM|30aNUGu7TO=Rx;z}{BlPbL^ANE{7`WM{V9Tr##2sXq{*
zNKQ|F^i{%QKuud#N_n}Us|%;;JbS{}xL2CxDos=RUm%PacA{VKn*=(pD4-1x3b|8J
z$l5PAvf4Q`=7hY_e5M#^xaPis9dv@k$&kgiI0Os&7VD{<Y-Qp7M?Xrh{40O8g4CRc
z^?nFkt?P~YDIuGCI`;lS8Ah(R6p$2QauUJgAbZ<BJ=B00UpbloqU%|Zq(x06aSB^D
zkPm<OD}n?K5{TkNDTlzhqY!7`KvO;(dc2n*M~Iw@@VeW6<!HURg0OGq#jVVwcS*<?
z>%Su^7V$l+CU7QMDd#SHGrk_YI}Y9T)L~*Hf_<AaVu&gUKCI!sDD%IIYz?69#uiN-
zFPR-V8qvw`GU#6qDyM(R`r4?Gb%4J;5QyOo#OI!@=Ofl31MoLspmPxViSbB=AK*S+
z_c)*YlD`YQ=(Wm^Y<DYJgAvLvR5>K31esNAYoh%~Lfj45>s8{<r4#brHz<hX-G}%<
zkR<lDwZH(8uT1%XXk#R-h(r>&y3B+D(p9}^CFR`}DgyN5kw$8s$-en96UIXVpkQG9
zJ`MPu9@+RlYI>Nu5GJG)LJCZMnm?GjR@Tq@6$$Usf*E-|nO+lqfZisQ1pFZvC!~g-
z1t6r*LxGDr6m>XsbQFk2|Li>G=2$y(ekMti$(E0VaeD9crof?Ka<qOZko1rI&O2jM
zfw<oYzGr}GK5Q7@ZRiHjp6{gyN&mG4sc^us4f(@PfS`^RIGjl6zDJ$ZRxJ?jApNpf
zO17fV_ncCcK$od~WkeEb1i7}^8-f_3uV<AV#{0W3q|(Z-oqQqFxbba>Kr@0)YqlaL
zAkugXSxFY%QS^CYw&%T;+3S+2E>tDSNx#%PQiv)cun&pqw@c>c+5&pIqx{u|w2%wi
z6C%%&09K=w>-x4n1i(huHKZLt12&m~7#MEl)3N=xUt~u6*myEa06xJNn;kca)X7LD
zavaDf2*>v!tT2auX-nt|XwCg*ZQhJX6B<Af*b$370Z1-d;IM&YBM@3q1EAS0WN6i2
zTol-3RM?$pE~Nkc`(HcfW%U*&9#f0T1Kw~3D>8Lig(x$z44SmOyz^anna|CN#3Cf7
z{C_OA1VFTPf<P+<zLgIavWKCGjck}Io*9X;#4|)<>jkr`HY)6GJpUO|r5_Mm^vXY;
zuB-sjcKG;`lc)6(Tz$@-#is3JU!9RC_7#8+{%5F3-^fluU&oomNKhgmOD}Sz`~|7s
zQ%~IqlBjbbMfCx}_5Yc4a1s<z2n+}U(c~FyK&DF}VjPULJ$vZy8)}XXE`{!^>Eg)$
zCt3zr8d~7pU1^-vsj#F>-hJN^7Pl1#1^vtG*M2k%Ad}M*{GU++!f8>yMI^KTdX|Bb
z5CT$~o0+QAX!80d+Yh8aiBWJ)f+S@JDS^Rngz{-R3QHTNjQ8h)asW&FCOV|B*BltU
z#n6BjN#q`6>&x0CEewBVh-~b_14U%&eggt@z$57w_Mq^9K5586J|?(E^|6N6YsKL+
z6hab33RbmhcFqopWaQlTzZ+hV_yTg^9lmq^%qKwD$xmP_uC+_+7f@j)#zCU~FhOC)
zceqTqK~`Z%B$b(vsZzVYePN{2x%O`#v1d?RoaA6<2za}SHLp&t8zTt*;KlX-DEKEX
ziX_Aqc=%`agA_o8M9|q5caIt#F=WoGsl#x-PM~y(g^84*vzvcgid3=;zIs>0OF}OT
zAs`^&`7oWKw4V|me{(<X>5=a!!|9E(cX+U-`e#XW|MrfnP~vT=P@ustz~FV$2gHCW
z;mgz?SYbK(-6u>{%}lwtu#}+J1BZ`uLMHaM5%GE45^bMuuCMDFVmMSf7XycKYT$$K
zpAB}f&ZLX}z760#5!2tm$)M~+M**WJrS|4YX{aCfUsu#O2|ci$q(al>IH*Ek(_WwG
z)b;j~qufsUXdr-bCohM^=AC^J99xUvfMOEnFgR2L#Y4=H@z=8mgzR$<ln?}CG606?
z$EVe~&KcUHNb=LTm_e2f`KxlNIF_is1V(K?nF2k$?>?Yu(prnv`mQ%e+G(Bp`}^$d
zv2o@v<R6=*<tSnmm#v1iJS&E^e?2Oae5B*I^Oik*n`dvMw>UIn@eDbzdQqhG0R8fy
z7RD!=D<|8D^jzNP^sH__^qZ~c1P`@>UVuiPEeSmxWOQ_N`@?Jn$-8)=oG&yqX$gi?
z0$5&NU*h1{v;L=LVqTDyeB|LHpCN+ywFcHX7mROV1e-*IgYB;Mx(P8mS!yVfAkXw7
z3waJ8XH2ev`f52ZI4+%CsC&mI!n8(a-03lzYClwHzaPQ<r~kwh5LbOPh5IDBL3}=_
zUZ)B29RS;AC{%Qot}w7p^bQW$$_F)jy${7(i#`x#FGo0nAG$)hCLp!*D-$a!gMMYj
zZkpoDn8Tcm=a5AmwR#&1zq{;Pd>Pml^wN+<_d{IX`TcLds6wnLoO&bm-2#=i=msYw
z+&Q^AjZkV+j9J%;zD>^Vp&FT)EjQaAuB~Ya3-=#ZbeuS}<lIspIDdofydCzm=q}QI
zlBN7dVDln=vt&I?QBiN4E3N*VPwGgek2E3*#K)Jlo7lq`BzY=Zw=ik-#(1*tNKg<V
z?CtH<8i0^wU0ob!9={vPnRDBdcj3%*2lM%o>|YuSkecER+=-PEp{n0*VAhZ(kEsPh
z4qTMdvNU2Tlov^!OGX&A-CY&A45*2$5YEod%QcZiY@D1ae_u#ZRJegmO2Zi9Dfag!
z0&E6IaFuue@k6pv&Y*mlSHd+?kW~wT0DsL@a8iU?>6~^(ZsyY0OVvU$)IehI-VkhH
zfN5;j{CP6kh?NQ@VOqO0^3*5;BZHcb>-w;M4jf0l+i@WY^8G&YdhY<;0_J%n7#Owk
zdUhZ1vtX20H+rXoFpD%F(C~MBD&NT978+3G_KnOCNGpupz~*!xV4t)BP2K65w$K_q
zs~G1oX!fJ6;9{xEyTluBVz&QVxt8&So{+aSL?MHCb~uf)_%%*9^@WV8y6(e$DYj8y
z+^55Ht}zN_krgy=V>n_|CI&5SqP3ZsnYRh|Mmuxiu2iGV`0f_WCoE?0cg;3{vaxH8
zsR|!3P*KplwSLU7?U~?Peez-#pcCjaOxg-<H5Bpr{&9jo`QE8!)}nzIz+bW8Yu>lD
zwmv1BmIpPUetvR#@&KKbooc_!<)e>GPja6N2opkgpN=}~z=C|!xGdDfx`^*a?@0fi
zvc?b&(pu6fW!heg^!ZHkK?A#tavclrm9o%2p3H1wLB0FRZNNY)1&7aW19<8<n&#%_
znwpxaNKDqhp!S!X4si6W=u!6e%_<f<IIWc@2L4)RA2I-Dt&|lGKnGt(HzII2HK|Kh
z_o!2ArBqZklNmLZ_|cIgr4{UxjxN%CKLX2^w&`)chQd?hu~(i*HZk>MxS_1hdil#M
z+P|BfAW+K~h~g|3ee4e8<3hK(hj?5vCwEnU@uFBF)>O=79c9>-SK`nqN-es5?9#{s
z4oZ0ld3oKYC_4^y4-XGHB7n@s3odKI@tV~a%k=W)zt{4iKpG)d66Xhnl0sO2&m7)h
zpWGE}r}CFmOUja(4=bDtMEFUf-wb#6X$se#AJX7EF*o;f{gOpVQPDTF(me4566~u|
zi-Nu?>C9T2#q;jRr}oK;1uQys+((ue|9?t?!VfrRuqbagV&dSpGw)o(Fk&{uF!xX|
z4)=r6nh1~d5bRne2zyfMlQHo%CJ2&2IQ))Kmn1@}WLnenQ8D>Ysu}+#`$Eh;`fHT&
z#KPYRhIpIcOmtyDYt~WsYFs03*;d*!B}i0a%g4S7YNMk9C(P-s55TJ7C&~OlF`Ph+
z9o?%(^=~tT0#s%vE@X~Rz>wZUR&F$ugJ$)$@jC`T7|RC;aX*@S80ukDc|Bu5aDP&n
z34Bv<zJGU&pf@iwdz39K0d|B6+>?HRYtMqv=F?)F90{f5Pk`c>W9Y3!*=x{M3(e-@
zS7i9V=YXkzO$LM0`X)_;D-GZVd=0a*OQ$x@xRS|52?=?{+1q#9^dgD3wQI4Wl~3MU
zstGOhh8C){*3w&;W=NjG5w1U@0u)(^zIX60Ebn*4R9-Z(NfTU%gw7u$8O?m!|IJ@M
z`Q@K*e+P>e3Tz|D6sr%ksEODR3x96qGHe$H{YdcSqQ4s-=v}wAE{$j*o{_^)^SWh|
zt&nOqOq~&>OixM3(tJmP^yzpNo}X*m(GRJmqO>cawBP@t{m0eaTM<O$^m45cGWuE+
zBGYao8!v{-^Ulh&V0iugh#p#NduI2xX3Ypn{a1t~+n$G)^7R&r!SW(ot}`RX<U#$7
zhS$ogO`zW@FYX_^^!+1!mm)#8t=MN(UQ-E{0UO4+S4Zir_*g5YOu09=?4LBG(B97X
zBFQ)u#<9R0dU?6(HCgTs*l6ZSs3jK%i&d8lDn;mdr@IiXC9LlEueAAUh|C?*il&v4
z&v2^0z+{-LxGw}>v~UKT^Jmcu!~JYFNNO*Zpo$4{h32xfz;n}G`tgcV(}mk_N`!#V
zrTw^qJltinruo{mIU&lqWb>J~f{pGzrD1y@iq-7t{F1l6<8lxMNZT{E_YZHuL4eM1
z&nw6pg-Yx2$Xm~9ftP0Hu(BW6xO94#>%sm*?yu?nw;(_r@3o#(#}CY?fn45T@sCJN
zDbPvV?Pyi7rtTpUVz^?LHg303`6oQm6T6ts)882?lstmnk38K!I*Jy>Gp;MOJsTY-
zzPLU6dRM#%vp6#6f)O1B_i{wAD#@A(C$;@qUbi^edwfiBH;E(V6<1z5LI~HuZF}ru
z7H!asK~;DTxZ;hOW^F)Bir#Wm%fOwwo3f2o21jU9kLJX>dHQ{#U8u>VFwpC`+_`LD
zyg0bZ`IUnsSNfkL`&WcOzGZaazH%!o0r)RJ$-$rkx7)AZ(E_UhLTD@Hk|(&{Zr}Vh
zJ9%tzdLBA6DD2U^cu0Gz)cSR9i048A=CwTmbPQ@7V_Pg%_my&(#x!<fU-9<sH$Oeb
zc`&L-YFXKTpK9`9Hr{Nzn5?<NgQbOnHM%6EqP5fRaTa%3po!l;ue_8`eSSl*?@$^k
zT>1KHnA<F+0+g!GR6TaDhrS8k_cIz>w0nVP|LsEc&-(B|`h5p(LzO!rrDPCQ-@(8e
z0v#+q*l==%j?GY!g;XsoqUTsrzdDsvRHdDV+Xxd=JpA6Ik$$d35Z7xGE2lR*pRMCK
zR85^oa<UJ7Z+7Bhl$AgB(iOj2LQ7Ah%7hhzKebnIi*?`c8rlR66Ru3;T(3KEq-#ow
zHmS~PsM+>aBGN%O<#Gb9MPan(JKdLQzQUS@PRTZHc{Dlh_k_}C+l~)F;`-H9M4!R%
z_6GW=^@(NlpPedu7@r>Fz&nzM1hpLgqi1iX)7lOno#f7al_sVtB9_&RG#?me!suzO
z(j$J8SIY%Lo99x}6TR-Q@PUG5-6JnTX3>UW{4!=T2DliP80TE<uOUPDm{3!oR_x}*
zsdZVFG0xz-El$e;w+*_qJ?Iecj#s72igxwVAE9M6y*7&#PnqRSwliV)H^$Iuwb_Ec
zdqyp`GlNGrkRT9yD0XV6qGqhktpDdKwpf_gFKP`+nU7nVoYtQdV-kv5PvM*7w<XT%
zm(aaVKR^}9mEwOz`?)OL+KCgfsg(APu0Av)aMWPf>>bXa`opg3vy*j!*?LIE*wfL@
zRiqf8dNm|gneLCjZ_I0&{Xf75g0;_d9%hQv0<hS@G9pBEs>ENI#Sb_O*r>6J0j`yn
z3<L{u%o1+@phjOxu`K^XF~ilxk0RD7gBQ=z0ej8*p4*v6<FgYRVbg>|PeSwaw3{}M
z>l$T6jmW9FV<AH7T6Trg#?u5z-WP)`DMm_cOq)UVh8?%v1j%I@HAOY>gIn@jjBjZc
zAWIL^M-((o>k#jhKkC<IQtc1VpaPW}qMCILilu%cifs;Uc;x4L%#U+s%AYYkZ-#19
zDkKt8vBovsD+viU4xkLl-Cs*;E<01%2ww3o1W#gXl1j25P!rj~=gx;++}FuV#}@gd
zx{{{R#l+oygUg;1zyOqW>e!%9oWKc~_-5b-2Yzq^E1v~9LJK0gxq7is9A`|RM?-qV
z`}UB3s6*|A)jT;&3r$$pQPh3i_A8}Ql+Lx?!k_Q}Ti;B<Zmki~6(R>A<AC+GVqF+S
zF(680Pf$_X>9bnepMEM>T@tJ#DW7B@n&hziZJ6p)GHyd9mDzf9o0B?&20@!e51{~@
zt~q_Q)_N~b__MJiWTgPw5LOG3_2$`k#~YV+cSG7(7Rssu)FlM)LEguTY#%dBj8j$*
zwT^qYX~PPM42mvPo#!ys#AWrsguYerqqe7vjCL+&DtYh3-5^>`560Mad8DE&SrU2y
zh}6x5+*5=gxLVx9>+i5k*~_?!R*x+2e_`#(MK1z7{VftSZTZF>n?~PjaLsakZETol
zsh&${(>8DSc;MXa@JD#O3g32KwI1jSmKlo-#pun@BpAi;XBsO7>yxKOZol;YL$?}f
ze@ymef%8`I9lE01ebXR&l9&Q1OD!8{W$=irhmc3}%u=;4Xq+kM=}(9(-k(&lro^_`
zggmYSj{Pfwk&fSdXO9sLS`j3%FrylcX|u&u6x*eCP%{<0C{K$-e^8X4BN`qW%m}tX
zWAUguVc3Lrub)QIE3%;}33&9(B4#*9P8V4`pJ#Q##4bX3>pi(HuIh%bLC-SjD(p8`
zmFhpq-WDG3M&hM&@UBOh+wCz00qUrM@JAO#|00+%8!!_9B^v-s80VQ}NUT0XegLva
zm!}_}ygdpcl=odcs@BtOYXo%}&Lkc}54d%Nz#<4<T@v7Ic8F5p6Ep|os{(Jkxw{oD
zCGKy9eNRt6s77&Ck(p@VFG{l=kvSY{sc~4^%LIZ6sWCOsV&g%)j_cC!HZ{=a#uR8C
z^qq*AZ5y%_=(c=nv0XOND_OZ+Hf;+8?XVbbxQKimf(~%kusmy;cex?dcc9-1&u5wc
zg9%;gY+#CoZF;5hfZn;D)pZ10sa+L%>e!Y2qvyM$ib_k_NY~_|{RiE$#Vu)ilMNj5
zn%Y%{AEpF7;~e69oa1^8JzDNbAM<89{RYj3zQBJ)rdUYorRyB2^0VVFu$IW|{<CVa
zk8{6BSkXPgytT7u`?Z;w-E_k~)S8#};R^lVX=cdZi4EKCZgQ9O?5>K3t4S6vJ{)th
z0<iVFw^&!dGD#_isYN6aU08oy{E=dIbUt(Q1yiRGH03rs-Y$=^Qm9q6r<yVB&*yGQ
zx{aw*>B$%!62goel&|ShaOzK!6I6-<fhbJd0-^)GRJ>Zg!=kTY7TL2u=lF!dDYeaT
zF3U^dx;AOBw<|tR-ch5wjE(siu{1|L-{26w^P83qXNfxz#2y#aSqn*Qt$a&|^&G(D
zvDtIUKi{?-NRMJc&4}t6k+wi)v@(o{pR)#yCiHICY=Pf<0-u`l47SznBF{m5`9Q-W
z6Xz4F#8f9fmNq7kyKdT!V`>WR!|eMz*&FPASB-}OmSSFDiA-W$RK^!P@e$4%)uLH7
zI6Gyoae_V96F$#~Fl)?W{b<wT=#JXYx}pIF<?7?Z&pP*wPve0X&p-zjSaPA}&5rO0
zrJa#)C>OisqfU4GH!v@ZnmGpiK2+k&fdV@pt`J?KC_*^Z)$;^SC}<s;OMf7452|lt
zM^c1%4#kt9oj05gbQ6j{hA(E0(`jTp?PYK-h(8Ogf?6kf<HyTb+%9iYgBo&n(wA)8
zuP=obBBLl@C+Fd{2&ufRzc4Gm3^<CvJg;|-31FF_j_}^hE8#80sHaa_$3=tfOlMt~
z!FK)**@5-gDQNYfT(x<+U$py_SZ{VwFdElz)<4`pNDBfIIyUBegzrahR9a8Um4-R|
z7QcZ*xNY8<ctK=s>c)R!c;D!z$#E_t*o^jryoJ+Y-QK<Tx>P`kFFvLS$fUpFJnN*@
z#6Q%qV8DsurGHpYW1{~>Rt%+Q@K88;G1A`NVERjWUopP;VY#?ACB6Vhj^8B*g-Ur8
zE~!6IhE(2T?}Y!U=S85TBwwZWX$!f}=eaT#n+}WZhJxRN8tLUB4%+T+@EhZlSWR5S
zie_{=1MNw&DVOrM&*-mfhfv5oi#~P=y!Y;^ilD|)^+x!Rn5@3M=(A>*@BT<TAKB*;
zEJy4bAwYN5?^qCNM-@NaVxGuTktu2<Ui8&Z_I4Y8X2)PSs4AIWB8qtMt2+Ifd!e`U
zlN&WL8O%qEoJDJvE_$NZ)WjO$42V)l<FlD;$UNJ8>fIyMtVsg+qUoM&-uKLMQdSV9
z4`G|HFR~+aeJ^1(r|H??>cQV2_#f2peD8LqN#FWk-Mi^fa~)dNd9)I$Q29!;VI2jD
z<3Z!Eb`XBJyL{m>I|u<EBHbvV49(C?Yj3xrY{F@wh&7qqNAy$rv_7-q-s2NjCA-vW
z;SXL-pNpulw0e6fM7zp1OVM%~uI8pp{J|EP@q4~O*KZKCao6{s(j73ywJ&!%w>{#8
zztK_eM+{1kmcW#YtU05Ne}^5NGe`?B)O6!IS&|;%7UPtkf}V38mC~LkPve)LW1tn@
zb==+T@pOs{JK!KKG0MLI8kOF^p9-}cMCmOMZZ)<4yg*KPJ?lk)y`??*B|ZuXtBXiJ
zrI9p00_o&U)>Y|Nv^=RL1^hZdWs#~B0;krO+YB9*MMvl!56y<VhcC&Kc}ky99*pVc
zjy}1vLBJJy-0OPkGdh>B5u#EZS=8~gbez_03ZzFN+FV9sG?a_AIP04vD-6_TaWV&>
z2zj~`6_o2UmB|f|onVA7qku0nuHCPr(+nVu*6kDBs6SqBE`L$IJ8F;$m|44O7MJPp
zV62gy?0IKBCjDCSczi6-N_;q}a3>pVWCE+=7V31DgcL#Uw33$-z8C31=v?1zLPWGd
zjg}P+Lili(KRnGajj_PTrpHT4jknYA26w@OvoM~ixdcADE=u1-x&>bC!0-z^lZde0
z9B1VCE1`wbTY3;*;dACLZ3ckN&~<rj8nD$6z&?(7k^P2+DB#;$oKo$)A@#yWd7&nJ
zZs7O~Zb?Ek@p|@-oWUD5ysduxzCzdcwHVh7Ur(+5tV~lT-p^<^OkXtmynPy$$8NRx
z;kt$(BE%lOZrcoz5B5BU&aNwtV+pUoA|kH4!DE*c&BA)rqLCUCK6Ft%A)aPx)kXf{
z)?;Oa!#=|)OE!zGdjSS^pLzHSn&7fyr>iE+4ZL(-EDAA%(d#{MvW}#J&GBABosC#x
zxQOdDd<Lh!5+!}i5e93j5Cs!Pw(N2J{2kRgH|iAS09(5=>QwOucX;W0BpKo>wa;bx
z1J6T&C)}%?2k?^fLp&`E*YyXrT$_zOKW&|dd_W;--ic5ZG58!|we*H&m9PjWxUl9t
z^heLz8Gjs!g2eJo<M>B{E<-Wy9ZyEOeO6sPIO_WvU4mZ7Z?T?lyCnxO!oG36xD_Z6
ze8ya6#*>X?c<^1xab=cQJP^B(zoSfsx9LNY0IGYDFPu|QN&YTl3J_4Dg`eIf9VtwP
zl@K64ie585K|R`z`faf`@=G(8s^8HYci&GvYQuGasW}P7YuEPk=tlb}EX*HFQTj^>
z2qk*i?*SyY%y4Urcgz6YM1z|JG64W?IbB_&#hRV1FYM*>ZQozV<SBFb!oY3BBbFfC
zu0-`GJ?z~4)_nSU6~U^oOUR|Y`R5G2qp^a5E@pCE$r(OsMB`!fR$Mk(2qbR#d@5UN
zwGHZ}E6Af5(@eX1I&4cwk7@Pr&#IZ9UgTV`;}}X#3y;HWe(Z>S%^_DMHadOeKe4U2
zMN$>$fOveePl6raad{a_Ycl@a%M1Fj!V7n;sA05Gp8X@TYzxxrXZYVFJ*{v^G!q)5
z0j;KEpPd2v8%ycbsJ<7qo>>3o0KTvKvrl*e_&XW*YUv^nPPA7$`x-}1Ow!W9$Nlv9
zMvA$(<CB@)w-0bV?8wJvRn_bDDotA#-}_8UB(URgwx$~G!8BY&hl<78I+}#Gti>;|
zKC)hfCWWz-QqS@@DX!lV8vB&oL|^x9huC$vxyT(RM{k*R?UHiWsG_;@J=-W}l8Y|6
zHSZ5}WUQnH;L91(%)XwSs(X6cN>p#?Nc9=9>|c(Fb)o6NYMDhtf^(g`M8!P!moD8T
zH9b^3RTAd6U!53*mxLYS)HIb;xYJi2o+S!AO4Hqzs%sBOq^a+il(YUL0{=r?_!@zm
zG`!Xcnl>mWN#dP#A{<%C(rce+AE>47H$(KISZ-`E9j&;}Nn7qnVSInt$@UuGxlRFz
zr<hG<i*mGn+(EZt_Qs!IG^uS8uVr*wA8My;i(~4K38s^@@y6@XmXHLVH)sds+QIrX
zBzMcjHe5Duv^Pxd{K@kE0BBLba6?N5+&b{ttCOkRvkoYy#d2`{!zsIt`_aAiV3irt
zt8a&~^VJL5d%qoup8y2^A2cU|0tDvJ^|Fl<t)<rFGA^H8E?w<+)XP{v10Q6Il<a;M
zt^Xm*mkf!y9{TF2-|EvT_9s<B=zV@lBE}pLAcC}-SSBA*?IEfL5!p5M^HWyFpuAFc
zxb+5Df9!b@|EO>09cg^$5fz^l;+Y;q)krE`X91PtCod*yUH)EUF}gMBp~M;<<D!68
z%z3-*<?Xh@D*6T6@zzzWPC}9B1XrlgVeKj~?)}#k&qKYKOW_XV=To{J?Vn7q8vg|=
z{sLaa?Qb~m>3!a0FC%zMe@ENk(7`HF$S(p)J8Xp;{#y;@D6=Wj3C}ZE-h|-{v#M3n
z=pi2@(}`mYUBk8Meog@A;&8`G^88rrdC{V96xnl%l!AON-DD%&@c3ZqXOZhy@=Iz#
z(}UHGg`mb>ZCqFVx>564Ywa3Y;MC;w-0k}JLxxAm-l^ry2{%W5;(flPv0`e<QwH)J
zr?8CbDVx##1@eK%S>4kGKjJ+3KQjG4patM2qU~K;yGfIV(OSdKTt{%YI@T|=7NEZ`
zFxJP8Bh@C#fe%I$Vt(%E+mX_-mNBua#FNspcJYw&<VI<B>vhiG)xc9Ng1<c)8mb~|
zd@9iGLn$ArVE4Vy)Hro^?6)$-t_i_(jNK`@sF5?%*dx<VKILIZ7EU&|y6%gm110)1
zw6^m)xiPt7P3gElVgm}4%bykay5NL_feC=-s1%GiOGgR`yiC#>S!47^)|;5pzIjzB
z-bHYGaW4LHU)NxtHI&F?acBE9R4s{}IEYOS!uL#C(KC^U&Uw0-+8c@2&K`IPt#7(O
zOB`GWN4+nVCAM{V;xV+ek}C0e-WwqyRYGPcfj&3L4lvNoq_*gtXhE>92jR)~4<Hn(
z@gf#{HVXm9Ix!iA%=R@iU2P^tnvyt~_J`hV(70xbckL8f(A~y$-w6-$9KGlMqrDkd
zy&UC31l2UJqa?KHWq`b>2=4P)4MF33U(dU12$_zLHKGM?1;@@5&YLdCCh}g5xVDj@
zZR?sxoqL6$A02NTq*m_#pOnX-k`h_Q_7<HmI+VMM{?m&(ivX3&nws$#QPK{!YDdM>
zMl!S~p3B;Y%W50fwD2<Z<8&`iNtHRB9Ai&U>Cp)zesB+6N_6ig6bc4RMLoG0I|6e8
zi|@RL@8<+cEzF+=j#G9xfi7)hWjvF%8@>;>1<Y&tn5_D^)wlJ>?uT0`Pkq=4n$--3
zWRPd44lnVVL^4v-`81;{97p&(Q}#XBXEaipsfHsZhb5+jCP>Dj1^fV1ue8S~a??)(
z6dkgv>~3!vZO-WpkQgIm$%_+-&GxRD2QxhNClejqI!beUAsfW?2x2lKKxigVE3qv>
zbX?(xCqBqo>6U&rpOXG{q%I<HeM1y)!|g{y9DH{UBi5~<L-l%DqrA}M7z{0|=A(2>
zq!Z6-3&Wt^aeuC*n*xvb`D4snU!73z{*{4g0^WjwX6x6(NnXcT?BWi0VT<#-yxxQ~
zQy-q!jD8g!cV)^sDccnpZ50TXl+k@VDYJZq68mO)(lP~8SJxInlEJ}2xFsze#dDRM
zC{s#C%5!e@ZockJUHT*X^=9StHZJvq@<__j^7R1kzWDPD&ICQ$Z@k*4W&7pUF2V)S
ztAuXBh)YLW{omZmw>7&8&ZcIjQgfHJ=oeU)-(Mc3PZDh2jT)$Gq@=s+d%&Hzl$03{
zY`)k{X4^8_+SEQ6Lsd%Aj?Wl{T<PAQeRi!Cq;9V(MN|A}$17W%2$G<Q%R*y5oT^dG
z&Ap^MKHBHv8X(P36d^?}SF!v-@souzR#M@zAtA#bNI2<rJbua?Mg@m`+LdAd4X4(;
zC-XFq71D#!S@dTnOds#u!m9XGZs7GiD0arCPE>b@Nl&U3Lq;}E8R|Mj>?vYZ&6>>7
zet_MN6)Uw1%!AwH2^^$au&SdvL|P3bgOvZIKc!d6EARjFyuZzw-TK+{IEK@Maj^x<
zmF^iRK=qFv#+D9uwbbVN$E-!wyk*HuxEbG!g9-s>%<mxer{QU^na$1Eks}`^dJ2Q@
zGlBO@__%t?Z<B#1YJC-k7_t!VNII1Yf>DULl;3VBsq5gquCIzhx9BW;`JSI>1{Btr
zyT=5Q-6z+DU1;QNur_SFkvkMJ6~rX^s;c~!?YE&m3+iaLj^Q|z?0)~AZ1_@v|8fx7
zvS()k@pyB*RAV^a!vbX2HC|1L-(T}&oX#o&?eC1%D5<EZSk3=HejS-5mCE8Mc*w2}
zyCV+y*x|O7S4l*68G4_g@nT%YKdjAOu(wRp|LUH(38os8HQZ>if4w{#$v^x9p4`h`
zY-Ky70@k=Q-64^alSWr`vgS&ewW8Ud83A$4sJgjy{P^{<2W6<TP4cI+`p3&KoYayZ
z9m*!h4+uN9&SmVa7a7?ZUuaj<WTHxDYY^9%ke1MjIdj{mEdYv=9QEXY5Qt9<u@C%q
zZyv_U^*2!A3dO>X0~<oWXd5MCFU!3Vk@s8^ufrfvXy?^1Rs6LP8+9xpHliJlyd);Z
zHm2Jl@OAUaB?8n9rxm1>9UJC>Fu<axs*Y7pCedrW;7H@4D2IjRz0cbKXUe5V1B(;4
z0e=w}_-kc)d%rS3`8cvDPA+c{J4tVlQuH~pA|K>hO6SI~jNhiG>&+lccMT;N*4^Hw
zzN!F!`7PBm*O=5$e^5M(!B@tIg&fBHmrG+_(Nlng@+Wjng;HvUp&xrykCW?JtJdXZ
z6L@HAt=gSXO)V|6?^l-C*s$RJ>=b}na&^uR%=gW<Ay;3LMf0Q}_&B;hipko#e}ZsY
z39hbG-_oNvfA4C1AXc~+X4?Jgp7zkk*yu9&K#!a}XSTOGJO*d`$<Rwk@;-wdr-mvw
zKi@$AD|~TN4v=VyeH5ptVQgj=JG?C~FMsC@lt$j{kJ$8`*%?h~YC+4Q->_LsHN}6f
zH>&=)*?nlJ;3o8zuIs_(ucl$>VFT_~Q|Df{Ok>f3ryU7+a1>Hs40vlce9Z>PQnTBJ
zcQ@v57hRiV*@7*V?WqVqz(R&Q5M4jCmDnim%Ri_puH4-9N8I~nc^)<570^&K=6%F_
zmpq&N>+JGR7lV^&)3mW=hUmLH;|ko#g;R%GoULHy{Smq?X{6(Tj@#f?lGsC<ZqG8_
z^CF+A?Jve`?gw{S9@w9(Iq`FX&Qt$o@apOaP24R^EL4j+`Ti7zc_S9u29IgCn6NhB
z$@dk9Ql^p+<G${bT);vGEUUT0x8HX)Xr0cr+v@kq-xZ%bji2YJ3tOn1<8ncq6P(Vp
zZ=N@?Dr&%Gg$Q@3KAwm?FZ|ML{k4`tr%>pq!f~GV!BDlKE`>_=BhOo@g9vAQyxzFH
zV!E=4Jz<$YTz5fv-5(y3v}CI;fKCKk3#5iy3rYiS51tK!*VF3t({OP@t}X6GJN1;z
zkA^8_7Z1K2yn3GJGkd#mcGfE-vjoF+2h&uftig$^HxAAojVlL<nMDctgM@&Qy-1aM
ztrEOCBV0PX-sH&)<>B#oJ%4z2cEW#EJ+=zouf&xuMC)CE9qcHXZed?8l>oMc{oOvj
z7di&^OXkX0raqq;TQ}@hp^8Wvd=#Ix^*I!_8omGa%F4=*4kN4US;d^M?>#y^Utga4
z!wEP6W<yMLeuPC@wk^2&(2U`#^-WsoG+qX=HAm9<E@s9!?4;J3rm!Z@BxiBvTn*R%
zY5~}w(%@o*nac(EJJS)~8;T%n^6t{YYWdM_ngA-}F>|Kf(dMbcty%+A)<^z+KN@3M
z>9M1xOB?D3tr6P}n~_f5V*TfV>M}{Re{$D`I2ZTOY*CiYZ?UV?W2gtMPQu_i{L$27
zR>bW(3TRl<GRuP27s@j(Hrzv^QGW?!T`sDqr|Ab`cJ3N(Kks!)f$k9aIM`!KS2u4v
zrYEC|3`lsb@d=Jh8zS^045@%n9Z=F!Ie@w}SKm^Y>Ee4H-r_A}%_TyIVN`J5`y`)`
zJHGKd<Pdsex0t#TeQc~B3vCW=?g7l$&n%z+5W&nb^Sv9+d!I1xPi$DI7N}ileM5OG
zOQV}D=jH(dvP`T#)m%&ZO3Jo|S>4KfQ+ji5OxyFT>nTJZ%4+Pzr}8h*HROw%Z_Ny{
zk{1aUK*#<PJe;aok->CdWUe_NJlVKz8t#|XdUxX)Jdu8>c@rEH0*SIb!r(-w^9uXn
z*N;*N^vPw!q7QW@G;SZ<kzUD<37x3tw<)HWrfRA&Uh9Nz*T@yxo0K^QU(+lnzL5Ty
z%&>DRO<%jPQ!ZAy5PeJ>j{)(d5BVa2&I$Xg2+2L>uGp#!=^8SzyCvp_fQlyLW7FSm
z74%K?7#I0i()R?NsiS97`Gng#D%6D_*oF#=T*Eto?A)JYV`B!h6-&qEMMc^b8)!`Q
z^9=3q?l<k)^YoAhK)!ZYf-A@$gv6=wg!+4f8)(_#9xB_xwp{|MWF`47Ssid6+1$b`
zq2{undKX6}6c0tRlO*2}_<M(xLjhszJ6Hmq5HAOv7z5^E*u}K<X-H_k!IF_0nW<>J
z(BuC})V|-T+O}n=?x=N2S~`7w2uF@A2sX7kEsp^D{J0df-S1!0?NZY1K=Es8%8kwD
z{76c*(RLtQ?p4bZE$V_VAhN4V=03S(6qbJwm$X;IqXZbN=$#O*<uPu$JnaTL(zeky
zjV|S21dnm{uW-NL((}6!hi7g5$#BKX3l|{g&n<bJeN@LI>YgJT(W;olGo05q;G6n(
z<5I`th2y`6K1+Wio4e(yKGrTLdp|L9cLDD&koIc=FF|;1Ge6>fv=E;N(2@Rru3)j4
zypA?AyDFmWWbv5p@uL?D<nk`tM-Y+nLz={zaJ0<RZHc5<63#<Bo!9uFemf2lq_3uj
zY2*0sT55@Cp0=d>obdQkFbkGPq9w!rnsg4M2G^w1eb2V}myi&I5(Z4u8cc>DSnug&
zYt=aDgLxuYp4#r_GV`kxGov<?2F7`fMySv#k52p6e&^7r79@=3vaD}B`bCs?PFYS_
zt|1a5!YCZsf<Q?&yuDInBzu^)klqW%Acyd1?HO}?^u4{k&OI@4@x`xQxA2Im>FKLW
zOT!w$n^l*;0-SaXZ@GOVibbx5Xv#NPwT91XMaU%hcz7H)$mbr!$f_+&=WFreiP;hV
zq^R%26r}Z;{bGDdVyUL6D)*E-P4j%HVX!cy8?DR;8g)r^X!E(p3x21e*_cjzu{a%>
z5vUZvMLU7ZkKd}s*fI~#TP8*OCsy%FOq^TM^3qw;tT-<H<c98=JYYGdPiEzZTzHR)
znr?l}1?dhl2ZLP4pJguyR~17-4zVwp>_c*aklxzlH7H)30r&!?0&GXDYGhx?oLC1Y
z4B1+BX>m_9Fj9H2v5q(G6;>C4OdzX-g>5vH&O&dG)yXF~$1k~Hx2J!6>|y<oiVXcZ
zRvjEz7+0zb2zG$TN`7R#-3J)RuHjrZ9Hnf;tlp#3dKe~~b4%nuj&@EO9Ut9l4GU<_
zdRc#+J0^xuGPd}(v~cZie?7F3XNVeR6{D3Ncf<cJ57a$CXyV*MNSs0QK)9r`-+bA~
zR(&gYFl%ESEH=fMooY?zM>~g>bEaLA0&KZ3<ZHZ*wX$Q|W@$sSJ{)VK?dV_xd;Mku
z(a#>m33^5p^+{xm$h^H`b!_bDcn~lyD!EPDmuG@5f)c1kL?*mb)_R*8VY0B5iyxLj
zpbq=PIUu2p`ebxuM6KQ|2}pp9C|ViQo6r|X`{;gqvXT-NRb?_;%)09I&N<ick?mVU
zLsJ2fWw5~&vI6*p7R@6QUVJD;PfQ!RCg;t8o~d=z2{SJ{k=0Gzv2PcG_<n$XhLC}=
z1UCfT;p1UFv&E($^TD>vXDyR~LDKv#@(U8#s9AIFW$V4=4MYwobV~ca{upv3-7wnP
z?ZYy}6{*L~ex&l@fdJpz?y<Q@9>v5&sODn_({a+t$zRZqQi#Z1_Myj7t0tDojUc+E
z_0c@ckKEF(f4t3<{w45JAns|DslA9@CibP*!<Yc<d!$-IFOIU2V!hYX5v#lF=WC?|
z)kw7kHUNG1gHH2R8jsM@HB(@!`n3^@CU>*=&_!#~NoMCGp&~+6*>3gxa^tRz{rYM6
zsvusCyXvyY6#D3SuXTDks1dW)jL=MBSdLSu=WK>`O8z4n&Mm8I;5*_JWr$U;y_4G!
zT1}L6r82H3)=~VDNa^?8w0%EA{JK}G_9%ZIM<P$oP!{224Xd-{e+y8EF4b|dz~L#2
zZX$H{Co38ee($Gbdw^ZA=cjJ}WZ;XZj)9jK*iw#najxFe%A->YD|l=mJsjC$zYvx&
zV!E)xv4v|F05Ql)`NHeE3l18vUojm)cn=<_b($t_)6`}hGE^)c??5wHPpVq4zgYc*
z-ycL%Krt5bgeEKsMAO;A^;M;oH$ID3>s9Do(;l1DeP3#fYrB2#1ElFBCfyPtu;cp>
z!#ZeL30?Z0EH_=Z5Ic;e+Kzk2wt(|nuGNrY@(k`M#Zsizd=BW{j(zwDc3WrNq|XuV
zam7?sh$;<%*XD8l^2%j<v9HRy>M|Ulst?}~X!?sb@VV^*OLIBEoDpAb1*p1$HQa+G
zb|er3rPU+E?=4#(^$ofmV3uwZf!{0aIczesu5f$=qq+$u&f2}gvt>=b>LVZL!bKZN
z-{2nj<$~LC&5y-rV319!u`$5BrSpkogwE6cLeU0Ef@IsTH3lUm(i+!kA@0S$N0vuT
z4~l&vdRX{k@xbnBEjxEKKElzJ!%9j+@>vsk>9iI>Eo1LAZ740urMl>bs9qB(j^XB+
zXGM*5vpv>2Gf#s6hOH2RAH`78;#}UME+UM_=AqE$-b5H)YC9TDQ0p`JQ<d5thvv%9
zwmhxj)*dah(cUktduMDuK39|k->6ih6@0{dX$6|{q*|x%PTDw6dKFezdR>v23FJW0
z(<tc?4FoAkbh~_9s~VNMJL+bOPERwNVm!H~sY7IBOhR7iP<1t#zTh!C_hT^4i)G5u
z1Mdl{Rm_9jJBZ5sqTnv4Rb|u5&+S4l&dU5@*sd-dOas+hl(DeJ@_6OqiCt$OHtj|$
zOQnVAQfd%h8(HD%Cq#6Kj<Ot1I|vB;uL#Xy@MY^bpN>DZhofq?bkB3oy|ZqZUPmmd
z{tRVVOQSjAl-Psu`HMV00oDWOLTYqoi(Qd9#DiBnvdch$G|#izwe1fmPp4_~BvEvm
zNw?i_t9GFChi|E>jEoLLl8UM-$mNiR!Vlzn%1wq4J<eLS{o9CX=m0b_BGDLBUXdVS
z9>oZfV%8+o(B5Y6lKFu5dhmEyg?!e0aY*GwBO9C!kx=#x#q9IaL+SMZ*Sxz$eqwOH
zopRI6=3XBQzuB>X8wPB5uQAzK$S2Da=E^BvH#TB^Y*Os56sC64$h_P5leo*Q&E&;u
zH`5}X`2qt{NR7cXd{}a@?&(>w$F=6ztEJ%i)|pkV9pqJ6-}56XYS|<QDC7y0N_yn6
zJX4ZNVhF1#kJ9@>Qs`Yvjf@8EZ{~jGkThQ<7_I19!IrsZAUhlvYC8&y#$n9+4PVkW
zZozqpvmW`>L}f%q0zRi-h=PR|%px(*s}4zgADo&8>l-|HBzJLpy?vhSXd!{~2wF!{
zX@`os_H5%qXfd)E&5a2iktIqx;|dyPRpH|0<utz(iZb6w$!GG{`2iuI60msFeahjZ
zig2JMN|!ZI*K)6oOx;XArmY4&b#^z)y7Oz|Fnzu2gMb$jE69Laj5$6xF<3^jm+f7U
znb~;ur)IcHcKxS4(e?)aQQE!^k4bK&4=ebPl{FZsAF_n38VSxm1w%gJI6rG-tX-aa
z@Sa{?@VN0;{@%ZkddA8c8Q#_Oxb7-ZEN{99FLT7m!yKQS4qb}WwWe4M{IzxMf=s~S
zhawydhR}q~Bb5asM4?sa$xS%^i|6Vim(4mFCg%65DG|S*U+MRUu;STD1Ecng#hz&F
z*e!G;0})J{{PSIh#g8}{p;}inNd+puRIN(p7ayN`d0)1fJ^h)uwns3$9I=k02?hgZ
zE<3%$RC@gm+zUJ|*H$aEF~z2b^uU!CwF?ce=S!PD5NPv$bUU~s&msB(Wkt2;g+@(b
zsGacm?mW2ivB9AHu2Y(M&cn7JQ=x5r$7kbRR%xvE2v@mH6ed%8TMSaU&&95*bNQv(
zkGLfEZ%|!oFN>BP_&enf3VI+z`>^{wL&mI(vN-1m!}JI?#wAc{oqqjq$cx>TZwqri
zmXw=6m+-`OtcI%&#%ef3bE=s7%d^#uVCgD}K>?PiVr%1&I*H#BIBi?#o*=YNPt0gK
z;juT$M;#I_HvPchI<2cGvI>$C20W}wFmKoT?)N`@;m@?u;yt@b)oMZ_q4FVoUdxqT
zq@+&x#b_89&hp83B4^;YgC-=Ff+cc*jS?;U4tl%oh;#0A$U>Lqg3d~erQfDe<Gcys
z&m>JM-^8fS4jGiLIP_v&G8(d{u3B*oyL&;=#_Ka*+I`u08-h(+)716TX8Oe+MvQAU
zo%t0*;@+jIkq{A!;<w_wx(=~bZjcKz)T?H*P5pjZ7A)MB_Z->r*rH&bn^sX9uz_{e
zft(-rT!e^EhKvJQL-wIs_$HwQw|kkgXJ{xW_&(@V4sS>MtBNR#XjN2nuXmnk!Vbp8
zP3_o<bluge<Yg>F;g<=N!51<cVm3Jbp?gi;o`pJtENxe_av??e4QolIx36dcQxb|_
zs9j?SDb2rg^K?ux$F%@i(kt@NyQ9H{zFDMr^C67Vh)9!#8VjOOYw06xRRYdEmakr8
zxY8G=aR$}lM$V<OflK%@QBH>HpD$r!3U?_8ny7eoOQ}dbM{OS~D00EfzVqemTSw0z
za=2@-Z$xp}f*YGrz!ozzk{5PTCq&1f9$ltx)9S;ZThW{d(=|5bwWe>D;5jQM&5Z;j
z>|bx}kICA$M|<f~wl4TM57a-IGeT*Z*?(m-#I#D?%pnC6Zl_hDVL!YTC_&G6{sNg<
z|2%IR6C)XIXaEU*BlX(wqB{TCa)^O1-R;WnvTo<R<b4>jSv|kWO2=pL4cb%@s$*jC
z^J`sCoa((K0`>rDOZo~)R<1_$$!NFhZuBt9uihQ!CwoaegKi~2&)CC-JtCg?@T&)e
z=Tr!K4@5fVdIg^169;c&*!?eXYRO6Bl4~-frLpudwC^(ZvD~vHGnlx+ET4Lg)rhB+
z3j4mnExU!EnrThjh{E9`QbB*ikRIRkphM8?cXz6cXA$stFwBr4Q5|6sIYRG-9@Dd}
z9yO~W6ET$Wq4}-lQ&;0XE5O0ug>xtPA<Xk|)>Af_a+Kovs$ANV7Pdm_XYhEM*T-5l
zk>{TH#6(!|yD-*OFD-;o`rQAIsc(+%vs>DZ(Ikx;+g9VGL1Q;bW7~FP+qP}nXlz@J
z-Pqrq=Q-!RU;g{8m9_7U*@J7(Ttgf0Q^3NDK?~w_GGRT*gRKY)F|DW>Aa?$eL+V*R
zxz1>79l0~B#xeU^s^C2HB-fd)q{oX<+k``luJMDjL#D;dPT;FuG=AE)h`IR&+p^q3
zdoIE7CXI0Uz#<}-R@t;#N(*`it|bpKhBqe*eS+?gAMDdwbdxQ05k>m#Uxk_@s_wTq
z$F!?~OSs-JOX*qbz)sh)vNQVx9DBMDn?()wuiHu(o{eUwf&n4ohT_A)XyFVwlD9_C
z*!uO5M=Rscx*TVy`<{<Dtrx><5szu)aa_Nq=Q&3zU{EmR_Mx+0bRoznLdPCGKAV}n
z1@c}$f=AQ#?yGuw4lt#eqJ7i1Z?})}GVmp&ecTIKKxO4g`eSs(-puJW8rY7&$Mv`r
z>rn6Y>Ny7Hl{09x*;#geD0PsMwzv^~hGMh0#)&nJ;WhC0xg<1P0yCsLDf5W{$QS^(
zUXV2^+^%o6l`zi)6i%x4&J?P@`~45))lZf)>Pr{6&Y8z4jYTGcf%r2FRvq(PZ+dw*
zzwghK80H#l723HcRigWy!lB-OexkaU4Z_%{%WN0?8nltAUrvxYh1e~~YWMp!m-dx7
zLVt;**Id~*Q<VhL@{?y3ZIT@CRUKuQ5leOKnL}|L>#^VU^h3NmT+SjfY{#Wu$JciS
zO1~l@79@Utoz6D#11!|1)#dVB6HNJ+aL^w_vGLrm{Xc_K`Q`aRe)oMMRTpm#Fu-|`
zN-S6l!4+Q%xWReMs?OycuGw3wyUrXPtqg9jbakmKaC3FFp&=s^rdv)-Oe7|lu~t)C
zS!sxMhaAq&$pM93ORXrmd?Y&}+lCu^uOtOYi-_&D*M%mIp)J>wrE4}xv|l(V=i>$T
zk~d{<>~2_8y<p)ycU=szCGZ$pz|DUL^D}nl_r+{^$e6^Lu^B$8OM)^3w$E%<6YJrU
zOT(jXfkcjd%IJ33(D?(YXVC<C#%(y_ykK{FKNuuBmo`{VGj_B1T6+9=GO{X`ysa<p
zZY+dBepdwjXb+lXZH%`*YsIdK;k`envHRt&6_aqUoW>v+y$v1JUSU8_&NQ3wG?qTJ
zIw>&{+HRAcgnJbw1P<z<!`wprG*VTZXrNPl)Saot5+IEb(;O)}e9d!URoV{gg^Y%^
z7YgED{D>s8)?s`?u`RR}@w7PK2@o1$c7klFdosy&CK+_j4V3~({x0)LI%rTJNB8fV
z=Bp@3wqCYQr+bB4ULJ5@Owo+BanwDSMw2kfq;S6}8GnK#8qaW(Z+S2aNfn1BwA^x#
zDKh3F6p=9sX2SYmH75jmhq@>KpdsrcU8taX+YKVSfN?<b2|&`p^#8ttBO@uX74DAr
zD?k;dKlqqGI6${z^}ud>_5}al&4sCdlcP)@-c{ds!(cA$5|i%2_htUIORL=>2frYb
zl^?y;d{A>ydEI+G^H}{_x^4ZuD9e+Jo&A2ryh<2^R6&$9zb^=pga}7~2El5j{%9zM
zq}l(5W_0zU>z&u3cS_7+iLu01QNo-HG>Pr9IGn1tr1qO!9=`2g(qSwK%wN_-5L+vq
zYRSZXX!cEcZR;DKzkhktl!H3Xt~_#kTrg4^HX0+SCrHA9fAYU^n{0HeUc^A`3`*Pd
zqsN%J5M}p}+F)KQT~UWYh@}PT;{x0i1(-C_swCVPj^aJCb_<84G~7Fgj<@08sW54H
zSCQ;dk@3s&vEayo>_vv2oput)mOG?F;!wL@=Pfd(Qz*d`36_ne%s=37UJ7*uLW<(^
zA&`Up`F(rZ%M94-J0&TfMqYOi2`D`2H%#3rVq>!58|iMs@3tb)PC0Bs__Ugxm5z7l
zsArlK)?4$ozLKFH>*a5w{J49fKj5={YI=Z_9g!uLfuTJ%C6vK5wMc~pJ#sd0Bo%-A
zGqz;SAVX<7KYN<xK&go<i%ioL&mmqbg7J7Va|`q38>6b$gwIWw(AieJYY`102+4J;
z-t2`r1?{g!W62-U9M!riGXC%JX$abZ=O{jm5KHyAL`<p<#AZ%#NloNZ;;pO<V6tZd
zQvu&gZjKyF@Ct^`_{o{DNU4-Puy2Bw$X}I)28W_=)a&bK7_j}DZx4AkwPTG|S682(
zp0Zau9F9<So&@BNPfz_P4{mO5%qv@r^ss&2zZ124JUh8`b2*)2n)SRUlv9c@l5(=e
zwpKUJI$L#?eaq9}8APn=LZGmFb9rkyJ~w+@plM)8Dohf9cwL)#jsXwgyxh57zJ~Vg
zl(D-Zao;2CEKO6K0WyG?igLMdkGK49L5Zn{oule;O>wLgCG<vZEw#s2%BjBz^11J_
z$Gg{mn>|aka~4OD&Lcs@<1^7&{*^-Zp8EzSRcH==H>p1JRrm3mJtH&obQsrlu7?B@
zZynbj60k#!7?z0k&P+|MqHSKTrxY%#g%<L``K<mJB9D<VpWD|ok~-)O(2Cvt{_2Y4
z|H<a^G>(^)=tl%a@ouPFFyaBf*1-+=9bzo;r<)1QE}d5{aufXMUb{*%(Xk8KZ2h7>
zq7O0A7vwwxSp+lb;K{w#_HQREEFH<qG(CemtG1@ei$*t|!zN~w)R$*5!(L@)mFb6j
zUQF&a&d+F9zolL`&r=>K9$lK$K+r!shij|q_+lKc5WPQodNl@gv`NT=byHjy^aMlb
z7^cS)g29n@qm|z-;$pO>EtLz1{D6Xl0}UC3bU9LxY=6n$)o9^7oem)NBaHY<A+#x6
zs)g}YLNS9Z#&a6qU3J}g(_?9Qb$vYoL~KZ0OpKC>s)t^?;k9n<8gLt6=$Hf`oE;np
zq3tdvGPv(gW9n0F9r-1hSKV`@<*j-;mVNA@tyJB@%A0&1J|TbUwDhG#i(xQ#D{U+F
zgU~OavN(Ibih1wM*$G78#JM7iFWB^{@u}0C4^k&}?09n7KV^Pi^uR1!w7WzbnxEG+
z)~fJO)HHgWAu7<mRnN(;WPtxMT=|1_{w1dXAJUF)A&Bi_Oe|W5*L6FdEC2GmJe^Oy
z%d&g-Z8YzKQo2PzSWf<2-WR5v*e801;qBNMNB-o`Gi@@S$MczW4(8i!4|+)1$Q^OS
zX0&$3LxEc7>q{jxlH<!j7y~6AZE>)D;~kZD9{^D=Oze1Gm*#8!n#DgPSjo7Fu2+<}
zuM!o}woE)tuUS<}^o)5sRAZJoy8Cl=F(|T!*L7L>GJ9OZw`wKLT({Y5x591IJn%Gq
z6atN1gz-5A8C;y2Bs8QrprXYDo{#<AaRqYx(x7kVoq&faP_u{f<u#4;;+oQrfE81c
zWJ!J~S@5_uo*Yb4*t@2Hc{pW9tZQn12(3cB)QENSGZ>7nHoC@9>+iv}xWuxNa%6cl
zb@6!=>*OGp0wr4V+S*#)+matw-}pE<hHP;g9|C`I_^CY{msJH`&|q!`GGK*K65}#A
zu5O3t+h}@OdU)Z5XKl||EU|u>K|p)kb~$||=*{Pp3Mak^@K&js>-0q}&HUpZ?^EO1
zUJJ_!)!Zx4UVuT*la-Miabrj0DHsWwG7!?}5l|p2ysbTT2D&&UHmRgCF?e={rJ7{C
zr<s`22TAG=PIr6Z1T>(I@7qn%Qgj2uua1|JK=L`H@a_`z=R(~I$<Q@GMS)0!<FoL8
z*2<~_O~W=ooLo}5daj#<c-`K$#*Ns*!}`_z36UB9JQk!pLlHmKgQ8-b<>Z<9_N5KH
zvh)uwCUsx+;|4<FjDgH&D~RbP-KF=upZW*T<Qs_{(_gjt{=A22hA{enb}8ufq(eT>
z$ZGxLS~g#1g>}T6bjc7T+GUr*x=L-S*!xqzZvDMq7+?_TA@if2AwyPC1Jlqg*kmHS
zX{^P93^!bP&L{xlB=tUYY5y=ASHk;V$(OlJDo^R^tXVylv<US6@ScO%3+OOA2P6+7
zSkbRyFH?p_P&iw{@=Uy=I+E4v`h!@WPocBrmjgD+p=o=zW2*3WtZb+gsuqu*zNnyX
zqf4%P#_2~&hYX9%W>v20eNu5I5t!LUNRolSDOJyA`5+Ws8V`FAIlj6NcPe8rE_D8K
z>OB_jUL5noG1Il_DueLI*$8bU#2Abe#N7Dy{j3<(_~B6l^HTd>o$8Ay>0q0sR=S9c
za%y={&R1fzVW+v{){4(>=GNha)kscoeR+y`>jYn9#5Esmitfdd*hhPf)RrdXw5|dR
z=mkxQtJfef!w|Hxi9oLD4sK5vw9n7=iamlsUG$<^Ix^+@Gp|bE`*ix!O=`(gV=rMt
zFpP|tSQxOWk%R5P2A^ED&P;mB$S{T5Uf$3ThH5%F@$Yq)UNY<{wm+SSX=4x*1*C74
z^lTWbV-M|flH!hp8-cNUuu>o=sfUJ=3L_ojopsDPQ@wa=SGnOa;Oh2+UhgjpZL*(i
zYQ$+lLI2%O%Wb;?xRbVARQ80&k-_Mk&H}B$e6P}d-1pFBQ9jpyAyC^+D`*qaNrCCc
zt7lvz;X0ES%OC4CJSHPg4VVhkOqIQs7}>aDy0y|ebc~Y<iJeM|4qk6(V#32FMGh7Q
z^OSqA9bbNoeEGxAFu~aH?c4iFV3_WwDLP`L42VmHX-QUwadV5}zjouJ+hv3{D;71g
zy~_D*D*$y@_1!|e(MQt~4G0b%<$A48A#+-z`36i-vl?jiP6QWoqH81^L{FbuOF9%U
zXTmAlV%O55{p%MBrLO@7oquQ@01A|kV8iy`<_Pq#Vni`u8`Xs1C!=hG;NX;Qx*Ml9
zQA_J2W*CH1=Mn<ezWJvSP3!Gf)#ogt#Qgs$0Okj}K<Tg|NC4abNTLwUvA1vbLH#~5
zOgvHI6H~`y$h$q;PD4*x1HD*2zmTn=ipDL}*D;0F24t@PkL4v7D822TZlP!Spk+zS
z0MW0lenb-hD4!q8J$JQ4tX1ylm8-#BKx6#17GWA6dRr>jnA_P$?HCj~b$9N|w-`%k
z{x=_Qm~u+M!YY4ZcN75#S`?7C>?DNUvN*VCfBDmAp*s+j{>IwY(fJcD+u@Xims^F>
z96ZkiQ%*hFQD4C>5UcQiT^*;WKP+`?Eeiv2wkjBJm(5>a`>Asr%sb^TX;n)`>JJK7
zfi$Z-eD9eYb0qK%wOEgE)@F+4kr7cu^?jF1)juwW!I`Q94VeFId`aUBG0fju{peHi
z-;Mid^&++T@mnvv`!e|bqH~oP@hQ_IB@D&ek?Xg?e(2(r^ufbIn3Oy=Jw`}ghw%%*
z%Q#4*kf7>hB^9fV<MaUJ#9O~Nm=64c4KwX>o;vv}CX+@7YvI(2Jdqys8wz?bFgiNT
z5Mp+UU(dOzC!f7iU4NL4DJXpT1RujJO@nouK2cZJ!ZKvpB!8+iOf{vsGA&JGjb{d%
z0)|obR*J^r=r;1ZW2Dk-a*0xr$h8{0519J*pgeshI+Hwl4ikN1+plma-n#}lrm28L
zjY)WqQz8XE_it-;9+h{RB}M8Q(Qz$C{KUxcx?eY{veuhCqp%u(iTm*<cZRv@j_-P<
zTM|0x?eg#`ASCs3(R<P4P5Z-nG^UB$Gt?{wFG;{<f+)nrxM`xov+NF^dzIVLwrpTZ
zobJQjX8fM9G@QxY)bZPsb1G3>5JTZw0R%G44?+s6NC+J%CF#6xRuDR43Ou%eV5abU
zqQG{ez}jS23Be<0E59*StKiIHym8=z&xW}K_Y>(UDA;U3G|xnE`HAD=?X+R<YpN=4
z4|bgd-oVvd*G7a4c|Ik)y%AN}hkKn%i;Fru-yXq5d)Cz5?+FUtzgnKbT}X*_nSA1{
zBz)~nv2SJVATHDU`9|JFbM5u+R-{%gT$2g9sr=r8tk18;tH#CSbyXE%kDf*=^G*R~
zk2+L`Hm)g_M@Aht!@|X!ijEu{%<n^|)bv@Hg@-yHAd>?b?C!OaDl&{s4B_bSPGSuW
z8X|!};>$_S;FJ=vo~v30Td$g0CR}<pLJuYl!s!3)#4fR6r<hv)fF`7AKltFo4z1H<
z!NTag8H**(ef)L(b))J{a<|EAVcX{Kv3s%m=+_Z83=4X3h8nUZOuXx{GH`vXVXhT3
zBZ4>i?e|wT@lxs9E1z<juuZ#Ln6Q%PT$Yc$9#o>mfnw-&A$CWcwsThRnO}vwD-{Lr
zF!{CwwW%iC!q6q~@BV|ZWYykQ?Z3bDl|P)n@U&e!2T}1i<wk&{@Qbd7`eRQ1W|;vA
z>K0HH;+NKO7<*sWc6xe^4Ngncdsy*6y~tn3e{-&aZ+CKOcJ4N3WIP$IP%kSdXd&Vm
z=DIq$ui~?cbDk$xZRuK54k;FM|H)dnJ#xXzWPpeXTeNiJ_1F?Dm3A2vO4raXb90?b
z7?L}~bdKuzz5;^sTqPbyHpA~EMBur>$FiWkxgRS@p(cE=)L-Q@U?Sd-PhG*G`I06Y
zv^P4rnPT6Usqn|e1J%#_=+>Ao)pDv18U1JKhun$tZ``czngkruU@SGAZ)D-UVl4CW
z86+f6^vAvSFZdnJRDCO{s$9KJ&}aC4195=s9)06hx{Fi_VHuQJhfJNV2u4uWdOf|n
zIeVPtm8|&F6HDv~L6C~eI>wBNYte9}Sm#M{q3d43?p|SP(QyUCkA4m!o5bVbVaTlr
zm*d_d(}o8!;gkeOs`$ICbtsn;j&~ng#K84_fY{;nOh9)DMy5<)_pqnNK!A-eLunvi
z=jiFRc{E$io_O7{A+D;lu3gMB`t?#Gg4@g8?UMU_*2h0npPsEXyM2!X?+!eu^a~fF
zR)#v1`h;WVZ8Z<OHpP)=RTuF##(ULQhFQ#70qHonx;X3M%%)5?djX<wsb|W~8LD5y
zq17rw^ptTh5Xc<!RN~)9YP?=MB-Hd_ABTCzAP6*?MD>3v{V;A^hO`V)QqFN`M{c%X
z&$wbU98-QX44!Nme6ouZLdKzam~`9GRQ@qzZQ=e?*)-nE-5ja6bnS7_dU&bMk(hA?
z5&weA$w^@%sA^X_L5b6&WcqeUzrxP-BGQ1<XR@wA|EYGo72@RRDMUwLsNG39R9<JI
zKZ!3T&19SKYN0`_aSEt>x&8edt9Q3g^RsS7aJ2H6t!5oVE5qE?%*@psY7j~|BUw+T
z^Zl;&{mJN&y;CK{C~aPl)mLEnY%9Rwd*m=PefL3P>t2s;3BUiq92%80gb~V8CPNBn
z-!*f5_lTy6AHmW!W4M0;?l@`oasS*G$NRBgJxEW_ZTEdLF8dY96F!dY`)GgOK81O<
z?h@{!O}cgIyQ(JXUo!f?9alo@!nWf^h+3vqzy2;CepQ^KmreE=Xj4IhlCEF(g@1|2
zdo#hA9|;fo^PaGco7chO?27M}D~a!}nDPkcEUuMg3%~3!vazUMCF5~;9WeBA2Ip~E
z5Z+&NEcc+;NOoMcX7oI%?KpB_JGl^{*+n6&U2`@zijhxVowd+=4%1v0%W&}GAHsT5
zZ%iN2GWh6dm<WeZ`MoX6&>?Fj3$3$q@#4(+4v`Dm-S@`0()bo@;U+v^Do)F8E1ip|
zWpd>=KY!<drN3zJf#k*Ki15EKNVjiCA@^Y5ps<|1dUZ~M?7{rrAVS|^TBCilAvV}e
zA?fPm8i($}8-Kf6kPdao+6j!okvx@lA%|wz_~|ni>XUpw514{`*ZQ7Y^-WdvI*Nhc
zUu7<svceK9l+5P9Bq;FXKM+pcCn%=bow_CgB|5g!^XX~%HIU*YfZ~MIZHR-D(LC03
z*PsG}P5QL@wP;XnuUZgE>HY0T*zHq@W^Ga`MdL*7UKxXAB9BfF=k<@Ql*7`-<qrFw
zC~WXm3{4uvNuRRHaQZ0pWw>S$2qt3puF*~qmbkd(h-%*p$Z!aS^JraPe&4G_H(NPN
zc;40X3mqql@Z@>qd61kVAG*avjd!Gkq?j($M_;+kqs^NZnfJ=98W?zZZVx9t+hRN!
z3xfnwnEeq_ky`&+5W+78hU8#~jIsJ1Ek~K2^B0wA$nIHkv`@nc!>3WYuEk`HJr{M|
z)C*h)azmZJFs#s&tsSjE9IB=Hc73i{1HsEjnI7bmFA~+=XpFwmWpZ67qU<tU=(y!b
z)gJA>=3#FXX%=Q79cSQAOYr{8r$!$4^S#Q{={v~p+l{l~T9CE1Z69X3LCj6#tZ0h+
zeTR@phu?`zigY`3X`*Mr0{%NqS{XncVH113E3MI8A&vaKCf$IvPXlv!`ZI2aRTp$p
zc_g4x4ap73QwiNBpS_FdTOtXAs|XqeXWPtw%A0=oor%^U?A4Q?17bQx2pyQ$onQk5
zIB`tV8R$UW0w48i_rP=IL{C=J!%834Tq?ksLISuPy-6U@ga^nCfHk8Dn+pi4vVtjF
zHsMv^2P_(fZv{99oj=J24vY=w`3&w}_Sr%DLgkDla9h0JDl}<4Xk?h180hg;%;&FW
zUR*6^EhwMqmH$)^=wqkZ3~+z$50mF8;8BnDyiA)&q#uSxi#$$c8tUY3g5!zAXJ808
z5auT-c4tOmj)wW7IwUG`+#khBOvG~)J9p91WE@dSOktQW5h1E#K}3?xbtTHr<R2&t
zA+CZRD#ldY!QiWQ6QIh`aXPhuG8-Pu-wt$%;n+}0-<O175eE63#haProzanuHkZi<
z)ZX+={uyO1r)K42=Un8ro><~J!gl@oBPoe>JAs;SR6!|vYL3WMPZu)6Tih;%#yKCe
zF1z^b?_$PO)oLH<SOcoEsag@Y!^|``k}G?>I$`eaM3xuz#o4aY=_k+QhKW;o@!xDX
zW1Nk+Ld<&Tczkk+*3*TP3{H2h$j7Go0k?Aju+Ta~lTvYzTd-K%?o9DTelS7;AUpIj
z$pZq2wA>=Gd?Y23hI)}88@5w$k;&?;*o*+#12a%9^(_u|@8hf_A<jFb|JJXulZM3G
zKzr=&QQ?e`i8qvv<x1ss&c7OGjr^oPQPW5u`{^9xHUBw{7DRcGqYY@?{@}Hcg!c3+
z%jDvI(KB1yi&H<@k)~><IX&9&?<gB7HE2+i#f`R!y{5?&!sieq5BoU#c^`Mb(#d<f
zK5QCactmJ0jJ$K;Kz31mGX6MyvX>h870c=1Kk!HGMjV2e6eI^GGq)Aj65GZdZ99Iq
zG#U3I=}VVw!y$_*akk}0=<DWT>LkSf41pqbn#7lIKTaUFt+F-txaqZVwJS=!)ly2i
zs1R!$YZ-;Sc__JA9@N3Yk|jF9fxYq#(W~S#kf-ERMwt`o`!T0@gvRW*8v7-)&ktTk
zm>!R8UgNgYrU&MHTiMY2`)|wNJe?Fi``sL^)}6))94#kS5^=wn)|9aIJ+0kJEZUQ6
zc~~DFDU<7A58LsUDlA5NY~whJxu5RCTTlm{RH@$=zTF8A-=n3=G&#6zaG3@5s#?7?
zp5$u|auCy!V-)@%M&blb7KFY78O+-)8={gE|2G~9h6203w!%grDP;O5MDc~`9%f$S
z9!+8V=D7nY{@GvistKQZbRwDYDM0Ayn(yZADas?-)Aru2>)0;phf8a(;jb7@<vo5l
zPM9c`?e~<u<`FzD``kn9y%U*Z{}MGy^uI3ObYeSddSjCg*vOkwq-N0f2;LO5J+z*N
zJItQrxA1CRWyx<^r({Np+E=k4*YLkj$PwdwN1-1|3~z;$yZ764>Ts|T!#6by!P07u
zXCt94j4y%!MC`x8Y`qW=iPBY&j|af?LxM)8!8rIYQy*2WrB!8(y^mje@Vw6OYMq9^
z-Up4)Z>Gi@WL$=mfv?mMUAZAvF{Ks0g7kh;i$J`a93jhNKVCea!$R$!Ci2=f6`%h0
zJUw-s*hi)57*J-}Jf6JewiTzL_7&RpOY5?^GdT&@^l5|On%q9-P9`<nb`rivv%BCx
zyeYdAdLPD(mwU$;*AXWC05D;*<k<ht7AWSN`V0zHDY3e;0uSR@vbY-uhf52W03Gy0
zO5shTJqjIx5eExvx|`PI6C7c5`ZqqrZn#6@#?p2#wZD}R^Lpj*ID8It8M~UVyI53#
zx$XXh)5<9Wn|v#OH>jZL>t+$U9+ecM|4_ANyh(~WdJ?3m4kcJAm_d@^;t#qRua+`A
zS#@evi@AAR%hSfvA{@+w7)_X@lRHAsYsN}K2QL5FQGsg9Mx~o2^>Ta$99?DAg?bAX
z&jB_nMl?Jce!`O&)Wf|oZ3}gu&SE&?Z1U>cwj$f*`}?F4W-7cu5FW2UAHk-5QY2->
z8kY@lBqANKpdXnBdp}6sd9yYz294$9rq|Mz_xmLv|EX)0lL4u^MEatPhoQ`)(?4N(
zbfbe<P5ZjD0ECS2v7Rx*$*8vpNxFR1Q=65{m@U2%jwE7kuN#ruce+hH+@j8IK2&@K
z{OBHgda@l*3EG8{>baix`=%?W(Rjitv<8|Z0Qb;;P>*2#a1=n(ieN+r0&N_-W0769
za2)N1h+Bjqq*~8fZ=x%hL#Q+!**f3yr{-a<G3l!`=*fcxs`8qQ^F^m%ar^d34~!@b
z<F=*50^|RW2o1?c5nwC7r0y-M1n7T)KY<-lK?#F&ZvTz%deZ2Tx~=*u%SQH7xiQ3=
zi^gH@#9gb><u!P8gLjQ-A}UWRm8^o0b+cPq2vf;S&i8*+vw(OLVgpD4E<zc<KJY__
z6_!w~YP!2zTYtH39?E&j{&Rrz<RTO9rotKi=^+YFUU~gCM2-jC?58-X`T$26PX&PS
zn9b)cQ^tZ?a&pAyB7P|oHX`%m14v1LcMv&hSR@XBH`&BClW*m2cV(3%;)O<c=#@v;
zOTr?5gfz9xJjs{8iS|Z}0CeW$jOVspu3NA{9++{An9^?6D_P14*rTYqHUDx$0zC%1
zubPipK4|sO1$Fv)X1L~#cRiN&()O?RIYi*~wKNS|Bj>({^^}IRS~ay57XG$iQ&vzQ
zO!g(;7m7<Jmi4+S2i~bi5AeEd_Q6rSiw<Q&|CuYv$6R9qa&-Y#V<bq3t<zHd=Df}2
zs2Y`sh1`1LI>IM&KBNpMAu)k+o!`kwkbU_?<)3}Fx3{z2Uk-vByw91LnSnROw|Ok+
z+g1yRr#9|+%X>%1Vg|rd|3?6szUwTL$p40b1faQ(jg|qUuR4*xCll)`kE9Z#Djq4R
z#iWz+RqT4R`yHDfmkUAgy?l#vH3v+MOjc8qPO>Xm$IHu06k1$VP5roi=j&~}-KWs`
zBmjZ`kUO7bfPdLWiWU{&ga2QVeCp(|<gDcCfyYQtKyjkgLcQ@T;cuOtQYU8dl2%*9
zo9<kDp%&qgW@03RYbo36`lhFXgp(O&inqIQ^pil#wt9BaROF9&@?S#?L8x6zN}&P*
zt|JHG-rn>p+t9)NON9ZM(S8wnwbW&qpoq2iYhBlNxXH!!BJQlRg>fu1`aF$d<ae+%
zc57bGm*#SaiII_!$;qf5@u}!OWJYZ1rVYo7DgLZMR;XKsQK<JX{$*14{}!MVa(&1n
z-U)vm@OeUNSopTU)xeb(-_369(AluK@!`79aeIXKPid1O;2CdEs2a=YY;?{Gy$*t5
z5V3J_T`zkKeXxlGdQ=Pyi#uOTWl((T!)d|3|9c8GK--M1B~5N@PGE7PV*E&tcR6=H
zHQ#SQTbf8KgeJ#t{e~HVXs&&O@`mL)!dR#(Xfy|jYP4BIZi(fE59k*{_X%1=P>mYQ
zV;%1jGJ>P~QP>dRT3t)$gOi+RYWPoc0ZAd9%7YfN<G|E^z|ejq(5A(8jwz0F0%J#u
z?`GeP<c<FL9fX!55h<8dp{<y0;i+l2ii<`K#q5Ud#pY7>LOiXt*dzHlUu;NAY^i9C
zP3aRHUwE7?7yWUoKxoj<i<C|}gVl_;`-cish)@l7>Mp@V6ASx;^SVr^`@DAXZh`-)
z0h9K`ZgE`lDIsWVFVPllmFPZHkf#&wB8=Yjoe?jUVrp*g=Dh9VGXjF6lN0az%k}Q=
zZfcfYyEIa(_H8_lIm7=izrfBVtC0UAzBEGF#`(~#+FD;`Dvn?r;&oJXG_=`R)w`}F
zsJ_J-k9l1MGcwY-AAXV!Y*keSyS=@Y2;$AEs;H1|$@gc2dGO%96+#(9za=a9&jQFl
z&Kz}A$nQhSmSJIXr@l?Can1}MIy_Q+Bx;1g>-Qzo$_H<afn{`GOB+8XUUSK*+?mQk
zmx*RqSIZvZzWH4L{R=#Rn)r36I^xWu4v!IuI-BADdq4W2Kv%$VaZZHtKE_vt?VhyP
z*Y=y`{>@}zDx%6^J$a1{ts$6Xg@W=EKtu(!+c@^OMw*z&uiIC$dus%;OG`^TI$mcA
zBw=A;m%uF=)btJiuuQ<f{`rHU>A4=H19RpSk)T*vwbIVh8~R_2H#g`5cCJHb`JiuC
z3i6J+pTD1P^ROZ@rk$i_$4OM-H)MvxGOz90uIFIe>9R>yuM3dQ3{tL`_Yvrr$O0L(
zZCbM%m1bXuxV<1Ahu+@=S`ZO|nU}KdXyi;3;{byK7e)mN%mAzdUbf`J)6xq9N!Oge
zn-h3qJwYwCTcB^bp^4L>WqW<1Nsgz@*c@EU+~PiQ%*Eu6Hp!0xA{!HzZfxB6T;u5+
zMKInhj3Omt(SLDslS~j(Z`Q7UmhZr@Mr0r@O`S~}6c6PhG!9*^PFP+jSRLQBTl_A}
zzHprcOh5^V`BEoO;~3-Nt_QP%>Feuvz1>#feTIh8QdND7iE<}hFyi0M@B^8Aj_P=Z
z0we4(<X4i}nCM{7&o>;C3$pr0y9e{fBNHOn#M8kb0KJQS5{S31ejU4=5WcRU#8TJM
zBq}~B?)UFiOjoUk@b~NtdB4Bt2KS86N%V910JXLwGYsVN%F2tIn*=A!xmVE0-iNCS
zZlHSAlrSBdcn3f5;i&nO{x#7^uOG_(jWrkfqov9XgwCVJBJ|N>R(iBXrfSdEwV8V+
z$*^!b&8}@~AQ}4L_JIL!kNbFt`-Zkyk9PIUsZ10;p!z9x2AgndMWrZHSber$@|N!7
zi2^th{<#n1Z<Z7Y1-uV*+aX^*b;O=0-IJxnj(i<e+R#SUXE`c!s^cu+8tT-H=)ArN
znb_V-rE6%DhhVcx{~HmXoUEdtP%qE(laEG-kd8!h{ig)iuezVtz;hZQpb*($Xm<mf
zmO%JFM44~`=HZu@hxR(hg>?MgYo%_AqATJMqlO$>TH>xXZ;?HB&L^X~(3ai?E~h<*
zY1_uXqrB_o<>k-7rGI(6Mh`QbEtI~5>^Rkwho+Itc7NRuo2PK;(mroAn{7-u%W?$>
zazCsK8DL#5QTX%80f`Gn1CpdyIi?P;qSWCN|CXaQxPJ}_7MEhOXpg<HKx$3%-%#q=
zC}LP2S{ka55mRG|PC@0+)5&J(heWO>CtrVDW@wmObkWcUEKXePPxLu>#ebh_eC9v=
z8?%|B4{m!ET`)_*iV54I80PK+W(=}crNF&U)H$E_0kyCH*=rnH$_P}sK63l;{#QU3
z-W(osa+>$FN$Fa(;kli{fBc)=1Q09};ggZ6=8ubF2G$X|0jT<=Z&kyz>^6Y~R-STa
z!#=*tz7lw&p|5yv_Rs;_ox%-b|Di_yk2hxoP_(;1p^N}~&mRVXi!WN#fyzt+K-rjd
z(;UL5pG2bbBWnE)Z2@nt>ni;4USwC+RO(+j1Ec}iF6j?|eZO_O7+6&@B52o^HI@ak
zqn?$WRVkSxucC4*ZJbVkpGl<)Ub}9H-#YNV<=<18fDdsi`mf3QXRHW7s8sUcBxixG
z;up?#tY$^Jp+p9&rsh_QgYPp+I%GdHjGcAlW!O|XtKz1L{1L{4Qz2Mn3v|i&XBHol
zQwqe&xbvfee!!vXTtPskgF7{4=r_mS$cqfpcJ?Hg`Y@&3nmgMT;5fQ=m|XN#>U4G}
z-8?H5Iv)r8e-2|RDZiEoYfCu`6)-e8jLV0U?4$uChhyFTPTuV`LjO9f>h2c7u|yUi
zacq6?cVzjLc-<_3A(GRVMdyFB@rEgeiH1^v^!tcdOd|P<I{YvoPoJgh3I`7VVCIQ;
z8HIWFp@q{)AKYJACb=(Rew)L~o6XVv_mcfXm7;?NET}#7vcw!1H8H9C@Zm7p9Md-H
zll-T|rlLLTj2d#ui5hBW#(klT!2$O4D{XgeTs*b6%o6DTZyF{+z%zllF`X$nFp*-|
z?gRTlS!g>u3(gvom-5W8Sfih{OMj$vv;8iLF)~QrBnOk{Xe+Bfb><~}1=3n*eq;|$
zyOv%fJ)Pm3YCdk13>uO}r)i|eDWn_IjMShpn2XMFeB4_dL%_nde@!pJ0KTo1+8u2_
zv}cdSsozNFR`9H~@U}(5RTnKix!aZ&kV$UaJZXKAWcPOz%g<ERt?>5;Hdn;;IpdrI
z^DnxgnKy`*+19s;SxcH`SGOK5gt6d4;E?&#fxJDAi7pTpkB<jM06-d}<0B&=pTbTj
z9kqSjvrx*JQf0VthViiM)uBlH`Fk&s*t;6)K=Nm(1km<VdErUmM>CHX0~KtZT@E@c
zW&0MtNBeH{4-`KP;kXZq8o(_E)TXa+HW3n_Hs>Hj)=2QXppUhiyVQ;w^NM+j-CJTK
zV6exW=LFDjkpfpq*{4$=|B!QqE{Nv|%6;h~eKK<hpeQ6W_s|7Hpm7#QTeFQG%W3G?
zVc{mu{`CQac!rqz3K8PN-f+1xot5X)28N_`cfn~<G!M)upLz?@c2<bs;%oz*kTMV~
zoS4!S`wtP|tP-hFd@dmj>Wl#tuP8sIZR+fz4sFz$hY*&eBBf+nC@~sjRj$uzK_Ux}
zRdUHfftBow!ghc3OWQ?osn4_yF~Bck^QXM{!z-`(-hJlS_s%?MgB5~R!?aU?Nfs9$
zC@bD88#T2~8OiA%$wivq(X&hzKHUC=M;1p&C)C>lo#x2X*y2-wrbAL*g|Wg42bUrd
z)X&;$3V8Q@T;nupKmBSe2biqe$e!g9AurDWx{kHPNZa$#Di~}!*&&)R2L3-PzSudE
z6)22vZ<{Q%_ta&D=ojKpO4a>JzJRl;#(+%+%*`GZ(@wm{2k9XxtZTj6LhZB6G}DkX
zdk6`*z>l!0)sg%?J!?k&n(^^S0NsRv;qOnF?^?RSQFtkk><V#gQBFZ7&mAK}(Y=_K
z6xCNdS0s;Ar9_1#0zbI$h=I>RQvn+4c}u|@v2W-cM)8Ktx*aSU2H3Pq^A#SH32!no
zbr7<+0FsL?-F=QNg0r&mii3}$FS%H?Ub5+e78es0yQ7l?7-X+A+u;6fni)-EBv?>N
z7diOflV(ZE(V<>WH`-r9m|~su3gGiSq!3WkExTnOJ@=NvLZ>*?Ym!I3TJk<$_nyv?
z4CV^5N8)l`COn}R>?ZQ#N_35=4PLLI!7wEO;=P|34h1y*;O79d%39qeV6T1>`l;7!
zXKNExLwYpIcG9FVx*vbY(ZTWcu<Etj>y1aZT9P8v7R0--Spz}`g1hbrgW(M-1$)DR
z;fKwBf6R4<q^RJ&If?!Lsgc=R1JlpcfnJ!yD4wS3(9{y)uQp?JWU$>#O$PsHu3qHo
zw$tVeJ@F9ed*y9@sSW*bSdD3}*M*ZMz`**6J4F1AnD0Dx*1@aTeT^$Pd>7KehcIBR
zTA^0iKnW+We=-wBKh@phL7kP%xMgN$O$0x&x(zoN?;>w_JvNo+LII2R)P=$o7e`2v
zyZE$l$<n~W3Zw|sr?Pw~4F~!vxGyNu;{5{B-rF}CRw=qC4H`$}8Juzlx0is5oVUI{
zYsfX0(u^%wcWn4C7r=~=PA7!HWcPIin);q$4?eMWG!aX__7d#if(AOHnu;?tmH<OG
za;X3Wixfy_73(+dGwBEjowEw6@nD#KRv)G+(g{`Rh2}z_uMieGkuO5pom~R=7OUF9
zJ>0tVTOIT(Mik8J88MZ=@vg|DkWQ?3`}?oI)RAw97Ynv5>ZxY^5Ia3*_N0u#f~4`e
zMex6TA~PGZV?H#93K;K35GrW2l<TbC>WqU28yQ^DA@26`YJUzsfLUfZX`Tp^v!;y?
z8CznhZH$y0C1@rL2dtsAQ<JFr$biRX{Pn=&bCokKWX>h70I@kH9)XSCqF_L>4gSku
zHgzcm@)=Cv!{h5`1a;}|J){$ngrC%f44NP%KS5<b3SETj<LTw6@TCBZ?l&2~kntfu
z(y`=WAW3|Y#HcN_tRwq-+<fN2!E$Hd74z&ej4Us33sZq!eAPyYvE%|kf2#=s#vN80
zC_N@bFxtVwgWWG3_`y9Kj+sn3ZCDig(uw_BHyR?=>7srLz~%a%A)W@Bvuyo0R=cLy
z!XRz>?V6b8rC6F1_ab~y(E}T1qMI#<d5k_N@=$}U`AkO688%L-^YiO4OKK-2u%Lg(
z;+Oi+_k~GOP(Y`kZWgfi?%mYg!z4@W#78a05Gq`mVU||quMzlINI`DD(xFJw62r#(
z0E0RhjX3aVSMc|L19cyxW)JqyYlCBh0xOgh=3fBmgI$nk#auk=He~5vuh*Dnr-ye6
z0msW7rMhX{nXAFomkbg}_F=S;3O1Ku`9+LW0Z}`S&eP}Anm*0N4+Nnq-@%|z+rRbB
zL*6}<>r~At#(y})5*UGj!oXa?V1}@DcqF?l;Jn$*(EwP&PQsD1pgK5EMy38fj6TTZ
zV)x90YaQ};EG3qhAf}8I8TgSZ(M$vfN%x^cR@vIt_Twh&{NG#^9qBb~6(=X4g@m@U
z3km@heHT?1=78s{4VC+F!*GfAX6?!Pc_fh4_c@Eb*v2;ZY_+YbCd#ezVdLa`Q~aoa
z`OJI^q=yv-_SL7C^Rczk`1&~Tj)NfR_z%-ADd0`D+FP;Om&Hxms43*PhDI<=R&aIk
ztpvw8z?y)p<&6D0Y2#q?MfxH3De9drE`EgIB}3NB&Pe<fPkV1c``qn~Y5N9;`C^1q
z$_Tmb$n52WJl#X|;J#L|Ev47dMB0LrT^(&CN)GHM88Z(~v=4xC2q8c-??8gGYYkK{
zLk3ji93c~?U?rnqqW!lyR`%jq`qrhnWF|?C#bRyj$PM<%PFPd1fxn$!!(*QNF)=Yc
zjM1)zctEJ#*5>Bo!a+nt1mIG1be1b;F0Iu78c??gF1M?*8%-l5w9I;BZfE%mYXLrL
zbCz{xnQM(}2Md<C|Eq<Z1ahb$nPJ59w=<G6pfXFwx;l_~AYDF24p~9D6W0lm9i9bZ
zomz^DdXiF<uF9+3tNh(!Q8k>Xc+8#Q-eAw8*#yC?V`k&qDPC8b!<i!I<Ksd;C*+op
zAJL#5owP(|ooIcQ1<Sft`@SIL07D}?-?{=cky42v0K8&pi|x^)h$MO#45G2+-4vzj
zv9Lx(zKkbkh;1q<+$E4$JGO~Q78VL04WLYIy7Q$e`gbtDHHJxvfI9aXUz!un;bW*z
zOitHx#)yyV+K&`=uH{gR)t;=3Vq(&J{MF5=+jxIs=x;Qwimq;;P~cI_+%S1KB?%u0
zr1jFPU7FQ<cvy@<zhB#b-p&dWTrbUy5C3pY247HSKHPCxm<LnD>Rvrg)M)FJF#)zZ
zS&Gn|LnKmN-F)o>C*piYzB#{4B5G!;6k1YUm@(a~-X!~E$+gD8-N&OJUR>&Vh`bNk
z!z|LLRaI49ueXaC6I53gKn&Kj;d)|0XTss-_I7tdW5tLwmb^<a@y06#B2$;|;j$hS
zHY-sG^W|KK{{sBr^W5DcWr|YX?KvF*gA|p5ozt<?FZayBA3Pg-hYDX~noIufmzGmI
zM#gr|xrx((FmvrkMi4B=w~14E_a~4kd)#k%72Bgnzp03GntgBibi}@B(Lv0OnB+)8
zMEVZNLa+R|@fasN@0n{s*S{5&pkP3z(&@(QzhmBb#~IjgNP)Ybv?>oZSb%BAL72D|
z3!#$&<v|Y%+W7aY_|yE6zta&zYTL1l`?!z~2Djg)2wgLGP1pE+UX|^lS8CbH_`WhG
z@AG6Q0Z(uS_q7SqIkPk>)0dR?Ps1u)Haf*pTAZ-m*MwMb!ay}`fMPDw2O^6F`i&)z
z5HKF$3-a;3aXxezeI;cmgX=)nvCc)@T(3S!YzGUz6}(8Yh~#!WN}OY&fze+dH>xMC
zBQ}-9iei`rnw7J=w>QtVon}++$+WbzEVpyc??`rbcA;TmIS^Ksmg5r>T1VfjoV-*+
zRG$~m7-YpOm_;2lA8%`K)Hk&^`4*Dm;(x}fh3XhNTem!SMZI7s)E4_Ptbn(5MW+)U
z33H#Gz3PKU`{&ThFp{pd?QUFj-52A6YgplaGH6ecbN1i#4;_>EGsK5HQjxakDVFF7
z{TnJZDD@{wEK{ugdKjzoT6&_YQQVxgBT3)Gi-|ZSjtc^*HgyNX*KLdeWp1_4w+`-|
zcDoHN0aeb8?#0=pld+WSX)%PB6F+`1Zfdv49UZR8zK8f|J<g0jw`ok|3W;ydZ&hn!
zX1c5mlGXP}paGuY0P0rdOY&Oql3bbOupYZsfMiXT^nrSLNr0;blJjfVGkcDE+S?r;
z#xu9j#vqW(ApvRuBBJIsPVwMPNq=x%^(sK|3DvOO%C<TTb`7oVIA8%zLbIkwRs5#_
z4iFzK{N|dW1un{zE;u7CrYfHPOq_b5;sY-uIWs<9{^ASLvj}vJqKZ76o5m$!g#8XO
zNe?w#UpT99EsMVXa6<jG$;+WAAGXk40EU(~h=!tK!Qzisw@)BbuREw<*LcorpjVg;
zgt6a4;YusdB!g=aPoI3hy=G41YXqiWj3#OMdb^hHI=u2{Xk=41JappSgDM*?th^bC
zgFtnlo)KuY?YFWYZ*punNzpqA4n!!&Yv|6TNytmm-)hQZ^R3ybh>wQQwWu3_K3F(6
z*wM_VyQ*#*Hd{0`@p=Ab=l$;L(MUQN6gKk5>4}FvnMFUV!W}l?5^N=igr-i5k4rzP
zYAt^B;=N~pIf`AwxAak;EJ1yS*{@X=%FjKkn+A-L9u+~}-I`&tYhgK6KXc0CyVyBq
z+E;ZLvk3Z-Zg*J57W1WE*f4n8=BT#qSt&vVBCX_!rjn4qFgH3ZCu?~`WpD^Z9efY=
zF9wX9WKZh^pQ-)W8;_;lBD8m>zf<)k7u<{HZjNTTM~G)UbfBb8PW*@~XAupdBxk%u
zbozoA8wj9M01lDnJ$m3fGibpwn3l}Mo{B~f8bZPOGbtT5p%@0#WsIK6Kf|ec!uMHv
zn)x>()C-7i2CaB(4U507io}WD#b)00^mHoraIQ5#Q)Tu$A|hf6UXXO7$vTVnZQBah
zlP;&d!R-`DcC*;6qq6Hf=j2U9T3mdW;l70V2UU_-JwlTn2EA0FE?&i-uFb!1F$*MS
z^XDlOvq;`@gnXRZbRaZ}@%`sJJYx5p&)NHmU)lF9`U~|m-mZG>B`IHXdnD9L*G5<V
z)Ys;J>H8Cw*+6AVClmA)gcK;gxHxb5oVqkfpXr0G<RK}eosw}sP&&T*?fu}Qt6*a%
z46i+5xI}h!M-&k{U)!B`!=<E$=qTORAcfA&{?nT0yX2X)-Dh5g(z$liLWuMs_p&z2
zer`|c3IF)F=Y7|LZ)CyUJFtw9u~z}^jKU{Nz72M%<5?qF?N$0Sb_iZiSv&km?~eqb
znndvV%LvLx_a1TwIQMT`lUqe*rFu>wFfl5P>UR=%FM6UG@3-2=U|;FzTgDd|8{s?O
z;+ME@NwR-hrY({cFpJM1M%wJttuMi}9bvcFzPoiLq281L9c=EqbI6|l2?!FSy=k_j
zP;elVs-?}$Vjz+s;AAvg>p|sbc3MQqW=)FlqA-Z>;G;Ng1i&fQ$6L_}Dzjd#E8V%1
zv?uoCt8HjH4h3(1y&inVZrp4>OcY?TIi8~`{sqA3cJ}u3P0&zKHma(sSoJh2n&kL1
zj3W<wA==%?E^B<BnK=GZ37#jg!{2iha%Rd&c9}@qD(>wSW%?Q4$;T?CW{|4#c}_WL
zc(AXh`iwSivz>~IIH!cDIxSY~yQg}W(i8k@UF1nLh>tJh$i5w@Hg<chVda6_Vfw~4
zS-6FF{g_=O&2o5$mdLxxMTXd2{kZQN8(A}LoO-fxauh$XB@%>Jw02QA2M^Ot-*wRx
zF~gmj0{zF>pjYtLo-RUcDCw4@?_db>MoJ~V4il^oRq5UiXU8T=MhQl;agZ@IrmGzl
zkI}r5Dcxt79$hmBtvz>;>d16FWUbQU<#|#@L2{gF?VZ7<pECWIdaSbH`d2nAf?qON
z9P0J>VAZnr4r~ll7C!ZTkO?n7MushTZ}t8A1Lq;KzxhKBf%w4YrW`WDA3#lok!>O+
zjoi?8{fRbnS8_*2zw^sKuGmOy)Y)`{fAZh%w$dg2^O*-4KjU~gz5hG>1pV(}LlU35
z;8E(p4VTg}4Jz9;)~9=C0NiVEzeDzzuWSjO-0fUEsi>?J2_U>>u-l@=&O!>0!sk%~
zknhFCq|{V306TWR&}#O}6eXz9R(LB5x4{>gNH&ldsoU#m#8Q-PDrBg?BxhGiRidVF
z6@Bh?s3{VYf7gq<Tt2Tm*27wG(1?tT;;lXbbxBM#RA>(IJlYA97W}F9(=h>NHcGQJ
zkil>$ak7c^u6eN2Yx`zz`Iqcv=lVSQT<-$QupXA3#Rcucv~l2*`I(?B9?7>E8ocq~
zGSViH3`PbR$c6kW%Qa9$6&tVleRw)Xh}&Wfr%28+=x4@K-YA1)gqB4!#&4@%$@FQ+
zsJ=rOfOR5j0c`(I5pF5oSML5QI&r67XBbk$A~{#^JFt)2GFaAS<Ki#S4AA0TCefO8
zXjuYYK@+^v7D`VjIFm4E4HnyK=b=%5DYT}4@iYh6-0U1OrezMEHK(k*@<8anoo!Mp
z5=#YxXJF=lG}L|B{y|ZnZj6HRdO;9e&4m_5_u=?0xK5h@$SsUCKN4h+y8Jq68d(;-
zLq7;;qF)CV1|w&j$SN^bMGD_*bytnrq3O1pdd)zXHE$5J34JkHNPl!h9U%^M{?4gh
z`-*5h9F$w1Z=`ob`uiHuptiR0Qpe;=iuJK18w8r_(%$3s!8QgL6O--P3Tzl}K}OH_
z;jF3czMyq0Q+bYPKX9TL-nXl$!8CYU)Zjm;8`Vx|(jEB^nzuirWsJ*UPWH?fHG<mc
ztIB>k{bF5@jYJZqbZWhh=R+cwHf0<qhV90&EA$|!W_mzXzj!=58bl5fr{dfcDx3B3
zXpyM+;K`v*k`S0=#F-_fy9s%lntZYwrbsh;*L~iTrP@@g-#^;t;=IPV#n3u8>8#S@
z*`e!+L4&W5F6U+LDQD4&r|h8cMJ=bP1-rwDW5*UftF2z=WqTSr%8Og(dYJ7k(EzI6
z#z+a9MPH2(pJY09mps8Ys6}wkW&T9H$p!u7#RY#$^5Uwqr3#v_Ba5A6%Xt$z1oP2&
zZ~K9L@e17zyLY$to4_6Wm!5UlMNL($dgc744a41>O<LtX;=2#sCT~SdciK;@^}ShQ
z#AgqIb!a=Lny&Tx2NDUi?S2}L1mJBjygS?&GGaWc5O}BMcSi!iVi+!>X%ki()Wo1G
zChLmvnU~?NpM|6xPywB6;+W^=14UD-pGs5?&4stf@QwRS3;rk&_lyX@e}2eF{G$uu
z3GbpF1NRWw@rV1Z_A2#9^2IA(bXJksI3Hx*LL9}9+>J)d)p*TL3FgbkZ~%5$TW_(a
z@HYTb;?5ctU0q#ePey2}6eQ#YqzS)gc~^_roYES5y1ZI;@m|rKA}J-w&9E!2C7Z>B
zyKGvzvWLUo0Gvp&XFHI~&}XPoEp~9#zm&>r8Sb>cEj`dT(vZksbvi!Zrh6K1R}R2*
zj}Z1zEc`=)vz(rOGlpCHvYhiKdDr7eb<~7b^{b@g*BIY+Ih@^T(`4pSTtXWe-F3$K
zUDr}Gcut^k<0VjZ{?quad7l=x)r>GclK~Wy$ZgYW!ueQQ6+YAYmT@m77GY{Hm)`|c
z#iA5_g}z4kq?xDbdQjWf9JWMSu6sk%dffIkB5Qk+z_*U3Pt%L1j-k;VM}~~xx9G;j
zT9t-8vFFFDFQ2(IGZ~l~Ipb-pP^3cH4Zl<n8%%YhLps-dU+6am-Dc54%Uw6J7!E?T
zCK!*i=+JFTxE}&w_<>Md#$<${8_t<G_^!X75(tv5UdGA?fR~o3DG(}*oTx^N<*#++
zJvx{K1fp}BX;!V`op5waBLv@Es>{mEjUL79(l?)HL-dY8_>SvcX)?IH8tY}urZzbW
ziqkE$dD2Z+ujknFTTw3vdlO(wQQrQxz|BPR3dyLYDLP6ovx@OU1>(CHRg8Y3k9$>P
zMPSQ3O;%KepmP3sZln-I)zC+x8cZ3qc#+Vw&xXkMy1jO>w>~hhIsZ5e$$hD9=Ob@t
z)a!M$WU!yR-`Q3D<xJ<^dR*hmC(Eq-bw84(+_i5Uasaweor>V>gm+<aoJs0nsTgIX
zcq-L|St6}+Tg%)<<8M>}Zr^U~@L})g%@)D$XdVZjB{=K!lFtGSiuB)eUz+l$nNOTq
zeZL;J9)p(r-BZj=@3pX$*+|+ipk|g#8<jKK=iuSCRz{$S{(p3R1yq#V7cU?P2$Iq%
zDGkz%B3%m74blzLEz%`Ow{&;M3@OrxbPbJk*HG^p^xpq{Z>{H=HEWj4eCM2fcAdR{
zd!IBL>utyFm)k{!o7svZTBg<SR0F~YtutDiF7KUM&U3K)RNrVTTu#!^9-7_7$W(T2
zB#U|(6j%0c`7TRMqnFm?7p@Xk^^oKyxPzYs%Q%PZ`yH0{fBTRIq|f*i@l*0;5NqYz
zN3NxGsFMuCk^v+gTdfc;4>z*ekEd<+Tr7Oc4jzODXSCp7!-k-inUfZ~qHn(&bgV$v
z6;HKkcV>_%=oO`3PeIRiSQ4;2hi!OLe{C_dv8gv?X0Q^?1JJs3BKO&AXayA;>AODN
zSh$GBL~J|^Rq1X$kO|*X2@$<~Ov9QDgA9}5$B057$>5g!!8(fKW+dU9>0c8{N{RUS
zPtBz|OhV`*m}wnj9a9P13#LL@dLsiAw()~>#b11l`+~TvNv5q)6!MvmF}acL_(d(<
z-j6RjPHjJD7z@|Jz6==!*rxu1SJ@;v4*P^?5GR$koO&F7zjYb|Q6QGSKg%De+#$UF
ze80SQEgt^GEdZI5^DsjDxRw209LFzjDB<H9>2}^d7Rk@?YPr)~-`qKbUnU1y_h8hv
zXL=Yj@*FU;baLSB24Fcy&$+B}!4s}Wny#vouPTAJuGjBltf)mYmz6+ha#*`W8~V3b
z%nHgbUNFEfXfo9l0Q}0pjdWD{DsmJMo_)A4?Zb=usC-!2^Ssqwt-VhzD;B)|i3*N{
z6+Gm1Ar6(@BC_H@W=@`)qaB$@)a4m!d~d<Y&rg)1hbW`$_=S)tX7MMp+oQ^}l4yn6
zd<?o$MY+58^q9_f)?0orqnXgmm&Z-$=8}$lRj<zq91>OHPMpWq$H?s^10Ngap@a9o
zypR9R#L09p>qWo=H@9$3uXxWBam3lb%RC<%wh(3e2CAy{7Khqa5OJy2kE|{hRew}^
zHJw;UohkVhYPsdb`{BGIn_87*r#!!7rAeFbxJ~+4de-4TmM67!ZGiY-l9kM7;GBnz
z8s#;O{yjP&PWv>-$`LISh0lvsrnZBX*j3-!?$c?waQocLY9BREMTabIP3Oh?;ES9h
z0kb@bUdd6hsO=UGRU;4CTQWiBy$_0ab~8{hRdrp{`j0e_6U~0OMoanPS^@p|$Y~So
zxJ<KTl-V@?;h3s+Nk0o`Rq<34&^FGm&Fp5*GKDjp*Kz)P=;v?)yjk8)lf?APJa^@a
zv(Xe^LT~juyT9eGN4H_gFm)#L&ZHhlP17`5Np@4`J#n4r#Zr%MA)O2GrSFwlDQ}Xp
zbe|uh@Q^f<+jN1@x$r*O3>YGc!+(K|2}{cbtLF3Lz_Z}C?}P4s`V6wq(G{uu1}?)x
zITT6iBC5Fkd{qu!Tbm~NWy`kqTJ65G#K|;&t<!Y_9-c6H`l7}AI*uTrzMkhpC->>#
zam-qh?VUAE&&IorFS*^OoUeC@(_3OZicnJNWHiG?mu`rHdS3xo+dPu|QK_va2e#sz
zT5P&vjatWQ{5?hQi}zuIlq*(&KNUwI^ha9JUA!Dd%N`O#AbW#P(FUyqDtbESz6*cz
zVHXua>J@|L2HSok2bj>)<LBcK@A*F;r0tRIZrxb-JQnJ;QyNi2Yo}n-M%$ViIO!i=
zR7$K6=g?52FfWpd$YZO3SWfOJkX}%1=IZW*^P377m<`63lm(LMfSx%AMM<NugEYaB
zG4J)8U&elB4h7AXPf?eazj|4t9~-dXgL{6O%^(AHR&0Zy{^Il9r*!?bd8leO;CdJa
z$K2OIA<445W>tMUu%>Rmb1uz7-54{_q3c|5cRVKn9^oB*e$Ewak!fp@3RkkX^>Y^%
z^APfXwMm)Q@>+pLbl1`c#MR-BZNT{?*4I(wh|Q<<{TSP6GdK6xU2XEu=s16yg=V}t
zKW!~7%0~mqC=oPh?MO(=Jc*1f=5+AO`1Rd<EJ3K+4oMb2_$zI`bH&^NZ2<Nc91a$=
z_a!g&*RuK}@p#Kn8*Ob#)8ImG>XKEfPs0y8eOnJnd+pi3CXB2hZbgcZKDWb>WX?kq
zCirCAm)JWS^?JWYsn=%5ZmK3$#K83@c~g-~%W1vQ6~>z#8^`IYR~LPnpH7E&J-P)K
zg&2vjX_O=hB?U%|+W5hQsC>P#3hAz<8`hW_YWMkf*#npa4W0Mn=~DhoH76B=dP@TY
z?*Y`lADmS^@x{F9-L5FH%Y5tSF*Ysy77|2r6Xcdl*Nli~+~-ZF(v!HO7mTW>Q@+HH
zaNEf5JIr$BgC-zQi5rS*?zN=$o1dFM(E<z<UA<KIsNPxl<2bzb<AU``<5Hl?Qb73h
zqYH%XG*Go}?i9pT(t~aAl@otT%zh8(Es6RGj?8WpU*DO37e1(D({<5(v)%vE+pA7>
z{Q5g8TlQk>#a2yS<r9mLQpaahCi#a}fw+mjLiak(uH4Vcsxvo>OP%=)J<*ZaY6V`5
z9_$7?ndYsS1Pa=tC0^bD{XpWqXn+!%d-vZh+i9`2W4kncG;8mBWvnk$A<AQyTYNw7
zI)<}#r>!GY`VL69_{LjXH)8%Y{y;fnMtq+K;m1YsM*O;^6@PnjUpzZl#eDNxd?tLG
zJ^1b`;}+WE-k)|K>t6N57|Dux8DJg+w`?I#+7^><yF$I3T;3ps07!tK^oF28eXsoK
zg|+KGae>|G;336s<W97m_daDw*=O?`R`0aKnxEODA$YT;HatFP@*25+tBgW|3!n`7
zt}#3p3UW0()V<}SvY$Bwzke$Ti`orqjmd|Ik>dO&-#R)H`E9Sv%;3Q1opRid`+H|c
zyr9x1A+UDlvEN?D^r^P4?!wQX{x7GYOoD+KM4T4&__Z;j8|f2$mY-fZQiPY)hd6&!
z-BO)HbD74mMtSvFzR*THNLvqd8rysDj*rjGu796MEvzq;%Zbs4sPgG$_pV6xyW_H;
z2KI<Zev<WxZiAG^sd|l<LfenI8%Yy^HXE88<kf;beKlSeDQTaEEMl?mI2D`~!E8Sb
z+}w8d->V=vE*b8CE1DT5%s;u6a>ZM7d0P$%e14_u_~I2}cDUFNu%PL-ASsttm8!{n
z$5vH1AyO`%d!-A|*=yizzAjS?!FOTw5oaG!ghk58Yuf|eo8$)PDE}<et(W957ZtNa
z-iZcbmd3AOLPUyfLoG?GaENHEG&{N-Xif5z={LW(=BrT&^jx6n%y-)cW1MLgQaytx
zP$=tAh(SpNr<b<<F?uAEVv<aO_OEZl64Hywsu_a!%)`l7&z%&VGX&<m@uQA9rI!j(
zD6~d0L=PQ@<SaJ0G(KEJoWDr*7w2h_|J%Ky^~LKW77})9G7ww1-u+b_$-Ddoe(39#
z4=7=jGV6V~wudGhgvqvGFl2SxsU-`3F)0Dto=O*T;1Fz=2DIIopl$z<Xy0<a<wous
zKfMy(5%Stx5W^%5$ZeT$<~^mmoANC>k!2g6R&Je6!OB=>)3QV)xyEK6S!A2No~{#o
zj=6KOxbAxdj+1<WEef+cnRWTeIPhgaUt(K=k5m~+WppKz8<HoXMhG%8F#>lS#F3hs
zvFe5bRL|kG%@c)}_IP5)oZ|hh{QRpzJ_@?UPYO3PKTqEvUhTd`u%enbDnjGs&)owV
zV(4Mb^-3<w>=e|Qt-p|MvsFJc$kcyU)zRoQII~JFj-g}N7fEA3A6?NrW65s7d012S
z%=ZPlR&yN`F)0F}n^!sd5zpB6K(fV~j{#OpjR9)&g47)!62r*2fwomW)+GCZze{j$
z9CZtQ&)7dNdPPPdE+uoVQU)U~@o9WWp~4=eg1-b2J4Cl*EBeTS@HeHL0O%E^9t!Es
zjz6YZp|9byrz5H?!!gF*PAF@upPsF{id#ajmR}+LqArML+{!{UqP)#LFU>H7>}{bm
zOC-LboJB$5mb${NczuhOtj4>K@2UN{X(bYs0P`9;*K<@POz^tPBCSRt@_q^L4LZIe
zm_r-Be~JgzB%lohgUBc#j84~LHW=DUSOh+99LfrK0It^{-egz$l{K+{6%l+E6Q=#x
zsjz_46!mBOY6RTD1^5(ll3p{-CXDyS!!7M56&zK|9{-EfU(+?g$~K?tIe;tRdJUI)
zs`WU<{hf4OZoVb~$rlysx8}tEriWozD{Pn-k0AXX7S%GR@>`-kM7CN(m#~P{MiT%G
zA0@)S-xm7};|i>2cmT+Zk`V;}Z?{M_V>9H^w7nl0ql+rkct-r+q8g(>03%yft<0tP
z2jNg+Qi(*lbjir@Tv@3VG3q~Qb6|uYz@zgY?)U|OI=$D#*CdGVepH%%n5#B69_5k+
zp78HnfLQ{8IIgnCkpOhfUlZjJ0Wu0%TK5jke=`deM5F2d1DpSwlurr(X5j>vJqHX@
zDgbZp{rtA`ZYGzvtWT$lJtPsh(c+&KR`w%){#2|={_5jLCDLqTGAc48)b^OzY)9BH
zpTHvue_F3`nzvYsh}Vo?yR=kQ^9L@mHbhyYBM5FPsnUM+wXCv7j;8)Hx#&BnYCxC_
z=jKCaw_y|5LT*k3wH>%~RtpBsV?Y&y+7O$6bd!8q`t4=QSRpT~$<8=FEIa?|p#{NG
zR$oGIBye`-)C~iN@>z=i&?k|q$t$vikyA@kCIuOLloVb=gcpNrc7b{nXk)70ey8cA
zl8cHB&w}-%rpNBhet#|(3-j|Ke-!38pnyL2=Jeny#P@;>O+xxi%^!G730!(J3@xpQ
zaOj~5Q5U6>18d@$2DlG10wo_njluIT#!LxM1GvG$zJF`;pNq2*W7c;x;J*jZO>dRb
z#@>iMUurwqkrfcZrMdk+-~1Jh)JabA5go!Ty<dowb6edp2vRp=#UdGgzA4X1gHR<d
zhVSZ0TGs#NqO66$;@$g~T=8!auPL|GGuG6n_I{3Ai!0DcLxm?CQ1U+2iw74=xgWiz
z%rIGU%kbRw0R#EMg}R&=TzDIxZFe+)fN%ENNAyO>g&>N5;@Om`p+evQu7)e1L1O5=
zJBvjx?Gwk}?UFxyr7+N5GsJ2xSWB0fL5KGoUgMP~`3;2zf|Q0HNza<*S0p#)@_Z3|
zWCde@Ys5+r0S7?gk%CVLW|^IY8q$^5<o4@dtwt&B=QnL^QME47wXadpug%<9rG+Xt
z4SzpYawUz}ni(P$dY@h$=DESbj~p}#fwbM{4MP(Jw@sOF!>=m$Gm0SJvj^lzVP)A4
z-0B8{VYKXX?*g2VJapn&DUW2$?zC{c)dTNiKguE;#v0^G0<5lqfN-00yVtdsttih?
z5N8@!iQa%1sf-KoA~QGqkLKy8XbdQ_OWt1*D(6FuXy!Q?Wq!yloP^aQHxbAxhPa1)
zp#XXIC^mL*XdDot>+_`?yxtF##=O^iE-X5b;_C%Z)r~X6nODWa?~h89B=nkvU(?cF
z1_rv!<tyR<#0~!q+;S8p^jz@zonUXm*TmS~-$_VyZ{lHdL;X`t%&0H%J6<rOHEo00
zlJ@&EByag2?XzbDf$IqnEBSKAXJQ2~G@%&ch75p;aYx8m`7`+n$ehqLdZK!16pJF8
zVvVv!OrE6t9=5*;B_+vgaZL1wqFvTUt1m2Z5=KUE0r2-Y_#M|v;wLakHOK%IMFu@P
zqav*Q3Wt!G#FE5vRbuf6QUA+H4TVWsn+#%@m^Goi2pYu-tE7D>m~GT)RIkvj`;As(
z?=e&5A@@ocz&uuR0guunjv9wO_=MI^8jR%~tRr3+q5vMfjU6btdYOCt#=sd>Y`%v<
z5EM&B-IrM+$hhsDjIu<A+_t1aS3k}S{E`W_y7*iLZvc<W{tE8#2+O0P)z(Cl>CW-a
zh;H=PuyAAqj^A5ErFXhfJWu&RVLxd#CJhIUd}NMVO1~6202ES-1%#4GCKU>U03-XV
zFGTHU#E`pr))TYj5t-1ng*F0&#QKG3fI&9>h%`E?!pLLU{16}~mOmc=thOg*6;Mb<
zDJAxIxOY1dJ4tdyXU(9s8|iaL7hlX!x8W}|1_t>@fp(Jsc4yV5#{%@mU;+hQ02ym1
zga8SsTo`(xz(rd=`}Y6(HkN-QYy=%vL4_2QQfBxUK6Amdl0q0CQ%z-<WSLepY)yj2
z+Wvz@hGCe<P}@&wVY@{HEB6o{TiE=K_mQgC9?P3y@ZjZ2em)R&2mbsQ?$ikb5HXWC
z1NCt2R4A0+?F!nu2ChdXgSdr(y1bE}cEePD%Bufa0g&p(&I<n7bCfd+JmWLf(s>gw
zDXCs5hhLVpRHHEyAD*gyIsRw80O^3mxAy}P6Ss8@6(s<L3bPp|2ivaa)crC36PtN!
zDiIJj4c8QE><}h|TjBIil(}Z>zt4giQ}`4TV1_CS9)@8xz_xe-6y%_w^C36yri*lp
z{7wRptZ(?K%+!BY^KeB0WeqMZR+g57rcM$PNWC#N4e=`=<=Y6)`3iEkPD2XG;Kw-@
z2MX6GVY2GQPTN2w1Z-*ve!%9-!NsHi6lv$*-zBuAIBE8y>Wh1yq-M^Ogo=h8!i&(=
z)g^j=HR7Jp+x@p1&5b$>z~1N!G0B1N!EL<J<v<q@;j*78Hdght1NGJeH61(#k9fXd
z1#o=%B9{N@lWZQNs>D<GlIy%X_qNHBv&rp=HmItqnk%E~7EQXW-xq8gN<@^L=je|y
z-7;)6Cz-XYY2_w&?{sblH|*($j)gCLFtrlB&u3Q6GM&6Yn-_D}qrX6l8ILG@DB(#j
z0?IMM06ZQMJn9l3$y;YB#QYSvu|(&LxnL28xQy8Evg%r!?!~=gXFcft!k*_z&^!qi
z7M8lYy7l#Sj$Z=Y9}rM#xyIe)EXpg+_8FNGs3;Mru&xnl{EU4g#$RKHyh9KlYXG$g
zR*vCi@-YrGu?{gQD9T3t+$h$hV!uNC<dyL?HkJ;oIKiHWxG`8#TEf3x%*>Lx+4&^I
z4+VH#e)1z%_2!Vb%th&@@~2jidJC3@%y61kFl+Zk=odjWNa^b=o}iZMwar>At*op7
zZR{9IbyO9Q{E<`#o`lJk<`0(c;#t`yg=wh<!yXvY-i`eQ$!$fWm<C%K4k4Hr<JNMM
zO;qI^JgQy;O;}4X&nrPBba!@mgJ?RKbo4tXx*A1IO>Ht;B3v>~D%4AYQrH`+izzhj
zQQy>3f_q};SdESfA{OOVLwqBKn6K~^Zc-DV0Xr1}o%hAm0sWa-(4baHznTm*DkL3;
z76*RPSFgrYf$EG8`#MEmBQ0b>EmJ}a@eL&_3UJ3w4|_2#6?-xw#yG|0S-Jj^9IfV-
zrfWs>oaI;GhMR51xkN-(ebCL_^})eh113?c&#ecMzc+ta7k6{hw}iT^D-3&0iS<?q
zRR#u+IAV<CsBmD#V$9g1x`GLk;x^d+8dRfmkdxk3U$3L~@QKZ03xctW4Al#3-8yb2
z;p_AT|G<jcP(N7r7Wd;dAXCD8+_ag|MdkrL-FjtFyJLk=#-iYRxyM$DRuE0GwQH{L
zyzp56LOPNF9vjR54K*cvnmKj(U0C}eV#;i)p1|eUPO$#Y?jDV^p5$UeysM3_JHeRi
z<)G|y1XTH@=_=#$3vX|4Zf@>y0yY<pC*APy*5F0GG(JZ$glV)lhS*r}*dg8sIPF!U
zk{v9iJB4L76|0Gl>h}C0mvfVeNP2~doAL4M+qfwzysd6_`$e}{Uk~<E77`0|^H+L$
z!W&Ab9gWu`ix@0arZ6UG5J0r-uKV+Co)suG2~sJXW>I!6*+IedqmZdh;V&`C>kFzH
zuw8sZd5#Kf#vP$|cHrDjy<LUp0q(n_Mq}@JJ>I9ZtsrY}As3E%==j9k6*Oi_U*J&L
z*pr$?PEMx9eR)V4(w`kzHSxAi645BN9Vk#6N#l0{?w5;*K;M8fGaIm=sz<gyEz@qa
zUN15Z)&XUY&9Ig}@Op?J8^8nCMo9>f-D}r+3!ct<&Yywn#&j{JH&=YcQBPd&tFKL-
zWaM^~Ta<OIT~Ai=dO|%5v)Ky{qt;y)L8s^Q5%V&|?|Q<-NO6~_+qHpoORGEQ283pR
ze0C*D%tEs#GP4<1>bIP3dc5jDV!0lPtM2>YhXoG<3%)k>%M>_$X2ZReO1V81`LzH3
zE)TO&7wNlFR!hb8?e>Mf;LUbNP=FdSglo2XrQG>sl9qm}CSeu16bB~}P6c&)d;1c@
z-q6r+MLA?AgH5M77Tma>EkF;`3P<w5mQv(|Z`N>g{mf-+lRPoL2=ep#*6Ul1fsV0T
zv;Z)r-8Uc4YflDtYL?ad;<<gDsyyqB(FX5c{a^qlg-AC#Gjnyh8r{&)&;^wLZG*1&
z<qQaq=FdQ&_FDi^DV!l#1Oj*$D7(P<0(aigzH*a>a^gcB`Psq;#ay9OIz$r37w9*f
z+Pmm+u_j2ipbj#qt^K%_FOkXvT!xgK!5@ngCyDsRKm(!F&ty9>PAZz*#=?Suk&&1u
z5$7_by<P17+@|6XKDT2apeN6%9P;sc&?_10&E;oV3{x%gUx86&+EYeE%-28g{3Hc0
zXC=4i^yti~4K#RhT=BSaX)hjYuIGD(JD%x?Xr;-rA#`Cie%y-XMS5(AYQXk|4~5!W
ziJaen%%Zqr0qk`BeaN-<6?hy8CI-@^fEa{wPKxXo5%~v$ZgTOyNpVG$rI#I~xm}m7
z+NBG4_P<;++qBbZbXZ+cI6>QpE<^#;4K|^$e>{`={&ZE>@%q}@`}gl7K<Mis76=7O
zq-XUN8#FCA?Rqp%9`r;hE^v9@8FsdJ=<fY)z;b9FUB-dsoMz3*-l`o%p{N1H@sRAu
z>|1wgI>>rWqLsp|1~F3|tqAHf0s_&S!>;R#12gPW)e^NT{EuGeoc^Bi`WiZ}(A-Dt
zHDcvl7(oxlVF?ph#~mSk9S%a>Ufl|otRJnJQo3;H{(`&5W?zju`GE3Q70nT%g_e9H
z7K*c{LwSUNW|5(KD^RPTyv%rBjH^)#T!}0!_!xR!Mk}XY*0iml{0PRwVu+FwVhC>U
z8{;$(fkP~WV^+Jtb!scUWq4Nr;=Gs=pOFG`9PTICsDQj}5@8Y+RGTe!fmsBxR;(Yx
zeQozK;Bpa{#+DMNR};tcM4YR6W`L~+zCiN?u#RttEY3JZP`Da+4R;q*YtZO7?>d<1
zLORnr>+r0m)Jnx~v;9|d3V^yS;1}I={->u~s!ZjfL-j?fFq=q;&;>9hIerXINV_T>
zJ0G8Y;}%Lbfv4Tx6_d}B%&*vD+2TpnQt^vnrX<(+)WU6;P5AfKjtN-QTXtDX;}vW|
zLQ;d*2j7Ck0n<fpDFi4X6LgL7?b&0istY~sDmpf5wxjmK-amu>eP?$8h;D3FkVeH`
zh3IkZ8O1{(IB);kpsOQiND2@+-76>4;f}HJHdl+SvADHo1QmZ3(u2hWKDYk>^h0!7
zyq&UXo(T&Zs@KUzcN1=zZduH%u&ZfLcBcd<r&)H3mVoy8<iXzlflFwpzE0!xp2s7b
z#M!7!VOtKOBBB!0ieqx;<pt-K1sYX?CQ5L%k($ISHF)j}TS47lF0*8^gJSA-o6Fy+
zO*e#pIwEvctor@d)ob?J+BF$4V`CcpnaD#*i1a_Q0Q51404URo!fIMm#-e?_)ze^>
zZ!*?da3O-H2FK}r>cn(_hEvWv0=eAdy`MO<a+)BM3r}p;wOe}o>p8ujQ~sv4rbpsM
zA=;E~VTE0VQw!q0?%j;lK>6ACR_)t;re3}C?=-KID$dAlg}f@4N0+~g7mTFWW1f#4
zt>vyE1)?Ryv+DDB&Qy=(xhHet_y<8>JaGBLjswJ3kpwuh|E-dTL=S(DD_cv8*T%e|
zRkLwldcMzyONQ`-ho$NF2=}X#3+~+$(^Bx;US!iYj-oz>@bKc0Et20S-?a%<ceyEX
zXU1lB6<p-j%kq6v*?2PfJdJ$rT4&syY}0&Kul7#_hrN~*h|HD&%@j#MTr#4Hd7Hj6
z<y{w&aon*e(G#AK@OZFQl~yikg~V(@-Sz(>A*Bn<^BC5MD51@3%F_ogvjH{x40%;K
zF$>Z?L;Y#a3-ddC9ve5wnfqSZcI*);>%ZqF?2zN_hjy*x;SOx3aX*GE@G7=OrC~%i
z5Z+WxB~;MLr%?DFW(wa5$6v)`mV1UI?etfKbHYc+xhq%=;q`ddLqG0VKzC>Z`gPye
zzA)HGZ%gwN(OC=3sr-lI9vD!b9FV*|W5GOH&OCgT?bGqC3R3SY^MRjs-rE$^s^IF6
zwB_}r-skO{G2?dAtvj1Gl;qbelB<=d*>6~xHIf8{6A|Z>z-E?*`AEFl(CoBqes`zs
zxt*L3(MRII1@ui5W{)Oy@3u##1S?Ff++VqL+<dw^LE9W*(-6zzYe?cn;8<kfR(jAa
zidj{_T^Y>{(h&RSKh<3b`MJQkX~M>O7W=LI?s$3b(6tQx#|nGT0FMRObUtD-3NquP
z+|1oej^Vx^av$vD5(qvJIM(Ku1#NZ6<FWQLn95puDtX2+lcr>XvuGMVw<B{ONGTDW
zo4<3Z>Y)(!jDy>;WBH-Kq`cC)hXx<P>14Ip^!+?P|NMLY`NlW>PKETg^l~;tjl3pn
zQ%$iWpVP#z*jV?ou)U>ZMcpm-wsPG|b(rCHeuB_CzGQb%Yhl%Ir>PB+k%xVy{Q#y?
zL_Se8+#8MbM7vT2KdC|EoBsLh=!^t3%&fyHQC)d*fGOfzefA;Oi-Zwj10v_0c+Ru?
zG<Cy&LSJ4<M#>Yj4BLAbxT}<kKv#CMpK4xo)Go5M?ik-iU*LFbqbJp2ZkSwP8>jcR
z-vx>pTZYZPwTNd`-nx;TwyU;^l!}~`-0$YeTKvR~u$w0}`$ik-f>yR#vRcfiuWbN}
z2WWj-gCPAHs1d!6cD;;brwo#h>XS_*<g??bt~;85ivAac%D}f!X(-`^{Mm2cz4uWQ
zgR6L<yKKXX8vyp&Q_q;cRS{8Gi)>)mXITl5`RqEi_oM`l|1*6JZALner_17QSTbJp
zp4Xt!<&X>}ioq!-c%5^D^+n+u)PvFm2dnimqCO&*aoUVeaF3mc+qM1L^)E*4lzMx<
zEubZ`E-5W8k}cARFj=X|==F{2Tgcct$mm&E=!GU&Wqf+Bf(OWdm1H}S53RScjX7Pt
zu<2P35;5C_A4B80LX)@>vtc|Pa8T$0_Mw3AQnef-(`=K{yK-wOmA;<CDJlA~ovw?k
zrR?^ZlN}0^AMfCt-#5bWedOl@+&LC3)m3fqyry)}<6D|;_5oQHW>t+~hBUDQF*a}m
zYim5jwHP89Xqsz+MV{IgCsF)v)gSEdL&tf6d3yFVFth`&)t9|;?$?x4)y2w}ZX1f&
z76LYmzJ+oS>vm*y6(1+A>k%f~FazTtYl{9$if;q+3#Wzq>+hb7KYwt^IT1F_nLQ2C
zo?7MZ8_Ypcct;jJvOc3q$riai{M`XCHyk2jxbv-xcX}VGEzifBzA7Df_KSS1E$~sA
zi8yw?;mr}M72!H5o+$|xo%iA!XYD@)?r8uoIaa+<J1M6JHEn_4_I$dLrT1&`c=QRE
zNFFa9DSmBMv*jz{8*V1YnRn{a({KvHTArsABw+4b=SN`#x1>Dl(o`0DiXOJMk{DqN
zcaF?oVp4g9E7%L{O*iDV83$!kIm9#9$WYbuumO+i8NvoWN#$*j{F5HGW>8yx6*arV
z_!OV@5q&e(Y_IgKz@pE-xfBz)cXmWV7Weun{NxG#I#OCseF6)HCCdxz5B%_wQM83v
zd%y`gq<w;x65h-CO38WeQ6h3>2-THhnxMt@l-B6vge)a5H9?bARDZb%pa(h8_O7|-
zbU(zw1x=zY5MX_ALu>hv-sXSRr)i<tz|tDo-ZF7uP%tDt#2({b)zFm}@l32bd-3Xo
zu3eGjQcgxePEk%lMveryC^$dwsl;*MH>Q3U4~(|!7ip>K84CW3+0XC+=>a^y=kPS;
z$-c>_BysB(!5N1w`_97I)a7i{*q-+z-!8n$Jav1w0(YbdpX$_ax%0mk)PNnjFTeO9
zR$?OCcqxGFw}cS*AUTQ*nELuYN3<AFBNl`+Xw#Ha;kP#bgU8X8rrj(IZTPcM-;kQI
z#s=?t7F$*aF>vBW(yWl8?61mc*X8cKhNgmRZN)C4h8#RT>%M&nn;4eAG$Q+<Bg&@P
zL9BY=$|j}=HbZ#Ds?AYBOQPu7UPXgclGpu#_<_6e3iZwFy?1w@ChGvA&t)oN?L5OJ
z@cgfPdta0gPyrJ~fCNk=yhWU4O)mh;g(Z3@WSyLB;`Y(#9gGcimon;_pz%q)yw9h}
zt9*mcu<+eO>nizbchUp#q|b?7=aZ`v*a||Sr&b*y{n63cs!ouY_De=WMrOR7sbvx5
zMb<}YnC7R8hf}Qlww?-&G=`+SI2K`@s32JxT@2K^(=~c<M*cZ1M%D&;1)?CE-W_t)
z3-Q5e%a7GYFL*ahwFaMXinL#_-ZQ(rS1zxZW~ZiR?>!s5YM1jqsQ1xZ+L6*Q$K)bE
z1Z@4;bv(EJRcb1En^PaYb|2B%^_8mr(tsol-yTDx9d*-s9r5fAf3wH=ww0;A_!3|V
z4HI*#w@;ZKybdfh#6gbf9XxB5PZo3Q168B#p>_eNo}{hf;dkB(Rii)n!aG{#=BR5v
z3*OrwJP&+`JDj8bKoU6bHP2;f^*wuZUPYC-oUwj!+`C_MojLQXvUkP7bkSiW04RZK
zG#%!?Y3g<+u!IQUT~21sZEUi==wmT-Ro_#j!)$RQXh#?1biz+qBVn{%!o;-H-b+S2
zPy=h9^szCv`P`f#Pl-q;1W(=;G5KG8w@df>wa56!Pg)X0sDD{`kRn|CIJHvhczFvr
z_e$Qb&<GW0-y|h5bTqnql6||KMyu0=?MH+kbNi7KU1hCf?(m0P6A#Qbmzz58r`PjT
z8iUuu;~#(b=_(zcQQB4C3~F{SWw++=u$%CH+}S_4yKA{W0E}#lM23u0{mHIXub%h%
z^uVhv4mQ!Ioq|n)3g!rzJ!YcY?&024Rvx6h@$$dkNH-mP>OE<yP3pK>Rr6VHLPaNx
zbO!w>KM;gW3hCRj%`k<!AkxLlo~_`8`&0sqdl7a`UJET_sT|y{#od-|mpz;50gvH#
zx!g7G`a;K4zV1ZsoG(o?_N-C0-ppzn3|*!8`fj$k>2t;tq?6L-@g{cuaowxrDR<+R
zG;9yuW_iYE6v`2Ivsp<Y{$fhvps;5UU9|&%AS>~Hi1w{fyN9=(hjXJpv4qKX_;cRp
z6jbGSQSqHJbr^C|7393wuGD<S@P|!m5OFM7&EJ|WY<@Cw`AAo682am1C{?~A@GPSQ
zKb<UN7xQuU2SI(%BQS}D32i9M(8h47CZN!u_!Bk3Z^p<i1fY)TJFEQXs6r_M^Co-w
ziV0u~STaU9f7zo~df7-~+5C@dCpHK>XI?#5e)PbAi>M!;y5p{y>}2M;QCOTkcw4|s
z%6Z_0ZFKgq-`-L!i6gA%ZPh~Ouavxa2ZC?ketr012I`00+_gL;+o=bqM+}h^z6@dS
z?F(RBc4Y)kM`dYCwU(HTcLLZU^6h&0gXzM;j<JLSV>2@|qoeHyrJ6NBp&94Pmz_N2
zZEbB$O-&^w;an0D5)2IfC6d~ou%uIX_C|`;K4PNZ9IwUr4<ruMIPGU>H#MB?whW#9
zM4jig`?*o=PUE?9`RzA@lw;f&NTX>jAmRJH)5!I=txeO-#g{FuSISfML9>e;{$~<3
ziNk{s_j(K8xe(ADmR6P#u*^5@1b_qZH^NB@pKqo2`?sho2yBpVOU=P6aA%2ShW+%s
z2hl(z`R+T3-R^9im4QJ!B|Sa8-F&0NE%Z!AMmmE@TU&chj;-yzipt5m?%MJ3@u5`S
z3az^S9vUr5CKfCAKF1g7e6HDbCEV5*1Z(PQgT*g?Fq&^!^DnqG=kI-dTOEjmb`|0E
zmZoKhKt`YJnNmMq9@EwQZTq_aMz{j~NILp$vHs#|YhWOnoTKc^U)9no5Iy|`wV@Zt
zc-%n?PkWs9i!`La6O5!;?(AKye4-_h8|bfg3dU>ax3I|5oI!I0`gYY)(O-<<SD>Vt
zddjWV2XPWH_zRw-bmI6}2@0C#BQLT#pPprZXHoZXJiga(Raty1B&Fo6bJ=TEzB$^4
z7w>z&Z}n6+JwYA}<18#+#M3omU*lr((DwIO?Pwm-a2GOgN=W;S<z0hdP!e3L&0IZD
z+6niw#h~L;b@fY{{bWwFMX!^gj*bohdE6&i)X;EI)l0s!wbdcgYQOv%heFT=UFN0}
zjqS^BidA{&P6s-qsm{bowC(bIuvQ*JwC$p(65(=jJ+rNTSIh3swFClFAB#y=8#*o7
zToK!XKId*<;6QoDliG}SN1%A%r0#Y$%`|6K--2LQ*to0`E|Q+HA~apiZv0O#fY0iV
zDBgEF!r*PP-_CvC@h>}XBtCREhC$QQlf6~?NL`}!P%3VE-%2Q2Lb;K83^_BlS}$kZ
z!$CSt-DI~nH$691*S+7H?G7LoM+`E3nnf1)dU3obIwQ1bk0NzZ4RXHe1A^NK2<~ox
zA<GC;g-ylTEAff$H&lKEwGr*1TuWak)H&~mSrnqZ@6FHyJTLZ<x`%inUaOJ3IAW)u
zJLrz|3bj-eA3ShdIml!n0SbjGr1BVE($3g4ECfLpcx!1>;8=$lK%O%T>ztdCqW+^L
z|KB4jR$RlLvNm97d8?bx;#^&2evWAqEXvB8*=@#bP&4!~s7k2*I1o&jci-@`@%AJO
z4yz8|FKouGnp#}&sa=;=Rz6<o>;Y6KVe)~d&%v+jjAMMh*~9Id?Eco|H35%rk^0?c
z$6o^c_M+-*Uu<Efi(Y)qLB5-sn8GvpaJvH{qfMT{WYyYG(1$oX%$nS#CS=6Q6W2V_
z{v`M4mbC0gpYes;_0=PrO&!V7j=w?KZVKQCdP(xDaqlOz`l-VludmA>k-r6KxBZT^
zt7P7CydpY5xdmV!S6AL239P!??JSzri171cV`C7AonxZ-o9ZSm!~{0|s5={L>o*df
zL$QloM+B@xEVt07zWz_s%DG**s!8gj;eexAf_USL`^$j)-K~S7!3r<?1@UejbsybA
zxN`8@`<8%_K$d>0lCTmKKWOm5ZB|=BI=kaVg&mXxK`yLV9&Xj-c4e7B)=`e*rAm&8
zm;IhN;4;5h1_Biw1IG8mSHgJlY6fzyz}SN|b-L)C_=FR7mH_76l5uh1TT=?FGnthr
zWb#*JW7)p>{g0L_*-kS>3Nx*P<nk!rnT8xH!Hat>U#pQNyeV(F7|vP|wS)F{ifzS2
zQ&Y_~&}72waQHW81|Wb6Sfn67HUIODw+ZWy@Aggy*-l=i0z60QhfUZ;CM?l4?W%+O
zZEAb<4fax6Q}uZ~#US`pfQ`)#dfNV`e{wRKOfv@59TykJcSe#h(&PkxLM&%U8wJe+
zhset}CK+bV+|Tv83gIW9#}Mi|6>Q>6`#^<%W%IH$&fpNNKO5>p<HL-$WEy0o^j6nT
zEYk0+T{BV=8#l=_Ysq#Q-*>wkJxGJnlB=+Tw~DqV$rBxG{fk>Q6HNLdZu;kwEyOF}
zLNs4;x*?qGmhNWyLNk09>`C-`4Xv7*J`CTx4v^hf-%Xybv4<C$<mcj>eaL%C#@IKQ
z!ol@zN?TFZaqLVY?|!b1WEV?oifkw|ql2QQf_q%&_ujW6m)}Jyy*k8yoJQdG6}W2y
z4FE%HZZevxOHu2YooY@>*Ze-7mldJ0EakDtuW4gY=_;dQGHwu@8QLcL!dc)+%~Q05
z!Tx?flY<$vOjzkkjaTxcn@Mdu>>Aqz0XbY~IN9-9-&fz8RSN!E)1j16L<iEY+BqN$
zapVfQYiN7w8GK{kby4@?x?g89$1FP5Xn!ya=?YCpIjvCF?X!PSl%#S#ZNboBYc`|V
zhru7@u^<J4)a+-<BGgO83lnqB-#m3h+7%K-^j<wF0j|x?m91cTAxS<m(1&KVM5}J5
zPvJ8ADPpk9Nz`;jR$E`_T9n7<yV@Ys&Wh)zXH0b;%l~|F@g8)N?zE7own5<IqGupc
z4ph}AW?4##<<-zla!$~rOz&5r*<9Bm)*9ymCo5PuAFUSiF+LjmB6x0Ru?vOtD)Sx1
z#}7gZpZzpDdsRY?6(7T=HoNCnO_jPI2WFuEa8S!X@j8!z);(`L85Tq(75MmjLS5g4
z-&`9F>W@s$Zb&L1Um6s+*HFQhC14A_J)bC156%xgAgpPTJTM+UCB-?#Jk?&&X0kK9
z$fIVn(Q8dk#F!D6YNM^hz-JPow!MA~O%Wh&NcXDwc8d$a7nt>01I|UpKW@JVfjf)6
z%6I1X!bJo2+Hwkj)(-G?@9<5x4+bNWOEz_C99;~^O4I8EU;m0=+<;*28M2tvt~+tl
z6SFz{Y_{){$ZfEXoS#8cvK-5Y*r<Y3Qyfe&1U|G-)Yp^pL&CO_Fp1kVJi`tck!W)?
zKvmr-BisaYRX8=DYI)&%?hYty?+4SKG=mwzg$t`vx>N2BBTc5&yspT_k{6~0dAIe@
zM&6bO-xBBr3j}~TN_Pe(r(DvCNVJ-}C|EMG)C7hw{ZSc}d*p@SD;`TeCK#0eik{)t
z@9-}BE9msQ>vkef3sGz7#~#ZO9=c#m3R4O5lc@739MsEa>`bECYZ=0xqkYUz_Y`v2
z5go@KAzUi!8{ipPSE4;(eAihx3XpV2dbl#@RhH@I5M7XSSx`cm)@jXxQiiqg))>~^
z-W_DV;rQg2N&)0$EiryD6#3fsaPi_O+@%jV%%>a;Dctu+>|0G=d=KTF-=9V(V5`5M
z>%i1qw27>{Y0@Q-R*>!F8Q70XFn8I?%oI9?Of4p*X873kbn2%+A?#Z?m+T@MKf8Ch
z{a#FTb>HfWobUm^+fj<e9&#hm5T}>?*=xfnSkNQCX4QAsXJilbUVA8WP8D#|0Hu}$
z9E|NAyNb^Q70hNHD>(Hoy!{H&XdO6azq7n5ad?!zhA@u<GJV2BB%iKH)R#<@V#(2W
zYTW3?%b%u_U2+}v?8B|S+FN4`cXVDM`CqKM&7UO_^D6P#^je*F)O507Ig|^CukZcc
zt+TUpw9qk1@pNkB0{FTG+;uZh5bLr#{Z3c+cI~T@&ngK-TCU}IkH~K24MqWmchw|F
z=tBuFSml;y{}+*kKT)v-1I4O<`#$26`htq<H#>cxJH1I4Nr(|G$Z0F#-fa^?CSE;w
z!S_zv%hHjNLfB*LNBDH4t}KGIxhaELzUi!yE|Z-4WQJ(hsexUJ%oDauRdfBF1$Ukl
zxW&2IPRo%2Q~Y^ByXAwCwBu%u=v>3#k%nRE)F?D)N4-;*PoNtO5@RIH;lE6WQB4vH
zdC9kNITgsJuA=RwN=D~=+t`iVtg!~KX7S}|ra!hlAgxtGRPi=gr?8<q#D>q5)wdGS
zA~+i`QoopY!lc6gdce{!udJ$i24nzFlJ&a}pYqNhzLOHY6J_AINk~ley=Z~#?e4x|
z9LW^DU+sGGbf^jG(aT0JN&awlYAM&reVQQWB+bZVq9%;7;4=!v)q|X}Z#mD+JXo2e
z2}}uAr1s{^?mr9#;MFi57Wo|gK$92M)2cnKm&ok2@=%ybncw0Uox81xeu8q7iOF`m
zQ}4TM)&Ac5<R;R|bg;>4W^xv-j#+z8frn_hB{=`=<@Lp(Jp}o#CzSfWc0Yf2yjHM(
z^Y;5{-rz2z;yo)vQijY4=zSASAa8F*BvEINxRu~)kOCKO=zXbWPq<le)vbpz!$U3s
zRSHO)nu$jde_$z`eXjr8O|{eOBI(_$!(S>x*Jm@RVL*Pp{biH288Lz!X)+;s*r*Z}
zj@Xe_!>#%8Q{u|}e7|Ijt8MP(1Pq&}PoKJQy$GM{As(a}8$_l{My%{I@*iIOc9#6B
z+E&|*gabIP2eiD*=quEBVLO*pu`(N;nx>C4HQ7jola$Eu>1zaA-0wFpAYyQl8Mw2k
z^n^bl$oZ_@BBIxuifBEZiOEZ0Yi@TLtN{6tsM<)U4L340tgEi^TDM|6ot)Ix9h2_&
z%brBL^F@(@PA0!2_YJmDe~Vu{2??6*x7FqGEH>*#DC}qIe{=u-h%mnu{7MQpg*nb*
z+&3Umn#DzyFGipY^qtecw6r}~nN1J9ko&+iV}zgIKeV*|NMR}NS*Zg>>Z<)`QxSHl
zD}ynqqSJdOM1dfYx1S*|YkaFN_W5w_MOib6G`=Jc%{bfe{w650=4h1HhV!=aSJ@QF
zz>AnWIdbY%ASC#J_xXvzK<CN`&(Iv6(Gl+5K=P6LfSOa#DJF)9{)vNN&ihj>@1ac9
zvb6O0fP7((Z$rxGPcektZw@EJki3wSD(;M^?&N2LFxsYc^eK*6AVVf6NsjZl)e&lO
zvd#~|rIlFV?5=}R0$@^MryBMS#L9Vcpd7NQ>ge)l6^(!uy)g0a?h!IZnuvEw%KYn5
zFQUt$f(%Ax<_{T_7N)UnH^&3!2J;0+ff-AtS71KV^Jc|XPv`=uqn&iYgm&OkVp6R^
zttF@CrP(s2O-&$+qhSXX!tc57QIEq7i_FlTnIPk9xTLE5*kns@_)$${vbV6uDjd^2
zZ50kxVrANUl3WP)GM>LJ?))bCt4$lcS+ZdRFUbzMX6vVoGL{#w;4%;Pd~)sv!|Nt`
zXXk90lOy4L>dN!WcUJbDhP;kle@T_-H5pwIt5_-Vwk$kS*CT2ae}MLgWn+JVQ>?{S
z_l2G1#Sp*0_N%Md7)~DuQ&SSX{pjN2;^5$5W5ZINP@TZ6+4-C)E)-OHKiJ?4zGyoz
zJQx}re8XwXYZ{r?vfqsMR4Ad@J2kkej-k(gV%XlIUh&YGO3jXLeqqXn0@=1@+@*Q%
zv{e)SSDyE%`PuHo)F3EmA%{h3p?S!Bfeq;Ab-I0moGH4XrmzSEXj@DbDK!@Y1?bRm
z4N5FZUSS$5f$FUl<je-DYI^ev<n^_xBe?VU!y*%<5vGRPd<J4!7H${V$bFWj2e7LL
z)A=uIm_!I(7|qt=nu$)X;d54j>1RhWtwl3qQlKZe!BQH>fr}X`WCV;Sro)6<R%M`)
z6G3Fx;0^DJre&3yO&`O%l`L^DrKI@UkX9Oa($A7D0B?j!QC8j2Dz+Y}M*pE0T@YM}
zp7&9>z86rrTnR^Qu9Pky(Zp#stW#yw1N12VkRWcv{>*pJO8>fx;_j`AN>{9U_Y#J%
z*>GAU39n<w!spq2{oD5JPQRE*n+s-eqNq#e!u?=IkTCu|^k|Ag=bEzk?3=Uiw(_xI
zZi6Cd%LT3aL?u?49YM5q|M?m#sGqJ(uvsue^i(j>dg-{`s#m`)XIn9$2YOS?*64<C
zDF=2uH3{F^Z|P=LPUCtO=sk^}LwD0(l{n{#aJT)nA$_;;u<QaNFQ>SF{hLXXx@f1j
z7h~zA_Zs#6rnF`~ciOU3M^PUIaP>lLm<TT$I~G}+zdFyK1Xm2;J<}imE;)cn4JASj
zrQhv&)VHVbgJGjcNJvCP>gcJ9%0SZ$paHy3?t3dMCc2gEY$~ow-d8K1k2IpjXCj^p
zR+5>pl+e50J~Pz$LS~Qtn9OC??EJod%gA7vV{Wm+9bA-S0VIrR`Dy)?@M#rxwhorR
zO0bc;bC@f#F(j+EI&^#onh0DsVl%zw)wRCqib=F$ORE|?=iN6;E-4$>|Gt;ZM)S?*
z%7}BK%@dmbC=ywu*vavpLhY9BXBEnve?2x!Ni>7d?q<}TQ6J+I+XIrAUgytrFSH)K
z4Szr}2t{N=AJ#|39*?MT+~2aTI$d0an)9WLTsG~;pP(aD+X=J*fn3?Tc<`XTP2Up=
zzvAU0$QToyzk7rZ2GY*c)>oh2nG=WekAM6k8fWuP@raT^Fco{^RcO(A6`81EQW8sA
zO4_7XRUb<cUYujKt7f13&OFkiM7A97DGZjU3U1kqLvnIvYW6awlcifkj{*WVo4fqd
z3!C3ZJy`fpfQ4rZl8FRTpAT`uOM1T^zObLu(CE{3PYG&6|ExNho_9FZ5jiMZFNo+5
z-@3a*l`Zb}3(fd+1ojeLR+LoebL{koC#~*nUehaTMb{Yiv%+>&J=_oRaDuAB;}63F
zTH=kt?D@v`M9UJ6`;})46A*pxqt5dUYz8mmhMc^u!JhE++hzI-ke+^5?9bfY-+Q+U
zKSY{xp99$*EdNV70PqM|Em?$NgdSeqT>f_h0T9tv*FgoZVyH%3YXxuGGMg*{8GxIC
z!P&l~nUksgRZy_e|9Rnj1vbYhs>OrlL2LinqK9{wwdPw6(johkg83Udg*~ksFlK2<
ztL1tysLg+0Vx2He*!WyM_<zg%GY};QjLSC~OQ!yC`TyR(*aOZxuI-Nr!@ptLBr${<
zvq1oFX4G1kHOxB96ms-f>HP^#K>@CW{5mjRH!~2&NFpQVmjAm9FR?5xUVlXUw`K&i
z5parW8PKIz6<lBn-+?8#dELZm|NSCPYI|C1*k`1-@u``W-s-)uS+*Czf|dgImi7OT
z648IG)qR67E$$iaUUI8sDFfKV=8DelYFYxfgZHxhxVX$Dyp2r#0bh3`2e>p~<AQ|0
zq-a;AG;nOFx~(no+^G&m(Fg5PtuQWq_WlB`Q@rZ}qAnA2_UWj~;1){=mFnon-}YC}
z9x!E9(g3mXr6g=%+XbUBA$?^DYu2ZEmy2V+$58`ApS|NSd^pRw?Q<8A6oR7$zNr@g
zd-(s@TuOwm5(YM!?N1w*J1r`(38j8l*j?K3p(?4BsaNR8r+<vZkhDaI8ii>3^7?ef
z;9PQ%AJ{_iYH#oYKrQDA9&taMz}^B`52V1B#zXnLBfx|R`QdXZUlZVc#&+AGH~Hp-
zW4p^2`I_84nIj2jAv^{*nLq;Sk-B&DIl3WJaMEYk^M}6SN4D(5v$jvU6=$8y_i1p{
z-76KKk~(1LL&bo_VoPdz|08ChG=8Jpp#vY^(tDJBigppL(ind;N!Dee`?LM1MekXc
z%>lOv@j4+nI=2FBC#kT2pgWx8&wrUH26YML_9oDemsvKca@RlRT~8ObP-fL_3N%tq
z>cWkX=Ij+9Zy$h-mijJJ^e^uVA*NAtWuwqqXG;gY!u-aE>XFB0yX-N8O}|=f8zP1P
z#P$`JI@G8BGP40G;+K}2W&CimX?)3Qh{Lm@QsBl1S5l7-?3S*a1V9!efOFMh$UBB_
z|A>Vc3j7;vCW(oLsqT(W_2=m--SG#v{f8wgz<eleVd;gTx5d<d*J1CB0@ySzWIk*H
zP_sa{YRSV>+BHyr3$`267I^);+<!lSr~t3BWLeqx{}nfY^<@FpFI|iKCkOHGqTjTu
z!x)}h$FlUFS^g`+z*qn_Dn9M_U%m3LcwdGAs<9$SE)wq#gZ}58kO`2-s#q0~|FO$I
z%0eH|2j>&^MOFV!`QH!5v|j`!Bl;h>|IdG-N@e9$+1lGzW;JqgbF(Z9RA4+v)jce{
z<cmJ>=%45N_tB63^4`jW+?3vWk*Mb7DM4zl_WAM9=)hVNe~nBG;u?bRLxu;o1hG%J
z06KAOf1w4FLPUt2{masem5S?LjD7AixhbfJCx+MMtDCcT!Vk)_k)9IGejc+*;12+b
zT>^1-cGl-Kha&lug^>|DI|bsAz$-~%cs@GzcC)OY2{hSK@)zvG2Bgt;!wr?G|7?ht
zn88Sf@bKZ>*qE|5lmA-4I}&%?&B2mWI#vJ}{tra=KWUQ(a$}<8=H|L-C&$IDEvQZ(
zAmYDgVS2$>rT4+qq(Z|f0OFZ@4x@`00uW64h=9@D{0FPf&VZ;^p?3=as#CEWfq$i?
z*2=~2zNv?b0g&ewa<{@WYbRHA`VGk12TknqG3i1r7(EG*fz5MhS5f;*+(WD+4&(1R
z(IWj%G=K(O;rJ}ar0>{$P}T_WdzH+_abaJR76L#Kp}ZU0Rev}%7yHNHpiYhHP%d7@
zr;3;U8$nu=pEd;BP4MDR@Ky72fAeoMMu!wX0IPrEj7ECacE{=cRmq*Wjb2wTSx2wW
z_rxDp=!5knmkyJ>Nakk8PJ<zLohiQ1%b4M)bJZ!ELmRts`-kD*BBX#~vmRC0{!zN}
zeEvW;9NW42G62k9UcL{&yn#$e@*(5<B~==~y(#VMP-^7XmIq+y0}TJaHvSOa-?%rb
zN$vdXY+`&IfC#VniTUbhHV_acYcA?O<dww`y<P!Yo}epN5(bX|9^uyxT%e-Mq)FvA
zoW^gf?$1YAX+I-t#}+1Q=IM&}$6g*H!J``Jqkkp-lc`*Kgdms5x-KVeVPOH}=Q8h3
z3u<a=03V*)p&L<lfYJ75JUx)MrpD<+t!%E+aSw`ZruzC}Py98WXGv5Vnb3@5{MjQg
zuC$EIOts0t#!xE9JsmCWRhyut?+gDxIrU=#;tBv{3KLE+))%B{HtIZ=f94E__NoS9
zvdL-FYgCQfK^_qb^|&HYQ8W2taT=kBAK*by<1G9?BHxYdKRi6#OX1tv)|S5iUR4z+
zM)p4X$#&L>f{uP_2RVO2Ax7LPq@g3Q2~}tq8Dx7#`e$5UpeA8je>HFN&$!*J{%xKY
zDbT#oKN#fDh5BNX9D2V~VfQt-mzT#&1}ffrcj<Fd`azC=M%FO_xJ%s~?tR+>cZtnE
z0E-*g2tT*AJh@J9-@=t@(=Ft`3f29a_kT$BBH9mPL=poiBtZU`I1!lCeOiT-6%`dF
zBmzeSvNj}Xzvyf13X9Za{rHctnq&OO+XFZOsJaNI@Nom8RsidlsFfM9m{V|RDUfpb
zOAM$}%-0xafgz5}x^<@Ann39wOr=t)!IXHvbRpRv9p)gG_0c>$AgU1U8)CJS<ALv5
zMM*T-{{FVk+d3iF?}MXUVK5I4K-T>Q7FlNeqlLvvv80tU_3BnqG%O-#pFgaG-2>rx
zm{^z-xPtHxb^rH%_#EIb3XGJLKhpn4?fq4L9smV%%<@V9%;~@HBCt3_*DIBWwDUhc
z;2+x{sRUSz)4@3LzmoYMixCX77<}fI)&I=(e-`66%wl9D|J}PkI~dX)hXt_c|7q(h
zprYKqw_zAyknR$MAq1qmr9(<YrMqRMyBs=)lI|7-0SToU8e|9w>6Va^Mgj4Ay?X!m
z-p?Ov)?(Jcns>kFJ?Gi`?EUQLWF+}MjQWRi{O{8G&yjP1Z0)H|zez<Sh+*+B9xgaA
zT9tadM*oGW;`$%=1E>b5sHw$tnIM|gNRVqvWk7q{zw9$}g;-fxscUv{JOYy>1J0KX
z%S0q!8yQ_x?CV3J9P+aAw?*&~NO5WDMMcjOM-)-Ibbv3ajwPH1ihff*q@WbwL@Y>H
zxEW1w{2pEvB2Y~SbH9uhOvGbWVU->IW|Vrm_af3>+>VOdg|5U;*@&<TXa<N<Ti*EA
z=pLxN*VC<-pBn>z2H7%hdDhDjZt!ZHb<9i!O&LlmZQ{x%N!jyjIs7yS=?rc=cf?R_
z^VrE=A=&okMVAW3BK;8f5F~D1xSWU<2fB@7j75s)bvj3lv-KMAjI6rDCb@`J+(9Bk
zxO#961hY8qsVVqM298Z46?|cyZ&8Tw4Ms@gksv>O3l)2huM#(E-q3BFyieyMQoNl2
zT(S=g6xBdnJX`SvY=Q$|(V4b$6Q-2u&msf$J?4kLU__T}PAGSQj#Ycq@FS3@c;11s
zo2%;y3AbdXchqDnlZn!U@4y^{Xu-vh8{r&G&fYT7IbhK6kD1bZEjj!{(_(trwP&$?
zQ}SdtZV!BYANgY*plRQ<6f2A+&c0P+ZEL%;xDpZcfEI9!y^3h)u>>7#=alW@tP%$e
z_c@N8!SnVTi!FF*@_kGsqfB-Rf;i7)7GszsF;C3j5C`9Q9!pDPsHLUl<>i&$6@A2r
zj@O>lCVf*x2%ymbyy@#5t_sD6KRi9KX}(s8BtLj>x+LlsYt5bo2_>qgyh9bp1;3yZ
zUzZzWw@3z`K*aBv9p)L0c|EkucK>#?o|&0hS0|Y2wMvPOOwG=QwI?g4F99xCJ0;65
z>hkgu(5l?3@2+kS&ppn@n#-sn9J+MaodCRNP!#mw?z_q3&3l(Cl$55r+=SwN@<Dtg
zyyaDcv3)@l&pZWLh2ebRpv#MkU43^8TwVJ&s_@%-e*PsszQG=rq17ysqM~-~M#Q1t
ztk*!YRfmS!+Kjl>Ov06Dwz)a}EzfCnW#9k3zID{l^g9a`zGUy`8zei++8kxiBL`)l
zLV4*y*($<QX|*wTapPaetRobV^wOsgnyC0yMTSU#VI(V4_ls2ZZ;SvilBo{OftWK7
zQJ(qdpLvA=2(er%HTpMr{CY19v_|dLqU*T*kD&7>M;tbvtoE-Z`fIr&ZGS?Du-TKp
zc}Rb+OJHtJ0}vXI$a4K>)&C7IUt@uwa|BC$=zj#Av_FGR7ai_@5b<w}%=;O1&cI(b
z{%N}<V7sKS<NIGJ%KvXXNRZOByh6Hv*lq>`Z13yUX#5ZK{B>Xczzt8^Vw7(Dv%3Gb
zJr)7L(R2fQ+8>w+U=a||!jKb2f7l-MhFIm>i)R-vfOIJ^1DS8%p5qAueqWZ{@7(u-
zd9eN8w;`z@Ehl4YKa)a0my)BS<9&cnU791|brgRZODzygfN(os?g&Xv$jOoFbTu$E
z1WtPkxW4+9l$1nlL+!)g)Chc#o11%eb(OdYWzmnLm%7ITRQi=t_#UhZ$j_a89tZeD
z(2_=u!y=lh!8D$B;8>^c-@gM%xjO8Y>ZhzTZ2_0w(wuB;kSwI4u!snt5W2a(eu(!O
zic?ot2h=GeYYWTD`f2axR_EZ=y=rKfP8lB^J(zbJ`4FxcL(!=6vvy39f#${AG*ab7
zdu6wFYiL5Dw5aX(PFe;<0yNe20Yx}FdaWzq3@(Bvn+{d2;ZXUjt06!af3)CmH&@c<
z$gBO5j>Ufk*OaQDP!wp1yY=I1pP1W5g+YCEEYOX|mdEx~CV;X0W0mPGMR?;b(AlHB
zsdEIOUE@!Rd0Y_q^F+UQ_4SQkRf2#+1W_oIigMJm%e{A>XIp%Z*?8~OuuBWh9*PHC
z)R}*~Z2xgNG4YTd;-h2sRH<SEki06VST*%ORIGD&^ytwEy$gM?H2^3;nI~RkJ&N=;
zz|qmL5{_s&T*G04+xzS5&%95$V=QJwS1(U{d(vadcypEf=d1-tq|9)pMD3Q}bHzvq
z6gf9#`YdOgI2wo=@t<IC2ZI$%{PyY>78YccyY?;aXliK@`t>V%y1PpPC+of45vpkf
zGvVY%XuMNajXhCR4S#jPrmy4y(LV3MzLl^Juz<w;zw%a*gb!W+oL}1DgPs`5L?1H#
z3Wl3+3vtwW!w<!sm(lR`8k`xo)6kNR4*PC-X{_QkelE>oqd-?@ZVf!0)ZJtI!XT%G
zQ&ANjR+QR99+u6jo|^9s6(cvUImB)d-|9Krn`<<=r=~VIIM`=edJnj{NGAYE4yD?*
zbAH|256E(Tm^or8Iy&0Wv5}<=qZ>H)a0t3YGaF12y3lj?TcR>Oj$c32&(ALp==B9|
ze`a4tOX_s8D$oOOzfJE-U6lY2&wIfl@e%81?e_CUzb~I&n$E^wC}QYb0+lp4p%`B}
zw)|<<sbIeeB8X-P7BTN+Y@8D&7Og$o6M@fZ(n6*6xjKTC*A;I~kz&5n9>a4v@9NWS
zuxJ{JKnrdxnelmHrq=d#PBtFZ7?&h4rS8LfDQ2SHQ1ZdpTiYL=kNmhAS)|Gy`*G&<
z<D-RUjyO3-yx7FlR78fz#NLu&oCr$D;=#?v>w_-B`0iR{ma#eTg#T$M{R<$v#nDmj
zRP}c2d+(O$F9g3Z-?(lqP-Z&iiuQTV+23RO<6?^SnAeqF!ZTJZyZvIas_mqN2l03?
zk-q3A4OUcG1~DyXQbSYIMUK~E0TdPs1m_|oALcYU5q6ADvA9`OMds?N9*K)+l^<k{
zyO<qWmjGVC+PFj1OTLpw!E|!P1(U`Z`Cq?(dG^IK1XQ{b0uAx}am4e(wQe-{9+jsT
zY^`V4v^T6%`z;JSnz3~8@g3x9L!{k&l<yP&#i&f$HK3zzu_%;#fa(w~pq=1=wXnYM
z8I(aAY!^Yd$XXcHnb-+GKnaZK@jEHut|eY0F$hC@BM>Vb%lEzk<EK?gQ%P49;y!&6
z4dj4SoPjBV69_81{Ds(j%4p9tXG3XljAbB`K`!Y<$D1R{Ihrct+Oc-VwaWn;0(tt)
zo?Mv`?D^eSCok@{{<yyEs;mvmI6;Uk=A)Os9Hn2nTs)sPe&@JwI%PWYUXM!cTfn#V
zG*h2-asgg`t@MmS6fXV~;Q<rxm9Tu3FOJFJ0=E=xhklMLm<Vionae8FoNP826SqPq
z74zHEy}l=V_4djfyebLG_k=gTzClnr399!w&NmQ`fXWv_#d#RwZUMs8u*MAor*M7V
znudqEx|C6TG;2T&fFvY?jx(FqZi9j6``MYNCYJkWV0TTkZjAQgU0SWsz;O15N*^U{
zBc2wPmDxlz;iL<|*+nV<88Q;;p5IuAe8d1}8H%+pxO0(D5qLSbWbs|Tc)_KQjt!Mq
zM`+$f!Op^w_NWS$QTDThL@s*|_M(jQgbQoBkKS(=XfEx-5H17LgbceRrsF?N+aQkW
zJ2m}2Y5GQC-0w^4=2b*S9<{ZLJq`6XCH@Tqxyt)9^V8E?_45X5qbsb(_pO=E3p`pG
z;2(}+Os@)K3U0s(4x$p*t9m6(D%j#o6jv9$*ATLC7+XpNT!wFBS#lPNO(6`iIegh+
zZDJS8A%ry4qR+mrM1+c|?d^8<<P62tu#uyy%x1t6ulS*hvMwc!U~u3;$SoO(J9l={
z+OJAPa;sBDK3hdpZ&&Hp_LdZ|xHCH+W=n|du1<2N{oEMg{7jdkV;dX)+G|G|gS-pJ
zL{Cf-zEL(_o{VcT$%#ha{C<7jez#NFe_JQ7lbJS?YAEEf6$#&lG#T+*eP*ID%%}2`
zU+bZA)fj7cE^G6?<Eh5t^6^#P^pDSQ8sHW-c}P9nOJzBuC{X*bN-f-x8Ag-7ozShK
zV-ZP6GD)Q=Pfq**``q50AV#2(pUdpt0BscOW{jv!>q*mWQaHuzh1TK;#oLpDLkjt<
z50(etfO$&Cj_A>mNaFF$JiJM_>75}WdZxFr(`3Ut+OLwe71ME(w#wczec4Wi0{Z5=
ztEMYxITc1N7TuG3R=vZDReO}-)7ad}$8h(so76E4S*nqhu(X(-&zm&2*yDWdH%FZu
zs}oF>xk-*Z2{UR?88yIJX0Vt=Xu`ejh{`(a(4_2iBr+*CY`?auWU8u_PnQ2+$RA#$
zqd!HJNtvY&=p6jt4k!rBVkTWCsfl@dOA1cLc(jq_w2>B;|AFIeYL!%I*ejkG!kzk<
zQEL{i@e<~*yS8^7grJs0(VX0f+B=oSc6g6_JF#MP1mpGX%m^}+<f>{I2cKqgk73U7
zXeBTUQ10iS&2dL@NkxT#ou^OyKZSqQueAx2+D0hEn^$%ReWd-|nJ?hWZNrTI#CDOB
zJ!2rYtyBC)gbKB62h6r&OM7=O@rZ!-?)BkpjWzBpe`Hq@iy9R{b~d#rJ)nR`)RZ8I
z9!oDAkH*ZhJ+){w`cPBRkC=28)~3Jb@!S(9eeLP{k3D*Dm2FqwNzFilm6Z{(&l6!R
zHl=(oq;7|Zy^F{t&+Zbn(dnOVSqhmgUFc>+4$^R+5noJrzi}4$M9%1Sw>enJyFUvi
z*QuS!$GF~S$_ThPk<#tNUoI{l=YUgjC(%$g0O=bp!Tkh~0*HGVN%{~U6wWhquoa%p
zh?wd*8MvLNAc~1&iPr+5dbdS3^3+==;t5VU9o^As)ib)4zF1S{JG~}kM?jWGUvhxN
zEXIu^?D6++c|RI^)=)6heMQM4)%%Z!L)9o=xCLKO)eSPee90;xj75h(YhB7WE5Vjz
zY_OU`b}xwavNe(UnC6`^qn<2!3}1#%tpbT>j)#2<daon1#;Fapu%z}{SmyVu&Aaj8
z-HS1;F_hHPY8k5zPIriUe;nTWAxmT8GfjJgMrnC&>Du!?u71c+HY#NGY1;EqlTk38
zwYwZ9ukmFMPoV5Qo7%N34W#rd1zJ1R(H4uiP6~9CN(Lw4t6<~iC%ZRpNWG#WPS*ov
z?~(O?@1FN;2~!sPq#?|>k~q~v-i@E}Ou3<(wfM;o3Ml&S(i@$@Ut5gT1h`aNgmiws
zrFQN|^V%4w*|aq|w2p-z%es>?fOkwh!dAz@hQ+hE+C1~3CosnFOEmeN`GRWnjU|g1
zdG6~K!e?fwJf(NRuSt=Mx9?h!$1v+~uAA`++Ui!su)=e`+~Ic(1x*L!L$qLIiEbVE
zPj5>J5!!yNlDn5N^D${<YG|WICJOs;DVx(m)1+cJ{_?0pD@N6TW%hti4^eWu>hRkw
z!3|{@F~7@>5NswfW9$?ndrBP+)1X}B;c93{Z4PnqQ{E2H$RLE7#l|o<DzUjm3Z0?3
z#a5Q1=!(wm+@dFStyd>m@GC90Q0~i4E4*kckqWjF|KTT^SwD{ew=?^wQcD^##cfrf
z+TvNjhxgbn$lP-G6^@}U;6Y>cLD@L!hR9n%xJyDwSvXTXw{}*Q1ZU;52eQ>F%c{}e
zZ@TX6?si9ol#g(!BDrD=(QPHdA9I6E_Iz4%x+ut{NQ(F{T?<{Ct3e^9uuz*#ioTSd
zo=%Srt{mM||Dm~sr*h-XRM{5ZRSHx6{YsKEK5EuVYafKWqOINag3)WmZZ?o3-(RQT
z%<*unmt-MmZe*u0Q0X7JX1EPBduqA>o5JXza`E50ok$h<CWg*ybNnRkEF3d|IVfX-
z>enskePTS7`$w4->x~FbSqd`+o_GbxxOvaHr>u{S-)Ms*r7ae$U3rqCW;#=oZqu?3
z>r=T{$H$i<d?afWlPV-6_oum|-iRx`?58U{EUk}ZL|xgo<$X%2;buX<h)kr|5hR)T
zRCc~a)k!s={WdjG`6=!}!gheBHJP6N4ThWRC0(!IEpB@R_O^UR?WP9QwF`@rikcMQ
z^WxsMjNky2@t?tLF$aj=`M0Ne-8sN}-$P6B5w9;D<-U_Izso<Lja6_cNgbi&3i>gS
zcZIV}nUo%UNH0R@dEC3HzF6--x%k2Ka(1f4On%UX&vSB`eG^K4z=RGazfD3*GPpr!
zcJ_`+lNL92o5<HmkHBcq2=^<o^X2NQ2PplLqbkC?HF()d$b*c3>Qdzfo*@$@WmWI}
z_LiBI@R1T_?`hD>Op|fReGenndBsM9Atxw|iz3QwgZsU4Oyk9T=*yT(f%h4`@vo`L
z25}V@GhMt^!-8Kr7+5=Xcb>&a&w6)|R;xJjyCyz}13M?b8E5=E4Mql%OsoE2NdGwa
z0;T3oFTt7AM+0J$QumP^nC`icR6?d&_g<1Qc5pwz#$X_PV0wL&Chvw%+okhxRPO#n
zTy=*+h#}o9hDS8|=trN@mzDL8`7ivZIa+W=?`{ZQrd0WdotF8y%DJqBBfeCMWZ)j3
zvZ5wT2Jzx+QEr|%oM!i8!-Bu5yNojCR<nnyNanS2%qlUn@iqH<r<xbGv$;)Uu`JIB
z_794)byPQR$V+RlVd5L^-muo3OjsdKMd*Mq5_7aAAJl#l8ae+cOn=dSobyF5y<?qJ
zKhy`l@d(1sCB2n425pp?Q>99#M<B3zb#LLLU~X}R{&=iQ<Ete&Og&Wywfl>s0D3_Y
zx^})jK=HX5;cO`@F%tm4GsSHJ=AE^#i>N?ueP7S)$q{wN)x6i)KM*Fvjn{4jfvDJg
zeV$`|)nGyt=(y^8!Y>~WEzoXhFyQ?jS_Cm@5`YD@V8}5W+Upq|YOTo8KSp!=mVY;+
z)#-JKiR%o)8a7m&mOFpkDB1W>W1ePC1=AHV4!hDIT0}BaiYS$q=l9C5sO!gaB6Y$I
z$bY9#0KJ-OfdgdU^LzIn(08Jyw^n^%uI5f~-Q7iFt7>-h&7N&3@eSU1Y2g4ehg$YK
zxg*|Vod$9l(_rs;M))B`7pIn!V~0s5A`@Z46R&J%KXx!WFisy$SI(qF_)ritJdhze
z`QgfGDl=9+%z~$m`v#6wHxoO1#sO?W_8_7y{D8tbRS8yLzDLETB<yriPOG%)YpR+~
zM{hy(^gh{{dTfPt(G(u{Yeg*4bMz|x6v4!c&g|oAflzt-W)e}Z!)HnuSqDnwdL?zy
z5wNSxLy6_683#WvpAeAeWIB`kDC6Em4BVcBjE4tav5v=Gm}b1s)g615a6YNWOqR|k
zwkh_+iv(62y0<{Y5jQ(iAI><~#|hu#^eC4kT257A#w^s8U$S@ItkcOXPkKhPCCZUJ
z7<6e^9M|CO=pOnZn?fFLa-U!!b__2~N>GNo#&WQppS=&B!2ckK6~0%v!Mz762-C8T
z1s^;ddu;qW$Ha?=PKw<4w5##nGC}p8I%ydwck`<x4^DOR5l7AoHcls5LZ7#tL^g(g
zR-X=s4VOi`$`mRn$|z0tvMfHmOdJC9zMAF?l4OU%eGHnupUu5il5Qb0Mk@-;dv@(Z
za{S3^Johu@(#CfnG#Gjg-O$f1RI(sZ5VJIPUnpkrSDe`+K^ob2jzIS?g9dn8NcGK7
z`cX@PmwWkBH>~(l`o~Q7zm2``i2TGVX{gS51?Ak6c$6)fEq9VL;O$P0jb1kE?%<1%
zka{gdX_wpYa+m(mTFB!JdUKOH?ruAr&tf9pNpEilLiv6i^$)AA-~3RNY_E#|JCi8{
ziiM7@+gN0h-o>mG8op6?E0@*C(Nfgvy(iwnW}7TG_p>i_$V+LvI_ojqng&X73SJ>K
zEqU7(L(r4%h~O4?Fl4t$7eku{nbIS{zL@PQz|7+$$4BG#gIO)vMuC0QG5&y1L*Ok)
zelR1G3TOG{N`=AiES#AFIQ>?bv^iF$DsdY2ElFWdKFs47Q9eR(ib2K5)xci=hmY-D
z9p4T6M)eAy??%%+LkqIHb*Wew8c_2|br2SN22rzwrM(&|BzcQ3i3yD#(*1}RqB%zD
zy&Qy{&J)c=T+;pAVw$8Su~>FZA1{^Y$TyzE#`9(sIZ9@QfKMp%wp!@BbLzBx1=nee
zwm}DU5f5Ir>+O94YA=jbLqGYBL9$Cc@)y{kblH_R>4<aOV!k=bq%P0b>n-k7X9}w@
z_tHS8XFiG+j^7qlD0>UnZx;J>UJp419s`+<Np}J#QoZxYM4BkHx2jWJl^&nAA2Foj
zm>DSOxKJM{g^(uICSHcLme9-<yz%(xC~L$j+%<m#ryNaLudS75E&Cmu+Ws}gE9YCZ
zxE%OX4tBf}a6cOA#(XwLHjORrAL`ZSdcq>E@0D>3YuJV$Tzx%y60e82T_rKG$oZ`S
z9i9IIiXJ-Ti>V-Qyo9+my_P_7rzIk#=eCwMot<26LbXz%0I^f#1HW5ZnTL|)ich%j
z;b4YQD5iSTIT-tr;bzUT9CVXvd3$w*=lO24?~>o_%ttixt7IPShS8-vNt<tV#Ztcw
zRY`22gX4|(S5WlUGF6dyCzY;K4ZI=odm0W=+&Fm<r;E0>K({?|HE4RBWK|JBZdKQ@
zP4beOk7@*EyJ&sDJM_tfQ*m)%BwKFLn0^T8*2{il-t06ol-Lx{)7q-MynueEyXFlf
zLqpWIWg36yg#IDT>-ATRV;@Ivh`%ykB9>XtRJ}FO_bti+tzCG>0~QgB=A`E=u)#6~
z`M$lk0ml(<!bY?T+`tvvO2DzV>6#4)L2KO7o^IhD+uuaJU1n9Xlrg7g;|{_M-d-JI
z(xn(}Xd38m$J`HCuO5QnzPCGQO96$vqJN9bKhgEl1%2H<(%t(F9tSv}>Gk`#)8YsB
z@OQQbyRfOfM>`fK*6U8SN0AM&(1+gd-{@X5SAS0X`az?@I%yK_BdLhfEbNUT37aY6
zAbbL$nq8w$?<XICpu~|V%$|VED*P~ygEi_MfDNGBVeukh_f21mkkXCg^!{M2Gezk8
z7gEK=Qe{Sx**+HveHKo5mz5nUQQCYHl`4#6!zlAwRC9MA4lnlxuEr&fJl4_1W8_Rv
zv4e@sGWLGcnhjS|`Y75L$7#8>qHbRB*$hX8Vaqb|YH(~7;$*UO&@f`(l~z_{<rUFj
zLPbzXXS?PaK?X!Sf(80C#Kz#=uw<N`H+1}v`MX2$l)9PKwdWyvhhq_Q1jCqL<&Iq=
zfORsK3a?2%%Z*EU)6fCcN!*#IF1#ssepDLuJbQf7aV`1oZaK@Mw`+;>h;oFR+6%sU
zzr!k*FCtySA%ZaPs!{7}oaMKu02KEp^DJTtvMEXycw81Q3ol!X-X|fpFQgG%ypY|=
zg%q^5rmIKIzq79X!SD=L?-sKhEwF0B=U8mkTC}1q^@#xJ@o1brt8vQ^c;oXYAUo-j
zxJG!;VjXW}9@F`3ZV3JQ-Lp#(3Tc;d7Z=yFz!y_lIh%vZw*n@lq<sk+dE-q1nfMoT
z2>N9y&|{aZmc9zziiWS_1{Cx+@18e~d<XIZ>*jH$ZRcw`bhJ4#TiT@Ls3%I_U26`_
z5Em@egf$9Bh&#FIVndNDQ8Opbc8rM@W>geRy`BQ*nAXfk8Me8yes1Bs6?jrfml1cb
z7`4vyu9OP3DrB%ScfxpWq-JkDjPd-gg8XJp<h)O1V{>zkF$5li{et?o>Xw0{tZm#L
zl;$wWY!&TxaqD2Mt{(wALiPfBuTemUA2gZa)<wUXI*iCkAz*ucQoLeJSl<BZ!fFU&
zf;XyUR3lqsa7hO=5c@qA(@kutcY<x)CTkBLCws0!Wh;S^$0765HW)TUyTqawdFrQ6
z{Zi(9I59A2qHN6NZM9TRW<T0~`CRbJ&o7?*DvJMPEi?cL=TZBXwLT#-`SN!&5DfZ&
z-Na7XTQo|G43@mGOopiacFN4}PkPjs1#nnpA44p+83JSzuoIb+u=U+}K(P^GlI1Qo
zz10Fi_zeblMH7SU=7F7(QqN;=`$_XDqLs6coJ&qwoCRUz1<=!C=f2+SQNB;>{K2c%
ze}VBPy0-*|zeV-8xl1xKf+fS%`+DctX(DXMl+M#mCebO)pV3D$8b66Lp@U@7NLUp0
z9OIp63C0&}FWwCZ$9xh>c;|n@m_@gm*32d_*SK?(8<v_L>ZXjttCPdd_?6ZT%Qpt$
z9=R>5&5r2qx@TG*`A*yDbqi#fq?7{6Cxl(kTt{7I{i>Q!G%@U%^w$<KEb|@X6Pr*>
zMMknncptDAE6=|U=Snz<;}X%^A#i&&!ztO*?rGb6)W*0a+{aCqwTkuf?~N7_I^>|G
zXY~OaDgDkN?rD=dlu!?sgM{VsUDmU1AHfa+)L>xlLm0PpF{ci-R=KxQcO2i_dvDD0
z?J+1qKUsB_!kDC_gF(+3?7f}mn>-wfORR}t>cShib%J=a%hCI|_z&m}?a|_s;?Aa<
z+#b2|Eu?AZKQW^CkfC1E8yWf%8v;%b8TvA=b$7_V*N=3bU)3y+tDtsz@##WEerm1N
zyW`YujHPD1N;P}UFLq{lrmRUHTC)q!g1Ae+`r3YL+VrRq7zNsR>s?W+R(mciq%tT0
zPjJJNLc%;iQ~*bfVN8QboG3JVCa;UN2&K}aByJ@x46{#!w%%?R*&V~4>={bMMLZ++
zwnlOdQ{2aEQYsW=dJtb0$ItX3@<G1C<^;IG;e)1=vEz9(+S{y#@4n;ge-~S!yr<w%
z3>2y5+MpC6(9KjW&|MKGs#y!;Ayn$ex)h;%!*_~^f5<d`k56Fsg9@Qm;t@&wX~-8e
zzt>BWLkgMGD8@E!hdY**X^{^&KWajB_#N!9rD(!8d{@FKTLxv1)pse!n@%wW*wIa}
zm+euM@%pZ@l;HG^Z(*NA+79tqm-wU7s6&bs_KI}rz#AEWLtA928R*}r0b}l#H8LM?
zI&OQd^&+%UZ>O8}h+=HLbjjNCxz*vy{*}bTo+jizkLpAaozR4Iu(!|qN4<XXQvv(B
zx`QX%v(Aq|vJXTU;9T$REgT+??mx0G=lES;1(>~X1hIbS`vKIfg?%}3Q^-+6h$Qc6
zOgX*7^Uz0}+6hPAp#>vtLL@91=R~X7j~>m>wp-b{T~Iin4axK-gbi3m>Q&rOVQ`9%
z?0|e`9rnRJ57&NyvXxIkkKml>e{NJ(AJi-0mHe0(QlCnybt|Ow2k|km59~3dG=GB5
zy6!i`a1u5`a~vCb(qm1@qRPOw_HaMWv&9)3d3ZVNP*sxH5VpoRpkQ~KJ+Z@1TX<O9
z<dNBW@BC9sWnUW(-)1Z;g2T6%JACY|5rq*$u9)JBqB0|Xtf4l=s@{S8r-{kgXl3r3
ziuO^B;&#k80q;~ZN<zj2!cl|!F{Fv{)HWQtVjjkWC?BqlE-O8SPBp=1&!TtNpEble
z3#?ub^SHy-Smnfpo3n^iZklYr{OvfpLFhM?`Ml#suV``cAJZzBZR41MH)cE@Iz26I
zOMImba1?Gp(%aS-ZlVi=t^mDgCje$pJWkP74KjuyDwJeqX(|&{-!)~MAN{4d_g8J4
zcvPTu7)(r+3ST6`k5R!<U?7I1Cwcg$ayM7wQbpWpgHr4W9V<nvg8jFPejD;nQ613V
z^k%74on_<8OXrjoPZJb;!6RPvo4@w2e}gcyqL0@O*GMos-#zpxf}?pBPGPnra=TfO
zJgoY&z;BTUe_m-G_FB<|7`Z#$hTE{O?_X^Em&Tsu;qxFgG)#9@1zAAC{oj`W-m6mw
zZ5d438{+D%!qEusB)|T!Se%Mt$*nPY3H_r84$w@X%PD0hpSLw^n$oD${1wp*pQtHM
zbJ0KLOPwfjQS=`CEpGa6DiEMp8x9|M@Zv#E$wv$IF#|Qu4NG(sC7dgIDc_wN1D#)w
zK2TLmsPzHY@2KlP)qfT^gU9LwNVAZnnzwzpMvZDl4F?^!S{Ds_EU?ZcGQYgH@To`{
zL7Ea!t^MPb&J1GJ)<}2|rdu*wIq7h?xD=0h02I($u?s_uqly`KpVW*0*0uTfMFF<9
zGSVSNNS{U#=}XAyXa5KZ%1%iMv!51zK;-<nVqq5xbKdd(y_l)0|9?Dx4k;P>ZOI(b
z`lN+Q5wj?bX%k?zhV+}%fWgiN1_r*qO%lr*PtC^~R*j}<*Pu9dq<@(GlfOdr*w2@V
z3sv=WxO7K>JD74t%@1@8p8-y;9?rY_g@6=UgW`#R+`s4Q%HKY`IRjnTzfYY<G(b@V
zh%x-}g#dHERQ+3tdLWnC_9QbGABA%>#Kb`c2|@u~jeS*WBD{6_Pl7%B12KC1=8Ibs
zL+k&fd_*F_B)r7$d8`enUek~bFcz1OS98M})en+3qA{rq_W`LBfXslC5MerJRP+Xo
zw9D~+3%PRfqc3B3{yVn6o-(N%@{X8B=z|K<0<ii;_;q3E@$s<+Drr3$jWszd%kOZt
zr>#x;c>{NtLuHSl5XISJ*npf{<L+<G=KoA%WEmuV+kJNYsK$YhVtGo{)b^4E*}H3M
zd(HBt4@9+RU}R*ZtE&uk3NdQ50eg;3*&Bn3-x!zY?(UbpWBW}d{SSu(&}S``&#4p~
zuuuF{kJkRSAP^_tN&|~@>&q7r^O*kAkL073i{JP6_e)DzU#Y69uBdfHnh1AZk$e`e
zAzB+!NiX7NEz|o$;_|QMr*NCd*cj?Q;J7^%807+*p5QrTVPT=Bre2H=#^mi2myiIc
z$!Y;xCePc@i6wvXWbcHu4jrZbO=bSilvC$K7pTWlHT4`ibKs|9QC9~zCqQ4@{XKIq
zFFT4r9eD@dx}8={ZUxfg7lo92{)rr{3GnA_k68_-2FzXrYM?!5m^gE2?8G&TGZzBL
zEBkwUiWo&s+AVL1-y#IN@0aWuAZHa~Q!4-0G^4^mf5DwIU5CbzHU^p7nBZxi4%9!5
z_Gw3L;u~5jpu<=IRzzKWJ+aa_7LJ)tqpU%i@e_Q*=g>c`QZV}jmcuOltns|<%mFmL
z`mLeLYiM&cI(({}Y+`Y7m@=svt0>4mXpSwentU5n;KBBnD8zprB0y+UN1kxaa3QPa
zh>&^#0B<g#t?T{R3TCwfG!L>5NC^YFEE1VR+qE}ZCL4Hhj7<J3{P_#T%$UKQ(f3Hx
zuUwPyZ`;28JpRJg+Pb8q1W~Lv7AuDqU#-CMzm_l+^T7{{w7GWk_-HRfG~h>7QB$E(
I&Mf%<0cEcB2><{9

literal 90233
zcmeFZWmHvb_Xi4_mXJ^yk?!tBDQN*I>F(|ZX=&+}knV1f?(XhR>As6|{zuQNXWS3>
z^VP-Ji?LVCXFfB2vj}`IC4%@2`xzJ*7^3JqL0K>`DBu({3=0B2`0>TSfe&ySS&_G3
zMT59Iz%M>}N}~Fbl3<j;IV>0yI4T&#(<Q)vFmUX@ZhpE&3>@d@xhy#O|6Kz-)87aT
z@~`W`z&-+>PyaN5pQn5N{)G4n{_BZfLH}G01@;x<pL5VKa5b2R;2T%q1J3fDvJDs*
zQv1^ncr+Cf4nQ}UsNkCqj^O*rFs`ayZd+bLBr<U6D6d<jKFd>Uzsxlj`;e{oQamQ<
zoq~1f%dRcrEpgh|^}*8QdA0ra(qzHVmnv#y1^R)6LNaCV0#Q2_U7)^0qcf-LU|gyp
zu)Dg#d%|miAJV!Xc@M2MIGt_|xGq^QJ#0RvKDJj?RJ0qSfukV*c6b?*A>+HkBqk&n
zo0#BWV<)JvMKP(Eno_gGHRkqaap1UaP*Q*hU;lm}8!CRl_A(MAhgwys&dkj8f`B0<
zCWh>xxhP|d2Fc6IZw;kdn3|qBa?kge55`1bt<%U$Knn8zetaU+w96MQsZJc)5|@yW
zkd%~^mToSfZVUz!zKMyA9iygvdv8zZDLF<V%=PKWPwcZNY`|{^e?24!Dr+QB;r<Ih
zSb6;28*gX=@43QWUHcqGD;ruWs<vGm3=D&bVmUAy9{+j2a#K>R!(J`2>T!xc*a42R
zo#ZJWt6-V{X&nnMnpi0RSY@PHJQc*k&c=rExNT2mp#e5EHI>R~_Zj|uvwQiGZ=w9|
zje~C7Ztx__t-ZxpiT`>g0r)yCOB@fJ&bghDCgVs;(m-FIxRex9gANy{CM#?6Y-jA9
z>Nr3k&O+a!`3Dis64{O4mkF$zzZ*^o%QTbDCBx^Qba@gHykFQIc*;qsDxxL4rfD;o
zbPDq>Mt&*7JvNr9T`@}IB&?~4?PskqY8NrM|DX%@3;)(GYOXks0t610sV$w$=4pcM
zSG+4!aEV%-u23to7j(N*2_B;1fvb8JtmeY4%*l|K<^IAqvu&^Iv$g+}3PMfT8ryFX
zNu-e=Vu@Me;WlFACmL8RwY1V~c#lb#yaSzu)TGW$SS-KZ*omnoR>ASG{s&>(1mHxr
zA)^(}W83P+tZ+X<B&X5o*;vw&;h#M-#i4zsslZLRS>AVSqWX1UadA{(S0YY-#yR?T
z;Ra;g>lJDV=eU>@s%}|4ZldL4fSi)e43Tw2oxNEmD|kQL<gMMTOY&&!-Q>+Z?+~$R
zBk9=Ugi~*f%-i236_DLJ$rcI@$=MISAQu1qWaB7-@-$<V@^=dr70hy9CBZTRb3ajM
zxKOm~k8MWHB=$|qWk@E@nb7^NI{@F(NHl%2bH_fvhs^C^=#ApRo^;Z%4zK8B!Tz2Y
z5%GP772NgV&WV!o^VI$U0bIQmxRG40<g^Rq=CqvHe+dQ~tWu##5lib>uQaOgUILGv
zL~E}KGySJ2Sk33zfO1;~S7q0xga|}xN@JB<T)GcRL{6&z#|q!RZOIkREkO(HrC_Df
zFYFdNCUmKtr1LZ}F*$%UFdEIO^@2+rq9~8YJrMdsmjz!}K+<kYJvI*}9HcR=(AmC$
zR>=+8-+0>$Zz~|+O)+x4IPb?u-2bYtOf*hzHt07!eiHB_6net(UfEdE%4=d(oU&Mj
zYnm47&~?tPG^0{UOT*qcS92Zf{<Mq#5WV3!$Y4R1Pf;!$@_8K0i1gQkJY}(R=HR9c
z-_%~txWvuX2v*g4{pX!9kl{HBNeMnEh4Zrk>XGz6Cf8M8v<MG#(v@sTjG2XG1=GyH
z;EmDzX}$zogjzn!Mbf87Gvbyh_Z1B=K;5Bh8jQ4v4V+iS(d<*^3jCLNGl7JY5*kMe
z_thM#IkMt3z_@}EDo(Loyn1Z$IK?Sx{zGEi1X@U>Af8Jixs;FOv4We<iWHgUNcOFp
z#FG>JaXE4dWPxp^c8vXOh3FMj$wD_{?Ya_I8Be~?AJ)?o)`tc>!ys8~no@OalNEfQ
zva2@Ky0t3bIPQ;Y`8|l1qiVeDRTV?$K&F};`SeBxQXUX_4}V%^9~v+I5o4$V$+%99
z7cEI8G1@kR^30|#`F??aZaWyHDkFNtUjGTarp>-=bCE#Wi{ISTlO`XNEu)ri4tFn#
zZ-Q|}TU}j>(frqCQm~j2Cg02x!H}Z5s|3mHcB1}R2e9Us;O(YgTUlt%;5DaeON{HV
ziT+^XYY-2yrmjUIRE@vgj`e?RBdiSwwMFZ}bDaB+FTIA5!@-acMJ5RUcr5ZJB(Z1P
z9eA$OpF*5Q@ERN!J2X$|57m6#5BCnt{~AK}^iLstE5Hw8XU3He`eUK|acBS;r!bkD
ze{$W&&lA$pkUbCmPvYsx05Ue8zZ>`yFu)>$!z~Y6exUi2cr7V_jDGy^1hPNZj16!q
zZ6)X9pTxH&0c6DSy=IaAbIr^Erv%z$D*v>2J{$lU^d9`iDSxin5EkH+UxqQtA2I}N
z*ooF6FALpgxFmKfLJkfN9v&WA+M-Bv1qFq}#YUGO>pc)KNc)*e%egl<H$FZ-gH+EO
z#5n$5>xjtm@^|lnfq}EWwUgjiJe)V2(-tltfLmo`-dvWKm6es3tKkkNakSBayBoE4
zcGgK%x+uxX+3Zg<@DjL6&C)!9126K|0CS<9GsxB-cj8zi@p+^;jNV<JZVe{SnX@66
z7B}7O*4k_-6sz+Xjb{47V?bXct@#g%(>40EJgj0gcQ-BcM*oe-hNWStRjPv7kdlRv
z+-~QVkjkdI!tjgp^Y<Do&CSg}eoUY#HyR^VSK2&IaXF-*q%6yhf_>@r<qIl16ZK#*
z$X%TNz0^Rt{y+ko#p0MWpPG^qyIyaUR-506w^#Yb#s-3~bRz3PR-$>GDMXdoT$S-e
zUVp!YvCg`h&UP$G7Kjiz5ZEE2lUyNzL^odiwSu$EZ{PG<Ji!m_bJNni6ft&V%V9t6
zw`g3oVtjhh($FH6$~)jo*Kpi=f4MZYZBbthD^EJGmK{B_J?jI9_Ex@p_wP-E^#h}W
zU&O|XK67r|{2(WX_8@}y62OPJ+>RwYw<99>(J?WzZT4ucD@#sW$rmq*y=P}X+8A0G
z4^fWTfJDMxxm|C>O7ftQNv$WF?9Deg+1S~!G^0;rKG4$A3g27Dz<h7<r<oMhzP&g|
z>d3r%xIGHPX6Z#R+h1yaJfG4yTBnraxn7T?prA;O9Z?2$js8h9NuQ_Vvp{SSX3}M;
zWft$S7Uws*Tz=Wy_})_3v;OUT)}$Eg+{C(OeX9B4e8FMKO<BXRbAPH>!=i}O<znAv
zi087KC`?yZH!f*$y7_7~2*7I<EMZtoq}>jMje>t8G_MrotA!(XhvgP8P2=Tn!!o5S
zZT@`6Ef9FgW^79oEr1mD52Ipo+L9LyUa`s@%vPG1ZQQ+^uCvSM5Ul?}$m@Dl!V{FX
zn8hWA%W2#Fu&b%shJAsxaJY@S0eD<NLhu30fc9+k88dZY=MycO0@)G{It^0Ygpua5
zQ{BZ#`A99zR$)H7J)imF$aBA|*!*^BHpw2%8yayH%1An`8mr#S)U<-*7YqR&iTnLn
znw7?&yA3HT!+oS>Jv%FF(SFX1I0<45P_o#Ag6OgN^o)4r*g`=lzy!3WdQ!KnJO<w=
z!UxK=lJn}T%$ccw3__>**yMVhE0^7^`}*Q~D;1y5otrMZ#S&wa(lrm?_4v(Q?7k-b
z;jnlNwQ_@_Rrss%i^KmTLlDv{+_f<yIVriL8Y|YwAXJj?w4ce5YfgaVCb-2P-`&t{
z!OFU`uzx;5kuMeeZpbMBp<rukiwlb0{b*3Yrbk{;P0w3RW+;M4M1pry<E?S!T*h8e
z{h<3h`-55Ek(veVUclMF8US`|<<2&}+${M{ctvQ{IW`!V<3~~bp_rJM^LCoQJD`Sy
zVTdmlIZXio-FVW8Gk0!AY6(>q->Lv{G*|t+?FWGMGtly#NuG@4ePT=F<>DNir^o%2
z2TN#y+Otm+qIUsOi+ah-0@=<|nr(iFle>F&1Db8o1hzBCrTYg5n2^;*i7k?|&z7U9
z6cg^QuC7dq8)M=-C5Y8aG`*-oNl(}d!8#G=X24VmQGs{-pILtYf_3Ol`1*Rt!+es4
ze@T1rTWZ57@6|GdqQ4Ww{ao{XVh=)+fv<?|7J+cU^Bz@gN(L5Wte{Fn&g(a8b@fPp
z!#%=JVD17Ijpqu>CatWCK5Fa8L5FniC-8~*ahj^pSec}$iosUA&#3iTl$I$rd?3I(
zx$^SzKAH9mCUcopFpbkSqs4LfHj(i6&{WT(>XJ~B0!D=5$%t%-3dwU_6KIdqHEN5|
z`zeDg76A<sY%623l<?>J!NX)QGK$AR5f7U7va&1##Tm6+33=>@YcLwz>JP<LguwRV
z!JTd3N^Ndo%f%fJZ}Nojc!lFYK|$%CK+kcLvdpBK>uNu*ZX3!%pg-UTQ`5hPcKM4x
zgv0o-$1H~FgivEMEnsMa`AOhJ!xIv9Rw?o~pV2gVV1@A=T~^`orZE>Y3kth~$}%G0
zUEr!TbRP6xlDOl<xoYbTBymI<j&82C_r<>ZIC$N*KF3yOQx{XH0H`zoTL8=PFhu@L
zC17Ln?3p5Sxf03|rFGoLws4w{=0hnw$+n43ybX(2A*;c*6EaS*E~v(6e8$}QT$K2;
zuGl@C5`*|EnBSB`hUa~EgvDcN5pmN=12Dwdl=1pN2uDq~MP}3C1Ol(z&SYG=Kjb`K
zg*}#3!TO;#oflg4unqnAJCXrH7wYt}gFZVg3*=?I-tHfB7R?Lh8x4q7<T^bXTiS{>
zoM`Al%1s5dT1DFANvX&PSWLD*M#br7L_75K^rU&tqfTP7iQ5M57`1w%8!_@_rYoML
z3q=fY`fu@7b=h!)3^+Xn%1#?wm8fr!T`0=URe9PijWN)*S&JE76VZ*h6nz;KK<FNn
zNA9QiWLi4xi*;#-ei*_mwIFrQrQIF?D1HJC!{>g=E-5*0Gcdkdb*GK!V%H6-&e0%M
zk>QVleL1Z6Wy~cOb8_P?G@0%+q9lMVxgqcZj99#u;F#4ShDw#G)!WzDgpu4%Bg^NU
zdc7}BQMGbjOsrGuj}Foux0LtpxPTBMEaqz>ScnRA5ltbUUjhnf;~Y-lchXoEqeA=U
zJ|V(EJxk#*A<t5{+-~*J^z#hv(|giA0i5!JyB&59L`UNu5hslC@})Ak1aJBoTk~~D
z$oBUBG|%OH8&wD!e#$#XNt`Ltx2m?Zo(!eX!aMB-f!#_90h~vuv&?F9Rc48WXe=&W
zcn+9$y(V!foD+0M`cgBPuN-w5`h%f2C;IBT8uAK>*xWU!A$=1oa%Y4Knf+^A=eQ{U
zLi+dNU}&PpQQxCPl!&s?kgd>)n;)E4NmrL|PP*_<M_2MO#lONKSSf?|W7OF7Tgi4%
z^f=|%7NaUPyEld?bc6(eBr~Z_8THJF7c(JmHHR?$<-mxnux$02%+{DR^=R7mf&;nu
z$g1w|IyK`KUp>7PnFUbMj7=F~2@!<?B`qO}Ae?ynQ-Sp^z6S>H6Di5<eN>B@A->0?
zr2OKh+4v==*@OhO4&Li^G(wA+%hWy7cStfN!TenL+8l_P1wCnNQbPvrkpn3_iE{XE
zXA#Lz1NqqZt^+Jn;X_BPRGu8f3L^EOxQKn;(?eFgk-q}f)(|kA0wvh^V{IH($74<0
zp!XfF#jDObzQ{I~>h9MYe0Obp6(nkK+3;sIR%_w%MIg?79Z&;WJh5IYmvjm@mf{xR
z-ew=H<CqMPIz4#7;x5$?bxNlFYJ2<oY*LZ|JV?}sz|7P=2wTt5p$QWilH4J26Cv`d
zREu57v}Z#DSxNl~2x`6K*VxdydY|4PifQe=L*PY@8M|S(f!mI_`Bnv*j&zGE{E{%^
z0WvBb%xt;Qt__iGx;0Jmm{M<q^j0j(I$ezMz1iWX+3G!x2m$Gk8<GLAs+TReWzgOz
zE&UqSe%)2tn5Vw?BqC1Z#daZ^?-QT!?HL*<C$`xAJl_^w1^>iFt+DfDYk+OZR&UkT
zJBtN86&@abU?ZwjUtK?Tnoem^#MQ36mU1QBDKici;xu{;2lDHHsd@_O_d155RdGGs
zxNESu6RQ*oh~dHNW+Uh$xq3=eaY(K?zi+W2sW1RaN$N4kgiyS;$ESJ#DS%z>($|&y
ziUHukC*~<+aLTLdL(@cTw08?pRb(XWGx5{FskyC_f^rIgYDq|Nibt7>h{YmRu;ExV
zZ=gQlE`7a+P=<-FZ*YZ}c?6^-_bbl=wDeu#l9LaDi32}XCM-$uK|m2rvSxkD^;!aF
zO^VBvd>D$!donNgpTT6?^RTHK2Q8NEIhGX!81y64gRZhVcunc5H%4UaaU(}MQ}6c;
zE~1#cOos3uPw=^Hq7LOj<nm{fbb={mc#@=Mf^<i2ya))Kr#PMtgvC;)iw=WD+6`?J
zZ;Q0CXiSa`w&ULuv7;Q@lWu3_mpnN-!en5bnS9^7P52bV+G!HP@evzL`x&8gc!gDz
zA-g;6h(E|n-v|##oK><Mqw6M20zN&SS64VF;;W#hI{*WmiFBh(XlK%ef|48<5KGL~
zlFiiTSi49a2Tm1Or5x^5%RzAxqy08EQeZKU<r`T*SkCW3+EPuTk<#hk-SJ(??WFR1
zf1mZ)iwrQNH`^+$c(tF1K6<C+qfQa%L=@rTT~LAxyDJu}AJjn|*&2|Zyop-~@qUS<
zY`;9G+Um);slBz~itxU9@G{rVCkr#<Vz70t+M>EVKF;8f`&$L@woD*C4UHmu$#bA<
z81tSmi*K^7ZwN{K-DdT>cXeW(Xa=UbnRFBB#L7c0v=lxbEMgN^nEvZoRj7-hQqmTg
z?3a}W_2ZK2y9!`q6e@7)!?fVkj|T7}PY%yr+|$Cn2?q<J5(S;+Srah|Q-e4CA%WU(
zk9|@UBm*qqvdps+5M{wsICL#C+h3Bk<gkU!F?$br-<Q5Yn$+0}XU4~jL9IX`hfq2E
zTqzn}*uvNg#03G=0QibHZ%EIptcg*c(oju)yiR?L|2kad&yL410Ii`N+c=KCP5d2<
zM%}Cm4BB9CPB<aH<wC7H5kZk0cg1uioLI@HEukzo+^DgAp3uEAmz!SKP&3rbPo^0c
zwVi~Ds*h7BW6|mRTAG2lwc*%b*b>Njw5+4tIbWIYZx?#i7o5i-`UtEO_j?wwYqHRn
zi*h-0X)=(0&B%q6v(Yr`-QfW>RK|~0m@jbJz>n_-V=+x1O_#PI@o=r_{jjc}bE91`
z@GLh|4M?<I{v3D(8$Q(efkN3ixjhQ~XJpt~*OElF$SjD?U~)Y>$@Hu*zb~|Jb*-Jf
zkq5{1Q*SJdihdu{QS5uHi}0Jky{rB5p#)slK)AFw@4JSjph+2FbcQZs(P@>K1MA}!
zXRffa5UE>$0OI*Hy8V~eFJj<)C9$%YIPNRgALrrNl2L)2_j5>0+I_)$XaP@Oh=4_p
z+k@)F)|{nK$P$~-Qb<dBQvoHvSW<{>1+dd#Sfjv!)Dbfq48O$W=Y!Xtj_@#{>^f+h
zu@J>F+#}O9F>g-oi8N*SuI)7wN?mZuiG1)r$OD?(D9I11sfNpUX9JHi6Uj$g!7*Ku
zcwwV~)y~jX0qHMjIa^jhzy3pdt)p|gM6C|2D_c>+?R>=_-+o6{Mc@(@(+eesb^2v<
zOhG-%p;80y$YPfM=aY<(*rG<1qYsQ$L**Q#Z$e+Tlvock13DEH{iMh@IN%kC-eC$*
zBW_Jb@y9(TzKChsFo^LG{bJTNRg7QQwcBBvLX;7D$g!Xet{1C>mqRfLtM_w<o48CX
z#cbcUBrH*Q+r>tQI|gjR{a~m$pHw-hWKWoZ!syY>aqIa)a=GA;iWSD%aW#$X>*Kh5
zQG1HDTsV*)uSf$vYHCLO%Hz)Jwmq2&gR_quNb3EQ`VrDP#Z+0ScPP%+xs&*Qf`9_V
zf^>iZ_2^bXJ~#2Uw<h4TQc__rfff#m7cf}}EERf+X0pJ&eCuPqMdO#0+7(J;nY=Ne
z`idFc?X>zTPsbebGg_R^zx1dYs@DbBFw>(bXGtX+(~)`EZZ(=T-YR_`O^JRi7fO4w
zG|eO}7`#^JGgqHBf}+^qH40rLe)#r(&3oC>U~)y-IUUqWpg<qAu60hr4VmU0_-y5w
z?*y$xwzR1sUchW)GNT%#qXttoY_VPB5pI~K@*ClJNnUe3cBd0wJM}@%7wt6(Tn<G8
z?KypOSk?B6&B1}kDxZ9?GCR=*NIVbZpR`Jl7D(T8yV*y~T0_!%pY*S2txW|gFUDvo
zx@WQ1w|@z~3jpGJhv1J{{KCS}P&Jdv{h3ZO1ayT0Q9Zi5NIG?cGU_e_#T70`jj=Bu
z_gx~`mYxzM<+iXo+9w&GDMWz+)MgWc6cf@w3zI*&<)mWC$7DH)kM@HqSqQrPx&}y*
z0vgCYiL7RfFJ~L?QfZ$31tpol*J?jU3C*;EpW+=sHTjH)OHu1jkGOK2@<`CbF48$H
zI+1CV3~J+jtDWEJ614RT6{Bp9g*~>u0}?auq8Pc-dKO_L>Dt;6(22C;(GG*7wEE)c
z;|(=W;l1MUw$*RTsyf~s6M0ETFo_ubD-{GNJm}rh-6or4MzR%!>H<Gbx$<@I5OzI!
zYO;z6?Mh>Z_+WyKB<TuOctUbN;U-z1n!`fJbV(y!vr#}Ti`gvm9;BYM9i10#2g*$d
z+hR%Vn6(18b{z^l?}>M?CzS%k93$%+CVELA+|9=PhV-K4hey?L6i_bNu7<p7ZQt?J
z64|20Bz(ny0*$ESX0Y6rxKY~mY7IU$?uF}Vq_@OsJvMmoUWiR^j#pq8vR1lN+H$ji
z(|D!ZnkKD&LDdptvn(E)OjGiyr>QtSJX87r=$({-qiI8db2q2xBzQ>nkd5xRx2P;N
z)pXGf3p}SLt^LP1EZI_slffl=X1_3)Lufq7S5-70fU3*#XCP<Uv>L{bXqeiP!sAjB
zJ1b9q72&1CqHb{EfIx>sy9glYdm8QCxA&+Dl*b~$ds5rN3fmjB7gMPDBzDsG_L&ve
z937BMxJCPg3@on!IEhbn*&9v805u04r(NO2SdjE$8VaO$YHf%3uJ3VXRUUZlR}WPF
zOYJKb<4I&qSX4B8joKt@hL!wiIx}c;AWzeOm8+(Wci=<b$_ERPaf<p3MnU`8vZUFf
z;NTCj%U9s(@(ke9=c5LK-j}blVRyf;@yC|Uu!h?_-d{2$1ZQwvXtCOS{t+B^%+R9I
zuh1Qan8HhE$ok<7p02^OxU%rGPv2C33Zpp8n%e+*^S~1yUUNTXe79_5^0kq@?vP7g
zA4>~Na+)=>vt!K!26TMw?JlC||0IC0;*j~y%$M}L4}<z=C2g$x4a8Zq$1NCq*J1f`
zp7lnPu_8zX!=xI_{LL*zAPZI&!>cW!DXc6KIo$2>qle7nx=&-angv&NajmF+`~6cA
zHa!Jwk)d1BWQnK%rPU7urm0to1`@_K2$>ri_L=|HUCwJ(qLgdsP2bg4A%^vE8}c!9
z&CXm&su37SN4<JKPb@?IhPY@@{7GN1d5qxdCD@=s7DI!<QOz0>+6!!w{$=(occ!XA
zPeu&c;PM7pIPBKW0B8X+w_%ipr~QA13he)<W4pZ|NYMGKJzRQgX}Bo*kxa*Gt&$G4
z5ZpyAgfh-GS>#&CSmJ_QYOD5uhYn}&cPE>-jZ3#Y5-@^pwjDu8tGmcAzN5dH`cwd$
z-2Yij;okaXdh(LZ8}%Y>z#9=FM?)gh00{;*jj$T3Q^JzAPmW{kQ1op<j)GiE><!v+
z8s6xwIIxfMO)>}LIArAg&a~kDDuH>(orBt9m#pB6ahhG`L*n@PN139L!8IFA4d0#4
zh^KK(==ok<IW4;iG1h%gf8Nfg!=3y*c%+Wow#r^*@QkXy%Ca6xHGa^gR%!>}^=nty
zcE)v4L%}A{m2_VU8#vApba{5#CeO&>?Q7S%v=~8h@K$l;tWTXfoy=o7n6V^;FYtvH
zIjKdyZ-vWkzU(lF)>L$T&vnBLU2ZQV@--)^)8}9uFQKc2wLE#IU+j4nQH#@RAQ>jg
zc8*3b##0sLK?2N#fR^<^gVo9^XUW{72d&s^hD}0o1*%<<R!SJp?POKU#5M2w+DC1c
zqU!e48&+${=~=@ws}F}hG$2f0Q^|WThc4w=sSQN#d|cpxup}+d^*@?tp_hqZ10`;E
zzQprU%;6}o(BZ9o{Yx&;<C*m1dQ{U{s)lv2F4cor^DTK!+tU{ObAUqvx#1K~_~@rV
zGZfOY+J-eqKp#W=o-_W*Y5sE=aFUERJpO&~db<GD2Oj(d-NTBK8{Ej7{^yey+wHeh
zs@R40|5GX8XGa05AKBSyRRR26kmfZj(5v#$eq;w%&ys(u4b=E}LLQT_+XCU8_-jka
z<r1?zY#=lBuUD^#^4oZ}oz~_&VVU0!0#YEuqy05c>dy+sPaOu->bK*q1dust=a*0Z
zvx4CWXaLgCR=UD}RBhsb&?LYskMqx}%`q`RM#_*-A%N(9tAxWc0R9#kLf-B-%7I^j
zg@M?)Q-ePKm5}_O?~%0uz)b+1xBDCAz^|>502z+F7?onbFH7)s`%~2h;lsp#5Kjh>
zaqLQK9R25-1D>oMW=`IJl$@lWlCIaP<CMQI3)u_#slLVVUj9EyPALEx|6ew&-QS@6
ze_rKfN&0?D>GCuzl~c{_<}mlNADfpdDbX2f&OSZwM@NW>8lt1)O##6UR*?iAPzgPI
zDv>p<6x9C`M*a^dhKA-!ZkjA=d1g6*d7-`)Oa>-{%~f_8`MoM#lHp+X3?pf<XIQ|U
zyaI(d|7P789Z1L8`ce10q<U(Y`4J`8^-9yieg5NaA*>Jn6F*%@jU)cWPyP?c?><Xk
z{iuk~qDmAK2l6(nxp`<2lKgK<2yd@*&;MtO|B~f5sNqoT@7_P<Vt>lEr4va0TwW#A
zJWKVhYHL!2jT(k2%|hMY`k)QVmbI*nux?m`^LEr#4WvPQGMRk}j|VC1B$LOPs{yZ3
zt9c<`S!lcb^_tD7wW@)OwUV-8^=9`QW6an@K5mne{5&(VP`u&-%<yo>g&c;959L$h
z4;PVL@f$8prCOF^yWIu*IKp8a>n44+M5PbgD3sLQ-AUY;!%o*fc(_zPe$;<~*e4}w
zx0!fW_oXc{439@mE;%)ZftAg|{v^Psrlv*vDP9B;b|t*fzm^1aT@Y9{HQm%7-5q_g
zA^G5Nn>m*Zs_B_K^ZvH9Waa9ADwSa){J7J~Hz3uRqtAxFaJRY1Mjn}(!pG@QQGQ%U
zwC8?PpBjFO5%j=V0b*xmy||@XG`qMq$K^S^t){bIj5@nq)Ud8dca^X&dfC#y(|Ed*
zsxUECFZOVoy|Yw*pAvWtRdl!fJawr=->hc^OCZR@`bc0f-%ver>b8CVI&7$EGJa`#
z{w}-O%}ys5zh<Fx3o#Aj+GvOMDY6C^=cgS;_kGHX{5%%O-jBUMbvSxRmTzw6J7O?U
zlP+}b&C$?3kW^gYZgk`{xJ+GqTySXGJ9jb@HMvr=F$@`C4jfXkk&TqiMo3=eoM>x1
zTVHo-6OrlJ6@W3u!AY(>;FI&aAu$+{M>BIz>SAIjeoevaK3Eb_U?lj#KqrpJu4&gI
z=Dw<E=L`0}d}G9w|MOU^b1njlZZ)**IQ4x_yVb<vW}lR!5UxBalmJ^$8JNfo+K1a;
z9V5%VXgOvD_Yb2-c$_u?S(>+Yxl0>dODdHXB-yXxPFmcU4%r6o9hdS_?+(ex@}=Bs
zZoPfc%o*Z4lskmHKZnNP3mx(@-l9bIG&SYA_l?jHmr!=OynTd6cdOrBZW6XQCG)>n
zVl@BMcmz{umB>?CIw&#ta8T&5`r_b>*?qTMeyHF!*w>>vm7TZTv8FKX61CW3p~AF!
zDgCelp}E?n>rwq-u(bEHgT1LTx6{X?1vQo+exD~jd5fQv@Gq~l^7d;}?%`4FgQmxf
zJNAnl_a0T7VT(b$7?%CT9gVUOb^6UZIDtFa)3tm2ISJHGSl7JW@f8IQGbuCPy4;by
z>ViRhyTIoqr>!ZOrO8<&Br@Jq@5?!ol$n#1n+9*jB4OAk=&}#vnI~SbyB-#l>mGgc
zs9tK$8QtDbT1sUZTHKh-CzYb1UbUP#OlFn)TS`FF>F)s~_0#2i?SsTlz<JP`;oIk^
z^rxDWZx*!RbnL{}HtsCJN|_dSca@?|lHmO~<uqkN_imoWpSSutwK}U@wyd+-SU(Xz
zPf*+SPEw~Ry=o{Fx4_7de&Ud8A@s5QG*kkb*R2UVcFj)YIX<sTXHskMKJ}QmQO+U7
zsZG6oyCK5(VEyYU4sLb%mHrPOAq88IVH+U=yZ_xUa)u9*E_R=_jWKGZ9WsdY$h&!g
zG@2QEpj366xnyX>*7_!rwwQ)Y5M3ri(%sy7aeBVgrSGDM<7_6@z&&1K(42bao%Ujm
z37nGNXJ1#3y_!G^v!%BM6s~C&IDCOOeACrI_ntmJdm<rr3q=*_cYwiOnk&yJ%I&es
zvp}-4CcR<4ycviIQ3;FXwD@S>l+eb+vIQ66TjG!+3sB7eNOFetZ+E)Q>s3p%rJZtK
zd1aqG?K}44cps&xF1VKj4XdA0qzLFx*)ypE#U+`DXas@rs#`Tw+-(oP5t<7%D>TU?
zYL2~2mBcBc#S~j#kDQS2zhwbkwYj;Mv+lBStbFMRQDWWcnbK&z=$nb~w&~Q}Lcoq&
zH8HwA-#pLC<DE_|;;=ZB9h)xMnI5q}dWT!kZZAzP2YK`4-retxC+vQC$ZZBMBcZXZ
zm(q_@VeWpyPrCNFz_X+SMPyJY0E5Wl&lcRca#PC2E<Ix_>slrm8OLS4$dt<CoumKb
z*p2CP@Z)KCFaeRxU1@@gQCn3%<VTQlAq~feh4<3z`J-YUcUyBsKUBPv=N_*u<7JvX
z8jq2PqB(+gYUrSj1K{^wF7djL9<1G`tb5^9?X^g31n~0#g|PV{KCs=UU*7603aqy(
zy=t|ilJ3K#yt_rulG{<rkscDRE|sLT)R5Ewug!ymt7>cer=TFX8IV_CzgK+ZGg332
zs_2gJCia6xJO3$}%~_dK2ys7F7&=2pdcUz~n2XhQiH!ma<_yEQJ=%UWQkbAp`Q{=J
z54S1Y>P<g5#Hs9<vLgint^3XJ>g%HSC;->^yu??LVFQ0r1~_k9@0Qivpg_+KU%d&v
zC6CM7$`F=8F=73%^>Di|_Pzci;t&jG17-Ou?*;rMi{tv+L5qQ%^)D%@*eNVmd8*CV
zH{Ol)Kqy?`zW$6s=qxuz!S|z@#!-WgsILdF4OwDxqpHl2!<M;2&}DnX&}tj|hdB`b
z!IHPr%&Xb<ntATg0vDgsS^cL1%<xmc%U{U%U!dYWq`Sr8(Gbp#M%Y$&Ez#p;<Kx`)
zzD8xYse@!~Vuwp0#{H9LbF;>HhI+Z#X7K#cup{hYeZ!*c^QiA9jK^di?JDJ?ON`Vz
zm|CJTkr%q?>f8$^6b)Z<Z%@An2*wkl7_JF*rAKnu9nZ(J6lQ6T_P5@zO{o)px8GJ(
zVK=lfy!6G2C%xa@M3gUFjc1pK8A_>wdWRr7q&YNmdATnLp*S(MqHsSYzGNL!y5pZc
zq)m}^vzf)`wl}2`8e1i6MqqvZ=z2K-lXC53wkGs&f%=q&(Y`L0m6iPx9*&HUKg3&P
zck0M}*Y}EF-@?DZ=YLy>kDVUcwjRNdmTDew*n;avz>F?f?=^RxSK%)WuJo@kJ?_JM
zbcTu9>_*<>Klb@QYLE7u^uTJC7twKqY1~!{p<%?!4c_z7K6;ouFJ|Eg>vump%s;YE
zIrw%~JDX6S`Vi01652E9wz<*;vN(HKO!lbXH;WwF{T^r5w|A#iH1_37JhwzE2ivsM
zHJiGNm5oVD-gI1CFgOI|?yj(|Uh{GHlxe)=Hxi#IM*rME(MrjX3SCWY!jmMces}GQ
zyDo!U#5H@BCWEa<=i)+={;TtwkNboY9?tizw?!%D;=s<!NVi<+U%B!+_b%?~B{M#z
z6z1jzJ__sy1qJDWhu%nk;w1kC1{&YJX5j6a9Hd_2Yu;!^#OF@JB|Uu5Uo*KFzZ-#X
za$lH=N05+mvuTuRZY%S<uU2UqE4ukMeK&$Zc0b$UW#-!$)r}p;nD6M5>nfAa!hS3a
z-z9Z*VW)u^xBR?Rbz#`^MlbK!0b}9*PVp6+{^A=57-)5&!N;caqM5?zwWZ)25`QnS
zR`$8pF+cRjlRF%=wYv;x{pgGyfoG}i$N5tgv<D_ZGmx)lJ)BMnKPg7GeUcEq4;>u5
z_UAf`zNw4?Qc`5#%AU#0QRx4QVYY=p(>ig`u34MZ!kXy<WMrzScQbZ6&mMcIJl;Af
zU_Jx^odBFJ9nVX9Ulo$`DJn8CQn^@)<rzI^%}LId3ho;Sv#|SSS{<P`A^$D<<%^aT
z4l)*+5`-@`nRlvgHm5a7-2Kg7P^ui$wZL2Q>Wuld2}jakDkyCfvG6|gkE6kkf(poo
zWgbP}!~DW9uT^1}QIb;`e3~_}&j6q(Ib7h9y?`Te%}X1JiO)xwXcuptbg4JH+<pf#
zkkaI2qe*UVaZQZ;635I-M=rRDN=l0~fZLv0_~xl-5(+e}IS2}0{{(ixiK1Ui8k0Zo
zbffn5;KqDPZM)8Cr&_%Ib`kKMj0h06?Y_$8B>uJi5faO_EJIC=l{6(|69UB#lah}t
zUtBV(o+@`3PmzN2E8~z~7VgXj#9>rh%1{bCb`YCkZxSvDb&ZY>t|}Ex?h;t%r>DjR
zZmQ^iH(74mfu=%~=?&VG`n}BZH!p7PZ6ThL3W7j#pO44vT>cm8XiaHpX^-+^yz#r&
zk%bU?{T9v;ZyDCj(zxmu3IAuz_@|y$9}@diWBg^`{yGN|AaMWxUH`D<|D7A{4uv)U
z!$KbtuL=KrKAzRb3_A~ZweOW}W36TJ#vh1LmIcl`3@-1g_uviB8nldV-V2Sk$*FJw
zt%>vCn0mjqfqxzO%7ZHG)L`y*T4L$MxR?h>P1cDln<j_BABez{n6_J98jr~nA|pX+
z1A!UP1%--=y1KSD(^YByD$L(wW=ya=EF=Wce=`s9-=ZxAn%;h}ny|XiRcB&8-?Q<L
z^C=G=B^*WrJwD99(LP?Xkj>~o#(2Du*4&+4B=RizW}Q03XWX{9cb>o#m<5bXZ0cWh
zbaa$~T`m&6ANcj?;XTOU8<x>nx8fyfwrvl{Sz-ClqwiY_1!%g8@py|Kwcdwi_;`NO
z6zcK*!1fa%-w=Si%ApW%FKW#53GY_pyMx`7^<C(6iVSiJUFt#D(xJe@0dg3w`GMqL
zubP4^Kw^NdYiepdoT7t^d!C5pv=a+9z7z1II45E6@qWU_?NmsKmaXEUp4fwG4|lMl
zcg5Ew@k5E%S85Tg+gVS`PJoz4bFNePr9J>{HyGf-Ez%8jbfZwm-@RejOsDBxuZ~AD
zM4n?a=VXW|DJWFA-P#Wh#xW2P5oKg(+u7OWD->e07>@^_5CxFzQ&;H^U{ew-TH4!R
z6eyP`W!EJ?oELjYYLd}51D$E7r>FI5(vJ=AK{Xz{4(Cr;_pjsiDqNgX+z*e?E0|m)
zRX7k1n>qJ*oxGyrlI@rznN$+cYDk4h@Ws-|h(gx>`zNTJ$sa#{obOFV@|n-qNI@QF
zNhVfRm_tA#I0EVA0Y=U&6&NI3cKdzI9XK@7xTKULBLaqy-0Y^Nrmf2JYHVW9+c`8v
zk6(rrpyKN-WH7v~3H$b;qP1SJ;2EL2Bo5F)R_%Pg`}y-{JTCibg^0i`7Q!*zrsGz4
zQZI_D%|weT64Cbv9A?(o*x2+?TtH)$%OtMsmI%JvIyZ~aC~<%5Anv!@r!F3R{>k54
z`CEO#gw@LRsS#T-5(Xy9rl+TYM!>^``l;xpLxSGgs;bGP-rnAi_4a1<9a2^1gL1yU
zzOb4__Y=kL8~toMot>TS?Sig(7PTAbu_|_&S{snkK)&UZ!M88J<mIoZJwkH%>SV1m
ze`Y3Retw?Lbp>87TZ$zf5M`UKLA3_Qlm2)n$w9j*wW%U_=C{rZb#@nd4Gr7|mESXS
zS6p3iKymwO_4XWidEUA2^*G61!&`2-+WxQD2)-7BWoBWaQ7&tb^B5Z&D_kWRz*XBz
z4^}+oI%*I|wK8JmdAvIv3K3zxSY$F7<i1+=CiMXNkFQu0nT<JESfXcIH^X@%?LyvQ
zp6pvEZJN@b<kM5wz-KeDV%)g$+Q5@yDk>;2o;dDLmy(Ly_C4k6sR>{Hl=i<*0-!-Y
zCi<X~ogSbKA^>FOBBZLvgvd@o5$H+^Jts$8fJ%B8CEwsk=W(^-pM{y0d6LlSfL%`W
zY({tXOPtMtuBOeiN>hpYo}QlPJZIrO6}QqrL(%p~2Clxoe)_ao6V;p7Cf3l;Ur~ea
z6OQ$yL0Xbo+WwY~eC-UYxkIvf`eUPSXLPT)*_^A>cK&3oYifKv+~#~j@i`Ww?rM8r
zW@)i@2g!F;RYIW*cZTYZ^(VJS&0*=R(VBTe_g{d%@M@-%7!L8$r-sXl8R=Bs1z63^
zOZ1m7Iiw@1DDkZJIKQ>M0=RHUz^_L8%O5{&Ju(C2aCNHt4Tb&3Yz+qS^K=VI{CCR~
zA;d*_d9BtajDTtw;)b0>={wWMQy<qG45hrc!|`Ui(4Ehe>8J?F8PC$UJulH}Q+435
zUJvNe+GYHND}O}!wN2{DWr9Sqf7-CWPtrew*?$zI7XGMn^vyzIUdU!vYSpFR5918z
zA~wtF%jv5u+6XljO{_T`<VvQUBz?^0yU(T3M3s1_UaAe1Piqyh-gJ9dA2KkLM3NU%
zD#TTMGZN;mJARAEHjnHGZy@>&0!Y-tFv^7fuczi8N9AXe0=mU>vs2RjiP33Q0}?vY
z_x6u-WHOFbXzA$Kgf*#4;o#t2yb~AKN&WKWEx7i34mzuEl9)7#`pX38bI$J??tb(E
z0dYqS#vU=leOzr5Gbw$r0?<@ZOAQ#`K0?`lVZtXF^CBnkJc$`da7Br^;*(BbhT}Sp
zW6)W2yHvvkN-lBg@yRZ`<GC~{Rl_!S;WpOR@0P7i`KgskTAod%d?nbNY<tcZe8^%x
z#I9K$|193IpLkv4;YX~n&zK)zV=vd$>(GJ3^9|;2h~x|d1hnwkIMbn(e@1-S+bev<
zjg#9Gtf6qZP;HUwtF0Qv(N1iF&Z+%C6Y0e;nh^f6DpS&OvT_(@anPdaI*UdVO=6V<
z`HZT#K|4b@QO+k?|DO1;d$wc!?$DuG0F|ikz*o%H8?aMsUw2S{1@wQdc$>g8@uYl+
zH>iqP9CB?1S7M1CM3llsS?h4L_~px&(80PND5Js<b0ksZ{Pe~bY>SR-K!uSX<gs6<
zQoUM!P^aLpMhG~05>-m--vsqLq@|s(QrRwD%1{;#E_SgFqa@Pe;OW+oh!g7847G+W
z&=|J-Vqj(&v82e?gDwbRV!(7gR^7QLMzzXxCbsE}WL0MEy20bo{Rc2kKn-qsZA(W0
zKF?!b_iv?qEen^#>l9342EDb})pgs3ZM3Hd8F$#%IsefBnVR=`yMcbZhWDrTA@>U=
zvY6^c=RRCi!KXGnhAL$PuNLN$_!D*ejbe@F#ppHeyY)!vB!7P-yw-#GX+`P<T}b)?
z{Yqj3tZ(%|TWU>y`-gwexB;(b9-nHw>=c)OxncX7fWhc{E7!BnB7(*S<A=y7Egynd
z;wmFp&F2mCsL9E<4MQ|sGXoP}_9vHa&ju)ek6LPS<LaZU6+?ZDk8hE<7ZOKvaGoqs
zR?8ccPecO70}8^t{-qQA9t0&8TM8NOJC<@fZJ`5ufS>CtKl+*~SVu^Wt{tuCQV2#$
zIg!L+Qv)(HeXCW9S*#2eC{ZsV10!FhS096P*g)@<%WyHvI6tT!N_2*QKZ4KmaJ6<(
zfXV~B?0?Y0>seUMIf6VyR&;bhIQKG*3Ymb#ha_IB{+ZgcwQqw0-)^6S<5<iT`1_cg
zd?67xy&Or})}k(&_6h+@;k2W)u`=`0M0E{;boZa$h)rVops0ujn#GPW7)<Ip(@{;f
z^2(atpD9oFjXop*6!8^keB-BA8xin)o&VH_WdvG5hS~zU27*$Wa>)uIpZSGwE39I?
z)bGRR+<z<kctHoMw?DA9$IK{F_M6g0eQ{GcrQU|Z$-xnii_rQitjm=tj(+6i<e)nz
zFOO0|X7!^S9ILKsY_bEv09$a+_o{wv@$vpCq}^B($%n6RyaSqrZmQ<Yb)c4kHvLez
z7Tok{t8if%wrcY%`a(vy18=h7!ASTA?SF+YUWSAvdVT0P&=)|z-nVbx1pJXgvXJuV
zh&n_0YFut-#<KYtG&OtMjmq0I@ljjKdVN&JP5{5IO<k@V!J$h^f1$*LF;&nc&bxb7
zyOmP@^*HvSldb6uGj*a4DwRS3eOg{W0quZPvA&{~f*ODqoPpBoqWi5`zPnLB(6JF6
zz8p3nT(Mj1alc18uu`hiwdiuhqe!xCpcsloC(aMLDhv4VD{0$|Y<W!u{m^ni_d2~g
zH84=Ldf~FWmPzltk|oYVk3VQpWI=f-V8v9T$s6XmdV?c_HfBC0#@BaG?fJYfeNqTj
zZR!tuUl29eylcXR<&iW41}vO`xtKt%kiIiu04Fsy)gsY+f{p{2ROn!sn@*JkZ}>p$
zNt3^fhT8JITvqfS+v7z}Mi0ydRhmp;6Fm(UDQ4dZaU_%Psw>!=zc?3G+hGL9O|+ta
zI2)6eX%-a~t-(zUY<kXn^>ri(QYD2!2U@+iAF-1qVL)nlLtilGSp!K~ZB9<WEJ)fe
z%9|u!&UHfbT&>P_2jV$5a*gSi#+U>Or`>T1a~~_rtzBS@-3YSl2OKX-ANgBRQ8;OA
z5&H`S*D|ls{oHO%#Gcn8#{<7e1xKkNgp@$0-rQVy*)x<zHR|`;BH>o;@l$$YGY?Jo
z4@!O5sAO^ybmq?L*42nM;joaP$TvBC_#wHE6@ezb51R?J8dyabaagqrN?HLYWm#FI
zb$U@Bs&Bhsev}!<;9$j19@Gn7`gU@g@9*wAG3#5Tpa{Ezp<`g|@wwW1AdGYUWLgo*
zGRAR*(U&MSZ}d0chLU+J?*<elyu<dlZ9N12`C9->a&l@c*VvE7Y_m5U;I3))A}to&
z2p#Wc^d{&Am?n1)E9DfG0Wb9Ls?U8g7&N5nSLGKku=+=dFuiWMB69Zlsx%Bzk@jZ@
z!1p23D_{kAz@Y|1Z$t`^ex}+X#h=F4s1%EIYf(T&s0kCa2B`bzlo%I~mY-~^7@S)8
zx6(!dy_S)F$}HfQ{z@z%Q-h<yc17t|VOq(4YLwj|^l8aCiA<sy=)qs*e#+{<-UTp$
z$UTw5uk^?#5`JVwl_&})U;^Xfec<-%a1ABy%TAT@Q@_m2Z_+6Y2BT*)BO`R@K%L_C
zJ0SeQB_@CQv-TU{4pLOJn*iLf!@+C^B}G3tYfzM+NA<1pa}hO`z-ISJBRfSPObB@@
z@jd%#j0lH?Jq?SV=7?%62{ttf!Ld5<gR-)OonynpF+1EoOaT~amIN@KwCH+2`En))
zg8W1ZLf->3Ffh23gOph?E3Upijiyop>zP{Z8=#A;UEb`c=GiWBS<hE2Zn~H?X)97T
ze*fXAgZ6V*j?_<l;PZ)JQgQ$o^HP+T7t#Z?3c&ML<i_%NT7qCZE|x<`V_)UE#H%f?
zTpwDwT65g)n<xZRTmX&y=6-t*lZF9K4y!=dDnIdaJrP2hdy|F2_oMs3oLLI58)w;U
z@uYf8O9X^VvYr@{y7e~qH`^t&l3hhm&C$wbDpxOP-Xo>bnerdkZixi~g2F*mOdkOL
zByos|aC#N&&+CXF&8q7nO`cZL7g>U;4XWsXCLkaJQLLe;bNhe>6uI*7i#dOm)Q4Y!
zB1zQ{kdhJ-^6*#HyfCozM5N<TF+4^<wiD|{5hI6&7T?A#D)?6Dcb7UIAGOBGS^hP^
zS_J6@L^@C1>p%-K8SLbGPh=pJ8_CBsmkUC#sPPKA`^Bl}M{{Z#Doon@J{7_J>J9OE
zNTFc6u^U}Cofq{MOHBj<e)J75RmTW3#(_ae=_Gar{r<Ra!^3FvZ;;2)?x4Ene;hB+
z^3iRv(3&e`EFJ(yOiCJ(>}VH2C2zMtqB&vVK(*a!2aJd~9W`EJPA5#&*{$@_)7}{E
zZJu5$wVL%tQE1JNS{fyEvb1f8=HUI@hNqL^Vp!zk_y_IV18;R;F3t7&$HqKtq0;;J
z!!Qo}i7J}ISt9d6iz8i4wMK$VLg>o@?yklS|4{XJCW{z++(Jf1W(m?&-|gsf$s?5~
z6X?<8biK0lE+{AnR&u~w0dkupBzCr}5<f(OG2eu-S}X=50Jyv(Ba9at2M34L41P%e
z|C+-72lv0`ge#dxaj$pFa`&nM1P_QQBf7i0YgYVls1*{ve=@ijj;^`Cm`nCLQ8nP=
z<OZe@0q>*qzOby!`f$EhSy>q`8bO|yhtqZ&xth!A2QklqaH7D(mw+4*+F_KFxbb)Y
zn6<wkI1t+Dmo7DZXnwDAQLN=KXI4!@N($Y>z*Nq~FdC3vZ92o4$?~zHsfoAS<vbIU
zCtV{8dTuP`1Lne1F9>&GNU`y!rvHU%EeR}zVz}~(iaLqmK{4ltx@P4-_??xV%_WNX
zihJ5=TY`<1b#ii2me;3rwNah!BuP$Ib`_7xj>BSBG{JqOek@yhOpY?JjD9NFwgD%b
z*s~s7GWMrl{(WK_((+QKnfU}Tf>~(*j}9_B`h`iqeyE31C{lG=??#bgpmLnAu>uAS
z!DS<{I)GTE246aHvMS;1X-aa7$$3tp%yvh%*D`<*m>F`Bd;msbS<Pm3N3E=^fCv>?
zeavLCAT1dY5s}<D{nJZy^rj!ZRNbbZWgs~8_379uub(1W?qknff1bt+d14?ZVtGFC
z*~a{P4d8Fh2|53r@&?!fO9Ng%FGI#UJ-j$F35*zPjRM1f<?(7_?;*xaYJD2v*z{;E
zjExDa(97Z{#=74SXJ{s~WS9;Re45-ubLtz{w^o9P?}#@g3e*!?r&%|*u_>qVE7Oa%
z?oH*efyTGCNi$i|aE8&9n#q%3I8Xz+Wz_g>|5Z$Ql6qt@kixxR+3453GSZofiV7*(
zw`|xZg%sWc=x8RIPLP!9y%L8VIzX%l7LC#Zj83<w2bokfKBEvv@)vGOa5e6%oi$zq
z8o4J5baaaeWigDX>+F>?Mn`4kycq-&zf7kekPw?5S$f%TQXK$s$v!Ckx4)O*6^^pq
z*Wo^ARuLlTYiU;P+2aayrzac0QL#Av&@~7Z1?sJ>zVJZ!W7eng{TjyO7$)kw#?9#v
zADiz{^W#Gci$4%kOOo(CoP<eYWw^tkOY&TCXQWHU(IPZF%^p#BM?2n}?PL~$2`h%Z
z;+aiiahc<q)7Vn}MgtC~8T9t4qW*u!b~B`u0^W?{zRrzD`Y7L&j0!Uf<`)KPJ~O2^
z&Q|WuY;K<Qk{NUuw+A^9_G+r8RSN-h8+rB*ch?`bRp+~@>GmlnzX>$N9@QT;0Ry+_
ziUv5&&ck2d%*@POam&3#*SvVA7gdrQAFftpIXOvqP)6pEOLCu90%_^t*ef$9vb1v0
zM8x$mbpNY=CQ(JI)fC^mKAtvGXFuuB!?c1L<y1p1;?g&5QYG>VY>7S>gu^h9jH7o)
z8)q*b34MhGzT7N_*7?F>f^fw77C+R9F{ej^d1K$9*c;6b?`1t#8)jSBzwL16+KojF
z3=Vvmx*qyD?JW!frsfbfpRUWc*qQ1(E~<uyo4wL)RB8CN!gJj$F!f<!Fd&%{6&pJ>
zF%e&)lw^I)7pa3dGKihzATtYi$VoB+AnYo3?Wq3|{m!g0V<8Jeg76JoSM_JDE>V)(
zD9@2b*#@^~YHamUp4V6MRnW*h&SfY(!N34W(~B>mZzWnV-9siYxK_?uq1-Hp5v*cA
zsDXh)vv=zRx80q4A+QGBqbkPJeC2RU)`FrhcjZ!^*{<6w+9Q8vTU-@K5;5>%6@^H+
z#@q*kc@Hj8BDh6i75auxuCuernr3r7PtG5R@DT)Gfd@AR2%9!XOr1%oNMv7$U+p^R
zJv)q&D^9W%U0N5E)_0zp(y{)sgq|%4dE>|L<{gGJ!FF@`Qhs1ttDRn~hMZ4^vBu)n
z8;|-RmOHT<;mZs*1r61&C)SsVpTrf<^SCNxnhWN~F2Pgh+(N0tO@1ij8;<A59K`H=
z>(^|^P)q3_j9K5<&<ZFjC?H1LGMH3iG=R8I?a6l7qz)Y;O>?V<JZmdbqwYm80Z9%$
zNS@_th|gpC9HgN(N`mdw>v$}Lx>b@R+FH2VuO7Fq-z5p!7GLijK<BulSfbLW*7a97
zK3tJABI|T&54WV6=WVX-QWsRfo+Wu&xpcmAyuA|9y*l6+qA&Im>G$5W8k1sLs%OKN
zXffEl_Y1rE7N(>i>9_@ekc;nkO4+gJfb&4m#R;s-??3n`;{P1KsuJpkZ;Z}aWaEr^
z_{;o6qOgOLvS-HawXoLFv1@3nI!B#PRd(19U;EcP9qS`#h}+N1H6@xDFD?j8<QHf_
z-I_LdlbWc(<J~XjX~OGr+(4Z)lNPs#aW6h=oSo!-iJW){%s9}%C8#C6LJL9M*Ad~F
z)^Ibo*uc8D&6`!QJjl^y-wG4O=jNmdLSN*yEyz#)N-rJroc~x!HQLtJFqZ2X+FY>_
zSpst84v-gC`f3Q+QXutdT73@;Pu6wW1lk<~f9Bv>RKkJ!UcYT;7a<|@NjjXgkZnGY
zKOV19I-0K?`)E>oJf15DOrH~6odR9<+XY>j@z4$K_s*lqx4`Pl?@)Q{Xg6OdrCAeu
zo?`_NgF3JOAEMqeDy}Bj8U{kp;O_1o+zC!_2<|RHgS!NGcXuD$T@#$(?(XjJ9-e#e
z_pNo-EdJ1Qx~i*sm+j$>(_E=+G=x-@sj!JXUJ_G%eTuZgG8UgNQ?NieK!X@0)>d4N
z_`)H=@hkWY?LyHTjl7EG{p%rMO)f6{M2D^OcOg*=oseXAZzl6;A#)v#+c&+=1q2A%
z&H7SIT*6wnKhseJLN)44Nqj9P%2di@LQcmaDJK)kd**f*64xI|Zqd3^Q&iCVK0g7#
ztLSBj$mazZ1&R@{-|DZ@X|tlBUIx<X$SUPJ;M(fyAso(C3^K2bAd4jQBE2GEcgvru
zc{&iuUw+kV38#`G3qa;ATrYlZdB2&Ny%gY0csgaBX;mzNc`&g%o^fPjCfZO?DR+Nj
z0RPf{Ltv|3yw6(paLB&i6vmRak#l#5OK?)6oZ{K__=rk}%S(%C|0o@Ony+^=zW9rf
zr_uhG@BvKZGHd*gOHb!DYR`Wux<Iu-(t~->(54}3@*9+cGbXF5VXuPI3@;p$ZhOjM
z+c<>e+{%i!nOuxTlJ>94`{S?Qr?K3P=Y;a2)ySjNV!UAE4Qs)I|Nd5B72QCEFtsk0
zu60D_fl%toH7ZSeO7OK;i6Ll~&y_eIv-3wdS&7S>h{wSTU!=V-X4{$U0gXMDJ9}Jh
zXJ$8~6A`4|oKe-C+ueO05fs-qlav3qS-o&>vOGa5BD!zL$Vj;e1jys5tijS}R;!F2
zrv#Phb=c*%-ut}k_Iq5@0jo~{mxBA*3b)lCN#)+JMre&$e}Qbp_*G^xP&P=at^H~w
zHHaIbTwllM#Zs*P8X~|WPqWGhl*5+?@<y2{a=;V~p7cq}Gy+h*$`xFBMwRRr4K||K
zE%{-fNfU)<Av2rm7OPdKqRM1Wm3gDwS#h~S|MF;>A>yZQ<!o=uBml;uvb3IMyUj4K
zV1sv~G6=rN6c-e%08Q}fhCmMO=<5U&=9wE}k`{hts6^l^<}yg7OQ$T=#P9xm{i9x>
zC3y6+s%6k3s)*xBIQjsqBR^WFtjh;8>GOZ}Bc2sl=4I}cbnKc_vIu1B<fq65=#roz
zbzVCf_|MUV#H6Iis1VNl1u-+2S&7&N(K~%8ONS4UPXqE?e9QQ~s++5kWc8sD7-g1y
zmNo18Jb?yxc<T>AKOwA{v2;tn3cf#1Om*L#ePJW^J<XNMsaXUNF<FUT730liE`7Jx
z7wskhR5r&!o{UP7kyIHgJKCZgfP)Kk2Qc1)P%8ps-F+34@3bIH-y8%_1g0uQ7LG~f
zxw9s)z5CYhj!&G7OGWXEt+zFh4uPbMQ>xGD;-8~r>pKjoKM<Z`)yG8u98wGNb@J}~
z+BB~tM(hZAVaVlHq$s{IiE?_*-oQ)2rI}mrd}ny_Q_Z);{FMC_&Om;DfM|=U0`oa?
z7&_R(1>i;LZy>#@%hL)xLXidw4lDRzJArY57<{4I-?#ITv(&SLRBv3u^<!1y{UVO5
zZ9+={!NQ*nkNXW-Co{71&jbN~xWcXD@zX>Y9|nj`?pe;>UgBQKTM}k8TTqbvwgi<5
zyhVuD;=fU|F~~AY&#4vu+sbzoeYRjZBgiu!9kpnn%vOaBK675WEuq*Y;f2-V08;<y
zXoPaW17!B9Sf??7ea1@p!p5^{*ZGiLAC}IZB6q{cR6Xi9IcRG9hY2kq#9tZPpZyfn
zDxO4h&SCz1Zar5&mh<|iuODRA%csh0#a&&xyAtYrmLjmgYMDl5>pI$9pQJ3|IdtEI
zY}-Q7&76{YOw&r+sPAa?U3}!PNN0YVR@9k+L5MW%=;(Dss=ZVcKegcDa@Q1L0|hFy
zYgOk|ycT{uTTbCt{rQIJdu78d2Ke#&iW=vPmuL<X%*JP(^#d~Wr1qR=h^8}=4_b}q
zu2(1BZ?QAB?{Da$BIgvo`I|IlNI|}4PrVQ6M3DqB!v@no1>umpYwYW6qT3GXYC`{7
z_ftN8(tkj-vT?tCA7GnnFd6K3En36(86p}Sq~Hp7YpSyHKBkf@#rGLGAJSo8*4>qH
zb*Z$6-B{SVguVBH=Ju*tc=1SIdvsYJ+{JQ8_-MrUV?<S;u3&^vwg>(`L*{ZiIhaGp
z&h;+VW^Lk~KgLCYq55cVzhRq6IztT^V~Fb7j^-2F<|!rSD5gG}8`4N<FFdNSomj$-
zhJLoTa&I)7nR#gIoO)S88f(ZpY$9KIbo$58Fxx4jWw?dPmtQ<ENHr+i(ph*Eao>k^
z!k`&-dYwk`*;-ZGb7f&}U@?ucYGF?>H8uHS_Z=lY<KLF`)u{%SvWtN8LjOWN{rZ~I
zof3t6x^F62L`y}JZNbz37G{ZmK>kBT#cLmn>;zM5P*^1naaZVC@Gc(Bpt{9_WWWdo
z1Ga&35i`?24%@#ME$O=TKIs1PO~H!_$?Zy_UaNE0QR@1ip6gXGXV<%ojEMEm)P(?v
zw?Wn`%ZZdjmaGTtY#)E>yyWk8c{c8s&n&ZMuLDp;RNlv>3jyR43#oG8Cpxe0KPj+W
zT)FVTPgbv{23As19*&7F%Js6F9&df_PM<1He^d-v$U7&g{eQ)5V45r>GW7Aa2JN_G
zO^;}$FXnzSVTLzM+=ky}uda4Gv&s6hdI}ysSn=fXwT*{q@lgZ!;&<w`Lmc#r<$07z
zVem48c0!!<YD}()Qv;oR0>@K(okNgzVrs+YXzA&0uEv$xQIpQeaD@5C{$C$vTm}7-
zrVCjxinZe6(${@3(=GqGWF3cu+rIvjmQc`Y_n0H`H9~{#FF*(@<vZ=Fe)%yy@lH<}
zlsq1Y)77BT`I^2pIB_YzE-M*jui-+#8J_NdCDB<Mmn5RaWIE)|7ym+X;>D|~_oE9R
zT8^*NHBu>;N+05LYR<P@kPdrTHwI}Am-_0b^_dyRA}3aOtD=GeM<t{{AZwzitDBXP
zkr5vspO`o+wRs@G&TOy|&<^{cM8M^-p?%7&X2xHWwKcj$a`?H$q6I<rR)Q{?klSU)
zbK6ag1(8OIKM*I7CbSg8X_u;8{)}<?6yBAgh^jDpm@qLpjg#0wfALXys62{@QE+AJ
zs-soGL(%l|;AATG(^tH7Jh}OdHFwXSUe|?d>R8{Q-p?~u{CUGA6ulRxM0O()?xV3e
z1-q)5DNbu4xY$WZeDsGy*oNAR@6OUTF44c-Of1)G#ZP#&Hx3ex591iZ$^0F*Py?fK
z=UdNYVd7^AmHvtrkEo*Ny?>Nia8673I5r``w^=egw^#^C0&1*!PLS$y3l!67RR|O#
z&iI%$xt>;B_9xr0wtSh@8(?F9IBk{s^t-L7G6ASVFSp3P>b5`lKe2N+B)%+fSw~%R
z=+OVNpmpvy_OYr=!9HK27-y~deKqQ6c)o`;Ia}k_XSju?DTn_R$_%KH{*TSLr-NNt
zOc%)lIakrSB@YAw9>>eAflttl*HDX1w(CHR+2`#=41?3{YG>J|ZA^FB2Xz|0c%5x;
z4;=Q>!PT*ro&)SgLVv<D$UBGnI!`7Ihqb)3^er%w2_M9>SC9~!ad{8{Ld13b3&%4=
z8{N@)+7Q+Xr}azqvI0+HJpnt}mBb7cHsId2v3=>F!}t)ikh0)G$&kfod=(h?<^%M@
zyl1Pv{z;vVyy@tZaKIQ;nK_REr@6j@<66-=RDD}5S=9D#ex1s|%Sg^H;eQ{>_BQ_&
zGo**ZzgA$jkC@6v%{y6whjomDy^dLH?C8F?7}V%X`9;ZYK?L0DlK?Qll^y#}QAlWd
zGjD^W44#E$e}u`E9a@5npSRIf_(ey4uwk(0s!DHe(WHj3=tL=JSH>b@Vp;KTGq=n0
z$c)N!W0hl4D8Y%3Uaeag6{Yw7V*mS9en03nyT8j-;BC!zsNVu|xcYziL7qao)7XCk
z>?BhwD||pB3XmuS!g(Hm-L1a<qgr$AzPf$^z#RAE$|eN>fj-umO%U=rTLG=6y1KeV
z4eVAn@#$&L3!_74DR#w*U4Ey+HeS|uXyUI)s`#spR@14tUGLVvgs;e03GH=mH)fdf
zy>UXhl)QK9`mzbi=?lr{HkPYeSLZU~;~Yj7v=qC5`I+PBs%3>%KS(nP1VX2M$ga9X
zhc=THAfx+h+DT&ml(z#bu>G{3!z|UNfTcA`W@4weBXReni_0^D3iG_WvCrnm!W4yW
z_PMe3*y0n%sb#pA+m1>gP3f3GHuvp*Jm@dp24Q~bH3t#M8ZUEEPo*Zm-RVg6Cx-fO
zYn4?=$yeu3X^f%h5KpfJH1gk1zYzHC%oMyoIcR0NEYqG#FfI0V2bdknW}W2jZ1>^2
z&h7LgGTuaF$t|_ni^(|T*I^frlCb(&cM6taF7et6U61%gTQ)xaFXh$^tsejf_f}dQ
zfNUcJz18zC0U)i&I>Dz5q!X2tz5=859xmAv!KcZuKvn*%WuK6g>KEK%&_bQblL)CG
z!~4&=EaufAwbZ_D-QS;6-TO-L)K0W&8h0F&H}+WcQaC+zl|27leCu;bY>*8ccu7y*
zBl;#p&a`+NMdP-f@I1ILi=D-eKk&1n?SYwTxr2>~!DpcJ9xn|~rUoSAW4yBwYgCJp
zM|jM{Z{D5rGps7NdnzoS$;!3!ugg@mZPn4;+xS-O-qQ4KLo*xe#2mgM@|k$%Wla|N
z<>jnw@{4e@g3oGvwl^~=!z+>5y8h2jd&#NQzL&LmCW3|6snGoQulGgu{rz3-?ss}s
z&)8Ex!(%07FYx~2b*$|UMeXP*{8=8)WUOpCXxyMDl36NS*M}>QfDy$95IxyhY-tZa
z1#)`UtdjCKNm}Jtvwsj1>;$}Z2*XAe6yKjjgg|a>`5vs#$=RYahdNC&DwG_o^E>ry
zGaRpb!3aL@3fsy)N2^VKGNh&hdzdZ5$Nx?4isszIkdu?I*bfl^1F!i&)0oi)MUSZ7
zz84Zcmx7`q3K7u<xdYzg(BfN>_u*H~`n=A(qME(RQ(J+iHw`LMv#064?6=oo!Rn)A
z<@9Llub->Wmg0UxBXS((V^DBhZ!G>U*f!i&7~yd6I&?>`Rq5I}=kEyiGW0amR7zvu
zpz%R<Pw87fbEOM7N`@OMYT~wt9{GctniMKh+j7_}b5DLj@<~~@^H44$^^&I%!GW@B
zjL!9`Rm+>}`Kf=-H*;M1w8)kT_i`to6g#6Si}!Ue_7x)%;l1-GeEt`)QVSn`YeWaH
zQxy%Vzc2O=o1t;TgHUOfavjd**$mUOkl@)ZqT#R3iRr@<$RBb(Feoj}C7D!G{rAu}
zRMY7$E*F~qP9fiO5U~87Q{yN<BJ~dc5XZpHzPZ^IMUWCyYwdnq%s72E5claHpK{gy
zWYhC?3a!iJKoUIN7tW3=B!=K7<%->z&As(E`m>3*ct@*E^(BXzGWgQ8hLN9`NWBs~
zNiF;pk|*;0dXnV*<m5FgEC}HQF=y+~XeY8uUH8Vj9#B{@4!HuabRSh36q$`oo!#59
z&H=Q#E&kl5&OAD12oWmIChPWpF{F~1u-kX|Jtyufj-ZL>(I-82xAe(8IX_%=7V^wg
z4yZ(jVMY$)FqSBV7{%t>epTg8=4o5)O6xNI^~uz!U*<tRf0`R>8f)M39L_fqtiDPQ
zOQ*y~fSlwkZN#kIR74U>Td1Cuo!GH;WD(T8Wb2kI?T$9IcP^`EZk!R?wUwr40x~(+
zNuW%^bF7<C)7{oXSdbzu)1TVTZvJw&h;Z$OTX6sCv~<;kx_Txu(|gaiK6X)kC?<^_
zyC`=g{n6$0;LE?FrqNm1Mv|l0rFnuCx0II-bhbDO>fKfuK}0$osH}(nmRffY6V5`3
z?_dPS&rZ46@R1Pz)%XZB+mlyc7d8y)IM9WY$L_zrWJ*swL~GIxzdRQ~<$Eu~>HFJQ
zUNBWA2(HX0IbCMYts^sdcdV`~{M&n+We_~vL6>(X(J_B+OCdx}PnB>y3UB)HUn@#)
zO7~^i;QQm+RM-2(Lj3g=QC3nWK2a?Q)Y{q#)UAE_YchfU`phpE347H!IldNs9`|Pq
zbaZ%Z=Ex?P^y)%f=4O9O<Xx(yd5_*gDmZ+ulxN@Wa~2g^WS$7pG}!9QDbc(*lWYL@
zWN6v*W4ww%WBK1&8zVnAKP$Jx_nz7KpoeXJYigZ!RkdTmMH=t;Urr*o^QK;rU^9cF
zdb(<FXX6ym6Q3h~@`Bp6pY&X;Ns_)UU7f~#qB^$pt~HuoX@}Tbd^>CQSa7#gMNCYb
z`;mRr&Fg;MGVMV-o~xrlXrXaPGN*EMuqOglq<Jfy3W`j}SO2A;bd@ci`uI?G&*fCH
z_mWg+QeRfFcAgS>CMzZBdVOKS=B%H&W8RYQTtm%D`%%)}HBu?|r&MrjEgZm-PAR8<
zhdCZVxP6|~bJH}^WB0kKwY?6;l5bJUdT37dMzUNF{lp;Q(kA!I9I{%Eq!{rE`uMAs
zc+}J=!#)$D(eh6>AEXR7>3{F8+=I(2|5kR8_)q2Q2Xi>MVYZiO{neiDo%WfEWD$=!
zGWj=oT}X>M2i01W1+}gR0;mw_SioCfmLBq$ZDh@`(i(N>EB@p4)mDTUyzr>6y<|#C
zda;|m6wJuHUts4x{LBA@P-irRX!tGtV*HOL1TU2?^L=V3Zr#PvY<cVuN3aZEA(88b
z-&>Ji+tZ7^bf>{gq;_D>-DIKgP2w1c@9VarDFo|bvY_(y75}-Hx4~8QwJtC{vaWfd
zXN{O!DZq0P%TFFVd!)?IvQAX~&qn48<;+}ox-Ri}(%6Y5MEJ41i%p|iC7;G{Hh+ES
z!@`1;hBw{K({!<wss7gPZ;v<UCvBNw7mR54TLq8vUHJJ7TT8z6nSj&ezy!vfhF7g~
z>ow=IQ6nR&S39j`>h7tuqjMWgqwo$j_Y^@7Y)|1MPFGc0oX?Q%H&-G4Z{_f>VZQ6@
z%|});4eKABSvlTP&r!TV(r9rnM=s4i1uc)i_dCk<Z0T0l1hf9a8!9$>U!PNy6D`&<
z>{{FQH^W|^z)4|e$b#!x@TR3Io9lPM4a_d8&fEroifVUH?AKF`1n&0EWwi1Nuh<@0
z%%U1t;l{L^{HN^uDEpDJu{o_!VJBi@zhb!%bX5T*ljZ;+kvdS`nwG}Aw(h*P#yPvi
zT?5x2cdfK`hDr~;_=%!d?lFP8&f04%GQ7+xi?_GnA@7&Jp+jbSc>xZWbf<HJt)2b;
z9La=0wH0W%gA8<@69q?9>;eFFI=6$Vr6p~he=?JvH^AA8fXAWjaoRB6`@Idu(_j>9
zR9J!zsmifcNI7CswN$FK>dGN#jDc6r`Cx@a4Pf^yB0>rw(l0V#-A<;SmO<hexNvLK
zUF4NN)ppXSm`>C%c(}WC=^q-Hpii4c13$5pk_bkFGNEd!I;`H5F@s21Y;U6-kD9>u
zoUc|qC*=Rpci`-SH$wahip-wn;GETcu!Bl^BJPGHP%o0^);wvFZvMdq2lQ)7^oabx
z3JHx}X)I8<3fxrs1y$dvXAft2>4D>6x`x?x02`4vCjH*mWTqpd>}55j0(<`w+Oy9)
ziCO+>EcN2zovl&te95JQS8eFa)lj+BvN}u3Y!Ct7CWy<DTW@puGL&pNmR|61wGQZF
zt7twZvZ_Nh+o`Wi4dA|C5RjNcrsAi;VWGjXAK3nMY;9rLFKYFpMvFX~k==Q_Xx6q-
zCnZIO0?_9mLiR#g7?rCw)O9x=wZsQG3UZ0fMOKNWqs3AfN9eM)M)0I{mA>Bm%0`E=
zzd6$74Ev+PRHrmmrgN#>4kMoTI5ZMrKl;mIadvG#itxOuaC1da5R~exPP1L^U*lc!
zAD2L`8hNxa1=SC-3deoy#K7T?pzEFQh>@G|+@IiLpFozixGOS{tw(0{L|vHK1UAp7
zT<Ms70BFf$LOQF4(7sI#6DdVJOwgZd#VFb>KP*erNvBH7)QG?2YMP-F@p#0T1ZYtq
z4_I+`7BU-AJ0Xr?A61kk|8qf)%rP~6KkHn1>IUI2Tz8p{N{7lfn;cYg^4uv2DC=?3
z@=wdWB3L<yiM+<;pBeaf8}{t?XGg5NZz&7wTGXs><dzy20K5ZHH&i8e&#>ex_xq+8
zq~T<nRkr;XSZLEXbMl^A-un}va)a*-HTkG#uZ`~nht`G+q_t8W>pqlFBX-A_>6|Mi
zdQn@ZtK->!IiHJ~-e;RE0>?rLSQg_sGepjVc3o+fJ=OBu4w?AKitLX2hrGLKt{Vq$
zTOT8dhS=uX;O@r^tb`4<*O=cRY=b%O2v<+}Yx_K0gYW;yoo}8lgmpY~UYfxV6`7C(
zMUtBm30gtKHl1kv$7C4+_LQX2470keB0E%uD<4;4!=rjQQEG7&%?wpXF*smKK4d~Z
zWQKTg4vi2pA`>-%jhyV?92zbg5^fS*?qHZPRIo_pD${8;n@d~KdB>=ik#f6kOOKt3
z;UC&8^J-EK0!e_ePR-N!0^R5KF{Zit9(t$&5vJ#1Sf}(kHwzi|O}Y&*i01QZP3@MV
zr2}7G9<*nef^BVl;zQfWlg_;FyB9wp$$7=RXo%IVmskxQ!{J?>)vi*N$-Vsbx3!0@
z3y%c5YjmC9%%Y;c@vDQ*<fH}NPOQsG%k_zB&(G}j$jSX_%1fxnS$tEx!WfFucIFC#
zZKc>R4^y7DWu!h61yf#jdJJ^Ie4ZDATR~J)3sMF1Q1<M)m+--KB?CrP(LdC?6}%kX
zI;S)}E~7c^V_Yot&<L{Rabtdqdf#&KpsfGpNm`Q$`{(5KrV=r-2^?lDKsTL$*Bqv%
z!jO;f{K*7hU=f{7-Q#?NeRi-45|o2Fch%Dfb-Be87#-Pc%8lHXklUQ#Kv1)!3wrH+
z_%oh#<S@1@us4x(xr07{kd4l1sPq!h0*kgs3)Vo99{?i?3EtnAx@1ab&t$ICHOzka
zv<G}I4Q$rSO~AKLF%6fgf34HzsI~5PjO+Kv9HA-uo$$mgOqP#IIitrP%G2Sfc9Bk;
zRZewNGEcMnfCf7X#tIx99Ci2d@>kL^8+t4mO*CHyWHm#padpgF69_voodM}|T}N&~
z<pr5V3d1_qIM!plnkptW1UY*U^G-#!^eD`)x$f`*+GASeZjDc`4zVZV^ydG@)=c+l
zzu#GvpdLKDfAxktzcJ0Wm6B2bZxZ0sy?QpHLOBdO81tZe6}Yn+y#+{g+eYL58b^=Z
z46<Tv2h08)&RW5>9>Ii>%A;UdV5x{%kxL8_;sR>Ph{44<95)F<*II&`=d}&>88p`J
zdmtkiw?tNSwS6GL457whNwYeAvFgF3l}NL(+}v(|EK!rn&BBh6spmiKw7rJFg0on2
z_*-i{vmG0u{CcE!o4#r$EA$$ba=dQrGLw7F)7Ycjt9e$z)3NFNM)56e^y{CR8hbKO
zRJNmaZ~x;Z+P>S@moEASfT1G*$&Zy?7J7V+h-<m}-KyjLT;?_Q3W{>wd8W6%pxOT>
z!2hP7#3Ix>)Dbl_@DP?iLUeYDK<5!V*bJ-iZFVfsAxvb$s&@wH9Cuplh4gf0_#FUN
z^yS*SSU%eZJ~`om3=9o-X^+|fHev+lzL4gAz-?=?X~NpIv8;1At2Xo~sB9EGRZ{iK
zyDH(3$5zdB5qS}Dy0w%lQW2C91xM-*_VMLqSvcdtt`kOo0%5YpY+KuUgSbALR=DAT
zrIx`TG(Bqk!3^E9*Z2Q^kZ3mbuJ~Rtxq?wE$)ky-@i4`=rznuE6H=1IS_FnB-HK$L
zvRcYH-qRw6!X$nbSrUdO!S`?s+wOd|)=EmXu9dCBXCjlgwKWX~V}#6OZ`{G>8gCrn
z#C4c>7W~aV(SGhWF*r^2{37DP5%HMP#H%SN@Dsd3U6)H1wYynFsf%#&-};l^TQP3%
zyp&V3jxvew5Iz%AobOlIh=)%(GH4bUu>B|@0r55+c=MKd#p=ERR!V5x7iP^}tmDCa
zvCsdiBa2E_6n<1`+Glb#N>T^xj$NQa%b&m!dQ!O>x|A3&>2{jE!y~Y%|LnL>TJ0Ul
z3AQ)FP3t3x_4S7(zMUyuOPRDjh#FocWKx}=Op8b{{<bB&D6UeafUN6|ZWZ*G*A|V4
zEi|p%bgv>ko--70+s03*_t!d57O&E3vRP|a_lE3e1=`gJ7=WKk**#5W)Cn_Ii;Rq%
z>}EBCyDXXfn+H}^!ABG>z5BbR+Jxl04w)xZOuPnu=r=PVN0#9=U$vDsbGgeEB>Fe7
zG=uexE+Ti;@;OqBx&>_7A6NGrj+{SsRgN3n1EkK)*P@sY4<Dy%zF;3=Many719g=W
z%iUXtsv)^vCV<3AeV*k+SUXY8>Dphbzx+Uye#1-aTGe>4_mp$2>oJfF@Au|L+0kqZ
z<>pZM^y}p_hLlTT!6fs7&#&tBg6Y>%5;uX7{^BnWUd8yI8o1qBY7@2>j317dIYJ|2
z_qi__YfNW|O2pgzZpnop@{x1E2tR)*m-2<Alo6_&wWKrKHfcV2ZKm0}hK#ljMn%N;
z#0tDP%ok|aePLiUST|br9}(rRV8FZ7ap;vd5<w;QQ-mcB()e}MI~0C(=<Tz0Z|drJ
z3@6J9AL$CB6YdGPtvBs3o$+S6`D_%%@fHYnc7A^U{0dAY;Q!L-*$pS3U|?XVMoLpX
zI}}5h10$Qg)&jbqfqvw^-Eg0M;zWBU)z3`2eC?7u!gbt46Tx~-RV8w71$g`G0a%uA
z-WQ8rr_Tz_C6<BIahGqQiP;I9&aMQ4t1oCZrt-&GkA?8xttb|r)mGlrEEi{%LuAIc
zN;x<D5&{Rk-}9E4e<IKRIf{^`?oxd}%CTK&iU{oCl|NV4@Vbn<qHvY!FlgEwE9Q_c
zR#xOX#C~|XYuao_2$<-dcxihQfk_qMK!1<$Gq|jFNGO=RGJvNmc8dXnE$|2XY)4C7
zi-bxHjsxB>RiWoep?iU-PqeN7dbW}4;*Z=H+!Vlz`|8^9#+6nM|NRyoh0F`bzcAKB
z^NUryQy(d8O!ot1wRFtFLD4(EJ2FWeEKO;>rHYgHj|1@rn;-XSlpRi!51+oDV=jE(
zpVP7pgmwjBw)z+y<3Ypnsoe$89l*iJh+CxXI3;FYXS*(-NN#ipN<r6LiKFVUmfbz5
zMwv2SP0jPx*LI3pD_UQsT8+w3=~}+*S}1}Etq=t<G4=?0R$MQX59!5{CLuZFi>A@B
zi7c=}6y$pMZC>E)r!vT%6C81o-%?_(aa}?MfeThYxIi9z%im>qzFjz6;0-logiRM5
zsa4{tR1qG9Q>^yu%ke^=yB~{91!i$ImXDNgup}M*wBlAu{S2HT2NEH0PsSTpCSdDa
zkTJG0g0>jCWk}u(sEEOGr@%2JmU)`=P=`PDc?P-W!WSgYF?9A;KZ(B%AG1$+B@P`X
zCrc62!3v!~)tK0Dk#<P0ty&jn3MrXSg`#2s<FjpA=4F354;l`SmpX{2Ll#W&7q&`@
zi=mIOhRpkXCkF^6)pXq`UIxvTwY4)c1!qYLa6nVkp|=x+o=~8g<q$Ozg=~Qf^x=gk
z>iLBE?IUMs@e?L$j$>!1cklgtFkLH#Ig6Xjan=i1s#Bt$q1oIIY_(EYDe%O6xfz?(
za!bFy(~&65tBt`JXi+9wy0Njd4I2rfL~T!TKn_MacWjPpTo0Z3sePE?H(v->)Ja!(
zKoZ6<CG5DXqlK=iHZ9QiMs*Y<;+i1|-q0Q>M#}~U`v#Gi<$<3m+MmR&rEZN0`#dCt
zzCm8RYQ(kqDTrR(f2aJO+vD@LP$6cLBpj~W+TXhXS$%vC>7ar0C8+sD-ROR_9F5!;
zUrh?l<gaaT!T^tf+nBk@!I87Xv$@)Yh*#lkP`&yUbS6H2Om>#_W551;Zl}#5<4MyG
z3xeAr+)^BPz=Ld~0v-el1rIp*GO*y*v)b)HI9DRqL<l1NGMS#61gK7`>V433%k+G7
zc#Ucd5E3qAulQ4ojHyo&ApZsVmbi*l@`i0;G!71Uw`_5=EGW({G8xymS{B9J215ff
z2qdkptlQpA5^wfFK|e)=!pr=$%tJ-<2an*l7VomNbEaF}YrXM!o7vKwip=??>}KQO
zzdChda1*o~Fx9)4e>|vvzCbMfJ6ysOG;6(dSa9H~-Y)E(+kb7-{nlO&4HEQ5O8;^^
zzXI7*ZPQbDWKNhcS{;^8?iY&E{dG-<`UFYr!v7#~J%DMNCv_$8EO2Z08w7bw5Tt+X
z1t|JV{%?1V$L>G16Evw}BAk`<IA8=C)|eX{ZiD_EY|;}|k_lqLVZn7);vx+4#m~zY
z?z`(U{DQ&4{k_D6((+Y}<U;ix<?Gdbscdf+4xc2k2&}$6aeb8_b;w$Cx9L;^U8`HJ
zH;pT+V;Hv;;7$Nbxgi$<&&ay&Rg4vCL{m6M2nwIuG-=t-oxIF^W0-hs5+JhS-t)PJ
zZU5m83@~Yu2t94xrnSde1&cki27m=r5xWPfagi@`e8yD+DdN>zeo}g!97-pt`)d#f
z1`8<Bm>PKbFPY8s1dXOoy>{C@^y~s!W8(eAHsjyh>9bv#XEc#0zBDm6Vj-TmqA+1p
zjq4eCu4e{~*eIu4FT#a77c+rVuaz8NkY)rs)1!))`yB*s%^K2xpgy;{O}oHxfBkPC
z;3g=5e&#&?;T9rK>OP_rro?^ct;eVvC3>ON-Rxw2J7t1w<cnsuI4KE8K302&L9lAS
zV|?|OR(h1Y6N505Cq|EY5Ju5cK<>D*Rv>o&%n4F8nuOJ;81FP%12iP`-(yz=N$oq4
zNPI4s4LQRO|KkQMTYl^CiC*@NZMs!{3*(aO^<3c8<Mw{C`)!`EPg+^mto=@Idnwui
zZsecS1Ag*XSfMlFn<sy=xf?@x-EWuTnH`#8x+dd%m85_&z)}B@L!fu3vT5O$7n%B1
zuS#IzSF^!a$oPfAc!<BS>gF~={n1~?^MPr~yx@Ccm@q;*NY*oJKVzgvRXuKIwS-fs
z3on4|MG09eIZNdBK$*0fDU0OknI1XVD_BvN`rmC}h57CY^QTNu_(>sm<8D}mAOuBL
zJED5lK4Mxw%8U#V{dvwdYP1zB?7C4+6vtb5jJx(AI_>&dblla2V!R>5;lowb?abvt
z(5Vnjw{Z9c(N$zE2l*(X#I*dIvi?-!!i}40rUoeYDHG!E<X0I?!tR`m%KYKHZAMMq
zFSu#j2<5MNCpC`WFKUzv0lc6(EMpo;z!M@;=pkWXG&gD%hM@AZK@#8kJy~$)wX^3c
zmB_r9DdNlBL)I&(hp8%zpN4d#BYi8ljyDj^w{9K{=H7$Y{Zq$T&Il1=0GWTCTJboG
zMR;W^Y5BO#4Czv8xd+CZqC$yV;T=6{xBcMUB0M@z`K75zbm3*vbq1s{pi>iO^-*L9
zIA;iv<>PaAW|2LT%HYz!G;FKC<j*FWc3*A?wx1?StlhTk`n)nx%zVf<q>rZ@><&f2
za>piH`Ogf@nBusP*=V^uuE#V#K6v0WI<(i*<?04&Wc-EP<Zj8&lm;2<9KsU}U@8Gc
zr@(+$foH)`G)gf+z#wtFEi3oP$_H`qr|OdNHcbgFOy7Ihz{IaqmTLti?@qs$@}P(4
zMv1-<Ca$A>b1eH?#-Ujqs}#4ao_GtnaW1A`$4PAb3)5gD9^$-8vD|MY`4{K0ATb=I
zLYngL?u|P?O3#_y#gRm_quOD*BsE>eCU|efeyDk*yFYY^YMr@;b5FyI!*$`9vE7S+
z{}s?Ow900L>{maqn<n`}?T}dAJcqSdx%s@?x?cKhRf<5F_#L?$@B$$dXqPQ2n+pB>
zA>{uiyA^tA5&8^@5Pc|bznn9E<@Tult!SqX{02gz6v*#p7etZDmW+Sw3MtyM%(4J^
zNY|(%cpkNG^ID}e3nD++o&lLZC+}5ux-1V~rkLE_a^1GInXsOOY9VGWV*a`zXJ!G6
z18uus)j|p^Oc6cOF{5brrC>K_<AHtoBJ81q7DR`7Bhfw{GGEA%_8F&QS1{Cq`=_!X
zwdeLdRG;g&`><XtKkz@BR&zb;(yP2cJ0z7h7et#DCkPnv!yX8Fbg|-lc?iTCM;Fj|
z@xg<Nx{G+;13fNoGUV%w-MFhK&jd8@PD(9T$3dct`^q5&%2JP!0IEa=e+Zc64ou4+
zZ6F*surk?3L~<0v_loI9Yt4>C|0XokVW>+-?l2f6uFw@?H!h}Bez2v><$ZXo(*I*R
zgd8$S4aT55#4QL-z4eRj#cKJvL`?OM{1gc7OlH|%E>uf_LI=TW)<PL}TZIu--yAtl
z!lZoyrPimfI8KK58rE_6EAd}ikaOC$wGS?J0hj)TDrdU<^zjIJ&b>8Y^1xRuFnK(u
z_e!6{GA-B;7RG+uuUfv*jcM*)_$<xQ^1JT9I1d7z6qpjSFcvNKIBbNfQjA@2J}jKu
zju(zI)G9m`mGK((KQ)^;bSlr@sr0FG|6C6e_t<qhxu>u}!+(n1(E9%BJ0a?nelk?R
zWpc>+=Q17)HiH$sQqFozCH)j7n{LYqUQWMQFz?$7opE)lM(ud2Ev^$X9K04z%O``1
zTMVRc_eX4${7$yGvS`7-)?kDV!cehBzEMok33weiiq@7~b5z4W6H9&4TQHDWon~3x
zI>!~M<8z8OoFI>h0t|TCUX_ay*gL$CP`)3OYPuCnaFB>P2BNt3CzK`;Nla_uT60G1
z7BGjnUWwja_|<S?vl@B&6LyK$j?w)L;Xfy|Xt2b{?%Te|2=EjUUtj%FxkAy1SV^-t
zpD|`Zq@Px)qWl@^QUN5+F(F`01&%67oTDm%0m5jb5aVN1p+>&s3NW6cWYMVS*o0Co
zU<dE#0s;;-YWfJY(n{q0FNg3$wwlrDzsdZr#f0Djf~fsbF~v{_e(%G-KYB!IKatXB
z2s&p7-gqiK0T-EE7x!j}q%Y(@Uoijd%P>e!;o1XVd3ADn^6*CD-}T=`a5A7++18Nz
zRXP_&)T~OTOGe!p3P3@_E_{ydS=NxmE|<dU^e^3phUAz0%Us5x9S@Pe1?`OgYEO?&
z!6<-5iwAu~Yvegf$C0!hiVP2aI{xz5Q&R%b)f@}P+e;faFP;JUjC!KH(u{h>PL0_0
zj*mtAp7uWuMZof4QuCIe(lKHlXuV2`CM5e`y$>H`vvD>h8Hs_b9v&t;ni9CkkRdcX
zmXeAQ7X$3fyRcBE{v=YIP(?KK2rDo|*As6biLJaXsET99sOHy-=4YnPax)YK|Na9B
z0TUcm1wKC5ua?Rzh))I^BV-A@Z*dTr2ViLm0^ooEcFTWz8xIN>9fWu&z=SpK*!2~_
z3*4^hFYF>g3)h&NS(yYVn34HseZ)@x`*ceJo`cNoA_5W+>L6tfYl#D#ia*gpZZA~t
zcqa@8TF{rlvmU;2CO=8hz!TLfA;}2m!7bhJZ=XO+I-UD2gb!^0gEIdA3z`miwKQbk
zc`POasp{oiI4IKJ{JlyB(ox?>e11#}p&R6amId20nLInxci}-y+fx(JUIM>Az8`qL
zrh;{qn_QjPp8#6GO7M+A$4$)(gq)HiQN9tvniiG64G?-FUBcn6+ISntoiD3|iVU3^
zS02lJ1q|zBPrgckROn17Ej}RaXA)np-?0cI<|tQ2u-tk17J0I&22JGbud$^Waa@Pt
zE90tr&T<s`0M7Xz9HRlm1YC4Qsp0@clVJd-=WW<4lbusfGv^BMl0nP-x)b_u-gL6}
zKD`#YnhY>1YQLzSqSeZDMJpn6Qq(|{ZVt)9JKPgT4B4AX=52FC*bD+d^L5(;b06z7
z)B35W9r(r&Ys#P@;CwL{eNoRR#oLG2%Fua>`ANNjqpSCQ-9F~>E38aX_gT`Ihvr(=
z$!a^(D(r>?Li=6Gj}cl>ch<zAfOb?gWKkU0=ZhczOxA&wH6+2LatGL^{zM0Ud;ld&
z24`{6>{Byvc(2S(1+Lb)<bU^8hc*1LG8w)H4;USt7if&2<_x*s(CLwcqzAuGA_KPg
zTj5{1lqsXOGvI(Tq5Lh;3lM@aFF1*8{Tem-&=oQM5(cd6XSM3Jlv8a=Q^C92z#D|1
zz&WVOB^%@J>;CQ<4A=~Q@V}SRhaPtqUk?$dj>D17MO)yjHj<if5HqE&hiZxv06+2F
zzLxdl(8R#NJl32@q7gXXl?(fY<g1x5!)sAkuqmNoZoxnbqXaYUAi>(`6*xEIG>l&0
z2Zt1s$7n(rF0j7(l@_KocJwrL2^5RJ%zpZgy<1N}3oQ<zECGacM+>!PAImEknCZ*f
z#8#`sEu&m|RBNHKRWF%Srg1^QI0emP8BCN6d3VNiV)FaYg#7MTMwMg%XQ5ZUc%`I=
z6VrBF)^`XNQRhnAD$ZIz>)(-gHO-66N7(7tpRku;T05=@qA-fq;0|<BkIq-B1f^h@
zK`Ml>h9h<N*YrE}Dx?0<21J<3>w?b>7{eg4kiR*kn1uGHUgw@F@5J@rA?AtV=`2t(
zmqPr0%=lfC-G5H3Sj=M%!#pHqS$;XoL(ocUPrZhVb=h<2a$UI=9qaxj#U@?+ic)hw
z8C!`{=|RzF5NIrkilA-(C=MkoU9JA-E5wTz{|IHq9-uUBY6x6<Qw9aC>mQZ~#&*qJ
z@HU(9>`6CnHq7{kPSDWp{!f7?4E0CVTggY9UX&qZip=0#t_B4D*}F8LoG_oZ+qO8v
zA90Tg&&&u=QKsnHo%c4&)S-h@X(rmQ;S56tSQYWn`0<GAT$cTjpq*rOO7MY?An*l!
zS_m)-Hd5aWGg%v!_8wXl(FF$BbxGkKHr#bLe7K}X(!G{tjQ%jae!l(G`p=k|h!ljt
z`P~l$^VdhquDiV0F8Og0t&ryz8kE0hCecV)sU~ic=M<XdW1{|@PE!9vtlOl9pFZ>}
zNdq1!Zap#tPcpf{$i+7qDKj<MN8=^l>JntE#$S~)%~bIqHtJBLV!IW#?wHLMC2s*K
z$_e75Ro6!S!dvsXi4;k3fvlT%sufG~7>y1?_4k2Ii&);iUhJB8ODcW55Gi1~qLdYY
zdnNXxp#q~~jx#Ea#M~?|8Un|ufP*S}DYdu&o4Q=yMkIZ}am(7g9Wxkpz#WAT7J@J|
z)i-fK4&*1-(<Ww{VcH5vwC1f4adgopuHTX^@*|J=umdIf3i6M&OQ~|^VA4O4Nf(O;
z3mshOH*KkXhNtrm#_v-7T{M|D1VBsZF{%&e)(r!(^|X(ovS{yrGPh_zT}kd&^Kog3
z1<!xDPyI635+|r046E9$Z@p#up1iQ|em%pyF-JI2>)kQi$$zU7I0x#f^I^$#P&1}5
zBUv7}jOvD%()g32Sf1NO0olHM`R{82DRWfe(?1!hRHqQT=fGR!G2NsnJ$eQZkWR4b
zQm5QHz7)kVJd^tUK>1VFkYhhc%XEEho*f2+E^H7LRN%-P0^KjzA1euIB6pYRH^>p$
z-;uE<Z9sD@&R}|IMx3lb`Bm?GBaya~Necen?L_Y0pCdX4E=NGEACKQ(v<<A-zjfQ0
zA8zxMI4kJ?xBy}dAr|PkiWRIe9c}xM(K)2xf|XuEu9q`8sRQ^Wu60V`8F<RpufwzD
z$^LJ(5CD4N%LnX#EM;c^TQb&YZd#Em8wc?Q&zmJBxVnqfbI*%@H_Go#g%HR2Ke0LR
z?gbHmiiQ<x0XGkvH4Hy>Q~C}?3|I+#ew<_iTn_?+0Z<>6@wISmxputjiZ`o@=K|9I
z-KxOl5e0bXo#so%kN-{qUYh)`ZVt!d1vUw9eH{@Vl>8-`^0XIM-jM@z>@`jv=S0PT
zvqb4(a>s|%{^#lDM$<>Fa1j54_@8cvVPM><`$yHi<;l@!7OqurPZRhVJ`)6!#R|B<
zco103lzG<4O;~#?gC*(!D`;awEEK(<)nU1c<O*i<1?}P|sxAkWExmTEYVj-&5>8gK
zJI$-k<ScGeMMbQBy)2Wf?D>s)T!{OE?!L6!E!b!%n>gz&reRV%)KS_oK!jLH%b1?7
zR$cx)+5_aKFfoCb+5zC@E*oI|fX3>{h>e5C8Q^%IeoQ8QTD8>5!p)tsaNB^_0BK1+
zR7{s#G4KrX7w^*BE08n0L11>6ywyK00Ibr*x$~=d^HZa}sh^Ylo4;o`^R%Ts;qKm=
zcC_$-ioSxBVC*j2<nOa>aLi*lkw>@(Gg8G^ix-PhZ<FNqQyY642RjG<#9W{)@1$Ov
zVvK!n$71)&>O@<miqlQg-#v=E!Yen+yOb`LzkT!~N@Llt{TBvT?xhWGHGM42Fo$!u
zQbSZQZ$8XGR?moDL7Vq9byPmsd0F$+H^By5gu|8wt)?Akg#1RmgA)Oy`PbEJQFqhJ
zex9#hiMK7YI}5gdhgg&XKm+f7rYZnIjL`vXAFoAy5`%sL%S*1|Fe@(IibJg2bp#Qv
z+NaWW$RUCs9U(-Fd=N!wTGvuhF>2W`%s3b(kZo&c$6Q0m-aKN8m#Y=Wp{%}p6}J1+
zOy|=nTwB)Cdy^=5dx7Vn|G&?nsv?2IpY2LJZt_P2P1z&#I}7bcj&DI?#BV`S;pI%7
ztu~e4eqxuYhd>0}>)pQ&5aG%pxSpOI?<I{ASh8+)NsQxjOMrVW-|*bP?9<NJrY^ew
zt^bulNED*>MwaEyL8Z_oNLcD5&r7hr-bCQ#>fh7BpIPT{4KKTA^xENY6`+UN=+ekU
zOU(gK^LaA^6R}d$XzFm_myVon^aNSbCD~^=8ecJ7Pbxnyz@^v=xqkmZR~Aylt>o&v
z&M?blEl}0`am`vvX%XyY-ZiVS-$9D|%CAL#E9|iU!gTvIe+(n1bA0<GJx@nR_rcT>
zZqk4L{k;8p9LTp9a9s6@Vd>O6pK7{A){am##vxpD{Mb{G?U#Ab!Sle|Wx(^0mnybH
zS#Q~5j9){C3%+YQzlZj6_`cU0-e&rgrt30sHn(axV)*mYsc!z;0D?Pov<rc9IlJBU
zUdpcx<4*fGS$Tqo^cjO?p`RJ@>cvyzv{{i*ev=pI(x+6q>e>q0>G8pLL(oqbZ*PZn
zqKh<Ha_!ln^(S_1R}tdz&JRDi3r^m7tFOz$Rkbb49u{*~vs2q#H4I?kh|;-jy__m%
zs5mri9eB&Fxl6cN7JN!T60MN7)jv%AASH$5^dH{Y+!#haycHlcNg;LAidkVW2|hU$
z>Vig+PR2dxX5V}<Aw#0hz;CaXv+DQZvt2+w(;C(a;K94z8&gnq*c+u`WIQ`K;Bq?p
zAuT;(6wQBkDDR_LPM~WPU0!E8Ff_-(#um_L&>^trAg#r!%*D)Qb>8_fjT;#=R@FD<
zH(kSPi)Zculo#?FQg!(7j<D3S7p{kt6%E=SXZGYlPclC~>5;;2FsjW<OXy{oGI>?L
zspw5o-QCsfy3AnC3B&%JNwX7`{2INzI_NUsf74lD6-w=U-*g^NOQqOsFKOoNwhCi0
z$fH$*#uY#{g{OMg>u@aDSgBJ!@>s}Vo1jr4*tL@;bz?ORFZaub`sVvj<x=iDvT?t)
zD$HaD)Q(F`)IU(b*;-^CsgDJO#tj*;VHU};brAl*U)B?YYf&?U#WnV;ixV40Z2mP3
z<*@>Prd~7_a-;q9^b}yxu@DmrG}o7xp8z-`c$k?dfo^!C!7qQ02Bt)K#K1Y{=I8UP
z^}odl>A6W$B<6}ecf0~k&kfrk!gHRt+wv}Z#yNvSCL3EKE3{dr;VfS>+vBYAqpBbW
zuJsHg=-P$%@uW<9B!4=<1?R9XMBag)mz<5Mu$S8#71t@di)ss^@nvSlGc{(!YbpGk
z=yP9Pu+aUM?;vW$SAQ(8s)rzdLKb}Ai;%wXUN}80$m>$Wg#NVUVGC34NoDs#^OUGO
zT@B6YbWKTF%?5>Z@Vp{jkdBjswk8@PAC@U$-Q1S&;<<`Gvh=1a6IGyu4{+3RK<Y{^
zEHLroP{njY#z0DEDq}m}i2J|&(T^U~wF6fcL2?)A)TiICtEXr1TC_LTkOv!I23p4c
zu%KgNCM6~H!mg~XF=BOJaTsbugj7{lGEhs#9nsWue6>U_e>oUmC&|FhQvb8z!1n!S
zB~RW>PzkC+Te*tdcNd}mmq``!@5llTqmuQ*&#Xm@#kq@7rUn$JE%;`9jBO;15J21m
zsYzx>Y!NICFHIaxq8iWRY9CIA?3+DTq*e(^BcTL+Uy|3}wVpNthdHJ#4o|KE;lBBa
zSM-n?pvUAsEe=AV_fJ3hb$*foXMot^g(W8gvMmvC#~&9b@fhsE4K4}0BM2^c=+kOi
zhH#?Q<$@bt+cJ@}QJ0=E5&QAM3%~8cW6lh!Z?zv9wpUU@Lc~<v&^EW-1{iLIdW~U(
zX;}NtO{N$#!<Bwda(IlX`5tRjlq}VHP?uV-;UwJD_LZ^P)bxT=vvXmR61cR_wTxT%
zNHRS=+Liw4_lqym42tSH49z~9DuWP4Zm;CS(fEtO+QXAc6YQLhuG&aMOLeB2-1zOb
zjqF3WjrBR$><o-Usfu~|_jk^rp%vBq|D+j;t3gWINLSMWUH8GyE;*(uQi~Xh(TrKm
z<!#EApWLB6+6I&Z<j;=}`%8E_g!MTbK`J1hqRWh5deTUSevk>@eIe9KS*6<mktE0o
z<p-W&80P+dV}9x8{#<szIdW~v(a8JjApm6GVp{3<{F=pi=Be-<R%osh;4*LxR&Hu-
zb&u%0KV8Q90ySj?a6uTcZBrmqkI?k-UWrLetIis<oc~>mCrzF6n@bgQy4aoDk;hUN
zAv<|Y`rH(vwtJX4fEz#VxW220IpQif>Ag`I)KoCtESy_dT~&gZ=%MKX-PhAxZsxJH
zga7il+3`;&ok#N`POi{ju2NTBAz(UF$E;wuzc*Ws@Okcv-HvAc2mduwaTFCtj3se&
zlXIid7&AoHz;~+)Ji_5<>q+w(%0-+nA<5Mw7r#9kzu$MR{0m8T9EJcOsS@Bgq-uav
zB_N8ge!eNVON+s$vAw@Lgz0Z4y|I<~-N`$T?gOfgLd8HV2FrSc<S`bIhy*+V+LLm{
z8_NMV9ROp@7m>@V(4qk0+|{-~$N{_eC`{;dSGC63j1vnx=#@_2rrdjD;sc4!aynDp
z&=Za0J>B>4dqNZo{8PSG(<ch|%D1ZUGfN_?;POTukR~U3cO3Te7ueIQwo#tCl)#?`
zhrLN})1f232gcRrD+W)9huw!PdVafmM?F4@8Q$&btQx^?ymshFJbCQxVyyjOy$+l%
z))s+tuK%{C&5Fhg8?M&Xv4!f!+E2goyoPs5cy>uw-1`+a<MT&4!grwPKTqHcdEqpX
z1VU|uxeFrTxAgGS#L}wgC=>}i$0F1>_H4upuG^D4L|f#BEl3j5(<9<*HO#iQwuZ6o
zJgFTK_vi<xr$`bb#f?-8yKo~1&2K%H@5(N4d6o!HIr6>ScCSc(#*UezZI?`NO}se0
z>j~EGkRjLS<-3-&T&#P`dqUCd)IMDn5gBmm7j(5cKAG&c>~fB3MYH$)kznXTG2zO<
zN@NfR$Hhyh8qmpXoko~)YEggnaBP3|%eLZzqWL*{2r92|b04MNoux2on#c%eA+ytr
zu*MwnabqKG^{&o7ayg<*;5YjOY}zWtWJwap>zP9U(e`Hqgp+$wC=Zo8PvgI7O21!o
zLz-`}dM5J815^L)*Eyg{f`k9j!IwPoyxNg!_Fo4W=nj?vVpGaf_kB4MGM0bB(VG-<
z?nX&!S!cFEU{C>`4u179527xw@@sGQvOPCf8NaAiAcfa!FH}#e0?4)2ayV&N0>nk;
zdW~KRN6tll<9udC{d^HN9KNAGID0y_9OwKMBT+^5IgFHKf9_|c>;j_KiG;qNO`QX>
z$DOXSE`Jc%;9H-bZZpJtBjM4p_r1(=R8^F2w(st6?RP~mK~*2u6X;7?AVge%#BSo?
zAkwAyK;@&vIgPsj4lO0^E!z;XS{|jrZEe1px12d>Ii5l%F>Trp2LlRjMg=P6s+)d8
z(Nub=p{KFq8Qi~#(vq04>hYsP(PA*S1`EB!3vOargY`f@)<cJ<7%doEYrSon&XKD?
zrvl1rIEQ2{#yl$TCr|~dce}5oz^V_=*%5js>HGTr9>X9s88)J=RTRT7!e<RzQ8e>J
z4J*S|(;EB0*}LKf&Ns)~*{wr0OhyU0!}#B?lBI!T@!pMlmRtehGJEn98Uau+^#UtQ
zJ6793wUOBZ;s#6}m%#SF$oYmer*Y3v2qha2S3OYO{57Fp*aO1g<f(kNqyh>`uy`KY
zH$RolFOQTY6y=A_KSI%aTOA!8o2rX0?C2>N;!KRW<6$(7G5QJ-qk`XOcJ)*pKb^+X
zewyipORIl*8802X;y@m}K;rd8EJbBkNawPSFHFP)G1BS;Q2$JrD1N^8!eCdQ4iC2B
z^QxT?%*`fPKQn)QsQ7<my#-Jm(b6r9yA#}<;KALU1b4UK9^4M@8Uh6O5Zql3P6EN*
zEx5bGKjhx;d+)DTHAPWS414DE-rc==t!~(!`1hexap+f(!Gmq}zpLrqJ)J^7)|{V$
zNLFp9tu|OHhkrjlY$lJ-^T)y|?hGo8KQo$`1;Wq*iG=6Zbx)$V6tIvY&;<49NMi|E
zEgKto6>s9%)^c^1Gt(c<+7zbxN~@UY{24xQyqRmCTejJCGo-o%g}5L4&@ix~8b+%O
z)Bj9d(PBa{cr<{kiQWg=&{>JfY6YG3neFOepqB`9CT1v_fmK(v6UIK_UI*apwBwyR
z&5tstwUwLlY2IwULwe&sVL~x;0gRtF%9M=c6%gwQ&bpzXmR^)Pkjmq(j58m3F^Xu;
zAheND3_U0hQg}UoOCf@L+$iSScLmw-@^{0d{vU2sjBSL|%TNkWKPh=Y&G}?r=lA&A
z7m^H2wAka+Tz{3<=w6?UtX?p}$Fn>;X((z88RI^(fM#34H#-JUb6%(*IO*@XYrzIV
zYMml%DKBAE3>}*GlV4yz4ft{L8gIO!Fx>*<VozJ$4tGW}=&-CE0hXDcz)(X&5Pr0P
z`!Uw0OI~bQY3U}*=dpcwT#)jzp)C9Tz&+1K=oFaD*WKt*_#ILOtZoCY;<|w5GGq(#
zbiM_^a3YEqWL=4XV&^mBvCNvmP;ic!X;&iiEM3A`n%A`3NA<)IMvZ-bk!s3glvIvR
z%UAKQc$pDfiy+pTLbmu=hm7p((R73)HLz%^B^>jGHOCdj*Y9!3X?1h0Kl1hlU^hAK
zk|wo)C?bpOV>cgkRJGZ8lp<~im__)Sk(a3Yxz^tUo0=Lxd6b|C9sglb^|S%kT?{h3
ztvssnv`w-&ZYzc6ec1tL+mjZ#51$Yf-Ca5nMTM_#0rJ<&Znn?Kano8@c|TegK>xy*
z`TY6wCYF)DkmnhBrRi<KrO>RaHz`zx3{l+s1NeVO(HQTjzQALvb)$7pij)nGVC#JC
zUXdB=bt^1<o9jC6Pos#xY8}OB^`|1s&b%rOq({66Chh*Ka3Mm6ocur6oOokUCiT)+
z6|T;4zh7=phG}`#A14;dC`nP2JZSX3sG$9Bi#{yQ3ijx@rflzwv{(3;f<8Ce*{VOE
zv51HCZ2TGrq??f=+7iHSM+AIzQow-Tzd&vU5y6Lw&znjN<XJ6q23;%;O?Cf;t$ean
zL)zgf<K%MeoQ4j<#2wJC_CUAWFEs}41-iSp`R)8kvz@DqjgB5Dii<;In&ZqE`P#<o
z1(vURe$2BxC!8Dl(fMP|?$MFgU%`&%Y{3-1ps<PjS%a5Y-1ri|m5`^0?&&crJ_uCP
z0OW!m{A0538#Y^4R$6^Pk1v8>R_93uR+2BK2=zuEN(m6u!)^>nKcU86%qs<M@j6Ht
zXX*MmI}>Q)v9izy9XFG-<bu8&K~Uuk(*7=^cG7%fO(5YBy%jG+!!WwE=zPS?t7UMI
zB+c@o)py%X5|>z;K_jlO7QbWydWmDZCigZj@4dafbN!uTW?cqi2!JMQtnLts(*p%7
zJ>IfLg{Gvz(B=%(hxn*}Q`hUsKFJPeh!G9Ksti|U=eQKjz-=&qW`B1>-tS8eaU8W6
z=@IMM`vWaTE`OVyx;1|KE8X~3x8(&KW@MeI!oQtI4`tIpTMR*JtU-_Od?SXQGrYI)
z>kJmwF)XbNG!{yA`iTf?{<^8X-FJDzszH|)M4F046wuW;8ked^xKS^qTrYrc=Za=0
z@JQ2k9sE4Tnf>bnesxW?Zx$OO@Z5z70M3SFQp@-cXXAjfi5)P+Al<`thjT|SW#&sF
zC2JH8dYZAGUi@-Ht>lf;4kUa){Vzq74eRB4;(1rNeXx0AqD8_Sotljnl9rtS8=dtH
z#1s92J#IB~<C`o`a^6}kbyiq$9v;G347c(#&46}=<DUch4@4MvDIEZH*Pgc%{AOnB
zJs8S|C^gT42GEHCAeUfKIHu)aD<C?Vc#p*Y!R87PffvM?hJg03Z1p1{V9^RFta?J=
zLYv8*QD?u4K{D<LBVCv4+G74s9uIuo7Y9%x1B;-oe*ouun%u_u8Sf+pEHnw|_$EG?
zP1!yH&UamrR&RFyFZZWT-~+6K!?KcB_3hR0@<0KgntU1dSMfIZvC?8E$xsL@b8!Ca
zZFzIehyMW$MO)vBq)h}Ho^Q`$JcM9uMy<z5kupYd?nV3Z-D&!@tmr9=m%Z`LfBw5<
z6@Wcv&Bsjq?(H5QG2d#_INTCZ&G59H`1qv8#5N8AoKi_W4sztEZ-kY?Zu-$FjLn#=
zWHrxhQr|qXB%u^Tt4UvfU7!S@c(}i@{%^Bx!%Ry@F9!5?C05sgf}#VZ(Anl*fB3S@
zQy><i2detuBChkA9o9-iSjHFaUxILDzJ|ROtDRJNsoxg%T^Gv6He0?xBNPg=$&6A7
zOQ?&`JAe)<+Fq8N1M%Cgy5&xn8r#9bP0+im9v0v~vWEa>6!!65_&+Ysduq0J{COP2
zyMg2Hr0dR@HIRtr{DG61gdf<n&%v(DW$mV3+uIlSK}MWJrooOsGdns>Q<j}l<j4gO
zl_4y5+ox=R=&AgTE-*5Y1(?DXoH%@b2E-vgbk=naA(S!}q{@jq3b&keMUDsjkR@0l
zeOgQxkJ^N+*uP&4WW9P&PwK}2hga<H(PSrG<vg6Hc20aF2DPsU7{Q8V#MT=+9r&J-
z9KpE45C=_4a0^B}8fw0ab6kxR`zQs5g*b4fA_(bg9O@-3YWXjTcQ<DEo;mqkXI8WQ
z%;B1Ur>E$#B7h{97(S%<%~}$qU^r*>wTaGK)w{c_EZ}=E%OPiN&NhW*3&c!?5Y0&g
zw{gVrogPJ#mJwq__u919;>kDu)LFJ;_Rb(q8LwNRVj?`Bm7+#qlU9g@%~G`zx%U@=
zdkRmjy@+r>UoM`aWGSOPE+g)Zb|ByU*E&mJFc9o(#Ua8CpwpN03pMY8O{R%*1Kx_u
z^brt+<RL8T7@1v%GDG6;Wt)2^U_vt|q$O^9ej}#wgk2>Q(f1?f;2)Kc9VHqKm9x9D
zO0r(~^vfAdAWdAxqj$m7n5P^QGb6@)0zx7?VE|<X9utW!mwSoIzbXN9aqFEH>>$Ar
zA_CNWVZkF08j6w}`4-~;AxG$Px$;x$s1Fbcet<S5)NZ-YXZtTR;scAF6qGzgm(f)+
zds6+s4NNN|TA>*oI8I783q5$ffiATU5q3NGb89V{mm7#bXfQCK^ETl9H-2qhXj{?D
zOA}!s7)O1WFg>dS=nvRT7O;ra6r$)(SoGy@T(!V*%G_BZ4LIzlt{`k)hA^7T6@M|T
zjB9l;78b6os0vJ>s8urz4;p7=engy@)QIymzN}G*P;{J8Na$8LI-CfjV~X_z3}A;!
z81FLP&YXa+h!KI~K$NQxq_H@k6K2f2i7IW}7z(BRJ4tD&HVfh}iy=aEsG0H=YSih%
zs8rs~77yA>SKfF_kq$PED5Ri@s-4W+3zVnLodHT%2<rerz@8O@+3gPImUX&HdQnvE
zH-Z%rqB$321f_YD4UwIu=w?}Y_AiwfyxYg3EsuAC<)bWbfE(9ZeahSUD@}#r2IWHu
znZvNIb%@$&JdYP6dcPPG10szjIFth(5(AqEHF^YKD@3Ks627@|T1fwj|2>;;FaiqZ
z%!6B;pr}q3Hn6{nELA^au7DRV337}6d-~<N0{>4w$7J!}%CTw5nIJT6t7*PY1+Rdp
zWMAw)oQ?H`oYzqN@5#4_z0Q+SpF@e3@V3BFB1pSP^G4WdZ!Kj{a~7UgA;-V><o`YM
z$OA9M18f7vkS&Bm{=ontqJ74sC{`K_4H{MKRx<?bHfTw2zxdBZD;Yq#j%Z@~uN3qP
z3o5wNNw#Q425L5!QQ_l{wEr$x6ly^N*xf!m=_zmi2VhrMpJH;qNKKYy=BjPq{>%;i
zzjzk`L2on#D|Tz7xAkX2Lwb-OU4&y^WjfC8qrhFgJ8vD!6IuOd_5ZoOHBj2-J^m2_
z{m;ZMl_1()(7a(mj&X9)MPPA$D+FUQ7&dpw&3}wcd8+Z53GW}ru59?q=_d8zfF}@y
z`WVDTN?`~PbjTr#u+PFNpH;4HIc)ws?4cL%cgUBig$7}QmF(HxlRz8;r_(P=DB-Hz
z?P6e$o(7M22cKWq@_f@8`$hR^&46ew1nC`6_d+EK0W5Ce6GZ2luo4@Vip~{b2IPH?
zS@@zcuDt)LGVH4Y)Pi`|);Z7^e-{`^l82Gn&FD0Fh<=JU!)k|o=NEo+qMVz^840Y<
z70B!2N5iz<-ni&KOs@Z<5QQY4#53icjzi_5Rh%a=CRhvAIi_730J{YcuCA}2$6lY}
z>HPo^y2$-+C5!MC9rMpxK4r^`qm8)t@81CQC^}K}>doTsaR1@~7bruyXTr^yDyLxS
zvRMioO&CJn`{#0Ce`C!9Ln;2=9UmOnSm*JpE^?;MO%Huys3=d&sr?9G2A+T=M&+0i
z0{DR_lpI3y^M|!6oP#;uo?C%seq7jNf=ZLfH&m^R<QyEFzJVT<aZXUTi-W6#J;JV6
zj+|mp&Wml00hoj~3_g?)E{Wm4+N2bgXpg0xH_TMRwS4CZ&!~1G7;w6jkYok9TfffK
zyJ2vF{(Zpgq6tKOp#O@BN}jP<-4thVw`VW>>E7|lRjYy1s}1KB+~-~RKut?lAR;-+
z^3hcUoIxl|b#~Jl(G@I}_H>5rY`UwN|7Gv3cwsOa9Hkgo*YS_IJ|`bC;@_Pe{|#g#
zAi#<4SJl!=4TY)g`x})1m8s^N1@OlDfJh<^8Xz+O?pT>A(3m&qo0jL?PmOzvEJFc*
z8^(rF{BGei$ebuB?HZu}8m>~89XG39BU5L}E)wPV!fKHI_=Zz+erw|oheq7C&U4^4
zzX+k8$b@Zwq=y0bH|K#=A{X34?uG`cg8(^{S@KL0twU^ELkj98vLRbG-cAC_`V%=;
zBst7OS0HpkH!!y;ADg$r(pEM2@R<K{h(jr=i93sT#|4F@)#|#?d-D_U@es%v|5<N}
zsgDT$PdOQ13?kp7i>L<~w$4z^YT}dnbE*1-<hYFneQp$jZJ1X=z$Rj*pqC4vnC|H4
zsHms_^fH-ayK3#f7c9tq!7fQeaU@^=A2Udpfx$Ri-a_knj@EB%p=CC-Or6H%a{`n`
zZ4|IiIwOe#mZ*Ub58l6LMahBc0#jCPE(%n)sHj84Z@d53s1iD0^k3MfSvlEyvN!HR
zA3fNaFkoY;WFZ9!JlpBE5Y#m^<jkb~*Do$y_P@b?#`w<Xn75p;Im!M%X5Pj1KlYgr
z3nRXPV4D4$hY%Bf(ys`%+`UWYm_mAs-s!8%(f}aX7-(h<sON;=M&+3I5E_@wl&UM#
z%~noE9dKz?Ns!kM9+zebflfBJb)tj9l0@Bs;=$;sSMdz+cI9c;Z^B8&J27#v3@COM
zcyA14wi1<X-4Z4el@q+G2PFCr<;inrY=DNL54KeuxF<&C5XwPv^%Q|!e_D{w<$nUc
zGC@=m;5Ls&S^r1`?x-UUF)<p<K3KKFd+w@LfIVpyYP*qu^flev*j2GTA0J8<CKg3|
z9=`eKPuUOB6A8RffmVjl9nF1ICxl9XisKy+AZSlaDQp1;M{O8HU&$0%&?(;P;x}IZ
z@ZVxr;?NQhTm38S;VspLAE8)M4}swuM8w1)UO;D~&g)sdWNS-YJsc$1CVOvGBJxnG
zjjxjz$*D$3T3tr`wRg~BQ+4rOg;@FKWVE`#NdQFgAG?T9JlddSy<o3xCv2n2AHJaY
z#Bt!NjQ<pS=c+HHBq!<xb91`JT59y&{ps$!vXW(c;rlkO*h99UI|4f|7Fv$AEnl;(
zUJ7*HJ#~UT5cAgA4_E_goPc};@|~73?4#R|gcJEH995y+@2Z$L#PD*iPpS}uCL1MK
zh@OI^EjmsJ!%8}u5P?6!wp<v~mEw4ljZD*kLo*S$7Y<(qXB6=LJwSCgX>n{~+(VYe
zxI|e&zD7nBq)90&05M@$j06LRmGMT;#<DDTMn!9@?mn(%mLIGXjZ4NQQuKB)6OfhB
zXG6?EF#1PXlLIT8L=X*cg`%KX=VOq?ytGr0t1bJ$+YijPkD&!vBSYlMs;Vw?1|B4W
zo)~h~z+eFYDIcni)|7=g*kKiJceJF(*PHs_F~Po%^`>K45CuFLkwqFea0bwa2hd@-
z-&GG+87Ha~OJ`e>Jb~5xB7W!WLuT8I9*GDce3Op9!bg@#^oG*Rc!nl>^)-7|saoPP
zyYcmLFg(cVCIxI@@;eaw6Dk4iwBJ4=cBo&j+gG7Adw6aD)9Z@sqe@rZQC<xttP>^n
zEZ}U-nIMC^d40OS#*hfZ1IMM4BJkqI5Xl_>@fa>eMOpkB2yqIl<UIU)+0CH7Q;hGL
zG~OfpZ|LwI(1i$wIxTSh^W0Q{y!*BsR-Ya&G0uraY#MZ-!C$Dc(jJTt?_>Z9{r|=g
zs<OaShq5i;y!};S7{v4s9t`Pp#t#7LZ|%#sPHoQR$&Ir2JfB>A3&KU)mh)y6*N*m6
z<Zc8Pma0$H)Y|Yo$}|oLlF!|{4Rb{7K3LN&37!5g#YLGG63O`UDC3(};+HbiFOF@r
zkQILuBO~Hn7C$L8y&E+DUA&Qg*oPT~BeKp;n9vV*A-#!fFBN8&qk&R&6$(4LsUvkb
zyHd&K=8_1m<oNzCBdc_Vd&I6`4(+AuQ)EmW1WE7~IS#k29aJYI$NPcCeOsti`sPZD
z5YS7`<L5h#FFwM${(B*hOCpZq936_!%dEJaO_u93w+~fdrq_Ha_oHCnv*yDbe^-XF
z$}%P{L8nvKvNU<#_bQri-Wj+=X90&Z+WNk@`)!}eL1YkiZzEqb?&wN8SeA(;l?Lou
z8Xktt7<2^gt{!!Kwx7U<5nLSyJw06AK%>=r`PqsX(ocUQVlAC2&$QKUX3C!`5%76p
z1uxxR2z0FY)%ZzfgUUQkRp!RPI;rZ=B2VFs&x87Af}AIlt-}}KyBZh29{ydj*UIe%
z<{nQM`&ODS_LBw?BmPIHS;e~T<M*~Hi(t30E3;Tq{bLW9=We!{DwrrhQ}-580T+_7
zKiu2Ly$*$q5JEZL5#bfb@2BzW7-iq~V*)6$;HfE`P@wfW^4jRdv;Qegv*g7o_|UjR
zkAJ1PWcLf%`&7j(q;6&NbK)`)jId~&7wvN!wT!BgPuERNLKX!DrGK>7{zfig?hhrm
zcq|JtmpsHCf+&kw!BeR@1&@7?3R{F=$4{N~0Xb{aROmkbwvQ0gtb{~Y2k~nR%Nk@j
zUG&qmk}`wWzyCS(w-p143Q#81nEGV)wud4hIH_Iq#U8{VqI=o*$^9DUH?4vS`Zkwl
zIpkof=kN|Op2<@lHU<~}k_bO~kIj@_Nb5D&HXR5zSK_l)v9{m-yo{}Qc046caJaqe
z84Ry4(vF1KAM-1;^OkyI&<AY!-K>#{)8MBmEJuC*F-<Ld{)r>hP<5vpc~t+`BZ8Wz
z`=#OjL}JGn#212Oi~nfe0899HLH-&0XC#@9P_p*hH{n8eO6or;E9!KrYWBFa+tV-d
zo{p1G)GC5J)cMz~UT%#zMSMX9hKgTBAQ6ZhtZq0teUvzT&TI}pQdSpLDhK%7|Hf-0
z*QqhqHe_W5?RM^OsH8xg3Lib)lj-`vo90au#vYJ4u!8pw#P5$y34~Yu1~XIkY*z0%
znE4v#YYm%ASPinFHR7R&=f>Js{q}2@IfNk3S;{el-EHO{nKf~@50NhibYZjZTxSzR
zxiR+e?G{&B2~rx-5s;6(=p#jS96ptF{17Z|<t&z#bDzM)`VJFFz2;9lf&35Sg~Y;7
z70n;Un;1>#-0d94BVF-o*pbP$iYMv~++z7H5Ow!gsS~uw`a)gbZMqImYW?ssXMum!
zYh9L0dip$yC@C=LMkz8<W3xM}i<a%wBJ@G(@KPor8L4U?XMm`RVcF?(pzcQk=C)5S
z?@C%hY<FcMO<U3>KU~r`7;}E=E7KuZ|8<h4wS0G05HLZGa$($Ym^#s2;M?3Ci-)v%
zK9?GbGs@cshhOL!bz5wBJfOgjgPhY^an;N7ZcyXm8%%BHfBDO!E(l26WFj`}4KhW#
znqK`EL&G?B?>|umIs^G_d~^irza68Gh`_S8$6(}~#`-RQ??UQF*_UH}@7G$d*+UlQ
zfTw6?syNN;lQW?+qfgpXjKZ5=$XMDoqJmO5g#UJnk0ip~f?xhlLmOo}H1z$YG(W(5
zQM!K?vH#|P>G%yimgeAlrZAPKxVFS`H`L}Ak(h!D&C~dxn0+%ea|(KD^%}#ZbEx`m
z@$_3{?AvYd1?a_t<H8~`nZJTC>gwjYKb_*-ckNa&S3<vIGk+QMtnaqmVU|NGKx5uT
zxE1l!^y7e4uL5;~5RBwt)!ubzj+0mawksBc<IOoVd`!<jTD7*9+Q(>G0Q>RWET8{Z
zcpi;|Fi%1EA%yLDp}>i{?m%$k7Q6c)eILi4J)p^|YR<PpQPW@A@BY*1TaC^{HWkYe
zVhlUG+4B~<;>#MVdTJ_uzlChY(*k;`(1m2i!q32B5C1IK?g719zHFa589TNP^}902
zR3_h1&jz;#3?CF4Kw;pqtR5t&ZOU=JvW;jGPW|nR9R;;b7;9_C@av3{dK8+;dwN12
zcE8)<sj}gZ_?KGXHK*QfShAKpUVNfEClEqSnDC(2n(=yMtU)hcn0%9gp1Q92_~DFF
z2iEBYi4E4{sd`BIpimIN(|!*_J;++*_~YZk-+}kuewa|P^d8+f%NN|ed2}*gJ>CaE
zz*a-iCepq+LlVfp4dOwJN)Q5bNM_jjo&2#2xf8{|wgnoymu?VGbRtwsbma0j(8mVZ
zr8JTWr66O<v`L@P(WgNdjgxw_xRizuR?{Bd$29jiQz+?s%0!AjYx9eA*Vrf_uTPT*
z=Q`i3z}xBKcmAkwv7RL^>E~ZR^G!0-i#`kA$<}>uL>l%ZyEBbl;3O{6*EA1!km|aO
ze`$hEoYAg-+O+7FA@Lw@!!e}O6I}D=y+4rrd9}pzjy20R_)xF)_V$$ze(d3Q0ke}%
z!Nq3(O%<pV>B7*a3+hdp`r#<;rHknvzw7_vsWW}ZwD=m32|Rr!+&_*N5Pbjw!Ic<t
zzhH?)>^EVF#Is_<u$J(N<yr)vU6K6nP{tWqSf<UDdb9N(Wk^PzZFrA}a@TUmO5oT8
z3yM;{bBrc5>F3XkE}JlH?JKII40Z@8AD-4zH^FYtFKHa}269I?y>obGZB$K`+JpJ4
z8%RPmHP~UY860wE^uK1rv<hD0$2?91c}+c)@5*p@U2g_lOh?j88izFz6ojgQfK5&m
zB^t*Uj2JDBiMPT%zr2Bg8)v~u{NWz^qinr1XPY9*4Y9}7W`{r9%i83GgIw>!8#SI!
zT)g`lr*1P0{vFUR7n;qP$vNxn8w`6Y5UlNtlE}Pesw^-tD@1+LotW?XK6Lv;O>2&K
zV6RQlhYpC^N7W3P-CA@0%=5R@Ov4B)&pKOGFuP5AD%JH{%fbm1{TpjF#K?q_GO3g2
zr<Z!VKi8TluiJk6FnsA~WJGy#%XoUs`0AYh*=mfA`bxKr0X>QYHDULD!*SN{are{s
z*j)K2$Y7^xKtu3wQ|e~wxJGc^ZDtuq4lQ}RoE9RIu@zLa$Ai{~EJHfxy27XfBSEc4
zOL;@eU&~eCR%Omxo`52kAIQkE_Dj?X5f@npC?W6;)9UN&oCsmhFA>bo5r|TJVb<gS
z1TK`EPu#|iW=gY_a*rccX$v|*l`f3+g<UDbuH~odxP&ziqF)2IFK^$32ww-P%4rY8
z4w_CbdtKJ&ymVe03G3NM!cm*GRMoTK#kM^_$$q0*X)q0BKDupkh1IY@6>rU>&J!#u
zyMV$)A6DvThbpak!1G};S)<y!wAI`ddJ3OE>09yZHWDHjHbR{{@9<EkUX4rlIW522
zCCd^Yt*{P#aD0(K#nOp}!cVO(o<Ij1wmGYfH9n)+VKRx_5WDvvqGYjZszMBJRA+9(
ztgpjD!iWs38H(XJ3O+Sc{sy9T?mu7&hpJ`OW?zuId0D$O!8V>=+?Lx~`%J!sHYXCs
zI?<pKG)jo(0Mk@d9T0T*YBtaF#v=G`UkAp_c3{bi4WJ`>+884$@Z%+nBaRx%8nv8o
ziQgVfdn$z|_GUdEv(Az?uupzs&T%9&lSN-KqBH35vY!~SHM5*A*dqgtlN;#PO}|w5
z{BT@YeCcvbG?GU+eK{AI!NtQbgu{Nn=X&rcV)Wc$#6^`ggYLgHIY9#MWy7U=y|gTq
z9#(EJk3&UHPRx5aLI2j;u~Fp*hRlGQ(@Ya_vd7Fu%Q*{UL^krLYt$zYcy_-<1V@`_
z70<0kAJ>1goO6C$i~RF$$s7?9rkhrmq11?JApxtMuJQLCA-?DB!DCW-uIx3V4$>j1
zVS^aJEzAb-25xf!;)0a79QbRb=C`zjXk~B|`+J)|1@OzB&wtbP??RF-v!IxeByQnC
zX*yNqEq!I)J$3LmP-rX>6ro{fwhEx}dczMO#&tc+w`bmoz-Ze)vWf`P^b_Ij>~~(A
z%Tw1zS%r(F-MPd>^_>qjiOIJwM#8q|{W{H#E82>(4PZ_;T$^OID2r>O&K|9*g9|pH
zo(dvbAj8P^&;Px36V}IRpxkc+ZaZiK*dDmuuct%}vQEr4#@1x(p>;{kKazwalBp9=
zVfwm^z0|9lsqq`>9&_{%WhG7GAx^I^Pa^7eLuVhF3AeK-TOSoJH5J?=vz^`x>z7&v
z!n{)=fANXmMEwznME>?_Mv%*WE(?NWqGbThSjHS4(xbWa=pEAM=~B#HyO26|uXg~Y
z=Xt`CUy*Zgwlj`9m+Up^gCc~-%^mo1*dhc~q3P-hUgRm6YO+KdNH601XV$M~ZIMJk
zZPjWjn-f!HUEH!&ol89R^4`se_>}2{LAYxzpc`#Q?zq<L^uMpjf>+vQ^)*SZuf6eu
z;wAm*Rci+K-ERE=nV$$jVN$C-<a6(&0TbY-`Y<s#pa(S=j?~}XB=|;LrND~=@T9D^
z$pCG7FikhYCGZ2fMiW#-bLhbOh}mJd@%j%MF#aCKo+_rL4<DQSzg3(~#kx<PixyJ!
zcy$pSxWaiaixn$HxQ9)19ZY-C+DB^SSk7jJclaj7F<a9}t~1{ff1FN{BZ^nK2U3`v
zSNG@h0d4M`54zbiG)JvhC6DnG!a9T$H%D1|M8h%-Rw>tkKE*^=HEUQ2WD2^=KAK8m
zW(d}W?X6aM7}tK=L;Cl}+|lma`8E07+p#)8x~t3$>HJ(*YyZ)Pq*jlv!jcBj9On($
zwQ1#8)&6M&gJ{`Kuth*#iDW^3<(a7pBH_#Q6YE}Jgyq{J&_#XfAe1$dAbj+}_JI33
z6?g-ruku{7WHk23)EYe!k5e*w9>lJ)T<@94SL)xX=&0ttE*3M?<lYjA2)-9GT@YLX
zgRCETK(q9O7twT!Ogq%zu~lC;3RP(ZAFho`f@E4(N-u99&Ngcrc&P*&QXrYOt~H8K
zxl%mN;@24_KwN?;+e*z_A^p9lTQZhp)DIPGg(RS~TM46p?Jgz13;D&4nhgg??u&yM
z9;pMr&;%UKzU$gWayGq{_#TM~gw|g{Se>$VMj<hP-`Q_!_b?6ntxM6s&d#QQQ`Nro
zxV6?GUu+6l_T`p@s3y2_dfmq;O+|y@Z(GmMQjQ>D+qvZ{KX%(`l)bRq>v;_h@8oBL
zPRd;%Iy%)$YVwv-^eF~+)HT&G<9=p7>8dxcJkAj|xLz^hGLr^&X_Sb=5usDe$GvjZ
z6}Q9s)2CWFLi`v8mhso)<oOr5pE9IO`wU1k+tP9nbKj6v)86!qRxq_T%vPB-lkQ>#
z-6|jbZnR6kzb~Lrd+TJv@UwQTgff66{zvH{=OK>|Q-|_;!Kh*PTJ*fd`(*4!7IA*Y
zh*eIb<qQPW{lwIfCb{eRMJ)!UYBt9o+iRW5myYOMn_3V@Dj||1^AvLJc;Z?g?=sDZ
zUXoOd)f9Ac6Jx!Ww}3c;^=BO=?>!I5{`GKJmPW|;TWVjeoKYj?Es!tu`j#7Hp+gET
zoBo7>eHpFn&f}QrSmSdZNpH6_jK6ljW-ytboY`GFSm*@J=f&duDodF!#>qC=u_@ts
z6O{bt`X*+4w-m#El!r4!OKy)>Xvbk<aHH*=T|9X#gJww)Tle><AEMf_irm{R{g2zt
zXgPOxop&5to+9|^94SKzKK@*wZ9uM`^t=~Dq}L~qxSRe-*V&qdUFA0{+l@`nRv~FM
zPLjGJlX3AT>r+lGxMR`phu$4CN*faJ>c2nqcgo!Qy7Ioxjt0lcWaB3iBQMl-J`V4Y
zJ*zQ8=V5o(hW&S)wc$V{bMuFbnI^ED3IhH#n|p57Vt1ByFm)%j`$f!%sZ=xg<7nFc
zQS#X4CSPL|mKYN5cKr4{N+^|KPPJE+XAEYg?@AG@M8&|p<NWE0$8;pjC`L-)UYumJ
z2_;`mjg7~QDFp$J`$?9eNsv}!qf5RxVUs9@V{_@*spHkt!Eg6_jG8}pADh-RnOz&K
zWkhB<!o!&cXmX64E~#4Z+$mlLl{9sjb?-agAiXz?1wg;h-wFk3wz~3AI$~Y>$j4UB
z4%RLX_U=d4ZujCf5SA(s8P|k&KIh`%jIis?r=wAk+JPf(=jpP;kxhuO5+Zja``LlH
zPq@@sUvuQQ8#y|cz=YsLtjZIC1Mi#bzb%$<SybMnC#6%jPkJ3hJpF4k-UFbuTf)vS
zYga&&({MO`X1ar3!Pt5-`NZni)Q$a&Xgq8<DD>*T`7)+8R+{$nAcb@UAnN{S#Q{)n
zg)(C-YapZ+2z1agCR%PE8D$=c3np>!^1N)vx=goOIv{KtVpSgEnz&9)SBh3FYjsH8
zj?@a%`r9KEEvYHzGZ;gz&$nL`sU=)f^M+Cs3;15>RWG)b{-NIql@7Ri^`lRb(Y5<B
zH3RDbQa*cn-702yea0IxrI|E+K2%bC-U$DK`hZw&kRlTE`3>#)P6$=!a-rBpysGTG
z1Kw}U^arC?m3T4v&;&981=q|XY^6Fm@&d%>r#uNuL3sY<$0dCMJz(?K`1Y_N9eSoF
z>uG8&%}&p=R@R#I8cs~!-k|JC3|TFWjjbonA^9A{J(tgX;qoD3va;Z|Ik5SorT<N!
zC@p1#Hdg=HbmG*Y>7#_Mb*yxU`?ax*7R1ui>ZNf9{(8kssj!R0?<}6w2wMGC!CTv$
za^JlgP5u4=@ICsBI@nB!r3ygX0w7*6pZbnq$BRJ1UMPszj1`Tj8V!#=ZB4FmvL6zD
z9n7Y;+A`XVADv^%1sQEF8mV(08>LkCNW<j#>}s^kW?3})zHTzQ5{{tXp3X1wnNEba
zhclEtN7W7~#`~!GM2isXYUp$GR2ggCrUm;^O`;Atnxp}s0I*+DKoC~Kh~{vCVvfoQ
zZO0Q@;g6C{TJkF>(0}+xqU0IhvAVJ%;R>y^Q~kiv`O$d>3d5E(i97<m7MV##ha@Sa
zYzyB;FNYj#AT`Xgl~G=8vEu#w)Ek)^&MKpj^X#<nNlQlP)ESS~>EUdvV#SXtbKsZj
zGm!QJ2%f_3Vx?iS&rHA9*N6^J6{gtPVqxWnOObktb^-zFNIe*Z_|}`RzII_x>r|gk
zK}MMF6e$Nfzr>*wi>J2EsR<ppGwd6wb5O&3CnhKJC#)D47`}4L9?6$*{YTAa)6n`)
z&6Y9!F?hDR&{r<9qA!;V&GV7STao*kYe<iU-XOsLFPG}Q@t~LzIX4$=mbJ<P<^I?9
z>S8w~Ho?s`__hf{Ep@F#J%UI{#akXTPZqF(|M1_TGKC?>^6W?-BYwZqvD3%#7{1hG
zO?B<#EhOU%LnE7-(dzi?s-L{nvATY{<@fXwd#l1<Dt$98D$tUD>Zqx9*0bGw$(}bJ
zPHXh*5HIx&mcCq%QgA`(Q9Sj6+j>9P#gkGldH>^J(Wj|>;zSV=<~-7u4w43dV>Ku3
zCULQp(I6$ckX@R3{c=}O_m}2*C?QZBR$Kb-9L#m}EesgiB`(=Bx%_WV+r4x>zzLLP
zrPBzY5?8O0N#ZuHn|RPY=Z5VR3_5~>-3%jlBOZZ9=S##KR~SSk3&#dm_vltSpCdA#
zfjFme|2V>V)?-Fam2|F~*hw|Bv&V{)RN(L27H>DhNv_qpVm<%ob-TN=t&>gbM$Gw^
zFS|F#OV|~Lz+7y%IRm;XbhzL#;YT|OiC}d;U~I_s;hY4D0@s3?wqcF$ak=duZ<FUI
zwa3>KbqK9(4UpCE@ba*YwSJZ?=Y@gZu~UZ?=Ad+o4ELpc^cc8`k}5f@F7ATkhZY`c
z`vv~-S#JELVpP<jqt9e|&f&alnJiWMCujVmOV^L29=^2!g&nafUVx@fKlBUELDL_*
z4)gRgh0XK8zeAuH|AFSKnzT!X3ilew%mFz)aks&lrk2cnh}lvuT!W*WzShikQlq0?
z=%?UFHKcW32Y_{w2m#9`f*3`aV5x4TVK2$Bczpb#IjD@KofcW7InrbLoC#&nDfcCx
z)w5c_=_e!oEseZA<59Y;O$?5^JzF{d0@?BesTFCAQKp*RL^;#c-1fdp3}HRrB2nLs
z)CKHMRY!Vl*8{hP0Rk`nccabXdrpqCcD78rY`QJ><LDL0{cYeC*!`swjBgpP-(3&9
zXoALZ42x2{rvAV&7)FlLhiVkq#i$#a_St^R7$^;k8Zc~AjdmI@L4u|7k6%o92vG$x
z>{L=}oB<MU*V9K9IhTUz;LzwU8eAPCdSL4?Vy8qX43_KE71nBd?xa~NW($_g9pbU*
zN8AF<B1wgP@h44z0ff%X$$m&4Ct+Sh440;0P^^VrHs9$@QB%g%4`p80^26^u>m{RA
zfsQwxbI$v?M!!7%e)Ls$vNx$vp?fO$i%t_sAm-!f<e7z>?$*LzgtkH7Y1W_RX~jz{
zJnl@6fmHre--Ku3RNr~7_f+s*RNw1HiUV;|b#rbrx6B>h>76Lq>Y9ijZhOPzeshyj
zA>>nilQh>&S;Z$l@7_|Z4d{C^pQi3LABh>1Z%QaPBF>w?M!4J*kfNO*06ueDM^K-=
z+o0;Rmv}dKQ{5u1WOwd)UZ=?jx+5FI8yST9O_ycflm3y$$t-KXPJ!7y_^kIS_!O;?
zfAcl2vWm;!tLRfzY=vFBMeEt_&5YXW>+(U2S_PSrd5dkH&XXG5CQxbsuO0&PM(5Xz
zU7eSRr&biock<l6&ixEob+3N}cPwluj!#ENxuF|oCs`7@6Z*Oa9t<vJjb-7V%NY2k
zY_8P^Oq3X|MUt`_qOSA^7(%aN8mX1Tjr6FB9ZE}8xw$94FHurDFP~fxz4NE442&4$
z!hzz=LfxJJCYIaScvD(dN!XhLFl&DraW-$K=#ArtD$~~kj9ZCtGz0gA&n+!mGEH$4
zUT_8s4XLYs=fzUR9^nPh#RaG@QHzYQ6oiN(e(NPvSs#+iG)t&TH`dY~g`Pnxuc^(X
zou2z0z+g3lfth9nUca)95r?^-!#a51So$O;j`|B&Bm8%U+T~HO2t5^lXZBj6(Yf<>
zrxTTh$_-9zyHOPq9NP7(@rLyG=yV)T6V@s2BE;NTxTtY<dV?Ib%7!;$!afv?CHEI;
z_c6M6Ru$JR+mw+VVZ)v!f7U=hTE&Wqx$|55fj4>jD3Pb7n;}0^Gk*cyVZdCu;d^Jv
zrOy4oO%E(X136q8jN0ZKb3LcKWR;ssMz3a~L;DS&JI^WsocE%C8_q8L%Q1>tvA|P?
zUoU8krHs?pH1UkCaE!>msvliuiv|bo&hu2qL|~dkaFVKAp!E05YTYuDh-j+7l|wX{
z-a&Z@+dI8_#$lA#=AoPQHmVEe<OR;PHugb_aZxGo(t*bvm4dvhl*LFJGgXiGL<MF1
zjTo5TxyGr9qSQ_4R>tEqiM4&U9HY&Ol*)vj9)yzrQE^lvs#gjNOs)@=LpZ~`2$-jX
zJ)UY;0)jy?s1kCg^)5(PHA6#|Qlp$PkF#~L8Z-SMIK_Sm_S|?DEiG^p8PqkPi0nyy
z1O$<ZuH$!jJ|_F(`ux+*vZ`R-<g&Fw9zacy;fM*v)5t{^si5Q?-R@$2kCjQeqoWRv
z=uV;LPod0-hRDvsMy5;qCxo0r@9!A<&1mI{M%OhsHOw@dQ{G9KJuicH8cL)oELh{a
zUw@%a4DSA)UI1gG21m%Dop-B5ztm{B?ha;~Dy!1Z<rTJG4ZS+l?}c^9ui!2Iq#USx
z&oT0J^TJu~SN$9~5rU`q|C30TrY-^)C!jX~06a7VC60JegU*}OLsNwpj2ZpZoF}!8
zvflVIW%bvmS>q;|yKBz5pZ*sqPz8#pevEisshUV4Kf<UI$2z9hwsCb8$7Wtm;Wp4I
zbfch}oyo7p74fpKqlH+sMDOe$iv{#W^fT)6r>k3+bEke{@G_HlFxQJdhxH_$w(ojA
zx*p9LS?%yP)lCb3K~@CqnX7M#A0n-;kdnQt5+FCjY(N#hJMc9#$dmKLK|JL^{zTJQ
z;}8C&Pb*K#*Ll{1c;x)^Y!Z)QL3J@D8Aex6&&0#PAj?X~7w9iSLqn65m9<&Klo#Z=
zBjfRcme=2ztAwJiXye(*XH<rXg>hoP6zx%dJ!9ia66ekvlGK>WpruhI?bRjV<oe5+
z$sk=eZ(cLV;(FynhsX9G#-g@9g~|N|+)+<`;LP%afN$@Vt>Ri7tBueO6RfP+?&I_9
z_c=d7f>|%_H)^@o;K;V-r<f544g_cOSCTw5+@jOPUENE^B0sLjEXbDAaN!E1Wik5l
ziG>|l5)mn5C>_E-ps~T$O9D+xWyurt8K^nUU=a&h1Ahc6hcntul!00XuMNvyThM7=
zDOYz;Ks){Z2*&TRY`gFlW>3KR^4h7klO^pzmRh`}M?E=C`Z$16H=(T~+bK|oD&EBZ
zhku{Zdsk#FHkfLiDi%)bQORVElhE;gUDJ1~b~kbdc*SXD{&_9}aM0SdOFL)1ZA-Y!
z(V>Q87?Rq&uJ3eR^ZRfbScbUn;daUidy*Djaexvj4&sA`f7K$}Z(psn*nk2Nps!-q
zA}+!`Ye|PBcCz++FAEQkTVOE5!{cL3b5ni&+n_UkVEnZdOKO6c77D;sSOI1R*IQ2k
z1G>(8kXgy&UF8Q7-e>XpZ7u0pMLwTbh>@1}lVSCK4bEGi7%c#aTpd~2IuE-Hm0gx~
zo9ymqDSwv>^mRH9PtYM;Y#W>M$ZvZ&PI6SpC%pEqINP$$k&*qVk*vj4U>w%FJ3rTY
zTe~=HA4bjBkt9rMy-g)^V-m|!zx`zdm4tMzH~gkNO%o0NG{b(x`8X990ohegKaQh7
zQs(sdn16N+dG14_jCaYl`ldhFG#rp5<IP<*7gziWo0*DKaq|up<=!(aGkpEHRXsr3
z1kX(#$VAPyx%R+RpF_(S0Pz%k+rhn#D!m@ra4?9N9{YH>c#7knh89K@xDi1;bKXgw
zU-C(pOFVTcOFY<G^HZnXUQ3=xWLFYC3q95g3RRyjaL7o}ZI*7~5&7=rb1OwRA3k*E
zE=w_8CkVsZ3A|HlL~H58844CAC{Lu~wwd8Tios|-+XHsfPg||UNDp(p?Ds(s#FQ33
zeL?}+R!GKDf2`68CytN2U55)mi|54|sms1IM`ft3-;GZ6!=kSNHKmbj(7Xk8bL;cX
z5_8Htmb|$-762$niw6U;BMIm#ojU0&$f(rO?fs#)rg1{-F0Eg_)%+C>CJW*Pqi4k(
zAbFdM1H$fS<lBpr6azV;+}e5CUkb#ZA8KneYY*BF)=nQfw1YoRn2P-&iIw`r>sNIy
zbl&9PS(r%4$P$<`?@xL9X|y|s47Yt@v!<i~wkoe~<MjaJ(Lg!m5>Us6*<#Cs_`Qzw
zhUdD9V%)$WJ~zRQR^@Y7vkqUf^=9t*pk{Nc$ST+U`r-5S?25_#Vdhv*x#Blullm=X
zeTU4*5hJR^S$J;;kGgg=i6vIs6Hff~y;=FA->V%5aSOPG;*?dUgE<bv#dbphJ^R8!
z?W;x`4KC_eg{m^HNS%fk;Ykjrhotjw{WK5oEKO9ngr7n5wfFU}k9s7C6Wx}!eG3if
zAwAEl;{kNjrvO!XVk-A;br<#8CupUTe7U7^LMANa&u4cDowz(f8KZ1$=J{)!mN3<}
zy!j|csI4bBXLl-#!+L-OuCorK85)dPMYLT{#tQ#E5yq8p<50f1;F9O`X@|A#rPgF3
z>~N>54xjektJl4AIE6WQHcQyAb;8Qd#>RUqmS-Kqe>cmc&^`ewP@B>_xSPBc1n@``
zX<IuD5gMdENxNhYiS4Fc^qpY7e}3B7J!m^XW`fn4tH^@2>#s|cX`NaixP2lv8-4nE
z|5I?>pIqgK_|yq+2eg&|+|m-<Qo^T)#f3RBl(}~w2Mzl+Hw`<a@2KLSv0B-ikQNFz
z%EMAReFwHpg`RpNg`!hcuZ2a(<OoB@b}LV6VA$9VNcK<DQnftQM*iR_=D5I`k+I#g
z&1z8`ryLzdJf+JQDH+`L{)+RGhSGU+T8BR};S^wiU{P}y=@prrSEp3c#8PJ6=alc|
z8mmpJN{rv?9E<wU((p(^zrLMj$UXSsx1QMoq4R@o!7b<peRoRylbhnvD|-o}I#B9q
zh^an)<Ut*{jTn}I*PnV(=Ed(3@SUFY;niiG32{cuV9onfuQN{;!|R*S9F&f;mS{}y
zxt)$>ki=X42~^=df)I&ZL4@5A28H~(5;2&(y=xOKw0YEPY78{!-ee`$d9lV{@eQeH
z^<ybs+rHw@Q`HyVAYt93ff<79?VfK_$6zcd_H!^HBRt1HLwRz3B+FTN{Nr|6r3ZGB
z$fo(x7FHSmYP6?KtSWF6{`dBg$8j}=IgT0<WhJ_O@C@3F(YP7ZVfZEkJcA}vbT0Ty
zpTcj_%~Kydk>rzOcVG*Xz%j}(M)LBgRrN$T1SnY}p*%ld_nW%x12SAJV180%YFsD%
z%+}55O8lC~ed-5f4kQ~X$Ro7Am-S7$uZ)(4fdhcN4O>`2qK!-rwa{PHa2{i&3ZV=X
zAJ-&umV`Rk37i#WiXel}BU8WgzhVA4N-FvlMRc$&fmpeD;018Hof={8q;BjYYdXXc
zzAbU)7}$h<kllJpE$FHAo(#P18dfk9VNgg;D4)OD+ilC7R5dxr`pQS8;~FQ%>@W%R
zOPbf#?i9oyHL0QTEfrbZS)M!?T<ys*G&L|V5#6*Zoa5)hAXABPQ<fo2mnXIRmYrP+
zRjWin&No-sFHp;}o9^nhGw+ivS3ZZUyFNFw8vuol^&KCQ;!el1OMX3KE;3>-a-~lb
zi2?&{>$U;1cx)r2IoZ5o4)K~2$v|bh)t6<uaNNSNE1FK;R&1<hcW6ld3WDIsy-ms)
zIXM(+_5lqI&Ged8@&e#}Pr%9JpK6w!?FNTuc8R*eQ+b+7T{9Z?6c)fa%v&R7(B-*!
z^}BEi%zVL${IP8is|j=${5#a+&}%wt#VPS>>cDX1sjkP1U97DT;~i~?pg$N6L(ndL
z$V_wnCYR2)-aBZRrTsff+@{1dZtsp}I<{&%RF;Hf%s9Cpzf32$n#Zw@=OOr2>y60`
z=n0?V1Q4y-X|@o%>>qQqws#0a|NNPUnHRY@-9oP%GEmPC=ef?y8r4#~XDMS}?wCiK
zX*KzQ=z=F#xP2qhxq72sB~@&wQu;a%b(tyt?8jK6r<&WzI$KgtcgDlRcjJykp@jOJ
zM`rg$&@H1{-^M?YMFnCjI`vNLoj1;5cp@v(1rhAIK^1{Y0ro)wDyKMfCSe0%1}2sk
zqxIs?<(cjD2JYa5wP<+6!t8+lO2VVaV?^RuxR1|N^IM@*5V4S6Q^!a9Zr83`+easE
z`Qs~FM}dy+n+)&7hPCVYp4b=4UvoNc1LBVuPG5>Wu4@k_x$W1kZ`_)kZx@Y&Q3vqN
z%wFWkA;SZb+F9jRpEkDr5apZ#MC8atQCN)Ai5%wVR~zQqY#q;U@{=_UblqY(JDx!v
zqen9<iJS}qlYf@)4Nfe5fkBno7agWWYl355q)96_wWd|HOrDb^csT>etf+(h@jVBO
z(9L$|+qZTPk~)Sh`d<=ZdBvkizd3&=MuUerJFEhunV<}_y?mA?@|537g7Oq}O6<X_
z#my_0ey+*Y@k$Y#&i#P$;vBE9T4M+^l&*3^rR^~h&tyx}6cj)tB6UqOtPC#x+++pe
zVWmGb6+y(WlX@3;H-%$+9*l_+Ze(YluGr-0+9<3HZe89HZQhyc{Q!pRTj1y8R6hQt
z^DQY{zx$5DHGBXnuFEtgJFikGkDRy|+T=YaA}~xKF#4@Y{)ekOJ83MoL$0-Eh9-Wk
zuR*U5t9yYb$Tu714BVp6o3ljBop?kvb9+2`Pi#v_8tn}|>d6JRWRb7e(8-VPZDbR5
z{`Z)_NxUV}N=(=+G^9gprtg9<^ZZo?KJ3Mk+u(6ev7~(EHdqf}2D*&sKhAdaZ=N!%
z^eSP=T0-f<(6BF23VZZ%m5;>s_sH!cesRFYa`Mg^uYWG^d#?1)RBq1~Tqne6HGNXk
zjm5>~3zwp>9YJebU{S9$_+_xnwP0`2rbu)dL9nK@N%&Eev$^o$s}Ikbo>n`X^JCiT
z@yW>m6)@pd{&SnthWNC^GcGPJiyrMhBYhHw<!Ekz9tVl|^)Y6?PPy~vg`wL~%PXmm
z7Agze%cL^Kwj-L;D9!MM543RzMRS`O%TN9u;3sl+W*prjquOH$dza5<psmG=hGy5t
z71J>`bsp2tc|U5Dymh{KkejgHT;;#wEv3UfV?QyFiCm4I#Emf-gc_X?MdAK}!XN2u
zJSFjE86A1ONhwPp+7BeD`ZZ>#se7K>kda`1x3S_ll>8R7=%WCIjOe^UOOAMm>C@K^
zS`P#DO<+LxwTs%5V|l3+8a0z0SRB9im;f;;giSj597;QYcNb|(KsQSh`AbdA4<B`Q
zSgIwbJSl<o*n1g@a-dJ&!G<t%lREA=;!G75!tlP5=py3Lt^E5$d{oBgwG`>CD-;hD
zH+K{_S2VZvI@@Ms$|;aP(e542Uu_qRou+w}m@!Hj=bD0_zv5g>@(K`U7tfEA^nxi4
z@TS+=w$&Jii@wX@eeo2`HhO)S+uq)u)Bl2sMV`lKF22}ci-**Mse9r(lFkK)*av8)
ztM1_MS3K52KjANFYE|gc@C=7R)uKicgAq!ZW}`)yXD=NF60MeL5!Tg&ir1rJl>Zov
zRyO8wBTQ6GkdLv=yQ6u~i!n3muq=OHbM#TtVNK2RKh*)D-#h@J3jZUTU5hf<qw@ae
zJjXKoG(*!<?iMsfzy>f(fQ_;66V|DMIdzI2ZO8Z?v5gCw4oa92cXp=5Zm<8^LgI#0
z%e~hGO0O-lg0LP~*MGJ=^~Lkohx8Zwr3RNG=JYJvz?sVO<+-`%zBFtXqPN1Hg{1K)
z$a=(z+wLRO7x^wM4R9(`!iDA29DHSQ++a-okeJUH{I|;3^oVUemuza23908ON@y(D
z+bl;`8*+UW-Wd@KjT1mtt8S=g`*Qr=`Vt?YYye$DoQ!*`>Ccj2*s}vPiyL;O3QYJK
zXzRit6{dD#O*2kf5=nIqrIEAd(*^v4oK#4Yn!k?6+8Fq#<aN-$PYWN2=LOz(vMu+l
zL#D-6-^k+PBA~4{UKDcPgt>SSfA8k%O1|?&MP*_}%c#N^7j6USh(r!GyV~J%{;tOe
zQR2f_ipXWzp@9PyklnF?LR2dKoafTel5_sfeZd&X0Y9}vhs(iss1!1V7}@+2xs5R!
zyrHkK&sAFUsix!&Ri8+(uZBBg>IQF?BXif5o=xMrWB_OLV02qshDQ@x<1gl#?K}0c
z-=B+yO|G98uR(Nk1-s`aO@G_u-gCyHh+M2H7AW#iHT@kVjO+gVpg#TTWnh9Rm@}wk
z;Y%Z}qDe|d$Pp6{%H#q#w2=Vcl5VHBElsS;W}L7f&J8W8P{cVGF0e!yA62qPrH*m>
zw5f6gyK&7@(QDP_ngUI;zTztIY*dyirYA8wz)7*wt)|F}x4w8PUVB7KBZD*|EcnDZ
zR5{YZV_L7Xej;uZ{Mc!$6^>53IYSc$Ucr6jx-m>ug$Va(cx0(!r$V|a30$98U5Cmz
zIoVeAMT7YwJfQ@Mf+eUfE*cf~xn2^=@HZyE%!T^j53ewS{z|*m=8MPpc6ho?OAA7)
zfdslul;C`JFqS3kXgiXuQ4QUfmtDc_2)S=-5ue>&pKr}99ksOZu*glU{;8S54Lapt
zEk6_iu7*_8v=G6;(NPA~^%Q6g(PY2Gy&a-4OD+b%p)ifcG>eS)U>PU)<+3*8vfS%u
zpl>LQUz1mA#5@y+n2`JN=7sWZ9<K>glh{c<+40MUn?jYIMkAp}nfSBm(*4G$L|Zz|
zmyV0Ok&QJwBWEK0Dw7gvA=m4?QFKG0>(bhh<zzZ_@H`>gLc}24VEy6LCpysFazM&9
z_al`p51w8j7`4;mD1g1_Y<99%#Hgin?C`!!$nm#dE8S2&_1b5kCmi_);H2yG_2l6|
zc-q3@(_<(!^0_$wHJd3@cr2CfcueYbUH*4BW~EX5Ip24eol$ZB=6=iQCN6>m{Qpt)
z)lqdcPn5Vj1ot2zXmEG;0KqM|dvFaN+)1z?3GVLh?(XjHw)4pE+dZ4pe}s4D&6}R?
zuCA`Sb+4q)<EBW7z^XoD)xpcj1!7B*n0nDGCvKPl_kqL+*_L4Jf+#r(Zy=b;9+KX-
z*IgkFy3Spm#FxirFNPxo@y*j!(m#i2dOtcf@cR>a+mn^6D)<H|qU)imZkGDW1TfCb
zJ&9>(F{19t&$`lkM{hEYagW;m4xAebFAZpNXy*0Rz6-Zaq-6W^=MO+sVEX~<;PiC%
z@Oo|oQHp(j;VX8_K|vwfBf>~+sFwVUKf*x<fHxc2r`vKm%@10cwDTS*-$H4Cr9u)3
z)cgMWa)P=xk;*CYnUv6Vdy1CRk-pw7@rhrJkr`5f6E>hjxaH4khU-^9L+}Ad>$@~N
zl)R#ETPvE)Xz0afomFJ``1srX_+jo#D~j6g=H}ghW0}3Kg3o^L1QF>>)Y4z9BTMTw
zdSs)QZApVn7DEug;MqO4S-CH)uOFLMm8@6dHX&dcUwQf?r~re_P9@0j(yP!4@$!ni
z9zEyuXZxBDp&ik27@n1$?F}0eRBKZ=xP+Oc9+aB6pm~6c_d~#A1a@nMX}rhMy6p-6
z{RY(|L}OJmtdDsb5yHzx-R|(rU7|heMJyC^l&?IaHH<T|#8Rh{QPEyv&5)Lu`zWr@
zMrRh{GnJRLhHj4a&ruR@-68yz>}|Jg>3T$&(s{Hnhtw6?l-YRz!w;`uD*2SH11OBA
zC0ap3%wh0u5q11b4kBcwwP#rh{ED|5Km5C}Q6fj*B%izB2qmCfDRO0tP*pdQarfs?
zhF<vy;q{4lP!9EI>fEf0jVBAJaE1be+;niOsGUN)%jL`F#EkMPVst%LR(klcPspSB
z%t>a6vxB#m7cMK-5v6%=6~=OvREm07g@1%CE?U@=sjtmVX}qaJ^s=1xqLfn7_4g1L
zzJI(d-Wp&K{f0L7%leluDtLKEwm-LMK>AY6-^lBc&W{^dr6F8c94E^Jr@AUlbq&7@
zICG6=+7mY)wkQEa%oY66@xFI;GoD^UC(Qy85_=TN>G8hw6DMKH>vf-ZK*z%JWT>np
zCOiL_&&m7_%avO?8VaqHzB2#|GVP5}Fop()(>z*`Yf^#R1Z6!vq3F>CWg;`#z7nX$
z`f|gW9pA_3mr`McxQbWRXn&)#;8%+Qf^(#yd41$A4E({clzOp^9NwP%rhVnWqyc!V
z->;LT@e-<WZEwG{IC5gLUIqzAWpJhc2Db%DxrYGW-!s`zfQTD-pV4h9P*s{~*`!BD
zVXiv({!$2$-G(0_>`YJsAkHkr+ZH(qY*RP>__=&cY*P4F2LTZWWQ@|WkZnO<2X2?{
z+YYyA+jSgIE=&+U^n;bGA2_bVLHCB~21K*zhZT&F(lx6zVNMtV@9N(-0LiQ~y5HyM
zZ#64^`S51+&gLw3ZPeB<BkLw>xSz;evNOh)EO&*3w}ns0ml3nnKcA=PcD(*qq!SAt
zzAYr@(0dg5hJw-m2w}R|EZ|YY!^_{Zpn}@7Ea2U9eKp8upRjM2|7}aAW>p`|dCe(V
zp<oBB{t($!qUpW=iI69G3Sv`Q3^=qf4xUX6<~uiK`-NfW0L#A*a?_R@b^ppffI>0s
zH7nOaZ4lW#H-_2i&2!XgDiJ=sbLyqQg<`@u)1WN{Aa3@OK~nPo8Dpn@*?&AKeaP&?
zS;eg*pIL=BcRKEhq*-YA5+r{u+0jGGo0{P0*TQzNzGxLto}{TJ74!z?0O2`cffC<K
zu%9BpTQb4{kK&jb+h}(y5zw#P`zS4UsKzOcASaEm?Df+6ERQ+G_|e5@?da%yR&|J3
zX$sNyM&vmwBZJRl#9(IG&8ytu_f*m~49$nDJyLREOGVXhf^<gY$N`Xk`d}F!2G6d6
zMC&FkN`L3iEVZ7F|9~z-0)UafHyuF-YH_Ay!E}dxZkH>cMb6=?h@Tg`X|Wf(2A=)S
zUOlg@R`rX9ariYpSzd>skhtYNFt&`7x<9T@>LC6IPbwajq3w#@dk0=F9$eLj6rQZk
zBB0N->M^%}DUnEDWuu+&o*UNzX8qA?@Jk@ucIDH9;ML^hsf$PFhfTz=i7dpH0yN~N
zma}}5+x<%7H2F%a%;J_23+70TqnPSGk_(aBNcShX;+LKouvn7W*`G=DRf}|HW`ZhK
z<EX$X(i))Vn07|4%{jh`<pJo_=hr8evS3VGE5wV9i&TnbHX9`MA3%t_(I50cM<w+U
zAV$X5)LNGJZX}hY-P+)qJY&9;xSd2jGu{6fOey)`>m6r1oE4p6c=tFu>wUc_2W~Vv
zZuW9GyR0>{g^#qL;l$<=B?(?0z1+K-2w||!$Yh0--hbX6I_`7lUCHFMS>I^$@nuP8
z`@_>ob&IL)sn2y<yPmgcpi+!{>nXb0S*wrB$#yMlK(q7ULTaf`Im5|$kLu{`OR+}s
zVRtcfchBqNcHkc|cdPBdt3WVuFUQ7Lt=D-DUgnz{vC1Dx1*@D{O|lXY##|Z{zUAuM
zJnFG*5V*8o7*dTf`s5*=ic`~0`IObX`oGWPMl#!1&sR>!0=(Qio@ZToMc%c=gZDj2
z2QT+AVi~Qugciv8+TH%|OU5P{Z+|csRr`3`ihW1PbwgzD_pl8+emOq4ZmnV=lEdr!
zk;9hEx(*N<2x5K-pVTJ$^}JQPtk^mhN1!Iv7~*pq+_K`=mdA7TSeuhz)B4v8`v8Yw
zz-Nx_Y-}~n+uT(4S)MZ^QU3J(D~6+L5<%)AqUXJq>90{_cYobHJtKPV+3fqCTSmoJ
zvv3oi>tZU|FW%8W9!3k|T|JvQPi=j=y4Q%97b4f}q~R;DR{KHmW9{@KYa93?+F@+)
zR6g3Y#f)UP)8{FTDBc|rmjqkgxXQmPFENKd7_~BJXJ0S=5P#sXciTnou2i&fP#fq7
zE~T&dW%!ySa4#ISNI)PwPt|Sg2^+2KYu&~KEx~p+hdtkgi5U1^?igc^fRWa9uY?&3
zjh&$3>Yn3az1E7^LcqB*yq3@9_M!DcL2lKpsFRBuIu9rq#MHBB<9S#g#S*xn7IWjm
zFjaTg^Xawzl<YXfbzk$O=3HkWKc%|7>RIye`fNZ?cWDOGSgyGL;gZzPiAph1i<Z!T
z)JG#}B(6EHzPPl(LS#B&fI%N;7-n@%tKh)4Si3-*6Yz-Ap!Oir{tdNM{<-N-ZkG`r
zS~w^X!>p1IJ{vyzt6XR@a9d^jwk-w_l_IZ-Yp@F65Oh_;PD+XMCJw9S{2$VK7sOt<
zoSy+T^>?sSHj|wR_zdlNB*e%>)^_da+$F=Fy22d9=60dzwoOg?i`?eSrKfn_x4wX~
zk0p7`V#%59l6uL{p4A1Ww8N@}XsYkq?<cA`0gb>)pLlGK%Y?xDdd%!dwzNF~_vXL(
z%d{tg`5%{45{4zT{Wxw=LVrcsjxN`<Lwq9S%xJkC<|_&2*R&ox)IJ$YIqm+%XV?4P
zvUVrCha`OXI>80z<k4=wDBF{Ex04y3BF1;_YVp|0@9N$1O2bA=#?k#>a!)M`2^lZ7
zyIyfRdim!cKfTPmYZy<wK3!L)4&rs?uR<Q%8dlXEk2!MjKT`QQkuhxw;7=HDq)Mn_
z_!=^eppN7(Wt_2CTA>z&ipdNN+@{8ay=<w;x9$Bvle;)Ny)VQRUMkkwxqC=D5alz{
zQt&x~y_=A6K&#TQVZ`}y5fM^#HR7F{Cj_;B$Vl&-ax&ueY5VCcmv*~n0KzE=tu4>$
z@WNUnyNT-?7uFBnn<FmcBZF-gD*uxg9_$a67)i4Xm9Mk54FS4=)!02}`b-y_dM=3h
z8mf7E8pWZcRM=J>%0%30&QcNAqH&MiM3AQ>L}HHqx*iq%$eZ*|N6Q?;b5CK!Xz`De
zBn;i&=AM>kW4!|{cdess-?Y==NcBxi1@;8&EL2up!~3+HD~}U6V3$|sw1|n}tDPR0
zIJ$ac^_t<vuAfq#D_EMAWKS}H<wpVm%e~Ta-2~QCR8!h?+P$feGkO)viJ9qL-q!!%
z>Dpa$nm)%ezbsqYdqAZvyyUzG4^m`O0ZLQUjTu#*2i>k3nk+M7hxkA8=XtZ7ZyT7F
zPCSKC_I2b}nGJnw-Aq-eDTz-?rq<fmThemd%R%(YYG>3vsy7f>vDJ;RCeUr3a=uK!
z4C}dwEkEl<Ym58Fufb=a{Q8hE_hEBU&~Zc(jIpHLdm}Mcuj#|L5Yb-S6Cwu>;fl=b
z^+(!aDqD)RX+cPyi(XV5wM%Le#@EMFHj#5~2}->^g=O6zTM8f63jOMyl<ZNd>Y6qi
zHmU~+Wh{HY$7R}6U=UwNkXI$R+SzgLkVc#`C#vptqP!j*;vAI*)e}RgqdY{IBp?or
zo8UaLQ2wG!MzW1*d%~PkblVQ=qz`#2Vuk3$e;TVPZD)5a^V)q<FqfAI$j78Qff8v$
ze|XfYZJioFb9mf`8fHGhZfg9x8kxeb+u+(g-*n3p3C~#h2J~&Rye`7RzZ>)k|JgBB
zS#U|)elUV_zbZ>^H=Nj{s6IJ%WFvsXLZRD2rgn5HrvKHAvKT=}Q<ax0d>bYUEJHV7
z<l#nP!5;oPBvlHsQ)z@ETj=rZ`HKT@ab513vUTl&_Big;fZxWi;YG>~hhy$FEEcz?
zdPj0eHu2V%iKpwr3sxbmxp|Uv4_1ca8UF4lK4!`1S&qaF8Sp5^CeO@c*K9;VCrxD5
zo1&!bSxe(<+Qnx7^=QS`zIjXLWZsjx#Q;WbnC~nsOM_n<R-fBLaMdJNTiTQL<(I5x
zl(+pUm~fzee=8@z2Bfaw!pn`Q*H6%;$VR*OE@!Bn7{gPe-70cjHZqL`)>%eg!bc*Y
zmJy|*?sPH5y?bO}VV}TcF=Y(Qnq(k;iUCQf$`u?_T6ABWtCU-80q3sg%J(*G=<N-_
zw7U)TzOI~3erkQqs(jWS6241-EwoC!GZLtP$BJ+~3Vnfo8LRnTyF%c78bVPO$<gCI
zby{DY(_p34SiU#89mAU9K&maj>#O~GV7gh0J&0;RQlXu00^X=w?sq@9Y7sF0xa8J*
z${S3)qn!`ykNz?m6C<=G-Z34IUq?FYI*i?~illbz^CZNApk_T%_(4t-(i(%L-44xr
zgj0<8J*zmcX<@&`M2ge+Q1iwj)RdNNgCG;#(b?@vjUaX#dHT;mOcpF^n?zS;psxTA
zkFc7gcCx4OIPG8imy3b>j4uNc;pY0+Jz*V(*sGSQK7%w8BY>;lgdusgJKH25;2+b5
z1mEY~5$q0u*G!Asfb%H>eHAefk6Hh6=>6|2rF3S+%OrlC`}xweSe^VZL?n`ofwg@u
zk|zzWG1gD*<nGHg`OPu8^C@OEo-xNamSJcm8r}z!BpT6&A<qZn_`~=bkP_sR=Yiq^
za2$bG!XHQj=CTDWC1Q0w$L*H?+;hlbeU>Fw)9_uohW5hQ(=FH0TF|j7!=-aDMDNE-
z3K4zoT^8~3Z<i}1`j%i=pv9VO!cwn=ElKJH2Pa`R=a(7q`7a-nm+r9k5LEhT*)zg5
z;^nC}QaisC=`#>x%6;Y8K%%B3wOo_ZI)j1F!Snld@yVXD=@+JKS?(%hBXah9n_^l1
za9Dh69N+g3$|HL<Us>~LNHERgs-p^fN2YmRHq^EMc$%}DXFRrB+&er#TY0Fmd%yPe
zS<hniv&F)U(1(X3Nw$n-3qw*fvvsQ7tBunQ*wMX4={b|bB<vlWnbT}s#pC0i3`e(I
zVCz981(nYlF&$R%UBt&jLs4KRg_vCz?!oMP)F%CCp3fp)mHy2%Y%-9pLFLCvM#>{B
zg7sCV3{8v`>2Lp{)COz(1dh%6Q^osGtNAZIAclfEwH^>}p%IfGw3ztO=DUiUvHo$M
z(hSz`pM;gXc1?*Ky6B4V`fXp2O^H@t8!2HryD-kr_CMEqRSTOd#3ePMI(OV;CdZuy
za8MU}9xt~)_vX|MUzFdT^+nzWm#pxbSj^zdE~Jth!9?CQ|B4YR&L$PI$<cu|O!=Wk
zSJCXEeu4U0=`rBaB7nqrzS_#h^b@RS;<tzWK*`8hvxz_6jjo#kCiV|R0|?yGqRQT=
zu^HN=In;Dqtr#<)qnIe|(ioCl0Kai6`B?&7I0e5l|0j8U2DmjI6z}#=IQsLZFzCq}
zE<P~D0m^SA!dKM3;rwO8>@`w&W~hWDf#csgWF_k!w-EV`mt)-~ji$(dO&N}+iriZT
z-_DlacsqE|3~WZZp!P6RudC{Ghts!(6o1j=%qMv<D)4w>-TLLX-iDfSf{|3Kr&V{l
zmnX?~Mbf&rP&Q%Tj&0`uIZ640`I@f+%P&dD*9%ITBB!hKxfcs7q!S`IK`@uwZV1(W
zOhGa%6gPieSDrBGqocqRF(=ycZnb%b4rZeoW*MfTR<oM}9>^^FX^1$ceTB;T01;px
zoCp9DMJE^g#;x@Q?e3#o^xtV#(H1>?@5zHdcFg%8Duj<0gh@cSO$NU0;F0ll890qQ
zp4#diK2KR=Qq1yA9{7#D^Ic=|yd9>T^IgE6?o@bg+5HjWwkh&e2&!Z0BXNFdWrre{
za!d4vz-#U{i`Pe?M-tw78UxXGFMNFOZG%UF=Q`wL^xuaPtp^VS{z`LY<&gNCwUR#&
ziO$5tAHGEjBUg~=xgPOwJNy-s_75lp3zEnwo8uh0zAtyix^ReZ9VdSwZAxnnIUuzD
zBcx&)Hf}H#MdP{luuNjm|3ehj%xx?F@bY!ew}WUFr#&5M-e>Y1w1Pxh2|9F9{p90}
zhlqpl&aqmrXMOIx>`*`kMRX0+8Vb=eWNL(8>BP++I|IO*m!d{{-4&aF)eru643~x=
zSx9UxW3Iu(UDPNaS98NL7Ug;wF+5%`Q$gOpJ5P~8^Sftp>2YHAv~PX9yg5G^5O|SG
z8YMy3;d4^^`61`*^4P1>P7NDVkg&)MX}2lxOL<`H%?TRP+WF)p!EZk{?q(`nIG#t=
z%;c_wl;;ad^W2jH${M!oo9Sz3Emk)4ELlXc2J5tV8wB|g;#Si>zN3rA-`?occvP#}
zGB%Nv68YZa4t;n5Vmhe~D5g0Y7;Ii5<wN3%9SMjzP=j_tucLa-%@-rTUD;$TiaB&Y
zB}Tjb8XiLh$%g+6gJ6MhxMZFvasb(v2?Sgj>-xnS^z(dFHx$66TI(|r^u#@oIQmkK
z+Fl|$94w#`p4#?7ubd3kS?9A`Rr~Y93EB30pCy*M&1ZFoqv1lw8G6SLrz1Y|yQr^g
z`SPC_kOo~=DU1&T!>;{Fh*(^FPR}EmSdEv+%-0N%kE+(Ajga|I8^TpXZo&hzNqO7W
ze?AGkR{j033dV)7c=RRZg5O(aJ<rx@js+=WH-su{cHf#xi}=N~B9o8<g#rEA-E;d6
zU-H)HIi;HxC#svcGfa$b&(`N#<}&xpF>6Z1X$B|*@ULA;2_muxTUr*Pf7L*O@jS>5
zme1|<IS<VbQFvNs&Y0X#2VEDf4RJ~w4?#7Z#?eewd#P~+W4gw1+apSsYSsGmQwsA;
ze*QjG{8sN(CJwGB;c!ggp*D;bXUG-uEIxb467tCepD6wYQiP4?qWW+0^4*jM2gZA!
zhfc$f_?7rhFyVg{)i-;c^*%|_v?YuKecBpv>w3pKzcqfyHh5s=yqJ6yL16rAcq6?b
zd2k11|1frNMh3=?cwYSX)!}2=7HUfq|04Ft_21Ms$|&M4Lid-i$^)hy08^2y;9YNE
zcDm*rQlRh#W+0%mg9LM~p{yLY)rz{cuJLcYB?Z?CQB~c%GM7mtE1srZU<5p^$2Wc@
z`*E}@W3D{(+cpL~RBHjz@Igct-DiWCyAifr#ZCOkyCuaAe65lha%*#OguFUBMYy9P
z7I(;Ty>G5?G@ipDG{tF{yHujb3r!{#F<gM9ZIS+u+Xe{LvH5Y`(|#?X9)1A@K1e6w
z+g@*co}`eo@H(^ZI5G;;s~@0YT_G3?YT7362vBF~e-{6c7fILjNS~pC9|>8+vq!ev
z!cxc^7i|J(Y)V`9=3sv&&#Bxxwi*^mF62^bHSY^n29X24wPa{;O<z;+h$v9lPY?qx
zIlRH=PS{!|mt&-WYqA9KGW_+akK8C<N0Uc};6hd+wf06cOeC8{R6JN8L0p!uPDH|q
zTdxfk;Ef75->Y^H(amA|RZC<4{}>d*sQ`;PUK$k#FbeirK`<@q<~+PRlwhU0&etnv
zwE~+V=fkLhf_-io7b<N>i)-O-o;Hg>JW8DxKu!h1pKZJtd&lC0Eq0&H@eJ06Hp>VB
z-YU{-AU34@io*FO@J8w<3We0;%QuT?Yf3|CC|WwMIqWRGD%#~51w@V<K>UQ$rrzs>
zu^71oayzuPbGn}^?Jjnj0Jh2B><~+kMKv4)*P#CU{(`#`@is5DZG*fHTUBRoU0uJ%
zZL--;)MqPBvXp{_AdcEyYxk#CNEcljb4o_t1*Si8FDl}7m<^=&YB}nPg3aqu1n_vn
z@M93EJB%TdZ}hEnl)hEsA@=W(V9UJ&>c4lg+&qY15kqywW{Ctta7*}^WI?rR41^8J
zWB9eVw`aUu<qAIl+9JGnYyMIP$;&y2fSe7=wu(FVVnPzAKrb&HjJ~bFr(2s86s$GE
z1&4BWzSog2#XL|e9RC3~N<NV=V>P{vE!6<%+MwQwJt-k*1L72-5Wy%!vB<3eeckb~
ziiA{73bxLdDF&sH?4klyw|-`z{|A6$R`~MH(eG_-e}c-okKjFXyMcX9uA0{ucX;oq
zTLuPfylO>knyfKQ6;Qp#k`2Ep871|1pspn4{&Gg^Y1(&Z;lt4t>3vqI5G?Als4UfN
z6+<rEzz2fff8~4`#wNwPgZ^0<M=7ALBBZGW7wS`q{$1eiWf!Eyw}n)Qh*|nSa6vpy
zV~q78hxY{52AV}_=zi6fvn@bsr~^)0Q&UqzgDbmtp7R+#S$0S3q`~%gY44$P`%~eh
z+{LNvLumjDz*?OA4*aE_iPp+9<ShVA>ISuTd35f9c8Z`wUd@<O`W4?o)w0|?qUUT6
zO$n-#NYiq3`j>To3YN!!5`>$Zo8Daq4jTBNNhQ5T1%(WaQF{eqm`tU9f;KrYDWQP*
zNA273@!z)K_I?fV;kUP#vz}-}MO&@gL-0!8AbsS#pH3%!tAgd|<XAe3m#-BUI(Xr9
zgZJ}8=t-G8C6s%^0y-kTn=h>;_B2EOtimP%M?z8RAh0gS%s%+uEB~{^(fAPKoTDZB
z>I1ASfuoM!;SHjwfEi997L4NhzSFyyKKSn%RGTa9CqGFF2%Nq55|M&1w#y9(;%i-X
z%;zV9r}YB7k5$QTgFlr^(18lqMP_@lR2HBMM{stFokw-&H2?Y#Mh@0#%R1sHiBV?K
z*m;!f)O*Sb2ssutG+`8v(~0$b$8bh5%W81PkE(!&*B1PppKsn9NdyTANkl}%*mU-N
zbhmMhosl^M%&K)jj5VG6Z<7&-Y!0+gzr6ma2lO5Rbv#ChxpSTkBB3T)*})u+ZH<ew
zp8+%nR|~1a#e90%(_-IS&J+Q;K560FBl1BwR#w(NS`;V<fNb%C67c}A(NOV-<?47m
zg8lx+7>Yn3T>rY&u;h)#bs`w-f`E&!9IBP+X+zfL7aq-LCfRnXLUGLY6@94Qi2#N>
zLk=%RJF0!D-vE<cI_?Ifnu<za5?!8u+s3=X1VkDdS~cA_7EgDONqA5jf(E5B0AWJG
zWLkAEvG1$%r*~;1N>1Fx@AWXtq-nm3fYS(8b!S#{v&!yq6S-@wn%rM(1F|R7@~LI&
zbaRkawTqR+p$lN~UuLx3kLBzFZt8Tx4%8U*8ilNBx7>jRfdO(SLV`I!h8_@K5(2Xs
z&2ITD+AM6^=U~L195-&6#a~9Eo}z|fA0_Hp65_(Tace>3rYXYgS&WH1=z*soSUS7v
zc{$9nWCuCa+W$?V&z1F~X4}Sgp?!gwkT$>>+lB-;2JH@0HW&Xd4TB8@kqNexp6QLg
z^Kmwo2lar1U5chfwS>J^(w~reUB7FdaX#REj0T-w6j0(1^<5mQ=;h_5Nb_3_Jv-Xj
z=1|QS$7W#pk_sX+`5*xg4YZwTFo!1~AdCc7YuZTD&*PoTVyo^|-S-aZeVHlihNA=o
ze=)t9<u9q4^?jsHb_=pKhk9b4C;QyVQ0VE|*;V^qA`1<?S@id42++4Du0-(BYd@7V
zRm<-O4lfYHqySP{QV%%5p7NdkqJ2AOxKaAbwc2@LAIw@*k&k~KAe8=8#s=G7&I<E>
z;=PzS?E7qyUv{p#_I71RWOjFFUo*Wwtxo1D+}_-n^mTC!?_>C0S#y6wdLvmpv=V6W
zId#e~;sGY;7l3O+wcB!w9Mmz=VYs$XrzswYUDIOm6vL5n+{w0$0**b0u&*!EW>x5|
z)VxcODNKA>lSi=B*OTY2yaQ5gq(x0e8qiRh_zJXY;|oshe=e{=>^%hl6=2c8?0^`E
zrCIPJd|Ub0zF5h7^GVxC%3fdkI&()Ly{6+0FKi_AAkO=KJ(KuOEO+>bGiC}?z1f|P
zJ+^Z_FF#-EIhE5t2jc@B!<U;RJ(aBgR@lT|6vlMr4#b<kKmZ5T+5Xw8Zd&w;n-3Uh
zze$^E?q>E}Ma;AJpP4Qw$e2~T4!=jSa=_#+r$~1PNXy8aw!Xe(OGGVL)v#I4kYYQ1
zG->~|8{HP0U>QXMC@sKr;||UiWdN94fXPts0XW*qx4LxTy>+Dr11?RiH6Ou^&C5YE
zTPj5jNzW`tdP1LLZSObCdc_)PgjWY|MT(%tRi6!vg>Lh5%w_rLlZIobROw=MnYXdL
zZp$yV!D`@M;Q&iHFA6;Ezd2<h1{NAAo>illr#I(qI^F9jki(|&^)AA7St)$)w*UYW
zrYve#+Mxi6!hWRGXa0GpR;;|gQAY=W@@U}BaGtPyT~q$ecy6ey0~a6yftTYwS}GG3
z(XLr3H_@i6)^*yQ&$d{t8XR;|x{G(-`fpRB_>BT&_zqm7v;hKAfO9HVkg9O?aw+;_
ze`0pEs4>$7^yBY<Wz8_i1@-Ldbla}~@}0mw%nlyp+;?=_I}fU%7aV|>#EbG&nkq!9
zdXDrDzEi*9H9|5;-m^DTf1_Roe$Ijvm=!^_eQa;O*8!a50ghV~+U2}WO|A{T6p@Cl
zV6vIDO$-(qErxjV-kBZaQ&t=|4A1{%a|FbP8U%B}xP#v~`lr$C?w9&J0<<MU-2Y7H
z4SZ1#`#n|<hj|=fA`{yoD&YiEJRMo5;q*gw7?lY}_|47#$18dq@wTQZqFEtUd}m26
zvKv{4Z&ShprG+x(c0y(`&m%25glNpmJVX(G8JC++Fm>BACl2xd8!1V_Zjgz8a;Se3
z_)Zpq0O)$)U6}w<!KaK}yPPSP2&Qp%8h-3p7!U1ViliHOLVbH?e{`}hs&mu%P5(P?
zNC7J(RW$hsaPEAeDuM;OwjIA#12Ky7(h8&b@tpP<$+ldfnjBw+fuCF7q!LscsVqs2
z`Wttc|JlwdkZf78ZQ>!wvGwDkSUdL+i9xG*(JUupA4CD{^mtLiQJZAK7J9A<e5;w~
z1*u;+<=C+m*VsAx-&MAy*z&NoE@~>pbTzF+Wvv)3<wPwWd&HSo!5I+!&M&p$z_-mH
z7LN2Ff#XA<sQ8>|0(8qSaI)slhkdg_j#<w7wMN)Ma<~cP(lbch27pX7A_QZa>-Po@
z`jxIFSqMg)U7-jQujwxY1tqB|LUXi0X*-a}9dcDjeM`CLpn^x~Ej(C$Qb%eidZql{
z)Lx@qJdJ+dkQwmjxIJ40U58aV5$|(_$~$ZxFK-C0xGfCd^;;mcAHx5YdP&iZG9sX#
zG8LtHo!*683$^AHi`v+Zy9sNA><d)Ii*1sM-|kzoJo+cd{?oNFJ!ys~4r#X&4rvzp
z!-$*hsmIeng*o#Wey$+($D_1FiLM+pLgyTNVaGyu&%Tnwp13-K)w5U&I96-2Z*po7
z$=yxaDBAG@KmxpiJ7}P_^P3ogxRoHx?_qkP3GY@_sLQG|bgEq`zUVgzzItr?9IjQ3
z#km)FXgB(%F+LjFflCvgA}$gDEg5dZJI0Ur^A(;2!^1T7IadPaEEJX?E5rOO%Y-)&
zNS>X`ddaWHE|G6{cD&-95}CXP*Lcafg#n3E3}CHlTx8YDzIhiA;67s{KLXGn2Rh6Y
z;x<JO^pQt?>p`}fwQ|((;R4_;tRSJeXnLVaYU(bYePOU3L0RLbhlJsdedh77<Y2|S
z$<@aPC5g_#<6K6AHYYcgq7CB+80ov2fj<N0LXew<$eyKs5v#Q&bqa644g=9(rA{&X
z#`aASjRn#28}(T<Eu+5i8$y<*Km6wkC+I(#TIul=G#J2{@T;kwYn|ExJt2z1Ij?P8
z8zH7|gj$G*u_T2`i_??+=Thb*Xu1PxkCsqq`JQ)FtEXvm*(leA+V54bx|<mh{A;wM
z(pEl*KvIK|a{vmU|I60I557tL)RUtj1eZPHGy~<%_4p!Q&mCu$<@*;uzPVA(Q520I
zu#%Yv+qv#(8#yU5qW~#OEObFhif}sKfNh#K`kKM{k2$s!<Z6YvcBBpKZXMU2w_WK&
z-(1t}#0I3*YZ8E{V7Sg|9(rhLd@X>%nFeWiKhyqi!{LHjdkv42WwI(5Vu~l^Rld&R
zAl0ohLUYCnacYlsx#|;iJ=5;ugZRQbeF?x*q^L-5ZVeoZmP*e;dj5R;!#ES@(?EK<
zZ9IS|K_*Y~(KbID$(p2A{411d??D{`Mlw3EOz_qX3_(NOrwh>%ZB)WaFf<=V3Qs#L
z&Ew~Y@a_JOre!3ITh1E(F;T)(R@(DfjB4?PBm}o}j1dHo4N5(SD=F)^<m&ItQFalY
zGyG}q-D-!bnz4K7dZwN|fv(x~5FTmA?j2D?=C=>5_jD9Wkh%@2pA|LO>n`9{FETp5
zQte8B!v_?j=y-<$zS58IKjYG$vvoRSh344k>ctDEVUh?vk0|e<0wkO+9_1>D17D?=
z4A3vRhW~P@P4=fJjJy-NDMSF~Yk_NoHq;v^=M#AOBOt84pZrH%<AztK9io_z#JK-{
zYBy0kyPN83D=gJU4(b4k6saYAh;3rPqYJjMqNZ=9-Muz5pl2cL-<1IcdMSV~I6PE#
zib_O?$&eufoFrF3u~LJ6K;MN2xpxK?R`dnDVFpuCrzCe^*C17;cy2~m`#d$gukXQg
z24>T?)tQfcndb_*pB1nHr&`;l9=`cl^Ju@JUD>Bh&XEj^H5_w}+t0XgAaF~@&q7e{
z$Ze1(Xr#14VvN*B^;Ro=2PGs)#YrtWS_(La*nH}w0OZCUfz!kP7%VH21St+e3PrF<
zh%ZIJQUYSw`weEvrLmDZn4m>qI_ZwuxgeCwDE!HSC`-*j`}w~%319_yb^fPEp&?6(
z9TN&4t#roXE8Ee*ga5fNfCe}5>s)X%L&WU6n3mYS&LVRDsHt#({Rr57K^w3z@UG#{
z&#2!1@)gI7JkTpx#d@V%gN7?C<wGUQrc7a?>s(idSa0_zj7akAt9#+@JQ%#LF1)Ky
zdaB^${db!NkdHpg(dqW)?<}DC?xQ=7ulw*$`1@|%ho6m0W(2GmrRTxixIuX6b%nxP
z5ZwoTNy1ar`Ks*|=zY#j&w-TNtF=idsgDhXt!@odT++$M9cFqD2l(azpi^X5hxETu
z`~<PS2cwVwt~Vq{K?<Wb7Hs5o{%6~Z8l=PuJh2z`(jxZUBZfSxjrvj0wpN5?i7zob
z-692a{0>O&jt@dJV#n{{%ZlQjnp|!)eDlD`oNn{pnc(V4`bZbi(&xslpaD%*kBy<w
zF8ZYHcTd9&^gIm<8Rj;2Fi-XomPGZhP1grx8Mg{6ZuBRKo*LGp^#x4@y_@3HFLq{@
zQuh~69nW67ktjF)*6P5dQv_a%>V!UU!~<MqeF%t8h-KJ5$QP2z5Di%lml3FIT~ES%
z*6oIh9gPrZokYm(s4HzW!;AXNbc<H%$b)Cwirt!pA_YS&hWh%XSO{`;CmS0Z=XzIA
z5Pl^kCGG7(05});r>@SqUOBI5&a$A&pbjq@@f-np;&(2it6f#cTbnhfdxY%H6U?It
zqZQQLX+Ml6Q%cneGc4^W?FDYTXs0zOIG87}((%)FSWmNw^+dy-YY&fi(uL|o^_%x_
z>;|Rl0Lj&LgFC7VaS!3f!qAn2mU*`|TiE#&t+go-kZQzXXv`|Am`G>&1LlkyVa)#6
zL1^ydy#e_QU>`|JbUc;69EVw(`Yb!)ldF1D%$iM5KLyX`OnP~38rS#51lhLB?o__-
z^l7$X8K|A5d)PSPXjo#Xrv;%#jeyz7jPO4$D=I3q@c?^~L9{W<O{qprFZ1e_tGFFY
zfzY3Uu%pmX&4`qQyfw5_o>&>2%?h2_I;DCJq39;-(@ZFO1&&xb%gj3_!n&omy#g=i
zMqUC>XPqXO(Bc<CK|!;+9@b7yvgySdl{<-AHb0AC-_6?QEuCflnbn9;Dym*3da+Ig
zW2kz!QnOLB(9!S-VmbvfvyDX}oom`dsiZ39$ffkr^_zFKcBMvTH^CXd+giW8X|Q%^
z2l6!s1EWq!QOqFqNSY#oezEvt%(P1pjoy0>!S#y<TH@t<BI9AY0g_^^@45Qgfe-Yx
z3yfNdeuI;pm>*s>oEV7jPsX2_ro9cunfunFX6Wgw=ZN_ld>)$jtGQFi64Sk;Y`j|)
z93I>J7-{UJ!0F5Y@csrs@ze{x{tu%l$m?gPz5vO)!i>EdIlC_*s8-hI)SbrpsrqbB
z@$9a#gPD-qk;%zjKwhV{tLHy1fMJ%^ZhEg_gy*d4hlPZPhA$5b)6rx5weed+lDU)g
zI{3C~g!uRe$H(3D&AO$8J3wU`AoQTkNytD;TUcBih+g;Sk8%5V=mGY5MTT$jHhSgF
z(wUmQr4I{~Bp3&^nYEd-)5?j;s%m9pc^oUvCnqE)FAB*<=Ws8`Zf1wO7j&^YRbF|;
zv(vDYNRH**X7#q4UaLO49_fOzt(o9ReI2)=#Dl*l8R_$TDV?f;7acKZ1Kf9X+QoUz
zs)Z7jg=^xQ=)4K`c6A_Sn8W4y+Wxwb=ZZ$H3JzP(k3kJ5&h_{0l3UX^JGG6A0$QyP
zzb+1DxqsOf6cm<qH?jPn$L9TFRL-vsRAW5#37)pJIBrZ}A~-ilSQ6IP@oo}wv(GVd
z__L`qRDwJ@(5W@29S95p_7n(teIHlsgdy@VmIb5sFK~+VoJ`cRHyG*5!s4yxuyew>
zL4s9iCb8i2bF`wLArz5CD*Yk7k<hS|Ro?hhoB5}#%L<Jb(QjVw*T+>6Fh;$WC4JmS
zvfz`zW1I}MA(Hz(3DT%@I0}s#FH9(!M?mv9blWA$X;Udwo}txqgA#5E@)(xjK|XBY
z*Y|}-julkx>pz3;qtXz#S2xwoKEoT9dbY05%`?qe^8oU`wdjPovRzwE(Iw0DDA-Qz
zlA+%5v$|S~JltBRPVkl%^vrj;=@h$p_Nkk#7ix%g#H#WoE9}5U3+&Kb_hy?qR>O?q
zx&R?p>}Im)glT<TyxKuEr)?CN*VauEUbh`6*<q66LOnGV42}R^yeZfYG7YfJiLddo
zegFrEfKyex20ESsH)-smj-d@=R%`~arG0Ok6S$)IckB{`*n}5lMMqdWS7&Y(w=9=2
zk7Kw;!~TBNky$B03A>+Yn7Lz^nYbB~N!(|cdcj-`ZLHV<)6Y+s&^0~yCC=H^$Y^Uz
zs$arovnS%h{j-^sRe&*W?A?r(?Yj%qg!#YT<wm%+!A&A)d8HZN$4;mF5+%=;l$7;H
zD0LYxYXG@M;7mLAQAgk)Yg6|2gG<Wl@^Xci`NH$>O;RW(e3hLqAEC>hLbT^J8<Dru
z$BC2Owg;w-3(NCyfn=QrL+Akx(abJ($mhiEcMJpl9OA9uLc<kL9Xp?M>nQmLt#2f1
zbr5BaT1j5POw_mOKeu=ab!X7&9U=z4Y%FucYk8LY*YcNwnP~O*if8*hbnnJRP>*m@
zrm#dR6&?>%d{kh%Q__mdYu~jG{8>9@)gC&)(V!Xp+)_Ab@bS6Ulwj-TAIs*O>dc$;
zAgLcBT!@{JJCSfX6Wk26k&2_=*jUg*1n2f}>H4~EX23a~6+gnJolzN2$mJS|VPQ|?
z*+uu~r2Xljg?A0H_&T2hYxMnYgmE^E$Pm7<nOAXpY3NjNtK2vO<R-~(v>!hX3=Sq-
zdwD6LEk8Uw)akT?mOo0Mh`{14Zd0U}5Q)**RT9!NEjyA6Ph-3S%{1e|w&Ir;MNcH7
zZRKx)h&Wr4BfF=yExARE6*!v}-^$*3#D3Ba&35YJ+q=>sRZKX})#Kl_-%h63{D`9N
zg^ByhNb@m}SG;SdAE~KC5X@OK__L$sb%&`|Plro;`F&48gY#^k?MS+JZlg%wn)oi7
z{HK#&-wojOU6{^PHs|;)>}5QK1+snNrUB{jEK&x7AlN7-s45K1K?*xEz@bKTJ9|56
zORfn+7&H<+XE5euUC`?2hT1H%^?aKR`L?0(dRCv9N5PNqSf;XP2IrFAjyL!Ggo~Jl
zf{!cB>8^V4Lkv74A(pqME0v{pL7@?g+r#K8<Ah`N%J&-6C(Lzr(%a@B$h-A*j11uY
z9eE1FhYIVV4meNe^N`QrU!I&)R#a3}R(9M@P$MV2n$juE>&~-<8L6Ubrs+*pj?n^N
zHDPM2r1qe~w*5ZV(Gi$sXOlw>UTMu1dykV6fa*e|%1&D&GjjjFB__CrH=u7~!-G2@
z)O-IfOb*geReAgUB;D&{s7S~kB<p)&OT*gU>t{n)Mjb_P$kUXxVtYPqr4Md&BE9J;
zT|5u|ek;l%kW57H`6g(OO=HxguE0|4J`k2v>^^NDM1=STo~adQzqe1LZaK1xAU-&4
zFLG~+H3X#7m(4tD+++=@y;EKOQv~$bEdYfi^c$c&$@*zWjY2ep|32a_=7)fZLKl_B
zf;%rdmlsL4ksNT+(|k=m&h79bT5lQYvs1`vr43MK5yI6f=2O7v=}uTk78d6!h<22z
zsv(S+j%n*A#XvF>7Fv}NxM_X~*sc+%T)I~4Ux@R(+WXuU=*&q7uor}R7(PEM@n-5Y
zI=k_f_sQn9`^8I=yx#Rz%0c$FOW6UckwEcSAF}tiJ@Y)}d*%|b(``#^y)fz8RWE0U
zW=$hn;UDi=dFJc|kNTn?X{w|kT))hJtcQWNLVD?<yyg9NCbjidX=XHUiTR+bMf*O6
zX!)3PTc%!r%t8%ET6NE>xx7u~g5G#NNiO$gHb~~HQcJVRdFg0Rjg-KQ-O=_<<t?L5
zsHY5^5wwJ5<%ps|`2gw+r-Pz6TG601?UpnaKEUiSXX6;*`MgGakG)~O9?u9$#wG*W
zpJxH;>TjBj6r||B%H%~p?#1cY`Y(bX;LReaM3ya52L>cR;GUc!+`5QA@SM}+8+_iA
z$fVuCM_E@1T2SH-uV90fR<|4!`);tW98d3D+>U#|X*+)5(cJpTaXKha?tLYb80Gm{
zX#~f9&D7)7TdJ^BuT^(toAx$1dGv$G^Tr8K6h;<XPJ4&yb0^~B!jazabTPP{NcRC=
z9SJ*!O<3O)Aa)yABw4+6JVH~gi5Z+_Y;I|z;yOPuTZn0ccGo&)_Y}a03;@b3^}Mm6
z?|27w=X*zqR_E&=7ZYOg?`GaDBD;6)9MI#u_f3GL{7_2wp=R%oK<;fu)DZ92%}&T>
z>YxX;Eu3ZD#=Ac?l?<M_n0&ttU+>Ratp98uBFL;9SUg@FL`bsnwgi_JE$0+HjrVtA
zHAs`v#kGY4uG1*o{{&>6(a&JbUWQ9JygwCo-%^ZYbz$ZzBJe!EE2xvf=oco7x{_FW
zk6$XYi5I$dbeigpl8!zaw|e#RBEhBSGgEdKo4=?qu`%?MMX_GetIB4%;ao0UJbQFk
zWM-AXrcP)nFah`2<z#7oo-0Bs^7IprMLN$79rlkQsX^%^z2-d&tlxfLVToHG<i4bc
zY8U=}>3KeW?BPITQ>?cfn9V{`v&g;uKHU8B`wE$;>U{p??<&zf{eYQs-ld|k?zH$5
zBO^AtMMZj?QfsrO!+OujYMk;mtarotlz>gskPXv{`j^L{K-~ck_lBDrC$cf&U`tVX
zV-;(ctzS8Evv8$sdvPx`iBUosYHwZ+lQQ6nvrzWjfX<!K^iXI|RA_R(6pQK=#@pJv
zglN8#6<f7UcEbT)646!*ELrE_;!E;->*Wd=1TUlQn~jW1Rz(~-9#PjNrF(^&&xzDW
zo)rULj}+t84%^Zx*59A|>+9>Yv$JIq=|1!8s!(t(bs%bL^k29_giMEHmh>HdoSA+%
zW6q}86{p5t$f)5wd6Dwj-=vlQ$}&?Y0eS19r$DZcI$Va!G1ik73qImOqI|oqyj5zx
z^S9PQYnoxdpR4K)b|Q(aYUV<EWw|=S@U^>y4ClvI%&TzZhT?4bI&M9+&zRJ{=U5j=
ztBM+r5&n%n-&TYk3N6{c&VIUqe=U7JMNvGbA|2GCU=jhn45*%+x0k^NRYr?y8TcSq
z#>HZ(Z<pyPBNzszdBck=KMeJfp&Lg@<r`sg8Ie)$c{KPi@hdD9jrZr`!opbpUpXAk
zq=Ds~?d|r7FbXLLWQ5Mn&buubeabi}W2o#7ohJeVj`>WL?Zj)!YnS3?L;~MnUXfPL
zI~5??QZ=vLjECyX)fm06b|S=p<Pk*bi<s>_<v?j5lug*xa=r!~q+BnggaDj)71WBl
z1)|#R?z(5pp_kmVE3bk0<2E~N2U`Yl;#$c2S+j;po6uqXriP{moN?dLZ;{$}Vw)#n
z)^duibC69fbyw86k$vD*BLV}UNd8c=Z#-ATe=&qEbip%Is1(0t7^?U>ttJY;dnz;p
zAadbk`=X#QC-A!0U8pytm+XT+U7sV0u+H=13nor^^Ze1ax<(q^7aboMWo9_iyUUIa
zG5Ze%+46m7TB-%B#*~96njRd?g=F^V7<AokY`xcIf2|@qj|8_}FH6n1_F|Y}+Ltx&
z`G~AW@{XLG4HnDH*l{vu)n*J77~O-!-_dyH5*kxG5Q!mo6a1iPEcf*E9B0nc^Z7t=
zdh|RM`%WF5w-7kj3r7B7ENa>kdB=7aPx2Kg57nOm!VRVok*J_hw(l=^*C(YdEzye4
zFB<tf(2myTvTb!Q4NtH9#vW%rhX@SO$d&2LM-9{p()DgVrUJ2#O<S=tWyp2)^%^s6
zlHn9kc3-AFtr!waV=o}O=v&}A%~^UpyV0?Ar`C9wWl^_BZQS-+B5s$PPi%5t#gK{X
zz4wvBvNKZ%9(!9v)m1B=3@uN;KXjvn?MCqhgL&A+VVkClJ@k;BpaC%=nSJ%!@;a>z
z2irqpNon<DTfO_Q=!LeH!|dZ<7Nf7MyO)UiW)`;yJ7AXe<YRMOp2k2G=ji>Rq^F)i
zU*l=5ZU|^CKMUH?tsgYi=U9nMRX&6UZJy{ep`pCq?q{3X-G3h##5o(piCz<ez!3v*
z2{?gKsG!7+??-sj5L))x_WLobc;T`$QokvTy1wR?O=_RDHa|N~Bm&zdY&~O{BXIG&
z-P#rR!=I+<e*HM*6=l~rZvN+e3)M=pe~-9GHN>#V-TFf;12F-o+3Q4cmJC-@EOmGL
z53OCtEiQ(dr^^h_LfG2Sg?~x`#|AdT`F-0C?6y0Wc+>mWo15%`Ukx3Bhz>cWynuju
zZ>!{hmIGeN_~XLLs&*xGN`(EuHBslWZHAXtOKO<#WZ&8Q)8ha)Y>00U&+o6%wf`#6
zJY~FQY+GJ)6Kx20&V_lep*-gf{vlz4iu7)-eD}A&vl9B=uQ`*nLr$Q|YB<wxWn7Rh
z<m#%|801j@1Y}3TzyD9MDin;4h1@E9*a&ln$bk$z0ex?Ozx@Zh)m-#kJNTl1`Tp%#
zrpWQ}u~}4cEBS}3yHu%<o0zqPNvrSF-s@>*X;G9-W7kKPsJnIt6-3l0YUhv&Lnd3N
zz^3T&pT}}=Vpq62U6ceh`8(8RDVou@=^}Yz*4kd+j+@>0{N!MY01h7Ai(N*)9#Xu0
zo}hUNX4kc~<@3BTp9X1Q-LT{88;UHfGq(a>Q~pk7xBGUQJuOgbAr2{F(1^}GtiR*H
zN*;>ty%@Tb-SNOF6~w2g4+6U7_Y;U-rPF+>c@sHh!xYR>O;Y&r#lMb?{GtGqk2I$B
zYdmcs&>d6msrWu7hLTfQ+Tv~|xnTBVxg!+1Qq#Ue4bOCAdOZV0UE97xuAxsC%8^0o
zBGPB8K6`Y7P*33NuwNu(a3jjD)+Oc#JKhjn%~4{no$WZrcbbUnG0S`t#o=&#Uq>B3
zYaI49SG#|OGyi$EEIs9ix7`Ifj}$b@5EpA+8xi@`B8QM2NFgP2k<-=38Gt0-j)`>R
zzRX9=LDyD@7?v%RL*U*#!SD_gHmwA*iM)tro^L|6Dl%YNJ|ZzpvJ9%2hI;uo^p0Oi
zqvPUO<WQ*M@~c#Sd>k_5hFU{BCXR*Zquv($(88~_>eTRkz1ET<VL$(0p|5;(KaKS*
zfLrK@VV{K~H-EmH`Whp)pW5q{*Gi2Ws_$<fY+1FqDU2-qHB_F?{W+?nZrp~|faR=`
z-W20%NDFu-c);tR_U#1ymm*pR>I{cMzG(hy4Yl3+Aj1c3dQf0N*1v5f-KNVf=pILY
zJVbk%m%FLf6hY_&QHIM~?Hv{o(NU7b-9tN{16PSJq2%kggEFDQ#qnigm#`$@u9MV2
zr@d6I-W)><Dqmm(&lzi84!%7d|K4#K1|^m$(f|ec^zIq$Iw=z3<it=d*}LPD$ehts
zqFBKiblk-+8P>GB?*Gz=MnLj1FodnH3YTu~nRXTw1o^L70Kng(zqS3<Z@~~NIMP7)
zDMo`i(t~%kFC#&u8K8v0TkAsuwotr_EKWJl2gw8wimf5DKNNDdfoPf|3!Dciy#BBG
zRRKemie2g#2l~J-9xWOmB6+sB=GsX;l0A>bxFGxo+5mwOC;{88{5{S8Ee&}9FPe3L
zBNcU}*os}SI@O9k0$lR1>6gGWjqGY;nt<x<D54{wdU!J^uMdA8a}eoa?27)^pJ*$H
zDlqDl507sEwJK^f1lTm)+^SQxLKn${q*la<mo)qD6imHP1D6)Nt^rra-sU!+ALJuh
zfa@jM0mxvST>SG}MBE(^v4bGrj1e-mOE!O$JFV@W2R<JH_q+b0HY`+%H?~dx<r<Gk
zMm`2=CmF2uI>WH-C>`{)6QRD0dzc5aIUM$@w%pBlBY{v#vcKshD!?qOY0|}|gY<+E
z?WF4*6)_}1DIhGr-7-*@m|CHtcV>@W>Yr_pEI(-;nV9hYTE%G_mn3b5SJ|4;{~jah
zKFTari5Zr_Q#eW!KX|}kG%7v)OkCd(2E?;GW5Dh?LG#WC3>^Jp0O!iE#5r!*qRON#
zhf53?gn9~6_Gf1vtu9jI`s$8P>eu4>beLgZvI3zw2|WGF#s3s*H9c6ZJQhFU>2nnV
z)7y0VaK`|cJryxv?9beMBZ{0klLrp;^;G^`1T=QTz$0S<dDQb7?dHsbfr}-8#L3V2
zYn1VTOd?{fD#I7A4|GMJbr})TMpQi!W?hT{)`Z{gzy$gqyiZUS^9+i2?h5hMG<yZ^
zx^Q;C5+4=^DDt*TZwr!^f(1%w`^5FNZ4?ciK9G5l9g&^Z0u^7pzIU%Z`<-`-KRuDH
zU(bG6+tYH+wP3Q@udLZyyGs54a1>t{D!nc43z#N-@C;KJ&z(^qIprG*w&WZ5SU3R}
zJ^)I#8Vkh+$`OP$eA~|5OwC9TTqAyZE?%78MT~d{6zsA8xnxoG`mIy(6m<)u1_3a*
z1L=74=&1*jdIsQ?7EysMBQ7$cwH?pfR1jP}&GHxe5ZAc^hq|_6+LOorblVO%B(5AM
zByqeTp>=ZFqX10)^p^zT_0B<@K`BzN1Vld~+?Xu+D5T#P+c%Q~T6ikhCrfC}>N2TU
z-5<{yx-Gx7Tp?)^<w`@~Ncs9;=uimq1Da8QHl!HXd5Jc^8WUkxl`Kr$uo>{()d|bL
zsmMTj=m5Tr@(#$KhbM_dhY5c&$rS%?fR**xOMcwWCAghL&uxub!Pxm_>eVNdrH>F8
zk)M|(oNtnd$v?m*p4^{owmywpR7pAoc(p3?wLb#Cry&RS5l0vfLOu0^!m9eO={08S
zbLsuC`pvK?^Iu&o)|sh{@UkGCdJA!@Hw?%=AZ6yQ<Bh}r>C2w(7Wae&-Zt6uDuJma
zL_Reb0i*mnHf{gf)My9`fU2-V3_g4$L}@FLB0UC`&pgv^K!J=FDH#C#+dy`05+c#u
zuhJ~+H<?Jm;BQX>o`(WW0SsUL=<%4?9G#)!oZdC9AF9jQEa2tuI!Bz|``vU<xBA!n
zbV0TQurSe^z`8PAWfbQi7z()=B5I{^LkCQdiXhm;hk{5d$+*Jr)AsP78<PSP|B@Q;
zDSe@sW5Jrz$h^eLXpL?IM=N!EeI{5gzBo*PE_-X2;=Vrg!vq#6Z^oye49tU3iSXXv
z+bLLIO*QUa&FYrZ@Y@soGhl+#AUMghdp##$CcmMFn31>mDp1^Y5A0nQmCO!KgUs(+
z8{z`20++-P_}kOdKt*rBwU>0DQ*gy@@Ggd{rpaf-r_aOx?_$t`hX<~wa~szNGJ=9I
z02->%wvCot=WAo>uo=tVeW?pftD=0`e|D7g3)CI8N<p8a_L~*|<twmtd-wG^;XChP
z6}Q!`@sI5M{PH)5(7&gV6$Zu?gQ@6E8#W$5m|Z_KXG+3VM(31{TQD;<+Dhxe!@jv2
zp!@ZCf+o}}N<GBCPM%yxaPf*fXomlv^8Pw1%C7qZ#)pwc1VKPLRJx=)rMtVN8)=3{
z5tUR@hEk+qhVBwX1RX*cx&-NN80x(+p69-w@B01ud;fV|EY`v`bDeYTv(G*|KIgMZ
zF$45RDVLnC?PG+LyPpD3cwpt=y&L2BkX}6k@Zrs`<9Ix~TfY*?I=2aLX9Y_uTCjXe
zPG~JhF$@ms#_vf0@An310i2b{q+wh(lBbfob{Hd&YSYZJ-M4($jQYlvA^SA#<)BUL
z-t$coemorsHg!PumLb=VCa{nD_2@*Rc2Wz&;McR*6nA3}jKxb^z5TP2$lMbE+`?Td
zs`FKiPzqcnN<w92WtyO!kHRzw)BS?s&ljR1QC;n5ZQEm5+d82BW6?SP`w1ez%NAMp
zzrMDTSyJ3o&$haJEu=ego*vXNbZLz|r3VoyJ_rYBz;O<vl@5-MYU}C@^z`yPWvE2Q
z(IHJDNoGghwQO9!8W9NspiiGR3mCvEK}U_#4)lmeSsmg>J|HH(^};;*W5-YV2uy%q
zpay+DD67WUO;&LePw8@nq$XO#xWD%zMGx6)dtG$X)sQMck$C>bIZL4D_)mu%b6+m|
z<;GmJ473D{h((P{A3`PIFL`@B!2m~jGQWqTqob{@ZORR;**&rmI5Vpe-H2_?xIx+M
z`&NEWIY8GFZv!QB9-h+cRSvfy3d`ng&it{@E)rQ+H69k*y5pPwgyn6<I2n$qSa@@D
zGgr_LJnRVDs__(dBhOvx$|&!90FKSQVZAlHl?FbEu@6^Qc&gdh!q69W4Y9=7q3W<5
zz1~t`AcKxcat!GkgJqV7$o0DhDU#Ip6I#&;uL3SmhpVEJeeC4uxX~(!gZO9Hy2cHN
zpZusp$PAd4Dm~#%jEb)Yw>%=N<rSBs6VGsX7x6u_j8uUB>CFJXS|N@q{N_xf4_j<|
z@ww8<s*?h{!%s9=sgZ8e2Xpvx_NU^Ye$zWRs#0NB?%5#RlIzU}1eWDhWQ-Oo=Hox3
zK?VaYF`Ht}AA%Clm)=V0=nTbCi+;)hAj06OcL=+EvHtK*1WS1Mj8~}tk>kTh|G_0M
zc|Y>KZuKXDUcXEqJcD5m=wZS~bUMElH2BbhHzac=hb)!*lpzz2?ICvv{RmId>6ZZG
z<KyqWzY#74TvQ3_i4ehVKPoX*Tqv>z&R0O)hSkDIuhk_P4zn$92*}CvDa;GV5%vN&
zJq!&JxgJ>7Lw1pGn_iV>3Y$K#+KB8ih;xf<?;Bfm{tms16m||}t=~~)(lj#*KJiec
zqZiYblatGbzu1qzca25nCoNI?jhk=0#?7By6bJakZ(jw-ubZDvTaxU_6o%WfJDP`W
z;XeZ>w4Njt;11%gs#wEsKEt@~zWg<n%iY;o^vV3QuE!r~ESsjY-r@bIX1Z7I-?dhS
z&-AnDf$gFvKx<9+7jUEh18jA2aoU<);%+4h^_^=D9lEH&@L4m-bke`SI<rD*5g;eu
z^6^7z?Fmm~^0(_z9Ked;YkV-!pc9|_YVT^4{DPGU8f0XP$QzwOS8#}*tSJmx+^eBv
zbnbxwBOPA%@|YC`5ZljCNGJZ+FL24Ckrx;ES2-P#wtH_F(y?Vk@K&QM4PQyy6T<q=
z&x8_ZIhNJI#Kd8#3JMBXdmu70GL5N-8gg~Z-94lbZ_w=wz#g@`T-%oC6xmAj;ncAe
zUowhy+hmZPO=m-t+ZyyXw>Yrr5=b7wg=`ri9KOfOu)Y^h9vD;tx}L*$-HUy<o7PVx
z(@-}!_=4JR>Rmqa2?tNORC|2opu-#IYc#?aOhCuScT$j5@`V;cI3@Pt3;GPY;<f0V
z2x#2E!p=7xj1D85!RTl5dkK(C8g*cWqa#dv08W+ba37qa*=9JsI#duC7^tGGtlRLt
z)J&K8&Q#Na&wZ&5vdlbN5-7Zxvn?V2vh?D~Tt`(Lh~uu&ac{$13|-jD2>C+|q^dT$
z7jOqdHtXH(ZEPY6oI|`pXWsFIUgps^&iuwjA$t3t8wiOMrP>#EnYTOspoHmyq3YC6
zZ^k|ATo##(-<mCnko$GK4gr3un3|?b3MqQRE;Gl{!{fv+0DwsR>!W*fO`#S8SY3G2
z>w67^)40laTM>3o$E|#SPVVi#<Y~zymi{SDq)8o)Ea|R&E<zQTo=$<}csNNm{N3O9
zWlqg%gvuhvuZ^Jqq&(IF3!KbfXK*SaqGMnjf%+m>aP3FcuP|%&q8O|Kz?eNfM#_&L
z@xp&;k~;XBn`<`oYA{#fHo7xFhxY;_Gm}cUd97pqdt3@*K=`Sg_mfmBfFpkm2+B$?
z{l1X^!HWNlhf$wz!+8tG#!HY6_}WDGl#Y4Qcth0z!(juq9h7agk+wxoDK!l|A86I&
zW*(^tLO_x^60Tuwiq{R`(WqtsOy?I%uv^=i?s1W|S$CWtwey-Q>U%z|^+TBp<=bW6
z@-NH_XK$L*7yNSj?sKz&eHHq;CHCzR_)INsqaCPZ;egYswdVvtWMXq4?Q%EuH9R&E
zII4lV!qINlh6KyYnLca81!8QTExiZoUr|7I8tAx@nLxw#%f$-B2JV@l^wulwTTEF1
zolynArt%*F?U9lvx_cOx5w^0K#NNVj!2x_f1&!A|*zuxwPmk@Z0VkJ<?_A-}HOvxs
zdCoW2BLd3$`$zE_{%NCWLkpPneMOM)E6ZuuHCKRl*lELc<L+7lR+NvQ(kc->BsG~s
z7G!^#BG3Dtx#~C8@V9G~5DR!pRl8+gi2Dgf=m|xI4e*8{ctu4WPB!&Z>dLodc;Q-p
zj;q>A2l}PYdVs6Vwj*moCjXrQU3kDX=Gwhbcp!+doZOX-tn|~Z{?C`6(T>|~Wc8Ov
z*;&lrxFe3Sf?HrSoj|)mY53ILLzU>%-qhZX9Qz&BS#mAwhlV3baIKl-uUMkDFgq*8
z-gqto=}vwOez{tPm@%HQ?;>d&!m+mCA+EWWN3P9kvB9w~EHEhH%}}z;_PU0~9EeuW
zd{<ZWj**F>b&mD^!H>${@Qz<Tp3OC*9ec=Wu?gyVFFvg?Bopb-)f?h>Qb&wy`Jv_X
z%bMu?v-L$E1F^<^QJ#3pHFs0<M$=YZQuPc`dOXW#I*kE9<)F#4!MeU`NO&nV8Z~JU
za`L8E<tHZdhTF^qq|>=K-G#IBbM$7Dha+hmV)N;ya#u8=zK@(w^m|XT>>9b6sa_~T
zlEYN=zn<i`bl@~D9o+rM$Dp~!Jl*;@P%q>#$*b|nxSGtxQ3I;)RtBQ(Cz5o8dR63o
zP`OwAJ))Nw+C+z#0HuzScyG9-)VOxiyI0AWHo8ZRkR$}m*t<rvO*~he+i`?sBxPCO
z)Yxw|!Oy{B@~k(-NSnr!0H6}>fK3Vyhiha6=LYxI$nK7ij&QOXp*J+u+dNUT;-H2m
z2LZ^;|1NGCH6Xe1Ckr}`k8;=xHr{b$53PEq=^QHxaxy_p!)q*c4jHFhDV+j6uZY8U
z(49#A{P?$Dty`I$iqMAv)zw!`kzea5W}juySa3Pb#kah3y3y;fKX!J7ue1EVLoR#5
zpVmo0&sDnx1eC#-Gp3(-l959eJm~%P<U+dM&vy~FXf|uM={7%k0mPfvUd!(vk6l1#
zxw7a36(6Fx6h*R-?1orKUQDdc48@zCjV7u&_>4QfCOA5^?pMnXVG8nf-V_+_48hCY
zeTGk@%gJe+VcjSFw1p!uCq%2><;UXt;Fq}{80y{+jlZ4S{nog6)HGkcCA=)`FjueF
z9@xwPf6vfX$<y|}GN+iQ%~M*vNWCE5`STyl!0G)z0C4#Y3cI9Nr|6Qj*2&Arl*M8F
zpCd_&BYoZeR8P^rrvYSk6m3-Mt`PJbcu4K`Lm?(vbMv$##>-QNz=y@gSSA(XcTFNy
zsPcBYd{7y?o1D!sHq&}Kd$hF~_u%ag(V<4xiqu!W1!wBHVJ9Ydcx1gA9RZ>X=;e|t
zv>u1Y4Ja)6y#C9<))3Qquj<)FzaAB043|bu1WTk387rB+?t%W2(f&Npjrvz?0=Txf
zs@sCggYBJ`+Xt89K&`{=0h+l+7Cy-5#ca!NbVsV-RSm#!Ud-OM7vc}snq3)=<x77Y
zcso7zM4o11kI?r=hcJ06_Qv`5T{0+UI^(*PNvzG~A-WiluhbY@g4Osz4;US`9b#6V
zXR3)Nqh(lbe$x4<sj0fRCTH+t52*v6DL=rhcb&}jW7-g?Nq+HIe2yY4f74H?SAg-!
zgNDiN19em~+IfoAgr3v%UbCkNZ^4nCr}wpTDymA|4T(gO`F7wZ8+=zxOEYAg=^~>_
z6KGu^1Q6?tt&jSIjQ|x%lzVew0}7Xc-VZZKF4OKKp?oU&q(@wXI*6#~WzymMm{K{#
zv}b!C<8CbQQoa<}u_2B0v<?Vx3s4I|^dDcD4$lo)y+P+b;FT!ZD<&i5h#;DoZQTau
zZ{kh*#K29AAkssKZ_TeEh*Q;iSafYqC0kqAcwsO0R^amrvw$)2(r+~-8F!D?Nyl(s
zQOR}1%`*gQz0SQm%RWcU59F|Ie|eX{5%xVJ%;hBSKy6>p=k*Y=zD2!M=T|cxjJoX)
zq6cyeiwkd6fR*r?rM8#g1@8o;P=AQe7HzG1g5`Vbp5sm#TP@|ma|F_a@lN}sQ{6|+
zo6%cm3myEjL$7+>?8&CmDhA0;6X~Ac)~A?$jQvp3J1#=<XZJEP8vc2?3DGoH>-x}G
zGfPW^mf6GbO}7M7%guHYVa6xcGJfd%GAp<&aqoy}$Josr*kaa9B0ts09*`~??MLp4
zJs|)XNv=0!!X^5%N#4!y)hmGGQg-af9Z^Oy3z5Rf%}8<sLT4LNz=nK-SY&K&;8-rR
zzM+(E$lP>CO~0Of^++K~gg|de&-K&QUh!u?d_;485XYLvQ3loaF`m+CZ%^uC0U<-l
zayv1B#cAr@$5uZWj6l&Zx)VO$eXKReAXd{BESVKi`1}hMEdhBQciqrtLEFyo^1@G;
z*htqM?m~pkQ)>bBrty$gIx`XWTTwk(&WJ9%Rj`RfuD01tdx>B32Y8q3yOe8ZpFm}P
zkWH_;Y|^|Ih|9l{A^N6?9xC&6*EwUO2%w-Dx_9Hm#p6h0gz;iMb%~UtCz)#2t<01{
z&?JY@om3Ju)J-&s!=*&$1vv5cTTKh!?B(h1gs*QiZ&b%#sP*!-J>5d{P6FzzQ?XTX
zZlx3V*{io}wle!H$IQewsQc=cI%N&r2xzU7T;(VEqv6t4e)~<_Ka6jZ-j0V1OET0Y
z;Ux?ttUoDw^27i>)Oleja`>wMNoraZ(xydfob?&!FxO@skJB$GD1h{qn#bMe61ey*
z?Z5ho_$@4Ok;ICA&p7|yQLEo$4Ir`z_+c2?oPfjUv6##SK-Zsl$)sG9jZ~6lO@F06
zx+x7JV;yGkrz7Q)uyQ65eq|#=SO_f<T&Vmy9@+fSGk88?jHy)hoR<iH07L85bX)oH
zmh)s3P4QldoFoI!$ce;y$r`YvZOxin6y1W>K&I?>vLz05v)P}pufI3JK(mXBCiJl{
zb^fUi!^zN5@-fS3Nd~WK>#TT%f>CbV9&ml)iA3{bC^vSr92(eV;lwE{ZeR_dXY7i>
zUa=cakG*bqc@y%S`wHMIPG%fv>=4m?ObqAo=5-oLDht0&64~>u4N^u!UpXKpL8wtO
zVEp2%Z=|K$ntKxEhTAyD9s%629GpDRgSdg%Gqe5Z!bc{myyuE>OC_$$fq$haB-#JZ
zQCM#X_K2XKjnr%#ypOZsUi^+RyxAZRl{`Csf{d*@{~8NmOMI>`GaR2GQjqj`x2e*e
zbPO4mk{9_s!rvR{y>nE%6~13JZPOOK7-eNDcQKOg8bHdz<O-A^<?8pwjM;1@BO;Fs
zk008$005Dhs>`f?i=#+r$}~HJFz|Q7QtlU*XP6wXW)disZo!d@8=t0Y7M(|v;j%xx
zw;lc3IYfRk{gp5i+K;=X2e_mr5f7sjZ6ug@LalME2(Y$yWm|^_xm&eu`FFPTVTy(w
zwpSk4PQ27KKqXhUbqwVwIUAd3dQ`~}@UgC}nVN|+TM{+(4kr7artjPDf}yQhmq>=^
zLfns|x_;%;-JiKIj~@{k81-TUt+ddnMMwiEbt%XhjlJiZS^61P4ZtsfdCe?so~E^m
z;B^mi>MYp#5=<${aU6E>*<En+Hz?=Yj}5;=MEE*fM<_htt}%9?qJ%$$jr!fYkRSKO
z2#6Io3CD<T3cBar^LAS998>~QY7S`XBmr?yRWNp$n33NOt^N#T;TxqwW84?%^78HD
zPYuKx)c&l5xXe(XPNsQ-Y%zHAd&=}~l;Fz6;1+G`EGmoYC%J2a#BuC%$<~=2W7EL2
z)NGL*n>IF5RifN`HV4FKw331lPS^vk<v1zxxP##AQL?Ni`Y~P{fH!mZ9!E&?awyQd
z6iluxwGrAk&|~qf`t~&HG0k$-^~JwxP|1S0-5G1vFLq%~DTx{Tc!~YJp41PBMq{;O
z#X9!q$?>!+LLT+&-1EXr2_s{Ov)&>Dk0oQzefHB}*i1d$_ugA3QN~vn)3ohp6g@ug
z5{avICAxk?Xo0c_K{!qwdVl}GzNE5ug+cE^2PbPP(kww=gp=(}W9l~m=H(AWvI}p^
z<uA}JPc|u5m7CQ+c|F%wo06ZBdo{Of6u}fk=qVEZK5OUpFU|-lFxb59=Wv2^fusRg
zv6-I(Y*a(W=T_m_nB(}m_ow_dk7S5S##sjO9Q@m#Z0YxKDZRHiLjb+!kQGnHjsH5f
z2~x^HoL+z~iUky@(%iuTx5S^{S*kpxfiApm&$vxEyQ-TCU3NkD1zKeM^5=@Li(<v2
zJzap6xKGzEWQa4jqt8fmm*TY;#a%Qu;#unD-ycn2z0LtL^gjXOsU;|=C1)8b)D0yA
zPl3d^(u9G#5P+2lyB@scr<^A_@NgZXFfu+D+noqIo)0WW71Ai;u+!Ab{?)5=Az7k&
ze=uo_#3*xQ1yH@ezIhb`&b$+|0aQNec(L2D#i)|;Z6BOlGw_;|+Y6J2r=eoy{h+1z
z>%@c}4W?#hW+&{-%*+7d+>o7Ez*i(wTwL6(j?xuKWgb9S(n0a;^f^cennH_3{Kycb
zH|w33y5rQ7C1li>SCdWqb3(8iZ3~}*pVGO3?<+>2`zJE6ydqN4s<c_lxepKeq9kWL
zUhES<om!=?=eys}IG$9et@NN`Kgznh#+S;Zw|8c*H^qgmk)YQ+^MgMvog(3}($sO!
zIc9v2ivZ@0o7gw)Ag$KJD?Z2T3&9k%=beEUjSIb4WwGHHG!`{mmb<KaXKiHt7%*XI
znaBij-nyit^CcIPM3!-=t?}pZMK)tBtXqP}c-5Hg9+OsjwzHMwl%dQjNMhIUjY>?k
zemuf3@z7{TIxzMWA$Mkb>&+?Al;n?BpqYescZ|SGs}^RwLl%f1pH~mJw_DG)3bI2)
zBqZE?<6~o|+d{7Z^ycHocLHF+BBG)eftxh|5&k+`%BSvbS}}i*^^r1PwQ3S=Vr@YZ
zmp9+@j#Q{`P=`R<7@MkXjFi-!)J;N7)a=z<?PE(OCNgTqi^gHe#x9#W7fz!P<dkXs
z1JMV8=WG7X7Aksy$YH@dc8s<#gqcZ#dBU57Vv$(!SY#%$@heOgVYS<L{$4?4#Hrh0
zozpMwreuZP#bw9*e02=@4G)NnjFr<wdQ4uphVh%MU1TL9WIbqjB&fcKQ@HPVyNJ30
z0|ndOMkpVs`HhN-yytT}QjUqe=!3PqO<b=z^mIRNn{G9M(y*~y7|=FP^9{Hc@5X|_
z>S&i&**Z^oz}Ws4?Y`iWA{)!?S$D45fm<OnrYUP(M;!jpTeK4AJxtlm2QZ_m{Q7#s
z+jTJ5R?G1WG%anc$qz1k@#V{xs(uMkF|pFi9{{06v8SzV9>Xphy!pM;WSzUkPRY$S
z;tlqh0E_Vp795twYK!ckkM5ulm!V}hwpK*ICarGhj@=?<AOB>u+ob6V)1g_j=O9TK
zLDGy@&Oz8doM?e~!CkNQRBKb=D9kTuYWJ<r@q^Ff(&8r7N~h<v8s|<nL7()YCO_~>
zMjaJ=V5}FM8cLHUnje6S(q-ZmmHKO%?0Rvg+3h%=i{NaNnyu_)Se=PvTcfI^@wv5E
z=ao?KaA|z>OSM=H?nR%sMw^{a^V#`0h{9qqXR+(ivD-NbNjr@#eU8@F;?~MrKLs=j
z)p%#ceX^PYuc4b8r5TQjJ(f>+6Fx1)9#sci;z#ida2?}ruj4nB=ycEZBr^FJogHm9
zt;3phHCKXx&Rch00^n;Gkh-dB(8{|g3Q9^qC*6F`izfi7mK+2+?Gd}82}z1yy^f79
z{bEdh;>!w8KbV{tg{=1GA;(Kn>`A9<P%zj#*gc=@`lC&%4etxQmd1t3sy<XR{&8uG
zf-_11#b(Sl|9GKyzn7$q*6_;G%pllW<Eg-6-lDkXWlo2Azh-}A?JHmjE2k>I{Z#eg
zk!)P8u*imd3~0CfI$61|%v)7G8o8w&%og-n{T3m2^hX*FsS7W&P02QorCFCIaW3J*
zz=F6tA3lgTxaC%bEJ)41DM9tW`BZO+e0b5G-!XTRR-5v{-f8!-#^~EV-=<v1Q`fg(
zFt!i|cDp)$?+;GRH#NP7+h0A}<{QkjjYUSy#@+4Ec%71NidEg=?@(=j8$y0ARtFuL
zo)+ih`w%SXGG-ZH9&!P}n5(U=t*CfN>{p}2c39z~J67$OxaaQWRi#~BW%AvqJ8-ch
zrbDu6!Flb5!BBc2v}UC)7CheYxIn=1#a_R}sbr^hXWn?8#uh}`+0Ej~*)V8oZ2IJ^
zs%<}zxvEmE%@jlH>SrhI@y+AH()zR5mMiVZ!+=FbkaN;u$+88@7iL|isy+wbAkSr;
zJmEa$j*5pB#0E^?dWC}|jkTSQoG2*<670n70Rj|yv8ddx?oaujx}6X9hJ#Hou~-8e
zMWUkaxRnG3!s6Xp^>_2qqamerZaK$I1#w9qY|lr<k8f(2QZ~9febDHO=jV~QgvhE{
z_10+77l=%(ot@=pMe}3R(V^LeFOAZ@K|fgjsn}==<B!3(Lo*znkEbhH9-P4w15Z_v
zwZvKVGY`Sx;pI(y6GWix>pgY%OYuqxKL!Sdzy(U&Ag~D@sHS5jr-9N7B;i3umbi_j
zs<)j?y|%yTb;uJj<9)-Uds4V0n<#e-8@Fd&&RZt2MPU+P9rmapv@XI2(Go-SMv@Qk
z&t%M;9;b^Bzee5T%06pRYcqz!EQ6UoGo`Or@IU29vghP&Dz!*AOMjireaZwXGs<2J
z2@42tn&8?FJP7ogDbeZ<>92(6tc23~&ou>ZDa9P}zBE=g4GQse>iC%-ku;o_NN^w$
zPfSKxB?{k}o%Ssl|4`~&XUFtlT_M_C5a}C#b6p#ePsV95A##UMs{Mf!K{?*Du5wbt
z8kZV!j4~}nnB?o{hdx*VPblQ<J_lno&?27_dmP<h!?d^k%u6LAB<&QXEXB3;9bPyy
zmq)xtAb4;wgWC+@QBhIp&lEkLoV`4155Hkj>jIR^PCIEYbF8<3o;8j4N@(}?7Qcp`
zFVN~)0lYCodiy^i;=X75_arH)Y4yISzB<0xY~N<$+MK8=C4-r2MkX6QaIPF3OQ(2L
z)=;!D?}Dq=f}rruB!ng;zd`bk<(Z{0a;ZUMS~-F_(BjG;7r7T6wSSR19^i;Yb0gpA
zS8P6VsDK3D@IISONrd}1vx*P7W5GG|L%nq`s#kGTZk3ttKSs!nc5U}qz-X)X;C@r9
z6BE2Vdx8qHSCeLEwKmJ@aZk;^OA0uxCvhF-c_UsPY9Brz`S#e>Z<!@OtXBRGVH$%J
zC`+c})eh;&keSBSCgtp|4XUOn>wvOyRvP2wx0n;&<knr6rPr1uFFw-mFF)eN70QLr
zJT7CI^5624uO?@^rg$pOy?GAY+;J3f;3YdqZ9RB^VcmA-B*1=n5f_Kj?!GvlZ37yS
zv?0ZszaKPVx>-WB8(Cvw<KOlkC(#VdJCnev*+mN_MLwvx`Orx3TRJ|sk2H~6PnlWj
z)Z6Bt&Pd>@*55F1FrjX+Xxr~cmP|<ugoKXUBadf9rvhtFWA-)kOBF(^-c;3+xXxBi
z2@;G9qVDOeqt`4&Evq|l+S-1dMVdR&Y+PNwwe};qvno94N8xPN-M}HL;moH}g~{6_
z@V0A#+Lgo%=wma27i(VDR(j0ZP`p|W>3*{m1lwHK;;OJq@YNr%x*FPzmoU+NzvPbS
zTYnOh>$b8jIyh52Z4wn!pueT2qUc{Sky(+ckQ)O6qg#exF=))KPG*PrqO=TOk7lhK
zxM;T+`vqfM-HZ&I|1?8Q?xWUu^xATWveb)-2}MJsq`nutFHOe>R&HK;RQuH+`qAuZ
zSDjfv`l@o3IP__@WT-i>40Ld?Z>T839HaDYHlml9Nu8O=*~!74x|c{%;{apsqt-0@
zr?sbMi8{siOYcB5R>gZNdhAN@oC5OUlREpxYU;qDNY<SNUn{Ki(GA%>aHpBw3-A%8
zP0PSnfqrKE9CH3+*3q=O%nr9_w`aEX%wjURAYHvBaMi3ys7^-BqW?-PaB3^CzQJ75
zcaU`6`th(}N!LBsa8zEXk>0ML=(cw1p7jIgP@nNpB{#`!0VIpr)$;V&*HpW!<3xqw
z#8RA!4SgN|pu@%+k)t#+u=VvClXX;Jo7aYH(}{6#O~?iV20Gymn-u8iYe#Q6>44Nq
zXy}e4Rjc<&OL3=F@H=Vq40*qjP|+`$g%XnBR)vUECKk-&1C5gzqA6Yh$?ipF?5T9n
z;PJ@$`G&ZVP$7+(TBM%7zVFHaeap(q$?gJe==m;CE2E^KXx&SOGn0t=4b9iJ9&-3x
zt?4NN<>Mk4EadWZx$W{0&UD{2@HnQ*lP`6FY1YtrM$G2(!xoDR4GM|OjJZG=e)=s;
z1HH2c55|5BzEh#r%eB6jK52BS-|~sT&3`4d<x1AM&`e(xQww^yTd@mS9R!rUcy??=
zSNgWG21~)Gg0!B-+B<GV+r>i*ANxe`bZ4sBN1MxzSCXaBPHYsQc7Zc#$@^o)HCOPh
zO0T>7E}R=d1^^Y*ef)5V$#IDVlNa`0QUI+K0*pTA(0cZI+E-M)zP5z%eZh16Eo4T2
z`mD-FiAr~+pB62_)!IsiWm<Pf>h?T-*2R!MiU}ivH|WcYat(;<jOd||HU{w$s6v_2
z#-PLd9svQTUj5<)qvxzQui1@sG|JM~PRuGEcM*i_JiWXOky}KT7-*D{BAgGtm8HY)
zHa}j)RqH4ff>d7?jyTZRAwIj*Qe-d0cBif^qY8@ZSj1Umc@>xQ7oDhTsNF8Oe8r3^
zOCMPmTa@`P+6?vJ2T*RA9h1kV&uBH@yT@`t)*bTX0@ND1)}=BldT!Q&Z&)x>2MHbg
z4)iRfDc**SRwMhI@U%i~^0u|?#V-Ow@{ey^b>_Xgs&{rb4(hnUrhoDIp>lxQ=kKBB
zjS@^Oa^0t%tEl>(RE}{K<if|(L@!b2yS4gD_X~n*g7!;%kZWf(KFoAsQksAubLtDJ
z%)tUTqDF0>@W1A=O!W9E7)eSO)~*Il-&6kj3f{*#)zPB?P%Vx_hHk}S9AY{XIf@gM
zI-y%)#lXiTd4wgsWY$`ow~_N$$ZhBPN_j@M3#SVA`<lij>&5(VP2-d|uHbU*>hEx0
zv1w0~Vdq1VzUqv@17k)K_*V`cqOH62598}tS8^|x_sf={ko3#>Eq7;t@sGnBWd1g#
zf~`(!8B+Dm?s5LA(m@!EW)~?MxXs1-1k*A$U?d)nrjoM3#V&wxRu)k9ZCKwo78i1m
z3fe$_7xVY^0PBQJ7X|{~W=}|83)FJ5$mS{&mbCln1!>%t*54l#4PTfarX=$U?jpi}
zHnQJtJdBsPp^Ph^<F|()M^RT=5Q>}){Lm+OZa5?aEvvN{<w|{DX#}Sq%FhXM#!a1c
z7b7XP>L;7zO1I2NOy}hXLCyG1s{+1F(tIk-K6bybJ3syGioz#{rujD<efGf=8k~%+
zvEZ1k6yrC0dnDsmP$Vq!@bbKCKT3IIMZ6ud4sU!RX|fTxx)4<s8>=(37+CI~Oe0K_
z#S^O^mRN~{hHeU&TQcnEUvGs?H)n))I0XcHwG9oY^Ig#Z`sFY$wW0#(_BT8{T!`>x
zaA+Yvi6k@sf<Pd>Iv9CNCMeyT-`y<zF+_p4X_V6-psH~+VJ2C4YU$l^9JBQ~A{M1z
z>LXE9&2IY^QxRGaiQshh8Y#*Nnw*-n8F47K*ZHEduU76NDL@Y;yXP3Z`+Yv^9gWFs
z>BG=k?4vG~BlaqG=KQs{=6WFwuwt)I$8+CevX9d#TeWMAQtNmNq|oY}ZC0i~HyW&$
zumy^2vl_xc=lZg)ol>(ENBS*$$6M=F=Hs1fuBz0Xvc^;t%i~lfGHBsBfOjpOSaIX`
zVq!lk3|ne7Zt%>rt41BdLo-uSQnIrxEG*!LB}=8iJus+h(?Je=DHK**j2es&`EWUt
zlyt||?vT<sE-#8U#E@J_1}a(ib)>51NyU>11KD)M?E_y1#7yblz)C`Zu<Np=y_!9u
z*tQj>vM-bC`nAs0qSY*#Y=Uzv0GjO67BrcfY+xaA=BZ|1bJP;twK*9bgrsPsJZLY+
zMGgCouo9F=p4QG&yI!~^8?YwMzY)0OGMw>!qFBPbO!vo8aucob)xf~m0N{2PIg|`=
zvQ_Daxb0`3+^VqY$zv1bX)xk#n@xo@7DF1}EG&cute&&SPl@vcHPkin@j9>mG<A->
zaWN|y=(5&ITPqN3ciPKU%IW3${p=ZkVv7DPqA)W)b_T*2Dens|e{P;(IS?8;p%e%W
zj^i*=!j$Ddzgah{Pf!ltT>P4f>?kcQML-3&r<+C(sGMR&US$U?y&bg(ZK<u**D-gD
zeJ)EzLb5sAW&y3ftC!8?cJ{r|)Pkw(LacH1;f2F)U4ezjpm#@U=<>X%##WGa(P5EU
zsFU+rmttrkq@Q!?gKc-$ry}B$A~Ow^EvM4Tmm@8*E!X~ZnLr4D`;K<M4%_m(Q0F6D
zV~4B`%?D7j8E)t2@>n&6%rIjWT_^}dtF81%T319Q2^EE~8D?!WI+gD)cW*{@1Q$b^
zuGSWgi5^=kz}p@;3oN6I7RmA7!s;b10~*bM#LBAA$K47+`MHvO^#i7oAi?*3pN^R*
zC9vtZ1<}AeQ&VGjza@jtpe=P#N1z&VCyf7|x4OEz=Uz>mntdP-4^Qh!7Z<BC&@-?w
zT8N8FgM7@09@0xuA!cTs$aEHt&_~!Fo)?6|f!)7Ed6!+}aH!QA)s-SK`^kD~|H)=I
zM+*nmS6XI8uAP=jX1ku9v2t^x1E;PMm_0;Kr=MioqDoSdW43upkyobffWOUrS3cM;
zQ+Q%^X()YZZQ!#4AEB|kqBaUi3H50taGH@E3R*%5lO1J;47tZp2q2bK3*dNupW_=l
zE?T!%oY(7|X0ry3V(YVZ*>$DpM1Wm07%=O||9jgEa^|qWGpfu_7d5lXi7IE+2CMe!
z?9IRTyG)o&>Ya5ShbE+?<>M5>4lJ~ew})H!v{6j77lzbrr>m!HRY=O1{E>&weKi@#
z_&2WRkjrOIM|G^aO|0we{WPZyZi!i>aq(&no6Z$FP7O|+2k-4XC8|9UC&-fCR#7J4
zln!WBPk)<GSP+4yt)2SdLA-`)HNk0kCfw@@6}lJ~-~*j=<cI$;Yhh9==)=}jIYVQn
zQSae127FLw?Hqmr60E{fODZ}=tg$CFf@O*-f>nZ(*7}FulY1Pbm!6Ybh_A2<`XwMT
zA3K*@H)-bfRiGmRWboR5wBGL57P$Tu&P{YuSaVu~a`L%y(mZG%GxV`IRw%1dKFP;d
zm@r-gE{%7eOHQ4sTbJd>=p$xczn<;iN>;IY)R{*|Xa}5{+)ebRxBgfn;2`~g6JwTn
z(zMUC9E9Z3HNYG@&de9NKrd`(L?=vZk=ocO(I)<*X4kv$*A%{x(18@TS{8b5|M{Ok
zABZ5N17U^B>HTN2|9|~>dm?~qgYDTgoeT6L$11;3wIQ49cp%1WErANrOIl$dvG_D9
z+`n^wp%~r~!;ISw`wWXt2T_T0#D2LV@*I3eL<fpePT#*iWq+;S4_3`2BO+L8?cAtd
z*6WtJ<vDb0Izj<JaODjorr3W4SFQ+-d|UFZeJ(9ct}#M0)3^K84N-%sO))4+F4xLs
zr<1LhfFxCzQk^_}<qjaN<=_J3AMGGSf*H32j)x5+Wht|@PuKLCI&?57H_TQ?`S!R3
zW>$+vP|h)I7a_)1SV&LtTbu5ZBlL6pXyEeEE#^(>Kh_Z4j%CO3DHq0g|2=3B`B)+?
z@x~3loyn}e_Mw`-L!oLWckx&mAm|49hL^wi^J+jk(bB%c{jP_OUu+ez;f;4!8+~mf
zbXMCn7G{}F=@dd{Lwtm&vp||bp&zTPk5(YDTl!6=Ll&#~v?ZY$9Iuw_+wL7a_Z+X|
zBn(}Tn#2C9?I7^$2RY1zIVE>KsL#m?cFTw=);HA2;|NzyEH)Z1n)`UNE@8ZA?K9gD
z`VlR@nJm89r}kP;e@kx#d2S9{aW=MsTpr?atE7B!5;cgHvP1)WSkl%q{9TcmJDLOh
zw+-T-P7FAwLxOknd)_w}ap&oc@|626M}OZG2pz2tNi85O2cv0Rr<{WW9jX2<6L(7(
zrcB$^CMAB!{ZgKb@FAT5t7v(NlI_tC78<v_k2}=f<KqFl*WBN_@9%in&+@{kvCA|+
z+;@?=P5sm=0PeQ>K4Z|Jv*Xmdo5Qiv>lrZ0y>m>@)4u{}=fGy(T2ttJj3jVjl;@eP
z^HB7~w?MmyeJbhkY<u%ZuM7~r-@@T#`p@ch7)rfU<dx$;8irWTmvGyeSF7-DpXDw1
z4Z4AtZZQE85Sqq^Vf<BI!~1CXQCUHlLKIA`#`itdqe0+ky7s^@GPF#c|H$e0Y@V5i
zfv6x}eg9eX-<n;H4QQ~O)N<0_Iseg#cVvM6&t&la&r{eVKxqEA2ZSH|736Q>NUZ?&
z=$+tl%>O(knhp>ly0`kvznb=YP(ldsA}a{td;fk)I|KG7t`6aUJv^FeU}TE>;ltO7
z7I$g0%l!>LzP&AFc^k;{Mu+vW{MXKq%31n5?9|Mjzb`1!vDZ*kZ9JR1C-=aabWvG|
z1&q!93M89D7MYp&=Y6D3aBtqaMI-9FaelhLu(0qWFxhlG1D&-$i*MB+Fh1^Pw(w<7
z#;s0uV2>Ap4?qfQnG217Mzf?x2TBj2sG;oi6=-Ve@i*Rn_D@DaOOJ7?`T2!3rY8)y
zO+Nr0dKOs@*4Tbs8s^_I3BlLAywq&~LGR%q`Ukp$jy9*kV(n!)Qkdc5pRdq?0xwC2
zr2be+Y#BOE&OReiM#j$#io)M9Mv~mW^{{c5DJrQ=HZQ~}y5Am+2Z5z=xY0$JIa%-h
zUW~AAj9S;pBLJ}qRi8UQKcAm}94{!;o1U7McCeG0wO0RKgl_=8H9KYqdHQ}sFl<S_
z1%xKF7K#D-Yqg`=zvrp6og&<wFiQc4+h=`5xK{HZPRiG<)sI3}g;0v_F0g>y#(#aV
zaArb9C8hBSYlS;}e9F+V30-(Y&LPd*{G0E3>%9x}Cs&<XD5z9bu1?rh$3IQpoW<N4
zvV;O0yf)0zH76c;G=Q^_&GLBEx4NeJa$Yj+E4;yQaCWll@JRGtEx)M{7#p3V-J0MZ
zKC{1JPI2+t&W}!j0~!Egx1CLIKaYwMpBiI!Nk@fbmbL0W0YpcR_J7V|!e>%I<)cho
zM8w#{#F>o6U&_+OdwBfS&m`St23sJ1(F{WSpVebCfK}J<%Xw&Ny*B$WhZbH#Stn%j
z+Ms^w|HlCB&+#b_7(YCF_ADkQ=4`8pi-UvXMP?Dj5je8zfnV^_$Ek=#NAkBOe$x%M
z%UR`ZHk^cL=u0|bO65yBiPrRgw$=x{PhDN&2LrNL1T?zG?y9P)9|WV;vsuf1J4r88
z&H5?O3148MLBeu>a1P1;M{lHvrJXTLkB*M$j@~&v!ikBCTVZ<7`8HY(6n=U;2g^T%
zN*MRg?(>(;X=}S`Sk78sUDfgeXl8))$`kkMX#Kn4ySo+fx7v!x=+sOzzi_cn1Rq}*
zjW^5z?!f`}zzr(#<Mfn2%H94A3~<r|n@5k!w0>Y@L||WH_yrZ3+-&hH-d7(Dm>7*I
z)-`A^m_1>cY``1>0FR*m21C?ejqAq-wxh`8`&(Aa42z0ng$>>x$Dd6ULrF8C%=f~=
zm;m#V)m+B+_taiuF1P&}yZZY3&=7!@Uh=2&#Zw92m<n3<v0eNrOvVCyWf{XC^MBS4
zXd$m5d2s+_j&yW%>fEM_8*-kGy)CxlDt8;ItzwFciI08DHeK$cFlNC+2H44c79hE*
zp%xeU$9mBaGH0Co=g{+66-yaIK9jZW#jf@4%ig$f?iI9UN2D7^0m=S3E8s+qa_3Z&
z{d*!4df?q>WK4FS*)snM)b1WdfpQ`57bJ$1|K$$RtpV?-b;SnyA5%#U*yok{{%WGX
zHvgB%UR+zy;VWFwZzcKr9pKq$LLytdWsm+d`1Qx%U)%n}HZbTv-pnsMJxDJFii<l_
zW&5ugy>=uE0n@K=0SAHpWz40#u?fR+|6iJRKhB0p<~srEqV0XtuMUKOqLyDLb|T*_
z*8gKt{u*-%w0uQcp*|X~kJII&-%A6piSPGT;Ezs*VPPD>_6|W%zWI+!gZBY(TcQC6
z2VPh&{ogkZk0j$pGnCCC$7tCZ%lMHV7BU`kU{yu>4Nl96{U`&F=DZs@+23>v_6hpI
z&2sYR%1qpCg!IJa3)zT!EA*mVOfr_Oz=QW6^gQ{GFRY2j3}TBa)Y)=wEB-($G>p>n
zl{j;@yV@hN1@VpE1Mku}Vj=#jKl*#^IW7VR&i9`~i?{SJFF$8S@|=7&`<kmAA<y+9
z?6mWhNQj#Bs^6Z0n{;27^lj{Lsc%63&e_?Sn22b8Vd0Qk@bqPDEK>5YjE#Ht;lqdY
z^%Uyif3<>+8!P<Ew_Z!qw>w)*%lGV+catJocmqzFxkVFPo{Ial3YkOb2F9&z{P6N6
z&c3*W1gx_4kQ}h6l$1k$N=i85?LT}M>S_M!E1d&c7m=FsL5LdsNSCNj=_N<+3p^C_
zMp!!njFRK&N3GSVNahE5k)#m5;07$yy^ZHj8ve0v*ILLKZgd3V#Yy=ZEBE)Ye^k~T
zmoTg)z`~K_-_AjpN*HJZY<2rz+d!%v3gnI4XAF%0?$JNP%n{LnnxqW>y$uL=@&TI;
zJx<pDV_W|U=ug@BuTuOOq8Zr!M@zwZdjC6hV1wg5`~T>)cV}Ek%Vhp#UF?AFD4Q+*
zyYt0*C6!fG_QiqLfpT(PD=URY0AnFwpDQQ9E|oq@C4{|Rh*5qn)RPr7^8=H1jDK3A
z_IYgJko5NR15h3qfvB{!w0G~`0SE31HZ1stizl-AuuC&*eFQE*6(>dDAvA>nL;I&D
zFvwd17tb0;0K&=MUgc3atg)ZP0qfCKlB2*jAsOxN?j9N%a=&Q49gGh4cr+`)N%N0y
zYv2qck^KDpu9LMK!ouSME|!*az$x+e?OOnr^U;l!g9Cv;)I{x>4D4!TiH*<B(o#~I
zXlqvnoqFo1iFdxL2k<;=4u~&b4C~x7y{fBbWiiZ!fx5+wqr=0luCBK?7#SHcXXLEQ
zfTJ<z-NY;S?(QzYlx5Q7Tjop9oLcMa?L9m)QtUXPMO!ww1)vXfOqM*zm%JNAfpOOk
zQl4VQepT)sW^BV6R*I()ciKuPI(bFH=51fI4R}w{uU>salf6O^t_(oE{yG4^49gBz
zj#S>a{CI|;mp%QTK0Pza9R_F(T(xKRLm9g#*4CUd9{{-@$9<qG>ihL{f7!&?n23ld
z=@>xNcngcvOjEc>7YKPR#dsFUlzs>9iLLK0blZ#NIQr=8>swj9+Y7L^&V|{0)?wq$
z7V%MT;FFY;WMWb{jE;^z-kN5MZ7_QtmqW9ylFI4mcOfmUsXU4bd^V!tC&jOJtP&ou
z`aN$gRDW-jmfssqq%UT)&4UEc3n7!Z|5)2={rHIUAurDnYw>|?L0_MGa`OCvmUM&G
zILnyYQdl^b%(!;v%VflX7E?iEL`|wl$l(h(_-DQvv^r2vFPR~GzN9BHoM6STB%%Zr
zGFobsD_o~5-C&G(yBmhv(&V=-fTbJ1ezx5PSB2pn1>!bUwzQa?Ry8+InU?jHv<yEj
z!}V&q>9g!q%l%*sAT(Qzzr#31F}ZrHaH?de%(Ow<Y@}n@9H=x8elk<OJQ9($_`g9@
zSSVUzQIh{Avqhv}q&Y`1neG{SlcT`X6#jIBK?5wo1sF1~s8U4h&=ta^$4!=RD6tGG
zeZC^JW<OHL!VGfGyH(f>IodF)nhDt+tLPM~EU7MP!zlcr{EmW0TujVmUDbel2=aEf
zr#Ls_rVkZAZ@aCkA79z1`GnciPQ*hWsvD05Rs)@yR6+WEqxxO`CIj;fAwcx>qQB^$
z_HK?54Z|!?GmpPaO-V^>Mf*VeNJULe?;yRCG10|cq<e!j$wyD?hTmaD;8-2)IDZva
zAxW_dEs7r_(GK}NA_6@6P8B0_cSu7L+3NIyu-f5@Z?1UTRM$NqIJo7xZ^@A18IUI>
zmo5`Q<LnGTH!y0MH@3c%nw#LOyU}=ys8SB>@ug7s_CIa@H})KuoGt4E@x#z!UVSt}
z7A*pVQ-6bN`f1XoQyR<~pHhFLdh&u%s)^s@<3VOI+2|crrZVAZ^>;sj`#GZn&W;ZA
z%xVmI)cj>hadUO~UU`sYweCuCdDsFQ4ixwIJjP86W{>3%n_;kpD3{kDDjp~GXMc}{
zYyIQJV_saFZZ0nPQczxClyu;l1<9Ob^in>wa!RXc)Hu9fy!jm8gWvb00#gyI(C)L!
zS=ro#O+<CpbN<X0RtK({FWarYd8-!4>Ym=WYXoGGt(*EL9+@hM9P6u(-#KovZ5B?s
z1$Njs-)z&AmyJJL3p@Id&%J<Vc1Y&;8q{2WnL+&zONH)6q{+x99*b+nnx@sw$lT|e
zDBRcqCGRdNDzn?Cpb_^hbtq7J$4_c}?^SXS2@B$m=2F-axd9?3kI9-uhh)_C%R!S;
zgMsxM{^TU0(mf|Nwb(d!8kg3h3qh{Jdj?uY$;qAkuai0D`-hxf)Ne)~1#%(>6^7J`
zdX&$4+tVAz#qvcLY)>M!3CiQ>M0}*zu^U;^<Bj1TwENFvu$mjBqnjUr%zsk0ul`fH
z+F2|`C~M>~01S%2bd1-e%`F(&ch($M(&9O>%wFSFQ)^NZife~lkiH1dn5!Jw3TsI9
zdHAXoH!r<I*@Q&X)eknS)|&tobRXgSB9gyW(g%cA-lWS#1t}z4Bw@({{MIQlaJvNH
z)(p9;M(M2AYWdpAi0wKTHp+pn8dg<Wsv3y!Cm)h_ovPO|fVF{{JJ&@H70~wi_Pnw9
zWNVPxdZa~K$oEFPHF@uhh;t<+9rE4LR&!rA3}Xg+KUtbIEomh?W|g)6X!O^?yIz&{
zPVlRUUVdc}=^8C*bpm>}pmglz34`uof9uHhqNq%_#JK$4UJIBkhT$+Rc-XPDsxYpX
z5iY#m)R$LXsx$TpMzcU5d9E4Um2Nb#MKZ?&mST}CZklutyg@aP<^2QK&ZeFm7v?_A
zzh4&dX_z7SKt11i1r}5yS9R54MynwIuX9+2g-~~?nk@gmBPx57!v5pvYaz8HU=BSM
zeNVp`3TzYdATw;6a@S4Q`1B3R9%qW=CHM1t8}ajxR+qtL!oH@#<R(<QGt}?3qh&7R
zOB-4FI(6_bw~&UZO+7exK4<5F`!7$;QW}GAxyn4)duvKKkTiB+Bxc0-Ap{pzxQ^Fu
zhxEQJ3~_J(GB5u)<mb@P5Nb8{{WOTQyur4$k0U3W<ElZM;m@Ir%#$Lberm(~&agvJ
zNmhy(x&InP|BC^_e~k!;8=`KwZyit{KE#h857z4@dG4OR^-aG9W7D#?kAEoh<>5ca
zyN->X8Cp6y)S!)!etTdB%&V*l%fFGI-VLYVzv0<$C)`p5&Hj^5oUg#4ne&u*yRW@L
z%c}Zk$iF54h`U3&9T^YE|Fb!i3pA-$J7>DOL0a3S^&e0EkABbvp}Tk=Qo0~|ozV>O
z?8Zr5c)y`mNjD+5|7V7(bRPOO<0E%eZ7o1Ylt~CV(UNqhTF)=WT`&KsY}ae;fg^OU
zn72`+<n2@mfBs$#$i)c?VbxGo6&g(|2I|Cp_q6}56F{m4XpNXMk>nKUgrFdHL>#8^
z3xYj@f|`x;+zrH=p5jh?+{krD-n5+*BKy~30m74)3Lk#1qf>rc4?}09ZgX7EsKVe3
z1qsVU8#6dYDL{4kn7D15Rz#x8WdG%i0kaOrAmV;IjIN#8@ysBQ6KaTnEFZ^$GLn*h
zP7&s~s9Uye8f~63|3f#f*NP6fxZBriC})uQKq}0~O?yMn)`Gyp$*H*UIYNP7xBT#%
zob#Ywc{D8DPJH%%#rQ2X3_nXCBmLf_oc%{#fsaSV1DR=>8%WMpP)0&RLRy-GppY}P
za&4@0ywWSytO!i|ze~HM((Zob4db&7hQ@CW)zBM+8&nvKE(G2(%sx0cfWbJMj4%$_
z*G-_h16q%*tq)zh#h}T)PxkH#M%q+8cmF?+(`vu36TF^=62M3_SNnjZ&?%3`ZC(Ng
ziMOL{?CjPiM<}z;(<WHc)s`mx{JXgwmz9%G|5qa1@nFVhYbM=%wzhhs%C6epHRK~H
z2y@1r;=URh%fm%ZliJeUTv?3GT=)G7vN9UWvcdPxEy5Z4=|ht!0ABYm13{QZhGzeh
zk6t&bhF%wgIJh8$4aeTz9?D%}2E(vS2Fij!kw{)aLG4ow|Hfka;Syi|hFC?BfDc!b
zD1hks_roHHxQmADG^*gF2nwBny4cp*Z3B$pg9G^HC9+izTwduM5)vXS`;=9f>kG}O
zH+XWzxeA6`Y)y(-t!bKG6T1WC*#7-QyF1*%!%ND<!U*L}XIzv3ZJq^5l8xF;eJdB2
zZ|EkGrppaM<H!avKEC1a-`@`bS+P~MkGL(U!czCLYTC{B{C(7VBl=CBeGHqj0O;z!
zMH!9(E>OWR+jRR5KOLc<3{yiPQ4tXlKY!XRznnrdoJ5_S!A%?9@3S1IudL&JOhg+C
z616VhugvJq`<FioJhuHDHw~t5aDaTjddC0IP|48Q)5~k<`*&0OW8yHq&Vw5zb2r=j
z4oWJ86L8u;S(35+MK%1=ap2cJvt=$^IKL7W`%&N`9aM^|a~6Uyzr0aiTQpi<Q{!V}
z^N8H=RR85@kgfnNa*!hPJ9~OW17q1kg=NZrIs@1HOc;C2+p#mB1@KZFSfTL%o>O-g
zZrAeNs|}Jhx=mhy-@fz$=(d=dnaRpF)CewDYJioN$Ymn8-x~f;Qa-GG10x?(HBnIQ
zfPa<|1U-Z_z`gpGi<r`d;cHSrBm|Lt19_Sp?t^iZ+gapt%Lz}X|09rm{P!X*v0Lty
z`3hnLPsW4GA;Cb@MG|ZulgEo?8Tb++x6|I<zOz#<udr_2XRkgd7Ryl*F`fE<7OU#^
z4kfEv`*2<DTCQ{->i&ZVdHMN__wRpODlaB}1j<^xUG)5)P8zT%Qg?CBL+e`wgC>>a
R13<t(B{}s+Fd55;{|CQHh#LR^

diff --git a/chapter_hashing/hash_map.assets/hash_map.png b/chapter_hashing/hash_map.assets/hash_map.png
deleted file mode 100644
index 124dacd3a61968186bf3d94bf3b26f70a3a3ed51..0000000000000000000000000000000000000000
GIT binary patch
literal 0
HcmV?d00001

literal 66528
zcmeFZcUV(f^9C9a6;K30<j_Sa0wPE+Qlv-+5eU6Y4Nd7Clp-BOq!;NBLg>8-BGRSz
zqV&*90we_PMm@jpJAU`i`#krbgAd6z?7jA^S+i!|d1rP)pQ*?a5mFI?Kp-M{IqByh
z&}HBd_ZvPg@Fqd8fCIeYI6aq@1eNsDtONfEG}o55P*w)90mt~D%Q&Q<OBbgA|3ElY
zKQF$xL;;8T|Bj#I-2Z(JFlLA~2=C|lAdoKbe(_@r{9au1>-|zD&VNSC#Qpp1%b?6l
ze;?z11I`BdNk8!h-UuA!beuq-8=o(JapKu;Py=#<<fWfzxZ`ZjUUg@bO*`7t?0-oP
zepw~7x|Uk;vW@c1Rt3)d-s=F7T9Mb^1zTsNxcIwXaNU>?{GM9T)Rp2i7Z28frY>Tr
z<Ev}jEO@Ep?`>JFh(xDPA`pn}BGsD8gN&k*8|&-ql%3ab@JJ*;|9J_Jpuj(B4xpu_
z?d$8av$IQU;*{z43<?aiB3_x@>{fuljzsbqaq;i?gZ}G<)R9^v88nRdk&R>y69)W5
zMn=AUyF0}3qLoYYGGb$cnwolgdRj_K%7t;m9G=A8^q8^ZANK_$*fneo(^Hn*8G|-7
zh;Vari;0Ondi1ij)Y%`T{n0^LIkG61mKBX80i_f{6A|Bic<zV(w+w(t{(3m$pyAIc
z;6rF2u5pu+uYy8Yn{iD8cM|pslxjs^P3@!Md}%2cJG$y>>y%-*aKsqGoOGo?_s~%e
z%<zvH;on)%X$^Y_GahEVwQVDn+Xodm+X@e8sIMQPPK}NIxHo9;wk-y-x3lBm<Q%^e
z=1V)<+-cbKv1C!1(!z~-jBm%DSc3V#RP<A0?YExQLPZnZn3Ujf_3On-9j&@4NlBEn
zv|FCi0yvK9>gwj^xsv)aEhx~$=O)h@!>P2P5)r1W|5=}3M;X_&O-c!TkoI>?WGNhX
z6md!oyH!<H$4|9Y$Q^I^j~?lP!4_FYNUD?)BeE-cFX059Fco7+G|G5FqeoW;_s{V-
zFF%$|AatpsXTQR4QX1-oEWvmvPgT($2ZFSh!@|Q|7-bs6d|}&0Oz#WdYVEA#zF{>f
zDhZ6T<VgNDu6tPSaZBpIZ0KV2R(!#Zc;+SEB(}^z`INvPCQP>ub<<kG*Hh!-%vykf
zMc(jj#G}lkePMr1@S&?hYQa+qj#Gcy#9w*-1kTDi)*UI#+oS2qk|%kp6KuveZ1P<D
z`}?aAj*mfOWYN5<73!UEN?f}+n3S$a6^l|;G4|bm8})@i#)-IK8k?Y0h5PE9ab`@L
zSBKb;D+q%pC6WdklX5;drQkJ>7Sx%c*BbP64lDBIF}umu_zPXxDtLK!%>NAb6&DpV
zoYPlwD<D~>X*yetBRL^U_i_cH3mGY?Qb03E`%#(e#|LCbMKOlpsbcOO3!WxOG<b?8
z-R+;-4F}Jg-56K3LX{m~Q^Mwz(u*Ruj#AVjn=Av2k_zT8z{)BQ!Qd`@`SNt@t90Ya
ztgc3zr}d@WJ{4G?%k^;@2sy!@;|1R_?x?rWBXigNo=<vVhiqn~V0Y+W+Bk3mf2pea
z>};t^*|5<mLr#w5z&Xt?jSZsdqQf~JvVSfh3ogn^L*$So%O>6s%mukzN9azDveA<T
z&CJZ$!b%gsQySxZCd-g`k0hG8n}29%7uH%<JG=+?85qkF{eIv1!S!lMgP^9VZ;$Zm
zVX(gUyQlUyvbhx!-H;Db0(Ck>{@f_{Sd3pkV}IZhCJ*ywN;M?((qxw<E~SfFs#FQj
z`vR5>&x`09H&KexS)%>JmIGpMb1@VV$hkc5dT(=E`La?o*1!Y~7P{JMQCT@0Rcw~n
zE_iuz1=M)&kNwU?h)bvjTNq(f`c@>Bk~z+(<PLcib+wf_v&z9Zo=39=W!0_CB>T~X
z=6|*i3l6&=9|2iqQN(Rzxu+|PM!j|Lk}W5qUcI78vzKjC<DJZ(%k)&a6)%5f_A|`W
zO}IYZEKCU3*h?+0+QH1um^<zE7L)w{h$oDz@~Lnmt81{qqYw<(YhlJKSeUMLy*CFL
z=^yU+jMX@(1k45X)U}Rt#A_W>)M3^V0*jYdeZc!u(Z1})KXkkpZDnfn`hh{!g<u<;
zoen7qe|qQF%B^%i>QRfr%YsKB>IayIN>k}%wwaX_|5Sgg!)5(9V0Qm1(!Bl7OUAHL
z&#*q>{4C#TUAEvqoi$!+oA%{86pbv%_Cs2hQNGOm|FI%JoP6W42g#*JfnNSwv1R8q
zVN`ejShj^Ht$20df@um+L-1EH0Wrpu{D0=ilxaN1*T%=^jMu8Naax4Xxbjb_K>;R&
ziKR90tL}*yQ>Q<d>Qvt!G%=t`GWv&)+l>U_lseE%Ui;_${4=hRfG{TnS)PBaO7qP-
zAXMZ%uP6W9X}eB1xW?k*Pc(@CDO9TfE?#T%%NLw~4CDJy0<^ix@)q$&z&d^kh$#@Y
zdHIiF1}@|KV^8taME{uAJU$@im)NF%Msob)I$%~A8Fz|8{<&TY)PR`tg5?x{3?ohf
z%<6zl8u^Fo_Pz&*NiB<d{l_q?z^r_IUl-8*p*06Qe1D(CuZDjN^RMzR^!KmwFRb)m
z%fIj(|GJ$E7xAy#xrl@RpZR==+Kln&-x0;}IUbna{%tg2iU`A4PqsjnTZc?Ak#=o1
z6tiwOs_3+s9}!JgTG}LGVmCcDWD!^KfK%+ASX=W4-rp|W{lfJ}lA8Z?<*yYpt12)k
zzfJL}nWVJ8USdxx9a2*k>#zem1t)$3bP>^nqAsRw>v5$0Y46@A&@5NVtEvt-iP-oa
zgZDlqS10a%bI8bW>MW0li6O~1#d0)zWuDC&3EGZ{c@B>p<TD*<z4QJZlh#!ILABzP
z`#*8SYpsQK*l3vV=-E4T6fyB=H1#Sg$akTAXs1P|xQ!!i_IySyn?5%`S0+P%Z~e4T
zo}J~(c(pUu$7%E)HS`9!hEhHL^b5O8hs)M{-JOA@#3RH?|2S%F%BlFUKI<tvb~_-r
zXbzzx1imZqX#Y??bnNcmV7wGS0MmSOKOr1md8^b0d&`N!N60nu;%4ND5ZKpC>xff~
zt?IV8*ihw}+~T_#clJ)!M?9h{c|nWwb4EsE-%MardZR@dSG5vkgMyr$kDQORAvB>8
zwY!{Y=`I`Z4#{41MtZrM<%Z^_?Wf)LYsi~n?bL02@st~<H22AGe98g@Y!;H+Kb3(C
z&a7z2hi!b8tE_>kB()ru+MW+Km*~RAuNe7!--WvMhuv@!cUlS>jzea@6X{N&pL>Q3
zaUpkolAi_{9q;cxYb#7DyJ>I#*Y-<w5lsKDx!v(^Ed|1MNJr<FpCAQ?xfEW6Y(9#1
zJ5L_lDz-Y=cM73vv?y0MbJ5%Rm|P7r?_06dvv!h+Gh3)!9fxbh$B)#U_Y6gN==Ag0
zTH8Q9uu2WN!uS0JydKJhD!hF~CJuptJ;a0|zmOrm1rF|lu^6WE0`%iQ5BORdvtt;8
zIbO+5iSC2i-a+V!IQW<vVag0miCDni(68zcK9`CWJMbzjO{qQJZ%-{rw383!4-SA%
zhU!d@%)u}L$O=Z5?UsQqA*cO4Jy!?aMAy;O5oIQ2AOm($-GXZ&BfXnVUBm3TTsh+C
zC?4_IImRhAYzNZ(GC5pre~_TR>O<w9*wB%a<R;at)&1UfzAY3;yXI^Tee6413#m?u
zA$fUDei>2Jv`Z|aEO)x-rl>1Y-{Rw2QZ)=uOKZw2cnP!fWP`-V*ZNqaIl_lWWlksZ
z*!p0av#%P%wL8NI-O?}DS2kn2TehqD-BR2a+PSf{CH3}(2zZI>cAhK8(;L4w-xKzQ
zGuOP#<;?FtSL74xw{K&}q|PHB=h{y;XP2~YF?I$H^haRxwkYKgJJ|7j;(}7vyoT53
z-q>3Qa)yzj&Aw;H^hO`fLm<&1nI;U2{pml}7Bt0oi8=e{PvcJri&kHJxi5=@I;a`Y
zkIgWqjr}{Nh^PdKw%+6DJ^Q&<rv?kpT&6qxW~`CeWQ0v`h3|VY*F`%c_Vg)mQ&H)6
zEiL7tIA8kX)<Gf>adxmlH<fSk;n>h^7Zi$|R^TDq<HOY*5x3EY{h`B|R(5BdRX)S!
z*y+NgICV_$Lr9!?-ODk$Vrg^r{4ZuHGRk^sG+Qfl3+mVK^EtSFXG66B+;)8<dHX^y
z63+<M9?7T-!jsRB`eZRu-`WF^WMntd--5f(x)V=VqPEYvH%m6DA+UGj{fe3({jqO`
z<A^oAvq=`h-WAl*s_Tf=_3ExV50j~r;hC9B#Z?XLdi(G0&8j@Io2Rz^Wecy>0b39p
z5P?0t2-AX3BvdzCd<+K(m~5|!*WTZ$KUoyGB`~$`9W(M?SJif108vf9;5R3jMeh|Q
zik)1h6t5MWPnV+l4c{X`I9yt|KZP&7W+lDnm!5{5WFfYCw_07Yjg*~HYI~3kUCpy+
zwcB1poNR_EapZjtG!hc&DBnP=dze_lsszROPY+)QCb*3!6I62lXj4s^*g0O>d)a)t
zQ=6MTU3BF??&^5oPaos^JLlvI#w$rotKaO|(+Q288~1o_bGQRfGwt38Xf;BwGC=hD
zHj6{9Wbg^S?854WA*SM6csb|TY{{Jz61yr>xpky}=Qs3(K!QOMXYeymi7>%&Nj=+z
z{YZZ)N;egg_Lm1{==wPBIri1}#p=PHjKs7o>X*bCH8$n!>a}%Edf_G1D=d&9Xfq4L
ztds9{O@B{WcLDT70NU-hZy1WyH|?t$9i24`wvi19DMq(77E5>b>Ummk9;(i9oU|yi
zr1LNho_tcs!`u0tK5^O801CzVsnBl(_t{{!h=MB7cUpLmXx_8aH_r!dUn@6F!(GTj
zl{mEM9`1f&!vrUnDu|;}-ENG)PnY?<qU7P&ACE=FySj;q*24{5-t1{*h&N_ub?D}H
zGK;<%<`s3){#4DaC*rm3({P-irHt5KKWTAO*!G%NJ4m6M#pDh%pN<O&JyfNrc9r_&
zqysW<-vQk~467~zyCz`a*0-fzC*S(X!Y!#aK?8${%-Dgk;m}l9!9W?JT;Cnzb|bM8
zcWW(J6N~3|V4|!;GCu>uE5z{{eT(|@S?YS|_z_vfbKi!%(>GF`^hT%O&<dha?w<9F
zYVD1`^Qu;PAWI|&{K-cI+#xT$ni}^!o7*#E1M*<(mXPXku^dtaPJgn6c!dGC2SDw&
zPcbV+EhX^B+OtQcMwq$u7CQ_5oW)Nqo~R+(9-iV=1|RgE56YD4+#7IkVR2hYIlp|h
zL@VhXQ1yMeU+LvHmfie~yxy*eDnVwfm6UqJ!AQ4WPx9>3mY!FOzDHfnU1blk!~H|S
zH?}Ng3>))0xJA5yP%ZAac?$aOXDfuB9go(Qbyi4R8-L+zFY_gv8XC4i>jcq(zfUaP
zNzHIO$l_%W`P&uM0+!d19P{QPbs|~7O@4wn>NM5h;}c_ZE+x7_KyWf0sSfwBI?8)z
zaXBN|2a!G=*6nFF`*rtQYEHA5Hsm$C=-StArMIsRmxY^djoGtVd)nw#b!8;dc+{c-
zNygbSZqc5JQ>^%&6<#u^KE{NqDjUVnTE;U3{7!c5ft-7`Jmx1qP4X4jgn@ygPma#w
z+Ty+TGf(UYM*Kb&ku>S~Iu>`~`{uKoNFS|R1zJL4Y@72cU5&OD-7<bNg`GF_FvV7z
z?ne?>5zNNn+~Dj1vZ7+gr{S}%7gDOh&++A%^0jrGYPsJkUbx8ri3oLm+B*(wOu{XX
zvr0xj4rXuvhx3<Yr#GEUkrQa$EpAWy-ROsDRs(x6U`MFf+}l!;K72cJ5fnb7>{Dm=
zwFb97f{nf*o+Oket)K0XP|Iv{)9G=<H#YBswn_tX*nsWM#v^;%on}m(R5H%SSnj%3
zzse}AZH(c!ApZVL5+GZ(n4gp&zGJ|(JeG~ll&5ohOTG?aL`A*SUXU%H>M8!aywb$C
zt9L$2w<McvSnkAI71==I)eoVkL><b+hCJ3bx|MtkAGpUU1lCve;J0SI<j-6VI`vZG
z{^lC*wF-RJC-^yE{D|OIAZ%_mbqg<f48JQ*3Ebi<utl6M%bKHT*l8(mXBDRVxxbv-
zKXs2xKAX~+^s99(R}XR3aR1tU>JIro2F;k@+oiunmoQ$#RWo4-Q>kk5aGO>0)c?%q
zq#iv|1APIOTq<uorlzRh$r+{XsNw88Zm%bVuvnLUr%+O?cl6xXQ73iTDT{}HCa+M}
zT48xyTYox0ua#I>bndwIzH#Zk7v<0|vF{iI_^FQc*XDG*?Y^03UBP2kJfrSg)hBjm
zvb%<5%*VRfXOPtn?d#{XDKDo2F`y8y;a10Se5!vO@AMoFI8G}e-p_^S$Hz~jSZn(S
zutU~lXSF4gHS8JOkG>xZKmYqqWcY)TPlJMjZr;54{rh)M;tijm;9!JN6Ew$TT#$Vl
z%=l~L;`0XV2cxu(MvxIsO76M#qwf<J=WmMFA+2P0q(Z)Q21BXGFdtg#8>$Pl6_+V2
zI+ax-QNB{~r)$sJ%NuLoa@m8aZczvQ9PG7*L;y^8Zgwm2iPVmPfx(JFXjD{Gf4@r8
z>gp;P=;}K1NyTq>@hfNq_}|>+2CaB4`wK1d;{6VVf4i<YfSF>U9s7g#!UH0uV{57c
z)t^k$g{O<VvGM!r-$4lv7uY6(#wtuif6{P_K++-~;__Qtf3u7@KrTbWmH#gI51Py!
z@NTG_cHw`rVSxC6J5N-Xm-^$bj|oUXUPC6d7vbl(j{uH<DhUbbYHwi<!#_R-;idyt
zA-Z0A<DUxnX)KpkG=@n2c~=}&fKy9%*8YRBBjLjRjx$X9TQ9BmuhA4)PiqXl&!DLj
zWbu7Z-1q&rkjD7H^->aMWIu;JCoQmBe^BTUO-P)^EjDFXAsP=POQI)TYI|xXC~u?O
z^X5W?<xYYjj{x!$#G3>}F<Q-6=~8HqA{?)D{xDX<&cnp~nEla^7N4c~uX*9+154zX
z?xq_F%pLE2Yfl4Y$9MZ%W#t<2xm`(<i5AwyP19+$T|lMD(X(81UVPZdYj0N%v!PjY
z-o&+Yz|N!0<cCz7yhQ(j)n}`5#K=f=QXHZJ`z8Nh?6@<R9)tUDA%7wdz~i9jwvG5+
zDXYC19jTIuWVVA<fn$F=jet);Y#;_l?EjK1;;ldBd9eYUb@Q61NPWFabeT|Mm8*1A
zpUN+@#J_<PEOE8dBQO5v`AxX-%CzSbuMV3oAwwY3HpvY`KiU95?0XVXtV8)oMY509
zfY_nH)7P>ub_x{}^Rm9dUB#l8wugKFU3RL1%}Y1)o}IDx(3<MzDhSx3S74woO@Lvn
zDsh#@4vPEe`^R|Yw5w6oDs=Qsu;SdR3Kssmm37$-AKhS+?RpplFT%@AUR}ma*6QtI
z`u85o+?i%x(Yu?0J5?ETu7{Ibd^Hc{wUT57z%Y>^?HE#@y@(vue(DT5itlyY#WFv4
zz@0llXu7mtIduQ$Vjtm#S+ro#H(}~Ze{tLEyC|-v7mcmDYP1}3R@`3xtTTOhc<2p8
zIrw%VkI>DJ46=x+dC_O*7(ViWd9ilu{#60gSW|s|bzzeT+k+e!G{5rW;=&*n(kwVI
zm6AX(-05ZWq%8%508{X@fzFQKX0sn3$`io13M-C4=e~A9-By|}wB@|CRONj_y8Rpr
zzJH|7n~JW=FGt4DR(U~nfi&FZNN}uRNj8M~*5mVou_V;H-v9%j6i5c|2o3U*UF?!p
zhRpj~>Pj5_p?Zn5P-D$EkuB&`hM;0`?}lUg8l{>D!zoQj*1VAc-}(>Au9vYNJ%0=W
zU`j)Er)_ibWjQOn!HL4W6MGu=I%$27p3bIr#lh>wSmjocRnqzp)OKs0Z*X>acw!EA
z%EKaryTBJjB*3Y_BLK?aV^zZ`#nLUn(_?cB^EJ777+x7^Ze)m;Jd-Qd)>=+j6&jFj
zI=7lGBqQ4v61VgP&lrtsogMWAL2n3%)fXaGf~-qM@BFIp2DDzF!Oa833#S!uhjc=3
zR2ajOvPm>{>l;cYu9{gp3ZL3-ZiF$C<ZMucX}TwQi;3^KZa9^f_j2m{uX8Uu;?%QS
z+)UD&BI3t3hgE$nJiT)k<rVW)6;eeQo=PRmi))A%fV649T7;~sD5Lu~WJj{0GDNyj
z(bo;$ZQ$2YPoW9#H$C7q6wf;ysaykyngbvW?HHKuNin!&9JEY4&pWE2DphMVqm$kI
zBf)i)1Vk<ItN8a?VIeRj=ylOD@9m5AxU-ALt1@x6_%Xl*mWJrpOtAKBT(s9_KjTeF
zeZ;CpFzey9?cnyfysW%PfNtBtp?-EeFd?rs5U+FCb6Ui!ljf)<Qn8uxdoe>F&yX4S
zk9#8_#p`fhQym;T)Ax(hHlp8Za~IvO7t<)mYU+<Sm(^N(dGs7QcZ&9^z__j^rFlpq
zAEu_~oVF$NSA6(gbbYPhPq&aMJo{5Z{1-Umt01V<L>1X_^ah)6OWvtORX+YRbwi({
z*E1I!kw{?6{^|FammvemsRfU^wEE;}8J_T50vidudeSyLUF3HXySUfFen3W=MeEb!
z$to8W>geqRGZ_%~fiKn3^3kr0&COLAHYXi77F5sn?EkKj--!X7`=xc;q1zWbFaQVd
ztg=K>;8RhIu%v2AV&?XI)>O6E{KJ>C02oYiT<?8vS)(Q1l5GLeIS{#uKxUtm(AAdT
z(WsEbpv^t~7qe;hwkYFha7usZ<!Y@!uO7RDiu+CC8&Arb>REKwsVO2d5=nDQPbla=
z*t0wA<vllPiXR`*@eGQPkZLTv^oyh;5!3-f0E=S!;?MG0M74yS;;JZ|e7#_Nfd0G(
z%AC{=!7rNzX+y3(&uaGe{NQ`|EbH7We<^8eRMl3<b9MjvxJPO5JSk6S{5p;pto0E{
zk2CV^Sh0cH_m9cJx@k?!a?Lx~=Q1sXpE4Tkg143UnKU19URo%!=-ldy>y*8Tr4s(z
zj{Lp+-yocawJ)rw;PT=9dr0rFg(;6tS?;3<>SGH7(bzSCait;ks7hE;(&TDXq+L`9
zsPo7b#kSk8{Axz7xGR?&%N9E!LO69jPVCuiQEG18OQ0o0h8VUcROUlZWBbg5h+<rX
z^FsePc(0WKKrqoSxOL$mUu)gT7bw!e2qd8TPKpalo3TaNs<l-W4P~=8UneI#6`MzW
zZpO;ee$4X_t*X+ER(|fOl4n-Wn$Z%41RY^pPB);;*zLHu^P{Y0kNm#-R>PN4)7IWb
zx@lHdyP*0)kt1W-JKJzAi>d}4xY4vaW)7!Qw@FNRBr~6h)x_ci(YHwSGw1`m-x%MS
zB+WKC>>_5?Nhm1Qrl(=%J_XY^8Jy02Lg%b;iC(QO@7gP1462^@fUV^xP~4xL8AKu}
zh{vm4o9Y|D(cB8r;m`6RCOgGyLZPwwN=knbd@(x$9nEex?0?Qq^e9z|@$M*oFJ26L
zc4FQ#;i=#&Der?xzT3$Ycj)QuG&<^}&c|M*!@HwQJ3B7gXt^CY5m->_A`?la0K<eK
zcUk@q$Kr(o<j<2=S=JXVFF?jK*t8gEpl9`kIK{03MWLng{CaW8%n>nvV`&BW=+oKW
z6l+UuxkP)4A~lUbCxV>%CJME>sxQjI_mEpj^{=5BtuS8~k!_cQ=SH<Yc|KQ)&!QkG
zo&q->{^>J8Cd^9MXjK6V!@5D)o+@WX!Rn<1KIgUSC1i(kLch}7>GBDX%9HoH)%9M3
zy&Sn#ZpIfq4#ba<Fm{XlQ$&$G3Oqq9{flP-JTCqqW6b{>D&AX3E9Az-2xneELV!Se
zFW^d3Vm<6rZ6R1TWjH@ocs4qdbD!lZ5`KHE+MG#xg-I5z`K@4Y!1JBDmt_sQ0EX`;
z>rs)8hVVV1ofY?LIZUoA1oE1?tTHJgwbfG13AU%dNdOSZGh-;&*-d1dc*sjjE5So6
zD?2;8qC$P=<mBXfzzu&VWwM{PdW9v1lKvw-hCg)hJGyK&vGVQ<b~#rAFH)ylo&DX8
z&D4{0Sm9CS0i~g6b>{Hj;41|rmHB2XV%YGPz5g5t*jjP`5O{O=dD!-!A5Y-TTt6b@
z$DIoQiBlyc2vbG)SlJ%GkePd{q(>WL%1ijuzb{<ih_hS65*L>POoDbg1w7-9-Q&KW
z?3YAq8gSRy!k9lXsUzTLaNHEEN&bn1{Y3z>+Kp}LPi&uhf$h_tQw9D9G+!Jor~ueL
zjnL!Q4F3;O<FEi=-7)|Dl|P25B?G9ye91pb&JwKvD8D+xn)~FBVYUGW{jcc%YW-h>
z`FETC;Trz+F#rEJM-n<mjx4}WbKwUN6Y~`SEI<3B>Bk32ly4>yvwp47aZT$e@z&V6
zb3Qp^s_>)l5KD86n|UEXxkLnmaCWWkJ6*>+RbS}b`LNbmG(9wP{0=B2{aw8>GsuKh
z$SOa(UQCZo$p0&m%e^>59TDBiby?EW)06PpwR?B(wzan->BcaGL`0)4p5t?UUUG6@
zxuQR>0O3d+7fq9C2vBJXVO~4JOg)UJ`N1Q<=_@0G$F)To4W5oJNs|mFrEud(Vq9OQ
z%vLaReS4e#f)!KPFo6FzEruD@$>s*6_8;AYNE$Uoe^C><@+(}j=t;zu61)iwP(>9k
z9OEAww)TJ$8NM~=TSns_SNM}-=c-=4UOz^zPCXa+71q7)8=ox#t;Xj>E?TAAM5yom
zlR$r51Objk03BI=sKVU^9vo}}+~+11ef>S{&$t=Eiqp}GR(+;f&FoL3KAK++s9hh(
zwZ9XVi{hHe`LDTMPkT^w0ZZ?2N#ceDxL~4_ZbJfZe6qhO0rdX?-DaqfXOHl_IlobW
zj#NCBF-;Y+zl8Y$ur1eM=ePU3W6W~KG=Rk2`wqamU6OVUXiX$3t@rDcwk!PITz-!w
zlg@a>pGL?K72z*_jf>!ecm^#Z*q`&VnDD0i+D&*Y*?p+E{&OSkF~{1<?cJ}m<~c{H
z@w_i3+oWmDUv5*1iQkq^m%r35Ye!QD#lJg{5Hoh=%HUT6NmmIM-1(E}rh2mD%GZ=A
zZ-9y=nE+r(fRC>=EpF%K-us+9Ya8wlS?LKHD-XUuqCL{RZWA<0GXJHOMCYqL8O~z%
zSmZZNyx3{>&U8vH>3hxulQ5tlF7b_Umu4YT6v_K|4UfC|sBEfnojv?@$@0A!V`NQZ
z?c(>FVqfK_vE~&HNil0{By|1P?hbecY-LvypR>LGdcc%Z6`;&}s#qZ28gyhgQWWO(
z0j1>+^fvq@g=;8wHPOqz^P5m^5nyi7xXfrGg1ydqq81gg&@G02@4L9uvUc=mfKaQ7
zUnN(F2mPPjx=3ySa{0;yKKpphR&c+0vNqpxO=NGHqc6mosE9^|h+)5&VnWOYvkSlb
z_OX$qF7<?TdrROIyc}S0@!|pO^(@Vv3IKx5x4wn+N6O9}EYo3ajhKtZ``oDvger@k
zEKPDO_>7#I7|M`%GzV7lFN6kr5D?+Z0T2<N|DsqgviP$_^sh>PiyFE^{wLKq(wEX5
z-`=5m*6M`wkYPaVf|ue1jHW3t>#qxB_aKvnPRR1|+J20l@Dfoc&C)kr;Y!#SnyA9v
zZ&V_cusc-Qxam+@4T?9GgkyL8TOENphGchE1B*C<JGS^5*U;oE2km~aS(LLC2kjKt
z>_(@CyHzA`L=vfnGcbCiDEt%8WuT$JSP)qA_CYhff8bwGz$1Y1eQcpZPX3E9`^lPJ
zy!;gfcoE0LiJ$bw|9vW9+zW8H(MjquGXEg5aqxogk%*;6PF|e8`=AtVYB@NFt>PF(
za_|W}IJb3{E?(XL&B^^7%y<cyh;07{(R==_wZy2#`a-L!fa9fi)15MS3G%kmo149p
z3=9mI=xw-tiL0IWE9X~+uMEMauKF+Zb)+U^>$9?^?v9&w%SS4w@tD}#DA{PKYRQ<L
z1Y}<=N-j!OV1CM^BA@b(GJ}%rCX|~A$rNI919^BTNX`=;YZ7~{oZ`i2OX*;l(W<d+
zanA+EK86}5S>9nDHD~w3#$pe9_R=zUGfTI8A5E|%*#4EFq=uxnm6eXq<Xlk`EDeUj
zRq&GMwQQr&?6uabsD;_;DawXVYu<amp7fQ*xwT^5Jp9V#hloOJb*Fc)Tq4OwZzJwH
z*f>xz;0-jSCG&GIG1paPyFezvHB9*t8Cmn?m9@MEq)aXyA&?v6RbxW&*NF)FRQt8c
zA_60-qsFr8v)V^PsHdsZ!aP{5?cx(sIdhj1mr(uH-Fe*{OnUm9iqPG!Ojj7Gc5QDU
zrbzP64wo61Kg$3OJ|k<<(<NaBv!b&qM29Plf_B`l6g?X~<FvY7d#T~=?KI~%Ka9pV
zHyq6pqkJ4^-)#(}y5^0RP*gw8xSi2_$L)#Ii->r6AaV0%2V9q)D(a%I`H<j2zmE5I
z<$>v48hX?8x&8MLP$QSu_uPty*RB!qQ1|vFLqC5Q;ux^QSPs;ZWsUK$WVoy>@sP_M
zZF$brmTZ>@95t8aIY!1;JoY;gQXkN~<NTnrOrV2N)&5M@OAAxh+w6z@cv^pXoE1^M
zubSeF4i_<;c-Hu-n=<ILzx1Bk9>qZ8XFKJv4Fv^6I7~C4uipFRwkbp{bn3$t3%{u0
zoVLBWr+khBNlDU?JcK<z&@_MWy8l(i=g2FMQ|4;EdO7;c?iMoDB=+dJkoZbL+ULi_
zohwfY;wIicM6fd&Fbognuir;2eB}d;3CJc4)O(xSeA=^F;@DV2xLa)SG_bqrB%uvz
z?LQ&W{N3F;{PuNs5wiS`O<Q^!6GnU`zXa(E9kJy*II6G<Vw;bAEojYekzOJ#yfK%m
zyaSKSS<6x7JW*1x4Qq1gaOqHW@KI=qXCCf3Fr9CoP~L#nXSBSWub0|53~4HEKJ6dg
z(a@vw-uXnEEArmmYSf5gmGd@y$gBJ4aV468sZFXKuI;!S*<-IUb>?ZYILvA9Gnl?8
z<g?z`Q=;P>xeAcscknOL-`$+y7r@Te!Eu2a@^5e>pLz;L;HLCg7?t4mZS`G+60==T
z7xuMr*FHWiK0(5e4m(~wQ?5_Zy%l+>xiT*Bt&$1YyW!z{_T5^?FETP!vc35ShqZ^-
z@{Mxvb*8rqXJ|=Dg*ohWO`WrZwI60+34FFIQF(#F+4lPGX3o-;S!=WL4SFKF`|8X^
z=a#C=bY5jQmA#~1z+3zG(^Rk)@yg`j07VN!(<~zwUfRc=cUYNqnpAC8h{Ekpm#?;P
zVO8eHs$8np9mo2WP4|zx)V`}JH29`0XbfqE8<KiB@rQi7JFtMb-e}&H??T|>=ElCF
z@wkrBO<vOZbz8cT_pbjH)?>m??Y<+OwXc4#qD}8-)riAd-l4%?rCYq%j}Xa8F<c+-
zn7`v6q>yMaKxWpzsQT#pa$Ealej9&o^vG>Zeoa<Vuv;0Gd(S()k-Ho0(NE+N0wdBb
zVZBI^begoBWLplGdD&SbY)IS=)1dJ{-YP_jyxHV?WSB4C!_3m^(wq`TaVFJvyb)^e
zu3km@>Ei<HSb<e@LAxWU9eE!D9&@65P(=$*=RSEaH0fk-=zCCecET~L?pJ9vgKi^I
zba+3}4mq>1p`)VmM2`&X>wV-j*O=pLX`zWUUvnTo!N;or;uu$k&s3DZIN^Odh!spZ
zQjz!?ZJb}`Aps_8*$uH6?noYOJqRloBZ0usZx2IDKf<1v^9~^uEoWfSD`5^>IJ<`t
z>$=c^r+(U444S`FmcHYaTN)a!&?}c=k8A7`<!3(LlSDu^H-YigvrGZ6BMUof?%S#}
z77u(veF{OSx&}TJogJ|C@wAjN%E?a_bP-8Oi}>7-AdQl0sW`VAXP5^E)RED&=MZbs
zd%kFI&&y>ZQx)<<UnaC(QAvcVxWJI<a%mc>_9r1#PI1S6`946^;R;&UKwIUqcf*=!
ztbnBxKF9v`lELHpz>%c{x26|QiI$jGi~7R?EMN3asBN!}Q>`a>u3MV-52;OwOuMWn
z!&&r+(fj=gz;@xMnXIiT+QHEJ%pN2$WvG1<5jA_d{6rR1Y*Z2*K9(lBoGO57E<;Te
zgdOCi`PqCboU(hO5P*dIXnLWb)IHRgJ5^_I<NgBMPCH9m;zGSn!x?(Ti(k};8lBst
z^i^ZnIj${S#E8qT(e<pVg4>cJ=eE_`uoJ?rlmqS|vFy6@fwa9k1M>!|X_|WozoRpU
zotEzb>q$H-tNrt@KJSgMZ_PTegM7V?^w`X7Tvn~!R`T4@gqj_PA+xt!eQM4>xfv(|
z4R8@%0|}}8z=j^i<+MG+q?^?s(gZMJmp#~(oW#VA&mhwog;w_mv+R{P<Su;qiS_V9
zE(lT_?J##1a3Ush_rd<PRiEk8BRDa<#TSEN7U$>QE^%sp`Re5@tI_H)gwp}Fm!Vb$
zV!Z#Pei}VeIdbZY+}VUCizFXuZVg*{x?owagW<_KDYr!o31EDK@FC$qF*)n6sZ)@x
z?~C{7^{nHbX_ewGeBG5pZtJ=|MmV*YN|H|)R?nif;T>w>zAg_qLzURCcx%m=zb+dM
z(bA#EjFH1c%=VLnuf=^)<;MXY4r7YlxM^w8%eyEveyhaAK!jAtkd)}e_C|%wwF-)Y
zQK|#mEThOzV>(<n>dU;HaTfr(y5)iJ7^J~S)ci*wJ2MJP`BIn`-QnRqyol;;OKzu9
z&U|!>DhRUd=e(A!8KSiw9U5Oz=$?&h%u%#4be3XD&J}vbh}5$<lMt=JX0R}!HIa>s
z`&*MV^Oz$A+3^~g5AiDxo`Gm?lja%8lYzWE42wl02Bj^vI%lKj?Y1Mwjp>KOhU$l=
z&t5@?z$z~4Rj)=GAbba$(6cOhj<ek&dJC3S?Gv!6VSl58k!y6-+WX^~_6(TaHnrV$
zWf;(`6a#d_B>>G^5k;*Z?rqFX>=g^WP}%=1G#Re!x%KIY&HxL6vTYgI5xzqX4-Gn>
zZ9?C}RpY`4u0fAdxXr6%CRxeiAHvwD^qOa1^!FH8kh1I<EQXz<_lz_&k)IL6bD1_-
z#6fIu(Y4O0(#nrY*@gEc@9|EII*S)Ycg!?HT0V`kIWWD7qoKt|N0`gB=xTJnuiJ1}
z?_%aaq(4PgCh)!2{g_>K@|7uAYDt%!NRuxK^=PPmU1ivxm20?GeO$Sirbc>9m%Z$+
zU+$3Uj7xF*j4q!f0cU8iH-E@v*5UDWKK<c{q?Hr~G_xHzk|f-x24Vc5n3blDqchB_
z57uLj%tg^oWg9K)CB&^h*}=+3?KC~ml$t$-w}<9d*L^|X=<%J2RrHcynyx4e;CMHp
z#WN`{H0Gu%)KzDbch;Qr@L7%W_D*9h$73+JNJ9e~HEs6wR73C@WLaccJAAg9)4aG%
zq0*(2e4H)=?^Cma^=!(*`}VuI_!B^++@b=iuEsAe+oVLF`SiV6`78FjT1~oZO%kz_
zUq^rE_*pfl_yZe-FU4;(qrBAPv$ua720j>8d@SxZ`O$3guOqE(Zk*lpayxJ?#flJa
zeB9aoF2jJ-EHA!?se>H6tQqC#tlF_{?$I+6i>ZsxFmiIQ65E3~=7|~EEF4CaH-DXP
z)|*8`tsPb@Ik_rqVB%$#6NrqY0*}%aBTKZ3NP{q+EVRDp>FT!fsB5Y8cz=t^8x~~H
zYtMdQWBTm0dfkqFrF7tuoi_XFGtZtH0ZJ(jrL?4BIE=fRzr=p9m=&F7%9#JI+2AnP
z%F1#$<+cZCJd~?ucC1p6nSXq%JnlKmy3LG!<N9Hj<!4#pm3_*z@yskEO+6`wa<U5K
zMm8c;YrHYUvq;Ut&ZB*=p)al5D@G~Y>G}*w4{guRvq#uA8?|wSqKM(+XFjdg;`eF<
z?+lXk=Y>FkTEKffeK+a($#wV#`>_ef7d}rAjLOIPnviSb^-;W(n;w)x(Ac?(kefX!
zA=PKKLd(+>M;e<a-DF19t1$rEzH?dSxOM?+@&2Oy;R<`^`N%nHkTWG(^!_s1Jflyp
zmtVxgVSpW+v8u(1{uG#_PmbBHIM4GnCZBj-IfmDYSn#nQzGo4KjTae6^o<2z6!669
z?zgvfLW;dpWyj52mLJ!9XMBsLrYj}s6EbE|y_!yN@Uff4j;(gL7IFU5XDM`MUS@n5
zeY2J{=NdVbZgZ38QBAGKa|6rWWv;oE%=6DHX~^kLj+FgsC{P*Bp5FC^N?>U)*z^OP
z*1<P)h*DI#drr9Q>=Yt=82e#mQZCt4w#Ku_A96J7FRcPI6dK%vh1DM-)#j{6<&9{j
zCJ*yu=vw=nt85yQs1yVk*kKHxqh1~^ep#26n?Q((u1kY2JIh;9IYRbA`=V34c3?DK
zl4aeK>iud_!ar`H=;59*N?Wu9#g@#IZcsWeWfJ7t7g^qfTG4aHybwozQGMz>1}di#
zp&@6MQhW4hbk~TS3#J$ej=Sn&SPc7O`h&9uJL>&i(0G~eHk!xp?9jjCKG4@A1(fgU
zxM`_@v~&T_*$<utuILNvvgG6toSiz`9rR&_)xk%2^k+r*AU58fI<q&I>BXi5Hibk@
zB*D+qfk%!HBph}k@6sdbQtT|vmCFfx{{Aii&Im+WV&{V>n41r`m>a^QsKVk{Ljc~i
zkFZmx2osgHM!F*2EJ7QM%IwMcFOSp|V){(m%z7W_*WXmDn3~%0(OfNMExb9!x#@1G
zzG$=b(KYvKmy%*e$#gV36=rMaRZ;u>2W+2*W*dcLo<b32Ul5-fjL|{pQ`n?4-#|s(
zxJJ`h@&_<ZWAg53#hJm!pk~=p`<-IQOW&Cde`%EKdflfA9t(C^Bc@}MX99s0>vb}7
z{t(_~hM}tbM@#hs`b~vs*M$gq%S3O3GGD7@{2mcq7`}8x_W9Ogh<=MCx3Zw$)X7T8
zjvH~~2AVdEb@9n_vvk-ry>onX&ACC}wM=$!wCHexa?kz;j4EgoJ9)S=#l@W*IS>X_
zj+)~$uQ{u>+81Z<WW3^Hm|9J%7moJvur-)xoUn(KeCnrS@xu;nAZd(iF27HTPi^8F
z7);w<hTiErIlsXvkn<OA00&SxnpjO3V_1;IrQh@!E$U;rJ!6|ot!u-_JN1C=5Ig5&
zR0&R!)-=<B$T|Vp`|Z`$hrlEIJ`g)iDIGICDZPBNoJvDq?z2e^i)TA%eD~q36tjC~
zE{h+&Fr<hnL5Kx7(eHy7Y~Js)HyDkHy6_BJri&tJF1v@ny3HirAzr=r2%1BRetS~k
z=2xT^M5uW9d2lmlQ_;e}GiUp)eJ@YPRFo*0b`vj<5wofbkczh~3I#<eK$_`W2>r=>
zA+8X0rzWU9IW--aqUOqb6@@fg<!Z*t;{rh+<;(&pCo5=<7$n)G9)-#1^S#1Yek1>L
z`RVcs6c6&s7&8@@PS-YhICIyb6_%+s-<Ha^ti(_(d>Z?3s^3giyqqxAncnO2Sshk~
z1Hqn7Ny#&i?EQf>EMSz_meXuV(J7&1Z3`vt=-e_)i-&5XW27ZhKbpG=4SBWB@WNv0
zbmd*2Csj;3MSRLqEyI|q;aC@tmwP(d6{y9jv&=UhtD}iVUzh<&pRQl{hgJA9D6%7N
zCHMTGUVJ^E6;<u!XSk^s8DAMp`rxZe?_c=|%_Tk_(|auz%)>|@v%xP71DO57I92l6
zv8S?v%<rshAi`5i$40MSO})U@+AlNYm)3LfGQMaP$`#!V(8R|}2NHsXG<DrT{|rJU
zl?;!}@}0bfaks}#$RB#jGMEkHG6A6aI*ZqOu>YZ{9?M#xP=hm$oC_-GC=)r;$q<1X
zxxb<8DasEPM8>RDl-J?7=$-H@TW5c;@jpy25@lvfPv%#SEwz{|(_`g$K0B|iYgDw#
zX07JNql@Ecpa^?)i#~a6+_pefm)TTfJhE$V+Kot0Qwe&~s&qB2Fkd);-tc@kP`dM;
zq1oLm^4$%QAof+m+^VY1Z4y_T*sFJ;Ig(bQB|71RX1p8~@jK$7pVIpnD!-EJYlVky
zAAZj6TFkdnbCd01<iGoL2Vq`iZ@Ei<AIcoH^Nfm}cR{j36XIO5G2D`uKTvD6(!mBd
zJ)by@KHEm49u!_HFKbe}bQ?u4YCJCmB<4kQw{stw^7zjbO>`+-U$w0_q_*i`y_}y&
zoel(oV#*h1`y~k|`dPpBHtP2+j~zOATvQwQU0V-+)ORI*9h@PWZ#>k?D;nDpPlu%6
zipzQO&`9i@9c2n3hMn{^w3Mx0=l2;fKkDsE5}1J9kCw;;y7R6gl5!33kJDO5!^IC;
zspq%WwgS8zj@T8M)6>O$!)%1a#P0EPH`mSX`Aav6xsCZDtSOo8nmT2elAY}p0)pjJ
z9t}~Q>JRIi?{}^pTgtQuaMXA8`XIN@+<JR^!O-~9;C;3$75n7H+amP?cwdsQbn$`s
znaJ-aOLR<y?)N<&LLZlOg&k7Pz8|R^>Q<{SJbDCh5f1ap#C7WLbGuw_?QY19f}KA$
zGc%3ctm)&IO@@Tekm_{Yw&3KxXCb?_E<5(IN$EPu_6AHwWuZRFXf`-GM87NxQJAlq
zglnN-w~@79PQa3zm?WsYczJ}-D~QiqLbX^Eo@R{nw<n(OBf4L>!+Z;r|0QpN+G<5_
z%<9I5$t<dhg-NuxV%^!UfM8|C6025D-2Cm{r1PCmQPCo2Ypmlal$)WxVpK<J!R{K|
z=r9A7ys<7jVCy~Qyp?>~aT4C*-k<Oz>&Iq?_d9;eZk7g97JNK^U@L%9rIY<zCrIQ%
zl^Y!U`8e%Q8j7Hf%Vkw9*y!+WzUU=2#zv@fg>`T<bB#Um!|gOS=6pB)d(c>_%h>*H
zimKWM+i>#I$d0{%dd&708G$5u)43_kN=S%U<&+hZ5=Gc;zKo*y!a(w~Boa9xs-|L0
z2yCCZ)45}9TL+>C>0g>8vw%DY$2lmw>y3B~S7{#SupDZ>753WVnJn6Q$oFNBQum0z
z0hXS1L%G!~k8JpxzKf$yM<Zi-H~g#7$4as89Z~+H+Ny3<(l??hm#V)iI=Za&4J32o
z_1!eL9~yJJpPZ^Bgn^>BSC7c<5`7wNHOmhz-uJx9uyNEuhwYck*y}nOM{vIDKL$vz
zoGQ9xuFMz8iZBbwF~^Mr*QOUPxG6@iSTQ!L!_osa!{z14!~H2ME9m%6u`dymgU_2x
z2lU7y3{G9#qBWP1pf>hbUHkfwuJFskDnHTBYs~__c@8|vQNfinji)O-`Dx~7R(c&u
zcOMB`E7UJyOq-ndXo?XH@wx*2FPMaUcdmFBF8Q0^_m|kcXbv8z%ge=2^$u{dFl<IG
zG{h4{+1C$Ewbi(a`F*146dVomU@rz8$7;6dR_*kqzJEPbFDbep@Q8VNBjMEOw2aP}
zJUyeP7q8W&^Jxuw`q<K^nkS&?$`2}MqCoYUoFS?^HgtGdYe#t<0x8Y&E<q3%5vZhy
zy7msjgvUqPGpc|xwUNs*_UU&-7gWtejfcl_o%t!bI(;~0as#i!WCzc~v0kZqGgr4|
zd%LWVVf{y|3Ki{GO`nRl)@lsH+hMa*jYVBvqeey6apd)hB6Q>$390U0>66}!b4?6G
zSGTDtW(&N0$W49RcQ19Y-L3bW<6Fs_X|D=WAs?QS5ej#K032k#9*GvMu6g`k`d3@-
zdp>!T=1nC9I}lumR(9NOu+=k5r`FpZ#Lb27aRmM@ml5TIRX$s%8@*TE#?`Lh`<&aZ
z(_-`}Hp=Ls3s>?yw~K31tz>x3!zSfR3P{i@z`GWH1sB!t=jSMEdR+De&jucJon(x_
zVaeHg-7+S?vd@*eS=hwkFlkySf45P7k{`1}RsnanUJWmLXTdtYlME)W)2|2fd8h0K
z%gG+D*n0Zet-&MHTVOYtsN_ppY^kR8W1eSD`^$VZ+uFeTe#RX9(2E(I*K>0l4=7rE
z<F-jYp;a~z=DWJu-(vGglggpIW#|NRPx);;O-kd7AEemCzM2Hv^9+h+$WTIW(^7D*
zz?7RJ(7)7p@r4pkL%D&f2{lfiKe~&lM)bJ9$-)h8?`30hMku=Cw*20Sow|E|=0tUw
zU2NpV;F$LyP=J8jd95Tf`3PKxN<5i5JYLKBGA0aFIpaUm!OE$7iJR#0jW~;-2Y)zC
zpVigX!1V_39}U8}`BI{MffUio*TSh2ZqMuunNOimX_2caVnbCV49X$|P>uGl4trm4
zAk1>R3mW9<f5^Zz6<W%UkmzbMbUAO*Sk7L(7XM1Mc})s8I<xql=ft~FGc)mTayfu4
zSgtK4-WpX_g%3twiAsK2C>CZ*KCeqYoPUr)JI{Qppp=_0A(43pyRd)(<1k&3$=P2a
z5I|E&eh=^w&;Ec4mW$szv%N8KcjuGKrIYP21H_yLd`Dnlr=deFJ~kdVeUPDB;cK&5
z2QA9Xy5QU|70b6=kg`WX|2Q+yREwu;xHm!vJ;;<pGOo`U9~qyVIyvQSJx6+w8$Z{#
z6I507vFiKk&b%cD+oQ~!?zQP$fE8Om(iNcI=$z6Y`08{1nSEGy`5;h0TDU;Kau@@V
z@~gE_P0SYha=2-9aBKuM2!RqOg>E#8bB<M;@s^<%k~3O7+Bz1i8T6uT2cxGoYcf1B
zOir9ta9y8;<0DUp9ZxUpcO<Gx#X6`@`l|}_gS&Tt7O97q0Cww1!0w!gq6<iwpNxts
z?{jbQWvceZ<+s^du!@Goy2$96mn(kvv7tc%GJ&$TZ2ER|J~=c^S@%r)Q(TsXcsO~&
zR}8R^4_<vJo;v>!zwWS@vDI!5Q%DZfU3$OhI!JZDpo*$s=G&M%I%k;Y2e;B{zF231
zz=x)44Dw!+YT$Fq+4UmplEWDC$o)|(smo!6xO`0&UqB9=)7#GYkz3wCH30Ew%$8j@
z*InXCk1P-dm^EG5#7V>FND8GeZctyZxypkTC4kj5Aj5+BH0@X?H+l8-jmXxv75Jpf
z!tV1Y*uF}uuz4mu6~A6O)Z3Je%Jq+{5Rjhw+*7fx9Nu_!{AI?>{*rmc!*K~uWTB1P
z{H?dx(b-N*PdA&W0SXs*U~`pPgZ@!5r<+oqO|B*Fx|`+8od=&+NQb0SZj91+daNp<
zEcy7Rg1bewN~^2Bq%TJ1u%3@K*BoL>e2vxRHCKS|??K!5AdV__Tp5SvNRk$Bxbru)
z@bf-j<lHzbZjq@kYda-fCqYP#x5kYhHRgTO3I|+&tTAPuk1Kr&)vVUltxd$S<N02S
zId8!eaXMGA^9h;}y6#fKfIGJwy*G@swf_R1!=a-qIVzn?5HnjhI*{*aY`}^$<2PAx
z<C<yRS@eoZ(iQMAkIfKxQiDW1k+q}cAba<UZ$5rnTnzEO@f_(z2&KLE7oRX%MC*(@
z>q!0hzQ9&A)Q>A!R^tVfOVtd)mdtjTKfU#_Bex-lkGV0cOy8%?z9&)1hv_3u62V|-
za?+SD%L~7hnX>&9ENnk!hyAXo6cej(T~T3qOPv!RTNMnt71N{s)L>&pH1^6TU9&-h
zqs3$%yt_sx?jHP24uk#+c_(eX5d#_;i{_m>@{D1TZ%6ev&|%WiOD>{rZ~FEOpR3ym
zZR-+K=EDonn5rszEF-B0aA_m|$bI#FEA{yGkQ#wu1)$z}{Zps#hw0C47=E^vAL)y3
ztMwfGmAynk)N}@zx6^h=4havRI-Okhik47#iIHdf{_DlXH~hEl8;|1Y>t{bs_cru5
zZp<XD))~k!<KnOypY;|IOTdQzr=9W;baiPmUkyLPB%rq7xR9~}4e@6V7t^l8#M`No
zYaY#NyP$d%RTU1Wjfi9)8sXR#+6lAQTph~r<&?Tf#HYo$5NF(Kr|g|l=&LdiN4h13
z3WVWAZ-~b7b&U999<N_+yr`#HNjMI_Fws?=5MIYmXV3hrxUPEAiE?M$le17TztU~&
z(vF*Nxq{~}O%OULpizyf59-gNpgL*DMc1w7u%>x;6t%_Zx#0=6@|d@#BbD2wX4hx@
zd}c48`Mi1g2-S#b8>8qA2G~6nFXNjyc);UJz2*Q1VJ5$T8JM^8Oa3tuF=;s<XySjU
zZFAk_S24R4f-{?)9+$dUcN}i#GYG#Dyp+4*@vv7H?>`SO8y6E=eJO62#jJFVG<_C;
zH}=%`xfk<?dj9%4g8={LrqK#N7am19IV&~gSXJGbxk>P}K2(RaSE}boa~tDmG_Tx7
z)~UL*E-UuLf+gUhDbs!R{cQ%IFF09>ouAv+bZTT$C;aemLBhVMp*koYg&o}P-UkSi
z2IV(Q#9254ywW5@_qmL5O0sZ5^{+KnZNNgn;!DZmsa(kHOHf~IKV1K)Fm*YOMwNRt
z2!vY#RPsxhmw+z-JSWuW-Vr{B&3qky&=>)72bsUU0vc*k)t9+M`GhxyL~GDr(w;C?
zeB+cw;PK>)Z(Gxv`f&aY7Lb@-w>2^REM?;sL2|%mn+`>7As+B3Wvghb{-yuw0gI^g
zrweyMEUC}WA2mOH0`c74T-pQ*6=IL(_ud{ev>d**5Z#a?zREv*w!!=zC`qp;4Lj(%
zs+;b-*$!^B<d?qVe|Zh(#zLIpFwmB9(MSutoXRXXS^64^H^cf8`myhPc|&Vlp_V!)
zuB)3w0sgmuM?$_1D`fxY{MR!6-vqS#dAAOOBnmiP+r<9!r(Z|AZa}E;6PFtK^DCuT
z07Z$JykG&EB_eQj<jLOTOiJ0W#|Y3kl}bU@zg1H?3Ffs)K{mftzqX1XbT4szW^g^7
zRU7C4X$P<dT@>B)U7!{Envxv;2ax-(HjC{xDqY2p>e0mZN91(6W+Bz&(q<a1PE~IZ
zrn^d?bpO#e@mlwe$fN&<y|0X_t4Z1gf(ExhaCdiif<th(5Zv7@xCaXk0TT4!?(XjH
z?(TMXX5M#ZzVH6M|L(B%Vr@8Q@9wUydb+B*s#>sM=}df!_%bpu#+0xm2sQ^C>W}XX
z7D3ui^CwJ?xS=5C{{G?XO_76gL-Fn}frgv?h$ahQ19`cI<tm*zOwhB;=_Iyyv^0};
z@0ZuZH65$+7a57WqAtWUyn;351*O?>#g)mA_yj!M>=v4O&nGghN=6FzGxtC)sP0NM
z3_`a=&`K-Yi>u|}pIRFlOFuC1eLe|yV##NG$8!{M7c|b%YW<M>ol8;lQu+w#r~|!4
z;ph1c__L93gu|Flx@YhBAw;Zc9nl49=l8$kX2`@uTmO!mNdwDT1mdk>OgxtwJ$%m9
zD$JLF#5EvAF6BDu)t!l+A*Z>bi|(|*Y(OTu(Ph<*e)YCn0IGsw%|lRS>UQ?^aScS{
zdpR`)q*iJ^+_kDMPvC;l?%nX$&^TJDE(LGq&4@>ht?&d;qTsQ@mHIMfI1dr3zY!7T
z>eChxI$T>aK!x(XNkf*$;GD+)9r(l)tH6*A4o(daT9~{YWgp0b5uVVXeN?q<^61r^
zC^LVSX|j;r>^vBFv7fGU_I^EhXPvQP13#a$)_P<49+z<O^Fi&oUkW=rd&rY7J0~Y{
zJq+L!@*gr;bC^70Lc?TIY*EnKi_eG@!wqRr&_{(Tig6>xImZd;XN@iM;v)>I0eDUY
z0zluH1Ee3l3}X>%imS`>r=bR-y-`zCX0#SFW~RAzJ;w>2di1F&sE&u-f#0SJUQ|nL
zPm6gqrc8ix4>n7RtCduHZj|LKr_0n~Kt>{tnKe?j>Y8uWJ!`~N$T-~der}Aw?Yz-#
z#?sW?s^{59Qw00{LT|xe5-LJl$Y&Z4BZv~KYi`>usQlwpXF9n}GbP*c0V3Ne%%8od
zE%bH&iema4=H>i%6cYgu#k9^n*D*Qypjk1t#<4XObLMHSkg@n&mjBh~?pyOWPfj*h
zu1&+0M@yo~EfS>XxtxOYtpFnFqb01hHt~$!-I}UNZ!oWa<}GR(17#zCA{4FmbIv8Y
zm{IsCaIxOFo-Ya(XT@!sfJ*RELbA3739|1rMhpQ$_S#g(o*wtN^76E1hD9IwPF~bj
z69W6Il-lnLQb?UJg|{EjCKvsPak6F1fKYuPQGw}?)!3zpRLVgi9#Tlj!I8sQ$v&mr
zBNmtnHgA)?U-zrkTUjc8m6lCP%~ionQZnhI4ZDqwqvu*w_pMyQYc~iZ-ti*xD=nB>
z^eG{M2$+}h+0X$BU9_UV5h1@s`PA!1lps6Tp(8<rG>W@`W$t?J`^ba8_)LV22o(y*
zE$IIfT=5J6yShurwfNXo7Xc)U896^7&5C&U-^wA))t2?wnf}?k_;>8p+n<EmvMXWh
zPZB@tOJC4^7gQIfxzoE2VkK`!o{pGnlkDZnwCik^YOPBjDE6AKMu)~Ii%w%g{x1IW
z2T7rUwT6$2Q5q(=y-a|nN}>%&h-@=f)G`t2#>(Wsf9-%~T+&!_5P9Y^_Nq?8U5qHv
zZJO;O(@@TrCkLx_gfeYxtn_**a_!4k(C`{eaq&kiUgg))Y~4<%Qkr5tc@RzxHfxVZ
zLKS=W9znye*i487AUP1a2w>x%V9G}g15v5?n!e}lenQ<i!Vg6UISOw0X$VJwvQM3T
z647U34^vY{$CfR!jM}xJk`miP^EtW7%1Ry9feUSaZ^RkT!=mffy4M0^T5jvN*y+aJ
z%gr299BEU$rL#JHPp{rrQZ0}B8`C@a0sbE+0lxX<(OIeAi|}<*c~@YXc<r&C4r5Nu
z3ud2^DW#qG<ew+g%_(bb>t#r{b1gCgfjNpv3fRIz%y|v_G@AcrR0)(p1lAHTu0Lx@
zHN06Xtz|_?ReoWM%vQ=<b!q47i?+s;O=1P5PfO!-^*6|os++1i8IadVbK*zePWp~n
znz68*7RE7S4PFXJg87EUI^m3&!`c0Q`{<7&ea33H{5^}AE})wOnUZpx%_VFurZ6w8
zcQNTP4BzA30oFa`ybjc73)Knz)Ze$m_4N<){&D|pY37eqv3}u5;=m2L?2S$lTmT`h
z-=gPtDe-x|JYQS^Wjg9-F*ru=FDRheGis?GZ-0N3@6kXY0C#>^Z8Mtbuc;%U=Pqv6
z62*u+j6vpMGWU+nts!;VPl~uZ+&f*!Pe$6<z!S$$yF1h2Pv>`Az5RuXzi@RK%kMe{
z)YH7=Q=jZwjJ=)6Cca#^RTJLM5_`nF8n9jPE6M#678%oi5%LpSA<di`B1<>+qap4U
z=<}>t+pXdF;IOpQT4Avykc2aufpS$-g<Xu-oHP^qsqKq(L^wz;Qn}N|JGJ@}NH9L|
zp5#G)Sv)#h;>r4&W7u~~dg6EqEGE#6n;~zAiU#`PU3VY%5y}aG8IlBMC{*4Bj8k<2
z#Q#%O=4M@gN)IT;VluHkmVxrLq#!>U%4-POy**u^ewuvKou6mUSM{E8EJlI%LRi8C
zIihmQs^Y4idMlTp*~38$yG=Tna(`8yr_vN-Q73ct?%F)x=qBk*#VR=hCzUsyzgeYu
z&dTSxH(=wqG|T!acb~B>YXyO4N$jSJ7zdw_9V8h3dI@7aF$Rrt^UjeEH)rd^sZ!US
zeVzIxAo^}l@~~jvlKg+f*!vfpk8j%2S8#5=(o!7s4K6$o!k1J_=?Kv798-sBOQ!<$
zUMPTaL<5o3l3|nWCM7F3gz%h+Y(Yz1I!nF!0^Xh9j_ad(<k;ymfFdPo+mzSpleMS=
z?HHf0i-kLL$7>tA>u38z_ivG&DiU(NJV#-FJF{j6yCYi@Rp;;`>f>dHFSvSEhRUj(
z5fusY1p1HX?vm1m9%Dr=v5DDe9;Z+SnI*Rw-#*6wK_W7tI?N>D^Y`5n!5LcL?S?j;
zpt^u&<*sRwMqpdWIQ0~5eAyPlVv|OsCxU?(bF`P+e6dzWC=n5w$&9lb=k04B<E^20
zH&u)yHY;N|Z36-aVu&+7MiUC+M29fDZX9BL^p8>*DkLMsYYH{}f0~3Q2H*;oF8oi@
zr3?5?#3Ggin=Z3J!_tRSnv!%>{v7W;QJca?@sp>I6W3A{I7%`SQxf+mh;C3K+hbz6
z&rd8wPypN-L;_+HGl4EqgDSMX4R5x7RG^we%Xe&Mk>kwuJJE<f+Ud(blr>Sa2@NtF
zIl@>GwsmKySV8ot%d;Ur3?Ne2pP2^e$|nW9nNMK;Khde`_%Hf1k$6I1aji@%@}Jg7
z_Gjlcj}LwZ?6-BeeDG|1qyJ_TmC*xy1r{d~Fgld|q{@4D-E(JiY0rVeC>Edg;owj;
z;bIqF_;AggEW0PZDgLBp$YbW<X>CwFlZGMf5V8(7Bg(c%5oY_@?gv#L4o#K=NY{N8
zkVp9H<x-H=2D{wAcU8n)2qf52<cVE$llpSg3Tq-?b*IMq*o-9S1(~%^!Te7o_FH>D
z{_eOgKREnPAp0nUgfd#?Q1s!7dr#QVqXjEBO=DxpP51FnjmtPHD!NDWUl~;FG&~e^
z&Giivg;qLlVxMHK42`_i$3g|#77of^E6pe`Kj#l8&!2z)tj>>|202W_7&g7SUtZon
zUj7(;>u3ICfIGRm@X#`+Cm9+o9~u5IT$yMet61teud8@_pBIxTNKAa;n4f;2)y|$@
z-1M}>_*T`B>+NDPdpvxch)x+461CcmQhGxS<IfCOaD2h?A5_JOn4oBI4sQwR9WAug
zzDNsO1S{`qXr^bS`bdA8eKMACndZq0Yqi*%PAJ&#Lq4`RJ-%LsOl&4H-7E@^3%NUS
z(ypXrbGl2=X=&26G|m(tzB_G*pw&ukJKw-vQ9BI_YpxGut#VM^U6~|3S<$7PtTLg<
zFD;{4Q)9(Z;KRX*{TB74z@2ZZGsb@;c*xj%CzL>dpId(_7L5J_*cEAAG9Y>^gBr>w
zqiEA{I!A7*Tco$i;Mi+U_kwEI*L;cQU(1|5;9{kv<mGtny4(yvyxGdl85<e3Jv#I#
zt}d_G3N%$)s=HLxLbh(ReoUV&Eu};{R!hjl#q!l$-KL*WeZ0Bw3I+Eas%~fq&&!W|
z8-p6UfxjHiZYjN3>b~zLEaNJ!ExB<dY+hYMeV1w0-X<Q0dhZ->3M!_1n%J!={Y-gR
zH(Vn?8mqjj0l0Nm79Gtb`!i@2>X0h(E1RoZZImpu<dqyWMPF!}YAq8xjetz#wGxlF
zjF;$qP#Ha6LQ;Aq-JAZstnEUaP<s_v8(pUNA0vpA;k?5?BgW>w{eUT7A@gCUiotad
zk2a!CAuFCRtAJ957HoF!Qaf){$wSxppf(lUBq};4G#Le#lbU!yRAwoMlvG3%(|LYK
zrIuqU_lTBKenRVJ-Q1RZMD8|@0{<h<V+(mc#jT4NP>BcMs^IDIo3YkS*z<tC&W&1O
zlbnt#OL}@X>H+s>i`eM25BNqgDj61&gcBpmrWxGCbA{#J6)nX_d3E}1+~5koOfs2?
zB__(yBBoeQ-|HGECe*QIWMt%v>-M^i@MM;yN1v7op01im>!qvPJzY0Q>nCWRFWl)r
zEj}Ah#VJ*DQ8ORBTI0&5#Cqzd#Cp58Zt?j3-Zzl*Tyl;#Nf#idq+~E`2b)h@V>wY%
zkG;*p_~_izO^vl9?^UtCE{JqIp)Rf#fksNwWu-t-b$JrjPBAEp>$_CVeS52Qz@BJ)
z_Tz(i2)Dpj2I-;cr`SB`mqNvy?A#R`HM>dQA<+96GZDqo1z(ph4uK`{w}te$nQN`$
z#SAIjcf-_E(5fMArP?=jH^n7#^3=(fyQ}D}9M)ErGSOiz28~<3gvHoEZ8Ijo*!@R&
zARuStN1ic_)i{Ccoy(h^GLu}E;I+T4zIRC((iP*>o?f!H!P?STU5RfSXns3AK2hC{
zF7S1E7;0_lJl2xZPD9e{xT1BuFl<0#No%;asOW<P510V8nBc-?h51%yW9sf`bkG(n
z#!%sJ9!>I*DB}@1fao)VMupIPvB76r6EY^U%TV0WwjXr#apDZdtWFNAAq?PU=Hgmo
zrJ@gU=L==}TL)l&mr*Ad@ms<M<g9^`>y=rnYU=YxnRh$Y%bw~==KMl&DaJlygY>r}
z_vfE#O9-b&-=$Fr@Huq2-EBFAr{a_)bE!Ign45u`y3XxE9t@}NjepWMnX&$bZhUjI
zivm@+b<($}y2^QNF0IwbzvkFj)$}w+*m`vrb#&a5xsNYkJ;r=M$yxTcVXU6tlW`tY
zXvysGpIIDj=o$j{TAys&XQx+hpHyw{bzh)0iLZzia8F8$XDN55SRE4>EI@M_Bf_VJ
zYnzW;rOwVL*7O+})QXCVEh}_+)iwug84ic&@=@U_NvXFf=8mtGu1!;|T8%uIHz`88
zu@5fVbJZRJ8SkIG?59Ij9K~z%rsgeru0rkzZ9u;3(~g34jPAep$76nEUDz8xD8t-6
z-yF+;Sfn92Vm%n!TFidiV5qw;>)%<u&1u4Siiir*Fe;X<_%iBb@7`TsKf90J{wR%Z
zGND%y%<mN`PQGmF!*3(6udF%qMAr@Jk&AjXA?D{%Ge%;+_Fh)^2-L$75p3Wbo)vb6
z)m7Xbg0I>y4sf}>ZuZ#zeri0fE^lhO)1v1k>Af<$9#Oq-hHvKO6!{Rv3bUf6`(Ury
zpz7~OsU+h%OE6P&adwq-c>HE{)c44;qpWPI2_e0&5LJq!%Nc8!O=I-vFX#Vfw#v3c
z^M;~d6xqScPgiEjw6#t5{Bsj`>#JC*4r5+8+)D>y7gNugAD>4rmBxBNHL7w^%zdp#
z)htqg8S-X&#@D`7Fv*Swn7(z&c=_BdoDk+hB8>1d+6IP(2X?Lp<xUzdg)$9xhQ!yY
zLL!vkSGT%d(0J`#mp#u$U$#jJV<al+WE^5&Msg(t9CxeTP05bZ-UQ#W!FKtDAjp_d
zAhnj3XpW9jm$dlPb@|d8={L|%PeQPu74`Hj?ZKCQ4pqdx>3yu-n)W&EG;g>2+}sQ)
zO3ct}sqdF_ERP4*I=oMi9AR~jPqLMqXg4MHessnscX9I)Y2XFfQs&V$a&slHb1YYx
z!so3DV}qh_;<eSUEPbMjpj=@jw%ZTx@|%whu%c`_g0s#jkESoacN5FBXyc*!D5!IC
z9%wZ%8$9EM47M0uM)pASXL<6}7)HY0$%Yp5`h?mJOZ6cJ!<8oIA(7HNt3V<0>G_-Z
z!&~agu<GnwfFQNVYecQ3bxtz`LB0b+HWs$=O=~+Q{VXpD8tB|w)sZm#^(V|}y2qQM
zrXn%W0>);D@$h>59{XL@MojGbDEPcH3f7?b0Aa&=Oe(1IuPl+MnC#P81*IS}i@^Gx
zDrD91YQzQeP{!}t`d4MYUSe$s#zu6*wZ+||ppTUE@I>E!pXt0U_{T5Y{|sXg;40tS
z3iO`8add97StU7m|N2t#>(b+-Bm$;`(dxhhrP<-RTdD)+EcmduHwNkS;dtD?SM3DS
z(^GqiwYP`byGRlAyX2&AIyZ-xi-@n<Axb;nGPr-67w$V4>}Rkm4kB>0eO&P5V1l=U
zh{s(Dm8y@%SK~zyI=n_&0<T+p_j^%ZjHYu>YC3*mCYl$Fedx%0#+b8C++Z+`o+aUF
zwI-9Y#7I$RuU+q!;x4PiA7Iq=wokVs!L;69U$kRc8F_A-sU5#sexD-5pReU7g<8Z-
z>BwA-|3*5R#exN=*}EC0!C3MrK4ib@v&HM$cW}hkJ#!M|K4d`PezH&8f;0&qAYvOD
zA)%73?P8-QFEGt(wcjpbG92>Rf7kb+Us#M-#EuAikZAxtYCUP3@jW7fD6^g!%tbhn
z^ADH9E=E>`ee30KDc&N1pY@cz-`)PeXth5sKgG6FiW$@5>R39<0FHT>n5O^9xi=h&
zjautk9fFl-mNR^KZl+y5<Bhu-dM*SxhcEaOe53M0_qI`n$6L)1uhr%mgB(rvqQz%P
zVGxgb3kxY_ZTnY1)_f5ExkkuUTjj5wsfx_hf!_IZRNRw|D9wvSUE4L#qRp*oyr6M%
zCeG2$yFFOL%iu?GEW$iOnc~^`^a{ghegaVYV+qEy1m-9P6>Br9vjKJx)ux@Zefdl`
zVX%J7xdLiPcT+|QB0)VLmo-5*lf(JA907i}LJFQ}8^!q=3?Yg!mIy-9%$&8{*<<C3
z8=I8o?p2p==Is^)1hHS8=`Z4FC+j{rDrpjpYf;+KOag*JP-rjV>jrL$<3nV_R2RuM
z13H-yL>w4YxmX7z+;=}kNG3T99Ig@-UiSlyiGdW<)X!{`v_nX)MN?4Bi-r17Gnj&T
zcuF<eI@&chZ$A!uA8Ab)Rq<JxwKa5!pR9R*Kd6GoR}OzX!6GZ>tY#B@m`Yl})PiB%
z#!^$?OiakS>Rw2CaET!zw@k?rx+XFv4MKG8B#K-c{|vjCR88k+UU0t=tx@TL*i5B1
zHwkeS+SFB0Me=3V_1PuCSrzUX%-dm>WaB78UeQv|0Cw<M?>js=LWbj1xA|6!_Zug9
z#qX^-Y@dZKs$*o_%E?%iCdwk3xJN<A>Wfezt5jRC;TWaWf>9hkaf}>zqc7R}kxndG
z`&%JcshwRA8<3}Frj(u3)Juf7p@G?G5ZI=OFeZ>ZYMHGph|;i-zj4o{h!(Zn(7*>!
zhSY~?2>nc{uyIdGkR_tv-*ISoUqnqS{~`n?+|H_3)-$=gt)DO2ym+%KO;0y0Y2P(G
zMi7!|H{LfPlf=PkErgTAzSZ%a=sDT}Ox~EXaDk1D&vyH0pD9E7@zL4_41ZDSlwVj}
zz&*8cl;gVV-JZ$EwS(?;6kpf7MTZe(Y^(ej{21}X)A{oSdiW$=KI^>x?k_S5Z;vmw
z_#1h#tfPYG!4DBV#I5mQa0P(q7yH>IK}!B~g@FIE8TY=Lp=JQ8K?F=@iSCdwboTvv
z3Tke~3I2K|=I+kX!Evgl8re!62iX~~pbrD6zU6MN4~@ycla6l2Hqw^J2hTLYoMKnl
zQ}AL6>rLP+Re;0X>LRf6iyMW)<pr;b-nVn^@f;?U4smoxIn_ffdXbe4{I>E9(So{n
zY~LicP)hAgUN^qxf&0VgTP{HCQgv!jx*9{sOt+6la!2+1uXF3DMXqdqlA9ZEu}jy>
z`du-0eP_Z)BG&c6z6d$NtTbcwB>s9j#B?}h;s6vnp?^cSA+~bnz;cU$CDgydZv3M^
zHnyVMM%;03aDeo^VshFOeSF>#xfKyQT4QB{6qV_Ge8ni@sf&*OJ5@U8{TibX)CxQW
zyVen@zWn1vQn;%C5qrV6JUd4e@04fifIX;V^9>sUSJ})kSdGx71ZC~1xeH`lu{h{{
z(q(?UU1oJWnb#tdm93|f0a4E%A)huq-NJ4C9E1ynpA!Z;?kqR;_jH<RdAC~S^mDPW
z9kTeYmakU5b+4)DyRhUkHq1=3v^87lMXwMMl6E8VE!gQ@OoJshR<KS*_VgTPB+fd|
zJ@+PeV84;is(Kh6F%AT|-(^-b{;K_836VuL<MXJ4k58ys^Jxd4{&DAjAU&(UyW-aB
z;ti`4g#`tcMWWpo;aao)fmK5fw@6vR#z(a7`frcoNY5Px$%&iX`8i*|l<(kI8$`%+
zrBFkIQTxnQ)<|~YKNffMOKz(qbTULa2aAIbwFba03tym({NUgy_@SP-vamGYPWDY#
z%pfkMF-(C)X=5J2Xl}8eIm?t_j-JTjC*;o~j@_^A8_GIZ#!{fui1G275_-Ws^D<Nu
zD8V1)+CThhK6GmAUh8+diIuMyVxtg;40=whgbc|j(F_@y^bIPwefp^bFMWr>q>Ng|
zDpDgKK&8KuQ&Z5sh`?*7rJ9uc8Y%)wdYG3<c^cf%Sez3LUz_}amRNLVUw23KL%9`%
z;V=`UdTrRix!Ztl3e%o)@VNb2)^M}MvKXii5|<0FB*W^YBB9!fZ*t|GIb??xN<m5v
zb=`HU^n;|O8!1{o0w+43pPR=m$*@g3I(dCH5z&ud#AtisF^RO_cW5$65jOK>**kp}
zovZ5v6?0x5Q$OIuY8T#QC9RBvMYdWVyg#;)5@dj6>OQBB_%Q&%g1WuYaC#~D(Bw(9
zx)gN5S{__(NAdP>U(x;Ce3%y;Jla#&)#8<@?J4Zk_lBjJ0f$BeP7eOwfE+PT$`3LU
z*osqA7RhC*!unk`7=DzBlYx&HgRvbx$l4_#`fez=7dns#VWwj_vhs0pF%O#C5F4ue
zb2gnxhnSYRdf@Pde>QoIs+msr0$R(jM2y>bFpgI`ipTp1ah7a(#A#_d#*SaovX0_(
z#b*wziK_vFT5sH`-xYO(^y3F*jkTopjdxKL#*Q@vFwmtDhZYrBl?YNQ!1UJk#G*T{
zAi5}bOwQ~clDQO3oZS%g1~0YY<y)P8tzng`-kO;#Duq6$r;~qJA*NOjndIk5a2$S4
z5bk?rwHGu&Hz48px|$Jh`lZlt<x2H{UzQEKyickz;J`9EB{cFFNujVAFMS;%ihHt!
zVcP0z+N=^?p-_|1%5=G%d3Itzo0W(9^81tpWs-5xs&;}}Rr~nP7Vp>Ai{i^@_N54n
ztJS?vJ$$u~criY9C1|==8IZv+;P2Nr?D5?{kTH!z8faodU_-a$ic_K*HMFuSRiuMO
zG80qGzMVe1tE&~2YF55|Lhz==^>sb71sEw-l95)2&*U48qo3<o^tdGB@T=T`_0FWi
zlrmvP1K6OovD@?<zZ>;CTRmMw&`*+IMW+oyiyy!DHSWOh!#FDUTpzq-RE>DzD1C7+
zbo&IxxX)N6A1XEK0pG=a<!|nYx(b)sIA{W>(jhLO_^<<z2jGvCg(ne7xJ1vW$Z%5l
z;Gc(bF2(7)zo)UST-#JH<TkoRN`ZwCVdseT`T+Yyed0x!V3Qcxo5dk;m$XwQNHCJ%
zYz}paP<UF!v4@#oW0~(<MIxUmSs$GjPFVzWbR@ZX2n5&R<B!hy6nBRNzPX4z1)f$O
zR8c|)dAZVk^r$Jb&f$Bl$fTm~oOV@RaimmeG4D|NI!k3Ef(0WH=>Iu!n*lD;4g#Z{
z^ci~nAl@$wa#t)Ws1h@_z~CuJPJ`{&weP3VG+y7ulm+92E=9f+hLeTQ=9^}X>Xu57
zng>2&O(6!v9#=4Q=%@jKCrA;w*N<jk=uXU4Nb<?&D<@K5M%$yew;Gpq`N~3mv`3FU
z)U)qxEG%D2rmBACD~k$vwHcE2v6*n?9y$k!fArK&Ym>`}f}2V9xHF!;`1Z&Hi@QzQ
zIeX>EF8DEiNCw8_mFBUs-$Yo<XLOXiCY7qygOiHK5~KaYa{~BHczHn|x{LQLH{wPn
zbrsVQ_EjM21{`zywFB;B$_HV{EYs%hfkUl+)Lm(@My1L2Y5k)|9wnq!g@dk#hS2Fy
zn(se*YGx>TUc5I&yON^A=nD!Pjb8F|gbjzpaW>UV9vd13t1qn<NWbxl$lFQ@UML@;
z9-Py~kW>&qFzF5A{nF<-n_P&UD3U#mYlo#20_W?r1<MqGOO^z)eCQ4NM80jDBajE)
z<jQbTeC;bgJoe)dtD}_ZBiAIQfv^0cV;X1je6jsZ?>!9ga+<+TJn!Cmo8kr{!Jk)q
zsrDzD^$8;dik$MH5`5TH6>{7kd#hWy1@}_t2Q=z21<7MvOM4#Yq^3}pG&x0B)C85Z
zgx?B6V~l0>MY9ngungt2BDd?FbwGR5N8fLgFuqV5Xl$1gfRw=21l)H^;!R-Vr^Cz5
zASnYzwzsYmWF%txBK5hl+7i6Z<0dL#odOwVf197B=r!TKhoTEAXlT*BpV<mS_(9$U
z>iiLXf4GUa;pzuTAo?@XP~tkfU5p!A#(Qu)FF#=GVZsP?%fnm}(uQDLtjRN+>L{5D
z@g|~=Vd~}G8zcLGP%_WXe6S<{H09S966VyV;=Km=26Rq=o+j=Z7^C*C_CBqnIh$_L
ze)BMHc1&VK*LO@TL(<|{_qA=WQ_dm?q^8oLy-5POASYY-A5=fRl2SsykVBsP-kmPT
z$EWBdGpZ>neK1Ldlx&9t7@b1M2opeOL~t`1V!x`vCN*58M?s?nVkrv`4cY24iabRN
z`_^GAi=#a2Wu7_oPyWXaCuh)_8i`beg`E~%Ay-u@5A*oAD0HmM;_jDmk`?Pr2yHO(
zd1F!G_{-c;_s+16<ex(I$G+GraxZ40X~SQY5^%z$x(Dlj$7mmSo?Jo^XsKlI383)}
zWkiI-f>8K?y$Pq2kwz)sMMT_K4iUwiYt8R$VQMcxaV@ghIi^{f0urlcro;!YGjx3v
z;H<h)c}g^*6uE4vaSMvi*nL|s&G8beWX~(h{@nX5R7gXp)pt<`%w6z=>b~F6%lwsP
znXin18?u>YiU#e+W5UMQjam4c2#I$NCX56$8(pCf@S%QDl%MN$0b@Vo`1m!$shws$
zR5&%Jpt9lO?s=I|-lW6V$LBLF<awDpx5ii8ObpoJX!aZxHWW)ajUim#$eg0wE{D5K
z^D4j>zP45t#zi$_o1Da%!*h4w<w!I1o3^GXXZ4`fZ8BenO+z)P2{2$V+M8h{{UBw@
zm?#~N(`suS=wYgJE`2{WOD|lnrnA+{s<Ta>3`xbOv=JzD>U_zT7k37YYwPJpIN2B<
zoanc_YqFQJzB$5LBN{Zws{lPcMiag)^C4$W8wvL`N(d9^iL<B9t3S+Oa(X@Xg8G?L
z4LaRZ5)p5bMl_r@rrj$u{1puFCn67}-ROKLuP(ET6b++NhEt0sGFSC7EVFXJzMLFW
zO$Vx*6FR@2<yQB6S=-~8>Q=EvZqR*p5^X1@<BNd$9qA?H=O{@<9}M=1%}Srrlz9my
z#r8MZ7btZy$efmp_^u6>sGHxJDOF+xYt=>JoY93Z&>?tOJ$}OyfzD26VOf~Fi#KqH
zb`!&2>V2LQR1GI8i+@Hd;89qMKn@O5BA@i88#eH=p#!rP1nh?#mz$D6W}w(sz58bB
z6lnUi-mPee>3iqK!gk*IlSvkHRq-pk!uw%~1bzLx!3oF}T(Ed}6c++Zi9#epLr2*;
z36ri+)OI(un<OY1O2{C-*C~pR6z|@sv=<i*R$81EK~ueEf|?TVujcT__rFqlKKX)p
zB!0$^S=efOJ)W8O^^klMU?@eI$!VW5%|ceUh*fJ<pPtKlxuqS%`=jP0KwiHYDE%-1
zB+U=<8qLnpArlA3TZmXV@pY^K4GWtBihg(JHKAx0d*S_5#r~I_`@$@;W0ZsD(f!YM
zzdsz&$RQxTy(Zt@skw+#>v_QJ8koMF7ex@xU)vi?%qJH0dQe$wUS5gvj)i9AOix~p
zx0A706up|BsbNPaL=U#OM2TyjgNSRU-ahW&YHL?iDwbhduOFDHE>VLt6Eh*I$eJCa
z2;G$24~iwwZWAyh6?FM7CCf@DBVdu?zdrAgV*XYD@^-6JaMunD64?k*kGC~eB+l+h
zF~&;7z#$nX-RPXGfa<jwHLIE~OmA9;%C~#<ZhYPWtlu<Fu}{Z2dwaIJQ8HhWp7F#!
zh{&>okP+f3zBTG|`n;drVd*vZWtwohwWb!!IB|Yz`b~tDMJ?N`zPq{0&1pgBV3F$i
zwyC66eapsX@wz;yUi(HNPnHYX?l_whbl-K~dKYkkmI50~k9J$@BGX%th40o>|Hb-O
zQE#xjBD1}J2kn{{oN`bJK75}7M1Z6pgd566l_gra2ZWuQ+IxfFZ>*z;v;-?v$LUG6
zHfX&X_O+H2qdIIRor0XURK>+9n9QG2eS0Qq;!O=>^|%ADQZz77$$KW;6)Pe>^;wUN
z%XW1I=Wj9XosJ5`mZDQ}^>;mOsA82YwXxSwDG0bqB!&rZ%nj>ugdWxzt*3If9L|}j
z)U8ESGNG|N(@iEfgny?=PAQ}#n%WbOQue_1;Nlt-RZAEz_CY*1x3E<X9)cjD^3~Oh
z@HFu;fTd9B`iy{+4E^l2DbV7L=&j}vVogTk7N&pmbjKy(7FHI9=WQ6-8ycu#iA*?O
zI9)e3tQUDd&lGcZ%x1OOnn<uKN*K$X#ge`<xqj}p21eG}&lOEceTsw>N^&}7zenUX
zofe^X&&5OC*0Fx)`H&1}H-i26bsKg>jBH7f{QOw@%t6AASxBnkwYF&1Zbe*nHwOKd
zdJIYCwYBl3j`s(Hx(SZFK8oOq9XJ6wI2uzX;EuTfX~aQF3dtE9%uBfyI$}Om_-8X_
zzU2>JZf>U12y(_yWr0;7o#SGy`K5G~z7Nq;gljddW8glDJAnV0lBTWAr>jHS{8AAf
zz!mQ9>Pn~UDEzDgIUM*lkKIND6vy^?))5cUm4aOMFz5-oXU|erR8rL6+ui<URaCre
zkdGpC1A>h@W2i2(D-l~f|4DRvepoo%lY8UVeWNl@bIBO~aqsLn{QH(bG|o);2)0<x
zFE3<!dtOpHw9FKy1!DB7Jj1WA9F#3{d0*j0xeXym_#iZ}F~ZyBNjh26bFvhcW86yy
zrvi_-Ts9hLAdIPzHPsgb6+SLQmf{P3%umtQu3}baoq^cM==FFAMaN>nHeZ$`kGe@-
zc@NLj$?F_wA;^5K+ufr{wI(O@3uMEEIK-Wa1ldsk4OfSCFt{1MWn=1KO7R)l<FzhJ
zns>{edx;lTVHZ#y9;cDu0iTG*cYw%HhLzO7;>{1a{v8h&B|Pa8`<GQ@76rwRRm5BE
z=4%2GiUfK+etgxPuFa5j?TOZ+W8!Mu(_Mydd4tTxD(VB(aByNjK7FUuRJ_L<)U}i)
zN{wcT#v+pt?i0HZ$QW|oqEt9bZVWT~q;ZC|;YAw~i<}J?S`K1UlZO_a2dluF%l}wN
zbF)O*EZSTSmsMGNs|=eG?B;BnPw~FkO;Pk^qw<TGPS>#}-F86XZh!1}`pNOD>x49@
zCupGksH%wsAHkl*!Ht3_&e>CL8C?(;{7{TpEbU#FUNJ%pgeoFp%=3Lz<YBXm((_E!
z?%P9^v$AN{lyt;JT)sOMqx!FnrRNQQeip(pU&MKzw~MV$Etb!Ne%h7z6aeBTKvMZ7
zvL#c1qY?T0Q<Ue|qf8hZz6K$6JkNj@X#yvi4N*!?^2<+QX?(uBs2t!eEzcrpXR)XL
zB7>x>WEo)uBZ1sgU7QDNGv=O9|8c;6ae6^|uC}7B1AAk6ax1$M&kjD}*%z}IT{%!#
zyr7scH&s33Oc^bI15af(-u=7ka0Fn7bh`3h#;@8AK@>Le^8_;Efz*>t9c!;8(_)^u
z+B+gT9x{MQgpNY3@YPpJ5jc`tAq%v2>4?IDvtyZ>hWbrj)7~xL_VKa{<Z$wWzO&`I
z7q>Htgk-Dd1tr3!|1{vqpYi1D^2~rtyqyRRP8T^)$@Iq^`U&kP7zY|gL@XHGccC^E
zznWQ+cxYzUtE{jm=a74;y#(_W(b>3waW%ITZY|L0WlTWRu+`UoHBN9;o8~&Drf*#b
z{53DX#oZ40zv`ysc@M4=WX&&mSV<!-@rXpzI)bRIaY)?1>6>JHH(!C=-J{LlKl*@O
z%B?<{es@2XX6It`3;`Jb#M6wE8><2hi92043GRAi2AIH<lx(ute+T;buWMFpeHbp@
z)#SI)M6QHdNo)t59fVKmsi|D@^75h)6^wgas2=eY%f{w9QI61?(aj?H<2L~nV2k4J
z^r({W&v0n~^@)aP89*Ljci`^}9>vXRMk_F<J<kdroQP1zzLq6l;UK20xwTNW>b+l6
zZhUSl=K8y3ehxj~2(zhN(qsLsMN>mG>|3CdAur^+aB%?j{=N_(z;{G6e;lrkOu#X|
zD-pJRYHa*S)h<fL)Cp&R>1y+@(fs>{=^5@b81kFtFe}-=d-YfMzyM#!D)hg<`!_jA
zzkxxWht?1CN&Raa|GEL5c=zWC0}_AxOdpEb>RJnmtil1zlBjX2snO|bEj1Vkg!$@t
z_L2{%n$+N3T?C4p0frcS(!e7~Kzok+6%26S+e0asX1iPi)7u72d0e{rNSRJ#<%*4e
zyJnbET58dgR4PFPhw$gvKzC8OB>*M@9zfgOaU)$oh*0H-W`}&mvf5B733<O{qGE%K
zDxh9Yy!-9>0o8dg+cYNhTFCIjADUgu`a#s2a`1@&vz&m9;PZDa00?Nfb_O0aoy$=K
zTvs(WkT4oQL151(qRNAcemgEZ6Srec!!22^c+^gqub~BVO97z>q%0{h8z$~RR}3Hl
zt|suu%E*@mM#KzJCzotmQ5$R_N>QwDF9I=9nC;=R8!1x+oUM3Pz88Q_mZN9OM8Xo;
zPvV8(+K~&8jx-9Ou4L0D-&(AUfnha_ywBUfVr;}u-_hsWu&by14dRI+@zK*;!^dQy
z0*|Y)(dQ4r-7Pt`C}O{2r0e)d4ueHa`;@$#a7>^9LiUpb7Og`W|5!ReCKAYX*q6cO
zstro3*x6utQajyV;BfI*X?GI4>lq@JnHa5w>F?5(s44jSmi3n%JtR4LXBvMxr{r~g
zd)ZqGu^o}$<pIwW4~$a-t(@?OX-_-}INCV5-B{c>zGmUQ@7rxpmt4_7=5hO;q~Jz%
z>LvP&@jF2<nVZn8G?bRmGh@_)V!Xs_bopY2Di5(tpHM!?jUql_)~T*wWG=H)5)u|S
zQIuF=z87csgA*s=gkJt|+&`lrHgG(gE=*6ygMoqZ^z>|Aa<;0it-X(M^+P%1;BffR
z+wb4SO73qcZXlsH@^F^FnLy-c8q|bb?6@`Xmv{&f!pV9PgR_SdX3q3^(8&Y)tzvLO
z^IyK6oSba7l$0QvHyc@+o10r(_jrE&N~ZfWWdCNXT(W%=a((AUP)2kDWcOI<_GI<_
zkD?4*pdi0{b*fi-t)XOYd4T^TP=12d!hYfqftVErdpjTwK!u6Gndf1^mXP`fjEo~g
zo-3S3tpG7`5cP!nl~QQfhku0l5p(livb_?L2^|}8lTeVo+_<BX{h#twOeAz;iJ24@
zK<58SDg?glYqh`vhae828$CYVE_(53C;Ly~d=Upj`aI|BBeLjY{(8bVZj}TX%mEJF
zfwMRll1u9UN_;*>|KJu@`^LhE9o9CCe2`T-PxBXSAW(qs>p3BJl}WA(Go@#r3nUwT
zSp#1CBGlebq=C`?(w-?7=a-1`dC&miV|I3fNL->04-&uu01?`$AebKBuh2?&9m;f-
zDXwdTLV~{g#X=+>foX5l?0lDM7lG_P1M6SUSYX#68yHxnnC==Cv99{~7hGU_LEO(#
zM7EGXLL;^X_)2j>pkZ4<RD&VkVj8^tb7=qhdl!{y5@MK0W7p8c`mZ<qjibPyw8TQ-
zR^(XWUH><bF~tB{i2Jif+Fw)m&k6j;2&92c8|{IhO(wt;`uD&8aX$=@+=@VO_Rre<
zKd*8$0B_VBvbkjc_a{W)SHKI?`eJJS@ArWMfnFr)Q2j-`|7@?F?+<`o82xux0Hyys
zTmQit|7F7ekiGxP*1sX@zmV}CnEYSJ_%CGqzg>=RcU4V+)!5&kXncBFMOir@Gc_#@
zCP(mA_-~ug01q4)85slPtaru$aBui`kO7)@^7R5I+_kijr2gTmo^Zv#472y(7lAlu
z<LwC@0S<8U)Nt2fU{H2hb`?x;2vp$DoIM;rbt_r_rA)-bhWai{w^MW&k)vUAL8QOq
zvjZ)l0}ly>-2Z+&L1+E&mrepS+Wxi@AeH4E?`IDvlTlmUN@PsskoSa62JTgyf4#6A
z0sI-J@0xt5x<?HFkVk)@Z9yU9crpVH@aHGCCPa?EEjuzMSjc+?FO;8EGH6VxfVwhK
zpz$3NIvniH9tp$zR`jp2|Dg06Ph^A8CZN?O1BXWi^j;K6j=w+rr^bd4c~6(d2?2+o
z31~K=x07}Tq)A|exG~F?W2}__A-Vesz~?VgN!IaxQjqnBWm5ARVSg!N!SBIeX$fi6
zziknL;{)H~kxc#<@&Danyg&A9U-6(LV2J$3Qt{`09MA|s0f8U?Q-}QLeOD}CW7#zq
z@lpQoXZ}BFsu$JF(w4P!T`0*ya7JKUw^Fc}e4OL*^hd3Wj}YkAXQy4N-3r1bM&Qv*
zRW%WaYcDA&ag*rm?ful8>-}q|X<?-TAh-W2-1PMHwO)S?IT|{8M0j{Q@RN~2KXV>3
zP?JSiY$?c2(?2pgA%Dd_Ii<F={3@(uEq6sNh_#d{ZK7TyP?LLkm)@({AwPN>tfdTC
zm>sEayedu9CE1OI-qJsFFUR|3>uPH$C@Fclxa#Zcuf>SS$$z)Dt_}?q=R^D$3Gw4o
zu`4KT7@eEJqOYs1qrjx_@jOmjo8%k|OSZJk^_EW4&uF7`jj3v>3W*OfhB1)0#6-j#
zvvPlwyg*f#r~|75yEvOnho)DmE2=n5s?J*Dz1K6cGy?g8#21g-KC!T{MC0=YXW?aL
zW}4i7%PT4_wm(AJ4l*;h^t3;_?auj@P`PQ}`ikV@(r6m1sCX-^)VbQc92tH|?cdP|
z<>dHN@~y`6XctudoO+ly`$LEm`I%*k-Xu0XCJtS1zNMt}H~I3^P)|n(i8a!~C;1E>
z=b!7_X)t$QPTS+(&Z*QxUSHbQH<$xk%Yu)^H`@PLqvui*X>RH^CmFb}a`W2FG8~eC
zqd^z){N#MmvMezvsjsh3@P0ku!$&XWqry7m88x<AU(cM4POiC-5AJu<#{-A6OFlGX
z1y<tV+G&dM@9;hZ@iIo*rS6{*`Sj!^)Ofj6+jLz#a*Wh16tq0ZDP-)j@=h1#Lnl5I
z8q+sjrhZ4?&E8WltlWl`0uGrKyy!-cjg1`>d~04+W}u_<dOXO-#la!)x!)Lwr#zz1
z9RzBEJ>M?b+BRQ&;uBKDKXm3SWI7nyW~9ZXO+QY5H62)cUU_C6VqN1uFD<C&_P!dl
zrxkxpGs0DpR^rI>I@;QFeEP=QtlPMv_<17c`O>azg&O|Z=)uUP)?@|qd(vCe-N<2{
zMRT}C1cAma(RD*5eB|ITLqf^NtktZ#x1?(Q&#!ycS?`u1_QZynTTk1Qo?q_PeD60x
zXiMu!=;(%%SFbKFU!T_A^n71#goT9%FYgVnHX|4}p<DNJA{ZLB(RPSsehWUIcb&Dp
zy$;fr>C{*xT2%pQE^`A`$AD+G!D&(@B}-FNPe&bh;{bpAG@3=*fyJ(WW_6=-VCw6~
zcVRK{$R`6s!v0<2P{gMM7sA=l@6#Oj>p<0IN^ujNbA<z^(b0R+SzqNXMcZtQERS$u
zT+}((zZ58(%|CaW7l*X$5<X%Dk&^iX#U8-<&W9IB;SlH{DCN`r9($5!L7GOx{XfOC
zMO4WpJeTx2OO6!pI4KXaeZ*4&J5BZt^9hD)1&!I-A?Tz#b<#DKzs*^~SbC*f?*;Pg
zs?_1rS}WdS?iio#7Ssmn)KviPv8u{snip|te!U{u<6zHu>*ngEF|!qxF6#WBKf&_R
zQBkw+epy&rzTK4h3cqYpMVfzlzn-M;^Dz~&a|_4{KPg5X8(OF;sz6&|uVMF&yT72n
zvc=yMWMCjd(!xq%GGd6<JKkK6(~6^U_|83Qn=buAg05}tSR#oq|MW<zk2P)Pwzx2_
z%X`I>?SqVk_sDMqFJDwtNVCZMI15#WIPdmVB0oleKbH>Q#eCZ<^?JZ;ZNjaRC`QY3
zGhRV}+w1;Z6hG}!eznb4&_*PEB}Y8MgI_{&XLIvQR}Y0;s?+Pk9-*Mma$g@M4bA(Y
zwA55!ZNDf5Y3P)-TtKX>;A6z7_(;mUu+t)vD@5S%Q>wgC$}dE-yzEr`x+zQ@qOASc
zVaV%H#dF8zd!(JppOKCwE|z9~!~iPsr&p=wV<me|pAQ?<qsx3f+j!YQ^k@w!i_H4C
zerR%Wdd&gb;5qjEJI3ar;YP*NMRlhs<Zg}6vUN3X7;s!*_x^DSUG(e}#sWdYJ})=w
z30;iM=2MX@a%7mCU4<Gm*T*Ol)PA(MOK(+eLlL;MD|>e;{N?3o1M+HZE~zkjl!MwX
z=~jzwIRYgjM(=x}U!IMEcZpk;d!H88_~$I6?Q8WlhwMa(oVt2~J0@&fAM$?xhHBfj
zXZYTs@AE*8W)~=M1gh#@P*qdw<Vuf^M<*cAQ&PI@fFb;eeQcGCV|0H##&<RBy6R3z
zPmg%|&MaF2hij7eFtTEZ*l9vsOLNh``5kMQ32+7k{kDyxHtY5FaJgm{r7uG-$~J-1
zL_!2&42;C@t?Hs*y_gm%A*B9?LTj#$#SR;B^oJR&8|m0<*s%<y^aG&r`N#4OF*>w&
z&q#_+JJ-dTD~||#)rLW<c2-@^Ri(J=%v4Rq#l^f1zhp+Kk%^-Qu-y7ys$9?XW{4Xi
z$|xixN{SEl-yY|}!{09t#0b9LD=YBtoR!Vo+KCFe*H;7v-`dcLySBVH(AU?${>HF7
zoZ>jff7jnpfJT1fOhUPwy9DyT4rhraJlM%C`eJ~Et~^JMzwEY|TsfS_HgZL@a`IH2
z@Rrgx-Pfaf_dS;TjGVyiB>DZ(*`~)+dXUNBfgbNlW}50k!Rwm8R&ie>ArpAy>E`o0
zfEU0IBG?et_r0rQOkSY?HO)U(6xjUT*0Ic_hKuBJzx-wKjhQ0obiU%9*%u=tX7n=3
zPc}9-=V>Pg1vGCDE2@cdTDhfM*AEqs4~Fvj62*HNKW6GWx-?rIiV=Izc{EpUy*&a#
zaz`M2Z$Kq>3Qa{6{A(sqHP+7bS{<yj5(?nzFg47Y&J0~9cg1C`ox^(eJmsffL>E_A
z^<dWnV31p1ZkK-l{tcw<w>+IT8A^HHE|^|?g(TU?OS6f?5oL@@q*aH8hVFEV)M9M8
zo_vSQ=l78AAw$F3rto58xvREqFj+RNpLG6;C8bqD%hD$Bcrz!_8tkoc+&Oh0n??A^
zL)z|nXNn;SGcj!G!!lA@K8r*iQ1JMf?m)T0QvOTV#EpmyOcM-awB{Fi<rl@dg${S?
z<;6SnRf(-+<){#NqnF-W35ninxUi-8A>hc0CZqVKB1i(zI=u8(68R4AyA_ysOsym9
zr7^h34|YaUa&qDjoE*_bMMEoXFDJH4dtdHSOf&t5*wF0Ed%K8+VMLY3f#W{TK_Af9
zFAh+UBfmPggvB+=gC7^7wkJ1Pni>HcZ$Fev?5*25X8X!&H9g-&q-U<eTNLXrR`Hi8
zbKj}R?j~_^a4j4?XvISzP{u{T-|g&$v#58E?Vl}_2g9(oOQ^@-zsc-|Eg#Z6d%7{&
zzX|@Z$k#$RXPU<cT-*kzOfSWb<)4Oq0MDT;#rcE;VTa;p+nX$2j+T(`AMx>DmL10m
zqf7DkHZ5$g4k~OItYN)sDy9UyJQ5uBtSv24K5g(dmN<Z7M1PT-wr}L@7Prx>))X%5
zVr)PfIXHyPLg6Ug9!+~R=RtBU*Nt1|h(Ny?g(0i3<)PCSlfIm8ERy0AOn+ZX4hQjs
zuk0{e$dziFxNRFmlM}c!zr8-)ulUZWs>4NvyJGt==Q`|-W^j!J!DDqc2d}-<FOR>g
z-;|P)s#|fvHR0>Tn)Wltf^O8dZNVgg+1beUc-VRTT^L6OYC<gWuo5mB&Qq&#K!Hl-
zC9kNIi!C*yVl0|DlMfqcY}}FSr!Jul`h|fxmf@zS0Bwq{Rcny=(U7(7tIa^^w5-BP
zVwEKdRC!(9-C~WUYCg2YW|q&RRAQJeU+jc44@!~hhu$l$0v)T(3&i6`I}H?xjoui!
zA1dVQki-tlD=V>PR#x3}1ZYWm9@Lqa>&jqr`*7$K1`y4s*eY^{cNf-ec+?DW7x5d_
z&nFkT*7@@8yiGbh%&je?knrIznHhQu1vgLyw$|=@;{pp9Udcu;5asYe&m$MPY4X3=
zYRucZkFBk+#Kaa{eSbh&p3J7pD&ohS+N8CN<IRM_YUfaQpK4)bI~#sCI*RF@xnS*q
zBXO92qvpDn&<|ef77Z`nG!<y@W(~)urtZuQL2-37D*t#ID*^CCFa{7sOYF?eg^h*{
z3t@-KCcs8M9Nf^LMeA>2ryPLSwS1BQ;ifIWHN{&jRw1OmB$4EnG+U=z+xn}}TE%&a
zx_@O({i)}{GB+~kF~gBhe}3t=)Oo!8K~|$j^-!vP=|@cZWasCRFzAEQNS5r=!?V&G
zAh;TDCiRQTRyTu)VVIdlktp08_g&pwR#9KaqHe1fH$wBdYB0H6Bfsrh>&qzbSzrjw
zC#aPODluFRtM8=gEXMEo#EH{5trx4^uXfwsUe3@d<r5@S;p)ROffeLvt}LYNCXQTY
zU801>z+lb|+<bUa;0SH@<Ngpy2ofe)sLQj?3k9Tnxn$bQM1RhH&q4?r#J!{<3*E_W
z?V*C4uT#+yg;y9Vmvl;uE#|yIEIJ+@9y)rJ<y>jim;f&^F}Uzz`HJ(LZcA`3GAyjy
z&5XJ@GpzYW3&cBH1x|v+?hH`)6m%V|SX3{Vyx@xyf(f8ZojVFE!@2~8hz)`t$<@_l
zb@D0g5EtklcMiGQ<{M)+rBzKP8n-Invr2eA34xuBjd{DTML){hM|YmXv>M-bN`VUx
zhJRiRouP9a4a;Dw@C0}7PlhDhZ+(u>A@lN!D*WP;(i5wdvNFENQV)T>$HLD=*FVxy
zAb(Z=^==^jYKtPx_nVbJu)U%Mi!j<IYMI?-AJ<+^=7&-U|ACI_aypuTKfGr$k{Ti9
z@%~mCvJ!1c@Q0fx&%&m2AKsX$tGNmT#&J!W^jXT0yKwrfkgIdE=O<$sLu=gb^J*dq
zkV>GPTHg>m2Z}A_66+T>W@m{fu4V4Iqp~W#HW|zNeM$Ncsvf5Zgjk;16GK0nNuf0y
z>{%O;T<RijYkl`VpG-`C=q~fIi@iH-rm*WTvxc{?>q_}@PBlC4acE#TH5xCMjHIiy
zrZzJlJ(FpGko95TZ9t6EcF$(-a;<yu7Adqex;9DH?uDrV3G>QQn;#DqbNC?D&6SA#
z1XR(AO7kU-?3<5~&lzb9AA}{-G$UTJ;m5A#!7+g+*}9#DD$`sh6L=Xyl@%5e3A&O%
z4#Q|sAy8&`;bl^k9yDnYO;x@w7s1<)3vC4n7`nI59flKg(<r%lBe`}`))yNh*7V1t
z@6$>UcARsrAtS4S!;skJW=^9|lMnfLy`q)0@{@iK74{VPEbbdCjgUOfou=!4;d9Hv
zWuEJjvK&gqWBUl+xF}y^$Z>fQHytJ%|FuF`cD?Yu&dvtb$=+Uw`xY*zO}Bx;R?pqA
zQ4GJ!{y6b6pItMdU@Mj?#WZ7j)?CRH-(@=~0o8ows7yUye^@tFaJZXBz@EUlN4sLb
zQF8PJ3XJdy6B!r#di<oaWy>xlrg^9R$A%8DqoZT3wH$9JE<wJ*kq*>d<7BEa99&8q
ze?9M)_R<x6`|Mcslbx%O0bSJmsAEY@gpS|YBC+q3uR!BAF~zg_6s}rjsDf*b@*2ND
zuq8-!h848P9R;4CU;l@@b6~DC3b%BUj%}MA+vp@6+qP}nwr$(CjZVk5ZO`dD_uiSQ
z`wyn-R4PfG;OuXo_j~u+>sk9nPX25BtRiCMEu)0I3Jfgp%&iwl%rdqIA{67YG$k3A
zmJ<1tpZz%)X<lp)9G<yzY=|4R+4uQG{pLKxmU$^gFw0a{l!E5MN#k#td4GOG1QR1Y
zjm6+C$r!L2fTzGJ5!YKm0ql!ErKVAcf&38A(-mOWnaHtu%hzhB{_{v%iodQCyfPy<
zjNv7pwQ$-*W606!f~~|5>2~|>;UgsYJHqSdlr8;fL!1`tFfE^4cfcX_yCnl0rZ!35
zgL}P)R-QETx6P!rR%%f*o1qMo3WEp+Vt4p3S+Mh(`BZvxwX0I9Z5s!o_QtDYd(G#o
zku*-yWyir9`^-Zo>Ktq3>*D7k^1xD-NYd%h3b?IZ&|e?Z=v?!`kS2b`7vtE|9(8qf
zu|XvmBoO1s(@r(Sp2k8O-(7kj3>DDcV5Jimep6A8WkV6h0DPjb8X2TdtZ=Z<V$u37
zWIN9%R~R)$m*A~JVn;!K0-Abwmo?!QSQfJ#Ir-?PnJ5G{36kcf<}Syb&43KAdGZ;s
z7WLIHK(iE3+psZA)#JYC4snlAgWY;Ib!!^_v38UZO^KcVvt_==@POwyY0vO3Zu%$A
z&*K>dK!6>Ne6z3+V-x2I2qrKjVg<COrY6o6mr%+;HJNB63kw78HRC<H%$QwQ?@j<r
z64;Jz-a|%6As^t|>UiuF*!_ha@7KM$E#$~IBN+Wt!dT|OA*wJ`d-`x}Q^X_F^rmBx
z5pH6ju4c-X6`K&~**S7)&l_~p&4FRvrdtU(z3&o9@hQ8^qfw#QL7~+QtpmmC78*%e
zxQJ1%^rop07`gVdvpD&OHQ8+MfklCx6Ra+t9Fhd|)UT6M?uT%2-&@_Rl@)?4R|eO1
z>si7RVGG2)ve)g|ib)h;-~zVP=T}_mBqVNNot{6z7(kp37tOp~?1=Z~9Jzf%vs7CA
zSZFHahPHD!-fs5L481><M59-E6%=0N8;+=9a6o$z`yi2@^c$AGL0;!pB!EAz^1Ubg
z^usvd%)+{y=YuGH(^#qti*0Nj2Z@7#W@@VZNV?6pD>pR`-~qs9GUCZ0M09c%SSVmK
zUk}=UXlN+sXi`5WixV92M`8F)Q>RtJ2*?IB#DGkDWoy@NA+1I+=b5f&MFUp~(vo$N
zcoiOx1?qq$kza}pu#thu-K8UsGXhpR$=}+aG>f$>!85Y8W_ai4bu1I=sz8xUWj@=s
zXu4XMkePKhvCxl|ylHZOqaL&9a`IU7&s9z-A;9TQ6joM8qH#)T0#CLj<cZ(~NC)vW
zK8S;oVZjg`$Ldt6j*th7Le74MlqWMx=%d&B6C}mi8NlW9Kj%H%Jyfe}CKvw6oS~Ub
z!(b$cB;7SjGfn#$Sf_S*nV|`spZ2(PMyVL4hAFw3&9Wd6y={?cp}EFd!ffSl<4>&r
zf@hyr{5Cw%w>;G*QiIvWYniF=NwxlZI}}?JV<TypLd;C32O`zOq^Bn0-htXTD#^Ms
z93n+;T06r#ts5l=sdr*w`~_5+&yeqFPqMqkzf7%C)pnF&iHrMJwu)gES7hh9=N+DT
zyq@ERzV{=5HF~EWp*m9Ir6B;P7nk#jg#%B^b<^4IB2**f8w9rfjuFnrEll(F6HsDH
z9-+AzH2NR}sB~5ekRG9DR>p?F$D?JT1I)cYAD7b*XgU|9`BzO;EQC*mzViasYUZ8`
zZvN)QotIeVh+a%jB7v;TFTuNLZ<gfkeKi}v?QyQJtq}4l9(~=V#9(S8+ENw|H&0JT
zXFCSwi(PBi!G=h0io7KS7KaPJ)?M{i#<vslNI>gVB`Ph+0YD%#Y!8JBU3sY{25M3*
zz_tB-bM9k*-GZS~1x6je;Cub6sFZ54wxN(dhRmIVE1OrwoAozu)Aom(p8Uc_P;zln
z^FMds|0N9Y(}N<SNDBQ}qGk7ZIN^iR11)K2#!6QD10s7A7(Cr!059@~n!M9HUE%u=
zv~C+?p=jHk2e-LZ=?a6ZOgSlUwiSb^8m>c2tNjuM{H_lTbl*>^AI9Oho31PV!IWyx
za@L`rD(u^1xN3g&;CH(Q)x;5Z4S_bZmGc$%dv9!zJIRbQVNr0!ywpRC8w>aj-lO9p
zSa;Z5uWp<?Wt~|1M%OR{*#kTmJ72VbXz;Guw*n5;A8QIr%H&U%>ky1U1oIacR{0Qm
zpdq3^K?gmryGv=pSxUmbU-o0=2myiwxmOVqjK&m-3Yy}TAhRAub$?hW|6E%wpnCU3
zR4E3O?vQEtK`E^&$)3u^&b`FFnCEZOaMoV?bT`OT3wl(T5fVfo$rr+*&hZ8{2Md)1
zRtHuV;<th*Cl?KnmT9HCZw=iKb~oXdrlY0nlKWC3OhaaKl30ODH3OX5OadkfJET>6
z=SJ6{hq+owG<OS=%qgxa+&Ugz%$yb(F_JB&rTF+lz)@n8Y0A`BTqjah)nw#}zY7fx
z+}1$Mp~I<N;u}34Ep|(R3a_s5Z~~OH-FAa-WJSj8QTq(EnaH<4Uhf&dKl=QCjOlhb
zQF@ie_l3;aApRkyRcgJ1g2%tfCq1AW38b7jJv~i(ixj_3Lx`e!N$ZOysDA8FLf&u^
z#z6V_!Aw0VtkF}8$1Y#uDgENyaYq-9i+6DZ+(?z>CSR#kZ+F#{H^+TU=W?!vRI$tk
zhx*fc4qA`E6hoO2Qcumpm^>>YRU~@EM!`N+GN!f>rmD68cB0qyg+C~jot)NCg?1wr
z1^OQ5yeakvVSZyJ)yUi1B=|dtKg_Mn0N*N8LF6vj{WXOse54eO2WUS2!4=UY;qKK*
zkSOvrp6ndqHKkv&T^hOnt~5Z`aMRVz!Gn5`0dhPZx{#JfwTXC{UiECgA|q7H{WZwm
z*}=*u*Bgg2{LM2xSm`)%4smSZ`>X#?80I`qj3sST7~bbKT92x?V!}#3)pho@^VZ9j
zvB>i-?8er<q<6rE6}@IHqm)4Dei7lF?nTr^@M`bavvd8ryK~r|5ly9IpCyVgf=WD7
z4fjeNV6P{&R0`R9fqXgF&eSJ!U%5ST0rTIUewN!bR0g}cZj_Ru#xIeA;ClX8O}`9B
zV9Vf1^Ad%%v@XY@z8ak?M}i_<ZcdC=8;t8V`@`66w|LCsndkm=jlJ%F7#ag_AcO~p
zzsp=DbH@3m%6{(ujVoswRe+*NTwg9Z$dDRIi=oD$`o;GVe?iRWc4iQK&upML?i|jj
z`&@ygnoo)>8W|IIGQBcgGZg?N0z&;u92nM+W6z(+O-)=o{O|XTZ_Kj5!EVv#@OBxB
ztY%C_FN&RD$k4FTJwUm_Xi>4BEawu=V^xOFDblmxx)`Z@i>R}1)2`1?Lu_jBszu5a
zc0c{5p`z32Qfu)GWtE#;*72-H>}w0%4U8@f0b^L=3UF6pK|Us^<EGavT8_yC>JHtR
z<(1}5{ydXrX=>tcclKd-LQ}_QzKT^WG3>1wJk-RsYiSMD?yQWPFCU31MfiDjS;giF
z-qt=?_%77Gv=T!&o(<AAIqR<DmgEHvfpO)0{3&3*A3Xn3a@~_)Usq48<O{R&`AV_Q
z{rl$(JY26~&C%WrbTo%t9EI$Gn|rwgP+?SQV<STdyAuc_HW3WK@2bWKFp5(5xZ!d^
zsRaR%uTf%n3_Ho8fHH`H7;EbM{kqa`Cdk7rO3a=fMtOX>A{I(f>iy|8=oH(Pv2-M(
zuQ0z7qP-d>7Ub^a?b_Wo&?+3Vh0S`_S~YU);wqey;^-uQ+q~GrxRnuM_A!o^{6*)&
zKKo!-zs#yy>A~D|erQBO;;_0BC0It)4JY`CzSxXMX+Gkq{@YXY{U_?xM?YIdK7{S{
zA)bEU+^4zxi~^7$1`OY$GSFZVI2I5RNVDH?#10-bOmAi7(>RD!f7*Fu3L}}Cb4y%d
z1@7kN!GRIxd7ST>dFd{mE2<4q7(^8*?6%V8T}2jREMk|@zk@%NDz;DanP<}LmPUtF
z(dEboczzd;P*>BNo6Yly2;fqRa#I+Kcb^ivPLodYS>NcRA3CR+DK!6xe(TS7ex!XQ
z-d-MlMo|3Dqe;|`Cvgqr4XE!(SP9l_L+#^C<^-s>L<9qv$f}Sgpv@DtGofTy^NmI@
z9bdB?q!8{FN&T<j4aq)YLPA1)dXa6@H~b=HrVl`>rbuq;wzfA(A-+rxXez}cAy9+e
z5?b@{OUNO=8pZZKrPyjLfm1@K#Br%<kw<<H#Zy(+re4k2fB6GiF3B@Xq%n!6S}kyK
zlYxf_xmgFG=xSQZVlvM=hn7PliBMB_RHz}B0m<~hhr!6yQ3z*m7bQ`+iwUrl2k2jz
z&c!xTbn^*PN@{-c{Hq*)ZPmT;a7&52sj+bgy{$!8#e~=Xey=fA3%;-RmkscC>ARp0
z{w|_(CpJGUW`b?T^)fWQu{P{EF{1rv%CE}iUyc>C{Dl&e3vjynL7^_Tur@g<if$J#
zekYaNub-Q1V(#J=t3kKr7vmYANxoA}e(QHHRmvF&zEC#jj!CuA39S))a9igOJ6q3Q
zRIFt!vidQPw(&HLoqy0rM4qwqe*NN8c%Gp8RW%i4-WnRg;_paUoy)7;+klLxe!$yV
zftFv*z+irNY1!yQw|UWRSD&*bx(iOBKm$heHf+Io<11374R98p!7}CJ);&5aHSk1r
ziw)+ZGT}h+$of}ONm(#(55_8;dQep+EvGKCocgLHEYv&EN_4DrRz+yz?V~7ess*N2
zMS>P71*w7}`{p<XPWc)iPo~L4X>(9)H=o$7L?05tkauxsN90=}Z9?BRd01#kIi!fH
zj@Gz1pWGSuAzW=#&;fr)uF<=V4=@3o{eNs?Yz#j}#?17w4zUmcU7w<{xc0XxZiPh^
zDwu~y0Ab~`CGpQPY8^bT08+L(HI}9QWE3a)6|u+21T{@HDIrnp2CQoX6!?!jdjuw=
zaP0b8uGm;A`eirzeKr-kA0f^m#=zZBSO{3mV%OUr-H3xfv6gpnvJ{oeT}=QZ35o{t
zGHECth7s(hYJf)8?XAv(VqYqpY4^EkjT>LKE&10i*^s)XGB_GFKgU=cz*j+|{#EjI
zIzTMyWO;S@i_^yLmGozF(#Ti0lzgAe)tI=tpfYMK2(Gt9_&ydWlPN7_Y!?vy(8oXy
z*oKRur<08aeM{}r47Hd(-QgEl7}TUbbW(TBkf1aF`cT_MIE7QQQ?p^0aqTrPp>U~9
zyZEZ*#m>BG*(mY7E`L+0FJkZzJ)q*uR$FS;1BvAMG&eMN4^)3*R}Hl>ISYZGJ>!E@
zVBbNk7=)+6_CGG2t4U8!Csu2+(&96V<E#KR`6jlaXQJ=CU^=~lC1FT`7crs<gAU?W
zQ0~9V^xWqEpxX2@h7b5v`|GV4ps(kX=4w1PZ3u(FKnkEl;DSc}JEviyu;cXCY>z-Y
zV!Vxijss72*FpY7NCeO`e|x1w8@ESO6T2kNMa%_W<ACX;a4eEIOo)~;+NQSo!bpC3
zzhW_v483e1`(rp$wYXgEH*<v&ix_a#Z7~5cjt%p!VU;V7TD+vKPi;EyH1HByUz%+d
z&J%8hrj!yo-Xm2P5_o$@`E4a?^iskZ#)9iE^2WJbGT5C(MT~QY0`+~o%Qb$kI&QGB
za=TewMMQijAKjY3gqa#ZT?<Uxqc-Ijgrw0fk(WCCjygm5`Z81=buu=F`H>zHQ+=)W
zXWXvzF<V0wJ#bN@==Sk!9qB|8-yi_+es=q(L~Jdmnu>ySqnMqn7;!FsaHVgT4t+3`
zy6bDaYuY$dgJ4uv_{J+d4?R&Sle>(*u61&*5c{{usWAgsq-gY~*^DC>P-PY6enEj+
zyfSf0OZh{Hjy34V$Pbu(t!*wPk^+nF?RGDuyV+>xcF&sB@yW9aj|+2*^EawR`aM-`
z#AE2|bBI=@i|J)-0*?yn`^wCYQ`2HJ?G#2PV0kJ!#uUBknwk-ADq<Fv18U?npep3P
zkj!8cx9`tqd6TI$#yElo1~0AU8twPj<6IITWI_FCJZ=?y<nR{7%^5N0zd@Uy?hprF
z8l;F46LuscL$!a_LA3I^v%9IeX(}m;%fUhGQX7viZdT7@YcMYRD&0Mop2!#_hiVG5
z4gEBM$ZsRGgDmmSOG|=&_ta?PLj$<J!+3h(*M|mJH-TkVOW*$UN8b>H7TEa1QZvye
zy$|kz((cD4O@<nS7<TfB3AKrl);!HWexv1o+$uHagK#&F%MOp0Sigzs=-`Qfj1`Fu
z&}F2jf>K|}$Tqv=je5ig4ek#UOJi?uJ&m{F%MtJ{FErNH>qO==>{05bs(!k6bs2e|
zAr;v_#BfG(S4Q?0)}(V;%IeTbRjr8Pl80H?@7Ug_Ql%39NeNNzEx+xs{gv8TLKd*W
zBP1Nu0-!)GON^Y>cMdkl{30Wh&g4(OyNDjc6h3Qkd9R|<>~F5XQH<xRY@{_kM#s1K
zhBkkT?21?&i+^qMzzc<{NvSO|!(J0Z=+_j>wpGBo{?p?DQ6W3}?&|Ieq;n7;uG`+O
z1QOH{f<_XLWm!p)#9?6G&RtK-A{y?IH9$J3SGZ?7k<E_sm<7*5?JBE$U1OdSqL{Q;
zpywUs_{5M)UjZfO?B(7oh+fpyg4I4~hJQ)5@vI2cPClQfwN1!`(tTXgXFu#rmB+tU
zf}J(kBGpu$X>S^ScU|z=5aXv+1+^_OSxbSW=uA}x`T3Wt$Rr5mnMgsQFCu|L`rE}X
zu|{H<5eS0$6b*#G$@;z}PN={FM{)Mq(RsffrsjIxi3_Euu%VrVwC%plf^5w*%_TY5
z)HQUJCXTe!ZXn-v?k!Q>KbF+1AU>3C{T?xrfzIe6@#L1kr{gGswJ6qfwSP$1Z1;q=
zgdWO|rraieY6cwOgNbvBM+RmWCwfD6n|jugH|0OhH9)PvA!BH~gU88zAm9Bp%Mf0O
zInl=#6`W+W+e6M!=n0t8Wx<`03ti3xrVq^mZn!*mV<fzb9fv8Ju%fvMX!eGN>2xn_
zk%s|DFmL6hImn_&ms;p3uB`YIW4JKn44W7-1Ap`}fphCjt~c*fVxDdXD;r6s8+okK
zXn81T1d9&2g|3wWVKA_>O?h>Ud_AhRFMlyTOR8)%3{1o@dqNm!##DpuGBER0q8RRp
z9U9Dd%G>y<ypq2g|I~8KE#gh`t*)Bo=uxp>j#D@E3Dk!YLUwzFMwb34BSx7x6C<%m
zMeW<g*I}Q@Dy7PEb#>K=8Oz1TEolW}{x@l;fj@hHg`BV6bpiSeC#ayHpcAh5@HnxK
z;ABqrshhT+HIropJbx{*bw+EepE}>x6DG;qzbUu8uY8-K^OqwkKpX|LuXJ}FSDvUq
z3p<PoG^H2HWn(O?4GKt2KCWgg*D|-8XeM4;t*Xtz7)z--*Oio~HSAQ8axGB<oEKYj
z92_wpPv^OcUt1}D-8`e5n*?+0x}Ir5X*25~ElJ9FvN>cita{%LV+_E9mjjV7Q1!g*
zMYc@{_84H?Q{2{Md9GUS*Fh8Kphr}zH<GilsVL(s`r3A0veBGJ*a-nddKxVqBn!!u
zcKw-XrfP|<_Ty+nve7tBc7rQpMS4}dOY`S9b>EOlCr!^v|2*yQwJ)Bi0<-?071aqJ
zq*x8eoreaest8iB>V_z>K`pQOgGimt$A}ec8_O@AQ)c(8`7L>fJ1$lc{XJL8OhiN+
za@`eY*W-(|)Yk9W#_x+`D&eG(=$9QgPDeM>78Ri9gKrv~WlI9|-%Ll^baFuhkZvYD
zKqHEnjJ8^~*9Nyb-Jwb8ZY=?wF!RgABqa0zw-4?BUd^(v0Hy<ypN4vODT~b0!FXaC
zDZy5KKTTCeUsXj|+SE4guZpRmgx+fk{5F?0E8~*ghYH4hIE=a%d0SHq&~xOPWlcvW
zCoqPn0=0E<RDLsRP9Q+L!88mZfg5~^!?ilRwLAKtRQ!s80BPhL&p$^4o7Ye;aN(1h
zg1mDE{+p#ld6Gl9u3%CFu{F&+N_bsoqfy#~3I(wb@N0!<wmvohmLl3%tVp{hx2hY<
zqj1{Q^k+IAY3y!cMh;s7>Ur>69ZaNZt7vn8xj<hQun1q#HOL`^dJx>n55-py@xLm5
zD3kZEaWT->@x-fb*Ey$x5%OIBb`fUKx?W4dmRB!ejy_R=L`YOGZ$@@CvHaFSJPwH)
zYZSyoihe!CTf>SSe!NV(>ZGm}UrW(dKh4x#&(J6_2c21b{#1E&G}#A`s3FVN3XjGE
zbQkNQlFd)i32#rv=g|Ju#hu^uLhl*%HTGX;b`ns+)1~<zW%3i8y{TuBMVse+43ros
zP88A^sOaeA0ea&1^k;NhZHSeP#K0J4V;ZD&98@hiS=##U?*PGwaT0^9erY~gRVO^?
zD&$ZnUy9IK&)o-L@VRc=hc_l9-n=_HaN`>6GaVaJRRO3yRiPds84DO*$@&2`HWeYY
zk0VLZsxr&IZv`-@IaqA>{9C~Fo=q<&{U3qMf~I<|A}dputLukaC%J!o1}3Nbt80Yc
z5s$kAzq`Hr@tCeyD)h(>q|0%H74NibdxRT39iGFO!is2NGUNEgn0ba*dc3(y#wOhN
z$(u+j^^6N^d)_3j&ZJMWo9QIbQO$BvclF`^(g#R>AJY3G$ye!R_w0t?BvpswsPP;M
zh#wNAi)b^RV?J5G(C~jk6Ig9@U}!tVPf%(sAw!w9v?4zdUe&KSH#B09Phc(S$qz}i
z3vS!YNQ@>7>*t(7fZ91PWoK1A_>QQHdb|~>CPgklgj)8#!sZZGXZM2%eIb~at8KV7
z$)+;@x-;zZMuu+QK*R)u(l@)Z8gULWK$r2P*nZjvnn_>37mTG5EX3wk&C682GLb>i
zBZyK!>dAivZ?5O4wP>6kf9NX&gek&N@)7Z$!xXmKn*i47u)hGV-NEaOyC|_fHITHX
za5Ap<3UR%c;YmA!T7s%qLiP8*+x#bno8hJ%(}IQ{_P?Qu3V9Cpqdeq-wb%E=qM4ah
zFyEAsKr}cvF+^pRnz|fYzPo#s2~ktZ!t18oq95yfol}nglzlmb_IM?{mo(Kl$FL~0
z43fyb5Jbf5DHrj#+VJ@k6I@ey?0;U^UcmKKRZ4{=D<yM=EF3#qc}()ld>sG!M%r~@
zOubvuv{lxIH>PFzk(`j02DyM6^sMc=87!=l3?|gkreYW&;P=z)Z-z;8w^(ZzBd1y*
z#t+99SCPD<x1%>{%1onb#vVhXwII+D_obIcKJmXpJt4`?;tvTwbASH0%wpcvqS>V`
z)b~#QICT5I4LgfkmUgri>8iN{uMXlTQTQYVB$<SP;O*m(;EdkMxQS2G+&uy!Zm#MP
zKkA5PBN--0l%5JCcBny!QAFh1rZdgIh8si(yl(s}yf?MA+Hyb{gg8K=BB>fprr*wW
zzaz%G+bEEZdAPVVLi7`@1u005m|cohVIF9M08Szs85#Jk;(n|@7{hgc8F-rN!|UuC
z@JN;JQ!FzwbT&GrMV$FaJTAac$hUi6A;j7)DxkZJHVcb|iQ%?Qq%x9U)rOb-E}x6L
zxi73-CkB}23n1-inWe?D@R`wD&I>v;#$LY3uYC39u_{FLF1(NDdSYs+FOibJnH^^F
zF+!a)5g{~_=0F>+Zu(E2K3ys{YaNGKSBHb`6_KIu4{M~XX2*Gc*)X|KK!B2fr$zmt
zfjN=pKj&*QdJXLTl>39V3_V=*CX6jfZHPsxg)NU~Nn$-Yje06cA+zYbjvo5*5AM|Z
zXAEDap1dap*p#!}kJ3G0c9%(|h+infbMxise-=9FENTj~H<qZs4vIgw)pOci2RT1%
z4$;Xs5pIav9xlTxrJljG;2!C>lKyemZ)?mfyp*K&*4@yo{yW0CSj|WGHe9-;<HVfJ
z)hp_(3N(Uxc<Te7X8ZAXhKlB!`dq|gjkkHKw50sgHj^3%TCv2tlirC`LI&Q>?@<kV
ztg!1Mhi`f`|5`E3xHkkPEQEaTumIENd>_9Lj&MUX9?=<KQH6lSM51whdpNaoxDqc5
zyJP4Vcpj+eGM+@2x)7SG2FQ2PQ!7b<0&_<gu3d!7lgY0$PjpPyf`Vi;#xQF5luN%<
zt};^6P#9e`m)MXjEI0F=U1>WcY3vWmY?Vo+IQf{Lq_E&BTiRV5-;SD5mI^GT&b!UG
zrf(us<|~HW?A8r;w;d^Rj<1huv55rr(TYE5m;tlWc6QCBO6`7p*ySq7@$!=ET0Va9
z`T6tx`S+&*Htk;VWB1cfEvFMx6siK~tCW9xic8azlak`%{ocXBNi&?sxbX<~p1Z*q
z6HIa~ZJyd%T6WueF~gV8a0F<@-eUe8Hxh9j7+>^qGlCDq`3|A|6nlUQ-%pCf66`Y{
ztVR8vzwMhuE()p>Fw0!P$lGq^tSx!J?Yk)9#7Ua2mg*!|(w&tB2dNj$*e;#Y>;=L%
zqB=bLaa==dhOO}s`tWygleZpe61rwyRHEq&Z&>MTb}anqsoU^suNCD<$z|k9kX%q<
zlg|{1<HPfrt?ReTo>YA8M%*hP^!kflzt&;i5ELqL$&g)iG}DyU&3PN1lLQ-quQrW|
zq_*R1nPwUV&MGDX2ZwJRfnNQq7vlM6cda})HS#PhTrZc8NnPhtJ8jpJ?pkMeA#gO&
zTU1&-@wDrIm;n1Wd?QFgQD>7tMc{#}247cAb17#rLii4CYR${YC>NC2q&7Q#a*l5c
zNKH65EkM&6*P|6?H&$riU5L1IuM!KPt2`^?C!4=8`#N?BjM+3H6Py5bUi}d}X5`bZ
z8GeCsUe>B@9O>wBECZ*T`}y(ws^k3_AaY^WWz;K%+tD*wj7~Q}MSsX_pmh|=EiiGU
z)a=2zI`YOD<Z0$3Tex?v3QDqF0|D%_$?_cj6$4qQytsnDYyOLOWnRZX*~J#Hk7GQL
zLaia#M|GkzM4SKz<7=Ka!*Gh>0OA33_e0TlSbfaE1I5h)gc*+<su$obyy1{5*Hx--
zZPw*_Yr0lk%+UApQ%4~|vQ@W`IqXY`)-m})?q>ke#r}q<;)z;}k~o)G!t)}aMkYa_
z2uN+<j_0#}VCr(Zj}KIvW1oGu6#nflAg%9gh<35qe?`P_|5T*0JXCFNW$t&~WCq8D
z1){miWJ2!id_Wx^csg-Qq?j!Fo*^=2$8+cB$w0LS?_Y5-qV+icUs(W_FhA){7Bl3K
zly@R(t00Rba1drbAjPYvR7;4Kl^vs0tJH{c_jXHozd!D8!$iY$(!7$LmCe&qcS&d$
zxzRgCmJ6ob?Gtr2OY7%E+}*c3f!LFeAkdW1O)4v}u^KwVc7n-#U9+b~Ah&s&=>IHe
zvSPguNUA<@y}0kjD+c~%qM87B3^(zz3c3M19UH^!gWShjQD`2QR*$~@w2}DC+$=nu
z70772yzsNfKj{fDLThR*L18@sdnrwFOL7=jr*IS&sDo}c8LYb3Wr7>L1nLbSB0C!u
z6A>dGWBZV@wG0UKQk*G=`d1;FJ#{VMobW9z>@#V$Q6vdfGk~b#z8gY-)WuUnG8^zO
z5mVg`5_6$)mf0leYO5QE7y{=&LP%%`FiowMAhLtMm<E4)oDoAm2<s+0;m_Y={7UBI
zk^O$)k;f*!2}axW0X;VtW-gxs9?`GDbdsq$$C{t<u&yXD$jTjbG<^XeAvWVSU3y)W
zTT3*V;bMOwO@mV_)P;i3<!hB+9oWaF>Bgo}$B8uOq<8S+m^t&I85G$$I56XVQfSmc
z>|sy{vVPgi+s*5vgkX-;s0o5U|1b#otud9(Tv}UGCr3DkGhrt&;Xe(P`#Bk&tDg~w
z`DFJ1c@Le7#%3wF18SV!Q-buo((i&YHEA~yl#V)ptl%i{H{dlM=4~x$>n?sP-Z#r-
z*cYKEawNY@b4_Dvevyx^$L;h|EIs^1EmMJg{6>|d$?F2z7`O=O6$^&7zZ#pUkWp}P
zzUOKH0`v@H;QFkxHspt+Ze`>hq(6BVxKvq8r=W6WDd%y+N&pxP!$nF8`o_ph#~@x!
z28bWxVS`<5c&2SndsP)|4t(4m1MB2%7CP&Zo&Y{gO6#=xiPbjQdY87A-592*v1;&2
z;-H^yQ=R)3qw9RuoLD+N3afN9yHBZi9}%;(%m$OEfVeho0H-05Ry&BIuIBHZN`O_(
zt(<D0nPX{o&b1SeHnJ7bfR`3y8uUOb#2nO=CQO4PPp+prIvk*miQ;FQ-Dp;2+e+v-
zkst-g_JK77VRM6oHYM_E9Na{@#_M&vZJI%cx}~Mx8XoM@hYctd0r?&32f51RG-CK6
zHgUF&&9%p>?@rn-h^*yyDA?vhC&z(3X<CcpWMvt8O`ihh(!gE;y=G;@UA!E!Vd?t2
zw6Dtb4yj1PioWVb9o<;}k=tp;sZS)p*YWe29#)__U^6he^6_cG9c>A<$8!g7@nU;*
z*YS(vGPZ-);E5g_{SfaozfmX2Mt_jgO(lS{buyJ+RLypfOms({#uSdyc(t=Kzqq*F
zP+CtF;7LDK*c<+&Nv^0YEM(GXpjjvdEnqbCxp;`Hi)Thd&mcf5eW$8^7g9z|VV;#P
zo1_A;WaNl_?4%aqr5|pg#~E&-AhN=@sQA|mKjuKJKr~f|01TRJ-)!^bf>cUhmU0^7
zVNE<#d2TcfeS~`F+vUP|LtQ*5O{J_-whU}m*~Dq7Hif5X@>@0{$1TFG@7y|GR{bt^
z^|PEV^DQDS-KcjptKh_Qs6h}y-5)r$RMIO`dQ(Y0jNh0C>iK7j;m+@PGMs8eP_?^G
zB0Ly?`w1U_%)3IN`)^oKfN<yXV&CjIEIDYNo%|DED)P`d;DOu}z=ZDnuh0ZbfU<2h
ztr}|xfb=k3K(BJnPtUDFmE%D+Z?;S)U+eb!QT`zNZC-zfWAq(hUZS9!;EU1yZ>SFN
zu>|lJ*`jeQ|1;93%?cUs{tfJc!OY30=xe8SaObZZ^nX5?K@aqVmsPK973u%v*ZgNv
zN1xum3>B%ji~pI|pw|b8S3tnDa1r`14D<hxfN2190wR&`{eR{)U@`y}B0oYh@c#W@
z|L+43e*wMIUo_hT5N802%>VrWj{-n~e)%S%|NZj*`;$O%z>1pTw9)o|;Di3afYb<{
z|F2(GA0(L_AdF>cN#zGcZfffDe(bNM#YL>23kyVm725I4W~b}3Qs0XgOSA9y*V~&1
zNu`pqa{hUtXe_pR&$5A8T~m{i`V<4Zv3UB-?Cf@{ZEgjgz0+h0?Px54t)*pR@U*Ov
zv2p(N)04|)iQQ)X=}~4@Vp5Wly1Kc8^JWAD0{##hsLSSW@&muurD{#!p`eZe32AA#
zkfiu{eFvCNRixHE82YZ8VGLchqR4}TgMW_y!^1;#^XTaRef1y0{k(G}8X5j$GVtd@
zvaqmpy`5FgVIuIo<TW-nZgl{3EGvC|A|E(imsMjA7|b!Dclw@}g2cpyF86y_)WlH2
zalX$7MQ-lSNctW%lL*iz#E`R-lNSK!_ROMWoSaA@TX255P%4|nA%E1`)MT~YqkTn%
zf_VU_@=2T(4-f=iK+zsc>ZaO`)2w@Q0H-MU_;cy6PpIxP=;x+)K+9aK+sg-#%AJ#q
zsi>&F?sLBhkE7YQZXO?%@tG(-0TkN7(Ged2zN@dVpKx(-aM1C*Z0_spTet1SYf284
zk|f}CIJg}p5LGl=0uX^sB1z4JYXJYXFFQN??`3y)cS?lxl&_1%Ss>p(MdGnMcVUdQ
zJ1SCQVq#KKU3(GK7niKPB0!e_NFqEuyq{tq4IR7+_AkBK?k!>s$d#<Bsw#8mR+~LZ
z4k`}-j013@Wxc(<>DBdI|23v^K+jMZ|03Yx__rbX^8l2QfcGchWpn|IT|)@o$|%&T
zHC}+-3;<I1en0zb8}qQdVyko$U=2F?9Y%ne1yD*XaBy(c@qSIj=P;Yba2f)f`(6M8
zmvQC<s8Jv=u$Gcill3}VQZAcyMj4n5B_*X;Xi(74b;c|{`#n(TsoY<>%CIK-2SUQa
zSaQ8`fu7G-%F07FW@aZR^M%g$#xXjQ^!OHiX;9<Pa8U_zawC{$w`qEt9nKBL@j%Ka
zIz{$6Zi4zzjX-a#UU-p_k@h`5(Q$FB&Ssi60p4;P5KLqwRX7Af4{K0Ue@(F25QZom
zo3{MryFg{2S*IM|FLyI%Sy@>zmHS0{8PL`t0GI}~4V>?Pn`cxv6Z82mwyO{FA2JR?
z&n24<*p}LX<hR-M{r;>A@ArMocHQbn@DAHeNI*V>92gv|hl&3I2m2#~C#Yk9D~Mo%
z_q9h*uh2_TF;VA`JOdgM(ob2ssIai`cK^LNRp;%h^E$7&Xc{YoW4EgVU`FBuN<`7u
z*QXL+s8qf=uk8(?8RaMjLJ#2K<J)oz1`jDOF9*aab%3bdq;oo!_$LOCdIGiuoMEzD
z*38+ry&7$L{IkZ!#sFR|47PPVZkH%5W|Qd*R<|eMON%^cC6=a?Ef6<8;wvn*WlyHM
zN-7W%8=my=1&mm5qZl*9sb8-LDCv~QfZ71~*(xf<3xlBV?XB!#DTQQTTm%M~sR6qE
z5E!n#pFaf1NDD-il<2hf=s;1>0!7H^Fj1np=ZAt|YNHC|>H1&_<e^4>PDBfIVS=%5
zAhHX^O{W8^kAAxzrGF2mD=sbqz@^WbF2^44`SKb*=ZZ7M$C-!PnR3Nzw^42pYty8B
z<wUJbZQR6J?<+@6U%=JA_S}9a>^Q5a%z3Ob<vr${J?)N(J2Yh#5Va(Jqix-2a5$8x
zslLG&9pXRCLN3y6NvWHlgH4L6-9yN_(_+U`eu?`H|9T?&OJWol9@-ZhAkfWAIXspv
za_Rzup~~f<G61Dw%TVX}fiz;|Eyhoc%li79BvOm1Z<6<@owN7cMmszfH6!@G3{Jf+
zwe}2m#~-S0nq!xDFdM>SCBUz|((cAtzucwvN*$5fiEN*WWhT9@E%&65RYJ8KJJ)(@
zvo=1H^j-rHi@)#6*HShF#rMp*^WgYkVW#ss60X~3SXbINNs2PzE;0(Z>M=G44=QAy
zh}VTYJ5A<|y-iX~p<Vqks><Cj!}R2ZM^ZH~T^Gjmk+Dt_-B%swca>n$bI=mHSAZ&)
zM(&FJ3gCP{c89}_=2f)N3N0B;;mdQ%R9aS4hbv;01B~g*il_!fnT}n1?z1hvLf~*J
zh8uxg<wmvly7TK@P3YFATQBCRbzddCPEuuLFWL?}*?COKBC}quTzlWAZGD*OaD<gb
z@tje$i9|L9{MKiEo|q;6fg*+r^c<=>?uUn|x-(#uH5T(nzv`MlqPqYE?VpwT3ZV7c
z(E3bjZZXNN)S}Aq1B03T)C0;PDp95c4E!g^#=zUZF;fyLyaG@|jq!<poE|m-((HJ?
z)qAu?!#XXkLsPkmGD<iWZ)L{#Wt(wIq-`gyJiYt4WSFMWK$~~!(RP$O`<9!bvZ+s0
ziUnT+af{6+_7CZLxQ))qr{3FW+o^<)lIs@gqt;C*V#HnlOVX;5R+bPHvvhJyQMN0(
zVO$%H7$B*L$@%J=qJf{XZN)RWUk|0Xw3jzs6%{fZyFtj&W7FE@@*(d9ze8Aj2I1J1
zVD93N__o@U_{~TGx-gvW&&<0Sj(ymMIrGwNwvDItYPKUney#7@SYN5P;(8|~F`Q;M
z&RpZk1;29`NW~qrS~p>LQO4=X#3+H`CoPZDV)b9_(fj<9H@l$(In1^lr{oTJ0$lVK
z2damlz8G1dT4OsMKfLo_E1uc>9pcMNSMh7e>o|M^M+tm+KEc`u2ihm9F9=@xAnrCM
z-#AUpJdgKbbZ$Vtz#V<AK{r`A)U+5+KU-YMKe@M_0Pa$F-|zSBW90DzUOW#=#}W|e
zpLu;jAmBSt`7|YdAkZ`tek}_a-6z5iA|)vwjMC7?3~EPN-cPHrHOv-ZrMW&Hk7#(7
zh4J^SweE12gFz5?6u*|j7am%Q+0B)E-s4&S?1(UsfP0-v>J|XO4Ik%t+O(27n(>f6
zG^D(+f!IkoQd1I$dn5UUi%e0#*DK5GU2un=i~f2;8eX|m%X;_sy$K{>2*u0qj`uHF
zuGQUM_e>{MT>8#=?xOgG+-DZEPr`T?L0zL4z@edStVbeFlUSrEh)v>bdblXmGJ6au
zj;lfk=XIu-YfxG-kmy@f$~DjXhyL?ebW>}yI?m)HZmO1}t?SP40fR6*$8m;}GZCtz
zUllm*_dP&#_Du`3gw7goDojyk41KTZtnNwLO?rP@?#&5~<$Y4SN;QGtOic^Nfg5<W
zX6<Kld@ae~92a$={X-A`AQPJ=o$4R!ePO5tuNR%kZd;<<Qgs&k>w}1-d!CqggJ+U*
zf;G=f@7MwM*usgPz7m^Ny6H#)R5kl$KiU^sB-yFwKQ2ZUC~RM2LK8lqOzDaF<<7_Z
zG$Otx2K|O1>h1c+_@>P=2nu0f7m7sd4Jo8*yQn{?k$*DX$q7jZpjQ&UGOVF9Z$Ff<
z!-b+R2?F0i8Is(4W}9o=n2k(LQ&YT1&yH5bmHjrvgGx-3=#^v3;ph*Ue~@5gBh1iT
z#YZoy=2&wuCyeG!7oSu|dt``nNSfWXgF2Whb<Pmu$DsjEvpF!l9w387p>Swamju<L
zLq{BW5j#5Og<%jlK7;zfAf43iZVZPD8Dd}X8WT7P&m^PZB{{M$vbth_R0mg>v2;qg
zY3&&$A;Wb_dbL@6nMzHLOD>aq%zN!Fu4*G970C7kuOGu9pJ=hV);PmesVUAGYB*7!
z=iKdS$<m*;UR`L1tHSk^3Y^ei|C*9W8ggxrv6;`91!ZKm6l2_Zy-~=0Lu>BX0fg&I
z9_1=syKiMwA_{)I63X{LB%{4Y_gO!A8Ez?M<$}L-x1MFPdQ!yC%<YT)m-%&(fNJ**
z<QV+7RN^-t9JO-xzlwE40jOBH)vVNc{O2GnVk2;g!2PwFIe?>7Q?(qRs;xg-e4abE
zrLpz-qLmKd{t!M#B0D!2$;_#yw~$A~)0$To`_h{e^^%1p#DuXIG5N?k{-DyXEi{>k
ziwRRuPlH;LjI`g_8*44P1)QLHnuz6Eb4N?S>~Wiz9m^7d?AIQgFug-!o^Q2e2v6(D
zQtQ0lyb^^A|5mB{X|Wie`FBE5Vf@(E_kF$GD4u>m{K3H3u9oUk!SO=1#R{RyQuW6f
z32m8r0>w76A8@{;^~{CLT&#zZsEx*?D41Rc?2S|Lg}Y4i14$Wn_oTCZwLS;XeVkE@
zywh39J*{`|<gjDL2F}7f>ALg&I<01lUCbe|)KIw6jD80Eh}J@Qx|KVqUZ3Z>66N?K
zWJ?5NeTB!%n3xg^tE@v^$0QR4zFIbWv?*3iwH;FEBNLMfmY?|PgHWE@wXOl(45;sN
zR^<l~V)EoGip+g$ALT?d@)sg(A4-9`6yP4M7Uc)*#^^y;2`EaiP;osIKvO$X@)?Y7
zZFr0wfB$3+7lya>CZ%sci@h1gRb1KHaIG@A$-*8;Dw4K0J&Q9N$&2I`{G#YRf?D6;
zlq%I)6DDCB((Y^@4l<ocG=$m>vKX)v(V9SnH+P5{PzIX8o(MM^Hs0TNF@6)iw`TEA
zV1&f?GD352WF$CE@Bko+smV9iQHUb@Y_FWX0r8$R_l8n-qo*r<ewZYBL{Dd`y%`}_
z6-az8brVW;H)RKE!Yqa(EKm_RneCIVN;Xw&weRsq{de~LxK4DYPLauu6AzOgXUHPz
z4tg2<o`4Q|Au}Vy3?AiuQhJ7SPPJXnNE_U6zs>HHG{a@`M||)peH>BBZan3<=c?EY
zmgLF^)##5|!fErRb!HxHAE=;i>n<(IG%g@Vcspmm=<DdEDN-OuXTs+gC=WQH?@Rf8
z|K#9yC3zpMIhIn!-SosnAfDIz8jL1rn15XmbQ0hepfG6uujr(JI9)|=&#{o*{!OgP
zsLyUcW#m)oCJRTz!UUA`s3<}_SCa(sF<K)AE-_JNyh7P|tKko;W)hS?R}vlM!?%eU
z@?qoYu=SGfID?l$*&EUlSH>AqGYjFXV`insEO}!LpfcETg$&nDCx_ljwN^b5n??cC
zk^aql<T^(;1<py<CIRbs%s?pV2HWO*!xVS4<>6COj+U$&ES<XWM%|T5+2`2n5>f?u
zm>3vg8CJ-Kc*(!TAHnqoke9Iy&<?pZXN<wP9vpsHo3uCdt(en+T5Ys3M%o)WdJI4X
zSfVXYf`wn%XIgS5n&Wfggl3xa^H0J+6iJBO6iC_?sSi-lF51mIb5iZ*{YXO_F@|3|
zp3HANd7YXsnyE^;V<be6l;vnaDaB>qXxJ(1!-BBfA)Si8kTIeUWGXPNPa78>+nR4B
zJ~G9p6MdQxHsS84g6wM_Syi#I2Hb1?K$87{+dys$0kxii*}u&><!nsJxH#%^C_11?
z<Zdu^N!4dTbRA<g1Y$Q%$-EXYY4O@On#Tq`&GX5!81m>=lV>W8tr@j>r$SQLudvC$
z?+x54%)Dm260GNGB;Ae{tLw6u5&g`$NVF4EF%2Sw$9Ctnvf|sa(kZjkFSuK060Ejg
zXIz=ol&WI14N1%!$PI?G+)Aez9Gp2DaXZpq2~(Hh4KmYX@vrS+=sdip#FjdBapQ5p
zGB(n*Q^yZBxNy3|Mz`Xou#ayG7+bn#TQtCU;VU?AZ>w#+so8H6KK!R03408X-tg@9
zgn>#lfmNl%hV6?u7$HNAd;K8$x?{Nuy4hvjsA8`cy4M%D6Me3yj;)SYyR<s<>r?Y9
zCQy>qWc*J->`Wx#ZCo$w(OsggO)ljL(FII8SY4Kx7$}%rY!3LvdldlX8C9(dP$q6e
zmj2CQ8Yw@diZHeKTQe@hzduusRXL*Tn-G~=5T$!qg8odhD3D3J6xBA|Ms$iymaZjL
zQpAts4Sg*6exB>f>h4+nrHXu%@dYgEV_T+AI<kx_E(F?&E$v}9r=)Wj73^8&{vjjn
zN*`6nB)5FXK0atDEHI4)RML+wF~!F>qI`Gp7PnWU4TJ8@FtD&9D0J-dC}68&eYH>2
zR6;w!^j`W>iJweB%+e~~Llk`d)fHM%KXZ*2Hxsrvc`#e7xMsq(G}~OsDMYS6cGFpI
zMlko0m?j5c1E)k|w6B395-unMg@>KAHpc{t3{156%Wa_OdLvGEU2Fcz`HlEm7`~Xv
z7`C0T$D7*XZk+D@jOSb0>U1Ob%9vvY8WparUk(XzwHUB9q+K*_fJ$vn`;T5j5Dc~t
z2CcCR@I{@P|3|;{JH=@#tazwG$IG7{(Ma6SI4Ii<aU4VGdM09nbf5I!Ij1dQBPNVA
zil93$X|F_l@VyHVtUi&cm#s9&t0V(B@!`_b>*3}P`|1rWv<|aIMO9j0_K{8FE+RNq
zGqbVA?>au*kD#>2umRbTiKAopukoJ-bF~OQH-Q_WQl+~1za~{LFz!8n%hRdJ%<)f<
zL3JqH52^009>9o@H8C<ZDX6FkKV)rl_m7|`VlhXpOt}v@M{gN0GQ%67=N&)w1qK(a
z@B_oUg735?qMub|h0l5&F(3LQ>q?6WZ4{5Ef|-{b)dmg<-P0c<@OEr}9I=ZAABwBh
z7$lr_J!i(L>jZ`w-%AKxk>3|)0_oZ(8|5u}Cp5>>qNEZrdB)P({#!iq`wv56`e76v
zH~j0JlR!YjC+T~$V&;kneJm0gPckJU2pJPX$ALDgxe)O&&)VO)`Pj&aC!8{e*GSA!
z*d{#v3azP@#5(E3qs%k%pb|Ig$6pkxVs7MkjZ@c+&1q;yy>e_SO`1_vvD}c6_pKZw
z>80DO81TGT<EiN2Yh!p^E}NGVzQyO$r$aEtZQVCyIQ>-6<{Q<nK?}p?7kLV>wNK0|
zFK9<7g@kIK!Xhc>lk++ur3<aVFLxP}Tw8%0F$*Y<N4+Pre!xPZYXjX?%A<ga)x;*X
z>bOdd7<NNG-9lOx?6@Cik0$5+>n(V`IYr<j;kOE9-fglEvo7fTHA8l35Yrx9=$=_d
z913Bd!H>x@wTxO&=Cyg)9a@q#Gylylelk6v8vc(mz&mqF)la7AW8*lLS3hJ&U|EZc
z>b@~&`?(36nTf%=WdlkI6LSS#!>m$djfSU!mJUXW5h<Um0b*ThR7r%Q1jA{oQ!<<M
z$wI00L{Dmg_%h{C0;(X2M0o~_TYAF)@~{F^+$8^zL4&?N8mFS&ob&CLt_dw;MAoCu
z@i0J7#d`LG&tcfV5^BRAx028kp(@gDM!MG+7@TN7+3|#sU-rFCH&wp|s?Uirua_5$
zqx@woI7*%~5&s>P1gH@`ry$E2UY4I1(Qh@!O$oWR&D7}_8jSh0d8T?e_w&NE{FlL*
zV63W@nu+99BQIdpTTxwn58^1c+3v!3L|nAc4zBlw7uH*=W!UWQqx7$6rBwrpR!h#(
zzXewm(oVi;)8`+Ylo9?BuZZIfM2eSWSp=g35OJopesHS2njL?-InK3vez;q-!u>l~
z1r73j5^I}yuRWF7H1VGiMwve#ok>8+!kZZdkr$e(m@2GkX0APTjGt$!D4?b8WVqdj
zP8;lk>K$fQ%#q;{OiM8JNpdI`H!*934(2wTrZ1Pqe|vc3E-cWhPwSstchP6ma-1mp
zZ^Z`r(h(oj?PjrUaN|8Qn7Y?w{#&kkk)ALesn1-?*j?Qc-~I{a7E!03)B=PI4Oxj)
z9>rL~o4qPaIX*E7umk6uOs3f7neQHF&+J}%Uwck|J>k;Rogi{>4sJizxH?xxa1suk
zP7Jz1bsIB&abb3Hk02a_mdOk>9ITjgDbDT4${Ie^yhkzGaF&En`8pK6Xy#Fa9`}_&
zu*Pa%lY-shR<h|O7}FL4#_=aZFkn!jSuo@QBV2+?h{muscUqb&<2IK24ofVYdi3Hw
z>*zFEqPrwb7Ipl$6Y15n<9XfTNLf{Tcr)K<v&*#Yy-ItcQJ)kSdD(6sXI3X-A{;BI
z61I;q@sl_$nbztsB`Ui_IzeYox&G8*G7U*{B^uEF<~(awTapvBJG$jR-iU3PU6bkO
zI4`M#3SLDWCV*b<&eMqR6UA!9&<*j-rc_e6hq}9JH?1c4q|ahnZ9YtTWyFM66=`9=
zx*N0aR8irN4x=G9*laLP?w4R;Mxlgv7j8Q^<(Gnk6O~e}rMG9g{^f1bV%*Ju*%6Yy
zdaqXCZ3Wk|>j$g1$j~pG{Ot}#)M}9c6>_&%8={yk3B?J^0rO{XS{g#iDf8i#gp7fi
z3&XX2LBJ!SSxTNfCv7?ylMYy_zAf@!V**X1)Cbfh$2j?~A%sB>E0OnczYomW80H_1
z_jy(SPOkML!;hY%*BgLE3O2L9YCnb_!c>_RQys*ShpW~?i{Z;f%ExMt*g>6*J?tMo
zw2rGsWekA|kWQAZ;MymVjxW+>VtxikNn2&TLM&Nkw618fU3lZNGjy~KW=yQoY@vHf
zDaySeOVvuyJuK99lwn0uh3;?-B9{G214G{fK?Cgb7pWZoNU0{(93F17+8vqx^We60
zmNPzWY{)UQU2dSi1F&Dv9^_B8AGDC|lZ1SF3sB^vR1Dtya{*4H#fUu;G@rMHT$3cL
zfGdh$ui_%DRE@;bbr1NZMyp_cD<jPa@LaQ31*~a~nbd@^+0)qVuBj%wXZ@1xIu7)%
ztfQ<LAum+#kVffQd6jGn55KNkR!q}(q25#*mDTE9Kd>C6UMr0<dvAj2>j+bY%@%4b
zc34&#jA1C4Wg|QmD|M8;xf5eKL}y*z77@P3XN{ay3jWPpKR@7=h5x7voj{j{_3(e_
zrQJc%zzGVB!$Y`z;!&)^;G7<d7^%Qxh%@JHmeyB<`G`URhs3t^H@B|P``kv3`LJ}}
z@~oe1y#f@;EP}VDWoL{ifY+w9+nFh`lwI3?80~?a>{ad<KqbhwnDU7Sq6@NR0-h(E
z@Y@XNy2e<kIdQf$JtK-;-<>U?zUt?OwM(IXBle6(p3E863tR7AyTq$maTez|sCEWc
zGxZ>IVZ8m9ow`5C*lGf6oR2K;<6rsHR2XU}=9qIDmSIPCGK>ouyVZaZmlzE7)T%M+
z+20m<?A)c&Xe#4_LK5hdp0T!DUFk`D6}w55L{am2pB<d{SbLS7WQVv3R0R7z{tjOU
z3r%j0Eso)#l`>YCo#UH#S}ghCC97Xok9afgbi7^wiFluAJ&JfFCRPJaJf{qI+X0`c
zAO2{e=oENMdRab=0-w2Gd`vk!ZNKy1?WnH{(Cpl!xA=genrZtfA@VAjj~twGgZ|)Z
zNa!h0PxBgE_+RZ^`9IX(_a6))+4mHYecxgzC4>x77-SjCj0lCYhf#^LFJs7(CX}6o
ztW(*S$(Ai!c7?HTSw1i7^Lf+z`yYJ!Z5}hPx#!$-&pr2?=RN1V5LnGnq@{2AayG30
zG5MK+Cu{}L<p#hN)99O1n(7nUAuB%VLfu*%t!tG_>4v@^7`*KC$JJDWmnKB(9UyaA
z&WZwxwcUV8Ojt5{#5e3B!_!?$@K$JwdNSkR6ed9~T_Cj8q*HlgkhIZ6=B(jz^Q1aE
z$g`Vz(77=>qN7loIwM$?B^5=-;C5!}9{)6|WtSf95lP0zjgi7ynY%9zLG&*Vdt^@B
z%nX$>ogCRUGB=g^rWW5jnT_JnFwAI7LO`${?Fv^vDVDeR^t*WSUwj+RQ6sOQs*S%y
z&GscK%@}sxM*zki%RoM}*TTyhCA}IQZ|zI<v&HzTlWMqqpHM$ikfAb2uuhiI9y#_V
zUhzxtj|%xvNT-Kd;JD0-!PwR?Jar|Bt_5&EHY=|F$W70X5o-hV5fXIwdrFZkT$kHU
zg`XhV6~dCScW7oVKIzVh4s`drsf)?&ubI?iaVn+$7@KXsm?&*;s&M7wm_4JG<fzwu
z^32QwH$gx`g@|N<N;2mva7a$m!L#`k9@Fbgb2W+kCa7R(Q{%jkYqCt-u~4X)x4&N=
z;U=_H2boG#vGny*@99kL=f}iWuVO{kJqxdR@q|Bhe8u8BA3a~_Bz2~>cr)^JR}rRG
zeUw=b{YsThp}SDsCPXBjA?A$k&N%-?OI-^$&&ioMCORFmK=yQyUgmcNo$79fp%CIv
zvbup-%`O{mi}4n{MZspOYZBDPA)izW984z?Q}^zE`3U7YKl3WOG$|J50Ab-Fe`=aP
zQhVdglABYem58udx`Z-pJlt=4OdnGc$582!;OxZ2>#D#<tvD;8qaS9sbvFnb8C`re
zAz)@X@foPua8UucKz!dzM7J1gt^F$e#IvXYC++z(9UTpB89%y2wVJW)j6^OO!@12w
zSW!J1k&aRF>^V+(S@yX$AK`-8TO^JxDyhAq7jc@tF6HiKPeN^}Q&cB|P8-p9VY3)k
zq9>!Y&*Nj-0o*H)?|~xO_#CU1YDztoK|<J;AFHh<EaE9ghrPsD#eEU`fmJkljc8nS
zOi_yq9T$4R2wOTBV@urrLR~jIIpOB~@r!LU63~)yOyk9_MJk{T-*~4gweOE>=E+e5
z^w1K=gn&&yR8TWopDj4|l`3NZr{ZM|c({?)d1HQ<s;-TX_?92KnqVxn=hqlzu|3LS
zcP*Va(Xcg<jiE@4`^qQ2VMB{pPP=cf?A$l{^oknV7x0Rykqe*8%Cdxi%qC5iT>`^*
zJ73X*Z>i+EC6a0;7llQ|@fnk59D4wMkzO2EwUQQ(vP^x04sV%CVyS;A=U<yHWg{6M
zZT;cdaRGg%Yi)D$<h87CpPG%-1jV|Q2f(zPjUTy2*_^ZtN4<fJI?xYB86Q7s5j(|W
zXyZbC;uy<`D09BMg)+Bihy0Ub^Th|`@E=Ccjz3C0EBbjEko0X1%!|GhF)9bDonA-^
z%igmfJUJD89XlIa*tt!V!Ot&+%p>8qjqg;S%)=Ej1ZCB2KdD78<Nekb@!*RWH)tNa
z@2*RN#LIbpkP-F(RAy(7wfqSXpJjtRSee)`fzD25r)6KSjw`BKONox#raV|ntm{tj
z(Gr2cfX!p-nPZB|1t5moqa38@CxA=j$-!T8oru(g{zYG+(^qM`$LUM~mX&2R=JvsF
zgCEF(<eV{sjSn>8A3?Jha6dbgU2h&-)c`<H3S&^@cVwa6JtesvylThQ{m@4c>=u3w
zQX3_9aB}T?4F|3RU|yx@B|zfXhZE^ShrR`Vhl&FT>JXlnX&+AgJv8tM9SQKpc1lFf
z;PAHqRWD!`KxFaepP~0Z<%a;Uc=I&;{hR+1{QZ09aaR9~5?9SbL+|s6I12}vUpdyS
zZE%DtBgPyDI$xQjB_zR*GRQJ)eS^&U{RE1acA<KS_mUeEC3GM3#kZ#Y!!6@9i&3T5
z{XG`E!6j6sC>%8ORUNk~+(u_q?fbwsS^ChEy6^&E)oLlrDu|_7MhXkeGLX6UkAHD3
z67Szr7#GsdB$%%YO!IQBNFMGw`3C3Ib%Ao~Uo)8G8u1%-z4Y!XDUuK1f-Q|n5U`5u
zs2zf9V6tJ_!K`r|<O{<kdk@7=yt}OjR{%!3=OmVf8z9~0yf<Hy`)kIic*+gGbtohU
zih56;jnT?6%mi*bX@j&Hz7{(^S3`8C{+8e}J$!+Bx5sT^%5&2skN7Qv1n4uqBY_d~
z@RF%k7?lHkGD*I{uSJ!pyhLSUw~}Pu#>-^n0?>_$F2795EJmySVX<l<&Fu2wwREHO
zpvj*?{ZB&<$X#Lpgu_SuR`HMZg@e{Ojw%S_t;;yjK#ipv{~ww|g-a&+LkYBjfc&|9
z%lxaO!~nm__2}~JzMvo?xy$gRFX<o<`-h?g$ea4NCjS--rOX*P$Z1rfJo*n}Wbn_2
zr@60fe1LLlb0FP;eRfzAaG+Vp(aj*x_6XRU!JlSz{@5j~{uhoN{wu(C0<FZs=KMpo
ziAeIN{>$QTj{gevuTcML>fi1E*QOpZjDKzF--GJtf&BOM|Nrh%8MW7#mmT%!E~&!-
zkJt|Y29q~x_)mL|M<$7@<2Qh;+`W;9G<7{d>sV93_h&w}A=KPrZzb3xo8>t4W3`vK
zqK5``@`!)utv-S}c6#G8aEsWcLL+)_^%%!p9MJaM{pVcC4V8DZIG90Wt)FSreNo@r
z>yOzTh=y3g0=^y@qWQ`QP(f{b6KJ_Nd2x3!{L2*@AA?xa?fS-^RiIUKc<JuKCz`yQ
zB~FV!%(`V+{o_`@xsDz3kbCpMySwYv!!FID{K+1pz#9S*72ODx>$^Y}lhR6?N{Q28
zSzBJ1;(RGKTuCA8d(w+ti`}KTb)b*=KI@P8&wrB)_k=QH5ttxvfb-6_GT)u845igK
zh&xk5nSr*z;CpEw=f0M3-fL6V`<7{t708mBx5~M@aIDOp!2+nga;~9MKR+RO&2sTu
z+Qu5te|r1t@NQjh0hjn>{sxdGS62lsU@K4v!&mRFinCWbzvz@V>}rHnG8J|JNhURV
zJgEJNPc;<IMklYls#jVo(EHX={gu>frqyi!-u!>^S~*Vpy1}6$2--vNn(Hm#nT*)7
zvQoB)T;J-^Z`o<K*!^g7diAw><T)U#E`56vNM{_(DH$pQaz~ej09oES_rzeT<aiRC
zsd}^ZPD9!wqYi>2&?_BiO&yvev9<*W+HVERsjajJlp{ByL(F7Ro3QFFruQot>oCao
z*I0qQ()tVY?>|2fWAAh%lWiM)FcvCTD9^&^&u!*<Az%|LWYZ&W4xao(tr)Uq8+DOI
zwiooBt$b%$7=C<V+absJuytbQ%XgbIVdfH#OagK|#nLsMD==JgQAx~O2Kw?9bT(RL
z4AHF~?G2hYB(&NWnnkO?4YudU*hF>#=HeUFeL~MeOf3l|U|7Fz%Jw+F^dvKB!<Sin
zFC|4~Mxx7AeT`>7WP40i_-r3~!y={k3-OnxI+NFmdQG~UuNT2@z{^@+K;qgzYUBe6
zo^Ri4(0x1Spl+ZskGNld+FL}s8(!E&!Jml3nVsDmz^A1E!G7iY+lQkllrO45|LoB0
zgq8=-%2K4EF4}k+7JbhoT~53`t_eFVtDOMt3~KT&GMAz|c|{~e0rZxqOGQzdAgK&O
z@-aohfUCygx@{jIFFAS)ZPvlpL)`0pUBE1T{{=51()Qeet50_uV=RePzFW#2J7=x$
z*kUWloZ;%xrFnsf-ePfRFpnHJ?o-8EHwETgA8iIzuq>LrJFG9WXD+qzK91_fcsHDR
zLR%JOZc{CLyPLK$eM2Z}?(`4LEQxVkz`cQqSgrBSa2NbI!z}6J<@8}pkW6#3Q*VB1
zrVwR*UCQ3}lt^=!Kd!z)MmJXcVu#5tfbKoa9h6~zEAk)~drTHVb`G1Jnviag2ysTe
z*s?F9%({x6#S(cmzBY?I%ufi*3%f|DS_gI~y3UALLNM|<(%7XeuP(1JPgUkrrz55}
zet4Y^x9#S^-LGR;8ybA;Rp`5X$}-_~F`b^<GOY4Xm0uY}Sf;&BEwO<_8&2FZ0y2ra
zuF;1PlRVe!*43_eTT>F>C%+Z<f0O5$SaL9LqT3|*4tZJQJ+P`U2rIbSFEN9JE(^N9
zL`u)%x^3326*OoVpY3*3l4j;{Yq-ie$gD|yxIU{#D1=D&!`RNnCu(}jGgeHMK=g8+
zeL%l2XO*d|vQl>OE`Ag~7-IgqZN$w&s3o?prk65n$$K4;17WM&?Qo#ntKtu36%BnP
z#`m(v8C*M4^|YVjPJ4J<Y7U<#6-@~T!yGGPLRH&}0ADnNpf&mH*Any22pf_45Z-k9
z9%-93U$yzPYf>tjk?_W>{cMgm7o8l2toPQpFR6&>#eW>XOIB!QU7CUx8|`BrEEj89
zuqqXFi!ZuHhMb-()pnmnu3T;>hMs6^2Wy|;V64MVM(P)}gy-D-e5$`Wg$n1r2`cqE
z%&!3H%YsM<RCNoXkiZ6%p9xK&iop6-XBZ~FV~|J)zY;w=(1fxjI^tHqBvG-*&Ctr0
zI@$*mX;hZACEzXx{M^n{s?8Q#rD)5DH_=Nmp1{$AH)%3(&j^kK!#ntRkaS*b$_Wjv
z>~DFC-Ocp1ROFtwGJ(zSJwhtVISn*ix0bVJ>`K>u-s_S}9PzDBM~t#&umLL+lG{Hk
z`1s5T1Espe`DC%yM3T~NoW?L{(F!iMhGIF%LMX_oAPnZ1vLEj`0^j{C0O>`Ts&p8)
zDbbIYQp7K?(dC+;6=v>0$!84}zYE)AB{s7%?MHZ6h;PXtMPn=#mQ0MROjzvV4Q#A3
zYBzvaT&3k;BGX*opjuh|xi5AM43<}uFil>alB2uu2`em5;CSa@ODwq-#PZpuKh%8U
zrc&L~@>iwXhDXpD^mVv$ytG`%S+=>)kc`CMz6g2lrm!s`7YF0U-WiWTT}I&y*AMn)
zGVGoDTG?2=1RtFq#8s*8duUrLxb&4dIxW2^flw4>^Qzbf8O!45cdaYSN$%E|sSxNn
zs9^tvyMCP?Ee8IQDV{6sC*%eqZl^vu$73>8@5Yz;x*W)s$=0KLe~Nuw|FCst?4<#-
zKL6fz;~Jty#A~l3KznaaldNip#_hZt%Hig@`72$akn)@Ug7s5EBtYjIIqvzO!&_Y-
zpY!<L6p1nGxq3x;`<|w0t#~0Sg5-cPb1MaN(2NWIwd}9bghLWR@iI>bc2ng;=$;oT
zg6anfNj<s}d50Ka8Ark#0DBccNsXc_ldwLr8BRp_$5}2|!%3gR8oLj4t&yTKPsN2x
z@|QT;g7C%=J-o>C$F7q6f51+Rz3yPCvNf`=nD>gH<ugiCs`FP`I9Da76pu;}AR9$N
zW&5S2Sd#8BkZ?2fg5#tabEuWEN8?%((|(5kp_5ubmm-GlT}UpXprNuQ_#?0^F<~xH
zLT>>!kwMLsngJ1dP>gZ-ANeuFbXwABNG->fV2zVs8C*|O;DCPALB<uZ2^S(hBQEr}
zq$sWTcXG9ktP_C7(Q-u~<wJu*UPEhS2z`akG6iu6_hL{Sk%w*Hp5G!<bU^?HAO1z5
zFofYS!F`TfG`Xbgz}F4wzRC8)2Fp&y5yHVEU$S6v7F5uB%B2fE2|rwqfSmj2AA};t
zu|O5pEkz4&&I_t!9O@&kK(?|c1dgdu@D-Xm$Z%!_ZyUviY*rnlTK?m|2uKK{sFK-q
zu#?+HI;!8ui_0I*hn=c1XYOP3hvk~SxBrs4{ZiyqXH4UFm$JlY>G*|T`0qcW#btxN
z-r7Q>(>=ps#WTnT-UWK^zT~8JqGc1n(HnFhPO^|zZk8hW)Pmn}c#NPbY*VH%@tp2o
z3e+{iAphn^1*MT*af6>ANjD?QE$V8;eUaY7n#8Rbw5$O5j-H=gXb4_vc6?)59>c~D
z+O^AoTzT<7^$aOMdnU&Hdx%}3y=-(|P;R`Xs{;BdPAh&;6jwBH8t@K*+7W&Rkx$+g
zE?7GvBsFK&rrs%O>s8|+ihqs8t$PJeo~r-+OiXZ4)u4OSLZtd>w&h$12m~Uo)l^m1
zw?wPC9fPNL1C@CXey#x(d=lJF=!VwN&4L7s7>uK~Olx9P=a9$`^fI3drI8eW!P*$G
zl$enV*gM5LQXig``@P+aLvT{yY<d9yZgTSZopjyz%EotOh;3I|vzx()QS0pF+U2i>
zLK%k~?gI>&RhSkc<BCwlV;T!3KX_MYR6`?dc*vv|fiOTVpLZPnqd(rP`7_{84+9=(
zlRdS<G*>bsbb6vzhS1W&@=PMbG{UZ`6=LuXGW;(g1d;}J@+!yG^6b<px=Ml6w-EbP
zJk&}XBQ9$9L6ha)Kq>}M;%NI|d?=_&QDq?)#6dt%iOFSU_t^bQpu)7;IR+~e)<rv4
zsQ4(Pr>3#t=H+gV@79t*(BNCgkT0ol2;f{3dJ1x&$~D^A&)zyDJqZ<5NR=MHv7GhY
z^kH%w<8<*(-Sr(J4B?h+)m-t{(;g#4QWBf!nv>$`V`^-Z`Ar+F3<cUP!Tk?lhYZ{P
zh6UR7L*v-aSqH>uIYR4&JH<Keej>Vr=YLN44h_kMQQ`E)iXFcmc*2cE2B5H*n+P+d
z!tNni$c;budn0KXk@ON$b=V^u#IfvIdIvJ;>aI4nEX3qESQg8Fww)bHhCIHcb|0#q
z25C2Y;`*n>!<cX_i9V|b6E?X)o!`ry1{GcsdW{s6KvR56K_ftY-TLlNLWa9co{>fN
z3sY^K8(eYs|78U<!Coo|Fmz}W&61SpnPXn*1=QjJ<&=r9OqxWvK-Y}0wSUs>Jx01q
Y(?7KRaueZ{2xv4&Q%y%T_cA=-KMmzSy#N3J

diff --git a/chapter_hashing/hash_map.assets/hash_table_lookup.png b/chapter_hashing/hash_map.assets/hash_table_lookup.png
new file mode 100644
index 0000000000000000000000000000000000000000..c234da571a6f399d826b971247760a757b493912
GIT binary patch
literal 61522
zcmeFZcRXC%`aeDhAqXNOdPERJ%NR9!5IySXgoNl~^fE|<M2+ZmqL)#l_mYT67<Ke6
z>M(knF?=WY-1E8jocsFy`TOtin%R5yYwf+tQ`WQI&wK6nPqkDiuQ6T&005M#Paf+6
z0L1uH!a-6({6UUQjR1cjfat0y0Ll@}8~7igFN{=eH8lae_;XSKF~JQ0(eEPoe*gjF
zzi$40iy8sb|DEd+-2ZnO{4>Mt0ayN29sn@GAAkQ@;Xl9c`Qu3RiQqp^{6zR?X=1=9
zqCd|G2l1r=L67AF@CP!tC&mx};QH6!AA&@_>rD7|15_W&>-!LF&0Y;)_RhQvGEH)t
zG_3Ngz4!C;%G?rT@)ZR?1;P+&!cgi>P|Q4wS;(7Zaj4r2%T;e#^Z*Me^rN!slQ)Or
z@BMc)>mHcSe&$zCat2+_4}&p&EqrB$Q$r3le%p$Z0d}iW^JfT%?Kn1d$GZ)P*<bmY
z>%$%lASAu>pD*eS!lBL`D|K~sJ-v~9^<)z%%ZQ94MrpqqHKCn?`{`rD3*_9~f4K#J
z^Nn@kA`yZDGKEC;rUQ`6OamD$*VnIKuWX1m4G0-9ATp)KCnhFlW|-;d^7$u|t8LR5
zesT4N{k7^~xm`k07Z6$NG}zxCJ5gn`ytH)V#tjUGI+iq;4wEGTQAX;@M?i_LbQEm<
zDDb<|&h+asfZz(X+<(44sSsQOM!u$tVhj`rDlKfGy1E~`7FZ)60{x@G$o|HH0_Czc
zn{QE7Llr>47$$AhwnkqtUdR;rJXrHH>0h4(2<adcZK~-kP`y8cj8IDl+nrC-5!Kh$
z7K6m4rOk1<{tsH#0H;gckw_%cM1IIsrP}ob4jkR~8KKb2c<<ToAIoIL_4lD-zjlAd
zfNa&AY-AHfOXOH!ZN=aJ{rkJ<=%aaSDuUg!gEdD-N4h0mj3-G47aG|dSS+58BY$!I
z@6RbGpAeb|ZSxb0b5o&pTT{pPHVu}PRIpbSz`MW%fN$5Al>B(y?f??iZ0Dk=dsRW^
z=gd*bKg2+h?l7rz@4pA__wbSG-f{CNehOZhxIGct`MYBD8p!_AYXMGZwZbPTIG%KK
zj~7$h->&wu;I2h$da`IiXmQhxsjN(q?21eZ_ml5`mu4`{?t4DX@AkI5Z*Fio--rlL
zd^+gJ6yi*g5g)(Y!gg9B^#-(=_`_YfU6kZF7MjUkt~q@robvB7peEM%<ak$;$u+G3
z%$Xj#nlAb*z0+xwVml)<(;4N)2^gb|6<Mv;{!+0)=sdU0<(!QOEl%Q3zVi10W4|^b
zJ{p#RZ@-0YjHb9)o{~d9viY^y+ot2mC*}l|x7K~z5yuvG>+rM874Jh|!>%Mp+o>{1
z`pHNCGg`MRgMq(9?DZ1vJ_Qzg+liE@9_Z@BtqikW0s>lk2k8KOT!u7hFP1D`4F4?X
zzkA?fIMS?EV_)q%NAq9G`g`2nz#Uhz3N)BPdGCNA8qZ6-yDJgf4lxQQBOnt3S8MB>
zBroEQ=;&zP?~hwnXSH~rS(?b(>lJBEIG+wwMLzj2%l(%P3jqk2P-&i;3-({MIW<Zh
z=MsDFIr+eE8xd5H1?Sc@<mW4~<ZfG+RU~t1D(w8Qne(5?f)uD8#Qe<^gZT&%FZGE@
zNOfwT2r~6e-2oF+bXk;5(*VRkph;rHj9U68hI=c3|Dhl--1{#ki0{=5-Fl3a)Wyz&
zNi9iQmei&%R!p0`TgV6&^G|~2P0!u0K*iE^SULNeO_DUb9xSo^UFMy%Lh?nF>Vej}
zQkG<}<Sq+jNiMMwmCC+xfvTQO`e0tK&8j2NHYWAg|K55_h`ogDNiDx!f&-T(abLh%
zbC(7GK4q|`t3B-XmS~@Cz-y;!g8z{N>6>5$eWr}GP%@KRd)h<%(X~H=kD!w5WhUQ5
zK*46+<M^IciZ3x$WPk5$z!fJqhZ|fk4OlfdUzmDrGskD=5>KQe+n-jq_1glmzn<Ut
zd;coQQWi#A(i;qRWK8QJ8g(%MeEGag)C66h229mXYxuuC@^86@s&sIRAHhT*hb|T+
z24H~GW?^Gpj;LmQ1&BT5ucBMfBw%WqvNAlXv5#LT4c=C-?lbGJ+Wzjv^FJ+r#Amf+
zY<JIz!%T0j95BHROF9zmscu&5{+n}9P74NpJ#y_iN?o2NbgIlyN~wV$o)EnV`kOL8
z;#**=nF5S)X{=OS=`gV}jp%;}E6tiU<^3Pua3!G2h`13U!9q}(di)+5$d&zfPu_tg
zl<6!@6?wK}Z~~Cxu-Vz61O2_so#0?HcjuyMIsi8OyQoU=XQR-+4n}Zr;gy?x7?p;C
zFnmn|548<4fBfBKsB?nJ{F_aJ6(2+*|JEVu-39<bWe*iKQt>}i%)hKwB^WTlqM|1M
z*USGDr*`{iWd6~af0W=KPw<Z?_-FROhqwPs2mee5|0uyf)4@NU;GgN>pXuPrKT7bA
z68!(K1adV!D3v2>xsGcs=2N>nj(j4;U+K$#j={_y6aE{Ex@)vBKUXw3|Ks(k<H2%m
z`Z>wF1)KhI$~pkSt`)hS450vNO3-lzG04oJ;^j*Sf<5}*$VwdVr=XKs$0ovZS<b^R
z!Rm`~ex;KYowsfWp6#!E{`@&5C1rj6Wozt4fRd8Z#--o*YCm>;DEDeJZ$d19@PZKI
zjh2pO7CE3_`xa=clr*e%y7v4}aQksxM^b#Wsg{UG3(QHxU+p&Yq)J9BDmj?Ybj8(m
zr@<ueq^?f%p!_jDJ>lpGpF7y!e@TE&=1rv`g$FyIg0cl)xf&f!-u?snWu+YyBsj2H
z2pR*II9yg|tI5(Od{U|DxqcJ5SA)lO3aO|PnR*FDF}S{cjgeickD!S^k<3cM<8T7u
zN<6qG_kl2qkmcUZNorC!V93>|@z1A!c`Em;viu`_2{UPhreqD1l24=|tp^aeHFQt1
z5_XcNuxi%eNNki?|G*2COM|0Bw%@UHB)w))x$}g8aN$n&_b|EBEAOCR?D~`bK-_Mx
z5=MmdM|ZBCd=Z*wDv9m*L{1H$k`!i=`_xW&PBdmIywC9m%=?kJkH7OAdb@WGfMspL
z*Sc%?>+v0C!c|K_^B<tgl(#nVPDK9}by#&U3rm_*Nch3CJoK|0RyWs$<f|F3U^uNX
z504z_9#YlGAsd&cf6R{>@}gp?j_blI&r83a_nih9Sm~fQJIhJ((ASnX$_v%rjGF5{
znmsz?(H!rW-TSo|WNBLU`O}0QO+4wHg`0N(UJf6Wt=5UhSX`fS-qMa?!<0OI<3ezd
z%l~<K4js5ny3?O!2x7KOsFnm~bKLgA5f?Y-`81)5hwpeM-_-V&=E0-?3N-&;ngkwN
z4Ln>Q%61C#q>;PxB;>HdSqH&#Y4_~IS+D2>;j~s;Bkq@pv(o(QWI?Lqu}9#Gt{G6d
z7_s7}08bX$Z&Q)<kLnl}=HC;~PnPF{ERC7(P(@O|vmzj_n`%Bj_Bxmw8!M=pJ94nM
zw|90%`de7Ao&Z#KB|6I4gXM|{kG<2cF@_9P9Gi5uQ!99Slv4e>1A272-l}^Z<0E^{
zYIwAl<h~r>k({`pA|T`){Zp7U&h7o_>=xwe+dC05)x_}xy1Bn@{cci;$dg&l?h$is
zJ;oi<JJdONIlc=n#bfa_d{$vC5fihhftW_6MMDW(akI)nlft4JJ1g;~UF}Sc8$1JQ
zI3GD_p6!-TEx38uuJ!bAJ_<yA`vG3FIzQ%{U7@}`Mz~ogrl8!qc_6g0YNu1gSvZgp
z0+e$IG-Ll=XClcTjkj0lz(dIF*Qf#Eq~AC3$g^B1c}hCWzRhh<NOALSK|~k6@RL0c
z^I$@n-GtwEbNy-}9{8*vU1yiGC|1iGCDQedz4zbUQNzQf^;bxPXFujKU!i_?p8z9^
zWkw9jD+qQLs(lH3`1k`gm<{cBaYV&(@9@UCBdByOl=Q~Z=9jeco*zWR9OOV6(suk{
zoc2%N{c9ShgPIg?5d@Oye}jVmEN)#%m~0{_QC(M8@4_>Cj?L7Tvg4f{4QR_R>$c;<
ztLeYY=Z~-8Sh<=3k$6&y#$dwPBTiJ-EY8W?W>#$eK+t~AzGOHOdvW?Ti5p@5sL;bN
z;M;!JN?q2x&mz+c&ld;oYy3Z&Z6_06(DrE7L~1NO>5m(3vXKE|Gcw{NfMPuL15VHX
zJJS=gco(k{W-+6rC2Kb6Y}NfOmwWs5muKY_Dk@4nJzOd4U}~z0%Z;3tw>G&wJgu!x
z*z8S3H7DNLnw8Teo?^X%sPv^b`AXW`r<ntNGTb{ByII)exp_O$hyUHB4mX-l<cDq&
zx*SDW-hvHMFRUXb7e7vYEcAMme;Cn42YhIkl3F+bv+(yR8!mI^m!00NOf5daCIvht
zsLZ^#m?LNE50A{(x%pqCu6S3DeD_0T^-vbEK%H4jz}bGvkPWNR-q23VIUCmqtto5!
zi?M#2oE+CI&x4Q>BHPt48zw_7^P|3UJ6?ogibOX<w^)DEhQh(yb>Sgl8*9J0jv}4n
zSH%w6Xy=W|f@*qG!Q(oQy#9G#>t)o{tcrHGri-rB*9kf8KI34OGypd8|3H1}XN0ZF
zgfw-qEkq^tX_u>vWnlSKdkK~F{)d4+b8hdz!^Nu^Kq^DFfZfGd2Q3Asu2|O7Do7j<
z7wa7W;$Z(G(UUso=J7_-Txu=qmq&l&51Yd4j3JTy^vVy3vHwYeQ8N%;>4<y9JQ>MH
zcx<@HSIx`=dI(RP5MD01_iWC9S>p=-2L_k~Hw3YwlPk(>8Ps;xa_MK&6P1}H$<N0w
z#UZ1J>m9HV_s_Zb8mFfc5GGmAryL!V29pj_bAL8`nwNB(v>CQZYxncmV5geFNkO7^
zV=HuPw4r9KZVW<?`Z<uuRwC_@ed2h_n9P{Gn!Z3o0~rj#z{SB;M_+Gg9|b-Y`_LUv
z-xI4|<Wf3i-Z+ge)y&g)Vw_U_T?=z>PV%_m5`FU?oko_3gp}~w{>pKfdUWC%ua^PZ
zp?wBjUCuSaRX|rbFc>$i<Jdl9Xkn@2wdylD`4E;N@m>NrVt3Y86Hjj<Sjrb@YHqTX
zk*#^?8!@$c<m-3n-IJ_gk#;-%<xg)eUPR)Fk0E^_-5NLDJ?$qE5sZ2kme60L&swFx
z%=;d&!Xk%>ih+WO1FjX+8)hb2c*Q$fJME+_2}9rV;UH}=eK~_zfemRCt0mU)_~<2a
z?b&u!jT?eu|0c3ggd<SdLf67WKdQ~?sJo%w!4+a!t!;qyAEVp^mut_aJO+fY)87HG
z?kma>ckzBwUafSAjaF(3w$4Kpw%Mr8-M~SI+cv!?(p98fo_e=^<h~bV)fre!tCtB(
zjxsSpK0W$b*8bAL-W>t<8$MN~GCLUhx(BunJI_1M_f=mTW5wX+3Nz!%?ruui%@#lH
zH|_%E-s0<kI$?8b*BmnsG%*DmV(_A&T$O1h45;yre`ioTPFl+DC2fShYr1bU1F0Or
z^H_q)cZN4h*UPf};m7)-X78DmV;KY2w!BfVUu$0wOOV56&O#4fzs*Sly>%?-H)5be
zz7pwo^fRftfl?c9bw6D}`?6dPy!%P|^y&+7Xw%_yoa!2{;>YW&H*4w0R}a^BVg~xt
z;^QX{-eH<_m)QXGlFMV=@yQdsnwqIiem@*C&zh{B*<E+Oo1#}^3DeB<bi7spf%1Bi
zDRW;QT+N#Ia)%EfEaLq&&l`MTsa_8`WN^vTP<w98yD48btJTE0-^ePBEDy^D^s8{i
zwC<N)4J@Z$c`z)1H9OcGHx?_hY+OuuZi=70^6>up!_(*F@Q$1oCC1Q3%k=ZJFqP}$
z%;<66=gM~;hcIjaT?N{VThT-bxi1$(y4eiiG5aEBPEQX?Sxw8vton5#dsJ@8?zW>Y
zdm5XpE2;P~mG7Z+C{`IyqcZ6T0uKoGux6vaui?nMImq!qw(^t!=QaA=*{008j7*sJ
zn%*@}sut)#pwoup<=Lutph?ORhrjW~!xdLYS1D*gP4SAtT;3yOkX`q6(^YCN{Y$1u
z*R*7i;HhL$)lY`bG&)DbxVXB{z|08(kx?eG32<K@&DKd)(Ns;%p;n;m+JOb_d`S;-
z0HTIFO1h9~qr#G2m?Fjq&y7yA#)i5DlYTS*L(25VLye6+U{8;S#c3rl@q4Doq{g*L
ziJ&LLof$cG*78}bMANSpvGqA@MU$@eE;q)tTjw6PHznyqkMp#KQa6B}(o3_|JHz>R
zJ=1o3*;acOw1*aC)0-r7`JPVEWC|HjCKe*bi#PoD^B#47sUK)D$9)Var`ftcFU;B4
zVb?=zP1{ee1D`jh|Ml#MN60C@6P6R<FYDe<MEgza>8!_5<we(I9$D|T_sFv43#F6G
z=OfzZDCWL@iSok08Xt=L$m5fn<SHSOr`Oik{GskpT({pmvCK%a;JC<WUte0j<#~KO
z7cBt0OELW1Suy`x&*!&-0!GsI3gbnyYl5Issr~)z%~m_ac*&W<L1gu6`TYR9^HWu>
zcH6ekm-fvr7VblbeG*>o<GuZ$wI)f)f^NHh*bGgH@3H63In~WV?;1)HXfa<Y;`!U=
zX)PE3iw?+*r%>ES?CEFiB0(6ml}Dl6rNtf94DBoKHu4=6KmLm7(S+i*F19w?M|~|4
zbn^;qr(c~E&uX{Yq5bFX`v&6njtUrsb%aj@PJ_D^UJbE4t3D{KhO$+peO8+s-98)I
zj!nvvu{9j(;oprW;+nQ<hZ}4M9?Z+i*tUp{&ds5n-cVNBZ~Lp7s|Hh$E#J^MG!4qW
zSmc)l`8z;W3%m1qNX9q;OexMXRmMH~vhRZG*SrhUwbHF4bt6ZE1-%lNDS{Ih<M?F{
zCTlh?li{+390uNPh{<c)@%)eC<+E}M9(Ka;s<GEppclL2^I$hd9j_MGh}otuQp$(!
zU$RuA%~GnL4lR6cSy5yHoS<$}UQ`#u!I;M=hh#tJb?6nvyx2{th`Hj!tv(5acGYT&
z#r_luT6j)5GMDctVp4*pD!6jMdj8C_oUYEJU2DkK_(1c})P3`Nt`sZM+s4Ubi+*lT
ztfZ{z_Af3i8RMX?!qv_U&o?KDC_M%)8o3TB{ERp!aclG!ZwO`2SkPtkjwJ}5{Jv|n
ztG#XSpn%9B*4QN-GF_6BC@pYJ2#DKs$tQ4+DN^Eh?w9pNNhQvnC>DHsQJ&^iO(Tx?
zy_xjw0d0+)uSYX0c#3B)j~A0=y_d&7N=gAx;H{+L`jRH>Tdjc<{IJ31E+U)IPu*S&
zMYB=`Yvz_u6^|vA8aOU;CkOpNHvqHWp}5nbrE(}E?~dYphZ-}>CawNPwKZ;faU!c(
zD|^FvgQ}6o?P>bc$!V|cUi1ws(^X7OY*}rG1o<ANbG7@9Q+{zxXvqc`#ba90=Nl~#
zTqjeCgwrnfvy+_<;i^Z;qNwZJ%>ooD>-Ae2ljK*kz=eaU46Sp|m;wwuD?as}du^DC
zB9hy=cCto>`kzA)giHXukNA?#cFbcY58l|&jVs|X0^dDvE|off`<LWc_D_0P$3reY
z<h^;Mq&chbNZM@j)zLSxwGKo?CKm?z3AZWm%t4&fH=>;3DDaubU@6u!g5+{?w1WWi
zNE9TN+3bNB!)@ER3ig{8@PRhpSlJyX4e}JabeK%J6?dM+jb~6(Il7v9I70D)CYE5?
z{)I6Nu$>34HowYRZX@A8q6&UfytWXyLQ?Iye<!%(!|$M)Op0mScp)Ax^TN-mpgW%x
zj&jJ_lz`iyhxAn1FV1Cyju1g6DdT(O9c>qtYi}bkYElvlUx#0FLfluc`y7#)?rm(h
z*9=u;X&x<<40L;mPJ%#U7Yos@61kSm%YGk*Pb{(Ru)uNIZci_|tmNiVl8*es>+s^9
z$1e&8#;4Z7D1q;$F6z6sOK))lf~hUP%4}RW?BHRV*Pg1rH9)M7|EhU4`ZXnnHSicY
z<JX(F{H=R3Rc&3_uoYzoQ-dH*wA1Gk(&i^-*3HrwVEL*?%d-ZJBNFo*_Qa1I5C$S>
zbXk_e0!Ye8XC7H+%SAQnA+4wRCF+RhQyACE&}|zT^B;kRqc6lMTXR!4eKy`&tl(W|
z3FLlZxT%yy!WbQj*H5G_(!HXJ?TWcfdYZ|vAnnoto!fZ2m-f({O#0>^N^kpTt^n$R
zE}#^m-BLFat}O~IW*sef9&Ni84@~$nwOluo$#Bk7GEm&eApd2Y2LT3oyn6nkGf{o|
zSV1+&QQXI}5m!cbhF{$};jQgiuB~DqdEd`g_Z`b!0yhiyER*1Pu6z7E4G&!+MC*z@
zMzSK{l5dX8-(<P3cReDg44Djc|7jY2`7#b|aT+(1M+iJS@SKNluzKCMSJ?FIt}ozz
zE?d0}PRtA(u36t;X+Is@mo-@RZB)0I!J1YZLZ<Wgf%(2XdLZ8hzY6@ipkd-`u|04*
zPmGq)T1|13qQOOVSqdY8@+{d%P)#}E@HF?95E!t`-U|n5l&_*(o_T&XSo%6iTgNcc
zn52nP$?kFo8vCs_WLAVS7^)F%@+OT1di%z6!57z`_gGcuD^8TGmM)sK?|sQo_t)UN
zKm2ZRuZry2mLntl2pzAPY#*?iqPn7As8=g?EGk!J4!`3Yp*)DpLw|N@W?rwepzLwZ
zsb!&)I(M`tr!dX2EPQ#tQ00SExsiacf|}D|1CSoEJ}}P?bsATKEf-2@nVT~LXZ=p}
z(W&vsR~4cC3+*mGs}u{rL#f@#8eb;`HeDcfumIWF*Ba4S&7v|RdvnI=O)+c3`{BqW
zS)ca{+B*I$kHzNFF%N#2=cQuM!?To|>)DaS3L|fcU{lAwW0Z6F*i;iAn-c7h9-jZ~
zkUGlc;xM#Y88sm1wnXMk`xNh`nzsjSFF0z&BbDH?wW}jdvqKW`hgPH+&XTzGZ+u@s
z#q8ckhw1%c9>h2~WTJ9+Y{gj%S(Hj_3}$}3-F}}LF8%yQW3S#v?t<dhagC(WEir=K
z?2=jAn7Oqz0m}VbPn&=2s;!5oS(E75NiTgj_U*0@ccju*Pal)`fb3DzN*o0tH&W#=
zN2ReHKfzRwoxr11o#(1&m@2r-m!=A%gZgCG@h|>PB+-d4lw%C!PPxY~igBRgTcWkR
z{toZVP1me$u$lR^_ZP5Cn%82fu3EU&jg+*0Kg>udJSZ@;Pbt4zFi^(-l}i#P4^ln3
z>X2gmcG4k6uh+{y_Wg@9mf2hS(fzFJmoqk${^<-$8#H|}D1rX=CUiw~V@bAhi`|Lz
zGDLglE5d@R$?H?r`H$-Rg*FW~fp<MnwPeBDzSGk&K5kGLte+KC%7i$I8^3$`?HTO6
z+aB0gMBra?JOSn8(ta0?v{O`+Vi*s6^(z1p?=bB9Dlhj89N3KvHzuf*$%_aHY-+s%
z8KWEqqX*rqJn;<J2XX-BiST?yE+J9B(u<7r%O$;_pprc`Q{&^jt*c2v`pZgE2jU|R
z3|^vL%%w6flWjR|Qwf0E8G!d&Ut_+(XfAYVzY2~8Y2z}Y-`t(RCIwEVWjumt$YT2Q
zvigho&`oSc@qRJzen?4GN%7fvD53}4*KdCQt+U)HC-1mJ%62Z>331D6=Om~O3#tqy
zIT|9>FaewAIx;#2TpKcyU#*hf#1uX8nJOxWX3Nf=$Iqe1Gvh>;$5QJj-9-cvv}+0q
zFVgZE)u!&<<mAmU>?>u9VYCLbCE=io`%{GBN(xdrG<oqo+_+KU%IdIL(ZumxgthPh
zIr6&^W6(6kr)}AHHNBT}jXNL?bV_gGiOlS>O@3(<y1`Jfm5U0=y0tAd*=M01>W=4L
zFN<Q3Xui+L?np~#Y(9hn2#Ho6XH1Y!1#4|Yxv9<9X*V#$5V*l$nwRnNZ$eUODr;Wq
zO)6hfAS8ZD^>~hF^uI{YI7qy{Qi-_<`W1gXXzA4Y=|@T=2O~I0<?J{Lp$<(eek4Os
zX^S^2o&l?Xl@cQhJj`fJKxj3<nnnYz8mmjHrr#vms%yHNo{u@vST>mzLD_O<uvZzE
z)YT?5+{|ZdIku@2@r=Wa4#?U|so?tigVKRKJp!CVg~1!WPSvvy*8;f`K#&;klPTnL
zNB^JWFkD9ehDL^XV2yb7vdd;;qq;L7pyoLE_1Y$6Wlg|~viqi(KqnRl%fuq*Ynry&
zAXAhk>QWc@Sm7KDOOr%;_>A54bQGbKSL3ttaTwU)9WcOD<X}G_^9q!25QmtQ?7={8
zRZ!$4QyB8Xeq47HcYd+f_rxR;LeJ+uX5w&-RhgjDYccUlMHCazP<~^mDYr?Eqe{xI
z)s!l7Snu7aUtN6(T&0z9@UZA!Ee($(uCF#I=a%QJKsM8x?SZAarXW;TsGrRA9Op@2
z^V+ynP@s{v&gM#OOZ6F;T<olyy|r{PdonwNH4uFodDSv4$z*h9&izpTeN3{;YRj`J
z$`MJyuQU1q2PfmWpj%zc3Fy^%rHF94MJK`ef~p>ktU1Y==^Kwy)(@&TEZ5Q_Tpy}D
z_AZ&GnL4kwkI53v7?)5>YVtp=rweyC@}HTZM%08`ByW0Tr8Ec43j~^ab4~<BIk6&v
zr`1}iSC{#`Ny{cg2uTll<N!0=Gz?w$o|=F$-Gyzp`@V@d4Fj9AhAdrE+kH^<^coiH
zW=)MA@zGGwWiP+Bc=B<Ig<(U0(qaTFeRM}^6Hk49?V0XczW4UUw2FnvqZhSP+>}a+
zFsjncKJV<amR`#g!_xcpRgmv`wY-iRr5qsh#fXP5ch^YKm!;S1Px#M2ZFphFs>E<X
z)g_b%<r3aM<-yL-W~|ueow80C9<0!rC=j+{HQC=|bH&76n)um%ytv8zvU17MogS|E
z=|(-GVLLUjU2L@uTzM_Px@Wn7T|creV<v~S3&W6^`N7%!dZf2f3rcO?%g_KP>zOad
zzm{g4@(@YV(ez_?{n#?lWABZF`}lTSlj~q((y;q+sts3A+Yt@tSKS0j&4E0f#U0os
zRLN0#uB9ZB@khb=5>gsj5c=#;W?_UQg=KuA1+nN$M<m;L(5qc>8s*2fp5S$Ts}!DL
z(-TWqn<fXo<?-mV<LsU%rc2EED6J-0K0MADZ=kTip@#ld<EKq|M?FMAyT+Tq#uop|
zj%aCfFNWP`N0SlsT*#2``d=t~S=g8=u0NRmQSVUD3Y=dZ>RT9SlE?fwB4qTG1BA@s
zAz%OaXBR@ZcG(_2-(IXm;EcUJG9jOPJj|T%@kyd;RA$ZdA8Cbkmot4j@jIsB7G`<@
zk*R&D`c@F$SKFg8tD2W!Wd$(2`R<y8#JH3Al&4fZW606ERl4kJtSo#{fwFovtaUcA
z*;3GV7G0~^;)sb>L#bQ}*5PJEhS8-njTN@AG%;jlu{seR=omQ&afaF{cmsH^j}paS
zIIX}?UgFbHrH_tg2PE;R*-zzm+u4#Z2jUJ!CBx1rw3yc|@s?q)qU~R3f^Ql)&_tqN
zta|Ppdo@2Z6HS}4umhw(dcjW&y8Nm%x-{!&NqgO~A!rJ<yP^8X?uY;FR#maiw7QdL
z-X|54D1zV1xmQXL7<Kxh1`<TrCq=vX@^o_ZwUo>Y*CX5{RXm#>`t0Y!Nkn({KKMdx
zg9i$#ySnYW#kAU0A&2Zpn~+Q@Wp`Vk{n4*+q;NiR<-+QuXcgf^BvXn|c=XX_>v}ME
zO!Nq_UZ2mLaO5QK#<J8^dvI6#Wp(v_Yo_O$!$j1Kh&?{nn1+Y!$78;KFN<~7^2q#D
z(zY*$47s?Ko;vtSicOHO(htLb&3KzODr@$r$YlkjebT?f{B3g8476Ra)s|&0;kvKO
z1Yj$k^v?5x8B6~bgAR)5K=#vBLPu?+<z8y5xpVcHCRuG5j~j?#>kAZAY!Ot!;%h)q
zIUFd8ESXf<{@_3`#`3DpcYCY5+JW5Q!!0oZi?`yI$%6G#+~KZM%H*OJpRspoYssc<
z7gLIEgGwBWH9T57Y*GBL&NWhv6M#J4re~rsCx-zr$4A?eK;3arK+^Td-jGbz>@6Rg
zwRoq{Ty~-dab#AbbB?TWtrw?~BjK{13gawWAso!6F?O`lP*Hq32eR0DfF26hA9o9C
zMu}apNIPl88-1+*>X9_*Ze3j+8Q(8j`NaWzqQ4YyQXA`ivsIC9qzvoz-4Oz>7GMxp
z!L3*AU)as!*G<Pp1h#jBgH`YfFYSJ(=vz@&O|fOuHXA-kcWha4QOLloWX>R4x1SAo
zt~U~qp$=zqNV@d^seKJnJJI-^yR3(6^4c#hPY@XMi=iss;lgizDK=;)G3X&7<Jnm+
zzwE`RXAr!1^t6x6W_gR+IJWdM2#@%)&!XWvpJHK>=fiD<qsRW^T~tyV1$KQ5^eq0x
zwKg^B+b>YtIZw7POV>|u2RleTjoL!LsPHK-r+Vq;9kq$+KvOAG(Tqr^foUsDcr1!p
zPHU}&MfwSMJM<y%J%J|zZnxky_Hkq3jz(ga4k}x;fpCOpROi^VI!!XVKy={dtZ8d~
zkAF$v7$_^vH@ndWzzR#A${pp`1JW@~r<Vur`vkaK6{_5qD%axtmREw^vriih90v~D
zrJPBc*Jn&v508vAE4v)92_v50R^GXQY3lh#OO}&A$B+zGoz9}?kA2Mxs=3`%6pJqU
zhd=B{U!&NnJT@BrFz_gFvF3O*U{F8xDBql3MP$9T5!qOfT`-`Af&B(4rtMyQ$7gjE
ze<$8TPo1W~R#0@nym5>@mI`@VwM@Sz==ETOqu81#*=fwx)zyF3j%o@Zp04xx+$?g~
z&LY0u9ko~PFL+|$H18EKn{)1%xOaSZBHehVVoO<j;}XA$jgDq5EKpi5&S={4c0u1T
zeSVmdVmwKnnO$LgGY$vy+?<<c!8!Dq&c2>DP06FyZ<V7fD9JX`>_iYm90hPF>iac~
zKIA3rjT-P<+5IUxh`bxUn=m^$-O_TA*Gl&E0M1mh^o`E`!F_&EEd7{<r$0iQ_o;%p
z?vad{MM*UpQYZUbvli@;6`_`#DLpqGQ`D)_ItW|>Cde;_Od&HRK${;WKb2&kT5THy
zDj#at#+Q8+o=Z>7E$3T}>BpxwL0=`*nJhLgvRLKO4Fb4Q9<yAPvQ3(?TaRgeMn%QQ
zfo;qrRQl!&svt)R$O7OQX835;CWl-^PfxO(dE*tRXESC>;ZfH5xSbvjkBjYCP%e&5
zjbVP3b01ZrWlmh=j|oRc<X<9U+Xo_W(xozRe>>gFgsqA>S;1yF{B5iF=jZ#ndcB!+
zQcliqWKkqXeB)!`_)S_qns~I)Q6&^Zk=k)lLR9e97&NH(ad>$oyp)%9Znv2p>Z5%o
zD#bYFS}$XkA)&3kV`h9<UZ74nu-)YDT9WoI6I<2x3uFf<Rr32-sSSA4f{}Inz7mD#
znR{u;6|F5Il^*}W8CuG>Uqf{Ha+GgY%HiP_d`b!!SfHBj4I<t_p$W<*B0d}~7~^Vi
zgE>@upAE2iexZo(DZb{5o?PuL?~GoJmjPXn8qsIxt5vl>ir;BT!#v|F$=I)tnSq{H
zeQSQGIml*q+PQWt3pX{@<I0;8M#Yr()n3&+Q#>snl(y|N(jzb@eyZRJ%u++WZ(9{E
z^s8ILk?(+OgrschNN&KLOASORaW6<3hN)I;JbMC;6&MN%wJcMrpTvbtT1E>U9%dD0
z4kfP!Sx<7;n&bUOeA@L0m+aBTR=*#-#U*lqvI(9iZ|hc2zKGRDX+}lU7gJ{zPp$+-
zl+@v*rC-nN`LDKCh`0KzBp5LL6n!av-+V+TKC}E`3VB+1Ije!`EVGBV9Mq1Rn6k4B
z4#cm)>-!t}Yp^`SsH$97@nSqog*}=aP5#n~_xl2(Q*qKre-9PZ3}R@18@iFZIWJ{n
zKld>HnO;Y@*2zibRCE~kP=%g{O1Bp+z|qMo^PXLr7HW(LTMTx+Zn_4=&rT<ajwnSu
z7o~+u4zN|rp%7S3nlPG_ArmBNt5M@OZ1K|N^H4FXhX?0~oZgDvPlJZ60|^-}!vU?q
z<pgNm#WT~1zEZftO{t*AoB>&1oQ|bm1q_!#=IvCz3_n3spo3Ns#B8I(Om^+uybgVi
zSQzMwlqo!PLbbjxaDKmdrv{>7ZF@}E>*&KS736aigwXymPU&B_&y^kCoU+zjgxzaz
z+1DHym{e~6VH3vVRi5v~kJqrP9Qj%rI#Gp&Kd|(H-&6JMrEiYTy(oF+Dsm;JBu-pr
zFUHs#^J^x+y4oe%1EGJKU8kw!ExC<kn{Ir$ycaz!slw!rpa{Yo8+)f@^&&Lq+t;DM
zv(=$m+lfki4sw)D_f-Nq>~{)663B-Mbn3BbIvSGDBiQUo4(tjowryiYVzI65;|oRz
zrzW=3=#S$^R;+JL{hn4|WT?~4$TV$(FIdJw*AjZ`sw&oMCDqBbB~SJAk2ZETXnw`O
z!>hAil&xCV=1hlqRAZ-d21ZIimyNiA4Vr#QBT1cp%^j|4#t%n*O!2H;CwH`mpn;;?
zQmjAnz07fETMO0LtUa<|kYQ3IM80#n_@FRgUy2*+Z<L7&W1p?i(-(_%5^s~Y8Q-uD
zDPNl0EIxP}rtfy_wSmtP;c>0HF#IOU4o5t!Wg&HUbS<L8wf@o;Vozm$ZP{8XEleR`
zgGa4`)hEAR!SJS+2a08}0u|vp0+a1J0=kUDE(7`-pRG1m2)31#mj7}Z*(gXlD5f0&
z(n4st@13Mbh}xbfqfZfHFf1ym&Nlv;lFq;vm6Ha{hk=^hkH<!|xTT$!_AN72Ps=Q9
zU&2`-B`jYgETc1GoqT`clX&)znWZt`ALx#hqoMjyo6I4q?2`lak8<ij(mmhjE=n>O
z2^_tV<*YDe?BQJD=xU>gYjJC0IXWQIMC<0M1WHKXUjFQAN8Q7M_ZsonNT4-~;p6n?
zvQm(kCXsZCOieWRyv%VDlyllZLm|&Lk5j3oY3vgpDK{eN?3Zx-64C|?B8<;sa$;-E
z)!K+?vyeQ@VJV#`cij0|R3r!vhe*wH{Dz+N78kT*7rX<uhib14yJSFZ3<K&IxBJ6x
zRwrgi?(Z)qduD#`QM-DA&oVSS9?vpv_0OQoJEIfMHd?jQu{;6$;l2;Q>v;fR{Q#*Y
zW~zbbdOcS%cO6K#_iWI5`n!0*q+3Yi_~a(C=P8FuQFHhPdk*6!(-xAWg0*OJr_{L}
z(Ik)i;W-w8U$6P7Sk;vKCMPC#fBpJcMFkb8v8H~xxqi7i&wAj3iSjL+8-0F{lv&#I
za0iO5zwpNgIM})7@AWJFvZf0XiARY+XQy`leevlD*oqw-cs6fpdAKtx^`bWBm8I7?
z3~mA=@y}fpw3H2?GTeq*k5CPWc!DhZ`b>5=P?rMdpbh6p*}2^yf76?FXV<1jug}bk
z>5e?zo<CkM4TD}Q?0NCTK$9&ZBs21SB*NmR5Ik;Me}t!27HhZejOa-YDy~=R>|>+Q
zmBxtk3z$21HOWzb3Mx&542X$sjHz9|gV(3QFUxWqyKOFBRSfVp*(l8FV)|CAlTs<(
zdI&u-fa4_r-EM#?<!Nf93wh<B)sF1_cXX6FJmK^n>i&@=ieprXtOut96y19HlqB};
zGU*roqtndh)+4y{O_o_x64+TMn<0!&k)4G?TTdDk9M<&w<)7~YaC{6;`{rQ&aksb<
z^10n^_D<l6B>ZMXVRgpbFnQaE@LiLBFh*EQ%~eU5EoAY&)kW*m9%=)N9cO3fRrB{r
zNl9a4hOKKWD?@~jn5ocDiXqP&o>{nCOm39dG2;AT(mejiQG*=|H}Luu<M+mXgK?KH
zs~9a%*@;w?28T=-C}rf0tf}LJBhHE`ruPPR(WHTE=X~Z<Vciy?*&i9FzqLzO_iUF)
z6xADQUY;|W799taU7XWXHcL3P4k-p=OTApb{30>Z$*#B{d|nxe@ucZ2UzvQoTd30R
zWhSeJ0fkj7Sk`{?H{>~uI6_r31XML8&;}gBt>4I&c8)(Ig_Ib~v_G3^m%&M+NH+M!
z+pYWL0U_CR_*}n9P~BX3$NbEp*yi1Q^>K`PwE9p-S77NNtlP5XC~{3ew5G1MCbo&0
z1*Dt|1=0eMg7va5K6u|D^t1X1#2_;}*er2pGHfi5KJZul$vXT^pt+7mm9CPg?vUki
zKc|>8>PvOFqSd!Qr=<does}}Yr&Y4NzVzBaY#`9m!A$wrj;Q~;|Kp?xjpCh}V&Iht
z8A1+iE3f06i4-#9_wh$!(5=w8tAnx9ta_72{If}(FB-O>rP_wF1W#~J6w*TMo&-pj
zQP^wq62ZdPI<}2yLrC#mj2R^Q>B7G7jDV7|OqL2fsAv#beiz_%<|el(aR09yt2=~O
za_(BOO%VTmM=}Oa#Y4xxqxcKk2|yTk2M=(Psl)~TH!%s%5nR^`1~h2j{R@!@-@C`J
z@frPl%u2@u|K<_?dspx$Z9K(H=Kb$*n?vUgpK#DUwAT)nS@Ov`=b=UOv&MV>Vs|Ay
zC*WiGeeFu=!mjD<yHDQ1sbnkK94MYxDm+lRqwzbx@!A%MZ(>K~t?yB55y3yNQtNul
z<4JUS`SO1-_H-EuiEiPgF2urjH(2f-`GX(EWwT7uk{?fm`>=TS+QQ$tgEKeq97Oex
z?$mO3a;`k2-A9^l@2|X@Dkj*8x_@iM%Z!F}g}7Kx(Bn6WQQ!VUlX^s9a~5Lw2}iKp
zeSCwm*Q*5Z{r((m-}dg8G=<;%zj$_^_|UUa<xd-Q-+4!4^nmsEXLt)`Jx^X*fbW~}
ze9e`^mEO9EyTTzw_~!TG<6Xl|JX7|IiCjNDIb@syW$u>0uR#5lPf6b4_Uzri@b1)>
z@w?X*@Ups2^8vr}_|8Y-(H-yS-#U(0?Y5!onXt@4(meFXB|PyGVeoIB;MzD3eo22j
zMeeY}(1sr`cdJm+^>I@#g}J(YF+Nmm><9BPm(A6+m~?%JA)KJ+s5R^l%I5#|HUYmC
z`#)Si>NCP?gs$q}=e_ndw;c?=?0t_3r8{vDyUKG|yLK%vsVnhHR=JQQdB|unjUVH{
zASDl88UAaOyNE~M4K;>mUk{rREU<LCtn0npTd~|6kN9#In1^QN`tNc6T{98w0_#FZ
zW7Vzy;+Oqa0U=tvm~F2{ZQlKZn)j!1QD_7Me5_nb-~M^w53-w3AAaE-K1q<<^fwhJ
zqP3zf{p0yj;vpQAg)mv)C(VJUX66%KP~(%N3+rXbY;Py-vL-Yk=k&QVJ|nmBra50H
zHzot_-*#SEcjGLNjE5ypVuU2|ruMim`+s<;B=|`6k&xJ!0w9Fuo|VG98;QN*JNRsk
zzod_F<r#~Um`Es=DNNH+Nm5)`D65=J<=-O1b0I^X;+v~DWMhu!LIx1jV%i2L)fno`
zqh0L#OQj)Dg{@T8Jw!BDrgO@KM-?xBF^G%Va(2oQH=73RKN2!3YZLUS%a=NFc{*aj
zj%@VUA1rGenRUMQ4bRKWjQF<}zri@GE|NxF32{4*U?hv#;=n6%p4@4!rSNL<cwUx_
zx9@0?H1JyKW@tg=NK8^JE6BkNqOK}mmnl0zMtk0Tn`j!=HATN|<6|**cbnp379$^3
z*qE}ERH*gjkDd(d2H1V3yK>hwSibTuo{Hg(C;fbsOPPjhnoq0ni8AM3j$U_itnlcW
z(aG)8m6D|(V=tm@FlBn!PHbQ@kz?un6OzYGRjg9Pm**3qL+aw2Hr$uJcyr~Zr&33T
zzCc!v3o^o;`gRrG5IK$qtCvad42B0Y?3cu9ys2#9^8CmHS~-+3ZPA?0_tLq2!$qfv
z|2{?S(R`><b<_`=5wGIQh&RGLX5Zc3b|os1RK^<iF)D`@9uw-ayG2}IP^7V<qn9Rf
zdaHzQ^`Cs{-;xx%mkEpBIeWkCNmMzklUyMppIWo(Xn#ueChXO<RvM%1x6b7h2Le73
zqs*h%hX)x$_C)OBOtW|?|4sN!_$GyaJ%a$=vo^7F{?<+ba(z!RLTtkHbO6lhjqrvc
z$F9{Vf67DuT$D3Z=tWqH%A))`PKw3N*2W`ISqcM|v8?@#=<@or4<xtN`^)OjLewEI
zHr!;D%;i5(UunVn?5(%CaxD1Z8A6yX<`ec=-Lsdh%qE~622wdt<nekrPFd9n{Q5(M
zl_!fm>&69Kantq259UXI=-cf_1oLc0Z|XVKl<}`B2#f0&l*u`E*VlJe8_(>xr3n$4
z*9w!M`R%7eKmUwVi6|U6qyGKtRKM6VJ|hRWv<Za#@;z?+iD$Eh+#wFzs@MN;#KD9&
zU!jM@B_mwsjYJKQzUTc6sW)A=L3u8!Y3{p!_24ud_^}ZV|Hy)$!{6O#5OHw|?0Vd+
zuI3n%c~2NX@Z@UnEi1Z5L<<y7G<if2lr#S$JcNv&O3m<=9|{9($>4)c@Fz+BUPDA`
z9Z>ZU+|j$PaZ=B`&qPp|4U8TLCeDaL90rp!FY-xJW^T|Ry3ia#UBo#mrx(>&)|=wc
zg7U?s?$C+7_ZX&m6s@Jn^fVRHFdehT&8f{SCGb7a-o+V*n=>cw<pGWWxnsz^%I=VJ
zGZ6}0%P@fNOr*T(=l26ob$?WG()rNjzy7!RDUKcAJBA+NoZ}@Gra3&aL$Iy8ANqa(
zx-{TFT~B|!bFs=7B&2?c&BD^JYM}WG2hMlO16PWrrTR3K5SK?;*x{w6z<r_j!Q5Ar
zW6QNN6Tmv~6P;WY{~Wb1tvB#BUin*%G{0-42^aqCm9uZwI+@*~3dRIEAc_y7VVAgy
zgLvI*db$<qlC6zp&HyZ~d3GAlVL{s2+0x>!2geyib)*dCP77MrDH<qwek)3&%^O%6
zjan}%+Aeeus6Fv}I9|YI3r228r#vj=((nU&&CLNlnH+dc-jpi~afWlpqI(&n{XEih
zS8sS}k(4WcJ0;UwqIDFsxG&)?Du;l^k=(a4dT{N4N0MC<a{!@-iO-*g$M^82Be2wg
z4KHn1Pv4tr8?+nxcG(RHrBS@CX)j!#$s0}jxqTIph3>cW^&9g{ZHzACzih2QmAJS{
zNK46n)ow-2=a8tam9+VaBK4C*JaBjR9^9eBJ63|<#1%la0SWk1$zsN&9MnAmqK<|0
zA=f57{1NZizK=X*o3C1t9dBEDaNwaglAIOvLqf$~X-ZFTSf<rlGx++13|vTpkl3X^
zbN@X91fGVtJZl2q+~<mBIl&q1FiJZd($}}pi35O!_EpQ5(9VbX?X8YKo6;iY0H(RQ
zu{Ui|t@RX$Gq(E=+PFZ=1v9U&&KEhqwD%HlFG$=T>(xWl*PQQvhdTSoyHC9tS<Cwt
z6I7P7)f0X!4haLYNK2{(_byvsI_}ho@oGDaunA^Crhj!sgAy;B93es=-}!`%oj!z=
zZ`-2ac>Aq8K~}m-H-X%oSB+*L`0f4L+b>X#&w3<$F#=qp<GklwT!xuz+wR}q4ibfQ
zMnrAxA5h9ZYQR3lrOK!?<xwokD$Sb;IYZT&F6y#M_Q`_tJ;2bo#wVk8fUSN#{cxVg
z!_dr}$@q_L4OWvA!Zu!GNEzs1M`xB+UMU%Ea)DiDqlfS=&#y^6k+0f;LG4PljdOm(
zHMRBi-W*y{F}~i=xN?sS=eAK(z}BQ*jX(FPEFtNY8>E{m2A>Fx!h+#=Zoa9ucRkb1
zduJpaUV1>_!}<(y7jCQuK5ED9V8ntNopZGjls&PSKH>OgzMn`+Y_s>g6p#bnL(%7P
z?NQ5K?Z|9rFyuld$t?Mn*avkwghET|*g%o@nzq5L6L}?6sQYpBP{tiB*94ojO%7&#
z+6+dW%$EE#!^a?;v{vi>L;atzM?<bNN<163`%_U{vRMymBQxHY?$Pe>KN!n6O{t=y
z8_+S`Qz;zCn(?LYaQ1!c3I;P5?bJ5*8pohEP}S~qxRQyw;~1{PuT{$~-x1)ur?)(D
zRt8Y~wxr<XC$8TS2ff9?hS6)VG-2)Z>y_okHM!+uBpneLTdmF0&$@%n*uG-Ss`|K{
z_e`8liqJ+|7lY+=Tid`e35Q~ew$AqJ^6VLz#=)(humO|xnd02c{+Fv6$-`7PTs;H~
zFuRSw%R0x%)D654JbsHyV#sEozV1FC3-+-<*4*N(GsN68u)9g7(snq#uxRtvQem6r
ze9jIcy=13}HBjUr?u$Q6#v-R;P*_K2<OWwNhi7)Jr>aST@e7D^qWO4rVNn@7{!KxD
zvLP046`@@&kYSqSl_br&Vmg}W3N&WTu4|&oH~!-rs^Fi9jEhY+n8Z`aie<%}6JDuj
zx*sG|eCq0BSj7E1>zi{mTv8i_bcq&_3=$j5+%MUvyuu=12@8v@cs+L1EaP_w@xTS7
zz%o`ZM>N@@#Y!Yi)cR5Jz}1q=O4WH;&u?{l$W4lw*4-bMnbHyQ-?}%)vmjbir+Zh!
za(ZB!fnfQ#;(Yd2V1?UEN(}k6H>0mHRU43Rmb2w(C&{tyw;XGTl2$EGpYwJ3qlf(&
zLVG^TjrAozcK9CLnxY$oD|!%z6tb{KJj#^#l6oEQwFDfZBxU(bfY_89{>YfCS);rl
z`t%1e2cd@uo|4VCsUGu_O|pU5#OZ^A^+!=Gw5{U&2iB(3-p5Y0Pdm9Yz;P{*h_Exg
z3fGMeYd+xTO9!;IT~>R_tS5`g+OO7%M>h1n$2V(1_wYMzLWoI&iLjL-0fd+5OAtY}
zxt()wOhp#-^YXZ_f3xxz%umqHjHRBvL$1$hIMZAJYJ$eJ(e4;MW9HSTH7DT@HB{)4
zj$ae7(1-8PO4SuTn-oB5ws+ezcnx#aB_@MFmKz{UF&!NLTC`VBPDy71IZaUO3w}Mn
z6mSX#OK!N-nAM-1zO^;=NQ?D%_MY6?+7ty@snzkiwNLsVAAB5Hvi^24d!BDOwVwnP
z#*Qk*DIdK(U|5#=mSE^KIXu^vTdrJ>aL}y>vOSU#!FeVZ+SzHp(_<M;)qB<K!r3ZO
zFBk8Z>NAmN9yG2Lnntb}5lZ(`g8cGJ@348HBl3F%;Iw#{<JFLG{TiJNq~&p-_q^;2
zKk$d~)~<43Z9y*>I2zV+(pQY;%q5&@wLhTHy_->3l=ibtD5$pvp>=H_iKVR3?IL@r
zajIhNM@*a9D>LrGrWMD}=%u$o)3wGp^+aPBedYkZ{dIG->mQdNAFc9~sD;Jrr;orJ
zTerRQRmKdn&JQNZBWdGd;(mjLk!>zmuxOx#jF;#1>P~F3_;f_8Z^ZT9!i&WH&noK2
zLC>d3QJ=Ze4`KZ#l|r@4+#zSz!3xPu_;+$Oea?-vl)?Eu@{jNuPrJmgC)w~}Y#^XY
z+=<XRdD@h@J*3Zz4#%6VHN+IlrYGWP%e%L`3iqSCSnRN{lTKdM)B&9TEMrRC4mjXk
z%W)(xfUXowA4PGlY2=?6fL*Z8shJYe{L5$w@~wOCI|$j#-EsMdwg!IZGTFIPhlM_x
zO8xCB-&yl!Pgo(EuldFP&1%b)wPrLqOVsS6p^4qMnvMqhRED$bPP!wp3$YsM#b+u5
znFhhxhzT~{G-GPmX`{q=fa4n1Ww6;|Rq<T)3r@8n!J5<=_mZheYCGGoHS_IOTSaau
zg89TuS@tG)<F_-L(W4&$ke+WWg^oB=D5f?$)J2Zvj=81~OQR;)0Brq?D-xP08{GFy
zMv1;452byi-%b?$D&LW(0MX>|DJHi`a8^S`&oJk<VwoKZ&NmmAS!haPm}l4Owv+<Y
z2TDl$M1-Y|il=y=1vpRpWrEdaM13Q0bydFKqTjc1xRzw<TRR&x>LK407V%2lgZWX$
zxD}k~DysMNb0klhB#uS5X-S&b`0YI}Zc}J)wo7MR^u+cCJ!rQ8-_7t%I9}k{)KkPW
zoAE(Afg6DNmhTg*K>PL}6;V-3{5uI9gqvMEKbC}H*j#*2)$n<Sky!(6DPvtQ7OX8h
zG%Ee_Lze7$^fda|{@KBYw<jf^{Tx&d^T*#Nt;SIU1l6{ikcQ1IcR0;ukDVzb1Ubv}
zx=u8`GXyk$>OUx)?(?vO?JObeXTe?r3HH3ZZ1v^UCwM-~h=gA5!ugliFEGRbRb@xA
z$4<zF0c{r9&-eIk{H#BtEwI0$d}SpYrYEcJ+9_nDE$F`v+tFpt2{lR52x*t_`flt#
zG3?OJi)Qt9@LRg4DfyO8W&`mY_TzCZD=z=-Pb6zwah>j~<^f%)V%uL#kbMx><jKiS
z4e*WXdYD7)S<07^<_b*>zD<Vry>-bI{5>@R4!Zk(^;y%}25gX-k!J_t?2A_@zVMVN
ze&Q2!d<X%NOlXhKSi6`AH=iLL%WJXlsxhajdvkh1n$8yknc}M%JDqy^NR(i4b74{2
za}7Duq0t8HVWI#DBwh*=Si}~tZTW^A9MtQxdy}Q35W3r@lvxNHZdx`0-)?VlJFEA0
z70xA-^uK@qjhMC$tknv?xsnhc^Ih$Drej3RYSa>-Ws3-E+50%T`Qvr5@%#7fbB+BP
zS&eQh*M))Tw+CXaE}WmeWqI3G9dECFQ>PEAc5GgK@DsL=$XS9pnSuWwdvE;~RrmG{
zlOiA>jUb_vAl)^9A|j2_jdZ7U45)y#gmef<clQj9bT`b<NDeT-&^+7g`&{pR-|zd&
z`v=?{$Na$FYwcBMe$I2PwLD)Zf6#{KGORYiO}B)qsJI({3k~<Jdm+w?fw%*y8A6~}
zzmBJ_2`0B$x;>V9ij#gCiFq-<=82dpY=Q1>M2AnrTkVYq2nrcA7nVHG#g*^b5p5XK
zd5oA1cMQkdx(&Wv<n}Oj)Zus68t9JR=0Oy3h#M?U4}t`_KDvL@R&&6cnn)r#C@z%B
zO^cci%t}jk^&j8IZZbS52M)RHktoZ^6-dD#R}w?u@K@#C*Ow0tXi{#<7CjkFIP+nX
zqdl17$ag=(igv;lKCD`+<>oX<922#kj3GJ{T0h*)Jsze_gVcSBI{cu8l`PI{B(*NU
z7hg1ede~7*R#xZfkvWtxH;(c`?JRTw`6?Swb*_>3#zb!YHuh6gf{(=H9n>q`-0+g8
zC-vRP&T$?F!ea$>+gk9~NKQ2}1A20(>4qFfLYz@bDdke)aF%>#CN@Lgs-58x{pzwK
zCk3KKiH|B@@5z?c)QhBA(rj_K+)f$mkQunL&=L8x`oK&v*=t4WHMUgH$2DP!3Yd{L
za?dO@J*n$cRl9fF3J6=4o-1{FZsKOzVUOb{xbrWg&%;&QUcz(is$B(#TAp;gTCXa)
zj%>TKT>jLignILbW($d=7&Jz5*BUlOD8$1gWF2nhfi10Bf5kCL>@y{dU^bg|v)%=?
zi}EJ?(>G6O&=wW^?04$23?O>((D}N9#R^Z^L3qpdU9f1p16|t1{w_^wsy>Xj%xgL!
z$Eo$^b67x~hN_0o(Rk?nU5Gwh!snvtw#DJ@n3vbMX(u|kiT2gIjkeTO?pxQrG!N(p
zR+hQM#SHR1kJxhV7ie1bVE?n7jLkeDsJw>o6ygQ9za=8EV(I2CXR3Ua*Z<^H^s+{|
zVh5%e&&kT$gVnyMLU(<eSzfR_G?KpmC=lFyJiUGHZiqLoNA1#l`l;+K%m;o$j^fmt
z-`+A9J<_w7ClK|vrJJJ4woRYPsJ$MYv3Y7Do5`JIyz|bffkxai(uQ2Z^-w9WfOMzt
zaNO-I7&pwP97r|khS5PkMocdU+OE_wiY}}37=k^DE`tmD=jGY%A^Xi09u4eiX%D9N
z&-Hq6IWwrG`VDxl4#s2wBd)AMBOzt+4f!y;mUe@V_wJoO!HennyqQBS?bo;Ol@<IQ
z{gXuV$v^KJSs$$66pY;TMn^?6x3Nqs&{Kl6BHS62SOl@tqUSv_W(E)NJcoa&V9J!W
za49cImLX44RKjlCq#)B2g73nfNy!Sv)ze+lcp*NGHX%FnhW7#S;=adi^R3{|t-4ij
z3~h<EgQn$3^KQ7DBB92az}Qb&{O?CwYzqL{=)-e%hd(-fP)pczLqb1lL^PK_E5;UK
z783IL)W><>+`U3}zQwj%`V4?r|22O<l8<$T?w@a2Y(kt(Vlo79>!e})PO+myXz>I0
zn`w^1PwoIBh+|dqG9P@vuM0lzgo9A}+s*U1Ven=o9SD6+ls|3)>3YH%O>5N>j3{ES
zK|eYSU-wWY_e)J&?TIhA!f9toGu=Tzj`uwe19<Y?HdtE@O_=T~!7cn(?v87-;<J5y
zy)el=>g^$(U*v@TrUwz~q$G+oBZj-J!u#~~t!4T>r;PpH@Qkwl^j|=j>yx6xPiy7N
zvszW8^9qql#_<^hL#U_UgH)jqeO}aN;)imSF6r77&E$FV*m|tcv=$qh7FmHrIO@)3
z(T8(+ovOJXn%<F#gyMJ<xi$8F;EOWE`yzF`MeoMaog|Q6C+IoTvE)*`1qWH}rX&3)
zn$a~;vU@IXcIC?6@__96Siju=5)j~LVc&&nwW`OK31!E6Ib1h^1D4-fYl%A7m#|2Q
z*Q#nWGa<4>?cG9d$T$^}e?fx|Duh+X@8Uwd!gs^u!oAK~9hU{msB{|m{d9?_5Pqo|
zU`@arv*o@zEArga*MQ^t3|-vH@(b){I)3oVTk9^1#~*t5Sw(00^x9T7<;upclw(-R
z{p{NnAOtebSOHZ2UyHjGqlLX$><<M?0ZVu9?y;;T@=902=H_d2KC)pbxr{g)M~hWZ
z&~IyDFQ2L4ZZcx@Dyh=T^={UwZ4m6tai8Ahsq$$mInR62NPNOw_f<yt0c5|pF%IG}
z@QD9@;q#7daYlNAn7Eni+s<F%SCfmXbS1VTc8OXU;=VVZ9NsTz@+NbRm34QdhG&Vq
zoz~M7F`G_!VteOrf4yi)Dz$u(ig6Zsfqpkd=L{kT(Un5kQ}KAT;tyZ&)8LKi&RUKU
zl-L@L75?I9VZL6P-B#DXeb^!dy6!i_na0Xko{ySm{c@;3dGMJ?CF|Dp@_68IE0=Ve
z=G4k9)6QnbxzEG(A*m#Rfi1%>r_uB`Nz1w24EH*gNFp@{Q1@>m^@n${t)82zf(Ol%
z`ua{oE*`i~%HZA2pG}CA-F#b!Oq`|()%rVh1ZoTZC~o!{Blb-no6O#MA1hox)wU8E
z&CKbD4+#k0{c;(>c%3EXvY)-<Hl?mjX==-5)F^3JP4|AUmhYDAlS)9f+nmGpb9V+|
zqSwfMw&H~c_y4TxI$3!|(O83>hf(_BllQ<0-KX=k!n_7&Bt>sS>p^7u+so!B`)oeb
zl01M9)drl8fpYAMtHih84@ell8Mzy3dD*hI`a?Y&@@d`SzQyt2dW)#FOtqo%?&CcS
zez4QXJhxrPU{!6pKHzqC<;FFkHbG25Vl19F_n>`u$iNfwYB{EaW@JXd0|@WNa1C<v
zJq%lCy}Rkka<4yTzt57m#9Vx??QuS3g43?Ak}x;S*`IdRw0EesOtDSw0P>!K@%R<y
z^WC6VA|-IsfxXHR;@9DOPk7Kjo9lnWs0a2*=Jyj(j9l~uqRwa~eD#LkSoWYbAns5Q
z+WMp4?+Qg{Z+H%>JZncKcXPgE{wbMxcN>@~$R^v>d}V%=r4*B4;-s1(z@@cZ;D7Rh
z(A)Ze-rtfC-rpf2D|nuK7g8brP0(|XY?>489^yL~zPlenL13^X!7Vy1@a{@O)okUG
zh~U;|GmI_^>#*jqGWltwy1-HN9!5HsbRjD=Q?+XQlr4&!UPMZfSlYx37eLo4*2(+p
zI4h(|q-sJp&#Y`|XcSc3Z{ztvAjSZLedV4S$W7;DqO^aq!xas;6#e4uSi<IIFt~o#
zr{$dsqCVcDc^37f3nyI_v;IlK-1~qv(io|=bh8O#$nm+pmC+OYKB=zCG=6Q$w!R+Q
z-!IkO1Tl=Y1$-NFFK5reLQlwU+5d2gYUZJUy*w`|G{4$2PAF!m#!+c}WnAtuwRzbT
z|6zLHUMML(*&cI+v4Gvd`0!QPP&*!w*lw{vBAiu>myd<*F1I^M#>_G-ufiFrDzTtl
z(C2BXO6XjZ=O{B>*3)6{NwwLOi%gLhBl?0HSZBPebC-ub_(QG5F$=vi;3U9e+!a}y
z2>^6+Y14H+ulzpu&S<?JwV3wpZhf#$raAQUI2@BSr3Hey{Ul#;86-QcVDt17_VA^P
zP+MtTVQsci4Dz^Y*P+%s%f8EWqDQ^f>%&BwdcIw)_rb+lt&*YE7|)K%*P&xlNkOwr
zvk|Ig`y8mh)h?_U;+mAmh$#<5`~m>`r3;ZPYa2y0V}MH}^y3EvRREv;LO*1uwcQp?
zsi$|^nsex_eG7j(l1f8Env06J8kK0X+MbE;(=6rOE_Q#r@zv)Q_h8ofKz6wc^js?g
zI2@YRKilEn>R4kY>vFnYSeQ=Ao)N~AW)u0e2j-CrU95W#2C#%^k(0R;nEaCA*qNWo
znGRvK7WL*Cw|Jke7EP*SJbr6pCWybm_sxs@bX$+RDSbn;o=a}pXg3O`f*s<%;>+Gt
zg)AJe^Lp_`mFZ;P?CC0lb$Fp>Sws3R>f%T6p!;ks-_6F#p&7y1Nc5qxZsTj@nTuNA
z6ik6C8i}(`_T$%muDZXo4-M8J>tbaZK(D8&R$T9%ik~mGH0)}5V?JNK*Y#fSPEJO0
zavIM!bH#NU-ZLJqu@#S>omvTHE5_3&FSrlJEEkITTOav}+mKQxrJ>E)ewQ|B{Cl_#
zijhk63<@c{=wN<H2V3IBh%!1CeL)R+XP7WNv;t3C)B^zI`FS7Gn`WVcw)?)3u)yv*
z>>eRBn7a3C=qm@b{r!8t;^QSLiF<2*lv;yK^}5)%^J5Kk_MgN}7#y?<vL*a(N@>{(
z4g=H`OWrh%S^%0ZIWDHHs-c&Wa=re=ci*9$dT6I4LM*d5m8ae;*>qd6;rg((IZxXY
zdk_8Hhy?NXXgb=n@tvCC=(%?c$+tdrYu%yYmbL=uXGR{;p0}|!HHVHiDN~nE*?u4a
zH$M5#Rah?05A`qhC9#*jz72aJN}w-OOTmTcC3YdFZp1@(53>4})ioBU)tvF3eJbDO
zzOa3xq%y1ezW<M?5#o1dDZ<MAqgVCy$K}7U;U8^9cgdGm(;k9qi6PbaJR>(evK~N|
z5U4#b>g*-I>#yuR(_Pct)ng@ATER-G<;xdN^e+s*O?A!r(P8h$hyEpBqrc?4=Oydv
za8_|$pjDa@n|W53l<8m#Ir$ybnV>OQm_|nlo=v|@T(Mqe6SoC6G4BHgu}es`7}$L$
zTY<jWa(=YA%cdof<aoW;|K6Y8b;Koq+VN&%q-;c#I59K+2c?vwUsql<;YRbB=U!Nx
z+cI=3<2EY`Rx|(P7N#L#Jo;84^)c#xM$!p$t0NIena=Ga)b@y3O3O%=5a*u-=kB=B
z9t6?(v6WtVZT}Vkc4X}3(h|i#I>~!w2P<dS#(7V`BJq-~N3?fhX=92Gf1F=0!0Ttp
zN4R-ofyu(HEJV2Cyz!7H^)jfa$J+(BxH9K9AWAUr`WYfiOeU%JlUqJNn$T)Fxmrne
zrco|$SEhuI+Lvw>MWqh`pf|ho)wvJUId@~8!t9VlsBV+=9OJoKAq#_2b4h+Th?l$I
zHUO5X6moMLWdA<siO-|9&_*(DNov-_lxO9zp9k6047ahK%MbcgkJEb78Y+HzE$O*d
zNOIq_MoW!jlobJnL7v5lftmus@3!W$g^N`(n?A`ePc>u}Umj<J8dNiLR0MXZKDcG~
zZyS)?Ul$HG$Ccv*8r$1VGI0Y@>qkJ!$8VA7*cwW^e3fgL6U;2Xo9(FOVV_W2yUe+&
zO&E4W!LMI;2jWguEydeti)a_B+D3@`rz=EU23H%=Wu$#k`mx5165#NKL?U;|ua-(0
z37uy8(W<5juG-r#vM!1Fi<XUzcn<Qu7}DC&FP|qa3tHW8GuCNe(Y@@vxj3Pz%^9{K
zxs$3H>I$&0$LI8K7&fxC<GoDNZz1t;XU@;F1k$;Mc`qktVH*a!$F+3rG_&4zSM-C5
zL{pvwHgx70f}i4>WIh}x69k^^Ki_r>QKT8g*467a*H4`}{$msM?ON*k`p=WYn!zjg
zl6*RXin3&no8&+E4rMG|X_~Ahsm+;xe9JfE^gPc@KAx4%G~H%^^rtiPdA-z4`_e3}
zK#wn==Z>>~L?nZW;PRBJ<D&9xW__O|c&8yl4X;ibk9{)BGK#+1G)&244*MYk&L{FD
zojg4$*5+&X3JMR^1PzHkZ8y<E4Yl2dFx$bp)y70+KYD>U6N*A9Eh{bn2-Ng~&r4Oo
zFSpj%u1exCuaFgij-umm&L(WBw!;CUM`_AL(hF0fWWl!+m47dWXg~U!F$L-4GPQ%v
zz{<BN#5@r#cE;mph&w{`G90$st&UNqXnLpctFv;45k5Iry|$mgX1CVsoeGlrbt(LU
zHsrIaw?%nnXQp<8Kwt#C1YMrL(O(yqjDIkkDiE+Xf5>_$0R{W&8GJrWk#MPZbYJ~3
z^KLoZ-nRfD;%)DJSL@zK2=Q_*xPO(Bm{@lX<hp{@=ZS;&5UG;FoLuiY=XQVJ_Qv{y
zQROWlajetDY4T~xRM?OBdt}%3jVI^P)2L@t6R>)eQbwkpjT<{!z`iw+)QWw`H&wrn
z>om3(#cgu}fhxbncWtNmE<bpu;8I2YpqpOjhm^SSJOd5Nb;<2LWJd<i%s3q`6*7{@
z{|1r_z<h46VpMZ7Gn0WsNsum+*1aR>QD?zNLE64v(ix+Au&hrgGR=ZpoC5dL%UO9l
zsq3CF`K|ORwlcW|>i9lILJkFa?f7dPya?eLtzC2}SOZ>u2=Lt?;R1b)(=JBaT7<h%
zMvAS|Y_l@RFo(c^1+b*rYXJF|2@+teH4P7d-c2Am1N@`tmLW}0^hzv;Q}Ne=zVipV
zDe<JHtaF*8EJ-!@HCr3Zc|WE!(`2ddFSCtr8=7P4>y4*z_K9%nE7(#sljByGMiLS}
zfw<;|=5>v(v^VouK#U-{j!Jo}Zq|kN>!>*YD}LlHTw6KgvJX>Sb;eVc7CPVb3S5uh
za01>wvw{X(<B-3<uGk9}^+Aidd!QDtc;G<qeTz*~Tts}KcDwWK^1V3P<C<`>P;qe{
zR7rYYG@W1RM*ICJ%)5Q@eS-hosgb-BQ;@VZIz~3?Iql2ym>iw=udwYkdN3|@CEs8Z
zcVl?G!g?hw?ZbM?^egoH_wO(oxEp`Jd5!Nv8!A1`O*Ioah%om6{?1dD-L|C=;)t0i
zgEQd6G*JSFdI6{?C46x7uvXl~lx?JWU@+6a^rK<Zs^9dLag*cwB?Z(1m2wgsFY;hD
zyns{p>!yVFS!>r5PZB@Rl(Dc&-aj%!Hu+(Eu$;#tHorZ-h|iX7uzoc<B4-t7r}TU>
z?8nT{2lcYx@MNRI8`?i2P{rc$@Oo}(cySscoF}Xv*>9P&N1;5EqD)GE$B0^v9cE>H
z1JzH^N%>KeoI>(ln*aGvG{?6Yn%By*w|5s%RBJQu(@!ykv@M>0M7&`J<u^-R(Ok1<
z-1>E55EC~2?Q~{Yqvcr8ulda>?^jOZ&n;Y(ucX{$S@-#_I^?<K#5obK{rY@jtYCeO
zclXT^`B1MY=iL*yur2gOV0;T*>gj;*+XEWcbDCx|vi5$yc>z6Crx{FDq+Ar&6J8l8
zN|wpzL<n18oRt&kr!yKBee@Aun7i0GeD&bwjFp~UEmL?Y!1dN=U5ADJd$Kw*tn;0E
z$B^!I6467+iO_TU)768w9!5@=x|Oayd83kgK96erriEH=IwhLYH#imMc<y55E0_2^
zpOSNV+;m>Ty-qqVB8d4aq&BEvg26f0dkMJDtoAOsA_d$dPJC*J9>LK?BDBgL**EcX
z)3t#sYu7PuCo!Xy%EWM)aGyGxz|rSa?C9)2W*P*XP&n{J1<;DS?srBFR#O|q;3!CA
zOv^~48-V<)>Ke@Nsx2s&z4s>hcRO>AUOhGNxM|Uiy)Kfvb({(eYVAQC9@7|nlnK&_
z8>Y$f+o(?x3-*IF98?Y4nC%+r#35zuSMQs4uF_jRq;zvBY)%br1$D`>VDof+`*qKs
zBwA~g<wgiPZtgqOt@P`{ljp;gcRzpD$8A`55{iQN3Rl<YUpL3TI+5AZ#i6|}={xMP
z6WeNVm=?3O;Zt3(;D)VT4@EZ5ajx>$S|RvR;&|CKLb%{Mmr?PtIZ9f$fx4Kbj8lju
zw*$=X$fF=iv=shUUtQvtEvYYRSMirtq@kbbw=KcF0p~PgYW6pw#S3;7Z@L!h>}BnX
z>pAsvo~mK2))hvrK1o+3COXiYzIFMfhaq@-SEv0A!!Ybz`(p+HM7B!F)d>MFxc_71
z|Aix^)_V2FsFZF<S_>ZUkELI|OF3CE8;wRHFlyoDF{j)YQn%>$x7D5_Cl=k#K5jiH
zUDrgGKhAJM5EsAqQv`9L9Szp~8THu=6-w)rCME?V{xkO}X>~3(s{VUbtyoNI!B}MN
znsaRWHt~>?7%90$?uTlX&&sE{RW7ZsXB?uN&ROSZklCwk9sPzfz7!<w{c*vQf|u04
zocl#2?l&Xd@Qv>RWIX5mSH|R>hPQ&-GZyRQNY<O5CL7$Z*04YXOEfK;GzyQ7h+Cqc
zRNqcrx`|X8rU|u)yD!&UIVC>so2+x1Jg1R^CZSLxI!9V*iDf!}7Oig643UDktNzDT
z^z9EN{5zH|2NP=@rY)Ug93FV=^~bI2Sk=5+aigI?^vvXZJtmGyBTzYVjB!cpo2OoA
zT0AP(q^57_NJ<f_R31!}BX~LyfLsjpO!*c5qfxZdY#R|RDnb!pbGKw111=JJ&fgQk
zo@#x>sc=*<im0|K%&JRxL;n0kH1kGwRA&*J+AZR_b<h{`j5+%t5|?Bh)S$-fg)Fjw
zTX!h++x*~V1IK___{YMHDC40D;(3wY(Guq0z&h?>qmN%tV#b&gc!-31GAQdVwbLj1
zWXyH~@@Dd}wPjade$bk3{lg&DL(j3M`wPY7s=F0BU$80s%WHlgk0tYk<>v&8sjA_&
zvg}B1Y;@LLS|6f!7A(TVL!v}ViSrO`sXJyjyaL_VPqm3DxpeD%pZqpu&h-}AD${F7
zJl@N#v4TKK-y5N@n0sYTxa0foJ!c{}g6a9K|KOH|kdBF@=$h>?+i9)KN32rH5ZH0+
z7Kz)8e_qUYIN>OqJ)0nY)3#9I35KP78XYR)PZTOP-gV#IWm{U&KZOYA=PKz`UX7K`
zx<ELOg!H~*u?$opw=_mIwab~Knq<Lu19RFGLurlPkAnuYz}3!nh;&}>PZg3xBR;pA
zQRsyDNlqTVG=32*6$wS?0m2kpU{&<kb4w1xr8;H(UZ$J&lNpy>X;$>qL}@oxKsFzO
zbi@zf;6EPp3vQ1PD<H&?naYAi7fH33cMB1fK+DGEEQIC@XHQo=E)3Ien2la>i)pf<
zRV1;2i`h*{@uvY+<+R^U)%BpJe&Kew1g2@iv-<(xa`w^#VN#<l<0k628qe;2l+<tO
zsG2#B+Zl20ENj4h&d0aj<##wZ4si|`DEW^LM$TcYPOD&*?r#cjQAE{&K%PSPYnDPm
zhqtax;F20EUO5bsxeowG>4&#&55HQ8zozx;9BJ9~lSin+uUDVqOtJ2r^5Ueo4jw)o
zFL&R|2KjD^pWf!aMJzQ)`MUU1^LtrCOt%!JF-X1#VlgqG<Gz!|7>*9aXq<P~<rHr8
zPZJWIcG4~PMszGDei;3E2)fW#kRJpJ{rB<_(pNv=!zE|+TL1m=KPA+jqhmXV{p4Wz
z=ga@SQX0^RH!7<v>Hlf>KW~Fba9;!}Vp;J1?aF_vKw=F8#yQ+_Z{PNBNB@1B@D7mn
z&tF8y|IZ5FrI9SaO2Tff_L%=OvVSYQ`}qa~Z-wNQt`abP%?~60G!M_Xcl4CkA4^jk
z%Tx&o)!as5P5kakds0f0y6D9aRgwMGQmEkhe;$$+O)Ri~pAgYiz#s=mrCh{R_3!6@
zK6q#k&$A*hkkvHoJXfhssFT{z)k=5&5mwv!Zd2DNbA~180jV0AFjdB16;-FSa`8%h
z>SWU)%uYOD<r}BVLMo_0Vh~pMoRj;5cVbdO9Wb6vz)s+zl;4XD#Ig-Xd!V{JZ5l%-
z?EGfk3ac^z>ldeKo4(6h<12B24|Kozy{`o_S?m67u75!ZSl6g$z!W?J#ryz1kRrX#
zY&<;1Mj6g<2`hiX71j9tZ86;0(z}=L1-_~+sf~B+KuxQJnF9+GLs0KypsOL7egAY7
zjgcpDR1eZQQC=4Lxbor0qL&A?f;#M}kU{KMnX6oEl>b#*#v$NuvrIs<OwvTa>e{BD
zC64k9K)2o%bBv7k<M%z+c-s_L+H^J9aXP%2G-%MzJP5QZix+hA{EUK=dvy0cyC#^V
zFaU!S7I1xFGnrop{M`3u{2KJ`ZRV?)?~%jUUlA0XYeVj5#tEDW()=t(nea$ouYt8a
zl_yoGpCiK;e75B~o<mgk6|<~UOBUqK3^RK<_b(}LE~95zZ|r(6UUL>U`MbZviEd}n
z3VRuEHD46|e^+UKAv3jVV@OI>#MwFtn$>LPQ6Wk)NBxk&zG(>PL@=VxZZ>W!ZFG0K
zWVTed3-$e(jGhw#N9)_a^cuzVn6d*>?*;oR>m*oRZ!0O$T~u6nN{~cf_OpW1$F4+L
zk9X(gC>}@+ma~cda`fb6Xy$zCw8xyT(jjS|%MF-!CUnkrdFp)T%1vC8yPk)Umz0c0
ziB3_R|MKTg(Z}sK5yTg*GB`&SqP4R^3O{eK6l&309yH$kDSHnrcp#D_6e%1Djw<Ri
z`<L+N6dvBJjSF{HzB+69aoU&!97Bz_(mRIK!PWRGeX-X=UlTs%nD;M#Og%@RcH%rQ
zp4A8dik<M+y~P!XlfJ<0)hMTKjAa5D{D(2skXTflH)~b82Kg9`Th|Nt9QXjY>+<M@
zVGSrTe0APHq);~wnU|^j-{LY@8c@Nh6e9&vVt}@YtyLL=e27h$j~>Wb3p%&8>+1Zc
zT;=rRcg4oTP<`bF-|Q&n6}#`$ieu}{YR@oMx#xcn4Lu4_PT%CeMpcY8mHsPnf-K)K
zl*We#RcJtm3la9a6aZtw)(lNBnZ74UD_|l$qh}cpK#llt?--ZRf8~du0>cZVN6=>-
zn$?!<tx`E}E9M5{q%UzV=>9Y2gbXwflRM^;+o6D4frqR?$%+4wRZ~1ce-55j#Ok^d
zKx0F2aixEDqtNWo&mCi>`57MH{l+G^`90M`q^i4=XE=y%s3-U(fAP(~;*4535PCgD
z9ND%_$0uFllpChkF{20^kvp@9GHUv_Xa8A<pallC9PGIlV|C-pM#2B{9Xc)<z}Z|F
zznA}Aw135=8Vw*P>&9dLx5j^|ga4hY|D}@u<&XcB4F4+=|9{Cuz1dz1FLJ<b6nw1H
z<jOp()9S?wFVQM14q=&p@Q)(1j>cN3cTlWZ1gs(8n(wW-fJF{;Tn$b@|4(~F5yVTo
zJr6vUMX~#&sb|e={jH*@#BlR!Ra~j~`4`Pj%_T!2WsKo4zy}aLOLX`lO-`bArS-93
zj_Gev!M6;*O@=z>zS`|iv_1ta>oCA2NTX^jh?iC-HhDwxfLYL8(<t&Eg{VOvbhQ0e
z-TCY+k~2=4pAp!=XF2mxNE?8FOxiBW^bhv{7wNC<G$w#`GdU@c4vN6CO$OQx5ua6z
zm&V2w!75@fDEUXT2i;)ZU?yZm`2uFx8lXgbp6I^DAbCgpa4$eT#St)s|9&Vn1dUpx
z)$^x~%C;_0P7g59%kyBTdQ4+)up-Zw-uwhb{nN3HXMqn!YWnQ|4k-BHi$MHwmn<x%
z@610Dx`|<;|LIaUR&x0C!=>&aPzILm7obx@SK}psvrg>XKK`i`6#t(OvHm0$k)lBX
z-|+_K0h#mHfcYLDcsD9qmCW{!U!|<n4wX}Wv@|LIQwV6vE|<Oy4_AN~eHf~YwJ-@(
z1eOvP>!w5lgDC>|FAXrioI<(?fSKh%FIdD!x>Wqr(tipH0zQhi8)8oApN0O%><ntf
zGI)?q86^%3SOS<B@AhO)bli>SKWlWk*th<h+a*8**o#}^s`Vc*G+#?o{$byFnD*?S
zE<Qf0h-(M}@E>EK#1%;m00sR|pG-gzcwss3Af)%7_4=>3yNZB&XKb4I|M3(p<)zV=
zI9i6^{!jlE7_2`qQG1F*C;xA)H^%Xok}MkLt^aFq|M5%<xr4Nl3|#v=gYot2Y^SR&
z29K0;WFsh6({|tWA+BZ|y@A>4eaK<d+Gta5y-;g|+#24SDk6m{ijFq=obAfd`_~#n
z11|A4B#LeM`(o(f<%TWw4vUGf&L+ieNy+u&j^zgp_V0y%h+6HW<FH5_g>E|?PUWu$
zmSdWMP|D3t<Ke-};-8$BtKEkL-h;4aN_CNQW-)DdS9@O`5ZIcR6z-;2W$wV*eA9#+
zsC6|r3BkKX1xCIHb(tVv*RCY5MEQ6Y(CL^A=rARU{NJ+xd`?$zvJ+$uv&4?+*Np>g
zM)n2wW(f8tIJch(Lob$Y)mbEuuTEjK;%9%xc&$=2wvaXO#*=XzmZ3CpaL<W~!@?)F
zrrRQ)B@Xc*F2m-8HkFqN01t2nHNXSXdXX77rHdCkGi7P(*;|WE^#*^vT2=7XB&n*z
z@sA2W3%EaO*gFGyIqY=UyjPy#2}{v!O~<ZInFabSdA(oLN9Swq=`f$ZGg$!M(}$Zb
z9Ir)i!yH=<!i6jkn(Krmk$aSuZAa(gu(uDgsu$Uwo`hBjtELObcEgSDu1EYmcIN6G
zm82~067-EB!EZ_^%A%JJf3M4BN{d}K`F1W7DM6%C)J6RNRLaEA9glQcD9pE5E>mNB
zqtyWyQPAIC^c8m8o-bCAeYz37U#GwS-8#xvFm>j8g8a=Gb8}iCWkJ0ObleUO@pskM
zofu5yyapaFSDE$Ml{e*gki-0t!%Ii-YZyv_l2c-z8+voH(H{@J=;2Oug>737`&nO+
zDR@{fTMh+w96$c*0#z}5;CTQma#$>YCG)zk`gsuSjk|fpIGCpRg*7B{-X5<Lap~2$
z4s>3klrt`x+E561o*ks~KM0NVf3YS2f>;ix_Vf_Zwb~q|njdG~-{71n5^Al9x^0~v
zE{it_TTweWkAhInD+Q8gMU2rR&#h88<C<)zi|KFw$ob{!E7YRb+s@lAFYc*91uj;L
zhz`cVF~n_e(;Fw{rMxftHaHCHPVf3r^w9O=7kR++3L21Ut&L-%28>n)>Ru+5>ctI@
zCe^qe6#KO(^xtoi&W`9y(np+5Oe>BqAdmtr3Ar5cOg!$pQ~Hig!D0J=mdNy2u<1~I
zNp`U<bua%}H#27!6-;R){f(t$IOVPLb011hz1m3?@n_?+0PnbN4x}@`O!Zz1V|^Y-
zA8@fs<hOz;;!g&eO}9{#NqJ=`oC1dHLG}w&B}q;yBoCKmU&>P?*L>>FyKloequ~>;
zvx%@<@>k#8N)rlzWj6R-W-k&VrmL7}&U$lG*Y1sD{B2<;7W4eKqlImi0anOi0ApbS
zTw1brL3oeRPpni@bU((vXj;XHFKCv(BY=dCw(|wMKV#Xe3Wu%8k-Z9N=FKyi5Tz8p
zO&a(`uQv2*`k(<Wxj&2=ei(3Zw0iO3ZjBPEQ)Sw7+((~PVXnTF`@TwXG@18Hd`=Mf
zBtFaJl&h!c8neaUd7@Q*P-`~I?*6os9_oF8-R1LWv1&GYeJh%A`*<hjS>R=+1o%T^
zItt;T0OgWRka5l<+*F7EInYq)5;D#}?k+UUhL~xW>W)_`q^`ejY~<FdWUv~nLW_^7
z?B0B4h0d3<_C&~DXKwI|^ZC4$Tgj43AMLjZBJf4mv-`{KtZf$t|NW}IkaP?<a(i@J
z_oW)c{#xeEbVY#R$Ih?xH!C<2j`JsE4`Xa?DM#iETRaY?OSIXc?JTOy?83(A<z#P?
zAw-fFEA}ap{#Q(_F=Hj!N)z|qYpo5hSu9s2X~nHx_9yXMbhIKse)LzO6gtg5)6=RT
zYGJdriVBGHZed&WvSVMeIstCvD!$g#vKc^)8fXQ{jevTyX9iY8UtZ2Pg~XZ;t2c_K
zk4m`yY!rOw_AVFq35r{{dczZXO{--PnP+@8k#xS~rs~HSi|+LbyhfTOvR~O1H&dx2
z|E@CdXhM-&R;UsyHkWD`0WftDpK@y$F_GXM{QfQp`CN}jZL+?k0&;}}jtlyJJAb|+
zdb4~Dsqu4PcJ{bTCHSJJbsum$Qo-y-QLgijaAsMji<A2{18kq^HkNedaY%zSGYvHo
z_j82StXZ<Vj4xAi={3Fhv17S|b$8wXtrBZ+_I_gt!N`3Z)x7c<e+_nvg3}|p)mg#!
z*Kp$A4o|UUFq>N!fpB+R5f-UD0(jj2E2NSF4ciyyz5RX>N9v*@H%5}0JX~x0(`x%j
zM#Mwe{K9}cWLCiliEu^pZZX8)ZOOh$nvd7>aOt1w>Gr9U$NgJ1YM)bbze9bN^=AHr
zoVIfr&bHkOxhT*1IovIM7j2ar#gHP)R=ThZ*saH{SUT;ju~SGx(+dvsGxW|6j~nIz
zR6SrBY%&9I1GlPOd>|IJtVxog$K^$zR5W-iUR6@m=k!mbk!L8aM|)^WEa=s>&gYA|
z3V(-<-?8aCr<1CECtqU2--{?v*-^=D+M&N?GUwm3ukx?jJqdqV&Oo9H>HINbRTw$L
zTuY>fs>!<D&km&<AkQA{@7N(DH4Y`Dt#&XuL$q!pt1sU_>N6}#Z|qN&Oq6HQD$^D8
z?cX<7;iDa{?^l}4BbCl3c-qLurz`SUUTMEXgPFr_v>cP3$3(h#?!6rCSuc%K>*<7I
zf)(W!d^^*ZD<MUMcPF)F-ep`#A))l~i#<Ri;OtW3@Ak81DG{pn4W;ly@6Iav<eX~O
z`Dxzd0SD^4u%hoamd}*wQ&ysF$N#MTh+6iH(fpD8kdUEb#2*=lb7*NJ-P)ttau#C;
zH=512DCr6z%xdBdgx3b+mxB-c|B(BkejPhG)>3&oE}mnGJBf%tt8fh15q)jcBlKtw
z=B9(9bKz&|9SLBh4wXCG0pFavLlrg8L>;D#Ue1<h%a_cS-%h)!YH2Ro|22VwIA2Sn
zx5`%fe!zXlAdLQC($87LQrKvqgQSO~8<<P0@xZq%>j9Egc)u9aN~5|z*P>v)S>U@%
z7j5>ABWhpD-sihF2TtIK5hZf#ROP2?xLUx;($&L!ibF2xs6b3Y>8rbwB<O|$FKTr*
zii2$|lfwPg)t-{RtW=%|kE$-urY{QIV691EO%>EdBqia_kf@Yz|Jx7Y3y<(mo_}Ir
zdBMUX-W8|qxUO-zza=Mi^<E<CIHcX4Cg;Pkb-MRf%6#0$igDn~CP#mpmxY_Hs|x6B
z>Srh%1wq}yuSPeMjEx2+d}e5n@-y;RJ(R{wg)|ZFF1v&;spGJ98b(=Oes7q!q_G5#
zh^$9C@2Z9T*1^t%n}g;BdSMAgLiXi)4Ibwc%-o~%JkT1i=>c&gUqQONt2Nmh{IoW)
zPmeIDp53mc>sCDqGYdgD?;iTr+11S#;`ZMjofc*5YzsMzQoBiq#h6!bDHIUV@o}V^
zUZzgtttd>^2LKkK?&G=rf>zzyxwn9OAgGEaXFVi0$Ijh))G0$Ky7BW1q3PJrZ`VFr
zPrtKiZEvebS!7rP>+RkE(OCU>Tg=30Z;qMr;&H;;nT14l<8$Sk^eS!SYqo_*vc8w(
zZci*5?ryKmX1aFB`rdbLWcnU9eZ91xV1UQ1An1L)TV~RBQv8$+n=CiA5kul^-w}oR
zLsm^EYd>gUmD4pcqvow#ramCPv(;la)*)j_qIDzG`LgFe$o2l&wY$x%V6F3-KI!@g
zD_26A0Ix`HWxtBPd<VUfCd7*W`g>(>_aZl!>*Y_A${l7;&U`y@S+U3mmfsn#Z#i%N
z(2l#zCh~vik|rk96z1~_Ee5w7>+5I6+kVvmzN|r)hfV3F-!WZsEJuR3Uw+e3>L`ux
zOAUW$_4$FFv!wQoIe+yIk7#gRN>3Mu&Tk3^R=o8X|9vxg^z<5@aBB3?NADHv`MD`(
zkT~G)>3tze`?c8TmYxUV&dy}*paoA6*ST{d)hyTX+j~jRdztlSUEt&!`a4yg@(*3C
za)=gXn+o-T%;<Fe-Zm=ESuaNfzw>1HUV)`b7R36a2>an$YsHW^vT2^*ibGEX+*952
zQoG(}x){7&F77y)*3(81AUoOEu+^RNSu#V6Uc~Fg_NK#!hA6P8K%f(uJNwLRgwsf~
z)ydbC2ue<!rX0IPk8V0~`^AIvKS>_?-vpEY`b?D;fTz*G0UqT-$Nh!ddbyQ$;bA&x
z>i%3Ic|}tMlXM5qj$A0uFV^>Q{G-oR*{cj0<t|8v2a}IdW$50nOu%z$y#)#8O@A;}
zcsAePU5h4*w7pw0S!2l&jBSJ69(sZ|80kNPSfl6PF{HQI!2D6mp{iaZn**gdklP+G
zg*A?AY;a58fwNx>p$&A{OCw9A&2zU+eTgHLD#5GEdAyUE!t3g+z=_V+jl*xik^Y;F
z(aC9UXu!MQf0B_i)eT;Yq*WE8qDSd;w7U{>fVFossx9n71#@dz1%-y5R6s5jmV!I{
zhJMzT@o6oZ<NE#3?Ng~`ujQIqV2qLAyL3EQj}|A4Qiv4Z;3Z}Dx~LfgQImT=9}(S7
zH&-7O+vCXm)<+LcS2|yNowcNxD#y|)_N~nxNUXre5y4JTV)x(T&+1@(uJkCF+Q@s8
z{Lz&4Nu};Znut#S%Fwe!atx~eRDulm^(f(-THWxcPoKsqhg+q9e1!&5f{!_tS>qc%
z*I;1uWRkUu=<yTx)(l;JV+fQx-$h<~f-iD#4pT*-BfoFzFbTH}<sR1PaE2ZDoG#^g
zN|Cf;iM(-#<$1yngdh)!z}o~B@gT?R*spOAv(6IM!^+9}Wgmmv4aSaSzdKMvRt@4+
zqu9OwQUut`hC^su?UGog0bh^TyWA&_K7-d`?S|lE^OgHy99cWme>KHAx3@=Zzj-b8
zx~7;;MmX-G9+%tr)6w`MisR0)z#iW?m47dvQutzm=wOD?fDAtke7{yx#X~L57U<-4
z*uO|h;qEu+txgu(0E13C(l1!VcqQQeRnGr6-{qqspbx|_o>4gNW)v>Bcy4q4ly9(7
z$Z@Yi@o}&W$LX2MeN^trtu9Zz$>RCb_vg(c_P4wCiEECjP)OYQPs=dvQ^0T#w|+#y
z&KPh~_T5~1G$Qu%6|=Me?AOJ+^<R41d<!|7zhN{KPs)9L55NUe*kkNB-kZbPDzyF!
znYXA%gMo{6<^1d<l0K^^*h~*RX@;Pkg1^ooRo0df6r2&g2`aQdoJhkI$@UtPw8dx}
z4}w0r%@<qDO1db2xa~E4b9r@XCUw7tZsqAX>urw6;JM_ZeSEHxD$I*#vfq3Bn6IS{
zK_Q$b8Dw>Be1D}KnUkJcE|;`btN%PK<@A{tbu(E~fEM98b|C$mBO^;f=6Tm{{!MSL
zhfR@%Zy&LqG35wD>R!AITrY_$j2CcCD2VK*gz(<1aVtL*OU!3gP2yLUX9A(D)CSXE
z7%(DuWH6EPwC;-z4bK9-HSk4@osmfKb__Eu7B?>)@}VX4QF{S}&=d|!96|}_E&`d#
zmv_pB^bReX;(9;rooJyp*>9|S`%rT@w{NM>sIYjr@g!Z|M2r56*>7gO1c`s@Zfx!n
zYBS2bW|3Q!^q>ENI(cAHnvwk)0v9I9Yxub7JXGqm7WiuMExLqVzv&D)jxV1NACMOD
zOQ+BqardPfLu6mC-sdbP%j-x^F6*muBV@SH=~A3ETCo@oT(9cA8O-IdnDITrp*q>-
zFPSK-0)WZs5GWS_kdn|amrNKeZl5`}Cv+VR{?2r{#3YgkB!A(}By-Md)@#Dh<Cg5C
z)aMt6?V6tzaAk86Bf3RpB;|%^L*3n>pmNc@@7;GF_b%yr?rEfSrggvQ>^c3rCOSu9
zviM<{aj1D}=dUb$6xBGan)|CUl2<Qm?<ceFKBZ|nNY)^%WG)}$i}~8K7bv!Hfy7Tm
z94aQ`FS&<&ByBz^AF}f*|F*`EOVSZB<~8-XJ)eiKWYgl=Pr9TLMJ*hCpm&`++nOMt
z4JW=H`xtt@vxKVGzB}$+6Z6#aSiTx4qhDUny$IrGJ6hYPlwl^_Ru*Ib1v`#DcI$Ie
zf?(RvPAaFHT&?@UuZ?u(qfORf>;CoDBRn*n29Nk+Zma`0dwVbGp=i%@*6Bv8ouA?)
zlfHVqmhzN3hSEQoXie*xCHbWE#~qIG<<4$A$S~FS^&bx^LSOjwZx?k)42Dj|#t>ns
zzVZtu8C|YlbR2wQMsP{;@j>|X;5%c9=J!y8hnm<8*qMB;p9^HFL#$__Q?fHF!*;09
zhg4rZZXd$nxkk?DI}vA#jZi;kjp_V4jIXuk%s|bTY#Zu<7|&KtE5hIEyOQ4@tI<}2
z_7C~(%m9gA0rL^!$FiYM{g-Q0vCR084nU3;(*?d6;ha<Mi(zd|w#yg#9BoxhDm|^5
z$-|VerCPEkt82ol+XSe~{^XYyce!oU!Bh$hNZf9#G>>M6m?67>D;?@TYE;#!z;u)Z
zxtmvhUq?tSkpNBxS4D+RF7uqTef5Dyd7LTKc8L8AGYbR)04DmF#2XBfLNfIIsz&h-
z*Pak$hBM)V4!^O6kEE1iD;qam^mmo$QSBRpJgJ!8RwQQ(#l%#NPt4v9>e85bQqXTL
zX_~SqprJ>utTwB$aO^)i;NEn8fVy~HBTZ(eE!6maQOjZUDYD-jgs;uf2p~LwyO`q9
zWwkBY;%7e^<8H4m9L<fuIas*BLr{74O<~iRKCH7H-#s0-s&$%_)M&9iU^k+Es(KvO
zHu`j`Y$Wj;D^gJP=J|$drj#g?$DS}d-bz1`h4>U-UDPR5uhR6(-D=_cTN=CEh^Qi`
z9Q_8zuO4P}IEJW9R4dK_HDcRbvjOH~=Sqs+zh-34L+^LpMHBWIaDV3>*>sz0sj`$j
z&meCX;go|~Or2DKZ|!y?F{r@d8U&X@@UwEy>{ZblzzfH8?9XQYt)WHB7*>SCe`b+n
z7-9_2#;+xUOA(jvCY+e?xzO>AMkyY<_G)ui9*lJ|<zIUYfua(PuD^`%pKd-s9P9Ql
zs<#yEtM}>?zeCJ<-mdmk;Sf9-u*8)7)^Gm>07I^)F$ud~`Rw?hPShL#Aj@mi8B=Av
zMSYtX<lFOel6yF%?LC^4UR&fuH0^Ske<&PsEhA6E{dRp6cHHpi2gqUkvjYA~f#rw}
zijW0sSJLdkBQY!Z7x{gV$<d@!D;>A_O=}b0%GuYOxInDpZvZWXi*@A#Lg$_21BgzZ
z4ocC0{<RG68mpMbDTO7eld3ecAxLqX!iX=DdX?;{dpEJ%O5#lt^afksZseT=Rmb;%
zyxA<yC;KM9S3-K~H~Geg=570JrmLsR{XL^vyu!vSvLMfVFgzV*&$?q-qn-$`L?@fc
zlVmJ<&@DO0BxE$ejfBm{BP$#H_s-kI9lq=IpUi*KD4sWD-ik~UKU`%a>gi-fd^%Y<
zOiQn_;z%E%-m0V|vZ4;D5lEw|U4Q15G}4ho<4uIa<oE(=Ivk!7VVRT2su6$Bk0`R7
zwrh=Q!b+^MG<GE8ifW2`j7-<hkhV_NL}I^=cwzcE$v5~3MLL@)3ob{MA1h~je_NE&
z`mbTykqHaGR(Umj9j*4|2vWhll-NEco6T18^`cx*`qP`X)vlM-mssdSZeP(XEnHuW
z4v`7jX6nMY$?X_A@a8JR;I5}H=qAd<$Fo)7{uNo0XAikrvfKBWX(IE$-j|nFR&8{A
z@VYLp+^cgU8whVnbOs0sVIyVbOs3>FGu_$Mqy!xy8lRBpSVP?|s)~k4gn4)0E>p=k
zgR&~o<nFiCp6#N_EEJoResNbwmiw+Bi|f6SZFco9gp#N(SDGGA4?LADRP-Dg$)<bm
z-h=P$09&F8Y5r(+{Nk^Eu>i6zxWqsFg@~zD(2@rC%3HX;=^H$)0-Fjj3Xln&d^UiD
zg^=4-AgnXnYd)gU9<;p!ZYZ1k%3Hk|iRu!Oe6+bP-(ZiixOIx{p1C?dT8piod$kNe
zVRDXOjTWtge9q)V_W2q!qUX;L6Q0_4!G;feO6V6?bbNmU2rvBjV(J<Bf}i!kmnzHW
zQuJasm5uVIwmF*yvlb|S029s6t};W=iq{>~E(<NTozK`k0|U_8!<Az<;diur4L|SQ
ztVup_76tUb5eU(~2*K!g(lGYhp}fp1F~&0!BoO1bsOs(=g#ALHk4#{t;BOPG#pgAN
zz(SuwJOLYF)c?@UrN$X!k~fsUgY2uY9qDUtSV=cy@0$7N@^!rTKjRq2*SjfR`mVNP
zd<AgMsF!#l#=F@?I$<(P+>d(tU*??b;0rfONr?FK-FNPIEaf|@SWPd~iBb-8>9(<N
zAr@NbF{tF_FG?u4hQbkeTx0uuhYR!-TibgS)<+$FAkX;^uR(o6Ot)EVN4;yZ!fmHZ
z>lLaIEby~F!DUL}xo&TFn82!x2G5<t(!%Mz9Sx(e!vG&M0PmP60zn_A9lE0%lJD(X
zSZfbOQfP;De}_CKc)?MmoXD2iD;v)@7oUq}X~XN{=>oEdVh+mJvC^rH<J33Vr!jN#
z+nSYK40QPc7L920OhVD}?SJ1WuX2*06!xYaSEQkw>>V=4m^a`GUMf*{QfkaT@gCf6
zleo^yxIQEqC5MNTxw*2ez5cU&eL#nO)a_kCD{;Dl>*Vk)u+HK(%S|XvX+Mwcm_m`{
zyJ-Gi+6pt|l}*76TCPeFyZ2jHo%E->M7Al2WSIc9o;+c+vcX@PI=f20n~z?z<kud>
zTIPZ5BI7Yc><9=8dJQGgiQ~EX4O;Ib@o<xRWQjBIOSti}<dQA$$$YoP;VHH-i%@#s
zo?Miiy7`=VwYK3@$%K@Hew~k3FB$AM9`rTo){?(px5`6#<U|yIdyuJ??}0hROb7;5
zkTz3kqx`*9?J+hAUgx|S?x!jEN|F?>qpS6(DY48*voX;3A4LfQqNJ1js7N4C<$}TS
z@DaKb?~UoJPGW(lT_giMZwMJz*2o<=IzGU{NLj0cU$K?)Kl1gueBAOFQzsKZnJXMQ
zjPmYDFPmC9yBe>ChLp2Czm*R`F$z{_Td@J6o~>exZaSD=T-&)j?aYEghR=_OdohK<
z@CkGoLf}3(;2tFz$-%(;s|jNnpEdpXqt9E|ogZsBj<bM!uV1k!93eIhTNvL){+>_v
zvB(j++>rSCqgE726aVCm`v){IG7TO{{-AD%+Qi%&uum~i;XeaJznd6x@K~0i+q|yh
zN4>dWueE!Gm(g}U)=4#vmnNEB^DsDg{p~kOWrxx*hH}BgRc6IR6H>xG{J4Ye#mf`M
znEU>9B2dkENlM$-kgXQqYr<^=Sck)}YmU`>oH(tu!y0i%<A=cUEQ^PKY4KpaLvpSg
zJs*y(iq|>3hRS78*}Y>4xExydRHn`vveBVt-B!i`Zhx0QOFjid+?N#P&#p&S8Ka*H
zeMXTRpKWxxkbml;R=awCpx3Zf_TI_<lP}#^-X2$*kVIs^f>(;O>tyX;Xw8-Z2=0a$
zRT2PP@c`q|PZuBa(#Q%kFBg11sy1p03gAp%3~W-~Sa${CIg+6#{)4MuC!TG&kqA?;
zb7*&0GK&dlS#S*Xw@oJ=jy22NbEVC^U`dmkdI5{2acyouz_OJ?H(<$!uxwwYcm@@|
zLF;(Y;K^3uM(3ajRK4BuouN4NT6lDcitw4q^g+cPvaJQeZST0~zi6(BLjbaF--;7y
zN)njuDc;(_-!p)C^B;9h(nVuaBkm(P6EsU#gWF1}Sa)4ZTRU*IuqmB`qQ^5MW>m?9
z4`Ij=aqfifD$&BFql>RfQ<jw#A!kV0J$q^N$HZl+n7W3l)OlB5&ge@U)5*Y=dcn92
z(!+1Wt(?f(e~mXhTzO0$Gt3RX9GvQ{JBofGgv-(Ac`jpLj3g4-A6mSNbaI=!t|_29
zfR%TZ`(GUZ@XK?g6h!IQni#soFZ~$v0FjMf#Nt)qUJa024}|ziP*HpU=)7n@j6L>C
zO49HC>@7-|AEREN`rW8JbPb3ffK5mJ_38@seKKy|EYtDpI~iGCUOoKi;v^J=>G3-<
zOyfz8hb+28p<;t7qRzNDFzs*Pw>Ta!Ld33nwB$`*G6x>EZ6@kBdXaITzu1@P{`nk@
zFXwOciGhC5*{jax+Y@~}7NdeUzpc{?pM0}2V^i<KWlazK5jGkn4Et8VJnpGb<Pnk3
zAuqDSnr`1Ub*T<MJqr0fXGQNth#*in98R*VJDMfBexMkU8}D7e5zn952tK)e26fsF
zn8zR(c>*#y%~hulgA5R<csrlAw}qTjDFnBPojq^XB-@61pEtbe&#7x1an19Do+BU`
z*Ew171$5I+8jst}CHdUHpm8PLyVVYuZg0R!W}BDH8O>6^s|*cx51T(%fS6m32#nyj
za#5Ah%s%4xPT&l?l1&J)Vs8;n`%=KmTVe%73I|~EDq>;7zqp1ISwr7xQ+bJEf6ThH
zER#eqwd~}ly>8w6V5)$#=kiU3Ql%sQ+Y`}NtmO2{EqZl{RH=eXVWItV+=@46iYz0|
zaNi3_j8~z;d%dREB;7i9`><=u7i!stwax`b{zkg@BOhPu_tXGNsDC3Uszs|pKSG7&
z^wf~Fk9inc`aIg=_2-|u$sLrXI&?w^uY+kI_FVPV>nbOhS49)pjIs9qo4yuxgTwMw
zUyPGpIXx;)8tvY5VdFcpduZox$ohR(J!`t4lOn|P<SS0T%H2Xx=-I&(v-h`uJltt%
zAXk8(&4dQvUIHv<pKjJCgH)IXWZbVRE2){av5kFp@;b1u)U&S0`b?g(aD57D_>mLf
zjs21?Q{!`}n@&=4XH@=GCnY41z~S!Zk|SFJh*JNb_TDP0jxCG(1p)~U!7aGEy9S4i
zySuw3xC9ICt|0`6;O_43?i$=Jd__)w-KWoexi9zOj?oz-54(1;Yt_=Z=KRh7GJ?)h
z9#~u=jc1jrJabtQaO)DpV@etOtz91k;jvbC^!W4cbjLtY4r@<<|0UQ7i9br!p&y1s
z?&%WF2exli^QpH+PP;2DixI3$S8b2z=^~8*>9k?R_W4s-Le!za;f=#fcp8xc#*3LP
z3n?BVM6+0NJ4onoI*{Xhi%y%+O#Q-DqCDv>OvDm|H$sV#*{O<}PQrC~JN^(o`RC}o
zilAgcfp-HVo~RY6F|8fiAOl?u?W>HLX@BTGM%gbrtsTcH<2&;|EbyNbbWU*PKA_5H
zaJx{aE!nks4I78>XVpu7$qPz&a*z>mw3Coa6*xs=;KQ73&gW2P2zEL33%0MdN8epP
z#Dlc2v;o$)i(uztCWqfa?bF>pzwZQoLvBwKZ}aHke(sOncs=(M8F6fMk<b_B`Ff{`
zgO{P14VDQsLKU^cu<T-0iCuUlBpkHD=I|8WgNq^abUlN4H}}Ja2hyJM{(B$3u?jmP
zZ{eF2z=HfQ7pk=wn7`cD`(_Q>-w5F!J2cSVs1>0J9|EuNyqji+Sj(VGsI7lM-n+rz
zeIB+31l+I<zBh(I%do^s2P!3~4UiLMs|$x|i=>WfRvvhLi?F~in}*EZtPwWgqVM>T
zm2&S~U@tfa9^vz-P-OGmc*Wy9{|$gL7`EFg?jk%WRv$;-yL3b#F5k496eq6opWL`Y
z+k{!5M9F%vQu!)eJZ-ti4=_jE`XJUAL~MHtf+69um&EMqE#FBiOhDPTnPqvgOQ=4D
z!c60NVwBGkYr8$#-n3`O#o6g}E{9GeOWo-oL>zY@L97f(>Cnf?Nwrp{7~@V(`v*fI
zAzoh=<wu8*_YsD}(~CYkLRaZb`%b+J<+yV<mJ>n598LYY-k(9+OLhtb&(U06AJFhJ
z)qY0l1wOP~6ri4DJT12AdZ5D{+HC2`&T<(|d?~-b!eyBy-_$u?t$P_iNek(9MI*|S
zYpJ1+*1f4J@f@nPIJ_R?OM%R|@Y(%E5sr1gUOiyNzUVhM$#B#}-eBl<ymVB1FwZnI
zeH*cSyrAJyMN~K@JVoASwq0h7@-9tKPx8^N$k-9J)MJB4T*rPb!+_0Y9({%(O$lRk
zk4>WBXj>ug)e^FH0GJ=TRVa3VP%0n*Pgm%oP!Fm&*+h#tPt@Er$Gsf_0<zrAS6|g&
zeE@$j)dM?;u8`+OAZBF%3c8;FMeI5dUHqvxl-hh{G)2&Ky`xo`Z&GN_Ue%qxXUgv}
zHJ|2)(c8yq=1sy9wX(qp;m~8Q{#m9z4r|l^;c|jxb)nLv_>ug#*+9|A6PMc%llU<Q
zY0GZ3yn2;h6Hjfv_U|#}dc&U3_4Kjg&xX%GC|vDq)QPnohz4SzhjPvMGsk}Q%nnwn
z?}mRI_#Vkkjo+Dzl#_Ho#J|5J&)=|(m1a|p<pe$UKC*ARR`(K-B;%?f8;k)4u9LI7
zP)aj7M4=BJ4GAt1tDaB1n2kC$n7;O%IDBeHH#l`t`{;JC`bkB5%k8Q(4i7tnupvJ6
z?jC47Tp3$7*yJt-TgfNhe)jne-{|Y`RmI8;uX(?Gju;=Sm(=K@J+7=fVx3)!9Y6Rm
z&8HzsXD9X`5bX@l?aAY0y38df)r;BSc&F11-(8~_fnGE;q>MyS)h*Z8I@Fi5ig)*7
zpFUa5@w;F!k1am>>hV278WeBQ=je(bIpo*c2-Mwz3wT{@U~Qxz8xjEG&_`hyt2{e3
z_7Y2~X+e>9)_TtU3UmCIuCYWtt|aHWZ{B9GTmA%&Z1RiDm3ehkf7GA)sa{jv{|Wej
zLMgGHYE=ev^1T@$@Jn}T#A@zD7dH5CnEE`A=bgQEn*u3X$=wI@^&y5fJSPk|s<@xl
zRG!lq%hJ}{K2dE}KvbST;v1Q8Ba%gU#-}Ua7F(~KS*(v-x;lHc8A!`F+4T$M-7lHt
z1__QA_Mnj@{OeL6R_wL?NgSX37o)CuvwjamBINC1y-XYZb5qUQS!KGh<RnETuS3t_
z4w8%)<@V{~=Q&R@rFR&sp65N7FwNaEfkC|Y+i`H1qYap+hT36HC)8wdU2#1?@DZMr
zKzD%(8+#~QB4tphx(_d&aUywZ7vJNTUz)Idv$|~|-N_)ie6t*14HfKk$2$VNA;MCw
zx%CczhWhm{5Jv&vuCLMm@8+K-@kV9>A12Oz8HN%ajlYi?Nr66It6K9V(rJ>@ss<C@
zFZ_PP4aC6EOckxw@xyFKi;9RYCxwrA31NM1a9NFSy`Rr-y^RKPMr{@mj#t0i<&PS?
zJ$s0g+dyb3y|_Bq5U#^z(I1}<gyTde;mRBnsXH0Zli~e9)KPYLZENXjbw4Sj)3hZb
z!*sK&g|^b>G#7@%g+s!KadA(RNE8K=$5$@Rk%-sF{o0}^1=PSGE;>ZSB>@IBar>cO
zxB`<St!+v_lIMq*yyOsd7`#;ocfh^F_|$X7YQNszg~&sTC-*cTM&I~Vfi179M0`Kb
z$ym`<U)OPf4E`w2>OISk!Ss&J;q8P(KqAW_3fzPL`9aB5sEWT<F25CkWB9C_WVrLM
ziVO#4OEsf@@m(~ejFsxV4E{)@(=@atV??KM<f%Kt3u80+Qj9z6q&~qyym+1zx$%?I
zXZl7QldmWqqU~|zRKD#Up1q)a<`2ABYX5b3hkm7dGFxK3II;$V){BInq)v(!p!$8S
z;buxne1zdDPKiFXUy4}IZUA?e7dcorFzBh;e~GsN>M;8H-I3Pq_x&Ero4}tU%q%An
zFc>o|(xM0(T(3l4Tr94*t)a>Jc*RAQFwPS@GlWn^%c)Qjul+4%FCJ&(OS|hQ6b~e<
z_#rPI4P#*(9!qM#X@x*S2Ju19VH&2e#o#h%FSFU>A|SnqI%(kgWU`6jMKPa{_zH0e
zEp&FZ!KNwwU9UUihkUSJoqH7MgYr;LJ@Cud8CDs|4}<o=00!A7u2YYkH~#J{iOO?o
z{7j7+M58L#WD^1`v!c)e=G<D_)0x#FFac0mBb$9bvzr<myk1_G*Qd!skDks^QHfAE
zi0$g+{=78OfvT}&(VBMYbn=FXaPF7b0@5W!D&awNnx_`S_Fq+g0>yQ@2ePAPdC;9K
zw@pTwO;sZWC%<JonpKzr5%UL_fNyYRlB@}KtBc63lI8A^k_N3zT;||qzssrvU+wl<
zFh5fwuQy4bN|*AcPi4J6{T?qsN(j^RM3rlxuFj<Ob6m08QE97=3p!WLwf2wWsz;`1
z`5M>sn(hW{scQhbRZS~u9{<%N1uQFmC&wP^;P{3jRr|Ne@B2^);P#FmW(@zBi+>&m
z0rcO}?6{UcDLQO2V7MzDpWGOv34(91X7j5~wF?hMZ#Mr$t45Fjd2M(CQGfBm)P&_P
z(a*)%=<GuOf>!-3DYAprYi^^D0Z!(>2v@&KAfYY^>U+X#ss2#4e}Sh!fnR}J52OYD
zKL!5VSCs!wr~0p70$P;^@F4u}A^)h!|5w!oi|PuD(=~wG>@>kC|9pKo^9pUIvRUES
zTaOB>mTBJu&~2$!9sS;FdP?<1+spH*KN5eklifjz)m)j^{<q+QqATH#11T(K{J=us
zv^P3}f7kv7DV#tcGqtKIbXV{?MjYQyY$8?^PJTuSnCz_=Ds#w${Q}`I9WC8!yDvn;
z6bwS;-khYsI*iWUQ7Pq(f9A65shjh;_%QGLgsJOl(D4Ndfs=8KXpHv~o)7xQ6Y4NQ
zZtYwfELT^Y430s!IhkB0m6a+*gYQ5Mh>Zg*qV!4*f)zf;4Z524d6du7cY|P$_*ehM
zA<=lFd#WK26$XcyP68X;dt7_rC#kaY+`{$vRUz($#2}CF_xZSH?&e@>FJIu<!q0F&
z5WwMX0erU`pm4?Bd;$nwfMPZsBDwJf96yZkAD9fg>sqf%RZBHZhK!w5OVm3Ss65X)
z-kIGdX0q6=HorW!y?lQn3dU1>P>62^&;`4Oox~Ut@yXq7KL9RldpIl}xbI=`o~SY#
z+b&a_97<w%0SdhgAfK-!Zv2JdZve!F4px%oB2&SqgCtJY`@G_Eyi_N5JYqWv(3481
z4SSh9r_D~wLn3cbAstv!vSVK7ab}8y-z%ryeWi|1=Y2rH^1uMIB-+y~-Qlg7B>HHb
z2GQuf?B^L3HJL2_=gJ}aC4=A(u_k#kX*U3I7Vh!;SJfE(Ife{=rc4`vh`nwh3PUYD
zuJ&W-<k#>-9$#5Wm10$ZofS9)=r1p%vBcMCCghXOr-dB=S{^+a*|n#6Wtu^a0LnsO
zwbEz{3B~IDB?tlc)BR48*^u2rI;Ngyj4IQ0FX^Jk>Sd-F``ehPX|vXlwIzUcYKbTr
z>H1?73%we}&}&MsX|!a%Ua=GE0ELR(nW&DrlSHqRO1lhj=|F9fJ7Jl<0I(wIJ7Ltr
z3g2E2t7o%;ShCMQU$VQ$+l_j|fs-~^T?`4mfa(CYNjEU4<np-Rw}Jk#rD5R*l~zTH
zi#!P}iW1(S=XE{vOV^S6^9ir{cy@ZzU@UfO3(#`;mT!2tmTa4Bz?ln$ajLjn4waob
zGd}iZ037d?S_z%=6!5-Ep$`$_KTtrdPfvRSawb7Cwxtjdt~b9HI`|1F^j`V&agFE4
z+c6D;(cxZuF$Ct9*wRn!zTjQKNMpNwcqhflks%sYrr(_EMJL*gbJ(Ssrdedpmezi=
ztD>ODi{8fW{@!Si;BzkQG>E&zI1$f8D@!tbez+de5cXn`<J^FRWc-++Ym}3}zo89P
z2P*)_x&`d+l_xH=%G>8FjD9v>NG;xv0)a@NZ+za;>U18!Y`YW9oBVwiEO18i;D_Xy
zeeR;^|2ka$M$%>TLgIVh8Bl+GsRojdyKyR3^(!RN$temkuu!)Wq_D#&Uctb&ryYj;
z!M+jQ7Iz}_anrkaLtG&`Ld5%O>je}e268<}=D>;~0~RiTLhX<0>+J>rc<cb}VM+3W
zr<^c)soieYM!2cZ%d~b7;4HSwoH*&|?LrQ~aMXnwg^u=Y{V6ox#h&j7=W=thl6L<k
z8lT&lGWwMqe#LjqOaI`zS!M8}#Q;Wc?Uxu|Z?)d;M<uB=O?`LU_L8ysEkgk;*c*?{
zQuzS3G$uX9xT86%5oBBY8mK57?o1O7g1=v!YYiGn?6Yh-uH`xJMrCr`y)yrLot;yW
z)i+`ckrWK@<k9{vd|7^c8kx?A-n%!@N^dIE3y^os%agHD9#5K1Z<g$`2I14H&*HM4
zj9WhiF#~B7lAlaNbr|ngZ(A{oO$HCrokqbY_->cGNat2PPBWbFi4qx%zBHhhjF{Vb
zJMDiU=Y&<}ci0rMZtI^0Hd2SES$86iqm+9Jch2pJ#WdPB$?%(!PeXdYJC~6^ON=fK
zzq$wHcK|S0WmSk>4oKn`1XIEt4W_~?VI(yJ5PU8+!AizdNJ(TTMpmdS5G1u&>^5a0
zUhhf#Q`XBp!4-Te1}c4Gj;l4hpH#PJ08^r!2u@~j_=G~#H`2|g?*z}3rW@&pNz8bn
zxRo=^#%-sqkNtf?aVye@TkFRBLFPft1L@I`A6dy2O~$#xy^P2YzuXwb=doWj<dnnt
zb!fi{g$u*x`ik1zy`@0pupJ{Fr1}gnmR$zSH5@hf{sd2i38)+gKjG->32lixxft?=
zorpR8Po2}*>NkRL4F{AV5?&b#frJ#ND&b&6p5tnzQ5`Opl$G}T6rG6%G?@3lek^N3
zsoFYGK=PPra0b^hG1w0?^#!mp9{{uC(86v`%5vzP;|oA;c5jdB1o!+rBeH8g7b{24
z58coV7ugQ#WBXq45ZafAMyn=7=3oapt6p_KDh0^XhnwRxZeEP`_ar4KV_Y(cEG+nG
zPbSbQ+7kd33s3O$a^8(7r!9MqM`L09Wq|YKX}Z&;nzE=>DPNY0W-lb$fR{>ihQa>M
z>k*ioh6B*r^yi<PRIymN7!=dRqv-kfv;7-CpW=T`d9`%LwSj!4G-<g7Ss3eM$g|;L
zGx1K*L^%V&aI`oGtSK3+WusvjYHqy9v#y?)4Q7<1+&Ec7<p_zc7St|@QL>Bzk#vd>
z)~<IO@0WZNf^Zn;vcHa3z{j6|?ZxpgW#%y!QMm}|>xDdbL2eH(1=iEyWDUZOb@XGM
zY{9`!Z0S5&yMi#R6<CE4b%A)1<;hVXjfeGDpcaY_Wfc&-d<z~fikN1}D=I-4qUZB`
ztxP`Tpd^(Ep&^ZS6|H4{TJDK?X&3J{-=yf$JF-tKdzJ}g3<a7CR{Pa7QDz}|pZQmi
zq7rB{87`;E_(CC8v)rrz(+0x{ffRALKl>=YC}LP5;M#@Tvxg<+C{`3sb(!#kzs0XJ
zsYOVB>^G+NTf%h-WuTdDR{ypCJxUDjgX_9qpiNtaCp9?u^rFx2OM+>J-bs`sw|r`t
zG`zHCgk(Km#wJ(BIGWIV4N9`N=*I>P-n{R_dN+K7K>Sgl9|lVz5`B^p>ij9LK+;N|
zSHH;HOGJZ1>XLV|iBxK-OR;N|t%b-=tb+ARLP892Zh))Bv<ZgrPS4)MX9G@;vSgS_
z%#6&ZUdrMonE#5%mN9W^4FE*1ubC--c>j?FDPRRm(;qNeZNLD<hX}@ZH)l3Q5*B2I
zS22nh7|j1gCG9NPvYTopui8KNnkl6GrIyGZ&A~7vy_+!}+`MuZK(ya)Ne&wzgW&wX
zz5U<{Y_=-HMBA|5Xb^(tiNbUG8F7Z8neow4pk2cm3y1Z!Kbq`R$LG8WX^H0!ka@dP
zsKB6FvhI>T&9xyY8#8q`yb9zBTvj*+2-PcYkJ!|$i19O1)tsaj8<Bnp-U=r0cID+I
zwJ$;FHE!;p0`W{_VJ$IHZb%Qrixhc&LKWsl*hQ;Hm{LM(mru9*1hz#~%_Utx0lgk=
zN=2164h_Mnz8fQ4P3<w6&P7?~aoUokQ_YJv>c0L;^>5n~fwJv!oew6-@{?Q#E$1Xg
zxzaG1-&+6%jan<j1pk;0nr-;ym_SycpEN^DHB(vXT_3Y3%Jk{=oL-ilgG;Rn7TueH
z`moU*RE{nsU+x|@64Tgr1b#B#1Dws?9xWyf&b*W+1O7m=9j0JNt`fa|O|OL>x<1RV
z>aJ(&9VJP-5W>*z^#;h19!fBa!&frYRoyb>gwAd`udA0h4oG(yFof@t^+NzEaMJ;i
zJBxyK^tbU?58dFY8Dlxihpv`E2FqIYQM`8MrOwLtrf$g-()9QP8mpk!y~>Oj;B2?y
zGkndLT!vJK9;7&dV^YKR@B-LW$;dS9TxL>}6iSk5_4;_o@48|E>e__}TlUISlm=pr
z$x>(iJ<BoG=0sWL^~4p?O$8kvfD?_Bf}y$;ek&jui7YFful1UK<shl8vG(8;^@FP5
z`V2*5SX;#4bs$|L3)*F=<~u5>>X(dM7Y3(w;d*z%%7e{}<A(;xNQ@EFPOiyXkmpM5
z?5zma=ZR9F8ZO#llyc7fdt1noxEgDLrJF(%DP<TA4TH`Z0cxMhP~J%)w_@F(7nDhp
zhdmV+iB9Y?{+80sm>Lxupttc*F<9YIIeN?m8Lg)95xZ6KtQ)W-{MR@!af@^CA*g~c
zh7$r<i2Dc3R3WfKToA!Q(d9We6&H??bNDF9lt!1aP5aQEsAu-3-`Fs*NZP-hpQ%D)
z%DO#pXIXrZJ21bModu;5+Ao*Qdpm$<r!kUmQQ}VgfUSb5_RRcH!N?amovW!ibcuiI
zM82=|0CD90NdvNzlO6=U66*A>?6d;kv{1q+F5pZjw;}zk{bNutSt5wcewMNvvu1%2
z9OThiHHM_A+?I~>hE1o7zA-kKG9;<MqeEMp)0wx<%U*H)U4*zlcH^X(4+MrSE<URD
z#YP<&RJY8ZRt5pBJknyc^rw}v?)jdtrhav`rYg5>6Y`cr&&&n%Fn(azDfdNv7Urbk
zKVKHP5(OhcI%Dd6Mmg@2^hYy}CkSOK-$mt(cHr;6>!p}QMu9hYKM*c|pFOr!@k_L_
z@{Cy}Q-RGf)d|YV%+hY7Cakd2WWjhGPgR`cK<O~)L4ny*Jj{xh1jEG?V;`-WY*zEB
zprNcDlW6elgIkw8{w}Rx&kSA$Dy%$(A~gnihdFK-6PRQbriYOug9Yfhqk*rQ!qPwc
z-98%R8T*p8Fbie4C^s9GVB5NC=vNsPX_k+Wgcm;7#d<&R8d5%FA01F7YUd$Zx0`lx
zn#pxP_fn)qiNArsB3zDGXkmKCG3Ob%tUh!Jvks)yK?r=!J&s|Uci^T{#Yg>G&<T;u
zMe;z&>2lf3vVayPLq6VOz>;iSbxYxKKOw<Cw;g~>rGaDtNooMl33Nyh$+$ds&bhEk
zv2FyK38^lyJ;^tn)9GH6iV53G;rPEm#JPjxUQh6j#qAVaELbNX?@HLm9^}L*kA!#N
zfmuZj@iLhv@hnk_heDJ)>VIb7`PbBCt!6muR~tzH!u2vIi8F|;MKXW?VW!gU;N^Mk
z1)(V1kH>21ENaEmXNATGtB2ShTiB?}SUtRhg*zq>)`*t)BZ!)%W}tu@TL0}yyqR6R
zWrcCS5Q6FFK<4ahl|m|CSJwqpkrrYUbTQG@qA%bWj|LZLAmZ{AyrZtYSI!N3dq`nl
zkv4ch_#+OT)D;!{L`h!n&)9@6&K*M^M3q35rgO^1kc)kFc=@lE-S#MmIUKD17gXSQ
zKqUVQdJ?pjL4)J|tv<w$zKU$cWF^RJbi`aUVdF}5B#$m>-+HE4?|1Xh^#+C&(fU19
zizEptizN(Zi0|NjN+DiDvY1M+5OjB%s^0HTMHDKTaWEl~XEBp%sJlngVLQbhCJj%c
ziP5TZb~tr}d7kB&=7rd9nzkRazkQIx$E~KP@3?|Pl4d+6=OM=E)gug5CoWcsJ<W|t
z=fS8zD6ZG!hqbV+N}saqI2+oQki}(Sfr@zF{#6S{j<)#MV=s`C;y>1sssx6q+6E4-
zgdPKWgL3CW;wub?YhNGy>a&>t^4dbkt@(f#=}^WOoM6HVny;rFP1?F8YRm~NQ8ICT
z(@Y{98&a+oP3ZHPtx0smIZJXCbU>V^05UA8y0`{JXr<^Bv!~g3`V^%2vjP-RBW$0p
z;Z>GqVX`$o`BXZMU!2KcLN9w5gpdn~AJ(H`hAejg1r+03F<pFARnr_vPFRGXu}_Rs
z22G|!toIX^?+|{K(W;B~7$|jOMUHlpBUyeF3%sdHWyP9-0gbpzEF1b~B<?H-brEuY
zd(VIo#&_Tux%n$6NIn^m;M3Gr=EXZQcb%e=%~Sv*N%@jbdBcJ6{MIYXa<ew~yV6Ep
z!;>-Lk!x9w>gFU@-z+mzhqmx?IE?0KH3VV{ZFYnv{RtgehX@$MRVdlPLNYy*pS_H1
zSZ?HI#{iesRmQ0&#e+N;r1^P_kV+*q1`<H3zt2)HYM^t_K}?uBkSxT@<BAR&7}s#+
zpGup?F5a0(Mh@$ehR1HF>+{5Zm-AL>4xPPASYe%f*iCsD{$?guB&tbp(BJo&mrSV3
zl(|xkH@7*&9v0fS0!CJCwO1<*@QNn95>Y!GzDW#zyCPsIet58maS}gmR~jeWyX}>k
zt>4P@)HBisz$Ib64TGXj5VH4t5oiD8z{`m3^-cvj5Zo~dSp)4mKJicHT2mQ@4V5la
zUS2bZfsC3kW@DtFDOZVF&^$V(eQ&IZBw<0$`*2wQWYYKPbX}A3XjEwm)TB@pz)VeB
z{S|eVMiFIi#=1+9p{nDew@3k?OlQ@CIaox!P}qgZzMAnbz{YV6+>l;MZdHXgiZQ&W
z{3>&jqE9coB0<Db<SfNJZgxOBc*Bx)58sjVu|^vwqT4uwxrgQXy|W7?Mypa@gP3C^
zn-gv~<@kQ@eq%U!p8|$LfI-#%mu+<|H&iU6xFc(&gstwhL722xZ%UY}+b}rpsb6`R
zu&WC@5@1>L;tVHehYHI%7-eI{d4mgq?P)WEC6=r5PU9`-JJnK{nW|s3uS5<pIdNcl
zxWzbLh>0dT>H9<3%U2Cxkf*)JC<eM_TQu!NJ_wa^(iK+O9Ym34_NoIQID-QCMs4Qi
z839I(1tQ#5;|zQ57gU8`EZ6O_69-M5H%ZY#c^JC0fsT2tG4ne+t#~J9iWJl2q1Xmv
zS&8qd$gcAX>X^ZGW_}gkH|ma9o0pO&hLlmfB*9bXu_~QjL~+qE^BsmvK@C{=8iHvk
zIu(LjsPmr;$>2+jQX#>M8R;tPF+&^|Op*fGb9*0>f641fZlM>8#o5(Js!9kra%~fC
z%X00Yd4~9<(8?2f^`NUkE}0g^6yA)>3{wS+kANZrBzigo`^dT<w&d~WX4hA6J_kaY
z8py^gDsg2Po#XxP<!FuJ=51P#82$DUy1UNv+j9;Wd4y`)-Da3Z(V#J;ch$mMw9yR(
zsnp0VWr>aNu^#7861IuSz3sT#xL^7~_&w>EX;(U<h_GZ0ll$y=<je((8j{I^l5{YL
zP=^ZT#$aF!!jd9F%AupB-R{YSL=op%!q5aGHt=P3fKTuI1R-NdAArxnulF7$VK@vf
zD8gtWs=z8@(51Td@Vzsroneas^*B;Me=F^ouV9?(kLZ>l2@GRVS1^k?Y0#De3*&hA
zO>7A-mSA+GB&z)6HDH(~^b%r=RTn;$4={2ZO@umxTxWGq%5X~+>PvTL$2$)qTn7kt
zaLIKjlo)k)VBuosebn}};G$0Y9EU=U{l)_8g1A<}E4~9I4gH4pdxX)HePRK8)lWUx
z<6-u<YrrW7mlH7QOt#F+6j(EAtrzIaJq}_$xam61u=frna!PTBNf7%fC8Dg;lInTm
z4F)WS!9e;DF2QuRy5by)Z7ktxH0Vl4TQ>Y4T;DVqqd`j%al4;RneQ0B_QdtDKBf8;
zNCT5)&2*YjG9v65kNC_%57S>YFC>Zt4^>~>g>zkwefmQYagSUm4}}GOA^bzKTLgr7
zplmo){eV+1MHG|-8l~W8ad13RL-ht^q&^c8Hyx%dk&v&^P05~AV~`ka?7WD{J`Fx+
z`=(5y1&nT}<Z=pzsT9z9v7WFjpfysn9dj-g&O6d~JKCEXII6TDVSDRC%zA?ww?CfU
zyjOiasl`lb2o!Td@SqiV4z6S-*26%|v!GCWHQ63;G1g7DFak&ZQefSL*NxAO%bYa8
zR2_`}77I=$#qi@NWq9k(uL-pjA$#RaAqvL4D6V+%-tUl(WjVRLu+g`qfhIpnh<8!G
z1c`%P9_sXVcskv)ruFnH_dxZ2<^Q&G&XXlIkVJq)%jd^zhQPj2sNo)J@xDSRPCkta
zJFX;p+(c5#&{1tNG+~&5EJ7DS3b!IA-4?o%DE+;PuO^|)*knS<JZU6m!ql(nrEm@U
zunJb}%Z7M%<ucG4PBUD8e3DMChpdIrf|1G|$KCYLt8N2enuUeY>A~HgoUa>0$l<*u
z5oQf`%LyPtk(m8Lo?vkv&H@VQAlAc3(=+2h`PBu8ZBi2h*UkEO&@dR<V2=2)!`)uK
z_c8HSVwGSAXPOKFUao;`+|g=z6~r0&$+rT*{RSN!JZm;tMT|`_koZrYa^mYL4;6-S
zYcv=IW>z$IvYb#Y7??uwb>6Q@(4_KQfS-1-qUJTIWepkqrKH-JP-0tAS7++Zoe4Kc
zesZA*I?I0-v<py)$@|8L7U7A>wOEu!haz!CNJ5d7f~;sp^Px70oC8cjsQ0v^;c((c
zHq*W{NfOcnOf-Nbs$Qr9S7XwhR)8MyTZW1ntOq49CtF3GKG+bMgbQcU`+z!B7Ki9q
z?7Kln^z(UlvVFL1NF^BBJcQpr0!zOS6B<*z@5H`b*gTxcRNf%O{c;0_7Fj4lVOmSP
z0HrTEA`aPS0Scp{g;wxHR?Met4p|-)W7tY8u;aVlNw-1ol{>*$y$)p@Iw_S$WI-Gz
zFNffoj=G_@C$?3<cqWHK4hWYUHgNw+cFPO5jl7EkFze#VX6y}x^Txy^S)(GzitymW
z8qllwN3`kdiS&fN7ILmCC|0POEIlCPloCXJi*q1vU*`}Br{>H_Asf3uqjU7#&qQS=
z+tchaB_=q|09=N9qgd{8?X(TF<*^RBAKEjTQLk=Va)8RTh3L-&w0S7s`01Nc35y;T
zx7(uXI-*jGtWFo3Zqs)ZFxh-7EXOc}gZ;kYuJX~Kw+|0re4u{Ia2ElGRs-D;GfIAy
zD)fPj5IJ}|oO|fb0}yP`)*K9G>0KY8Cl_HaSLa|0lFe)sOm%nx)GFLy8Fvv)&pO{X
za4PUu@m9eMq<n#(Fu@f1T<&L-0^d{K0JVdf=pF<TQIM~#kc=Ksm2L}$mi*QEWuz(N
zBer{@++-cgY+Na+9^%c7wc1;z#M9{X`ycjVaDivj)5xA=iYn)^ndzqolITOW%nAO^
z;rHhK$@I~J{!Ah572n|5jb~-^cde2~?w?Nq;o1OtrZL!Qv4Btf&~)1MkATCDdSDxk
zIn8{gq<-|CP%eWzLD(L3eZ{CcAaWOG6L-)4i8l84&DC6jny#ceRp!x{_f1tHYL5(I
zz>-UUG!d^eQx@c<Gpzyic~=9tB8NexF_lFoZ77lN#1rq_fbjT}0ZV*HQ)g8;_m0EY
zICBR(Y}5@KEriDdN+XsMsn>=24dBPa1sf3t+Q(GRcf;|MkoAFD;1O-FFdCI@djz(L
zA&_#4&S03BYq&35U#ZGcoEj|{KK+U_=ZrI!d>e6OuK|Y*_T$e=uStl-ezzvXy&F$Z
zf&UTXJqL{~IVu;MR;3_l&1sBp7>cnz$||Vpbnypc=bJ$PO=@e;trh8SrlzdOYJkHV
zr0W#O7<SV#AB2JmqBq8j;3%ohNq^rSsF$Z=m{!%J&Xqnwo9<utvHUiNQQ#sbiV#`@
zdng|A=Bzv(=ZMVi1(v@1yLi;D0`(cPK@|X8iFIn5%`n_2N5+&CXoo*}R>smcM}}b|
zSKF#%4RgCe_&bm|xZKgb!*sVKgyvE?SFTLu;L$=WOT|Xr)dm}_h6CiIitv5bu@a-m
zP&#&qxcud@bSzI_<7>~*7Q7;{3JVQ&{tO%(VuNqE>aQ+oIv6BJ=dBBsSgldpkjS?<
z*$?p7%8Pja)bkWzmU8epjZp%yg(SpR)=lXhJjuCYje6{S-iRX?SK4q(6DlKqoo*}~
z0*QEbb{cqXk$~PJu_ydZ*$vDLSZmxPYtJv>&f4ZOHXB~KP(=u^7(V?FCXAOD^Fw8w
zt??c2StZOtJJ9)Ozvqj~8mSxBS<;D{ao-xmO;T{-`ck1>hne=4Me6qkqQ~(-yh)=j
zyHIaX!njUPFlITJ%5`DV@=bSi5ECS3i_8D2&=i|;Ek*L<;#%U+M7GfK0B5;WLrPH4
z?rzH|l2q)xlAk~TksB_{Cyy~(D&3wqbnknBdovIR^iN1W_%_`c;HpUdG+Wmy`otA*
zLYAc6ITbS<P#`{y6BtJirf!?^m_4Q7z^ef*YAUFX*p98yG-RxF*du+ey|1gv7R-hD
z(UZ&z(l8|%nqBc}40oL$nfe<x<gMxMS2qG>)?*QuEs^$%h;=9M_UR9@ZB_0mW)VO7
zpK4iu%|;|eGrY&=OYQTRxJ+Qu`-dr-O$-Ty^;GX#XrW7ym)SD;>*ae#9>|fEH&o~i
zmeW7Pid_%s^QnJ^ISp5%nB+(mv*?oLITjg$X%Y?W4(#ph0!vcq>nKoJQ$?qb3V}IR
zs0S^FSrhi6r0s_$r+~8M>Z^@qN1eg>#?S->{lM0}YMT{8aIieTYgWveAi;BU;mA5=
zMh-h{^=>$g!dcft9vUyOXC7~VCoV^xv~~x7Bt7Cq5_mfMrE#I6<?h|U>4cQqsex(!
z22)GlZaMI36O}_+ZhaEuTuqr7A{IoIoR)|m9@#V<<VrHH#eW@^fW=`HnM0a)$1=uS
zCHN+}wtZgK=bMW{r)SPY0*-55y^W$FI$wBUqHyf$mb$jWfy02{Vfb(mG92HX%hq<f
zwr~tJHoJdBH4{F@wEseS*vF;Ieio9hp?SjqvrI4DvqU~NC87X2Fv1O#Wbz>lXf8@O
zZ-bAikI|5rSZm}F?>O<dxT46ywfDt=eeI~m<X`SaK<-OB<Jqtnm}52}zdj7Xxhf69
z#!-oHBI0cBbZfeX&^t2OVn`sHrpWn0T(1NsAYH2Qh6?$B@=<6>5g|DH8E=?ZP0~k*
zM8FJDtx!f&rh}}Fe209o1Qa_7lXTvE2WPbZk($IBW<YP03dW%z){gbPygmns>A6R^
z9|-mNU~?R$34VY|z(wqa5QESO#f!LUF%D+_B7Vi((Ect2Wso8XZ>u5n1JAGt<Cbqu
zdpJfuDdRo)cWejxZr;dBXUNuBZD`xW{-Sjntu-qu`PTFF1~UCl6--XJO9pL*ypR0L
z`b3@z{3&YLncMW#9co#Y1G$UkVZkxi6`uCwd%`L9cHM6dgicgICwO62tOO<Bu~r*u
z`uh@xI37|wLS*4v{HMFu{OG@HR<rKGUMijEesg4H{5{6|ffsW+$`tXwLnS$(kvC}h
zhq82W`G_L9nD1WQmsAU0wkpLB4WksUm`+thnT4TCz6}(q5r*Osd+>tKfE1Q}%N6un
zH(9hz2u3?}hBj~*e5Puz<g-n3q(e+|UP7jA-6Bn_)+3$MPKhCfC)?~pC8$pFOTqz@
zOCpxt?J()!LSD$#y+&9_m?1YYmOo$;3=k(sa1Iy&qCkKTgo!37GCjDWks)C$n=v8I
zE^fnh(7a1N6KwQ;FmCKDRk$-uuCfQZ#bZJglS$W1Jsdmq+@TiKZy=A4QjIY&bceze
zjk8}BqS^H!K8BAOYeDtl#}1DjI{}oUtMgDzu68Q6lXw*_x}iE;S^mPH^uWfMG1IJ@
z<Ay8AUYtz<rmAVsfxkUrDsq)g31pYIc6!M2$HAO<$~Tf2`g_{cAZ$o<1~>8ohA&0G
z4wGuxGFd(-)aP@;$yP~>eEkA>3sSgrt@LD<!DFV~BND(-QxLyH%BLM(K5IH{^-yO<
zK0ziYK@J6}pLL{TB{?bKhF$vmzm-FkLqPA{|9p3~d5x^~aUdBH#x$&aX)6DmKR3)j
z1{KK?)N#k#C%i6Je0Sz;N6sS{;Q8Zc%+)u8Z=^Kj;~vuk2q6JtZjP8lQAT_NkU2~{
z935VPG_IAPH<QYpk1gd##6=CnC&ISt(_<ftH1Wltw>bO;aGr<9B#OY&hSQ8$fWXtI
zJilb2Y=i}v%Fez<wbyy>8sL=F<n-oI0K1kHBD@8wikK7o)YKn-r#L5mgTG7LTBtrY
z4-d}4r28yZ#~f!2{q3zo9AuZ(C{`{NaelWv6TB9-vC+K2y~$OWtSau*zTjdAlKqB*
zJ!RAgb(WK331f=>glQ|ZU<FnYK38Z9G?TDV`LFX356O1Y#frFlvb=*ZV@d7|U*Umt
zWt{brXyeT{G}vMmXb|@G!iG$?$pDap74oqy+f~7&1OkB%e<)gTqdXQ!02>&Io>EHE
zmrkd#ELG2hEP`3DCQ3<>NeXnTU9?8TVOEE0KtG^`)-MiLFCyhmT%t<LqQ+on@-sw)
zVyh8VB3%iXW6jenBF?ho*Qn`5Xjtv%MmeJQ#xozie!In0Zzqo)0iWM4og&8zcm`{R
zSI_Kw;(8%Sb3P09i*Q$VW10+=U=Ubl_gN?=mq|6APDb&{dnOBS&|+mdU<e)<m?P8?
z!&x<$?axBMtvJkb0{oC0Wj#~9m=rUc>iTDrg^L`Evc{|YWN8u*_ZI>^6LPd<O#K7#
z2_-aoK{+oVJFP<|715-W%}b}g`A;gDGMyjB@N^|@@S4=`g0m4hc7orKL3WED#MA<V
z4OKkc*a3liN(Mh<t%7D3O~9)Ka6o{lH8<WRn=SL5^<Fwd!5p^3zW(Uffe+ix4a#0E
zIP%$yRdi4{jljlo-W?heGq;>G(r$OZivz~A{a$4|Z9oL-Y}QHI^#@>k10xulQ1exo
z+K-&5JsC-Se_w31-^mcGuO#BFtudd8fHt`Hr(9J^KU1k}5%3Z?XO?5Vw7=w}UJ*Fh
z_w8vvwGWe~w&9%Q3!qN^?5eyV*+pziT7wpd|B1sz3vvOPDnpV}jsL*mB(g1mFN$le
ztdk*&Vgy6p8x~g_)Jg)K8Bm{(^z})wER${_gi%fh@_{zL@&PK8Kt23{#{|isw>>yq
z$wo~wfSzvy^!zz70e5s1b7F{Q^16`GZHs^3`nuz@1$KOns5O5B^?(=8hI5Y7zad2_
zpaQ;4J(Oh-gGe9;lrjGbg1*+cY<rv3kE+UCNK$0LN^U^~>g(aXePfGvGwolMkwCP*
z_I=R4Mipk76R6aP&*e!JewC>9*!BxCn&18u7s#&PU3)8di3}7R{1+eav(r&vZxAU~
zj)I3L|L}xB>4tl`iL`7BW-0tizxYD97Vn!fC<4M=>&f4nc}r#f)W@N8d*S?F`kVhQ
zj5}&ObjjN?4mKp9!hpgtzhAeD{yk=5Xu*aue+U%0u95!s3z<9y1U&y;{10lHSEana
zUQ9snuNMP!O~FQ)Uyq}p4Dl6?j%C!4`180y@pb{e9U}`FlzAzb>Q$+qOGALudr-*N
z54yM<V907*&o>>X%|84^L;_L7JEty!4}4ipQ%t~QM41A#n6WYjfO|N;*QZ4ZBC%Z8
zb{+nMR{He<lCkWG*?j;e1q0MPBzzpugu*Z)S**rqg9$W+Z>#KuX)ZbcH1zx;OaS57
zlLNR&vgyiVi0d<OYYOmULy(h}zzbhP=Ab10TNeJcEJYE%LghuJ;?}P_&VO~5zg}87
z04Ni&da3fC_xszIz@I?WFS>W%{OMVL-TYT469t|`^JPZrb=~{>m)VQJ7sda3$bZ+Q
z;Qy-Yf4%E}<K+L=!2hO||BoifyO*1jtG>`2yEpd6NyqO+?AILTy0MIMUfRyXdgr{>
z6oep+<77Nf&il03%|_F)#Vje^%6^X*mX(ziwLVPo&EyAzfkQw-BV)-3g5e*BBqRO#
zL@4O{=d$yAWZ$Op!}!1M`PWr3RAgUq58_?nzwSZ)>#`0c<T`x`H`%}b^3PSj3E<*H
z=GXgw-2*%axLFVr9K0T`SQh5*SM^!J!Ck8<4Eg`M=U)#T7Zn6M=`2!uE#dzy)BlS4
zzgqoYU;W>(`rl;rzj^il$E(%+<PWtBlz%U3go666ek^9AuPM4wychj|X6_vSf}Ftf
z)y2-x%<r>}uBAFVyE%H!nZ@OjPO(Urs$I{a#|j9~Ap*a@FQoQXkiZcKSAeE~PJ`o)
zSa2JlU`nrDZ~t_6e#Pi?{6&d{?&W?%Eb@BHjOQbgs;{^!?C#%|?DjUX^@IGZQSB%^
zt_wg^eGKH@QJ9kW@??K(^bC9sIr0HAaZXm6UheB(4)Gz^eXh4y-2SsX*Cn*yuKB!7
z$qBRo2}nGjewlN80wgE^U3LA_)s}p@tkwyoD1qO1esA7ssyV?Oya2i3Jb=_UkirC{
zs%!wM7(Y`@OgP`)P8TX^n6CioRj<<AUQ2GaYGE`!FVDBmuUR=GX&h?7OSLvyo|3CI
zuSriAMV~g066v&Vj+bt`QRTKTdenA)0m4JAzz;5K(hn!5YX1gwv$u6;nIdrL<@WZn
zd`5FV<6TU;mQ0$-jvO=kw*v8+>*?5bKs~5~cR~9RK-E`)=gn;Np0+@=obQT}{->7o
zTY-~cn6+v}@?IXTn%u7~XGpJAHiBfyPDcnV6dy-8){Nr;nPUozOF&=W_D_l(5Q_t-
zD>k>&Bt7o|XJ%&}kMDu-=NrKU<Vob+<j?p(O|5)h)2ZodJZb_?nE(<@WcXhI$$geM
zm0($YZ{Wq_q>=D>T>;JI{AWPo^6cU0r?`>VlmwE-`R|J%1}C@Q*~kUCM^Ajj*EBB4
zT0@so`o95YJnnjr^yNu`1XV(yc(hIL4Nd#A^)=`}hFg0C%&)~78cb3KGM)@xH|Cw(
zdTT0D4sxEA{lY{0bJAG4OKyisjaphqQz}k1lMN1ma~WUHlZHLVdo?|;g#M&EO*cn}
zV5c$ideh_Eiaz`yj=D+02JX5l%V3xmK#1PbB^iB=W6hH#g%>rGN2K@(pu*z>vfK{~
zQ*C-jR5Utd{jX(6h8pfQ)lq)Y{A`XDP*kp`TT0*tos8Hc@m<L$miVU>>$+|Pde+kn
zw2e4z!9kq$rs2l?$0YT;he#-lbzRbGg|UNa;TonkFKd`kvU0QFvb!XI$h&ku<(5vR
zGJDVVsM!MgMxLnNdIFY?D=DC1Hrfgc(_RP)9w;X8x>A^_dj@j!wFMSr7Khg$9JeID
zxtTm{_Joy=NCiHWsI_FJvr~05K5w&Qf{cEwDrOZsy6GbR<e!rBn=bs7w5A3HC_|>p
zgxdw;t#-<QwFce=k^iU9taJN8uH=sA)=UFJ_!%%dA-V(JK*tANY4#OL)y_p!)cPB*
zunvbcEi9rRw-MB&)?hkfS}c2CX$4AEHB15dGb7F_2+W&6&S0FC6Nym2!Q)gr=<&cn
zb;###Be;1nLv%|!?Q_Br!eO-rV}u0~%T7sXe%^0EMkh<J52MbN2Eh<#K?=BE|5k4^
zP?gompoH9{>oMA1axe<AUGb_0N3VQU0!Q62P3}>vu8@r5r)9|bQF{96MGIAjV)?LY
zHmRWgqd_NzvEsRj{^0Ky?+dk)$E1D)H_+uLXsDD0?zl(rK2yM``9n=5-!Lkbxs5*i
zC>$Nx=e;2Cp!sryFADz6mM@`?j!%0TN&6Jy3FC1es(5o<Ja?T@L{t@&G8bOunW~pl
zYcda2W$}|>59$DF<k0J&0l`#OC3^IyfmH=ZpmqXJs)tQ+$@PpUI~Nzr(Z;v_)(o4#
zl!}Xrou@`l^ZOeWdXTLh%|@}T5xug-_Fn5jIf7=O3QxL)j};Qsy4I1M^MB?p$TCz3
z@{)w!fHJhh(k<A~BOa9&isl)Q=KJay&EE)e-j3<!Nl_p7boQGS(m|OL8d<(Yh({b{
z_spu^*lEeB^{XFumz4%u+$gxRVx_*w=mJxU-IULB`F-PK+iya+hLAyvbi7O?4HM>j
zJ{#Tlc2*NkeNt)G_shz*TowY@oLRPISqEj@5e@Ph;Ic^HhESZ{`-KN?3oaQ7E1BCY
zgXh-9>G)B6?atpY^8Rg`rsSt-4U&OP@K!1_=>=+U^b*MeRUQ>iDH$=zkvgBvC3zgc
z@ECRlh)iI(U)tH{Mm;^a;v}zRC`Twt9NEEZ==MhW65#KjF30v*`VUx+r*?rudIl(`
zz9l80GNAg#v0wI-1gv@ramVnG)F#X~82wnHbv9ePhx=ID44vVI&+o~pR>~cbke%su
zvoOr-10@jzWGRXJJ+NI!eV8p?Y?xw2v?$yyw@h3+=$&4U5fIpxUIQOYL~`1}uQYM2
z`PpFVV`bLBgds-sw*kYBA%O-elbmb-gvFwVqM}jxX*x%=)A%o29X_sK*s5_StWI*?
zTjdo)1>Xw`Vnnb=E#_*w*(`dSmgMfhPoQ|HhOYt1U?u2#LzBlvP*dt)2~Wv8Ck?kv
z*<I}BZ68~(b$@;_%gR@ML?ce*8BBZ`a7OSVU)wD&JLM4IL;d^8Oaf&~=~Np+COP}y
zRGfm5h=HQ^wUQ>I2#@F3c*gM=>6;}xT^*cR?_iEYq9y84C1r+ZrdrYz^IEFyv64Dt
zM8XNB+K;gWRt#s(51-!*!c+~R+D3TLfvGK{yK}4?V14<|pah4|fw~ykdpi0KER*#S
zu^iQaqS>drHl^f{MrrW+BGu6T7arD=|Jsq)`3bhlTmz@3?}TZ%J#x^@yZLy~5wx}<
z*f!e|EqrRM*HWmnEGq@e*NHS^KD$U=66=om&vu$naGf2a|1{vz3pfVpty*J^#g$B2
z3Zv)B-l*o3YCn`p=4=UTtoz@_39uJ0?|>K*wt_1!l~-!S@Gbt-2+^!K@^&p`<8S+P
zpa$EeAf~?Zcr7(7j!h4jfz^eXEtaw-|Kqn9zqAi?+aea{jo46u)fK5GtI8$?E}6jo
zZJq#1tB>c0p|kgPsi+yl*Gaywblmp)p&GaK^*?Xxg2XVJNwg`Jk4S<zTh7*w%VaM#
zEj<rfN$~qe*}~gdb7a3CRcq|5PAhL&f!AxQHO2qbZQ(90%qt}iw1^t~M+r!vs1s}B
z7ga5b^N4Lm@-2TOwrkZ|7Z&|8TdaXo?1yrZxv^-7xizKz@4AwQfXSsxSN$eBjaHQI
zrL`c#RlzYwUkWDo=1g(vWzCVg2Pb>**xodJR?P439RU*B8KnTE>BlOp>}q3F)2(?u
z^}Gh|3XoD$sBnX9f=hJ@ORoQT{p`4QXFB!?w(qpi<x@%_Ef&qy5Y0e-KP|#sA_i6U
zC$<B;QMAPk&`?nw#ec@yt3ALWoeedHAzQrniIYxw3$}Ld%gIb}NK1n;6`0*hqYGed
z9d}o|BmjpP&katcs-}F2`0uhV)A}_mIB9C^{IasLYNXpHKO?^}<(F=IGg|9$djjND
z)=W_un{Yj*OA)nLFIH1M-i$h_)ONK!)YFryMezM?J_BmKJ_I5GR3(?Sp!RLjN_25r
z`P&EbvsuVQRo|-Pl_rkI*^{WYTFVT>jG|}7+qk*h`~<3{f3&U)S^;vZ*F%Y8<sryK
zmaMTBereD}1!}drp%x;&X4&iUCWF&~I8Zyz%f@CBm~Uke%?^v3lxNRMTOj^X7%GUV
zehnhlm0IM~kD_ZkkE9zwF1T9q2-zHjy_CnzFD~H!&QKD~W-W$Iql#XavKzNOo0hjq
zllDK_b2(b@$7mwo(ITFz40@&AL|y4~UNl|XZ=0dEhMQBc^k42k!W)TrWbTCX$I>-T
zNZW}zlNGedJVdKI?bT7)CdI!Q6t8Vo46BT2(@;rlrn0+8ZLFs?X$LD=iSDmd@3<oc
zwG^;?pf0`O;_kW883@>)rpbWWye9xfab+sa^{8A+my~PjZZOETWNF%H^Zyt|744hO
zDcNa5G|#jAY`{$QAoKi9IQY}Ad8QBM>|lG#4NiNJfLg?PtOv~lec*Z<g#B?olPh<r
zMcY3{&H66vwBixyYQ&)QSruLuMRo+R{XZQqvavj*gQa8CAf|V+g2_$U4bCV)=`*<o
z%@F-p?JtY?VR#jf8LwdYYdw^LrN14T^FAuN2j|?YwDkNnUm=}DPxgjljr@Ez(b2{t
zE)`xQSfzmLN1ppX`}YyD`9Wpi2sP<WUR}JE)d5Ga#^Z?E&x@wDr_9eMUuoX1AD#n8
z<xt3Fg1AyXk%OrXW(+iP4Hr0xD@y*yUViQKv-IV>`l_oX`&y5%?J8M5Cp^!)mluAj
zW5oyiR|iw~NRk=|vTsM>7ZXnu%Vf0-?y)TY(Kj2RsMmHcsEyZZA=gVDPF7oZCO*#q
z=ShLtDh;<m^ZWdM>IuWV{N!AV^Yd*o;?$tUc$v!I)}z<rSiMiirKZt0&8k|sh;^z3
zq$N&)HaVItwK`z8u_XliSs_01kEi-Vyg+RWuVdfu{tN*F{z;0;ij;lS|MGtTrbnCV

literal 0
HcmV?d00001

diff --git a/chapter_hashing/hash_map/index.html b/chapter_hashing/hash_map/index.html
index 3f8240949..757598370 100644
--- a/chapter_hashing/hash_map/index.html
+++ b/chapter_hashing/hash_map/index.html
@@ -1021,7 +1021,7 @@
       
         <li class="md-nav__item">
   <a href="#612" class="md-nav__link">
-    6.1.2. &nbsp; 哈希函数
+    6.1.2. &nbsp; 哈希表简单实现
   </a>
   
 </li>
@@ -2063,7 +2063,7 @@
       
         <li class="md-nav__item">
   <a href="#612" class="md-nav__link">
-    6.1.2. &nbsp; 哈希函数
+    6.1.2. &nbsp; 哈希表简单实现
   </a>
   
 </li>
@@ -2099,9 +2099,9 @@
 
 
 <h1 id="61">6.1. &nbsp; 哈希表<a class="headerlink" href="#61" title="Permanent link">&para;</a></h1>
-<p>哈希表通过建立「键 key」与「值 value」之间的映射，实现高效的元素查询。具体而言，我们向哈希表输入一个 key，则可以在 <span class="arithmatex">\(O(1)\)</span> 时间内获取对应的 value 。</p>
+<p>「哈希表 Hash Table」通过建立键 <code>key</code> 与值 <code>value</code> 之间的映射，实现高效的元素查询。具体而言，我们向哈希表输入一个 <code>key</code> ，则可以在 <span class="arithmatex">\(O(1)\)</span> 时间内获取对应的 <code>value</code> 。</p>
 <p>以一个包含 <span class="arithmatex">\(n\)</span> 个学生的数据库为例，每个学生都有“姓名 <code>name</code>”和“学号 <code>id</code>”两项数据。假如我们希望实现查询功能，例如“输入一个学号，返回对应的姓名”，则可以采用哈希表来实现。</p>
-<p><img alt="哈希表的抽象表示" src="../hash_map.assets/hash_map.png" /></p>
+<p><img alt="哈希表的抽象表示" src="../hash_map.assets/hash_table_lookup.png" /></p>
 <p align="center"> Fig. 哈希表的抽象表示 </p>
 
 <p>除哈希表外，我们还可以使用数组或链表实现元素查询，其中：</p>
@@ -2110,7 +2110,6 @@
 <li>添加元素仅需添加至尾部即可，使用 <span class="arithmatex">\(O(1)\)</span> 时间；</li>
 <li>删除元素需要先查询再删除，使用 <span class="arithmatex">\(O(n)\)</span> 时间；</li>
 </ul>
-<p>然而，在哈希表中进行增删查的时间复杂度都是 <span class="arithmatex">\(O(1)\)</span> 。哈希表全面胜出！因此，哈希表常用于对查找效率要求较高的场景。</p>
 <div class="center-table">
 <table>
 <thead>
@@ -2143,6 +2142,7 @@
 </tbody>
 </table>
 </div>
+<p>观察发现，在哈希表中进行增删查改的时间复杂度都是 <span class="arithmatex">\(O(1)\)</span> ，非常高效。因此，哈希表常用于对查找效率要求较高的场景。</p>
 <h2 id="611">6.1.1. &nbsp; 哈希表常用操作<a class="headerlink" href="#611" title="Permanent link">&para;</a></h2>
 <p>哈希表的基本操作包括 <strong>初始化、查询操作、添加与删除键值对</strong>。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="1:11"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Java</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Python</label><label for="__tabbed_1_4">Go</label><label for="__tabbed_1_5">JavaScript</label><label for="__tabbed_1_6">TypeScript</label><label for="__tabbed_1_7">C</label><label for="__tabbed_1_8">C#</label><label for="__tabbed_1_9">Swift</label><label for="__tabbed_1_10">Zig</label><label for="__tabbed_1_11">Dart</label></div>
@@ -2508,23 +2508,19 @@
 </div>
 </div>
 </div>
-<h2 id="612">6.1.2. &nbsp; 哈希函数<a class="headerlink" href="#612" title="Permanent link">&para;</a></h2>
-<p>哈希表的底层实现为数组，同时可能包含链表、二叉树（红黑树）等数据结构，以提高查询性能（将在下节讨论）。</p>
-<p>首先考虑最简单的情况，<strong>仅使用一个数组来实现哈希表</strong>。通常，我们将数组中的每个空位称为「桶 Bucket」，用于存储键值对。</p>
-<p>我们将键值对 key, value 封装成一个类 <code>Pair</code> ，并将所有 <code>Pair</code> 放入数组中。这样，数组中的每个 <code>Pair</code> 都具有唯一的索引。为了建立 key 和索引之间的映射关系，我们需要使用「哈希函数 Hash Function」。</p>
-<p>设哈希表的数组为 <code>buckets</code> ，哈希函数为 <code>f(x)</code> ，那么查询操作的步骤如下：</p>
-<ol>
-<li>输入 <code>key</code> ，通过哈希函数计算出索引 <code>index</code> ，即 <code>index = f(key)</code> ；</li>
-<li>通过索引在数组中访问到键值对 <code>pair</code> ，即 <code>pair = buckets[index]</code> ，然后从 <code>pair</code> 中获取对应的 <code>value</code> ；</li>
-</ol>
-<p>以学生数据 <code>key 学号 -&gt; value 姓名</code> 为例，我们可以设计如下哈希函数：</p>
+<h2 id="612">6.1.2. &nbsp; 哈希表简单实现<a class="headerlink" href="#612" title="Permanent link">&para;</a></h2>
+<p>我们先考虑最简单的情况，<strong>仅用一个数组来实现哈希表</strong>。在哈希表中，我们通常将数组中的每个空位称为「桶 Bucket」，每个桶可存储一个键值对。因此，查询操作就是定位输入的 <code>key</code> 对应的桶，从而得到 <code>value</code> 。</p>
+<p>那么，如何基于 <code>key</code> 来定位对应的桶呢？这是通过「哈希函数 Hash Function」实现的。哈希函数的作用是将一个较大的输入空间映射到一个较小的输出空间。在哈希表中，输入空间是所有 <code>key</code> ，输出空间是所有桶（数组索引）。换句话说，<strong>输入一个 <code>key</code> ，我们可以通过哈希函数得到该 <code>key</code> 对应的键值对存储在数组中的位置</strong>。</p>
+<p>哈希函数的计算过程分为两步：输入一个 <code>key</code> ，首先通过函数 <code>hash(key)</code> 计算得到哈希值，接下来将哈希值对桶数量（数组长度）取模，从而获取该 <code>key</code> 对应的数组索引 <code>index</code> 。计算公式如下</p>
 <div class="arithmatex">\[
-f(x) = x \bmod {100}
+index = \text{hash}(key) \bmod {c}
 \]</div>
-<p>其中 <span class="arithmatex">\(\bmod\)</span> 表示取余运算。</p>
+<p>其中， <span class="arithmatex">\(\bmod\)</span> 表示取余运算， <span class="arithmatex">\(c\)</span> 为桶数量（数组长度）。随后，我们就可以利用 <code>index</code> 在哈希表中访问对应的桶，从而获取 <code>value</code> 。</p>
+<p>设数组长度 <span class="arithmatex">\(c = 100\)</span> , <span class="arithmatex">\(\text{hash}(key) = key\)</span> ，易得哈希函数为 <span class="arithmatex">\(key \bmod 100\)</span> 。下图以 <code>key</code> 学号和 <code>value</code> 姓名为例，展示了哈希函数的工作原理。</p>
 <p><img alt="哈希函数工作原理" src="../hash_map.assets/hash_function.png" /></p>
 <p align="center"> Fig. 哈希函数工作原理 </p>
 
+<p>以下代码给出了一个简单哈希表实现。其中，我们将 <code>key</code> 和 <code>value</code> 封装成一个类 <code>Pair</code> ，以表示键值对。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="3:11"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Java</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Python</label><label for="__tabbed_3_4">Go</label><label for="__tabbed_3_5">JavaScript</label><label for="__tabbed_3_6">TypeScript</label><label for="__tabbed_3_7">C</label><label for="__tabbed_3_8">C#</label><label for="__tabbed_3_9">Swift</label><label for="__tabbed_3_10">Zig</label><label for="__tabbed_3_11">Dart</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
@@ -3455,21 +3451,15 @@ f(x) = x \bmod {100}
 </div>
 </div>
 <h2 id="613">6.1.3. &nbsp; 哈希冲突<a class="headerlink" href="#613" title="Permanent link">&para;</a></h2>
-<p>细心的你可能已经注意到，<strong>在某些情况下，哈希函数 <span class="arithmatex">\(f(x) = x \bmod 100\)</span> 可能无法正常工作</strong>。具体来说，当输入的 key 后两位相同时，哈希函数的计算结果也会相同，从而指向同一个 value 。例如，查询学号为 <span class="arithmatex">\(12836\)</span> 和 <span class="arithmatex">\(20336\)</span> 的两个学生时，我们得到：</p>
+<p>本质上看，哈希函数的是将一个庞大的输入空间（<code>key</code> 范围）映射到一个较小的输出空间（数组索引范围）。因此，<strong>理论上一定存在”多个输入对应相同输出”的情况</strong>。</p>
+<p>对于上述示例中的哈希函数，当输入的 <code>key</code> 后两位相同时，哈希函数的输出结果也相同。例如，查询学号为 <span class="arithmatex">\(12836\)</span> 和 <span class="arithmatex">\(20336\)</span> 的两个学生时，我们得到：</p>
 <div class="arithmatex">\[
-f(12836) = f(20336) = 36
+12836 \bmod 100 = 20336 \bmod 100 = 36
 \]</div>
-<p>这两个学号指向了同一个姓名，这显然是错误的。我们把这种情况称为「哈希冲突 Hash Collision」。在后续章节中，我们将讨论如何解决哈希冲突的问题。</p>
+<p>两个学号指向了同一个姓名，这显然是不对的。我们把这种情况称为“哈希冲突”。在下节中，我们将重点讨论如何解决冲突问题。</p>
 <p><img alt="哈希冲突示例" src="../hash_map.assets/hash_collision.png" /></p>
 <p align="center"> Fig. 哈希冲突示例 </p>
 
-<p>综上所述，一个优秀的哈希函数应具备以下特性：</p>
-<ul>
-<li>尽可能减少哈希冲突的发生；</li>
-<li>查询效率高且稳定，能够在绝大多数情况下达到 <span class="arithmatex">\(O(1)\)</span> 时间复杂度；</li>
-<li>较高的空间利用率，即使“键值对占用空间 / 哈希表总占用空间”比例最大化；</li>
-</ul>
-
 
 
 
diff --git a/search/search_index.json b/search/search_index.json
index 747212c59..e9bfea1cd 100644
--- a/search/search_index.json
+++ b/search/search_index.json
@@ -1 +1 @@
-{"config":{"lang":["ja"],"separator":"[\\s\\-\uff0c\u3002]+","pipeline":["stemmer"]},"docs":[{"location":"","title":"Home","text":"<p>  \u300a Hello \u7b97\u6cd5 \u300b  <p> \u52a8\u753b\u56fe\u89e3\u3001\u80fd\u8fd0\u884c\u3001\u53ef\u63d0\u95ee\u7684\u6570\u636e\u7ed3\u6784\u4e0e\u7b97\u6cd5\u5feb\u901f\u5165\u95e8\u6559\u7a0b </p> <p> </p> @Krahets </p>  \u63a8\u8350\u8bed  <p>Quote</p> <p>\u201c\u4e00\u672c\u901a\u4fd7\u6613\u61c2\u7684\u6570\u636e\u7ed3\u6784\u4e0e\u7b97\u6cd5\u5165\u95e8\u4e66\uff0c\u5f15\u5bfc\u8bfb\u8005\u624b\u8111\u5e76\u7528\u5730\u5b66\u4e60\uff0c\u5f3a\u70c8\u63a8\u8350\u7b97\u6cd5\u521d\u5b66\u8005\u9605\u8bfb\u3002\u201d</p> <p>\u2014\u2014 \u9093\u4fca\u8f89\uff0c\u6e05\u534e\u5927\u5b66\u8ba1\u7b97\u673a\u7cfb\u6559\u6388</p> <p>Quote</p> <p>\u201c\u5982\u679c\u6211\u5f53\u5e74\u5b66\u6570\u636e\u7ed3\u6784\u4e0e\u7b97\u6cd5\u7684\u65f6\u5019\u6709\u300aHello \u7b97\u6cd5\u300b\uff0c\u5b66\u8d77\u6765\u5e94\u8be5\u4f1a\u7b80\u5355 10 \u500d\uff01\u201d</p> <p>\u2014\u2014 \u674e\u6c90\uff0c\u4e9a\u9a6c\u900a\u8d44\u6df1\u9996\u5e2d\u79d1\u5b66\u5bb6</p>  \u300c\u5168\u4e66\u52a8\u753b\u56fe\u89e3\u300d  <p> \u5185\u5bb9\u6e05\u6670\u6613\u61c2\u3001\u5b66\u4e60\u66f2\u7ebf\u5e73\u6ed1\u7535\u8111\u3001\u5e73\u677f\u3001\u624b\u673a\u5168\u7ec8\u7aef\u9605\u8bfb </p> <p></p> <p><p> \"A picture is worth a thousand words.\" </p> <p> \u201c\u4e00\u56fe\u80dc\u5343\u8a00\u201d </p></p>  \u300c\u4ee3\u7801\u4e00\u952e\u8fd0\u884c\u300d  <p> \u63d0\u4f9b\u5404\u4e2a\u7b97\u6cd5\u4e0e\u6570\u636e\u7ed3\u6784\u7684\u7b80\u6d01\u5b9e\u73b0\u4e0e\u6d4b\u8bd5\u6837\u4f8b\uff0c\u7686\u53ef\u76f4\u63a5\u8fd0\u884c\u652f\u6301 Java, C++, Python, Go, JS, TS, C#, Swift, Zig \u7b49\u8bed\u8a00 </p> <p></p> <p><p> \"Talk is cheap. Show me the code.\" </p> <p> \u201c\u5c11\u5439\u725b\uff0c\u770b\u4ee3\u7801\u201d </p></p>  \u300c\u53ef\u8ba8\u8bba\u4e0e\u63d0\u95ee\u300d  <p> \u9f13\u52b1\u5c0f\u4f19\u4f34\u4eec\u4e92\u5e2e\u4e92\u52a9\u3001\u5171\u540c\u6210\u957f\u63d0\u95ee\u4e0e\u8bc4\u8bba\u4e00\u822c\u80fd\u5728\u4e24\u65e5\u5185\u5f97\u5230\u56de\u590d </p> <p></p> <p><p> \u201c\u8ffd\u98ce\u8d76\u6708\u83ab\u505c\u7559\uff0c\u5e73\u829c\u5c3d\u5904\u662f\u6625\u5c71\u201d </p> <p> \u4e00\u8d77\u52a0\u6cb9\uff01 </p></p>  \u5e8f  <p>\u4e24\u5e74\u524d\uff0c\u6211\u5728\u529b\u6263\u4e0a\u5206\u4eab\u4e86\u300a\u5251\u6307 Offer\u300b\u7cfb\u5217\u9898\u89e3\uff0c\u53d7\u5230\u4e86\u8bb8\u591a\u670b\u53cb\u7684\u559c\u7231\u4e0e\u652f\u6301\u3002\u5728\u6b64\u671f\u95f4\uff0c\u6211\u56de\u7b54\u4e86\u4f17\u591a\u8bfb\u8005\u7684\u8bc4\u8bba\u95ee\u9898\uff0c\u5176\u4e2d\u6700\u5e38\u89c1\u7684\u4e00\u4e2a\u95ee\u9898\u662f\u201c\u5982\u4f55\u5165\u95e8\u5b66\u4e60\u7b97\u6cd5\u201d\u3002\u6211\u9010\u6e10\u4e5f\u5bf9\u8fd9\u4e2a\u95ee\u9898\u4ea7\u751f\u4e86\u6d53\u539a\u7684\u5174\u8da3\u3002</p> <p>\u4e24\u773c\u4e00\u62b9\u9ed1\u5730\u5237\u9898\u4f3c\u4e4e\u662f\u6700\u53d7\u6b22\u8fce\u7684\u65b9\u6cd5\uff0c\u7b80\u5355\u76f4\u63a5\u4e14\u6709\u6548\u3002\u7136\u800c\uff0c\u5237\u9898\u5c31\u5982\u540c\u73a9\u201c\u626b\u96f7\u201d\u6e38\u620f\uff0c\u81ea\u5b66\u80fd\u529b\u5f3a\u7684\u540c\u5b66\u80fd\u591f\u987a\u5229\u5730\u5c06\u5730\u96f7\u9010\u4e2a\u6392\u6389\uff0c\u800c\u57fa\u7840\u4e0d\u8db3\u7684\u540c\u5b66\u5f88\u53ef\u80fd\u88ab\u70b8\u7684\u6ee1\u5934\u662f\u5305\uff0c\u5e76\u5728\u632b\u6298\u4e2d\u6b65\u6b65\u9000\u7f29\u3002\u901a\u8bfb\u6559\u6750\u4e66\u7c4d\u4e5f\u662f\u4e00\u79cd\u5e38\u89c1\u505a\u6cd5\uff0c\u4f46\u5bf9\u4e8e\u9762\u5411\u6c42\u804c\u7684\u540c\u5b66\u6765\u8bf4\uff0c\u6bd5\u4e1a\u5b63\u3001\u6295\u9012\u7b80\u5386\u3001\u51c6\u5907\u7b14\u8bd5\u9762\u8bd5\u5df2\u7ecf\u5360\u636e\u4e86\u5927\u90e8\u5206\u7cbe\u529b\uff0c\u539a\u91cd\u7684\u4e66\u7c4d\u5f80\u5f80\u53d8\u6210\u4e86\u4e00\u9879\u8270\u5de8\u7684\u6311\u6218\u3002</p> <p>\u5982\u679c\u4f60\u4e5f\u9762\u4e34\u7c7b\u4f3c\u7684\u56f0\u6270\uff0c\u90a3\u4e48\u5f88\u5e78\u8fd0\u8fd9\u672c\u4e66\u627e\u5230\u4e86\u4f60\u3002\u672c\u4e66\u662f\u6211\u5bf9\u6b64\u95ee\u9898\u7684\u7ed9\u51fa\u7684\u7b54\u6848\uff0c\u867d\u7136\u4e0d\u4e00\u5b9a\u6b63\u786e\uff0c\u4f46\u81f3\u5c11\u662f\u4e00\u6b21\u79ef\u6781\u7684\u5c1d\u8bd5\u3002\u8fd9\u672c\u4e66\u867d\u7136\u4e0d\u8db3\u4ee5\u8ba9\u4f60\u76f4\u63a5\u62ff\u5230 Offer \uff0c\u4f46\u4f1a\u5f15\u5bfc\u4f60\u63a2\u7d22\u6570\u636e\u7ed3\u6784\u4e0e\u7b97\u6cd5\u7684\u201c\u77e5\u8bc6\u5730\u56fe\u201d\uff0c\u5e26\u4f60\u4e86\u89e3\u4e0d\u540c\u201c\u5730\u96f7\u201d\u7684\u5f62\u72b6\u5927\u5c0f\u548c\u5206\u5e03\u4f4d\u7f6e\uff0c\u8ba9\u4f60\u638c\u63e1\u5404\u79cd\u201c\u6392\u96f7\u65b9\u6cd5\u201d\u3002\u6709\u4e86\u8fd9\u4e9b\u672c\u9886\uff0c\u76f8\u4fe1\u4f60\u53ef\u4ee5\u66f4\u52a0\u81ea\u5982\u5730\u5e94\u5bf9\u5237\u9898\u548c\u9605\u8bfb\u6587\u732e\uff0c\u9010\u6b65\u6784\u5efa\u8d77\u5b8c\u6574\u7684\u77e5\u8bc6\u4f53\u7cfb\u3002</p>  \u4f5c\u8005\u7b80\u4ecb  <p>\u9773\u5b87\u680b (Krahets)\uff0c\u5927\u5382\u9ad8\u7ea7\u7b97\u6cd5\u5de5\u7a0b\u5e08\uff0c\u4e0a\u6d77\u4ea4\u901a\u5927\u5b66\u7855\u58eb\u3002\u529b\u6263\uff08LeetCode\uff09\u5168\u7f51\u9605\u8bfb\u91cf\u6700\u9ad8\u535a\u4e3b\uff0c\u5176 LeetBook\u300a\u56fe\u89e3\u7b97\u6cd5\u6570\u636e\u7ed3\u6784\u300b\u5df2\u88ab\u8ba2\u9605 24 \u4e07\u672c\u3002</p>  \u81f4\u8c22  <p>\u672c\u4e66\u5728\u5f00\u6e90\u793e\u533a\u4f17\u591a\u8d21\u732e\u8005\u7684\u5171\u540c\u52aa\u529b\u4e0b\u4e0d\u65ad\u6210\u957f\u3002\u611f\u8c22\u6bcf\u4e00\u4f4d\u6295\u5165\u65f6\u95f4\u4e0e\u7cbe\u529b\u7684\u64b0\u7a3f\u4eba\uff0c\u662f\u4ed6\u4eec\u65e0\u79c1\u5949\u732e\u4f7f\u8fd9\u672c\u4e66\u8d8a\u53d8\u8d8a\u597d\uff0c\u4ed6\u4eec\u662f\uff08\u6309\u7167 GitHub \u81ea\u52a8\u751f\u6210\u7684\u987a\u5e8f\u6392\u5217\uff09\uff1a</p> <p> </p> <p>\u672c\u4e66\u7684\u4ee3\u7801\u5ba1\u9605\u5de5\u4f5c\u7531 Gonglja, gvenusleo, justin\u2010tse, krahets, nuomi1, Reanon, sjinzh \u5b8c\u6210\uff08\u6309\u7167\u9996\u5b57\u6bcd\u987a\u5e8f\u6392\u5217\uff09\u3002\u611f\u8c22\u4ed6\u4eec\u4ed8\u51fa\u7684\u65f6\u95f4\u4e0e\u7cbe\u529b\uff0c\u6b63\u662f\u4ed6\u4eec\u786e\u4fdd\u4e86\u5404\u8bed\u8a00\u4ee3\u7801\u7684\u89c4\u8303\u4e0e\u7edf\u4e00\u3002</p> GongljaC / C++ gvenusleoDart justin-tseJS / TS krahetsJava / Python nuomi1Swift ReanonGo / C sjinzhRust / Zig"},{"location":"chapter_appendix/contribution/","title":"13.2. \u00a0 \u4e00\u8d77\u53c2\u4e0e\u521b\u4f5c","text":"<p>\u5f00\u6e90\u7684\u9b45\u529b</p> <p>\u7eb8\u8d28\u4e66\u7c4d\u7684\u4e24\u6b21\u5370\u5237\u7684\u95f4\u9694\u65f6\u95f4\u5f80\u5f80\u9700\u8981\u6570\u5e74\uff0c\u5185\u5bb9\u66f4\u65b0\u975e\u5e38\u4e0d\u65b9\u4fbf\u3002\u4f46\u5728\u672c\u5f00\u6e90\u4e66\u4e2d\uff0c\u5185\u5bb9\u66f4\u8fed\u7684\u65f6\u95f4\u88ab\u7f29\u77ed\u81f3\u6570\u65e5\u751a\u81f3\u51e0\u4e2a\u5c0f\u65f6\u3002</p> <p>\u7531\u4e8e\u4f5c\u8005\u80fd\u529b\u6709\u9650\uff0c\u4e66\u4e2d\u96be\u514d\u5b58\u5728\u4e00\u4e9b\u9057\u6f0f\u548c\u9519\u8bef\uff0c\u8bf7\u60a8\u8c05\u89e3\u3002\u5982\u679c\u60a8\u53d1\u73b0\u4e86\u7b14\u8bef\u3001\u5931\u6548\u94fe\u63a5\u3001\u5185\u5bb9\u7f3a\u5931\u3001\u6587\u5b57\u6b67\u4e49\u3001\u89e3\u91ca\u4e0d\u6e05\u6670\u6216\u884c\u6587\u7ed3\u6784\u4e0d\u5408\u7406\u7b49\u95ee\u9898\uff0c\u8bf7\u534f\u52a9\u6211\u4eec\u8fdb\u884c\u4fee\u6b63\uff0c\u4ee5\u5e2e\u52a9\u5176\u4ed6\u8bfb\u8005\u83b7\u5f97\u66f4\u4f18\u8d28\u7684\u5b66\u4e60\u8d44\u6e90\u3002\u6240\u6709\u64b0\u7a3f\u4eba\u5c06\u5728\u4ed3\u5e93\u548c\u7f51\u7ad9\u4e3b\u9875\u4e0a\u5c55\u793a\uff0c\u4ee5\u611f\u8c22\u4ed6\u4eec\u5bf9\u5f00\u6e90\u793e\u533a\u7684\u65e0\u79c1\u5949\u732e\uff01</p>"},{"location":"chapter_appendix/contribution/#1321","title":"13.2.1. \u00a0 \u5185\u5bb9\u5fae\u8c03","text":"<p>\u5728\u6bcf\u4e2a\u9875\u9762\u7684\u53f3\u4e0a\u89d2\u6709\u4e00\u4e2a\u300c\u7f16\u8f91\u300d\u56fe\u6807\uff0c\u60a8\u53ef\u4ee5\u6309\u7167\u4ee5\u4e0b\u6b65\u9aa4\u4fee\u6539\u6587\u672c\u6216\u4ee3\u7801\uff1a</p> <ol> <li>\u70b9\u51fb\u7f16\u8f91\u6309\u94ae\uff0c\u5982\u679c\u9047\u5230\u201c\u9700\u8981 Fork \u6b64\u4ed3\u5e93\u201d\u7684\u63d0\u793a\uff0c\u8bf7\u540c\u610f\u8be5\u64cd\u4f5c\uff1b</li> <li>\u4fee\u6539 Markdown \u6e90\u6587\u4ef6\u5185\u5bb9\uff0c\u5e76\u786e\u4fdd\u5185\u5bb9\u6b63\u786e\uff0c\u540c\u65f6\u5c3d\u91cf\u4fdd\u6301\u6392\u7248\u683c\u5f0f\u7684\u7edf\u4e00\uff1b</li> <li>\u5728\u9875\u9762\u5e95\u90e8\u586b\u5199\u4fee\u6539\u8bf4\u660e\uff0c\u7136\u540e\u70b9\u51fb\u201cPropose file change\u201d\u6309\u94ae\uff1b\u9875\u9762\u8df3\u8f6c\u540e\uff0c\u70b9\u51fb\u201cCreate pull request\u201d\u6309\u94ae\u5373\u53ef\u53d1\u8d77\u62c9\u53d6\u8bf7\u6c42\u3002</li> </ol> <p></p> <p> Fig. \u9875\u9762\u7f16\u8f91\u6309\u952e </p> <p>\u7531\u4e8e\u56fe\u7247\u65e0\u6cd5\u76f4\u63a5\u4fee\u6539\uff0c\u56e0\u6b64\u9700\u8981\u901a\u8fc7\u65b0\u5efa Issue \u6216\u8bc4\u8bba\u7559\u8a00\u6765\u63cf\u8ff0\u56fe\u7247\u95ee\u9898\uff0c\u6211\u4eec\u4f1a\u5c3d\u5feb\u91cd\u65b0\u7ed8\u5236\u5e76\u66ff\u6362\u56fe\u7247\u3002</p>"},{"location":"chapter_appendix/contribution/#1322","title":"13.2.2. \u00a0 \u5185\u5bb9\u521b\u4f5c","text":"<p>\u5982\u679c\u60a8\u6709\u5174\u8da3\u53c2\u4e0e\u6b64\u5f00\u6e90\u9879\u76ee\uff0c\u5305\u62ec\u5c06\u4ee3\u7801\u7ffb\u8bd1\u6210\u5176\u4ed6\u7f16\u7a0b\u8bed\u8a00\u3001\u6269\u5c55\u6587\u7ae0\u5185\u5bb9\u7b49\uff0c\u90a3\u4e48\u9700\u8981\u5b9e\u65bd Pull Request \u5de5\u4f5c\u6d41\u7a0b\uff1a</p> <ol> <li>\u767b\u5f55 GitHub \uff0c\u5c06\u672c\u4ed3\u5e93 Fork \u5230\u4e2a\u4eba\u8d26\u53f7\u4e0b\uff1b</li> <li>\u8fdb\u5165\u60a8\u7684 Fork \u4ed3\u5e93\u7f51\u9875\uff0c\u4f7f\u7528 git clone \u547d\u4ee4\u5c06\u4ed3\u5e93\u514b\u9686\u81f3\u672c\u5730\uff1b</li> <li>\u5728\u672c\u5730\u8fdb\u884c\u5185\u5bb9\u521b\u4f5c\uff0c\u5e76\u901a\u8fc7\u8fd0\u884c\u6d4b\u8bd5\u4ee5\u9a8c\u8bc1\u4ee3\u7801\u7684\u6b63\u786e\u6027\uff1b</li> <li>\u5c06\u672c\u5730\u6240\u505a\u66f4\u6539 Commit \uff0c\u7136\u540e Push \u81f3\u8fdc\u7a0b\u4ed3\u5e93\uff1b</li> <li>\u5237\u65b0\u4ed3\u5e93\u7f51\u9875\uff0c\u70b9\u51fb\u201cCreate pull request\u201d\u6309\u94ae\u5373\u53ef\u53d1\u8d77\u62c9\u53d6\u8bf7\u6c42\uff1b</li> </ol>"},{"location":"chapter_appendix/contribution/#1323-docker","title":"13.2.3. \u00a0 Docker \u90e8\u7f72","text":"<p>\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7 Docker \u6765\u90e8\u7f72\u672c\u9879\u76ee\u3002\u6267\u884c\u4ee5\u4e0b\u811a\u672c\uff0c\u7a0d\u7b49\u7247\u523b\u540e\uff0c\u5373\u53ef\u4f7f\u7528\u6d4f\u89c8\u5668\u6253\u5f00 <code>http://localhost:8000</code> \u6765\u8bbf\u95ee\u672c\u9879\u76ee\u3002</p> <pre><code>git clone https://github.com/krahets/hello-algo.git\ncd hello-algo\ndocker-compose up -d\n</code></pre> <p>\u4f7f\u7528\u4ee5\u4e0b\u547d\u4ee4\u5373\u53ef\u5220\u9664\u90e8\u7f72\u3002</p> <pre><code>docker-compose down\n</code></pre>"},{"location":"chapter_appendix/installation/","title":"13.1. \u00a0 \u7f16\u7a0b\u73af\u5883\u5b89\u88c5","text":""},{"location":"chapter_appendix/installation/#1311-vscode","title":"13.1.1. \u00a0 VSCode","text":"<p>\u672c\u4e66\u63a8\u8350\u4f7f\u7528\u5f00\u6e90\u8f7b\u91cf\u7684 VSCode \u4f5c\u4e3a\u672c\u5730 IDE \uff0c\u4e0b\u8f7d\u5e76\u5b89\u88c5 VSCode \u3002</p>"},{"location":"chapter_appendix/installation/#1312-java","title":"13.1.2. \u00a0 Java \u73af\u5883","text":"<ol> <li>\u4e0b\u8f7d\u5e76\u5b89\u88c5 OpenJDK\uff08\u7248\u672c\u9700\u6ee1\u8db3 &gt; JDK 9\uff09\u3002</li> <li>\u5728 VSCode \u7684\u63d2\u4ef6\u5e02\u573a\u4e2d\u641c\u7d22 <code>java</code> \uff0c\u5b89\u88c5 Extension Pack for Java \u3002</li> </ol>"},{"location":"chapter_appendix/installation/#1313-cc","title":"13.1.3. \u00a0 C/C++ \u73af\u5883","text":"<ol> <li>Windows \u7cfb\u7edf\u9700\u8981\u5b89\u88c5 MinGW\uff08\u914d\u7f6e\u6559\u7a0b\uff09\uff0cMacOS \u81ea\u5e26 Clang \u65e0\u9700\u5b89\u88c5\u3002</li> <li>\u5728 VSCode \u7684\u63d2\u4ef6\u5e02\u573a\u4e2d\u641c\u7d22 <code>c++</code> \uff0c\u5b89\u88c5 C/C++ Extension Pack \u3002</li> <li>\uff08\u53ef\u9009\uff09\u6253\u5f00 Settings \u9875\u9762\uff0c\u641c\u7d22 <code>Clang_format_fallback Style</code> \u4ee3\u7801\u683c\u5f0f\u5316\u9009\u9879\uff0c\u8bbe\u7f6e\u4e3a <code>{ BasedOnStyle: Microsoft, BreakBeforeBraces: Attach }</code> \u3002</li> </ol>"},{"location":"chapter_appendix/installation/#1314-python","title":"13.1.4. \u00a0 Python \u73af\u5883","text":"<ol> <li>\u4e0b\u8f7d\u5e76\u5b89\u88c5 Miniconda3 \u3002</li> <li>\u5728 VSCode \u7684\u63d2\u4ef6\u5e02\u573a\u4e2d\u641c\u7d22 <code>python</code> \uff0c\u5b89\u88c5 Python Extension Pack \u3002</li> <li>\uff08\u53ef\u9009\uff09\u5728\u547d\u4ee4\u884c\u8f93\u5165 <code>pip install black</code> \uff0c\u5b89\u88c5\u4ee3\u7801\u683c\u5f0f\u5316\u5de5\u5177\u3002</li> </ol>"},{"location":"chapter_appendix/installation/#1315-go","title":"13.1.5. \u00a0 Go \u73af\u5883","text":"<ol> <li>\u4e0b\u8f7d\u5e76\u5b89\u88c5 go \u3002</li> <li>\u5728 VSCode \u7684\u63d2\u4ef6\u5e02\u573a\u4e2d\u641c\u7d22 <code>go</code> \uff0c\u5b89\u88c5 Go \u3002</li> <li>\u5feb\u6377\u952e <code>Ctrl + Shift + P</code> \u547c\u51fa\u547d\u4ee4\u680f\uff0c\u8f93\u5165 go \uff0c\u9009\u62e9 <code>Go: Install/Update Tools</code> \uff0c\u5168\u90e8\u52fe\u9009\u5e76\u5b89\u88c5\u5373\u53ef\u3002</li> </ol>"},{"location":"chapter_appendix/installation/#1316-javascript","title":"13.1.6. \u00a0 JavaScript \u73af\u5883","text":"<ol> <li>\u4e0b\u8f7d\u5e76\u5b89\u88c5 node.js \u3002</li> <li>\u5728 VSCode \u7684\u63d2\u4ef6\u5e02\u573a\u4e2d\u641c\u7d22 <code>javascript</code> \uff0c\u5b89\u88c5 JavaScript (ES6) code snippets \u3002</li> <li>\uff08\u53ef\u9009\uff09\u5728 VSCode \u7684\u63d2\u4ef6\u5e02\u573a\u4e2d\u641c\u7d22 <code>Prettier</code> \uff0c\u5b89\u88c5\u4ee3\u7801\u683c\u5f0f\u5316\u5de5\u5177\u3002</li> </ol>"},{"location":"chapter_appendix/installation/#1317-c","title":"13.1.7. \u00a0 C# \u73af\u5883","text":"<ol> <li>\u4e0b\u8f7d\u5e76\u5b89\u88c5 .Net 6.0 \uff1b</li> <li>\u5728 VSCode \u7684\u63d2\u4ef6\u5e02\u573a\u4e2d\u641c\u7d22 <code>c#</code> \uff0c\u5b89\u88c5 c# \u3002</li> </ol>"},{"location":"chapter_appendix/installation/#1318-swift","title":"13.1.8. \u00a0 Swift \u73af\u5883","text":"<ol> <li>\u4e0b\u8f7d\u5e76\u5b89\u88c5 Swift\uff1b</li> <li>\u5728 VSCode \u7684\u63d2\u4ef6\u5e02\u573a\u4e2d\u641c\u7d22 <code>swift</code> \uff0c\u5b89\u88c5 Swift for Visual Studio Code\u3002</li> </ol>"},{"location":"chapter_appendix/installation/#1319-rust","title":"13.1.9. \u00a0 Rust \u73af\u5883","text":"<ol> <li>\u4e0b\u8f7d\u5e76\u5b89\u88c5 Rust\uff1b</li> <li>\u5728 VSCode \u7684\u63d2\u4ef6\u5e02\u573a\u4e2d\u641c\u7d22 <code>rust</code> \uff0c\u5b89\u88c5 rust-analyzer\u3002</li> </ol>"},{"location":"chapter_array_and_linkedlist/","title":"4. \u00a0 \u6570\u7ec4\u4e0e\u94fe\u8868","text":""},{"location":"chapter_array_and_linkedlist/array/","title":"4.1. \u00a0 \u6570\u7ec4","text":"<p>\u300c\u6570\u7ec4 Array\u300d\u662f\u4e00\u79cd\u7ebf\u6027\u6570\u636e\u7ed3\u6784\uff0c\u5176\u5c06\u76f8\u540c\u7c7b\u578b\u5143\u7d20\u5b58\u50a8\u5728\u8fde\u7eed\u7684\u5185\u5b58\u7a7a\u95f4\u4e2d\u3002\u6211\u4eec\u5c06\u5143\u7d20\u5728\u6570\u7ec4\u4e2d\u7684\u4f4d\u7f6e\u79f0\u4e3a\u5143\u7d20\u7684\u300c\u7d22\u5f15 Index\u300d\u3002</p> <p></p> <p> Fig. \u6570\u7ec4\u5b9a\u4e49\u4e0e\u5b58\u50a8\u65b9\u5f0f </p> <p>\u6570\u7ec4\u521d\u59cb\u5316\u3002\u901a\u5e38\u6709\u65e0\u521d\u59cb\u503c\u548c\u7ed9\u5b9a\u521d\u59cb\u503c\u4e24\u79cd\u65b9\u5f0f\uff0c\u6211\u4eec\u53ef\u6839\u636e\u9700\u6c42\u9009\u62e9\u5408\u9002\u7684\u65b9\u6cd5\u3002\u5728\u672a\u7ed9\u5b9a\u521d\u59cb\u503c\u7684\u60c5\u51b5\u4e0b\uff0c\u6570\u7ec4\u7684\u6240\u6709\u5143\u7d20\u901a\u5e38\u4f1a\u88ab\u521d\u59cb\u5316\u4e3a\u9ed8\u8ba4\u503c \\(0\\) \u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart array.java<pre><code>/* \u521d\u59cb\u5316\u6570\u7ec4 */\nint[] arr = new int[5]; // { 0, 0, 0, 0, 0 }\nint[] nums = { 1, 3, 2, 5, 4 };\n</code></pre> array.cpp<pre><code>/* \u521d\u59cb\u5316\u6570\u7ec4 */\n// \u5b58\u50a8\u5728\u6808\u4e0a\nint arr[5];\nint nums[5] { 1, 3, 2, 5, 4 };\n// \u5b58\u50a8\u5728\u5806\u4e0a\nint* arr1 = new int[5];\nint* nums1 = new int[5] { 1, 3, 2, 5, 4 };\n</code></pre> array.py<pre><code># \u521d\u59cb\u5316\u6570\u7ec4\narr: List[int] = [0] * 5  # [ 0, 0, 0, 0, 0 ]\nnums: List[int] = [1, 3, 2, 5, 4]  \n</code></pre> array.go<pre><code>/* \u521d\u59cb\u5316\u6570\u7ec4 */\nvar arr [5]int\n// \u5728 Go \u4e2d\uff0c\u6307\u5b9a\u957f\u5ea6\u65f6\uff08[5]int\uff09\u4e3a\u6570\u7ec4\uff0c\u4e0d\u6307\u5b9a\u957f\u5ea6\u65f6\uff08[]int\uff09\u4e3a\u5207\u7247\n// \u7531\u4e8e Go \u7684\u6570\u7ec4\u88ab\u8bbe\u8ba1\u4e3a\u5728\u7f16\u8bd1\u671f\u786e\u5b9a\u957f\u5ea6\uff0c\u56e0\u6b64\u53ea\u80fd\u4f7f\u7528\u5e38\u91cf\u6765\u6307\u5b9a\u957f\u5ea6\n// \u4e3a\u4e86\u65b9\u4fbf\u5b9e\u73b0\u6269\u5bb9 extend() \u65b9\u6cd5\uff0c\u4ee5\u4e0b\u5c06\u5207\u7247\uff08Slice\uff09\u770b\u4f5c\u6570\u7ec4\uff08Array\uff09\nnums := []int{1, 3, 2, 5, 4}\n</code></pre> array.js<pre><code>/* \u521d\u59cb\u5316\u6570\u7ec4 */\nvar arr = new Array(5).fill(0);\nvar nums = [1, 3, 2, 5, 4];\n</code></pre> array.ts<pre><code>/* \u521d\u59cb\u5316\u6570\u7ec4 */\nlet arr: number[] = new Array(5).fill(0);\nlet nums: number[] = [1, 3, 2, 5, 4];\n</code></pre> array.c<pre><code>int arr[5] = { 0 }; // { 0, 0, 0, 0, 0 }\nint nums[5] = { 1, 3, 2, 5, 4 };\n</code></pre> array.cs<pre><code>/* \u521d\u59cb\u5316\u6570\u7ec4 */\nint[] arr = new int[5]; // { 0, 0, 0, 0, 0 }\nint[] nums = { 1, 3, 2, 5, 4 };\n</code></pre> array.swift<pre><code>/* \u521d\u59cb\u5316\u6570\u7ec4 */\nlet arr = Array(repeating: 0, count: 5) // [0, 0, 0, 0, 0]\nlet nums = [1, 3, 2, 5, 4]\n</code></pre> array.zig<pre><code>// \u521d\u59cb\u5316\u6570\u7ec4\nvar arr = [_]i32{0} ** 5; // { 0, 0, 0, 0, 0 }\nvar nums = [_]i32{ 1, 3, 2, 5, 4 };\n</code></pre> array.dart<pre><code>/* \u521d\u59cb\u5316\u6570\u7ec4 */\nList&lt;int&gt; arr = List.filled(5, 0); // [0, 0, 0, 0, 0]\nList&lt;int&gt; nums = [1, 3, 2, 5, 4];\n</code></pre>"},{"location":"chapter_array_and_linkedlist/array/#411","title":"4.1.1. \u00a0 \u6570\u7ec4\u4f18\u70b9","text":"<p>\u5728\u6570\u7ec4\u4e2d\u8bbf\u95ee\u5143\u7d20\u975e\u5e38\u9ad8\u6548\u3002\u7531\u4e8e\u6570\u7ec4\u5143\u7d20\u88ab\u5b58\u50a8\u5728\u8fde\u7eed\u7684\u5185\u5b58\u7a7a\u95f4\u4e2d\uff0c\u56e0\u6b64\u8ba1\u7b97\u6570\u7ec4\u5143\u7d20\u7684\u5185\u5b58\u5730\u5740\u975e\u5e38\u5bb9\u6613\u3002\u7ed9\u5b9a\u6570\u7ec4\u9996\u4e2a\u5143\u7d20\u7684\u5730\u5740\u548c\u67d0\u4e2a\u5143\u7d20\u7684\u7d22\u5f15\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u4ee5\u4e0b\u516c\u5f0f\u8ba1\u7b97\u5f97\u5230\u8be5\u5143\u7d20\u7684\u5185\u5b58\u5730\u5740\uff0c\u4ece\u800c\u76f4\u63a5\u8bbf\u95ee\u6b64\u5143\u7d20\u3002</p> <p></p> <p> Fig. \u6570\u7ec4\u5143\u7d20\u7684\u5185\u5b58\u5730\u5740\u8ba1\u7b97 </p> <pre><code># \u5143\u7d20\u5185\u5b58\u5730\u5740 = \u6570\u7ec4\u5185\u5b58\u5730\u5740 + \u5143\u7d20\u957f\u5ea6 * \u5143\u7d20\u7d22\u5f15\nelementAddr = firtstElementAddr + elementLength * elementIndex\n</code></pre> <p>\u4e3a\u4ec0\u4e48\u6570\u7ec4\u5143\u7d20\u7684\u7d22\u5f15\u8981\u4ece \\(0\\) \u5f00\u59cb\u7f16\u53f7\u5462\uff1f</p> <p>\u89c2\u5bdf\u4e0a\u56fe\uff0c\u6211\u4eec\u53d1\u73b0\u6570\u7ec4\u9996\u4e2a\u5143\u7d20\u7684\u7d22\u5f15\u4e3a \\(0\\) \uff0c\u8fd9\u4f3c\u4e4e\u6709\u4e9b\u53cd\u76f4\u89c9\uff0c\u56e0\u4e3a\u4ece \\(1\\) \u5f00\u59cb\u8ba1\u6570\u4f1a\u66f4\u81ea\u7136\u3002</p> <p>\u7136\u800c\uff0c\u4ece\u5730\u5740\u8ba1\u7b97\u516c\u5f0f\u7684\u89d2\u5ea6\u770b\uff0c\u7d22\u5f15\u672c\u8d28\u4e0a\u8868\u793a\u7684\u662f\u5185\u5b58\u5730\u5740\u7684\u504f\u79fb\u91cf\u3002\u9996\u4e2a\u5143\u7d20\u7684\u5730\u5740\u504f\u79fb\u91cf\u662f \\(0\\) \uff0c\u56e0\u6b64\u7d22\u5f15\u4e3a \\(0\\) \u4e5f\u662f\u5408\u7406\u7684\u3002</p> <p>\u8bbf\u95ee\u5143\u7d20\u7684\u9ad8\u6548\u6027\u5e26\u6765\u4e86\u8bf8\u591a\u4fbf\u5229\u3002\u4f8b\u5982\uff0c\u6211\u4eec\u53ef\u4ee5\u5728 \\(O(1)\\) \u65f6\u95f4\u5185\u968f\u673a\u83b7\u53d6\u6570\u7ec4\u4e2d\u7684\u4efb\u610f\u4e00\u4e2a\u5143\u7d20\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart array.java<pre><code>/* \u968f\u673a\u8fd4\u56de\u4e00\u4e2a\u6570\u7ec4\u5143\u7d20 */\nint randomAccess(int[] nums) {\n// \u5728\u533a\u95f4 [0, nums.length) \u4e2d\u968f\u673a\u62bd\u53d6\u4e00\u4e2a\u6570\u5b57\nint randomIndex = ThreadLocalRandom.current().nextInt(0, nums.length);\n// \u83b7\u53d6\u5e76\u8fd4\u56de\u968f\u673a\u5143\u7d20\nint randomNum = nums[randomIndex];\nreturn randomNum;\n}\n</code></pre> array.cpp<pre><code>/* \u968f\u673a\u8fd4\u56de\u4e00\u4e2a\u6570\u7ec4\u5143\u7d20 */\nint randomAccess(int *nums, int size) {\n// \u5728\u533a\u95f4 [0, size) \u4e2d\u968f\u673a\u62bd\u53d6\u4e00\u4e2a\u6570\u5b57\nint randomIndex = rand() % size;\n// \u83b7\u53d6\u5e76\u8fd4\u56de\u968f\u673a\u5143\u7d20\nint randomNum = nums[randomIndex];\nreturn randomNum;\n}\n</code></pre> array.py<pre><code>def random_access(nums: list[int]) -&gt; int:\n\"\"\"\u968f\u673a\u8bbf\u95ee\u5143\u7d20\"\"\"\n# \u5728\u533a\u95f4 [0, len(nums)-1] \u4e2d\u968f\u673a\u62bd\u53d6\u4e00\u4e2a\u6570\u5b57\nrandom_index = random.randint(0, len(nums) - 1)\n# \u83b7\u53d6\u5e76\u8fd4\u56de\u968f\u673a\u5143\u7d20\nrandom_num = nums[random_index]\nreturn random_num\n</code></pre> array.go<pre><code>/* \u968f\u673a\u8fd4\u56de\u4e00\u4e2a\u6570\u7ec4\u5143\u7d20 */\nfunc randomAccess(nums []int) (randomNum int) {\n// \u5728\u533a\u95f4 [0, nums.length) \u4e2d\u968f\u673a\u62bd\u53d6\u4e00\u4e2a\u6570\u5b57\nrandomIndex := rand.Intn(len(nums))\n// \u83b7\u53d6\u5e76\u8fd4\u56de\u968f\u673a\u5143\u7d20\nrandomNum = nums[randomIndex]\nreturn\n}\n</code></pre> array.js<pre><code>/* \u968f\u673a\u8fd4\u56de\u4e00\u4e2a\u6570\u7ec4\u5143\u7d20 */\nfunction randomAccess(nums) {\n// \u5728\u533a\u95f4 [0, nums.length) \u4e2d\u968f\u673a\u62bd\u53d6\u4e00\u4e2a\u6570\u5b57\nconst random_index = Math.floor(Math.random() * nums.length);\n// \u83b7\u53d6\u5e76\u8fd4\u56de\u968f\u673a\u5143\u7d20\nconst random_num = nums[random_index];\nreturn random_num;\n}\n</code></pre> array.ts<pre><code>/* \u968f\u673a\u8fd4\u56de\u4e00\u4e2a\u6570\u7ec4\u5143\u7d20 */\nfunction randomAccess(nums: number[]): number {\n// \u5728\u533a\u95f4 [0, nums.length) \u4e2d\u968f\u673a\u62bd\u53d6\u4e00\u4e2a\u6570\u5b57\nconst random_index = Math.floor(Math.random() * nums.length);\n// \u83b7\u53d6\u5e76\u8fd4\u56de\u968f\u673a\u5143\u7d20\nconst random_num = nums[random_index];\nreturn random_num;\n}\n</code></pre> array.c<pre><code>/* \u968f\u673a\u8fd4\u56de\u4e00\u4e2a\u6570\u7ec4\u5143\u7d20 */\nint randomAccess(int *nums, int size) {\n// \u5728\u533a\u95f4 [0, size) \u4e2d\u968f\u673a\u62bd\u53d6\u4e00\u4e2a\u6570\u5b57\nint randomIndex = rand() % size;\n// \u83b7\u53d6\u5e76\u8fd4\u56de\u968f\u673a\u5143\u7d20\nint randomNum = nums[randomIndex];\nreturn randomNum;\n}\n</code></pre> array.cs<pre><code>/* \u968f\u673a\u8fd4\u56de\u4e00\u4e2a\u6570\u7ec4\u5143\u7d20 */\nint randomAccess(int[] nums) {\nRandom random = new();\n// \u5728\u533a\u95f4 [0, nums.Length) \u4e2d\u968f\u673a\u62bd\u53d6\u4e00\u4e2a\u6570\u5b57\nint randomIndex = random.Next(nums.Length);\n// \u83b7\u53d6\u5e76\u8fd4\u56de\u968f\u673a\u5143\u7d20\nint randomNum = nums[randomIndex];\nreturn randomNum;\n}\n</code></pre> array.swift<pre><code>/* \u968f\u673a\u8fd4\u56de\u4e00\u4e2a\u6570\u7ec4\u5143\u7d20 */\nfunc randomAccess(nums: [Int]) -&gt; Int {\n// \u5728\u533a\u95f4 [0, nums.count) \u4e2d\u968f\u673a\u62bd\u53d6\u4e00\u4e2a\u6570\u5b57\nlet randomIndex = nums.indices.randomElement()!\n// \u83b7\u53d6\u5e76\u8fd4\u56de\u968f\u673a\u5143\u7d20\nlet randomNum = nums[randomIndex]\nreturn randomNum\n}\n</code></pre> array.zig<pre><code>// \u968f\u673a\u8fd4\u56de\u4e00\u4e2a\u6570\u7ec4\u5143\u7d20\nfn randomAccess(nums: []i32) i32 {\n// \u5728\u533a\u95f4 [0, nums.len) \u4e2d\u968f\u673a\u62bd\u53d6\u4e00\u4e2a\u6574\u6570\nvar randomIndex = std.crypto.random.intRangeLessThan(usize, 0, nums.len);\n// \u83b7\u53d6\u5e76\u8fd4\u56de\u968f\u673a\u5143\u7d20\nvar randomNum = nums[randomIndex];\nreturn randomNum;\n}\n</code></pre> array.dart<pre><code>/* \u968f\u673a\u8fd4\u56de\u4e00\u4e2a\u6570\u7ec4\u5143\u7d20 */\nint randomAccess(List nums) {\n// \u5728\u533a\u95f4 [0, nums.length) \u4e2d\u968f\u673a\u62bd\u53d6\u4e00\u4e2a\u6570\u5b57\nint randomIndex = Random().nextInt(nums.length);\n// \u83b7\u53d6\u5e76\u8fd4\u56de\u968f\u673a\u5143\u7d20\nint randomNum = nums[randomIndex];\nreturn randomNum;\n}\n</code></pre>"},{"location":"chapter_array_and_linkedlist/array/#412","title":"4.1.2. \u00a0 \u6570\u7ec4\u7f3a\u70b9","text":"<p>\u6570\u7ec4\u5728\u521d\u59cb\u5316\u540e\u957f\u5ea6\u4e0d\u53ef\u53d8\u3002\u7531\u4e8e\u7cfb\u7edf\u65e0\u6cd5\u4fdd\u8bc1\u6570\u7ec4\u4e4b\u540e\u7684\u5185\u5b58\u7a7a\u95f4\u662f\u53ef\u7528\u7684\uff0c\u56e0\u6b64\u6570\u7ec4\u957f\u5ea6\u65e0\u6cd5\u6269\u5c55\u3002\u800c\u82e5\u5e0c\u671b\u6269\u5bb9\u6570\u7ec4\uff0c\u5219\u9700\u65b0\u5efa\u4e00\u4e2a\u6570\u7ec4\uff0c\u7136\u540e\u628a\u539f\u6570\u7ec4\u5143\u7d20\u4f9d\u6b21\u62f7\u8d1d\u5230\u65b0\u6570\u7ec4\uff0c\u5728\u6570\u7ec4\u5f88\u5927\u7684\u60c5\u51b5\u4e0b\uff0c\u8fd9\u662f\u975e\u5e38\u8017\u65f6\u7684\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart array.java<pre><code>/* \u6269\u5c55\u6570\u7ec4\u957f\u5ea6 */\nint[] extend(int[] nums, int enlarge) {\n// \u521d\u59cb\u5316\u4e00\u4e2a\u6269\u5c55\u957f\u5ea6\u540e\u7684\u6570\u7ec4\nint[] res = new int[nums.length + enlarge];\n// \u5c06\u539f\u6570\u7ec4\u4e2d\u7684\u6240\u6709\u5143\u7d20\u590d\u5236\u5230\u65b0\u6570\u7ec4\nfor (int i = 0; i &lt; nums.length; i++) {\nres[i] = nums[i];\n}\n// \u8fd4\u56de\u6269\u5c55\u540e\u7684\u65b0\u6570\u7ec4\nreturn res;\n}\n</code></pre> array.cpp<pre><code>/* \u6269\u5c55\u6570\u7ec4\u957f\u5ea6 */\nint *extend(int *nums, int size, int enlarge) {\n// \u521d\u59cb\u5316\u4e00\u4e2a\u6269\u5c55\u957f\u5ea6\u540e\u7684\u6570\u7ec4\nint *res = new int[size + enlarge];\n// \u5c06\u539f\u6570\u7ec4\u4e2d\u7684\u6240\u6709\u5143\u7d20\u590d\u5236\u5230\u65b0\u6570\u7ec4\nfor (int i = 0; i &lt; size; i++) {\nres[i] = nums[i];\n}\n// \u91ca\u653e\u5185\u5b58\ndelete[] nums;\n// \u8fd4\u56de\u6269\u5c55\u540e\u7684\u65b0\u6570\u7ec4\nreturn res;\n}\n</code></pre> array.py<pre><code>def extend(nums: list[int], enlarge: int) -&gt; list[int]:\n\"\"\"\u6269\u5c55\u6570\u7ec4\u957f\u5ea6\"\"\"\n# \u521d\u59cb\u5316\u4e00\u4e2a\u6269\u5c55\u957f\u5ea6\u540e\u7684\u6570\u7ec4\nres = [0] * (len(nums) + enlarge)\n# \u5c06\u539f\u6570\u7ec4\u4e2d\u7684\u6240\u6709\u5143\u7d20\u590d\u5236\u5230\u65b0\u6570\u7ec4\nfor i in range(len(nums)):\nres[i] = nums[i]\n# \u8fd4\u56de\u6269\u5c55\u540e\u7684\u65b0\u6570\u7ec4\nreturn res\n</code></pre> array.go<pre><code>/* \u6269\u5c55\u6570\u7ec4\u957f\u5ea6 */\nfunc extend(nums []int, enlarge int) []int {\n// \u521d\u59cb\u5316\u4e00\u4e2a\u6269\u5c55\u957f\u5ea6\u540e\u7684\u6570\u7ec4\nres := make([]int, len(nums)+enlarge)\n// \u5c06\u539f\u6570\u7ec4\u4e2d\u7684\u6240\u6709\u5143\u7d20\u590d\u5236\u5230\u65b0\u6570\u7ec4\nfor i, num := range nums {\nres[i] = num\n}\n// \u8fd4\u56de\u6269\u5c55\u540e\u7684\u65b0\u6570\u7ec4\nreturn res\n}\n</code></pre> array.js<pre><code>/* \u6269\u5c55\u6570\u7ec4\u957f\u5ea6 */\n// \u8bf7\u6ce8\u610f\uff0cJavaScript \u7684 Array \u662f\u52a8\u6001\u6570\u7ec4\uff0c\u53ef\u4ee5\u76f4\u63a5\u6269\u5c55\n// \u4e3a\u4e86\u65b9\u4fbf\u5b66\u4e60\uff0c\u672c\u51fd\u6570\u5c06 Array \u770b\u4f5c\u662f\u957f\u5ea6\u4e0d\u53ef\u53d8\u7684\u6570\u7ec4\nfunction extend(nums, enlarge) {\n// \u521d\u59cb\u5316\u4e00\u4e2a\u6269\u5c55\u957f\u5ea6\u540e\u7684\u6570\u7ec4\nconst res = new Array(nums.length + enlarge).fill(0);\n// \u5c06\u539f\u6570\u7ec4\u4e2d\u7684\u6240\u6709\u5143\u7d20\u590d\u5236\u5230\u65b0\u6570\u7ec4\nfor (let i = 0; i &lt; nums.length; i++) {\nres[i] = nums[i];\n}\n// \u8fd4\u56de\u6269\u5c55\u540e\u7684\u65b0\u6570\u7ec4\nreturn res;\n}\n</code></pre> array.ts<pre><code>/* \u6269\u5c55\u6570\u7ec4\u957f\u5ea6 */\n// \u8bf7\u6ce8\u610f\uff0cTypeScript \u7684 Array \u662f\u52a8\u6001\u6570\u7ec4\uff0c\u53ef\u4ee5\u76f4\u63a5\u6269\u5c55\n// \u4e3a\u4e86\u65b9\u4fbf\u5b66\u4e60\uff0c\u672c\u51fd\u6570\u5c06 Array \u770b\u4f5c\u662f\u957f\u5ea6\u4e0d\u53ef\u53d8\u7684\u6570\u7ec4\nfunction extend(nums: number[], enlarge: number): number[] {\n// \u521d\u59cb\u5316\u4e00\u4e2a\u6269\u5c55\u957f\u5ea6\u540e\u7684\u6570\u7ec4\nconst res = new Array(nums.length + enlarge).fill(0);\n// \u5c06\u539f\u6570\u7ec4\u4e2d\u7684\u6240\u6709\u5143\u7d20\u590d\u5236\u5230\u65b0\u6570\u7ec4\nfor (let i = 0; i &lt; nums.length; i++) {\nres[i] = nums[i];\n}\n// \u8fd4\u56de\u6269\u5c55\u540e\u7684\u65b0\u6570\u7ec4\nreturn res;\n}\n</code></pre> array.c<pre><code>/* \u6269\u5c55\u6570\u7ec4\u957f\u5ea6 */\nint *extend(int *nums, int size, int enlarge) {\n// \u521d\u59cb\u5316\u4e00\u4e2a\u6269\u5c55\u957f\u5ea6\u540e\u7684\u6570\u7ec4\nint *res = (int *)malloc(sizeof(int) * (size + enlarge));\n// \u5c06\u539f\u6570\u7ec4\u4e2d\u7684\u6240\u6709\u5143\u7d20\u590d\u5236\u5230\u65b0\u6570\u7ec4\nfor (int i = 0; i &lt; size; i++) {\nres[i] = nums[i];\n}\n// \u521d\u59cb\u5316\u6269\u5c55\u540e\u7684\u7a7a\u95f4\nfor (int i = size; i &lt; size + enlarge; i++) {\nres[i] = 0;\n}\n// \u8fd4\u56de\u6269\u5c55\u540e\u7684\u65b0\u6570\u7ec4\nreturn res;\n}\n</code></pre> array.cs<pre><code>/* \u6269\u5c55\u6570\u7ec4\u957f\u5ea6 */\nint[] extend(int[] nums, int enlarge) {\n// \u521d\u59cb\u5316\u4e00\u4e2a\u6269\u5c55\u957f\u5ea6\u540e\u7684\u6570\u7ec4\nint[] res = new int[nums.Length + enlarge];\n// \u5c06\u539f\u6570\u7ec4\u4e2d\u7684\u6240\u6709\u5143\u7d20\u590d\u5236\u5230\u65b0\u6570\u7ec4\nfor (int i = 0; i &lt; nums.Length; i++) {\nres[i] = nums[i];\n}\n// \u8fd4\u56de\u6269\u5c55\u540e\u7684\u65b0\u6570\u7ec4\nreturn res;\n}\n</code></pre> array.swift<pre><code>/* \u6269\u5c55\u6570\u7ec4\u957f\u5ea6 */\nfunc extend(nums: [Int], enlarge: Int) -&gt; [Int] {\n// \u521d\u59cb\u5316\u4e00\u4e2a\u6269\u5c55\u957f\u5ea6\u540e\u7684\u6570\u7ec4\nvar res = Array(repeating: 0, count: nums.count + enlarge)\n// \u5c06\u539f\u6570\u7ec4\u4e2d\u7684\u6240\u6709\u5143\u7d20\u590d\u5236\u5230\u65b0\u6570\u7ec4\nfor i in nums.indices {\nres[i] = nums[i]\n}\n// \u8fd4\u56de\u6269\u5c55\u540e\u7684\u65b0\u6570\u7ec4\nreturn res\n}\n</code></pre> array.zig<pre><code>// \u6269\u5c55\u6570\u7ec4\u957f\u5ea6\nfn extend(mem_allocator: std.mem.Allocator, nums: []i32, enlarge: usize) ![]i32 {\n// \u521d\u59cb\u5316\u4e00\u4e2a\u6269\u5c55\u957f\u5ea6\u540e\u7684\u6570\u7ec4\nvar res = try mem_allocator.alloc(i32, nums.len + enlarge);\nstd.mem.set(i32, res, 0);\n// \u5c06\u539f\u6570\u7ec4\u4e2d\u7684\u6240\u6709\u5143\u7d20\u590d\u5236\u5230\u65b0\u6570\u7ec4\nstd.mem.copy(i32, res, nums);\n// \u8fd4\u56de\u6269\u5c55\u540e\u7684\u65b0\u6570\u7ec4\nreturn res;\n}\n</code></pre> array.dart<pre><code>/* \u6269\u5c55\u6570\u7ec4\u957f\u5ea6 */\nList extend(List nums, int enlarge) {\n// \u521d\u59cb\u5316\u4e00\u4e2a\u6269\u5c55\u957f\u5ea6\u540e\u7684\u6570\u7ec4\nList&lt;int&gt; res = List.filled(nums.length + enlarge, 0);\n// \u5c06\u539f\u6570\u7ec4\u4e2d\u7684\u6240\u6709\u5143\u7d20\u590d\u5236\u5230\u65b0\u6570\u7ec4\nfor (var i = 0; i &lt; nums.length; i++) {\nres[i] = nums[i];\n}\n// \u8fd4\u56de\u6269\u5c55\u540e\u7684\u65b0\u6570\u7ec4\nreturn res;\n}\n</code></pre> <p>\u6570\u7ec4\u4e2d\u63d2\u5165\u6216\u5220\u9664\u5143\u7d20\u6548\u7387\u4f4e\u4e0b\u3002\u5982\u679c\u6211\u4eec\u60f3\u8981\u5728\u6570\u7ec4\u4e2d\u95f4\u63d2\u5165\u4e00\u4e2a\u5143\u7d20\uff0c\u7531\u4e8e\u6570\u7ec4\u5143\u7d20\u5728\u5185\u5b58\u4e2d\u662f\u201c\u7d27\u6328\u7740\u7684\u201d\uff0c\u5b83\u4eec\u4e4b\u95f4\u6ca1\u6709\u7a7a\u95f4\u518d\u653e\u4efb\u4f55\u6570\u636e\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u4e0d\u5f97\u4e0d\u5c06\u6b64\u7d22\u5f15\u4e4b\u540e\u7684\u6240\u6709\u5143\u7d20\u90fd\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\uff0c\u7136\u540e\u518d\u628a\u5143\u7d20\u8d4b\u503c\u7ed9\u8be5\u7d22\u5f15\u3002</p> <p></p> <p> Fig. \u6570\u7ec4\u63d2\u5165\u5143\u7d20 </p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart array.java<pre><code>/* \u5728\u6570\u7ec4\u7684\u7d22\u5f15 index \u5904\u63d2\u5165\u5143\u7d20 num */\nvoid insert(int[] nums, int num, int index) {\n// \u628a\u7d22\u5f15 index \u4ee5\u53ca\u4e4b\u540e\u7684\u6240\u6709\u5143\u7d20\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\nfor (int i = nums.length - 1; i &gt; index; i--) {\nnums[i] = nums[i - 1];\n}\n// \u5c06 num \u8d4b\u7ed9 index \u5904\u5143\u7d20\nnums[index] = num;\n}\n</code></pre> array.cpp<pre><code>/* \u5728\u6570\u7ec4\u7684\u7d22\u5f15 index \u5904\u63d2\u5165\u5143\u7d20 num */\nvoid insert(int *nums, int size, int num, int index) {\n// \u628a\u7d22\u5f15 index \u4ee5\u53ca\u4e4b\u540e\u7684\u6240\u6709\u5143\u7d20\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\nfor (int i = size - 1; i &gt; index; i--) {\nnums[i] = nums[i - 1];\n}\n// \u5c06 num \u8d4b\u7ed9 index \u5904\u5143\u7d20\nnums[index] = num;\n}\n</code></pre> array.py<pre><code>def insert(nums: list[int], num: int, index: int) -&gt; None:\n\"\"\"\u5728\u6570\u7ec4\u7684\u7d22\u5f15 index \u5904\u63d2\u5165\u5143\u7d20 num\"\"\"\n# \u628a\u7d22\u5f15 index \u4ee5\u53ca\u4e4b\u540e\u7684\u6240\u6709\u5143\u7d20\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\nfor i in range(len(nums) - 1, index, -1):\nnums[i] = nums[i - 1]\n# \u5c06 num \u8d4b\u7ed9 index \u5904\u5143\u7d20\nnums[index] = num\n</code></pre> array.go<pre><code>/* \u5728\u6570\u7ec4\u7684\u7d22\u5f15 index \u5904\u63d2\u5165\u5143\u7d20 num */\nfunc insert(nums []int, num int, index int) {\n// \u628a\u7d22\u5f15 index \u4ee5\u53ca\u4e4b\u540e\u7684\u6240\u6709\u5143\u7d20\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\nfor i := len(nums) - 1; i &gt; index; i-- {\nnums[i] = nums[i-1]\n}\n// \u5c06 num \u8d4b\u7ed9 index \u5904\u5143\u7d20\nnums[index] = num\n}\n</code></pre> array.js<pre><code>/* \u5728\u6570\u7ec4\u7684\u7d22\u5f15 index \u5904\u63d2\u5165\u5143\u7d20 num */\nfunction insert(nums, num, index) {\n// \u628a\u7d22\u5f15 index \u4ee5\u53ca\u4e4b\u540e\u7684\u6240\u6709\u5143\u7d20\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\nfor (let i = nums.length - 1; i &gt; index; i--) {\nnums[i] = nums[i - 1];\n}\n// \u5c06 num \u8d4b\u7ed9 index \u5904\u5143\u7d20\nnums[index] = num;\n}\n</code></pre> array.ts<pre><code>/* \u5728\u6570\u7ec4\u7684\u7d22\u5f15 index \u5904\u63d2\u5165\u5143\u7d20 num */\nfunction insert(nums: number[], num: number, index: number): void {\n// \u628a\u7d22\u5f15 index \u4ee5\u53ca\u4e4b\u540e\u7684\u6240\u6709\u5143\u7d20\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\nfor (let i = nums.length - 1; i &gt; index; i--) {\nnums[i] = nums[i - 1];\n}\n// \u5c06 num \u8d4b\u7ed9 index \u5904\u5143\u7d20\nnums[index] = num;\n}\n</code></pre> array.c<pre><code>/* \u5728\u6570\u7ec4\u7684\u7d22\u5f15 index \u5904\u63d2\u5165\u5143\u7d20 num */\nvoid insert(int *nums, int size, int num, int index) {\n// \u628a\u7d22\u5f15 index \u4ee5\u53ca\u4e4b\u540e\u7684\u6240\u6709\u5143\u7d20\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\nfor (int i = size - 1; i &gt; index; i--) {\nnums[i] = nums[i - 1];\n}\n// \u5c06 num \u8d4b\u7ed9 index \u5904\u5143\u7d20\nnums[index] = num;\n}\n</code></pre> array.cs<pre><code>/* \u5728\u6570\u7ec4\u7684\u7d22\u5f15 index \u5904\u63d2\u5165\u5143\u7d20 num */\nvoid insert(int[] nums, int num, int index) {\n// \u628a\u7d22\u5f15 index \u4ee5\u53ca\u4e4b\u540e\u7684\u6240\u6709\u5143\u7d20\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\nfor (int i = nums.Length - 1; i &gt; index; i--) {\nnums[i] = nums[i - 1];\n}\n// \u5c06 num \u8d4b\u7ed9 index \u5904\u5143\u7d20\nnums[index] = num;\n}\n</code></pre> array.swift<pre><code>/* \u5728\u6570\u7ec4\u7684\u7d22\u5f15 index \u5904\u63d2\u5165\u5143\u7d20 num */\nfunc insert(nums: inout [Int], num: Int, index: Int) {\n// \u628a\u7d22\u5f15 index \u4ee5\u53ca\u4e4b\u540e\u7684\u6240\u6709\u5143\u7d20\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\nfor i in sequence(first: nums.count - 1, next: { $0 &gt; index + 1 ? $0 - 1 : nil }) {\nnums[i] = nums[i - 1]\n}\n// \u5c06 num \u8d4b\u7ed9 index \u5904\u5143\u7d20\nnums[index] = num\n}\n</code></pre> array.zig<pre><code>// \u5728\u6570\u7ec4\u7684\u7d22\u5f15 index \u5904\u63d2\u5165\u5143\u7d20 num\nfn insert(nums: []i32, num: i32, index: usize) void {\n// \u628a\u7d22\u5f15 index \u4ee5\u53ca\u4e4b\u540e\u7684\u6240\u6709\u5143\u7d20\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\nvar i = nums.len - 1;\nwhile (i &gt; index) : (i -= 1) {\nnums[i] = nums[i - 1];\n}\n// \u5c06 num \u8d4b\u7ed9 index \u5904\u5143\u7d20\nnums[index] = num;\n}\n</code></pre> array.dart<pre><code>/* \u5728\u6570\u7ec4\u7684\u7d22\u5f15 index \u5904\u63d2\u5165\u5143\u7d20 num */\nvoid insert(List nums, int num, int index) {\n// \u628a\u7d22\u5f15 index \u4ee5\u53ca\u4e4b\u540e\u7684\u6240\u6709\u5143\u7d20\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\nfor (var i = nums.length - 1; i &gt; index; i--) {\nnums[i] = nums[i - 1];\n}\n// \u5c06 num \u8d4b\u7ed9 index \u5904\u5143\u7d20\nnums[index] = num;\n}\n</code></pre> <p>\u5220\u9664\u5143\u7d20\u4e5f\u7c7b\u4f3c\uff0c\u5982\u679c\u6211\u4eec\u60f3\u8981\u5220\u9664\u7d22\u5f15 \\(i\\) \u5904\u7684\u5143\u7d20\uff0c\u5219\u9700\u8981\u628a\u7d22\u5f15 \\(i\\) \u4e4b\u540e\u7684\u5143\u7d20\u90fd\u5411\u524d\u79fb\u52a8\u4e00\u4f4d\u3002\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u5220\u9664\u5143\u7d20\u540e\uff0c\u539f\u5148\u672b\u5c3e\u7684\u5143\u7d20\u53d8\u5f97\u201c\u65e0\u610f\u4e49\u201d\u4e86\uff0c\u6211\u4eec\u65e0\u9700\u7279\u610f\u53bb\u4fee\u6539\u5b83\u3002</p> <p></p> <p> Fig. \u6570\u7ec4\u5220\u9664\u5143\u7d20 </p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart array.java<pre><code>/* \u5220\u9664\u7d22\u5f15 index \u5904\u5143\u7d20 */\nvoid remove(int[] nums, int index) {\n// \u628a\u7d22\u5f15 index \u4e4b\u540e\u7684\u6240\u6709\u5143\u7d20\u5411\u524d\u79fb\u52a8\u4e00\u4f4d\nfor (int i = index; i &lt; nums.length - 1; i++) {\nnums[i] = nums[i + 1];\n}\n}\n</code></pre> array.cpp<pre><code>/* \u5220\u9664\u7d22\u5f15 index \u5904\u5143\u7d20 */\nvoid remove(int *nums, int size, int index) {\n// \u628a\u7d22\u5f15 index \u4e4b\u540e\u7684\u6240\u6709\u5143\u7d20\u5411\u524d\u79fb\u52a8\u4e00\u4f4d\nfor (int i = index; i &lt; size - 1; i++) {\nnums[i] = nums[i + 1];\n}\n}\n</code></pre> array.py<pre><code>def remove(nums: list[int], index: int) -&gt; None:\n\"\"\"\u5220\u9664\u7d22\u5f15 index \u5904\u5143\u7d20\"\"\"\n# \u628a\u7d22\u5f15 index \u4e4b\u540e\u7684\u6240\u6709\u5143\u7d20\u5411\u524d\u79fb\u52a8\u4e00\u4f4d\nfor i in range(index, len(nums) - 1):\nnums[i] = nums[i + 1]\n</code></pre> array.go<pre><code>/* \u5220\u9664\u7d22\u5f15 index \u5904\u5143\u7d20 */\nfunc remove(nums []int, index int) {\n// \u628a\u7d22\u5f15 index \u4e4b\u540e\u7684\u6240\u6709\u5143\u7d20\u5411\u524d\u79fb\u52a8\u4e00\u4f4d\nfor i := index; i &lt; len(nums)-1; i++ {\nnums[i] = nums[i+1]\n}\n}\n</code></pre> array.js<pre><code>/* \u5220\u9664\u7d22\u5f15 index \u5904\u5143\u7d20 */\nfunction remove(nums, index) {\n// \u628a\u7d22\u5f15 index \u4e4b\u540e\u7684\u6240\u6709\u5143\u7d20\u5411\u524d\u79fb\u52a8\u4e00\u4f4d\nfor (let i = index; i &lt; nums.length - 1; i++) {\nnums[i] = nums[i + 1];\n}\n}\n</code></pre> array.ts<pre><code>/* \u5220\u9664\u7d22\u5f15 index \u5904\u5143\u7d20 */\nfunction remove(nums: number[], index: number): void {\n// \u628a\u7d22\u5f15 index \u4e4b\u540e\u7684\u6240\u6709\u5143\u7d20\u5411\u524d\u79fb\u52a8\u4e00\u4f4d\nfor (let i = index; i &lt; nums.length - 1; i++) {\nnums[i] = nums[i + 1];\n}\n}\n</code></pre> array.c<pre><code>/* \u5220\u9664\u7d22\u5f15 index \u5904\u5143\u7d20 */\n// \u6ce8\u610f\uff1astdio.h \u5360\u7528\u4e86 remove \u5173\u952e\u8bcd\nvoid removeItem(int *nums, int size, int index) {\n// \u628a\u7d22\u5f15 index \u4e4b\u540e\u7684\u6240\u6709\u5143\u7d20\u5411\u524d\u79fb\u52a8\u4e00\u4f4d\nfor (int i = index; i &lt; size - 1; i++) {\nnums[i] = nums[i + 1];\n}\n}\n</code></pre> array.cs<pre><code>/* \u5220\u9664\u7d22\u5f15 index \u5904\u5143\u7d20 */\nvoid remove(int[] nums, int index) {\n// \u628a\u7d22\u5f15 index \u4e4b\u540e\u7684\u6240\u6709\u5143\u7d20\u5411\u524d\u79fb\u52a8\u4e00\u4f4d\nfor (int i = index; i &lt; nums.Length - 1; i++) {\nnums[i] = nums[i + 1];\n}\n}\n</code></pre> array.swift<pre><code>/* \u5220\u9664\u7d22\u5f15 index \u5904\u5143\u7d20 */\nfunc remove(nums: inout [Int], index: Int) {\nlet count = nums.count\n// \u628a\u7d22\u5f15 index \u4e4b\u540e\u7684\u6240\u6709\u5143\u7d20\u5411\u524d\u79fb\u52a8\u4e00\u4f4d\nfor i in sequence(first: index, next: { $0 &lt; count - 1 - 1 ? $0 + 1 : nil }) {\nnums[i] = nums[i + 1]\n}\n}\n</code></pre> array.zig<pre><code>// \u5220\u9664\u7d22\u5f15 index \u5904\u5143\u7d20\nfn remove(nums: []i32, index: usize) void {\n// \u628a\u7d22\u5f15 index \u4e4b\u540e\u7684\u6240\u6709\u5143\u7d20\u5411\u524d\u79fb\u52a8\u4e00\u4f4d\nvar i = index;\nwhile (i &lt; nums.len - 1) : (i += 1) {\nnums[i] = nums[i + 1];\n}\n}\n</code></pre> array.dart<pre><code>/* \u5220\u9664\u7d22\u5f15 index \u5904\u5143\u7d20 */\nvoid remove(List nums, int index) {\n// \u628a\u7d22\u5f15 index \u4e4b\u540e\u7684\u6240\u6709\u5143\u7d20\u5411\u524d\u79fb\u52a8\u4e00\u4f4d\nfor (var i = index; i &lt; nums.length - 1; i++) {\nnums[i] = nums[i + 1];\n}\n}\n</code></pre> <p>\u603b\u7ed3\u6765\u770b\uff0c\u6570\u7ec4\u7684\u63d2\u5165\u4e0e\u5220\u9664\u64cd\u4f5c\u6709\u4ee5\u4e0b\u7f3a\u70b9\uff1a</p> <ul> <li>\u65f6\u95f4\u590d\u6742\u5ea6\u9ad8\uff1a\u6570\u7ec4\u7684\u63d2\u5165\u548c\u5220\u9664\u7684\u5e73\u5747\u65f6\u95f4\u590d\u6742\u5ea6\u5747\u4e3a \\(O(n)\\) \uff0c\u5176\u4e2d \\(n\\) \u4e3a\u6570\u7ec4\u957f\u5ea6\u3002</li> <li>\u4e22\u5931\u5143\u7d20\uff1a\u7531\u4e8e\u6570\u7ec4\u7684\u957f\u5ea6\u4e0d\u53ef\u53d8\uff0c\u56e0\u6b64\u5728\u63d2\u5165\u5143\u7d20\u540e\uff0c\u8d85\u51fa\u6570\u7ec4\u957f\u5ea6\u8303\u56f4\u7684\u5143\u7d20\u4f1a\u4e22\u5931\u3002</li> <li>\u5185\u5b58\u6d6a\u8d39\uff1a\u6211\u4eec\u53ef\u4ee5\u521d\u59cb\u5316\u4e00\u4e2a\u6bd4\u8f83\u957f\u7684\u6570\u7ec4\uff0c\u53ea\u7528\u524d\u9762\u4e00\u90e8\u5206\uff0c\u8fd9\u6837\u5728\u63d2\u5165\u6570\u636e\u65f6\uff0c\u4e22\u5931\u7684\u672b\u5c3e\u5143\u7d20\u90fd\u662f\u6211\u4eec\u4e0d\u5173\u5fc3\u7684\uff0c\u4f46\u8fd9\u6837\u505a\u540c\u65f6\u4e5f\u4f1a\u9020\u6210\u5185\u5b58\u7a7a\u95f4\u7684\u6d6a\u8d39\u3002</li> </ul>"},{"location":"chapter_array_and_linkedlist/array/#413","title":"4.1.3. \u00a0 \u6570\u7ec4\u5e38\u7528\u64cd\u4f5c","text":"<p>\u6570\u7ec4\u904d\u5386\u3002\u4ee5\u4e0b\u4ecb\u7ecd\u4e24\u79cd\u5e38\u7528\u7684\u904d\u5386\u65b9\u6cd5\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart array.java<pre><code>/* \u904d\u5386\u6570\u7ec4 */\nvoid traverse(int[] nums) {\nint count = 0;\n// \u901a\u8fc7\u7d22\u5f15\u904d\u5386\u6570\u7ec4\nfor (int i = 0; i &lt; nums.length; i++) {\ncount++;\n}\n// \u76f4\u63a5\u904d\u5386\u6570\u7ec4\nfor (int num : nums) {\ncount++;\n}\n}\n</code></pre> array.cpp<pre><code>/* \u904d\u5386\u6570\u7ec4 */\nvoid traverse(int *nums, int size) {\nint count = 0;\n// \u901a\u8fc7\u7d22\u5f15\u904d\u5386\u6570\u7ec4\nfor (int i = 0; i &lt; size; i++) {\ncount++;\n}\n}\n</code></pre> array.py<pre><code>def traverse(nums: list[int]) -&gt; None:\n\"\"\"\u904d\u5386\u6570\u7ec4\"\"\"\ncount = 0\n# \u901a\u8fc7\u7d22\u5f15\u904d\u5386\u6570\u7ec4\nfor i in range(len(nums)):\ncount += 1\n# \u76f4\u63a5\u904d\u5386\u6570\u7ec4\nfor num in nums:\ncount += 1\n# \u540c\u65f6\u904d\u5386\u6570\u636e\u7d22\u5f15\u548c\u5143\u7d20\nfor i, num in enumerate(nums):\ncount += 1\n</code></pre> array.go<pre><code>/* \u904d\u5386\u6570\u7ec4 */\nfunc traverse(nums []int) {\ncount := 0\n// \u901a\u8fc7\u7d22\u5f15\u904d\u5386\u6570\u7ec4\nfor i := 0; i &lt; len(nums); i++ {\ncount++\n}\ncount = 0\n// \u76f4\u63a5\u904d\u5386\u6570\u7ec4\nfor range nums {\ncount++\n}\n}\n</code></pre> array.js<pre><code>/* \u904d\u5386\u6570\u7ec4 */\nfunction traverse(nums) {\nlet count = 0;\n// \u901a\u8fc7\u7d22\u5f15\u904d\u5386\u6570\u7ec4\nfor (let i = 0; i &lt; nums.length; i++) {\ncount++;\n}\n// \u76f4\u63a5\u904d\u5386\u6570\u7ec4\nfor (let num of nums) {\ncount += 1;\n}\n}\n</code></pre> array.ts<pre><code>/* \u904d\u5386\u6570\u7ec4 */\nfunction traverse(nums: number[]): void {\nlet count = 0;\n// \u901a\u8fc7\u7d22\u5f15\u904d\u5386\u6570\u7ec4\nfor (let i = 0; i &lt; nums.length; i++) {\ncount++;\n}\n// \u76f4\u63a5\u904d\u5386\u6570\u7ec4\nfor (let num of nums) {\ncount += 1;\n}\n}\n</code></pre> array.c<pre><code>/* \u904d\u5386\u6570\u7ec4 */\nvoid traverse(int *nums, int size) {\nint count = 0;\n// \u901a\u8fc7\u7d22\u5f15\u904d\u5386\u6570\u7ec4\nfor (int i = 0; i &lt; size; i++) {\ncount++;\n}\n}\n</code></pre> array.cs<pre><code>/* \u904d\u5386\u6570\u7ec4 */\nvoid traverse(int[] nums) {\nint count = 0;\n// \u901a\u8fc7\u7d22\u5f15\u904d\u5386\u6570\u7ec4\nfor (int i = 0; i &lt; nums.Length; i++) {\ncount++;\n}\n// \u76f4\u63a5\u904d\u5386\u6570\u7ec4\nforeach (int num in nums) {\ncount++;\n}\n}\n</code></pre> array.swift<pre><code>/* \u904d\u5386\u6570\u7ec4 */\nfunc traverse(nums: [Int]) {\nvar count = 0\n// \u901a\u8fc7\u7d22\u5f15\u904d\u5386\u6570\u7ec4\nfor _ in nums.indices {\ncount += 1\n}\n// \u76f4\u63a5\u904d\u5386\u6570\u7ec4\nfor _ in nums {\ncount += 1\n}\n}\n</code></pre> array.zig<pre><code>// \u904d\u5386\u6570\u7ec4\nfn traverse(nums: []i32) void {\nvar count: i32 = 0;\n// \u901a\u8fc7\u7d22\u5f15\u904d\u5386\u6570\u7ec4\nvar i: i32 = 0;\nwhile (i &lt; nums.len) : (i += 1) {\ncount += 1;\n}\ncount = 0;\n// \u76f4\u63a5\u904d\u5386\u6570\u7ec4\nfor (nums) |_| {\ncount += 1;\n}\n}\n</code></pre> array.dart<pre><code>/* \u904d\u5386\u6570\u7ec4\u5143\u7d20 */\nvoid traverse(List nums) {\nvar count = 0;\n// \u901a\u8fc7\u7d22\u5f15\u904d\u5386\u6570\u7ec4\nfor (var i = 0; i &lt; nums.length; i++) {\ncount++;\n}\n// \u76f4\u63a5\u904d\u5386\u6570\u7ec4\nfor (var num in nums) {\ncount++;\n}\n// \u901a\u8fc7 forEach \u65b9\u6cd5\u904d\u5386\u6570\u7ec4\nnums.forEach((element) {\ncount++;\n});\n}\n</code></pre> <p>\u6570\u7ec4\u67e5\u627e\u3002\u901a\u8fc7\u904d\u5386\u6570\u7ec4\uff0c\u67e5\u627e\u6570\u7ec4\u5185\u7684\u6307\u5b9a\u5143\u7d20\uff0c\u5e76\u8f93\u51fa\u5bf9\u5e94\u7d22\u5f15\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart array.java<pre><code>/* \u5728\u6570\u7ec4\u4e2d\u67e5\u627e\u6307\u5b9a\u5143\u7d20 */\nint find(int[] nums, int target) {\nfor (int i = 0; i &lt; nums.length; i++) {\nif (nums[i] == target)\nreturn i;\n}\nreturn -1;\n}\n</code></pre> array.cpp<pre><code>/* \u5728\u6570\u7ec4\u4e2d\u67e5\u627e\u6307\u5b9a\u5143\u7d20 */\nint find(int *nums, int size, int target) {\nfor (int i = 0; i &lt; size; i++) {\nif (nums[i] == target)\nreturn i;\n}\nreturn -1;\n}\n</code></pre> array.py<pre><code>def find(nums: list[int], target: int) -&gt; int:\n\"\"\"\u5728\u6570\u7ec4\u4e2d\u67e5\u627e\u6307\u5b9a\u5143\u7d20\"\"\"\nfor i in range(len(nums)):\nif nums[i] == target:\nreturn i\nreturn -1\n</code></pre> array.go<pre><code>/* \u5728\u6570\u7ec4\u4e2d\u67e5\u627e\u6307\u5b9a\u5143\u7d20 */\nfunc find(nums []int, target int) (index int) {\nindex = -1\nfor i := 0; i &lt; len(nums); i++ {\nif nums[i] == target {\nindex = i\nbreak\n}\n}\nreturn\n}\n</code></pre> array.js<pre><code>/* \u5728\u6570\u7ec4\u4e2d\u67e5\u627e\u6307\u5b9a\u5143\u7d20 */\nfunction find(nums, target) {\nfor (let i = 0; i &lt; nums.length; i++) {\nif (nums[i] == target) return i;\n}\nreturn -1;\n}\n</code></pre> array.ts<pre><code>/* \u5728\u6570\u7ec4\u4e2d\u67e5\u627e\u6307\u5b9a\u5143\u7d20 */\nfunction find(nums: number[], target: number): number {\nfor (let i = 0; i &lt; nums.length; i++) {\nif (nums[i] === target) {\nreturn i;\n}\n}\nreturn -1;\n}\n</code></pre> array.c<pre><code>/* \u5728\u6570\u7ec4\u4e2d\u67e5\u627e\u6307\u5b9a\u5143\u7d20 */\nint find(int *nums, int size, int target) {\nfor (int i = 0; i &lt; size; i++) {\nif (nums[i] == target)\nreturn i;\n}\nreturn -1;\n}\n</code></pre> array.cs<pre><code>/* \u5728\u6570\u7ec4\u4e2d\u67e5\u627e\u6307\u5b9a\u5143\u7d20 */\nint find(int[] nums, int target) {\nfor (int i = 0; i &lt; nums.Length; i++) {\nif (nums[i] == target)\nreturn i;\n}\nreturn -1;\n}\n</code></pre> array.swift<pre><code>/* \u5728\u6570\u7ec4\u4e2d\u67e5\u627e\u6307\u5b9a\u5143\u7d20 */\nfunc find(nums: [Int], target: Int) -&gt; Int {\nfor i in nums.indices {\nif nums[i] == target {\nreturn i\n}\n}\nreturn -1\n}\n</code></pre> array.zig<pre><code>// \u5728\u6570\u7ec4\u4e2d\u67e5\u627e\u6307\u5b9a\u5143\u7d20\nfn find(nums: []i32, target: i32) i32 {\nfor (nums) |num, i| {\nif (num == target) return @intCast(i32, i);\n}\nreturn -1;\n}\n</code></pre> array.dart<pre><code>/* \u5728\u6570\u7ec4\u4e2d\u67e5\u627e\u6307\u5b9a\u5143\u7d20 */\nint find(List nums, int target) {\nfor (var i = 0; i &lt; nums.length; i++) {\nif (nums[i] == target) return i;\n}\nreturn -1;\n}\n</code></pre>"},{"location":"chapter_array_and_linkedlist/array/#414","title":"4.1.4. \u00a0 \u6570\u7ec4\u5178\u578b\u5e94\u7528","text":"<p>\u968f\u673a\u8bbf\u95ee\u3002\u5982\u679c\u6211\u4eec\u60f3\u8981\u968f\u673a\u62bd\u53d6\u4e00\u4e9b\u6837\u672c\uff0c\u90a3\u4e48\u53ef\u4ee5\u7528\u6570\u7ec4\u5b58\u50a8\uff0c\u5e76\u751f\u6210\u4e00\u4e2a\u968f\u673a\u5e8f\u5217\uff0c\u6839\u636e\u7d22\u5f15\u5b9e\u73b0\u6837\u672c\u7684\u968f\u673a\u62bd\u53d6\u3002</p> <p>\u4e8c\u5206\u67e5\u627e\u3002\u4f8b\u5982\u524d\u6587\u67e5\u5b57\u5178\u7684\u4f8b\u5b50\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u5b57\u5178\u4e2d\u7684\u6240\u6709\u5b57\u6309\u7167\u62fc\u97f3\u987a\u5e8f\u5b58\u50a8\u5728\u6570\u7ec4\u4e2d\uff0c\u7136\u540e\u4f7f\u7528\u4e0e\u65e5\u5e38\u67e5\u7eb8\u8d28\u5b57\u5178\u76f8\u540c\u7684\u201c\u7ffb\u5f00\u4e2d\u95f4\uff0c\u6392\u9664\u4e00\u534a\u201d\u7684\u65b9\u5f0f\uff0c\u6765\u5b9e\u73b0\u4e00\u4e2a\u67e5\u7535\u5b50\u5b57\u5178\u7684\u7b97\u6cd5\u3002</p> <p>\u6df1\u5ea6\u5b66\u4e60\u3002\u795e\u7ecf\u7f51\u7edc\u4e2d\u5927\u91cf\u4f7f\u7528\u4e86\u5411\u91cf\u3001\u77e9\u9635\u3001\u5f20\u91cf\u4e4b\u95f4\u7684\u7ebf\u6027\u4ee3\u6570\u8fd0\u7b97\uff0c\u8fd9\u4e9b\u6570\u636e\u90fd\u662f\u4ee5\u6570\u7ec4\u7684\u5f62\u5f0f\u6784\u5efa\u7684\u3002\u6570\u7ec4\u662f\u795e\u7ecf\u7f51\u7edc\u7f16\u7a0b\u4e2d\u6700\u5e38\u4f7f\u7528\u7684\u6570\u636e\u7ed3\u6784\u3002</p>"},{"location":"chapter_array_and_linkedlist/linked_list/","title":"4.2. \u00a0 \u94fe\u8868","text":"<p>\u5185\u5b58\u7a7a\u95f4\u662f\u6240\u6709\u7a0b\u5e8f\u7684\u516c\u5171\u8d44\u6e90\uff0c\u6392\u9664\u5df2\u88ab\u5360\u7528\u7684\u5185\u5b58\u7a7a\u95f4\uff0c\u7a7a\u95f2\u5185\u5b58\u7a7a\u95f4\u901a\u5e38\u6563\u843d\u5728\u5185\u5b58\u5404\u5904\u3002\u5728\u4e0a\u4e00\u8282\u4e2d\uff0c\u6211\u4eec\u63d0\u5230\u5b58\u50a8\u6570\u7ec4\u7684\u5185\u5b58\u7a7a\u95f4\u5fc5\u987b\u662f\u8fde\u7eed\u7684\uff0c\u800c\u5f53\u6211\u4eec\u9700\u8981\u7533\u8bf7\u4e00\u4e2a\u975e\u5e38\u5927\u7684\u6570\u7ec4\u65f6\uff0c\u7a7a\u95f2\u5185\u5b58\u4e2d\u53ef\u80fd\u6ca1\u6709\u8fd9\u4e48\u5927\u7684\u8fde\u7eed\u7a7a\u95f4\u3002\u4e0e\u6570\u7ec4\u76f8\u6bd4\uff0c\u94fe\u8868\u66f4\u5177\u7075\u6d3b\u6027\uff0c\u5b83\u53ef\u4ee5\u88ab\u5b58\u50a8\u5728\u975e\u8fde\u7eed\u7684\u5185\u5b58\u7a7a\u95f4\u4e2d\u3002</p> <p>\u300c\u94fe\u8868 Linked List\u300d\u662f\u4e00\u79cd\u7ebf\u6027\u6570\u636e\u7ed3\u6784\uff0c\u5176\u6bcf\u4e2a\u5143\u7d20\u90fd\u662f\u4e00\u4e2a\u8282\u70b9\u5bf9\u8c61\uff0c\u5404\u4e2a\u8282\u70b9\u4e4b\u95f4\u901a\u8fc7\u6307\u9488\u8fde\u63a5\uff0c\u4ece\u5f53\u524d\u8282\u70b9\u901a\u8fc7\u6307\u9488\u53ef\u4ee5\u8bbf\u95ee\u5230\u4e0b\u4e00\u4e2a\u8282\u70b9\u3002\u7531\u4e8e\u6307\u9488\u8bb0\u5f55\u4e86\u4e0b\u4e2a\u8282\u70b9\u7684\u5185\u5b58\u5730\u5740\uff0c\u56e0\u6b64\u65e0\u9700\u4fdd\u8bc1\u5185\u5b58\u5730\u5740\u7684\u8fde\u7eed\u6027\uff0c\u4ece\u800c\u53ef\u4ee5\u5c06\u5404\u4e2a\u8282\u70b9\u5206\u6563\u5b58\u50a8\u5728\u5185\u5b58\u5404\u5904\u3002</p> <p>\u94fe\u8868\u300c\u8282\u70b9 Node\u300d\u5305\u542b\u4e24\u9879\u6570\u636e\uff0c\u4e00\u662f\u8282\u70b9\u300c\u503c Value\u300d\uff0c\u4e8c\u662f\u6307\u5411\u4e0b\u4e00\u8282\u70b9\u7684\u300c\u6307\u9488 Pointer\u300d\uff0c\u6216\u79f0\u300c\u5f15\u7528 Reference\u300d\u3002</p> <p></p> <p> Fig. \u94fe\u8868\u5b9a\u4e49\u4e0e\u5b58\u50a8\u65b9\u5f0f </p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart <pre><code>/* \u94fe\u8868\u8282\u70b9\u7c7b */\nclass ListNode {\nint val;        // \u8282\u70b9\u503c\nListNode next;  // \u6307\u5411\u4e0b\u4e00\u8282\u70b9\u7684\u6307\u9488\uff08\u5f15\u7528\uff09\nListNode(int x) { val = x; }  // \u6784\u9020\u51fd\u6570\n}\n</code></pre> <pre><code>/* \u94fe\u8868\u8282\u70b9\u7ed3\u6784\u4f53 */\nstruct ListNode {\nint val;         // \u8282\u70b9\u503c\nListNode *next;  // \u6307\u5411\u4e0b\u4e00\u8282\u70b9\u7684\u6307\u9488\uff08\u5f15\u7528\uff09\nListNode(int x) : val(x), next(nullptr) {}  // \u6784\u9020\u51fd\u6570\n};\n</code></pre> <pre><code>class ListNode:\n\"\"\"\u94fe\u8868\u8282\u70b9\u7c7b\"\"\"\ndef __init__(self, val: int):\nself.val: int = val                  # \u8282\u70b9\u503c\nself.next: Optional[ListNode] = None # \u6307\u5411\u4e0b\u4e00\u8282\u70b9\u7684\u6307\u9488\uff08\u5f15\u7528\uff09\n</code></pre> <pre><code>/* \u94fe\u8868\u8282\u70b9\u7ed3\u6784\u4f53 */\ntype ListNode struct {\nVal  int       // \u8282\u70b9\u503c\nNext *ListNode // \u6307\u5411\u4e0b\u4e00\u8282\u70b9\u7684\u6307\u9488\uff08\u5f15\u7528\uff09\n}\n// NewListNode \u6784\u9020\u51fd\u6570\uff0c\u521b\u5efa\u4e00\u4e2a\u65b0\u7684\u94fe\u8868\nfunc NewListNode(val int) *ListNode {\nreturn &amp;ListNode{\nVal:  val,\nNext: nil,\n}\n}\n</code></pre> <pre><code>/* \u94fe\u8868\u8282\u70b9\u7c7b */\nclass ListNode {\nval;\nnext;\nconstructor(val, next) {\nthis.val = (val === undefined ? 0 : val);       // \u8282\u70b9\u503c\nthis.next = (next === undefined ? null : next); // \u6307\u5411\u4e0b\u4e00\u8282\u70b9\u7684\u5f15\u7528\n}\n}\n</code></pre> <pre><code>/* \u94fe\u8868\u8282\u70b9\u7c7b */\nclass ListNode {\nval: number;\nnext: ListNode | null;\nconstructor(val?: number, next?: ListNode | null) {\nthis.val = val === undefined ? 0 : val;        // \u8282\u70b9\u503c\nthis.next = next === undefined ? null : next;  // \u6307\u5411\u4e0b\u4e00\u8282\u70b9\u7684\u5f15\u7528\n}\n}\n</code></pre> <pre><code>/* \u94fe\u8868\u8282\u70b9\u7ed3\u6784\u4f53 */\nstruct ListNode {\nint val;               // \u8282\u70b9\u503c\nstruct ListNode *next; // \u6307\u5411\u4e0b\u4e00\u8282\u70b9\u7684\u6307\u9488\uff08\u5f15\u7528\uff09\n};\ntypedef struct ListNode ListNode;\n/* \u6784\u9020\u51fd\u6570 */\nListNode *newListNode(int val) {\nListNode *node, *next;\nnode = (ListNode *) malloc(sizeof(ListNode));\nnode-&gt;val = val;\nnode-&gt;next = NULL;\nreturn node;\n}\n</code></pre> <pre><code>/* \u94fe\u8868\u8282\u70b9\u7c7b */\nclass ListNode\n{\nint val;         // \u8282\u70b9\u503c\nListNode next;   // \u6307\u5411\u4e0b\u4e00\u8282\u70b9\u7684\u5f15\u7528\nListNode(int x) =&gt; val = x;  //\u6784\u9020\u51fd\u6570\n}\n</code></pre> <pre><code>/* \u94fe\u8868\u8282\u70b9\u7c7b */\nclass ListNode {\nvar val: Int // \u8282\u70b9\u503c\nvar next: ListNode? // \u6307\u5411\u4e0b\u4e00\u8282\u70b9\u7684\u6307\u9488\uff08\u5f15\u7528\uff09\ninit(x: Int) { // \u6784\u9020\u51fd\u6570\nval = x\n}\n}\n</code></pre> <pre><code>// \u94fe\u8868\u8282\u70b9\u7c7b\npub fn ListNode(comptime T: type) type {\nreturn struct {\nconst Self = @This();\nval: T = 0, // \u8282\u70b9\u503c\nnext: ?*Self = null, // \u6307\u5411\u4e0b\u4e00\u8282\u70b9\u7684\u6307\u9488\uff08\u5f15\u7528\uff09\n// \u6784\u9020\u51fd\u6570\npub fn init(self: *Self, x: i32) void {\nself.val = x;\nself.next = null;\n}\n};\n}\n</code></pre> <pre><code>/* \u94fe\u8868\u8282\u70b9\u7c7b */\nclass ListNode {\nint val; // \u8282\u70b9\u503c\nListNode? next; // \u6307\u5411\u4e0b\u4e00\u8282\u70b9\u7684\u6307\u9488\uff08\u5f15\u7528\uff09\nListNode(this.val, [this.next]); // \u6784\u9020\u51fd\u6570\n}\n</code></pre> <p>\u5c3e\u8282\u70b9\u6307\u5411\u4ec0\u4e48\uff1f</p> <p>\u6211\u4eec\u5c06\u94fe\u8868\u7684\u6700\u540e\u4e00\u4e2a\u8282\u70b9\u79f0\u4e3a\u300c\u5c3e\u8282\u70b9\u300d\uff0c\u5176\u6307\u5411\u7684\u662f\u201c\u7a7a\u201d\uff0c\u5728 Java, C++, Python \u4e2d\u5206\u522b\u8bb0\u4e3a \\(\\text{null}\\) , \\(\\text{nullptr}\\) , \\(\\text{None}\\) \u3002\u5728\u4e0d\u5f15\u8d77\u6b67\u4e49\u7684\u524d\u63d0\u4e0b\uff0c\u672c\u4e66\u90fd\u4f7f\u7528 \\(\\text{null}\\) \u6765\u8868\u793a\u7a7a\u3002</p> <p>\u5982\u4f55\u79f0\u547c\u94fe\u8868\uff1f</p> <p>\u5728\u7f16\u7a0b\u8bed\u8a00\u4e2d\uff0c\u6570\u7ec4\u6574\u4f53\u5c31\u662f\u4e00\u4e2a\u53d8\u91cf\uff0c\u4f8b\u5982\u6570\u7ec4 <code>nums</code> \uff0c\u5305\u542b\u5404\u4e2a\u5143\u7d20 <code>nums[0]</code> , <code>nums[1]</code> \u7b49\u7b49\u3002\u800c\u94fe\u8868\u662f\u7531\u591a\u4e2a\u8282\u70b9\u5bf9\u8c61\u7ec4\u6210\uff0c\u6211\u4eec\u901a\u5e38\u5c06\u5934\u8282\u70b9\u5f53\u4f5c\u94fe\u8868\u7684\u4ee3\u79f0\uff0c\u4f8b\u5982\u5934\u8282\u70b9 <code>head</code> \u548c\u94fe\u8868 <code>head</code> \u5b9e\u9645\u4e0a\u662f\u540c\u4e49\u7684\u3002</p> <p>\u94fe\u8868\u521d\u59cb\u5316\u65b9\u6cd5\u3002\u5efa\u7acb\u94fe\u8868\u5206\u4e3a\u4e24\u6b65\uff0c\u7b2c\u4e00\u6b65\u662f\u521d\u59cb\u5316\u5404\u4e2a\u8282\u70b9\u5bf9\u8c61\uff0c\u7b2c\u4e8c\u6b65\u662f\u6784\u5efa\u5f15\u7528\u6307\u5411\u5173\u7cfb\u3002\u5b8c\u6210\u540e\uff0c\u5373\u53ef\u4ee5\u4ece\u94fe\u8868\u7684\u5934\u8282\u70b9\uff08\u5373\u9996\u4e2a\u8282\u70b9\uff09\u51fa\u53d1\uff0c\u901a\u8fc7\u6307\u9488 <code>next</code> \u4f9d\u6b21\u8bbf\u95ee\u6240\u6709\u8282\u70b9\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart linked_list.java<pre><code>/* \u521d\u59cb\u5316\u94fe\u8868 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */\n// \u521d\u59cb\u5316\u5404\u4e2a\u8282\u70b9 \nListNode n0 = new ListNode(1);\nListNode n1 = new ListNode(3);\nListNode n2 = new ListNode(2);\nListNode n3 = new ListNode(5);\nListNode n4 = new ListNode(4);\n// \u6784\u5efa\u5f15\u7528\u6307\u5411\nn0.next = n1;\nn1.next = n2;\nn2.next = n3;\nn3.next = n4;\n</code></pre> linked_list.cpp<pre><code>/* \u521d\u59cb\u5316\u94fe\u8868 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */\n// \u521d\u59cb\u5316\u5404\u4e2a\u8282\u70b9 \nListNode* n0 = new ListNode(1);\nListNode* n1 = new ListNode(3);\nListNode* n2 = new ListNode(2);\nListNode* n3 = new ListNode(5);\nListNode* n4 = new ListNode(4);\n// \u6784\u5efa\u5f15\u7528\u6307\u5411\nn0-&gt;next = n1;\nn1-&gt;next = n2;\nn2-&gt;next = n3;\nn3-&gt;next = n4;\n</code></pre> linked_list.py<pre><code># \u521d\u59cb\u5316\u94fe\u8868 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4\n# \u521d\u59cb\u5316\u5404\u4e2a\u8282\u70b9 \nn0 = ListNode(1)\nn1 = ListNode(3)\nn2 = ListNode(2)\nn3 = ListNode(5)\nn4 = ListNode(4)\n# \u6784\u5efa\u5f15\u7528\u6307\u5411\nn0.next = n1\nn1.next = n2\nn2.next = n3\nn3.next = n4\n</code></pre> linked_list.go<pre><code>/* \u521d\u59cb\u5316\u94fe\u8868 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */\n// \u521d\u59cb\u5316\u5404\u4e2a\u8282\u70b9\nn0 := NewListNode(1)\nn1 := NewListNode(3)\nn2 := NewListNode(2)\nn3 := NewListNode(5)\nn4 := NewListNode(4)\n// \u6784\u5efa\u5f15\u7528\u6307\u5411\nn0.Next = n1\nn1.Next = n2\nn2.Next = n3\nn3.Next = n4\n</code></pre> linked_list.js<pre><code>/* \u521d\u59cb\u5316\u94fe\u8868 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */\n// \u521d\u59cb\u5316\u5404\u4e2a\u8282\u70b9\nconst n0 = new ListNode(1);\nconst n1 = new ListNode(3);\nconst n2 = new ListNode(2);\nconst n3 = new ListNode(5);\nconst n4 = new ListNode(4);\n// \u6784\u5efa\u5f15\u7528\u6307\u5411\nn0.next = n1;\nn1.next = n2;\nn2.next = n3;\nn3.next = n4;\n</code></pre> linked_list.ts<pre><code>/* \u521d\u59cb\u5316\u94fe\u8868 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */\n// \u521d\u59cb\u5316\u5404\u4e2a\u8282\u70b9\nconst n0 = new ListNode(1);\nconst n1 = new ListNode(3);\nconst n2 = new ListNode(2);\nconst n3 = new ListNode(5);\nconst n4 = new ListNode(4);\n// \u6784\u5efa\u5f15\u7528\u6307\u5411\nn0.next = n1;\nn1.next = n2;\nn2.next = n3;\nn3.next = n4;\n</code></pre> linked_list.c<pre><code>/* \u521d\u59cb\u5316\u94fe\u8868 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */\n// \u521d\u59cb\u5316\u5404\u4e2a\u8282\u70b9 \nListNode* n0 = newListNode(1);\nListNode* n1 = newListNode(3);\nListNode* n2 = newListNode(2);\nListNode* n3 = newListNode(5);\nListNode* n4 = newListNode(4);\n// \u6784\u5efa\u5f15\u7528\u6307\u5411\nn0-&gt;next = n1;\nn1-&gt;next = n2;\nn2-&gt;next = n3;\nn3-&gt;next = n4;\n</code></pre> linked_list.cs<pre><code>/* \u521d\u59cb\u5316\u94fe\u8868 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */\n// \u521d\u59cb\u5316\u5404\u4e2a\u8282\u70b9 \nListNode n0 = new ListNode(1);\nListNode n1 = new ListNode(3);\nListNode n2 = new ListNode(2);\nListNode n3 = new ListNode(5);\nListNode n4 = new ListNode(4);\n// \u6784\u5efa\u5f15\u7528\u6307\u5411\nn0.next = n1;\nn1.next = n2;\nn2.next = n3;\nn3.next = n4;\n</code></pre> linked_list.swift<pre><code>/* \u521d\u59cb\u5316\u94fe\u8868 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */\n// \u521d\u59cb\u5316\u5404\u4e2a\u8282\u70b9\nlet n0 = ListNode(x: 1)\nlet n1 = ListNode(x: 3)\nlet n2 = ListNode(x: 2)\nlet n3 = ListNode(x: 5)\nlet n4 = ListNode(x: 4)\n// \u6784\u5efa\u5f15\u7528\u6307\u5411\nn0.next = n1\nn1.next = n2\nn2.next = n3\nn3.next = n4\n</code></pre> linked_list.zig<pre><code>// \u521d\u59cb\u5316\u94fe\u8868\n// \u521d\u59cb\u5316\u5404\u4e2a\u8282\u70b9 \nvar n0 = inc.ListNode(i32){.val = 1};\nvar n1 = inc.ListNode(i32){.val = 3};\nvar n2 = inc.ListNode(i32){.val = 2};\nvar n3 = inc.ListNode(i32){.val = 5};\nvar n4 = inc.ListNode(i32){.val = 4};\n// \u6784\u5efa\u5f15\u7528\u6307\u5411\nn0.next = &amp;n1;\nn1.next = &amp;n2;\nn2.next = &amp;n3;\nn3.next = &amp;n4;\n</code></pre> linked_list.dart<pre><code>/* \u521d\u59cb\u5316\u94fe\u8868 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */\\\n// \u521d\u59cb\u5316\u5404\u4e2a\u8282\u70b9\nListNode n0 = ListNode(1);\nListNode n1 = ListNode(3);\nListNode n2 = ListNode(2);\nListNode n3 = ListNode(5);\nListNode n4 = ListNode(4);\n// \u6784\u5efa\u5f15\u7528\u6307\u5411\nn0.next = n1;\nn1.next = n2;\nn2.next = n3;\nn3.next = n4;\n</code></pre>"},{"location":"chapter_array_and_linkedlist/linked_list/#421","title":"4.2.1. \u00a0 \u94fe\u8868\u4f18\u70b9","text":"<p>\u94fe\u8868\u4e2d\u63d2\u5165\u4e0e\u5220\u9664\u8282\u70b9\u7684\u64cd\u4f5c\u6548\u7387\u9ad8\u3002\u4f8b\u5982\uff0c\u5982\u679c\u6211\u4eec\u60f3\u5728\u94fe\u8868\u4e2d\u95f4\u7684\u4e24\u4e2a\u8282\u70b9 <code>A</code> , <code>B</code> \u4e4b\u95f4\u63d2\u5165\u4e00\u4e2a\u65b0\u8282\u70b9 <code>P</code> \uff0c\u6211\u4eec\u53ea\u9700\u8981\u6539\u53d8\u4e24\u4e2a\u8282\u70b9\u6307\u9488\u5373\u53ef\uff0c\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(1)\\) \uff1b\u76f8\u6bd4\u4e4b\u4e0b\uff0c\u6570\u7ec4\u7684\u63d2\u5165\u64cd\u4f5c\u6548\u7387\u8981\u4f4e\u5f97\u591a\u3002</p> <p></p> <p> Fig. \u94fe\u8868\u63d2\u5165\u8282\u70b9 </p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart linked_list.java<pre><code>/* \u5728\u94fe\u8868\u7684\u8282\u70b9 n0 \u4e4b\u540e\u63d2\u5165\u8282\u70b9 P */\nvoid insert(ListNode n0, ListNode P) {\nListNode n1 = n0.next;\nP.next = n1;\nn0.next = P;\n}\n</code></pre> linked_list.cpp<pre><code>/* \u5728\u94fe\u8868\u7684\u8282\u70b9 n0 \u4e4b\u540e\u63d2\u5165\u8282\u70b9 P */\nvoid insert(ListNode *n0, ListNode *P) {\nListNode *n1 = n0-&gt;next;\nP-&gt;next = n1;\nn0-&gt;next = P;\n}\n</code></pre> linked_list.py<pre><code>def insert(n0: ListNode, P: ListNode) -&gt; None:\n\"\"\"\u5728\u94fe\u8868\u7684\u8282\u70b9 n0 \u4e4b\u540e\u63d2\u5165\u8282\u70b9 P\"\"\"\nn1 = n0.next\nP.next = n1\nn0.next = P\n</code></pre> linked_list.go<pre><code>/* \u5728\u94fe\u8868\u7684\u8282\u70b9 n0 \u4e4b\u540e\u63d2\u5165\u8282\u70b9 P */\nfunc insertNode(n0 *ListNode, P *ListNode) {\nn1 := n0.Next\nP.Next = n1\nn0.Next = P\n}\n</code></pre> linked_list.js<pre><code>/* \u5728\u94fe\u8868\u7684\u8282\u70b9 n0 \u4e4b\u540e\u63d2\u5165\u8282\u70b9 P */\nfunction insert(n0, P) {\nconst n1 = n0.next;\nP.next = n1;\nn0.next = P;\n}\n</code></pre> linked_list.ts<pre><code>/* \u5728\u94fe\u8868\u7684\u8282\u70b9 n0 \u4e4b\u540e\u63d2\u5165\u8282\u70b9 P */\nfunction insert(n0: ListNode, P: ListNode): void {\nconst n1 = n0.next;\nP.next = n1;\nn0.next = P;\n}\n</code></pre> linked_list.c<pre><code>/* \u5728\u94fe\u8868\u7684\u8282\u70b9 n0 \u4e4b\u540e\u63d2\u5165\u8282\u70b9 P */\nvoid insert(ListNode *n0, ListNode *P) {\nListNode *n1 = n0-&gt;next;\nP-&gt;next = n1;\nn0-&gt;next = P;\n}\n</code></pre> linked_list.cs<pre><code>/* \u5728\u94fe\u8868\u7684\u8282\u70b9 n0 \u4e4b\u540e\u63d2\u5165\u8282\u70b9 P */\nvoid insert(ListNode n0, ListNode P) {\nListNode? n1 = n0.next;\nP.next = n1;\nn0.next = P;\n}\n</code></pre> linked_list.swift<pre><code>/* \u5728\u94fe\u8868\u7684\u8282\u70b9 n0 \u4e4b\u540e\u63d2\u5165\u8282\u70b9 P */\nfunc insert(n0: ListNode, P: ListNode) {\nlet n1 = n0.next\nP.next = n1\nn0.next = P\n}\n</code></pre> linked_list.zig<pre><code>// \u5728\u94fe\u8868\u7684\u8282\u70b9 n0 \u4e4b\u540e\u63d2\u5165\u8282\u70b9 P\nfn insert(n0: ?*inc.ListNode(i32), P: ?*inc.ListNode(i32)) void {\nvar n1 = n0.?.next;\nP.?.next = n1;\nn0.?.next = P;\n}\n</code></pre> linked_list.dart<pre><code>/* \u5728\u94fe\u8868\u7684\u8282\u70b9 n0 \u4e4b\u540e\u63d2\u5165\u8282\u70b9 P */\nvoid insert(ListNode n0, ListNode P) {\nListNode? n1 = n0.next;\nP.next = n1;\nn0.next = P;\n}\n</code></pre> <p>\u5728\u94fe\u8868\u4e2d\u5220\u9664\u8282\u70b9\u4e5f\u975e\u5e38\u65b9\u4fbf\uff0c\u53ea\u9700\u6539\u53d8\u4e00\u4e2a\u8282\u70b9\u7684\u6307\u9488\u5373\u53ef\u3002\u5982\u4e0b\u56fe\u6240\u793a\uff0c\u5c3d\u7ba1\u5728\u5220\u9664\u64cd\u4f5c\u5b8c\u6210\u540e\uff0c\u8282\u70b9 <code>P</code> \u4ecd\u7136\u6307\u5411 <code>n1</code> \uff0c\u4f46\u5b9e\u9645\u4e0a <code>P</code> \u5df2\u7ecf\u4e0d\u518d\u5c5e\u4e8e\u6b64\u94fe\u8868\uff0c\u56e0\u4e3a\u904d\u5386\u6b64\u94fe\u8868\u65f6\u65e0\u6cd5\u8bbf\u95ee\u5230 <code>P</code> \u3002</p> <p></p> <p> Fig. \u94fe\u8868\u5220\u9664\u8282\u70b9 </p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart linked_list.java<pre><code>/* \u5220\u9664\u94fe\u8868\u7684\u8282\u70b9 n0 \u4e4b\u540e\u7684\u9996\u4e2a\u8282\u70b9 */\nvoid remove(ListNode n0) {\nif (n0.next == null)\nreturn;\n// n0 -&gt; P -&gt; n1\nListNode P = n0.next;\nListNode n1 = P.next;\nn0.next = n1;\n}\n</code></pre> linked_list.cpp<pre><code>/* \u5220\u9664\u94fe\u8868\u7684\u8282\u70b9 n0 \u4e4b\u540e\u7684\u9996\u4e2a\u8282\u70b9 */\nvoid remove(ListNode *n0) {\nif (n0-&gt;next == nullptr)\nreturn;\n// n0 -&gt; P -&gt; n1\nListNode *P = n0-&gt;next;\nListNode *n1 = P-&gt;next;\nn0-&gt;next = n1;\n// \u91ca\u653e\u5185\u5b58\ndelete P;\n}\n</code></pre> linked_list.py<pre><code>def remove(n0: ListNode) -&gt; None:\n\"\"\"\u5220\u9664\u94fe\u8868\u7684\u8282\u70b9 n0 \u4e4b\u540e\u7684\u9996\u4e2a\u8282\u70b9\"\"\"\nif not n0.next:\nreturn\n# n0 -&gt; P -&gt; n1\nP = n0.next\nn1 = P.next\nn0.next = n1\n</code></pre> linked_list.go<pre><code>/* \u5220\u9664\u94fe\u8868\u7684\u8282\u70b9 n0 \u4e4b\u540e\u7684\u9996\u4e2a\u8282\u70b9 */\nfunc removeNode(n0 *ListNode) {\nif n0.Next == nil {\nreturn\n}\n// n0 -&gt; P -&gt; n1\nP := n0.Next\nn1 := P.Next\nn0.Next = n1\n}\n</code></pre> linked_list.js<pre><code>/* \u5220\u9664\u94fe\u8868\u7684\u8282\u70b9 n0 \u4e4b\u540e\u7684\u9996\u4e2a\u8282\u70b9 */\nfunction remove(n0) {\nif (!n0.next) return;\n// n0 -&gt; P -&gt; n1\nconst P = n0.next;\nconst n1 = P.next;\nn0.next = n1;\n}\n</code></pre> linked_list.ts<pre><code>/* \u5220\u9664\u94fe\u8868\u7684\u8282\u70b9 n0 \u4e4b\u540e\u7684\u9996\u4e2a\u8282\u70b9 */\nfunction remove(n0: ListNode): void {\nif (!n0.next) {\nreturn;\n}\n// n0 -&gt; P -&gt; n1\nconst P = n0.next;\nconst n1 = P.next;\nn0.next = n1;\n}\n</code></pre> linked_list.c<pre><code>/* \u5220\u9664\u94fe\u8868\u7684\u8282\u70b9 n0 \u4e4b\u540e\u7684\u9996\u4e2a\u8282\u70b9 */\n// \u6ce8\u610f\uff1astdio.h \u5360\u7528\u4e86 remove \u5173\u952e\u8bcd\nvoid removeNode(ListNode *n0) {\nif (!n0-&gt;next)\nreturn;\n// n0 -&gt; P -&gt; n1\nListNode *P = n0-&gt;next;\nListNode *n1 = P-&gt;next;\nn0-&gt;next = n1;\n// \u91ca\u653e\u5185\u5b58\nfree(P);\n}\n</code></pre> linked_list.cs<pre><code>/* \u5220\u9664\u94fe\u8868\u7684\u8282\u70b9 n0 \u4e4b\u540e\u7684\u9996\u4e2a\u8282\u70b9 */\nvoid remove(ListNode n0) {\nif (n0.next == null)\nreturn;\n// n0 -&gt; P -&gt; n1\nListNode P = n0.next;\nListNode? n1 = P.next;\nn0.next = n1;\n}\n</code></pre> linked_list.swift<pre><code>/* \u5220\u9664\u94fe\u8868\u7684\u8282\u70b9 n0 \u4e4b\u540e\u7684\u9996\u4e2a\u8282\u70b9 */\nfunc remove(n0: ListNode) {\nif n0.next == nil {\nreturn\n}\n// n0 -&gt; P -&gt; n1\nlet P = n0.next\nlet n1 = P?.next\nn0.next = n1\nP?.next = nil\n}\n</code></pre> linked_list.zig<pre><code>// \u5220\u9664\u94fe\u8868\u7684\u8282\u70b9 n0 \u4e4b\u540e\u7684\u9996\u4e2a\u8282\u70b9\nfn remove(n0: ?*inc.ListNode(i32)) void {\nif (n0.?.next == null) return;\n// n0 -&gt; P -&gt; n1\nvar P = n0.?.next;\nvar n1 = P.?.next;\nn0.?.next = n1;\n}\n</code></pre> linked_list.dart<pre><code>/* \u5220\u9664\u94fe\u8868\u7684\u8282\u70b9 n0 \u4e4b\u540e\u7684\u9996\u4e2a\u8282\u70b9 */\nvoid remove(ListNode n0) {\nif (n0.next == null) return;\n// n0 -&gt; P -&gt; n1\nListNode P = n0.next!;\nListNode? n1 = P.next;\nn0.next = n1;\n}\n</code></pre>"},{"location":"chapter_array_and_linkedlist/linked_list/#422","title":"4.2.2. \u00a0 \u94fe\u8868\u7f3a\u70b9","text":"<p>\u94fe\u8868\u8bbf\u95ee\u8282\u70b9\u6548\u7387\u8f83\u4f4e\u3002\u5982\u4e0a\u8282\u6240\u8ff0\uff0c\u6570\u7ec4\u53ef\u4ee5\u5728 \\(O(1)\\) \u65f6\u95f4\u4e0b\u8bbf\u95ee\u4efb\u610f\u5143\u7d20\u3002\u7136\u800c\uff0c\u94fe\u8868\u65e0\u6cd5\u76f4\u63a5\u8bbf\u95ee\u4efb\u610f\u8282\u70b9\uff0c\u8fd9\u662f\u56e0\u4e3a\u7cfb\u7edf\u9700\u8981\u4ece\u5934\u8282\u70b9\u51fa\u53d1\uff0c\u9010\u4e2a\u5411\u540e\u904d\u5386\u76f4\u81f3\u627e\u5230\u76ee\u6807\u8282\u70b9\u3002\u4f8b\u5982\uff0c\u82e5\u8981\u8bbf\u95ee\u94fe\u8868\u7d22\u5f15\u4e3a <code>index</code>\uff08\u5373\u7b2c <code>index + 1</code> \u4e2a\uff09\u7684\u8282\u70b9\uff0c\u5219\u9700\u8981\u5411\u540e\u904d\u5386 <code>index</code> \u8f6e\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart linked_list.java<pre><code>/* \u8bbf\u95ee\u94fe\u8868\u4e2d\u7d22\u5f15\u4e3a index \u7684\u8282\u70b9 */\nListNode access(ListNode head, int index) {\nfor (int i = 0; i &lt; index; i++) {\nif (head == null)\nreturn null;\nhead = head.next;\n}\nreturn head;\n}\n</code></pre> linked_list.cpp<pre><code>/* \u8bbf\u95ee\u94fe\u8868\u4e2d\u7d22\u5f15\u4e3a index \u7684\u8282\u70b9 */\nListNode *access(ListNode *head, int index) {\nfor (int i = 0; i &lt; index; i++) {\nif (head == nullptr)\nreturn nullptr;\nhead = head-&gt;next;\n}\nreturn head;\n}\n</code></pre> linked_list.py<pre><code>def access(head: ListNode, index: int) -&gt; ListNode | None:\n\"\"\"\u8bbf\u95ee\u94fe\u8868\u4e2d\u7d22\u5f15\u4e3a index \u7684\u8282\u70b9\"\"\"\nfor _ in range(index):\nif not head:\nreturn None\nhead = head.next\nreturn head\n</code></pre> linked_list.go<pre><code>/* \u8bbf\u95ee\u94fe\u8868\u4e2d\u7d22\u5f15\u4e3a index \u7684\u8282\u70b9 */\nfunc access(head *ListNode, index int) *ListNode {\nfor i := 0; i &lt; index; i++ {\nif head == nil {\nreturn nil\n}\nhead = head.Next\n}\nreturn head\n}\n</code></pre> linked_list.js<pre><code>/* \u8bbf\u95ee\u94fe\u8868\u4e2d\u7d22\u5f15\u4e3a index \u7684\u8282\u70b9 */\nfunction access(head, index) {\nfor (let i = 0; i &lt; index; i++) {\nif (!head) {\nreturn null;\n}\nhead = head.next;\n}\nreturn head;\n}\n</code></pre> linked_list.ts<pre><code>/* \u8bbf\u95ee\u94fe\u8868\u4e2d\u7d22\u5f15\u4e3a index \u7684\u8282\u70b9 */\nfunction access(head: ListNode | null, index: number): ListNode | null {\nfor (let i = 0; i &lt; index; i++) {\nif (!head) {\nreturn null;\n}\nhead = head.next;\n}\nreturn head;\n}\n</code></pre> linked_list.c<pre><code>/* \u8bbf\u95ee\u94fe\u8868\u4e2d\u7d22\u5f15\u4e3a index \u7684\u8282\u70b9 */\nListNode *access(ListNode *head, int index) {\nwhile (head &amp;&amp; head-&gt;next &amp;&amp; index) {\nhead = head-&gt;next;\nindex--;\n}\nreturn head;\n}\n</code></pre> linked_list.cs<pre><code>/* \u8bbf\u95ee\u94fe\u8868\u4e2d\u7d22\u5f15\u4e3a index \u7684\u8282\u70b9 */\nListNode? access(ListNode head, int index) {\nfor (int i = 0; i &lt; index; i++) {\nif (head == null)\nreturn null;\nhead = head.next;\n}\nreturn head;\n}\n</code></pre> linked_list.swift<pre><code>/* \u8bbf\u95ee\u94fe\u8868\u4e2d\u7d22\u5f15\u4e3a index \u7684\u8282\u70b9 */\nfunc access(head: ListNode, index: Int) -&gt; ListNode? {\nvar head: ListNode? = head\nfor _ in 0 ..&lt; index {\nif head == nil {\nreturn nil\n}\nhead = head?.next\n}\nreturn head\n}\n</code></pre> linked_list.zig<pre><code>// \u8bbf\u95ee\u94fe\u8868\u4e2d\u7d22\u5f15\u4e3a index \u7684\u8282\u70b9\nfn access(node: ?*inc.ListNode(i32), index: i32) ?*inc.ListNode(i32) {\nvar head = node;\nvar i: i32 = 0;\nwhile (i &lt; index) : (i += 1) {\nhead = head.?.next;\nif (head == null) return null;\n}\nreturn head;\n}\n</code></pre> linked_list.dart<pre><code>/* \u8bbf\u95ee\u94fe\u8868\u4e2d\u7d22\u5f15\u4e3a index \u7684\u8282\u70b9 */\nListNode? access(ListNode? head, int index) {\nfor (var i = 0; i &lt; index; i++) {\nif (head == null) return null;\nhead = head.next;\n}\nreturn head;\n}\n</code></pre> <p>\u94fe\u8868\u7684\u5185\u5b58\u5360\u7528\u8f83\u5927\u3002\u94fe\u8868\u4ee5\u8282\u70b9\u4e3a\u5355\u4f4d\uff0c\u6bcf\u4e2a\u8282\u70b9\u9664\u4e86\u4fdd\u5b58\u503c\u4e4b\u5916\uff0c\u8fd8\u9700\u989d\u5916\u4fdd\u5b58\u6307\u9488\uff08\u5f15\u7528\uff09\u3002\u8fd9\u610f\u5473\u7740\u5728\u76f8\u540c\u6570\u636e\u91cf\u7684\u60c5\u51b5\u4e0b\uff0c\u94fe\u8868\u6bd4\u6570\u7ec4\u9700\u8981\u5360\u7528\u66f4\u591a\u7684\u5185\u5b58\u7a7a\u95f4\u3002</p>"},{"location":"chapter_array_and_linkedlist/linked_list/#423","title":"4.2.3. \u00a0 \u94fe\u8868\u5e38\u7528\u64cd\u4f5c","text":"<p>\u904d\u5386\u94fe\u8868\u67e5\u627e\u3002\u904d\u5386\u94fe\u8868\uff0c\u67e5\u627e\u94fe\u8868\u5185\u503c\u4e3a <code>target</code> \u7684\u8282\u70b9\uff0c\u8f93\u51fa\u8282\u70b9\u5728\u94fe\u8868\u4e2d\u7684\u7d22\u5f15\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart linked_list.java<pre><code>/* \u5728\u94fe\u8868\u4e2d\u67e5\u627e\u503c\u4e3a target \u7684\u9996\u4e2a\u8282\u70b9 */\nint find(ListNode head, int target) {\nint index = 0;\nwhile (head != null) {\nif (head.val == target)\nreturn index;\nhead = head.next;\nindex++;\n}\nreturn -1;\n}\n</code></pre> linked_list.cpp<pre><code>/* \u5728\u94fe\u8868\u4e2d\u67e5\u627e\u503c\u4e3a target \u7684\u9996\u4e2a\u8282\u70b9 */\nint find(ListNode *head, int target) {\nint index = 0;\nwhile (head != nullptr) {\nif (head-&gt;val == target)\nreturn index;\nhead = head-&gt;next;\nindex++;\n}\nreturn -1;\n}\n</code></pre> linked_list.py<pre><code>def find(head: ListNode, target: int) -&gt; int:\n\"\"\"\u5728\u94fe\u8868\u4e2d\u67e5\u627e\u503c\u4e3a target \u7684\u9996\u4e2a\u8282\u70b9\"\"\"\nindex = 0\nwhile head:\nif head.val == target:\nreturn index\nhead = head.next\nindex += 1\nreturn -1\n</code></pre> linked_list.go<pre><code>/* \u5728\u94fe\u8868\u4e2d\u67e5\u627e\u503c\u4e3a target \u7684\u9996\u4e2a\u8282\u70b9 */\nfunc findNode(head *ListNode, target int) int {\nindex := 0\nfor head != nil {\nif head.Val == target {\nreturn index\n}\nhead = head.Next\nindex++\n}\nreturn -1\n}\n</code></pre> linked_list.js<pre><code>/* \u5728\u94fe\u8868\u4e2d\u67e5\u627e\u503c\u4e3a target \u7684\u9996\u4e2a\u8282\u70b9 */\nfunction find(head, target) {\nlet index = 0;\nwhile (head !== null) {\nif (head.val === target) {\nreturn index;\n}\nhead = head.next;\nindex += 1;\n}\nreturn -1;\n}\n</code></pre> linked_list.ts<pre><code>/* \u5728\u94fe\u8868\u4e2d\u67e5\u627e\u503c\u4e3a target \u7684\u9996\u4e2a\u8282\u70b9 */\nfunction find(head: ListNode | null, target: number): number {\nlet index = 0;\nwhile (head !== null) {\nif (head.val === target) {\nreturn index;\n}\nhead = head.next;\nindex += 1;\n}\nreturn -1;\n}\n</code></pre> linked_list.c<pre><code>/* \u5728\u94fe\u8868\u4e2d\u67e5\u627e\u503c\u4e3a target \u7684\u9996\u4e2a\u8282\u70b9 */\nint find(ListNode *head, int target) {\nint index = 0;\nwhile (head) {\nif (head-&gt;val == target)\nreturn index;\nhead = head-&gt;next;\nindex++;\n}\nreturn -1;\n}\n</code></pre> linked_list.cs<pre><code>/* \u5728\u94fe\u8868\u4e2d\u67e5\u627e\u503c\u4e3a target \u7684\u9996\u4e2a\u8282\u70b9 */\nint find(ListNode head, int target) {\nint index = 0;\nwhile (head != null) {\nif (head.val == target)\nreturn index;\nhead = head.next;\nindex++;\n}\nreturn -1;\n}\n</code></pre> linked_list.swift<pre><code>/* \u5728\u94fe\u8868\u4e2d\u67e5\u627e\u503c\u4e3a target \u7684\u9996\u4e2a\u8282\u70b9 */\nfunc find(head: ListNode, target: Int) -&gt; Int {\nvar head: ListNode? = head\nvar index = 0\nwhile head != nil {\nif head?.val == target {\nreturn index\n}\nhead = head?.next\nindex += 1\n}\nreturn -1\n}\n</code></pre> linked_list.zig<pre><code>// \u5728\u94fe\u8868\u4e2d\u67e5\u627e\u503c\u4e3a target \u7684\u9996\u4e2a\u8282\u70b9\nfn find(node: ?*inc.ListNode(i32), target: i32) i32 {\nvar head = node;\nvar index: i32 = 0;\nwhile (head != null) {\nif (head.?.val == target) return index;\nhead = head.?.next;\nindex += 1;\n}\nreturn -1;\n}\n</code></pre> linked_list.dart<pre><code>/* \u5728\u94fe\u8868\u4e2d\u67e5\u627e\u503c\u4e3a target \u7684\u9996\u4e2a\u8282\u70b9 */\nint find(ListNode? head, int target) {\nint index = 0;\nwhile (head != null) {\nif (head.val == target) {\nreturn index;\n}\nhead = head.next;\nindex++;\n}\nreturn -1;\n}\n</code></pre>"},{"location":"chapter_array_and_linkedlist/linked_list/#424","title":"4.2.4. \u00a0 \u5e38\u89c1\u94fe\u8868\u7c7b\u578b","text":"<p>\u5355\u5411\u94fe\u8868\u3002\u5373\u4e0a\u8ff0\u4ecb\u7ecd\u7684\u666e\u901a\u94fe\u8868\u3002\u5355\u5411\u94fe\u8868\u7684\u8282\u70b9\u5305\u542b\u503c\u548c\u6307\u5411\u4e0b\u4e00\u8282\u70b9\u7684\u6307\u9488\uff08\u5f15\u7528\uff09\u4e24\u9879\u6570\u636e\u3002\u6211\u4eec\u5c06\u9996\u4e2a\u8282\u70b9\u79f0\u4e3a\u5934\u8282\u70b9\uff0c\u5c06\u6700\u540e\u4e00\u4e2a\u8282\u70b9\u6210\u4e3a\u5c3e\u8282\u70b9\uff0c\u5c3e\u8282\u70b9\u6307\u5411 \\(\\text{null}\\) \u3002</p> <p>\u73af\u5f62\u94fe\u8868\u3002\u5982\u679c\u6211\u4eec\u4ee4\u5355\u5411\u94fe\u8868\u7684\u5c3e\u8282\u70b9\u6307\u5411\u5934\u8282\u70b9\uff08\u5373\u9996\u5c3e\u76f8\u63a5\uff09\uff0c\u5219\u5f97\u5230\u4e00\u4e2a\u73af\u5f62\u94fe\u8868\u3002\u5728\u73af\u5f62\u94fe\u8868\u4e2d\uff0c\u4efb\u610f\u8282\u70b9\u90fd\u53ef\u4ee5\u89c6\u4f5c\u5934\u8282\u70b9\u3002</p> <p>\u53cc\u5411\u94fe\u8868\u3002\u4e0e\u5355\u5411\u94fe\u8868\u76f8\u6bd4\uff0c\u53cc\u5411\u94fe\u8868\u8bb0\u5f55\u4e86\u4e24\u4e2a\u65b9\u5411\u7684\u6307\u9488\uff08\u5f15\u7528\uff09\u3002\u53cc\u5411\u94fe\u8868\u7684\u8282\u70b9\u5b9a\u4e49\u540c\u65f6\u5305\u542b\u6307\u5411\u540e\u7ee7\u8282\u70b9\uff08\u4e0b\u4e00\u8282\u70b9\uff09\u548c\u524d\u9a71\u8282\u70b9\uff08\u4e0a\u4e00\u8282\u70b9\uff09\u7684\u6307\u9488\u3002\u76f8\u8f83\u4e8e\u5355\u5411\u94fe\u8868\uff0c\u53cc\u5411\u94fe\u8868\u66f4\u5177\u7075\u6d3b\u6027\uff0c\u53ef\u4ee5\u671d\u4e24\u4e2a\u65b9\u5411\u904d\u5386\u94fe\u8868\uff0c\u4f46\u76f8\u5e94\u5730\u4e5f\u9700\u8981\u5360\u7528\u66f4\u591a\u7684\u5185\u5b58\u7a7a\u95f4\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart <pre><code>/* \u53cc\u5411\u94fe\u8868\u8282\u70b9\u7c7b */\nclass ListNode {\nint val;        // \u8282\u70b9\u503c\nListNode next;  // \u6307\u5411\u540e\u7ee7\u8282\u70b9\u7684\u6307\u9488\uff08\u5f15\u7528\uff09\nListNode prev;  // \u6307\u5411\u524d\u9a71\u8282\u70b9\u7684\u6307\u9488\uff08\u5f15\u7528\uff09\nListNode(int x) { val = x; }  // \u6784\u9020\u51fd\u6570\n}\n</code></pre> <pre><code>/* \u53cc\u5411\u94fe\u8868\u8282\u70b9\u7ed3\u6784\u4f53 */\nstruct ListNode {\nint val;         // \u8282\u70b9\u503c\nListNode *next;  // \u6307\u5411\u540e\u7ee7\u8282\u70b9\u7684\u6307\u9488\uff08\u5f15\u7528\uff09\nListNode *prev;  // \u6307\u5411\u524d\u9a71\u8282\u70b9\u7684\u6307\u9488\uff08\u5f15\u7528\uff09\nListNode(int x) : val(x), next(nullptr), prev(nullptr) {}  // \u6784\u9020\u51fd\u6570\n};\n</code></pre> <pre><code>class ListNode:\n\"\"\"\u53cc\u5411\u94fe\u8868\u8282\u70b9\u7c7b\"\"\"\ndef __init__(self, val: int):\nself.val: int = val                   # \u8282\u70b9\u503c\nself.next: Optional[ListNode] = None  # \u6307\u5411\u540e\u7ee7\u8282\u70b9\u7684\u6307\u9488\uff08\u5f15\u7528\uff09\nself.prev: Optional[ListNode] = None  # \u6307\u5411\u524d\u9a71\u8282\u70b9\u7684\u6307\u9488\uff08\u5f15\u7528\uff09\n</code></pre> <pre><code>/* \u53cc\u5411\u94fe\u8868\u8282\u70b9\u7ed3\u6784\u4f53 */\ntype DoublyListNode struct {\nVal  int             // \u8282\u70b9\u503c\nNext *DoublyListNode // \u6307\u5411\u540e\u7ee7\u8282\u70b9\u7684\u6307\u9488\uff08\u5f15\u7528\uff09\nPrev *DoublyListNode // \u6307\u5411\u524d\u9a71\u8282\u70b9\u7684\u6307\u9488\uff08\u5f15\u7528\uff09\n}\n// NewDoublyListNode \u521d\u59cb\u5316\nfunc NewDoublyListNode(val int) *DoublyListNode {\nreturn &amp;DoublyListNode{\nVal:  val,\nNext: nil,\nPrev: nil,\n}\n}\n</code></pre> <pre><code>/* \u53cc\u5411\u94fe\u8868\u8282\u70b9\u7c7b */\nclass ListNode {\nval;\nnext;\nprev;\nconstructor(val, next, prev) {\nthis.val = val  ===  undefined ? 0 : val;        // \u8282\u70b9\u503c\nthis.next = next  ===  undefined ? null : next;  // \u6307\u5411\u540e\u7ee7\u8282\u70b9\u7684\u6307\u9488\uff08\u5f15\u7528\uff09\nthis.prev = prev  ===  undefined ? null : prev;  // \u6307\u5411\u524d\u9a71\u8282\u70b9\u7684\u6307\u9488\uff08\u5f15\u7528\uff09\n}\n}\n</code></pre> <pre><code>/* \u53cc\u5411\u94fe\u8868\u8282\u70b9\u7c7b */\nclass ListNode {\nval: number;\nnext: ListNode | null;\nprev: ListNode | null;\nconstructor(val?: number, next?: ListNode | null, prev?: ListNode | null) {\nthis.val = val  ===  undefined ? 0 : val;        // \u8282\u70b9\u503c\nthis.next = next  ===  undefined ? null : next;  // \u6307\u5411\u540e\u7ee7\u8282\u70b9\u7684\u6307\u9488\uff08\u5f15\u7528\uff09\nthis.prev = prev  ===  undefined ? null : prev;  // \u6307\u5411\u524d\u9a71\u8282\u70b9\u7684\u6307\u9488\uff08\u5f15\u7528\uff09\n}\n}\n</code></pre> <pre><code>/* \u53cc\u5411\u94fe\u8868\u8282\u70b9\u7ed3\u6784\u4f53 */\nstruct ListNode {\nint val;               // \u8282\u70b9\u503c\nstruct ListNode *next; // \u6307\u5411\u540e\u7ee7\u8282\u70b9\u7684\u6307\u9488\uff08\u5f15\u7528\uff09\nstruct ListNode *prev; // \u6307\u5411\u524d\u9a71\u8282\u70b9\u7684\u6307\u9488\uff08\u5f15\u7528\uff09\n};\ntypedef struct ListNode ListNode;\n/* \u6784\u9020\u51fd\u6570 */\nListNode *newListNode(int val) {\nListNode *node, *next;\nnode = (ListNode *) malloc(sizeof(ListNode));\nnode-&gt;val = val;\nnode-&gt;next = NULL;\nnode-&gt;prev = NULL;\nreturn node;\n}\n</code></pre> <pre><code>/* \u53cc\u5411\u94fe\u8868\u8282\u70b9\u7c7b */\nclass ListNode {\nint val;        // \u8282\u70b9\u503c\nListNode next;  // \u6307\u5411\u540e\u7ee7\u8282\u70b9\u7684\u6307\u9488\uff08\u5f15\u7528\uff09\nListNode prev;  // \u6307\u5411\u524d\u9a71\u8282\u70b9\u7684\u6307\u9488\uff08\u5f15\u7528\uff09\nListNode(int x) =&gt; val = x;  // \u6784\u9020\u51fd\u6570\n}\n</code></pre> <pre><code>/* \u53cc\u5411\u94fe\u8868\u8282\u70b9\u7c7b */\nclass ListNode {\nvar val: Int // \u8282\u70b9\u503c\nvar next: ListNode? // \u6307\u5411\u540e\u7ee7\u8282\u70b9\u7684\u6307\u9488\uff08\u5f15\u7528\uff09\nvar prev: ListNode? // \u6307\u5411\u524d\u9a71\u8282\u70b9\u7684\u6307\u9488\uff08\u5f15\u7528\uff09\ninit(x: Int) { // \u6784\u9020\u51fd\u6570\nval = x\n}\n}\n</code></pre> <pre><code>// \u53cc\u5411\u94fe\u8868\u8282\u70b9\u7c7b\npub fn ListNode(comptime T: type) type {\nreturn struct {\nconst Self = @This();\nval: T = 0, // \u8282\u70b9\u503c\nnext: ?*Self = null, // \u6307\u5411\u540e\u7ee7\u8282\u70b9\u7684\u6307\u9488\uff08\u5f15\u7528\uff09\nprev: ?*Self = null, // \u6307\u5411\u524d\u9a71\u8282\u70b9\u7684\u6307\u9488\uff08\u5f15\u7528\uff09\n// \u6784\u9020\u51fd\u6570\npub fn init(self: *Self, x: i32) void {\nself.val = x;\nself.next = null;\nself.prev = null;\n}\n};\n}\n</code></pre> <pre><code>/* \u53cc\u5411\u94fe\u8868\u8282\u70b9\u7c7b */\nclass ListNode {\nint val;        // \u8282\u70b9\u503c\nListNode next;  // \u6307\u5411\u540e\u7ee7\u8282\u70b9\u7684\u6307\u9488\uff08\u5f15\u7528\uff09\nListNode prev;  // \u6307\u5411\u524d\u9a71\u8282\u70b9\u7684\u6307\u9488\uff08\u5f15\u7528\uff09\nListNode(this.val, [this.next, this.prev]);  // \u6784\u9020\u51fd\u6570\n}\n</code></pre> <p></p> <p> Fig. \u5e38\u89c1\u94fe\u8868\u79cd\u7c7b </p>"},{"location":"chapter_array_and_linkedlist/list/","title":"4.3. \u00a0 \u5217\u8868","text":"<p>\u6570\u7ec4\u957f\u5ea6\u4e0d\u53ef\u53d8\u5bfc\u81f4\u5b9e\u7528\u6027\u964d\u4f4e\u3002\u5728\u8bb8\u591a\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u4e8b\u5148\u65e0\u6cd5\u786e\u5b9a\u9700\u8981\u5b58\u50a8\u591a\u5c11\u6570\u636e\uff0c\u8fd9\u4f7f\u6570\u7ec4\u957f\u5ea6\u7684\u9009\u62e9\u53d8\u5f97\u56f0\u96be\u3002\u82e5\u957f\u5ea6\u8fc7\u5c0f\uff0c\u9700\u8981\u5728\u6301\u7eed\u6dfb\u52a0\u6570\u636e\u65f6\u9891\u7e41\u6269\u5bb9\u6570\u7ec4\uff1b\u82e5\u957f\u5ea6\u8fc7\u5927\uff0c\u5219\u4f1a\u9020\u6210\u5185\u5b58\u7a7a\u95f4\u7684\u6d6a\u8d39\u3002</p> <p>\u4e3a\u89e3\u51b3\u6b64\u95ee\u9898\uff0c\u51fa\u73b0\u4e86\u4e00\u79cd\u88ab\u79f0\u4e3a\u300c\u52a8\u6001\u6570\u7ec4 Dynamic Array\u300d\u7684\u6570\u636e\u7ed3\u6784\uff0c\u5373\u957f\u5ea6\u53ef\u53d8\u7684\u6570\u7ec4\uff0c\u4e5f\u5e38\u88ab\u79f0\u4e3a\u300c\u5217\u8868 List\u300d\u3002\u5217\u8868\u57fa\u4e8e\u6570\u7ec4\u5b9e\u73b0\uff0c\u7ee7\u627f\u4e86\u6570\u7ec4\u7684\u4f18\u70b9\uff0c\u5e76\u4e14\u53ef\u4ee5\u5728\u7a0b\u5e8f\u8fd0\u884c\u8fc7\u7a0b\u4e2d\u52a8\u6001\u6269\u5bb9\u3002\u5728\u5217\u8868\u4e2d\uff0c\u6211\u4eec\u53ef\u4ee5\u81ea\u7531\u6dfb\u52a0\u5143\u7d20\uff0c\u800c\u65e0\u9700\u62c5\u5fc3\u8d85\u8fc7\u5bb9\u91cf\u9650\u5236\u3002</p>"},{"location":"chapter_array_and_linkedlist/list/#431","title":"4.3.1. \u00a0 \u5217\u8868\u5e38\u7528\u64cd\u4f5c","text":"<p>\u521d\u59cb\u5316\u5217\u8868\u3002\u901a\u5e38\u6211\u4eec\u4f1a\u4f7f\u7528\u201c\u65e0\u521d\u59cb\u503c\u201d\u548c\u201c\u6709\u521d\u59cb\u503c\u201d\u7684\u4e24\u79cd\u521d\u59cb\u5316\u65b9\u6cd5\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart list.java<pre><code>/* \u521d\u59cb\u5316\u5217\u8868 */\n// \u65e0\u521d\u59cb\u503c\nList&lt;Integer&gt; list1 = new ArrayList&lt;&gt;();\n// \u6709\u521d\u59cb\u503c\uff08\u6ce8\u610f\u6570\u7ec4\u7684\u5143\u7d20\u7c7b\u578b\u9700\u4e3a int[] \u7684\u5305\u88c5\u7c7b Integer[]\uff09\nInteger[] numbers = new Integer[] { 1, 3, 2, 5, 4 };\nList&lt;Integer&gt; list = new ArrayList&lt;&gt;(Arrays.asList(numbers));\n</code></pre> list.cpp<pre><code>/* \u521d\u59cb\u5316\u5217\u8868 */\n// \u9700\u6ce8\u610f\uff0cC++ \u4e2d vector \u5373\u662f\u672c\u6587\u63cf\u8ff0\u7684 list\n// \u65e0\u521d\u59cb\u503c\nvector&lt;int&gt; list1;\n// \u6709\u521d\u59cb\u503c\nvector&lt;int&gt; list = { 1, 3, 2, 5, 4 };\n</code></pre> list.py<pre><code># \u521d\u59cb\u5316\u5217\u8868\n# \u65e0\u521d\u59cb\u503c\nlist1: List[int] = []\n# \u6709\u521d\u59cb\u503c\nlist: List[int] = [1, 3, 2, 5, 4]\n</code></pre> list_test.go<pre><code>/* \u521d\u59cb\u5316\u5217\u8868 */\n// \u65e0\u521d\u59cb\u503c\nlist1 := []int\n// \u6709\u521d\u59cb\u503c\nlist := []int{1, 3, 2, 5, 4}\n</code></pre> list.js<pre><code>/* \u521d\u59cb\u5316\u5217\u8868 */\n// \u65e0\u521d\u59cb\u503c\nconst list1 = [];\n// \u6709\u521d\u59cb\u503c\nconst list = [1, 3, 2, 5, 4];\n</code></pre> list.ts<pre><code>/* \u521d\u59cb\u5316\u5217\u8868 */\n// \u65e0\u521d\u59cb\u503c\nconst list1: number[] = [];\n// \u6709\u521d\u59cb\u503c\nconst list: number[] = [1, 3, 2, 5, 4];\n</code></pre> list.c<pre><code>// C \u672a\u63d0\u4f9b\u5185\u7f6e\u52a8\u6001\u6570\u7ec4\n</code></pre> list.cs<pre><code>/* \u521d\u59cb\u5316\u5217\u8868 */\n// \u65e0\u521d\u59cb\u503c\nList&lt;int&gt; list1 = new ();\n// \u6709\u521d\u59cb\u503c\nint[] numbers = new int[] { 1, 3, 2, 5, 4 };\nList&lt;int&gt; list = numbers.ToList();\n</code></pre> list.swift<pre><code>/* \u521d\u59cb\u5316\u5217\u8868 */\n// \u65e0\u521d\u59cb\u503c\nlet list1: [Int] = []\n// \u6709\u521d\u59cb\u503c\nvar list = [1, 3, 2, 5, 4]\n</code></pre> list.zig<pre><code>// \u521d\u59cb\u5316\u5217\u8868\nvar list = std.ArrayList(i32).init(std.heap.page_allocator);\ndefer list.deinit();\ntry list.appendSlice(&amp;[_]i32{ 1, 3, 2, 5, 4 });\n</code></pre> list.dart<pre><code>/* \u521d\u59cb\u5316\u5217\u8868 */\n// \u65e0\u521d\u59cb\u503c\nList&lt;int&gt; list1 = [];\n// \u6709\u521d\u59cb\u503c\nList&lt;int&gt; list = [1, 3, 2, 5, 4];\n</code></pre> <p>\u8bbf\u95ee\u4e0e\u66f4\u65b0\u5143\u7d20\u3002\u7531\u4e8e\u5217\u8868\u7684\u5e95\u5c42\u6570\u636e\u7ed3\u6784\u662f\u6570\u7ec4\uff0c\u56e0\u6b64\u53ef\u4ee5\u5728 \\(O(1)\\) \u65f6\u95f4\u5185\u8bbf\u95ee\u548c\u66f4\u65b0\u5143\u7d20\uff0c\u6548\u7387\u5f88\u9ad8\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart list.java<pre><code>/* \u8bbf\u95ee\u5143\u7d20 */\nint num = list.get(1);  // \u8bbf\u95ee\u7d22\u5f15 1 \u5904\u7684\u5143\u7d20\n/* \u66f4\u65b0\u5143\u7d20 */\nlist.set(1, 0);  // \u5c06\u7d22\u5f15 1 \u5904\u7684\u5143\u7d20\u66f4\u65b0\u4e3a 0\n</code></pre> list.cpp<pre><code>/* \u8bbf\u95ee\u5143\u7d20 */\nint num = list[1];  // \u8bbf\u95ee\u7d22\u5f15 1 \u5904\u7684\u5143\u7d20\n/* \u66f4\u65b0\u5143\u7d20 */\nlist[1] = 0;  // \u5c06\u7d22\u5f15 1 \u5904\u7684\u5143\u7d20\u66f4\u65b0\u4e3a 0\n</code></pre> list.py<pre><code># \u8bbf\u95ee\u5143\u7d20\nnum: int = list[1]  # \u8bbf\u95ee\u7d22\u5f15 1 \u5904\u7684\u5143\u7d20\n# \u66f4\u65b0\u5143\u7d20\nlist[1] = 0    # \u5c06\u7d22\u5f15 1 \u5904\u7684\u5143\u7d20\u66f4\u65b0\u4e3a 0\n</code></pre> list_test.go<pre><code>/* \u8bbf\u95ee\u5143\u7d20 */\nnum := list[1]  // \u8bbf\u95ee\u7d22\u5f15 1 \u5904\u7684\u5143\u7d20\n/* \u66f4\u65b0\u5143\u7d20 */\nlist[1] = 0     // \u5c06\u7d22\u5f15 1 \u5904\u7684\u5143\u7d20\u66f4\u65b0\u4e3a 0\n</code></pre> list.js<pre><code>/* \u8bbf\u95ee\u5143\u7d20 */\nconst num = list[1];  // \u8bbf\u95ee\u7d22\u5f15 1 \u5904\u7684\u5143\u7d20\n/* \u66f4\u65b0\u5143\u7d20 */\nlist[1] = 0;  // \u5c06\u7d22\u5f15 1 \u5904\u7684\u5143\u7d20\u66f4\u65b0\u4e3a 0\n</code></pre> list.ts<pre><code>/* \u8bbf\u95ee\u5143\u7d20 */\nconst num: number = list[1];  // \u8bbf\u95ee\u7d22\u5f15 1 \u5904\u7684\u5143\u7d20\n/* \u66f4\u65b0\u5143\u7d20 */\nlist[1] = 0;  // \u5c06\u7d22\u5f15 1 \u5904\u7684\u5143\u7d20\u66f4\u65b0\u4e3a 0\n</code></pre> list.c<pre><code>// C \u672a\u63d0\u4f9b\u5185\u7f6e\u52a8\u6001\u6570\u7ec4\n</code></pre> list.cs<pre><code>/* \u8bbf\u95ee\u5143\u7d20 */\nint num = list[1];  // \u8bbf\u95ee\u7d22\u5f15 1 \u5904\u7684\u5143\u7d20\n/* \u66f4\u65b0\u5143\u7d20 */\nlist[1] = 0;  // \u5c06\u7d22\u5f15 1 \u5904\u7684\u5143\u7d20\u66f4\u65b0\u4e3a 0\n</code></pre> list.swift<pre><code>/* \u8bbf\u95ee\u5143\u7d20 */\nlet num = list[1] // \u8bbf\u95ee\u7d22\u5f15 1 \u5904\u7684\u5143\u7d20\n/* \u66f4\u65b0\u5143\u7d20 */\nlist[1] = 0 // \u5c06\u7d22\u5f15 1 \u5904\u7684\u5143\u7d20\u66f4\u65b0\u4e3a 0\n</code></pre> list.zig<pre><code>// \u8bbf\u95ee\u5143\u7d20\nvar num = list.items[1]; // \u8bbf\u95ee\u7d22\u5f15 1 \u5904\u7684\u5143\u7d20\n// \u66f4\u65b0\u5143\u7d20\nlist.items[1] = 0; // \u5c06\u7d22\u5f15 1 \u5904\u7684\u5143\u7d20\u66f4\u65b0\u4e3a 0  \n</code></pre> list.dart<pre><code>/* \u8bbf\u95ee\u5143\u7d20 */\nint num = list[1];  // \u8bbf\u95ee\u7d22\u5f15 1 \u5904\u7684\u5143\u7d20\n/* \u66f4\u65b0\u5143\u7d20 */\nlist[1] = 0;  // \u5c06\u7d22\u5f15 1 \u5904\u7684\u5143\u7d20\u66f4\u65b0\u4e3a 0\n</code></pre> <p>\u5728\u5217\u8868\u4e2d\u6dfb\u52a0\u3001\u63d2\u5165\u3001\u5220\u9664\u5143\u7d20\u3002\u76f8\u8f83\u4e8e\u6570\u7ec4\uff0c\u5217\u8868\u53ef\u4ee5\u81ea\u7531\u5730\u6dfb\u52a0\u4e0e\u5220\u9664\u5143\u7d20\u3002\u5728\u5217\u8868\u5c3e\u90e8\u6dfb\u52a0\u5143\u7d20\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(1)\\) \uff0c\u4f46\u63d2\u5165\u548c\u5220\u9664\u5143\u7d20\u7684\u6548\u7387\u4ecd\u4e0e\u6570\u7ec4\u76f8\u540c\uff0c\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(N)\\) \u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart list.java<pre><code>/* \u6e05\u7a7a\u5217\u8868 */\nlist.clear();\n/* \u5c3e\u90e8\u6dfb\u52a0\u5143\u7d20 */\nlist.add(1);\nlist.add(3);\nlist.add(2);\nlist.add(5);\nlist.add(4);\n/* \u4e2d\u95f4\u63d2\u5165\u5143\u7d20 */\nlist.add(3, 6);  // \u5728\u7d22\u5f15 3 \u5904\u63d2\u5165\u6570\u5b57 6\n/* \u5220\u9664\u5143\u7d20 */\nlist.remove(3);  // \u5220\u9664\u7d22\u5f15 3 \u5904\u7684\u5143\u7d20\n</code></pre> list.cpp<pre><code>/* \u6e05\u7a7a\u5217\u8868 */\nlist.clear();\n/* \u5c3e\u90e8\u6dfb\u52a0\u5143\u7d20 */\nlist.push_back(1);\nlist.push_back(3);\nlist.push_back(2);\nlist.push_back(5);\nlist.push_back(4);\n/* \u4e2d\u95f4\u63d2\u5165\u5143\u7d20 */\nlist.insert(list.begin() + 3, 6);  // \u5728\u7d22\u5f15 3 \u5904\u63d2\u5165\u6570\u5b57 6\n/* \u5220\u9664\u5143\u7d20 */\nlist.erase(list.begin() + 3);      // \u5220\u9664\u7d22\u5f15 3 \u5904\u7684\u5143\u7d20\n</code></pre> list.py<pre><code># \u6e05\u7a7a\u5217\u8868\nlist.clear()\n# \u5c3e\u90e8\u6dfb\u52a0\u5143\u7d20\nlist.append(1)\nlist.append(3)\nlist.append(2)\nlist.append(5)\nlist.append(4)\n# \u4e2d\u95f4\u63d2\u5165\u5143\u7d20\nlist.insert(3, 6)  # \u5728\u7d22\u5f15 3 \u5904\u63d2\u5165\u6570\u5b57 6\n# \u5220\u9664\u5143\u7d20\nlist.pop(3)        # \u5220\u9664\u7d22\u5f15 3 \u5904\u7684\u5143\u7d20\n</code></pre> list_test.go<pre><code>/* \u6e05\u7a7a\u5217\u8868 */\nlist = nil\n/* \u5c3e\u90e8\u6dfb\u52a0\u5143\u7d20 */\nlist = append(list, 1)\nlist = append(list, 3)\nlist = append(list, 2)\nlist = append(list, 5)\nlist = append(list, 4)\n/* \u4e2d\u95f4\u63d2\u5165\u5143\u7d20 */\nlist = append(list[:3], append([]int{6}, list[3:]...)...) // \u5728\u7d22\u5f15 3 \u5904\u63d2\u5165\u6570\u5b57 6\n/* \u5220\u9664\u5143\u7d20 */\nlist = append(list[:3], list[4:]...) // \u5220\u9664\u7d22\u5f15 3 \u5904\u7684\u5143\u7d20\n</code></pre> list.js<pre><code>/* \u6e05\u7a7a\u5217\u8868 */\nlist.length = 0;\n/* \u5c3e\u90e8\u6dfb\u52a0\u5143\u7d20 */\nlist.push(1);\nlist.push(3);\nlist.push(2);\nlist.push(5);\nlist.push(4);\n/* \u4e2d\u95f4\u63d2\u5165\u5143\u7d20 */\nlist.splice(3, 0, 6);\n/* \u5220\u9664\u5143\u7d20 */\nlist.splice(3, 1);\n</code></pre> list.ts<pre><code>/* \u6e05\u7a7a\u5217\u8868 */\nlist.length = 0;\n/* \u5c3e\u90e8\u6dfb\u52a0\u5143\u7d20 */\nlist.push(1);\nlist.push(3);\nlist.push(2);\nlist.push(5);\nlist.push(4);\n/* \u4e2d\u95f4\u63d2\u5165\u5143\u7d20 */\nlist.splice(3, 0, 6);\n/* \u5220\u9664\u5143\u7d20 */\nlist.splice(3, 1);\n</code></pre> list.c<pre><code>// C \u672a\u63d0\u4f9b\u5185\u7f6e\u52a8\u6001\u6570\u7ec4\n</code></pre> list.cs<pre><code>/* \u6e05\u7a7a\u5217\u8868 */\nlist.Clear();\n/* \u5c3e\u90e8\u6dfb\u52a0\u5143\u7d20 */\nlist.Add(1);\nlist.Add(3);\nlist.Add(2);\nlist.Add(5);\nlist.Add(4);\n/* \u4e2d\u95f4\u63d2\u5165\u5143\u7d20 */\nlist.Insert(3, 6);\n/* \u5220\u9664\u5143\u7d20 */\nlist.RemoveAt(3);\n</code></pre> list.swift<pre><code>/* \u6e05\u7a7a\u5217\u8868 */\nlist.removeAll()\n/* \u5c3e\u90e8\u6dfb\u52a0\u5143\u7d20 */\nlist.append(1)\nlist.append(3)\nlist.append(2)\nlist.append(5)\nlist.append(4)\n/* \u4e2d\u95f4\u63d2\u5165\u5143\u7d20 */\nlist.insert(6, at: 3) // \u5728\u7d22\u5f15 3 \u5904\u63d2\u5165\u6570\u5b57 6\n/* \u5220\u9664\u5143\u7d20 */\nlist.remove(at: 3) // \u5220\u9664\u7d22\u5f15 3 \u5904\u7684\u5143\u7d20\n</code></pre> list.zig<pre><code>// \u6e05\u7a7a\u5217\u8868\nlist.clearRetainingCapacity();\n// \u5c3e\u90e8\u6dfb\u52a0\u5143\u7d20\ntry list.append(1);\ntry list.append(3);\ntry list.append(2);\ntry list.append(5);\ntry list.append(4);\n// \u4e2d\u95f4\u63d2\u5165\u5143\u7d20\ntry list.insert(3, 6); // \u5728\u7d22\u5f15 3 \u5904\u63d2\u5165\u6570\u5b57 6\n// \u5220\u9664\u5143\u7d20\n_ = list.orderedRemove(3); // \u5220\u9664\u7d22\u5f15 3 \u5904\u7684\u5143\u7d20\n</code></pre> list.dart<pre><code>/* \u6e05\u7a7a\u5217\u8868 */\nlist.clear();\n/* \u5c3e\u90e8\u6dfb\u52a0\u5143\u7d20 */\nlist.add(1);\nlist.add(3);\nlist.add(2);\nlist.add(5);\nlist.add(4);\n/* \u4e2d\u95f4\u63d2\u5165\u5143\u7d20 */\nlist.insert(3, 6); // \u5728\u7d22\u5f15 3 \u5904\u63d2\u5165\u6570\u5b57 6\n/* \u5220\u9664\u5143\u7d20 */\nlist.removeAt(3); // \u5220\u9664\u7d22\u5f15 3 \u5904\u7684\u5143\u7d20\n</code></pre> <p>\u904d\u5386\u5217\u8868\u3002\u4e0e\u6570\u7ec4\u4e00\u6837\uff0c\u5217\u8868\u53ef\u4ee5\u6839\u636e\u7d22\u5f15\u904d\u5386\uff0c\u4e5f\u53ef\u4ee5\u76f4\u63a5\u904d\u5386\u5404\u5143\u7d20\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart list.java<pre><code>/* \u901a\u8fc7\u7d22\u5f15\u904d\u5386\u5217\u8868 */\nint count = 0;\nfor (int i = 0; i &lt; list.size(); i++) {\ncount++;\n}\n/* \u76f4\u63a5\u904d\u5386\u5217\u8868\u5143\u7d20 */\ncount = 0;\nfor (int n : list) {\ncount++;\n}\n</code></pre> list.cpp<pre><code>/* \u901a\u8fc7\u7d22\u5f15\u904d\u5386\u5217\u8868 */\nint count = 0;\nfor (int i = 0; i &lt; list.size(); i++) {\ncount++;\n}\n/* \u76f4\u63a5\u904d\u5386\u5217\u8868\u5143\u7d20 */\ncount = 0;\nfor (int n : list) {\ncount++;\n}\n</code></pre> list.py<pre><code># \u901a\u8fc7\u7d22\u5f15\u904d\u5386\u5217\u8868\ncount = 0\nfor i in range(len(list)):\ncount += 1\n# \u76f4\u63a5\u904d\u5386\u5217\u8868\u5143\u7d20\ncount = 0\nfor n in list:\ncount += 1\n</code></pre> list_test.go<pre><code>/* \u901a\u8fc7\u7d22\u5f15\u904d\u5386\u5217\u8868 */\ncount := 0\nfor i := 0; i &lt; len(list); i++ {\ncount++\n}\n/* \u76f4\u63a5\u904d\u5386\u5217\u8868\u5143\u7d20 */\ncount = 0\nfor range list {\ncount++\n}\n</code></pre> list.js<pre><code>/* \u901a\u8fc7\u7d22\u5f15\u904d\u5386\u5217\u8868 */\nlet count = 0;\nfor (let i = 0; i &lt; list.length; i++) {\ncount++;\n}\n/* \u76f4\u63a5\u904d\u5386\u5217\u8868\u5143\u7d20 */\ncount = 0;\nfor (const n of list) {\ncount++;\n}\n</code></pre> list.ts<pre><code>/* \u901a\u8fc7\u7d22\u5f15\u904d\u5386\u5217\u8868 */\nlet count = 0;\nfor (let i = 0; i &lt; list.length; i++) {\ncount++;\n}\n/* \u76f4\u63a5\u904d\u5386\u5217\u8868\u5143\u7d20 */\ncount = 0;\nfor (const n of list) {\ncount++;\n}\n</code></pre> list.c<pre><code>// C \u672a\u63d0\u4f9b\u5185\u7f6e\u52a8\u6001\u6570\u7ec4\n</code></pre> list.cs<pre><code>/* \u901a\u8fc7\u7d22\u5f15\u904d\u5386\u5217\u8868 */\nint count = 0;\nfor (int i = 0; i &lt; list.Count(); i++)\n{\ncount++;\n}\n/* \u76f4\u63a5\u904d\u5386\u5217\u8868\u5143\u7d20 */\ncount = 0;\nforeach (int n in list)\n{\ncount++;\n}\n</code></pre> list.swift<pre><code>/* \u901a\u8fc7\u7d22\u5f15\u904d\u5386\u5217\u8868 */\nvar count = 0\nfor _ in list.indices {\ncount += 1\n}\n/* \u76f4\u63a5\u904d\u5386\u5217\u8868\u5143\u7d20 */\ncount = 0\nfor _ in list {\ncount += 1\n}\n</code></pre> list.zig<pre><code>// \u901a\u8fc7\u7d22\u5f15\u904d\u5386\u5217\u8868\nvar count: i32 = 0;\nvar i: i32 = 0;\nwhile (i &lt; list.items.len) : (i += 1) {\ncount += 1;\n}\n// \u76f4\u63a5\u904d\u5386\u5217\u8868\u5143\u7d20\ncount = 0;\nfor (list.items) |_| {\ncount += 1;\n}\n</code></pre> list.dart<pre><code>/* \u901a\u8fc7\u7d22\u5f15\u904d\u5386\u5217\u8868 */\nint count = 0;\nfor (int i = 0; i &lt; list.length; i++) {\ncount++;\n}\n/* \u76f4\u63a5\u904d\u5386\u5217\u8868\u5143\u7d20 */\ncount = 0;\nfor (int n in list) {\ncount++;\n}\n</code></pre> <p>\u62fc\u63a5\u4e24\u4e2a\u5217\u8868\u3002\u7ed9\u5b9a\u4e00\u4e2a\u65b0\u5217\u8868 <code>list1</code> \uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u8be5\u5217\u8868\u62fc\u63a5\u5230\u539f\u5217\u8868\u7684\u5c3e\u90e8\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart list.java<pre><code>/* \u62fc\u63a5\u4e24\u4e2a\u5217\u8868 */\nList&lt;Integer&gt; list1 = new ArrayList&lt;&gt;(Arrays.asList(new Integer[] { 6, 8, 7, 10, 9 }));\nlist.addAll(list1);  // \u5c06\u5217\u8868 list1 \u62fc\u63a5\u5230 list \u4e4b\u540e\n</code></pre> list.cpp<pre><code>/* \u62fc\u63a5\u4e24\u4e2a\u5217\u8868 */\nvector&lt;int&gt; list1 = { 6, 8, 7, 10, 9 };\n// \u5c06\u5217\u8868 list1 \u62fc\u63a5\u5230 list \u4e4b\u540e\nlist.insert(list.end(), list1.begin(), list1.end());\n</code></pre> list.py<pre><code># \u62fc\u63a5\u4e24\u4e2a\u5217\u8868\nlist1: List[int] = [6, 8, 7, 10, 9]\nlist += list1  # \u5c06\u5217\u8868 list1 \u62fc\u63a5\u5230 list \u4e4b\u540e\n</code></pre> list_test.go<pre><code>/* \u62fc\u63a5\u4e24\u4e2a\u5217\u8868 */\nlist1 := []int{6, 8, 7, 10, 9}\nlist = append(list, list1...)  // \u5c06\u5217\u8868 list1 \u62fc\u63a5\u5230 list \u4e4b\u540e\n</code></pre> list.js<pre><code>/* \u62fc\u63a5\u4e24\u4e2a\u5217\u8868 */\nconst list1 = [6, 8, 7, 10, 9];\nlist.push(...list1);  // \u5c06\u5217\u8868 list1 \u62fc\u63a5\u5230 list \u4e4b\u540e\n</code></pre> list.ts<pre><code>/* \u62fc\u63a5\u4e24\u4e2a\u5217\u8868 */\nconst list1: number[] = [6, 8, 7, 10, 9];\nlist.push(...list1);  // \u5c06\u5217\u8868 list1 \u62fc\u63a5\u5230 list \u4e4b\u540e\n</code></pre> list.c<pre><code>// C \u672a\u63d0\u4f9b\u5185\u7f6e\u52a8\u6001\u6570\u7ec4\n</code></pre> list.cs<pre><code>/* \u62fc\u63a5\u4e24\u4e2a\u5217\u8868 */\nList&lt;int&gt; list1 = new() { 6, 8, 7, 10, 9 };\nlist.AddRange(list1);  // \u5c06\u5217\u8868 list1 \u62fc\u63a5\u5230 list \u4e4b\u540e\n</code></pre> list.swift<pre><code>/* \u62fc\u63a5\u4e24\u4e2a\u5217\u8868 */\nlet list1 = [6, 8, 7, 10, 9]\nlist.append(contentsOf: list1) // \u5c06\u5217\u8868 list1 \u62fc\u63a5\u5230 list \u4e4b\u540e\n</code></pre> list.zig<pre><code>// \u62fc\u63a5\u4e24\u4e2a\u5217\u8868\nvar list1 = std.ArrayList(i32).init(std.heap.page_allocator);\ndefer list1.deinit();\ntry list1.appendSlice(&amp;[_]i32{ 6, 8, 7, 10, 9 });\ntry list.insertSlice(list.items.len, list1.items); // \u5c06\u5217\u8868 list1 \u62fc\u63a5\u5230 list \u4e4b\u540e\n</code></pre> list.dart<pre><code>/* \u62fc\u63a5\u4e24\u4e2a\u5217\u8868 */\nList&lt;int&gt; list1 = [6, 8, 7, 10, 9];\nlist.addAll(list1);  // \u5c06\u5217\u8868 list1 \u62fc\u63a5\u5230 list \u4e4b\u540e\n</code></pre> <p>\u6392\u5e8f\u5217\u8868\u3002\u6392\u5e8f\u4e5f\u662f\u5e38\u7528\u7684\u65b9\u6cd5\u4e4b\u4e00\u3002\u5b8c\u6210\u5217\u8868\u6392\u5e8f\u540e\uff0c\u6211\u4eec\u4fbf\u53ef\u4ee5\u4f7f\u7528\u5728\u6570\u7ec4\u7c7b\u7b97\u6cd5\u9898\u4e2d\u7ecf\u5e38\u8003\u5bdf\u7684\u300c\u4e8c\u5206\u67e5\u627e\u300d\u548c\u300c\u53cc\u6307\u9488\u300d\u7b97\u6cd5\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart list.java<pre><code>/* \u6392\u5e8f\u5217\u8868 */\nCollections.sort(list);  // \u6392\u5e8f\u540e\uff0c\u5217\u8868\u5143\u7d20\u4ece\u5c0f\u5230\u5927\u6392\u5217\n</code></pre> list.cpp<pre><code>/* \u6392\u5e8f\u5217\u8868 */\nsort(list.begin(), list.end());  // \u6392\u5e8f\u540e\uff0c\u5217\u8868\u5143\u7d20\u4ece\u5c0f\u5230\u5927\u6392\u5217\n</code></pre> list.py<pre><code># \u6392\u5e8f\u5217\u8868\nlist.sort()  # \u6392\u5e8f\u540e\uff0c\u5217\u8868\u5143\u7d20\u4ece\u5c0f\u5230\u5927\u6392\u5217\n</code></pre> list_test.go<pre><code>/* \u6392\u5e8f\u5217\u8868 */\nsort.Ints(list)  // \u6392\u5e8f\u540e\uff0c\u5217\u8868\u5143\u7d20\u4ece\u5c0f\u5230\u5927\u6392\u5217\n</code></pre> list.js<pre><code>/* \u6392\u5e8f\u5217\u8868 */  list.sort((a, b) =&gt; a - b);  // \u6392\u5e8f\u540e\uff0c\u5217\u8868\u5143\u7d20\u4ece\u5c0f\u5230\u5927\u6392\u5217\n</code></pre> list.ts<pre><code>/* \u6392\u5e8f\u5217\u8868 */\nlist.sort((a, b) =&gt; a - b);  // \u6392\u5e8f\u540e\uff0c\u5217\u8868\u5143\u7d20\u4ece\u5c0f\u5230\u5927\u6392\u5217\n</code></pre> list.c<pre><code>// C \u672a\u63d0\u4f9b\u5185\u7f6e\u52a8\u6001\u6570\u7ec4\n</code></pre> list.cs<pre><code>/* \u6392\u5e8f\u5217\u8868 */\nlist.Sort(); // \u6392\u5e8f\u540e\uff0c\u5217\u8868\u5143\u7d20\u4ece\u5c0f\u5230\u5927\u6392\u5217\n</code></pre> list.swift<pre><code>/* \u6392\u5e8f\u5217\u8868 */\nlist.sort() // \u6392\u5e8f\u540e\uff0c\u5217\u8868\u5143\u7d20\u4ece\u5c0f\u5230\u5927\u6392\u5217\n</code></pre> list.zig<pre><code>// \u6392\u5e8f\u5217\u8868\nstd.sort.sort(i32, list.items, {}, comptime std.sort.asc(i32));\n</code></pre> list.dart<pre><code>/* \u6392\u5e8f\u5217\u8868 */\nlist.sort(); // \u6392\u5e8f\u540e\uff0c\u5217\u8868\u5143\u7d20\u4ece\u5c0f\u5230\u5927\u6392\u5217\n</code></pre>"},{"location":"chapter_array_and_linkedlist/list/#432","title":"4.3.2. \u00a0 \u5217\u8868\u5b9e\u73b0 *","text":"<p>\u4e3a\u4e86\u5e2e\u52a9\u52a0\u6df1\u5bf9\u5217\u8868\u7684\u7406\u89e3\uff0c\u6211\u4eec\u5728\u6b64\u63d0\u4f9b\u4e00\u4e2a\u7b80\u6613\u7248\u5217\u8868\u5b9e\u73b0\u3002\u9700\u8981\u5173\u6ce8\u4e09\u4e2a\u6838\u5fc3\u70b9\uff1a</p> <ul> <li>\u521d\u59cb\u5bb9\u91cf\uff1a\u9009\u53d6\u4e00\u4e2a\u5408\u7406\u7684\u6570\u7ec4\u521d\u59cb\u5bb9\u91cf\u3002\u5728\u672c\u793a\u4f8b\u4e2d\uff0c\u6211\u4eec\u9009\u62e9 10 \u4f5c\u4e3a\u521d\u59cb\u5bb9\u91cf\u3002</li> <li>\u6570\u91cf\u8bb0\u5f55\uff1a\u58f0\u660e\u4e00\u4e2a\u53d8\u91cf size\uff0c\u7528\u4e8e\u8bb0\u5f55\u5217\u8868\u5f53\u524d\u5143\u7d20\u6570\u91cf\uff0c\u5e76\u968f\u7740\u5143\u7d20\u63d2\u5165\u548c\u5220\u9664\u5b9e\u65f6\u66f4\u65b0\u3002\u6839\u636e\u6b64\u53d8\u91cf\uff0c\u6211\u4eec\u53ef\u4ee5\u5b9a\u4f4d\u5217\u8868\u5c3e\u90e8\uff0c\u4ee5\u53ca\u5224\u65ad\u662f\u5426\u9700\u8981\u6269\u5bb9\u3002</li> <li>\u6269\u5bb9\u673a\u5236\uff1a\u63d2\u5165\u5143\u7d20\u65f6\u53ef\u80fd\u8d85\u51fa\u5217\u8868\u5bb9\u91cf\uff0c\u6b64\u65f6\u9700\u8981\u6269\u5bb9\u5217\u8868\u3002\u6269\u5bb9\u65b9\u6cd5\u662f\u6839\u636e\u6269\u5bb9\u500d\u6570\u521b\u5efa\u4e00\u4e2a\u66f4\u5927\u7684\u6570\u7ec4\uff0c\u5e76\u5c06\u5f53\u524d\u6570\u7ec4\u7684\u6240\u6709\u5143\u7d20\u4f9d\u6b21\u79fb\u52a8\u81f3\u65b0\u6570\u7ec4\u3002\u5728\u672c\u793a\u4f8b\u4e2d\uff0c\u6211\u4eec\u89c4\u5b9a\u6bcf\u6b21\u5c06\u6570\u7ec4\u6269\u5bb9\u81f3\u4e4b\u524d\u7684 2 \u500d\u3002</li> </ul> <p>\u672c\u793a\u4f8b\u65e8\u5728\u5e2e\u52a9\u8bfb\u8005\u76f4\u89c2\u7406\u89e3\u5217\u8868\u7684\u5de5\u4f5c\u673a\u5236\u3002\u5b9e\u9645\u7f16\u7a0b\u8bed\u8a00\u4e2d\uff0c\u5217\u8868\u5b9e\u73b0\u66f4\u52a0\u6807\u51c6\u548c\u590d\u6742\uff0c\u5404\u4e2a\u53c2\u6570\u7684\u8bbe\u5b9a\u4e5f\u975e\u5e38\u6709\u8003\u7a76\uff0c\u4f8b\u5982\u521d\u59cb\u5bb9\u91cf\u3001\u6269\u5bb9\u500d\u6570\u7b49\u3002\u611f\u5174\u8da3\u7684\u8bfb\u8005\u53ef\u4ee5\u67e5\u9605\u6e90\u7801\u8fdb\u884c\u5b66\u4e60\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart my_list.java<pre><code>/* \u5217\u8868\u7c7b\u7b80\u6613\u5b9e\u73b0 */\nclass MyList {\nprivate int[] nums; // \u6570\u7ec4\uff08\u5b58\u50a8\u5217\u8868\u5143\u7d20\uff09\nprivate int capacity = 10; // \u5217\u8868\u5bb9\u91cf\nprivate int size = 0; // \u5217\u8868\u957f\u5ea6\uff08\u5373\u5f53\u524d\u5143\u7d20\u6570\u91cf\uff09\nprivate int extendRatio = 2; // \u6bcf\u6b21\u5217\u8868\u6269\u5bb9\u7684\u500d\u6570\n/* \u6784\u9020\u65b9\u6cd5 */\npublic MyList() {\nnums = new int[capacity];\n}\n/* \u83b7\u53d6\u5217\u8868\u957f\u5ea6\uff08\u5373\u5f53\u524d\u5143\u7d20\u6570\u91cf\uff09 */\npublic int size() {\nreturn size;\n}\n/* \u83b7\u53d6\u5217\u8868\u5bb9\u91cf */\npublic int capacity() {\nreturn capacity;\n}\n/* \u8bbf\u95ee\u5143\u7d20 */\npublic int get(int index) {\n// \u7d22\u5f15\u5982\u679c\u8d8a\u754c\u5219\u629b\u51fa\u5f02\u5e38\uff0c\u4e0b\u540c\nif (index &lt; 0 || index &gt;= size)\nthrow new IndexOutOfBoundsException(\"\u7d22\u5f15\u8d8a\u754c\");\nreturn nums[index];\n}\n/* \u66f4\u65b0\u5143\u7d20 */\npublic void set(int index, int num) {\nif (index &lt; 0 || index &gt;= size)\nthrow new IndexOutOfBoundsException(\"\u7d22\u5f15\u8d8a\u754c\");\nnums[index] = num;\n}\n/* \u5c3e\u90e8\u6dfb\u52a0\u5143\u7d20 */\npublic void add(int num) {\n// \u5143\u7d20\u6570\u91cf\u8d85\u51fa\u5bb9\u91cf\u65f6\uff0c\u89e6\u53d1\u6269\u5bb9\u673a\u5236\nif (size == capacity())\nextendCapacity();\nnums[size] = num;\n// \u66f4\u65b0\u5143\u7d20\u6570\u91cf\nsize++;\n}\n/* \u4e2d\u95f4\u63d2\u5165\u5143\u7d20 */\npublic void insert(int index, int num) {\nif (index &lt; 0 || index &gt;= size)\nthrow new IndexOutOfBoundsException(\"\u7d22\u5f15\u8d8a\u754c\");\n// \u5143\u7d20\u6570\u91cf\u8d85\u51fa\u5bb9\u91cf\u65f6\uff0c\u89e6\u53d1\u6269\u5bb9\u673a\u5236\nif (size == capacity())\nextendCapacity();\n// \u5c06\u7d22\u5f15 index \u4ee5\u53ca\u4e4b\u540e\u7684\u5143\u7d20\u90fd\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\nfor (int j = size - 1; j &gt;= index; j--) {\nnums[j + 1] = nums[j];\n}\nnums[index] = num;\n// \u66f4\u65b0\u5143\u7d20\u6570\u91cf\nsize++;\n}\n/* \u5220\u9664\u5143\u7d20 */\npublic int remove(int index) {\nif (index &lt; 0 || index &gt;= size)\nthrow new IndexOutOfBoundsException(\"\u7d22\u5f15\u8d8a\u754c\");\nint num = nums[index];\n// \u5c06\u7d22\u5f15 index \u4e4b\u540e\u7684\u5143\u7d20\u90fd\u5411\u524d\u79fb\u52a8\u4e00\u4f4d\nfor (int j = index; j &lt; size - 1; j++) {\nnums[j] = nums[j + 1];\n}\n// \u66f4\u65b0\u5143\u7d20\u6570\u91cf\nsize--;\n// \u8fd4\u56de\u88ab\u5220\u9664\u5143\u7d20\nreturn num;\n}\n/* \u5217\u8868\u6269\u5bb9 */\npublic void extendCapacity() {\n// \u65b0\u5efa\u4e00\u4e2a\u957f\u5ea6\u4e3a\u539f\u6570\u7ec4 extendRatio \u500d\u7684\u65b0\u6570\u7ec4\uff0c\u5e76\u5c06\u539f\u6570\u7ec4\u62f7\u8d1d\u5230\u65b0\u6570\u7ec4\nnums = Arrays.copyOf(nums, capacity() * extendRatio);\n// \u66f4\u65b0\u5217\u8868\u5bb9\u91cf\ncapacity = nums.length;\n}\n/* \u5c06\u5217\u8868\u8f6c\u6362\u4e3a\u6570\u7ec4 */\npublic int[] toArray() {\nint size = size();\n// \u4ec5\u8f6c\u6362\u6709\u6548\u957f\u5ea6\u8303\u56f4\u5185\u7684\u5217\u8868\u5143\u7d20\nint[] nums = new int[size];\nfor (int i = 0; i &lt; size; i++) {\nnums[i] = get(i);\n}\nreturn nums;\n}\n}\n</code></pre> my_list.cpp<pre><code>/* \u5217\u8868\u7c7b\u7b80\u6613\u5b9e\u73b0 */\nclass MyList {\nprivate:\nint *nums;             // \u6570\u7ec4\uff08\u5b58\u50a8\u5217\u8868\u5143\u7d20\uff09\nint numsCapacity = 10; // \u5217\u8868\u5bb9\u91cf\nint numsSize = 0;      // \u5217\u8868\u957f\u5ea6\uff08\u5373\u5f53\u524d\u5143\u7d20\u6570\u91cf\uff09\nint extendRatio = 2;   // \u6bcf\u6b21\u5217\u8868\u6269\u5bb9\u7684\u500d\u6570\npublic:\n/* \u6784\u9020\u65b9\u6cd5 */\nMyList() {\nnums = new int[numsCapacity];\n}\n/* \u6790\u6784\u65b9\u6cd5 */\n~MyList() {\ndelete[] nums;\n}\n/* \u83b7\u53d6\u5217\u8868\u957f\u5ea6\uff08\u5373\u5f53\u524d\u5143\u7d20\u6570\u91cf\uff09*/\nint size() {\nreturn numsSize;\n}\n/* \u83b7\u53d6\u5217\u8868\u5bb9\u91cf */\nint capacity() {\nreturn numsCapacity;\n}\n/* \u8bbf\u95ee\u5143\u7d20 */\nint get(int index) {\n// \u7d22\u5f15\u5982\u679c\u8d8a\u754c\u5219\u629b\u51fa\u5f02\u5e38\uff0c\u4e0b\u540c\nif (index &lt; 0 || index &gt;= size())\nthrow out_of_range(\"\u7d22\u5f15\u8d8a\u754c\");\nreturn nums[index];\n}\n/* \u66f4\u65b0\u5143\u7d20 */\nvoid set(int index, int num) {\nif (index &lt; 0 || index &gt;= size())\nthrow out_of_range(\"\u7d22\u5f15\u8d8a\u754c\");\nnums[index] = num;\n}\n/* \u5c3e\u90e8\u6dfb\u52a0\u5143\u7d20 */\nvoid add(int num) {\n// \u5143\u7d20\u6570\u91cf\u8d85\u51fa\u5bb9\u91cf\u65f6\uff0c\u89e6\u53d1\u6269\u5bb9\u673a\u5236\nif (size() == capacity())\nextendCapacity();\nnums[size()] = num;\n// \u66f4\u65b0\u5143\u7d20\u6570\u91cf\nnumsSize++;\n}\n/* \u4e2d\u95f4\u63d2\u5165\u5143\u7d20 */\nvoid insert(int index, int num) {\nif (index &lt; 0 || index &gt;= size())\nthrow out_of_range(\"\u7d22\u5f15\u8d8a\u754c\");\n// \u5143\u7d20\u6570\u91cf\u8d85\u51fa\u5bb9\u91cf\u65f6\uff0c\u89e6\u53d1\u6269\u5bb9\u673a\u5236\nif (size() == capacity())\nextendCapacity();\n// \u7d22\u5f15 i \u4ee5\u53ca\u4e4b\u540e\u7684\u5143\u7d20\u90fd\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\nfor (int j = size() - 1; j &gt;= index; j--) {\nnums[j + 1] = nums[j];\n}\nnums[index] = num;\n// \u66f4\u65b0\u5143\u7d20\u6570\u91cf\nnumsSize++;\n}\n/* \u5220\u9664\u5143\u7d20 */\nint remove(int index) {\nif (index &lt; 0 || index &gt;= size())\nthrow out_of_range(\"\u7d22\u5f15\u8d8a\u754c\");\nint num = nums[index];\n// \u7d22\u5f15 i \u4e4b\u540e\u7684\u5143\u7d20\u90fd\u5411\u524d\u79fb\u52a8\u4e00\u4f4d\nfor (int j = index; j &lt; size() - 1; j++) {\nnums[j] = nums[j + 1];\n}\n// \u66f4\u65b0\u5143\u7d20\u6570\u91cf\nnumsSize--;\n// \u8fd4\u56de\u88ab\u5220\u9664\u5143\u7d20\nreturn num;\n}\n/* \u5217\u8868\u6269\u5bb9 */\nvoid extendCapacity() {\n// \u65b0\u5efa\u4e00\u4e2a\u957f\u5ea6\u4e3a\u539f\u6570\u7ec4 extendRatio \u500d\u7684\u65b0\u6570\u7ec4\nint newCapacity = capacity() * extendRatio;\nint *tmp = nums;\nnums = new int[newCapacity];\n// \u5c06\u539f\u6570\u7ec4\u4e2d\u7684\u6240\u6709\u5143\u7d20\u590d\u5236\u5230\u65b0\u6570\u7ec4\nfor (int i = 0; i &lt; size(); i++) {\nnums[i] = tmp[i];\n}\n// \u91ca\u653e\u5185\u5b58\ndelete[] tmp;\nnumsCapacity = newCapacity;\n}\n/* \u5c06\u5217\u8868\u8f6c\u6362\u4e3a Vector \u7528\u4e8e\u6253\u5370 */\nvector&lt;int&gt; toVector() {\n// \u4ec5\u8f6c\u6362\u6709\u6548\u957f\u5ea6\u8303\u56f4\u5185\u7684\u5217\u8868\u5143\u7d20\nvector&lt;int&gt; vec(size());\nfor (int i = 0; i &lt; size(); i++) {\nvec[i] = nums[i];\n}\nreturn vec;\n}\n};\n</code></pre> my_list.py<pre><code>class MyList:\n\"\"\"\u5217\u8868\u7c7b\u7b80\u6613\u5b9e\u73b0\"\"\"\ndef __init__(self):\n\"\"\"\u6784\u9020\u65b9\u6cd5\"\"\"\nself.__capacity: int = 10  # \u5217\u8868\u5bb9\u91cf\nself.__nums: list[int] = [0] * self.__capacity  # \u6570\u7ec4\uff08\u5b58\u50a8\u5217\u8868\u5143\u7d20\uff09\nself.__size: int = 0  # \u5217\u8868\u957f\u5ea6\uff08\u5373\u5f53\u524d\u5143\u7d20\u6570\u91cf\uff09\nself.__extend_ratio: int = 2  # \u6bcf\u6b21\u5217\u8868\u6269\u5bb9\u7684\u500d\u6570\ndef size(self) -&gt; int:\n\"\"\"\u83b7\u53d6\u5217\u8868\u957f\u5ea6\uff08\u5373\u5f53\u524d\u5143\u7d20\u6570\u91cf\uff09\"\"\"\nreturn self.__size\ndef capacity(self) -&gt; int:\n\"\"\"\u83b7\u53d6\u5217\u8868\u5bb9\u91cf\"\"\"\nreturn self.__capacity\ndef get(self, index: int) -&gt; int:\n\"\"\"\u8bbf\u95ee\u5143\u7d20\"\"\"\n# \u7d22\u5f15\u5982\u679c\u8d8a\u754c\u5219\u629b\u51fa\u5f02\u5e38\uff0c\u4e0b\u540c\nif index &lt; 0 or index &gt;= self.__size:\nraise IndexError(\"\u7d22\u5f15\u8d8a\u754c\")\nreturn self.__nums[index]\ndef set(self, num: int, index: int) -&gt; None:\n\"\"\"\u66f4\u65b0\u5143\u7d20\"\"\"\nif index &lt; 0 or index &gt;= self.__size:\nraise IndexError(\"\u7d22\u5f15\u8d8a\u754c\")\nself.__nums[index] = num\ndef add(self, num: int) -&gt; None:\n\"\"\"\u5c3e\u90e8\u6dfb\u52a0\u5143\u7d20\"\"\"\n# \u5143\u7d20\u6570\u91cf\u8d85\u51fa\u5bb9\u91cf\u65f6\uff0c\u89e6\u53d1\u6269\u5bb9\u673a\u5236\nif self.size() == self.capacity():\nself.extend_capacity()\nself.__nums[self.__size] = num\nself.__size += 1\ndef insert(self, num: int, index: int) -&gt; None:\n\"\"\"\u4e2d\u95f4\u63d2\u5165\u5143\u7d20\"\"\"\nif index &lt; 0 or index &gt;= self.__size:\nraise IndexError(\"\u7d22\u5f15\u8d8a\u754c\")\n# \u5143\u7d20\u6570\u91cf\u8d85\u51fa\u5bb9\u91cf\u65f6\uff0c\u89e6\u53d1\u6269\u5bb9\u673a\u5236\nif self.__size == self.capacity():\nself.extend_capacity()\n# \u7d22\u5f15 i \u4ee5\u53ca\u4e4b\u540e\u7684\u5143\u7d20\u90fd\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\nfor j in range(self.__size - 1, index - 1, -1):\nself.__nums[j + 1] = self.__nums[j]\nself.__nums[index] = num\n# \u66f4\u65b0\u5143\u7d20\u6570\u91cf\nself.__size += 1\ndef remove(self, index: int) -&gt; int:\n\"\"\"\u5220\u9664\u5143\u7d20\"\"\"\nif index &lt; 0 or index &gt;= self.__size:\nraise IndexError(\"\u7d22\u5f15\u8d8a\u754c\")\nnum = self.__nums[index]\n# \u7d22\u5f15 i \u4e4b\u540e\u7684\u5143\u7d20\u90fd\u5411\u524d\u79fb\u52a8\u4e00\u4f4d\nfor j in range(index, self.__size - 1):\nself.__nums[j] = self.__nums[j + 1]\n# \u66f4\u65b0\u5143\u7d20\u6570\u91cf\nself.__size -= 1\n# \u8fd4\u56de\u88ab\u5220\u9664\u5143\u7d20\nreturn num\ndef extend_capacity(self) -&gt; None:\n\"\"\"\u5217\u8868\u6269\u5bb9\"\"\"\n# \u65b0\u5efa\u4e00\u4e2a\u957f\u5ea6\u4e3a\u539f\u6570\u7ec4 __extend_ratio \u500d\u7684\u65b0\u6570\u7ec4\uff0c\u5e76\u5c06\u539f\u6570\u7ec4\u62f7\u8d1d\u5230\u65b0\u6570\u7ec4\nself.__nums = self.__nums + [0] * self.capacity() * (self.__extend_ratio - 1)\n# \u66f4\u65b0\u5217\u8868\u5bb9\u91cf\nself.__capacity = len(self.__nums)\ndef to_array(self) -&gt; list[int]:\n\"\"\"\u8fd4\u56de\u6709\u6548\u957f\u5ea6\u7684\u5217\u8868\"\"\"\nreturn self.__nums[: self.__size]\n</code></pre> my_list.go<pre><code>/* \u5217\u8868\u7c7b\u7b80\u6613\u5b9e\u73b0 */\ntype myList struct {\nnumsCapacity int\nnums         []int\nnumsSize     int\nextendRatio  int\n}\n/* \u6784\u9020\u65b9\u6cd5 */\nfunc newMyList() *myList {\nreturn &amp;myList{\nnumsCapacity: 10,              // \u5217\u8868\u5bb9\u91cf\nnums:         make([]int, 10), // \u6570\u7ec4\uff08\u5b58\u50a8\u5217\u8868\u5143\u7d20\uff09\nnumsSize:     0,               // \u5217\u8868\u957f\u5ea6\uff08\u5373\u5f53\u524d\u5143\u7d20\u6570\u91cf\uff09\nextendRatio:  2,               // \u6bcf\u6b21\u5217\u8868\u6269\u5bb9\u7684\u500d\u6570\n}\n}\n/* \u83b7\u53d6\u5217\u8868\u957f\u5ea6\uff08\u5373\u5f53\u524d\u5143\u7d20\u6570\u91cf\uff09 */\nfunc (l *myList) size() int {\nreturn l.numsSize\n}\n/*  \u83b7\u53d6\u5217\u8868\u5bb9\u91cf */\nfunc (l *myList) capacity() int {\nreturn l.numsCapacity\n}\n/* \u8bbf\u95ee\u5143\u7d20 */\nfunc (l *myList) get(index int) int {\n// \u7d22\u5f15\u5982\u679c\u8d8a\u754c\u5219\u629b\u51fa\u5f02\u5e38\uff0c\u4e0b\u540c\nif index &lt; 0 || index &gt;= l.numsSize {\npanic(\"\u7d22\u5f15\u8d8a\u754c\")\n}\nreturn l.nums[index]\n}\n/* \u66f4\u65b0\u5143\u7d20 */\nfunc (l *myList) set(num, index int) {\nif index &lt; 0 || index &gt;= l.numsSize {\npanic(\"\u7d22\u5f15\u8d8a\u754c\")\n}\nl.nums[index] = num\n}\n/* \u5c3e\u90e8\u6dfb\u52a0\u5143\u7d20 */\nfunc (l *myList) add(num int) {\n// \u5143\u7d20\u6570\u91cf\u8d85\u51fa\u5bb9\u91cf\u65f6\uff0c\u89e6\u53d1\u6269\u5bb9\u673a\u5236\nif l.numsSize == l.numsCapacity {\nl.extendCapacity()\n}\nl.nums[l.numsSize] = num\n// \u66f4\u65b0\u5143\u7d20\u6570\u91cf\nl.numsSize++\n}\n/* \u4e2d\u95f4\u63d2\u5165\u5143\u7d20 */\nfunc (l *myList) insert(num, index int) {\nif index &lt; 0 || index &gt;= l.numsSize {\npanic(\"\u7d22\u5f15\u8d8a\u754c\")\n}\n// \u5143\u7d20\u6570\u91cf\u8d85\u51fa\u5bb9\u91cf\u65f6\uff0c\u89e6\u53d1\u6269\u5bb9\u673a\u5236\nif l.numsSize == l.numsCapacity {\nl.extendCapacity()\n}\n// \u7d22\u5f15 i \u4ee5\u53ca\u4e4b\u540e\u7684\u5143\u7d20\u90fd\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\nfor j := l.numsSize - 1; j &gt;= index; j-- {\nl.nums[j+1] = l.nums[j]\n}\nl.nums[index] = num\n// \u66f4\u65b0\u5143\u7d20\u6570\u91cf\nl.numsSize++\n}\n/* \u5220\u9664\u5143\u7d20 */\nfunc (l *myList) remove(index int) int {\nif index &lt; 0 || index &gt;= l.numsSize {\npanic(\"\u7d22\u5f15\u8d8a\u754c\")\n}\nnum := l.nums[index]\n// \u7d22\u5f15 i \u4e4b\u540e\u7684\u5143\u7d20\u90fd\u5411\u524d\u79fb\u52a8\u4e00\u4f4d\nfor j := index; j &lt; l.numsSize-1; j++ {\nl.nums[j] = l.nums[j+1]\n}\n// \u66f4\u65b0\u5143\u7d20\u6570\u91cf\nl.numsSize--\n// \u8fd4\u56de\u88ab\u5220\u9664\u5143\u7d20\nreturn num\n}\n/* \u5217\u8868\u6269\u5bb9 */\nfunc (l *myList) extendCapacity() {\n// \u65b0\u5efa\u4e00\u4e2a\u957f\u5ea6\u4e3a\u539f\u6570\u7ec4 extendRatio \u500d\u7684\u65b0\u6570\u7ec4\uff0c\u5e76\u5c06\u539f\u6570\u7ec4\u62f7\u8d1d\u5230\u65b0\u6570\u7ec4\nl.nums = append(l.nums, make([]int, l.numsCapacity*(l.extendRatio-1))...)\n// \u66f4\u65b0\u5217\u8868\u5bb9\u91cf\nl.numsCapacity = len(l.nums)\n}\n/* \u8fd4\u56de\u6709\u6548\u957f\u5ea6\u7684\u5217\u8868 */\nfunc (l *myList) toArray() []int {\n// \u4ec5\u8f6c\u6362\u6709\u6548\u957f\u5ea6\u8303\u56f4\u5185\u7684\u5217\u8868\u5143\u7d20\nreturn l.nums[:l.numsSize]\n}\n</code></pre> my_list.js<pre><code>/* \u5217\u8868\u7c7b\u7b80\u6613\u5b9e\u73b0 */\nclass MyList {\n#nums = new Array(); // \u6570\u7ec4\uff08\u5b58\u50a8\u5217\u8868\u5143\u7d20\uff09\n#capacity = 10; // \u5217\u8868\u5bb9\u91cf\n#size = 0; // \u5217\u8868\u957f\u5ea6\uff08\u5373\u5f53\u524d\u5143\u7d20\u6570\u91cf\uff09\n#extendRatio = 2; // \u6bcf\u6b21\u5217\u8868\u6269\u5bb9\u7684\u500d\u6570\n/* \u6784\u9020\u65b9\u6cd5 */\nconstructor() {\nthis.#nums = new Array(this.#capacity);\n}\n/* \u83b7\u53d6\u5217\u8868\u957f\u5ea6\uff08\u5373\u5f53\u524d\u5143\u7d20\u6570\u91cf\uff09*/\nsize() {\nreturn this.#size;\n}\n/* \u83b7\u53d6\u5217\u8868\u5bb9\u91cf */\ncapacity() {\nreturn this.#capacity;\n}\n/* \u8bbf\u95ee\u5143\u7d20 */\nget(index) {\n// \u7d22\u5f15\u5982\u679c\u8d8a\u754c\u5219\u629b\u51fa\u5f02\u5e38\uff0c\u4e0b\u540c\nif (index &lt; 0 || index &gt;= this.#size) throw new Error('\u7d22\u5f15\u8d8a\u754c');\nreturn this.#nums[index];\n}\n/* \u66f4\u65b0\u5143\u7d20 */\nset(index, num) {\nif (index &lt; 0 || index &gt;= this.#size) throw new Error('\u7d22\u5f15\u8d8a\u754c');\nthis.#nums[index] = num;\n}\n/* \u5c3e\u90e8\u6dfb\u52a0\u5143\u7d20 */\nadd(num) {\n// \u5982\u679c\u957f\u5ea6\u7b49\u4e8e\u5bb9\u91cf\uff0c\u5219\u9700\u8981\u6269\u5bb9\nif (this.#size === this.#capacity) {\nthis.extendCapacity();\n}\n// \u5c06\u65b0\u5143\u7d20\u6dfb\u52a0\u5230\u5217\u8868\u5c3e\u90e8\nthis.#nums[this.#size] = num;\nthis.#size++;\n}\n/* \u4e2d\u95f4\u63d2\u5165\u5143\u7d20 */\ninsert(index, num) {\nif (index &lt; 0 || index &gt;= this.#size) throw new Error('\u7d22\u5f15\u8d8a\u754c');\n// \u5143\u7d20\u6570\u91cf\u8d85\u51fa\u5bb9\u91cf\u65f6\uff0c\u89e6\u53d1\u6269\u5bb9\u673a\u5236\nif (this.#size === this.#capacity) {\nthis.extendCapacity();\n}\n// \u5c06\u7d22\u5f15 index \u4ee5\u53ca\u4e4b\u540e\u7684\u5143\u7d20\u90fd\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\nfor (let j = this.#size - 1; j &gt;= index; j--) {\nthis.#nums[j + 1] = this.#nums[j];\n}\n// \u66f4\u65b0\u5143\u7d20\u6570\u91cf\nthis.#nums[index] = num;\nthis.#size++;\n}\n/* \u5220\u9664\u5143\u7d20 */\nremove(index) {\nif (index &lt; 0 || index &gt;= this.#size) throw new Error('\u7d22\u5f15\u8d8a\u754c');\nlet num = this.#nums[index];\n// \u5c06\u7d22\u5f15 index \u4e4b\u540e\u7684\u5143\u7d20\u90fd\u5411\u524d\u79fb\u52a8\u4e00\u4f4d\nfor (let j = index; j &lt; this.#size - 1; j++) {\nthis.#nums[j] = this.#nums[j + 1];\n}\n// \u66f4\u65b0\u5143\u7d20\u6570\u91cf\nthis.#size--;\n// \u8fd4\u56de\u88ab\u5220\u9664\u5143\u7d20\nreturn num;\n}\n/* \u5217\u8868\u6269\u5bb9 */\nextendCapacity() {\n// \u65b0\u5efa\u4e00\u4e2a\u957f\u5ea6\u4e3a\u539f\u6570\u7ec4 extendRatio \u500d\u7684\u65b0\u6570\u7ec4\uff0c\u5e76\u5c06\u539f\u6570\u7ec4\u62f7\u8d1d\u5230\u65b0\u6570\u7ec4\nthis.#nums = this.#nums.concat(\nnew Array(this.capacity() * (this.#extendRatio - 1))\n);\n// \u66f4\u65b0\u5217\u8868\u5bb9\u91cf\nthis.#capacity = this.#nums.length;\n}\n/* \u5c06\u5217\u8868\u8f6c\u6362\u4e3a\u6570\u7ec4 */\ntoArray() {\nlet size = this.size();\n// \u4ec5\u8f6c\u6362\u6709\u6548\u957f\u5ea6\u8303\u56f4\u5185\u7684\u5217\u8868\u5143\u7d20\nconst nums = new Array(size);\nfor (let i = 0; i &lt; size; i++) {\nnums[i] = this.get(i);\n}\nreturn nums;\n}\n}\n</code></pre> my_list.ts<pre><code>/* \u5217\u8868\u7c7b\u7b80\u6613\u5b9e\u73b0 */\nclass MyList {\nprivate nums: Array&lt;number&gt;; // \u6570\u7ec4\uff08\u5b58\u50a8\u5217\u8868\u5143\u7d20\uff09\nprivate _capacity: number = 10; // \u5217\u8868\u5bb9\u91cf\nprivate _size: number = 0; // \u5217\u8868\u957f\u5ea6\uff08\u5373\u5f53\u524d\u5143\u7d20\u6570\u91cf\uff09\nprivate extendRatio: number = 2; // \u6bcf\u6b21\u5217\u8868\u6269\u5bb9\u7684\u500d\u6570\n/* \u6784\u9020\u65b9\u6cd5 */\nconstructor() {\nthis.nums = new Array(this._capacity);\n}\n/* \u83b7\u53d6\u5217\u8868\u957f\u5ea6\uff08\u5373\u5f53\u524d\u5143\u7d20\u6570\u91cf\uff09*/\npublic size(): number {\nreturn this._size;\n}\n/* \u83b7\u53d6\u5217\u8868\u5bb9\u91cf */\npublic capacity(): number {\nreturn this._capacity;\n}\n/* \u8bbf\u95ee\u5143\u7d20 */\npublic get(index: number): number {\n// \u7d22\u5f15\u5982\u679c\u8d8a\u754c\u5219\u629b\u51fa\u5f02\u5e38\uff0c\u4e0b\u540c\nif (index &lt; 0 || index &gt;= this._size) throw new Error('\u7d22\u5f15\u8d8a\u754c');\nreturn this.nums[index];\n}\n/* \u66f4\u65b0\u5143\u7d20 */\npublic set(index: number, num: number): void {\nif (index &lt; 0 || index &gt;= this._size) throw new Error('\u7d22\u5f15\u8d8a\u754c');\nthis.nums[index] = num;\n}\n/* \u5c3e\u90e8\u6dfb\u52a0\u5143\u7d20 */\npublic add(num: number): void {\n// \u5982\u679c\u957f\u5ea6\u7b49\u4e8e\u5bb9\u91cf\uff0c\u5219\u9700\u8981\u6269\u5bb9\nif (this._size === this._capacity) this.extendCapacity();\n// \u5c06\u65b0\u5143\u7d20\u6dfb\u52a0\u5230\u5217\u8868\u5c3e\u90e8\nthis.nums[this._size] = num;\nthis._size++;\n}\n/* \u4e2d\u95f4\u63d2\u5165\u5143\u7d20 */\npublic insert(index: number, num: number): void {\nif (index &lt; 0 || index &gt;= this._size) throw new Error('\u7d22\u5f15\u8d8a\u754c');\n// \u5143\u7d20\u6570\u91cf\u8d85\u51fa\u5bb9\u91cf\u65f6\uff0c\u89e6\u53d1\u6269\u5bb9\u673a\u5236\nif (this._size === this._capacity) {\nthis.extendCapacity();\n}\n// \u5c06\u7d22\u5f15 index \u4ee5\u53ca\u4e4b\u540e\u7684\u5143\u7d20\u90fd\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\nfor (let j = this._size - 1; j &gt;= index; j--) {\nthis.nums[j + 1] = this.nums[j];\n}\n// \u66f4\u65b0\u5143\u7d20\u6570\u91cf\nthis.nums[index] = num;\nthis._size++;\n}\n/* \u5220\u9664\u5143\u7d20 */\npublic remove(index: number): number {\nif (index &lt; 0 || index &gt;= this._size) throw new Error('\u7d22\u5f15\u8d8a\u754c');\nlet num = this.nums[index];\n// \u5c06\u7d22\u5f15 index \u4e4b\u540e\u7684\u5143\u7d20\u90fd\u5411\u524d\u79fb\u52a8\u4e00\u4f4d\nfor (let j = index; j &lt; this._size - 1; j++) {\nthis.nums[j] = this.nums[j + 1];\n}\n// \u66f4\u65b0\u5143\u7d20\u6570\u91cf\nthis._size--;\n// \u8fd4\u56de\u88ab\u5220\u9664\u5143\u7d20\nreturn num;\n}\n/* \u5217\u8868\u6269\u5bb9 */\npublic extendCapacity(): void {\n// \u65b0\u5efa\u4e00\u4e2a\u957f\u5ea6\u4e3a size \u7684\u6570\u7ec4\uff0c\u5e76\u5c06\u539f\u6570\u7ec4\u62f7\u8d1d\u5230\u65b0\u6570\u7ec4\nthis.nums = this.nums.concat(\nnew Array(this.capacity() * (this.extendRatio - 1))\n);\n// \u66f4\u65b0\u5217\u8868\u5bb9\u91cf\nthis._capacity = this.nums.length;\n}\n/* \u5c06\u5217\u8868\u8f6c\u6362\u4e3a\u6570\u7ec4 */\npublic toArray(): number[] {\nlet size = this.size();\n// \u4ec5\u8f6c\u6362\u6709\u6548\u957f\u5ea6\u8303\u56f4\u5185\u7684\u5217\u8868\u5143\u7d20\nconst nums = new Array(size);\nfor (let i = 0; i &lt; size; i++) {\nnums[i] = this.get(i);\n}\nreturn nums;\n}\n}\n</code></pre> my_list.c<pre><code>/* \u5217\u8868\u7c7b\u7b80\u6613\u5b9e\u73b0 */\nstruct myList {\nint *nums;       // \u6570\u7ec4\uff08\u5b58\u50a8\u5217\u8868\u5143\u7d20\uff09\nint capacity;    // \u5217\u8868\u5bb9\u91cf\nint size;        // \u5217\u8868\u5927\u5c0f\nint extendRatio; // \u5217\u8868\u6bcf\u6b21\u6269\u5bb9\u7684\u500d\u6570\n};\ntypedef struct myList myList;\n/* \u6784\u9020\u51fd\u6570 */\nmyList *newMyList() {\nmyList *list = malloc(sizeof(myList));\nlist-&gt;capacity = 10;\nlist-&gt;nums = malloc(sizeof(int) * list-&gt;capacity);\nlist-&gt;size = 0;\nlist-&gt;extendRatio = 2;\nreturn list;\n}\n/* \u6790\u6784\u51fd\u6570 */\nvoid delMyList(myList *list) {\nfree(list-&gt;nums);\nfree(list);\n}\n/* \u83b7\u53d6\u5217\u8868\u957f\u5ea6 */\nint size(myList *list) {\nreturn list-&gt;size;\n}\n/* \u83b7\u53d6\u5217\u8868\u5bb9\u91cf */\nint capacity(myList *list) {\nreturn list-&gt;capacity;\n}\n/* \u8bbf\u95ee\u5143\u7d20 */\nint get(myList *list, int index) {\nassert(index &gt;= 0 &amp;&amp; index &lt; list-&gt;size);\nreturn list-&gt;nums[index];\n}\n/* \u66f4\u65b0\u5143\u7d20 */\nvoid set(myList *list, int index, int num) {\nassert(index &gt;= 0 &amp;&amp; index &lt; list-&gt;size);\nlist-&gt;nums[index] = num;\n}\n/* \u5c3e\u90e8\u6dfb\u52a0\u5143\u7d20 */\nvoid add(myList *list, int num) {\nif (size(list) == capacity(list)) {\nextendCapacity(list); // \u6269\u5bb9\n}\nlist-&gt;nums[size(list)] = num;\nlist-&gt;size++;\n}\n/* \u4e2d\u95f4\u63d2\u5165\u5143\u7d20 */\nvoid insert(myList *list, int index, int num) {\nassert(index &gt;= 0 &amp;&amp; index &lt; size(list));\nfor (int i = size(list); i &gt; index; --i) {\nlist-&gt;nums[i] = list-&gt;nums[i - 1];\n}\nlist-&gt;nums[index] = num;\nlist-&gt;size++;\n}\n/* \u5220\u9664\u5143\u7d20 */\n// \u6ce8\u610f\uff1astdio.h \u5360\u7528\u4e86 remove \u5173\u952e\u8bcd\nint removeNum(myList *list, int index) {\nassert(index &gt;= 0 &amp;&amp; index &lt; size(list));\nint num = list-&gt;nums[index];\nfor (int i = index; i &lt; size(list) - 1; i++) {\nlist-&gt;nums[i] = list-&gt;nums[i + 1];\n}\nlist-&gt;size--;\nreturn num;\n}\n/* \u5217\u8868\u6269\u5bb9 */\nvoid extendCapacity(myList *list) {\n// \u5148\u5206\u914d\u7a7a\u95f4\nint newCapacity = capacity(list) * list-&gt;extendRatio;\nint *extend = (int *)malloc(sizeof(int) * newCapacity);\nint *temp = list-&gt;nums;\n// \u62f7\u8d1d\u65e7\u6570\u636e\u5230\u65b0\u6570\u636e\nfor (int i = 0; i &lt; size(list); i++)\nextend[i] = list-&gt;nums[i];\n// \u91ca\u653e\u65e7\u6570\u636e\nfree(temp);\n// \u66f4\u65b0\u65b0\u6570\u636e\nlist-&gt;nums = extend;\nlist-&gt;capacity = newCapacity;\n}\n/* \u5c06\u5217\u8868\u8f6c\u6362\u4e3a Array \u7528\u4e8e\u6253\u5370 */\nint *toArray(myList *list) {\nreturn list-&gt;nums;\n}\n</code></pre> my_list.cs<pre><code>/* \u5217\u8868\u7c7b\u7b80\u6613\u5b9e\u73b0 */\nclass MyList {\nprivate int[] nums;           // \u6570\u7ec4\uff08\u5b58\u50a8\u5217\u8868\u5143\u7d20\uff09\nprivate int numsCapacity = 10;    // \u5217\u8868\u5bb9\u91cf\nprivate int numsSize = 0;         // \u5217\u8868\u957f\u5ea6\uff08\u5373\u5f53\u524d\u5143\u7d20\u6570\u91cf\uff09\nprivate int extendRatio = 2;  // \u6bcf\u6b21\u5217\u8868\u6269\u5bb9\u7684\u500d\u6570\n/* \u6784\u9020\u65b9\u6cd5 */\npublic MyList() {\nnums = new int[numsCapacity];\n}\n/* \u83b7\u53d6\u5217\u8868\u957f\u5ea6\uff08\u5373\u5f53\u524d\u5143\u7d20\u6570\u91cf\uff09*/\npublic int size() {\nreturn numsSize;\n}\n/* \u83b7\u53d6\u5217\u8868\u5bb9\u91cf */\npublic int capacity() {\nreturn numsCapacity;\n}\n/* \u8bbf\u95ee\u5143\u7d20 */\npublic int get(int index) {\n// \u7d22\u5f15\u5982\u679c\u8d8a\u754c\u5219\u629b\u51fa\u5f02\u5e38\uff0c\u4e0b\u540c\nif (index &lt; 0 || index &gt;= numsSize)\nthrow new IndexOutOfRangeException(\"\u7d22\u5f15\u8d8a\u754c\");\nreturn nums[index];\n}\n/* \u66f4\u65b0\u5143\u7d20 */\npublic void set(int index, int num) {\nif (index &lt; 0 || index &gt;= numsSize)\nthrow new IndexOutOfRangeException(\"\u7d22\u5f15\u8d8a\u754c\");\nnums[index] = num;\n}\n/* \u5c3e\u90e8\u6dfb\u52a0\u5143\u7d20 */\npublic void add(int num) {\n// \u5143\u7d20\u6570\u91cf\u8d85\u51fa\u5bb9\u91cf\u65f6\uff0c\u89e6\u53d1\u6269\u5bb9\u673a\u5236\nif (numsSize == numsCapacity)\nextendCapacity();\nnums[numsSize] = num;\n// \u66f4\u65b0\u5143\u7d20\u6570\u91cf\nnumsSize++;\n}\n/* \u4e2d\u95f4\u63d2\u5165\u5143\u7d20 */\npublic void insert(int index, int num) {\nif (index &lt; 0 || index &gt;= numsSize)\nthrow new IndexOutOfRangeException(\"\u7d22\u5f15\u8d8a\u754c\");\n// \u5143\u7d20\u6570\u91cf\u8d85\u51fa\u5bb9\u91cf\u65f6\uff0c\u89e6\u53d1\u6269\u5bb9\u673a\u5236\nif (numsSize == numsCapacity)\nextendCapacity();\n// \u5c06\u7d22\u5f15 index \u4ee5\u53ca\u4e4b\u540e\u7684\u5143\u7d20\u90fd\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\nfor (int j = numsSize - 1; j &gt;= index; j--) {\nnums[j + 1] = nums[j];\n}\nnums[index] = num;\n// \u66f4\u65b0\u5143\u7d20\u6570\u91cf\nnumsSize++;\n}\n/* \u5220\u9664\u5143\u7d20 */\npublic int remove(int index) {\nif (index &lt; 0 || index &gt;= numsSize)\nthrow new IndexOutOfRangeException(\"\u7d22\u5f15\u8d8a\u754c\");\nint num = nums[index];\n// \u5c06\u7d22\u5f15 index \u4e4b\u540e\u7684\u5143\u7d20\u90fd\u5411\u524d\u79fb\u52a8\u4e00\u4f4d\nfor (int j = index; j &lt; numsSize - 1; j++) {\nnums[j] = nums[j + 1];\n}\n// \u66f4\u65b0\u5143\u7d20\u6570\u91cf\nnumsSize--;\n// \u8fd4\u56de\u88ab\u5220\u9664\u5143\u7d20\nreturn num;\n}\n/* \u5217\u8868\u6269\u5bb9 */\npublic void extendCapacity() {\n// \u65b0\u5efa\u4e00\u4e2a\u957f\u5ea6\u4e3a numsCapacity * extendRatio \u7684\u6570\u7ec4\uff0c\u5e76\u5c06\u539f\u6570\u7ec4\u62f7\u8d1d\u5230\u65b0\u6570\u7ec4\nSystem.Array.Resize(ref nums, numsCapacity * extendRatio);\n// \u66f4\u65b0\u5217\u8868\u5bb9\u91cf\nnumsCapacity = nums.Length;\n}\n/* \u5c06\u5217\u8868\u8f6c\u6362\u4e3a\u6570\u7ec4 */\npublic int[] toArray() {\n// \u4ec5\u8f6c\u6362\u6709\u6548\u957f\u5ea6\u8303\u56f4\u5185\u7684\u5217\u8868\u5143\u7d20\nint[] nums = new int[numsSize];\nfor (int i = 0; i &lt; numsSize; i++) {\nnums[i] = get(i);\n}\nreturn nums;\n}\n}\n</code></pre> my_list.swift<pre><code>/* \u5217\u8868\u7c7b\u7b80\u6613\u5b9e\u73b0 */\nclass MyList {\nprivate var nums: [Int] // \u6570\u7ec4\uff08\u5b58\u50a8\u5217\u8868\u5143\u7d20\uff09\nprivate var _capacity = 10 // \u5217\u8868\u5bb9\u91cf\nprivate var _size = 0 // \u5217\u8868\u957f\u5ea6\uff08\u5373\u5f53\u524d\u5143\u7d20\u6570\u91cf\uff09\nprivate let extendRatio = 2 // \u6bcf\u6b21\u5217\u8868\u6269\u5bb9\u7684\u500d\u6570\n/* \u6784\u9020\u65b9\u6cd5 */\ninit() {\nnums = Array(repeating: 0, count: _capacity)\n}\n/* \u83b7\u53d6\u5217\u8868\u957f\u5ea6\uff08\u5373\u5f53\u524d\u5143\u7d20\u6570\u91cf\uff09*/\nfunc size() -&gt; Int {\n_size\n}\n/* \u83b7\u53d6\u5217\u8868\u5bb9\u91cf */\nfunc capacity() -&gt; Int {\n_capacity\n}\n/* \u8bbf\u95ee\u5143\u7d20 */\nfunc get(index: Int) -&gt; Int {\n// \u7d22\u5f15\u5982\u679c\u8d8a\u754c\u5219\u629b\u51fa\u9519\u8bef\uff0c\u4e0b\u540c\nif index &lt; 0 || index &gt;= _size {\nfatalError(\"\u7d22\u5f15\u8d8a\u754c\")\n}\nreturn nums[index]\n}\n/* \u66f4\u65b0\u5143\u7d20 */\nfunc set(index: Int, num: Int) {\nif index &lt; 0 || index &gt;= _size {\nfatalError(\"\u7d22\u5f15\u8d8a\u754c\")\n}\nnums[index] = num\n}\n/* \u5c3e\u90e8\u6dfb\u52a0\u5143\u7d20 */\nfunc add(num: Int) {\n// \u5143\u7d20\u6570\u91cf\u8d85\u51fa\u5bb9\u91cf\u65f6\uff0c\u89e6\u53d1\u6269\u5bb9\u673a\u5236\nif _size == _capacity {\nextendCapacity()\n}\nnums[_size] = num\n// \u66f4\u65b0\u5143\u7d20\u6570\u91cf\n_size += 1\n}\n/* \u4e2d\u95f4\u63d2\u5165\u5143\u7d20 */\nfunc insert(index: Int, num: Int) {\nif index &lt; 0 || index &gt;= _size {\nfatalError(\"\u7d22\u5f15\u8d8a\u754c\")\n}\n// \u5143\u7d20\u6570\u91cf\u8d85\u51fa\u5bb9\u91cf\u65f6\uff0c\u89e6\u53d1\u6269\u5bb9\u673a\u5236\nif _size == _capacity {\nextendCapacity()\n}\n// \u5c06\u7d22\u5f15 index \u4ee5\u53ca\u4e4b\u540e\u7684\u5143\u7d20\u90fd\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\nfor j in sequence(first: _size - 1, next: { $0 &gt;= index + 1 ? $0 - 1 : nil }) {\nnums[j + 1] = nums[j]\n}\nnums[index] = num\n// \u66f4\u65b0\u5143\u7d20\u6570\u91cf\n_size += 1\n}\n/* \u5220\u9664\u5143\u7d20 */\n@discardableResult\nfunc remove(index: Int) -&gt; Int {\nif index &lt; 0 || index &gt;= _size {\nfatalError(\"\u7d22\u5f15\u8d8a\u754c\")\n}\nlet num = nums[index]\n// \u5c06\u7d22\u5f15 index \u4e4b\u540e\u7684\u5143\u7d20\u90fd\u5411\u524d\u79fb\u52a8\u4e00\u4f4d\nfor j in index ..&lt; (_size - 1) {\nnums[j] = nums[j + 1]\n}\n// \u66f4\u65b0\u5143\u7d20\u6570\u91cf\n_size -= 1\n// \u8fd4\u56de\u88ab\u5220\u9664\u5143\u7d20\nreturn num\n}\n/* \u5217\u8868\u6269\u5bb9 */\nfunc extendCapacity() {\n// \u65b0\u5efa\u4e00\u4e2a\u957f\u5ea6\u4e3a\u539f\u6570\u7ec4 extendRatio \u500d\u7684\u65b0\u6570\u7ec4\uff0c\u5e76\u5c06\u539f\u6570\u7ec4\u62f7\u8d1d\u5230\u65b0\u6570\u7ec4\nnums = nums + Array(repeating: 0, count: _capacity * (extendRatio - 1))\n// \u66f4\u65b0\u5217\u8868\u5bb9\u91cf\n_capacity = nums.count\n}\n/* \u5c06\u5217\u8868\u8f6c\u6362\u4e3a\u6570\u7ec4 */\nfunc toArray() -&gt; [Int] {\nvar nums = Array(repeating: 0, count: _size)\nfor i in 0 ..&lt; _size {\nnums[i] = get(index: i)\n}\nreturn nums\n}\n}\n</code></pre> my_list.zig<pre><code>// \u5217\u8868\u7c7b\u7b80\u6613\u5b9e\u73b0\nfn MyList(comptime T: type) type {\nreturn struct {\nconst Self = @This();\nnums: []T = undefined,                        // \u6570\u7ec4\uff08\u5b58\u50a8\u5217\u8868\u5143\u7d20\uff09\nnums_capacity: usize = 10,                     // \u5217\u8868\u5bb9\u91cf\nnum_size: usize = 0,                           // \u5217\u8868\u957f\u5ea6\uff08\u5373\u5f53\u524d\u5143\u7d20\u6570\u91cf\uff09\nextend_ratio: usize = 2,                       // \u6bcf\u6b21\u5217\u8868\u6269\u5bb9\u7684\u500d\u6570\nmem_arena: ?std.heap.ArenaAllocator = null,\nmem_allocator: std.mem.Allocator = undefined, // \u5185\u5b58\u5206\u914d\u5668\n// \u6784\u9020\u65b9\u6cd5\uff08\u5206\u914d\u5185\u5b58+\u521d\u59cb\u5316\u5217\u8868\uff09\npub fn init(self: *Self, allocator: std.mem.Allocator) !void {\nif (self.mem_arena == null) {\nself.mem_arena = std.heap.ArenaAllocator.init(allocator);\nself.mem_allocator = self.mem_arena.?.allocator();\n}\nself.nums = try self.mem_allocator.alloc(T, self.nums_capacity);\nstd.mem.set(T, self.nums, @as(T, 0));\n}\n// \u6790\u6784\u65b9\u6cd5\uff08\u91ca\u653e\u5185\u5b58\uff09\npub fn deinit(self: *Self) void {\nif (self.mem_arena == null) return;\nself.mem_arena.?.deinit();\n}\n// \u83b7\u53d6\u5217\u8868\u957f\u5ea6\uff08\u5373\u5f53\u524d\u5143\u7d20\u6570\u91cf\uff09\npub fn size(self: *Self) usize {\nreturn self.num_size;\n}\n// \u83b7\u53d6\u5217\u8868\u5bb9\u91cf\npub fn capacity(self: *Self) usize {\nreturn self.nums_capacity;\n}\n// \u8bbf\u95ee\u5143\u7d20\npub fn get(self: *Self, index: usize) T {\n// \u7d22\u5f15\u5982\u679c\u8d8a\u754c\u5219\u629b\u51fa\u5f02\u5e38\uff0c\u4e0b\u540c\nif (index &lt; 0 or index &gt;= self.size()) @panic(\"\u7d22\u5f15\u8d8a\u754c\");\nreturn self.nums[index];\n}  // \u66f4\u65b0\u5143\u7d20\npub fn set(self: *Self, index: usize, num: T) void {\n// \u7d22\u5f15\u5982\u679c\u8d8a\u754c\u5219\u629b\u51fa\u5f02\u5e38\uff0c\u4e0b\u540c\nif (index &lt; 0 or index &gt;= self.size()) @panic(\"\u7d22\u5f15\u8d8a\u754c\");\nself.nums[index] = num;\n}  // \u5c3e\u90e8\u6dfb\u52a0\u5143\u7d20\npub fn add(self: *Self, num: T) !void {\n// \u5143\u7d20\u6570\u91cf\u8d85\u51fa\u5bb9\u91cf\u65f6\uff0c\u89e6\u53d1\u6269\u5bb9\u673a\u5236\nif (self.size() == self.capacity()) try self.extendCapacity();\nself.nums[self.size()] = num;\n// \u66f4\u65b0\u5143\u7d20\u6570\u91cf\nself.num_size += 1;\n}  // \u4e2d\u95f4\u63d2\u5165\u5143\u7d20\npub fn insert(self: *Self, index: usize, num: T) !void {\nif (index &lt; 0 or index &gt;= self.size()) @panic(\"\u7d22\u5f15\u8d8a\u754c\");\n// \u5143\u7d20\u6570\u91cf\u8d85\u51fa\u5bb9\u91cf\u65f6\uff0c\u89e6\u53d1\u6269\u5bb9\u673a\u5236\nif (self.size() == self.capacity()) try self.extendCapacity();\n// \u7d22\u5f15 i \u4ee5\u53ca\u4e4b\u540e\u7684\u5143\u7d20\u90fd\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\nvar j = self.size() - 1;\nwhile (j &gt;= index) : (j -= 1) {\nself.nums[j + 1] = self.nums[j];\n}\nself.nums[index] = num;\n// \u66f4\u65b0\u5143\u7d20\u6570\u91cf\nself.num_size += 1;\n}\n// \u5220\u9664\u5143\u7d20\npub fn remove(self: *Self, index: usize) T {\nif (index &lt; 0 or index &gt;= self.size()) @panic(\"\u7d22\u5f15\u8d8a\u754c\");\nvar num = self.nums[index];\n// \u7d22\u5f15 i \u4e4b\u540e\u7684\u5143\u7d20\u90fd\u5411\u524d\u79fb\u52a8\u4e00\u4f4d\nvar j = index;\nwhile (j &lt; self.size() - 1) : (j += 1) {\nself.nums[j] = self.nums[j + 1];\n}\n// \u66f4\u65b0\u5143\u7d20\u6570\u91cf\nself.num_size -= 1;\n// \u8fd4\u56de\u88ab\u5220\u9664\u5143\u7d20\nreturn num;\n}\n// \u5217\u8868\u6269\u5bb9\npub fn extendCapacity(self: *Self) !void {\n// \u65b0\u5efa\u4e00\u4e2a\u957f\u5ea6\u4e3a\u539f\u6570\u7ec4 extendRatio \u500d\u7684\u65b0\u6570\u7ec4\uff0c\u5e76\u5c06\u539f\u6570\u7ec4\u62f7\u8d1d\u5230\u65b0\u6570\u7ec4\nvar newCapacity = self.capacity() * self.extend_ratio;\nvar extend = try self.mem_allocator.alloc(T, newCapacity);\nstd.mem.set(T, extend, @as(T, 0));\n// \u5c06\u539f\u6570\u7ec4\u4e2d\u7684\u6240\u6709\u5143\u7d20\u590d\u5236\u5230\u65b0\u6570\u7ec4\nstd.mem.copy(T, extend, self.nums);\nself.nums = extend;\n// \u66f4\u65b0\u5217\u8868\u5bb9\u91cf\nself.nums_capacity = newCapacity;\n}\n// \u5c06\u5217\u8868\u8f6c\u6362\u4e3a\u6570\u7ec4\npub fn toArray(self: *Self) ![]T {\n// \u4ec5\u8f6c\u6362\u6709\u6548\u957f\u5ea6\u8303\u56f4\u5185\u7684\u5217\u8868\u5143\u7d20\nvar nums = try self.mem_allocator.alloc(T, self.size());\nstd.mem.set(T, nums, @as(T, 0));\nfor (nums) |*num, i| {\nnum.* = self.get(i);\n}\nreturn nums;\n}\n};\n}\n</code></pre> my_list.dart<pre><code>/* \u5217\u8868\u7c7b\u7b80\u6613\u5b9e\u73b0 */\nclass MyList {\nlate List&lt;int&gt; _nums; // \u6570\u7ec4\uff08\u5b58\u50a8\u5217\u8868\u5143\u7d20\uff09\nint _capacity = 10; // \u5217\u8868\u5bb9\u91cf\nint _size = 0; // \u5217\u8868\u957f\u5ea6\uff08\u5373\u5f53\u524d\u5143\u7d20\u6570\u91cf\uff09\nint _extendRatio = 2; // \u6bcf\u6b21\u5217\u8868\u6269\u5bb9\u7684\u500d\u6570\n/* \u6784\u9020\u65b9\u6cd5 */\nMyList() {\n_nums = List.filled(_capacity, 0);\n}\n/* \u83b7\u53d6\u5217\u8868\u957f\u5ea6\uff08\u5373\u5f53\u524d\u5143\u7d20\u6570\u91cf\uff09*/\nint size() =&gt; _size;\n/* \u83b7\u53d6\u5217\u8868\u5bb9\u91cf */\nint capacity() =&gt; _capacity;\n/* \u8bbf\u95ee\u5143\u7d20 */\nint get(int index) {\nif (index &gt;= _size) throw RangeError('\u7d22\u5f15\u8d8a\u754c');\nreturn _nums[index];\n}\n/* \u66f4\u65b0\u5143\u7d20 */\nvoid set(int index, int num) {\nif (index &gt;= _size) throw RangeError('\u7d22\u5f15\u8d8a\u754c');\n_nums[index] = num;\n}\n/* \u5c3e\u90e8\u6dfb\u52a0\u5143\u7d20 */\nvoid add(int num) {\n// \u5143\u7d20\u6570\u91cf\u8d85\u51fa\u5bb9\u91cf\u65f6\uff0c\u89e6\u53d1\u6269\u5bb9\u673a\u5236\nif (_size == _capacity) extendCapacity();\n_nums[_size] = num;\n// \u66f4\u65b0\u5143\u7d20\u6570\u91cf\n_size++;\n}\n/* \u4e2d\u95f4\u63d2\u5165\u5143\u7d20 */\nvoid insert(int index, int num) {\nif (index &gt;= _size) throw RangeError('\u7d22\u5f15\u8d8a\u754c');\n// \u5143\u7d20\u6570\u91cf\u8d85\u51fa\u5bb9\u91cf\u65f6\uff0c\u89e6\u53d1\u6269\u5bb9\u673a\u5236\nif (_size == _capacity) extendCapacity();\n// \u5c06\u7d22\u5f15 index \u4ee5\u53ca\u4e4b\u540e\u7684\u5143\u7d20\u90fd\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\nfor (var j = _size - 1; j &gt;= index; j--) {\n_nums[j + 1] = _nums[j];\n}\n_nums[index] = num;\n// \u66f4\u65b0\u5143\u7d20\u6570\u91cf\n_size++;\n}\n/* \u5220\u9664\u5143\u7d20 */\nint remove(int index) {\nif (index &gt;= _size) throw RangeError('\u7d22\u5f15\u8d8a\u754c');\nint num = _nums[index];\n// \u5c06\u7d22\u5f15 index \u4e4b\u540e\u7684\u5143\u7d20\u90fd\u5411\u524d\u79fb\u52a8\u4e00\u4f4d\nfor (var j = index; j &lt; _size - 1; j++) {\n_nums[j] = _nums[j + 1];\n}\n// \u66f4\u65b0\u5143\u7d20\u6570\u91cf\n_size--;\n// \u8fd4\u56de\u88ab\u5220\u9664\u5143\u7d20\nreturn num;\n}\n/* \u5217\u8868\u6269\u5bb9 */\nvoid extendCapacity() {\n// \u65b0\u5efa\u4e00\u4e2a\u957f\u5ea6\u4e3a\u539f\u6570\u7ec4 _extendRatio \u500d\u7684\u65b0\u6570\u7ec4\nfinal _newNums = List.filled(_capacity * _extendRatio, 0);\n// \u5c06\u539f\u6570\u7ec4\u62f7\u8d1d\u5230\u65b0\u6570\u7ec4\nList.copyRange(_newNums, 0, _nums);\n// \u66f4\u65b0 _nums \u7684\u5f15\u7528\n_nums = _newNums;\n// \u66f4\u65b0\u5217\u8868\u5bb9\u91cf\n_capacity = _nums.length;\n}\n/* \u5c06\u5217\u8868\u8f6c\u6362\u4e3a\u6570\u7ec4 */\nList&lt;int&gt; toArray() {\nList&lt;int&gt; nums = [];\nfor (var i = 0; i &lt; _size; i++) {\nnums.add(get(i));\n}\nreturn nums;\n}\n}\n</code></pre>"},{"location":"chapter_array_and_linkedlist/summary/","title":"4.4. \u00a0 \u5c0f\u7ed3","text":"<ul> <li>\u6570\u7ec4\u548c\u94fe\u8868\u662f\u4e24\u79cd\u57fa\u672c\u6570\u636e\u7ed3\u6784\uff0c\u5206\u522b\u4ee3\u8868\u6570\u636e\u5728\u8ba1\u7b97\u673a\u5185\u5b58\u4e2d\u7684\u8fde\u7eed\u7a7a\u95f4\u5b58\u50a8\u548c\u79bb\u6563\u7a7a\u95f4\u5b58\u50a8\u65b9\u5f0f\u3002\u4e24\u8005\u7684\u4f18\u7f3a\u70b9\u5448\u73b0\u51fa\u4e92\u8865\u7684\u7279\u6027\u3002</li> <li>\u6570\u7ec4\u652f\u6301\u968f\u673a\u8bbf\u95ee\u3001\u5360\u7528\u5185\u5b58\u8f83\u5c11\uff1b\u4f46\u63d2\u5165\u548c\u5220\u9664\u5143\u7d20\u6548\u7387\u4f4e\uff0c\u4e14\u521d\u59cb\u5316\u540e\u957f\u5ea6\u4e0d\u53ef\u53d8\u3002</li> <li>\u94fe\u8868\u901a\u8fc7\u66f4\u6539\u6307\u9488\u5b9e\u73b0\u9ad8\u6548\u7684\u8282\u70b9\u63d2\u5165\u4e0e\u5220\u9664\uff0c\u4e14\u53ef\u4ee5\u7075\u6d3b\u8c03\u6574\u957f\u5ea6\uff1b\u4f46\u8282\u70b9\u8bbf\u95ee\u6548\u7387\u4f4e\u3001\u5360\u7528\u5185\u5b58\u8f83\u591a\u3002\u5e38\u89c1\u7684\u94fe\u8868\u7c7b\u578b\u5305\u62ec\u5355\u5411\u94fe\u8868\u3001\u5faa\u73af\u94fe\u8868\u3001\u53cc\u5411\u94fe\u8868\u3002</li> <li>\u52a8\u6001\u6570\u7ec4\uff0c\u53c8\u79f0\u5217\u8868\uff0c\u662f\u57fa\u4e8e\u6570\u7ec4\u5b9e\u73b0\u7684\u4e00\u79cd\u6570\u636e\u7ed3\u6784\u3002\u5b83\u4fdd\u7559\u4e86\u6570\u7ec4\u7684\u4f18\u52bf\uff0c\u540c\u65f6\u53ef\u4ee5\u7075\u6d3b\u8c03\u6574\u957f\u5ea6\u3002\u5217\u8868\u7684\u51fa\u73b0\u6781\u5927\u5730\u63d0\u9ad8\u4e86\u6570\u7ec4\u7684\u6613\u7528\u6027\uff0c\u4f46\u53ef\u80fd\u5bfc\u81f4\u90e8\u5206\u5185\u5b58\u7a7a\u95f4\u6d6a\u8d39\u3002</li> <li>\u4e0b\u8868\u603b\u7ed3\u5e76\u5bf9\u6bd4\u4e86\u6570\u7ec4\u4e0e\u94fe\u8868\u7684\u5404\u9879\u7279\u6027\u4e0e\u64cd\u4f5c\u6548\u7387\u3002</li> </ul> \u6570\u7ec4 \u94fe\u8868 \u5b58\u50a8\u65b9\u5f0f \u8fde\u7eed\u5185\u5b58\u7a7a\u95f4 \u79bb\u6563\u5185\u5b58\u7a7a\u95f4 \u6570\u636e\u7ed3\u6784\u957f\u5ea6 \u957f\u5ea6\u4e0d\u53ef\u53d8 \u957f\u5ea6\u53ef\u53d8 \u5185\u5b58\u4f7f\u7528\u7387 \u5360\u7528\u5185\u5b58\u5c11\u3001\u7f13\u5b58\u5c40\u90e8\u6027\u597d \u5360\u7528\u5185\u5b58\u591a \u4f18\u52bf\u64cd\u4f5c \u968f\u673a\u8bbf\u95ee \u63d2\u5165\u3001\u5220\u9664 \u8bbf\u95ee\u5143\u7d20 \\(O(1)\\) \\(O(N)\\) \u6dfb\u52a0\u5143\u7d20 \\(O(N)\\) \\(O(1)\\) \u5220\u9664\u5143\u7d20 \\(O(N)\\) \\(O(1)\\) <p>\u7f13\u5b58\u5c40\u90e8\u6027</p> <p>\u5728\u8ba1\u7b97\u673a\u4e2d\uff0c\u6570\u636e\u8bfb\u5199\u901f\u5ea6\u6392\u5e8f\u662f\u201c\u786c\u76d8 &lt; \u5185\u5b58 &lt; CPU \u7f13\u5b58\u201d\u3002\u5f53\u6211\u4eec\u8bbf\u95ee\u6570\u7ec4\u5143\u7d20\u65f6\uff0c\u8ba1\u7b97\u673a\u4e0d\u4ec5\u4f1a\u52a0\u8f7d\u5b83\uff0c\u8fd8\u4f1a\u7f13\u5b58\u5176\u5468\u56f4\u7684\u5176\u4ed6\u6570\u636e\uff0c\u4ece\u800c\u501f\u52a9\u9ad8\u901f\u7f13\u5b58\u6765\u63d0\u5347\u540e\u7eed\u64cd\u4f5c\u7684\u6267\u884c\u901f\u5ea6\u3002\u94fe\u8868\u5219\u4e0d\u7136\uff0c\u8ba1\u7b97\u673a\u53ea\u80fd\u6328\u4e2a\u5730\u7f13\u5b58\u5404\u4e2a\u8282\u70b9\uff0c\u8fd9\u6837\u7684\u591a\u6b21\u201c\u642c\u8fd0\u201d\u964d\u4f4e\u4e86\u6574\u4f53\u6548\u7387\u3002</p>"},{"location":"chapter_array_and_linkedlist/summary/#441-q-a","title":"4.4.1. \u00a0 Q &amp; A","text":"<p>\u6570\u7ec4\u5b58\u50a8\u5728\u6808\u4e0a\u548c\u5b58\u50a8\u5728\u5806\u4e0a\uff0c\u5bf9\u65f6\u95f4\u6548\u7387\u548c\u7a7a\u95f4\u6548\u7387\u662f\u5426\u6709\u5f71\u54cd\uff1f</p> <p>\u6808\u5185\u5b58\u5206\u914d\u7531\u7f16\u8bd1\u5668\u81ea\u52a8\u5b8c\u6210\uff0c\u800c\u5806\u5185\u5b58\u7531\u7a0b\u5e8f\u5458\u5728\u4ee3\u7801\u4e2d\u5206\u914d\uff08\u6ce8\u610f\uff0c\u8fd9\u91cc\u7684\u6808\u548c\u5806\u548c\u6570\u636e\u7ed3\u6784\u4e2d\u7684\u6808\u548c\u5806\u4e0d\u662f\u540c\u4e00\u6982\u5ff5\uff09\u3002</p> <ol> <li>\u6808\u4e0d\u7075\u6d3b\uff0c\u5206\u914d\u7684\u5185\u5b58\u5927\u5c0f\u4e0d\u53ef\u66f4\u6539\uff1b\u5806\u76f8\u5bf9\u7075\u6d3b\uff0c\u53ef\u4ee5\u52a8\u6001\u5206\u914d\u5185\u5b58\uff1b</li> <li>\u6808\u662f\u4e00\u5757\u6bd4\u8f83\u5c0f\u7684\u5185\u5b58\uff0c\u5bb9\u6613\u51fa\u73b0\u5185\u5b58\u4e0d\u8db3\uff1b\u5806\u5185\u5b58\u5f88\u5927\uff0c\u4f46\u662f\u7531\u4e8e\u662f\u52a8\u6001\u5206\u914d\uff0c\u5bb9\u6613\u788e\u7247\u5316\uff0c\u7ba1\u7406\u5806\u5185\u5b58\u7684\u96be\u5ea6\u66f4\u5927\u3001\u6210\u672c\u66f4\u9ad8\uff1b</li> <li>\u8bbf\u95ee\u6808\u6bd4\u8bbf\u95ee\u5806\u66f4\u5feb\uff0c\u56e0\u4e3a\u6808\u5185\u5b58\u8f83\u5c0f\u3001\u5bf9\u7f13\u5b58\u53cb\u597d\uff0c\u5806\u5e27\u5206\u6563\u5728\u5f88\u5927\u7684\u7a7a\u95f4\u5185\uff0c\u4f1a\u51fa\u73b0\u66f4\u591a\u7684\u7f13\u5b58\u672a\u547d\u4e2d\uff1b</li> </ol> <p>\u4e3a\u4ec0\u4e48\u6570\u7ec4\u4f1a\u5f3a\u8c03\u8981\u6c42\u76f8\u540c\u7c7b\u578b\u7684\u5143\u7d20\uff0c\u800c\u5728\u94fe\u8868\u4e2d\u5374\u6ca1\u6709\u5f3a\u8c03\u540c\u7c7b\u578b\u5462\uff1f</p> <p>\u94fe\u8868\u7531\u7ed3\u70b9\u7ec4\u6210\uff0c\u7ed3\u70b9\u4e4b\u95f4\u7531\u6307\u9488\u8fde\u63a5\uff0c\u5404\u4e2a\u7ed3\u70b9\u53ef\u4ee5\u5b58\u50a8\u4e0d\u540c\u7c7b\u578b\u7684\u6570\u636e\uff0c\u4f8b\u5982 int, double, string, object \u7b49\u3002</p> <p>\u76f8\u5bf9\u5730\uff0c\u6570\u7ec4\u5143\u7d20\u5219\u5fc5\u987b\u662f\u76f8\u540c\u7c7b\u578b\u7684\uff0c\u8fd9\u6837\u624d\u80fd\u901a\u8fc7\u8ba1\u7b97\u504f\u79fb\u91cf\u6765\u83b7\u53d6\u5bf9\u5e94\u5143\u7d20\u4f4d\u7f6e\u3002\u4f8b\u5982\uff0c\u5982\u679c\u6570\u7ec4\u540c\u65f6\u5305\u542b int \u548c long \u4e24\u79cd\u7c7b\u578b\uff0c\u5355\u4e2a\u5143\u7d20\u5206\u522b\u5360\u7528 4 bytes \u548c 8 bytes \uff0c\u90a3\u4e48\u6b64\u65f6\u5c31\u4e0d\u80fd\u7528\u4ee5\u4e0b\u516c\u5f0f\u8ba1\u7b97\u504f\u79fb\u91cf\u4e86\uff0c\u56e0\u4e3a\u6570\u7ec4\u4e2d\u5305\u542b\u4e86\u4e24\u79cd <code>elementLength</code> \u3002</p> <pre><code>// \u5143\u7d20\u5185\u5b58\u5730\u5740 = \u6570\u7ec4\u5185\u5b58\u5730\u5740 + \u5143\u7d20\u957f\u5ea6 * \u5143\u7d20\u7d22\u5f15\nelementAddr = firtstElementAddr + elementLength * elementIndex\n</code></pre> <p>\u5220\u9664\u8282\u70b9\u540e\uff0c\u662f\u5426\u9700\u8981\u628a <code>P.next</code> \u8bbe\u4e3a \\(\\text{None}\\) \u5462\uff1f</p> <p>\u4e0d\u4fee\u6539 <code>P.next</code> \u4e5f\u53ef\u4ee5\u3002\u4ece\u8be5\u94fe\u8868\u7684\u89d2\u5ea6\u770b\uff0c\u4ece\u5934\u7ed3\u70b9\u904d\u5386\u5230\u5c3e\u7ed3\u70b9\u5df2\u7ecf\u9047\u4e0d\u5230 <code>P</code> \u4e86\u3002\u8fd9\u610f\u5473\u7740\u7ed3\u70b9 <code>P</code> \u5df2\u7ecf\u4ece\u94fe\u8868\u4e2d\u5220\u9664\u4e86\uff0c\u6b64\u65f6\u7ed3\u70b9 <code>P</code> \u6307\u5411\u54ea\u91cc\u90fd\u4e0d\u4f1a\u5bf9\u8fd9\u6761\u94fe\u8868\u4ea7\u751f\u5f71\u54cd\u4e86\u3002</p> <p>\u4ece\u5783\u573e\u56de\u6536\u7684\u89d2\u5ea6\u770b\uff0c\u5bf9\u4e8e Java, Python, Go \u7b49\u62e5\u6709\u81ea\u52a8\u5783\u573e\u56de\u6536\u7684\u8bed\u8a00\u6765\u8bf4\uff0c\u8282\u70b9 <code>P</code> \u662f\u5426\u88ab\u56de\u6536\u53d6\u51b3\u4e8e\u662f\u5426\u6709\u4ecd\u5b58\u5728\u6307\u5411\u5b83\u7684\u5f15\u7528\uff0c\u800c\u4e0d\u662f <code>P.next</code> \u7684\u503c\u3002\u5728 C, C++ \u7b49\u8bed\u8a00\u4e2d\uff0c\u6211\u4eec\u9700\u8981\u624b\u52a8\u91ca\u653e\u8282\u70b9\u5185\u5b58\u3002</p> <p>\u5728\u94fe\u8868\u4e2d\u63d2\u5165\u548c\u5220\u9664\u64cd\u4f5c\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u662f \\(O(1)\\) \u3002\u4f46\u662f\u589e\u5220\u4e4b\u524d\u90fd\u9700\u8981 \\(O(n)\\) \u67e5\u627e\u5143\u7d20\uff0c\u90a3\u4e3a\u4ec0\u4e48\u65f6\u95f4\u590d\u6742\u5ea6\u4e0d\u662f \\(O(n)\\) \u5462\uff1f</p> <p>\u5982\u679c\u662f\u5148\u67e5\u627e\u5143\u7d20\u3001\u518d\u5220\u9664\u5143\u7d20\uff0c\u786e\u5b9e\u662f \\(O(n)\\) \u3002\u7136\u800c\uff0c\u94fe\u8868\u7684 \\(O(1)\\) \u589e\u5220\u7684\u4f18\u52bf\u53ef\u4ee5\u5728\u5176\u4ed6\u5e94\u7528\u4e0a\u5f97\u5230\u4f53\u73b0\u3002\u4f8b\u5982\uff0c\u53cc\u5411\u961f\u5217\u9002\u5408\u4f7f\u7528\u94fe\u8868\u5b9e\u73b0\uff0c\u6211\u4eec\u7ef4\u62a4\u4e00\u4e2a\u6307\u9488\u53d8\u91cf\u59cb\u7ec8\u6307\u5411\u5934\u7ed3\u70b9\u3001\u5c3e\u7ed3\u70b9\uff0c\u6bcf\u6b21\u63d2\u5165\u4e0e\u5220\u9664\u64cd\u4f5c\u90fd\u662f \\(O(1)\\) \u3002</p> <p>\u56fe\u7247\u201c\u94fe\u8868\u5b9a\u4e49\u4e0e\u5b58\u50a8\u65b9\u5f0f\u201d\u4e2d\uff0c\u6d45\u84dd\u8272\u7684\u5b58\u50a8\u7ed3\u70b9\u6307\u9488\u662f\u5360\u7528\u4e00\u5757\u5185\u5b58\u5730\u5740\u5417\uff1f\u8fd8\u662f\u548c\u7ed3\u70b9\u503c\u5404\u5360\u4e00\u534a\u5462\uff1f</p> <p>\u6587\u4e2d\u53ea\u662f\u4e00\u4e2a\u793a\u610f\u56fe\uff0c\u53ea\u662f\u5b9a\u6027\u8868\u793a\u3002\u5b9a\u91cf\u7684\u8bdd\u9700\u8981\u6839\u636e\u5177\u4f53\u60c5\u51b5\u5206\u6790\uff1a</p> <ul> <li>\u4e0d\u540c\u7c7b\u578b\u7684\u7ed3\u70b9\u503c\u5360\u7528\u7684\u7a7a\u95f4\u662f\u4e0d\u540c\u7684\uff0c\u6bd4\u5982 int, long, double, \u6216\u8005\u662f\u7c7b\u7684\u5b9e\u4f8b\u7b49\u7b49\u3002</li> <li>\u6307\u9488\u53d8\u91cf\u5360\u7528\u7684\u5185\u5b58\u7a7a\u95f4\u5927\u5c0f\u6839\u636e\u6240\u4f7f\u7528\u7684\u64cd\u4f5c\u7cfb\u7edf\u53ca\u7f16\u8bd1\u73af\u5883\u800c\u5b9a\uff0c\u5927\u591a\u4e3a 8 \u5b57\u8282\u6216 4 \u5b57\u8282\u3002</li> </ul> <p>\u5728\u5217\u8868\u672b\u5c3e\u6dfb\u52a0\u5143\u7d20\u662f\u5426\u65f6\u65f6\u523b\u523b\u90fd\u4e3a \\(O(1)\\) \uff1f</p> <p>\u5982\u679c\u6dfb\u52a0\u5143\u7d20\u65f6\u8d85\u51fa\u5217\u8868\u957f\u5ea6\uff0c\u5219\u9700\u8981\u5148\u6269\u5bb9\u5217\u8868\u518d\u6dfb\u52a0\u3002\u7cfb\u7edf\u4f1a\u7533\u8bf7\u4e00\u5757\u65b0\u7684\u5185\u5b58\uff0c\u5e76\u5c06\u539f\u5217\u8868\u7684\u6240\u6709\u5143\u7d20\u642c\u8fd0\u8fc7\u53bb\uff0c\u8fd9\u65f6\u5019\u65f6\u95f4\u590d\u6742\u5ea6\u5c31\u4f1a\u662f \\(O(n)\\) \u3002</p> <p>\u201c\u5217\u8868\u7684\u51fa\u73b0\u5927\u5927\u63d0\u5347\u4e86\u6570\u7ec4\u7684\u5b9e\u7528\u6027\uff0c\u4f46\u526f\u4f5c\u7528\u662f\u4f1a\u9020\u6210\u90e8\u5206\u5185\u5b58\u7a7a\u95f4\u6d6a\u8d39\u201d\uff0c\u8fd9\u91cc\u7684\u7a7a\u95f4\u6d6a\u8d39\u662f\u6307\u989d\u5916\u589e\u52a0\u7684\u53d8\u91cf\u5982\u5bb9\u91cf\u3001\u957f\u5ea6\u3001\u6269\u5bb9\u500d\u6570\u6240\u5360\u7684\u5185\u5b58\u5417\uff1f</p> <p>\u8fd9\u91cc\u7684\u7a7a\u95f4\u6d6a\u8d39\u4e3b\u8981\u6709\u4e24\u65b9\u9762\u542b\u4e49\uff1a\u4e00\u65b9\u9762\uff0c\u5217\u8868\u90fd\u4f1a\u8bbe\u5b9a\u4e00\u4e2a\u521d\u59cb\u957f\u5ea6\uff0c\u6211\u4eec\u4e0d\u4e00\u5b9a\u9700\u8981\u7528\u8fd9\u4e48\u591a\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u4e3a\u4e86\u9632\u6b62\u9891\u7e41\u6269\u5bb9\uff0c\u6269\u5bb9\u4e00\u822c\u90fd\u4f1a\u4e58\u4ee5\u4e00\u4e2a\u7cfb\u6570\uff0c\u6bd4\u5982 \\(\\times 1.5\\) \u3002\u8fd9\u6837\u4e00\u6765\uff0c\u4e5f\u4f1a\u51fa\u73b0\u5f88\u591a\u7a7a\u4f4d\uff0c\u6211\u4eec\u901a\u5e38\u4e0d\u80fd\u5b8c\u5168\u586b\u6ee1\u5b83\u4eec\u3002</p>"},{"location":"chapter_backtracking/","title":"12. \u00a0 \u56de\u6eaf","text":""},{"location":"chapter_backtracking/backtracking_algorithm/","title":"12.1. \u00a0 \u56de\u6eaf\u7b97\u6cd5","text":"<p>\u300c\u56de\u6eaf\u7b97\u6cd5 Backtracking Algorithm\u300d\u662f\u4e00\u79cd\u901a\u8fc7\u7a77\u4e3e\u6765\u89e3\u51b3\u95ee\u9898\u7684\u65b9\u6cd5\uff0c\u5b83\u7684\u6838\u5fc3\u601d\u60f3\u662f\u4ece\u4e00\u4e2a\u521d\u59cb\u72b6\u6001\u51fa\u53d1\uff0c\u66b4\u529b\u641c\u7d22\u6240\u6709\u53ef\u80fd\u7684\u89e3\u51b3\u65b9\u6848\uff0c\u5f53\u9047\u5230\u6b63\u786e\u7684\u89e3\u5219\u5c06\u5176\u8bb0\u5f55\uff0c\u76f4\u5230\u627e\u5230\u89e3\u6216\u8005\u5c1d\u8bd5\u4e86\u6240\u6709\u53ef\u80fd\u7684\u9009\u62e9\u90fd\u65e0\u6cd5\u627e\u5230\u89e3\u4e3a\u6b62\u3002</p> <p>\u56de\u6eaf\u7b97\u6cd5\u901a\u5e38\u91c7\u7528\u300c\u6df1\u5ea6\u4f18\u5148\u641c\u7d22\u300d\u6765\u904d\u5386\u89e3\u7a7a\u95f4\u3002\u5728\u4e8c\u53c9\u6811\u7ae0\u8282\u4e2d\uff0c\u6211\u4eec\u63d0\u5230\u524d\u5e8f\u3001\u4e2d\u5e8f\u548c\u540e\u5e8f\u904d\u5386\u90fd\u5c5e\u4e8e\u6df1\u5ea6\u4f18\u5148\u641c\u7d22\u3002\u4e0b\u9762\uff0c\u6211\u4eec\u4ece\u4e8c\u53c9\u6811\u7684\u524d\u5e8f\u904d\u5386\u5165\u624b\uff0c\u9010\u6b65\u4e86\u89e3\u56de\u6eaf\u7b97\u6cd5\u7684\u5de5\u4f5c\u539f\u7406\u3002</p> <p>\u4f8b\u9898\u4e00</p> <p>\u7ed9\u5b9a\u4e00\u4e2a\u4e8c\u53c9\u6811\uff0c\u641c\u7d22\u5e76\u8bb0\u5f55\u6240\u6709\u503c\u4e3a \\(7\\) \u7684\u8282\u70b9\uff0c\u8fd4\u56de\u8282\u70b9\u5217\u8868\u3002</p> <p>\u89e3\u9898\u601d\u8def\uff1a\u524d\u5e8f\u904d\u5386\u8fd9\u9897\u6811\uff0c\u5e76\u5224\u65ad\u5f53\u524d\u8282\u70b9\u7684\u503c\u662f\u5426\u4e3a \\(7\\) \uff0c\u82e5\u662f\u5219\u5c06\u8be5\u8282\u70b9\u7684\u503c\u52a0\u5165\u5230\u7ed3\u679c\u5217\u8868 <code>res</code> \u4e4b\u4e2d\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart preorder_traversal_i_compact.java<pre><code>/* \u524d\u5e8f\u904d\u5386\uff1a\u4f8b\u9898\u4e00 */\nvoid preOrder(TreeNode root) {\nif (root == null) {\nreturn;\n}\nif (root.val == 7) {\n// \u8bb0\u5f55\u89e3\nres.add(root);\n}\npreOrder(root.left);\npreOrder(root.right);\n}\n</code></pre> preorder_traversal_i_compact.cpp<pre><code>/* \u524d\u5e8f\u904d\u5386\uff1a\u4f8b\u9898\u4e00 */\nvoid preOrder(TreeNode *root) {\nif (root == nullptr) {\nreturn;\n}\nif (root-&gt;val == 7) {\n// \u8bb0\u5f55\u89e3\nres.push_back(root);\n}\npreOrder(root-&gt;left);\npreOrder(root-&gt;right);\n}\n</code></pre> preorder_traversal_i_compact.py<pre><code>def pre_order(root: TreeNode) -&gt; None:\n\"\"\"\u524d\u5e8f\u904d\u5386\uff1a\u4f8b\u9898\u4e00\"\"\"\nif root is None:\nreturn\nif root.val == 7:\n# \u8bb0\u5f55\u89e3\nres.append(root)\npre_order(root.left)\npre_order(root.right)\n</code></pre> preorder_traversal_i_compact.go<pre><code>/* \u524d\u5e8f\u904d\u5386\uff1a\u4f8b\u9898\u4e00 */\nfunc preOrderI(root *TreeNode, res *[]*TreeNode) {\nif root == nil {\nreturn\n}\nif int(root.Val) == 7 {\n// \u8bb0\u5f55\u89e3\n*res = append(*res, root)\n}\npreOrderI(root.Left, res)\npreOrderI(root.Right, res)\n}\n</code></pre> preorder_traversal_i_compact.js<pre><code>/* \u524d\u5e8f\u904d\u5386\uff1a\u4f8b\u9898\u4e00 */\nfunction preOrder(root, res) {\nif (root === null) {\nreturn;\n}\nif (root.val === 7) {\n// \u8bb0\u5f55\u89e3\nres.push(root);\n}\npreOrder(root.left, res);\npreOrder(root.right, res);\n}\n</code></pre> preorder_traversal_i_compact.ts<pre><code>/* \u524d\u5e8f\u904d\u5386\uff1a\u4f8b\u9898\u4e00 */\nfunction preOrder(root: TreeNode | null, res: TreeNode[]): void {\nif (root === null) {\nreturn;\n}\nif (root.val === 7) {\n// \u8bb0\u5f55\u89e3\nres.push(root);\n}\npreOrder(root.left, res);\npreOrder(root.right, res);\n}\n</code></pre> preorder_traversal_i_compact.c<pre><code>[class]{}-[func]{preOrder}\n</code></pre> preorder_traversal_i_compact.cs<pre><code>/* \u524d\u5e8f\u904d\u5386\uff1a\u4f8b\u9898\u4e00 */\nvoid preOrder(TreeNode root) {\nif (root == null) {\nreturn;\n}\nif (root.val == 7) {\n// \u8bb0\u5f55\u89e3\nres.Add(root);\n}\npreOrder(root.left);\npreOrder(root.right);\n}\n</code></pre> preorder_traversal_i_compact.swift<pre><code>/* \u524d\u5e8f\u904d\u5386\uff1a\u4f8b\u9898\u4e00 */\nfunc preOrder(root: TreeNode?) {\nguard let root = root else {\nreturn\n}\nif root.val == 7 {\n// \u8bb0\u5f55\u89e3\nres.append(root)\n}\npreOrder(root: root.left)\npreOrder(root: root.right)\n}\n</code></pre> preorder_traversal_i_compact.zig<pre><code>[class]{}-[func]{preOrder}\n</code></pre> preorder_traversal_i_compact.dart<pre><code>[class]{}-[func]{preOrder}\n</code></pre> <p></p> <p> Fig. \u5728\u524d\u5e8f\u904d\u5386\u4e2d\u641c\u7d22\u8282\u70b9 </p>"},{"location":"chapter_backtracking/backtracking_algorithm/#1211","title":"12.1.1. \u00a0 \u5c1d\u8bd5\u4e0e\u56de\u9000","text":"<p>\u4e4b\u6240\u4ee5\u79f0\u4e4b\u4e3a\u56de\u6eaf\u7b97\u6cd5\uff0c\u662f\u56e0\u4e3a\u8be5\u7b97\u6cd5\u5728\u641c\u7d22\u89e3\u7a7a\u95f4\u65f6\u4f1a\u91c7\u7528\u201c\u5c1d\u8bd5\u201d\u4e0e\u201c\u56de\u9000\u201d\u7684\u7b56\u7565\u3002\u5f53\u7b97\u6cd5\u5728\u641c\u7d22\u8fc7\u7a0b\u4e2d\u9047\u5230\u67d0\u4e2a\u72b6\u6001\u65e0\u6cd5\u7ee7\u7eed\u524d\u8fdb\u6216\u65e0\u6cd5\u5f97\u5230\u6ee1\u8db3\u6761\u4ef6\u7684\u89e3\u65f6\uff0c\u5b83\u4f1a\u64a4\u9500\u4e0a\u4e00\u6b65\u7684\u9009\u62e9\uff0c\u9000\u56de\u5230\u4e4b\u524d\u7684\u72b6\u6001\uff0c\u5e76\u5c1d\u8bd5\u5176\u4ed6\u53ef\u80fd\u7684\u9009\u62e9\u3002</p> <p>\u5bf9\u4e8e\u4f8b\u9898\u4e00\uff0c\u8bbf\u95ee\u6bcf\u4e2a\u8282\u70b9\u90fd\u4ee3\u8868\u4e00\u6b21\u201c\u5c1d\u8bd5\u201d\uff0c\u800c\u8d8a\u8fc7\u53f6\u7ed3\u70b9\u6216\u8fd4\u56de\u7236\u8282\u70b9\u7684 <code>return</code> \u5219\u8868\u793a\u201c\u56de\u9000\u201d\u3002</p> <p>\u503c\u5f97\u8bf4\u660e\u7684\u662f\uff0c\u56de\u9000\u5e76\u4e0d\u7b49\u4ef7\u4e8e\u51fd\u6570\u8fd4\u56de\u3002\u4e3a\u89e3\u91ca\u8fd9\u4e00\u70b9\uff0c\u6211\u4eec\u5bf9\u4f8b\u9898\u4e00\u7a0d\u4f5c\u62d3\u5c55\u3002</p> <p>\u4f8b\u9898\u4e8c</p> <p>\u5728\u4e8c\u53c9\u6811\u4e2d\u641c\u7d22\u6240\u6709\u503c\u4e3a \\(7\\) \u7684\u8282\u70b9\uff0c\u8fd4\u56de\u6839\u8282\u70b9\u5230\u8fd9\u4e9b\u8282\u70b9\u7684\u8def\u5f84\u3002</p> <p>\u89e3\u9898\u601d\u8def\uff1a\u5728\u4f8b\u9898\u4e00\u4ee3\u7801\u7684\u57fa\u7840\u4e0a\uff0c\u6211\u4eec\u9700\u8981\u501f\u52a9\u4e00\u4e2a\u5217\u8868 <code>path</code> \u8bb0\u5f55\u8bbf\u95ee\u8fc7\u7684\u8282\u70b9\u8def\u5f84\u3002\u5f53\u8bbf\u95ee\u5230\u503c\u4e3a \\(7\\) \u7684\u8282\u70b9\u65f6\uff0c\u5219\u590d\u5236 <code>path</code> \u5e76\u6dfb\u52a0\u8fdb\u7ed3\u679c\u5217\u8868 <code>res</code> \u3002\u904d\u5386\u5b8c\u6210\u540e\uff0c<code>res</code> \u4e2d\u4fdd\u5b58\u7684\u5c31\u662f\u6240\u6709\u7684\u89e3\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart preorder_traversal_ii_compact.java<pre><code>/* \u524d\u5e8f\u904d\u5386\uff1a\u4f8b\u9898\u4e8c */\nvoid preOrder(TreeNode root) {\nif (root == null) {\nreturn;\n}\n// \u5c1d\u8bd5\npath.add(root);\nif (root.val == 7) {\n// \u8bb0\u5f55\u89e3\nres.add(new ArrayList&lt;&gt;(path));\n}\npreOrder(root.left);\npreOrder(root.right);\n// \u56de\u9000\npath.remove(path.size() - 1);\n}\n</code></pre> preorder_traversal_ii_compact.cpp<pre><code>/* \u524d\u5e8f\u904d\u5386\uff1a\u4f8b\u9898\u4e8c */\nvoid preOrder(TreeNode *root) {\nif (root == nullptr) {\nreturn;\n}\n// \u5c1d\u8bd5\npath.push_back(root);\nif (root-&gt;val == 7) {\n// \u8bb0\u5f55\u89e3\nres.push_back(path);\n}\npreOrder(root-&gt;left);\npreOrder(root-&gt;right);\n// \u56de\u9000\npath.pop_back();\n}\n</code></pre> preorder_traversal_ii_compact.py<pre><code>def pre_order(root: TreeNode) -&gt; None:\n\"\"\"\u524d\u5e8f\u904d\u5386\uff1a\u4f8b\u9898\u4e8c\"\"\"\nif root is None:\nreturn\n# \u5c1d\u8bd5\npath.append(root)\nif root.val == 7:\n# \u8bb0\u5f55\u89e3\nres.append(list(path))\npre_order(root.left)\npre_order(root.right)\n# \u56de\u9000\npath.pop()\n</code></pre> preorder_traversal_ii_compact.go<pre><code>/* \u524d\u5e8f\u904d\u5386\uff1a\u4f8b\u9898\u4e8c */\nfunc preOrderII(root *TreeNode, res *[][]*TreeNode, path *[]*TreeNode) {\nif root == nil {\nreturn\n}\n// \u5c1d\u8bd5\n*path = append(*path, root)\nif int(root.Val) == 7 {\n// \u8bb0\u5f55\u89e3\n*res = append(*res, *path)\n}\npreOrderII(root.Left, res, path)\npreOrderII(root.Right, res, path)\n// \u56de\u9000\n*path = (*path)[:len(*path)-1]\n}\n</code></pre> preorder_traversal_ii_compact.js<pre><code>/* \u524d\u5e8f\u904d\u5386\uff1a\u4f8b\u9898\u4e8c */\nfunction preOrder(root, path, res) {\nif (root === null) {\nreturn;\n}\n// \u5c1d\u8bd5\npath.push(root);\nif (root.val === 7) {\n// \u8bb0\u5f55\u89e3\nres.push([...path]);\n}\npreOrder(root.left, path, res);\npreOrder(root.right, path, res);\n// \u56de\u9000\npath.pop();\n}\n</code></pre> preorder_traversal_ii_compact.ts<pre><code>/* \u524d\u5e8f\u904d\u5386\uff1a\u4f8b\u9898\u4e8c */\nfunction preOrder(\nroot: TreeNode | null,\npath: TreeNode[],\nres: TreeNode[][]\n): void {\nif (root === null) {\nreturn;\n}\n// \u5c1d\u8bd5\npath.push(root);\nif (root.val === 7) {\n// \u8bb0\u5f55\u89e3\nres.push([...path]);\n}\npreOrder(root.left, path, res);\npreOrder(root.right, path, res);\n// \u56de\u9000\npath.pop();\n}\n</code></pre> preorder_traversal_ii_compact.c<pre><code>[class]{}-[func]{preOrder}\n</code></pre> preorder_traversal_ii_compact.cs<pre><code>/* \u524d\u5e8f\u904d\u5386\uff1a\u4f8b\u9898\u4e8c */\nvoid preOrder(TreeNode root) {\nif (root == null) {\nreturn;\n}\n// \u5c1d\u8bd5\npath.Add(root);\nif (root.val == 7) {\n// \u8bb0\u5f55\u89e3\nres.Add(new List&lt;TreeNode&gt;(path));\n}\npreOrder(root.left);\npreOrder(root.right);\n// \u56de\u9000\npath.RemoveAt(path.Count - 1);\n}\n</code></pre> preorder_traversal_ii_compact.swift<pre><code>/* \u524d\u5e8f\u904d\u5386\uff1a\u4f8b\u9898\u4e8c */\nfunc preOrder(root: TreeNode?) {\nguard let root = root else {\nreturn\n}\n// \u5c1d\u8bd5\npath.append(root)\nif root.val == 7 {\n// \u8bb0\u5f55\u89e3\nres.append(path)\n}\npreOrder(root: root.left)\npreOrder(root: root.right)\n// \u56de\u9000\npath.removeLast()\n}\n</code></pre> preorder_traversal_ii_compact.zig<pre><code>[class]{}-[func]{preOrder}\n</code></pre> preorder_traversal_ii_compact.dart<pre><code>[class]{}-[func]{preOrder}\n</code></pre> <p>\u5728\u6bcf\u6b21\u201c\u5c1d\u8bd5\u201d\u4e2d\uff0c\u6211\u4eec\u901a\u8fc7\u5c06\u5f53\u524d\u8282\u70b9\u6dfb\u52a0\u8fdb <code>path</code> \u6765\u8bb0\u5f55\u8def\u5f84\uff1b\u800c\u5728\u201c\u56de\u9000\u201d\u524d\uff0c\u6211\u4eec\u9700\u8981\u5c06\u8be5\u8282\u70b9\u4ece <code>path</code> \u4e2d\u5f39\u51fa\uff0c\u4ee5\u6062\u590d\u672c\u6b21\u5c1d\u8bd5\u4e4b\u524d\u7684\u72b6\u6001\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u5c1d\u8bd5\u548c\u56de\u9000\u7406\u89e3\u4e3a\u201c\u524d\u8fdb\u201d\u4e0e\u201c\u64a4\u9500\u201d\uff0c\u4e24\u4e2a\u64cd\u4f5c\u662f\u4e92\u4e3a\u76f8\u53cd\u7684\u3002</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt;&lt;11&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p>"},{"location":"chapter_backtracking/backtracking_algorithm/#1212","title":"12.1.2. \u00a0 \u526a\u679d","text":"<p>\u590d\u6742\u7684\u56de\u6eaf\u95ee\u9898\u901a\u5e38\u5305\u542b\u4e00\u4e2a\u6216\u591a\u4e2a\u7ea6\u675f\u6761\u4ef6\uff0c\u7ea6\u675f\u6761\u4ef6\u901a\u5e38\u53ef\u7528\u4e8e\u201c\u526a\u679d\u201d\u3002</p> <p>\u4f8b\u9898\u4e09</p> <p>\u5728\u4e8c\u53c9\u6811\u4e2d\u641c\u7d22\u6240\u6709\u503c\u4e3a \\(7\\) \u7684\u8282\u70b9\uff0c\u8fd4\u56de\u6839\u8282\u70b9\u5230\u8fd9\u4e9b\u8282\u70b9\u7684\u8def\u5f84\uff0c\u8def\u5f84\u4e2d\u4e0d\u80fd\u5305\u542b\u503c\u4e3a \\(3\\) \u7684\u8282\u70b9\u3002</p> <p>\u89e3\u9898\u601d\u8def\uff1a\u5728\u4f8b\u9898\u4e8c\u7684\u57fa\u7840\u4e0a\u6dfb\u52a0\u526a\u679d\u64cd\u4f5c\uff0c\u5f53\u9047\u5230\u503c\u4e3a \\(3\\) \u7684\u8282\u70b9\u65f6\uff0c\u5219\u7ec8\u6b62\u7ee7\u7eed\u641c\u7d22\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart preorder_traversal_iii_compact.java<pre><code>/* \u524d\u5e8f\u904d\u5386\uff1a\u4f8b\u9898\u4e09 */\nvoid preOrder(TreeNode root) {\n// \u526a\u679d\nif (root == null || root.val == 3) {\nreturn;\n}\n// \u5c1d\u8bd5\npath.add(root);\nif (root.val == 7) {\n// \u8bb0\u5f55\u89e3\nres.add(new ArrayList&lt;&gt;(path));\n}\npreOrder(root.left);\npreOrder(root.right);\n// \u56de\u9000\npath.remove(path.size() - 1);\n}\n</code></pre> preorder_traversal_iii_compact.cpp<pre><code>/* \u524d\u5e8f\u904d\u5386\uff1a\u4f8b\u9898\u4e09 */\nvoid preOrder(TreeNode *root) {\n// \u526a\u679d\nif (root == nullptr || root-&gt;val == 3) {\nreturn;\n}\n// \u5c1d\u8bd5\npath.push_back(root);\nif (root-&gt;val == 7) {\n// \u8bb0\u5f55\u89e3\nres.push_back(path);\n}\npreOrder(root-&gt;left);\npreOrder(root-&gt;right);\n// \u56de\u9000\npath.pop_back();\n}\n</code></pre> preorder_traversal_iii_compact.py<pre><code>def pre_order(root: TreeNode) -&gt; None:\n\"\"\"\u524d\u5e8f\u904d\u5386\uff1a\u4f8b\u9898\u4e09\"\"\"\n# \u526a\u679d\nif root is None or root.val == 3:\nreturn\n# \u5c1d\u8bd5\npath.append(root)\nif root.val == 7:\n# \u8bb0\u5f55\u89e3\nres.append(list(path))\npre_order(root.left)\npre_order(root.right)\n# \u56de\u9000\npath.pop()\n</code></pre> preorder_traversal_iii_compact.go<pre><code>/* \u524d\u5e8f\u904d\u5386\uff1a\u4f8b\u9898\u4e09 */\nfunc preOrderIII(root *TreeNode, res *[][]*TreeNode, path *[]*TreeNode) {\n// \u526a\u679d\nif root == nil || root.Val == 3 {\nreturn\n}\n// \u5c1d\u8bd5\n*path = append(*path, root)\nif int(root.Val) == 7 {\n// \u8bb0\u5f55\u89e3\n*res = append(*res, *path)\n}\npreOrderIII(root.Left, res, path)\npreOrderIII(root.Right, res, path)\n// \u56de\u9000\n*path = (*path)[:len(*path)-1]\n}\n</code></pre> preorder_traversal_iii_compact.js<pre><code>/* \u524d\u5e8f\u904d\u5386\uff1a\u4f8b\u9898\u4e09 */\nfunction preOrder(root, path, res) {\n// \u526a\u679d\nif (root === null || root.val === 3) {\nreturn;\n}\n// \u5c1d\u8bd5\npath.push(root);\nif (root.val === 7) {\n// \u8bb0\u5f55\u89e3\nres.push([...path]);\n}\npreOrder(root.left, path, res);\npreOrder(root.right, path, res);\n// \u56de\u9000\npath.pop();\n}\n</code></pre> preorder_traversal_iii_compact.ts<pre><code>/* \u524d\u5e8f\u904d\u5386\uff1a\u4f8b\u9898\u4e09 */\nfunction preOrder(\nroot: TreeNode | null,\npath: TreeNode[],\nres: TreeNode[][]\n): void {\n// \u526a\u679d\nif (root === null || root.val === 3) {\nreturn;\n}\n// \u5c1d\u8bd5\npath.push(root);\nif (root.val === 7) {\n// \u8bb0\u5f55\u89e3\nres.push([...path]);\n}\npreOrder(root.left, path, res);\npreOrder(root.right, path, res);\n// \u56de\u9000\npath.pop();\n}\n</code></pre> preorder_traversal_iii_compact.c<pre><code>[class]{}-[func]{preOrder}\n</code></pre> preorder_traversal_iii_compact.cs<pre><code>/* \u524d\u5e8f\u904d\u5386\uff1a\u4f8b\u9898\u4e09 */\nvoid preOrder(TreeNode root) {\n// \u526a\u679d\nif (root == null || root.val == 3) {\nreturn;\n}\n// \u5c1d\u8bd5\npath.Add(root);\nif (root.val == 7) {\n// \u8bb0\u5f55\u89e3\nres.Add(new List&lt;TreeNode&gt;(path));\n}\npreOrder(root.left);\npreOrder(root.right);\n// \u56de\u9000\npath.RemoveAt(path.Count - 1);\n}\n</code></pre> preorder_traversal_iii_compact.swift<pre><code>/* \u524d\u5e8f\u904d\u5386\uff1a\u4f8b\u9898\u4e09 */\nfunc preOrder(root: TreeNode?) {\n// \u526a\u679d\nguard let root = root, root.val != 3 else {\nreturn\n}\n// \u5c1d\u8bd5\npath.append(root)\nif root.val == 7 {\n// \u8bb0\u5f55\u89e3\nres.append(path)\n}\npreOrder(root: root.left)\npreOrder(root: root.right)\n// \u56de\u9000\npath.removeLast()\n}\n</code></pre> preorder_traversal_iii_compact.zig<pre><code>[class]{}-[func]{preOrder}\n</code></pre> preorder_traversal_iii_compact.dart<pre><code>[class]{}-[func]{preOrder}\n</code></pre> <p>\u526a\u679d\u662f\u4e00\u4e2a\u975e\u5e38\u5f62\u8c61\u7684\u540d\u8bcd\u3002\u5728\u641c\u7d22\u8fc7\u7a0b\u4e2d\uff0c\u6211\u4eec\u5229\u7528\u7ea6\u675f\u6761\u4ef6\u201c\u526a\u6389\u201d\u4e86\u4e0d\u6ee1\u8db3\u7ea6\u675f\u6761\u4ef6\u7684\u641c\u7d22\u5206\u652f\uff0c\u907f\u514d\u8bb8\u591a\u65e0\u610f\u4e49\u7684\u5c1d\u8bd5\uff0c\u4ece\u800c\u63d0\u5347\u641c\u7d22\u6548\u7387\u3002</p> <p></p> <p> Fig. \u6839\u636e\u7ea6\u675f\u6761\u4ef6\u526a\u679d </p>"},{"location":"chapter_backtracking/backtracking_algorithm/#1213","title":"12.1.3. \u00a0 \u5e38\u7528\u672f\u8bed","text":"<p>\u4e3a\u4e86\u66f4\u6e05\u6670\u5730\u5206\u6790\u7b97\u6cd5\u95ee\u9898\uff0c\u6211\u4eec\u603b\u7ed3\u4e00\u4e0b\u56de\u6eaf\u7b97\u6cd5\u4e2d\u5e38\u7528\u672f\u8bed\u7684\u542b\u4e49\uff0c\u5e76\u5bf9\u7167\u4f8b\u9898\u4e09\u7ed9\u51fa\u5bf9\u5e94\u793a\u4f8b\u3002</p> \u540d\u8bcd \u5b9a\u4e49 \u4f8b\u9898\u4e09 \u89e3 Solution \u89e3\u662f\u6ee1\u8db3\u95ee\u9898\u7279\u5b9a\u6761\u4ef6\u7684\u7b54\u6848\u3002\u56de\u6eaf\u7b97\u6cd5\u7684\u76ee\u6807\u662f\u627e\u5230\u4e00\u4e2a\u6216\u591a\u4e2a\u6ee1\u8db3\u6761\u4ef6\u7684\u89e3 \u6839\u8282\u70b9\u5230\u8282\u70b9 \\(7\\) \u7684\u6240\u6709\u8def\u5f84\uff0c\u4e14\u8def\u5f84\u4e2d\u4e0d\u5305\u542b\u503c\u4e3a \\(3\\) \u7684\u8282\u70b9 \u72b6\u6001 State \u72b6\u6001\u8868\u793a\u95ee\u9898\u5728\u67d0\u4e00\u65f6\u523b\u7684\u60c5\u51b5\uff0c\u5305\u62ec\u5df2\u7ecf\u505a\u51fa\u7684\u9009\u62e9 \u5f53\u524d\u5df2\u8bbf\u95ee\u7684\u8282\u70b9\u8def\u5f84\uff0c\u5373 <code>path</code> \u8282\u70b9\u5217\u8868 \u7ea6\u675f\u6761\u4ef6 Constraint \u7ea6\u675f\u6761\u4ef6\u662f\u95ee\u9898\u4e2d\u9650\u5236\u89e3\u7684\u53ef\u884c\u6027\u7684\u6761\u4ef6\uff0c\u901a\u5e38\u7528\u4e8e\u526a\u679d \u8981\u6c42\u8def\u5f84\u4e2d\u4e0d\u80fd\u5305\u542b\u503c\u4e3a \\(3\\) \u7684\u8282\u70b9 \u5c1d\u8bd5 Attempt \u5c1d\u8bd5\u662f\u5728\u641c\u7d22\u8fc7\u7a0b\u4e2d\uff0c\u6839\u636e\u5f53\u524d\u72b6\u6001\u548c\u53ef\u7528\u9009\u62e9\u6765\u63a2\u7d22\u89e3\u7a7a\u95f4\u7684\u8fc7\u7a0b\u3002\u5c1d\u8bd5\u5305\u62ec\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\uff0c\u68c0\u67e5\u662f\u5426\u4e3a\u89e3 \u9012\u5f52\u8bbf\u95ee\u5de6\uff08\u53f3\uff09\u5b50\u8282\u70b9\uff0c\u5c06\u8282\u70b9\u6dfb\u52a0\u8fdb <code>path</code> \uff0c\u5224\u65ad\u8282\u70b9\u7684\u503c\u662f\u5426\u4e3a \\(7\\) \u56de\u9000 Backtracking \u56de\u9000\u6307\u5728\u641c\u7d22\u4e2d\u9047\u5230\u5230\u4e0d\u6ee1\u8db3\u7ea6\u675f\u6761\u4ef6\u6216\u65e0\u6cd5\u7ee7\u7eed\u641c\u7d22\u7684\u72b6\u6001\u65f6\uff0c\u64a4\u9500\u524d\u9762\u505a\u51fa\u7684\u9009\u62e9\uff0c\u56de\u5230\u4e0a\u4e00\u4e2a\u72b6\u6001 \u5f53\u8d8a\u8fc7\u53f6\u7ed3\u70b9\u3001\u7ed3\u675f\u7ed3\u70b9\u8bbf\u95ee\u3001\u9047\u5230\u503c\u4e3a \\(3\\) \u7684\u8282\u70b9\u65f6\u7ec8\u6b62\u641c\u7d22\uff0c\u51fd\u6570\u8fd4\u56de \u526a\u679d Pruning \u526a\u679d\u662f\u6839\u636e\u95ee\u9898\u7279\u6027\u548c\u7ea6\u675f\u6761\u4ef6\u907f\u514d\u65e0\u610f\u4e49\u7684\u641c\u7d22\u8def\u5f84\u7684\u65b9\u6cd5\uff0c\u53ef\u63d0\u9ad8\u641c\u7d22\u6548\u7387 \u5f53\u9047\u5230\u503c\u4e3a \\(3\\) \u7684\u8282\u70b9\u65f6\uff0c\u5219\u7ec8\u6b62\u7ee7\u7eed\u641c\u7d22 <p>Tip</p> <p>\u89e3\u3001\u72b6\u6001\u3001\u7ea6\u675f\u6761\u4ef6\u7b49\u672f\u8bed\u662f\u901a\u7528\u7684\uff0c\u9002\u7528\u4e8e\u56de\u6eaf\u7b97\u6cd5\u3001\u52a8\u6001\u89c4\u5212\u3001\u8d2a\u5fc3\u7b97\u6cd5\u7b49\u3002</p>"},{"location":"chapter_backtracking/backtracking_algorithm/#1214","title":"12.1.4. \u00a0 \u6846\u67b6\u4ee3\u7801","text":"<p>\u56de\u6eaf\u7b97\u6cd5\u53ef\u7528\u4e8e\u89e3\u51b3\u8bb8\u591a\u641c\u7d22\u95ee\u9898\u3001\u7ea6\u675f\u6ee1\u8db3\u95ee\u9898\u548c\u7ec4\u5408\u4f18\u5316\u95ee\u9898\u3002\u4e3a\u63d0\u5347\u4ee3\u7801\u901a\u7528\u6027\uff0c\u6211\u4eec\u5e0c\u671b\u5c06\u56de\u6eaf\u7b97\u6cd5\u7684\u201c\u5c1d\u8bd5\u3001\u56de\u9000\u3001\u526a\u679d\u201d\u7684\u4e3b\u4f53\u6846\u67b6\u63d0\u70bc\u51fa\u6765\u3002</p> <p>\u8bbe <code>state</code> \u4e3a\u95ee\u9898\u7684\u5f53\u524d\u72b6\u6001\uff0c<code>choices</code> \u8868\u793a\u5f53\u524d\u72b6\u6001\u4e0b\u53ef\u4ee5\u505a\u51fa\u7684\u9009\u62e9\uff0c\u5219\u53ef\u5f97\u5230\u4ee5\u4e0b\u56de\u6eaf\u7b97\u6cd5\u7684\u6846\u67b6\u4ee3\u7801\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart <pre><code>/* \u56de\u6eaf\u7b97\u6cd5\u6846\u67b6 */\nvoid backtrack(State state, List&lt;Choice&gt; choices, List&lt;State&gt; res) {\n// \u5224\u65ad\u662f\u5426\u4e3a\u89e3\nif (isSolution(state)) {\n// \u8bb0\u5f55\u89e3\nrecordSolution(state, res);\nreturn;\n}\n// \u904d\u5386\u6240\u6709\u9009\u62e9\nfor (Choice choice : choices) {\n// \u526a\u679d\uff1a\u5224\u65ad\u9009\u62e9\u662f\u5426\u5408\u6cd5\nif (isValid(state, choice)) {\n// \u5c1d\u8bd5\uff1a\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\nmakeChoice(state, choice);\nbacktrack(state, choices, res);\n// \u56de\u9000\uff1a\u64a4\u9500\u9009\u62e9\uff0c\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001\nundoChoice(state, choice);\n}\n}\n}\n</code></pre> <pre><code>/* \u56de\u6eaf\u7b97\u6cd5\u6846\u67b6 */\nvoid backtrack(State *state, vector&lt;Choice *&gt; &amp;choices, vector&lt;State *&gt; &amp;res) {\n// \u5224\u65ad\u662f\u5426\u4e3a\u89e3\nif (isSolution(state)) {\n// \u8bb0\u5f55\u89e3\nrecordSolution(state, res);\nreturn;\n}\n// \u904d\u5386\u6240\u6709\u9009\u62e9\nfor (Choice choice : choices) {\n// \u526a\u679d\uff1a\u5224\u65ad\u9009\u62e9\u662f\u5426\u5408\u6cd5\nif (isValid(state, choice)) {\n// \u5c1d\u8bd5\uff1a\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\nmakeChoice(state, choice);\nbacktrack(state, choices, res);\n// \u56de\u9000\uff1a\u64a4\u9500\u9009\u62e9\uff0c\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001\nundoChoice(state, choice);\n}\n}\n}\n</code></pre> <pre><code>def backtrack(state: State, choices: list[choice], res: list[state]) -&gt; None:\n\"\"\"\u56de\u6eaf\u7b97\u6cd5\u6846\u67b6\"\"\"\n# \u5224\u65ad\u662f\u5426\u4e3a\u89e3\nif is_solution(state):\n# \u8bb0\u5f55\u89e3\nrecord_solution(state, res)\nreturn\n# \u904d\u5386\u6240\u6709\u9009\u62e9\nfor choice in choices:\n# \u526a\u679d\uff1a\u5224\u65ad\u9009\u62e9\u662f\u5426\u5408\u6cd5\nif is_valid(state, choice):\n# \u5c1d\u8bd5\uff1a\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\nmake_choice(state, choice)\nbacktrack(state, choices, res)\n# \u56de\u9000\uff1a\u64a4\u9500\u9009\u62e9\uff0c\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001\nundo_choice(state, choice)\n</code></pre> <pre><code>/* \u56de\u6eaf\u7b97\u6cd5\u6846\u67b6 */\nfunc backtrack(state *State, choices []Choice, res *[]State) {\n// \u5224\u65ad\u662f\u5426\u4e3a\u89e3\nif isSolution(state) {\n// \u8bb0\u5f55\u89e3\nrecordSolution(state, res)\nreturn\n}\n// \u904d\u5386\u6240\u6709\u9009\u62e9\nfor _, choice := range choices {\n// \u526a\u679d\uff1a\u5224\u65ad\u9009\u62e9\u662f\u5426\u5408\u6cd5\nif isValid(state, choice) {\n// \u5c1d\u8bd5\uff1a\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\nmakeChoice(state, choice)\nbacktrack(state, choices, res)\n// \u56de\u9000\uff1a\u64a4\u9500\u9009\u62e9\uff0c\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001\nundoChoice(state, choice)\n}\n}\n}\n</code></pre> <pre><code>/* \u56de\u6eaf\u7b97\u6cd5\u6846\u67b6 */\nfunction backtrack(state, choices, res) {\n// \u5224\u65ad\u662f\u5426\u4e3a\u89e3\nif (isSolution(state)) {\n// \u8bb0\u5f55\u89e3\nrecordSolution(state, res);\nreturn;\n}\n// \u904d\u5386\u6240\u6709\u9009\u62e9\nfor (let choice of choices) {\n// \u526a\u679d\uff1a\u5224\u65ad\u9009\u62e9\u662f\u5426\u5408\u6cd5\nif (isValid(state, choice)) {\n// \u5c1d\u8bd5\uff1a\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\nmakeChoice(state, choice);\nbacktrack(state, choices, res);\n// \u56de\u9000\uff1a\u64a4\u9500\u9009\u62e9\uff0c\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001\nundoChoice(state, choice);\n}\n}\n}\n</code></pre> <pre><code>/* \u56de\u6eaf\u7b97\u6cd5\u6846\u67b6 */\nfunction backtrack(state: State, choices: Choice[], res: State[]): void {\n// \u5224\u65ad\u662f\u5426\u4e3a\u89e3\nif (isSolution(state)) {\n// \u8bb0\u5f55\u89e3\nrecordSolution(state, res);\nreturn;\n}\n// \u904d\u5386\u6240\u6709\u9009\u62e9\nfor (let choice of choices) {\n// \u526a\u679d\uff1a\u5224\u65ad\u9009\u62e9\u662f\u5426\u5408\u6cd5\nif (isValid(state, choice)) {\n// \u5c1d\u8bd5\uff1a\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\nmakeChoice(state, choice);\nbacktrack(state, choices, res);\n// \u56de\u9000\uff1a\u64a4\u9500\u9009\u62e9\uff0c\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001\nundoChoice(state, choice);\n}\n}\n}\n</code></pre> <pre><code>/* \u56de\u6eaf\u7b97\u6cd5\u6846\u67b6 */\nvoid backtrack(State *state, Choice *choices, int numChoices, State *res, int numRes) {\n// \u5224\u65ad\u662f\u5426\u4e3a\u89e3\nif (isSolution(state)) {\n// \u8bb0\u5f55\u89e3\nrecordSolution(state, res, numRes);\nreturn;\n}\n// \u904d\u5386\u6240\u6709\u9009\u62e9\nfor (int i = 0; i &lt; numChoices; i++) {\n// \u526a\u679d\uff1a\u5224\u65ad\u9009\u62e9\u662f\u5426\u5408\u6cd5\nif (isValid(state, &amp;choices[i])) {\n// \u5c1d\u8bd5\uff1a\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\nmakeChoice(state, &amp;choices[i]);\nbacktrack(state, choices, numChoices, res, numRes);\n// \u56de\u9000\uff1a\u64a4\u9500\u9009\u62e9\uff0c\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001\nundoChoice(state, &amp;choices[i]);\n}\n}\n}\n</code></pre> <pre><code>/* \u56de\u6eaf\u7b97\u6cd5\u6846\u67b6 */\nvoid backtrack(State state, List&lt;Choice&gt; choices, List&lt;State&gt; res) {\n// \u5224\u65ad\u662f\u5426\u4e3a\u89e3\nif (isSolution(state)) {\n// \u8bb0\u5f55\u89e3\nrecordSolution(state, res);\nreturn;\n}\n// \u904d\u5386\u6240\u6709\u9009\u62e9\nforeach (Choice choice in choices) {\n// \u526a\u679d\uff1a\u5224\u65ad\u9009\u62e9\u662f\u5426\u5408\u6cd5\nif (isValid(state, choice)) {\n// \u5c1d\u8bd5\uff1a\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\nmakeChoice(state, choice);\nbacktrack(state, choices, res);\n// \u56de\u9000\uff1a\u64a4\u9500\u9009\u62e9\uff0c\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001\nundoChoice(state, choice);\n}\n}\n}\n</code></pre> <pre><code>/* \u56de\u6eaf\u7b97\u6cd5\u6846\u67b6 */\nfunc backtrack(state: inout State, choices: [Choice], res: inout [State]) {\n// \u5224\u65ad\u662f\u5426\u4e3a\u89e3\nif isSolution(state: state) {\n// \u8bb0\u5f55\u89e3\nrecordSolution(state: state, res: &amp;res)\nreturn\n}\n// \u904d\u5386\u6240\u6709\u9009\u62e9\nfor choice in choices {\n// \u526a\u679d\uff1a\u5224\u65ad\u9009\u62e9\u662f\u5426\u5408\u6cd5\nif isValid(state: state, choice: choice) {\n// \u5c1d\u8bd5\uff1a\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\nmakeChoice(state: &amp;state, choice: choice)\nbacktrack(state: &amp;state, choices: choices, res: &amp;res)\n// \u56de\u9000\uff1a\u64a4\u9500\u9009\u62e9\uff0c\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001\nundoChoice(state: &amp;state, choice: choice)\n}\n}\n}\n</code></pre> <pre><code>\n</code></pre> <pre><code>/* \u56de\u6eaf\u7b97\u6cd5\u6846\u67b6 */\nvoid backtrack(State state, List&lt;Choice&gt;, List&lt;State&gt; res) {\n// \u5224\u65ad\u662f\u5426\u4e3a\u89e3\nif (isSolution(state)) {\n// \u8bb0\u5f55\u89e3\nrecordSolution(state, res);\nreturn;\n}\n// \u904d\u5386\u6240\u6709\u9009\u62e9\nfor (Choice choice in choices) {\n// \u526a\u679d\uff1a\u5224\u65ad\u9009\u62e9\u662f\u5426\u5408\u6cd5\nif (isValid(state, choice)) {\n// \u5c1d\u8bd5\uff1a\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\nmakeChoice(state, choice);\nbacktrack(state, choices, res);\n// \u56de\u9000\uff1a\u64a4\u9500\u9009\u62e9\uff0c\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001\nundoChoice(state, choice);\n}\n}\n}\n</code></pre> <p>\u4e0b\u9762\uff0c\u6211\u4eec\u5c1d\u8bd5\u57fa\u4e8e\u6b64\u6846\u67b6\u6765\u89e3\u51b3\u4f8b\u9898\u4e09\u3002\u5728\u4f8b\u9898\u4e09\u4e2d\uff0c\u72b6\u6001 <code>state</code> \u662f\u8282\u70b9\u904d\u5386\u8def\u5f84\uff0c\u9009\u62e9 <code>choices</code> \u662f\u5f53\u524d\u8282\u70b9\u7684\u5de6\u5b50\u8282\u70b9\u548c\u53f3\u5b50\u8282\u70b9\uff0c\u7ed3\u679c <code>res</code> \u662f\u8def\u5f84\u5217\u8868\uff0c\u5b9e\u73b0\u4ee3\u7801\u5982\u4e0b\u6240\u793a\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart preorder_traversal_iii_template.java<pre><code>/* \u5224\u65ad\u5f53\u524d\u72b6\u6001\u662f\u5426\u4e3a\u89e3 */\nboolean isSolution(List&lt;TreeNode&gt; state) {\nreturn !state.isEmpty() &amp;&amp; state.get(state.size() - 1).val == 7;\n}\n/* \u8bb0\u5f55\u89e3 */\nvoid recordSolution(List&lt;TreeNode&gt; state, List&lt;List&lt;TreeNode&gt;&gt; res) {\nres.add(new ArrayList&lt;&gt;(state));\n}\n/* \u5224\u65ad\u5728\u5f53\u524d\u72b6\u6001\u4e0b\uff0c\u8be5\u9009\u62e9\u662f\u5426\u5408\u6cd5 */\nboolean isValid(List&lt;TreeNode&gt; state, TreeNode choice) {\nreturn choice != null &amp;&amp; choice.val != 3;\n}\n/* \u66f4\u65b0\u72b6\u6001 */\nvoid makeChoice(List&lt;TreeNode&gt; state, TreeNode choice) {\nstate.add(choice);\n}\n/* \u6062\u590d\u72b6\u6001 */\nvoid undoChoice(List&lt;TreeNode&gt; state, TreeNode choice) {\nstate.remove(state.size() - 1);\n}\n/* \u56de\u6eaf\u7b97\u6cd5\uff1a\u4f8b\u9898\u4e09 */\nvoid backtrack(List&lt;TreeNode&gt; state, List&lt;TreeNode&gt; choices, List&lt;List&lt;TreeNode&gt;&gt; res) {\n// \u68c0\u67e5\u662f\u5426\u4e3a\u89e3\nif (isSolution(state)) {\n// \u8bb0\u5f55\u89e3\nrecordSolution(state, res);\nreturn;\n}\n// \u904d\u5386\u6240\u6709\u9009\u62e9\nfor (TreeNode choice : choices) {\n// \u526a\u679d\uff1a\u68c0\u67e5\u9009\u62e9\u662f\u5426\u5408\u6cd5\nif (isValid(state, choice)) {\n// \u5c1d\u8bd5\uff1a\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\nmakeChoice(state, choice);\n// \u8fdb\u884c\u4e0b\u4e00\u8f6e\u9009\u62e9\nbacktrack(state, Arrays.asList(choice.left, choice.right), res);\n// \u56de\u9000\uff1a\u64a4\u9500\u9009\u62e9\uff0c\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001\nundoChoice(state, choice);\n}\n}\n}\n</code></pre> preorder_traversal_iii_template.cpp<pre><code>/* \u5224\u65ad\u5f53\u524d\u72b6\u6001\u662f\u5426\u4e3a\u89e3 */\nbool isSolution(vector&lt;TreeNode *&gt; &amp;state) {\nreturn !state.empty() &amp;&amp; state.back()-&gt;val == 7;\n}\n/* \u8bb0\u5f55\u89e3 */\nvoid recordSolution(vector&lt;TreeNode *&gt; &amp;state, vector&lt;vector&lt;TreeNode *&gt;&gt; &amp;res) {\nres.push_back(state);\n}\n/* \u5224\u65ad\u5728\u5f53\u524d\u72b6\u6001\u4e0b\uff0c\u8be5\u9009\u62e9\u662f\u5426\u5408\u6cd5 */\nbool isValid(vector&lt;TreeNode *&gt; &amp;state, TreeNode *choice) {\nreturn choice != nullptr &amp;&amp; choice-&gt;val != 3;\n}\n/* \u66f4\u65b0\u72b6\u6001 */\nvoid makeChoice(vector&lt;TreeNode *&gt; &amp;state, TreeNode *choice) {\nstate.push_back(choice);\n}\n/* \u6062\u590d\u72b6\u6001 */\nvoid undoChoice(vector&lt;TreeNode *&gt; &amp;state, TreeNode *choice) {\nstate.pop_back();\n}\n/* \u56de\u6eaf\u7b97\u6cd5\uff1a\u4f8b\u9898\u4e09 */\nvoid backtrack(vector&lt;TreeNode *&gt; &amp;state, vector&lt;TreeNode *&gt; &amp;choices, vector&lt;vector&lt;TreeNode *&gt;&gt; &amp;res) {\n// \u68c0\u67e5\u662f\u5426\u4e3a\u89e3\nif (isSolution(state)) {\n// \u8bb0\u5f55\u89e3\nrecordSolution(state, res);\nreturn;\n}\n// \u904d\u5386\u6240\u6709\u9009\u62e9\nfor (TreeNode *choice : choices) {\n// \u526a\u679d\uff1a\u68c0\u67e5\u9009\u62e9\u662f\u5426\u5408\u6cd5\nif (isValid(state, choice)) {\n// \u5c1d\u8bd5\uff1a\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\nmakeChoice(state, choice);\n// \u8fdb\u884c\u4e0b\u4e00\u8f6e\u9009\u62e9\nvector&lt;TreeNode *&gt; nextChoices{choice-&gt;left, choice-&gt;right};\nbacktrack(state, nextChoices, res);\n// \u56de\u9000\uff1a\u64a4\u9500\u9009\u62e9\uff0c\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001\nundoChoice(state, choice);\n}\n}\n}\n</code></pre> preorder_traversal_iii_template.py<pre><code>def is_solution(state: list[TreeNode]) -&gt; bool:\n\"\"\"\u5224\u65ad\u5f53\u524d\u72b6\u6001\u662f\u5426\u4e3a\u89e3\"\"\"\nreturn state and state[-1].val == 7\ndef record_solution(state: list[TreeNode], res: list[list[TreeNode]]):\n\"\"\"\u8bb0\u5f55\u89e3\"\"\"\nres.append(list(state))\ndef is_valid(state: list[TreeNode], choice: TreeNode) -&gt; bool:\n\"\"\"\u5224\u65ad\u5728\u5f53\u524d\u72b6\u6001\u4e0b\uff0c\u8be5\u9009\u62e9\u662f\u5426\u5408\u6cd5\"\"\"\nreturn choice is not None and choice.val != 3\ndef make_choice(state: list[TreeNode], choice: TreeNode):\n\"\"\"\u66f4\u65b0\u72b6\u6001\"\"\"\nstate.append(choice)\ndef undo_choice(state: list[TreeNode], choice: TreeNode):\n\"\"\"\u6062\u590d\u72b6\u6001\"\"\"\nstate.pop()\ndef backtrack(\nstate: list[TreeNode], choices: list[TreeNode], res: list[list[TreeNode]]\n):\n\"\"\"\u56de\u6eaf\u7b97\u6cd5\uff1a\u4f8b\u9898\u4e09\"\"\"\n# \u68c0\u67e5\u662f\u5426\u4e3a\u89e3\nif is_solution(state):\n# \u8bb0\u5f55\u89e3\nrecord_solution(state, res)\nreturn\n# \u904d\u5386\u6240\u6709\u9009\u62e9\nfor choice in choices:\n# \u526a\u679d\uff1a\u68c0\u67e5\u9009\u62e9\u662f\u5426\u5408\u6cd5\nif is_valid(state, choice):\n# \u5c1d\u8bd5\uff1a\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\nmake_choice(state, choice)\n# \u8fdb\u884c\u4e0b\u4e00\u8f6e\u9009\u62e9\nbacktrack(state, [choice.left, choice.right], res)\n# \u56de\u9000\uff1a\u64a4\u9500\u9009\u62e9\uff0c\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001\nundo_choice(state, choice)\n</code></pre> preorder_traversal_iii_template.go<pre><code>/* \u5224\u65ad\u5f53\u524d\u72b6\u6001\u662f\u5426\u4e3a\u89e3 */\nfunc isSolution(state *[]*TreeNode) bool {\nreturn len(*state) != 0 &amp;&amp; (*state)[len(*state)-1].Val == 7\n}\n/* \u8bb0\u5f55\u89e3 */\nfunc recordSolution(state *[]*TreeNode, res *[][]*TreeNode) {\n*res = append(*res, *state)\n}\n/* \u5224\u65ad\u5728\u5f53\u524d\u72b6\u6001\u4e0b\uff0c\u8be5\u9009\u62e9\u662f\u5426\u5408\u6cd5 */\nfunc isValid(state *[]*TreeNode, choice *TreeNode) bool {\nreturn choice != nil &amp;&amp; choice.Val != 3\n}\n/* \u66f4\u65b0\u72b6\u6001 */\nfunc makeChoice(state *[]*TreeNode, choice *TreeNode) {\n*state = append(*state, choice)\n}\n/* \u6062\u590d\u72b6\u6001 */\nfunc undoChoice(state *[]*TreeNode, choice *TreeNode) {\n*state = (*state)[:len(*state)-1]\n}\n/* \u56de\u6eaf\u7b97\u6cd5\uff1a\u4f8b\u9898\u4e09 */\nfunc backtrackIII(state *[]*TreeNode, choices *[]*TreeNode, res *[][]*TreeNode) {\n// \u68c0\u67e5\u662f\u5426\u4e3a\u89e3\nif isSolution(state) {\n// \u8bb0\u5f55\u89e3\nrecordSolution(state, res)\nreturn\n}\n// \u904d\u5386\u6240\u6709\u9009\u62e9\nfor _, choice := range *choices {\n// \u526a\u679d\uff1a\u68c0\u67e5\u9009\u62e9\u662f\u5426\u5408\u6cd5\nif isValid(state, choice) {\n// \u5c1d\u8bd5\uff1a\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\nmakeChoice(state, choice)\n// \u8fdb\u884c\u4e0b\u4e00\u8f6e\u9009\u62e9\ntemp := make([]*TreeNode, 0)\ntemp = append(temp, choice.Left, choice.Right)\nbacktrackIII(state, &amp;temp, res)\n// \u56de\u9000\uff1a\u64a4\u9500\u9009\u62e9\uff0c\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001\nundoChoice(state, choice)\n}\n}\n}\n</code></pre> preorder_traversal_iii_template.js<pre><code>/* \u5224\u65ad\u5f53\u524d\u72b6\u6001\u662f\u5426\u4e3a\u89e3 */\nfunction isSolution(state) {\nreturn state &amp;&amp; state[state.length - 1]?.val === 7;\n}\n/* \u8bb0\u5f55\u89e3 */\nfunction recordSolution(state, res) {\nres.push([...state]);\n}\n/* \u5224\u65ad\u5728\u5f53\u524d\u72b6\u6001\u4e0b\uff0c\u8be5\u9009\u62e9\u662f\u5426\u5408\u6cd5 */\nfunction isValid(state, choice) {\nreturn choice !== null &amp;&amp; choice.val !== 3;\n}\n/* \u66f4\u65b0\u72b6\u6001 */\nfunction makeChoice(state, choice) {\nstate.push(choice);\n}\n/* \u6062\u590d\u72b6\u6001 */\nfunction undoChoice(state) {\nstate.pop();\n}\n/* \u56de\u6eaf\u7b97\u6cd5\uff1a\u4f8b\u9898\u4e09 */\nfunction backtrack(state, choices, res) {\n// \u68c0\u67e5\u662f\u5426\u4e3a\u89e3\nif (isSolution(state)) {\n// \u8bb0\u5f55\u89e3\nrecordSolution(state, res);\nreturn;\n}\n// \u904d\u5386\u6240\u6709\u9009\u62e9\nfor (const choice of choices) {\n// \u526a\u679d\uff1a\u68c0\u67e5\u9009\u62e9\u662f\u5426\u5408\u6cd5\nif (isValid(state, choice)) {\n// \u5c1d\u8bd5\uff1a\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\nmakeChoice(state, choice);\n// \u8fdb\u884c\u4e0b\u4e00\u8f6e\u9009\u62e9\nbacktrack(state, [choice.left, choice.right], res);\n// \u56de\u9000\uff1a\u64a4\u9500\u9009\u62e9\uff0c\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001\nundoChoice(state);\n}\n}\n}\n</code></pre> preorder_traversal_iii_template.ts<pre><code>/* \u5224\u65ad\u5f53\u524d\u72b6\u6001\u662f\u5426\u4e3a\u89e3 */\nfunction isSolution(state: TreeNode[]): boolean {\nreturn state &amp;&amp; state[state.length - 1]?.val === 7;\n}\n/* \u8bb0\u5f55\u89e3 */\nfunction recordSolution(state: TreeNode[], res: TreeNode[][]): void {\nres.push([...state]);\n}\n/* \u5224\u65ad\u5728\u5f53\u524d\u72b6\u6001\u4e0b\uff0c\u8be5\u9009\u62e9\u662f\u5426\u5408\u6cd5 */\nfunction isValid(state: TreeNode[], choice: TreeNode): boolean {\nreturn choice !== null &amp;&amp; choice.val !== 3;\n}\n/* \u66f4\u65b0\u72b6\u6001 */\nfunction makeChoice(state: TreeNode[], choice: TreeNode): void {\nstate.push(choice);\n}\n/* \u6062\u590d\u72b6\u6001 */\nfunction undoChoice(state: TreeNode[]): void {\nstate.pop();\n}\n/* \u56de\u6eaf\u7b97\u6cd5\uff1a\u4f8b\u9898\u4e09 */\nfunction backtrack(\nstate: TreeNode[],\nchoices: TreeNode[],\nres: TreeNode[][]\n): void {\n// \u68c0\u67e5\u662f\u5426\u4e3a\u89e3\nif (isSolution(state)) {\n// \u8bb0\u5f55\u89e3\nrecordSolution(state, res);\nreturn;\n}\n// \u904d\u5386\u6240\u6709\u9009\u62e9\nfor (const choice of choices) {\n// \u526a\u679d\uff1a\u68c0\u67e5\u9009\u62e9\u662f\u5426\u5408\u6cd5\nif (isValid(state, choice)) {\n// \u5c1d\u8bd5\uff1a\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\nmakeChoice(state, choice);\n// \u8fdb\u884c\u4e0b\u4e00\u8f6e\u9009\u62e9\nbacktrack(state, [choice.left, choice.right], res);\n// \u56de\u9000\uff1a\u64a4\u9500\u9009\u62e9\uff0c\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001\nundoChoice(state);\n}\n}\n}\n</code></pre> preorder_traversal_iii_template.c<pre><code>[class]{}-[func]{isSolution}\n[class]{}-[func]{recordSolution}\n[class]{}-[func]{isValid}\n[class]{}-[func]{makeChoice}\n[class]{}-[func]{undoChoice}\n[class]{}-[func]{backtrack}\n</code></pre> preorder_traversal_iii_template.cs<pre><code>/* \u5224\u65ad\u5f53\u524d\u72b6\u6001\u662f\u5426\u4e3a\u89e3 */\nbool isSolution(List&lt;TreeNode&gt; state) {\nreturn state.Count != 0 &amp;&amp; state[^1].val == 7;\n}\n/* \u8bb0\u5f55\u89e3 */\nvoid recordSolution(List&lt;TreeNode&gt; state, List&lt;List&lt;TreeNode&gt;&gt; res) {\nres.Add(new List&lt;TreeNode&gt;(state));\n}\n/* \u5224\u65ad\u5728\u5f53\u524d\u72b6\u6001\u4e0b\uff0c\u8be5\u9009\u62e9\u662f\u5426\u5408\u6cd5 */\nbool isValid(List&lt;TreeNode&gt; state, TreeNode choice) {\nreturn choice != null &amp;&amp; choice.val != 3;\n}\n/* \u66f4\u65b0\u72b6\u6001 */\nvoid makeChoice(List&lt;TreeNode&gt; state, TreeNode choice) {\nstate.Add(choice);\n}\n/* \u6062\u590d\u72b6\u6001 */\nvoid undoChoice(List&lt;TreeNode&gt; state, TreeNode choice) {\nstate.RemoveAt(state.Count - 1);\n}\n/* \u56de\u6eaf\u7b97\u6cd5\uff1a\u4f8b\u9898\u4e09 */\nvoid backtrack(List&lt;TreeNode&gt; state, List&lt;TreeNode&gt; choices, List&lt;List&lt;TreeNode&gt;&gt; res) {\n// \u68c0\u67e5\u662f\u5426\u4e3a\u89e3\nif (isSolution(state)) {\n// \u8bb0\u5f55\u89e3\nrecordSolution(state, res);\nreturn;\n}\n// \u904d\u5386\u6240\u6709\u9009\u62e9\nforeach (TreeNode choice in choices) {\n// \u526a\u679d\uff1a\u68c0\u67e5\u9009\u62e9\u662f\u5426\u5408\u6cd5\nif (isValid(state, choice)) {\n// \u5c1d\u8bd5\uff1a\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\nmakeChoice(state, choice);\n// \u8fdb\u884c\u4e0b\u4e00\u8f6e\u9009\u62e9\nbacktrack(state, new List&lt;TreeNode&gt; { choice.left, choice.right }, res);\n// \u56de\u9000\uff1a\u64a4\u9500\u9009\u62e9\uff0c\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001\nundoChoice(state, choice);\n}\n}\n}\n</code></pre> preorder_traversal_iii_template.swift<pre><code>/* \u5224\u65ad\u5f53\u524d\u72b6\u6001\u662f\u5426\u4e3a\u89e3 */\nfunc isSolution(state: [TreeNode]) -&gt; Bool {\n!state.isEmpty &amp;&amp; state.last!.val == 7\n}\n/* \u8bb0\u5f55\u89e3 */\nfunc recordSolution(state: [TreeNode], res: inout [[TreeNode]]) {\nres.append(state)\n}\n/* \u5224\u65ad\u5728\u5f53\u524d\u72b6\u6001\u4e0b\uff0c\u8be5\u9009\u62e9\u662f\u5426\u5408\u6cd5 */\nfunc isValid(state: [TreeNode], choice: TreeNode?) -&gt; Bool {\nchoice != nil &amp;&amp; choice!.val != 3\n}\n/* \u66f4\u65b0\u72b6\u6001 */\nfunc makeChoice(state: inout [TreeNode], choice: TreeNode) {\nstate.append(choice)\n}\n/* \u6062\u590d\u72b6\u6001 */\nfunc undoChoice(state: inout [TreeNode], choice: TreeNode) {\nstate.removeLast()\n}\n/* \u56de\u6eaf\u7b97\u6cd5\uff1a\u4f8b\u9898\u4e09 */\nfunc backtrack(state: inout [TreeNode], choices: [TreeNode], res: inout [[TreeNode]]) {\n// \u68c0\u67e5\u662f\u5426\u4e3a\u89e3\nif isSolution(state: state) {\nrecordSolution(state: state, res: &amp;res)\nreturn\n}\n// \u904d\u5386\u6240\u6709\u9009\u62e9\nfor choice in choices {\n// \u526a\u679d\uff1a\u68c0\u67e5\u9009\u62e9\u662f\u5426\u5408\u6cd5\nif isValid(state: state, choice: choice) {\n// \u5c1d\u8bd5\uff1a\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\nmakeChoice(state: &amp;state, choice: choice)\n// \u8fdb\u884c\u4e0b\u4e00\u8f6e\u9009\u62e9\nbacktrack(state: &amp;state, choices: [choice.left, choice.right].compactMap { $0 }, res: &amp;res)\n// \u56de\u9000\uff1a\u64a4\u9500\u9009\u62e9\uff0c\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001\nundoChoice(state: &amp;state, choice: choice)\n}\n}\n}\n</code></pre> preorder_traversal_iii_template.zig<pre><code>[class]{}-[func]{isSolution}\n[class]{}-[func]{recordSolution}\n[class]{}-[func]{isValid}\n[class]{}-[func]{makeChoice}\n[class]{}-[func]{undoChoice}\n[class]{}-[func]{backtrack}\n</code></pre> preorder_traversal_iii_template.dart<pre><code>[class]{}-[func]{isSolution}\n[class]{}-[func]{recordSolution}\n[class]{}-[func]{isValid}\n[class]{}-[func]{makeChoice}\n[class]{}-[func]{undoChoice}\n[class]{}-[func]{backtrack}\n</code></pre> <p>\u76f8\u8f83\u4e8e\u57fa\u4e8e\u524d\u5e8f\u904d\u5386\u7684\u5b9e\u73b0\u4ee3\u7801\uff0c\u57fa\u4e8e\u56de\u6eaf\u7b97\u6cd5\u6846\u67b6\u7684\u5b9e\u73b0\u4ee3\u7801\u867d\u7136\u663e\u5f97\u5570\u55e6\uff0c\u4f46\u901a\u7528\u6027\u66f4\u597d\u3002\u5b9e\u9645\u4e0a\uff0c\u6240\u6709\u56de\u6eaf\u95ee\u9898\u90fd\u53ef\u4ee5\u5728\u8be5\u6846\u67b6\u4e0b\u89e3\u51b3\u3002\u6211\u4eec\u9700\u8981\u6839\u636e\u5177\u4f53\u95ee\u9898\u6765\u5b9a\u4e49 <code>state</code> \u548c <code>choices</code> \uff0c\u5e76\u5b9e\u73b0\u6846\u67b6\u4e2d\u7684\u5404\u4e2a\u65b9\u6cd5\u3002</p>"},{"location":"chapter_backtracking/backtracking_algorithm/#1215","title":"12.1.5. \u00a0 \u5178\u578b\u4f8b\u9898","text":"<p>\u641c\u7d22\u95ee\u9898\uff1a\u8fd9\u7c7b\u95ee\u9898\u7684\u76ee\u6807\u662f\u627e\u5230\u6ee1\u8db3\u7279\u5b9a\u6761\u4ef6\u7684\u89e3\u51b3\u65b9\u6848\u3002</p> <ul> <li>\u5168\u6392\u5217\u95ee\u9898\uff1a\u7ed9\u5b9a\u4e00\u4e2a\u96c6\u5408\uff0c\u6c42\u51fa\u5176\u6240\u6709\u53ef\u80fd\u7684\u6392\u5217\u7ec4\u5408\u3002</li> <li>\u5b50\u96c6\u548c\u95ee\u9898\uff1a\u7ed9\u5b9a\u4e00\u4e2a\u96c6\u5408\u548c\u4e00\u4e2a\u76ee\u6807\u548c\uff0c\u627e\u5230\u96c6\u5408\u4e2d\u6240\u6709\u548c\u4e3a\u76ee\u6807\u548c\u7684\u5b50\u96c6\u3002</li> <li>\u6c49\u8bfa\u5854\u95ee\u9898\uff1a\u7ed9\u5b9a\u4e09\u4e2a\u67f1\u5b50\u548c\u4e00\u7cfb\u5217\u5927\u5c0f\u4e0d\u540c\u7684\u5706\u76d8\uff0c\u8981\u6c42\u5c06\u6240\u6709\u5706\u76d8\u4ece\u4e00\u4e2a\u67f1\u5b50\u79fb\u52a8\u5230\u53e6\u4e00\u4e2a\u67f1\u5b50\uff0c\u6bcf\u6b21\u53ea\u80fd\u79fb\u52a8\u4e00\u4e2a\u5706\u76d8\uff0c\u4e14\u4e0d\u80fd\u5c06\u5927\u5706\u76d8\u653e\u5728\u5c0f\u5706\u76d8\u4e0a\u3002</li> </ul> <p>\u7ea6\u675f\u6ee1\u8db3\u95ee\u9898\uff1a\u8fd9\u7c7b\u95ee\u9898\u7684\u76ee\u6807\u662f\u627e\u5230\u6ee1\u8db3\u6240\u6709\u7ea6\u675f\u6761\u4ef6\u7684\u89e3\u3002</p> <ul> <li>\\(n\\) \u7687\u540e\uff1a\u5728 \\(n \\times n\\) \u7684\u68cb\u76d8\u4e0a\u653e\u7f6e \\(n\\) \u4e2a\u7687\u540e\uff0c\u4f7f\u5f97\u5b83\u4eec\u4e92\u4e0d\u653b\u51fb\u3002</li> <li>\u6570\u72ec\uff1a\u5728 \\(9 \\times 9\\) \u7684\u7f51\u683c\u4e2d\u586b\u5165\u6570\u5b57 \\(1\\) ~ \\(9\\) \uff0c\u4f7f\u5f97\u6bcf\u884c\u3001\u6bcf\u5217\u548c\u6bcf\u4e2a \\(3 \\times 3\\) \u5b50\u7f51\u683c\u4e2d\u7684\u6570\u5b57\u4e0d\u91cd\u590d\u3002</li> <li>\u56fe\u7740\u8272\u95ee\u9898\uff1a\u7ed9\u5b9a\u4e00\u4e2a\u65e0\u5411\u56fe\uff0c\u7528\u6700\u5c11\u7684\u989c\u8272\u7ed9\u56fe\u7684\u6bcf\u4e2a\u9876\u70b9\u7740\u8272\uff0c\u4f7f\u5f97\u76f8\u90bb\u9876\u70b9\u989c\u8272\u4e0d\u540c\u3002</li> </ul> <p>\u7ec4\u5408\u4f18\u5316\u95ee\u9898\uff1a\u8fd9\u7c7b\u95ee\u9898\u7684\u76ee\u6807\u662f\u5728\u4e00\u4e2a\u7ec4\u5408\u7a7a\u95f4\u4e2d\u627e\u5230\u6ee1\u8db3\u67d0\u4e9b\u6761\u4ef6\u7684\u6700\u4f18\u89e3\u3002</p> <ul> <li>0-1 \u80cc\u5305\u95ee\u9898\uff1a\u7ed9\u5b9a\u4e00\u7ec4\u7269\u54c1\u548c\u4e00\u4e2a\u80cc\u5305\uff0c\u6bcf\u4e2a\u7269\u54c1\u6709\u4e00\u5b9a\u7684\u4ef7\u503c\u548c\u91cd\u91cf\uff0c\u8981\u6c42\u5728\u80cc\u5305\u5bb9\u91cf\u9650\u5236\u5185\uff0c\u9009\u62e9\u7269\u54c1\u4f7f\u5f97\u603b\u4ef7\u503c\u6700\u5927\u3002</li> <li>\u65c5\u884c\u5546\u95ee\u9898\uff1a\u5728\u4e00\u4e2a\u56fe\u4e2d\uff0c\u4ece\u4e00\u4e2a\u70b9\u51fa\u53d1\uff0c\u8bbf\u95ee\u6240\u6709\u5176\u4ed6\u70b9\u6070\u597d\u4e00\u6b21\u540e\u8fd4\u56de\u8d77\u70b9\uff0c\u6c42\u6700\u77ed\u8def\u5f84\u3002</li> <li>\u6700\u5927\u56e2\u95ee\u9898\uff1a\u7ed9\u5b9a\u4e00\u4e2a\u65e0\u5411\u56fe\uff0c\u627e\u5230\u6700\u5927\u7684\u5b8c\u5168\u5b50\u56fe\uff0c\u5373\u5b50\u56fe\u4e2d\u7684\u4efb\u610f\u4e24\u4e2a\u9876\u70b9\u4e4b\u95f4\u90fd\u6709\u8fb9\u76f8\u8fde\u3002</li> </ul> <p>\u5728\u63a5\u4e0b\u6765\u7684\u7ae0\u8282\u4e2d\uff0c\u6211\u4eec\u5c06\u4e00\u8d77\u653b\u514b\u51e0\u4e2a\u7ecf\u5178\u7684\u56de\u6eaf\u7b97\u6cd5\u95ee\u9898\u3002</p>"},{"location":"chapter_backtracking/n_queens_problem/","title":"12.3. \u00a0 N \u7687\u540e\u95ee\u9898","text":"<p>Question</p> <p>\u6839\u636e\u56fd\u9645\u8c61\u68cb\u7684\u89c4\u5219\uff0c\u7687\u540e\u53ef\u4ee5\u653b\u51fb\u4e0e\u4e4b\u5904\u5728\u540c\u4e00\u884c\u6216\u540c\u4e00\u5217\u6216\u540c\u4e00\u659c\u7ebf\u4e0a\u7684\u68cb\u5b50\u3002\u7ed9\u5b9a \\(n\\) \u4e2a\u7687\u540e\u548c\u4e00\u4e2a \\(n \\times n\\) \u5927\u5c0f\u7684\u68cb\u76d8\uff0c\u5bfb\u627e\u4f7f\u5f97\u6240\u6709\u7687\u540e\u4e4b\u95f4\u65e0\u6cd5\u76f8\u4e92\u653b\u51fb\u7684\u6446\u653e\u65b9\u6848\u3002</p> <p>\u5982\u4e0b\u56fe\u6240\u793a\uff0c\u5f53 \\(n = 4\\) \u65f6\uff0c\u5171\u53ef\u4ee5\u627e\u5230\u4e24\u4e2a\u89e3\u3002\u4ece\u56de\u6eaf\u7b97\u6cd5\u7684\u89d2\u5ea6\u770b\uff0c\\(n \\times n\\) \u5927\u5c0f\u7684\u68cb\u76d8\u5171\u6709 \\(n^2\\) \u4e2a\u683c\u5b50\uff0c\u7ed9\u51fa\u4e86\u6240\u6709\u7684\u9009\u62e9 <code>choices</code> \u3002\u5728\u9010\u4e2a\u653e\u7f6e\u7687\u540e\u7684\u8fc7\u7a0b\u4e2d\uff0c\u68cb\u76d8\u72b6\u6001\u5728\u4e0d\u65ad\u5730\u53d8\u5316\uff0c\u6bcf\u4e2a\u65f6\u523b\u7684\u68cb\u76d8\u5c31\u662f\u72b6\u6001 <code>state</code> \u3002</p> <p></p> <p> Fig. 4 \u7687\u540e\u95ee\u9898\u7684\u89e3 </p> <p>\u672c\u9898\u5171\u6709\u4e09\u4e2a\u7ea6\u675f\u6761\u4ef6\uff1a\u591a\u4e2a\u7687\u540e\u4e0d\u80fd\u5728\u540c\u4e00\u884c\u3001\u540c\u4e00\u5217\u548c\u540c\u4e00\u5bf9\u89d2\u7ebf\u3002\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u5bf9\u89d2\u7ebf\u5206\u4e3a\u4e3b\u5bf9\u89d2\u7ebf <code>\\</code> \u548c\u526f\u5bf9\u89d2\u7ebf <code>/</code> \u4e24\u79cd\u3002</p> <p></p> <p> Fig. n \u7687\u540e\u95ee\u9898\u7684\u7ea6\u675f\u6761\u4ef6 </p> <p>\u7687\u540e\u7684\u6570\u91cf\u548c\u68cb\u76d8\u7684\u884c\u6570\u90fd\u4e3a \\(n\\) \uff0c\u56e0\u6b64\u6211\u4eec\u5bb9\u6613\u5f97\u5230\u7b2c\u4e00\u4e2a\u63a8\u8bba\uff1a\u68cb\u76d8\u6bcf\u884c\u90fd\u5141\u8bb8\u4e14\u53ea\u5141\u8bb8\u653e\u7f6e\u4e00\u4e2a\u7687\u540e\u3002\u8fd9\u610f\u5473\u7740\uff0c\u6211\u4eec\u53ef\u4ee5\u91c7\u53d6\u9010\u884c\u653e\u7f6e\u7b56\u7565\uff1a\u4ece\u7b2c\u4e00\u884c\u5f00\u59cb\uff0c\u5728\u6bcf\u884c\u653e\u7f6e\u4e00\u4e2a\u7687\u540e\uff0c\u76f4\u81f3\u6700\u540e\u4e00\u884c\u7ed3\u675f\u3002\u6b64\u7b56\u7565\u8d77\u5230\u4e86\u526a\u679d\u7684\u4f5c\u7528\uff0c\u5b83\u907f\u514d\u4e86\u540c\u4e00\u884c\u51fa\u73b0\u591a\u4e2a\u7687\u540e\u7684\u6240\u6709\u641c\u7d22\u5206\u652f\u3002</p> <p>\u4e0b\u56fe\u5c55\u793a\u4e86 \\(4\\) \u7687\u540e\u95ee\u9898\u7684\u9010\u884c\u653e\u7f6e\u8fc7\u7a0b\u3002\u53d7\u7bc7\u5e45\u9650\u5236\uff0c\u4e0b\u56fe\u4ec5\u5c55\u5f00\u4e86\u7b2c\u4e00\u884c\u7684\u4e00\u4e2a\u641c\u7d22\u5206\u652f\u3002\u5728\u641c\u7d22\u8fc7\u7a0b\u4e2d\uff0c\u6211\u4eec\u5c06\u4e0d\u6ee1\u8db3\u5217\u7ea6\u675f\u548c\u5bf9\u89d2\u7ebf\u7ea6\u675f\u7684\u65b9\u6848\u90fd\u526a\u679d\u4e86\u3002</p> <p></p> <p> Fig. \u9010\u884c\u653e\u7f6e\u7b56\u7565 </p> <p>\u4e3a\u4e86\u5b9e\u73b0\u6839\u636e\u5217\u7ea6\u675f\u526a\u679d\uff0c\u6211\u4eec\u53ef\u4ee5\u5229\u7528\u4e00\u4e2a\u957f\u5ea6\u4e3a \\(n\\) \u7684\u5e03\u5c14\u578b\u6570\u7ec4 <code>cols</code> \u8bb0\u5f55\u6bcf\u4e00\u5217\u662f\u5426\u6709\u7687\u540e\u3002\u5728\u6bcf\u6b21\u51b3\u5b9a\u653e\u7f6e\u524d\uff0c\u6211\u4eec\u901a\u8fc7 <code>cols</code> \u5c06\u5df2\u6709\u7687\u540e\u7684\u5217\u526a\u679d\uff0c\u5e76\u5728\u56de\u6eaf\u4e2d\u52a8\u6001\u66f4\u65b0 <code>cols</code> \u7684\u72b6\u6001\u3002</p> <p>\u90a3\u4e48\uff0c\u5982\u4f55\u5904\u7406\u5bf9\u89d2\u7ebf\u7ea6\u675f\u5462\uff1f\u8bbe\u68cb\u76d8\u4e2d\u67d0\u4e2a\u683c\u5b50\u7684\u884c\u5217\u7d22\u5f15\u4e3a <code>(row, col)</code> \uff0c\u89c2\u5bdf\u77e9\u9635\u7684\u67d0\u6761\u4e3b\u5bf9\u89d2\u7ebf\uff0c\u6211\u4eec\u53d1\u73b0\u8be5\u5bf9\u89d2\u7ebf\u4e0a\u6240\u6709\u683c\u5b50\u7684\u884c\u7d22\u5f15\u51cf\u5217\u7d22\u5f15\u76f8\u7b49\uff0c\u5373 <code>row - col</code> \u4e3a\u6052\u5b9a\u503c\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u82e5\u4e24\u4e2a\u683c\u5b50\u6ee1\u8db3 <code>row1 - col1 == row2 - col2</code> \uff0c\u5219\u8fd9\u4e24\u4e2a\u683c\u5b50\u4e00\u5b9a\u5904\u5728\u4e00\u6761\u4e3b\u5bf9\u89d2\u7ebf\u4e0a\u3002</p> <p>\u5229\u7528\u8be5\u6027\u8d28\uff0c\u6211\u4eec\u53ef\u4ee5\u501f\u52a9\u4e00\u4e2a\u6570\u7ec4 <code>diag1</code> \u6765\u8bb0\u5f55\u6bcf\u6761\u4e3b\u5bf9\u89d2\u7ebf\u4e0a\u662f\u5426\u6709\u7687\u540e\u3002\u6ce8\u610f\uff0c\\(n\\) \u7ef4\u65b9\u9635 <code>row - col</code> \u7684\u8303\u56f4\u662f \\([-n + 1, n - 1]\\) \uff0c\u56e0\u6b64\u5171\u6709 \\(2n - 1\\) \u6761\u4e3b\u5bf9\u89d2\u7ebf\u3002</p> <p></p> <p> Fig. \u5904\u7406\u5217\u7ea6\u675f\u548c\u5bf9\u89d2\u7ebf\u7ea6\u675f </p> <p>\u540c\u7406\uff0c\u6b21\u5bf9\u89d2\u7ebf\u4e0a\u7684\u6240\u6709\u683c\u5b50\u7684 <code>row + col</code> \u662f\u6052\u5b9a\u503c\u3002\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u540c\u6837\u7684\u65b9\u6cd5\uff0c\u501f\u52a9\u6570\u7ec4 <code>diag2</code> \u6765\u5904\u7406\u6b21\u5bf9\u89d2\u7ebf\u7ea6\u675f\u3002</p> <p>\u6839\u636e\u4ee5\u4e0a\u5206\u6790\uff0c\u6211\u4eec\u4fbf\u53ef\u4ee5\u5199\u51fa \\(n\\) \u7687\u540e\u7684\u89e3\u9898\u4ee3\u7801\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart n_queens.java<pre><code>/* \u56de\u6eaf\u7b97\u6cd5\uff1aN \u7687\u540e */\nvoid backtrack(int row, int n, List&lt;List&lt;String&gt;&gt; state, List&lt;List&lt;List&lt;String&gt;&gt;&gt; res,\nboolean[] cols, boolean[] diags1, boolean[] diags2) {\n// \u5f53\u653e\u7f6e\u5b8c\u6240\u6709\u884c\u65f6\uff0c\u8bb0\u5f55\u89e3\nif (row == n) {\nList&lt;List&lt;String&gt;&gt; copyState = new ArrayList&lt;&gt;();\nfor (List&lt;String&gt; sRow : state) {\ncopyState.add(new ArrayList&lt;&gt;(sRow));\n}\nres.add(copyState);\nreturn;\n}\n// \u904d\u5386\u6240\u6709\u5217\nfor (int col = 0; col &lt; n; col++) {\n// \u8ba1\u7b97\u8be5\u683c\u5b50\u5bf9\u5e94\u7684\u4e3b\u5bf9\u89d2\u7ebf\u548c\u526f\u5bf9\u89d2\u7ebf\nint diag1 = row - col + n - 1;\nint diag2 = row + col;\n// \u526a\u679d\uff1a\u4e0d\u5141\u8bb8\u8be5\u683c\u5b50\u6240\u5728 (\u5217 \u6216 \u4e3b\u5bf9\u89d2\u7ebf \u6216 \u526f\u5bf9\u89d2\u7ebf) \u5305\u542b\u7687\u540e\nif (!(cols[col] || diags1[diag1] || diags2[diag2])) {\n// \u5c1d\u8bd5\uff1a\u5c06\u7687\u540e\u653e\u7f6e\u5728\u8be5\u683c\u5b50\nstate.get(row).set(col, \"Q\");\ncols[col] = diags1[diag1] = diags2[diag2] = true;\n// \u653e\u7f6e\u4e0b\u4e00\u884c\nbacktrack(row + 1, n, state, res, cols, diags1, diags2);\n// \u56de\u9000\uff1a\u5c06\u8be5\u683c\u5b50\u6062\u590d\u4e3a\u7a7a\u4f4d\nstate.get(row).set(col, \"#\");\ncols[col] = diags1[diag1] = diags2[diag2] = false;\n}\n}\n}\n/* \u6c42\u89e3 N \u7687\u540e */\nList&lt;List&lt;List&lt;String&gt;&gt;&gt; nQueens(int n) {\n// \u521d\u59cb\u5316 n*n \u5927\u5c0f\u7684\u68cb\u76d8\uff0c\u5176\u4e2d 'Q' \u4ee3\u8868\u7687\u540e\uff0c'#' \u4ee3\u8868\u7a7a\u4f4d\nList&lt;List&lt;String&gt;&gt; state = new ArrayList&lt;&gt;();\nfor (int i = 0; i &lt; n; i++) {\nList&lt;String&gt; row = new ArrayList&lt;&gt;();\nfor (int j = 0; j &lt; n; j++) {\nrow.add(\"#\");\n}\nstate.add(row);\n}\nboolean[] cols = new boolean[n]; // \u8bb0\u5f55\u5217\u662f\u5426\u6709\u7687\u540e\nboolean[] diags1 = new boolean[2 * n - 1]; // \u8bb0\u5f55\u4e3b\u5bf9\u89d2\u7ebf\u662f\u5426\u6709\u7687\u540e\nboolean[] diags2 = new boolean[2 * n - 1]; // \u8bb0\u5f55\u526f\u5bf9\u89d2\u7ebf\u662f\u5426\u6709\u7687\u540e\nList&lt;List&lt;List&lt;String&gt;&gt;&gt; res = new ArrayList&lt;&gt;();\nbacktrack(0, n, state, res, cols, diags1, diags2);\nreturn res;\n}\n</code></pre> n_queens.cpp<pre><code>/* \u56de\u6eaf\u7b97\u6cd5\uff1aN \u7687\u540e */\nvoid backtrack(int row, int n, vector&lt;vector&lt;string&gt;&gt; &amp;state, vector&lt;vector&lt;vector&lt;string&gt;&gt;&gt; &amp;res, vector&lt;bool&gt; &amp;cols,\nvector&lt;bool&gt; &amp;diags1, vector&lt;bool&gt; &amp;diags2) {\n// \u5f53\u653e\u7f6e\u5b8c\u6240\u6709\u884c\u65f6\uff0c\u8bb0\u5f55\u89e3\nif (row == n) {\nres.push_back(state);\nreturn;\n}\n// \u904d\u5386\u6240\u6709\u5217\nfor (int col = 0; col &lt; n; col++) {\n// \u8ba1\u7b97\u8be5\u683c\u5b50\u5bf9\u5e94\u7684\u4e3b\u5bf9\u89d2\u7ebf\u548c\u526f\u5bf9\u89d2\u7ebf\nint diag1 = row - col + n - 1;\nint diag2 = row + col;\n// \u526a\u679d\uff1a\u4e0d\u5141\u8bb8\u8be5\u683c\u5b50\u6240\u5728 (\u5217 \u6216 \u4e3b\u5bf9\u89d2\u7ebf \u6216 \u526f\u5bf9\u89d2\u7ebf) \u5305\u542b\u7687\u540e\nif (!(cols[col] || diags1[diag1] || diags2[diag2])) {\n// \u5c1d\u8bd5\uff1a\u5c06\u7687\u540e\u653e\u7f6e\u5728\u8be5\u683c\u5b50\nstate[row][col] = \"Q\";\ncols[col] = diags1[diag1] = diags2[diag2] = true;\n// \u653e\u7f6e\u4e0b\u4e00\u884c\nbacktrack(row + 1, n, state, res, cols, diags1, diags2);\n// \u56de\u9000\uff1a\u5c06\u8be5\u683c\u5b50\u6062\u590d\u4e3a\u7a7a\u4f4d\nstate[row][col] = \"#\";\ncols[col] = diags1[diag1] = diags2[diag2] = false;\n}\n}\n}\n/* \u6c42\u89e3 N \u7687\u540e */\nvector&lt;vector&lt;vector&lt;string&gt;&gt;&gt; nQueens(int n) {\n// \u521d\u59cb\u5316 n*n \u5927\u5c0f\u7684\u68cb\u76d8\uff0c\u5176\u4e2d 'Q' \u4ee3\u8868\u7687\u540e\uff0c'#' \u4ee3\u8868\u7a7a\u4f4d\nvector&lt;vector&lt;string&gt;&gt; state(n, vector&lt;string&gt;(n, \"#\"));\nvector&lt;bool&gt; cols(n, false);           // \u8bb0\u5f55\u5217\u662f\u5426\u6709\u7687\u540e\nvector&lt;bool&gt; diags1(2 * n - 1, false); // \u8bb0\u5f55\u4e3b\u5bf9\u89d2\u7ebf\u662f\u5426\u6709\u7687\u540e\nvector&lt;bool&gt; diags2(2 * n - 1, false); // \u8bb0\u5f55\u526f\u5bf9\u89d2\u7ebf\u662f\u5426\u6709\u7687\u540e\nvector&lt;vector&lt;vector&lt;string&gt;&gt;&gt; res;\nbacktrack(0, n, state, res, cols, diags1, diags2);\nreturn res;\n}\n</code></pre> n_queens.py<pre><code>def backtrack(\nrow: int,\nn: int,\nstate: list[list[str]],\nres: list[list[list[str]]],\ncols: list[bool],\ndiags1: list[bool],\ndiags2: list[bool],\n):\n\"\"\"\u56de\u6eaf\u7b97\u6cd5\uff1aN \u7687\u540e\"\"\"\n# \u5f53\u653e\u7f6e\u5b8c\u6240\u6709\u884c\u65f6\uff0c\u8bb0\u5f55\u89e3\nif row == n:\nres.append([list(row) for row in state])\nreturn\n# \u904d\u5386\u6240\u6709\u5217\nfor col in range(n):\n# \u8ba1\u7b97\u8be5\u683c\u5b50\u5bf9\u5e94\u7684\u4e3b\u5bf9\u89d2\u7ebf\u548c\u526f\u5bf9\u89d2\u7ebf\ndiag1 = row - col + n - 1\ndiag2 = row + col\n# \u526a\u679d\uff1a\u4e0d\u5141\u8bb8\u8be5\u683c\u5b50\u6240\u5728 (\u5217 \u6216 \u4e3b\u5bf9\u89d2\u7ebf \u6216 \u526f\u5bf9\u89d2\u7ebf) \u5305\u542b\u7687\u540e\nif not (cols[col] or diags1[diag1] or diags2[diag2]):\n# \u5c1d\u8bd5\uff1a\u5c06\u7687\u540e\u653e\u7f6e\u5728\u8be5\u683c\u5b50\nstate[row][col] = \"Q\"\ncols[col] = diags1[diag1] = diags2[diag2] = True\n# \u653e\u7f6e\u4e0b\u4e00\u884c\nbacktrack(row + 1, n, state, res, cols, diags1, diags2)\n# \u56de\u9000\uff1a\u5c06\u8be5\u683c\u5b50\u6062\u590d\u4e3a\u7a7a\u4f4d\nstate[row][col] = \"#\"\ncols[col] = diags1[diag1] = diags2[diag2] = False\ndef n_queens(n: int) -&gt; list[list[list[str]]]:\n\"\"\"\u6c42\u89e3 N \u7687\u540e\"\"\"\n# \u521d\u59cb\u5316 n*n \u5927\u5c0f\u7684\u68cb\u76d8\uff0c\u5176\u4e2d 'Q' \u4ee3\u8868\u7687\u540e\uff0c'#' \u4ee3\u8868\u7a7a\u4f4d\nstate = [[\"#\" for _ in range(n)] for _ in range(n)]\ncols = [False] * n  # \u8bb0\u5f55\u5217\u662f\u5426\u6709\u7687\u540e\ndiags1 = [False] * (2 * n - 1)  # \u8bb0\u5f55\u4e3b\u5bf9\u89d2\u7ebf\u662f\u5426\u6709\u7687\u540e\ndiags2 = [False] * (2 * n - 1)  # \u8bb0\u5f55\u526f\u5bf9\u89d2\u7ebf\u662f\u5426\u6709\u7687\u540e\nres = []\nbacktrack(0, n, state, res, cols, diags1, diags2)\nreturn res\n</code></pre> n_queens.go<pre><code>/* \u56de\u6eaf\u7b97\u6cd5\uff1aN \u7687\u540e */\nfunc backtrack(row, n int, state *[][]string, res *[][][]string, cols, diags1, diags2 *[]bool) {\n// \u5f53\u653e\u7f6e\u5b8c\u6240\u6709\u884c\u65f6\uff0c\u8bb0\u5f55\u89e3\nif row == n {\nnewState := make([][]string, len(*state))\nfor i, _ := range newState {\nnewState[i] = make([]string, len((*state)[0]))\ncopy(newState[i], (*state)[i])\n}\n*res = append(*res, newState)\n}\n// \u904d\u5386\u6240\u6709\u5217\nfor col := 0; col &lt; n; col++ {\n// \u8ba1\u7b97\u8be5\u683c\u5b50\u5bf9\u5e94\u7684\u4e3b\u5bf9\u89d2\u7ebf\u548c\u526f\u5bf9\u89d2\u7ebf\ndiag1 := row - col + n - 1\ndiag2 := row + col\n// \u526a\u679d\uff1a\u4e0d\u5141\u8bb8\u8be5\u683c\u5b50\u6240\u5728 (\u5217 \u6216 \u4e3b\u5bf9\u89d2\u7ebf \u6216 \u526f\u5bf9\u89d2\u7ebf) \u5305\u542b\u7687\u540e\nif !((*cols)[col] || (*diags1)[diag1] || (*diags2)[diag2]) {\n// \u5c1d\u8bd5\uff1a\u5c06\u7687\u540e\u653e\u7f6e\u5728\u8be5\u683c\u5b50\n(*state)[row][col] = \"Q\"\n(*cols)[col], (*diags1)[diag1], (*diags2)[diag2] = true, true, true\n// \u653e\u7f6e\u4e0b\u4e00\u884c\nbacktrack(row+1, n, state, res, cols, diags1, diags2)\n// \u56de\u9000\uff1a\u5c06\u8be5\u683c\u5b50\u6062\u590d\u4e3a\u7a7a\u4f4d\n(*state)[row][col] = \"#\"\n(*cols)[col], (*diags1)[diag1], (*diags2)[diag2] = false, false, false\n}\n}\n}\n/* \u56de\u6eaf\u7b97\u6cd5\uff1aN \u7687\u540e */\nfunc backtrack(row, n int, state *[][]string, res *[][][]string, cols, diags1, diags2 *[]bool) {\n// \u5f53\u653e\u7f6e\u5b8c\u6240\u6709\u884c\u65f6\uff0c\u8bb0\u5f55\u89e3\nif row == n {\nnewState := make([][]string, len(*state))\nfor i, _ := range newState {\nnewState[i] = make([]string, len((*state)[0]))\ncopy(newState[i], (*state)[i])\n}\n*res = append(*res, newState)\n}\n// \u904d\u5386\u6240\u6709\u5217\nfor col := 0; col &lt; n; col++ {\n// \u8ba1\u7b97\u8be5\u683c\u5b50\u5bf9\u5e94\u7684\u4e3b\u5bf9\u89d2\u7ebf\u548c\u526f\u5bf9\u89d2\u7ebf\ndiag1 := row - col + n - 1\ndiag2 := row + col\n// \u526a\u679d\uff1a\u4e0d\u5141\u8bb8\u8be5\u683c\u5b50\u6240\u5728 (\u5217 \u6216 \u4e3b\u5bf9\u89d2\u7ebf \u6216 \u526f\u5bf9\u89d2\u7ebf) \u5305\u542b\u7687\u540e\nif !((*cols)[col] || (*diags1)[diag1] || (*diags2)[diag2]) {\n// \u5c1d\u8bd5\uff1a\u5c06\u7687\u540e\u653e\u7f6e\u5728\u8be5\u683c\u5b50\n(*state)[row][col] = \"Q\"\n(*cols)[col], (*diags1)[diag1], (*diags2)[diag2] = true, true, true\n// \u653e\u7f6e\u4e0b\u4e00\u884c\nbacktrack(row+1, n, state, res, cols, diags1, diags2)\n// \u56de\u9000\uff1a\u5c06\u8be5\u683c\u5b50\u6062\u590d\u4e3a\u7a7a\u4f4d\n(*state)[row][col] = \"#\"\n(*cols)[col], (*diags1)[diag1], (*diags2)[diag2] = false, false, false\n}\n}\n}\nfunc nQueens(n int) [][][]string {\n// \u521d\u59cb\u5316 n*n \u5927\u5c0f\u7684\u68cb\u76d8\uff0c\u5176\u4e2d 'Q' \u4ee3\u8868\u7687\u540e\uff0c'#' \u4ee3\u8868\u7a7a\u4f4d\nstate := make([][]string, n)\nfor i := 0; i &lt; n; i++ {\nrow := make([]string, n)\nfor i := 0; i &lt; n; i++ {\nrow[i] = \"#\"\n}\nstate[i] = row\n}\n// \u8bb0\u5f55\u5217\u662f\u5426\u6709\u7687\u540e\ncols := make([]bool, n)\ndiags1 := make([]bool, 2*n-1)\ndiags2 := make([]bool, 2*n-1)\nres := make([][][]string, 0)\nbacktrack(0, n, &amp;state, &amp;res, &amp;cols, &amp;diags1, &amp;diags2)\nreturn res\n}\n</code></pre> n_queens.js<pre><code>/* \u56de\u6eaf\u7b97\u6cd5\uff1aN \u7687\u540e */\nfunction backtrack(row, n, state, res, cols, diags1, diags2) {\n// \u5f53\u653e\u7f6e\u5b8c\u6240\u6709\u884c\u65f6\uff0c\u8bb0\u5f55\u89e3\nif (row === n) {\nres.push(state.map((row) =&gt; row.slice()));\nreturn;\n}\n// \u904d\u5386\u6240\u6709\u5217\nfor (let col = 0; col &lt; n; col++) {\n// \u8ba1\u7b97\u8be5\u683c\u5b50\u5bf9\u5e94\u7684\u4e3b\u5bf9\u89d2\u7ebf\u548c\u526f\u5bf9\u89d2\u7ebf\nconst diag1 = row - col + n - 1;\nconst diag2 = row + col;\n// \u526a\u679d\uff1a\u4e0d\u5141\u8bb8\u8be5\u683c\u5b50\u6240\u5728 (\u5217 \u6216 \u4e3b\u5bf9\u89d2\u7ebf \u6216 \u526f\u5bf9\u89d2\u7ebf) \u5305\u542b\u7687\u540e\nif (!(cols[col] || diags1[diag1] || diags2[diag2])) {\n// \u5c1d\u8bd5\uff1a\u5c06\u7687\u540e\u653e\u7f6e\u5728\u8be5\u683c\u5b50\nstate[row][col] = 'Q';\ncols[col] = diags1[diag1] = diags2[diag2] = true;\n// \u653e\u7f6e\u4e0b\u4e00\u884c\nbacktrack(row + 1, n, state, res, cols, diags1, diags2);\n// \u56de\u9000\uff1a\u5c06\u8be5\u683c\u5b50\u6062\u590d\u4e3a\u7a7a\u4f4d\nstate[row][col] = '#';\ncols[col] = diags1[diag1] = diags2[diag2] = false;\n}\n}\n}\n/* \u6c42\u89e3 N \u7687\u540e */\nfunction nQueens(n) {\n// \u521d\u59cb\u5316 n*n \u5927\u5c0f\u7684\u68cb\u76d8\uff0c\u5176\u4e2d 'Q' \u4ee3\u8868\u7687\u540e\uff0c'#' \u4ee3\u8868\u7a7a\u4f4d\nconst state = Array.from({ length: n }, () =&gt; Array(n).fill('#'));\nconst cols = Array(n).fill(false); // \u8bb0\u5f55\u5217\u662f\u5426\u6709\u7687\u540e\nconst diags1 = Array(2 * n - 1).fill(false); // \u8bb0\u5f55\u4e3b\u5bf9\u89d2\u7ebf\u662f\u5426\u6709\u7687\u540e\nconst diags2 = Array(2 * n - 1).fill(false); // \u8bb0\u5f55\u526f\u5bf9\u89d2\u7ebf\u662f\u5426\u6709\u7687\u540e\nconst res = [];\nbacktrack(0, n, state, res, cols, diags1, diags2);\nreturn res;\n}\n</code></pre> n_queens.ts<pre><code>/* \u56de\u6eaf\u7b97\u6cd5\uff1aN \u7687\u540e */\nfunction backtrack(\nrow: number,\nn: number,\nstate: string[][],\nres: string[][][],\ncols: boolean[],\ndiags1: boolean[],\ndiags2: boolean[]\n): void {\n// \u5f53\u653e\u7f6e\u5b8c\u6240\u6709\u884c\u65f6\uff0c\u8bb0\u5f55\u89e3\nif (row === n) {\nres.push(state.map((row) =&gt; row.slice()));\nreturn;\n}\n// \u904d\u5386\u6240\u6709\u5217\nfor (let col = 0; col &lt; n; col++) {\n// \u8ba1\u7b97\u8be5\u683c\u5b50\u5bf9\u5e94\u7684\u4e3b\u5bf9\u89d2\u7ebf\u548c\u526f\u5bf9\u89d2\u7ebf\nconst diag1 = row - col + n - 1;\nconst diag2 = row + col;\n// \u526a\u679d\uff1a\u4e0d\u5141\u8bb8\u8be5\u683c\u5b50\u6240\u5728 (\u5217 \u6216 \u4e3b\u5bf9\u89d2\u7ebf \u6216 \u526f\u5bf9\u89d2\u7ebf) \u5305\u542b\u7687\u540e\nif (!(cols[col] || diags1[diag1] || diags2[diag2])) {\n// \u5c1d\u8bd5\uff1a\u5c06\u7687\u540e\u653e\u7f6e\u5728\u8be5\u683c\u5b50\nstate[row][col] = 'Q';\ncols[col] = diags1[diag1] = diags2[diag2] = true;\n// \u653e\u7f6e\u4e0b\u4e00\u884c\nbacktrack(row + 1, n, state, res, cols, diags1, diags2);\n// \u56de\u9000\uff1a\u5c06\u8be5\u683c\u5b50\u6062\u590d\u4e3a\u7a7a\u4f4d\nstate[row][col] = '#';\ncols[col] = diags1[diag1] = diags2[diag2] = false;\n}\n}\n}\n/* \u6c42\u89e3 N \u7687\u540e */\nfunction nQueens(n: number): string[][][] {\n// \u521d\u59cb\u5316 n*n \u5927\u5c0f\u7684\u68cb\u76d8\uff0c\u5176\u4e2d 'Q' \u4ee3\u8868\u7687\u540e\uff0c'#' \u4ee3\u8868\u7a7a\u4f4d\nconst state = Array.from({ length: n }, () =&gt; Array(n).fill('#'));\nconst cols = Array(n).fill(false); // \u8bb0\u5f55\u5217\u662f\u5426\u6709\u7687\u540e\nconst diags1 = Array(2 * n - 1).fill(false); // \u8bb0\u5f55\u4e3b\u5bf9\u89d2\u7ebf\u662f\u5426\u6709\u7687\u540e\nconst diags2 = Array(2 * n - 1).fill(false); // \u8bb0\u5f55\u526f\u5bf9\u89d2\u7ebf\u662f\u5426\u6709\u7687\u540e\nconst res: string[][][] = [];\nbacktrack(0, n, state, res, cols, diags1, diags2);\nreturn res;\n}\n</code></pre> n_queens.c<pre><code>[class]{}-[func]{backtrack}\n[class]{}-[func]{nQueens}\n</code></pre> n_queens.cs<pre><code>/* \u56de\u6eaf\u7b97\u6cd5\uff1aN \u7687\u540e */\nvoid backtrack(int row, int n, List&lt;List&lt;string&gt;&gt; state, List&lt;List&lt;List&lt;string&gt;&gt;&gt; res,\nbool[] cols, bool[] diags1, bool[] diags2) {\n// \u5f53\u653e\u7f6e\u5b8c\u6240\u6709\u884c\u65f6\uff0c\u8bb0\u5f55\u89e3\nif (row == n) {\nList&lt;List&lt;string&gt;&gt; copyState = new List&lt;List&lt;string&gt;&gt;();\nforeach (List&lt;string&gt; sRow in state) {\ncopyState.Add(new List&lt;string&gt;(sRow));\n}\nres.Add(copyState);\nreturn;\n}\n// \u904d\u5386\u6240\u6709\u5217\nfor (int col = 0; col &lt; n; col++) {\n// \u8ba1\u7b97\u8be5\u683c\u5b50\u5bf9\u5e94\u7684\u4e3b\u5bf9\u89d2\u7ebf\u548c\u526f\u5bf9\u89d2\u7ebf\nint diag1 = row - col + n - 1;\nint diag2 = row + col;\n// \u526a\u679d\uff1a\u4e0d\u5141\u8bb8\u8be5\u683c\u5b50\u6240\u5728 (\u5217 \u6216 \u4e3b\u5bf9\u89d2\u7ebf \u6216 \u526f\u5bf9\u89d2\u7ebf) \u5305\u542b\u7687\u540e\nif (!(cols[col] || diags1[diag1] || diags2[diag2])) {\n// \u5c1d\u8bd5\uff1a\u5c06\u7687\u540e\u653e\u7f6e\u5728\u8be5\u683c\u5b50\nstate[row][col] = \"Q\";\ncols[col] = diags1[diag1] = diags2[diag2] = true;\n// \u653e\u7f6e\u4e0b\u4e00\u884c\nbacktrack(row + 1, n, state, res, cols, diags1, diags2);\n// \u56de\u9000\uff1a\u5c06\u8be5\u683c\u5b50\u6062\u590d\u4e3a\u7a7a\u4f4d\nstate[row][col] = \"#\";\ncols[col] = diags1[diag1] = diags2[diag2] = false;\n}\n}\n}\n/* \u6c42\u89e3 N \u7687\u540e */\nList&lt;List&lt;List&lt;string&gt;&gt;&gt; nQueens(int n) {\n// \u521d\u59cb\u5316 n*n \u5927\u5c0f\u7684\u68cb\u76d8\uff0c\u5176\u4e2d 'Q' \u4ee3\u8868\u7687\u540e\uff0c'#' \u4ee3\u8868\u7a7a\u4f4d\nList&lt;List&lt;string&gt;&gt; state = new List&lt;List&lt;string&gt;&gt;();\nfor (int i = 0; i &lt; n; i++) {\nList&lt;string&gt; row = new List&lt;string&gt;();\nfor (int j = 0; j &lt; n; j++) {\nrow.Add(\"#\");\n}\nstate.Add(row);\n}\nbool[] cols = new bool[n]; // \u8bb0\u5f55\u5217\u662f\u5426\u6709\u7687\u540e\nbool[] diags1 = new bool[2 * n - 1]; // \u8bb0\u5f55\u4e3b\u5bf9\u89d2\u7ebf\u662f\u5426\u6709\u7687\u540e\nbool[] diags2 = new bool[2 * n - 1]; // \u8bb0\u5f55\u526f\u5bf9\u89d2\u7ebf\u662f\u5426\u6709\u7687\u540e\nList&lt;List&lt;List&lt;string&gt;&gt;&gt; res = new List&lt;List&lt;List&lt;string&gt;&gt;&gt;();\nbacktrack(0, n, state, res, cols, diags1, diags2);\nreturn res;\n}\n</code></pre> n_queens.swift<pre><code>/* \u56de\u6eaf\u7b97\u6cd5\uff1aN \u7687\u540e */\nfunc backtrack(row: Int, n: Int, state: inout [[String]], res: inout [[[String]]], cols: inout [Bool], diags1: inout [Bool], diags2: inout [Bool]) {\n// \u5f53\u653e\u7f6e\u5b8c\u6240\u6709\u884c\u65f6\uff0c\u8bb0\u5f55\u89e3\nif row == n {\nres.append(state)\nreturn\n}\n// \u904d\u5386\u6240\u6709\u5217\nfor col in 0 ..&lt; n {\n// \u8ba1\u7b97\u8be5\u683c\u5b50\u5bf9\u5e94\u7684\u4e3b\u5bf9\u89d2\u7ebf\u548c\u526f\u5bf9\u89d2\u7ebf\nlet diag1 = row - col + n - 1\nlet diag2 = row + col\n// \u526a\u679d\uff1a\u4e0d\u5141\u8bb8\u8be5\u683c\u5b50\u6240\u5728 (\u5217 \u6216 \u4e3b\u5bf9\u89d2\u7ebf \u6216 \u526f\u5bf9\u89d2\u7ebf) \u5305\u542b\u7687\u540e\nif !(cols[col] || diags1[diag1] || diags2[diag2]) {\n// \u5c1d\u8bd5\uff1a\u5c06\u7687\u540e\u653e\u7f6e\u5728\u8be5\u683c\u5b50\nstate[row][col] = \"Q\"\ncols[col] = true\ndiags1[diag1] = true\ndiags2[diag2] = true\n// \u653e\u7f6e\u4e0b\u4e00\u884c\nbacktrack(row: row + 1, n: n, state: &amp;state, res: &amp;res, cols: &amp;cols, diags1: &amp;diags1, diags2: &amp;diags2)\n// \u56de\u9000\uff1a\u5c06\u8be5\u683c\u5b50\u6062\u590d\u4e3a\u7a7a\u4f4d\nstate[row][col] = \"#\"\ncols[col] = false\ndiags1[diag1] = false\ndiags2[diag2] = false\n}\n}\n}\n/* \u6c42\u89e3 N \u7687\u540e */\nfunc nQueens(n: Int) -&gt; [[[String]]] {\n// \u521d\u59cb\u5316 n*n \u5927\u5c0f\u7684\u68cb\u76d8\uff0c\u5176\u4e2d 'Q' \u4ee3\u8868\u7687\u540e\uff0c'#' \u4ee3\u8868\u7a7a\u4f4d\nvar state = Array(repeating: Array(repeating: \"#\", count: n), count: n)\nvar cols = Array(repeating: false, count: n) // \u8bb0\u5f55\u5217\u662f\u5426\u6709\u7687\u540e\nvar diags1 = Array(repeating: false, count: 2 * n - 1) // \u8bb0\u5f55\u4e3b\u5bf9\u89d2\u7ebf\u662f\u5426\u6709\u7687\u540e\nvar diags2 = Array(repeating: false, count: 2 * n - 1) // \u8bb0\u5f55\u526f\u5bf9\u89d2\u7ebf\u662f\u5426\u6709\u7687\u540e\nvar res: [[[String]]] = []\nbacktrack(row: 0, n: n, state: &amp;state, res: &amp;res, cols: &amp;cols, diags1: &amp;diags1, diags2: &amp;diags2)\nreturn res\n}\n</code></pre> n_queens.zig<pre><code>[class]{}-[func]{backtrack}\n[class]{}-[func]{nQueens}\n</code></pre> n_queens.dart<pre><code>[class]{}-[func]{backtrack}\n[class]{}-[func]{nQueens}\n</code></pre>"},{"location":"chapter_backtracking/n_queens_problem/#1231","title":"12.3.1. \u00a0 \u590d\u6742\u5ea6\u5206\u6790","text":"<p>\u9010\u884c\u653e\u7f6e \\(n\\) \u6b21\uff0c\u8003\u8651\u5217\u7ea6\u675f\uff0c\u5219\u4ece\u7b2c\u4e00\u884c\u5230\u6700\u540e\u4e00\u884c\u5206\u522b\u6709 \\(n, n-1, \\cdots, 2, 1\\) \u4e2a\u9009\u62e9\uff0c\u56e0\u6b64\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(n!)\\) \u3002\u5b9e\u9645\u4e0a\uff0c\u6839\u636e\u5bf9\u89d2\u7ebf\u7ea6\u675f\u7684\u526a\u679d\u4e5f\u80fd\u591f\u5927\u5e45\u5730\u7f29\u5c0f\u641c\u7d22\u7a7a\u95f4\uff0c\u56e0\u800c\u641c\u7d22\u6548\u7387\u5f80\u5f80\u4f18\u4e8e\u4ee5\u4e0a\u65f6\u95f4\u590d\u6742\u5ea6\u3002</p> <p><code>state</code> \u4f7f\u7528 \\(O(n^2)\\) \u7a7a\u95f4\uff0c<code>cols</code> , <code>diags1</code> , <code>diags2</code> \u7686\u4f7f\u7528 \\(O(n)\\) \u7a7a\u95f4\u3002\u6700\u5927\u9012\u5f52\u6df1\u5ea6\u4e3a \\(n\\) \uff0c\u4f7f\u7528 \\(O(n)\\) \u6808\u5e27\u7a7a\u95f4\u3002\u56e0\u6b64\uff0c\u7a7a\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(n^2)\\) \u3002</p>"},{"location":"chapter_backtracking/permutations_problem/","title":"12.2. \u00a0 \u5168\u6392\u5217\u95ee\u9898","text":"<p>\u5168\u6392\u5217\u95ee\u9898\u662f\u56de\u6eaf\u7b97\u6cd5\u7684\u4e00\u4e2a\u5178\u578b\u5e94\u7528\u3002\u5b83\u7684\u5b9a\u4e49\u662f\u5728\u7ed9\u5b9a\u4e00\u4e2a\u96c6\u5408\uff08\u5982\u4e00\u4e2a\u6570\u7ec4\u6216\u5b57\u7b26\u4e32\uff09\u7684\u60c5\u51b5\u4e0b\uff0c\u627e\u51fa\u8fd9\u4e2a\u96c6\u5408\u4e2d\u5143\u7d20\u7684\u6240\u6709\u53ef\u80fd\u7684\u6392\u5217\u3002</p> <p>\u5982\u4e0b\u8868\u6240\u793a\uff0c\u5217\u4e3e\u4e86\u51e0\u4e2a\u793a\u4f8b\u6570\u7ec4\u548c\u5176\u5bf9\u5e94\u7684\u6240\u6709\u6392\u5217\u3002</p> \u8f93\u5165\u6570\u7ec4 \u6240\u6709\u6392\u5217 \\([1]\\) \\([1]\\) \\([1, 2]\\) \\([1, 2], [2, 1]\\) \\([1, 2, 3]\\) \\([1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2], [3, 2, 1]\\)"},{"location":"chapter_backtracking/permutations_problem/#1221","title":"12.2.1. \u00a0 \u65e0\u91cd\u590d\u7684\u60c5\u51b5","text":"<p>Question</p> <p>\u8f93\u5165\u4e00\u4e2a\u6574\u6570\u6570\u7ec4\uff0c\u6570\u7ec4\u4e2d\u4e0d\u5305\u542b\u91cd\u590d\u5143\u7d20\uff0c\u8fd4\u56de\u6240\u6709\u53ef\u80fd\u7684\u6392\u5217\u3002</p> <p>\u4ece\u56de\u6eaf\u7b97\u6cd5\u7684\u89d2\u5ea6\u770b\uff0c\u6211\u4eec\u53ef\u4ee5\u628a\u751f\u6210\u6392\u5217\u7684\u8fc7\u7a0b\u60f3\u8c61\u6210\u4e00\u7cfb\u5217\u9009\u62e9\u7684\u7ed3\u679c\u3002\u5047\u8bbe\u8f93\u5165\u6570\u7ec4\u4e3a \\([1, 2, 3]\\) \uff0c\u5982\u679c\u6211\u4eec\u5148\u9009\u62e9 \\(1\\) \u3001\u518d\u9009\u62e9 \\(3\\) \u3001\u6700\u540e\u9009\u62e9 \\(2\\) \uff0c\u5219\u83b7\u5f97\u6392\u5217 \\([1, 3, 2]\\) \u3002\u56de\u9000\u8868\u793a\u64a4\u9500\u4e00\u4e2a\u9009\u62e9\uff0c\u4e4b\u540e\u7ee7\u7eed\u5c1d\u8bd5\u5176\u4ed6\u9009\u62e9\u3002</p> <p>\u4ece\u56de\u6eaf\u7b97\u6cd5\u4ee3\u7801\u7684\u89d2\u5ea6\u770b\uff0c\u5019\u9009\u96c6\u5408 <code>choices</code> \u662f\u8f93\u5165\u6570\u7ec4\u4e2d\u7684\u6240\u6709\u5143\u7d20\uff0c\u72b6\u6001 <code>state</code> \u662f\u76f4\u81f3\u76ee\u524d\u5df2\u88ab\u9009\u62e9\u7684\u5143\u7d20\u3002\u6ce8\u610f\uff0c\u6bcf\u4e2a\u5143\u7d20\u53ea\u5141\u8bb8\u88ab\u9009\u62e9\u4e00\u6b21\uff0c\u56e0\u6b64\u5728\u904d\u5386\u9009\u62e9\u65f6\uff0c\u5e94\u5f53\u6392\u9664\u5df2\u7ecf\u9009\u62e9\u8fc7\u7684\u5143\u7d20\u3002</p> <p>\u5982\u4e0b\u56fe\u6240\u793a\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u641c\u7d22\u8fc7\u7a0b\u5c55\u5f00\u6210\u4e00\u4e2a\u9012\u5f52\u6811\uff0c\u6811\u4e2d\u7684\u6bcf\u4e2a\u8282\u70b9\u4ee3\u8868\u5f53\u524d\u72b6\u6001 <code>state</code> \u3002\u4ece\u6839\u8282\u70b9\u5f00\u59cb\uff0c\u7ecf\u8fc7\u4e09\u8f6e\u9009\u62e9\u540e\u5230\u8fbe\u53f6\u8282\u70b9\uff0c\u6bcf\u4e2a\u53f6\u8282\u70b9\u90fd\u5bf9\u5e94\u4e00\u4e2a\u6392\u5217\u3002</p> <p></p> <p> Fig. \u5168\u6392\u5217\u7684\u9012\u5f52\u6811 </p> <p>\u60f3\u6e05\u695a\u4ee5\u4e0a\u4fe1\u606f\u4e4b\u540e\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u5728\u6846\u67b6\u4ee3\u7801\u4e2d\u505a\u201c\u5b8c\u5f62\u586b\u7a7a\u201d\u4e86\u3002\u4e3a\u4e86\u7f29\u77ed\u4ee3\u7801\u884c\u6570\uff0c\u6211\u4eec\u4e0d\u5355\u72ec\u5b9e\u73b0\u6846\u67b6\u4ee3\u7801\u4e2d\u7684\u5404\u4e2a\u51fd\u6570\uff0c\u800c\u662f\u5c06\u4ed6\u4eec\u5c55\u5f00\u5728 <code>backtrack()</code> \u51fd\u6570\u4e2d\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart permutations_i.java<pre><code>/* \u56de\u6eaf\u7b97\u6cd5\uff1a\u5168\u6392\u5217 I */\nvoid backtrack(List&lt;Integer&gt; state, int[] choices, boolean[] selected, List&lt;List&lt;Integer&gt;&gt; res) {\n// \u5f53\u72b6\u6001\u957f\u5ea6\u7b49\u4e8e\u5143\u7d20\u6570\u91cf\u65f6\uff0c\u8bb0\u5f55\u89e3\nif (state.size() == choices.length) {\nres.add(new ArrayList&lt;Integer&gt;(state));\nreturn;\n}\n// \u904d\u5386\u6240\u6709\u9009\u62e9\nfor (int i = 0; i &lt; choices.length; i++) {\nint choice = choices[i];\n// \u526a\u679d\uff1a\u4e0d\u5141\u8bb8\u91cd\u590d\u9009\u62e9\u5143\u7d20 \u4e14 \u4e0d\u5141\u8bb8\u91cd\u590d\u9009\u62e9\u76f8\u7b49\u5143\u7d20\nif (!selected[i]) {\n// \u5c1d\u8bd5\uff1a\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\nselected[i] = true;\nstate.add(choice);\n// \u8fdb\u884c\u4e0b\u4e00\u8f6e\u9009\u62e9\nbacktrack(state, choices, selected, res);\n// \u56de\u9000\uff1a\u64a4\u9500\u9009\u62e9\uff0c\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001\nselected[i] = false;\nstate.remove(state.size() - 1);\n}\n}\n}\n/* \u5168\u6392\u5217 I */\nList&lt;List&lt;Integer&gt;&gt; permutationsI(int[] nums) {\nList&lt;List&lt;Integer&gt;&gt; res = new ArrayList&lt;List&lt;Integer&gt;&gt;();\nbacktrack(new ArrayList&lt;Integer&gt;(), nums, new boolean[nums.length], res);\nreturn res;\n}\n</code></pre> permutations_i.cpp<pre><code>/* \u56de\u6eaf\u7b97\u6cd5\uff1a\u5168\u6392\u5217 I */\nvoid backtrack(vector&lt;int&gt; &amp;state, const vector&lt;int&gt; &amp;choices, vector&lt;bool&gt; &amp;selected, vector&lt;vector&lt;int&gt;&gt; &amp;res) {\n// \u5f53\u72b6\u6001\u957f\u5ea6\u7b49\u4e8e\u5143\u7d20\u6570\u91cf\u65f6\uff0c\u8bb0\u5f55\u89e3\nif (state.size() == choices.size()) {\nres.push_back(state);\nreturn;\n}\n// \u904d\u5386\u6240\u6709\u9009\u62e9\nfor (int i = 0; i &lt; choices.size(); i++) {\nint choice = choices[i];\n// \u526a\u679d\uff1a\u4e0d\u5141\u8bb8\u91cd\u590d\u9009\u62e9\u5143\u7d20 \u4e14 \u4e0d\u5141\u8bb8\u91cd\u590d\u9009\u62e9\u76f8\u7b49\u5143\u7d20\nif (!selected[i]) {\n// \u5c1d\u8bd5\uff1a\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\nselected[i] = true;\nstate.push_back(choice);\n// \u8fdb\u884c\u4e0b\u4e00\u8f6e\u9009\u62e9\nbacktrack(state, choices, selected, res);\n// \u56de\u9000\uff1a\u64a4\u9500\u9009\u62e9\uff0c\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001\nselected[i] = false;\nstate.pop_back();\n}\n}\n}\n/* \u5168\u6392\u5217 I */\nvector&lt;vector&lt;int&gt;&gt; permutationsI(vector&lt;int&gt; nums) {\nvector&lt;int&gt; state;\nvector&lt;bool&gt; selected(nums.size(), false);\nvector&lt;vector&lt;int&gt;&gt; res;\nbacktrack(state, nums, selected, res);\nreturn res;\n}\n</code></pre> permutations_i.py<pre><code>def backtrack(\nstate: list[int], choices: list[int], selected: list[bool], res: list[list[int]]\n):\n\"\"\"\u56de\u6eaf\u7b97\u6cd5\uff1a\u5168\u6392\u5217 I\"\"\"\n# \u5f53\u72b6\u6001\u957f\u5ea6\u7b49\u4e8e\u5143\u7d20\u6570\u91cf\u65f6\uff0c\u8bb0\u5f55\u89e3\nif len(state) == len(choices):\nres.append(list(state))\nreturn\n# \u904d\u5386\u6240\u6709\u9009\u62e9\nfor i, choice in enumerate(choices):\n# \u526a\u679d\uff1a\u4e0d\u5141\u8bb8\u91cd\u590d\u9009\u62e9\u5143\u7d20\nif not selected[i]:\n# \u5c1d\u8bd5\uff1a\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\nselected[i] = True\nstate.append(choice)\n# \u8fdb\u884c\u4e0b\u4e00\u8f6e\u9009\u62e9\nbacktrack(state, choices, selected, res)\n# \u56de\u9000\uff1a\u64a4\u9500\u9009\u62e9\uff0c\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001\nselected[i] = False\nstate.pop()\ndef permutations_i(nums: list[int]) -&gt; list[list[int]]:\n\"\"\"\u5168\u6392\u5217 I\"\"\"\nres = []\nbacktrack(state=[], choices=nums, selected=[False] * len(nums), res=res)\nreturn res\n</code></pre> permutations_i.go<pre><code>/* \u56de\u6eaf\u7b97\u6cd5\uff1a\u5168\u6392\u5217 I */\nfunc backtrackI(state *[]int, choices *[]int, selected *[]bool, res *[][]int) {\n// \u5f53\u72b6\u6001\u957f\u5ea6\u7b49\u4e8e\u5143\u7d20\u6570\u91cf\u65f6\uff0c\u8bb0\u5f55\u89e3\nif len(*state) == len(*choices) {\nnewState := append([]int{}, *state...)\n*res = append(*res, newState)\n}\n// \u904d\u5386\u6240\u6709\u9009\u62e9\nfor i := 0; i &lt; len(*choices); i++ {\nchoice := (*choices)[i]\n// \u526a\u679d\uff1a\u4e0d\u5141\u8bb8\u91cd\u590d\u9009\u62e9\u5143\u7d20 \u4e14 \u4e0d\u5141\u8bb8\u91cd\u590d\u9009\u62e9\u76f8\u7b49\u5143\u7d20\nif !(*selected)[i] {\n// \u5c1d\u8bd5\uff1a\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\n(*selected)[i] = true\n*state = append(*state, choice)\n// \u8fdb\u884c\u4e0b\u4e00\u8f6e\u9009\u62e9\nbacktrackI(state, choices, selected, res)\n// \u56de\u9000\uff1a\u64a4\u9500\u9009\u62e9\uff0c\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001\n(*selected)[i] = false\n*state = (*state)[:len(*state)-1]\n}\n}\n}\n/* \u5168\u6392\u5217 I */\nfunc permutationsI(nums []int) [][]int {\nres := make([][]int, 0)\nstate := make([]int, 0)\nselected := make([]bool, len(nums))\nbacktrackI(&amp;state, &amp;nums, &amp;selected, &amp;res)\nreturn res\n}\n</code></pre> permutations_i.js<pre><code>/* \u56de\u6eaf\u7b97\u6cd5\uff1a\u5168\u6392\u5217 I */\nfunction backtrack(state, choices, selected, res) {\n// \u5f53\u72b6\u6001\u957f\u5ea6\u7b49\u4e8e\u5143\u7d20\u6570\u91cf\u65f6\uff0c\u8bb0\u5f55\u89e3\nif (state.length === choices.length) {\nres.push([...state]);\nreturn;\n}\n// \u904d\u5386\u6240\u6709\u9009\u62e9\nchoices.forEach((choice, i) =&gt; {\n// \u526a\u679d\uff1a\u4e0d\u5141\u8bb8\u91cd\u590d\u9009\u62e9\u5143\u7d20 \u4e14 \u4e0d\u5141\u8bb8\u91cd\u590d\u9009\u62e9\u76f8\u7b49\u5143\u7d20\nif (!selected[i]) {\n// \u5c1d\u8bd5\uff1a\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\nselected[i] = true;\nstate.push(choice);\n// \u8fdb\u884c\u4e0b\u4e00\u8f6e\u9009\u62e9\nbacktrack(state, choices, selected, res);\n// \u56de\u9000\uff1a\u64a4\u9500\u9009\u62e9\uff0c\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001\nselected[i] = false;\nstate.pop();\n}\n});\n}\n/* \u5168\u6392\u5217 I */\nfunction permutationsI(nums) {\nconst res = [];\nbacktrack([], nums, Array(nums.length).fill(false), res);\nreturn res;\n}\n</code></pre> permutations_i.ts<pre><code>/* \u56de\u6eaf\u7b97\u6cd5\uff1a\u5168\u6392\u5217 I */\nfunction backtrack(\nstate: number[],\nchoices: number[],\nselected: boolean[],\nres: number[][]\n): void {\n// \u5f53\u72b6\u6001\u957f\u5ea6\u7b49\u4e8e\u5143\u7d20\u6570\u91cf\u65f6\uff0c\u8bb0\u5f55\u89e3\nif (state.length === choices.length) {\nres.push([...state]);\nreturn;\n}\n// \u904d\u5386\u6240\u6709\u9009\u62e9\nchoices.forEach((choice, i) =&gt; {\n// \u526a\u679d\uff1a\u4e0d\u5141\u8bb8\u91cd\u590d\u9009\u62e9\u5143\u7d20 \u4e14 \u4e0d\u5141\u8bb8\u91cd\u590d\u9009\u62e9\u76f8\u7b49\u5143\u7d20\nif (!selected[i]) {\n// \u5c1d\u8bd5\uff1a\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\nselected[i] = true;\nstate.push(choice);\n// \u8fdb\u884c\u4e0b\u4e00\u8f6e\u9009\u62e9\nbacktrack(state, choices, selected, res);\n// \u56de\u9000\uff1a\u64a4\u9500\u9009\u62e9\uff0c\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001\nselected[i] = false;\nstate.pop();\n}\n});\n}\n/* \u5168\u6392\u5217 I */\nfunction permutationsI(nums: number[]): number[][] {\nconst res: number[][] = [];\nbacktrack([], nums, Array(nums.length).fill(false), res);\nreturn res;\n}\n</code></pre> permutations_i.c<pre><code>[class]{}-[func]{backtrack}\n[class]{}-[func]{permutationsI}\n</code></pre> permutations_i.cs<pre><code>/* \u56de\u6eaf\u7b97\u6cd5\uff1a\u5168\u6392\u5217 I */\nvoid backtrack(List&lt;int&gt; state, int[] choices, bool[] selected, List&lt;List&lt;int&gt;&gt; res) {\n// \u5f53\u72b6\u6001\u957f\u5ea6\u7b49\u4e8e\u5143\u7d20\u6570\u91cf\u65f6\uff0c\u8bb0\u5f55\u89e3\nif (state.Count == choices.Length) {\nres.Add(new List&lt;int&gt;(state));\nreturn;\n}\n// \u904d\u5386\u6240\u6709\u9009\u62e9\nfor (int i = 0; i &lt; choices.Length; i++) {\nint choice = choices[i];\n// \u526a\u679d\uff1a\u4e0d\u5141\u8bb8\u91cd\u590d\u9009\u62e9\u5143\u7d20 \u4e14 \u4e0d\u5141\u8bb8\u91cd\u590d\u9009\u62e9\u76f8\u7b49\u5143\u7d20\nif (!selected[i]) {\n// \u5c1d\u8bd5\uff1a\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\nselected[i] = true;\nstate.Add(choice);\n// \u8fdb\u884c\u4e0b\u4e00\u8f6e\u9009\u62e9\nbacktrack(state, choices, selected, res);\n// \u56de\u9000\uff1a\u64a4\u9500\u9009\u62e9\uff0c\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001\nselected[i] = false;\nstate.RemoveAt(state.Count - 1);\n}\n}\n}\n/* \u5168\u6392\u5217 I */\nList&lt;List&lt;int&gt;&gt; permutationsI(int[] nums) {\nList&lt;List&lt;int&gt;&gt; res = new List&lt;List&lt;int&gt;&gt;();\nbacktrack(new List&lt;int&gt;(), nums, new bool[nums.Length], res);\nreturn res;\n}\n</code></pre> permutations_i.swift<pre><code>/* \u56de\u6eaf\u7b97\u6cd5\uff1a\u5168\u6392\u5217 I */\nfunc backtrack(state: inout [Int], choices: [Int], selected: inout [Bool], res: inout [[Int]]) {\n// \u5f53\u72b6\u6001\u957f\u5ea6\u7b49\u4e8e\u5143\u7d20\u6570\u91cf\u65f6\uff0c\u8bb0\u5f55\u89e3\nif state.count == choices.count {\nres.append(state)\nreturn\n}\n// \u904d\u5386\u6240\u6709\u9009\u62e9\nfor (i, choice) in choices.enumerated() {\n// \u526a\u679d\uff1a\u4e0d\u5141\u8bb8\u91cd\u590d\u9009\u62e9\u5143\u7d20 \u4e14 \u4e0d\u5141\u8bb8\u91cd\u590d\u9009\u62e9\u76f8\u7b49\u5143\u7d20\nif !selected[i] {\n// \u5c1d\u8bd5\uff1a\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\nselected[i] = true\nstate.append(choice)\n// \u8fdb\u884c\u4e0b\u4e00\u8f6e\u9009\u62e9\nbacktrack(state: &amp;state, choices: choices, selected: &amp;selected, res: &amp;res)\n// \u56de\u9000\uff1a\u64a4\u9500\u9009\u62e9\uff0c\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001\nselected[i] = false\nstate.removeLast()\n}\n}\n}\n/* \u5168\u6392\u5217 I */\nfunc permutationsI(nums: [Int]) -&gt; [[Int]] {\nvar state: [Int] = []\nvar selected = Array(repeating: false, count: nums.count)\nvar res: [[Int]] = []\nbacktrack(state: &amp;state, choices: nums, selected: &amp;selected, res: &amp;res)\nreturn res\n}\n</code></pre> permutations_i.zig<pre><code>[class]{}-[func]{backtrack}\n[class]{}-[func]{permutationsI}\n</code></pre> permutations_i.dart<pre><code>[class]{}-[func]{backtrack}\n[class]{}-[func]{permutationsI}\n</code></pre> <p>\u9700\u8981\u91cd\u70b9\u5173\u6ce8\u7684\u662f\uff0c\u6211\u4eec\u5f15\u5165\u4e86\u4e00\u4e2a\u5e03\u5c14\u578b\u6570\u7ec4 <code>selected</code> \uff0c\u5b83\u7684\u957f\u5ea6\u4e0e\u8f93\u5165\u6570\u7ec4\u957f\u5ea6\u76f8\u7b49\uff0c\u5176\u4e2d <code>selected[i]</code> \u8868\u793a <code>choices[i]</code> \u662f\u5426\u5df2\u88ab\u9009\u62e9\u3002\u6211\u4eec\u5229\u7528 <code>selected</code> \u907f\u514d\u67d0\u4e2a\u5143\u7d20\u88ab\u91cd\u590d\u9009\u62e9\uff0c\u4ece\u800c\u5b9e\u73b0\u526a\u679d\u3002</p> <p>\u5982\u4e0b\u56fe\u6240\u793a\uff0c\u5047\u8bbe\u6211\u4eec\u7b2c\u4e00\u8f6e\u9009\u62e9 1 \uff0c\u7b2c\u4e8c\u8f6e\u9009\u62e9 3 \uff0c\u7b2c\u4e09\u8f6e\u9009\u62e9 2 \uff0c\u5219\u9700\u8981\u5728\u7b2c\u4e8c\u8f6e\u526a\u6389\u5143\u7d20 1 \u7684\u5206\u652f\uff0c\u5728\u7b2c\u4e09\u8f6e\u526a\u6389\u5143\u7d20 1, 3 \u7684\u5206\u652f\u3002\u4ece\u672c\u8d28\u4e0a\u7406\u89e3\uff0c\u6b64\u526a\u679d\u64cd\u4f5c\u53ef\u5c06\u641c\u7d22\u7a7a\u95f4\u5927\u5c0f\u4ece \\(O(n^n)\\) \u964d\u4f4e\u81f3 \\(O(n!)\\) \u3002</p> <p></p> <p> Fig. \u5168\u6392\u5217\u526a\u679d\u793a\u4f8b </p>"},{"location":"chapter_backtracking/permutations_problem/#1222","title":"12.2.2. \u00a0 \u8003\u8651\u91cd\u590d\u7684\u60c5\u51b5","text":"<p>Question</p> <p>\u8f93\u5165\u4e00\u4e2a\u6574\u6570\u6570\u7ec4\uff0c\u6570\u7ec4\u4e2d\u53ef\u80fd\u5305\u542b\u91cd\u590d\u5143\u7d20\uff0c\u8fd4\u56de\u6240\u6709\u4e0d\u91cd\u590d\u7684\u6392\u5217\u3002</p> <p>\u5047\u8bbe\u8f93\u5165\u6570\u7ec4\u4e3a \\([1, 1, 2]\\) \u3002\u4e3a\u4e86\u65b9\u4fbf\u533a\u5206\u4e24\u4e2a\u91cd\u590d\u7684\u5143\u7d20 \\(1\\) \uff0c\u63a5\u4e0b\u6765\u6211\u4eec\u5c06\u7b2c\u4e8c\u4e2a\u5143\u7d20\u8bb0\u4e3a \\(\\hat{1}\\) \u3002\u5982\u4e0b\u56fe\u6240\u793a\uff0c\u4e0a\u8ff0\u65b9\u6cd5\u751f\u6210\u7684\u6392\u5217\u6709\u4e00\u534a\u90fd\u662f\u91cd\u590d\u7684\u3002</p> <p></p> <p> Fig. \u91cd\u590d\u6392\u5217 </p> <p>\u90a3\u4e48\uff0c\u5982\u4f55\u53bb\u9664\u91cd\u590d\u7684\u6392\u5217\u5462\uff1f\u6700\u76f4\u63a5\u5730\uff0c\u6211\u4eec\u53ef\u4ee5\u501f\u52a9\u4e00\u4e2a\u54c8\u5e0c\u8868\uff0c\u76f4\u63a5\u5bf9\u6392\u5217\u7ed3\u679c\u8fdb\u884c\u53bb\u91cd\u3002\u7136\u800c\uff0c\u8fd9\u6837\u505a\u4e0d\u591f\u4f18\u96c5\uff0c\u56e0\u4e3a\u751f\u6210\u91cd\u590d\u6392\u5217\u7684\u641c\u7d22\u5206\u652f\u662f\u6ca1\u6709\u5fc5\u8981\u7684\uff0c\u5e94\u5f53\u88ab\u63d0\u524d\u8bc6\u522b\u5e76\u526a\u679d\uff0c\u8fd9\u6837\u53ef\u4ee5\u63d0\u5347\u7b97\u6cd5\u6548\u7387\u3002</p> <p>\u89c2\u5bdf\u53d1\u73b0\uff0c\u5728\u7b2c\u4e00\u8f6e\u4e2d\uff0c\u9009\u62e9 \\(1\\) \u6216\u9009\u62e9 \\(\\hat{1}\\) \u662f\u7b49\u4ef7\u7684\uff0c\u56e0\u4e3a\u5728\u8fd9\u4e24\u4e2a\u9009\u62e9\u4e4b\u4e0b\u751f\u6210\u7684\u6240\u6709\u6392\u5217\u90fd\u662f\u91cd\u590d\u7684\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u5e94\u8be5\u628a \\(\\hat{1}\\) \u526a\u679d\u6389\u3002\u540c\u7406\uff0c\u5728\u7b2c\u4e00\u8f6e\u9009\u62e9 \\(2\\) \u540e\uff0c\u7b2c\u4e8c\u8f6e\u9009\u62e9\u4e2d\u7684 \\(1\\) \u548c \\(\\hat{1}\\) \u4e5f\u4f1a\u4ea7\u751f\u91cd\u590d\u5206\u652f\uff0c\u56e0\u6b64\u4e5f\u9700\u8981\u5c06\u7b2c\u4e8c\u8f6e\u7684 \\(\\hat{1}\\) \u526a\u679d\u3002</p> <p></p> <p> Fig. \u91cd\u590d\u6392\u5217\u526a\u679d </p> <p>\u672c\u8d28\u4e0a\u770b\uff0c\u6211\u4eec\u7684\u76ee\u6807\u662f\u5b9e\u73b0\u5728\u67d0\u4e00\u8f6e\u9009\u62e9\u4e2d\uff0c\u591a\u4e2a\u76f8\u7b49\u7684\u5143\u7d20\u4ec5\u88ab\u9009\u62e9\u4e00\u6b21\u3002\u56e0\u6b64\uff0c\u5728\u4e0a\u4e00\u9898\u7684\u4ee3\u7801\u7684\u57fa\u7840\u4e0a\uff0c\u6211\u4eec\u8003\u8651\u5728\u6bcf\u4e00\u8f6e\u9009\u62e9\u4e2d\u5f00\u542f\u4e00\u4e2a\u54c8\u5e0c\u8868 <code>duplicated</code> \uff0c\u7528\u4e8e\u8bb0\u5f55\u8be5\u8f6e\u4e2d\u5df2\u7ecf\u5c1d\u8bd5\u8fc7\u7684\u5143\u7d20\uff0c\u5e76\u5c06\u91cd\u590d\u5143\u7d20\u526a\u679d\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart permutations_ii.java<pre><code>/* \u56de\u6eaf\u7b97\u6cd5\uff1a\u5168\u6392\u5217 II */\nvoid backtrack(List&lt;Integer&gt; state, int[] choices, boolean[] selected, List&lt;List&lt;Integer&gt;&gt; res) {\n// \u5f53\u72b6\u6001\u957f\u5ea6\u7b49\u4e8e\u5143\u7d20\u6570\u91cf\u65f6\uff0c\u8bb0\u5f55\u89e3\nif (state.size() == choices.length) {\nres.add(new ArrayList&lt;Integer&gt;(state));\nreturn;\n}\n// \u904d\u5386\u6240\u6709\u9009\u62e9\nSet&lt;Integer&gt; duplicated = new HashSet&lt;Integer&gt;();\nfor (int i = 0; i &lt; choices.length; i++) {\nint choice = choices[i];\n// \u526a\u679d\uff1a\u4e0d\u5141\u8bb8\u91cd\u590d\u9009\u62e9\u5143\u7d20 \u4e14 \u4e0d\u5141\u8bb8\u91cd\u590d\u9009\u62e9\u76f8\u7b49\u5143\u7d20\nif (!selected[i] &amp;&amp; !duplicated.contains(choice)) {\n// \u5c1d\u8bd5\uff1a\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\nduplicated.add(choice); // \u8bb0\u5f55\u9009\u62e9\u8fc7\u7684\u5143\u7d20\u503c\nselected[i] = true;\nstate.add(choice);\n// \u8fdb\u884c\u4e0b\u4e00\u8f6e\u9009\u62e9\nbacktrack(state, choices, selected, res);\n// \u56de\u9000\uff1a\u64a4\u9500\u9009\u62e9\uff0c\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001\nselected[i] = false;\nstate.remove(state.size() - 1);\n}\n}\n}\n/* \u5168\u6392\u5217 II */\nList&lt;List&lt;Integer&gt;&gt; permutationsII(int[] nums) {\nList&lt;List&lt;Integer&gt;&gt; res = new ArrayList&lt;List&lt;Integer&gt;&gt;();\nbacktrack(new ArrayList&lt;Integer&gt;(), nums, new boolean[nums.length], res);\nreturn res;\n}\n</code></pre> permutations_ii.cpp<pre><code>/* \u56de\u6eaf\u7b97\u6cd5\uff1a\u5168\u6392\u5217 II */\nvoid backtrack(vector&lt;int&gt; &amp;state, const vector&lt;int&gt; &amp;choices, vector&lt;bool&gt; &amp;selected, vector&lt;vector&lt;int&gt;&gt; &amp;res) {\n// \u5f53\u72b6\u6001\u957f\u5ea6\u7b49\u4e8e\u5143\u7d20\u6570\u91cf\u65f6\uff0c\u8bb0\u5f55\u89e3\nif (state.size() == choices.size()) {\nres.push_back(state);\nreturn;\n}\n// \u904d\u5386\u6240\u6709\u9009\u62e9\nunordered_set&lt;int&gt; duplicated;\nfor (int i = 0; i &lt; choices.size(); i++) {\nint choice = choices[i];\n// \u526a\u679d\uff1a\u4e0d\u5141\u8bb8\u91cd\u590d\u9009\u62e9\u5143\u7d20 \u4e14 \u4e0d\u5141\u8bb8\u91cd\u590d\u9009\u62e9\u76f8\u7b49\u5143\u7d20\nif (!selected[i] &amp;&amp; duplicated.find(choice) == duplicated.end()) {\n// \u5c1d\u8bd5\uff1a\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\nduplicated.emplace(choice); // \u8bb0\u5f55\u9009\u62e9\u8fc7\u7684\u5143\u7d20\u503c\nselected[i] = true;\nstate.push_back(choice);\n// \u8fdb\u884c\u4e0b\u4e00\u8f6e\u9009\u62e9\nbacktrack(state, choices, selected, res);\n// \u56de\u9000\uff1a\u64a4\u9500\u9009\u62e9\uff0c\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001\nselected[i] = false;\nstate.pop_back();\n}\n}\n}\n/* \u5168\u6392\u5217 II */\nvector&lt;vector&lt;int&gt;&gt; permutationsII(vector&lt;int&gt; nums) {\nvector&lt;int&gt; state;\nvector&lt;bool&gt; selected(nums.size(), false);\nvector&lt;vector&lt;int&gt;&gt; res;\nbacktrack(state, nums, selected, res);\nreturn res;\n}\n</code></pre> permutations_ii.py<pre><code>def backtrack(\nstate: list[int], choices: list[int], selected: list[bool], res: list[list[int]]\n):\n\"\"\"\u56de\u6eaf\u7b97\u6cd5\uff1a\u5168\u6392\u5217 II\"\"\"\n# \u5f53\u72b6\u6001\u957f\u5ea6\u7b49\u4e8e\u5143\u7d20\u6570\u91cf\u65f6\uff0c\u8bb0\u5f55\u89e3\nif len(state) == len(choices):\nres.append(list(state))\nreturn\n# \u904d\u5386\u6240\u6709\u9009\u62e9\nduplicated = set[int]()\nfor i, choice in enumerate(choices):\n# \u526a\u679d\uff1a\u4e0d\u5141\u8bb8\u91cd\u590d\u9009\u62e9\u5143\u7d20 \u4e14 \u4e0d\u5141\u8bb8\u91cd\u590d\u9009\u62e9\u76f8\u7b49\u5143\u7d20\nif not selected[i] and choice not in duplicated:\n# \u5c1d\u8bd5\uff1a\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\nduplicated.add(choice)  # \u8bb0\u5f55\u9009\u62e9\u8fc7\u7684\u5143\u7d20\u503c\nselected[i] = True\nstate.append(choice)\n# \u8fdb\u884c\u4e0b\u4e00\u8f6e\u9009\u62e9\nbacktrack(state, choices, selected, res)\n# \u56de\u9000\uff1a\u64a4\u9500\u9009\u62e9\uff0c\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001\nselected[i] = False\nstate.pop()\ndef permutations_ii(nums: list[int]) -&gt; list[list[int]]:\n\"\"\"\u5168\u6392\u5217 II\"\"\"\nres = []\nbacktrack(state=[], choices=nums, selected=[False] * len(nums), res=res)\nreturn res\n</code></pre> permutations_ii.go<pre><code>/* \u56de\u6eaf\u7b97\u6cd5\uff1a\u5168\u6392\u5217 II */\nfunc backtrackII(state *[]int, choices *[]int, selected *[]bool, res *[][]int) {\n// \u5f53\u72b6\u6001\u957f\u5ea6\u7b49\u4e8e\u5143\u7d20\u6570\u91cf\u65f6\uff0c\u8bb0\u5f55\u89e3\nif len(*state) == len(*choices) {\nnewState := append([]int{}, *state...)\n*res = append(*res, newState)\n}\n// \u904d\u5386\u6240\u6709\u9009\u62e9\nduplicated := make(map[int]struct{}, 0)\nfor i := 0; i &lt; len(*choices); i++ {\nchoice := (*choices)[i]\n// \u526a\u679d\uff1a\u4e0d\u5141\u8bb8\u91cd\u590d\u9009\u62e9\u5143\u7d20 \u4e14 \u4e0d\u5141\u8bb8\u91cd\u590d\u9009\u62e9\u76f8\u7b49\u5143\u7d20\nif _, ok := duplicated[choice]; !ok &amp;&amp; !(*selected)[i] {\n// \u5c1d\u8bd5\uff1a\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\n// \u8bb0\u5f55\u9009\u62e9\u8fc7\u7684\u5143\u7d20\u503c\nduplicated[choice] = struct{}{}\n(*selected)[i] = true\n*state = append(*state, choice)\n// \u8fdb\u884c\u4e0b\u4e00\u8f6e\u9009\u62e9\nbacktrackI(state, choices, selected, res)\n// \u56de\u9000\uff1a\u64a4\u9500\u9009\u62e9\uff0c\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001\n(*selected)[i] = false\n*state = (*state)[:len(*state)-1]\n}\n}\n}\n/* \u5168\u6392\u5217 II */\nfunc permutationsII(nums []int) [][]int {\nres := make([][]int, 0)\nstate := make([]int, 0)\nselected := make([]bool, len(nums))\nbacktrackII(&amp;state, &amp;nums, &amp;selected, &amp;res)\nreturn res\n}\n</code></pre> permutations_ii.js<pre><code>/* \u56de\u6eaf\u7b97\u6cd5\uff1a\u5168\u6392\u5217 II */\nfunction backtrack(state, choices, selected, res) {\n// \u5f53\u72b6\u6001\u957f\u5ea6\u7b49\u4e8e\u5143\u7d20\u6570\u91cf\u65f6\uff0c\u8bb0\u5f55\u89e3\nif (state.length === choices.length) {\nres.push([...state]);\nreturn;\n}\n// \u904d\u5386\u6240\u6709\u9009\u62e9\nconst duplicated = new Set();\nchoices.forEach((choice, i) =&gt; {\n// \u526a\u679d\uff1a\u4e0d\u5141\u8bb8\u91cd\u590d\u9009\u62e9\u5143\u7d20 \u4e14 \u4e0d\u5141\u8bb8\u91cd\u590d\u9009\u62e9\u76f8\u7b49\u5143\u7d20\nif (!selected[i] &amp;&amp; !duplicated.has(choice)) {\n// \u5c1d\u8bd5\uff1a\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\nduplicated.add(choice); // \u8bb0\u5f55\u9009\u62e9\u8fc7\u7684\u5143\u7d20\u503c\nselected[i] = true;\nstate.push(choice);\n// \u8fdb\u884c\u4e0b\u4e00\u8f6e\u9009\u62e9\nbacktrack(state, choices, selected, res);\n// \u56de\u9000\uff1a\u64a4\u9500\u9009\u62e9\uff0c\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001\nselected[i] = false;\nstate.pop();\n}\n});\n}\n/* \u5168\u6392\u5217 II */\nfunction permutationsII(nums) {\nconst res = [];\nbacktrack([], nums, Array(nums.length).fill(false), res);\nreturn res;\n}\n</code></pre> permutations_ii.ts<pre><code>/* \u56de\u6eaf\u7b97\u6cd5\uff1a\u5168\u6392\u5217 II */\nfunction backtrack(\nstate: number[],\nchoices: number[],\nselected: boolean[],\nres: number[][]\n): void {\n// \u5f53\u72b6\u6001\u957f\u5ea6\u7b49\u4e8e\u5143\u7d20\u6570\u91cf\u65f6\uff0c\u8bb0\u5f55\u89e3\nif (state.length === choices.length) {\nres.push([...state]);\nreturn;\n}\n// \u904d\u5386\u6240\u6709\u9009\u62e9\nconst duplicated = new Set();\nchoices.forEach((choice, i) =&gt; {\n// \u526a\u679d\uff1a\u4e0d\u5141\u8bb8\u91cd\u590d\u9009\u62e9\u5143\u7d20 \u4e14 \u4e0d\u5141\u8bb8\u91cd\u590d\u9009\u62e9\u76f8\u7b49\u5143\u7d20\nif (!selected[i] &amp;&amp; !duplicated.has(choice)) {\n// \u5c1d\u8bd5\uff1a\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\nduplicated.add(choice); // \u8bb0\u5f55\u9009\u62e9\u8fc7\u7684\u5143\u7d20\u503c\nselected[i] = true;\nstate.push(choice);\n// \u8fdb\u884c\u4e0b\u4e00\u8f6e\u9009\u62e9\nbacktrack(state, choices, selected, res);\n// \u56de\u9000\uff1a\u64a4\u9500\u9009\u62e9\uff0c\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001\nselected[i] = false;\nstate.pop();\n}\n});\n}\n/* \u5168\u6392\u5217 II */\nfunction permutationsII(nums: number[]): number[][] {\nconst res: number[][] = [];\nbacktrack([], nums, Array(nums.length).fill(false), res);\nreturn res;\n}\n</code></pre> permutations_ii.c<pre><code>[class]{}-[func]{backtrack}\n[class]{}-[func]{permutationsII}\n</code></pre> permutations_ii.cs<pre><code>/* \u56de\u6eaf\u7b97\u6cd5\uff1a\u5168\u6392\u5217 II */\nvoid backtrack(List&lt;int&gt; state, int[] choices, bool[] selected, List&lt;List&lt;int&gt;&gt; res) {\n// \u5f53\u72b6\u6001\u957f\u5ea6\u7b49\u4e8e\u5143\u7d20\u6570\u91cf\u65f6\uff0c\u8bb0\u5f55\u89e3\nif (state.Count == choices.Length) {\nres.Add(new List&lt;int&gt;(state));\nreturn;\n}\n// \u904d\u5386\u6240\u6709\u9009\u62e9\nISet&lt;int&gt; duplicated = new HashSet&lt;int&gt;();\nfor (int i = 0; i &lt; choices.Length; i++) {\nint choice = choices[i];\n// \u526a\u679d\uff1a\u4e0d\u5141\u8bb8\u91cd\u590d\u9009\u62e9\u5143\u7d20 \u4e14 \u4e0d\u5141\u8bb8\u91cd\u590d\u9009\u62e9\u76f8\u7b49\u5143\u7d20\nif (!selected[i] &amp;&amp; !duplicated.Contains(choice)) {\n// \u5c1d\u8bd5\uff1a\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\nduplicated.Add(choice); // \u8bb0\u5f55\u9009\u62e9\u8fc7\u7684\u5143\u7d20\u503c\nselected[i] = true;\nstate.Add(choice);\n// \u8fdb\u884c\u4e0b\u4e00\u8f6e\u9009\u62e9\nbacktrack(state, choices, selected, res);\n// \u56de\u9000\uff1a\u64a4\u9500\u9009\u62e9\uff0c\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001\nselected[i] = false;\nstate.RemoveAt(state.Count - 1);\n}\n}\n}\n/* \u5168\u6392\u5217 II */\nList&lt;List&lt;int&gt;&gt; permutationsII(int[] nums) {\nList&lt;List&lt;int&gt;&gt; res = new List&lt;List&lt;int&gt;&gt;();\nbacktrack(new List&lt;int&gt;(), nums, new bool[nums.Length], res);\nreturn res;\n}\n</code></pre> permutations_ii.swift<pre><code>/* \u56de\u6eaf\u7b97\u6cd5\uff1a\u5168\u6392\u5217 II */\nfunc backtrack(state: inout [Int], choices: [Int], selected: inout [Bool], res: inout [[Int]]) {\n// \u5f53\u72b6\u6001\u957f\u5ea6\u7b49\u4e8e\u5143\u7d20\u6570\u91cf\u65f6\uff0c\u8bb0\u5f55\u89e3\nif state.count == choices.count {\nres.append(state)\nreturn\n}\n// \u904d\u5386\u6240\u6709\u9009\u62e9\nvar duplicated: Set&lt;Int&gt; = []\nfor (i, choice) in choices.enumerated() {\n// \u526a\u679d\uff1a\u4e0d\u5141\u8bb8\u91cd\u590d\u9009\u62e9\u5143\u7d20 \u4e14 \u4e0d\u5141\u8bb8\u91cd\u590d\u9009\u62e9\u76f8\u7b49\u5143\u7d20\nif !selected[i], !duplicated.contains(choice) {\n// \u5c1d\u8bd5\uff1a\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\nduplicated.insert(choice) // \u8bb0\u5f55\u9009\u62e9\u8fc7\u7684\u5143\u7d20\u503c\nselected[i] = true\nstate.append(choice)\n// \u8fdb\u884c\u4e0b\u4e00\u8f6e\u9009\u62e9\nbacktrack(state: &amp;state, choices: choices, selected: &amp;selected, res: &amp;res)\n// \u56de\u9000\uff1a\u64a4\u9500\u9009\u62e9\uff0c\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001\nselected[i] = false\nstate.removeLast()\n}\n}\n}\n/* \u5168\u6392\u5217 II */\nfunc permutationsII(nums: [Int]) -&gt; [[Int]] {\nvar state: [Int] = []\nvar selected = Array(repeating: false, count: nums.count)\nvar res: [[Int]] = []\nbacktrack(state: &amp;state, choices: nums, selected: &amp;selected, res: &amp;res)\nreturn res\n}\n</code></pre> permutations_ii.zig<pre><code>[class]{}-[func]{backtrack}\n[class]{}-[func]{permutationsII}\n</code></pre> permutations_ii.dart<pre><code>[class]{}-[func]{backtrack}\n[class]{}-[func]{permutationsII}\n</code></pre> <p>\u6ce8\u610f\uff0c\u867d\u7136 <code>selected</code> \u548c <code>duplicated</code> \u90fd\u8d77\u5230\u526a\u679d\u7684\u4f5c\u7528\uff0c\u4f46\u4ed6\u4eec\u526a\u6389\u7684\u662f\u4e0d\u540c\u7684\u5206\u652f\uff1a</p> <ul> <li>\u526a\u679d\u6761\u4ef6\u4e00\uff1a\u6574\u4e2a\u641c\u7d22\u8fc7\u7a0b\u4e2d\u53ea\u6709\u4e00\u4e2a <code>selected</code> \u3002\u5b83\u8bb0\u5f55\u7684\u662f\u5f53\u524d\u72b6\u6001\u4e2d\u5305\u542b\u54ea\u4e9b\u5143\u7d20\uff0c\u4f5c\u7528\u662f\u907f\u514d\u67d0\u4e2a\u5143\u7d20\u5728 <code>state</code> \u4e2d\u91cd\u590d\u51fa\u73b0\u3002</li> <li>\u526a\u679d\u6761\u4ef6\u4e8c\uff1a\u6bcf\u8f6e\u9009\u62e9\uff08\u5373\u6bcf\u4e2a\u5f00\u542f\u7684 <code>backtrack</code> \u51fd\u6570\uff09\u90fd\u5305\u542b\u4e00\u4e2a <code>duplicated</code> \u3002\u5b83\u8bb0\u5f55\u7684\u662f\u5728\u904d\u5386\u4e2d\u54ea\u4e9b\u5143\u7d20\u5df2\u88ab\u9009\u62e9\u8fc7\uff0c\u4f5c\u7528\u662f\u4fdd\u8bc1\u76f8\u7b49\u5143\u7d20\u53ea\u88ab\u9009\u62e9\u4e00\u6b21\uff0c\u4ee5\u907f\u514d\u4ea7\u751f\u91cd\u590d\u7684\u641c\u7d22\u5206\u652f\u3002</li> </ul> <p>\u4e0b\u56fe\u5c55\u793a\u4e86\u4e24\u4e2a\u526a\u679d\u6761\u4ef6\u7684\u751f\u6548\u8303\u56f4\u3002\u6ce8\u610f\uff0c\u6811\u4e2d\u7684\u6bcf\u4e2a\u8282\u70b9\u4ee3\u8868\u4e00\u4e2a\u9009\u62e9\uff0c\u4ece\u6839\u8282\u70b9\u5230\u53f6\u8282\u70b9\u7684\u8def\u5f84\u4e0a\u7684\u5404\u4e2a\u8282\u70b9\u6784\u6210\u4e00\u4e2a\u6392\u5217\u3002</p> <p></p> <p> Fig. \u4e24\u79cd\u526a\u679d\u6761\u4ef6\u7684\u4f5c\u7528\u8303\u56f4 </p>"},{"location":"chapter_backtracking/permutations_problem/#1223","title":"12.2.3. \u00a0 \u590d\u6742\u5ea6\u5206\u6790","text":"<p>\u5047\u8bbe\u5143\u7d20\u4e24\u4e24\u4e4b\u95f4\u4e92\u4e0d\u76f8\u540c\uff0c\u5219 \\(n\\) \u4e2a\u5143\u7d20\u5171\u6709 \\(n!\\)  \u79cd\u6392\u5217\uff08\u9636\u4e58\uff09\uff1b\u5728\u8bb0\u5f55\u7ed3\u679c\u65f6\uff0c\u9700\u8981\u590d\u5236\u957f\u5ea6\u4e3a \\(n\\) \u7684\u5217\u8868\uff0c\u4f7f\u7528 \\(O(n)\\) \u65f6\u95f4\u3002\u56e0\u6b64\uff0c\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(n!n)\\) \u3002</p> <p>\u6700\u5927\u9012\u5f52\u6df1\u5ea6\u4e3a \\(n\\) \uff0c\u4f7f\u7528 \\(O(n)\\) \u6808\u5e27\u7a7a\u95f4\u3002<code>selected</code> \u4f7f\u7528 \\(O(n)\\) \u7a7a\u95f4\u3002\u540c\u4e00\u65f6\u523b\u6700\u591a\u5171\u6709 \\(n\\) \u4e2a <code>duplicated</code> \uff0c\u4f7f\u7528 \\(O(n^2)\\) \u7a7a\u95f4\u3002\u56e0\u6b64\uff0c\u5168\u6392\u5217 I \u7684\u7a7a\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(n)\\) \uff0c\u5168\u6392\u5217 II \u7684\u7a7a\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(n^2)\\) \u3002</p>"},{"location":"chapter_computational_complexity/","title":"2. \u00a0 \u590d\u6742\u5ea6\u5206\u6790","text":""},{"location":"chapter_computational_complexity/performance_evaluation/","title":"2.1. \u00a0 \u7b97\u6cd5\u6548\u7387\u8bc4\u4f30","text":""},{"location":"chapter_computational_complexity/performance_evaluation/#211","title":"2.1.1. \u00a0 \u7b97\u6cd5\u8bc4\u4ef7\u7ef4\u5ea6","text":"<p>\u4ece\u603b\u4f53\u4e0a\u770b\uff0c\u7b97\u6cd5\u8bbe\u8ba1\u8ffd\u6c42\u4ee5\u4e0b\u4e24\u4e2a\u5c42\u9762\u7684\u76ee\u6807\uff1a</p> <ol> <li>\u627e\u5230\u95ee\u9898\u89e3\u6cd5\u3002\u7b97\u6cd5\u9700\u8981\u5728\u89c4\u5b9a\u7684\u8f93\u5165\u8303\u56f4\u5185\uff0c\u53ef\u9760\u5730\u6c42\u5f97\u95ee\u9898\u7684\u6b63\u786e\u89e3\u3002</li> <li>\u5bfb\u6c42\u6700\u4f18\u89e3\u6cd5\u3002\u540c\u4e00\u4e2a\u95ee\u9898\u53ef\u80fd\u5b58\u5728\u591a\u79cd\u89e3\u6cd5\uff0c\u6211\u4eec\u5e0c\u671b\u627e\u5230\u5c3d\u53ef\u80fd\u9ad8\u6548\u7684\u7b97\u6cd5\u3002</li> </ol> <p>\u56e0\u6b64\uff0c\u5728\u80fd\u591f\u89e3\u51b3\u95ee\u9898\u7684\u524d\u63d0\u4e0b\uff0c\u7b97\u6cd5\u6548\u7387\u6210\u4e3a\u4e3b\u8981\u7684\u8bc4\u4ef7\u7ef4\u5ea6\uff0c\u4e3b\u8981\u5305\u62ec\uff1a</p> <ul> <li>\u65f6\u95f4\u6548\u7387\uff0c\u5373\u7b97\u6cd5\u8fd0\u884c\u901f\u5ea6\u7684\u5feb\u6162\u3002</li> <li>\u7a7a\u95f4\u6548\u7387\uff0c\u5373\u7b97\u6cd5\u5360\u7528\u5185\u5b58\u7a7a\u95f4\u7684\u5927\u5c0f\u3002</li> </ul> <p>\u7b80\u800c\u8a00\u4e4b\uff0c\u6211\u4eec\u7684\u76ee\u6807\u662f\u8bbe\u8ba1\u201c\u65e2\u5feb\u53c8\u7701\u201d\u7684\u6570\u636e\u7ed3\u6784\u4e0e\u7b97\u6cd5\u3002\u638c\u63e1\u8bc4\u4f30\u7b97\u6cd5\u6548\u7387\u7684\u65b9\u6cd5\u5219\u81f3\u5173\u91cd\u8981\uff0c\u56e0\u4e3a\u53ea\u6709\u4e86\u89e3\u8bc4\u4ef7\u6807\u51c6\uff0c\u6211\u4eec\u624d\u80fd\u8fdb\u884c\u7b97\u6cd5\u4e4b\u95f4\u7684\u5bf9\u6bd4\u5206\u6790\uff0c\u4ece\u800c\u6307\u5bfc\u7b97\u6cd5\u8bbe\u8ba1\u4e0e\u4f18\u5316\u8fc7\u7a0b\u3002</p>"},{"location":"chapter_computational_complexity/performance_evaluation/#212","title":"2.1.2. \u00a0 \u6548\u7387\u8bc4\u4f30\u65b9\u6cd5","text":""},{"location":"chapter_computational_complexity/performance_evaluation/#_1","title":"\u5b9e\u9645\u6d4b\u8bd5","text":"<p>\u5047\u8bbe\u6211\u4eec\u73b0\u5728\u6709\u7b97\u6cd5 A \u548c\u7b97\u6cd5 B\uff0c\u5b83\u4eec\u90fd\u80fd\u89e3\u51b3\u540c\u4e00\u95ee\u9898\uff0c\u73b0\u5728\u9700\u8981\u5bf9\u6bd4\u8fd9\u4e24\u4e2a\u7b97\u6cd5\u7684\u6548\u7387\u3002\u6211\u4eec\u6700\u76f4\u63a5\u7684\u65b9\u6cd5\u5c31\u662f\u627e\u4e00\u53f0\u8ba1\u7b97\u673a\uff0c\u8fd0\u884c\u8fd9\u4e24\u4e2a\u7b97\u6cd5\uff0c\u5e76\u76d1\u63a7\u8bb0\u5f55\u5b83\u4eec\u7684\u8fd0\u884c\u65f6\u95f4\u548c\u5185\u5b58\u5360\u7528\u60c5\u51b5\u3002\u8fd9\u79cd\u8bc4\u4f30\u65b9\u5f0f\u80fd\u591f\u53cd\u6620\u771f\u5b9e\u60c5\u51b5\uff0c\u4f46\u4e5f\u5b58\u5728\u8f83\u5927\u5c40\u9650\u6027\u3002</p> <p>\u96be\u4ee5\u6392\u9664\u6d4b\u8bd5\u73af\u5883\u7684\u5e72\u6270\u56e0\u7d20\u3002\u786c\u4ef6\u914d\u7f6e\u4f1a\u5f71\u54cd\u7b97\u6cd5\u7684\u6027\u80fd\u8868\u73b0\u3002\u4f8b\u5982\uff0c\u5728\u67d0\u53f0\u8ba1\u7b97\u673a\u4e2d\uff0c\u7b97\u6cd5 A \u7684\u8fd0\u884c\u65f6\u95f4\u6bd4\u7b97\u6cd5 B \u77ed\uff1b\u4f46\u5728\u53e6\u4e00\u53f0\u914d\u7f6e\u4e0d\u540c\u7684\u8ba1\u7b97\u673a\u4e2d\uff0c\u6211\u4eec\u53ef\u80fd\u5f97\u5230\u76f8\u53cd\u7684\u6d4b\u8bd5\u7ed3\u679c\u3002\u8fd9\u610f\u5473\u7740\u6211\u4eec\u9700\u8981\u5728\u5404\u79cd\u673a\u5668\u4e0a\u8fdb\u884c\u6d4b\u8bd5\uff0c\u800c\u8fd9\u662f\u4e0d\u73b0\u5b9e\u7684\u3002</p> <p>\u5c55\u5f00\u5b8c\u6574\u6d4b\u8bd5\u975e\u5e38\u8017\u8d39\u8d44\u6e90\u3002\u968f\u7740\u8f93\u5165\u6570\u636e\u91cf\u7684\u53d8\u5316\uff0c\u7b97\u6cd5\u4f1a\u8868\u73b0\u51fa\u4e0d\u540c\u7684\u6548\u7387\u3002\u4f8b\u5982\uff0c\u8f93\u5165\u6570\u636e\u91cf\u8f83\u5c0f\u65f6\uff0c\u7b97\u6cd5 A \u7684\u8fd0\u884c\u65f6\u95f4\u53ef\u80fd\u77ed\u4e8e\u7b97\u6cd5 B\uff1b\u800c\u8f93\u5165\u6570\u636e\u91cf\u8f83\u5927\u65f6\uff0c\u6d4b\u8bd5\u7ed3\u679c\u53ef\u80fd\u76f8\u53cd\u3002\u56e0\u6b64\uff0c\u4e3a\u4e86\u5f97\u5230\u6709\u8bf4\u670d\u529b\u7684\u7ed3\u8bba\uff0c\u6211\u4eec\u9700\u8981\u6d4b\u8bd5\u5404\u79cd\u89c4\u6a21\u7684\u8f93\u5165\u6570\u636e\uff0c\u8fd9\u6837\u9700\u8981\u5360\u7528\u5927\u91cf\u7684\u8ba1\u7b97\u8d44\u6e90\u3002</p>"},{"location":"chapter_computational_complexity/performance_evaluation/#_2","title":"\u7406\u8bba\u4f30\u7b97","text":"<p>\u7531\u4e8e\u5b9e\u9645\u6d4b\u8bd5\u5177\u6709\u8f83\u5927\u7684\u5c40\u9650\u6027\uff0c\u6211\u4eec\u53ef\u4ee5\u8003\u8651\u4ec5\u901a\u8fc7\u4e00\u4e9b\u8ba1\u7b97\u6765\u8bc4\u4f30\u7b97\u6cd5\u7684\u6548\u7387\u3002\u8fd9\u79cd\u4f30\u7b97\u65b9\u6cd5\u88ab\u79f0\u4e3a\u300c\u590d\u6742\u5ea6\u5206\u6790 Complexity Analysis\u300d\u6216\u300c\u6e10\u8fd1\u590d\u6742\u5ea6\u5206\u6790 Asymptotic Complexity Analysis\u300d\u3002</p> <p>\u590d\u6742\u5ea6\u5206\u6790\u8bc4\u4f30\u7684\u662f\u7b97\u6cd5\u8fd0\u884c\u6548\u7387\u968f\u7740\u8f93\u5165\u6570\u636e\u91cf\u589e\u591a\u65f6\u7684\u589e\u957f\u8d8b\u52bf\u3002\u8fd9\u4e2a\u5b9a\u4e49\u6709\u4e9b\u62d7\u53e3\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u5176\u5206\u4e3a\u4e09\u4e2a\u91cd\u70b9\u6765\u7406\u89e3\uff1a</p> <ul> <li>\u201c\u7b97\u6cd5\u8fd0\u884c\u6548\u7387\u201d\u53ef\u5206\u4e3a\u201c\u8fd0\u884c\u65f6\u95f4\u201d\u548c\u201c\u5360\u7528\u7a7a\u95f4\u201d\uff0c\u56e0\u6b64\u6211\u4eec\u53ef\u4ee5\u5c06\u590d\u6742\u5ea6\u5206\u4e3a\u300c\u65f6\u95f4\u590d\u6742\u5ea6 Time Complexity\u300d\u548c\u300c\u7a7a\u95f4\u590d\u6742\u5ea6 Space Complexity\u300d\uff1b</li> <li>\u201c\u968f\u7740\u8f93\u5165\u6570\u636e\u91cf\u589e\u591a\u65f6\u201d\u8868\u793a\u590d\u6742\u5ea6\u4e0e\u8f93\u5165\u6570\u636e\u91cf\u6709\u5173\uff0c\u53cd\u6620\u4e86\u7b97\u6cd5\u8fd0\u884c\u6548\u7387\u4e0e\u8f93\u5165\u6570\u636e\u91cf\u4e4b\u95f4\u7684\u5173\u7cfb\uff1b</li> <li>\u201c\u589e\u957f\u8d8b\u52bf\u201d\u8868\u793a\u590d\u6742\u5ea6\u5206\u6790\u5173\u6ce8\u7684\u662f\u7b97\u6cd5\u65f6\u95f4\u4e0e\u7a7a\u95f4\u7684\u589e\u957f\u8d8b\u52bf\uff0c\u800c\u975e\u5177\u4f53\u7684\u8fd0\u884c\u65f6\u95f4\u6216\u5360\u7528\u7a7a\u95f4\uff1b</li> </ul> <p>\u590d\u6742\u5ea6\u5206\u6790\u514b\u670d\u4e86\u5b9e\u9645\u6d4b\u8bd5\u65b9\u6cd5\u7684\u5f0a\u7aef\u3002\u9996\u5148\uff0c\u5b83\u72ec\u7acb\u4e8e\u6d4b\u8bd5\u73af\u5883\uff0c\u56e0\u6b64\u5206\u6790\u7ed3\u679c\u9002\u7528\u4e8e\u6240\u6709\u8fd0\u884c\u5e73\u53f0\u3002\u5176\u6b21\uff0c\u5b83\u53ef\u4ee5\u4f53\u73b0\u4e0d\u540c\u6570\u636e\u91cf\u4e0b\u7684\u7b97\u6cd5\u6548\u7387\uff0c\u5c24\u5176\u662f\u5728\u5927\u6570\u636e\u91cf\u4e0b\u7684\u7b97\u6cd5\u6027\u80fd\u3002</p> <p>\u5982\u679c\u4f60\u5bf9\u590d\u6742\u5ea6\u5206\u6790\u7684\u6982\u5ff5\u4ecd\u611f\u5230\u56f0\u60d1\uff0c\u65e0\u9700\u62c5\u5fc3\uff0c\u6211\u4eec\u4f1a\u5728\u540e\u7eed\u7ae0\u8282\u8be6\u7ec6\u4ecb\u7ecd\u3002</p>"},{"location":"chapter_computational_complexity/performance_evaluation/#213","title":"2.1.3. \u00a0 \u590d\u6742\u5ea6\u5206\u6790\u91cd\u8981\u6027","text":"<p>\u590d\u6742\u5ea6\u5206\u6790\u4e3a\u6211\u4eec\u63d0\u4f9b\u4e86\u4e00\u628a\u8bc4\u4f30\u7b97\u6cd5\u6548\u7387\u7684\u201c\u6807\u5c3a\u201d\uff0c\u544a\u8bc9\u6211\u4eec\u6267\u884c\u67d0\u4e2a\u7b97\u6cd5\u6240\u9700\u7684\u65f6\u95f4\u548c\u7a7a\u95f4\u8d44\u6e90\uff0c\u5e76\u4f7f\u6211\u4eec\u80fd\u591f\u5bf9\u6bd4\u4e0d\u540c\u7b97\u6cd5\u4e4b\u95f4\u7684\u6548\u7387\u3002</p> <p>\u590d\u6742\u5ea6\u662f\u4e2a\u6570\u5b66\u6982\u5ff5\uff0c\u5bf9\u4e8e\u521d\u5b66\u8005\u53ef\u80fd\u6bd4\u8f83\u62bd\u8c61\uff0c\u5b66\u4e60\u96be\u5ea6\u76f8\u5bf9\u8f83\u9ad8\u3002\u4ece\u8fd9\u4e2a\u89d2\u5ea6\u770b\uff0c\u590d\u6742\u5ea6\u5206\u6790\u53ef\u80fd\u4e0d\u592a\u9002\u5408\u4f5c\u4e3a\u7b2c\u4e00\u7ae0\u7684\u5185\u5bb9\u3002\u7136\u800c\uff0c\u5f53\u6211\u4eec\u8ba8\u8bba\u67d0\u4e2a\u6570\u636e\u7ed3\u6784\u6216\u7b97\u6cd5\u7684\u7279\u70b9\u65f6\uff0c\u6211\u4eec\u96be\u4ee5\u907f\u514d\u8981\u5206\u6790\u5176\u8fd0\u884c\u901f\u5ea6\u548c\u7a7a\u95f4\u4f7f\u7528\u60c5\u51b5\u3002\u56e0\u6b64\uff0c\u5728\u6df1\u5165\u5b66\u4e60\u6570\u636e\u7ed3\u6784\u4e0e\u7b97\u6cd5\u4e4b\u524d\uff0c\u5efa\u8bae\u8bfb\u8005\u5148\u5bf9\u590d\u6742\u5ea6\u5efa\u7acb\u521d\u6b65\u7684\u4e86\u89e3\uff0c\u5e76\u80fd\u591f\u5b8c\u6210\u7b80\u5355\u6848\u4f8b\u7684\u590d\u6742\u5ea6\u5206\u6790\u3002</p>"},{"location":"chapter_computational_complexity/space_complexity/","title":"2.3. \u00a0 \u7a7a\u95f4\u590d\u6742\u5ea6","text":"<p>\u300c\u7a7a\u95f4\u590d\u6742\u5ea6 Space Complexity\u300d\u7528\u4e8e\u8861\u91cf\u7b97\u6cd5\u4f7f\u7528\u5185\u5b58\u7a7a\u95f4\u968f\u7740\u6570\u636e\u91cf\u53d8\u5927\u65f6\u7684\u589e\u957f\u8d8b\u52bf\u3002\u8fd9\u4e2a\u6982\u5ff5\u4e0e\u65f6\u95f4\u590d\u6742\u5ea6\u975e\u5e38\u7c7b\u4f3c\u3002</p>"},{"location":"chapter_computational_complexity/space_complexity/#231","title":"2.3.1. \u00a0 \u7b97\u6cd5\u76f8\u5173\u7a7a\u95f4","text":"<p>\u7b97\u6cd5\u8fd0\u884c\u8fc7\u7a0b\u4e2d\u4f7f\u7528\u7684\u5185\u5b58\u7a7a\u95f4\u4e3b\u8981\u5305\u62ec\u4ee5\u4e0b\u51e0\u79cd\uff1a</p> <ul> <li>\u300c\u8f93\u5165\u7a7a\u95f4\u300d\u7528\u4e8e\u5b58\u50a8\u7b97\u6cd5\u7684\u8f93\u5165\u6570\u636e\uff1b</li> <li>\u300c\u6682\u5b58\u7a7a\u95f4\u300d\u7528\u4e8e\u5b58\u50a8\u7b97\u6cd5\u8fd0\u884c\u8fc7\u7a0b\u4e2d\u7684\u53d8\u91cf\u3001\u5bf9\u8c61\u3001\u51fd\u6570\u4e0a\u4e0b\u6587\u7b49\u6570\u636e\uff1b</li> <li>\u300c\u8f93\u51fa\u7a7a\u95f4\u300d\u7528\u4e8e\u5b58\u50a8\u7b97\u6cd5\u7684\u8f93\u51fa\u6570\u636e\uff1b</li> </ul> <p>\u901a\u5e38\u60c5\u51b5\u4e0b\uff0c\u7a7a\u95f4\u590d\u6742\u5ea6\u7edf\u8ba1\u8303\u56f4\u662f\u300c\u6682\u5b58\u7a7a\u95f4\u300d+\u300c\u8f93\u51fa\u7a7a\u95f4\u300d\u3002</p> <p>\u6682\u5b58\u7a7a\u95f4\u53ef\u4ee5\u8fdb\u4e00\u6b65\u5212\u5206\u4e3a\u4e09\u4e2a\u90e8\u5206\uff1a</p> <ul> <li>\u300c\u6682\u5b58\u6570\u636e\u300d\u7528\u4e8e\u4fdd\u5b58\u7b97\u6cd5\u8fd0\u884c\u8fc7\u7a0b\u4e2d\u7684\u5404\u79cd\u5e38\u91cf\u3001\u53d8\u91cf\u3001\u5bf9\u8c61\u7b49\u3002</li> <li>\u300c\u6808\u5e27\u7a7a\u95f4\u300d\u7528\u4e8e\u4fdd\u5b58\u8c03\u7528\u51fd\u6570\u7684\u4e0a\u4e0b\u6587\u6570\u636e\u3002\u7cfb\u7edf\u5728\u6bcf\u6b21\u8c03\u7528\u51fd\u6570\u65f6\u90fd\u4f1a\u5728\u6808\u9876\u90e8\u521b\u5efa\u4e00\u4e2a\u6808\u5e27\uff0c\u51fd\u6570\u8fd4\u56de\u540e\uff0c\u6808\u5e27\u7a7a\u95f4\u4f1a\u88ab\u91ca\u653e\u3002</li> <li>\u300c\u6307\u4ee4\u7a7a\u95f4\u300d\u7528\u4e8e\u4fdd\u5b58\u7f16\u8bd1\u540e\u7684\u7a0b\u5e8f\u6307\u4ee4\uff0c\u5728\u5b9e\u9645\u7edf\u8ba1\u4e2d\u901a\u5e38\u5ffd\u7565\u4e0d\u8ba1\u3002</li> </ul> <p>\u56e0\u6b64\uff0c\u5728\u5206\u6790\u4e00\u6bb5\u7a0b\u5e8f\u7684\u7a7a\u95f4\u590d\u6742\u5ea6\u65f6\uff0c\u6211\u4eec\u4e00\u822c\u7edf\u8ba1 \u6682\u5b58\u6570\u636e\u3001\u8f93\u51fa\u6570\u636e\u3001\u6808\u5e27\u7a7a\u95f4 \u4e09\u90e8\u5206\u3002</p> <p></p> <p> Fig. \u7b97\u6cd5\u4f7f\u7528\u7684\u76f8\u5173\u7a7a\u95f4 </p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart <pre><code>/* \u7c7b */\nclass Node {\nint val;\nNode next;\nNode(int x) { val = x; }\n}\n/* \u51fd\u6570 */\nint function() {\n// do something...\nreturn 0;\n}\nint algorithm(int n) {        // \u8f93\u5165\u6570\u636e\nfinal int a = 0;          // \u6682\u5b58\u6570\u636e\uff08\u5e38\u91cf\uff09\nint b = 0;                // \u6682\u5b58\u6570\u636e\uff08\u53d8\u91cf\uff09\nNode node = new Node(0);  // \u6682\u5b58\u6570\u636e\uff08\u5bf9\u8c61\uff09\nint c = function();       // \u6808\u5e27\u7a7a\u95f4\uff08\u8c03\u7528\u51fd\u6570\uff09\nreturn a + b + c;         // \u8f93\u51fa\u6570\u636e\n}\n</code></pre> <pre><code>/* \u7ed3\u6784\u4f53 */\nstruct Node {\nint val;\nNode *next;\nNode(int x) : val(x), next(nullptr) {}\n};\n/* \u51fd\u6570 */\nint func() {\n// do something...\nreturn 0;\n}\nint algorithm(int n) {        // \u8f93\u5165\u6570\u636e\nconst int a = 0;          // \u6682\u5b58\u6570\u636e\uff08\u5e38\u91cf\uff09\nint b = 0;                // \u6682\u5b58\u6570\u636e\uff08\u53d8\u91cf\uff09\nNode* node = new Node(0); // \u6682\u5b58\u6570\u636e\uff08\u5bf9\u8c61\uff09\nint c = func();           // \u6808\u5e27\u7a7a\u95f4\uff08\u8c03\u7528\u51fd\u6570\uff09\nreturn a + b + c;         // \u8f93\u51fa\u6570\u636e\n}\n</code></pre> <pre><code>class Node:\n\"\"\"\u7c7b\"\"\"\ndef __init__(self, x: int):\nself.val: int = x                 # \u8282\u70b9\u503c\nself.next: Optional[Node] = None  # \u6307\u5411\u4e0b\u4e00\u8282\u70b9\u7684\u6307\u9488\uff08\u5f15\u7528\uff09\ndef function() -&gt; int:\n\"\"\"\u51fd\u6570\"\"\"\n# do something...\nreturn 0\ndef algorithm(n) -&gt; int:  # \u8f93\u5165\u6570\u636e\nA = 0                 # \u6682\u5b58\u6570\u636e\uff08\u5e38\u91cf\uff0c\u4e00\u822c\u7528\u5927\u5199\u5b57\u6bcd\u8868\u793a\uff09\nb = 0                 # \u6682\u5b58\u6570\u636e\uff08\u53d8\u91cf\uff09\nnode = Node(0)        # \u6682\u5b58\u6570\u636e\uff08\u5bf9\u8c61\uff09\nc = function()        # \u6808\u5e27\u7a7a\u95f4\uff08\u8c03\u7528\u51fd\u6570\uff09\nreturn A + b + c      # \u8f93\u51fa\u6570\u636e\n</code></pre> <pre><code>/* \u7ed3\u6784\u4f53 */\ntype node struct {\nval  int\nnext *node\n}\n/* \u521b\u5efa node \u7ed3\u6784\u4f53  */\nfunc newNode(val int) *node {\nreturn &amp;node{val: val}\n}\n/* \u51fd\u6570 */\nfunc function() int {\n// do something...\nreturn 0\n}\nfunc algorithm(n int) int { // \u8f93\u5165\u6570\u636e\nconst a = 0             // \u6682\u5b58\u6570\u636e\uff08\u5e38\u91cf\uff09\nb := 0                  // \u6682\u5b58\u6570\u636e\uff08\u53d8\u91cf\uff09\nnewNode(0)              // \u6682\u5b58\u6570\u636e\uff08\u5bf9\u8c61\uff09\nc := function()         // \u6808\u5e27\u7a7a\u95f4\uff08\u8c03\u7528\u51fd\u6570\uff09\nreturn a + b + c        // \u8f93\u51fa\u6570\u636e\n}\n</code></pre> <pre><code>/* \u7c7b */\nclass Node {\nval;\nnext;\nconstructor(val) {\nthis.val = val === undefined ? 0 : val; // \u8282\u70b9\u503c\nthis.next = null;                       // \u6307\u5411\u4e0b\u4e00\u8282\u70b9\u7684\u5f15\u7528\n}\n}\n/* \u51fd\u6570 */\nfunction constFunc() {\n// do something\nreturn 0;\n}\nfunction algorithm(n) {       // \u8f93\u5165\u6570\u636e\nconst a = 0;              // \u6682\u5b58\u6570\u636e\uff08\u5e38\u91cf\uff09\nlet b = 0;                // \u6682\u5b58\u6570\u636e\uff08\u53d8\u91cf\uff09\nconst node = new Node(0); // \u6682\u5b58\u6570\u636e\uff08\u5bf9\u8c61\uff09\nconst c = constFunc();    // \u6808\u5e27\u7a7a\u95f4\uff08\u8c03\u7528\u51fd\u6570\uff09\nreturn a + b + c;         // \u8f93\u51fa\u6570\u636e\n}\n</code></pre> <pre><code>/* \u7c7b */\nclass Node {\nval: number;\nnext: Node | null;\nconstructor(val?: number) {\nthis.val = val === undefined ? 0 : val; // \u8282\u70b9\u503c\nthis.next = null;                       // \u6307\u5411\u4e0b\u4e00\u8282\u70b9\u7684\u5f15\u7528\n}\n}\n/* \u51fd\u6570 */\nfunction constFunc(): number {\n// do something\nreturn 0;\n}\nfunction algorithm(n: number): number { // \u8f93\u5165\u6570\u636e\nconst a = 0;                        // \u6682\u5b58\u6570\u636e\uff08\u5e38\u91cf\uff09\nlet b = 0;                          // \u6682\u5b58\u6570\u636e\uff08\u53d8\u91cf\uff09\nconst node = new Node(0);           // \u6682\u5b58\u6570\u636e\uff08\u5bf9\u8c61\uff09\nconst c = constFunc();              // \u6808\u5e27\u7a7a\u95f4\uff08\u8c03\u7528\u51fd\u6570\uff09\nreturn a + b + c;                   // \u8f93\u51fa\u6570\u636e\n}\n</code></pre> <pre><code>/* \u51fd\u6570 */\nint func() {\n// do something...\nreturn 0;\n}\nint algorithm(int n) { // \u8f93\u5165\u6570\u636e\nconst int a = 0;   // \u6682\u5b58\u6570\u636e\uff08\u5e38\u91cf\uff09\nint b = 0;         // \u6682\u5b58\u6570\u636e\uff08\u53d8\u91cf\uff09\nint c = func();    // \u6808\u5e27\u7a7a\u95f4\uff08\u8c03\u7528\u51fd\u6570\uff09\nreturn a + b + c;  // \u8f93\u51fa\u6570\u636e\n}\n</code></pre> <pre><code>/* \u7c7b */\nclass Node\n{\nint val;\nNode next;\nNode(int x) { val = x; }\n}\n/* \u51fd\u6570 */\nint function()\n{\n// do something...\nreturn 0;\n}\nint algorithm(int n)          // \u8f93\u5165\u6570\u636e\n{\nconst int a = 0;          // \u6682\u5b58\u6570\u636e\uff08\u5e38\u91cf\uff09\nint b = 0;                // \u6682\u5b58\u6570\u636e\uff08\u53d8\u91cf\uff09\nNode node = new Node(0);  // \u6682\u5b58\u6570\u636e\uff08\u5bf9\u8c61\uff09\nint c = function();       // \u6808\u5e27\u7a7a\u95f4\uff08\u8c03\u7528\u51fd\u6570\uff09\nreturn a + b + c;         // \u8f93\u51fa\u6570\u636e\n}\n</code></pre> <pre><code>/* \u7c7b */\nclass Node {\nvar val: Int\nvar next: Node?\ninit(x: Int) {\nval = x\n}\n}\n/* \u51fd\u6570 */\nfunc function() -&gt; Int {\n// do something...\nreturn 0\n}\nfunc algorithm(n: Int) -&gt; Int { // \u8f93\u5165\u6570\u636e\nlet a = 0             // \u6682\u5b58\u6570\u636e\uff08\u5e38\u91cf\uff09\nvar b = 0             // \u6682\u5b58\u6570\u636e\uff08\u53d8\u91cf\uff09\nlet node = Node(x: 0) // \u6682\u5b58\u6570\u636e\uff08\u5bf9\u8c61\uff09\nlet c = function()    // \u6808\u5e27\u7a7a\u95f4\uff08\u8c03\u7528\u51fd\u6570\uff09\nreturn a + b + c      // \u8f93\u51fa\u6570\u636e\n}\n</code></pre> <pre><code>\n</code></pre> <pre><code>/* \u7c7b */\nclass Node {\nint val;\nNode next;\nNode(this.val, [this.next]);\n}\n/* \u51fd\u6570 */\nint function() {\n// do something...\nreturn 0;\n}\nint algorithm(int n) {  // \u8f93\u5165\u6570\u636e\nconst int a = 0;      // \u6682\u5b58\u6570\u636e\uff08\u5e38\u91cf\uff09\nint b = 0;            // \u6682\u5b58\u6570\u636e\uff08\u53d8\u91cf\uff09\nNode node = Node(0);  // \u6682\u5b58\u6570\u636e\uff08\u5bf9\u8c61\uff09\nint c = function();   // \u6808\u5e27\u7a7a\u95f4\uff08\u8c03\u7528\u51fd\u6570\uff09\nreturn a + b + c;     // \u8f93\u51fa\u6570\u636e\n}\n</code></pre>"},{"location":"chapter_computational_complexity/space_complexity/#232","title":"2.3.2. \u00a0 \u63a8\u7b97\u65b9\u6cd5","text":"<p>\u7a7a\u95f4\u590d\u6742\u5ea6\u7684\u63a8\u7b97\u65b9\u6cd5\u4e0e\u65f6\u95f4\u590d\u6742\u5ea6\u5927\u81f4\u76f8\u540c\uff0c\u53ea\u662f\u5c06\u7edf\u8ba1\u5bf9\u8c61\u4ece\u201c\u8ba1\u7b97\u64cd\u4f5c\u6570\u91cf\u201d\u8f6c\u4e3a\u201c\u4f7f\u7528\u7a7a\u95f4\u5927\u5c0f\u201d\u3002\u4e0e\u65f6\u95f4\u590d\u6742\u5ea6\u4e0d\u540c\u7684\u662f\uff0c\u6211\u4eec\u901a\u5e38\u53ea\u5173\u6ce8\u300c\u6700\u5dee\u7a7a\u95f4\u590d\u6742\u5ea6\u300d\uff0c\u8fd9\u662f\u56e0\u4e3a\u5185\u5b58\u7a7a\u95f4\u662f\u4e00\u9879\u786c\u6027\u8981\u6c42\uff0c\u6211\u4eec\u5fc5\u987b\u786e\u4fdd\u5728\u6240\u6709\u8f93\u5165\u6570\u636e\u4e0b\u90fd\u6709\u8db3\u591f\u7684\u5185\u5b58\u7a7a\u95f4\u9884\u7559\u3002</p> <p>\u6700\u5dee\u7a7a\u95f4\u590d\u6742\u5ea6\u4e2d\u7684\u201c\u6700\u5dee\u201d\u6709\u4e24\u5c42\u542b\u4e49\uff0c\u5206\u522b\u662f\u8f93\u5165\u6570\u636e\u7684\u6700\u5dee\u5206\u5e03\u548c\u7b97\u6cd5\u8fd0\u884c\u8fc7\u7a0b\u4e2d\u7684\u6700\u5dee\u65f6\u95f4\u70b9\u3002</p> <ul> <li>\u4ee5\u6700\u5dee\u8f93\u5165\u6570\u636e\u4e3a\u51c6\u3002\u5f53 \\(n &lt; 10\\) \u65f6\uff0c\u7a7a\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(1)\\) \uff1b\u4f46\u5f53 \\(n &gt; 10\\) \u65f6\uff0c\u521d\u59cb\u5316\u7684\u6570\u7ec4 <code>nums</code> \u5360\u7528 \\(O(n)\\) \u7a7a\u95f4\uff1b\u56e0\u6b64\u6700\u5dee\u7a7a\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(n)\\) \uff1b</li> <li>\u4ee5\u7b97\u6cd5\u8fd0\u884c\u8fc7\u7a0b\u4e2d\u7684\u5cf0\u503c\u5185\u5b58\u4e3a\u51c6\u3002\u4f8b\u5982\uff0c\u7a0b\u5e8f\u5728\u6267\u884c\u6700\u540e\u4e00\u884c\u4e4b\u524d\uff0c\u5360\u7528 \\(O(1)\\) \u7a7a\u95f4\uff1b\u5f53\u521d\u59cb\u5316\u6570\u7ec4 <code>nums</code> \u65f6\uff0c\u7a0b\u5e8f\u5360\u7528 \\(O(n)\\) \u7a7a\u95f4\uff1b\u56e0\u6b64\u6700\u5dee\u7a7a\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(n)\\) \uff1b</li> </ul> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart <pre><code>void algorithm(int n) {\nint a = 0;                   // O(1)\nint[] b = new int[10000];    // O(1)\nif (n &gt; 10)\nint[] nums = new int[n]; // O(n)\n}\n</code></pre> <pre><code>void algorithm(int n) {\nint a = 0;               // O(1)\nvector&lt;int&gt; b(10000);    // O(1)\nif (n &gt; 10)\nvector&lt;int&gt; nums(n); // O(n)\n}\n</code></pre> <pre><code>def algorithm(n: int) -&gt; None:\na = 0                     # O(1)\nb = [0] * 10000     # O(1)\nif n &gt; 10:\nnums = [0] * n  # O(n)\n</code></pre> <pre><code>func algorithm(n int) {\na := 0                      // O(1)\nb := make([]int, 10000)     // O(1)\nvar nums []int\nif n &gt; 10 {\nnums := make([]int, n)  // O(n)\n}\nfmt.Println(a, b, nums)\n}\n</code></pre> <pre><code>function algorithm(n) {\nconst a = 0;                   // O(1)\nconst b = new Array(10000);    // O(1)\nif (n &gt; 10) {\nconst nums = new Array(n); // O(n)\n}\n}\n</code></pre> <pre><code>function algorithm(n: number): void {\nconst a = 0;                   // O(1)\nconst b = new Array(10000);    // O(1)\nif (n &gt; 10) {\nconst nums = new Array(n); // O(n)\n}\n}\n</code></pre> <pre><code>void algorithm(int n) {\nint a = 0;               // O(1)\nint b[10000];            // O(1)\nif (n &gt; 10)\nvector&lt;int&gt; nums(n); // O(n)\n}\n</code></pre> <pre><code>void algorithm(int n)\n{\nint a = 0;                   // O(1)\nint[] b = new int[10000];    // O(1)\nif (n &gt; 10)\n{\nint[] nums = new int[n]; // O(n)\n}\n}\n</code></pre> <pre><code>func algorithm(n: Int) {\nlet a = 0 // O(1)\nlet b = Array(repeating: 0, count: 10000) // O(1)\nif n &gt; 10 {\nlet nums = Array(repeating: 0, count: n) // O(n)\n}\n}\n</code></pre> <pre><code>\n</code></pre> <pre><code>void algorithm(int n) {\nint a = 0;                            // O(1)\nList&lt;int&gt; b = List.filled(10000, 0);  // O(1)\nif (n &gt; 10) {\nList&lt;int&gt; nums = List.filled(n, 0); // O(n)\n}\n}\n</code></pre> <p>\u5728\u9012\u5f52\u51fd\u6570\u4e2d\uff0c\u9700\u8981\u6ce8\u610f\u7edf\u8ba1\u6808\u5e27\u7a7a\u95f4\u3002\u4f8b\u5982\uff0c\u51fd\u6570 <code>loop()</code> \u5728\u5faa\u73af\u4e2d\u8c03\u7528\u4e86 \\(n\\) \u6b21 <code>function()</code> \uff0c\u6bcf\u8f6e\u4e2d\u7684 <code>function()</code> \u90fd\u8fd4\u56de\u5e76\u91ca\u653e\u4e86\u6808\u5e27\u7a7a\u95f4\uff0c\u56e0\u6b64\u7a7a\u95f4\u590d\u6742\u5ea6\u4ecd\u4e3a \\(O(1)\\) \u3002\u800c\u9012\u5f52\u51fd\u6570 <code>recur()</code> \u5728\u8fd0\u884c\u8fc7\u7a0b\u4e2d\u4f1a\u540c\u65f6\u5b58\u5728 \\(n\\) \u4e2a\u672a\u8fd4\u56de\u7684 <code>recur()</code> \uff0c\u4ece\u800c\u5360\u7528 \\(O(n)\\) \u7684\u6808\u5e27\u7a7a\u95f4\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart <pre><code>int function() {\n// do something\nreturn 0;\n}\n/* \u5faa\u73af O(1) */\nvoid loop(int n) {\nfor (int i = 0; i &lt; n; i++) {\nfunction();\n}\n}\n/* \u9012\u5f52 O(n) */\nvoid recur(int n) {\nif (n == 1) return;\nreturn recur(n - 1);\n}\n</code></pre> <pre><code>int func() {\n// do something\nreturn 0;\n}\n/* \u5faa\u73af O(1) */\nvoid loop(int n) {\nfor (int i = 0; i &lt; n; i++) {\nfunc();\n}\n}\n/* \u9012\u5f52 O(n) */\nvoid recur(int n) {\nif (n == 1) return;\nreturn recur(n - 1);\n}\n</code></pre> <pre><code>def function() -&gt; int:\n# do something\nreturn 0\ndef loop(n: int) -&gt; None:\n\"\"\"\u5faa\u73af O(1)\"\"\"\nfor _ in range(n):\nfunction()\ndef recur(n: int) -&gt; int:\n\"\"\"\u9012\u5f52 O(n)\"\"\"\nif n == 1: return\nreturn recur(n - 1)\n</code></pre> <pre><code>func function() int {\n// do something\nreturn 0\n}\n/* \u5faa\u73af O(1) */\nfunc loop(n int) {\nfor i := 0; i &lt; n; i++ {\nfunction()\n}\n}\n/* \u9012\u5f52 O(n) */\nfunc recur(n int) {\nif n == 1 {\nreturn\n}\nrecur(n - 1)\n}\n</code></pre> <pre><code>function constFunc() {\n// do something\nreturn 0;\n}\n/* \u5faa\u73af O(1) */\nfunction loop(n) {\nfor (let i = 0; i &lt; n; i++) {\nconstFunc();\n}\n}\n/* \u9012\u5f52 O(n) */\nfunction recur(n) {\nif (n === 1) return;\nreturn recur(n - 1);\n}\n</code></pre> <pre><code>function constFunc(): number {\n// do something\nreturn 0;\n}\n/* \u5faa\u73af O(1) */\nfunction loop(n: number): void {\nfor (let i = 0; i &lt; n; i++) {\nconstFunc();\n}\n}\n/* \u9012\u5f52 O(n) */\nfunction recur(n: number): void {\nif (n === 1) return;\nreturn recur(n - 1);\n}\n</code></pre> <pre><code>int func() {\n// do something\nreturn 0;\n}\n/* \u5faa\u73af O(1) */\nvoid loop(int n) {\nfor (int i = 0; i &lt; n; i++) {\nfunc();\n}\n}\n/* \u9012\u5f52 O(n) */\nvoid recur(int n) {\nif (n == 1) return;\nreturn recur(n - 1);\n}\n</code></pre> <pre><code>int function()\n{\n// do something\nreturn 0;\n}\n/* \u5faa\u73af O(1) */\nvoid loop(int n)\n{\nfor (int i = 0; i &lt; n; i++)\n{\nfunction();\n}\n}\n/* \u9012\u5f52 O(n) */\nint recur(int n)\n{\nif (n == 1) return 1;\nreturn recur(n - 1);\n}\n</code></pre> <pre><code>@discardableResult\nfunc function() -&gt; Int {\n// do something\nreturn 0\n}\n/* \u5faa\u73af O(1) */\nfunc loop(n: Int) {\nfor _ in 0 ..&lt; n {\nfunction()\n}\n}\n/* \u9012\u5f52 O(n) */\nfunc recur(n: Int) {\nif n == 1 {\nreturn\n}\nrecur(n: n - 1)\n}\n</code></pre> <pre><code>\n</code></pre> <pre><code>int function() {\n// do something\nreturn 0;\n}\n/* \u5faa\u73af O(1) */\nvoid loop(int n) {\nfor (int i = 0; i &lt; n; i++) {\nfunction();\n}\n}\n/* \u9012\u5f52 O(n) */\nvoid recur(int n) {\nif (n == 1) return;\nreturn recur(n - 1);\n}\n</code></pre>"},{"location":"chapter_computational_complexity/space_complexity/#233","title":"2.3.3. \u00a0 \u5e38\u89c1\u7c7b\u578b","text":"<p>\u8bbe\u8f93\u5165\u6570\u636e\u5927\u5c0f\u4e3a \\(n\\) \uff0c\u5e38\u89c1\u7684\u7a7a\u95f4\u590d\u6742\u5ea6\u7c7b\u578b\u6709\uff08\u4ece\u4f4e\u5230\u9ad8\u6392\u5217\uff09</p> \\[ \\begin{aligned} O(1) &lt; O(\\log n) &lt; O(n) &lt; O(n^2) &lt; O(2^n) \\newline \\text{\u5e38\u6570\u9636} &lt; \\text{\u5bf9\u6570\u9636} &lt; \\text{\u7ebf\u6027\u9636} &lt; \\text{\u5e73\u65b9\u9636} &lt; \\text{\u6307\u6570\u9636} \\end{aligned} \\] <p></p> <p> Fig. \u7a7a\u95f4\u590d\u6742\u5ea6\u7684\u5e38\u89c1\u7c7b\u578b </p> <p>Tip</p> <p>\u90e8\u5206\u793a\u4f8b\u4ee3\u7801\u9700\u8981\u4e00\u4e9b\u524d\u7f6e\u77e5\u8bc6\uff0c\u5305\u62ec\u6570\u7ec4\u3001\u94fe\u8868\u3001\u4e8c\u53c9\u6811\u3001\u9012\u5f52\u7b97\u6cd5\u7b49\u3002\u5982\u679c\u9047\u5230\u770b\u4e0d\u61c2\u7684\u5730\u65b9\u65e0\u9700\u62c5\u5fc3\uff0c\u53ef\u4ee5\u5728\u5b66\u4e60\u5b8c\u540e\u9762\u7ae0\u8282\u540e\u518d\u6765\u590d\u4e60\uff0c\u73b0\u9636\u6bb5\u6211\u4eec\u5148\u4e13\u6ce8\u4e8e\u7406\u89e3\u7a7a\u95f4\u590d\u6742\u5ea6\u7684\u542b\u4e49\u548c\u63a8\u7b97\u65b9\u6cd5\u3002</p>"},{"location":"chapter_computational_complexity/space_complexity/#o1","title":"\u5e38\u6570\u9636 \\(O(1)\\)","text":"<p>\u5e38\u6570\u9636\u5e38\u89c1\u4e8e\u6570\u91cf\u4e0e\u8f93\u5165\u6570\u636e\u5927\u5c0f \\(n\\) \u65e0\u5173\u7684\u5e38\u91cf\u3001\u53d8\u91cf\u3001\u5bf9\u8c61\u3002</p> <p>\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u5728\u5faa\u73af\u4e2d\u521d\u59cb\u5316\u53d8\u91cf\u6216\u8c03\u7528\u51fd\u6570\u800c\u5360\u7528\u7684\u5185\u5b58\uff0c\u5728\u8fdb\u5165\u4e0b\u4e00\u5faa\u73af\u540e\u5c31\u4f1a\u88ab\u91ca\u653e\uff0c\u5373\u4e0d\u4f1a\u7d2f\u79ef\u5360\u7528\u7a7a\u95f4\uff0c\u7a7a\u95f4\u590d\u6742\u5ea6\u4ecd\u4e3a \\(O(1)\\) \u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart space_complexity.java<pre><code>/* \u5e38\u6570\u9636 */\nvoid constant(int n) {\n// \u5e38\u91cf\u3001\u53d8\u91cf\u3001\u5bf9\u8c61\u5360\u7528 O(1) \u7a7a\u95f4\nfinal int a = 0;\nint b = 0;\nint[] nums = new int[10000];\nListNode node = new ListNode(0);\n// \u5faa\u73af\u4e2d\u7684\u53d8\u91cf\u5360\u7528 O(1) \u7a7a\u95f4\nfor (int i = 0; i &lt; n; i++) {\nint c = 0;\n}\n// \u5faa\u73af\u4e2d\u7684\u51fd\u6570\u5360\u7528 O(1) \u7a7a\u95f4\nfor (int i = 0; i &lt; n; i++) {\nfunction();\n}\n}\n</code></pre> space_complexity.cpp<pre><code>/* \u5e38\u6570\u9636 */\nvoid constant(int n) {\n// \u5e38\u91cf\u3001\u53d8\u91cf\u3001\u5bf9\u8c61\u5360\u7528 O(1) \u7a7a\u95f4\nconst int a = 0;\nint b = 0;\nvector&lt;int&gt; nums(10000);\nListNode node(0);\n// \u5faa\u73af\u4e2d\u7684\u53d8\u91cf\u5360\u7528 O(1) \u7a7a\u95f4\nfor (int i = 0; i &lt; n; i++) {\nint c = 0;\n}\n// \u5faa\u73af\u4e2d\u7684\u51fd\u6570\u5360\u7528 O(1) \u7a7a\u95f4\nfor (int i = 0; i &lt; n; i++) {\nfunc();\n}\n}\n</code></pre> space_complexity.py<pre><code>def constant(n: int) -&gt; None:\n\"\"\"\u5e38\u6570\u9636\"\"\"\n# \u5e38\u91cf\u3001\u53d8\u91cf\u3001\u5bf9\u8c61\u5360\u7528 O(1) \u7a7a\u95f4\na = 0\nnums = [0] * 10000\nnode = ListNode(0)\n# \u5faa\u73af\u4e2d\u7684\u53d8\u91cf\u5360\u7528 O(1) \u7a7a\u95f4\nfor _ in range(n):\nc = 0\n# \u5faa\u73af\u4e2d\u7684\u51fd\u6570\u5360\u7528 O(1) \u7a7a\u95f4\nfor _ in range(n):\nfunction()\n</code></pre> space_complexity.go<pre><code>/* \u5e38\u6570\u9636 */\nfunc spaceConstant(n int) {\n// \u5e38\u91cf\u3001\u53d8\u91cf\u3001\u5bf9\u8c61\u5360\u7528 O(1) \u7a7a\u95f4\nconst a = 0\nb := 0\nnums := make([]int, 10000)\nListNode := newNode(0)\n// \u5faa\u73af\u4e2d\u7684\u53d8\u91cf\u5360\u7528 O(1) \u7a7a\u95f4\nvar c int\nfor i := 0; i &lt; n; i++ {\nc = 0\n}\n// \u5faa\u73af\u4e2d\u7684\u51fd\u6570\u5360\u7528 O(1) \u7a7a\u95f4\nfor i := 0; i &lt; n; i++ {\nfunction()\n}\nfmt.Println(a, b, nums, c, ListNode)\n}\n</code></pre> space_complexity.js<pre><code>/* \u5e38\u6570\u9636 */\nfunction constant(n) {\n// \u5e38\u91cf\u3001\u53d8\u91cf\u3001\u5bf9\u8c61\u5360\u7528 O(1) \u7a7a\u95f4\nconst a = 0;\nconst b = 0;\nconst nums = new Array(10000);\nconst node = new ListNode(0);\n// \u5faa\u73af\u4e2d\u7684\u53d8\u91cf\u5360\u7528 O(1) \u7a7a\u95f4\nfor (let i = 0; i &lt; n; i++) {\nconst c = 0;\n}\n// \u5faa\u73af\u4e2d\u7684\u51fd\u6570\u5360\u7528 O(1) \u7a7a\u95f4\nfor (let i = 0; i &lt; n; i++) {\nconstFunc();\n}\n}\n</code></pre> space_complexity.ts<pre><code>/* \u5e38\u6570\u9636 */\nfunction constant(n: number): void {\n// \u5e38\u91cf\u3001\u53d8\u91cf\u3001\u5bf9\u8c61\u5360\u7528 O(1) \u7a7a\u95f4\nconst a = 0;\nconst b = 0;\nconst nums = new Array(10000);\nconst node = new ListNode(0);\n// \u5faa\u73af\u4e2d\u7684\u53d8\u91cf\u5360\u7528 O(1) \u7a7a\u95f4\nfor (let i = 0; i &lt; n; i++) {\nconst c = 0;\n}\n// \u5faa\u73af\u4e2d\u7684\u51fd\u6570\u5360\u7528 O(1) \u7a7a\u95f4\nfor (let i = 0; i &lt; n; i++) {\nconstFunc();\n}\n}\n</code></pre> space_complexity.c<pre><code>/* \u5e38\u6570\u9636 */\nvoid constant(int n) {\n// \u5e38\u91cf\u3001\u53d8\u91cf\u3001\u5bf9\u8c61\u5360\u7528 O(1) \u7a7a\u95f4\nconst int a = 0;\nint b = 0;\nint nums[1000];\nListNode *node = newListNode(0);\nfree(node);\n// \u5faa\u73af\u4e2d\u7684\u53d8\u91cf\u5360\u7528 O(1) \u7a7a\u95f4\nfor (int i = 0; i &lt; n; i++) {\nint c = 0;\n}\n// \u5faa\u73af\u4e2d\u7684\u51fd\u6570\u5360\u7528 O(1) \u7a7a\u95f4\nfor (int i = 0; i &lt; n; i++) {\nfunc();\n}\n}\n</code></pre> space_complexity.cs<pre><code>/* \u5e38\u6570\u9636 */\nvoid constant(int n) {\n// \u5e38\u91cf\u3001\u53d8\u91cf\u3001\u5bf9\u8c61\u5360\u7528 O(1) \u7a7a\u95f4\nint a = 0;\nint b = 0;\nint[] nums = new int[10000];\nListNode node = new ListNode(0);\n// \u5faa\u73af\u4e2d\u7684\u53d8\u91cf\u5360\u7528 O(1) \u7a7a\u95f4\nfor (int i = 0; i &lt; n; i++) {\nint c = 0;\n}\n// \u5faa\u73af\u4e2d\u7684\u51fd\u6570\u5360\u7528 O(1) \u7a7a\u95f4\nfor (int i = 0; i &lt; n; i++) {\nfunction();\n}\n}\n</code></pre> space_complexity.swift<pre><code>/* \u5e38\u6570\u9636 */\nfunc constant(n: Int) {\n// \u5e38\u91cf\u3001\u53d8\u91cf\u3001\u5bf9\u8c61\u5360\u7528 O(1) \u7a7a\u95f4\nlet a = 0\nvar b = 0\nlet nums = Array(repeating: 0, count: 10000)\nlet node = ListNode(x: 0)\n// \u5faa\u73af\u4e2d\u7684\u53d8\u91cf\u5360\u7528 O(1) \u7a7a\u95f4\nfor _ in 0 ..&lt; n {\nlet c = 0\n}\n// \u5faa\u73af\u4e2d\u7684\u51fd\u6570\u5360\u7528 O(1) \u7a7a\u95f4\nfor _ in 0 ..&lt; n {\nfunction()\n}\n}\n</code></pre> space_complexity.zig<pre><code>// \u5e38\u6570\u9636\nfn constant(n: i32) void {\n// \u5e38\u91cf\u3001\u53d8\u91cf\u3001\u5bf9\u8c61\u5360\u7528 O(1) \u7a7a\u95f4\nconst a: i32 = 0;\nvar b: i32 = 0;\nvar nums = [_]i32{0}**10000;\nvar node = inc.ListNode(i32){.val = 0};\nvar i: i32 = 0;\n// \u5faa\u73af\u4e2d\u7684\u53d8\u91cf\u5360\u7528 O(1) \u7a7a\u95f4\nwhile (i &lt; n) : (i += 1) {\nvar c: i32 = 0;\n_ = c;\n}\n// \u5faa\u73af\u4e2d\u7684\u51fd\u6570\u5360\u7528 O(1) \u7a7a\u95f4\ni = 0;\nwhile (i &lt; n) : (i += 1) {\n_ = function();\n}\n_ = a;\n_ = b;\n_ = nums;\n_ = node;\n}\n</code></pre> space_complexity.dart<pre><code>/* \u5e38\u6570\u9636 */\nvoid constant(int n) {\n// \u5e38\u91cf\u3001\u53d8\u91cf\u3001\u5bf9\u8c61\u5360\u7528 O(1) \u7a7a\u95f4\nfinal int a = 0;\nint b = 0;\nList&lt;int&gt; nums = List.filled(10000, 0);\n// \u5faa\u73af\u4e2d\u7684\u53d8\u91cf\u5360\u7528 O(1) \u7a7a\u95f4\nfor (var i = 0; i &lt; n; i++) {\nint c = 0;\n}\n// \u5faa\u73af\u4e2d\u7684\u51fd\u6570\u5360\u7528 O(1) \u7a7a\u95f4\nfor (var i = 0; i &lt; n; i++) {\nfunction();\n}\n}\n</code></pre>"},{"location":"chapter_computational_complexity/space_complexity/#on","title":"\u7ebf\u6027\u9636 \\(O(n)\\)","text":"<p>\u7ebf\u6027\u9636\u5e38\u89c1\u4e8e\u5143\u7d20\u6570\u91cf\u4e0e \\(n\\) \u6210\u6b63\u6bd4\u7684\u6570\u7ec4\u3001\u94fe\u8868\u3001\u6808\u3001\u961f\u5217\u7b49\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart space_complexity.java<pre><code>/* \u7ebf\u6027\u9636 */\nvoid linear(int n) {\n// \u957f\u5ea6\u4e3a n \u7684\u6570\u7ec4\u5360\u7528 O(n) \u7a7a\u95f4\nint[] nums = new int[n];\n// \u957f\u5ea6\u4e3a n \u7684\u5217\u8868\u5360\u7528 O(n) \u7a7a\u95f4\nList&lt;ListNode&gt; nodes = new ArrayList&lt;&gt;();\nfor (int i = 0; i &lt; n; i++) {\nnodes.add(new ListNode(i));\n}\n// \u957f\u5ea6\u4e3a n \u7684\u54c8\u5e0c\u8868\u5360\u7528 O(n) \u7a7a\u95f4\nMap&lt;Integer, String&gt; map = new HashMap&lt;&gt;();\nfor (int i = 0; i &lt; n; i++) {\nmap.put(i, String.valueOf(i));\n}\n}\n</code></pre> space_complexity.cpp<pre><code>/* \u7ebf\u6027\u9636 */\nvoid linear(int n) {\n// \u957f\u5ea6\u4e3a n \u7684\u6570\u7ec4\u5360\u7528 O(n) \u7a7a\u95f4\nvector&lt;int&gt; nums(n);\n// \u957f\u5ea6\u4e3a n \u7684\u5217\u8868\u5360\u7528 O(n) \u7a7a\u95f4\nvector&lt;ListNode&gt; nodes;\nfor (int i = 0; i &lt; n; i++) {\nnodes.push_back(ListNode(i));\n}\n// \u957f\u5ea6\u4e3a n \u7684\u54c8\u5e0c\u8868\u5360\u7528 O(n) \u7a7a\u95f4\nunordered_map&lt;int, string&gt; map;\nfor (int i = 0; i &lt; n; i++) {\nmap[i] = to_string(i);\n}\n}\n</code></pre> space_complexity.py<pre><code>def linear(n: int) -&gt; None:\n\"\"\"\u7ebf\u6027\u9636\"\"\"\n# \u957f\u5ea6\u4e3a n \u7684\u5217\u8868\u5360\u7528 O(n) \u7a7a\u95f4\nnums = [0] * n\n# \u957f\u5ea6\u4e3a n \u7684\u54c8\u5e0c\u8868\u5360\u7528 O(n) \u7a7a\u95f4\nmapp = dict[int, str]()\nfor i in range(n):\nmapp[i] = str(i)\n</code></pre> space_complexity.go<pre><code>/* \u7ebf\u6027\u9636 */\nfunc spaceLinear(n int) {\n// \u957f\u5ea6\u4e3a n \u7684\u6570\u7ec4\u5360\u7528 O(n) \u7a7a\u95f4\n_ = make([]int, n)\n// \u957f\u5ea6\u4e3a n \u7684\u5217\u8868\u5360\u7528 O(n) \u7a7a\u95f4\nvar nodes []*node\nfor i := 0; i &lt; n; i++ {\nnodes = append(nodes, newNode(i))\n}\n// \u957f\u5ea6\u4e3a n \u7684\u54c8\u5e0c\u8868\u5360\u7528 O(n) \u7a7a\u95f4\nm := make(map[int]string, n)\nfor i := 0; i &lt; n; i++ {\nm[i] = strconv.Itoa(i)\n}\n}\n</code></pre> space_complexity.js<pre><code>/* \u7ebf\u6027\u9636 */\nfunction linear(n) {\n// \u957f\u5ea6\u4e3a n \u7684\u6570\u7ec4\u5360\u7528 O(n) \u7a7a\u95f4\nconst nums = new Array(n);\n// \u957f\u5ea6\u4e3a n \u7684\u5217\u8868\u5360\u7528 O(n) \u7a7a\u95f4\nconst nodes = [];\nfor (let i = 0; i &lt; n; i++) {\nnodes.push(new ListNode(i));\n}\n// \u957f\u5ea6\u4e3a n \u7684\u54c8\u5e0c\u8868\u5360\u7528 O(n) \u7a7a\u95f4\nconst map = new Map();\nfor (let i = 0; i &lt; n; i++) {\nmap.set(i, i.toString());\n}\n}\n</code></pre> space_complexity.ts<pre><code>/* \u7ebf\u6027\u9636 */\nfunction linear(n: number): void {\n// \u957f\u5ea6\u4e3a n \u7684\u6570\u7ec4\u5360\u7528 O(n) \u7a7a\u95f4\nconst nums = new Array(n);\n// \u957f\u5ea6\u4e3a n \u7684\u5217\u8868\u5360\u7528 O(n) \u7a7a\u95f4\nconst nodes: ListNode[] = [];\nfor (let i = 0; i &lt; n; i++) {\nnodes.push(new ListNode(i));\n}\n// \u957f\u5ea6\u4e3a n \u7684\u54c8\u5e0c\u8868\u5360\u7528 O(n) \u7a7a\u95f4\nconst map = new Map();\nfor (let i = 0; i &lt; n; i++) {\nmap.set(i, i.toString());\n}\n}\n</code></pre> space_complexity.c<pre><code>/* \u54c8\u5e0c\u8868 */\nstruct hashTable {\nint key;\nint val;\nUT_hash_handle hh; // \u57fa\u4e8e uthash.h \u5b9e\u73b0\n};\ntypedef struct hashTable hashTable;\n/* \u7ebf\u6027\u9636 */\nvoid linear(int n) {\n// \u957f\u5ea6\u4e3a n \u7684\u6570\u7ec4\u5360\u7528 O(n) \u7a7a\u95f4\nint *nums = malloc(sizeof(int) * n);\nfree(nums);\n// \u957f\u5ea6\u4e3a n \u7684\u5217\u8868\u5360\u7528 O(n) \u7a7a\u95f4\nListNode **nodes = malloc(sizeof(ListNode *) * n);\nfor (int i = 0; i &lt; n; i++) {\nnodes[i] = newListNode(i);\n}\n// \u5185\u5b58\u91ca\u653e\nfor (int i = 0; i &lt; n; i++) {\nfree(nodes[i]);\n}\nfree(nodes);\n// \u957f\u5ea6\u4e3a n \u7684\u54c8\u5e0c\u8868\u5360\u7528 O(n) \u7a7a\u95f4\nhashTable *h = NULL;\nfor (int i = 0; i &lt; n; i++) {\nhashTable *tmp = malloc(sizeof(hashTable));\ntmp-&gt;key = i;\ntmp-&gt;val = i;\nHASH_ADD_INT(h, key, tmp);\n}\n// \u5185\u5b58\u91ca\u653e\nhashTable *curr, *tmp;\nHASH_ITER(hh, h, curr, tmp) {\nHASH_DEL(h, curr);\nfree(curr);\n}\n}\n</code></pre> space_complexity.cs<pre><code>/* \u7ebf\u6027\u9636 */\nvoid linear(int n) {\n// \u957f\u5ea6\u4e3a n \u7684\u6570\u7ec4\u5360\u7528 O(n) \u7a7a\u95f4\nint[] nums = new int[n];\n// \u957f\u5ea6\u4e3a n \u7684\u5217\u8868\u5360\u7528 O(n) \u7a7a\u95f4\nList&lt;ListNode&gt; nodes = new();\nfor (int i = 0; i &lt; n; i++) {\nnodes.Add(new ListNode(i));\n}\n// \u957f\u5ea6\u4e3a n \u7684\u54c8\u5e0c\u8868\u5360\u7528 O(n) \u7a7a\u95f4\nDictionary&lt;int, string&gt; map = new();\nfor (int i = 0; i &lt; n; i++) {\nmap.Add(i, i.ToString());\n}\n}\n</code></pre> space_complexity.swift<pre><code>/* \u7ebf\u6027\u9636 */\nfunc linear(n: Int) {\n// \u957f\u5ea6\u4e3a n \u7684\u6570\u7ec4\u5360\u7528 O(n) \u7a7a\u95f4\nlet nums = Array(repeating: 0, count: n)\n// \u957f\u5ea6\u4e3a n \u7684\u5217\u8868\u5360\u7528 O(n) \u7a7a\u95f4\nlet nodes = (0 ..&lt; n).map { ListNode(x: $0) }\n// \u957f\u5ea6\u4e3a n \u7684\u54c8\u5e0c\u8868\u5360\u7528 O(n) \u7a7a\u95f4\nlet map = Dictionary(uniqueKeysWithValues: (0 ..&lt; n).map { ($0, \"\\($0)\") })\n}\n</code></pre> space_complexity.zig<pre><code>// \u7ebf\u6027\u9636\nfn linear(comptime n: i32) !void {\n// \u957f\u5ea6\u4e3a n \u7684\u6570\u7ec4\u5360\u7528 O(n) \u7a7a\u95f4\nvar nums = [_]i32{0}**n;\n// \u957f\u5ea6\u4e3a n \u7684\u5217\u8868\u5360\u7528 O(n) \u7a7a\u95f4\nvar nodes = std.ArrayList(i32).init(std.heap.page_allocator);\ndefer nodes.deinit();\nvar i: i32 = 0;\nwhile (i &lt; n) : (i += 1) {\ntry nodes.append(i);\n}\n// \u957f\u5ea6\u4e3a n \u7684\u54c8\u5e0c\u8868\u5360\u7528 O(n) \u7a7a\u95f4\nvar map = std.AutoArrayHashMap(i32, []const u8).init(std.heap.page_allocator);\ndefer map.deinit();\nvar j: i32 = 0;\nwhile (j &lt; n) : (j += 1) {\nconst string = try std.fmt.allocPrint(std.heap.page_allocator, \"{d}\", .{j});\ndefer std.heap.page_allocator.free(string);\ntry map.put(i, string);\n}\n_ = nums;\n}\n</code></pre> space_complexity.dart<pre><code>/* \u7ebf\u6027\u9636 */\nvoid linear(int n) {\n// \u957f\u5ea6\u4e3a n \u7684\u6570\u7ec4\u5360\u7528 O(n) \u7a7a\u95f4\nList&lt;int&gt; nums = List.filled(n, 0);\n// \u957f\u5ea6\u4e3a n \u7684\u5217\u8868\u5360\u7528 O(n) \u7a7a\u95f4\nList&lt;ListNode&gt; nodes = [];\nfor (var i = 0; i &lt; n; i++) {\nnodes.add(ListNode(i));\n}\n// \u957f\u5ea6\u4e3a n \u7684\u54c8\u5e0c\u8868\u5360\u7528 O(n) \u7a7a\u95f4\nMap&lt;int, String&gt; map = HashMap();\nfor (var i = 0; i &lt; n; i++) {\nmap.putIfAbsent(i, () =&gt; i.toString());\n}\n}\n</code></pre> <p>\u4ee5\u4e0b\u9012\u5f52\u51fd\u6570\u4f1a\u540c\u65f6\u5b58\u5728 \\(n\\) \u4e2a\u672a\u8fd4\u56de\u7684 <code>algorithm()</code> \u51fd\u6570\uff0c\u4f7f\u7528 \\(O(n)\\) \u5927\u5c0f\u7684\u6808\u5e27\u7a7a\u95f4\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart space_complexity.java<pre><code>/* \u7ebf\u6027\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nvoid linearRecur(int n) {\nSystem.out.println(\"\u9012\u5f52 n = \" + n);\nif (n == 1)\nreturn;\nlinearRecur(n - 1);\n}\n</code></pre> space_complexity.cpp<pre><code>/* \u7ebf\u6027\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nvoid linearRecur(int n) {\ncout &lt;&lt; \"\u9012\u5f52 n = \" &lt;&lt; n &lt;&lt; endl;\nif (n == 1)\nreturn;\nlinearRecur(n - 1);\n}\n</code></pre> space_complexity.py<pre><code>def linear_recur(n: int) -&gt; None:\n\"\"\"\u7ebf\u6027\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09\"\"\"\nprint(\"\u9012\u5f52 n =\", n)\nif n == 1:\nreturn\nlinear_recur(n - 1)\n</code></pre> space_complexity.go<pre><code>/* \u7ebf\u6027\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nfunc spaceLinearRecur(n int) {\nfmt.Println(\"\u9012\u5f52 n =\", n)\nif n == 1 {\nreturn\n}\nspaceLinearRecur(n - 1)\n}\n</code></pre> space_complexity.js<pre><code>/* \u7ebf\u6027\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nfunction linearRecur(n) {\nconsole.log(`\u9012\u5f52 n = ${n}`);\nif (n === 1) return;\nlinearRecur(n - 1);\n}\n</code></pre> space_complexity.ts<pre><code>/* \u7ebf\u6027\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nfunction linearRecur(n: number): void {\nconsole.log(`\u9012\u5f52 n = ${n}`);\nif (n === 1) return;\nlinearRecur(n - 1);\n}\n</code></pre> space_complexity.c<pre><code>/* \u7ebf\u6027\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nvoid linearRecur(int n) {\nprintf(\"\u9012\u5f52 n = %d\\r\\n\", n);\nif (n == 1)\nreturn;\nlinearRecur(n - 1);\n}\n</code></pre> space_complexity.cs<pre><code>/* \u7ebf\u6027\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nvoid linearRecur(int n) {\nConsole.WriteLine(\"\u9012\u5f52 n = \" + n);\nif (n == 1) return;\nlinearRecur(n - 1);\n}\n</code></pre> space_complexity.swift<pre><code>/* \u7ebf\u6027\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nfunc linearRecur(n: Int) {\nprint(\"\u9012\u5f52 n = \\(n)\")\nif n == 1 {\nreturn\n}\nlinearRecur(n: n - 1)\n}\n</code></pre> space_complexity.zig<pre><code>// \u7ebf\u6027\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09\nfn linearRecur(comptime n: i32) void {\nstd.debug.print(\"\u9012\u5f52 n = {}\\n\", .{n});\nif (n == 1) return;\nlinearRecur(n - 1);\n}\n</code></pre> space_complexity.dart<pre><code>/* \u7ebf\u6027\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nvoid linearRecur(int n) {\nprint('\u9012\u5f52 n = $n');\nif (n == 1) return;\nlinearRecur(n - 1);\n}\n</code></pre> <p></p> <p> Fig. \u9012\u5f52\u51fd\u6570\u4ea7\u751f\u7684\u7ebf\u6027\u9636\u7a7a\u95f4\u590d\u6742\u5ea6 </p>"},{"location":"chapter_computational_complexity/space_complexity/#on2","title":"\u5e73\u65b9\u9636 \\(O(n^2)\\)","text":"<p>\u5e73\u65b9\u9636\u5e38\u89c1\u4e8e\u77e9\u9635\u548c\u56fe\uff0c\u5143\u7d20\u6570\u91cf\u4e0e \\(n\\) \u6210\u5e73\u65b9\u5173\u7cfb\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart space_complexity.java<pre><code>/* \u5e73\u65b9\u9636 */\nvoid quadratic(int n) {\n// \u77e9\u9635\u5360\u7528 O(n^2) \u7a7a\u95f4\nint[][] numMatrix = new int[n][n];\n// \u4e8c\u7ef4\u5217\u8868\u5360\u7528 O(n^2) \u7a7a\u95f4\nList&lt;List&lt;Integer&gt;&gt; numList = new ArrayList&lt;&gt;();\nfor (int i = 0; i &lt; n; i++) {\nList&lt;Integer&gt; tmp = new ArrayList&lt;&gt;();\nfor (int j = 0; j &lt; n; j++) {\ntmp.add(0);\n}\nnumList.add(tmp);\n}\n}\n</code></pre> space_complexity.cpp<pre><code>/* \u5e73\u65b9\u9636 */\nvoid quadratic(int n) {\n// \u4e8c\u7ef4\u5217\u8868\u5360\u7528 O(n^2) \u7a7a\u95f4\nvector&lt;vector&lt;int&gt;&gt; numMatrix;\nfor (int i = 0; i &lt; n; i++) {\nvector&lt;int&gt; tmp;\nfor (int j = 0; j &lt; n; j++) {\ntmp.push_back(0);\n}\nnumMatrix.push_back(tmp);\n}\n}\n</code></pre> space_complexity.py<pre><code>def quadratic(n: int) -&gt; None:\n\"\"\"\u5e73\u65b9\u9636\"\"\"\n# \u4e8c\u7ef4\u5217\u8868\u5360\u7528 O(n^2) \u7a7a\u95f4\nnum_matrix = [[0] * n for _ in range(n)]\n</code></pre> space_complexity.go<pre><code>/* \u5e73\u65b9\u9636 */\nfunc spaceQuadratic(n int) {\n// \u77e9\u9635\u5360\u7528 O(n^2) \u7a7a\u95f4\nnumMatrix := make([][]int, n)\nfor i := 0; i &lt; n; i++ {\nnumMatrix[i] = make([]int, n)\n}\n}\n</code></pre> space_complexity.js<pre><code>/* \u5e73\u65b9\u9636 */\nfunction quadratic(n) {\n// \u77e9\u9635\u5360\u7528 O(n^2) \u7a7a\u95f4\nconst numMatrix = Array(n)\n.fill(null)\n.map(() =&gt; Array(n).fill(null));\n// \u4e8c\u7ef4\u5217\u8868\u5360\u7528 O(n^2) \u7a7a\u95f4\nconst numList = [];\nfor (let i = 0; i &lt; n; i++) {\nconst tmp = [];\nfor (let j = 0; j &lt; n; j++) {\ntmp.push(0);\n}\nnumList.push(tmp);\n}\n}\n</code></pre> space_complexity.ts<pre><code>/* \u5e73\u65b9\u9636 */\nfunction quadratic(n: number): void {\n// \u77e9\u9635\u5360\u7528 O(n^2) \u7a7a\u95f4\nconst numMatrix = Array(n)\n.fill(null)\n.map(() =&gt; Array(n).fill(null));\n// \u4e8c\u7ef4\u5217\u8868\u5360\u7528 O(n^2) \u7a7a\u95f4\nconst numList = [];\nfor (let i = 0; i &lt; n; i++) {\nconst tmp = [];\nfor (let j = 0; j &lt; n; j++) {\ntmp.push(0);\n}\nnumList.push(tmp);\n}\n}\n</code></pre> space_complexity.c<pre><code>/* \u5e73\u65b9\u9636 */\nvoid quadratic(int n) {\n// \u4e8c\u7ef4\u5217\u8868\u5360\u7528 O(n^2) \u7a7a\u95f4\nint **numMatrix = malloc(sizeof(int *) * n);\nfor (int i = 0; i &lt; n; i++) {\nint *tmp = malloc(sizeof(int) * n);\nfor (int j = 0; j &lt; n; j++) {\ntmp[j] = 0;\n}\nnumMatrix[i] = tmp;\n}\n// \u5185\u5b58\u91ca\u653e\nfor (int i = 0; i &lt; n; i++) {\nfree(numMatrix[i]);\n}\nfree(numMatrix);\n}\n</code></pre> space_complexity.cs<pre><code>/* \u5e73\u65b9\u9636 */\nvoid quadratic(int n) {\n// \u77e9\u9635\u5360\u7528 O(n^2) \u7a7a\u95f4\nint[,] numMatrix = new int[n, n];\n// \u4e8c\u7ef4\u5217\u8868\u5360\u7528 O(n^2) \u7a7a\u95f4\nList&lt;List&lt;int&gt;&gt; numList = new();\nfor (int i = 0; i &lt; n; i++) {\nList&lt;int&gt; tmp = new();\nfor (int j = 0; j &lt; n; j++) {\ntmp.Add(0);\n}\nnumList.Add(tmp);\n}\n}\n</code></pre> space_complexity.swift<pre><code>/* \u5e73\u65b9\u9636 */\nfunc quadratic(n: Int) {\n// \u4e8c\u7ef4\u5217\u8868\u5360\u7528 O(n^2) \u7a7a\u95f4\nlet numList = Array(repeating: Array(repeating: 0, count: n), count: n)\n}\n</code></pre> space_complexity.zig<pre><code>// \u5e73\u65b9\u9636\nfn quadratic(n: i32) !void {\n// \u4e8c\u7ef4\u5217\u8868\u5360\u7528 O(n^2) \u7a7a\u95f4\nvar nodes = std.ArrayList(std.ArrayList(i32)).init(std.heap.page_allocator);\ndefer nodes.deinit();\nvar i: i32 = 0;\nwhile (i &lt; n) : (i += 1) {\nvar tmp = std.ArrayList(i32).init(std.heap.page_allocator);\ndefer tmp.deinit();\nvar j: i32 = 0;\nwhile (j &lt; n) : (j += 1) {\ntry tmp.append(0);\n}\ntry nodes.append(tmp);\n}\n}\n</code></pre> space_complexity.dart<pre><code>/* \u5e73\u65b9\u9636 */\nvoid quadratic(int n) {\n// \u77e9\u9635\u5360\u7528 O(n^2) \u7a7a\u95f4\nList&lt;List&lt;int&gt;&gt; numMatrix = List.generate(n, (_) =&gt; List.filled(n, 0));\n// \u4e8c\u7ef4\u5217\u8868\u5360\u7528 O(n^2) \u7a7a\u95f4\nList&lt;List&lt;int&gt;&gt; numList = [];\nfor (var i = 0; i &lt; n; i++) {\nList&lt;int&gt; tmp = [];\nfor (int j = 0; j &lt; n; j++) {\ntmp.add(0);\n}\nnumList.add(tmp);\n}\n}\n</code></pre> <p>\u5728\u4ee5\u4e0b\u9012\u5f52\u51fd\u6570\u4e2d\uff0c\u540c\u65f6\u5b58\u5728 \\(n\\) \u4e2a\u672a\u8fd4\u56de\u7684 <code>algorithm()</code> \uff0c\u5e76\u4e14\u6bcf\u4e2a\u51fd\u6570\u4e2d\u90fd\u521d\u59cb\u5316\u4e86\u4e00\u4e2a\u6570\u7ec4\uff0c\u957f\u5ea6\u5206\u522b\u4e3a \\(n, n-1, n-2, ..., 2, 1\\) \uff0c\u5e73\u5747\u957f\u5ea6\u4e3a \\(\\frac{n}{2}\\) \uff0c\u56e0\u6b64\u603b\u4f53\u5360\u7528 \\(O(n^2)\\) \u7a7a\u95f4\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart space_complexity.java<pre><code>/* \u5e73\u65b9\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nint quadraticRecur(int n) {\nif (n &lt;= 0)\nreturn 0;\n// \u6570\u7ec4 nums \u957f\u5ea6\u4e3a n, n-1, ..., 2, 1\nint[] nums = new int[n];\nSystem.out.println(\"\u9012\u5f52 n = \" + n + \" \u4e2d\u7684 nums \u957f\u5ea6 = \" + nums.length);\nreturn quadraticRecur(n - 1);\n}\n</code></pre> space_complexity.cpp<pre><code>/* \u5e73\u65b9\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nint quadraticRecur(int n) {\nif (n &lt;= 0)\nreturn 0;\nvector&lt;int&gt; nums(n);\ncout &lt;&lt; \"\u9012\u5f52 n = \" &lt;&lt; n &lt;&lt; \" \u4e2d\u7684 nums \u957f\u5ea6 = \" &lt;&lt; nums.size() &lt;&lt; endl;\nreturn quadraticRecur(n - 1);\n}\n</code></pre> space_complexity.py<pre><code>def quadratic_recur(n: int) -&gt; int:\n\"\"\"\u5e73\u65b9\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09\"\"\"\nif n &lt;= 0:\nreturn 0\n# \u6570\u7ec4 nums \u957f\u5ea6\u4e3a n, n-1, ..., 2, 1\nnums = [0] * n\nreturn quadratic_recur(n - 1)\n</code></pre> space_complexity.go<pre><code>/* \u5e73\u65b9\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nfunc spaceQuadraticRecur(n int) int {\nif n &lt;= 0 {\nreturn 0\n}\nnums := make([]int, n)\nfmt.Printf(\"\u9012\u5f52 n = %d \u4e2d\u7684 nums \u957f\u5ea6 = %d \\n\", n, len(nums))\nreturn spaceQuadraticRecur(n - 1)\n}\n</code></pre> space_complexity.js<pre><code>/* \u5e73\u65b9\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nfunction quadraticRecur(n) {\nif (n &lt;= 0) return 0;\nconst nums = new Array(n);\nconsole.log(`\u9012\u5f52 n = ${n} \u4e2d\u7684 nums \u957f\u5ea6 = ${nums.length}`);\nreturn quadraticRecur(n - 1);\n}\n</code></pre> space_complexity.ts<pre><code>/* \u5e73\u65b9\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nfunction quadraticRecur(n: number): number {\nif (n &lt;= 0) return 0;\nconst nums = new Array(n);\nconsole.log(`\u9012\u5f52 n = ${n} \u4e2d\u7684 nums \u957f\u5ea6 = ${nums.length}`);\nreturn quadraticRecur(n - 1);\n}\n</code></pre> space_complexity.c<pre><code>/* \u5e73\u65b9\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nint quadraticRecur(int n) {\nif (n &lt;= 0)\nreturn 0;\nint *nums = malloc(sizeof(int) * n);\nprintf(\"\u9012\u5f52 n = %d \u4e2d\u7684 nums \u957f\u5ea6 = %d\\r\\n\", n, n);\nfree(nums);\nreturn quadraticRecur(n - 1);\n}\n</code></pre> space_complexity.cs<pre><code>/* \u5e73\u65b9\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nint quadraticRecur(int n) {\nif (n &lt;= 0) return 0;\nint[] nums = new int[n];\nConsole.WriteLine(\"\u9012\u5f52 n = \" + n + \" \u4e2d\u7684 nums \u957f\u5ea6 = \" + nums.Length);\nreturn quadraticRecur(n - 1);\n}\n</code></pre> space_complexity.swift<pre><code>/* \u5e73\u65b9\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\n@discardableResult\nfunc quadraticRecur(n: Int) -&gt; Int {\nif n &lt;= 0 {\nreturn 0\n}\n// \u6570\u7ec4 nums \u957f\u5ea6\u4e3a n, n-1, ..., 2, 1\nlet nums = Array(repeating: 0, count: n)\nprint(\"\u9012\u5f52 n = \\(n) \u4e2d\u7684 nums \u957f\u5ea6 = \\(nums.count)\")\nreturn quadraticRecur(n: n - 1)\n}\n</code></pre> space_complexity.zig<pre><code>// \u5e73\u65b9\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09\nfn quadraticRecur(comptime n: i32) i32 {\nif (n &lt;= 0) return 0;\nvar nums = [_]i32{0}**n;\nstd.debug.print(\"\u9012\u5f52 n = {} \u4e2d\u7684 nums \u957f\u5ea6 = {}\\n\", .{n, nums.len});\nreturn quadraticRecur(n - 1);\n}\n</code></pre> space_complexity.dart<pre><code>/* \u5e73\u65b9\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nint quadraticRecur(int n) {\nif (n &lt;= 0) return 0;\nList&lt;int&gt; nums = List.filled(n, 0);\nprint('\u9012\u5f52 n = $n \u4e2d\u7684 nums \u957f\u5ea6 = ${nums.length}');\nreturn quadraticRecur(n - 1);\n}\n</code></pre> <p></p> <p> Fig. \u9012\u5f52\u51fd\u6570\u4ea7\u751f\u7684\u5e73\u65b9\u9636\u7a7a\u95f4\u590d\u6742\u5ea6 </p>"},{"location":"chapter_computational_complexity/space_complexity/#o2n","title":"\u6307\u6570\u9636 \\(O(2^n)\\)","text":"<p>\u6307\u6570\u9636\u5e38\u89c1\u4e8e\u4e8c\u53c9\u6811\u3002\u9ad8\u5ea6\u4e3a \\(n\\) \u7684\u300c\u6ee1\u4e8c\u53c9\u6811\u300d\u7684\u8282\u70b9\u6570\u91cf\u4e3a \\(2^n - 1\\) \uff0c\u5360\u7528 \\(O(2^n)\\) \u7a7a\u95f4\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart space_complexity.java<pre><code>/* \u6307\u6570\u9636\uff08\u5efa\u7acb\u6ee1\u4e8c\u53c9\u6811\uff09 */\nTreeNode buildTree(int n) {\nif (n == 0)\nreturn null;\nTreeNode root = new TreeNode(0);\nroot.left = buildTree(n - 1);\nroot.right = buildTree(n - 1);\nreturn root;\n}\n</code></pre> space_complexity.cpp<pre><code>/* \u6307\u6570\u9636\uff08\u5efa\u7acb\u6ee1\u4e8c\u53c9\u6811\uff09 */\nTreeNode *buildTree(int n) {\nif (n == 0)\nreturn nullptr;\nTreeNode *root = new TreeNode(0);\nroot-&gt;left = buildTree(n - 1);\nroot-&gt;right = buildTree(n - 1);\nreturn root;\n}\n</code></pre> space_complexity.py<pre><code>def build_tree(n: int) -&gt; TreeNode | None:\n\"\"\"\u6307\u6570\u9636\uff08\u5efa\u7acb\u6ee1\u4e8c\u53c9\u6811\uff09\"\"\"\nif n == 0:\nreturn None\nroot = TreeNode(0)\nroot.left = build_tree(n - 1)\nroot.right = build_tree(n - 1)\nreturn root\n</code></pre> space_complexity.go<pre><code>/* \u6307\u6570\u9636\uff08\u5efa\u7acb\u6ee1\u4e8c\u53c9\u6811\uff09 */\nfunc buildTree(n int) *treeNode {\nif n == 0 {\nreturn nil\n}\nroot := newTreeNode(0)\nroot.left = buildTree(n - 1)\nroot.right = buildTree(n - 1)\nreturn root\n}\n</code></pre> space_complexity.js<pre><code>/* \u6307\u6570\u9636\uff08\u5efa\u7acb\u6ee1\u4e8c\u53c9\u6811\uff09 */\nfunction buildTree(n) {\nif (n === 0) return null;\nconst root = new TreeNode(0);\nroot.left = buildTree(n - 1);\nroot.right = buildTree(n - 1);\nreturn root;\n}\n</code></pre> space_complexity.ts<pre><code>/* \u6307\u6570\u9636\uff08\u5efa\u7acb\u6ee1\u4e8c\u53c9\u6811\uff09 */\nfunction buildTree(n: number): TreeNode | null {\nif (n === 0) return null;\nconst root = new TreeNode(0);\nroot.left = buildTree(n - 1);\nroot.right = buildTree(n - 1);\nreturn root;\n}\n</code></pre> space_complexity.c<pre><code>/* \u6307\u6570\u9636\uff08\u5efa\u7acb\u6ee1\u4e8c\u53c9\u6811\uff09 */\nTreeNode *buildTree(int n) {\nif (n == 0)\nreturn NULL;\nTreeNode *root = newTreeNode(0);\nroot-&gt;left = buildTree(n - 1);\nroot-&gt;right = buildTree(n - 1);\nreturn root;\n}\n</code></pre> space_complexity.cs<pre><code>/* \u6307\u6570\u9636\uff08\u5efa\u7acb\u6ee1\u4e8c\u53c9\u6811\uff09 */\nTreeNode? buildTree(int n) {\nif (n == 0) return null;\nTreeNode root = new TreeNode(0);\nroot.left = buildTree(n - 1);\nroot.right = buildTree(n - 1);\nreturn root;\n}\n</code></pre> space_complexity.swift<pre><code>/* \u6307\u6570\u9636\uff08\u5efa\u7acb\u6ee1\u4e8c\u53c9\u6811\uff09 */\nfunc buildTree(n: Int) -&gt; TreeNode? {\nif n == 0 {\nreturn nil\n}\nlet root = TreeNode(x: 0)\nroot.left = buildTree(n: n - 1)\nroot.right = buildTree(n: n - 1)\nreturn root\n}\n</code></pre> space_complexity.zig<pre><code>// \u6307\u6570\u9636\uff08\u5efa\u7acb\u6ee1\u4e8c\u53c9\u6811\uff09\nfn buildTree(mem_allocator: std.mem.Allocator, n: i32) !?*inc.TreeNode(i32) {\nif (n == 0) return null;\nconst root = try mem_allocator.create(inc.TreeNode(i32));\nroot.init(0);\nroot.left = try buildTree(mem_allocator, n - 1);\nroot.right = try buildTree(mem_allocator, n - 1);\nreturn root;\n}\n</code></pre> space_complexity.dart<pre><code>/* \u6307\u6570\u9636\uff08\u5efa\u7acb\u6ee1\u4e8c\u53c9\u6811\uff09 */\nTreeNode? buildTree(int n) {\nif (n == 0) return null;\nTreeNode root = TreeNode(0);\nroot.left = buildTree(n - 1);\nroot.right = buildTree(n - 1);\nreturn root;\n}\n</code></pre> <p></p> <p> Fig. \u6ee1\u4e8c\u53c9\u6811\u4ea7\u751f\u7684\u6307\u6570\u9636\u7a7a\u95f4\u590d\u6742\u5ea6 </p>"},{"location":"chapter_computational_complexity/space_complexity/#olog-n","title":"\u5bf9\u6570\u9636 \\(O(\\log n)\\)","text":"<p>\u5bf9\u6570\u9636\u5e38\u89c1\u4e8e\u5206\u6cbb\u7b97\u6cd5\u548c\u6570\u636e\u7c7b\u578b\u8f6c\u6362\u7b49\u3002</p> <p>\u4f8b\u5982\u201c\u5f52\u5e76\u6392\u5e8f\u201d\u7b97\u6cd5\uff0c\u8f93\u5165\u957f\u5ea6\u4e3a \\(n\\) \u7684\u6570\u7ec4\uff0c\u6bcf\u8f6e\u9012\u5f52\u5c06\u6570\u7ec4\u4ece\u4e2d\u70b9\u5212\u5206\u4e3a\u4e24\u534a\uff0c\u5f62\u6210\u9ad8\u5ea6\u4e3a \\(\\log n\\) \u7684\u9012\u5f52\u6811\uff0c\u4f7f\u7528 \\(O(\\log n)\\) \u6808\u5e27\u7a7a\u95f4\u3002</p> <p>\u518d\u4f8b\u5982\u201c\u6570\u5b57\u8f6c\u5316\u4e3a\u5b57\u7b26\u4e32\u201d\uff0c\u8f93\u5165\u4efb\u610f\u6b63\u6574\u6570 \\(n\\) \uff0c\u5b83\u7684\u4f4d\u6570\u4e3a \\(\\log_{10} n\\) \uff0c\u5373\u5bf9\u5e94\u5b57\u7b26\u4e32\u957f\u5ea6\u4e3a \\(\\log_{10} n\\) \uff0c\u56e0\u6b64\u7a7a\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(\\log_{10} n) = O(\\log n)\\) \u3002</p>"},{"location":"chapter_computational_complexity/space_complexity/#234","title":"2.3.4. \u00a0 \u6743\u8861\u65f6\u95f4\u4e0e\u7a7a\u95f4","text":"<p>\u7406\u60f3\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u5e0c\u671b\u7b97\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u548c\u7a7a\u95f4\u590d\u6742\u5ea6\u90fd\u80fd\u8fbe\u5230\u6700\u4f18\u3002\u7136\u800c\u5728\u5b9e\u9645\u60c5\u51b5\u4e2d\uff0c\u540c\u65f6\u4f18\u5316\u65f6\u95f4\u590d\u6742\u5ea6\u548c\u7a7a\u95f4\u590d\u6742\u5ea6\u901a\u5e38\u662f\u975e\u5e38\u56f0\u96be\u7684\u3002</p> <p>\u964d\u4f4e\u65f6\u95f4\u590d\u6742\u5ea6\u901a\u5e38\u9700\u8981\u4ee5\u63d0\u5347\u7a7a\u95f4\u590d\u6742\u5ea6\u4e3a\u4ee3\u4ef7\uff0c\u53cd\u4e4b\u4ea6\u7136\u3002\u6211\u4eec\u5c06\u727a\u7272\u5185\u5b58\u7a7a\u95f4\u6765\u63d0\u5347\u7b97\u6cd5\u8fd0\u884c\u901f\u5ea6\u7684\u601d\u8def\u79f0\u4e3a\u201c\u4ee5\u7a7a\u95f4\u6362\u65f6\u95f4\u201d\uff1b\u53cd\u4e4b\uff0c\u5219\u79f0\u4e3a\u201c\u4ee5\u65f6\u95f4\u6362\u7a7a\u95f4\u201d\u3002</p> <p>\u9009\u62e9\u54ea\u79cd\u601d\u8def\u53d6\u51b3\u4e8e\u6211\u4eec\u66f4\u770b\u91cd\u54ea\u4e2a\u65b9\u9762\u3002\u5728\u5927\u591a\u6570\u60c5\u51b5\u4e0b\uff0c\u65f6\u95f4\u6bd4\u7a7a\u95f4\u66f4\u5b9d\u8d35\uff0c\u56e0\u6b64\u4ee5\u7a7a\u95f4\u6362\u65f6\u95f4\u901a\u5e38\u662f\u66f4\u5e38\u7528\u7684\u7b56\u7565\u3002\u5f53\u7136\uff0c\u5728\u6570\u636e\u91cf\u5f88\u5927\u7684\u60c5\u51b5\u4e0b\uff0c\u63a7\u5236\u7a7a\u95f4\u590d\u6742\u5ea6\u4e5f\u662f\u975e\u5e38\u91cd\u8981\u7684\u3002</p>"},{"location":"chapter_computational_complexity/summary/","title":"2.4. \u00a0 \u5c0f\u7ed3","text":"<p>\u7b97\u6cd5\u6548\u7387\u8bc4\u4f30</p> <ul> <li>\u65f6\u95f4\u6548\u7387\u548c\u7a7a\u95f4\u6548\u7387\u662f\u8bc4\u4ef7\u7b97\u6cd5\u6027\u80fd\u7684\u4e24\u4e2a\u5173\u952e\u7ef4\u5ea6\u3002</li> <li>\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u5b9e\u9645\u6d4b\u8bd5\u6765\u8bc4\u4f30\u7b97\u6cd5\u6548\u7387\uff0c\u4f46\u96be\u4ee5\u6d88\u9664\u6d4b\u8bd5\u73af\u5883\u7684\u5f71\u54cd\uff0c\u4e14\u4f1a\u8017\u8d39\u5927\u91cf\u8ba1\u7b97\u8d44\u6e90\u3002</li> <li>\u590d\u6742\u5ea6\u5206\u6790\u53ef\u4ee5\u514b\u670d\u5b9e\u9645\u6d4b\u8bd5\u7684\u5f0a\u7aef\uff0c\u5206\u6790\u7ed3\u679c\u9002\u7528\u4e8e\u6240\u6709\u8fd0\u884c\u5e73\u53f0\uff0c\u5e76\u4e14\u80fd\u591f\u63ed\u793a\u7b97\u6cd5\u5728\u4e0d\u540c\u6570\u636e\u89c4\u6a21\u4e0b\u7684\u6548\u7387\u3002</li> </ul> <p>\u65f6\u95f4\u590d\u6742\u5ea6</p> <ul> <li>\u65f6\u95f4\u590d\u6742\u5ea6\u7528\u4e8e\u8861\u91cf\u7b97\u6cd5\u8fd0\u884c\u65f6\u95f4\u968f\u6570\u636e\u91cf\u589e\u957f\u7684\u8d8b\u52bf\uff0c\u53ef\u4ee5\u6709\u6548\u8bc4\u4f30\u7b97\u6cd5\u6548\u7387\uff0c\u4f46\u5728\u67d0\u4e9b\u60c5\u51b5\u4e0b\u53ef\u80fd\u5931\u6548\uff0c\u5982\u5728\u8f93\u5165\u6570\u636e\u91cf\u8f83\u5c0f\u6216\u65f6\u95f4\u590d\u6742\u5ea6\u76f8\u540c\u65f6\uff0c\u65e0\u6cd5\u7cbe\u786e\u5bf9\u6bd4\u7b97\u6cd5\u6548\u7387\u7684\u4f18\u52a3\u3002</li> <li>\u6700\u5dee\u65f6\u95f4\u590d\u6742\u5ea6\u4f7f\u7528\u5927 \\(O\\) \u7b26\u53f7\u8868\u793a\uff0c\u5373\u51fd\u6570\u6e10\u8fd1\u4e0a\u754c\uff0c\u53cd\u6620\u5f53 \\(n\\) \u8d8b\u5411\u6b63\u65e0\u7a77\u65f6\uff0c\\(T(n)\\) \u7684\u589e\u957f\u7ea7\u522b\u3002</li> <li>\u63a8\u7b97\u65f6\u95f4\u590d\u6742\u5ea6\u5206\u4e3a\u4e24\u6b65\uff0c\u9996\u5148\u7edf\u8ba1\u8ba1\u7b97\u64cd\u4f5c\u6570\u91cf\uff0c\u7136\u540e\u5224\u65ad\u6e10\u8fd1\u4e0a\u754c\u3002</li> <li>\u5e38\u89c1\u65f6\u95f4\u590d\u6742\u5ea6\u4ece\u5c0f\u5230\u5927\u6392\u5217\u6709 \\(O(1)\\) , \\(O(\\log n)\\) , \\(O(n)\\) , \\(O(n \\log n)\\) , \\(O(n^2)\\) , \\(O(2^n)\\) , \\(O(n!)\\) \u7b49\u3002</li> <li>\u67d0\u4e9b\u7b97\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u975e\u56fa\u5b9a\uff0c\u800c\u662f\u4e0e\u8f93\u5165\u6570\u636e\u7684\u5206\u5e03\u6709\u5173\u3002\u65f6\u95f4\u590d\u6742\u5ea6\u5206\u4e3a\u6700\u5dee\u3001\u6700\u4f73\u3001\u5e73\u5747\u65f6\u95f4\u590d\u6742\u5ea6\uff0c\u6700\u4f73\u65f6\u95f4\u590d\u6742\u5ea6\u51e0\u4e4e\u4e0d\u7528\uff0c\u56e0\u4e3a\u8f93\u5165\u6570\u636e\u4e00\u822c\u9700\u8981\u6ee1\u8db3\u4e25\u683c\u6761\u4ef6\u624d\u80fd\u8fbe\u5230\u6700\u4f73\u60c5\u51b5\u3002</li> <li>\u5e73\u5747\u65f6\u95f4\u590d\u6742\u5ea6\u53cd\u6620\u7b97\u6cd5\u5728\u968f\u673a\u6570\u636e\u8f93\u5165\u4e0b\u7684\u8fd0\u884c\u6548\u7387\uff0c\u6700\u63a5\u8fd1\u5b9e\u9645\u5e94\u7528\u4e2d\u7684\u7b97\u6cd5\u6027\u80fd\u3002\u8ba1\u7b97\u5e73\u5747\u65f6\u95f4\u590d\u6742\u5ea6\u9700\u8981\u7edf\u8ba1\u8f93\u5165\u6570\u636e\u5206\u5e03\u4ee5\u53ca\u7efc\u5408\u540e\u7684\u6570\u5b66\u671f\u671b\u3002</li> </ul> <p>\u7a7a\u95f4\u590d\u6742\u5ea6</p> <ul> <li>\u7c7b\u4f3c\u4e8e\u65f6\u95f4\u590d\u6742\u5ea6\uff0c\u7a7a\u95f4\u590d\u6742\u5ea6\u7528\u4e8e\u8861\u91cf\u7b97\u6cd5\u5360\u7528\u7a7a\u95f4\u968f\u6570\u636e\u91cf\u589e\u957f\u7684\u8d8b\u52bf\u3002</li> <li>\u7b97\u6cd5\u8fd0\u884c\u8fc7\u7a0b\u4e2d\u7684\u76f8\u5173\u5185\u5b58\u7a7a\u95f4\u53ef\u5206\u4e3a\u8f93\u5165\u7a7a\u95f4\u3001\u6682\u5b58\u7a7a\u95f4\u3001\u8f93\u51fa\u7a7a\u95f4\u3002\u901a\u5e38\u60c5\u51b5\u4e0b\uff0c\u8f93\u5165\u7a7a\u95f4\u4e0d\u8ba1\u5165\u7a7a\u95f4\u590d\u6742\u5ea6\u8ba1\u7b97\u3002\u6682\u5b58\u7a7a\u95f4\u53ef\u5206\u4e3a\u6307\u4ee4\u7a7a\u95f4\u3001\u6570\u636e\u7a7a\u95f4\u3001\u6808\u5e27\u7a7a\u95f4\uff0c\u5176\u4e2d\u6808\u5e27\u7a7a\u95f4\u901a\u5e38\u4ec5\u5728\u9012\u5f52\u51fd\u6570\u4e2d\u5f71\u54cd\u7a7a\u95f4\u590d\u6742\u5ea6\u3002</li> <li>\u6211\u4eec\u901a\u5e38\u53ea\u5173\u6ce8\u6700\u5dee\u7a7a\u95f4\u590d\u6742\u5ea6\uff0c\u5373\u7edf\u8ba1\u7b97\u6cd5\u5728\u6700\u5dee\u8f93\u5165\u6570\u636e\u548c\u6700\u5dee\u8fd0\u884c\u65f6\u95f4\u70b9\u4e0b\u7684\u7a7a\u95f4\u590d\u6742\u5ea6\u3002</li> <li>\u5e38\u89c1\u7a7a\u95f4\u590d\u6742\u5ea6\u4ece\u5c0f\u5230\u5927\u6392\u5217\u6709 \\(O(1)\\) , \\(O(\\log n)\\) , \\(O(n)\\) , \\(O(n^2)\\) , \\(O(2^n)\\) \u7b49\u3002</li> </ul>"},{"location":"chapter_computational_complexity/summary/#241-q-a","title":"2.4.1. \u00a0 Q &amp; A","text":"<p>\u5c3e\u9012\u5f52\u7684\u7a7a\u95f4\u590d\u6742\u5ea6\u662f \\(O(1)\\) \u5417\uff1f</p> <p>\u7406\u8bba\u4e0a\uff0c\u5c3e\u9012\u5f52\u51fd\u6570\u7684\u7a7a\u95f4\u590d\u6742\u5ea6\u53ef\u4ee5\u88ab\u4f18\u5316\u81f3 \\(O(1)\\) \u3002\u4e0d\u8fc7\u7edd\u5927\u591a\u6570\u7f16\u7a0b\u8bed\u8a00\uff08\u4f8b\u5982 Java, Python, C++, Go, C# \u7b49\uff09 \u90fd\u4e0d\u652f\u6301\u81ea\u52a8\u4f18\u5316\u5c3e\u9012\u5f52\uff0c\u56e0\u6b64\u4e00\u822c\u6765\u8bf4\u7a7a\u95f4\u590d\u6742\u5ea6\u662f \\(O(n)\\) \u3002</p> <p>\u51fd\u6570\u548c\u65b9\u6cd5\u8fd9\u4e24\u4e2a\u672f\u8bed\u7684\u533a\u522b\u662f\u4ec0\u4e48\uff1f</p> <p>\u51fd\u6570\uff08function\uff09\u53ef\u4ee5\u72ec\u7acb\u88ab\u6267\u884c\uff0c\u6240\u6709\u53c2\u6570\u90fd\u4ee5\u663e\u5f0f\u4f20\u9012\u3002 \u65b9\u6cd5\uff08method\uff09\u4e0e\u4e00\u4e2a\u5bf9\u8c61\u5173\u8054\uff0c\u65b9\u6cd5\u88ab\u9690\u5f0f\u4f20\u9012\u7ed9\u8c03\u7528\u5b83\u7684\u5bf9\u8c61\uff0c\u65b9\u6cd5\u80fd\u591f\u5bf9\u7c7b\u7684\u5b9e\u4f8b\u4e2d\u5305\u542b\u7684\u6570\u636e\u8fdb\u884c\u64cd\u4f5c\u3002</p> <p>\u56fe\u7247\u201c\u7a7a\u95f4\u590d\u6742\u5ea6\u7684\u5e38\u89c1\u7c7b\u578b\u201d\u53cd\u6620\u7684\u662f\u5426\u662f\u5360\u7528\u7a7a\u95f4\u7684\u7edd\u5bf9\u5927\u5c0f\uff1f</p> <p>\u4e0d\u662f\uff0c\u8be5\u56fe\u7247\u5c55\u793a\u7684\u662f\u7a7a\u95f4\u590d\u6742\u5ea6\uff08\u5373\u589e\u957f\u8d8b\u52bf\uff09\uff0c\u800c\u4e0d\u662f\u5360\u7528\u7a7a\u95f4\u7684\u7edd\u5bf9\u5927\u5c0f\u3002\u6bcf\u4e2a\u66f2\u7ebf\u90fd\u5305\u542b\u4e00\u4e2a\u5e38\u6570\u9879\uff0c\u7528\u6765\u628a\u6240\u6709\u66f2\u7ebf\u7684\u53d6\u503c\u8303\u56f4\u538b\u7f29\u5230\u4e00\u4e2a\u89c6\u89c9\u8212\u9002\u7684\u8303\u56f4\u5185\u3002 \u5b9e\u9645\u4e2d\uff0c\u56e0\u4e3a\u6211\u4eec\u901a\u5e38\u4e0d\u77e5\u9053\u6bcf\u4e2a\u65b9\u6cd5\u7684\u201c\u5e38\u6570\u9879\u201d\u590d\u6742\u5ea6\u662f\u591a\u5c11\uff0c\u6240\u4ee5\u4e00\u822c\u65e0\u6cd5\u4ec5\u51ed\u590d\u6742\u5ea6\u6765\u9009\u62e9 \\(n = 8\\) \u4e4b\u4e0b\u7684\u6700\u4f18\u89e3\u6cd5\uff1b\u4f46\u76f8\u5bf9\u5730 \\(n = 8^5\\) \u5c31\u5f88\u597d\u9009\u4e86\uff0c\u8fd9\u662f\u590d\u6742\u5ea6\u5360\u4e3b\u5bfc\u7684\u60c5\u51b5\u3002</p>"},{"location":"chapter_computational_complexity/time_complexity/","title":"2.2. \u00a0 \u65f6\u95f4\u590d\u6742\u5ea6","text":""},{"location":"chapter_computational_complexity/time_complexity/#221","title":"2.2.1. \u00a0 \u7edf\u8ba1\u7b97\u6cd5\u8fd0\u884c\u65f6\u95f4","text":"<p>\u8fd0\u884c\u65f6\u95f4\u53ef\u4ee5\u76f4\u89c2\u4e14\u51c6\u786e\u5730\u53cd\u6620\u7b97\u6cd5\u7684\u6548\u7387\u3002\u7136\u800c\uff0c\u5982\u679c\u6211\u4eec\u60f3\u8981\u51c6\u786e\u9884\u4f30\u4e00\u6bb5\u4ee3\u7801\u7684\u8fd0\u884c\u65f6\u95f4\uff0c\u5e94\u8be5\u5982\u4f55\u64cd\u4f5c\u5462\uff1f</p> <ol> <li>\u786e\u5b9a\u8fd0\u884c\u5e73\u53f0\uff0c\u5305\u62ec\u786c\u4ef6\u914d\u7f6e\u3001\u7f16\u7a0b\u8bed\u8a00\u3001\u7cfb\u7edf\u73af\u5883\u7b49\uff0c\u8fd9\u4e9b\u56e0\u7d20\u90fd\u4f1a\u5f71\u54cd\u4ee3\u7801\u7684\u8fd0\u884c\u6548\u7387\u3002</li> <li>\u8bc4\u4f30\u5404\u79cd\u8ba1\u7b97\u64cd\u4f5c\u6240\u9700\u7684\u8fd0\u884c\u65f6\u95f4\uff0c\u4f8b\u5982\u52a0\u6cd5\u64cd\u4f5c <code>+</code> \u9700\u8981 1 ns\uff0c\u4e58\u6cd5\u64cd\u4f5c <code>*</code> \u9700\u8981 10 ns\uff0c\u6253\u5370\u64cd\u4f5c\u9700\u8981 5 ns \u7b49\u3002</li> <li>\u7edf\u8ba1\u4ee3\u7801\u4e2d\u6240\u6709\u7684\u8ba1\u7b97\u64cd\u4f5c\uff0c\u5e76\u5c06\u6240\u6709\u64cd\u4f5c\u7684\u6267\u884c\u65f6\u95f4\u6c42\u548c\uff0c\u4ece\u800c\u5f97\u5230\u8fd0\u884c\u65f6\u95f4\u3002</li> </ol> <p>\u4f8b\u5982\u4ee5\u4e0b\u4ee3\u7801\uff0c\u8f93\u5165\u6570\u636e\u5927\u5c0f\u4e3a \\(n\\) \uff0c\u6839\u636e\u4ee5\u4e0a\u65b9\u6cd5\uff0c\u53ef\u4ee5\u5f97\u5230\u7b97\u6cd5\u8fd0\u884c\u65f6\u95f4\u4e3a \\(6n + 12\\) ns \u3002</p> \\[ 1 + 1 + 10 + (1 + 5) \\times n = 6n + 12 \\] JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart <pre><code>// \u5728\u67d0\u8fd0\u884c\u5e73\u53f0\u4e0b\nvoid algorithm(int n) {\nint a = 2;  // 1 ns\na = a + 1;  // 1 ns\na = a * 2;  // 10 ns\n// \u5faa\u73af n \u6b21\nfor (int i = 0; i &lt; n; i++) {  // 1 ns \uff0c\u6bcf\u8f6e\u90fd\u8981\u6267\u884c i++\nSystem.out.println(0);     // 5 ns\n}\n}\n</code></pre> <pre><code>// \u5728\u67d0\u8fd0\u884c\u5e73\u53f0\u4e0b\nvoid algorithm(int n) {\nint a = 2;  // 1 ns\na = a + 1;  // 1 ns\na = a * 2;  // 10 ns\n// \u5faa\u73af n \u6b21\nfor (int i = 0; i &lt; n; i++) {  // 1 ns \uff0c\u6bcf\u8f6e\u90fd\u8981\u6267\u884c i++\ncout &lt;&lt; 0 &lt;&lt; endl;         // 5 ns\n}\n}\n</code></pre> <pre><code># \u5728\u67d0\u8fd0\u884c\u5e73\u53f0\u4e0b\ndef algorithm(n: int) -&gt; None:\na = 2      # 1 ns\na = a + 1  # 1 ns\na = a * 2  # 10 ns\n# \u5faa\u73af n \u6b21\nfor _ in range(n):  # 1 ns\nprint(0)        # 5 ns\n</code></pre> <pre><code>// \u5728\u67d0\u8fd0\u884c\u5e73\u53f0\u4e0b\nfunc algorithm(n int) {\na := 2      // 1 ns\na = a + 1   // 1 ns\na = a * 2   // 10 ns\n// \u5faa\u73af n \u6b21\nfor i := 0; i &lt; n; i++ {    // 1 ns\nfmt.Println(a)          // 5 ns\n}\n}\n</code></pre> <pre><code>// \u5728\u67d0\u8fd0\u884c\u5e73\u53f0\u4e0b\nfunction algorithm(n) {\nvar a = 2; // 1 ns\na = a + 1; // 1 ns\na = a * 2; // 10 ns\n// \u5faa\u73af n \u6b21\nfor(let i = 0; i &lt; n; i++) { // 1 ns \uff0c\u6bcf\u8f6e\u90fd\u8981\u6267\u884c i++\nconsole.log(0); // 5 ns\n}\n}\n</code></pre> <pre><code>// \u5728\u67d0\u8fd0\u884c\u5e73\u53f0\u4e0b\nfunction algorithm(n: number): void {\nvar a: number = 2; // 1 ns\na = a + 1; // 1 ns\na = a * 2; // 10 ns\n// \u5faa\u73af n \u6b21\nfor(let i = 0; i &lt; n; i++) { // 1 ns \uff0c\u6bcf\u8f6e\u90fd\u8981\u6267\u884c i++\nconsole.log(0); // 5 ns\n}\n}\n</code></pre> <pre><code>// \u5728\u67d0\u8fd0\u884c\u5e73\u53f0\u4e0b\nvoid algorithm(int n) {\nint a = 2;  // 1 ns\na = a + 1;  // 1 ns\na = a * 2;  // 10 ns\n// \u5faa\u73af n \u6b21\nfor (int i = 0; i &lt; n; i++) {   // 1 ns \uff0c\u6bcf\u8f6e\u90fd\u8981\u6267\u884c i++\nprintf(\"%d\", 0);            // 5 ns\n}\n}\n</code></pre> <pre><code>// \u5728\u67d0\u8fd0\u884c\u5e73\u53f0\u4e0b\nvoid algorithm(int n)\n{\nint a = 2;  // 1 ns\na = a + 1;  // 1 ns\na = a * 2;  // 10 ns\n// \u5faa\u73af n \u6b21\nfor (int i = 0; i &lt; n; i++)\n{  // 1 ns \uff0c\u6bcf\u8f6e\u90fd\u8981\u6267\u884c i++\nConsole.WriteLine(0);     // 5 ns\n}\n}\n</code></pre> <pre><code>// \u5728\u67d0\u8fd0\u884c\u5e73\u53f0\u4e0b\nfunc algorithm(n: Int) {\nvar a = 2 // 1 ns\na = a + 1 // 1 ns\na = a * 2 // 10 ns\n// \u5faa\u73af n \u6b21\nfor _ in 0 ..&lt; n { // 1 ns\nprint(0) // 5 ns\n}\n}\n</code></pre> <pre><code>\n</code></pre> <pre><code>// \u5728\u67d0\u8fd0\u884c\u5e73\u53f0\u4e0b\nvoid algorithm(int n) {\nint a = 2; // 1 ns\na = a + 1; // 1 ns\na = a * 2; // 10 ns\n// \u5faa\u73af n \u6b21\nfor (int i = 0; i &lt; n; i++) { // 1 ns \uff0c\u6bcf\u8f6e\u90fd\u8981\u6267\u884c i++\nprint(0); // 5 ns\n}\n}\n</code></pre> <p>\u7136\u800c\u5b9e\u9645\u4e0a\uff0c\u7edf\u8ba1\u7b97\u6cd5\u7684\u8fd0\u884c\u65f6\u95f4\u65e2\u4e0d\u5408\u7406\u4e5f\u4e0d\u73b0\u5b9e\u3002\u9996\u5148\uff0c\u6211\u4eec\u4e0d\u5e0c\u671b\u9884\u4f30\u65f6\u95f4\u548c\u8fd0\u884c\u5e73\u53f0\u7ed1\u5b9a\uff0c\u56e0\u4e3a\u7b97\u6cd5\u9700\u8981\u5728\u5404\u79cd\u4e0d\u540c\u7684\u5e73\u53f0\u4e0a\u8fd0\u884c\u3002\u5176\u6b21\uff0c\u6211\u4eec\u5f88\u96be\u83b7\u77e5\u6bcf\u79cd\u64cd\u4f5c\u7684\u8fd0\u884c\u65f6\u95f4\uff0c\u8fd9\u7ed9\u9884\u4f30\u8fc7\u7a0b\u5e26\u6765\u4e86\u6781\u5927\u7684\u96be\u5ea6\u3002</p>"},{"location":"chapter_computational_complexity/time_complexity/#222","title":"2.2.2. \u00a0 \u7edf\u8ba1\u65f6\u95f4\u589e\u957f\u8d8b\u52bf","text":"<p>\u300c\u65f6\u95f4\u590d\u6742\u5ea6\u5206\u6790\u300d\u91c7\u53d6\u4e86\u4e00\u79cd\u4e0d\u540c\u7684\u65b9\u6cd5\uff0c\u5176\u7edf\u8ba1\u7684\u4e0d\u662f\u7b97\u6cd5\u8fd0\u884c\u65f6\u95f4\uff0c\u800c\u662f\u7b97\u6cd5\u8fd0\u884c\u65f6\u95f4\u968f\u7740\u6570\u636e\u91cf\u53d8\u5927\u65f6\u7684\u589e\u957f\u8d8b\u52bf\u3002</p> <p>\u201c\u65f6\u95f4\u589e\u957f\u8d8b\u52bf\u201d\u8fd9\u4e2a\u6982\u5ff5\u8f83\u4e3a\u62bd\u8c61\uff0c\u6211\u4eec\u901a\u8fc7\u4e00\u4e2a\u4f8b\u5b50\u6765\u52a0\u4ee5\u7406\u89e3\u3002\u5047\u8bbe\u8f93\u5165\u6570\u636e\u5927\u5c0f\u4e3a \\(n\\) \uff0c\u7ed9\u5b9a\u4e09\u4e2a\u7b97\u6cd5 <code>A</code> , <code>B</code> , <code>C</code> \u3002</p> <ul> <li>\u7b97\u6cd5 <code>A</code> \u53ea\u6709 \\(1\\) \u4e2a\u6253\u5370\u64cd\u4f5c\uff0c\u7b97\u6cd5\u8fd0\u884c\u65f6\u95f4\u4e0d\u968f\u7740 \\(n\\) \u589e\u5927\u800c\u589e\u957f\u3002\u6211\u4eec\u79f0\u6b64\u7b97\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a\u300c\u5e38\u6570\u9636\u300d\u3002</li> <li>\u7b97\u6cd5 <code>B</code> \u4e2d\u7684\u6253\u5370\u64cd\u4f5c\u9700\u8981\u5faa\u73af \\(n\\) \u6b21\uff0c\u7b97\u6cd5\u8fd0\u884c\u65f6\u95f4\u968f\u7740 \\(n\\) \u589e\u5927\u5448\u7ebf\u6027\u589e\u957f\u3002\u6b64\u7b97\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u88ab\u79f0\u4e3a\u300c\u7ebf\u6027\u9636\u300d\u3002</li> <li>\u7b97\u6cd5 <code>C</code> \u4e2d\u7684\u6253\u5370\u64cd\u4f5c\u9700\u8981\u5faa\u73af \\(1000000\\) \u6b21\uff0c\u4f46\u8fd0\u884c\u65f6\u95f4\u4ecd\u4e0e\u8f93\u5165\u6570\u636e\u5927\u5c0f \\(n\\) \u65e0\u5173\u3002\u56e0\u6b64 <code>C</code> \u7684\u65f6\u95f4\u590d\u6742\u5ea6\u548c <code>A</code> \u76f8\u540c\uff0c\u4ecd\u4e3a\u300c\u5e38\u6570\u9636\u300d\u3002</li> </ul> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart <pre><code>// \u7b97\u6cd5 A \u65f6\u95f4\u590d\u6742\u5ea6\uff1a\u5e38\u6570\u9636\nvoid algorithm_A(int n) {\nSystem.out.println(0);\n}\n// \u7b97\u6cd5 B \u65f6\u95f4\u590d\u6742\u5ea6\uff1a\u7ebf\u6027\u9636\nvoid algorithm_B(int n) {\nfor (int i = 0; i &lt; n; i++) {\nSystem.out.println(0);\n}\n}\n// \u7b97\u6cd5 C \u65f6\u95f4\u590d\u6742\u5ea6\uff1a\u5e38\u6570\u9636\nvoid algorithm_C(int n) {\nfor (int i = 0; i &lt; 1000000; i++) {\nSystem.out.println(0);\n}\n}\n</code></pre> <pre><code>// \u7b97\u6cd5 A \u65f6\u95f4\u590d\u6742\u5ea6\uff1a\u5e38\u6570\u9636\nvoid algorithm_A(int n) {\ncout &lt;&lt; 0 &lt;&lt; endl;\n}\n// \u7b97\u6cd5 B \u65f6\u95f4\u590d\u6742\u5ea6\uff1a\u7ebf\u6027\u9636\nvoid algorithm_B(int n) {\nfor (int i = 0; i &lt; n; i++) {\ncout &lt;&lt; 0 &lt;&lt; endl;\n}\n}\n// \u7b97\u6cd5 C \u65f6\u95f4\u590d\u6742\u5ea6\uff1a\u5e38\u6570\u9636\nvoid algorithm_C(int n) {\nfor (int i = 0; i &lt; 1000000; i++) {\ncout &lt;&lt; 0 &lt;&lt; endl;\n}\n}\n</code></pre> <pre><code># \u7b97\u6cd5 A \u65f6\u95f4\u590d\u6742\u5ea6\uff1a\u5e38\u6570\u9636\ndef algorithm_A(n: int) -&gt; None:\nprint(0)\n# \u7b97\u6cd5 B \u65f6\u95f4\u590d\u6742\u5ea6\uff1a\u7ebf\u6027\u9636\ndef algorithm_B(n: int) -&gt; None:\nfor _ in range(n):\nprint(0)\n# \u7b97\u6cd5 C \u65f6\u95f4\u590d\u6742\u5ea6\uff1a\u5e38\u6570\u9636\ndef algorithm_C(n: int) -&gt; None:\nfor _ in range(1000000):\nprint(0)\n</code></pre> <pre><code>// \u7b97\u6cd5 A \u65f6\u95f4\u590d\u6742\u5ea6\uff1a\u5e38\u6570\u9636\nfunc algorithm_A(n int) {\nfmt.Println(0)\n}\n// \u7b97\u6cd5 B \u65f6\u95f4\u590d\u6742\u5ea6\uff1a\u7ebf\u6027\u9636\nfunc algorithm_B(n int) {\nfor i := 0; i &lt; n; i++ {\nfmt.Println(0)\n}\n}\n// \u7b97\u6cd5 C \u65f6\u95f4\u590d\u6742\u5ea6\uff1a\u5e38\u6570\u9636\nfunc algorithm_C(n int) {\nfor i := 0; i &lt; 1000000; i++ {\nfmt.Println(0)\n}\n}\n</code></pre> <pre><code>// \u7b97\u6cd5 A \u65f6\u95f4\u590d\u6742\u5ea6\uff1a\u5e38\u6570\u9636\nfunction algorithm_A(n) {\nconsole.log(0);\n}\n// \u7b97\u6cd5 B \u65f6\u95f4\u590d\u6742\u5ea6\uff1a\u7ebf\u6027\u9636\nfunction algorithm_B(n) {\nfor (let i = 0; i &lt; n; i++) {\nconsole.log(0);\n}\n}\n// \u7b97\u6cd5 C \u65f6\u95f4\u590d\u6742\u5ea6\uff1a\u5e38\u6570\u9636\nfunction algorithm_C(n) {\nfor (let i = 0; i &lt; 1000000; i++) {\nconsole.log(0);\n}\n}\n</code></pre> <pre><code>// \u7b97\u6cd5 A \u65f6\u95f4\u590d\u6742\u5ea6\uff1a\u5e38\u6570\u9636\nfunction algorithm_A(n: number): void {\nconsole.log(0);\n}\n// \u7b97\u6cd5 B \u65f6\u95f4\u590d\u6742\u5ea6\uff1a\u7ebf\u6027\u9636\nfunction algorithm_B(n: number): void {\nfor (let i = 0; i &lt; n; i++) {\nconsole.log(0);\n}\n}\n// \u7b97\u6cd5 C \u65f6\u95f4\u590d\u6742\u5ea6\uff1a\u5e38\u6570\u9636\nfunction algorithm_C(n: number): void {\nfor (let i = 0; i &lt; 1000000; i++) {\nconsole.log(0);\n}\n}\n</code></pre> <pre><code>// \u7b97\u6cd5 A \u65f6\u95f4\u590d\u6742\u5ea6\uff1a\u5e38\u6570\u9636\nvoid algorithm_A(int n) {\nprintf(\"%d\", 0);\n}\n// \u7b97\u6cd5 B \u65f6\u95f4\u590d\u6742\u5ea6\uff1a\u7ebf\u6027\u9636\nvoid algorithm_B(int n) {\nfor (int i = 0; i &lt; n; i++) {\nprintf(\"%d\", 0);\n}\n}\n// \u7b97\u6cd5 C \u65f6\u95f4\u590d\u6742\u5ea6\uff1a\u5e38\u6570\u9636\nvoid algorithm_C(int n) {\nfor (int i = 0; i &lt; 1000000; i++) {\nprintf(\"%d\", 0);\n}\n}\n</code></pre> <pre><code>// \u7b97\u6cd5 A \u65f6\u95f4\u590d\u6742\u5ea6\uff1a\u5e38\u6570\u9636\nvoid algorithm_A(int n)\n{\nConsole.WriteLine(0);\n}\n// \u7b97\u6cd5 B \u65f6\u95f4\u590d\u6742\u5ea6\uff1a\u7ebf\u6027\u9636\nvoid algorithm_B(int n)\n{\nfor (int i = 0; i &lt; n; i++)\n{\nConsole.WriteLine(0);\n}\n}\n// \u7b97\u6cd5 C \u65f6\u95f4\u590d\u6742\u5ea6\uff1a\u5e38\u6570\u9636\nvoid algorithm_C(int n)\n{\nfor (int i = 0; i &lt; 1000000; i++)\n{\nConsole.WriteLine(0);\n}\n}\n</code></pre> <pre><code>// \u7b97\u6cd5 A \u65f6\u95f4\u590d\u6742\u5ea6\uff1a\u5e38\u6570\u9636\nfunc algorithmA(n: Int) {\nprint(0)\n}\n// \u7b97\u6cd5 B \u65f6\u95f4\u590d\u6742\u5ea6\uff1a\u7ebf\u6027\u9636\nfunc algorithmB(n: Int) {\nfor _ in 0 ..&lt; n {\nprint(0)\n}\n}\n// \u7b97\u6cd5 C \u65f6\u95f4\u590d\u6742\u5ea6\uff1a\u5e38\u6570\u9636\nfunc algorithmC(n: Int) {\nfor _ in 0 ..&lt; 1000000 {\nprint(0)\n}\n}\n</code></pre> <pre><code>\n</code></pre> <pre><code>// \u7b97\u6cd5 A \u65f6\u95f4\u590d\u6742\u5ea6\uff1a\u5e38\u6570\u9636\nvoid algorithmA(int n) {\nprint(0);\n}\n// \u7b97\u6cd5 B \u65f6\u95f4\u590d\u6742\u5ea6\uff1a\u7ebf\u6027\u9636\nvoid algorithmB(int n) {\nfor (int i = 0; i &lt; n; i++) {\nprint(0);\n}\n}\n// \u7b97\u6cd5 C \u65f6\u95f4\u590d\u6742\u5ea6\uff1a\u5e38\u6570\u9636\nvoid algorithmC(int n) {\nfor (int i = 0; i &lt; 1000000; i++) {\nprint(0);\n}\n}\n</code></pre> <p></p> <p> Fig. \u7b97\u6cd5 A, B, C \u7684\u65f6\u95f4\u589e\u957f\u8d8b\u52bf </p> <p>\u76f8\u8f83\u4e8e\u76f4\u63a5\u7edf\u8ba1\u7b97\u6cd5\u8fd0\u884c\u65f6\u95f4\uff0c\u65f6\u95f4\u590d\u6742\u5ea6\u5206\u6790\u6709\u54ea\u4e9b\u4f18\u52bf\u548c\u5c40\u9650\u6027\u5462\uff1f</p> <p>\u65f6\u95f4\u590d\u6742\u5ea6\u80fd\u591f\u6709\u6548\u8bc4\u4f30\u7b97\u6cd5\u6548\u7387\u3002\u4f8b\u5982\uff0c\u7b97\u6cd5 <code>B</code> \u7684\u8fd0\u884c\u65f6\u95f4\u5448\u7ebf\u6027\u589e\u957f\uff0c\u5728 \\(n &gt; 1\\) \u65f6\u6bd4\u7b97\u6cd5 <code>A</code> \u6162\uff0c\u5728 \\(n &gt; 1000000\\) \u65f6\u6bd4\u7b97\u6cd5 <code>C</code> \u6162\u3002\u4e8b\u5b9e\u4e0a\uff0c\u53ea\u8981\u8f93\u5165\u6570\u636e\u5927\u5c0f \\(n\\) \u8db3\u591f\u5927\uff0c\u590d\u6742\u5ea6\u4e3a\u300c\u5e38\u6570\u9636\u300d\u7684\u7b97\u6cd5\u4e00\u5b9a\u4f18\u4e8e\u300c\u7ebf\u6027\u9636\u300d\u7684\u7b97\u6cd5\uff0c\u8fd9\u6b63\u662f\u65f6\u95f4\u589e\u957f\u8d8b\u52bf\u6240\u8868\u8fbe\u7684\u542b\u4e49\u3002</p> <p>\u65f6\u95f4\u590d\u6742\u5ea6\u7684\u63a8\u7b97\u65b9\u6cd5\u66f4\u7b80\u4fbf\u3002\u663e\u7136\uff0c\u8fd0\u884c\u5e73\u53f0\u548c\u8ba1\u7b97\u64cd\u4f5c\u7c7b\u578b\u90fd\u4e0e\u7b97\u6cd5\u8fd0\u884c\u65f6\u95f4\u7684\u589e\u957f\u8d8b\u52bf\u65e0\u5173\u3002\u56e0\u6b64\u5728\u65f6\u95f4\u590d\u6742\u5ea6\u5206\u6790\u4e2d\uff0c\u6211\u4eec\u53ef\u4ee5\u7b80\u5355\u5730\u5c06\u6240\u6709\u8ba1\u7b97\u64cd\u4f5c\u7684\u6267\u884c\u65f6\u95f4\u89c6\u4e3a\u76f8\u540c\u7684\u201c\u5355\u4f4d\u65f6\u95f4\u201d\uff0c\u4ece\u800c\u5c06\u201c\u8ba1\u7b97\u64cd\u4f5c\u7684\u8fd0\u884c\u65f6\u95f4\u7684\u7edf\u8ba1\u201d\u7b80\u5316\u4e3a\u201c\u8ba1\u7b97\u64cd\u4f5c\u7684\u6570\u91cf\u7684\u7edf\u8ba1\u201d\uff0c\u8fd9\u6837\u7684\u7b80\u5316\u65b9\u6cd5\u5927\u5927\u964d\u4f4e\u4e86\u4f30\u7b97\u96be\u5ea6\u3002</p> <p>\u65f6\u95f4\u590d\u6742\u5ea6\u4e5f\u5b58\u5728\u4e00\u5b9a\u7684\u5c40\u9650\u6027\u3002\u4f8b\u5982\uff0c\u5c3d\u7ba1\u7b97\u6cd5 <code>A</code> \u548c <code>C</code> \u7684\u65f6\u95f4\u590d\u6742\u5ea6\u76f8\u540c\uff0c\u4f46\u5b9e\u9645\u8fd0\u884c\u65f6\u95f4\u5dee\u522b\u5f88\u5927\u3002\u540c\u6837\uff0c\u5c3d\u7ba1\u7b97\u6cd5 <code>B</code> \u7684\u65f6\u95f4\u590d\u6742\u5ea6\u6bd4 <code>C</code> \u9ad8\uff0c\u4f46\u5728\u8f93\u5165\u6570\u636e\u5927\u5c0f \\(n\\) \u8f83\u5c0f\u65f6\uff0c\u7b97\u6cd5 <code>B</code> \u660e\u663e\u4f18\u4e8e\u7b97\u6cd5 <code>C</code> \u3002\u5728\u8fd9\u4e9b\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u5f88\u96be\u4ec5\u51ed\u65f6\u95f4\u590d\u6742\u5ea6\u5224\u65ad\u7b97\u6cd5\u6548\u7387\u9ad8\u4f4e\u3002\u5f53\u7136\uff0c\u5c3d\u7ba1\u5b58\u5728\u4e0a\u8ff0\u95ee\u9898\uff0c\u590d\u6742\u5ea6\u5206\u6790\u4ecd\u7136\u662f\u8bc4\u5224\u7b97\u6cd5\u6548\u7387\u6700\u6709\u6548\u4e14\u5e38\u7528\u7684\u65b9\u6cd5\u3002</p>"},{"location":"chapter_computational_complexity/time_complexity/#223","title":"2.2.3. \u00a0 \u51fd\u6570\u6e10\u8fd1\u4e0a\u754c","text":"<p>\u8bbe\u7b97\u6cd5\u7684\u8ba1\u7b97\u64cd\u4f5c\u6570\u91cf\u662f\u4e00\u4e2a\u5173\u4e8e\u8f93\u5165\u6570\u636e\u5927\u5c0f \\(n\\) \u7684\u51fd\u6570\uff0c\u8bb0\u4e3a \\(T(n)\\) \uff0c\u5219\u4ee5\u4e0b\u7b97\u6cd5\u7684\u64cd\u4f5c\u6570\u91cf\u4e3a</p> \\[ T(n) = 3 + 2n \\] JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart <pre><code>void algorithm(int n) {\nint a = 1;  // +1\na = a + 1;  // +1\na = a * 2;  // +1\n// \u5faa\u73af n \u6b21\nfor (int i = 0; i &lt; n; i++) { // +1\uff08\u6bcf\u8f6e\u90fd\u6267\u884c i ++\uff09\nSystem.out.println(0);    // +1\n}\n}\n</code></pre> <pre><code>void algorithm(int n) {\nint a = 1;  // +1\na = a + 1;  // +1\na = a * 2;  // +1\n// \u5faa\u73af n \u6b21\nfor (int i = 0; i &lt; n; i++) { // +1\uff08\u6bcf\u8f6e\u90fd\u6267\u884c i ++\uff09\ncout &lt;&lt; 0 &lt;&lt; endl;    // +1\n}\n}\n</code></pre> <pre><code>def algorithm(n: int) -&gt; None:\na = 1      # +1\na = a + 1  # +1\na = a * 2  # +1\n# \u5faa\u73af n \u6b21\nfor i in range(n):  # +1\nprint(0)        # +1\n</code></pre> <pre><code>func algorithm(n int) {\na := 1      // +1\na = a + 1   // +1\na = a * 2   // +1\n// \u5faa\u73af n \u6b21\nfor i := 0; i &lt; n; i++ {   // +1\nfmt.Println(a)         // +1\n}\n}\n</code></pre> <pre><code>function algorithm(n) {\nvar a = 1; // +1\na += 1; // +1\na *= 2; // +1\n// \u5faa\u73af n \u6b21\nfor(let i = 0; i &lt; n; i++){ // +1\uff08\u6bcf\u8f6e\u90fd\u6267\u884c i ++\uff09\nconsole.log(0); // +1\n}\n}\n</code></pre> <pre><code>function algorithm(n: number): void{\nvar a: number = 1; // +1\na += 1; // +1\na *= 2; // +1\n// \u5faa\u73af n \u6b21\nfor(let i = 0; i &lt; n; i++){ // +1\uff08\u6bcf\u8f6e\u90fd\u6267\u884c i ++\uff09\nconsole.log(0); // +1\n}\n}\n</code></pre> <pre><code>void algorithm(int n) {\nint a = 1;  // +1\na = a + 1;  // +1\na = a * 2;  // +1\n// \u5faa\u73af n \u6b21\nfor (int i = 0; i &lt; n; i++) {   // +1\uff08\u6bcf\u8f6e\u90fd\u6267\u884c i ++\uff09\nprintf(\"%d\", 0);            // +1\n}\n}  </code></pre> <pre><code>void algorithm(int n)\n{\nint a = 1;  // +1\na = a + 1;  // +1\na = a * 2;  // +1\n// \u5faa\u73af n \u6b21\nfor (int i = 0; i &lt; n; i++) // +1\uff08\u6bcf\u8f6e\u90fd\u6267\u884c i ++\uff09\n{\nConsole.WriteLine(0);   // +1\n}\n}\n</code></pre> <pre><code>func algorithm(n: Int) {\nvar a = 1 // +1\na = a + 1 // +1\na = a * 2 // +1\n// \u5faa\u73af n \u6b21\nfor _ in 0 ..&lt; n { // +1\nprint(0) // +1\n}\n}\n</code></pre> <pre><code>\n</code></pre> <pre><code>void algorithm(int n) {\nint a = 1; // +1\na = a + 1; // +1\na = a * 2; // +1\n// \u5faa\u73af n \u6b21\nfor (int i = 0; i &lt; n; i++) { // +1\uff08\u6bcf\u8f6e\u90fd\u6267\u884c i ++\uff09\nprint(0); // +1\n}\n}\n</code></pre> <p>\\(T(n)\\) \u662f\u4e00\u6b21\u51fd\u6570\uff0c\u8bf4\u660e\u65f6\u95f4\u589e\u957f\u8d8b\u52bf\u662f\u7ebf\u6027\u7684\uff0c\u56e0\u6b64\u53ef\u4ee5\u5f97\u51fa\u65f6\u95f4\u590d\u6742\u5ea6\u662f\u7ebf\u6027\u9636\u3002</p> <p>\u6211\u4eec\u5c06\u7ebf\u6027\u9636\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u8bb0\u4e3a \\(O(n)\\) \uff0c\u8fd9\u4e2a\u6570\u5b66\u7b26\u53f7\u79f0\u4e3a\u300c\u5927 \\(O\\) \u8bb0\u53f7 Big-\\(O\\) Notation\u300d\uff0c\u8868\u793a\u51fd\u6570 \\(T(n)\\) \u7684\u300c\u6e10\u8fd1\u4e0a\u754c Asymptotic Upper Bound\u300d\u3002</p> <p>\u63a8\u7b97\u65f6\u95f4\u590d\u6742\u5ea6\u672c\u8d28\u4e0a\u662f\u8ba1\u7b97\u201c\u64cd\u4f5c\u6570\u91cf\u51fd\u6570 \\(T(n)\\)\u201d\u7684\u6e10\u8fd1\u4e0a\u754c\u3002\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u6765\u770b\u51fd\u6570\u6e10\u8fd1\u4e0a\u754c\u7684\u6570\u5b66\u5b9a\u4e49\u3002</p> <p>\u51fd\u6570\u6e10\u8fd1\u4e0a\u754c</p> <p>\u82e5\u5b58\u5728\u6b63\u5b9e\u6570 \\(c\\) \u548c\u5b9e\u6570 \\(n_0\\) \uff0c\u4f7f\u5f97\u5bf9\u4e8e\u6240\u6709\u7684 \\(n &gt; n_0\\) \uff0c\u5747\u6709 $$ T(n) \\leq c \\cdot f(n) $$ \u5219\u53ef\u8ba4\u4e3a \\(f(n)\\) \u7ed9\u51fa\u4e86 \\(T(n)\\) \u7684\u4e00\u4e2a\u6e10\u8fd1\u4e0a\u754c\uff0c\u8bb0\u4e3a $$ T(n) = O(f(n)) $$</p> <p></p> <p> Fig. \u51fd\u6570\u7684\u6e10\u8fd1\u4e0a\u754c </p> <p>\u4ece\u672c\u8d28\u4e0a\u8bb2\uff0c\u8ba1\u7b97\u6e10\u8fd1\u4e0a\u754c\u5c31\u662f\u5bfb\u627e\u4e00\u4e2a\u51fd\u6570 \\(f(n)\\) \uff0c\u4f7f\u5f97\u5f53 \\(n\\) \u8d8b\u5411\u4e8e\u65e0\u7a77\u5927\u65f6\uff0c\\(T(n)\\) \u548c \\(f(n)\\) \u5904\u4e8e\u76f8\u540c\u7684\u589e\u957f\u7ea7\u522b\uff0c\u4ec5\u76f8\u5dee\u4e00\u4e2a\u5e38\u6570\u9879 \\(c\\) \u7684\u500d\u6570\u3002</p>"},{"location":"chapter_computational_complexity/time_complexity/#224","title":"2.2.4. \u00a0 \u63a8\u7b97\u65b9\u6cd5","text":"<p>\u6e10\u8fd1\u4e0a\u754c\u7684\u6570\u5b66\u5473\u513f\u6709\u70b9\u91cd\uff0c\u5982\u679c\u4f60\u611f\u89c9\u6ca1\u6709\u5b8c\u5168\u7406\u89e3\uff0c\u4e5f\u65e0\u9700\u62c5\u5fc3\u3002\u56e0\u4e3a\u5728\u5b9e\u9645\u4f7f\u7528\u4e2d\uff0c\u6211\u4eec\u53ea\u9700\u8981\u638c\u63e1\u63a8\u7b97\u65b9\u6cd5\uff0c\u6570\u5b66\u610f\u4e49\u53ef\u4ee5\u9010\u6e10\u9886\u609f\u3002</p> <p>\u6839\u636e\u5b9a\u4e49\uff0c\u786e\u5b9a \\(f(n)\\) \u4e4b\u540e\uff0c\u6211\u4eec\u4fbf\u53ef\u5f97\u5230\u65f6\u95f4\u590d\u6742\u5ea6 \\(O(f(n))\\) \u3002\u90a3\u4e48\u5982\u4f55\u786e\u5b9a\u6e10\u8fd1\u4e0a\u754c \\(f(n)\\) \u5462\uff1f\u603b\u4f53\u5206\u4e3a\u4e24\u6b65\uff1a\u9996\u5148\u7edf\u8ba1\u64cd\u4f5c\u6570\u91cf\uff0c\u7136\u540e\u5224\u65ad\u6e10\u8fd1\u4e0a\u754c\u3002</p>"},{"location":"chapter_computational_complexity/time_complexity/#_1","title":"\u7b2c\u4e00\u6b65\uff1a\u7edf\u8ba1\u64cd\u4f5c\u6570\u91cf","text":"<p>\u9488\u5bf9\u4ee3\u7801\uff0c\u9010\u884c\u4ece\u4e0a\u5230\u4e0b\u8ba1\u7b97\u5373\u53ef\u3002\u7136\u800c\uff0c\u7531\u4e8e\u4e0a\u8ff0 \\(c \\cdot f(n)\\) \u4e2d\u7684\u5e38\u6570\u9879 \\(c\\) \u53ef\u4ee5\u53d6\u4efb\u610f\u5927\u5c0f\uff0c\u56e0\u6b64\u64cd\u4f5c\u6570\u91cf \\(T(n)\\) \u4e2d\u7684\u5404\u79cd\u7cfb\u6570\u3001\u5e38\u6570\u9879\u90fd\u53ef\u4ee5\u88ab\u5ffd\u7565\u3002\u6839\u636e\u6b64\u539f\u5219\uff0c\u53ef\u4ee5\u603b\u7ed3\u51fa\u4ee5\u4e0b\u8ba1\u6570\u7b80\u5316\u6280\u5de7\uff1a</p> <ol> <li>\u5ffd\u7565\u4e0e \\(n\\) \u65e0\u5173\u7684\u64cd\u4f5c\u3002\u56e0\u4e3a\u5b83\u4eec\u90fd\u662f \\(T(n)\\) \u4e2d\u7684\u5e38\u6570\u9879\uff0c\u5bf9\u65f6\u95f4\u590d\u6742\u5ea6\u4e0d\u4ea7\u751f\u5f71\u54cd\u3002</li> <li>\u7701\u7565\u6240\u6709\u7cfb\u6570\u3002\u4f8b\u5982\uff0c\u5faa\u73af \\(2n\\) \u6b21\u3001\\(5n + 1\\) \u6b21\u7b49\uff0c\u90fd\u53ef\u4ee5\u7b80\u5316\u8bb0\u4e3a \\(n\\) \u6b21\uff0c\u56e0\u4e3a \\(n\\) \u524d\u9762\u7684\u7cfb\u6570\u5bf9\u65f6\u95f4\u590d\u6742\u5ea6\u6ca1\u6709\u5f71\u54cd\u3002</li> <li>\u5faa\u73af\u5d4c\u5957\u65f6\u4f7f\u7528\u4e58\u6cd5\u3002\u603b\u64cd\u4f5c\u6570\u91cf\u7b49\u4e8e\u5916\u5c42\u5faa\u73af\u548c\u5185\u5c42\u5faa\u73af\u64cd\u4f5c\u6570\u91cf\u4e4b\u79ef\uff0c\u6bcf\u4e00\u5c42\u5faa\u73af\u4f9d\u7136\u53ef\u4ee5\u5206\u522b\u5957\u7528\u4e0a\u8ff0 <code>1.</code> \u548c <code>2.</code> \u6280\u5de7\u3002</li> </ol> <p>\u4ee5\u4e0b\u793a\u4f8b\u5c55\u793a\u4e86\u4f7f\u7528\u4e0a\u8ff0\u6280\u5de7\u524d\u3001\u540e\u7684\u7edf\u8ba1\u7ed3\u679c\u3002</p> \\[ \\begin{aligned} T(n) &amp; = 2n(n + 1) + (5n + 1) + 2 &amp; \\text{\u5b8c\u6574\u7edf\u8ba1 (-.-|||)} \\newline &amp; = 2n^2 + 7n + 3 \\newline T(n) &amp; = n^2 + n &amp; \\text{\u5077\u61d2\u7edf\u8ba1 (o.O)} \\end{aligned} \\] <p>\u6700\u7ec8\uff0c\u4e24\u8005\u90fd\u80fd\u63a8\u51fa\u76f8\u540c\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u7ed3\u679c\uff0c\u5373 \\(O(n^2)\\) \u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart <pre><code>void algorithm(int n) {\nint a = 1;  // +0\uff08\u6280\u5de7 1\uff09\na = a + n;  // +0\uff08\u6280\u5de7 1\uff09\n// +n\uff08\u6280\u5de7 2\uff09\nfor (int i = 0; i &lt; 5 * n + 1; i++) {\nSystem.out.println(0);\n}\n// +n*n\uff08\u6280\u5de7 3\uff09\nfor (int i = 0; i &lt; 2 * n; i++) {\nfor (int j = 0; j &lt; n + 1; j++) {\nSystem.out.println(0);\n}\n}\n}\n</code></pre> <pre><code>void algorithm(int n) {\nint a = 1;  // +0\uff08\u6280\u5de7 1\uff09\na = a + n;  // +0\uff08\u6280\u5de7 1\uff09\n// +n\uff08\u6280\u5de7 2\uff09\nfor (int i = 0; i &lt; 5 * n + 1; i++) {\ncout &lt;&lt; 0 &lt;&lt; endl;\n}\n// +n*n\uff08\u6280\u5de7 3\uff09\nfor (int i = 0; i &lt; 2 * n; i++) {\nfor (int j = 0; j &lt; n + 1; j++) {\ncout &lt;&lt; 0 &lt;&lt; endl;\n}\n}\n}\n</code></pre> <pre><code>def algorithm(n: int) -&gt; None:\na = 1      # +0\uff08\u6280\u5de7 1\uff09\na = a + n  # +0\uff08\u6280\u5de7 1\uff09\n# +n\uff08\u6280\u5de7 2\uff09\nfor i in range(5 * n + 1):\nprint(0)\n# +n*n\uff08\u6280\u5de7 3\uff09\nfor i in range(2 * n):\nfor j in range(n + 1):\nprint(0)\n</code></pre> <pre><code>func algorithm(n int) {\na := 1     // +0\uff08\u6280\u5de7 1\uff09\na = a + n  // +0\uff08\u6280\u5de7 1\uff09\n// +n\uff08\u6280\u5de7 2\uff09\nfor i := 0; i &lt; 5 * n + 1; i++ {\nfmt.Println(0)\n}\n// +n*n\uff08\u6280\u5de7 3\uff09\nfor i := 0; i &lt; 2 * n; i++ {\nfor j := 0; j &lt; n + 1; j++ {\nfmt.Println(0)\n}\n}\n}\n</code></pre> <pre><code>function algorithm(n) {\nlet a = 1;  // +0\uff08\u6280\u5de7 1\uff09\na = a + n;  // +0\uff08\u6280\u5de7 1\uff09\n// +n\uff08\u6280\u5de7 2\uff09\nfor (let i = 0; i &lt; 5 * n + 1; i++) {\nconsole.log(0);\n}\n// +n*n\uff08\u6280\u5de7 3\uff09\nfor (let i = 0; i &lt; 2 * n; i++) {\nfor (let j = 0; j &lt; n + 1; j++) {\nconsole.log(0);\n}\n}\n}\n</code></pre> <pre><code>function algorithm(n: number): void {\nlet a = 1;  // +0\uff08\u6280\u5de7 1\uff09\na = a + n;  // +0\uff08\u6280\u5de7 1\uff09\n// +n\uff08\u6280\u5de7 2\uff09\nfor (let i = 0; i &lt; 5 * n + 1; i++) {\nconsole.log(0);\n}\n// +n*n\uff08\u6280\u5de7 3\uff09\nfor (let i = 0; i &lt; 2 * n; i++) {\nfor (let j = 0; j &lt; n + 1; j++) {\nconsole.log(0);\n}\n}\n}\n</code></pre> <pre><code>void algorithm(int n) {\nint a = 1;  // +0\uff08\u6280\u5de7 1\uff09\na = a + n;  // +0\uff08\u6280\u5de7 1\uff09\n// +n\uff08\u6280\u5de7 2\uff09\nfor (int i = 0; i &lt; 5 * n + 1; i++) {\nprintf(\"%d\", 0);\n}\n// +n*n\uff08\u6280\u5de7 3\uff09\nfor (int i = 0; i &lt; 2 * n; i++) {\nfor (int j = 0; j &lt; n + 1; j++) {\nprintf(\"%d\", 0);\n}\n}\n}\n</code></pre> <pre><code>void algorithm(int n)\n{\nint a = 1;  // +0\uff08\u6280\u5de7 1\uff09\na = a + n;  // +0\uff08\u6280\u5de7 1\uff09\n// +n\uff08\u6280\u5de7 2\uff09\nfor (int i = 0; i &lt; 5 * n + 1; i++)\n{\nConsole.WriteLine(0);\n}\n// +n*n\uff08\u6280\u5de7 3\uff09\nfor (int i = 0; i &lt; 2 * n; i++)\n{\nfor (int j = 0; j &lt; n + 1; j++)\n{\nConsole.WriteLine(0);\n}\n}\n}\n</code></pre> <pre><code>func algorithm(n: Int) {\nvar a = 1 // +0\uff08\u6280\u5de7 1\uff09\na = a + n // +0\uff08\u6280\u5de7 1\uff09\n// +n\uff08\u6280\u5de7 2\uff09\nfor _ in 0 ..&lt; (5 * n + 1) {\nprint(0)\n}\n// +n*n\uff08\u6280\u5de7 3\uff09\nfor _ in 0 ..&lt; (2 * n) {\nfor _ in 0 ..&lt; (n + 1) {\nprint(0)\n}\n}\n}\n</code></pre> <pre><code>\n</code></pre> <pre><code>void algorithm(int n) {\nint a = 1; // +0\uff08\u6280\u5de7 1\uff09\na = a + n; // +0\uff08\u6280\u5de7 1\uff09\n// +n\uff08\u6280\u5de7 2\uff09\nfor (int i = 0; i &lt; 5 * n + 1; i++) {\nprint(0);\n}\n// +n*n\uff08\u6280\u5de7 3\uff09\nfor (int i = 0; i &lt; 2 * n; i++) {\nfor (int j = 0; j &lt; n + 1; j++) {\nprint(0);\n}\n}\n}\n</code></pre>"},{"location":"chapter_computational_complexity/time_complexity/#_2","title":"\u7b2c\u4e8c\u6b65\uff1a\u5224\u65ad\u6e10\u8fd1\u4e0a\u754c","text":"<p>\u65f6\u95f4\u590d\u6742\u5ea6\u7531\u591a\u9879\u5f0f \\(T(n)\\) \u4e2d\u6700\u9ad8\u9636\u7684\u9879\u6765\u51b3\u5b9a\u3002\u8fd9\u662f\u56e0\u4e3a\u5728 \\(n\\) \u8d8b\u4e8e\u65e0\u7a77\u5927\u65f6\uff0c\u6700\u9ad8\u9636\u7684\u9879\u5c06\u53d1\u6325\u4e3b\u5bfc\u4f5c\u7528\uff0c\u5176\u4ed6\u9879\u7684\u5f71\u54cd\u90fd\u53ef\u4ee5\u88ab\u5ffd\u7565\u3002</p> <p>\u4ee5\u4e0b\u8868\u683c\u5c55\u793a\u4e86\u4e00\u4e9b\u4f8b\u5b50\uff0c\u5176\u4e2d\u4e00\u4e9b\u5938\u5f20\u7684\u503c\u662f\u4e3a\u4e86\u5f3a\u8c03\u201c\u7cfb\u6570\u65e0\u6cd5\u64bc\u52a8\u9636\u6570\u201d\u8fd9\u4e00\u7ed3\u8bba\u3002\u5f53 \\(n\\) \u8d8b\u4e8e\u65e0\u7a77\u5927\u65f6\uff0c\u8fd9\u4e9b\u5e38\u6570\u53d8\u5f97\u65e0\u8db3\u8f7b\u91cd\u3002</p> \u64cd\u4f5c\u6570\u91cf \\(T(n)\\) \u65f6\u95f4\u590d\u6742\u5ea6 \\(O(f(n))\\) \\(100000\\) \\(O(1)\\) \\(3n + 2\\) \\(O(n)\\) \\(2n^2 + 3n + 2\\) \\(O(n^2)\\) \\(n^3 + 10000n^2\\) \\(O(n^3)\\) \\(2^n + 10000n^{10000}\\) \\(O(2^n)\\)"},{"location":"chapter_computational_complexity/time_complexity/#225","title":"2.2.5. \u00a0 \u5e38\u89c1\u7c7b\u578b","text":"<p>\u8bbe\u8f93\u5165\u6570\u636e\u5927\u5c0f\u4e3a \\(n\\) \uff0c\u5e38\u89c1\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u7c7b\u578b\u5305\u62ec\uff08\u6309\u7167\u4ece\u4f4e\u5230\u9ad8\u7684\u987a\u5e8f\u6392\u5217\uff09\uff1a</p> \\[ \\begin{aligned} O(1) &lt; O(\\log n) &lt; O(n) &lt; O(n \\log n) &lt; O(n^2) &lt; O(2^n) &lt; O(n!) \\newline \\text{\u5e38\u6570\u9636} &lt; \\text{\u5bf9\u6570\u9636} &lt; \\text{\u7ebf\u6027\u9636} &lt; \\text{\u7ebf\u6027\u5bf9\u6570\u9636} &lt; \\text{\u5e73\u65b9\u9636} &lt; \\text{\u6307\u6570\u9636} &lt; \\text{\u9636\u4e58\u9636} \\end{aligned} \\] <p></p> <p> Fig. \u65f6\u95f4\u590d\u6742\u5ea6\u7684\u5e38\u89c1\u7c7b\u578b </p> <p>Tip</p> <p>\u90e8\u5206\u793a\u4f8b\u4ee3\u7801\u9700\u8981\u4e00\u4e9b\u9884\u5907\u77e5\u8bc6\uff0c\u5305\u62ec\u6570\u7ec4\u3001\u9012\u5f52\u7b97\u6cd5\u7b49\u3002\u5982\u679c\u9047\u5230\u4e0d\u7406\u89e3\u7684\u90e8\u5206\uff0c\u8bf7\u4e0d\u8981\u62c5\u5fc3\uff0c\u53ef\u4ee5\u5728\u5b66\u4e60\u5b8c\u540e\u9762\u7ae0\u8282\u540e\u518d\u56de\u987e\u3002\u73b0\u9636\u6bb5\uff0c\u8bf7\u5148\u4e13\u6ce8\u4e8e\u7406\u89e3\u65f6\u95f4\u590d\u6742\u5ea6\u7684\u542b\u4e49\u548c\u63a8\u7b97\u65b9\u6cd5\u3002</p>"},{"location":"chapter_computational_complexity/time_complexity/#o1","title":"\u5e38\u6570\u9636 \\(O(1)\\)","text":"<p>\u5e38\u6570\u9636\u7684\u64cd\u4f5c\u6570\u91cf\u4e0e\u8f93\u5165\u6570\u636e\u5927\u5c0f \\(n\\) \u65e0\u5173\uff0c\u5373\u4e0d\u968f\u7740 \\(n\\) \u7684\u53d8\u5316\u800c\u53d8\u5316\u3002</p> <p>\u5bf9\u4e8e\u4ee5\u4e0b\u7b97\u6cd5\uff0c\u5c3d\u7ba1\u64cd\u4f5c\u6570\u91cf <code>size</code> \u53ef\u80fd\u5f88\u5927\uff0c\u4f46\u7531\u4e8e\u5176\u4e0e\u6570\u636e\u5927\u5c0f \\(n\\) \u65e0\u5173\uff0c\u56e0\u6b64\u65f6\u95f4\u590d\u6742\u5ea6\u4ecd\u4e3a \\(O(1)\\) \u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart time_complexity.java<pre><code>/* \u5e38\u6570\u9636 */\nint constant(int n) {\nint count = 0;\nint size = 100000;\nfor (int i = 0; i &lt; size; i++)\ncount++;\nreturn count;\n}\n</code></pre> time_complexity.cpp<pre><code>/* \u5e38\u6570\u9636 */\nint constant(int n) {\nint count = 0;\nint size = 100000;\nfor (int i = 0; i &lt; size; i++)\ncount++;\nreturn count;\n}\n</code></pre> time_complexity.py<pre><code>def constant(n: int) -&gt; int:\n\"\"\"\u5e38\u6570\u9636\"\"\"\ncount = 0\nsize = 100000\nfor _ in range(size):\ncount += 1\nreturn count\n</code></pre> time_complexity.go<pre><code>/* \u5e38\u6570\u9636 */\nfunc constant(n int) int {\ncount := 0\nsize := 100000\nfor i := 0; i &lt; size; i++ {\ncount++\n}\nreturn count\n}\n</code></pre> time_complexity.js<pre><code>/* \u5e38\u6570\u9636 */\nfunction constant(n) {\nlet count = 0;\nconst size = 100000;\nfor (let i = 0; i &lt; size; i++) count++;\nreturn count;\n}\n</code></pre> time_complexity.ts<pre><code>/* \u5e38\u6570\u9636 */\nfunction constant(n: number): number {\nlet count = 0;\nconst size = 100000;\nfor (let i = 0; i &lt; size; i++) count++;\nreturn count;\n}\n</code></pre> time_complexity.c<pre><code>/* \u5e38\u6570\u9636 */\nint constant(int n) {\nint count = 0;\nint size = 100000;\nint i = 0;\nfor (int i = 0; i &lt; size; i++) {\ncount++;\n}\nreturn count;\n}\n</code></pre> time_complexity.cs<pre><code>/* \u5e38\u6570\u9636 */\nint constant(int n) {\nint count = 0;\nint size = 100000;\nfor (int i = 0; i &lt; size; i++)\ncount++;\nreturn count;\n}\n</code></pre> time_complexity.swift<pre><code>/* \u5e38\u6570\u9636 */\nfunc constant(n: Int) -&gt; Int {\nvar count = 0\nlet size = 100_000\nfor _ in 0 ..&lt; size {\ncount += 1\n}\nreturn count\n}\n</code></pre> time_complexity.zig<pre><code>// \u5e38\u6570\u9636\nfn constant(n: i32) i32 {\n_ = n;\nvar count: i32 = 0;\nconst size: i32 = 100_000;\nvar i: i32 = 0;\nwhile(i&lt;size) : (i += 1) {\ncount += 1;\n}\nreturn count;\n}\n</code></pre> time_complexity.dart<pre><code>/* \u5e38\u6570\u9636 */\nint constant(int n) {\nint count = 0;\nint size = 100000;\nfor (var i = 0; i &lt; size; i++) {\ncount++;\n}\nreturn count;\n}\n</code></pre>"},{"location":"chapter_computational_complexity/time_complexity/#on","title":"\u7ebf\u6027\u9636 \\(O(n)\\)","text":"<p>\u7ebf\u6027\u9636\u7684\u64cd\u4f5c\u6570\u91cf\u76f8\u5bf9\u4e8e\u8f93\u5165\u6570\u636e\u5927\u5c0f\u4ee5\u7ebf\u6027\u7ea7\u522b\u589e\u957f\u3002\u7ebf\u6027\u9636\u901a\u5e38\u51fa\u73b0\u5728\u5355\u5c42\u5faa\u73af\u4e2d\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart time_complexity.java<pre><code>/* \u7ebf\u6027\u9636 */\nint linear(int n) {\nint count = 0;\nfor (int i = 0; i &lt; n; i++)\ncount++;\nreturn count;\n}\n</code></pre> time_complexity.cpp<pre><code>/* \u7ebf\u6027\u9636 */\nint linear(int n) {\nint count = 0;\nfor (int i = 0; i &lt; n; i++)\ncount++;\nreturn count;\n}\n</code></pre> time_complexity.py<pre><code>def linear(n: int) -&gt; int:\n\"\"\"\u7ebf\u6027\u9636\"\"\"\ncount = 0\nfor _ in range(n):\ncount += 1\nreturn count\n</code></pre> time_complexity.go<pre><code>/* \u7ebf\u6027\u9636 */\nfunc linear(n int) int {\ncount := 0\nfor i := 0; i &lt; n; i++ {\ncount++\n}\nreturn count\n}\n</code></pre> time_complexity.js<pre><code>/* \u7ebf\u6027\u9636 */\nfunction linear(n) {\nlet count = 0;\nfor (let i = 0; i &lt; n; i++) count++;\nreturn count;\n}\n</code></pre> time_complexity.ts<pre><code>/* \u7ebf\u6027\u9636 */\nfunction linear(n: number): number {\nlet count = 0;\nfor (let i = 0; i &lt; n; i++) count++;\nreturn count;\n}\n</code></pre> time_complexity.c<pre><code>/* \u7ebf\u6027\u9636 */\nint linear(int n) {\nint count = 0;\nfor (int i = 0; i &lt; n; i++) {\ncount++;\n}\nreturn count;\n}\n</code></pre> time_complexity.cs<pre><code>/* \u7ebf\u6027\u9636 */\nint linear(int n) {\nint count = 0;\nfor (int i = 0; i &lt; n; i++)\ncount++;\nreturn count;\n}\n</code></pre> time_complexity.swift<pre><code>/* \u7ebf\u6027\u9636 */\nfunc linear(n: Int) -&gt; Int {\nvar count = 0\nfor _ in 0 ..&lt; n {\ncount += 1\n}\nreturn count\n}\n</code></pre> time_complexity.zig<pre><code>// \u7ebf\u6027\u9636\nfn linear(n: i32) i32 {\nvar count: i32 = 0;\nvar i: i32 = 0;\nwhile (i &lt; n) : (i += 1) {\ncount += 1;\n}\nreturn count;\n}\n</code></pre> time_complexity.dart<pre><code>/* \u7ebf\u6027\u9636 */\nint linear(int n) {\nint count = 0;\nfor (var i = 0; i &lt; n; i++) {\ncount++;\n}\nreturn count;\n}\n</code></pre> <p>\u904d\u5386\u6570\u7ec4\u548c\u904d\u5386\u94fe\u8868\u7b49\u64cd\u4f5c\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u5747\u4e3a \\(O(n)\\) \uff0c\u5176\u4e2d \\(n\\) \u4e3a\u6570\u7ec4\u6216\u94fe\u8868\u7684\u957f\u5ea6\u3002</p> <p>\u5982\u4f55\u786e\u5b9a\u8f93\u5165\u6570\u636e\u5927\u5c0f \\(n\\) \uff1f</p> <p>\u6570\u636e\u5927\u5c0f \\(n\\) \u9700\u6839\u636e\u8f93\u5165\u6570\u636e\u7684\u7c7b\u578b\u6765\u5177\u4f53\u786e\u5b9a\u3002\u4f8b\u5982\uff0c\u5728\u4e0a\u8ff0\u793a\u4f8b\u4e2d\uff0c\u6211\u4eec\u76f4\u63a5\u5c06 \\(n\\) \u89c6\u4e3a\u8f93\u5165\u6570\u636e\u5927\u5c0f\uff1b\u5728\u4e0b\u9762\u904d\u5386\u6570\u7ec4\u7684\u793a\u4f8b\u4e2d\uff0c\u6570\u636e\u5927\u5c0f \\(n\\) \u4e3a\u6570\u7ec4\u7684\u957f\u5ea6\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart time_complexity.java<pre><code>/* \u7ebf\u6027\u9636\uff08\u904d\u5386\u6570\u7ec4\uff09 */\nint arrayTraversal(int[] nums) {\nint count = 0;\n// \u5faa\u73af\u6b21\u6570\u4e0e\u6570\u7ec4\u957f\u5ea6\u6210\u6b63\u6bd4\nfor (int num : nums) {\ncount++;\n}\nreturn count;\n}\n</code></pre> time_complexity.cpp<pre><code>/* \u7ebf\u6027\u9636\uff08\u904d\u5386\u6570\u7ec4\uff09 */\nint arrayTraversal(vector&lt;int&gt; &amp;nums) {\nint count = 0;\n// \u5faa\u73af\u6b21\u6570\u4e0e\u6570\u7ec4\u957f\u5ea6\u6210\u6b63\u6bd4\nfor (int num : nums) {\ncount++;\n}\nreturn count;\n}\n</code></pre> time_complexity.py<pre><code>def array_traversal(nums: list[int]) -&gt; int:\n\"\"\"\u7ebf\u6027\u9636\uff08\u904d\u5386\u6570\u7ec4\uff09\"\"\"\ncount = 0\n# \u5faa\u73af\u6b21\u6570\u4e0e\u6570\u7ec4\u957f\u5ea6\u6210\u6b63\u6bd4\nfor num in nums:\ncount += 1\nreturn count\n</code></pre> time_complexity.go<pre><code>/* \u7ebf\u6027\u9636\uff08\u904d\u5386\u6570\u7ec4\uff09 */\nfunc arrayTraversal(nums []int) int {\ncount := 0\n// \u5faa\u73af\u6b21\u6570\u4e0e\u6570\u7ec4\u957f\u5ea6\u6210\u6b63\u6bd4\nfor range nums {\ncount++\n}\nreturn count\n}\n</code></pre> time_complexity.js<pre><code>/* \u7ebf\u6027\u9636\uff08\u904d\u5386\u6570\u7ec4\uff09 */\nfunction arrayTraversal(nums) {\nlet count = 0;\n// \u5faa\u73af\u6b21\u6570\u4e0e\u6570\u7ec4\u957f\u5ea6\u6210\u6b63\u6bd4\nfor (let i = 0; i &lt; nums.length; i++) {\ncount++;\n}\nreturn count;\n}\n</code></pre> time_complexity.ts<pre><code>/* \u7ebf\u6027\u9636\uff08\u904d\u5386\u6570\u7ec4\uff09 */\nfunction arrayTraversal(nums: number[]): number {\nlet count = 0;\n// \u5faa\u73af\u6b21\u6570\u4e0e\u6570\u7ec4\u957f\u5ea6\u6210\u6b63\u6bd4\nfor (let i = 0; i &lt; nums.length; i++) {\ncount++;\n}\nreturn count;\n}\n</code></pre> time_complexity.c<pre><code>/* \u7ebf\u6027\u9636\uff08\u904d\u5386\u6570\u7ec4\uff09 */\nint arrayTraversal(int *nums, int n) {\nint count = 0;\n// \u5faa\u73af\u6b21\u6570\u4e0e\u6570\u7ec4\u957f\u5ea6\u6210\u6b63\u6bd4\nfor (int i = 0; i &lt; n; i++) {\ncount++;\n}\nreturn count;\n}\n</code></pre> time_complexity.cs<pre><code>/* \u7ebf\u6027\u9636\uff08\u904d\u5386\u6570\u7ec4\uff09 */\nint arrayTraversal(int[] nums) {\nint count = 0;\n// \u5faa\u73af\u6b21\u6570\u4e0e\u6570\u7ec4\u957f\u5ea6\u6210\u6b63\u6bd4\nforeach (int num in nums) {\ncount++;\n}\nreturn count;\n}\n</code></pre> time_complexity.swift<pre><code>/* \u7ebf\u6027\u9636\uff08\u904d\u5386\u6570\u7ec4\uff09 */\nfunc arrayTraversal(nums: [Int]) -&gt; Int {\nvar count = 0\n// \u5faa\u73af\u6b21\u6570\u4e0e\u6570\u7ec4\u957f\u5ea6\u6210\u6b63\u6bd4\nfor _ in nums {\ncount += 1\n}\nreturn count\n}\n</code></pre> time_complexity.zig<pre><code>// \u7ebf\u6027\u9636\uff08\u904d\u5386\u6570\u7ec4\uff09\nfn arrayTraversal(nums: []i32) i32 {\nvar count: i32 = 0;\n// \u5faa\u73af\u6b21\u6570\u4e0e\u6570\u7ec4\u957f\u5ea6\u6210\u6b63\u6bd4\nfor (nums) |_| {\ncount += 1;\n}\nreturn count;\n}\n</code></pre> time_complexity.dart<pre><code>/* \u7ebf\u6027\u9636\uff08\u904d\u5386\u6570\u7ec4\uff09 */\nint arrayTraversal(List&lt;int&gt; nums) {\nint count = 0;\n// \u5faa\u73af\u6b21\u6570\u4e0e\u6570\u7ec4\u957f\u5ea6\u6210\u6b63\u6bd4\nfor (var num in nums) {\ncount++;\n}\nreturn count;\n}\n</code></pre>"},{"location":"chapter_computational_complexity/time_complexity/#on2","title":"\u5e73\u65b9\u9636 \\(O(n^2)\\)","text":"<p>\u5e73\u65b9\u9636\u7684\u64cd\u4f5c\u6570\u91cf\u76f8\u5bf9\u4e8e\u8f93\u5165\u6570\u636e\u5927\u5c0f\u4ee5\u5e73\u65b9\u7ea7\u522b\u589e\u957f\u3002\u5e73\u65b9\u9636\u901a\u5e38\u51fa\u73b0\u5728\u5d4c\u5957\u5faa\u73af\u4e2d\uff0c\u5916\u5c42\u5faa\u73af\u548c\u5185\u5c42\u5faa\u73af\u90fd\u4e3a \\(O(n)\\) \uff0c\u56e0\u6b64\u603b\u4f53\u4e3a \\(O(n^2)\\) \u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart time_complexity.java<pre><code>/* \u5e73\u65b9\u9636 */\nint quadratic(int n) {\nint count = 0;\n// \u5faa\u73af\u6b21\u6570\u4e0e\u6570\u7ec4\u957f\u5ea6\u6210\u5e73\u65b9\u5173\u7cfb\nfor (int i = 0; i &lt; n; i++) {\nfor (int j = 0; j &lt; n; j++) {\ncount++;\n}\n}\nreturn count;\n}\n</code></pre> time_complexity.cpp<pre><code>/* \u5e73\u65b9\u9636 */\nint quadratic(int n) {\nint count = 0;\n// \u5faa\u73af\u6b21\u6570\u4e0e\u6570\u7ec4\u957f\u5ea6\u6210\u5e73\u65b9\u5173\u7cfb\nfor (int i = 0; i &lt; n; i++) {\nfor (int j = 0; j &lt; n; j++) {\ncount++;\n}\n}\nreturn count;\n}\n</code></pre> time_complexity.py<pre><code>def quadratic(n: int) -&gt; int:\n\"\"\"\u5e73\u65b9\u9636\"\"\"\ncount = 0\n# \u5faa\u73af\u6b21\u6570\u4e0e\u6570\u7ec4\u957f\u5ea6\u6210\u5e73\u65b9\u5173\u7cfb\nfor i in range(n):\nfor j in range(n):\ncount += 1\nreturn count\n</code></pre> time_complexity.go<pre><code>/* \u5e73\u65b9\u9636 */\nfunc quadratic(n int) int {\ncount := 0\n// \u5faa\u73af\u6b21\u6570\u4e0e\u6570\u7ec4\u957f\u5ea6\u6210\u5e73\u65b9\u5173\u7cfb\nfor i := 0; i &lt; n; i++ {\nfor j := 0; j &lt; n; j++ {\ncount++\n}\n}\nreturn count\n}\n</code></pre> time_complexity.js<pre><code>/* \u5e73\u65b9\u9636 */\nfunction quadratic(n) {\nlet count = 0;\n// \u5faa\u73af\u6b21\u6570\u4e0e\u6570\u7ec4\u957f\u5ea6\u6210\u5e73\u65b9\u5173\u7cfb\nfor (let i = 0; i &lt; n; i++) {\nfor (let j = 0; j &lt; n; j++) {\ncount++;\n}\n}\nreturn count;\n}\n</code></pre> time_complexity.ts<pre><code>/* \u5e73\u65b9\u9636 */\nfunction quadratic(n: number): number {\nlet count = 0;\n// \u5faa\u73af\u6b21\u6570\u4e0e\u6570\u7ec4\u957f\u5ea6\u6210\u5e73\u65b9\u5173\u7cfb\nfor (let i = 0; i &lt; n; i++) {\nfor (let j = 0; j &lt; n; j++) {\ncount++;\n}\n}\nreturn count;\n}\n</code></pre> time_complexity.c<pre><code>/* \u5e73\u65b9\u9636 */\nint quadratic(int n) {\nint count = 0;\n// \u5faa\u73af\u6b21\u6570\u4e0e\u6570\u7ec4\u957f\u5ea6\u6210\u5e73\u65b9\u5173\u7cfb\nfor (int i = 0; i &lt; n; i++) {\nfor (int j = 0; j &lt; n; j++) {\ncount++;\n}\n}\nreturn count;\n}\n</code></pre> time_complexity.cs<pre><code>/* \u5e73\u65b9\u9636 */\nint quadratic(int n) {\nint count = 0;\n// \u5faa\u73af\u6b21\u6570\u4e0e\u6570\u7ec4\u957f\u5ea6\u6210\u5e73\u65b9\u5173\u7cfb\nfor (int i = 0; i &lt; n; i++) {\nfor (int j = 0; j &lt; n; j++) {\ncount++;\n}\n}\nreturn count;\n}\n</code></pre> time_complexity.swift<pre><code>/* \u5e73\u65b9\u9636 */\nfunc quadratic(n: Int) -&gt; Int {\nvar count = 0\n// \u5faa\u73af\u6b21\u6570\u4e0e\u6570\u7ec4\u957f\u5ea6\u6210\u5e73\u65b9\u5173\u7cfb\nfor _ in 0 ..&lt; n {\nfor _ in 0 ..&lt; n {\ncount += 1\n}\n}\nreturn count\n}\n</code></pre> time_complexity.zig<pre><code>// \u5e73\u65b9\u9636\nfn quadratic(n: i32) i32 {\nvar count: i32 = 0;\nvar i: i32 = 0;\n// \u5faa\u73af\u6b21\u6570\u4e0e\u6570\u7ec4\u957f\u5ea6\u6210\u5e73\u65b9\u5173\u7cfb\nwhile (i &lt; n) : (i += 1) {\nvar j: i32 = 0;\nwhile (j &lt; n) : (j += 1) {\ncount += 1;\n}\n}\nreturn count;\n}\n</code></pre> time_complexity.dart<pre><code>/* \u5e73\u65b9\u9636 */\nint quadratic(int n) {\nint count = 0;\n// \u5faa\u73af\u6b21\u6570\u4e0e\u6570\u7ec4\u957f\u5ea6\u6210\u5e73\u65b9\u5173\u7cfb\nfor (int i = 0; i &lt; n; i++) {\nfor (int j = 0; j &lt; n; j++) {\ncount++;\n}\n}\nreturn count;\n}\n</code></pre> <p></p> <p> Fig. \u5e38\u6570\u9636\u3001\u7ebf\u6027\u9636\u3001\u5e73\u65b9\u9636\u7684\u65f6\u95f4\u590d\u6742\u5ea6 </p> <p>\u4ee5\u300c\u5192\u6ce1\u6392\u5e8f\u300d\u4e3a\u4f8b\uff0c\u5916\u5c42\u5faa\u73af\u6267\u884c \\(n - 1\\) \u6b21\uff0c\u5185\u5c42\u5faa\u73af\u6267\u884c \\(n-1, n-2, \\cdots, 2, 1\\) \u6b21\uff0c\u5e73\u5747\u4e3a \\(\\frac{n}{2}\\) \u6b21\uff0c\u56e0\u6b64\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(n^2)\\) \u3002</p> \\[ O((n - 1) \\frac{n}{2}) = O(n^2) \\] JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart time_complexity.java<pre><code>/* \u5e73\u65b9\u9636\uff08\u5192\u6ce1\u6392\u5e8f\uff09 */\nint bubbleSort(int[] nums) {\nint count = 0; // \u8ba1\u6570\u5668\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [0, i]\nfor (int i = nums.length - 1; i &gt; 0; i--) {\n// \u5185\u5faa\u73af\uff1a\u5c06\u672a\u6392\u5e8f\u533a\u95f4 [0, i] \u4e2d\u7684\u6700\u5927\u5143\u7d20\u4ea4\u6362\u81f3\u8be5\u533a\u95f4\u7684\u6700\u53f3\u7aef \nfor (int j = 0; j &lt; i; j++) {\nif (nums[j] &gt; nums[j + 1]) {\n// \u4ea4\u6362 nums[j] \u4e0e nums[j + 1]\nint tmp = nums[j];\nnums[j] = nums[j + 1];\nnums[j + 1] = tmp;\ncount += 3; // \u5143\u7d20\u4ea4\u6362\u5305\u542b 3 \u4e2a\u5355\u5143\u64cd\u4f5c\n}\n}\n}\nreturn count;\n}\n</code></pre> time_complexity.cpp<pre><code>/* \u5e73\u65b9\u9636\uff08\u5192\u6ce1\u6392\u5e8f\uff09 */\nint bubbleSort(vector&lt;int&gt; &amp;nums) {\nint count = 0; // \u8ba1\u6570\u5668\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [0, i]\nfor (int i = nums.size() - 1; i &gt; 0; i--) {\n// \u5185\u5faa\u73af\uff1a\u5c06\u672a\u6392\u5e8f\u533a\u95f4 [0, i] \u4e2d\u7684\u6700\u5927\u5143\u7d20\u4ea4\u6362\u81f3\u8be5\u533a\u95f4\u7684\u6700\u53f3\u7aef \nfor (int j = 0; j &lt; i; j++) {\nif (nums[j] &gt; nums[j + 1]) {\n// \u4ea4\u6362 nums[j] \u4e0e nums[j + 1]\nint tmp = nums[j];\nnums[j] = nums[j + 1];\nnums[j + 1] = tmp;\ncount += 3; // \u5143\u7d20\u4ea4\u6362\u5305\u542b 3 \u4e2a\u5355\u5143\u64cd\u4f5c\n}\n}\n}\nreturn count;\n}\n</code></pre> time_complexity.py<pre><code>def bubble_sort(nums: list[int]) -&gt; int:\n\"\"\"\u5e73\u65b9\u9636\uff08\u5192\u6ce1\u6392\u5e8f\uff09\"\"\"\ncount = 0  # \u8ba1\u6570\u5668\n# \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [0, i]\nfor i in range(len(nums) - 1, 0, -1):\n# \u5185\u5faa\u73af\uff1a\u5c06\u672a\u6392\u5e8f\u533a\u95f4 [0, i] \u4e2d\u7684\u6700\u5927\u5143\u7d20\u4ea4\u6362\u81f3\u8be5\u533a\u95f4\u7684\u6700\u53f3\u7aef \nfor j in range(i):\nif nums[j] &gt; nums[j + 1]:\n# \u4ea4\u6362 nums[j] \u4e0e nums[j + 1]\ntmp: int = nums[j]\nnums[j] = nums[j + 1]\nnums[j + 1] = tmp\ncount += 3  # \u5143\u7d20\u4ea4\u6362\u5305\u542b 3 \u4e2a\u5355\u5143\u64cd\u4f5c\nreturn count\n</code></pre> time_complexity.go<pre><code>/* \u5e73\u65b9\u9636\uff08\u5192\u6ce1\u6392\u5e8f\uff09 */\nfunc bubbleSort(nums []int) int {\ncount := 0 // \u8ba1\u6570\u5668\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [0, i]\nfor i := len(nums) - 1; i &gt; 0; i-- {\n// \u5185\u5faa\u73af\uff1a\u5c06\u672a\u6392\u5e8f\u533a\u95f4 [0, i] \u4e2d\u7684\u6700\u5927\u5143\u7d20\u4ea4\u6362\u81f3\u8be5\u533a\u95f4\u7684\u6700\u53f3\u7aef\nfor j := 0; j &lt; i; j++ {\nif nums[j] &gt; nums[j+1] {\n// \u4ea4\u6362 nums[j] \u4e0e nums[j + 1]\ntmp := nums[j]\nnums[j] = nums[j+1]\nnums[j+1] = tmp\ncount += 3 // \u5143\u7d20\u4ea4\u6362\u5305\u542b 3 \u4e2a\u5355\u5143\u64cd\u4f5c\n}\n}\n}\nreturn count\n}\n</code></pre> time_complexity.js<pre><code>/* \u5e73\u65b9\u9636\uff08\u5192\u6ce1\u6392\u5e8f\uff09 */\nfunction bubbleSort(nums) {\nlet count = 0; // \u8ba1\u6570\u5668\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [0, i]\nfor (let i = nums.length - 1; i &gt; 0; i--) {\n// \u5185\u5faa\u73af\uff1a\u5c06\u672a\u6392\u5e8f\u533a\u95f4 [0, i] \u4e2d\u7684\u6700\u5927\u5143\u7d20\u4ea4\u6362\u81f3\u8be5\u533a\u95f4\u7684\u6700\u53f3\u7aef \nfor (let j = 0; j &lt; i; j++) {\nif (nums[j] &gt; nums[j + 1]) {\n// \u4ea4\u6362 nums[j] \u4e0e nums[j + 1]\nlet tmp = nums[j];\nnums[j] = nums[j + 1];\nnums[j + 1] = tmp;\ncount += 3; // \u5143\u7d20\u4ea4\u6362\u5305\u542b 3 \u4e2a\u5355\u5143\u64cd\u4f5c\n}\n}\n}\nreturn count;\n}\n</code></pre> time_complexity.ts<pre><code>/* \u5e73\u65b9\u9636\uff08\u5192\u6ce1\u6392\u5e8f\uff09 */\nfunction bubbleSort(nums: number[]): number {\nlet count = 0; // \u8ba1\u6570\u5668\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [0, i]\nfor (let i = nums.length - 1; i &gt; 0; i--) {\n// \u5185\u5faa\u73af\uff1a\u5c06\u672a\u6392\u5e8f\u533a\u95f4 [0, i] \u4e2d\u7684\u6700\u5927\u5143\u7d20\u4ea4\u6362\u81f3\u8be5\u533a\u95f4\u7684\u6700\u53f3\u7aef \nfor (let j = 0; j &lt; i; j++) {\nif (nums[j] &gt; nums[j + 1]) {\n// \u4ea4\u6362 nums[j] \u4e0e nums[j + 1]\nlet tmp = nums[j];\nnums[j] = nums[j + 1];\nnums[j + 1] = tmp;\ncount += 3; // \u5143\u7d20\u4ea4\u6362\u5305\u542b 3 \u4e2a\u5355\u5143\u64cd\u4f5c\n}\n}\n}\nreturn count;\n}\n</code></pre> time_complexity.c<pre><code>/* \u5e73\u65b9\u9636\uff08\u5192\u6ce1\u6392\u5e8f\uff09 */\nint bubbleSort(int *nums, int n) {\nint count = 0; // \u8ba1\u6570\u5668\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [0, i]\nfor (int i = n - 1; i &gt; 0; i--) {\n// \u5185\u5faa\u73af\uff1a\u5c06\u672a\u6392\u5e8f\u533a\u95f4 [0, i] \u4e2d\u7684\u6700\u5927\u5143\u7d20\u4ea4\u6362\u81f3\u8be5\u533a\u95f4\u7684\u6700\u53f3\u7aef \nfor (int j = 0; j &lt; i; j++) {\nif (nums[j] &gt; nums[j + 1]) {\n// \u4ea4\u6362 nums[j] \u4e0e nums[j + 1]\nint tmp = nums[j];\nnums[j] = nums[j + 1];\nnums[j + 1] = tmp;\ncount += 3; // \u5143\u7d20\u4ea4\u6362\u5305\u542b 3 \u4e2a\u5355\u5143\u64cd\u4f5c\n}\n}\n}\nreturn count;\n}\n</code></pre> time_complexity.cs<pre><code>/* \u5e73\u65b9\u9636\uff08\u5192\u6ce1\u6392\u5e8f\uff09 */\nint bubbleSort(int[] nums) {\nint count = 0;  // \u8ba1\u6570\u5668\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [0, i]\nfor (int i = nums.Length - 1; i &gt; 0; i--) {\n// \u5185\u5faa\u73af\uff1a\u5c06\u672a\u6392\u5e8f\u533a\u95f4 [0, i] \u4e2d\u7684\u6700\u5927\u5143\u7d20\u4ea4\u6362\u81f3\u8be5\u533a\u95f4\u7684\u6700\u53f3\u7aef \nfor (int j = 0; j &lt; i; j++) {\nif (nums[j] &gt; nums[j + 1]) {\n// \u4ea4\u6362 nums[j] \u4e0e nums[j + 1]\nint tmp = nums[j];\nnums[j] = nums[j + 1];\nnums[j + 1] = tmp;\ncount += 3;  // \u5143\u7d20\u4ea4\u6362\u5305\u542b 3 \u4e2a\u5355\u5143\u64cd\u4f5c\n}\n}\n}\nreturn count;\n}\n</code></pre> time_complexity.swift<pre><code>/* \u5e73\u65b9\u9636\uff08\u5192\u6ce1\u6392\u5e8f\uff09 */\nfunc bubbleSort(nums: inout [Int]) -&gt; Int {\nvar count = 0 // \u8ba1\u6570\u5668\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [0, i]\nfor i in stride(from: nums.count - 1, to: 0, by: -1) {\n// \u5185\u5faa\u73af\uff1a\u5c06\u672a\u6392\u5e8f\u533a\u95f4 [0, i] \u4e2d\u7684\u6700\u5927\u5143\u7d20\u4ea4\u6362\u81f3\u8be5\u533a\u95f4\u7684\u6700\u53f3\u7aef \nfor j in 0 ..&lt; i {\nif nums[j] &gt; nums[j + 1] {\n// \u4ea4\u6362 nums[j] \u4e0e nums[j + 1]\nlet tmp = nums[j]\nnums[j] = nums[j + 1]\nnums[j + 1] = tmp\ncount += 3 // \u5143\u7d20\u4ea4\u6362\u5305\u542b 3 \u4e2a\u5355\u5143\u64cd\u4f5c\n}\n}\n}\nreturn count\n}\n</code></pre> time_complexity.zig<pre><code>// \u5e73\u65b9\u9636\uff08\u5192\u6ce1\u6392\u5e8f\uff09\nfn bubbleSort(nums: []i32) i32 {\nvar count: i32 = 0;  // \u8ba1\u6570\u5668 \n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [0, i]\nvar i: i32 = @intCast(i32, nums.len ) - 1;\nwhile (i &gt; 0) : (i -= 1) {\nvar j: usize = 0;\n// \u5185\u5faa\u73af\uff1a\u5c06\u672a\u6392\u5e8f\u533a\u95f4 [0, i] \u4e2d\u7684\u6700\u5927\u5143\u7d20\u4ea4\u6362\u81f3\u8be5\u533a\u95f4\u7684\u6700\u53f3\u7aef \nwhile (j &lt; i) : (j += 1) {\nif (nums[j] &gt; nums[j + 1]) {\n// \u4ea4\u6362 nums[j] \u4e0e nums[j + 1]\nvar tmp = nums[j];\nnums[j] = nums[j + 1];\nnums[j + 1] = tmp;\ncount += 3;  // \u5143\u7d20\u4ea4\u6362\u5305\u542b 3 \u4e2a\u5355\u5143\u64cd\u4f5c\n}\n}\n}\nreturn count;\n}\n</code></pre> time_complexity.dart<pre><code>/* \u5e73\u65b9\u9636\uff08\u5192\u6ce1\u6392\u5e8f\uff09 */\nint bubbleSort(List&lt;int&gt; nums) {\nint count = 0; // \u8ba1\u6570\u5668\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [0, i]\nfor (var i = nums.length - 1; i &gt; 0; i--) {\n// \u5185\u5faa\u73af\uff1a\u5c06\u672a\u6392\u5e8f\u533a\u95f4 [0, i] \u4e2d\u7684\u6700\u5927\u5143\u7d20\u4ea4\u6362\u81f3\u8be5\u533a\u95f4\u7684\u6700\u53f3\u7aef\nfor (var j = 0; j &lt; i; j++) {\nif (nums[j] &gt; nums[j + 1]) {\n// \u4ea4\u6362 nums[j] \u4e0e nums[j + 1]\nint tmp = nums[j];\nnums[j] = nums[j + 1];\nnums[j + 1] = tmp;\ncount += 3; // \u5143\u7d20\u4ea4\u6362\u5305\u542b 3 \u4e2a\u5355\u5143\u64cd\u4f5c\n}\n}\n}\nreturn count;\n}\n</code></pre>"},{"location":"chapter_computational_complexity/time_complexity/#o2n","title":"\u6307\u6570\u9636 \\(O(2^n)\\)","text":"<p>Note</p> <p>\u751f\u7269\u5b66\u7684\u201c\u7ec6\u80de\u5206\u88c2\u201d\u662f\u6307\u6570\u9636\u589e\u957f\u7684\u5178\u578b\u4f8b\u5b50\uff1a\u521d\u59cb\u72b6\u6001\u4e3a \\(1\\) \u4e2a\u7ec6\u80de\uff0c\u5206\u88c2\u4e00\u8f6e\u540e\u53d8\u4e3a \\(2\\) \u4e2a\uff0c\u5206\u88c2\u4e24\u8f6e\u540e\u53d8\u4e3a \\(4\\) \u4e2a\uff0c\u4ee5\u6b64\u7c7b\u63a8\uff0c\u5206\u88c2 \\(n\\) \u8f6e\u540e\u6709 \\(2^n\\) \u4e2a\u7ec6\u80de\u3002</p> <p>\u6307\u6570\u9636\u589e\u957f\u975e\u5e38\u8fc5\u901f\uff0c\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\u901a\u5e38\u662f\u4e0d\u53ef\u63a5\u53d7\u7684\u3002\u82e5\u4e00\u4e2a\u95ee\u9898\u4f7f\u7528\u300c\u66b4\u529b\u679a\u4e3e\u300d\u6c42\u89e3\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(2^n)\\) \uff0c\u90a3\u4e48\u901a\u5e38\u9700\u8981\u4f7f\u7528\u300c\u52a8\u6001\u89c4\u5212\u300d\u6216\u300c\u8d2a\u5fc3\u7b97\u6cd5\u300d\u7b49\u65b9\u6cd5\u6765\u89e3\u51b3\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart time_complexity.java<pre><code>/* \u6307\u6570\u9636\uff08\u5faa\u73af\u5b9e\u73b0\uff09 */\nint exponential(int n) {\nint count = 0, base = 1;\n// cell \u6bcf\u8f6e\u4e00\u5206\u4e3a\u4e8c\uff0c\u5f62\u6210\u6570\u5217 1, 2, 4, 8, ..., 2^(n-1)\nfor (int i = 0; i &lt; n; i++) {\nfor (int j = 0; j &lt; base; j++) {\ncount++;\n}\nbase *= 2;\n}\n// count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\nreturn count;\n}\n</code></pre> time_complexity.cpp<pre><code>/* \u6307\u6570\u9636\uff08\u5faa\u73af\u5b9e\u73b0\uff09 */\nint exponential(int n) {\nint count = 0, base = 1;\n// cell \u6bcf\u8f6e\u4e00\u5206\u4e3a\u4e8c\uff0c\u5f62\u6210\u6570\u5217 1, 2, 4, 8, ..., 2^(n-1)\nfor (int i = 0; i &lt; n; i++) {\nfor (int j = 0; j &lt; base; j++) {\ncount++;\n}\nbase *= 2;\n}\n// count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\nreturn count;\n}\n</code></pre> time_complexity.py<pre><code>def exponential(n: int) -&gt; int:\n\"\"\"\u6307\u6570\u9636\uff08\u5faa\u73af\u5b9e\u73b0\uff09\"\"\"\ncount = 0\nbase = 1\n# cell \u6bcf\u8f6e\u4e00\u5206\u4e3a\u4e8c\uff0c\u5f62\u6210\u6570\u5217 1, 2, 4, 8, ..., 2^(n-1)\nfor _ in range(n):\nfor _ in range(base):\ncount += 1\nbase *= 2\n# count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\nreturn count\n</code></pre> time_complexity.go<pre><code>/* \u6307\u6570\u9636\uff08\u5faa\u73af\u5b9e\u73b0\uff09*/\nfunc exponential(n int) int {\ncount, base := 0, 1\n// cell \u6bcf\u8f6e\u4e00\u5206\u4e3a\u4e8c\uff0c\u5f62\u6210\u6570\u5217 1, 2, 4, 8, ..., 2^(n-1)\nfor i := 0; i &lt; n; i++ {\nfor j := 0; j &lt; base; j++ {\ncount++\n}\nbase *= 2\n}\n// count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\nreturn count\n}\n</code></pre> time_complexity.js<pre><code>/* \u6307\u6570\u9636\uff08\u5faa\u73af\u5b9e\u73b0\uff09 */\nfunction exponential(n) {\nlet count = 0,\nbase = 1;\n// cell \u6bcf\u8f6e\u4e00\u5206\u4e3a\u4e8c\uff0c\u5f62\u6210\u6570\u5217 1, 2, 4, 8, ..., 2^(n-1)\nfor (let i = 0; i &lt; n; i++) {\nfor (let j = 0; j &lt; base; j++) {\ncount++;\n}\nbase *= 2;\n}\n// count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\nreturn count;\n}\n</code></pre> time_complexity.ts<pre><code>/* \u6307\u6570\u9636\uff08\u5faa\u73af\u5b9e\u73b0\uff09 */\nfunction exponential(n: number): number {\nlet count = 0,\nbase = 1;\n// cell \u6bcf\u8f6e\u4e00\u5206\u4e3a\u4e8c\uff0c\u5f62\u6210\u6570\u5217 1, 2, 4, 8, ..., 2^(n-1)\nfor (let i = 0; i &lt; n; i++) {\nfor (let j = 0; j &lt; base; j++) {\ncount++;\n}\nbase *= 2;\n}\n// count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\nreturn count;\n}\n</code></pre> time_complexity.c<pre><code>/* \u6307\u6570\u9636\uff08\u5faa\u73af\u5b9e\u73b0\uff09 */\nint exponential(int n) {\nint count = 0;\nint bas = 1;\n// cell \u6bcf\u8f6e\u4e00\u5206\u4e3a\u4e8c\uff0c\u5f62\u6210\u6570\u5217 1, 2, 4, 8, ..., 2^(n-1)\nfor (int i = 0; i &lt; n; i++) {\nfor (int j = 0; j &lt; bas; j++) {\ncount++;\n}\nbas *= 2;\n}\n// count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\nreturn count;\n}\n</code></pre> time_complexity.cs<pre><code>/* \u6307\u6570\u9636\uff08\u5faa\u73af\u5b9e\u73b0\uff09 */\nint exponential(int n) {\nint count = 0, bas = 1;\n// cell \u6bcf\u8f6e\u4e00\u5206\u4e3a\u4e8c\uff0c\u5f62\u6210\u6570\u5217 1, 2, 4, 8, ..., 2^(n-1)\nfor (int i = 0; i &lt; n; i++) {\nfor (int j = 0; j &lt; bas; j++) {\ncount++;\n}\nbas *= 2;\n}\n// count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\nreturn count;\n}\n</code></pre> time_complexity.swift<pre><code>/* \u6307\u6570\u9636\uff08\u5faa\u73af\u5b9e\u73b0\uff09 */\nfunc exponential(n: Int) -&gt; Int {\nvar count = 0\nvar base = 1\n// cell \u6bcf\u8f6e\u4e00\u5206\u4e3a\u4e8c\uff0c\u5f62\u6210\u6570\u5217 1, 2, 4, 8, ..., 2^(n-1)\nfor _ in 0 ..&lt; n {\nfor _ in 0 ..&lt; base {\ncount += 1\n}\nbase *= 2\n}\n// count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\nreturn count\n}\n</code></pre> time_complexity.zig<pre><code>// \u6307\u6570\u9636\uff08\u5faa\u73af\u5b9e\u73b0\uff09\nfn exponential(n: i32) i32 {\nvar count: i32 = 0;\nvar bas: i32 = 1;\nvar i: i32 = 0;\n// cell \u6bcf\u8f6e\u4e00\u5206\u4e3a\u4e8c\uff0c\u5f62\u6210\u6570\u5217 1, 2, 4, 8, ..., 2^(n-1)\nwhile (i &lt; n) : (i += 1) {\nvar j: i32 = 0;\nwhile (j &lt; bas) : (j += 1) {\ncount += 1;\n}\nbas *= 2;\n}\n// count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\nreturn count;\n}\n</code></pre> time_complexity.dart<pre><code>/* \u6307\u6570\u9636\uff08\u5faa\u73af\u5b9e\u73b0\uff09 */\nint exponential(int n) {\nint count = 0, base = 1;\n// cell \u6bcf\u8f6e\u4e00\u5206\u4e3a\u4e8c\uff0c\u5f62\u6210\u6570\u5217 1, 2, 4, 8, ..., 2^(n-1)\nfor (var i = 0; i &lt; n; i++) {\nfor (var j = 0; j &lt; base; j++) {\ncount++;\n}\nbase *= 2;\n}\n// count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\nreturn count;\n}\n</code></pre> <p></p> <p> Fig. \u6307\u6570\u9636\u7684\u65f6\u95f4\u590d\u6742\u5ea6 </p> <p>\u5728\u5b9e\u9645\u7b97\u6cd5\u4e2d\uff0c\u6307\u6570\u9636\u5e38\u51fa\u73b0\u4e8e\u9012\u5f52\u51fd\u6570\u3002\u4f8b\u5982\u4ee5\u4e0b\u4ee3\u7801\uff0c\u4e0d\u65ad\u5730\u4e00\u5206\u4e3a\u4e8c\uff0c\u7ecf\u8fc7 \\(n\\) \u6b21\u5206\u88c2\u540e\u505c\u6b62\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart time_complexity.java<pre><code>/* \u6307\u6570\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nint expRecur(int n) {\nif (n == 1)\nreturn 1;\nreturn expRecur(n - 1) + expRecur(n - 1) + 1;\n}\n</code></pre> time_complexity.cpp<pre><code>/* \u6307\u6570\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nint expRecur(int n) {\nif (n == 1)\nreturn 1;\nreturn expRecur(n - 1) + expRecur(n - 1) + 1;\n}\n</code></pre> time_complexity.py<pre><code>def exp_recur(n: int) -&gt; int:\n\"\"\"\u6307\u6570\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09\"\"\"\nif n == 1:\nreturn 1\nreturn exp_recur(n - 1) + exp_recur(n - 1) + 1\n</code></pre> time_complexity.go<pre><code>/* \u6307\u6570\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09*/\nfunc expRecur(n int) int {\nif n == 1 {\nreturn 1\n}\nreturn expRecur(n-1) + expRecur(n-1) + 1\n}\n</code></pre> time_complexity.js<pre><code>/* \u6307\u6570\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nfunction expRecur(n) {\nif (n == 1) return 1;\nreturn expRecur(n - 1) + expRecur(n - 1) + 1;\n}\n</code></pre> time_complexity.ts<pre><code>/* \u6307\u6570\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nfunction expRecur(n: number): number {\nif (n == 1) return 1;\nreturn expRecur(n - 1) + expRecur(n - 1) + 1;\n}\n</code></pre> time_complexity.c<pre><code>/* \u6307\u6570\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nint expRecur(int n) {\nif (n == 1)\nreturn 1;\nreturn expRecur(n - 1) + expRecur(n - 1) + 1;\n}\n</code></pre> time_complexity.cs<pre><code>/* \u6307\u6570\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nint expRecur(int n) {\nif (n == 1) return 1;\nreturn expRecur(n - 1) + expRecur(n - 1) + 1;\n}\n</code></pre> time_complexity.swift<pre><code>/* \u6307\u6570\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nfunc expRecur(n: Int) -&gt; Int {\nif n == 1 {\nreturn 1\n}\nreturn expRecur(n: n - 1) + expRecur(n: n - 1) + 1\n}\n</code></pre> time_complexity.zig<pre><code>// \u6307\u6570\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09\nfn expRecur(n: i32) i32 {\nif (n == 1) return 1;\nreturn expRecur(n - 1) + expRecur(n - 1) + 1;\n}\n</code></pre> time_complexity.dart<pre><code>/* \u6307\u6570\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nint expRecur(int n) {\nif (n == 1) return 1;\nreturn expRecur(n - 1) + expRecur(n - 1) + 1;\n}\n</code></pre>"},{"location":"chapter_computational_complexity/time_complexity/#olog-n","title":"\u5bf9\u6570\u9636 \\(O(\\log n)\\)","text":"<p>\u4e0e\u6307\u6570\u9636\u76f8\u53cd\uff0c\u5bf9\u6570\u9636\u53cd\u6620\u4e86\u201c\u6bcf\u8f6e\u7f29\u51cf\u5230\u4e00\u534a\u7684\u60c5\u51b5\u201d\u3002\u5bf9\u6570\u9636\u4ec5\u6b21\u4e8e\u5e38\u6570\u9636\uff0c\u65f6\u95f4\u589e\u957f\u7f13\u6162\uff0c\u662f\u7406\u60f3\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u3002</p> <p>\u5bf9\u6570\u9636\u5e38\u51fa\u73b0\u4e8e\u300c\u4e8c\u5206\u67e5\u627e\u300d\u548c\u300c\u5206\u6cbb\u7b97\u6cd5\u300d\u4e2d\uff0c\u4f53\u73b0\u4e86\u201c\u4e00\u5206\u4e3a\u591a\u201d\u548c\u201c\u5316\u7e41\u4e3a\u7b80\u201d\u7684\u7b97\u6cd5\u601d\u60f3\u3002</p> <p>\u8bbe\u8f93\u5165\u6570\u636e\u5927\u5c0f\u4e3a \\(n\\) \uff0c\u7531\u4e8e\u6bcf\u8f6e\u7f29\u51cf\u5230\u4e00\u534a\uff0c\u56e0\u6b64\u5faa\u73af\u6b21\u6570\u662f \\(\\log_2 n\\) \uff0c\u5373 \\(2^n\\) \u7684\u53cd\u51fd\u6570\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart time_complexity.java<pre><code>/* \u5bf9\u6570\u9636\uff08\u5faa\u73af\u5b9e\u73b0\uff09 */\nint logarithmic(float n) {\nint count = 0;\nwhile (n &gt; 1) {\nn = n / 2;\ncount++;\n}\nreturn count;\n}\n</code></pre> time_complexity.cpp<pre><code>/* \u5bf9\u6570\u9636\uff08\u5faa\u73af\u5b9e\u73b0\uff09 */\nint logarithmic(float n) {\nint count = 0;\nwhile (n &gt; 1) {\nn = n / 2;\ncount++;\n}\nreturn count;\n}\n</code></pre> time_complexity.py<pre><code>def logarithmic(n: float) -&gt; int:\n\"\"\"\u5bf9\u6570\u9636\uff08\u5faa\u73af\u5b9e\u73b0\uff09\"\"\"\ncount = 0\nwhile n &gt; 1:\nn = n / 2\ncount += 1\nreturn count\n</code></pre> time_complexity.go<pre><code>/* \u5bf9\u6570\u9636\uff08\u5faa\u73af\u5b9e\u73b0\uff09*/\nfunc logarithmic(n float64) int {\ncount := 0\nfor n &gt; 1 {\nn = n / 2\ncount++\n}\nreturn count\n}\n</code></pre> time_complexity.js<pre><code>/* \u5bf9\u6570\u9636\uff08\u5faa\u73af\u5b9e\u73b0\uff09 */\nfunction logarithmic(n) {\nlet count = 0;\nwhile (n &gt; 1) {\nn = n / 2;\ncount++;\n}\nreturn count;\n}\n</code></pre> time_complexity.ts<pre><code>/* \u5bf9\u6570\u9636\uff08\u5faa\u73af\u5b9e\u73b0\uff09 */\nfunction logarithmic(n: number): number {\nlet count = 0;\nwhile (n &gt; 1) {\nn = n / 2;\ncount++;\n}\nreturn count;\n}\n</code></pre> time_complexity.c<pre><code>/* \u5bf9\u6570\u9636\uff08\u5faa\u73af\u5b9e\u73b0\uff09 */\nint logarithmic(float n) {\nint count = 0;\nwhile (n &gt; 1) {\nn = n / 2;\ncount++;\n}\nreturn count;\n}\n</code></pre> time_complexity.cs<pre><code>/* \u5bf9\u6570\u9636\uff08\u5faa\u73af\u5b9e\u73b0\uff09 */\nint logarithmic(float n) {\nint count = 0;\nwhile (n &gt; 1) {\nn = n / 2;\ncount++;\n}\nreturn count;\n}\n</code></pre> time_complexity.swift<pre><code>/* \u5bf9\u6570\u9636\uff08\u5faa\u73af\u5b9e\u73b0\uff09 */\nfunc logarithmic(n: Double) -&gt; Int {\nvar count = 0\nvar n = n\nwhile n &gt; 1 {\nn = n / 2\ncount += 1\n}\nreturn count\n}\n</code></pre> time_complexity.zig<pre><code>// \u5bf9\u6570\u9636\uff08\u5faa\u73af\u5b9e\u73b0\uff09\nfn logarithmic(n: f32) i32 {\nvar count: i32 = 0;\nvar n_var = n;\nwhile (n_var &gt; 1)\n{\nn_var = n_var / 2;\ncount +=1;\n}\nreturn count;\n}\n</code></pre> time_complexity.dart<pre><code>/* \u5bf9\u6570\u9636\uff08\u5faa\u73af\u5b9e\u73b0\uff09 */\nint logarithmic(num n) {\nint count = 0;\nwhile (n &gt; 1) {\nn = n / 2;\ncount++;\n}\nreturn count;\n}\n</code></pre> <p></p> <p> Fig. \u5bf9\u6570\u9636\u7684\u65f6\u95f4\u590d\u6742\u5ea6 </p> <p>\u4e0e\u6307\u6570\u9636\u7c7b\u4f3c\uff0c\u5bf9\u6570\u9636\u4e5f\u5e38\u51fa\u73b0\u4e8e\u9012\u5f52\u51fd\u6570\u3002\u4ee5\u4e0b\u4ee3\u7801\u5f62\u6210\u4e86\u4e00\u4e2a\u9ad8\u5ea6\u4e3a \\(\\log_2 n\\) \u7684\u9012\u5f52\u6811\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart time_complexity.java<pre><code>/* \u5bf9\u6570\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nint logRecur(float n) {\nif (n &lt;= 1)\nreturn 0;\nreturn logRecur(n / 2) + 1;\n}\n</code></pre> time_complexity.cpp<pre><code>/* \u5bf9\u6570\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nint logRecur(float n) {\nif (n &lt;= 1)\nreturn 0;\nreturn logRecur(n / 2) + 1;\n}\n</code></pre> time_complexity.py<pre><code>def log_recur(n: float) -&gt; int:\n\"\"\"\u5bf9\u6570\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09\"\"\"\nif n &lt;= 1:\nreturn 0\nreturn log_recur(n / 2) + 1\n</code></pre> time_complexity.go<pre><code>/* \u5bf9\u6570\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09*/\nfunc logRecur(n float64) int {\nif n &lt;= 1 {\nreturn 0\n}\nreturn logRecur(n/2) + 1\n}\n</code></pre> time_complexity.js<pre><code>/* \u5bf9\u6570\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nfunction logRecur(n) {\nif (n &lt;= 1) return 0;\nreturn logRecur(n / 2) + 1;\n}\n</code></pre> time_complexity.ts<pre><code>/* \u5bf9\u6570\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nfunction logRecur(n: number): number {\nif (n &lt;= 1) return 0;\nreturn logRecur(n / 2) + 1;\n}\n</code></pre> time_complexity.c<pre><code>/* \u5bf9\u6570\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nint logRecur(float n) {\nif (n &lt;= 1)\nreturn 0;\nreturn logRecur(n / 2) + 1;\n}\n</code></pre> time_complexity.cs<pre><code>/* \u5bf9\u6570\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nint logRecur(float n) {\nif (n &lt;= 1) return 0;\nreturn logRecur(n / 2) + 1;\n}\n</code></pre> time_complexity.swift<pre><code>/* \u5bf9\u6570\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nfunc logRecur(n: Double) -&gt; Int {\nif n &lt;= 1 {\nreturn 0\n}\nreturn logRecur(n: n / 2) + 1\n}\n</code></pre> time_complexity.zig<pre><code>// \u5bf9\u6570\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09\nfn logRecur(n: f32) i32 {\nif (n &lt;= 1) return 0;\nreturn logRecur(n / 2) + 1;\n}\n</code></pre> time_complexity.dart<pre><code>/* \u5bf9\u6570\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nint logRecur(num n) {\nif (n &lt;= 1) return 0;\nreturn logRecur(n / 2) + 1;\n}\n</code></pre>"},{"location":"chapter_computational_complexity/time_complexity/#on-log-n","title":"\u7ebf\u6027\u5bf9\u6570\u9636 \\(O(n \\log n)\\)","text":"<p>\u7ebf\u6027\u5bf9\u6570\u9636\u5e38\u51fa\u73b0\u4e8e\u5d4c\u5957\u5faa\u73af\u4e2d\uff0c\u4e24\u5c42\u5faa\u73af\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u5206\u522b\u4e3a \\(O(\\log n)\\) \u548c \\(O(n)\\) \u3002</p> <p>\u4e3b\u6d41\u6392\u5e8f\u7b97\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u901a\u5e38\u4e3a \\(O(n \\log n)\\) \uff0c\u4f8b\u5982\u5feb\u901f\u6392\u5e8f\u3001\u5f52\u5e76\u6392\u5e8f\u3001\u5806\u6392\u5e8f\u7b49\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart time_complexity.java<pre><code>/* \u7ebf\u6027\u5bf9\u6570\u9636 */\nint linearLogRecur(float n) {\nif (n &lt;= 1)\nreturn 1;\nint count = linearLogRecur(n / 2) +\nlinearLogRecur(n / 2);\nfor (int i = 0; i &lt; n; i++) {\ncount++;\n}\nreturn count;\n}\n</code></pre> time_complexity.cpp<pre><code>/* \u7ebf\u6027\u5bf9\u6570\u9636 */\nint linearLogRecur(float n) {\nif (n &lt;= 1)\nreturn 1;\nint count = linearLogRecur(n / 2) + linearLogRecur(n / 2);\nfor (int i = 0; i &lt; n; i++) {\ncount++;\n}\nreturn count;\n}\n</code></pre> time_complexity.py<pre><code>def linear_log_recur(n: float) -&gt; int:\n\"\"\"\u7ebf\u6027\u5bf9\u6570\u9636\"\"\"\nif n &lt;= 1:\nreturn 1\ncount: int = linear_log_recur(n // 2) + linear_log_recur(n // 2)\nfor _ in range(n):\ncount += 1\nreturn count\n</code></pre> time_complexity.go<pre><code>/* \u7ebf\u6027\u5bf9\u6570\u9636 */\nfunc linearLogRecur(n float64) int {\nif n &lt;= 1 {\nreturn 1\n}\ncount := linearLogRecur(n/2) +\nlinearLogRecur(n/2)\nfor i := 0.0; i &lt; n; i++ {\ncount++\n}\nreturn count\n}\n</code></pre> time_complexity.js<pre><code>/* \u7ebf\u6027\u5bf9\u6570\u9636 */\nfunction linearLogRecur(n) {\nif (n &lt;= 1) return 1;\nlet count = linearLogRecur(n / 2) + linearLogRecur(n / 2);\nfor (let i = 0; i &lt; n; i++) {\ncount++;\n}\nreturn count;\n}\n</code></pre> time_complexity.ts<pre><code>/* \u7ebf\u6027\u5bf9\u6570\u9636 */\nfunction linearLogRecur(n: number): number {\nif (n &lt;= 1) return 1;\nlet count = linearLogRecur(n / 2) + linearLogRecur(n / 2);\nfor (let i = 0; i &lt; n; i++) {\ncount++;\n}\nreturn count;\n}\n</code></pre> time_complexity.c<pre><code>/* \u7ebf\u6027\u5bf9\u6570\u9636 */\nint linearLogRecur(float n) {\nif (n &lt;= 1)\nreturn 1;\nint count = linearLogRecur(n / 2) + linearLogRecur(n / 2);\nfor (int i = 0; i &lt; n; i++) {\ncount++;\n}\nreturn count;\n}\n</code></pre> time_complexity.cs<pre><code>/* \u7ebf\u6027\u5bf9\u6570\u9636 */\nint linearLogRecur(float n) {\nif (n &lt;= 1) return 1;\nint count = linearLogRecur(n / 2) +\nlinearLogRecur(n / 2);\nfor (int i = 0; i &lt; n; i++) {\ncount++;\n}\nreturn count;\n}\n</code></pre> time_complexity.swift<pre><code>/* \u7ebf\u6027\u5bf9\u6570\u9636 */\nfunc linearLogRecur(n: Double) -&gt; Int {\nif n &lt;= 1 {\nreturn 1\n}\nvar count = linearLogRecur(n: n / 2) + linearLogRecur(n: n / 2)\nfor _ in stride(from: 0, to: n, by: 1) {\ncount += 1\n}\nreturn count\n}\n</code></pre> time_complexity.zig<pre><code>// \u7ebf\u6027\u5bf9\u6570\u9636\nfn linearLogRecur(n: f32) i32 {\nif (n &lt;= 1) return 1;\nvar count: i32 = linearLogRecur(n / 2) +\nlinearLogRecur(n / 2);\nvar i: f32 = 0;\nwhile (i &lt; n) : (i += 1) {\ncount += 1;\n}\nreturn count;\n}\n</code></pre> time_complexity.dart<pre><code>/* \u7ebf\u6027\u5bf9\u6570\u9636 */\nint linearLogRecur(num n) {\nif (n &lt;= 1) return 1;\nint count = linearLogRecur(n / 2) + linearLogRecur(n / 2);\nfor (var i = 0; i &lt; n; i++) {\ncount++;\n}\nreturn count;\n}\n</code></pre> <p></p> <p> Fig. \u7ebf\u6027\u5bf9\u6570\u9636\u7684\u65f6\u95f4\u590d\u6742\u5ea6 </p>"},{"location":"chapter_computational_complexity/time_complexity/#on_1","title":"\u9636\u4e58\u9636 \\(O(n!)\\)","text":"<p>\u9636\u4e58\u9636\u5bf9\u5e94\u6570\u5b66\u4e0a\u7684\u300c\u5168\u6392\u5217\u300d\u95ee\u9898\u3002\u7ed9\u5b9a \\(n\\) \u4e2a\u4e92\u4e0d\u91cd\u590d\u7684\u5143\u7d20\uff0c\u6c42\u5176\u6240\u6709\u53ef\u80fd\u7684\u6392\u5217\u65b9\u6848\uff0c\u65b9\u6848\u6570\u91cf\u4e3a\uff1a</p> \\[ n! = n \\times (n - 1) \\times (n - 2) \\times \\cdots \\times 2 \\times 1 \\] <p>\u9636\u4e58\u901a\u5e38\u4f7f\u7528\u9012\u5f52\u5b9e\u73b0\u3002\u4f8b\u5982\u4ee5\u4e0b\u4ee3\u7801\uff0c\u7b2c\u4e00\u5c42\u5206\u88c2\u51fa \\(n\\) \u4e2a\uff0c\u7b2c\u4e8c\u5c42\u5206\u88c2\u51fa \\(n - 1\\) \u4e2a\uff0c\u4ee5\u6b64\u7c7b\u63a8\uff0c\u76f4\u81f3\u7b2c \\(n\\) \u5c42\u65f6\u7ec8\u6b62\u5206\u88c2\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart time_complexity.java<pre><code>/* \u9636\u4e58\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nint factorialRecur(int n) {\nif (n == 0)\nreturn 1;\nint count = 0;\n// \u4ece 1 \u4e2a\u5206\u88c2\u51fa n \u4e2a\nfor (int i = 0; i &lt; n; i++) {\ncount += factorialRecur(n - 1);\n}\nreturn count;\n}\n</code></pre> time_complexity.cpp<pre><code>/* \u9636\u4e58\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nint factorialRecur(int n) {\nif (n == 0)\nreturn 1;\nint count = 0;\n// \u4ece 1 \u4e2a\u5206\u88c2\u51fa n \u4e2a\nfor (int i = 0; i &lt; n; i++) {\ncount += factorialRecur(n - 1);\n}\nreturn count;\n}\n</code></pre> time_complexity.py<pre><code>def factorial_recur(n: int) -&gt; int:\n\"\"\"\u9636\u4e58\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09\"\"\"\nif n == 0:\nreturn 1\ncount = 0\n# \u4ece 1 \u4e2a\u5206\u88c2\u51fa n \u4e2a\nfor _ in range(n):\ncount += factorial_recur(n - 1)\nreturn count\n</code></pre> time_complexity.go<pre><code>/* \u9636\u4e58\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nfunc factorialRecur(n int) int {\nif n == 0 {\nreturn 1\n}\ncount := 0\n// \u4ece 1 \u4e2a\u5206\u88c2\u51fa n \u4e2a\nfor i := 0; i &lt; n; i++ {\ncount += factorialRecur(n - 1)\n}\nreturn count\n}\n</code></pre> time_complexity.js<pre><code>/* \u9636\u4e58\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nfunction factorialRecur(n) {\nif (n == 0) return 1;\nlet count = 0;\n// \u4ece 1 \u4e2a\u5206\u88c2\u51fa n \u4e2a\nfor (let i = 0; i &lt; n; i++) {\ncount += factorialRecur(n - 1);\n}\nreturn count;\n}\n</code></pre> time_complexity.ts<pre><code>/* \u9636\u4e58\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nfunction factorialRecur(n: number): number {\nif (n == 0) return 1;\nlet count = 0;\n// \u4ece 1 \u4e2a\u5206\u88c2\u51fa n \u4e2a\nfor (let i = 0; i &lt; n; i++) {\ncount += factorialRecur(n - 1);\n}\nreturn count;\n}\n</code></pre> time_complexity.c<pre><code>/* \u9636\u4e58\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nint factorialRecur(int n) {\nif (n == 0)\nreturn 1;\nint count = 0;\nfor (int i = 0; i &lt; n; i++) {\ncount += factorialRecur(n - 1);\n}\nreturn count;\n}\n</code></pre> time_complexity.cs<pre><code>/* \u9636\u4e58\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nint factorialRecur(int n) {\nif (n == 0) return 1;\nint count = 0;\n// \u4ece 1 \u4e2a\u5206\u88c2\u51fa n \u4e2a\nfor (int i = 0; i &lt; n; i++) {\ncount += factorialRecur(n - 1);\n}\nreturn count;\n}\n</code></pre> time_complexity.swift<pre><code>/* \u9636\u4e58\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nfunc factorialRecur(n: Int) -&gt; Int {\nif n == 0 {\nreturn 1\n}\nvar count = 0\n// \u4ece 1 \u4e2a\u5206\u88c2\u51fa n \u4e2a\nfor _ in 0 ..&lt; n {\ncount += factorialRecur(n: n - 1)\n}\nreturn count\n}\n</code></pre> time_complexity.zig<pre><code>// \u9636\u4e58\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09\nfn factorialRecur(n: i32) i32 {\nif (n == 0) return 1;\nvar count: i32 = 0;\nvar i: i32 = 0;\n// \u4ece 1 \u4e2a\u5206\u88c2\u51fa n \u4e2a\nwhile (i &lt; n) : (i += 1) {\ncount += factorialRecur(n - 1);\n}\nreturn count;\n}\n</code></pre> time_complexity.dart<pre><code>/* \u9636\u4e58\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nint factorialRecur(int n) {\nif (n == 0) return 1;\nint count = 0;\n// \u4ece 1 \u4e2a\u5206\u88c2\u51fa n \u4e2a\nfor (var i = 0; i &lt; n; i++) {\ncount += factorialRecur(n - 1);\n}\nreturn count;\n}\n</code></pre> <p></p> <p> Fig. \u9636\u4e58\u9636\u7684\u65f6\u95f4\u590d\u6742\u5ea6 </p>"},{"location":"chapter_computational_complexity/time_complexity/#226","title":"2.2.6. \u00a0 \u6700\u5dee\u3001\u6700\u4f73\u3001\u5e73\u5747\u65f6\u95f4\u590d\u6742\u5ea6","text":"<p>\u67d0\u4e9b\u7b97\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e0d\u662f\u56fa\u5b9a\u7684\uff0c\u800c\u662f\u4e0e\u8f93\u5165\u6570\u636e\u7684\u5206\u5e03\u6709\u5173\u3002\u4f8b\u5982\uff0c\u5047\u8bbe\u8f93\u5165\u4e00\u4e2a\u957f\u5ea6\u4e3a \\(n\\) \u7684\u6570\u7ec4 <code>nums</code> \uff0c\u5176\u4e2d <code>nums</code> \u7531\u4ece \\(1\\) \u81f3 \\(n\\) \u7684\u6570\u5b57\u7ec4\u6210\uff0c\u4f46\u5143\u7d20\u987a\u5e8f\u662f\u968f\u673a\u6253\u4e71\u7684\uff1b\u7b97\u6cd5\u7684\u4efb\u52a1\u662f\u8fd4\u56de\u5143\u7d20 \\(1\\) \u7684\u7d22\u5f15\u3002\u6211\u4eec\u53ef\u4ee5\u5f97\u51fa\u4ee5\u4e0b\u7ed3\u8bba\uff1a</p> <ul> <li>\u5f53 <code>nums = [?, ?, ..., 1]</code> \uff0c\u5373\u5f53\u672b\u5c3e\u5143\u7d20\u662f \\(1\\) \u65f6\uff0c\u9700\u8981\u5b8c\u6574\u904d\u5386\u6570\u7ec4\uff0c\u6b64\u65f6\u8fbe\u5230 \u6700\u5dee\u65f6\u95f4\u590d\u6742\u5ea6 \\(O(n)\\)\uff1b</li> <li>\u5f53 <code>nums = [1, ?, ?, ...]</code> \uff0c\u5373\u5f53\u9996\u4e2a\u6570\u5b57\u4e3a \\(1\\) \u65f6\uff0c\u65e0\u8bba\u6570\u7ec4\u591a\u957f\u90fd\u4e0d\u9700\u8981\u7ee7\u7eed\u904d\u5386\uff0c\u6b64\u65f6\u8fbe\u5230 \u6700\u4f73\u65f6\u95f4\u590d\u6742\u5ea6 \\(\\Omega(1)\\)\uff1b</li> </ul> <p>\u201c\u51fd\u6570\u6e10\u8fd1\u4e0a\u754c\u201d\u4f7f\u7528\u5927 \\(O\\) \u8bb0\u53f7\u8868\u793a\uff0c\u4ee3\u8868\u300c\u6700\u5dee\u65f6\u95f4\u590d\u6742\u5ea6\u300d\u3002\u76f8\u5e94\u5730\uff0c\u201c\u51fd\u6570\u6e10\u8fd1\u4e0b\u754c\u201d\u7528 \\(\\Omega\\) \u8bb0\u53f7\u6765\u8868\u793a\uff0c\u4ee3\u8868\u300c\u6700\u4f73\u65f6\u95f4\u590d\u6742\u5ea6\u300d\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart worst_best_time_complexity.java<pre><code>/* \u751f\u6210\u4e00\u4e2a\u6570\u7ec4\uff0c\u5143\u7d20\u4e3a { 1, 2, ..., n }\uff0c\u987a\u5e8f\u88ab\u6253\u4e71 */\nint[] randomNumbers(int n) {\nInteger[] nums = new Integer[n];\n// \u751f\u6210\u6570\u7ec4 nums = { 1, 2, 3, ..., n }\nfor (int i = 0; i &lt; n; i++) {\nnums[i] = i + 1;\n}\n// \u968f\u673a\u6253\u4e71\u6570\u7ec4\u5143\u7d20\nCollections.shuffle(Arrays.asList(nums));\n// Integer[] -&gt; int[]\nint[] res = new int[n];\nfor (int i = 0; i &lt; n; i++) {\nres[i] = nums[i];\n}\nreturn res;\n}\n/* \u67e5\u627e\u6570\u7ec4 nums \u4e2d\u6570\u5b57 1 \u6240\u5728\u7d22\u5f15 */\nint findOne(int[] nums) {\nfor (int i = 0; i &lt; nums.length; i++) {\n// \u5f53\u5143\u7d20 1 \u5728\u6570\u7ec4\u5934\u90e8\u65f6\uff0c\u8fbe\u5230\u6700\u4f73\u65f6\u95f4\u590d\u6742\u5ea6 O(1)\n// \u5f53\u5143\u7d20 1 \u5728\u6570\u7ec4\u5c3e\u90e8\u65f6\uff0c\u8fbe\u5230\u6700\u5dee\u65f6\u95f4\u590d\u6742\u5ea6 O(n)\nif (nums[i] == 1)\nreturn i;\n}\nreturn -1;\n}\n</code></pre> worst_best_time_complexity.cpp<pre><code>/* \u751f\u6210\u4e00\u4e2a\u6570\u7ec4\uff0c\u5143\u7d20\u4e3a { 1, 2, ..., n }\uff0c\u987a\u5e8f\u88ab\u6253\u4e71 */\nvector&lt;int&gt; randomNumbers(int n) {\nvector&lt;int&gt; nums(n);\n// \u751f\u6210\u6570\u7ec4 nums = { 1, 2, 3, ..., n }\nfor (int i = 0; i &lt; n; i++) {\nnums[i] = i + 1;\n}\n// \u4f7f\u7528\u7cfb\u7edf\u65f6\u95f4\u751f\u6210\u968f\u673a\u79cd\u5b50\nunsigned seed = chrono::system_clock::now().time_since_epoch().count();\n// \u968f\u673a\u6253\u4e71\u6570\u7ec4\u5143\u7d20\nshuffle(nums.begin(), nums.end(), default_random_engine(seed));\nreturn nums;\n}\n/* \u67e5\u627e\u6570\u7ec4 nums \u4e2d\u6570\u5b57 1 \u6240\u5728\u7d22\u5f15 */\nint findOne(vector&lt;int&gt; &amp;nums) {\nfor (int i = 0; i &lt; nums.size(); i++) {\n// \u5f53\u5143\u7d20 1 \u5728\u6570\u7ec4\u5934\u90e8\u65f6\uff0c\u8fbe\u5230\u6700\u4f73\u65f6\u95f4\u590d\u6742\u5ea6 O(1)\n// \u5f53\u5143\u7d20 1 \u5728\u6570\u7ec4\u5c3e\u90e8\u65f6\uff0c\u8fbe\u5230\u6700\u5dee\u65f6\u95f4\u590d\u6742\u5ea6 O(n)\nif (nums[i] == 1)\nreturn i;\n}\nreturn -1;\n}\n</code></pre> worst_best_time_complexity.py<pre><code>def random_numbers(n: int) -&gt; list[int]:\n\"\"\"\u751f\u6210\u4e00\u4e2a\u6570\u7ec4\uff0c\u5143\u7d20\u4e3a: 1, 2, ..., n \uff0c\u987a\u5e8f\u88ab\u6253\u4e71\"\"\"\n# \u751f\u6210\u6570\u7ec4 nums =: 1, 2, 3, ..., n\nnums = [i for i in range(1, n + 1)]\n# \u968f\u673a\u6253\u4e71\u6570\u7ec4\u5143\u7d20\nrandom.shuffle(nums)\nreturn nums\ndef find_one(nums: list[int]) -&gt; int:\n\"\"\"\u67e5\u627e\u6570\u7ec4 nums \u4e2d\u6570\u5b57 1 \u6240\u5728\u7d22\u5f15\"\"\"\nfor i in range(len(nums)):\n# \u5f53\u5143\u7d20 1 \u5728\u6570\u7ec4\u5934\u90e8\u65f6\uff0c\u8fbe\u5230\u6700\u4f73\u65f6\u95f4\u590d\u6742\u5ea6 O(1)\n# \u5f53\u5143\u7d20 1 \u5728\u6570\u7ec4\u5c3e\u90e8\u65f6\uff0c\u8fbe\u5230\u6700\u5dee\u65f6\u95f4\u590d\u6742\u5ea6 O(n)\nif nums[i] == 1:\nreturn i\nreturn -1\n</code></pre> worst_best_time_complexity.go<pre><code>/* \u751f\u6210\u4e00\u4e2a\u6570\u7ec4\uff0c\u5143\u7d20\u4e3a { 1, 2, ..., n }\uff0c\u987a\u5e8f\u88ab\u6253\u4e71 */\nfunc randomNumbers(n int) []int {\nnums := make([]int, n)\n// \u751f\u6210\u6570\u7ec4 nums = { 1, 2, 3, ..., n }\nfor i := 0; i &lt; n; i++ {\nnums[i] = i + 1\n}\n// \u968f\u673a\u6253\u4e71\u6570\u7ec4\u5143\u7d20\nrand.Shuffle(len(nums), func(i, j int) {\nnums[i], nums[j] = nums[j], nums[i]\n})\nreturn nums\n}\n/* \u67e5\u627e\u6570\u7ec4 nums \u4e2d\u6570\u5b57 1 \u6240\u5728\u7d22\u5f15 */\nfunc findOne(nums []int) int {\nfor i := 0; i &lt; len(nums); i++ {\n// \u5f53\u5143\u7d20 1 \u5728\u6570\u7ec4\u5934\u90e8\u65f6\uff0c\u8fbe\u5230\u6700\u4f73\u65f6\u95f4\u590d\u6742\u5ea6 O(1)\n// \u5f53\u5143\u7d20 1 \u5728\u6570\u7ec4\u5c3e\u90e8\u65f6\uff0c\u8fbe\u5230\u6700\u5dee\u65f6\u95f4\u590d\u6742\u5ea6 O(n)\nif nums[i] == 1 {\nreturn i\n}\n}\nreturn -1\n}\n</code></pre> worst_best_time_complexity.js<pre><code>/* \u751f\u6210\u4e00\u4e2a\u6570\u7ec4\uff0c\u5143\u7d20\u4e3a { 1, 2, ..., n }\uff0c\u987a\u5e8f\u88ab\u6253\u4e71 */\nfunction randomNumbers(n) {\nconst nums = Array(n);\n// \u751f\u6210\u6570\u7ec4 nums = { 1, 2, 3, ..., n }\nfor (let i = 0; i &lt; n; i++) {\nnums[i] = i + 1;\n}\n// \u968f\u673a\u6253\u4e71\u6570\u7ec4\u5143\u7d20\nfor (let i = 0; i &lt; n; i++) {\nconst r = Math.floor(Math.random() * (i + 1));\nconst temp = nums[i];\nnums[i] = nums[r];\nnums[r] = temp;\n}\nreturn nums;\n}\n/* \u67e5\u627e\u6570\u7ec4 nums \u4e2d\u6570\u5b57 1 \u6240\u5728\u7d22\u5f15 */\nfunction findOne(nums) {\nfor (let i = 0; i &lt; nums.length; i++) {\n// \u5f53\u5143\u7d20 1 \u5728\u6570\u7ec4\u5934\u90e8\u65f6\uff0c\u8fbe\u5230\u6700\u4f73\u65f6\u95f4\u590d\u6742\u5ea6 O(1)\n// \u5f53\u5143\u7d20 1 \u5728\u6570\u7ec4\u5c3e\u90e8\u65f6\uff0c\u8fbe\u5230\u6700\u5dee\u65f6\u95f4\u590d\u6742\u5ea6 O(n)\nif (nums[i] === 1) {\nreturn i;\n}\n}\nreturn -1;\n}\n</code></pre> worst_best_time_complexity.ts<pre><code>/* \u751f\u6210\u4e00\u4e2a\u6570\u7ec4\uff0c\u5143\u7d20\u4e3a { 1, 2, ..., n }\uff0c\u987a\u5e8f\u88ab\u6253\u4e71 */\nfunction randomNumbers(n: number): number[] {\nconst nums = Array(n);\n// \u751f\u6210\u6570\u7ec4 nums = { 1, 2, 3, ..., n }\nfor (let i = 0; i &lt; n; i++) {\nnums[i] = i + 1;\n}\n// \u968f\u673a\u6253\u4e71\u6570\u7ec4\u5143\u7d20\nfor (let i = 0; i &lt; n; i++) {\nconst r = Math.floor(Math.random() * (i + 1));\nconst temp = nums[i];\nnums[i] = nums[r];\nnums[r] = temp;\n}\nreturn nums;\n}\n/* \u67e5\u627e\u6570\u7ec4 nums \u4e2d\u6570\u5b57 1 \u6240\u5728\u7d22\u5f15 */\nfunction findOne(nums: number[]): number {\nfor (let i = 0; i &lt; nums.length; i++) {\n// \u5f53\u5143\u7d20 1 \u5728\u6570\u7ec4\u5934\u90e8\u65f6\uff0c\u8fbe\u5230\u6700\u4f73\u65f6\u95f4\u590d\u6742\u5ea6 O(1)\n// \u5f53\u5143\u7d20 1 \u5728\u6570\u7ec4\u5c3e\u90e8\u65f6\uff0c\u8fbe\u5230\u6700\u5dee\u65f6\u95f4\u590d\u6742\u5ea6 O(n)\nif (nums[i] === 1) {\nreturn i;\n}\n}\nreturn -1;\n}\n</code></pre> worst_best_time_complexity.c<pre><code>/* \u751f\u6210\u4e00\u4e2a\u6570\u7ec4\uff0c\u5143\u7d20\u4e3a { 1, 2, ..., n }\uff0c\u987a\u5e8f\u88ab\u6253\u4e71 */\nint *randomNumbers(int n) {\n// \u5206\u914d\u5806\u533a\u5185\u5b58\uff08\u521b\u5efa\u4e00\u7ef4\u53ef\u53d8\u957f\u6570\u7ec4\uff1a\u6570\u7ec4\u4e2d\u5143\u7d20\u6570\u91cf\u4e3an\uff0c\u5143\u7d20\u7c7b\u578b\u4e3aint\uff09\nint *nums = (int *)malloc(n * sizeof(int));\n// \u751f\u6210\u6570\u7ec4 nums = { 1, 2, 3, ..., n }\nfor (int i = 0; i &lt; n; i++) {\nnums[i] = i + 1;\n}\n// \u968f\u673a\u6253\u4e71\u6570\u7ec4\u5143\u7d20\nfor (int i = n - 1; i &gt; 0; i--) {\nint j = rand() % (i + 1);\nint temp = nums[i];\nnums[i] = nums[j];\nnums[j] = temp;\n}\nreturn nums;\n}\n/* \u67e5\u627e\u6570\u7ec4 nums \u4e2d\u6570\u5b57 1 \u6240\u5728\u7d22\u5f15 */\nint findOne(int *nums, int n) {\nfor (int i = 0; i &lt; n; i++) {\n// \u5f53\u5143\u7d20 1 \u5728\u6570\u7ec4\u5934\u90e8\u65f6\uff0c\u8fbe\u5230\u6700\u4f73\u65f6\u95f4\u590d\u6742\u5ea6 O(1)\n// \u5f53\u5143\u7d20 1 \u5728\u6570\u7ec4\u5c3e\u90e8\u65f6\uff0c\u8fbe\u5230\u6700\u5dee\u65f6\u95f4\u590d\u6742\u5ea6 O(n)\nif (nums[i] == 1)\nreturn i;\n}\nreturn -1;\n}\n</code></pre> worst_best_time_complexity.cs<pre><code>/* \u751f\u6210\u4e00\u4e2a\u6570\u7ec4\uff0c\u5143\u7d20\u4e3a { 1, 2, ..., n }\uff0c\u987a\u5e8f\u88ab\u6253\u4e71 */\nint[] randomNumbers(int n) {\nint[] nums = new int[n];\n// \u751f\u6210\u6570\u7ec4 nums = { 1, 2, 3, ..., n }\nfor (int i = 0; i &lt; n; i++) {\nnums[i] = i + 1;\n}\n// \u968f\u673a\u6253\u4e71\u6570\u7ec4\u5143\u7d20\nfor (int i = 0; i &lt; nums.Length; i++) {\nvar index = new Random().Next(i, nums.Length);\nvar tmp = nums[i];\nvar ran = nums[index];\nnums[i] = ran;\nnums[index] = tmp;\n}\nreturn nums;\n}\n/* \u67e5\u627e\u6570\u7ec4 nums \u4e2d\u6570\u5b57 1 \u6240\u5728\u7d22\u5f15 */\nint findOne(int[] nums) {\nfor (int i = 0; i &lt; nums.Length; i++) {\n// \u5f53\u5143\u7d20 1 \u5728\u6570\u7ec4\u5934\u90e8\u65f6\uff0c\u8fbe\u5230\u6700\u4f73\u65f6\u95f4\u590d\u6742\u5ea6 O(1)\n// \u5f53\u5143\u7d20 1 \u5728\u6570\u7ec4\u5c3e\u90e8\u65f6\uff0c\u8fbe\u5230\u6700\u5dee\u65f6\u95f4\u590d\u6742\u5ea6 O(n)\nif (nums[i] == 1)\nreturn i;\n}\nreturn -1;\n}\n</code></pre> worst_best_time_complexity.swift<pre><code>/* \u751f\u6210\u4e00\u4e2a\u6570\u7ec4\uff0c\u5143\u7d20\u4e3a { 1, 2, ..., n }\uff0c\u987a\u5e8f\u88ab\u6253\u4e71 */\nfunc randomNumbers(n: Int) -&gt; [Int] {\n// \u751f\u6210\u6570\u7ec4 nums = { 1, 2, 3, ..., n }\nvar nums = Array(1 ... n)\n// \u968f\u673a\u6253\u4e71\u6570\u7ec4\u5143\u7d20\nnums.shuffle()\nreturn nums\n}\n/* \u67e5\u627e\u6570\u7ec4 nums \u4e2d\u6570\u5b57 1 \u6240\u5728\u7d22\u5f15 */\nfunc findOne(nums: [Int]) -&gt; Int {\nfor i in nums.indices {\n// \u5f53\u5143\u7d20 1 \u5728\u6570\u7ec4\u5934\u90e8\u65f6\uff0c\u8fbe\u5230\u6700\u4f73\u65f6\u95f4\u590d\u6742\u5ea6 O(1)\n// \u5f53\u5143\u7d20 1 \u5728\u6570\u7ec4\u5c3e\u90e8\u65f6\uff0c\u8fbe\u5230\u6700\u5dee\u65f6\u95f4\u590d\u6742\u5ea6 O(n)\nif nums[i] == 1 {\nreturn i\n}\n}\nreturn -1\n}\n</code></pre> worst_best_time_complexity.zig<pre><code>// \u751f\u6210\u4e00\u4e2a\u6570\u7ec4\uff0c\u5143\u7d20\u4e3a { 1, 2, ..., n }\uff0c\u987a\u5e8f\u88ab\u6253\u4e71\npub fn randomNumbers(comptime n: usize) [n]i32 {\nvar nums: [n]i32 = undefined;\n// \u751f\u6210\u6570\u7ec4 nums = { 1, 2, 3, ..., n }\nfor (nums) |*num, i| {\nnum.* = @intCast(i32, i) + 1;\n}\n// \u968f\u673a\u6253\u4e71\u6570\u7ec4\u5143\u7d20\nconst rand = std.crypto.random;\nrand.shuffle(i32, &amp;nums);\nreturn nums;\n}\n// \u67e5\u627e\u6570\u7ec4 nums \u4e2d\u6570\u5b57 1 \u6240\u5728\u7d22\u5f15\npub fn findOne(nums: []i32) i32 {\nfor (nums) |num, i| {\n// \u5f53\u5143\u7d20 1 \u5728\u6570\u7ec4\u5934\u90e8\u65f6\uff0c\u8fbe\u5230\u6700\u4f73\u65f6\u95f4\u590d\u6742\u5ea6 O(1)\n// \u5f53\u5143\u7d20 1 \u5728\u6570\u7ec4\u5c3e\u90e8\u65f6\uff0c\u8fbe\u5230\u6700\u5dee\u65f6\u95f4\u590d\u6742\u5ea6 O(n)\nif (num == 1) return @intCast(i32, i);\n}\nreturn -1;\n}\n</code></pre> worst_best_time_complexity.dart<pre><code>/* \u751f\u6210\u4e00\u4e2a\u6570\u7ec4\uff0c\u5143\u7d20\u4e3a { 1, 2, ..., n }\uff0c\u987a\u5e8f\u88ab\u6253\u4e71 */\nList&lt;int&gt; randomNumbers(int n) {\nfinal nums = List.filled(n, 0);\n// \u751f\u6210\u6570\u7ec4 nums = { 1, 2, 3, ..., n }\nfor (var i = 0; i &lt; n; i++) {\nnums[i] = i + 1;\n}\n// \u968f\u673a\u6253\u4e71\u6570\u7ec4\u5143\u7d20\nnums.shuffle();\nreturn nums;\n}\n/* \u67e5\u627e\u6570\u7ec4 nums \u4e2d\u6570\u5b57 1 \u6240\u5728\u7d22\u5f15 */\nint findOne(List&lt;int&gt; nums) {\nfor (var i = 0; i &lt; nums.length; i++) {\n// \u5f53\u5143\u7d20 1 \u5728\u6570\u7ec4\u5934\u90e8\u65f6\uff0c\u8fbe\u5230\u6700\u4f73\u65f6\u95f4\u590d\u6742\u5ea6 O(1)\n// \u5f53\u5143\u7d20 1 \u5728\u6570\u7ec4\u5c3e\u90e8\u65f6\uff0c\u8fbe\u5230\u6700\u5dee\u65f6\u95f4\u590d\u6742\u5ea6 O(n)\nif (nums[i] == 1) return i;\n}\nreturn -1;\n}\n</code></pre> <p>Tip</p> <p>\u5b9e\u9645\u5e94\u7528\u4e2d\u6211\u4eec\u5f88\u5c11\u4f7f\u7528\u300c\u6700\u4f73\u65f6\u95f4\u590d\u6742\u5ea6\u300d\uff0c\u56e0\u4e3a\u901a\u5e38\u53ea\u6709\u5728\u5f88\u5c0f\u6982\u7387\u4e0b\u624d\u80fd\u8fbe\u5230\uff0c\u53ef\u80fd\u4f1a\u5e26\u6765\u4e00\u5b9a\u7684\u8bef\u5bfc\u6027\u3002\u76f8\u53cd\uff0c\u300c\u6700\u5dee\u65f6\u95f4\u590d\u6742\u5ea6\u300d\u66f4\u4e3a\u5b9e\u7528\uff0c\u56e0\u4e3a\u5b83\u7ed9\u51fa\u4e86\u4e00\u4e2a\u201c\u6548\u7387\u5b89\u5168\u503c\u201d\uff0c\u8ba9\u6211\u4eec\u53ef\u4ee5\u653e\u5fc3\u5730\u4f7f\u7528\u7b97\u6cd5\u3002</p> <p>\u4ece\u4e0a\u8ff0\u793a\u4f8b\u53ef\u4ee5\u770b\u51fa\uff0c\u6700\u5dee\u6216\u6700\u4f73\u65f6\u95f4\u590d\u6742\u5ea6\u53ea\u51fa\u73b0\u5728\u201c\u7279\u6b8a\u5206\u5e03\u7684\u6570\u636e\u201d\u4e2d\uff0c\u8fd9\u4e9b\u60c5\u51b5\u7684\u51fa\u73b0\u6982\u7387\u53ef\u80fd\u5f88\u5c0f\uff0c\u56e0\u6b64\u5e76\u4e0d\u80fd\u6700\u771f\u5b9e\u5730\u53cd\u6620\u7b97\u6cd5\u8fd0\u884c\u6548\u7387\u3002\u76f8\u8f83\u4e4b\u4e0b\uff0c\u300c\u5e73\u5747\u65f6\u95f4\u590d\u6742\u5ea6\u300d\u53ef\u4ee5\u4f53\u73b0\u7b97\u6cd5\u5728\u968f\u673a\u8f93\u5165\u6570\u636e\u4e0b\u7684\u8fd0\u884c\u6548\u7387\uff0c\u7528 \\(\\Theta\\) \u8bb0\u53f7\u6765\u8868\u793a\u3002</p> <p>\u5bf9\u4e8e\u90e8\u5206\u7b97\u6cd5\uff0c\u6211\u4eec\u53ef\u4ee5\u7b80\u5355\u5730\u63a8\u7b97\u51fa\u968f\u673a\u6570\u636e\u5206\u5e03\u4e0b\u7684\u5e73\u5747\u60c5\u51b5\u3002\u6bd4\u5982\u4e0a\u8ff0\u793a\u4f8b\uff0c\u7531\u4e8e\u8f93\u5165\u6570\u7ec4\u662f\u88ab\u6253\u4e71\u7684\uff0c\u56e0\u6b64\u5143\u7d20 \\(1\\) \u51fa\u73b0\u5728\u4efb\u610f\u7d22\u5f15\u7684\u6982\u7387\u90fd\u662f\u76f8\u7b49\u7684\uff0c\u90a3\u4e48\u7b97\u6cd5\u7684\u5e73\u5747\u5faa\u73af\u6b21\u6570\u5219\u662f\u6570\u7ec4\u957f\u5ea6\u7684\u4e00\u534a \\(\\frac{n}{2}\\) \uff0c\u5e73\u5747\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(\\Theta(\\frac{n}{2}) = \\Theta(n)\\) \u3002</p> <p>\u4f46\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u5c24\u5176\u662f\u8f83\u4e3a\u590d\u6742\u7684\u7b97\u6cd5\uff0c\u8ba1\u7b97\u5e73\u5747\u65f6\u95f4\u590d\u6742\u5ea6\u6bd4\u8f83\u56f0\u96be\uff0c\u56e0\u4e3a\u5f88\u96be\u7b80\u4fbf\u5730\u5206\u6790\u51fa\u5728\u6570\u636e\u5206\u5e03\u4e0b\u7684\u6574\u4f53\u6570\u5b66\u671f\u671b\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u901a\u5e38\u4f7f\u7528\u6700\u5dee\u65f6\u95f4\u590d\u6742\u5ea6\u4f5c\u4e3a\u7b97\u6cd5\u6548\u7387\u7684\u8bc4\u5224\u6807\u51c6\u3002</p> <p>\u4e3a\u4ec0\u4e48\u5f88\u5c11\u770b\u5230 \\(\\Theta\\) \u7b26\u53f7\uff1f</p> <p>\u53ef\u80fd\u7531\u4e8e \\(O\\) \u7b26\u53f7\u8fc7\u4e8e\u6717\u6717\u4e0a\u53e3\uff0c\u6211\u4eec\u5e38\u5e38\u4f7f\u7528\u5b83\u6765\u8868\u793a\u300c\u5e73\u5747\u590d\u6742\u5ea6\u300d\uff0c\u4f46\u4ece\u4e25\u683c\u610f\u4e49\u4e0a\u770b\uff0c\u8fd9\u79cd\u505a\u6cd5\u5e76\u4e0d\u89c4\u8303\u3002\u5728\u672c\u4e66\u548c\u5176\u4ed6\u8d44\u6599\u4e2d\uff0c\u82e5\u9047\u5230\u7c7b\u4f3c\u201c\u5e73\u5747\u65f6\u95f4\u590d\u6742\u5ea6 \\(O(n)\\)\u201d\u7684\u8868\u8ff0\uff0c\u8bf7\u5c06\u5176\u76f4\u63a5\u7406\u89e3\u4e3a \\(\\Theta(n)\\) \u3002</p>"},{"location":"chapter_data_structure/","title":"3. \u00a0 \u6570\u636e\u7ed3\u6784\u7b80\u4ecb","text":""},{"location":"chapter_data_structure/basic_data_types/","title":"3.2. \u00a0 \u57fa\u672c\u6570\u636e\u7c7b\u578b","text":"<p>\u8c08\u53ca\u8ba1\u7b97\u673a\u4e2d\u7684\u6570\u636e\uff0c\u6211\u4eec\u4f1a\u60f3\u5230\u6587\u672c\u3001\u56fe\u7247\u3001\u89c6\u9891\u3001\u8bed\u97f3\u30013D \u6a21\u578b\u7b49\u5404\u79cd\u5f62\u5f0f\u3002\u5c3d\u7ba1\u8fd9\u4e9b\u6570\u636e\u7684\u7ec4\u7ec7\u5f62\u5f0f\u5404\u5f02\uff0c\u4f46\u5b83\u4eec\u90fd\u7531\u5404\u79cd\u57fa\u672c\u6570\u636e\u7c7b\u578b\u6784\u6210\u3002</p> <p>\u57fa\u672c\u6570\u636e\u7c7b\u578b\u662f CPU \u53ef\u4ee5\u76f4\u63a5\u8fdb\u884c\u8fd0\u7b97\u7684\u7c7b\u578b\uff0c\u5728\u7b97\u6cd5\u4e2d\u76f4\u63a5\u88ab\u4f7f\u7528\u3002\u5b83\u5305\u62ec\uff1a</p> <ul> <li>\u6574\u6570\u7c7b\u578b <code>byte</code> , <code>short</code> , <code>int</code> , <code>long</code> \uff1b</li> <li>\u6d6e\u70b9\u6570\u7c7b\u578b <code>float</code> , <code>double</code> \uff0c\u7528\u4e8e\u8868\u793a\u5c0f\u6570\uff1b</li> <li>\u5b57\u7b26\u7c7b\u578b <code>char</code> \uff0c\u7528\u4e8e\u8868\u793a\u5404\u79cd\u8bed\u8a00\u7684\u5b57\u6bcd\u3001\u6807\u70b9\u7b26\u53f7\u3001\u751a\u81f3\u8868\u60c5\u7b26\u53f7\u7b49\uff1b</li> <li>\u5e03\u5c14\u7c7b\u578b <code>bool</code> \uff0c\u7528\u4e8e\u8868\u793a\u201c\u662f\u201d\u4e0e\u201c\u5426\u201d\u5224\u65ad\uff1b</li> </ul> <p>\u6240\u6709\u57fa\u672c\u6570\u636e\u7c7b\u578b\u90fd\u4ee5\u4e8c\u8fdb\u5236\u7684\u5f62\u5f0f\u5b58\u50a8\u5728\u8ba1\u7b97\u673a\u4e2d\u3002\u5728\u8ba1\u7b97\u673a\u4e2d\uff0c\u6211\u4eec\u5c06 \\(1\\) \u4e2a\u4e8c\u8fdb\u5236\u4f4d\u79f0\u4e3a \\(1\\) \u6bd4\u7279\uff0c\u5e76\u89c4\u5b9a \\(1\\) \u5b57\u8282\uff08byte\uff09\u7531 \\(8\\) \u6bd4\u7279\uff08bits\uff09\u7ec4\u6210\u3002\u57fa\u672c\u6570\u636e\u7c7b\u578b\u7684\u53d6\u503c\u8303\u56f4\u53d6\u51b3\u4e8e\u5176\u5360\u7528\u7684\u7a7a\u95f4\u5927\u5c0f\uff0c\u4f8b\u5982\uff1a</p> <ul> <li>\u6574\u6570\u7c7b\u578b <code>byte</code> \u5360\u7528 \\(1\\) byte = \\(8\\) bits \uff0c\u53ef\u4ee5\u8868\u793a \\(2^{8}\\) \u4e2a\u4e0d\u540c\u7684\u6570\u5b57\uff1b</li> <li>\u6574\u6570\u7c7b\u578b <code>int</code> \u5360\u7528 \\(4\\) bytes = \\(32\\) bits \uff0c\u53ef\u4ee5\u8868\u793a \\(2^{32}\\) \u4e2a\u6570\u5b57\uff1b</li> </ul> <p>\u4e0b\u8868\u5217\u4e3e\u4e86\u5404\u79cd\u57fa\u672c\u6570\u636e\u7c7b\u578b\u7684\u5360\u7528\u7a7a\u95f4\u3001\u53d6\u503c\u8303\u56f4\u548c\u9ed8\u8ba4\u503c\u3002\u6b64\u8868\u683c\u65e0\u9700\u786c\u80cc\uff0c\u5927\u81f4\u7406\u89e3\u5373\u53ef\uff0c\u9700\u8981\u65f6\u53ef\u4ee5\u901a\u8fc7\u67e5\u8868\u6765\u56de\u5fc6\u3002</p> \u7c7b\u578b \u7b26\u53f7 \u5360\u7528\u7a7a\u95f4 \u6700\u5c0f\u503c \u6700\u5927\u503c \u9ed8\u8ba4\u503c \u6574\u6570 <code>byte</code> 1 byte \\(-2^7\\) (\\(-128\\)) \\(2^7 - 1\\) (\\(127\\)) \\(0\\) <code>short</code> 2 bytes \\(-2^{15}\\) \\(2^{15} - 1\\) \\(0\\) <code>int</code> 4 bytes \\(-2^{31}\\) \\(2^{31} - 1\\) \\(0\\) <code>long</code> 8 bytes \\(-2^{63}\\) \\(2^{63} - 1\\) \\(0\\) \u6d6e\u70b9\u6570 <code>float</code> 4 bytes \\(1.175 \\times 10^{-38}\\) \\(3.403 \\times 10^{38}\\) \\(0.0 f\\) <code>double</code> 8 bytes \\(2.225 \\times 10^{-308}\\) \\(1.798 \\times 10^{308}\\) \\(0.0\\) \u5b57\u7b26 <code>char</code> 2 bytes / 1 byte \\(0\\) \\(2^{16} - 1\\) \\(0\\) \u5e03\u5c14 <code>bool</code> 1 byte \\(\\text{false}\\) \\(\\text{true}\\) \\(\\text{false}\\) <p>Tip</p> <p>\u5b57\u7b26\u7684\u5360\u7528\u7a7a\u95f4\u5927\u5c0f\u53d6\u51b3\u4e8e\u7f16\u7a0b\u8bed\u8a00\u91c7\u7528\u7684\u5b57\u7b26\u7f16\u7801\u65b9\u6cd5\uff0c\u8be6\u89c1\u300c\u5b57\u7b26\u7f16\u7801\u300d\u7ae0\u8282\u3002</p> <p>\u73b0\u4ee3\u8ba1\u7b97\u673a CPU \u901a\u5e38\u5c06 1 \u5b57\u8282\u4f5c\u4e3a\u6700\u5c0f\u5bfb\u5740\u5185\u5b58\u5355\u5143\u3002\u56e0\u6b64\uff0c\u5373\u4f7f\u8868\u793a\u5e03\u5c14\u91cf\u4ec5\u9700 1 \u4f4d\uff08\\(0\\) \u6216 \\(1\\)\uff09\uff0c\u5b83\u5728\u5185\u5b58\u4e2d\u901a\u5e38\u88ab\u5b58\u50a8\u4e3a 1 \u5b57\u8282\u3002</p> <p>\u90a3\u4e48\uff0c\u57fa\u672c\u6570\u636e\u7c7b\u578b\u4e0e\u6570\u636e\u7ed3\u6784\u4e4b\u95f4\u6709\u4ec0\u4e48\u8054\u7cfb\u4e0e\u533a\u522b\u5462\uff1f\u6211\u4eec\u77e5\u9053\uff0c\u6570\u636e\u7ed3\u6784\u662f\u5728\u8ba1\u7b97\u673a\u4e2d\u7ec4\u7ec7\u4e0e\u5b58\u50a8\u6570\u636e\u7684\u65b9\u5f0f\u3002\u5b83\u7684\u4e3b\u8bed\u662f\u201c\u7ed3\u6784\u201d\uff0c\u800c\u975e\u201c\u6570\u636e\u201d\u3002\u5982\u679c\u60f3\u8981\u8868\u793a\u201c\u4e00\u6392\u6570\u5b57\u201d\uff0c\u6211\u4eec\u81ea\u7136\u4f1a\u60f3\u5230\u4f7f\u7528\u6570\u7ec4\u3002\u8fd9\u662f\u56e0\u4e3a\u6570\u7ec4\u7684\u7ebf\u6027\u7ed3\u6784\u53ef\u4ee5\u8868\u793a\u6570\u5b57\u7684\u76f8\u90bb\u5173\u7cfb\u548c\u987a\u5e8f\u5173\u7cfb\uff0c\u4f46\u81f3\u4e8e\u5b58\u50a8\u7684\u5185\u5bb9\u662f\u6574\u6570 <code>int</code> \u3001\u5c0f\u6570 <code>float</code> \u3001\u8fd8\u662f\u5b57\u7b26 <code>char</code> \uff0c\u5219\u4e0e\u201c\u6570\u636e\u7ed3\u6784\u201d\u65e0\u5173\u3002</p> <p>\u6362\u53e5\u8bdd\u8bf4\uff0c\u57fa\u672c\u6570\u636e\u7c7b\u578b\u63d0\u4f9b\u4e86\u6570\u636e\u7684\u201c\u5185\u5bb9\u7c7b\u578b\u201d\uff0c\u800c\u6570\u636e\u7ed3\u6784\u63d0\u4f9b\u4e86\u6570\u636e\u7684\u201c\u7ec4\u7ec7\u65b9\u5f0f\u201d\u3002\u5982\u4ee5\u4e0b\u4ee3\u7801\u6240\u793a\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u4e0d\u540c\u57fa\u672c\u6570\u636e\u7c7b\u578b\u6765\u521d\u59cb\u5316\u6570\u7ec4\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart <pre><code>/* \u4f7f\u7528\u591a\u79cd\u300c\u57fa\u672c\u6570\u636e\u7c7b\u578b\u300d\u6765\u521d\u59cb\u5316\u300c\u6570\u7ec4\u300d */\nint[] numbers = new int[5];\nfloat[] decimals = new float[5];\nchar[] characters = new char[5];\nboolean[] booleans = new boolean[5];\n</code></pre> <pre><code>/* \u4f7f\u7528\u591a\u79cd\u300c\u57fa\u672c\u6570\u636e\u7c7b\u578b\u300d\u6765\u521d\u59cb\u5316\u300c\u6570\u7ec4\u300d */\nint numbers[5];\nfloat decimals[5];\nchar characters[5];\nbool booleans[5];\n</code></pre> <pre><code># Python \u7684 list \u53ef\u4ee5\u81ea\u7531\u5b58\u50a8\u5404\u79cd\u57fa\u672c\u6570\u636e\u7c7b\u578b\u548c\u5bf9\u8c61\nlist = [0, 0.0, 'a', False]\n</code></pre> <pre><code>// \u4f7f\u7528\u591a\u79cd\u300c\u57fa\u672c\u6570\u636e\u7c7b\u578b\u300d\u6765\u521d\u59cb\u5316\u300c\u6570\u7ec4\u300d\nvar numbers = [5]int{}\nvar decimals = [5]float64{}\nvar characters = [5]byte{}\nvar booleans = [5]bool{}\n</code></pre> <pre><code>/* JavaScript \u7684\u6570\u7ec4\u53ef\u4ee5\u81ea\u7531\u5b58\u50a8\u5404\u79cd\u57fa\u672c\u6570\u636e\u7c7b\u578b\u548c\u5bf9\u8c61 */\nconst array = [0, 0.0, 'a', false];\n</code></pre> <pre><code>/* \u4f7f\u7528\u591a\u79cd\u300c\u57fa\u672c\u6570\u636e\u7c7b\u578b\u300d\u6765\u521d\u59cb\u5316\u300c\u6570\u7ec4\u300d */\nconst numbers: number[] = [];\nconst characters: string[] = [];\nconst booleans: boolean[] = [];\n</code></pre> <pre><code>/* \u4f7f\u7528\u591a\u79cd\u300c\u57fa\u672c\u6570\u636e\u7c7b\u578b\u300d\u6765\u521d\u59cb\u5316\u300c\u6570\u7ec4\u300d */\nint numbers[10];\nfloat decimals[10];\nchar characters[10];\nbool booleans[10];\n</code></pre> <pre><code>/* \u4f7f\u7528\u591a\u79cd\u300c\u57fa\u672c\u6570\u636e\u7c7b\u578b\u300d\u6765\u521d\u59cb\u5316\u300c\u6570\u7ec4\u300d */\nint[] numbers = new int[5];\nfloat[] decimals = new float[5];\nchar[] characters = new char[5];\nbool[] booleans = new bool[5];\n</code></pre> <pre><code>/* \u4f7f\u7528\u591a\u79cd\u300c\u57fa\u672c\u6570\u636e\u7c7b\u578b\u300d\u6765\u521d\u59cb\u5316\u300c\u6570\u7ec4\u300d */\nlet numbers = Array(repeating: Int(), count: 5)\nlet decimals = Array(repeating: Double(), count: 5)\nlet characters = Array(repeating: Character(\"a\"), count: 5)\nlet booleans = Array(repeating: Bool(), count: 5)\n</code></pre> <pre><code>\n</code></pre> <pre><code>/* \u4f7f\u7528\u591a\u79cd\u300c\u57fa\u672c\u6570\u636e\u7c7b\u578b\u300d\u6765\u521d\u59cb\u5316\u300c\u6570\u7ec4\u300d */\nList&lt;int&gt; numbers = List.filled(5, 0);\nList&lt;double&gt; decimals = List.filled(5, 0.0);\nList&lt;String&gt; characters = List.filled(5, 'a');\nList&lt;bool&gt; booleans = List.filled(5, false);\n</code></pre>"},{"location":"chapter_data_structure/character_encoding/","title":"3.4. \u00a0 \u5b57\u7b26\u7f16\u7801 *","text":"<p>\u5728\u8ba1\u7b97\u673a\u4e2d\uff0c\u6240\u6709\u6570\u636e\u90fd\u662f\u4ee5\u4e8c\u8fdb\u5236\u6570\u7684\u5f62\u5f0f\u5b58\u50a8\u7684\uff0c\u5b57\u7b26 <code>char</code> \u4e5f\u4e0d\u4f8b\u5916\u3002\u4e3a\u4e86\u8868\u793a\u5b57\u7b26\uff0c\u6211\u4eec\u9700\u8981\u5efa\u7acb\u4e00\u5957\u300c\u5b57\u7b26\u96c6\u300d\uff0c\u89c4\u5b9a\u6bcf\u4e2a\u5b57\u7b26\u548c\u4e8c\u8fdb\u5236\u6570\u4e4b\u95f4\u7684\u4e00\u4e00\u5bf9\u5e94\u5173\u7cfb\u3002\u6709\u4e86\u5b57\u7b26\u96c6\u4e4b\u540e\uff0c\u8ba1\u7b97\u673a\u5c31\u53ef\u4ee5\u901a\u8fc7\u67e5\u8868\u5b8c\u6210\u4e8c\u8fdb\u5236\u6570\u5230\u5b57\u7b26\u7684\u8f6c\u6362\u3002</p>"},{"location":"chapter_data_structure/character_encoding/#341-ascii","title":"3.4.1. \u00a0 ASCII \u5b57\u7b26\u96c6","text":"<p>\u300cASCII \u7801\u300d\u662f\u6700\u65e9\u51fa\u73b0\u7684\u5b57\u7b26\u96c6\uff0c\u5168\u79f0\u4e3a\u201c\u7f8e\u56fd\u6807\u51c6\u4fe1\u606f\u4ea4\u6362\u4ee3\u7801\u201d\u3002\u5b83\u4f7f\u7528 7 \u4f4d\u4e8c\u8fdb\u5236\u6570\uff08\u5373\u4e00\u4e2a\u5b57\u8282\u7684\u4f4e 7 \u4f4d\uff09\u8868\u793a\u4e00\u4e2a\u5b57\u7b26\uff0c\u6700\u591a\u80fd\u591f\u8868\u793a 128 \u4e2a\u4e0d\u540c\u7684\u5b57\u7b26\u3002\u8fd9\u5305\u62ec\u82f1\u6587\u5b57\u6bcd\u7684\u5927\u5c0f\u5199\u3001\u6570\u5b57 0-9 \u3001\u4e00\u4e9b\u6807\u70b9\u7b26\u53f7\uff0c\u4ee5\u53ca\u4e00\u4e9b\u63a7\u5236\u5b57\u7b26\uff08\u5982\u6362\u884c\u7b26\u548c\u5236\u8868\u7b26\uff09\u3002</p> <p></p> <p> Fig. ASCII \u7801 </p> <p>\u7136\u800c\uff0cASCII \u7801\u4ec5\u80fd\u591f\u8868\u793a\u82f1\u6587\u3002\u968f\u7740\u8ba1\u7b97\u673a\u7684\u5168\u7403\u5316\uff0c\u8bde\u751f\u4e86\u4e00\u79cd\u80fd\u591f\u8868\u793a\u66f4\u591a\u8bed\u8a00\u7684\u5b57\u7b26\u96c6\u300cEASCII\u300d\u3002\u5b83\u5728 ASCII \u7684 7 \u4f4d\u57fa\u7840\u4e0a\u6269\u5c55\u5230 8 \u4f4d\uff0c\u80fd\u591f\u8868\u793a 256 \u4e2a\u4e0d\u540c\u7684\u5b57\u7b26\u3002\u5728\u4e16\u754c\u8303\u56f4\u5185\uff0c\u9646\u7eed\u51fa\u73b0\u4e86\u4e00\u6279\u9002\u7528\u4e8e\u4e0d\u540c\u5730\u533a\u7684 EASCII \u5b57\u7b26\u96c6\u3002\u8fd9\u4e9b\u5b57\u7b26\u96c6\u7684\u524d 128 \u4e2a\u5b57\u7b26\u7edf\u4e00\u4e3a ASCII \u7801\uff0c\u540e 128 \u4e2a\u5b57\u7b26\u5b9a\u4e49\u4e0d\u540c\uff0c\u4ee5\u9002\u5e94\u4e0d\u540c\u8bed\u8a00\u7684\u9700\u6c42\u3002</p>"},{"location":"chapter_data_structure/character_encoding/#342-gbk","title":"3.4.2. \u00a0 GBK \u5b57\u7b26\u96c6","text":"<p>\u540e\u6765\u4eba\u4eec\u53d1\u73b0\uff0cEASCII \u7801\u4ecd\u7136\u65e0\u6cd5\u6ee1\u8db3\u8bb8\u591a\u8bed\u8a00\u7684\u5b57\u7b26\u6570\u91cf\u8981\u6c42\u3002\u4f8b\u5982\uff0c\u6c49\u5b57\u5927\u7ea6\u6709\u8fd1\u5341\u4e07\u4e2a\uff0c\u5149\u65e5\u5e38\u4f7f\u7528\u7684\u5c31\u6709\u51e0\u5343\u4e2a\u3002\u4e2d\u56fd\u56fd\u5bb6\u6807\u51c6\u603b\u5c40\u4e8e 1980 \u5e74\u53d1\u5e03\u4e86\u300cGB2312\u300d\u5b57\u7b26\u96c6\uff0c\u5176\u6536\u5f55\u4e86 6763 \u4e2a\u6c49\u5b57\uff0c\u57fa\u672c\u6ee1\u8db3\u4e86\u6c49\u5b57\u7684\u8ba1\u7b97\u673a\u5904\u7406\u9700\u8981\u3002</p> <p>\u7136\u800c\uff0cGB2312 \u65e0\u6cd5\u5904\u7406\u90e8\u5206\u7684\u7f55\u89c1\u5b57\u548c\u7e41\u4f53\u5b57\u3002\u4e4b\u540e\u5728 GB2312 \u7684\u57fa\u7840\u4e0a\uff0c\u6269\u5c55\u5f97\u5230\u4e86\u300cGBK\u300d\u5b57\u7b26\u96c6\uff0c\u5b83\u5171\u6536\u5f55\u4e86 21886 \u4e2a\u6c49\u5b57\u3002\u5728 GBK \u7f16\u7801\u65b9\u6848\u4e2d\uff0cASCII \u5b57\u7b26\u4f7f\u7528\u4e00\u4e2a\u5b57\u8282\u8868\u793a\uff0c\u6c49\u5b57\u4f7f\u7528\u4e24\u4e2a\u5b57\u8282\u8868\u793a\u3002</p>"},{"location":"chapter_data_structure/character_encoding/#343-unicode","title":"3.4.3. \u00a0 Unicode \u5b57\u7b26\u96c6","text":"<p>\u968f\u7740\u8ba1\u7b97\u673a\u7684\u84ec\u52c3\u53d1\u5c55\uff0c\u5b57\u7b26\u96c6\u4e0e\u7f16\u7801\u6807\u51c6\u767e\u82b1\u9f50\u653e\uff0c\u800c\u8fd9\u5e26\u6765\u4e86\u8bb8\u591a\u95ee\u9898\u3002\u4e00\u65b9\u9762\uff0c\u8fd9\u4e9b\u5b57\u7b26\u96c6\u4e00\u822c\u53ea\u5b9a\u4e49\u4e86\u7279\u5b9a\u8bed\u8a00\u7684\u5b57\u7b26\uff0c\u65e0\u6cd5\u5728\u591a\u8bed\u8a00\u73af\u5883\u4e0b\u6b63\u5e38\u5de5\u4f5c\uff1b\u53e6\u4e00\u65b9\u9762\uff0c\u540c\u4e00\u79cd\u8bed\u8a00\u4e5f\u5b58\u5728\u591a\u79cd\u5b57\u7b26\u96c6\u6807\u51c6\uff0c\u5982\u679c\u4e24\u53f0\u7535\u8111\u5b89\u88c5\u7684\u662f\u4e0d\u540c\u7684\u7f16\u7801\u6807\u51c6\uff0c\u5219\u5728\u4fe1\u606f\u4f20\u9012\u65f6\u5c31\u4f1a\u51fa\u73b0\u4e71\u7801\u3002</p> <p>\u90a3\u4e2a\u65f6\u4ee3\u7684\u4eba\u4eec\u5c31\u5728\u60f3\uff1a\u5982\u679c\u63a8\u51fa\u4e00\u4e2a\u8db3\u591f\u5b8c\u6574\u7684\u5b57\u7b26\u96c6\uff0c\u5c06\u4e16\u754c\u8303\u56f4\u5185\u7684\u6240\u6709\u8bed\u8a00\u548c\u7b26\u53f7\u90fd\u6536\u5f55\u5176\u4e2d\uff0c\u4e0d\u5c31\u53ef\u4ee5\u89e3\u51b3\u8de8\u8bed\u8a00\u73af\u5883\u548c\u4e71\u7801\u95ee\u9898\u4e86\u5417\uff1f\u5728\u8fd9\u79cd\u60f3\u6cd5\u7684\u9a71\u52a8\u4e0b\uff0c\u4e00\u4e2a\u5927\u800c\u5168\u7684\u5b57\u7b26\u96c6 Unicode \u5e94\u8fd0\u800c\u751f\u3002</p> <p>\u300cUnicode\u300d\u7684\u5168\u79f0\u4e3a\u201c\u7edf\u4e00\u5b57\u7b26\u7f16\u7801\u201d\uff0c\u7406\u8bba\u4e0a\u80fd\u5bb9\u7eb3\u4e00\u767e\u591a\u4e07\u4e2a\u5b57\u7b26\u3002\u5b83\u81f4\u529b\u4e8e\u5c06\u5168\u7403\u8303\u56f4\u5185\u7684\u5b57\u7b26\u7eb3\u5165\u5230\u7edf\u4e00\u7684\u5b57\u7b26\u96c6\u4e4b\u4e2d\uff0c\u63d0\u4f9b\u4e00\u79cd\u901a\u7528\u7684\u5b57\u7b26\u96c6\u6765\u5904\u7406\u548c\u663e\u793a\u5404\u79cd\u8bed\u8a00\u6587\u5b57\uff0c\u51cf\u5c11\u56e0\u4e3a\u7f16\u7801\u6807\u51c6\u4e0d\u540c\u800c\u4ea7\u751f\u7684\u4e71\u7801\u95ee\u9898\u3002</p> <p>\u81ea 1991 \u5e74\u53d1\u5e03\u4ee5\u6765\uff0cUnicode \u4e0d\u65ad\u6269\u5145\u65b0\u7684\u8bed\u8a00\u4e0e\u5b57\u7b26\u3002\u622a\u6b62 2022 \u5e74 9 \u6708\uff0cUnicode \u5df2\u7ecf\u5305\u542b 149186 \u4e2a\u5b57\u7b26\uff0c\u5305\u62ec\u5404\u79cd\u8bed\u8a00\u7684\u5b57\u7b26\u3001\u7b26\u53f7\u3001\u751a\u81f3\u662f\u8868\u60c5\u7b26\u53f7\u7b49\u3002\u5728\u5e9e\u5927\u7684 Unicode \u5b57\u7b26\u96c6\u4e2d\uff0c\u5e38\u7528\u7684\u5b57\u7b26\u5360\u7528 2 \u5b57\u8282\uff0c\u6709\u4e9b\u751f\u50fb\u7684\u5b57\u7b26\u5360 3 \u5b57\u8282\u751a\u81f3 4 \u5b57\u8282\u3002</p> <p>Unicode \u662f\u4e00\u79cd\u5b57\u7b26\u96c6\u6807\u51c6\uff0c\u672c\u8d28\u4e0a\u662f\u7ed9\u6bcf\u4e2a\u5b57\u7b26\u5206\u914d\u4e00\u4e2a\u7f16\u53f7\uff08\u79f0\u4e3a\u201c\u7801\u70b9\u201d\uff09\uff0c\u4f46\u5b83\u5e76\u6ca1\u6709\u89c4\u5b9a\u5728\u8ba1\u7b97\u673a\u4e2d\u5982\u4f55\u5b58\u50a8\u8fd9\u4e9b\u5b57\u7b26\u7801\u70b9\u3002\u6211\u4eec\u4e0d\u7981\u4f1a\u95ee\uff1a\u5f53\u591a\u79cd\u957f\u5ea6\u7684 Unicode \u7801\u70b9\u540c\u65f6\u51fa\u73b0\u5728\u540c\u4e00\u4e2a\u6587\u672c\u4e2d\u65f6\uff0c\u7cfb\u7edf\u5982\u4f55\u89e3\u6790\u5b57\u7b26\uff1f\u4f8b\u5982\uff0c\u7ed9\u5b9a\u4e00\u4e2a\u957f\u5ea6\u4e3a 2 \u5b57\u8282\u7684\u7f16\u7801\uff0c\u7cfb\u7edf\u5982\u4f55\u786e\u8ba4\u5b83\u662f\u4e00\u4e2a 2 \u5b57\u8282\u7684\u5b57\u7b26\u8fd8\u662f\u4e24\u4e2a 1 \u5b57\u8282\u7684\u5b57\u7b26\uff1f</p> <p>\u5bf9\u4e8e\u4ee5\u4e0a\u95ee\u9898\uff0c\u4e00\u79cd\u76f4\u63a5\u7684\u89e3\u51b3\u65b9\u6848\u662f\u5c06\u6240\u6709\u5b57\u7b26\u5b58\u50a8\u4e3a\u7b49\u957f\u7684\u7f16\u7801\u3002\u5982\u4e0b\u56fe\u6240\u793a\uff0c\u201cHello\u201d\u4e2d\u7684\u6bcf\u4e2a\u5b57\u7b26\u5360\u7528 1 \u5b57\u8282\uff0c\u201c\u7b97\u6cd5\u201d\u4e2d\u7684\u6bcf\u4e2a\u5b57\u7b26\u5360\u7528 2 \u5b57\u8282\u3002\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u9ad8\u4f4d\u586b 0 \uff0c\u5c06\u201cHello \u7b97\u6cd5\u201d\u4e2d\u7684\u6240\u6709\u5b57\u7b26\u90fd\u7f16\u7801\u4e3a 2 \u5b57\u8282\u957f\u5ea6\u3002\u8fd9\u6837\u7cfb\u7edf\u5c31\u53ef\u4ee5\u6bcf\u9694 2 \u5b57\u8282\u89e3\u6790\u4e00\u4e2a\u5b57\u7b26\uff0c\u6062\u590d\u51fa\u8fd9\u4e2a\u77ed\u8bed\u7684\u5185\u5bb9\u4e86\u3002</p> <p></p> <p> Fig. Unicode \u7f16\u7801\u793a\u4f8b </p> <p>\u7136\u800c\uff0cASCII \u7801\u5df2\u7ecf\u5411\u6211\u4eec\u8bc1\u660e\uff0c\u7f16\u7801\u82f1\u6587\u53ea\u9700\u8981 1 \u5b57\u8282\u3002\u82e5\u91c7\u7528\u4e0a\u8ff0\u65b9\u6848\uff0c\u82f1\u6587\u6587\u672c\u5360\u7528\u7a7a\u95f4\u7684\u5927\u5c0f\u5c06\u4f1a\u662f ASCII \u7f16\u7801\u4e0b\u5927\u5c0f\u7684 2 \u500d\uff0c\u975e\u5e38\u6d6a\u8d39\u5185\u5b58\u7a7a\u95f4\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u9700\u8981\u4e00\u79cd\u66f4\u52a0\u9ad8\u6548\u7684 Unicode \u7f16\u7801\u65b9\u6cd5\u3002</p>"},{"location":"chapter_data_structure/character_encoding/#344-utf-8","title":"3.4.4. \u00a0 UTF-8 \u7f16\u7801","text":"<p>\u76ee\u524d\uff0cUTF-8 \u5df2\u6210\u4e3a\u56fd\u9645\u4e0a\u4f7f\u7528\u6700\u5e7f\u6cdb\u7684 Unicode \u7f16\u7801\u65b9\u6cd5\u3002\u5b83\u662f\u4e00\u79cd\u53ef\u53d8\u957f\u7684\u7f16\u7801\uff0c\u4f7f\u7528 1 \u5230 4 \u4e2a\u5b57\u8282\u6765\u8868\u793a\u4e00\u4e2a\u5b57\u7b26\uff0c\u6839\u636e\u5b57\u7b26\u7684\u590d\u6742\u6027\u800c\u53d8\u3002ASCII \u5b57\u7b26\u53ea\u9700\u8981 1 \u4e2a\u5b57\u8282\uff0c\u62c9\u4e01\u5b57\u6bcd\u548c\u5e0c\u814a\u5b57\u6bcd\u9700\u8981 2 \u4e2a\u5b57\u8282\uff0c\u5e38\u7528\u7684\u4e2d\u6587\u5b57\u7b26\u9700\u8981 3 \u4e2a\u5b57\u8282\uff0c\u5176\u4ed6\u7684\u4e00\u4e9b\u751f\u50fb\u5b57\u7b26\u9700\u8981 4 \u4e2a\u5b57\u8282\u3002</p> <p>UTF-8 \u7684\u7f16\u7801\u89c4\u5219\u5e76\u4e0d\u590d\u6742\uff0c\u5206\u4e3a\u4e24\u79cd\u60c5\u51b5\uff1a</p> <ul> <li>\u5bf9\u4e8e\u957f\u5ea6\u4e3a 1 \u5b57\u8282\u7684\u5b57\u7b26\uff0c\u5c06\u6700\u9ad8\u4f4d\u8bbe\u7f6e\u4e3a \\(0\\) \u3001\u5176\u4f59 7 \u4f4d\u8bbe\u7f6e\u4e3a Unicode \u7801\u70b9\u3002\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0cASCII \u5b57\u7b26\u5728 Unicode \u5b57\u7b26\u96c6\u4e2d\u5360\u636e\u4e86\u524d 128 \u4e2a\u7801\u70b9\u3002\u4e5f\u5c31\u662f\u8bf4\uff0cUTF-8 \u7f16\u7801\u53ef\u4ee5\u5411\u4e0b\u517c\u5bb9 ASCII \u7801\u3002\u8fd9\u610f\u5473\u7740\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528 UTF-8 \u6765\u89e3\u6790\u5e74\u4ee3\u4e45\u8fdc\u7684 ASCII \u7801\u6587\u672c\u3002</li> <li>\u5bf9\u4e8e\u957f\u5ea6\u4e3a \\(n\\) \u5b57\u8282\u7684\u5b57\u7b26\uff08\u5176\u4e2d \\(n &gt; 1\\)\uff09\uff0c\u5c06\u9996\u4e2a\u5b57\u8282\u7684\u9ad8 \\(n\\) \u4f4d\u90fd\u8bbe\u7f6e\u4e3a \\(1\\) \u3001\u7b2c \\(n + 1\\) \u4f4d\u8bbe\u7f6e\u4e3a \\(0\\) \uff1b\u4ece\u7b2c\u4e8c\u4e2a\u5b57\u8282\u5f00\u59cb\uff0c\u5c06\u6bcf\u4e2a\u5b57\u8282\u7684\u9ad8 2 \u4f4d\u90fd\u8bbe\u7f6e\u4e3a \\(10\\) \uff1b\u5176\u4f59\u6240\u6709\u4f4d\u7528\u4e8e\u586b\u5145\u5b57\u7b26\u7684 Unicode \u7801\u70b9\u3002</li> </ul> <p>\u4e0b\u56fe\u5c55\u793a\u4e86\u201cHello\u7b97\u6cd5\u201d\u5bf9\u5e94\u7684 UTF-8 \u7f16\u7801\u3002\u5c06\u6700\u9ad8 \\(n\\) \u4f4d\u8bbe\u7f6e\u4e3a \\(1\\) \u6bd4\u8f83\u5bb9\u6613\u7406\u89e3\uff0c\u53ef\u4ee5\u5411\u7cfb\u7edf\u6307\u51fa\u5b57\u7b26\u7684\u957f\u5ea6\u4e3a \\(n\\) \u3002\u90a3\u4e48\uff0c\u4e3a\u4ec0\u4e48\u8981\u5c06\u5176\u4f59\u6240\u6709\u5b57\u8282\u7684\u9ad8 2 \u4f4d\u90fd\u8bbe\u7f6e\u4e3a \\(10\\) \u5462\uff1f\u5b9e\u9645\u4e0a\uff0c\u8fd9\u4e2a \\(10\\) \u80fd\u591f\u8d77\u5230\u6821\u9a8c\u7b26\u7684\u4f5c\u7528\uff0c\u56e0\u4e3a\u5728 UTF-8 \u7f16\u7801\u89c4\u5219\u4e0b\uff0c\u4e0d\u53ef\u80fd\u6709\u5b57\u7b26\u7684\u6700\u9ad8\u4e24\u4f4d\u662f \\(10\\) \u3002\u8fd9\u662f\u56e0\u4e3a\u957f\u5ea6\u4e3a 1 \u5b57\u8282\u7684\u5b57\u7b26\u7684\u6700\u9ad8\u4e00\u4f4d\u662f \\(0\\) \u3002\u5047\u8bbe\u7cfb\u7edf\u4ece\u4e00\u4e2a\u9519\u8bef\u7684\u5b57\u8282\u5f00\u59cb\u89e3\u6790\u6587\u672c\uff0c\u5b57\u8282\u5934\u90e8\u7684 \\(10\\) \u80fd\u591f\u5e2e\u52a9\u7cfb\u7edf\u5feb\u901f\u7684\u5224\u65ad\u51fa\u5f02\u5e38\u3002</p> <p></p> <p> Fig. UTF-8 \u7f16\u7801\u793a\u4f8b </p> <p>\u9664\u4e86 UTF-8 \u4e4b\u5916\uff0c\u5e38\u89c1\u7684\u7f16\u7801\u65b9\u5f0f\u8fd8\u5305\u62ec UTF-16 \u548c UTF-32 \u3002\u5b83\u4eec\u4e3a Unicode \u5b57\u7b26\u96c6\u63d0\u4f9b\u4e86\u4e0d\u540c\u7684\u7f16\u7801\u65b9\u6cd5\u3002</p> <ul> <li>UTF-16 \u7f16\u7801\uff1a\u4f7f\u7528 2 \u6216 4 \u4e2a\u5b57\u8282\u6765\u8868\u793a\u4e00\u4e2a\u5b57\u7b26\u3002\u6240\u6709\u7684 ASCII \u5b57\u7b26\u548c\u5f88\u591a\u5e38\u7528\u7684\u975e\u82f1\u6587\u5b57\u7b26\uff0c\u90fd\u7528 2 \u4e2a\u5b57\u8282\u8868\u793a\uff1b\u5c11\u6570\u5b57\u7b26\u9700\u8981\u7528\u5230 4 \u4e2a\u5b57\u8282\u8868\u793a\u3002\u5bf9\u4e8e 2 \u5b57\u8282\u7684\u5b57\u7b26\uff0cUTF-16 \u7f16\u7801\u4e0e Unicode \u7801\u70b9\u76f8\u7b49\u3002</li> <li>UTF-32 \u7f16\u7801\uff1a\u6bcf\u4e2a\u5b57\u7b26\u90fd\u4f7f\u7528 4 \u4e2a\u5b57\u8282\u3002\u8fd9\u610f\u5473\u7740 UTF-32 \u4f1a\u6bd4 UTF-8 \u548c UTF-16 \u66f4\u5360\u7528\u7a7a\u95f4\uff0c\u7279\u522b\u662f\u5bf9\u4e8e\u4e3b\u8981\u4f7f\u7528 ASCII \u5b57\u7b26\u7684\u6587\u672c\u3002</li> </ul> <p>\u4ece\u5b58\u50a8\u7a7a\u95f4\u7684\u89d2\u5ea6\u770b\uff0c\u4f7f\u7528 UTF-8 \u8868\u793a\u82f1\u6587\u5b57\u7b26\u975e\u5e38\u9ad8\u6548\uff0c\u56e0\u4e3a\u5b83\u4ec5\u9700 1 \u4e2a\u5b57\u8282\uff1b\u4f7f\u7528 UTF-16 \u7f16\u7801\u67d0\u4e9b\u975e\u82f1\u6587\u5b57\u7b26\uff08\u4f8b\u5982\u4e2d\u6587\uff09\u4f1a\u66f4\u52a0\u9ad8\u6548\uff0c\u56e0\u4e3a\u5b83\u53ea\u9700\u8981 2 \u4e2a\u5b57\u8282\uff0c\u800c UTF-8 \u53ef\u80fd\u9700\u8981 3 \u4e2a\u5b57\u8282\u3002\u4ece\u517c\u5bb9\u6027\u7684\u89d2\u5ea6\u770b\uff0cUTF-8 \u7684\u901a\u7528\u6027\u6700\u4f73\uff0c\u8bb8\u591a\u5de5\u5177\u548c\u5e93\u90fd\u4f18\u5148\u652f\u6301 UTF-8 \u3002</p>"},{"location":"chapter_data_structure/character_encoding/#345","title":"3.4.5. \u00a0 \u7f16\u7a0b\u8bed\u8a00\u7684\u5b57\u7b26\u7f16\u7801","text":"<p>\u5bf9\u4e8e\u4ee5\u5f80\u7684\u5927\u591a\u6570\u7f16\u7a0b\u8bed\u8a00\uff0c\u7a0b\u5e8f\u8fd0\u884c\u4e2d\u7684\u5b57\u7b26\u4e32\u90fd\u91c7\u7528 UTF-16 \u6216 UTF-32 \u8fd9\u7c7b\u7b49\u957f\u7684\u7f16\u7801\u3002\u8fd9\u662f\u56e0\u4e3a\u5728\u7b49\u957f\u7f16\u7801\u4e0b\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u5b57\u7b26\u4e32\u770b\u4f5c\u6570\u7ec4\u6765\u5904\u7406\uff0c\u5177\u4f53\u6765\u8bf4\uff1a</p> <ul> <li>\u968f\u673a\u8bbf\u95ee: UTF-16 \u7f16\u7801\u7684\u5b57\u7b26\u4e32\u53ef\u4ee5\u5f88\u5bb9\u6613\u5730\u8fdb\u884c\u968f\u673a\u8bbf\u95ee\u3002UTF-8 \u662f\u4e00\u79cd\u53d8\u957f\u7f16\u7801\uff0c\u8981\u627e\u5230\u7b2c \\(i\\) \u4e2a\u5b57\u7b26\uff0c\u6211\u4eec\u9700\u8981\u4ece\u5b57\u7b26\u4e32\u7684\u5f00\u59cb\u5904\u904d\u5386\u5230\u7b2c \\(i\\) \u4e2a\u5b57\u7b26\uff0c\u8fd9\u9700\u8981 \\(O(n)\\) \u7684\u65f6\u95f4\u3002</li> <li>\u5b57\u7b26\u8ba1\u6570: \u4e0e\u968f\u673a\u8bbf\u95ee\u7c7b\u4f3c\uff0c\u8ba1\u7b97 UTF-16 \u5b57\u7b26\u4e32\u7684\u957f\u5ea6\u4e5f\u662f \\(O(1)\\) \u7684\u64cd\u4f5c\u3002\u4f46\u662f\uff0c\u8ba1\u7b97 UTF-8 \u7f16\u7801\u7684\u5b57\u7b26\u4e32\u7684\u957f\u5ea6\u9700\u8981\u904d\u5386\u6574\u4e2a\u5b57\u7b26\u4e32\u3002</li> <li>\u5b57\u7b26\u4e32\u64cd\u4f5c: \u5728 UTF-16 \u7f16\u7801\u7684\u5b57\u7b26\u4e32\u4e2d\uff0c\u5f88\u591a\u5b57\u7b26\u4e32\u64cd\u4f5c\uff08\u5982\u5206\u5272\u3001\u8fde\u63a5\u3001\u63d2\u5165\u3001\u5220\u9664\u7b49\uff09\u90fd\u66f4\u5bb9\u6613\u8fdb\u884c\u3002\u5728 UTF-8 \u7f16\u7801\u7684\u5b57\u7b26\u4e32\u4e0a\u8fdb\u884c\u8fd9\u4e9b\u64cd\u4f5c\u901a\u5e38\u9700\u8981\u989d\u5916\u7684\u8ba1\u7b97\uff0c\u4ee5\u786e\u4fdd\u4e0d\u4f1a\u4ea7\u751f\u65e0\u6548\u7684 UTF-8 \u7f16\u7801\u3002</li> </ul> <p>\u7f16\u7a0b\u8bed\u8a00\u7684\u5b57\u7b26\u7f16\u7801\u65b9\u6848\u8bbe\u8ba1\u662f\u4e00\u4e2a\u5f88\u6709\u8da3\u7684\u8bdd\u9898\uff0c\u6d89\u53ca\u5230\u8bb8\u591a\u56e0\u7d20\uff1a</p> <ul> <li>Java \u7684 <code>String</code> \u7c7b\u578b\u4f7f\u7528 UTF-16 \u7f16\u7801\uff0c\u6bcf\u4e2a\u5b57\u7b26\u5360\u7528 2 \u5b57\u8282\u3002\u8fd9\u662f\u56e0\u4e3a Java \u8bed\u8a00\u8bbe\u8ba1\u4e4b\u521d\uff0c\u4eba\u4eec\u8ba4\u4e3a 16 \u4f4d\u8db3\u4ee5\u8868\u793a\u6240\u6709\u53ef\u80fd\u7684\u5b57\u7b26\u3002\u7136\u800c\uff0c\u8fd9\u662f\u4e00\u4e2a\u4e0d\u6b63\u786e\u7684\u5224\u65ad\u3002\u540e\u6765 Unicode \u89c4\u8303\u6269\u5c55\u5230\u4e86\u8d85\u8fc7 16 \u4f4d\uff0c\u6240\u4ee5 Java \u4e2d\u7684\u5b57\u7b26\u73b0\u5728\u53ef\u80fd\u7531\u4e00\u5bf9 16 \u4f4d\u7684\u503c\uff08\u79f0\u4e3a\u201c\u4ee3\u7406\u5bf9\u201d\uff09\u8868\u793a\u3002</li> <li>JavaScript \u548c TypeScript \u7684\u5b57\u7b26\u4e32\u4f7f\u7528 UTF-16 \u7f16\u7801\u7684\u539f\u56e0\u4e0e Java \u7c7b\u4f3c\u3002\u5f53 JavaScript \u8bed\u8a00\u5728 1995 \u5e74\u88ab Netscape \u516c\u53f8\u9996\u6b21\u5f15\u5165\u65f6\uff0cUnicode \u8fd8\u5904\u4e8e\u76f8\u5bf9\u65e9\u671f\u7684\u9636\u6bb5\uff0c\u90a3\u65f6\u5019\u4f7f\u7528 16 \u4f4d\u7684\u7f16\u7801\u5c31\u8db3\u591f\u8868\u793a\u6240\u6709\u7684 Unicode \u5b57\u7b26\u4e86\u3002</li> <li>C# \u4f7f\u7528 UTF-16 \u7f16\u7801\uff0c\u4e3b\u8981\u56e0\u4e3a .NET \u5e73\u53f0\u662f\u7531 Microsoft \u8bbe\u8ba1\u7684\uff0c\u800c Microsoft \u7684\u5f88\u591a\u6280\u672f\uff0c\u5305\u62ec Windows \u64cd\u4f5c\u7cfb\u7edf\uff0c\u90fd\u5e7f\u6cdb\u5730\u4f7f\u7528 UTF-16 \u7f16\u7801\u3002</li> </ul> <p>\u7531\u4e8e\u4ee5\u4e0a\u7f16\u7a0b\u8bed\u8a00\u5bf9\u5b57\u7b26\u6570\u91cf\u7684\u4f4e\u4f30\uff0c\u5b83\u4eec\u4e0d\u5f97\u4e0d\u91c7\u53d6\u201c\u4ee3\u7406\u5bf9\u201d\u7684\u65b9\u5f0f\u6765\u8868\u793a\u8d85\u8fc7 16 \u4f4d\u957f\u5ea6\u7684 Unicode \u5b57\u7b26\u3002\u8fd9\u662f\u4e00\u4e2a\u4e0d\u5f97\u5df2\u4e3a\u4e4b\u7684\u65e0\u5948\u4e4b\u4e3e\u3002\u4e00\u65b9\u9762\uff0c\u5305\u542b\u4ee3\u7406\u5bf9\u7684\u5b57\u7b26\u4e32\u4e2d\uff0c\u4e00\u4e2a\u5b57\u7b26\u53ef\u80fd\u5360\u7528 2 \u5b57\u8282\u6216 4 \u5b57\u8282\uff0c\u56e0\u6b64\u4e27\u5931\u4e86\u7b49\u957f\u7f16\u7801\u7684\u4f18\u52bf\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u5904\u7406\u4ee3\u7406\u5bf9\u9700\u8981\u589e\u52a0\u989d\u5916\u4ee3\u7801\uff0c\u8fd9\u589e\u52a0\u4e86\u7f16\u7a0b\u7684\u590d\u6742\u6027\u548c Debug \u96be\u5ea6\u3002</p> <p>\u51fa\u4e8e\u4ee5\u4e0a\u539f\u56e0\uff0c\u90e8\u5206\u7f16\u7a0b\u8bed\u8a00\u63d0\u51fa\u4e86\u4e0d\u540c\u7684\u7f16\u7801\u65b9\u6848\uff1a</p> <ul> <li>Python 3 \u4f7f\u7528\u4e00\u79cd\u7075\u6d3b\u7684\u5b57\u7b26\u4e32\u8868\u793a\uff0c\u5b58\u50a8\u7684\u5b57\u7b26\u957f\u5ea6\u53d6\u51b3\u4e8e\u5b57\u7b26\u4e32\u4e2d\u6700\u5927\u7684 Unicode \u7801\u70b9\u3002\u5bf9\u4e8e\u5168\u90e8\u662f ASCII \u5b57\u7b26\u7684\u5b57\u7b26\u4e32\uff0c\u6bcf\u4e2a\u5b57\u7b26\u5360\u7528 1 \u4e2a\u5b57\u8282\uff1b\u5982\u679c\u5b57\u7b26\u4e32\u4e2d\u5305\u542b\u7684\u5b57\u7b26\u8d85\u51fa\u4e86 ASCII \u8303\u56f4\uff0c\u4f46\u5168\u90e8\u5728\u57fa\u672c\u591a\u8bed\u8a00\u5e73\u9762\uff08BMP\uff09\u5185\uff0c\u6bcf\u4e2a\u5b57\u7b26\u5360\u7528 2 \u4e2a\u5b57\u8282\uff1b\u5982\u679c\u5b57\u7b26\u4e32\u4e2d\u6709\u8d85\u51fa BMP \u7684\u5b57\u7b26\uff0c\u90a3\u4e48\u6bcf\u4e2a\u5b57\u7b26\u5360\u7528 4 \u4e2a\u5b57\u8282\u3002</li> <li>Go \u8bed\u8a00\u7684 <code>string</code> \u7c7b\u578b\u5728\u5185\u90e8\u4f7f\u7528 UTF-8 \u7f16\u7801\u3002Go \u8bed\u8a00\u8fd8\u63d0\u4f9b\u4e86 <code>rune</code> \u7c7b\u578b\uff0c\u5b83\u7528\u4e8e\u8868\u793a\u5355\u4e2a Unicode \u7801\u70b9\u3002</li> <li>Rust \u8bed\u8a00\u7684 str \u548c String \u7c7b\u578b\u5728\u5185\u90e8\u4f7f\u7528 UTF-8 \u7f16\u7801\u3002Rust \u4e5f\u63d0\u4f9b\u4e86 char \u7c7b\u578b\uff0c\u7528\u4e8e\u8868\u793a\u5355\u4e2a Unicode \u7801\u70b9\u3002</li> </ul> <p>\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u4ee5\u4e0a\u8ba8\u8bba\u7684\u90fd\u662f\u5b57\u7b26\u4e32\u5728\u7f16\u7a0b\u8bed\u8a00\u4e2d\u7684\u5b58\u50a8\u65b9\u5f0f\uff0c\u8fd9\u548c\u5b57\u7b26\u4e32\u5982\u4f55\u5728\u6587\u4ef6\u4e2d\u5b58\u50a8\u6216\u5728\u7f51\u7edc\u4e2d\u4f20\u8f93\u662f\u4e24\u4e2a\u4e0d\u540c\u7684\u95ee\u9898\u3002\u5728\u6587\u4ef6\u5b58\u50a8\u6216\u7f51\u7edc\u4f20\u8f93\u4e2d\uff0c\u6211\u4eec\u4e00\u822c\u4f1a\u5c06\u5b57\u7b26\u4e32\u7f16\u7801\u4e3a UTF-8 \u683c\u5f0f\uff0c\u4ee5\u8fbe\u5230\u6700\u4f18\u7684\u517c\u5bb9\u6027\u548c\u7a7a\u95f4\u6548\u7387\u3002</p>"},{"location":"chapter_data_structure/classification_of_data_structure/","title":"3.1. \u00a0 \u6570\u636e\u7ed3\u6784\u5206\u7c7b","text":"<p>\u6570\u636e\u7ed3\u6784\u53ef\u4ee5\u4ece\u903b\u8f91\u7ed3\u6784\u548c\u7269\u7406\u7ed3\u6784\u4e24\u4e2a\u7ef4\u5ea6\u8fdb\u884c\u5206\u7c7b\u3002</p>"},{"location":"chapter_data_structure/classification_of_data_structure/#311","title":"3.1.1. \u00a0 \u903b\u8f91\u7ed3\u6784\uff1a\u7ebf\u6027\u4e0e\u975e\u7ebf\u6027","text":"<p>\u300c\u903b\u8f91\u7ed3\u6784\u300d\u63ed\u793a\u4e86\u6570\u636e\u5143\u7d20\u4e4b\u95f4\u7684\u903b\u8f91\u5173\u7cfb\u3002\u5728\u6570\u7ec4\u548c\u94fe\u8868\u4e2d\uff0c\u6570\u636e\u6309\u7167\u987a\u5e8f\u4f9d\u6b21\u6392\u5217\uff0c\u4f53\u73b0\u4e86\u6570\u636e\u4e4b\u95f4\u7684\u7ebf\u6027\u5173\u7cfb\uff1b\u800c\u5728\u6811\u4e2d\uff0c\u6570\u636e\u4ece\u9876\u90e8\u5411\u4e0b\u6309\u5c42\u6b21\u6392\u5217\uff0c\u8868\u73b0\u51fa\u7956\u5148\u4e0e\u540e\u4ee3\u4e4b\u95f4\u7684\u6d3e\u751f\u5173\u7cfb\uff1b\u56fe\u5219\u7531\u8282\u70b9\u548c\u8fb9\u6784\u6210\uff0c\u53cd\u6620\u4e86\u590d\u6742\u7684\u7f51\u7edc\u5173\u7cfb\u3002</p> <p>\u903b\u8f91\u7ed3\u6784\u901a\u5e38\u5206\u4e3a\u300c\u7ebf\u6027\u300d\u548c\u300c\u975e\u7ebf\u6027\u300d\u4e24\u7c7b\u3002\u7ebf\u6027\u7ed3\u6784\u6bd4\u8f83\u76f4\u89c2\uff0c\u6307\u6570\u636e\u5728\u903b\u8f91\u5173\u7cfb\u4e0a\u5448\u7ebf\u6027\u6392\u5217\uff1b\u975e\u7ebf\u6027\u7ed3\u6784\u5219\u76f8\u53cd\uff0c\u5448\u975e\u7ebf\u6027\u6392\u5217\uff0c\u4f8b\u5982\u7f51\u72b6\u6216\u6811\u72b6\u7ed3\u6784\u3002</p> <ul> <li>\u7ebf\u6027\u6570\u636e\u7ed3\u6784\uff1a\u6570\u7ec4\u3001\u94fe\u8868\u3001\u6808\u3001\u961f\u5217\u3001\u54c8\u5e0c\u8868\uff1b</li> <li>\u975e\u7ebf\u6027\u6570\u636e\u7ed3\u6784\uff1a\u6811\u3001\u56fe\u3001\u5806\u3001\u54c8\u5e0c\u8868\uff1b</li> </ul> <p></p> <p> Fig. \u7ebf\u6027\u4e0e\u975e\u7ebf\u6027\u6570\u636e\u7ed3\u6784 </p>"},{"location":"chapter_data_structure/classification_of_data_structure/#312","title":"3.1.2. \u00a0 \u7269\u7406\u7ed3\u6784\uff1a\u8fde\u7eed\u4e0e\u79bb\u6563","text":"<p>\u5728\u8ba1\u7b97\u673a\u4e2d\uff0c\u5185\u5b58\u548c\u786c\u76d8\u662f\u4e24\u79cd\u4e3b\u8981\u7684\u5b58\u50a8\u786c\u4ef6\u8bbe\u5907\u3002\u300c\u786c\u76d8\u300d\u4e3b\u8981\u7528\u4e8e\u957f\u671f\u5b58\u50a8\u6570\u636e\uff0c\u5bb9\u91cf\u8f83\u5927\uff08\u901a\u5e38\u53ef\u8fbe\u5230 TB \u7ea7\u522b\uff09\u3001\u901f\u5ea6\u8f83\u6162\u3002\u300c\u5185\u5b58\u300d\u7528\u4e8e\u8fd0\u884c\u7a0b\u5e8f\u65f6\u6682\u5b58\u6570\u636e\uff0c\u901f\u5ea6\u8f83\u5feb\uff0c\u4f46\u5bb9\u91cf\u8f83\u5c0f\uff08\u901a\u5e38\u4e3a GB \u7ea7\u522b\uff09\u3002</p> <p>\u5728\u7b97\u6cd5\u8fd0\u884c\u8fc7\u7a0b\u4e2d\uff0c\u76f8\u5173\u6570\u636e\u90fd\u5b58\u50a8\u5728\u5185\u5b58\u4e2d\u3002\u4e0b\u56fe\u5c55\u793a\u4e86\u4e00\u4e2a\u8ba1\u7b97\u673a\u5185\u5b58\u6761\uff0c\u5176\u4e2d\u6bcf\u4e2a\u9ed1\u8272\u65b9\u5757\u90fd\u5305\u542b\u4e00\u5757\u5185\u5b58\u7a7a\u95f4\u3002\u6211\u4eec\u53ef\u4ee5\u5c06\u5185\u5b58\u60f3\u8c61\u6210\u4e00\u4e2a\u5de8\u5927\u7684 Excel \u8868\u683c\uff0c\u5176\u4e2d\u6bcf\u4e2a\u5355\u5143\u683c\u90fd\u53ef\u4ee5\u5b58\u50a8 1 byte \u7684\u6570\u636e\uff0c\u5728\u7b97\u6cd5\u8fd0\u884c\u65f6\uff0c\u6240\u6709\u6570\u636e\u90fd\u88ab\u5b58\u50a8\u5728\u8fd9\u4e9b\u5355\u5143\u683c\u4e2d\u3002</p> <p>\u7cfb\u7edf\u901a\u8fc7\u300c\u5185\u5b58\u5730\u5740 Memory Location\u300d\u6765\u8bbf\u95ee\u76ee\u6807\u5185\u5b58\u4f4d\u7f6e\u7684\u6570\u636e\u3002\u8ba1\u7b97\u673a\u6839\u636e\u7279\u5b9a\u89c4\u5219\u4e3a\u8868\u683c\u4e2d\u7684\u6bcf\u4e2a\u5355\u5143\u683c\u5206\u914d\u7f16\u53f7\uff0c\u786e\u4fdd\u6bcf\u4e2a\u5185\u5b58\u7a7a\u95f4\u90fd\u6709\u552f\u4e00\u7684\u5185\u5b58\u5730\u5740\u3002\u6709\u4e86\u8fd9\u4e9b\u5730\u5740\uff0c\u7a0b\u5e8f\u4fbf\u53ef\u4ee5\u8bbf\u95ee\u5185\u5b58\u4e2d\u7684\u6570\u636e\u3002</p> <p></p> <p> Fig. \u5185\u5b58\u6761\u3001\u5185\u5b58\u7a7a\u95f4\u3001\u5185\u5b58\u5730\u5740 </p> <p>\u5185\u5b58\u662f\u6240\u6709\u7a0b\u5e8f\u7684\u5171\u4eab\u8d44\u6e90\uff0c\u5f53\u5185\u5b58\u88ab\u67d0\u4e2a\u7a0b\u5e8f\u5360\u7528\u65f6\uff0c\u5176\u4ed6\u7a0b\u5e8f\u65e0\u6cd5\u540c\u65f6\u4f7f\u7528\u3002\u56e0\u6b64\uff0c\u5728\u6570\u636e\u7ed3\u6784\u4e0e\u7b97\u6cd5\u7684\u8bbe\u8ba1\u4e2d\uff0c\u5185\u5b58\u8d44\u6e90\u662f\u4e00\u4e2a\u91cd\u8981\u7684\u8003\u8651\u56e0\u7d20\u3002\u4f8b\u5982\uff0c\u7b97\u6cd5\u6240\u5360\u7528\u7684\u5185\u5b58\u5cf0\u503c\u4e0d\u5e94\u8d85\u8fc7\u7cfb\u7edf\u5269\u4f59\u7a7a\u95f2\u5185\u5b58\uff1b\u5982\u679c\u8fd0\u884c\u7684\u7a0b\u5e8f\u5f88\u591a\u5e76\u4e14\u7f3a\u5c11\u5927\u91cf\u8fde\u7eed\u7684\u5185\u5b58\u7a7a\u95f4\uff0c\u90a3\u4e48\u6240\u9009\u7528\u7684\u6570\u636e\u7ed3\u6784\u5fc5\u987b\u80fd\u591f\u5b58\u50a8\u5728\u79bb\u6563\u7684\u5185\u5b58\u7a7a\u95f4\u5185\u3002</p> <p>\u300c\u7269\u7406\u7ed3\u6784\u300d\u53cd\u6620\u4e86\u6570\u636e\u5728\u8ba1\u7b97\u673a\u5185\u5b58\u4e2d\u7684\u5b58\u50a8\u65b9\u5f0f\uff0c\u53ef\u5206\u4e3a\u6570\u7ec4\u7684\u8fde\u7eed\u7a7a\u95f4\u5b58\u50a8\u548c\u94fe\u8868\u7684\u79bb\u6563\u7a7a\u95f4\u5b58\u50a8\u3002\u7269\u7406\u7ed3\u6784\u4ece\u5e95\u5c42\u51b3\u5b9a\u4e86\u6570\u636e\u7684\u8bbf\u95ee\u3001\u66f4\u65b0\u3001\u589e\u5220\u7b49\u64cd\u4f5c\u65b9\u6cd5\uff0c\u540c\u65f6\u5728\u65f6\u95f4\u6548\u7387\u548c\u7a7a\u95f4\u6548\u7387\u65b9\u9762\u5448\u73b0\u51fa\u4e92\u8865\u7684\u7279\u70b9\u3002</p> <p></p> <p> Fig. \u8fde\u7eed\u7a7a\u95f4\u5b58\u50a8\u4e0e\u79bb\u6563\u7a7a\u95f4\u5b58\u50a8 </p> <p>\u6240\u6709\u6570\u636e\u7ed3\u6784\u90fd\u662f\u57fa\u4e8e\u6570\u7ec4\u3001\u94fe\u8868\u6216\u4e8c\u8005\u7684\u7ec4\u5408\u5b9e\u73b0\u7684\u3002\u4f8b\u5982\uff0c\u6808\u548c\u961f\u5217\u65e2\u53ef\u4ee5\u4f7f\u7528\u6570\u7ec4\u5b9e\u73b0\uff0c\u4e5f\u53ef\u4ee5\u4f7f\u7528\u94fe\u8868\u5b9e\u73b0\uff1b\u800c\u54c8\u5e0c\u8868\u7684\u5b9e\u73b0\u53ef\u80fd\u540c\u65f6\u5305\u542b\u6570\u7ec4\u548c\u94fe\u8868\u3002</p> <ul> <li>\u57fa\u4e8e\u6570\u7ec4\u53ef\u5b9e\u73b0\uff1a\u6808\u3001\u961f\u5217\u3001\u54c8\u5e0c\u8868\u3001\u6811\u3001\u5806\u3001\u56fe\u3001\u77e9\u9635\u3001\u5f20\u91cf\uff08\u7ef4\u5ea6 \\(\\geq 3\\) \u7684\u6570\u7ec4\uff09\u7b49\uff1b</li> <li>\u57fa\u4e8e\u94fe\u8868\u53ef\u5b9e\u73b0\uff1a\u6808\u3001\u961f\u5217\u3001\u54c8\u5e0c\u8868\u3001\u6811\u3001\u5806\u3001\u56fe\u7b49\uff1b</li> </ul> <p>\u57fa\u4e8e\u6570\u7ec4\u5b9e\u73b0\u7684\u6570\u636e\u7ed3\u6784\u4e5f\u88ab\u79f0\u4e3a\u300c\u9759\u6001\u6570\u636e\u7ed3\u6784\u300d\uff0c\u8fd9\u610f\u5473\u7740\u6b64\u7c7b\u6570\u636e\u7ed3\u6784\u5728\u521d\u59cb\u5316\u540e\u957f\u5ea6\u4e0d\u53ef\u53d8\u3002\u76f8\u5bf9\u5e94\u5730\uff0c\u57fa\u4e8e\u94fe\u8868\u5b9e\u73b0\u7684\u6570\u636e\u7ed3\u6784\u88ab\u79f0\u4e3a\u300c\u52a8\u6001\u6570\u636e\u7ed3\u6784\u300d\uff0c\u8fd9\u7c7b\u6570\u636e\u7ed3\u6784\u5728\u521d\u59cb\u5316\u540e\uff0c\u4ecd\u53ef\u4ee5\u5728\u7a0b\u5e8f\u8fd0\u884c\u8fc7\u7a0b\u4e2d\u5bf9\u5176\u957f\u5ea6\u8fdb\u884c\u8c03\u6574\u3002</p> <p>Tip</p> <p>\u5982\u82e5\u611f\u89c9\u7406\u89e3\u7269\u7406\u7ed3\u6784\u6709\u56f0\u96be\uff0c\u5efa\u8bae\u5148\u9605\u8bfb\u4e0b\u4e00\u7ae0\u201c\u6570\u7ec4\u4e0e\u94fe\u8868\u201d\uff0c\u7136\u540e\u518d\u56de\u5934\u7406\u89e3\u7269\u7406\u7ed3\u6784\u7684\u542b\u4e49\u3002\u6570\u7ec4\u4e0e\u94fe\u8868\u662f\u5176\u4ed6\u6240\u6709\u6570\u636e\u7ed3\u6784\u7684\u57fa\u77f3\uff0c\u5efa\u8bae\u4f60\u6295\u5165\u66f4\u591a\u65f6\u95f4\u6df1\u5165\u4e86\u89e3\u8fd9\u4e24\u79cd\u57fa\u672c\u6570\u636e\u7ed3\u6784\u3002</p>"},{"location":"chapter_data_structure/number_encoding/","title":"3.3. \u00a0 \u6570\u5b57\u7f16\u7801 *","text":"<p>Note</p> <p>\u5728\u672c\u4e66\u4e2d\uff0c\u6807\u9898\u5e26\u6709\u7684 * \u7b26\u53f7\u7684\u662f\u9009\u8bfb\u7ae0\u8282\u3002\u5982\u679c\u4f60\u65f6\u95f4\u6709\u9650\u6216\u611f\u5230\u7406\u89e3\u56f0\u96be\uff0c\u5efa\u8bae\u5148\u8df3\u8fc7\uff0c\u7b49\u5b66\u5b8c\u5fc5\u8bfb\u7ae0\u8282\u540e\u518d\u5355\u72ec\u653b\u514b\u3002</p>"},{"location":"chapter_data_structure/number_encoding/#331","title":"3.3.1. \u00a0 \u539f\u7801\u3001\u53cd\u7801\u548c\u8865\u7801","text":"<p>\u4ece\u4e0a\u4e00\u8282\u7684\u8868\u683c\u4e2d\u6211\u4eec\u53d1\u73b0\uff0c\u6240\u6709\u6574\u6570\u7c7b\u578b\u80fd\u591f\u8868\u793a\u7684\u8d1f\u6570\u90fd\u6bd4\u6b63\u6570\u591a\u4e00\u4e2a\u3002\u4f8b\u5982\uff0c<code>byte</code> \u7684\u53d6\u503c\u8303\u56f4\u662f \\([-128, 127]\\) \u3002\u8fd9\u4e2a\u73b0\u8c61\u6bd4\u8f83\u53cd\u76f4\u89c9\uff0c\u5b83\u7684\u5185\u5728\u539f\u56e0\u6d89\u53ca\u5230\u539f\u7801\u3001\u53cd\u7801\u3001\u8865\u7801\u7684\u76f8\u5173\u77e5\u8bc6\u3002\u5728\u5c55\u5f00\u5206\u6790\u4e4b\u524d\uff0c\u6211\u4eec\u9996\u5148\u7ed9\u51fa\u4e09\u8005\u7684\u5b9a\u4e49\uff1a</p> <ul> <li>\u539f\u7801\uff1a\u6211\u4eec\u5c06\u6570\u5b57\u7684\u4e8c\u8fdb\u5236\u8868\u793a\u7684\u6700\u9ad8\u4f4d\u89c6\u4e3a\u7b26\u53f7\u4f4d\uff0c\u5176\u4e2d \\(0\\) \u8868\u793a\u6b63\u6570\uff0c\\(1\\) \u8868\u793a\u8d1f\u6570\uff0c\u5176\u4f59\u4f4d\u8868\u793a\u6570\u5b57\u7684\u503c\u3002</li> <li>\u53cd\u7801\uff1a\u6b63\u6570\u7684\u53cd\u7801\u4e0e\u5176\u539f\u7801\u76f8\u540c\uff0c\u8d1f\u6570\u7684\u53cd\u7801\u662f\u5bf9\u5176\u539f\u7801\u9664\u7b26\u53f7\u4f4d\u5916\u7684\u6240\u6709\u4f4d\u53d6\u53cd\u3002</li> <li>\u8865\u7801\uff1a\u6b63\u6570\u7684\u8865\u7801\u4e0e\u5176\u539f\u7801\u76f8\u540c\uff0c\u8d1f\u6570\u7684\u8865\u7801\u662f\u5728\u5176\u53cd\u7801\u7684\u57fa\u7840\u4e0a\u52a0 \\(1\\) \u3002</li> </ul> <p></p> <p> Fig. \u539f\u7801\u3001\u53cd\u7801\u4e0e\u8865\u7801\u4e4b\u95f4\u7684\u76f8\u4e92\u8f6c\u6362 </p> <p>\u663e\u7136\uff0c\u300c\u539f\u7801\u300d\u6700\u4e3a\u76f4\u89c2\uff0c\u7136\u800c\u6570\u5b57\u5374\u662f\u4ee5\u300c\u8865\u7801\u300d\u7684\u5f62\u5f0f\u5b58\u50a8\u5728\u8ba1\u7b97\u673a\u4e2d\u7684\u3002\u8fd9\u662f\u56e0\u4e3a\u539f\u7801\u5b58\u5728\u4e00\u4e9b\u5c40\u9650\u6027\u3002</p> <p>\u4e00\u65b9\u9762\uff0c\u8d1f\u6570\u7684\u539f\u7801\u4e0d\u80fd\u76f4\u63a5\u7528\u4e8e\u8fd0\u7b97\u3002\u4f8b\u5982\uff0c\u6211\u4eec\u5728\u539f\u7801\u4e0b\u8ba1\u7b97 \\(1 + (-2)\\) \uff0c\u5f97\u5230\u7684\u7ed3\u679c\u662f \\(-3\\) \uff0c\u8fd9\u663e\u7136\u662f\u4e0d\u5bf9\u7684\u3002</p> \\[ \\begin{aligned} &amp; 1 + (-2) \\newline &amp; = 0000 \\space 0001 + 1000 \\space 0010 \\newline &amp; = 1000 \\space 0011 \\newline &amp; = -3 \\end{aligned} \\] <p>\u4e3a\u4e86\u89e3\u51b3\u6b64\u95ee\u9898\uff0c\u8ba1\u7b97\u673a\u5f15\u5165\u4e86\u300c\u53cd\u7801\u300d\u3002\u4f8b\u5982\uff0c\u6211\u4eec\u5148\u5c06\u539f\u7801\u8f6c\u6362\u4e3a\u53cd\u7801\uff0c\u5e76\u5728\u53cd\u7801\u4e0b\u8ba1\u7b97 \\(1 + (-2)\\) \uff0c\u5e76\u5c06\u7ed3\u679c\u4ece\u53cd\u7801\u8f6c\u5316\u56de\u539f\u7801\uff0c\u5219\u53ef\u5f97\u5230\u6b63\u786e\u7ed3\u679c \\(-1\\) \u3002</p> \\[ \\begin{aligned} &amp; 1 + (-2) \\newline &amp; = 0000 \\space 0001 \\space \\text{(\u539f\u7801)} + 1000 \\space 0010 \\space \\text{(\u539f\u7801)} \\newline &amp; = 0000 \\space 0001 \\space \\text{(\u53cd\u7801)} + 1111  \\space 1101 \\space \\text{(\u53cd\u7801)} \\newline &amp; = 1111 \\space 1110 \\space \\text{(\u53cd\u7801)} \\newline &amp; = 1000 \\space 0001 \\space \\text{(\u539f\u7801)} \\newline &amp; = -1 \\end{aligned} \\] <p>\u53e6\u4e00\u65b9\u9762\uff0c\u6570\u5b57\u96f6\u7684\u539f\u7801\u6709 \\(+0\\) \u548c \\(-0\\) \u4e24\u79cd\u8868\u793a\u65b9\u5f0f\u3002\u8fd9\u610f\u5473\u7740\u6570\u5b57\u96f6\u5bf9\u5e94\u7740\u4e24\u4e2a\u4e0d\u540c\u7684\u4e8c\u8fdb\u5236\u7f16\u7801\uff0c\u800c\u8fd9\u53ef\u80fd\u4f1a\u5e26\u6765\u6b67\u4e49\u95ee\u9898\u3002\u4f8b\u5982\uff0c\u5728\u6761\u4ef6\u5224\u65ad\u4e2d\uff0c\u5982\u679c\u6ca1\u6709\u533a\u5206\u6b63\u96f6\u548c\u8d1f\u96f6\uff0c\u53ef\u80fd\u4f1a\u5bfc\u81f4\u9519\u8bef\u7684\u5224\u65ad\u7ed3\u679c\u3002\u5982\u679c\u6211\u4eec\u60f3\u8981\u5904\u7406\u6b63\u96f6\u548c\u8d1f\u96f6\u6b67\u4e49\uff0c\u5219\u9700\u8981\u5f15\u5165\u989d\u5916\u7684\u5224\u65ad\u64cd\u4f5c\uff0c\u5176\u53ef\u80fd\u4f1a\u964d\u4f4e\u8ba1\u7b97\u673a\u7684\u8fd0\u7b97\u6548\u7387\u3002</p> \\[ \\begin{aligned} +0 &amp; = 0000 \\space 0000 \\newline -0 &amp; = 1000 \\space 0000 \\end{aligned} \\] <p>\u4e0e\u539f\u7801\u4e00\u6837\uff0c\u53cd\u7801\u4e5f\u5b58\u5728\u6b63\u8d1f\u96f6\u6b67\u4e49\u95ee\u9898\u3002\u4e3a\u6b64\uff0c\u8ba1\u7b97\u673a\u8fdb\u4e00\u6b65\u5f15\u5165\u4e86\u300c\u8865\u7801\u300d\u3002\u90a3\u4e48\uff0c\u8865\u7801\u6709\u4ec0\u4e48\u4f5c\u7528\u5462\uff1f\u6211\u4eec\u5148\u6765\u5206\u6790\u4e00\u4e0b\u8d1f\u96f6\u7684\u8865\u7801\u7684\u8ba1\u7b97\u8fc7\u7a0b\uff1a</p> \\[ \\begin{aligned} -0 = \\space &amp; 1000 \\space 0000 \\space \\text{(\u539f\u7801)} \\newline = \\space &amp; 1111 \\space 1111 \\space \\text{(\u53cd\u7801)} \\newline = 1 \\space &amp; 0000 \\space 0000 \\space \\text{(\u8865\u7801)} \\newline \\end{aligned} \\] <p>\u5728\u8d1f\u96f6\u7684\u53cd\u7801\u57fa\u7840\u4e0a\u52a0 \\(1\\) \u4f1a\u4ea7\u751f\u8fdb\u4f4d\uff0c\u800c\u7531\u4e8e byte \u7684\u957f\u5ea6\u53ea\u6709 8 \u4f4d\uff0c\u56e0\u6b64\u6ea2\u51fa\u5230\u7b2c 9 \u4f4d\u7684 \\(1\\) \u4f1a\u88ab\u820d\u5f03\u3002\u4ece\u800c\u5f97\u5230\u8d1f\u96f6\u7684\u8865\u7801\u4e3a \\(0000 \\space 0000\\) \uff0c\u4e0e\u6b63\u96f6\u7684\u8865\u7801\u76f8\u540c\u3002\u8fd9\u610f\u5473\u7740\u5728\u8865\u7801\u8868\u793a\u4e2d\u53ea\u5b58\u5728\u4e00\u4e2a\u96f6\uff0c\u4ece\u800c\u89e3\u51b3\u4e86\u6b63\u8d1f\u96f6\u6b67\u4e49\u95ee\u9898\u3002</p> <p>\u8fd8\u5269\u4f59\u6700\u540e\u4e00\u4e2a\u7591\u60d1\uff1abyte \u7684\u53d6\u503c\u8303\u56f4\u662f \\([-128, 127]\\) \uff0c\u591a\u51fa\u6765\u7684\u4e00\u4e2a\u8d1f\u6570 \\(-128\\) \u662f\u5982\u4f55\u5f97\u5230\u7684\u5462\uff1f\u6211\u4eec\u6ce8\u610f\u5230\uff0c\u533a\u95f4 \\([-127, +127]\\) \u5185\u7684\u6240\u6709\u6574\u6570\u90fd\u6709\u5bf9\u5e94\u7684\u539f\u7801\u3001\u53cd\u7801\u548c\u8865\u7801\uff0c\u5e76\u4e14\u539f\u7801\u548c\u8865\u7801\u4e4b\u95f4\u662f\u53ef\u4ee5\u4e92\u76f8\u8f6c\u6362\u7684\u3002</p> <p>\u7136\u800c\uff0c\u8865\u7801 \\(1000 \\space 0000\\) \u662f\u4e00\u4e2a\u4f8b\u5916\uff0c\u5b83\u5e76\u6ca1\u6709\u5bf9\u5e94\u7684\u539f\u7801\u3002\u6839\u636e\u8f6c\u6362\u65b9\u6cd5\uff0c\u6211\u4eec\u5f97\u5230\u8be5\u8865\u7801\u7684\u539f\u7801\u4e3a \\(0000 \\space 0000\\) \u3002\u8fd9\u663e\u7136\u662f\u77db\u76fe\u7684\uff0c\u56e0\u4e3a\u8be5\u539f\u7801\u8868\u793a\u6570\u5b57 \\(0\\) \uff0c\u5b83\u7684\u8865\u7801\u5e94\u8be5\u662f\u81ea\u8eab\u3002\u8ba1\u7b97\u673a\u89c4\u5b9a\u8fd9\u4e2a\u7279\u6b8a\u7684\u8865\u7801 \\(1000 \\space 0000\\) \u4ee3\u8868 \\(-128\\) \u3002\u5b9e\u9645\u4e0a\uff0c\\((-1) + (-127)\\) \u5728\u8865\u7801\u4e0b\u7684\u8ba1\u7b97\u7ed3\u679c\u5c31\u662f \\(-128\\) \u3002</p> \\[ \\begin{aligned} &amp; (-127) + (-1) \\newline &amp; = 1111 \\space 1111 \\space \\text{(\u539f\u7801)} + 1000 \\space 0001 \\space \\text{(\u539f\u7801)} \\newline &amp; = 1000 \\space 0000 \\space \\text{(\u53cd\u7801)} + 1111  \\space 1110 \\space \\text{(\u53cd\u7801)} \\newline &amp; = 1000 \\space 0001 \\space \\text{(\u8865\u7801)} + 1111  \\space 1111 \\space \\text{(\u8865\u7801)} \\newline &amp; = 1000 \\space 0000 \\space \\text{(\u8865\u7801)} \\newline &amp; = -128 \\end{aligned} \\] <p>\u4f60\u53ef\u80fd\u5df2\u7ecf\u53d1\u73b0\uff0c\u4e0a\u8ff0\u7684\u6240\u6709\u8ba1\u7b97\u90fd\u662f\u52a0\u6cd5\u8fd0\u7b97\u3002\u8fd9\u6697\u793a\u7740\u4e00\u4e2a\u91cd\u8981\u4e8b\u5b9e\uff1a\u8ba1\u7b97\u673a\u5185\u90e8\u7684\u786c\u4ef6\u7535\u8def\u4e3b\u8981\u662f\u57fa\u4e8e\u52a0\u6cd5\u8fd0\u7b97\u8bbe\u8ba1\u7684\u3002\u8fd9\u662f\u56e0\u4e3a\u52a0\u6cd5\u8fd0\u7b97\u76f8\u5bf9\u4e8e\u5176\u4ed6\u8fd0\u7b97\uff08\u6bd4\u5982\u4e58\u6cd5\u3001\u9664\u6cd5\u548c\u51cf\u6cd5\uff09\u6765\u8bf4\uff0c\u786c\u4ef6\u5b9e\u73b0\u8d77\u6765\u66f4\u7b80\u5355\uff0c\u66f4\u5bb9\u6613\u8fdb\u884c\u5e76\u884c\u5316\u5904\u7406\uff0c\u4ece\u800c\u63d0\u9ad8\u8fd0\u7b97\u901f\u5ea6\u3002</p> <p>\u7136\u800c\uff0c\u8fd9\u5e76\u4e0d\u610f\u5473\u7740\u8ba1\u7b97\u673a\u53ea\u80fd\u505a\u52a0\u6cd5\u3002\u901a\u8fc7\u5c06\u52a0\u6cd5\u4e0e\u4e00\u4e9b\u57fa\u672c\u903b\u8f91\u8fd0\u7b97\u7ed3\u5408\uff0c\u8ba1\u7b97\u673a\u80fd\u591f\u5b9e\u73b0\u5404\u79cd\u5176\u4ed6\u7684\u6570\u5b66\u8fd0\u7b97\u3002\u4f8b\u5982\uff0c\u8ba1\u7b97\u51cf\u6cd5 \\(a - b\\) \u53ef\u4ee5\u8f6c\u6362\u4e3a\u8ba1\u7b97\u52a0\u6cd5 \\(a + (-b)\\) \uff1b\u8ba1\u7b97\u4e58\u6cd5\u548c\u9664\u6cd5\u53ef\u4ee5\u8f6c\u6362\u4e3a\u8ba1\u7b97\u591a\u6b21\u52a0\u6cd5\u6216\u51cf\u6cd5\u3002</p> <p>\u73b0\u5728\uff0c\u6211\u4eec\u53ef\u4ee5\u603b\u7ed3\u51fa\u8ba1\u7b97\u673a\u4f7f\u7528\u8865\u7801\u7684\u539f\u56e0\uff1a\u57fa\u4e8e\u8865\u7801\u8868\u793a\uff0c\u8ba1\u7b97\u673a\u53ef\u4ee5\u7528\u540c\u6837\u7684\u7535\u8def\u548c\u64cd\u4f5c\u6765\u5904\u7406\u6b63\u6570\u548c\u8d1f\u6570\u7684\u52a0\u6cd5\uff0c\u4e0d\u9700\u8981\u8bbe\u8ba1\u7279\u6b8a\u7684\u786c\u4ef6\u7535\u8def\u6765\u5904\u7406\u51cf\u6cd5\uff0c\u5e76\u4e14\u65e0\u9700\u7279\u522b\u5904\u7406\u6b63\u8d1f\u96f6\u7684\u6b67\u4e49\u95ee\u9898\u3002\u8fd9\u5927\u5927\u7b80\u5316\u4e86\u786c\u4ef6\u8bbe\u8ba1\uff0c\u5e76\u63d0\u9ad8\u4e86\u8fd0\u7b97\u6548\u7387\u3002</p> <p>\u8865\u7801\u7684\u8bbe\u8ba1\u975e\u5e38\u7cbe\u5999\uff0c\u7531\u4e8e\u7bc7\u5e45\u5173\u7cfb\u6211\u4eec\u5148\u4ecb\u7ecd\u5230\u8fd9\u91cc\u3002\u5efa\u8bae\u6709\u5174\u8da3\u7684\u8bfb\u8005\u8fdb\u4e00\u6b65\u6df1\u5ea6\u4e86\u89e3\u3002</p>"},{"location":"chapter_data_structure/number_encoding/#332","title":"3.3.2. \u00a0 \u6d6e\u70b9\u6570\u7f16\u7801","text":"<p>\u7ec6\u5fc3\u7684\u4f60\u53ef\u80fd\u4f1a\u53d1\u73b0\uff1a<code>int</code> \u548c <code>float</code> \u957f\u5ea6\u76f8\u540c\uff0c\u90fd\u662f 4 bytes\uff0c\u4f46\u4e3a\u4ec0\u4e48 <code>float</code> \u7684\u53d6\u503c\u8303\u56f4\u8fdc\u5927\u4e8e <code>int</code> \uff1f\u8fd9\u975e\u5e38\u53cd\u76f4\u89c9\uff0c\u56e0\u4e3a\u6309\u7406\u8bf4 <code>float</code> \u9700\u8981\u8868\u793a\u5c0f\u6570\uff0c\u53d6\u503c\u8303\u56f4\u5e94\u8be5\u53d8\u5c0f\u624d\u5bf9\u3002</p> <p>\u5b9e\u9645\u4e0a\uff0c\u8fd9\u662f\u56e0\u4e3a\u6d6e\u70b9\u6570 <code>float</code> \u91c7\u7528\u4e86\u4e0d\u540c\u7684\u8868\u793a\u65b9\u5f0f\u3002\u6839\u636e IEEE 754 \u6807\u51c6\uff0c32-bit \u957f\u5ea6\u7684 <code>float</code> \u7531\u4ee5\u4e0b\u90e8\u5206\u6784\u6210\uff1a</p> <ul> <li>\u7b26\u53f7\u4f4d \\(\\mathrm{S}\\) \uff1a\u5360 1 bit \uff1b</li> <li>\u6307\u6570\u4f4d \\(\\mathrm{E}\\) \uff1a\u5360 8 bits \uff1b</li> <li>\u5206\u6570\u4f4d \\(\\mathrm{N}\\) \uff1a\u5360 24 bits \uff0c\u5176\u4e2d 23 \u4f4d\u663e\u5f0f\u5b58\u50a8\uff1b</li> </ul> <p>\u8bbe 32-bit \u4e8c\u8fdb\u5236\u6570\u7684\u7b2c \\(i\\) \u4f4d\u4e3a \\(b_i\\) \uff0c\u5219 <code>float</code> \u503c\u7684\u8ba1\u7b97\u65b9\u6cd5\u5b9a\u4e49\u4e3a\uff1a</p> \\[ \\text { val } = (-1)^{b_{31}} \\times 2^{\\left(b_{30} b_{29} \\ldots b_{23}\\right)_2-127} \\times\\left(1 . b_{22} b_{21} \\ldots b_0\\right)_2 \\] <p>\u8f6c\u5316\u5230\u5341\u8fdb\u5236\u4e0b\u7684\u8ba1\u7b97\u516c\u5f0f\u4e3a</p> \\[ \\text { val }=(-1)^{\\mathrm{S}} \\times 2^{\\mathrm{E} -127} \\times (1 + \\mathrm{N}) \\] <p>\u5176\u4e2d\u5404\u9879\u7684\u53d6\u503c\u8303\u56f4\u4e3a</p> \\[ \\begin{aligned} \\mathrm{S} \\in &amp; \\{ 0, 1\\} , \\quad \\mathrm{E} \\in \\{ 1, 2, \\dots, 254 \\} \\newline (1 + \\mathrm{N}) = &amp; (1 + \\sum_{i=1}^{23} b_{23-i} 2^{-i}) \\subset [1, 2 - 2^{-23}] \\end{aligned} \\] <p></p> <p> Fig. IEEE 754 \u6807\u51c6\u4e0b\u7684 float \u8868\u793a\u65b9\u5f0f </p> <p>\u4ee5\u4e0a\u56fe\u4e3a\u4f8b\uff0c\\(\\mathrm{S} = 0\\) \uff0c \\(\\mathrm{E} = 124\\) \uff0c\\(\\mathrm{N} = 2^{-2} + 2^{-3} = 0.375\\) \uff0c\u6613\u5f97</p> \\[ \\text { val } = (-1)^0 \\times 2^{124 - 127} \\times (1 + 0.375) = 0.171875 \\] <p>\u73b0\u5728\u6211\u4eec\u53ef\u4ee5\u56de\u7b54\u6700\u521d\u7684\u95ee\u9898\uff1a<code>float</code> \u7684\u8868\u793a\u65b9\u5f0f\u5305\u542b\u6307\u6570\u4f4d\uff0c\u5bfc\u81f4\u5176\u53d6\u503c\u8303\u56f4\u8fdc\u5927\u4e8e <code>int</code> \u3002\u6839\u636e\u4ee5\u4e0a\u8ba1\u7b97\uff0c<code>float</code> \u53ef\u8868\u793a\u7684\u6700\u5927\u6b63\u6570\u4e3a \\(2^{254 - 127} \\times (2 - 2^{-23}) \\approx 3.4 \\times 10^{38}\\) \uff0c\u5207\u6362\u7b26\u53f7\u4f4d\u4fbf\u53ef\u5f97\u5230\u6700\u5c0f\u8d1f\u6570\u3002</p> <p>\u5c3d\u7ba1\u6d6e\u70b9\u6570 <code>float</code> \u6269\u5c55\u4e86\u53d6\u503c\u8303\u56f4\uff0c\u4f46\u5176\u526f\u4f5c\u7528\u662f\u727a\u7272\u4e86\u7cbe\u5ea6\u3002\u6574\u6570\u7c7b\u578b <code>int</code> \u5c06\u5168\u90e8 32 \u4f4d\u7528\u4e8e\u8868\u793a\u6570\u5b57\uff0c\u6570\u5b57\u662f\u5747\u5300\u5206\u5e03\u7684\uff1b\u800c\u7531\u4e8e\u6307\u6570\u4f4d\u7684\u5b58\u5728\uff0c\u6d6e\u70b9\u6570 <code>float</code> \u7684\u6570\u503c\u8d8a\u5927\uff0c\u76f8\u90bb\u4e24\u4e2a\u6570\u5b57\u4e4b\u95f4\u7684\u5dee\u503c\u5c31\u4f1a\u8d8b\u5411\u8d8a\u5927\u3002</p> <p>\u8fdb\u4e00\u6b65\u5730\uff0c\u6307\u6570\u4f4d \\(E = 0\\) \u548c \\(E = 255\\) \u5177\u6709\u7279\u6b8a\u542b\u4e49\uff0c\u7528\u4e8e\u8868\u793a\u96f6\u3001\u65e0\u7a77\u5927\u3001\\(\\mathrm{NaN}\\) \u7b49\u3002</p> \u6307\u6570\u4f4d E \u5206\u6570\u4f4d \\(\\mathrm{N} = 0\\) \u5206\u6570\u4f4d \\(\\mathrm{N} \\ne 0\\) \u8ba1\u7b97\u516c\u5f0f \\(0\\) \\(\\pm 0\\) \u6b21\u6b63\u89c4\u6570 \\((-1)^{\\mathrm{S}} \\times 2^{-126} \\times (0.\\mathrm{N})\\) \\(1, 2, \\dots, 254\\) \u6b63\u89c4\u6570 \u6b63\u89c4\u6570 \\((-1)^{\\mathrm{S}} \\times 2^{(\\mathrm{E} -127)} \\times (1.\\mathrm{N})\\) \\(255\\) \\(\\pm \\infty\\) \\(\\mathrm{NaN}\\) <p>\u7279\u522b\u5730\uff0c\u6b21\u6b63\u89c4\u6570\u663e\u8457\u63d0\u5347\u4e86\u6d6e\u70b9\u6570\u7684\u7cbe\u5ea6\uff0c\u8fd9\u662f\u56e0\u4e3a\uff1a</p> <ul> <li>\u6700\u5c0f\u6b63\u6b63\u89c4\u6570\u4e3a \\(2^{-126} \\approx 1.18 \\times 10^{-38}\\) \uff1b</li> <li>\u6700\u5c0f\u6b63\u6b21\u6b63\u89c4\u6570\u4e3a \\(2^{-126} \\times 2^{-23} \\approx 1.4 \\times 10^{-45}\\) \uff1b</li> </ul> <p>\u53cc\u7cbe\u5ea6 <code>double</code> \u4e5f\u91c7\u7528\u7c7b\u4f3c <code>float</code> \u7684\u8868\u793a\u65b9\u6cd5\uff0c\u6b64\u5904\u4e0d\u518d\u8be6\u8ff0\u3002</p>"},{"location":"chapter_data_structure/summary/","title":"3.5. \u00a0 \u5c0f\u7ed3","text":"<p>\u6570\u636e\u7ed3\u6784\u5206\u7c7b</p> <ul> <li>\u6570\u636e\u7ed3\u6784\u53ef\u4ee5\u4ece\u903b\u8f91\u7ed3\u6784\u548c\u7269\u7406\u7ed3\u6784\u4e24\u4e2a\u89d2\u5ea6\u8fdb\u884c\u5206\u7c7b\u3002\u903b\u8f91\u7ed3\u6784\u63cf\u8ff0\u4e86\u6570\u636e\u5143\u7d20\u4e4b\u95f4\u7684\u903b\u8f91\u5173\u7cfb\uff0c\u800c\u7269\u7406\u7ed3\u6784\u63cf\u8ff0\u4e86\u6570\u636e\u5728\u8ba1\u7b97\u673a\u5185\u5b58\u4e2d\u7684\u5b58\u50a8\u65b9\u5f0f\u3002</li> <li>\u5e38\u89c1\u7684\u903b\u8f91\u7ed3\u6784\u5305\u62ec\u7ebf\u6027\u3001\u6811\u72b6\u548c\u7f51\u72b6\u7b49\u3002\u901a\u5e38\u6211\u4eec\u6839\u636e\u903b\u8f91\u7ed3\u6784\u5c06\u6570\u636e\u7ed3\u6784\u5206\u4e3a\u7ebf\u6027\uff08\u6570\u7ec4\u3001\u94fe\u8868\u3001\u6808\u3001\u961f\u5217\uff09\u548c\u975e\u7ebf\u6027\uff08\u6811\u3001\u56fe\u3001\u5806\uff09\u4e24\u79cd\u3002\u54c8\u5e0c\u8868\u7684\u5b9e\u73b0\u53ef\u80fd\u540c\u65f6\u5305\u542b\u7ebf\u6027\u548c\u975e\u7ebf\u6027\u7ed3\u6784\u3002</li> <li>\u5f53\u7a0b\u5e8f\u8fd0\u884c\u65f6\uff0c\u6570\u636e\u88ab\u5b58\u50a8\u5728\u8ba1\u7b97\u673a\u5185\u5b58\u4e2d\u3002\u6bcf\u4e2a\u5185\u5b58\u7a7a\u95f4\u90fd\u62e5\u6709\u5bf9\u5e94\u7684\u5185\u5b58\u5730\u5740\uff0c\u7a0b\u5e8f\u901a\u8fc7\u8fd9\u4e9b\u5185\u5b58\u5730\u5740\u8bbf\u95ee\u6570\u636e\u3002</li> <li>\u7269\u7406\u7ed3\u6784\u4e3b\u8981\u5206\u4e3a\u8fde\u7eed\u7a7a\u95f4\u5b58\u50a8\uff08\u6570\u7ec4\uff09\u548c\u79bb\u6563\u7a7a\u95f4\u5b58\u50a8\uff08\u94fe\u8868\uff09\u3002\u6240\u6709\u6570\u636e\u7ed3\u6784\u90fd\u662f\u7531\u6570\u7ec4\u3001\u94fe\u8868\u6216\u4e24\u8005\u7684\u7ec4\u5408\u5b9e\u73b0\u7684\u3002</li> </ul> <p>\u6570\u636e\u7c7b\u578b\u4e0e\u7f16\u7801</p> <ul> <li>\u8ba1\u7b97\u673a\u4e2d\u7684\u57fa\u672c\u6570\u636e\u7c7b\u578b\u5305\u62ec\u6574\u6570 byte, short, int, long \u3001\u6d6e\u70b9\u6570 float, double \u3001\u5b57\u7b26 char \u548c\u5e03\u5c14 boolean \u3002\u5b83\u4eec\u7684\u53d6\u503c\u8303\u56f4\u53d6\u51b3\u4e8e\u5360\u7528\u7a7a\u95f4\u5927\u5c0f\u548c\u8868\u793a\u65b9\u5f0f\u3002</li> <li>\u539f\u7801\u3001\u53cd\u7801\u548c\u8865\u7801\u662f\u5728\u8ba1\u7b97\u673a\u4e2d\u7f16\u7801\u6570\u5b57\u7684\u4e09\u79cd\u65b9\u6cd5\uff0c\u5b83\u4eec\u4e4b\u95f4\u662f\u53ef\u4ee5\u76f8\u4e92\u8f6c\u6362\u7684\u3002\u6574\u6570\u7684\u539f\u7801\u7684\u6700\u9ad8\u4f4d\u662f\u7b26\u53f7\u4f4d\uff0c\u5176\u4f59\u4f4d\u662f\u6570\u5b57\u7684\u503c\u3002</li> <li>\u6574\u6570\u5728\u8ba1\u7b97\u673a\u4e2d\u662f\u4ee5\u8865\u7801\u7684\u5f62\u5f0f\u5b58\u50a8\u7684\u3002\u5728\u8865\u7801\u8868\u793a\u4e0b\uff0c\u8ba1\u7b97\u673a\u53ef\u4ee5\u5bf9\u6b63\u6570\u548c\u8d1f\u6570\u7684\u52a0\u6cd5\u4e00\u89c6\u540c\u4ec1\uff0c\u4e0d\u9700\u8981\u4e3a\u51cf\u6cd5\u64cd\u4f5c\u5355\u72ec\u8bbe\u8ba1\u7279\u6b8a\u7684\u786c\u4ef6\u7535\u8def\uff0c\u5e76\u4e14\u4e0d\u5b58\u5728\u6b63\u8d1f\u96f6\u6b67\u4e49\u7684\u95ee\u9898\u3002</li> <li>\u6d6e\u70b9\u6570\u7684\u7f16\u7801\u7531 1 \u4f4d\u7b26\u53f7\u4f4d\u30018 \u4f4d\u6307\u6570\u4f4d\u548c 23 \u4f4d\u5206\u6570\u4f4d\u6784\u6210\u3002\u7531\u4e8e\u5b58\u5728\u6307\u6570\u4f4d\uff0c\u6d6e\u70b9\u6570\u7684\u53d6\u503c\u8303\u56f4\u8fdc\u5927\u4e8e\u6574\u6570\uff0c\u4ee3\u4ef7\u662f\u727a\u7272\u4e86\u7cbe\u5ea6\u3002</li> <li>ASCII \u7801\u662f\u6700\u65e9\u51fa\u73b0\u7684\u82f1\u6587\u5b57\u7b26\u96c6\uff0c\u957f\u5ea6\u4e3a 1 \u5b57\u8282\uff0c\u5171\u6536\u5f55 127 \u4e2a\u5b57\u7b26\u3002GBK \u5b57\u7b26\u96c6\u662f\u5e38\u7528\u7684\u4e2d\u6587\u5b57\u7b26\u96c6\uff0c\u5171\u6536\u5f55\u4e24\u4e07\u591a\u4e2a\u6c49\u5b57\u3002Unicode \u81f4\u529b\u4e8e\u63d0\u4f9b\u4e00\u4e2a\u5b8c\u6574\u7684\u5b57\u7b26\u96c6\u6807\u51c6\uff0c\u6536\u5f55\u4e16\u754c\u5185\u5404\u79cd\u8bed\u8a00\u7684\u5b57\u7b26\uff0c\u4ece\u800c\u89e3\u51b3\u7531\u4e8e\u5b57\u7b26\u7f16\u7801\u65b9\u6cd5\u4e0d\u4e00\u81f4\u800c\u5bfc\u81f4\u7684\u4e71\u7801\u95ee\u9898\u3002</li> <li>UTF-8 \u662f\u6700\u53d7\u6b22\u8fce\u7684 Unicode \u7f16\u7801\u65b9\u6cd5\uff0c\u901a\u7528\u6027\u975e\u5e38\u597d\u3002\u5b83\u662f\u4e00\u79cd\u53d8\u957f\u7684\u7f16\u7801\u65b9\u6cd5\uff0c\u5177\u6709\u5f88\u597d\u7684\u6269\u5c55\u6027\uff0c\u6709\u6548\u63d0\u5347\u4e86\u5b58\u50a8\u7a7a\u95f4\u7684\u4f7f\u7528\u6548\u7387\u3002UTF-16 \u548c UTF-32 \u662f\u7b49\u957f\u7684\u7f16\u7801\u65b9\u6cd5\u3002\u5728\u7f16\u7801\u4e2d\u6587\u65f6\uff0cUTF-16 \u6bd4 UTF-8 \u7684\u5360\u7528\u7a7a\u95f4\u66f4\u5c0f\u3002Java, C# \u7b49\u7f16\u7a0b\u8bed\u8a00\u9ed8\u8ba4\u4f7f\u7528 UTF-16 \u7f16\u7801\u3002</li> </ul>"},{"location":"chapter_data_structure/summary/#351-q-a","title":"3.5.1. \u00a0 Q &amp; A","text":"<p>\u4e3a\u4ec0\u4e48\u54c8\u5e0c\u8868\u540c\u65f6\u5305\u542b\u7ebf\u6027\u6570\u636e\u7ed3\u6784\u548c\u975e\u7ebf\u6027\u6570\u636e\u7ed3\u6784\uff1f</p> <p>\u54c8\u5e0c\u8868\u5e95\u5c42\u662f\u6570\u7ec4\uff0c\u800c\u4e3a\u4e86\u89e3\u51b3\u54c8\u5e0c\u51b2\u7a81\uff0c\u6211\u4eec\u53ef\u80fd\u4f1a\u4f7f\u7528\u201c\u62c9\u94fe\u6cd5\u201d\uff08\u540e\u7eed\u6563\u5217\u8868\u7ae0\u8282\u4f1a\u8bb2\uff09\u3002\u5728\u62c9\u94fe\u6cd5\u4e2d\uff0c\u6570\u7ec4\u4e2d\u6bcf\u4e2a\u5730\u5740\uff08\u6876\uff09\u6307\u5411\u4e00\u4e2a\u94fe\u8868\uff1b\u5f53\u8fd9\u4e2a\u94fe\u8868\u957f\u5ea6\u8d85\u8fc7\u4e00\u5b9a\u9608\u503c\u65f6\uff0c\u53c8\u53ef\u80fd\u88ab\u8f6c\u5316\u4e3a\u6811\uff08\u901a\u5e38\u4e3a\u7ea2\u9ed1\u6811\uff09\u3002\u56e0\u6b64\uff0c\u54c8\u5e0c\u8868\u53ef\u80fd\u540c\u65f6\u5305\u542b\u7ebf\u6027\uff08\u6570\u7ec4\u3001\u94fe\u8868\uff09\u548c\u975e\u7ebf\u6027\uff08\u6811\uff09\u6570\u636e\u7ed3\u6784\u3002</p> <p>char \u7c7b\u578b\u7684\u957f\u5ea6\u662f 1 bytes \u5417\uff1f</p> <p>\u8fd9\u4e2a\u4e0e\u7f16\u7a0b\u8bed\u8a00\u91c7\u7528\u7684\u7f16\u7801\u65b9\u6cd5\u6709\u5173\u3002\u4f8b\u5982\uff0cJava, JS, TS, C# \u90fd\u91c7\u7528 UTF-16 \u7f16\u7801\uff08\u4fdd\u5b58 Unicode \u7801\u70b9\uff09\uff0c\u56e0\u6b64 char \u7c7b\u578b\u7684\u957f\u5ea6\u4e3a 2 bytes \u3002</p>"},{"location":"chapter_graph/","title":"9. \u00a0 \u56fe","text":""},{"location":"chapter_graph/graph/","title":"9.1. \u00a0 \u56fe","text":"<p>\u300c\u56fe Graph\u300d\u662f\u4e00\u79cd\u975e\u7ebf\u6027\u6570\u636e\u7ed3\u6784\uff0c\u7531\u300c\u9876\u70b9 Vertex\u300d\u548c\u300c\u8fb9 Edge\u300d\u7ec4\u6210\u3002\u6211\u4eec\u53ef\u4ee5\u5c06\u56fe \\(G\\) \u62bd\u8c61\u5730\u8868\u793a\u4e3a\u4e00\u7ec4\u9876\u70b9 \\(V\\) \u548c\u4e00\u7ec4\u8fb9 \\(E\\) \u7684\u96c6\u5408\u3002\u4ee5\u4e0b\u793a\u4f8b\u5c55\u793a\u4e86\u4e00\u4e2a\u5305\u542b 5 \u4e2a\u9876\u70b9\u548c 7 \u6761\u8fb9\u7684\u56fe\u3002</p> \\[ \\begin{aligned} V &amp; = \\{ 1, 2, 3, 4, 5 \\} \\newline E &amp; = \\{ (1,2), (1,3), (1,5), (2,3), (2,4), (2,5), (4,5) \\} \\newline G &amp; = \\{ V, E \\} \\newline \\end{aligned} \\] <p></p> <p> Fig. \u94fe\u8868\u3001\u6811\u3001\u56fe\u4e4b\u95f4\u7684\u5173\u7cfb </p> <p>\u90a3\u4e48\uff0c\u56fe\u4e0e\u5176\u4ed6\u6570\u636e\u7ed3\u6784\u7684\u5173\u7cfb\u662f\u4ec0\u4e48\uff1f\u5982\u679c\u6211\u4eec\u628a\u300c\u9876\u70b9\u300d\u770b\u4f5c\u8282\u70b9\uff0c\u628a\u300c\u8fb9\u300d\u770b\u4f5c\u8fde\u63a5\u5404\u4e2a\u8282\u70b9\u7684\u6307\u9488\uff0c\u5219\u53ef\u5c06\u300c\u56fe\u300d\u770b\u4f5c\u662f\u4e00\u79cd\u4ece\u300c\u94fe\u8868\u300d\u62d3\u5c55\u800c\u6765\u7684\u6570\u636e\u7ed3\u6784\u3002\u76f8\u8f83\u4e8e\u7ebf\u6027\u5173\u7cfb\uff08\u94fe\u8868\uff09\u548c\u5206\u6cbb\u5173\u7cfb\uff08\u6811\uff09\uff0c\u7f51\u7edc\u5173\u7cfb\uff08\u56fe\uff09\u7684\u81ea\u7531\u5ea6\u66f4\u9ad8\uff0c\u4ece\u800c\u66f4\u4e3a\u590d\u6742\u3002</p>"},{"location":"chapter_graph/graph/#911","title":"9.1.1. \u00a0 \u56fe\u5e38\u89c1\u7c7b\u578b","text":"<p>\u6839\u636e\u8fb9\u662f\u5426\u5177\u6709\u65b9\u5411\uff0c\u53ef\u5206\u4e3a\u300c\u65e0\u5411\u56fe Undirected Graph\u300d\u548c\u300c\u6709\u5411\u56fe Directed Graph\u300d\u3002</p> <ul> <li>\u5728\u65e0\u5411\u56fe\u4e2d\uff0c\u8fb9\u8868\u793a\u4e24\u9876\u70b9\u4e4b\u95f4\u7684\u201c\u53cc\u5411\u201d\u8fde\u63a5\u5173\u7cfb\uff0c\u4f8b\u5982\u5fae\u4fe1\u6216 QQ \u4e2d\u7684\u201c\u597d\u53cb\u5173\u7cfb\u201d\uff1b</li> <li>\u5728\u6709\u5411\u56fe\u4e2d\uff0c\u8fb9\u5177\u6709\u65b9\u5411\u6027\uff0c\u5373 \\(A \\rightarrow B\\) \u548c \\(A \\leftarrow B\\) \u4e24\u4e2a\u65b9\u5411\u7684\u8fb9\u662f\u76f8\u4e92\u72ec\u7acb\u7684\uff0c\u4f8b\u5982\u5fae\u535a\u6216\u6296\u97f3\u4e0a\u7684\u201c\u5173\u6ce8\u201d\u4e0e\u201c\u88ab\u5173\u6ce8\u201d\u5173\u7cfb\uff1b</li> </ul> <p></p> <p> Fig. \u6709\u5411\u56fe\u4e0e\u65e0\u5411\u56fe </p> <p>\u6839\u636e\u6240\u6709\u9876\u70b9\u662f\u5426\u8fde\u901a\uff0c\u53ef\u5206\u4e3a\u300c\u8fde\u901a\u56fe Connected Graph\u300d\u548c\u300c\u975e\u8fde\u901a\u56fe Disconnected Graph\u300d\u3002</p> <ul> <li>\u5bf9\u4e8e\u8fde\u901a\u56fe\uff0c\u4ece\u67d0\u4e2a\u9876\u70b9\u51fa\u53d1\uff0c\u53ef\u4ee5\u5230\u8fbe\u5176\u4f59\u4efb\u610f\u9876\u70b9\uff1b</li> <li>\u5bf9\u4e8e\u975e\u8fde\u901a\u56fe\uff0c\u4ece\u67d0\u4e2a\u9876\u70b9\u51fa\u53d1\uff0c\u81f3\u5c11\u6709\u4e00\u4e2a\u9876\u70b9\u65e0\u6cd5\u5230\u8fbe\uff1b</li> </ul> <p></p> <p> Fig. \u8fde\u901a\u56fe\u4e0e\u975e\u8fde\u901a\u56fe </p> <p>\u6211\u4eec\u8fd8\u53ef\u4ee5\u4e3a\u8fb9\u6dfb\u52a0\u201c\u6743\u91cd\u201d\u53d8\u91cf\uff0c\u4ece\u800c\u5f97\u5230\u300c\u6709\u6743\u56fe Weighted Graph\u300d\u3002\u4f8b\u5982\uff0c\u5728\u738b\u8005\u8363\u8000\u7b49\u624b\u6e38\u4e2d\uff0c\u7cfb\u7edf\u4f1a\u6839\u636e\u5171\u540c\u6e38\u620f\u65f6\u95f4\u6765\u8ba1\u7b97\u73a9\u5bb6\u4e4b\u95f4\u7684\u201c\u4eb2\u5bc6\u5ea6\u201d\uff0c\u8fd9\u79cd\u4eb2\u5bc6\u5ea6\u7f51\u7edc\u5c31\u53ef\u4ee5\u7528\u6709\u6743\u56fe\u6765\u8868\u793a\u3002</p> <p></p> <p> Fig. \u6709\u6743\u56fe\u4e0e\u65e0\u6743\u56fe </p>"},{"location":"chapter_graph/graph/#912","title":"9.1.2. \u00a0 \u56fe\u5e38\u7528\u672f\u8bed","text":"<ul> <li>\u300c\u90bb\u63a5 Adjacency\u300d\uff1a\u5f53\u4e24\u9876\u70b9\u4e4b\u95f4\u5b58\u5728\u8fb9\u76f8\u8fde\u65f6\uff0c\u79f0\u8fd9\u4e24\u9876\u70b9\u201c\u90bb\u63a5\u201d\u3002\u5728\u4e0a\u56fe\u4e2d\uff0c\u9876\u70b9 1 \u7684\u90bb\u63a5\u9876\u70b9\u4e3a\u9876\u70b9 2\u30013\u30015\u3002</li> <li>\u300c\u8def\u5f84 Path\u300d\uff1a\u4ece\u9876\u70b9 A \u5230\u9876\u70b9 B \u7ecf\u8fc7\u7684\u8fb9\u6784\u6210\u7684\u5e8f\u5217\u88ab\u79f0\u4e3a\u4ece A \u5230 B \u7684\u201c\u8def\u5f84\u201d\u3002\u5728\u4e0a\u56fe\u4e2d\uff0c\u8fb9\u5e8f\u5217 1-5-2-4 \u662f\u9876\u70b9 1 \u5230\u9876\u70b9 4 \u7684\u4e00\u6761\u8def\u5f84\u3002</li> <li>\u300c\u5ea6 Degree\u300d\u8868\u793a\u4e00\u4e2a\u9876\u70b9\u62e5\u6709\u7684\u8fb9\u6570\u3002\u5bf9\u4e8e\u6709\u5411\u56fe\uff0c\u300c\u5165\u5ea6 In-Degree\u300d\u8868\u793a\u6709\u591a\u5c11\u6761\u8fb9\u6307\u5411\u8be5\u9876\u70b9\uff0c\u300c\u51fa\u5ea6 Out-Degree\u300d\u8868\u793a\u6709\u591a\u5c11\u6761\u8fb9\u4ece\u8be5\u9876\u70b9\u6307\u51fa\u3002</li> </ul>"},{"location":"chapter_graph/graph/#913","title":"9.1.3. \u00a0 \u56fe\u7684\u8868\u793a","text":"<p>\u56fe\u7684\u5e38\u7528\u8868\u793a\u65b9\u6cd5\u5305\u62ec\u300c\u90bb\u63a5\u77e9\u9635\u300d\u548c\u300c\u90bb\u63a5\u8868\u300d\u3002\u4ee5\u4e0b\u4f7f\u7528\u65e0\u5411\u56fe\u8fdb\u884c\u4e3e\u4f8b\u3002</p>"},{"location":"chapter_graph/graph/#_1","title":"\u90bb\u63a5\u77e9\u9635","text":"<p>\u8bbe\u56fe\u7684\u9876\u70b9\u6570\u91cf\u4e3a \\(n\\) \uff0c\u300c\u90bb\u63a5\u77e9\u9635 Adjacency Matrix\u300d\u4f7f\u7528\u4e00\u4e2a \\(n \\times n\\) \u5927\u5c0f\u7684\u77e9\u9635\u6765\u8868\u793a\u56fe\uff0c\u6bcf\u4e00\u884c\uff08\u5217\uff09\u4ee3\u8868\u4e00\u4e2a\u9876\u70b9\uff0c\u77e9\u9635\u5143\u7d20\u4ee3\u8868\u8fb9\uff0c\u7528 \\(1\\) \u6216 \\(0\\) \u8868\u793a\u4e24\u4e2a\u9876\u70b9\u4e4b\u95f4\u662f\u5426\u5b58\u5728\u8fb9\u3002</p> <p>\u5982\u4e0b\u56fe\u6240\u793a\uff0c\u8bbe\u90bb\u63a5\u77e9\u9635\u4e3a \\(M\\) \u3001\u9876\u70b9\u5217\u8868\u4e3a \\(V\\) \uff0c\u90a3\u4e48\u77e9\u9635\u5143\u7d20 \\(M[i][j] = 1\\) \u8868\u793a\u9876\u70b9 \\(V[i]\\) \u5230\u9876\u70b9 \\(V[j]\\) \u4e4b\u95f4\u5b58\u5728\u8fb9\uff0c\u53cd\u4e4b \\(M[i][j] = 0\\) \u8868\u793a\u4e24\u9876\u70b9\u4e4b\u95f4\u65e0\u8fb9\u3002</p> <p></p> <p> Fig. \u56fe\u7684\u90bb\u63a5\u77e9\u9635\u8868\u793a </p> <p>\u90bb\u63a5\u77e9\u9635\u5177\u6709\u4ee5\u4e0b\u7279\u6027\uff1a</p> <ul> <li>\u9876\u70b9\u4e0d\u80fd\u4e0e\u81ea\u8eab\u76f8\u8fde\uff0c\u56e0\u6b64\u90bb\u63a5\u77e9\u9635\u4e3b\u5bf9\u89d2\u7ebf\u5143\u7d20\u6ca1\u6709\u610f\u4e49\u3002</li> <li>\u5bf9\u4e8e\u65e0\u5411\u56fe\uff0c\u4e24\u4e2a\u65b9\u5411\u7684\u8fb9\u7b49\u4ef7\uff0c\u6b64\u65f6\u90bb\u63a5\u77e9\u9635\u5173\u4e8e\u4e3b\u5bf9\u89d2\u7ebf\u5bf9\u79f0\u3002</li> <li>\u5c06\u90bb\u63a5\u77e9\u9635\u7684\u5143\u7d20\u4ece \\(1\\) , \\(0\\) \u66ff\u6362\u4e3a\u6743\u91cd\uff0c\u5219\u53ef\u8868\u793a\u6709\u6743\u56fe\u3002</li> </ul> <p>\u4f7f\u7528\u90bb\u63a5\u77e9\u9635\u8868\u793a\u56fe\u65f6\uff0c\u6211\u4eec\u53ef\u4ee5\u76f4\u63a5\u8bbf\u95ee\u77e9\u9635\u5143\u7d20\u4ee5\u83b7\u53d6\u8fb9\uff0c\u56e0\u6b64\u589e\u5220\u67e5\u64cd\u4f5c\u7684\u6548\u7387\u5f88\u9ad8\uff0c\u65f6\u95f4\u590d\u6742\u5ea6\u5747\u4e3a \\(O(1)\\) \u3002\u7136\u800c\uff0c\u77e9\u9635\u7684\u7a7a\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(n^2)\\) \uff0c\u5185\u5b58\u5360\u7528\u8f83\u591a\u3002</p>"},{"location":"chapter_graph/graph/#_2","title":"\u90bb\u63a5\u8868","text":"<p>\u300c\u90bb\u63a5\u8868 Adjacency List\u300d\u4f7f\u7528 \\(n\\) \u4e2a\u94fe\u8868\u6765\u8868\u793a\u56fe\uff0c\u94fe\u8868\u8282\u70b9\u8868\u793a\u9876\u70b9\u3002\u7b2c \\(i\\) \u6761\u94fe\u8868\u5bf9\u5e94\u9876\u70b9 \\(i\\) \uff0c\u5176\u4e2d\u5b58\u50a8\u4e86\u8be5\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\uff08\u5373\u4e0e\u8be5\u9876\u70b9\u76f8\u8fde\u7684\u9876\u70b9\uff09\u3002</p> <p></p> <p> Fig. \u56fe\u7684\u90bb\u63a5\u8868\u8868\u793a </p> <p>\u90bb\u63a5\u8868\u4ec5\u5b58\u50a8\u5b9e\u9645\u5b58\u5728\u7684\u8fb9\uff0c\u800c\u8fb9\u7684\u603b\u6570\u901a\u5e38\u8fdc\u5c0f\u4e8e \\(n^2\\) \uff0c\u56e0\u6b64\u5b83\u66f4\u52a0\u8282\u7701\u7a7a\u95f4\u3002\u7136\u800c\uff0c\u5728\u90bb\u63a5\u8868\u4e2d\u9700\u8981\u901a\u8fc7\u904d\u5386\u94fe\u8868\u6765\u67e5\u627e\u8fb9\uff0c\u56e0\u6b64\u5176\u65f6\u95f4\u6548\u7387\u4e0d\u5982\u90bb\u63a5\u77e9\u9635\u3002</p> <p>\u89c2\u5bdf\u4e0a\u56fe\u53ef\u53d1\u73b0\uff0c\u90bb\u63a5\u8868\u7ed3\u6784\u4e0e\u54c8\u5e0c\u8868\u4e2d\u7684\u300c\u94fe\u5730\u5740\u6cd5\u300d\u975e\u5e38\u76f8\u4f3c\uff0c\u56e0\u6b64\u6211\u4eec\u4e5f\u53ef\u4ee5\u91c7\u7528\u7c7b\u4f3c\u65b9\u6cd5\u6765\u4f18\u5316\u6548\u7387\u3002\u4f8b\u5982\uff0c\u5f53\u94fe\u8868\u8f83\u957f\u65f6\uff0c\u53ef\u4ee5\u5c06\u94fe\u8868\u8f6c\u5316\u4e3a AVL \u6811\u6216\u7ea2\u9ed1\u6811\uff0c\u4ece\u800c\u5c06\u65f6\u95f4\u6548\u7387\u4ece \\(O(n)\\) \u4f18\u5316\u81f3 \\(O(\\log n)\\) \uff0c\u8fd8\u53ef\u4ee5\u901a\u8fc7\u4e2d\u5e8f\u904d\u5386\u83b7\u53d6\u6709\u5e8f\u5e8f\u5217\uff1b\u6b64\u5916\uff0c\u8fd8\u53ef\u4ee5\u5c06\u94fe\u8868\u8f6c\u6362\u4e3a\u54c8\u5e0c\u8868\uff0c\u5c06\u65f6\u95f4\u590d\u6742\u5ea6\u964d\u4f4e\u81f3 \\(O(1)\\) \u3002</p>"},{"location":"chapter_graph/graph/#914","title":"9.1.4. \u00a0 \u56fe\u5e38\u89c1\u5e94\u7528","text":"<p>\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u8bb8\u591a\u7cfb\u7edf\u90fd\u53ef\u4ee5\u7528\u56fe\u6765\u5efa\u6a21\uff0c\u76f8\u5e94\u7684\u5f85\u6c42\u89e3\u95ee\u9898\u4e5f\u53ef\u4ee5\u7ea6\u5316\u4e3a\u56fe\u8ba1\u7b97\u95ee\u9898\u3002</p> \u9876\u70b9 \u8fb9 \u56fe\u8ba1\u7b97\u95ee\u9898 \u793e\u4ea4\u7f51\u7edc \u7528\u6237 \u597d\u53cb\u5173\u7cfb \u6f5c\u5728\u597d\u53cb\u63a8\u8350 \u5730\u94c1\u7ebf\u8def \u7ad9\u70b9 \u7ad9\u70b9\u95f4\u7684\u8fde\u901a\u6027 \u6700\u77ed\u8def\u7ebf\u63a8\u8350 \u592a\u9633\u7cfb \u661f\u4f53 \u661f\u4f53\u95f4\u7684\u4e07\u6709\u5f15\u529b\u4f5c\u7528 \u884c\u661f\u8f68\u9053\u8ba1\u7b97"},{"location":"chapter_graph/graph_operations/","title":"9.2. \u00a0 \u56fe\u57fa\u7840\u64cd\u4f5c","text":"<p>\u56fe\u7684\u57fa\u7840\u64cd\u4f5c\u53ef\u5206\u4e3a\u5bf9\u300c\u8fb9\u300d\u7684\u64cd\u4f5c\u548c\u5bf9\u300c\u9876\u70b9\u300d\u7684\u64cd\u4f5c\u3002\u5728\u300c\u90bb\u63a5\u77e9\u9635\u300d\u548c\u300c\u90bb\u63a5\u8868\u300d\u4e24\u79cd\u8868\u793a\u65b9\u6cd5\u4e0b\uff0c\u5b9e\u73b0\u65b9\u5f0f\u6709\u6240\u4e0d\u540c\u3002</p>"},{"location":"chapter_graph/graph_operations/#921","title":"9.2.1. \u00a0 \u57fa\u4e8e\u90bb\u63a5\u77e9\u9635\u7684\u5b9e\u73b0","text":"<p>\u7ed9\u5b9a\u4e00\u4e2a\u9876\u70b9\u6570\u91cf\u4e3a \\(n\\) \u7684\u65e0\u5411\u56fe\uff0c\u5219\u6709\uff1a</p> <ul> <li>\u6dfb\u52a0\u6216\u5220\u9664\u8fb9\uff1a\u76f4\u63a5\u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u4fee\u6539\u6307\u5b9a\u7684\u8fb9\u5373\u53ef\uff0c\u4f7f\u7528 \\(O(1)\\) \u65f6\u95f4\u3002\u800c\u7531\u4e8e\u662f\u65e0\u5411\u56fe\uff0c\u56e0\u6b64\u9700\u8981\u540c\u65f6\u66f4\u65b0\u4e24\u4e2a\u65b9\u5411\u7684\u8fb9\u3002</li> <li>\u6dfb\u52a0\u9876\u70b9\uff1a\u5728\u90bb\u63a5\u77e9\u9635\u7684\u5c3e\u90e8\u6dfb\u52a0\u4e00\u884c\u4e00\u5217\uff0c\u5e76\u5168\u90e8\u586b \\(0\\) \u5373\u53ef\uff0c\u4f7f\u7528 \\(O(n)\\) \u65f6\u95f4\u3002</li> <li>\u5220\u9664\u9876\u70b9\uff1a\u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u5220\u9664\u4e00\u884c\u4e00\u5217\u3002\u5f53\u5220\u9664\u9996\u884c\u9996\u5217\u65f6\u8fbe\u5230\u6700\u5dee\u60c5\u51b5\uff0c\u9700\u8981\u5c06 \\((n-1)^2\\) \u4e2a\u5143\u7d20\u201c\u5411\u5de6\u4e0a\u79fb\u52a8\u201d\uff0c\u4ece\u800c\u4f7f\u7528 \\(O(n^2)\\) \u65f6\u95f4\u3002</li> <li>\u521d\u59cb\u5316\uff1a\u4f20\u5165 \\(n\\) \u4e2a\u9876\u70b9\uff0c\u521d\u59cb\u5316\u957f\u5ea6\u4e3a \\(n\\) \u7684\u9876\u70b9\u5217\u8868 <code>vertices</code> \uff0c\u4f7f\u7528 \\(O(n)\\) \u65f6\u95f4\uff1b\u521d\u59cb\u5316 \\(n \\times n\\) \u5927\u5c0f\u7684\u90bb\u63a5\u77e9\u9635 <code>adjMat</code> \uff0c\u4f7f\u7528 \\(O(n^2)\\) \u65f6\u95f4\u3002</li> </ul> \u521d\u59cb\u5316\u90bb\u63a5\u77e9\u9635\u6dfb\u52a0\u8fb9\u5220\u9664\u8fb9\u6dfb\u52a0\u9876\u70b9\u5220\u9664\u9876\u70b9 <p></p> <p></p> <p></p> <p></p> <p></p> <p>\u4ee5\u4e0b\u662f\u57fa\u4e8e\u90bb\u63a5\u77e9\u9635\u8868\u793a\u56fe\u7684\u5b9e\u73b0\u4ee3\u7801\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart graph_adjacency_matrix.java<pre><code>/* \u57fa\u4e8e\u90bb\u63a5\u77e9\u9635\u5b9e\u73b0\u7684\u65e0\u5411\u56fe\u7c7b */\nclass GraphAdjMat {\nList&lt;Integer&gt; vertices; // \u9876\u70b9\u5217\u8868\uff0c\u5143\u7d20\u4ee3\u8868\u201c\u9876\u70b9\u503c\u201d\uff0c\u7d22\u5f15\u4ee3\u8868\u201c\u9876\u70b9\u7d22\u5f15\u201d\nList&lt;List&lt;Integer&gt;&gt; adjMat; // \u90bb\u63a5\u77e9\u9635\uff0c\u884c\u5217\u7d22\u5f15\u5bf9\u5e94\u201c\u9876\u70b9\u7d22\u5f15\u201d\n/* \u6784\u9020\u65b9\u6cd5 */\npublic GraphAdjMat(int[] vertices, int[][] edges) {\nthis.vertices = new ArrayList&lt;&gt;();\nthis.adjMat = new ArrayList&lt;&gt;();\n// \u6dfb\u52a0\u9876\u70b9\nfor (int val : vertices) {\naddVertex(val);\n}\n// \u6dfb\u52a0\u8fb9\n// \u8bf7\u6ce8\u610f\uff0cedges \u5143\u7d20\u4ee3\u8868\u9876\u70b9\u7d22\u5f15\uff0c\u5373\u5bf9\u5e94 vertices \u5143\u7d20\u7d22\u5f15\nfor (int[] e : edges) {\naddEdge(e[0], e[1]);\n}\n}\n/* \u83b7\u53d6\u9876\u70b9\u6570\u91cf */\npublic int size() {\nreturn vertices.size();\n}\n/* \u6dfb\u52a0\u9876\u70b9 */\npublic void addVertex(int val) {\nint n = size();\n// \u5411\u9876\u70b9\u5217\u8868\u4e2d\u6dfb\u52a0\u65b0\u9876\u70b9\u7684\u503c\nvertices.add(val);\n// \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u6dfb\u52a0\u4e00\u884c\nList&lt;Integer&gt; newRow = new ArrayList&lt;&gt;(n);\nfor (int j = 0; j &lt; n; j++) {\nnewRow.add(0);\n}\nadjMat.add(newRow);\n// \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u6dfb\u52a0\u4e00\u5217\nfor (List&lt;Integer&gt; row : adjMat) {\nrow.add(0);\n}\n}\n/* \u5220\u9664\u9876\u70b9 */\npublic void removeVertex(int index) {\nif (index &gt;= size())\nthrow new IndexOutOfBoundsException();\n// \u5728\u9876\u70b9\u5217\u8868\u4e2d\u79fb\u9664\u7d22\u5f15 index \u7684\u9876\u70b9\nvertices.remove(index);\n// \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u5220\u9664\u7d22\u5f15 index \u7684\u884c\nadjMat.remove(index);\n// \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u5220\u9664\u7d22\u5f15 index \u7684\u5217\nfor (List&lt;Integer&gt; row : adjMat) {\nrow.remove(index);\n}\n}\n/* \u6dfb\u52a0\u8fb9 */\n// \u53c2\u6570 i, j \u5bf9\u5e94 vertices \u5143\u7d20\u7d22\u5f15\npublic void addEdge(int i, int j) {\n// \u7d22\u5f15\u8d8a\u754c\u4e0e\u76f8\u7b49\u5904\u7406\nif (i &lt; 0 || j &lt; 0 || i &gt;= size() || j &gt;= size() || i == j)\nthrow new IndexOutOfBoundsException();\n// \u5728\u65e0\u5411\u56fe\u4e2d\uff0c\u90bb\u63a5\u77e9\u9635\u6cbf\u4e3b\u5bf9\u89d2\u7ebf\u5bf9\u79f0\uff0c\u5373\u6ee1\u8db3 (i, j) == (j, i)\nadjMat.get(i).set(j, 1);\nadjMat.get(j).set(i, 1);\n}\n/* \u5220\u9664\u8fb9 */\n// \u53c2\u6570 i, j \u5bf9\u5e94 vertices \u5143\u7d20\u7d22\u5f15\npublic void removeEdge(int i, int j) {\n// \u7d22\u5f15\u8d8a\u754c\u4e0e\u76f8\u7b49\u5904\u7406\nif (i &lt; 0 || j &lt; 0 || i &gt;= size() || j &gt;= size() || i == j)\nthrow new IndexOutOfBoundsException();\nadjMat.get(i).set(j, 0);\nadjMat.get(j).set(i, 0);\n}\n/* \u6253\u5370\u90bb\u63a5\u77e9\u9635 */\npublic void print() {\nSystem.out.print(\"\u9876\u70b9\u5217\u8868 = \");\nSystem.out.println(vertices);\nSystem.out.println(\"\u90bb\u63a5\u77e9\u9635 =\");\nPrintUtil.printMatrix(adjMat);\n}\n}\n</code></pre> graph_adjacency_matrix.cpp<pre><code>/* \u57fa\u4e8e\u90bb\u63a5\u77e9\u9635\u5b9e\u73b0\u7684\u65e0\u5411\u56fe\u7c7b */\nclass GraphAdjMat {\nvector&lt;int&gt; vertices;       // \u9876\u70b9\u5217\u8868\uff0c\u5143\u7d20\u4ee3\u8868\u201c\u9876\u70b9\u503c\u201d\uff0c\u7d22\u5f15\u4ee3\u8868\u201c\u9876\u70b9\u7d22\u5f15\u201d\nvector&lt;vector&lt;int&gt;&gt; adjMat; // \u90bb\u63a5\u77e9\u9635\uff0c\u884c\u5217\u7d22\u5f15\u5bf9\u5e94\u201c\u9876\u70b9\u7d22\u5f15\u201d\npublic:\n/* \u6784\u9020\u65b9\u6cd5 */\nGraphAdjMat(const vector&lt;int&gt; &amp;vertices, const vector&lt;vector&lt;int&gt;&gt; &amp;edges) {\n// \u6dfb\u52a0\u9876\u70b9\nfor (int val : vertices) {\naddVertex(val);\n}\n// \u6dfb\u52a0\u8fb9\n// \u8bf7\u6ce8\u610f\uff0cedges \u5143\u7d20\u4ee3\u8868\u9876\u70b9\u7d22\u5f15\uff0c\u5373\u5bf9\u5e94 vertices \u5143\u7d20\u7d22\u5f15\nfor (const vector&lt;int&gt; &amp;edge : edges) {\naddEdge(edge[0], edge[1]);\n}\n}\n/* \u83b7\u53d6\u9876\u70b9\u6570\u91cf */\nint size() const {\nreturn vertices.size();\n}\n/* \u6dfb\u52a0\u9876\u70b9 */\nvoid addVertex(int val) {\nint n = size();\n// \u5411\u9876\u70b9\u5217\u8868\u4e2d\u6dfb\u52a0\u65b0\u9876\u70b9\u7684\u503c\nvertices.push_back(val);\n// \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u6dfb\u52a0\u4e00\u884c\nadjMat.emplace_back(n, 0);\n// \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u6dfb\u52a0\u4e00\u5217\nfor (vector&lt;int&gt; &amp;row : adjMat) {\nrow.push_back(0);\n}\n}\n/* \u5220\u9664\u9876\u70b9 */\nvoid removeVertex(int index) {\nif (index &gt;= size()) {\nthrow out_of_range(\"\u9876\u70b9\u4e0d\u5b58\u5728\");\n}\n// \u5728\u9876\u70b9\u5217\u8868\u4e2d\u79fb\u9664\u7d22\u5f15 index \u7684\u9876\u70b9\nvertices.erase(vertices.begin() + index);\n// \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u5220\u9664\u7d22\u5f15 index \u7684\u884c\nadjMat.erase(adjMat.begin() + index);\n// \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u5220\u9664\u7d22\u5f15 index \u7684\u5217\nfor (vector&lt;int&gt; &amp;row : adjMat) {\nrow.erase(row.begin() + index);\n}\n}\n/* \u6dfb\u52a0\u8fb9 */\n// \u53c2\u6570 i, j \u5bf9\u5e94 vertices \u5143\u7d20\u7d22\u5f15\nvoid addEdge(int i, int j) {\n// \u7d22\u5f15\u8d8a\u754c\u4e0e\u76f8\u7b49\u5904\u7406\nif (i &lt; 0 || j &lt; 0 || i &gt;= size() || j &gt;= size() || i == j) {\nthrow out_of_range(\"\u9876\u70b9\u4e0d\u5b58\u5728\");\n}\n// \u5728\u65e0\u5411\u56fe\u4e2d\uff0c\u90bb\u63a5\u77e9\u9635\u6cbf\u4e3b\u5bf9\u89d2\u7ebf\u5bf9\u79f0\uff0c\u5373\u6ee1\u8db3 (i, j) == (j, i)\nadjMat[i][j] = 1;\nadjMat[j][i] = 1;\n}\n/* \u5220\u9664\u8fb9 */\n// \u53c2\u6570 i, j \u5bf9\u5e94 vertices \u5143\u7d20\u7d22\u5f15\nvoid removeEdge(int i, int j) {\n// \u7d22\u5f15\u8d8a\u754c\u4e0e\u76f8\u7b49\u5904\u7406\nif (i &lt; 0 || j &lt; 0 || i &gt;= size() || j &gt;= size() || i == j) {\nthrow out_of_range(\"\u9876\u70b9\u4e0d\u5b58\u5728\");\n}\nadjMat[i][j] = 0;\nadjMat[j][i] = 0;\n}\n/* \u6253\u5370\u90bb\u63a5\u77e9\u9635 */\nvoid print() {\ncout &lt;&lt; \"\u9876\u70b9\u5217\u8868 = \";\nprintVector(vertices);\ncout &lt;&lt; \"\u90bb\u63a5\u77e9\u9635 =\" &lt;&lt; endl;\nprintVectorMatrix(adjMat);\n}\n};\n</code></pre> graph_adjacency_matrix.py<pre><code>class GraphAdjMat:\n\"\"\"\u57fa\u4e8e\u90bb\u63a5\u77e9\u9635\u5b9e\u73b0\u7684\u65e0\u5411\u56fe\u7c7b\"\"\"\n# \u9876\u70b9\u5217\u8868\uff0c\u5143\u7d20\u4ee3\u8868\u201c\u9876\u70b9\u503c\u201d\uff0c\u7d22\u5f15\u4ee3\u8868\u201c\u9876\u70b9\u7d22\u5f15\u201d\nvertices: list[int] = []\n# \u90bb\u63a5\u77e9\u9635\uff0c\u884c\u5217\u7d22\u5f15\u5bf9\u5e94\u201c\u9876\u70b9\u7d22\u5f15\u201d\nadj_mat: list[list[int]] = []\ndef __init__(self, vertices: list[int], edges: list[list[int]]) -&gt; None:\n\"\"\"\u6784\u9020\u65b9\u6cd5\"\"\"\nself.vertices: list[int] = []\nself.adj_mat: list[list[int]] = []\n# \u6dfb\u52a0\u9876\u70b9\nfor val in vertices:\nself.add_vertex(val)\n# \u6dfb\u52a0\u8fb9\n# \u8bf7\u6ce8\u610f\uff0cedges \u5143\u7d20\u4ee3\u8868\u9876\u70b9\u7d22\u5f15\uff0c\u5373\u5bf9\u5e94 vertices \u5143\u7d20\u7d22\u5f15\nfor e in edges:\nself.add_edge(e[0], e[1])\ndef size(self) -&gt; int:\n\"\"\"\u83b7\u53d6\u9876\u70b9\u6570\u91cf\"\"\"\nreturn len(self.vertices)\ndef add_vertex(self, val: int) -&gt; None:\n\"\"\"\u6dfb\u52a0\u9876\u70b9\"\"\"\nn = self.size()\n# \u5411\u9876\u70b9\u5217\u8868\u4e2d\u6dfb\u52a0\u65b0\u9876\u70b9\u7684\u503c\nself.vertices.append(val)\n# \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u6dfb\u52a0\u4e00\u884c\nnew_row = [0] * n\nself.adj_mat.append(new_row)\n# \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u6dfb\u52a0\u4e00\u5217\nfor row in self.adj_mat:\nrow.append(0)\ndef remove_vertex(self, index: int) -&gt; None:\n\"\"\"\u5220\u9664\u9876\u70b9\"\"\"\nif index &gt;= self.size():\nraise IndexError()\n# \u5728\u9876\u70b9\u5217\u8868\u4e2d\u79fb\u9664\u7d22\u5f15 index \u7684\u9876\u70b9\nself.vertices.pop(index)\n# \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u5220\u9664\u7d22\u5f15 index \u7684\u884c\nself.adj_mat.pop(index)\n# \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u5220\u9664\u7d22\u5f15 index \u7684\u5217\nfor row in self.adj_mat:\nrow.pop(index)\ndef add_edge(self, i: int, j: int) -&gt; None:\n\"\"\"\u6dfb\u52a0\u8fb9\"\"\"\n# \u53c2\u6570 i, j \u5bf9\u5e94 vertices \u5143\u7d20\u7d22\u5f15\n# \u7d22\u5f15\u8d8a\u754c\u4e0e\u76f8\u7b49\u5904\u7406\nif i &lt; 0 or j &lt; 0 or i &gt;= self.size() or j &gt;= self.size() or i == j:\nraise IndexError()\n# \u5728\u65e0\u5411\u56fe\u4e2d\uff0c\u90bb\u63a5\u77e9\u9635\u6cbf\u4e3b\u5bf9\u89d2\u7ebf\u5bf9\u79f0\uff0c\u5373\u6ee1\u8db3 (i, j) == (j, i)\nself.adj_mat[i][j] = 1\nself.adj_mat[j][i] = 1\ndef remove_edge(self, i: int, j: int) -&gt; None:\n\"\"\"\u5220\u9664\u8fb9\"\"\"\n# \u53c2\u6570 i, j \u5bf9\u5e94 vertices \u5143\u7d20\u7d22\u5f15\n# \u7d22\u5f15\u8d8a\u754c\u4e0e\u76f8\u7b49\u5904\u7406\nif i &lt; 0 or j &lt; 0 or i &gt;= self.size() or j &gt;= self.size() or i == j:\nraise IndexError()\nself.adj_mat[i][j] = 0\nself.adj_mat[j][i] = 0\ndef print(self) -&gt; None:\n\"\"\"\u6253\u5370\u90bb\u63a5\u77e9\u9635\"\"\"\nprint(\"\u9876\u70b9\u5217\u8868 =\", self.vertices)\nprint(\"\u90bb\u63a5\u77e9\u9635 =\")\nprint_matrix(self.adj_mat)\n</code></pre> graph_adjacency_matrix.go<pre><code>/* \u57fa\u4e8e\u90bb\u63a5\u77e9\u9635\u5b9e\u73b0\u7684\u65e0\u5411\u56fe\u7c7b */\ntype graphAdjMat struct {\n// \u9876\u70b9\u5217\u8868\uff0c\u5143\u7d20\u4ee3\u8868\u201c\u9876\u70b9\u503c\u201d\uff0c\u7d22\u5f15\u4ee3\u8868\u201c\u9876\u70b9\u7d22\u5f15\u201d\nvertices []int\n// \u90bb\u63a5\u77e9\u9635\uff0c\u884c\u5217\u7d22\u5f15\u5bf9\u5e94\u201c\u9876\u70b9\u7d22\u5f15\u201d\nadjMat [][]int\n}\n/* \u6784\u9020\u65b9\u6cd5 */\nfunc newGraphAdjMat(vertices []int, edges [][]int) *graphAdjMat {\n// \u6dfb\u52a0\u9876\u70b9\nn := len(vertices)\nadjMat := make([][]int, n)\nfor i := range adjMat {\nadjMat[i] = make([]int, n)\n}\n// \u521d\u59cb\u5316\u56fe\ng := &amp;graphAdjMat{\nvertices: vertices,\nadjMat:   adjMat,\n}\n// \u6dfb\u52a0\u8fb9\n// \u8bf7\u6ce8\u610f\uff0cedges \u5143\u7d20\u4ee3\u8868\u9876\u70b9\u7d22\u5f15\uff0c\u5373\u5bf9\u5e94 vertices \u5143\u7d20\u7d22\u5f15\nfor i := range edges {\ng.addEdge(edges[i][0], edges[i][1])\n}\nreturn g\n}\n/* \u83b7\u53d6\u9876\u70b9\u6570\u91cf */\nfunc (g *graphAdjMat) size() int {\nreturn len(g.vertices)\n}\n/* \u6dfb\u52a0\u9876\u70b9 */\nfunc (g *graphAdjMat) addVertex(val int) {\nn := g.size()\n// \u5411\u9876\u70b9\u5217\u8868\u4e2d\u6dfb\u52a0\u65b0\u9876\u70b9\u7684\u503c\ng.vertices = append(g.vertices, val)\n// \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u6dfb\u52a0\u4e00\u884c\nnewRow := make([]int, n)\ng.adjMat = append(g.adjMat, newRow)\n// \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u6dfb\u52a0\u4e00\u5217\nfor i := range g.adjMat {\ng.adjMat[i] = append(g.adjMat[i], 0)\n}\n}\n/* \u5220\u9664\u9876\u70b9 */\nfunc (g *graphAdjMat) removeVertex(index int) {\nif index &gt;= g.size() {\nreturn\n}\n// \u5728\u9876\u70b9\u5217\u8868\u4e2d\u79fb\u9664\u7d22\u5f15 index \u7684\u9876\u70b9\ng.vertices = append(g.vertices[:index], g.vertices[index+1:]...)\n// \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u5220\u9664\u7d22\u5f15 index \u7684\u884c\ng.adjMat = append(g.adjMat[:index], g.adjMat[index+1:]...)\n// \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u5220\u9664\u7d22\u5f15 index \u7684\u5217\nfor i := range g.adjMat {\ng.adjMat[i] = append(g.adjMat[i][:index], g.adjMat[i][index+1:]...)\n}\n}\n/* \u6dfb\u52a0\u8fb9 */\n// \u53c2\u6570 i, j \u5bf9\u5e94 vertices \u5143\u7d20\u7d22\u5f15\nfunc (g *graphAdjMat) addEdge(i, j int) {\n// \u7d22\u5f15\u8d8a\u754c\u4e0e\u76f8\u7b49\u5904\u7406\nif i &lt; 0 || j &lt; 0 || i &gt;= g.size() || j &gt;= g.size() || i == j {\nfmt.Errorf(\"%s\", \"Index Out Of Bounds Exception\")\n}\n// \u5728\u65e0\u5411\u56fe\u4e2d\uff0c\u90bb\u63a5\u77e9\u9635\u6cbf\u4e3b\u5bf9\u89d2\u7ebf\u5bf9\u79f0\uff0c\u5373\u6ee1\u8db3 (i, j) == (j, i)\ng.adjMat[i][j] = 1\ng.adjMat[j][i] = 1\n}\n/* \u5220\u9664\u8fb9 */\n// \u53c2\u6570 i, j \u5bf9\u5e94 vertices \u5143\u7d20\u7d22\u5f15\nfunc (g *graphAdjMat) removeEdge(i, j int) {\n// \u7d22\u5f15\u8d8a\u754c\u4e0e\u76f8\u7b49\u5904\u7406\nif i &lt; 0 || j &lt; 0 || i &gt;= g.size() || j &gt;= g.size() || i == j {\nfmt.Errorf(\"%s\", \"Index Out Of Bounds Exception\")\n}\ng.adjMat[i][j] = 0\ng.adjMat[j][i] = 0\n}\n/* \u6253\u5370\u90bb\u63a5\u77e9\u9635 */\nfunc (g *graphAdjMat) print() {\nfmt.Printf(\"\\t\u9876\u70b9\u5217\u8868 = %v\\n\", g.vertices)\nfmt.Printf(\"\\t\u90bb\u63a5\u77e9\u9635 = \\n\")\nfor i := range g.adjMat {\nfmt.Printf(\"\\t\\t\\t%v\\n\", g.adjMat[i])\n}\n}\n</code></pre> graph_adjacency_matrix.js<pre><code>/* \u57fa\u4e8e\u90bb\u63a5\u77e9\u9635\u5b9e\u73b0\u7684\u65e0\u5411\u56fe\u7c7b */\nclass GraphAdjMat {\nvertices; // \u9876\u70b9\u5217\u8868\uff0c\u5143\u7d20\u4ee3\u8868\u201c\u9876\u70b9\u503c\u201d\uff0c\u7d22\u5f15\u4ee3\u8868\u201c\u9876\u70b9\u7d22\u5f15\u201d\nadjMat; // \u90bb\u63a5\u77e9\u9635\uff0c\u884c\u5217\u7d22\u5f15\u5bf9\u5e94\u201c\u9876\u70b9\u7d22\u5f15\u201d\n/* \u6784\u9020\u51fd\u6570 */\nconstructor(vertices, edges) {\nthis.vertices = [];\nthis.adjMat = [];\n// \u6dfb\u52a0\u9876\u70b9\nfor (const val of vertices) {\nthis.addVertex(val);\n}\n// \u6dfb\u52a0\u8fb9\n// \u8bf7\u6ce8\u610f\uff0cedges \u5143\u7d20\u4ee3\u8868\u9876\u70b9\u7d22\u5f15\uff0c\u5373\u5bf9\u5e94 vertices \u5143\u7d20\u7d22\u5f15\nfor (const e of edges) {\nthis.addEdge(e[0], e[1]);\n}\n}\n/* \u83b7\u53d6\u9876\u70b9\u6570\u91cf */\nsize() {\nreturn this.vertices.length;\n}\n/* \u6dfb\u52a0\u9876\u70b9 */\naddVertex(val) {\nconst n = this.size();\n// \u5411\u9876\u70b9\u5217\u8868\u4e2d\u6dfb\u52a0\u65b0\u9876\u70b9\u7684\u503c\nthis.vertices.push(val);\n// \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u6dfb\u52a0\u4e00\u884c\nconst newRow = [];\nfor (let j = 0; j &lt; n; j++) {\nnewRow.push(0);\n}\nthis.adjMat.push(newRow);\n// \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u6dfb\u52a0\u4e00\u5217\nfor (const row of this.adjMat) {\nrow.push(0);\n}\n}\n/* \u5220\u9664\u9876\u70b9 */\nremoveVertex(index) {\nif (index &gt;= this.size()) {\nthrow new RangeError('Index Out Of Bounds Exception');\n}\n// \u5728\u9876\u70b9\u5217\u8868\u4e2d\u79fb\u9664\u7d22\u5f15 index \u7684\u9876\u70b9\nthis.vertices.splice(index, 1);\n// \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u5220\u9664\u7d22\u5f15 index \u7684\u884c\nthis.adjMat.splice(index, 1);\n// \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u5220\u9664\u7d22\u5f15 index \u7684\u5217\nfor (const row of this.adjMat) {\nrow.splice(index, 1);\n}\n}\n/* \u6dfb\u52a0\u8fb9 */\n// \u53c2\u6570 i, j \u5bf9\u5e94 vertices \u5143\u7d20\u7d22\u5f15\naddEdge(i, j) {\n// \u7d22\u5f15\u8d8a\u754c\u4e0e\u76f8\u7b49\u5904\u7406\nif (i &lt; 0 || j &lt; 0 || i &gt;= this.size() || j &gt;= this.size() || i === j) {\nthrow new RangeError('Index Out Of Bounds Exception');\n}\n// \u5728\u65e0\u5411\u56fe\u4e2d\uff0c\u90bb\u63a5\u77e9\u9635\u6cbf\u4e3b\u5bf9\u89d2\u7ebf\u5bf9\u79f0\uff0c\u5373\u6ee1\u8db3 (i, j) == (j, i)\nthis.adjMat[i][j] = 1;\nthis.adjMat[j][i] = 1;\n}\n/* \u5220\u9664\u8fb9 */\n// \u53c2\u6570 i, j \u5bf9\u5e94 vertices \u5143\u7d20\u7d22\u5f15\nremoveEdge(i, j) {\n// \u7d22\u5f15\u8d8a\u754c\u4e0e\u76f8\u7b49\u5904\u7406\nif (i &lt; 0 || j &lt; 0 || i &gt;= this.size() || j &gt;= this.size() || i === j) {\nthrow new RangeError('Index Out Of Bounds Exception');\n}\nthis.adjMat[i][j] = 0;\nthis.adjMat[j][i] = 0;\n}\n/* \u6253\u5370\u90bb\u63a5\u77e9\u9635 */\nprint() {\nconsole.log('\u9876\u70b9\u5217\u8868 = ', this.vertices);\nconsole.log('\u90bb\u63a5\u77e9\u9635 =', this.adjMat);\n}\n}\n</code></pre> graph_adjacency_matrix.ts<pre><code>/* \u57fa\u4e8e\u90bb\u63a5\u77e9\u9635\u5b9e\u73b0\u7684\u65e0\u5411\u56fe\u7c7b */\nclass GraphAdjMat {\nvertices: number[]; // \u9876\u70b9\u5217\u8868\uff0c\u5143\u7d20\u4ee3\u8868\u201c\u9876\u70b9\u503c\u201d\uff0c\u7d22\u5f15\u4ee3\u8868\u201c\u9876\u70b9\u7d22\u5f15\u201d\nadjMat: number[][]; // \u90bb\u63a5\u77e9\u9635\uff0c\u884c\u5217\u7d22\u5f15\u5bf9\u5e94\u201c\u9876\u70b9\u7d22\u5f15\u201d\n/* \u6784\u9020\u51fd\u6570 */\nconstructor(vertices: number[], edges: number[][]) {\nthis.vertices = [];\nthis.adjMat = [];\n// \u6dfb\u52a0\u9876\u70b9\nfor (const val of vertices) {\nthis.addVertex(val);\n}\n// \u6dfb\u52a0\u8fb9\n// \u8bf7\u6ce8\u610f\uff0cedges \u5143\u7d20\u4ee3\u8868\u9876\u70b9\u7d22\u5f15\uff0c\u5373\u5bf9\u5e94 vertices \u5143\u7d20\u7d22\u5f15\nfor (const e of edges) {\nthis.addEdge(e[0], e[1]);\n}\n}\n/* \u83b7\u53d6\u9876\u70b9\u6570\u91cf */\nsize(): number {\nreturn this.vertices.length;\n}\n/* \u6dfb\u52a0\u9876\u70b9 */\naddVertex(val: number): void {\nconst n: number = this.size();\n// \u5411\u9876\u70b9\u5217\u8868\u4e2d\u6dfb\u52a0\u65b0\u9876\u70b9\u7684\u503c\nthis.vertices.push(val);\n// \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u6dfb\u52a0\u4e00\u884c\nconst newRow: number[] = [];\nfor (let j: number = 0; j &lt; n; j++) {\nnewRow.push(0);\n}\nthis.adjMat.push(newRow);\n// \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u6dfb\u52a0\u4e00\u5217\nfor (const row of this.adjMat) {\nrow.push(0);\n}\n}\n/* \u5220\u9664\u9876\u70b9 */\nremoveVertex(index: number): void {\nif (index &gt;= this.size()) {\nthrow new RangeError('Index Out Of Bounds Exception');\n}\n// \u5728\u9876\u70b9\u5217\u8868\u4e2d\u79fb\u9664\u7d22\u5f15 index \u7684\u9876\u70b9\nthis.vertices.splice(index, 1);\n// \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u5220\u9664\u7d22\u5f15 index \u7684\u884c\nthis.adjMat.splice(index, 1);\n// \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u5220\u9664\u7d22\u5f15 index \u7684\u5217\nfor (const row of this.adjMat) {\nrow.splice(index, 1);\n}\n}\n/* \u6dfb\u52a0\u8fb9 */\n// \u53c2\u6570 i, j \u5bf9\u5e94 vertices \u5143\u7d20\u7d22\u5f15\naddEdge(i: number, j: number): void {\n// \u7d22\u5f15\u8d8a\u754c\u4e0e\u76f8\u7b49\u5904\u7406\nif (i &lt; 0 || j &lt; 0 || i &gt;= this.size() || j &gt;= this.size() || i === j) {\nthrow new RangeError('Index Out Of Bounds Exception');\n}\n// \u5728\u65e0\u5411\u56fe\u4e2d\uff0c\u90bb\u63a5\u77e9\u9635\u6cbf\u4e3b\u5bf9\u89d2\u7ebf\u5bf9\u79f0\uff0c\u5373\u6ee1\u8db3 (i, j) == (j, i)\nthis.adjMat[i][j] = 1;\nthis.adjMat[j][i] = 1;\n}\n/* \u5220\u9664\u8fb9 */\n// \u53c2\u6570 i, j \u5bf9\u5e94 vertices \u5143\u7d20\u7d22\u5f15\nremoveEdge(i: number, j: number): void {\n// \u7d22\u5f15\u8d8a\u754c\u4e0e\u76f8\u7b49\u5904\u7406\nif (i &lt; 0 || j &lt; 0 || i &gt;= this.size() || j &gt;= this.size() || i === j) {\nthrow new RangeError('Index Out Of Bounds Exception');\n}\nthis.adjMat[i][j] = 0;\nthis.adjMat[j][i] = 0;\n}\n/* \u6253\u5370\u90bb\u63a5\u77e9\u9635 */\nprint(): void {\nconsole.log('\u9876\u70b9\u5217\u8868 = ', this.vertices);\nconsole.log('\u90bb\u63a5\u77e9\u9635 =', this.adjMat);\n}\n}\n</code></pre> graph_adjacency_matrix.c<pre><code>[class]{graphAdjMat}-[func]{}\n</code></pre> graph_adjacency_matrix.cs<pre><code>/* \u57fa\u4e8e\u90bb\u63a5\u77e9\u9635\u5b9e\u73b0\u7684\u65e0\u5411\u56fe\u7c7b */\nclass GraphAdjMat {\nList&lt;int&gt; vertices;     // \u9876\u70b9\u5217\u8868\uff0c\u5143\u7d20\u4ee3\u8868\u201c\u9876\u70b9\u503c\u201d\uff0c\u7d22\u5f15\u4ee3\u8868\u201c\u9876\u70b9\u7d22\u5f15\u201d\nList&lt;List&lt;int&gt;&gt; adjMat; // \u90bb\u63a5\u77e9\u9635\uff0c\u884c\u5217\u7d22\u5f15\u5bf9\u5e94\u201c\u9876\u70b9\u7d22\u5f15\u201d\n/* \u6784\u9020\u51fd\u6570 */\npublic GraphAdjMat(int[] vertices, int[][] edges) {\nthis.vertices = new List&lt;int&gt;();\nthis.adjMat = new List&lt;List&lt;int&gt;&gt;();\n// \u6dfb\u52a0\u9876\u70b9\nforeach (int val in vertices) {\naddVertex(val);\n}\n// \u6dfb\u52a0\u8fb9\n// \u8bf7\u6ce8\u610f\uff0cedges \u5143\u7d20\u4ee3\u8868\u9876\u70b9\u7d22\u5f15\uff0c\u5373\u5bf9\u5e94 vertices \u5143\u7d20\u7d22\u5f15\nforeach (int[] e in edges) {\naddEdge(e[0], e[1]);\n}\n}\n/* \u83b7\u53d6\u9876\u70b9\u6570\u91cf */\npublic int size() {\nreturn vertices.Count;\n}\n/* \u6dfb\u52a0\u9876\u70b9 */\npublic void addVertex(int val) {\nint n = size();\n// \u5411\u9876\u70b9\u5217\u8868\u4e2d\u6dfb\u52a0\u65b0\u9876\u70b9\u7684\u503c\nvertices.Add(val);\n// \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u6dfb\u52a0\u4e00\u884c\nList&lt;int&gt; newRow = new List&lt;int&gt;(n);\nfor (int j = 0; j &lt; n; j++) {\nnewRow.Add(0);\n}\nadjMat.Add(newRow);\n// \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u6dfb\u52a0\u4e00\u5217\nforeach (List&lt;int&gt; row in adjMat) {\nrow.Add(0);\n}\n}\n/* \u5220\u9664\u9876\u70b9 */\npublic void removeVertex(int index) {\nif (index &gt;= size())\nthrow new IndexOutOfRangeException();\n// \u5728\u9876\u70b9\u5217\u8868\u4e2d\u79fb\u9664\u7d22\u5f15 index \u7684\u9876\u70b9\nvertices.RemoveAt(index);\n// \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u5220\u9664\u7d22\u5f15 index \u7684\u884c\nadjMat.RemoveAt(index);\n// \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u5220\u9664\u7d22\u5f15 index \u7684\u5217\nforeach (List&lt;int&gt; row in adjMat) {\nrow.RemoveAt(index);\n}\n}\n/* \u6dfb\u52a0\u8fb9 */\n// \u53c2\u6570 i, j \u5bf9\u5e94 vertices \u5143\u7d20\u7d22\u5f15\npublic void addEdge(int i, int j) {\n// \u7d22\u5f15\u8d8a\u754c\u4e0e\u76f8\u7b49\u5904\u7406\nif (i &lt; 0 || j &lt; 0 || i &gt;= size() || j &gt;= size() || i == j)\nthrow new IndexOutOfRangeException();\n// \u5728\u65e0\u5411\u56fe\u4e2d\uff0c\u90bb\u63a5\u77e9\u9635\u6cbf\u4e3b\u5bf9\u89d2\u7ebf\u5bf9\u79f0\uff0c\u5373\u6ee1\u8db3 (i, j) == (j, i)\nadjMat[i][j] = 1;\nadjMat[j][i] = 1;\n}\n/* \u5220\u9664\u8fb9 */\n// \u53c2\u6570 i, j \u5bf9\u5e94 vertices \u5143\u7d20\u7d22\u5f15\npublic void removeEdge(int i, int j) {\n// \u7d22\u5f15\u8d8a\u754c\u4e0e\u76f8\u7b49\u5904\u7406\nif (i &lt; 0 || j &lt; 0 || i &gt;= size() || j &gt;= size() || i == j)\nthrow new IndexOutOfRangeException();\nadjMat[i][j] = 0;\nadjMat[j][i] = 0;\n}\n/* \u6253\u5370\u90bb\u63a5\u77e9\u9635 */\npublic void print() {\nConsole.Write(\"\u9876\u70b9\u5217\u8868 = \");\nPrintUtil.PrintList(vertices);\nConsole.WriteLine(\"\u90bb\u63a5\u77e9\u9635 =\");\nPrintUtil.PrintMatrix(adjMat);\n}\n}\n</code></pre> graph_adjacency_matrix.swift<pre><code>/* \u57fa\u4e8e\u90bb\u63a5\u77e9\u9635\u5b9e\u73b0\u7684\u65e0\u5411\u56fe\u7c7b */\nclass GraphAdjMat {\nprivate var vertices: [Int] // \u9876\u70b9\u5217\u8868\uff0c\u5143\u7d20\u4ee3\u8868\u201c\u9876\u70b9\u503c\u201d\uff0c\u7d22\u5f15\u4ee3\u8868\u201c\u9876\u70b9\u7d22\u5f15\u201d\nprivate var adjMat: [[Int]] // \u90bb\u63a5\u77e9\u9635\uff0c\u884c\u5217\u7d22\u5f15\u5bf9\u5e94\u201c\u9876\u70b9\u7d22\u5f15\u201d\n/* \u6784\u9020\u65b9\u6cd5 */\ninit(vertices: [Int], edges: [[Int]]) {\nself.vertices = []\nadjMat = []\n// \u6dfb\u52a0\u9876\u70b9\nfor val in vertices {\naddVertex(val: val)\n}\n// \u6dfb\u52a0\u8fb9\n// \u8bf7\u6ce8\u610f\uff0cedges \u5143\u7d20\u4ee3\u8868\u9876\u70b9\u7d22\u5f15\uff0c\u5373\u5bf9\u5e94 vertices \u5143\u7d20\u7d22\u5f15\nfor e in edges {\naddEdge(i: e[0], j: e[1])\n}\n}\n/* \u83b7\u53d6\u9876\u70b9\u6570\u91cf */\nfunc size() -&gt; Int {\nvertices.count\n}\n/* \u6dfb\u52a0\u9876\u70b9 */\nfunc addVertex(val: Int) {\nlet n = size()\n// \u5411\u9876\u70b9\u5217\u8868\u4e2d\u6dfb\u52a0\u65b0\u9876\u70b9\u7684\u503c\nvertices.append(val)\n// \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u6dfb\u52a0\u4e00\u884c\nlet newRow = Array(repeating: 0, count: n)\nadjMat.append(newRow)\n// \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u6dfb\u52a0\u4e00\u5217\nfor i in adjMat.indices {\nadjMat[i].append(0)\n}\n}\n/* \u5220\u9664\u9876\u70b9 */\nfunc removeVertex(index: Int) {\nif index &gt;= size() {\nfatalError(\"\u8d8a\u754c\")\n}\n// \u5728\u9876\u70b9\u5217\u8868\u4e2d\u79fb\u9664\u7d22\u5f15 index \u7684\u9876\u70b9\nvertices.remove(at: index)\n// \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u5220\u9664\u7d22\u5f15 index \u7684\u884c\nadjMat.remove(at: index)\n// \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u5220\u9664\u7d22\u5f15 index \u7684\u5217\nfor i in adjMat.indices {\nadjMat[i].remove(at: index)\n}\n}\n/* \u6dfb\u52a0\u8fb9 */\n// \u53c2\u6570 i, j \u5bf9\u5e94 vertices \u5143\u7d20\u7d22\u5f15\nfunc addEdge(i: Int, j: Int) {\n// \u7d22\u5f15\u8d8a\u754c\u4e0e\u76f8\u7b49\u5904\u7406\nif i &lt; 0 || j &lt; 0 || i &gt;= size() || j &gt;= size() || i == j {\nfatalError(\"\u8d8a\u754c\")\n}\n// \u5728\u65e0\u5411\u56fe\u4e2d\uff0c\u90bb\u63a5\u77e9\u9635\u6cbf\u4e3b\u5bf9\u89d2\u7ebf\u5bf9\u79f0\uff0c\u5373\u6ee1\u8db3 (i, j) == (j, i)\nadjMat[i][j] = 1\nadjMat[j][i] = 1\n}\n/* \u5220\u9664\u8fb9 */\n// \u53c2\u6570 i, j \u5bf9\u5e94 vertices \u5143\u7d20\u7d22\u5f15\nfunc removeEdge(i: Int, j: Int) {\n// \u7d22\u5f15\u8d8a\u754c\u4e0e\u76f8\u7b49\u5904\u7406\nif i &lt; 0 || j &lt; 0 || i &gt;= size() || j &gt;= size() || i == j {\nfatalError(\"\u8d8a\u754c\")\n}\nadjMat[i][j] = 0\nadjMat[j][i] = 0\n}\n/* \u6253\u5370\u90bb\u63a5\u77e9\u9635 */\nfunc print() {\nSwift.print(\"\u9876\u70b9\u5217\u8868 = \", terminator: \"\")\nSwift.print(vertices)\nSwift.print(\"\u90bb\u63a5\u77e9\u9635 =\")\nPrintUtil.printMatrix(matrix: adjMat)\n}\n}\n</code></pre> graph_adjacency_matrix.zig<pre><code>\n</code></pre> graph_adjacency_matrix.dart<pre><code>/* \u57fa\u4e8e\u90bb\u63a5\u77e9\u9635\u5b9e\u73b0\u7684\u65e0\u5411\u56fe\u7c7b */\nclass GraphAdjMat {\nList&lt;int&gt; vertices = []; // \u9876\u70b9\u5143\u7d20\uff0c\u5143\u7d20\u4ee3\u8868\u201c\u9876\u70b9\u503c\u201d\uff0c\u7d22\u5f15\u4ee3\u8868\u201c\u9876\u70b9\u7d22\u5f15\u201d\nList&lt;List&lt;int&gt;&gt; adjMat = []; //\u90bb\u63a5\u77e9\u9635\uff0c\u884c\u5217\u7d22\u5f15\u5bf9\u5e94\u201c\u9876\u70b9\u7d22\u5f15\u201d\n/* \u6784\u9020\u65b9\u6cd5 */\nGraphAdjMat(List&lt;int&gt; vertices, List&lt;List&lt;int&gt;&gt; edges) {\nthis.vertices = [];\nthis.adjMat = [];\n// \u6dfb\u52a0\u9876\u70b9\nfor (int val in vertices) {\naddVertex(val);\n}\n// \u6dfb\u52a0\u8fb9\n// \u8bf7\u6ce8\u610f\uff0cedges \u5143\u7d20\u4ee3\u8868\u9876\u70b9\u7d22\u5f15\uff0c\u5373\u5bf9\u5e94 vertices \u5143\u7d20\u7d22\u5f15\nfor (List&lt;int&gt; e in edges) {\naddEdge(e[0], e[1]);\n}\n}\n/* \u83b7\u53d6\u9876\u70b9\u6570\u91cf */\nint size() {\nreturn vertices.length;\n}\n/* \u6dfb\u52a0\u9876\u70b9 */\nvoid addVertex(int val) {\nint n = size();\n// \u5411\u9876\u70b9\u5217\u8868\u4e2d\u6dfb\u52a0\u65b0\u9876\u70b9\u7684\u503c\nvertices.add(val);\n// \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u6dfb\u52a0\u4e00\u884c\nList&lt;int&gt; newRow = List.filled(n, 0, growable: true);\nadjMat.add(newRow);\n// \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u6dfb\u52a0\u4e00\u5217\nfor (List&lt;int&gt; row in adjMat) {\nrow.add(0);\n}\n}\n/* \u5220\u9664\u9876\u70b9 */\nvoid removeVertex(int index) {\nif (index &gt;= size()) {\nthrow IndexError;\n}\n// \u5728\u9876\u70b9\u5217\u8868\u4e2d\u79fb\u9664\u7d22\u5f15 index \u7684\u9876\u70b9\nvertices.removeAt(index);\n// \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u5220\u9664\u7d22\u5f15 index \u7684\u884c\nadjMat.removeAt(index);\n// \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u5220\u9664\u7d22\u5f15 index \u7684\u5217\nfor (List&lt;int&gt; row in adjMat) {\nrow.removeAt(index);\n}\n}\n/* \u6dfb\u52a0\u8fb9 */\n// \u53c2\u6570 i, j \u5bf9\u5e94 vertices \u5143\u7d20\u7d22\u5f15\nvoid addEdge(int i, int j) {\n// \u7d22\u5f15\u8d8a\u754c\u4e0e\u76f8\u7b49\u5904\u7406\nif (i &lt; 0 || j &lt; 0 || i &gt;= size() || j &gt;= size() || i == j) {\nthrow IndexError;\n}\n// \u5728\u65e0\u5411\u56fe\u4e2d\uff0c\u90bb\u63a5\u77e9\u9635\u6cbf\u4e3b\u5bf9\u89d2\u7ebf\u5bf9\u79f0\uff0c\u5373\u6ee1\u8db3 (i, j) == (j, i)\nadjMat[i][j] = 1;\nadjMat[j][i] = 1;\n}\n/* \u5220\u9664\u8fb9 */\n// \u53c2\u6570 i, j \u5bf9\u5e94 vertices \u5143\u7d20\u7d22\u5f15\nvoid removeEdge(int i, int j) {\n// \u7d22\u5f15\u8d8a\u754c\u4e0e\u76f8\u7b49\u5904\u7406\nif (i &lt; 0 || j &lt; 0 || i &gt;= size() || j &gt;= size() || i == j) {\nthrow IndexError;\n}\nadjMat[i][j] = 0;\nadjMat[j][i] = 0;\n}\n/* \u6253\u5370\u90bb\u63a5\u77e9\u9635 */\nvoid printAdjMat() {\nprint(\"\u9876\u70b9\u5217\u8868 = $vertices\");\nprint(\"\u90bb\u63a5\u77e9\u9635 = \");\nprintMatrix(adjMat);\n}\n}\n</code></pre>"},{"location":"chapter_graph/graph_operations/#922","title":"9.2.2. \u00a0 \u57fa\u4e8e\u90bb\u63a5\u8868\u7684\u5b9e\u73b0","text":"<p>\u8bbe\u65e0\u5411\u56fe\u7684\u9876\u70b9\u603b\u6570\u4e3a \\(n\\) \u3001\u8fb9\u603b\u6570\u4e3a \\(m\\) \uff0c\u5219\u6709\uff1a</p> <ul> <li>\u6dfb\u52a0\u8fb9\uff1a\u5728\u9876\u70b9\u5bf9\u5e94\u94fe\u8868\u7684\u672b\u5c3e\u6dfb\u52a0\u8fb9\u5373\u53ef\uff0c\u4f7f\u7528 \\(O(1)\\) \u65f6\u95f4\u3002\u56e0\u4e3a\u662f\u65e0\u5411\u56fe\uff0c\u6240\u4ee5\u9700\u8981\u540c\u65f6\u6dfb\u52a0\u4e24\u4e2a\u65b9\u5411\u7684\u8fb9\u3002</li> <li>\u5220\u9664\u8fb9\uff1a\u5728\u9876\u70b9\u5bf9\u5e94\u94fe\u8868\u4e2d\u67e5\u627e\u5e76\u5220\u9664\u6307\u5b9a\u8fb9\uff0c\u4f7f\u7528 \\(O(m)\\) \u65f6\u95f4\u3002\u5728\u65e0\u5411\u56fe\u4e2d\uff0c\u9700\u8981\u540c\u65f6\u5220\u9664\u4e24\u4e2a\u65b9\u5411\u7684\u8fb9\u3002</li> <li>\u6dfb\u52a0\u9876\u70b9\uff1a\u5728\u90bb\u63a5\u8868\u4e2d\u6dfb\u52a0\u4e00\u4e2a\u94fe\u8868\uff0c\u5e76\u5c06\u65b0\u589e\u9876\u70b9\u4f5c\u4e3a\u94fe\u8868\u5934\u8282\u70b9\uff0c\u4f7f\u7528 \\(O(1)\\) \u65f6\u95f4\u3002</li> <li>\u5220\u9664\u9876\u70b9\uff1a\u9700\u904d\u5386\u6574\u4e2a\u90bb\u63a5\u8868\uff0c\u5220\u9664\u5305\u542b\u6307\u5b9a\u9876\u70b9\u7684\u6240\u6709\u8fb9\uff0c\u4f7f\u7528 \\(O(n + m)\\) \u65f6\u95f4\u3002</li> <li>\u521d\u59cb\u5316\uff1a\u5728\u90bb\u63a5\u8868\u4e2d\u521b\u5efa \\(n\\) \u4e2a\u9876\u70b9\u548c \\(2m\\) \u6761\u8fb9\uff0c\u4f7f\u7528 \\(O(n + m)\\) \u65f6\u95f4\u3002</li> </ul> \u521d\u59cb\u5316\u90bb\u63a5\u8868\u6dfb\u52a0\u8fb9\u5220\u9664\u8fb9\u6dfb\u52a0\u9876\u70b9\u5220\u9664\u9876\u70b9 <p></p> <p></p> <p></p> <p></p> <p></p> <p>\u4ee5\u4e0b\u662f\u57fa\u4e8e\u90bb\u63a5\u8868\u5b9e\u73b0\u56fe\u7684\u4ee3\u7801\u793a\u4f8b\u3002\u7ec6\u5fc3\u7684\u540c\u5b66\u53ef\u80fd\u6ce8\u610f\u5230\uff0c\u6211\u4eec\u5728\u90bb\u63a5\u8868\u4e2d\u4f7f\u7528 <code>Vertex</code> \u8282\u70b9\u7c7b\u6765\u8868\u793a\u9876\u70b9\uff0c\u8fd9\u6837\u505a\u7684\u539f\u56e0\u6709\uff1a</p> <ul> <li>\u5982\u679c\u6211\u4eec\u9009\u62e9\u901a\u8fc7\u9876\u70b9\u503c\u6765\u533a\u5206\u4e0d\u540c\u9876\u70b9\uff0c\u90a3\u4e48\u503c\u91cd\u590d\u7684\u9876\u70b9\u5c06\u65e0\u6cd5\u88ab\u533a\u5206\u3002</li> <li>\u5982\u679c\u7c7b\u4f3c\u90bb\u63a5\u77e9\u9635\u90a3\u6837\uff0c\u4f7f\u7528\u9876\u70b9\u5217\u8868\u7d22\u5f15\u6765\u533a\u5206\u4e0d\u540c\u9876\u70b9\u3002\u90a3\u4e48\uff0c\u5047\u8bbe\u6211\u4eec\u60f3\u8981\u5220\u9664\u7d22\u5f15\u4e3a \\(i\\) \u7684\u9876\u70b9\uff0c\u5219\u9700\u8981\u904d\u5386\u6574\u4e2a\u90bb\u63a5\u8868\uff0c\u5c06\u5176\u4e2d \\(&gt; i\\) \u7684\u7d22\u5f15\u5168\u90e8\u51cf \\(1\\) \uff0c\u8fd9\u6837\u64cd\u4f5c\u6548\u7387\u8f83\u4f4e\u3002</li> <li>\u56e0\u6b64\u6211\u4eec\u8003\u8651\u5f15\u5165\u9876\u70b9\u7c7b <code>Vertex</code> \uff0c\u4f7f\u5f97\u6bcf\u4e2a\u9876\u70b9\u90fd\u662f\u552f\u4e00\u7684\u5bf9\u8c61\uff0c\u6b64\u65f6\u5220\u9664\u9876\u70b9\u65f6\u5c31\u65e0\u9700\u6539\u52a8\u5176\u4f59\u9876\u70b9\u4e86\u3002</li> </ul> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart graph_adjacency_list.java<pre><code>/* \u57fa\u4e8e\u90bb\u63a5\u8868\u5b9e\u73b0\u7684\u65e0\u5411\u56fe\u7c7b */\nclass GraphAdjList {\n// \u90bb\u63a5\u8868\uff0ckey: \u9876\u70b9\uff0cvalue\uff1a\u8be5\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nMap&lt;Vertex, List&lt;Vertex&gt;&gt; adjList;\n/* \u6784\u9020\u65b9\u6cd5 */\npublic GraphAdjList(Vertex[][] edges) {\nthis.adjList = new HashMap&lt;&gt;();\n// \u6dfb\u52a0\u6240\u6709\u9876\u70b9\u548c\u8fb9\nfor (Vertex[] edge : edges) {\naddVertex(edge[0]);\naddVertex(edge[1]);\naddEdge(edge[0], edge[1]);\n}\n}\n/* \u83b7\u53d6\u9876\u70b9\u6570\u91cf */\npublic int size() {\nreturn adjList.size();\n}\n/* \u6dfb\u52a0\u8fb9 */\npublic void addEdge(Vertex vet1, Vertex vet2) {\nif (!adjList.containsKey(vet1) || !adjList.containsKey(vet2) || vet1 == vet2)\nthrow new IllegalArgumentException();\n// \u6dfb\u52a0\u8fb9 vet1 - vet2\nadjList.get(vet1).add(vet2);\nadjList.get(vet2).add(vet1);\n}\n/* \u5220\u9664\u8fb9 */\npublic void removeEdge(Vertex vet1, Vertex vet2) {\nif (!adjList.containsKey(vet1) || !adjList.containsKey(vet2) || vet1 == vet2)\nthrow new IllegalArgumentException();\n// \u5220\u9664\u8fb9 vet1 - vet2\nadjList.get(vet1).remove(vet2);\nadjList.get(vet2).remove(vet1);\n}\n/* \u6dfb\u52a0\u9876\u70b9 */\npublic void addVertex(Vertex vet) {\nif (adjList.containsKey(vet))\nreturn;\n// \u5728\u90bb\u63a5\u8868\u4e2d\u6dfb\u52a0\u4e00\u4e2a\u65b0\u94fe\u8868\nadjList.put(vet, new ArrayList&lt;&gt;());\n}\n/* \u5220\u9664\u9876\u70b9 */\npublic void removeVertex(Vertex vet) {\nif (!adjList.containsKey(vet))\nthrow new IllegalArgumentException();\n// \u5728\u90bb\u63a5\u8868\u4e2d\u5220\u9664\u9876\u70b9 vet \u5bf9\u5e94\u7684\u94fe\u8868\nadjList.remove(vet);\n// \u904d\u5386\u5176\u4ed6\u9876\u70b9\u7684\u94fe\u8868\uff0c\u5220\u9664\u6240\u6709\u5305\u542b vet \u7684\u8fb9\nfor (List&lt;Vertex&gt; list : adjList.values()) {\nlist.remove(vet);\n}\n}\n/* \u6253\u5370\u90bb\u63a5\u8868 */\npublic void print() {\nSystem.out.println(\"\u90bb\u63a5\u8868 =\");\nfor (Map.Entry&lt;Vertex, List&lt;Vertex&gt;&gt; pair : adjList.entrySet()) {\nList&lt;Integer&gt; tmp = new ArrayList&lt;&gt;();\nfor (Vertex vertex : pair.getValue())\ntmp.add(vertex.val);\nSystem.out.println(pair.getKey().val + \": \" + tmp + \",\");\n}\n}\n}\n</code></pre> graph_adjacency_list.cpp<pre><code>/* \u57fa\u4e8e\u90bb\u63a5\u8868\u5b9e\u73b0\u7684\u65e0\u5411\u56fe\u7c7b */\nclass GraphAdjList {\npublic:\n// \u90bb\u63a5\u8868\uff0ckey: \u9876\u70b9\uff0cvalue\uff1a\u8be5\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nunordered_map&lt;Vertex *, vector&lt;Vertex *&gt;&gt; adjList;\n/* \u5728 vector \u4e2d\u5220\u9664\u6307\u5b9a\u8282\u70b9 */\nvoid remove(vector&lt;Vertex *&gt; &amp;vec, Vertex *vet) {\nfor (int i = 0; i &lt; vec.size(); i++) {\nif (vec[i] == vet) {\nvec.erase(vec.begin() + i);\nbreak;\n}\n}\n}\n/* \u6784\u9020\u65b9\u6cd5 */\nGraphAdjList(const vector&lt;vector&lt;Vertex *&gt;&gt; &amp;edges) {\n// \u6dfb\u52a0\u6240\u6709\u9876\u70b9\u548c\u8fb9\nfor (const vector&lt;Vertex *&gt; &amp;edge : edges) {\naddVertex(edge[0]);\naddVertex(edge[1]);\naddEdge(edge[0], edge[1]);\n}\n}\n/* \u83b7\u53d6\u9876\u70b9\u6570\u91cf */\nint size() {\nreturn adjList.size();\n}\n/* \u6dfb\u52a0\u8fb9 */\nvoid addEdge(Vertex *vet1, Vertex *vet2) {\nif (!adjList.count(vet1) || !adjList.count(vet2) || vet1 == vet2)\nthrow invalid_argument(\"\u4e0d\u5b58\u5728\u9876\u70b9\");\n// \u6dfb\u52a0\u8fb9 vet1 - vet2\nadjList[vet1].push_back(vet2);\nadjList[vet2].push_back(vet1);\n}\n/* \u5220\u9664\u8fb9 */\nvoid removeEdge(Vertex *vet1, Vertex *vet2) {\nif (!adjList.count(vet1) || !adjList.count(vet2) || vet1 == vet2)\nthrow invalid_argument(\"\u4e0d\u5b58\u5728\u9876\u70b9\");\n// \u5220\u9664\u8fb9 vet1 - vet2\nremove(adjList[vet1], vet2);\nremove(adjList[vet2], vet1);\n}\n/* \u6dfb\u52a0\u9876\u70b9 */\nvoid addVertex(Vertex *vet) {\nif (adjList.count(vet))\nreturn;\n// \u5728\u90bb\u63a5\u8868\u4e2d\u6dfb\u52a0\u4e00\u4e2a\u65b0\u94fe\u8868\nadjList[vet] = vector&lt;Vertex *&gt;();\n}\n/* \u5220\u9664\u9876\u70b9 */\nvoid removeVertex(Vertex *vet) {\nif (!adjList.count(vet))\nthrow invalid_argument(\"\u4e0d\u5b58\u5728\u9876\u70b9\");\n// \u5728\u90bb\u63a5\u8868\u4e2d\u5220\u9664\u9876\u70b9 vet \u5bf9\u5e94\u7684\u94fe\u8868\nadjList.erase(vet);\n// \u904d\u5386\u5176\u4ed6\u9876\u70b9\u7684\u94fe\u8868\uff0c\u5220\u9664\u6240\u6709\u5305\u542b vet \u7684\u8fb9\nfor (auto &amp;adj : adjList) {\nremove(adj.second, vet);\n}\n}\n/* \u6253\u5370\u90bb\u63a5\u8868 */\nvoid print() {\ncout &lt;&lt; \"\u90bb\u63a5\u8868 =\" &lt;&lt; endl;\nfor (auto &amp;adj : adjList) {\nconst auto &amp;key = adj.first;\nconst auto &amp;vec = adj.second;\ncout &lt;&lt; key-&gt;val &lt;&lt; \": \";\nprintVector(vetsToVals(vec));\n}\n}\n};\n</code></pre> graph_adjacency_list.py<pre><code>class GraphAdjList:\n\"\"\"\u57fa\u4e8e\u90bb\u63a5\u8868\u5b9e\u73b0\u7684\u65e0\u5411\u56fe\u7c7b\"\"\"\ndef __init__(self, edges: list[list[Vertex]]) -&gt; None:\n\"\"\"\u6784\u9020\u65b9\u6cd5\"\"\"\n# \u90bb\u63a5\u8868\uff0ckey: \u9876\u70b9\uff0cvalue\uff1a\u8be5\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nself.adj_list = dict[Vertex, Vertex]()\n# \u6dfb\u52a0\u6240\u6709\u9876\u70b9\u548c\u8fb9\nfor edge in edges:\nself.add_vertex(edge[0])\nself.add_vertex(edge[1])\nself.add_edge(edge[0], edge[1])\ndef size(self) -&gt; int:\n\"\"\"\u83b7\u53d6\u9876\u70b9\u6570\u91cf\"\"\"\nreturn len(self.adj_list)\ndef add_edge(self, vet1: Vertex, vet2: Vertex) -&gt; None:\n\"\"\"\u6dfb\u52a0\u8fb9\"\"\"\nif vet1 not in self.adj_list or vet2 not in self.adj_list or vet1 == vet2:\nraise ValueError()\n# \u6dfb\u52a0\u8fb9 vet1 - vet2\nself.adj_list[vet1].append(vet2)\nself.adj_list[vet2].append(vet1)\ndef remove_edge(self, vet1: Vertex, vet2: Vertex) -&gt; None:\n\"\"\"\u5220\u9664\u8fb9\"\"\"\nif vet1 not in self.adj_list or vet2 not in self.adj_list or vet1 == vet2:\nraise ValueError()\n# \u5220\u9664\u8fb9 vet1 - vet2\nself.adj_list[vet1].remove(vet2)\nself.adj_list[vet2].remove(vet1)\ndef add_vertex(self, vet: Vertex) -&gt; None:\n\"\"\"\u6dfb\u52a0\u9876\u70b9\"\"\"\nif vet in self.adj_list:\nreturn\n# \u5728\u90bb\u63a5\u8868\u4e2d\u6dfb\u52a0\u4e00\u4e2a\u65b0\u94fe\u8868\nself.adj_list[vet] = []\ndef remove_vertex(self, vet: Vertex) -&gt; None:\n\"\"\"\u5220\u9664\u9876\u70b9\"\"\"\nif vet not in self.adj_list:\nraise ValueError()\n# \u5728\u90bb\u63a5\u8868\u4e2d\u5220\u9664\u9876\u70b9 vet \u5bf9\u5e94\u7684\u94fe\u8868\nself.adj_list.pop(vet)\n# \u904d\u5386\u5176\u4ed6\u9876\u70b9\u7684\u94fe\u8868\uff0c\u5220\u9664\u6240\u6709\u5305\u542b vet \u7684\u8fb9\nfor vertex in self.adj_list:\nif vet in self.adj_list[vertex]:\nself.adj_list[vertex].remove(vet)\ndef print(self) -&gt; None:\n\"\"\"\u6253\u5370\u90bb\u63a5\u8868\"\"\"\nprint(\"\u90bb\u63a5\u8868 =\")\nfor vertex in self.adj_list:\ntmp = [v.val for v in self.adj_list[vertex]]\nprint(f\"{vertex.val}: {tmp},\")\n</code></pre> graph_adjacency_list.go<pre><code>/* \u57fa\u4e8e\u90bb\u63a5\u8868\u5b9e\u73b0\u7684\u65e0\u5411\u56fe\u7c7b */\ntype graphAdjList struct {\n// \u90bb\u63a5\u8868\uff0ckey: \u9876\u70b9\uff0cvalue\uff1a\u8be5\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nadjList map[Vertex][]Vertex\n}\n/* \u6784\u9020\u65b9\u6cd5 */\nfunc newGraphAdjList(edges [][]Vertex) *graphAdjList {\ng := &amp;graphAdjList{\nadjList: make(map[Vertex][]Vertex),\n}\n// \u6dfb\u52a0\u6240\u6709\u9876\u70b9\u548c\u8fb9\nfor _, edge := range edges {\ng.addVertex(edge[0])\ng.addVertex(edge[1])\ng.addEdge(edge[0], edge[1])\n}\nreturn g\n}\n/* \u83b7\u53d6\u9876\u70b9\u6570\u91cf */\nfunc (g *graphAdjList) size() int {\nreturn len(g.adjList)\n}\n/* \u6dfb\u52a0\u8fb9 */\nfunc (g *graphAdjList) addEdge(vet1 Vertex, vet2 Vertex) {\n_, ok1 := g.adjList[vet1]\n_, ok2 := g.adjList[vet2]\nif !ok1 || !ok2 || vet1 == vet2 {\npanic(\"error\")\n}\n// \u6dfb\u52a0\u8fb9 vet1 - vet2, \u6dfb\u52a0\u533f\u540d struct{},\ng.adjList[vet1] = append(g.adjList[vet1], vet2)\ng.adjList[vet2] = append(g.adjList[vet2], vet1)\n}\n/* \u5220\u9664\u8fb9 */\nfunc (g *graphAdjList) removeEdge(vet1 Vertex, vet2 Vertex) {\n_, ok1 := g.adjList[vet1]\n_, ok2 := g.adjList[vet2]\nif !ok1 || !ok2 || vet1 == vet2 {\npanic(\"error\")\n}\n// \u5220\u9664\u8fb9 vet1 - vet2\nDeleteSliceElms(g.adjList[vet1], vet2)\nDeleteSliceElms(g.adjList[vet2], vet1)\n}\n/* \u6dfb\u52a0\u9876\u70b9 */\nfunc (g *graphAdjList) addVertex(vet Vertex) {\n_, ok := g.adjList[vet]\nif ok {\nreturn\n}\n// \u5728\u90bb\u63a5\u8868\u4e2d\u6dfb\u52a0\u4e00\u4e2a\u65b0\u94fe\u8868\ng.adjList[vet] = make([]Vertex, 0)\n}\n/* \u5220\u9664\u9876\u70b9 */\nfunc (g *graphAdjList) removeVertex(vet Vertex) {\n_, ok := g.adjList[vet]\nif !ok {\npanic(\"error\")\n}\n// \u5728\u90bb\u63a5\u8868\u4e2d\u5220\u9664\u9876\u70b9 vet \u5bf9\u5e94\u7684\u94fe\u8868\ndelete(g.adjList, vet)\n// \u904d\u5386\u5176\u4ed6\u9876\u70b9\u7684\u94fe\u8868\uff0c\u5220\u9664\u6240\u6709\u5305\u542b vet \u7684\u8fb9\nfor _, list := range g.adjList {\nDeleteSliceElms(list, vet)\n}\n}\n/* \u6253\u5370\u90bb\u63a5\u8868 */\nfunc (g *graphAdjList) print() {\nvar builder strings.Builder\nfmt.Printf(\"\u90bb\u63a5\u8868 = \\n\")\nfor k, v := range g.adjList {\nbuilder.WriteString(\"\\t\\t\" + strconv.Itoa(k.Val) + \": \")\nfor _, vet := range v {\nbuilder.WriteString(strconv.Itoa(vet.Val) + \" \")\n}\nfmt.Println(builder.String())\nbuilder.Reset()\n}\n}\n</code></pre> graph_adjacency_list.js<pre><code>/* \u57fa\u4e8e\u90bb\u63a5\u8868\u5b9e\u73b0\u7684\u65e0\u5411\u56fe\u7c7b */\nclass GraphAdjList {\n// \u90bb\u63a5\u8868\uff0ckey: \u9876\u70b9\uff0cvalue\uff1a\u8be5\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nadjList;\n/* \u6784\u9020\u65b9\u6cd5 */\nconstructor(edges) {\nthis.adjList = new Map();\n// \u6dfb\u52a0\u6240\u6709\u9876\u70b9\u548c\u8fb9\nfor (const edge of edges) {\nthis.addVertex(edge[0]);\nthis.addVertex(edge[1]);\nthis.addEdge(edge[0], edge[1]);\n}\n}\n/* \u83b7\u53d6\u9876\u70b9\u6570\u91cf */\nsize() {\nreturn this.adjList.size;\n}\n/* \u6dfb\u52a0\u8fb9 */\naddEdge(vet1, vet2) {\nif (\n!this.adjList.has(vet1) ||\n!this.adjList.has(vet2) ||\nvet1 === vet2\n) {\nthrow new Error('Illegal Argument Exception');\n}\n// \u6dfb\u52a0\u8fb9 vet1 - vet2\nthis.adjList.get(vet1).push(vet2);\nthis.adjList.get(vet2).push(vet1);\n}\n/* \u5220\u9664\u8fb9 */\nremoveEdge(vet1, vet2) {\nif (\n!this.adjList.has(vet1) ||\n!this.adjList.has(vet2) ||\nvet1 === vet2\n) {\nthrow new Error('Illegal Argument Exception');\n}\n// \u5220\u9664\u8fb9 vet1 - vet2\nthis.adjList.get(vet1).splice(this.adjList.get(vet1).indexOf(vet2), 1);\nthis.adjList.get(vet2).splice(this.adjList.get(vet2).indexOf(vet1), 1);\n}\n/* \u6dfb\u52a0\u9876\u70b9 */\naddVertex(vet) {\nif (this.adjList.has(vet)) return;\n// \u5728\u90bb\u63a5\u8868\u4e2d\u6dfb\u52a0\u4e00\u4e2a\u65b0\u94fe\u8868\nthis.adjList.set(vet, []);\n}\n/* \u5220\u9664\u9876\u70b9 */\nremoveVertex(vet) {\nif (!this.adjList.has(vet)) {\nthrow new Error('Illegal Argument Exception');\n}\n// \u5728\u90bb\u63a5\u8868\u4e2d\u5220\u9664\u9876\u70b9 vet \u5bf9\u5e94\u7684\u94fe\u8868\nthis.adjList.delete(vet);\n// \u904d\u5386\u5176\u4ed6\u9876\u70b9\u7684\u94fe\u8868\uff0c\u5220\u9664\u6240\u6709\u5305\u542b vet \u7684\u8fb9\nfor (let set of this.adjList.values()) {\nconst index = set.indexOf(vet);\nif (index &gt; -1) {\nset.splice(index, 1);\n}\n}\n}\n/* \u6253\u5370\u90bb\u63a5\u8868 */\nprint() {\nconsole.log('\u90bb\u63a5\u8868 =');\nfor (const [key, value] of this.adjList) {\nconst tmp = [];\nfor (const vertex of value) {\ntmp.push(vertex.val);\n}\nconsole.log(key.val + ': ' + tmp.join());\n}\n}\n}\n</code></pre> graph_adjacency_list.ts<pre><code>/* \u57fa\u4e8e\u90bb\u63a5\u8868\u5b9e\u73b0\u7684\u65e0\u5411\u56fe\u7c7b */\nclass GraphAdjList {\n// \u90bb\u63a5\u8868\uff0ckey: \u9876\u70b9\uff0cvalue\uff1a\u8be5\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nadjList: Map&lt;Vertex, Vertex[]&gt;;\n/* \u6784\u9020\u65b9\u6cd5 */\nconstructor(edges: Vertex[][]) {\nthis.adjList = new Map();\n// \u6dfb\u52a0\u6240\u6709\u9876\u70b9\u548c\u8fb9\nfor (const edge of edges) {\nthis.addVertex(edge[0]);\nthis.addVertex(edge[1]);\nthis.addEdge(edge[0], edge[1]);\n}\n}\n/* \u83b7\u53d6\u9876\u70b9\u6570\u91cf */\nsize(): number {\nreturn this.adjList.size;\n}\n/* \u6dfb\u52a0\u8fb9 */\naddEdge(vet1: Vertex, vet2: Vertex): void {\nif (\n!this.adjList.has(vet1) ||\n!this.adjList.has(vet2) ||\nvet1 === vet2\n) {\nthrow new Error('Illegal Argument Exception');\n}\n// \u6dfb\u52a0\u8fb9 vet1 - vet2\nthis.adjList.get(vet1).push(vet2);\nthis.adjList.get(vet2).push(vet1);\n}\n/* \u5220\u9664\u8fb9 */\nremoveEdge(vet1: Vertex, vet2: Vertex): void {\nif (\n!this.adjList.has(vet1) ||\n!this.adjList.has(vet2) ||\nvet1 === vet2\n) {\nthrow new Error('Illegal Argument Exception');\n}\n// \u5220\u9664\u8fb9 vet1 - vet2\nthis.adjList.get(vet1).splice(this.adjList.get(vet1).indexOf(vet2), 1);\nthis.adjList.get(vet2).splice(this.adjList.get(vet2).indexOf(vet1), 1);\n}\n/* \u6dfb\u52a0\u9876\u70b9 */\naddVertex(vet: Vertex): void {\nif (this.adjList.has(vet)) return;\n// \u5728\u90bb\u63a5\u8868\u4e2d\u6dfb\u52a0\u4e00\u4e2a\u65b0\u94fe\u8868\nthis.adjList.set(vet, []);\n}\n/* \u5220\u9664\u9876\u70b9 */\nremoveVertex(vet: Vertex): void {\nif (!this.adjList.has(vet)) {\nthrow new Error('Illegal Argument Exception');\n}\n// \u5728\u90bb\u63a5\u8868\u4e2d\u5220\u9664\u9876\u70b9 vet \u5bf9\u5e94\u7684\u94fe\u8868\nthis.adjList.delete(vet);\n// \u904d\u5386\u5176\u4ed6\u9876\u70b9\u7684\u94fe\u8868\uff0c\u5220\u9664\u6240\u6709\u5305\u542b vet \u7684\u8fb9\nfor (let set of this.adjList.values()) {\nconst index: number = set.indexOf(vet);\nif (index &gt; -1) {\nset.splice(index, 1);\n}\n}\n}\n/* \u6253\u5370\u90bb\u63a5\u8868 */\nprint(): void {\nconsole.log('\u90bb\u63a5\u8868 =');\nfor (const [key, value] of this.adjList.entries()) {\nconst tmp = [];\nfor (const vertex of value) {\ntmp.push(vertex.val);\n}\nconsole.log(key.val + ': ' + tmp.join());\n}\n}\n}\n</code></pre> graph_adjacency_list.c<pre><code>[class]{graphAdjList}-[func]{}\n</code></pre> graph_adjacency_list.cs<pre><code>/* \u57fa\u4e8e\u90bb\u63a5\u8868\u5b9e\u73b0\u7684\u65e0\u5411\u56fe\u7c7b */\nclass GraphAdjList {\n// \u90bb\u63a5\u8868\uff0ckey: \u9876\u70b9\uff0cvalue\uff1a\u8be5\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\npublic Dictionary&lt;Vertex, List&lt;Vertex&gt;&gt; adjList;\n/* \u6784\u9020\u51fd\u6570 */\npublic GraphAdjList(Vertex[][] edges) {\nthis.adjList = new Dictionary&lt;Vertex, List&lt;Vertex&gt;&gt;();\n// \u6dfb\u52a0\u6240\u6709\u9876\u70b9\u548c\u8fb9\nforeach (Vertex[] edge in edges) {\naddVertex(edge[0]);\naddVertex(edge[1]);\naddEdge(edge[0], edge[1]);\n}\n}\n/* \u83b7\u53d6\u9876\u70b9\u6570\u91cf */\npublic int size() {\nreturn adjList.Count;\n}\n/* \u6dfb\u52a0\u8fb9 */\npublic void addEdge(Vertex vet1, Vertex vet2) {\nif (!adjList.ContainsKey(vet1) || !adjList.ContainsKey(vet2) || vet1 == vet2)\nthrow new InvalidOperationException();\n// \u6dfb\u52a0\u8fb9 vet1 - vet2\nadjList[vet1].Add(vet2);\nadjList[vet2].Add(vet1);\n}\n/* \u5220\u9664\u8fb9 */\npublic void removeEdge(Vertex vet1, Vertex vet2) {\nif (!adjList.ContainsKey(vet1) || !adjList.ContainsKey(vet2) || vet1 == vet2)\nthrow new InvalidOperationException();\n// \u5220\u9664\u8fb9 vet1 - vet2\nadjList[vet1].Remove(vet2);\nadjList[vet2].Remove(vet1);\n}\n/* \u6dfb\u52a0\u9876\u70b9 */\npublic void addVertex(Vertex vet) {\nif (adjList.ContainsKey(vet))\nreturn;\n// \u5728\u90bb\u63a5\u8868\u4e2d\u6dfb\u52a0\u4e00\u4e2a\u65b0\u94fe\u8868\nadjList.Add(vet, new List&lt;Vertex&gt;());\n}\n/* \u5220\u9664\u9876\u70b9 */\npublic void removeVertex(Vertex vet) {\nif (!adjList.ContainsKey(vet))\nthrow new InvalidOperationException();\n// \u5728\u90bb\u63a5\u8868\u4e2d\u5220\u9664\u9876\u70b9 vet \u5bf9\u5e94\u7684\u94fe\u8868\nadjList.Remove(vet);\n// \u904d\u5386\u5176\u4ed6\u9876\u70b9\u7684\u94fe\u8868\uff0c\u5220\u9664\u6240\u6709\u5305\u542b vet \u7684\u8fb9\nforeach (List&lt;Vertex&gt; list in adjList.Values) {\nlist.Remove(vet);\n}\n}\n/* \u6253\u5370\u90bb\u63a5\u8868 */\npublic void print() {\nConsole.WriteLine(\"\u90bb\u63a5\u8868 =\");\nforeach (KeyValuePair&lt;Vertex, List&lt;Vertex&gt;&gt; pair in adjList) {\nList&lt;int&gt; tmp = new List&lt;int&gt;();\nforeach (Vertex vertex in pair.Value)\ntmp.Add(vertex.val);\nConsole.WriteLine(pair.Key.val + \": [\" + string.Join(\", \", tmp) + \"],\");\n}\n}\n}\n</code></pre> graph_adjacency_list.swift<pre><code>/* \u57fa\u4e8e\u90bb\u63a5\u8868\u5b9e\u73b0\u7684\u65e0\u5411\u56fe\u7c7b */\nclass GraphAdjList {\n// \u90bb\u63a5\u8868\uff0ckey: \u9876\u70b9\uff0cvalue\uff1a\u8be5\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\npublic private(set) var adjList: [Vertex: [Vertex]]\n/* \u6784\u9020\u65b9\u6cd5 */\npublic init(edges: [[Vertex]]) {\nadjList = [:]\n// \u6dfb\u52a0\u6240\u6709\u9876\u70b9\u548c\u8fb9\nfor edge in edges {\naddVertex(vet: edge[0])\naddVertex(vet: edge[1])\naddEdge(vet1: edge[0], vet2: edge[1])\n}\n}\n/* \u83b7\u53d6\u9876\u70b9\u6570\u91cf */\npublic func size() -&gt; Int {\nadjList.count\n}\n/* \u6dfb\u52a0\u8fb9 */\npublic func addEdge(vet1: Vertex, vet2: Vertex) {\nif adjList[vet1] == nil || adjList[vet2] == nil || vet1 == vet2 {\nfatalError(\"\u53c2\u6570\u9519\u8bef\")\n}\n// \u6dfb\u52a0\u8fb9 vet1 - vet2\nadjList[vet1]?.append(vet2)\nadjList[vet2]?.append(vet1)\n}\n/* \u5220\u9664\u8fb9 */\npublic func removeEdge(vet1: Vertex, vet2: Vertex) {\nif adjList[vet1] == nil || adjList[vet2] == nil || vet1 == vet2 {\nfatalError(\"\u53c2\u6570\u9519\u8bef\")\n}\n// \u5220\u9664\u8fb9 vet1 - vet2\nadjList[vet1]?.removeAll(where: { $0 == vet2 })\nadjList[vet2]?.removeAll(where: { $0 == vet1 })\n}\n/* \u6dfb\u52a0\u9876\u70b9 */\npublic func addVertex(vet: Vertex) {\nif adjList[vet] != nil {\nreturn\n}\n// \u5728\u90bb\u63a5\u8868\u4e2d\u6dfb\u52a0\u4e00\u4e2a\u65b0\u94fe\u8868\nadjList[vet] = []\n}\n/* \u5220\u9664\u9876\u70b9 */\npublic func removeVertex(vet: Vertex) {\nif adjList[vet] == nil {\nfatalError(\"\u53c2\u6570\u9519\u8bef\")\n}\n// \u5728\u90bb\u63a5\u8868\u4e2d\u5220\u9664\u9876\u70b9 vet \u5bf9\u5e94\u7684\u94fe\u8868\nadjList.removeValue(forKey: vet)\n// \u904d\u5386\u5176\u4ed6\u9876\u70b9\u7684\u94fe\u8868\uff0c\u5220\u9664\u6240\u6709\u5305\u542b vet \u7684\u8fb9\nfor key in adjList.keys {\nadjList[key]?.removeAll(where: { $0 == vet })\n}\n}\n/* \u6253\u5370\u90bb\u63a5\u8868 */\npublic func print() {\nSwift.print(\"\u90bb\u63a5\u8868 =\")\nfor pair in adjList {\nvar tmp: [Int] = []\nfor vertex in pair.value {\ntmp.append(vertex.val)\n}\nSwift.print(\"\\(pair.key.val): \\(tmp),\")\n}\n}\n}\n</code></pre> graph_adjacency_list.zig<pre><code>[class]{GraphAdjList}-[func]{}\n</code></pre> graph_adjacency_list.dart<pre><code>/* \u57fa\u4e8e\u90bb\u63a5\u8868\u5b9e\u73b0\u7684\u65e0\u5411\u56fe\u7c7b */\nclass GraphAdjList {\n// \u90bb\u63a5\u8868\uff0ckey: \u9876\u70b9\uff0cvalue\uff1a\u8be5\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nMap&lt;Vertex, List&lt;Vertex&gt;&gt; adjList = {};\n/* \u6784\u9020\u65b9\u6cd5 */\nGraphAdjList(List&lt;List&lt;Vertex&gt;&gt; edges) {\nfor (List&lt;Vertex&gt; edge in edges) {\naddVertex(edge[0]);\naddVertex(edge[1]);\naddEdge(edge[0], edge[1]);\n}\n}\n/* \u83b7\u53d6\u9876\u70b9\u6570\u91cf */\nint size() {\nreturn adjList.length;\n}\n/* \u6dfb\u52a0\u8fb9 */\nvoid addEdge(Vertex vet1, Vertex vet2) {\nif (!adjList.containsKey(vet1) ||\n!adjList.containsKey(vet2) ||\nvet1 == vet2) {\nthrow ArgumentError;\n}\n// \u6dfb\u52a0\u8fb9 vet1 - vet2\nadjList[vet1]!.add(vet2);\nadjList[vet2]!.add(vet1);\n}\n/* \u5220\u9664\u8fb9 */\nvoid removeEdge(Vertex vet1, Vertex vet2) {\nif (!adjList.containsKey(vet1) ||\n!adjList.containsKey(vet2) ||\nvet1 == vet2) {\nthrow ArgumentError;\n}\n// \u5220\u9664\u8fb9 vet1 - vet2\nadjList[vet1]!.remove(vet2);\nadjList[vet2]!.remove(vet1);\n}\n/* \u6dfb\u52a0\u9876\u70b9 */\nvoid addVertex(Vertex vet) {\nif (adjList.containsKey(vet)) return;\n// \u5728\u90bb\u63a5\u8868\u4e2d\u6dfb\u52a0\u4e00\u4e2a\u65b0\u94fe\u8868\nadjList[vet] = [];\n}\n/* \u5220\u9664\u9876\u70b9 */\nvoid removeVertex(Vertex vet) {\nif (!adjList.containsKey(vet)) {\nthrow ArgumentError;\n}\n// \u5728\u90bb\u63a5\u8868\u4e2d\u5220\u9664\u9876\u70b9 vet \u5bf9\u5e94\u7684\u94fe\u8868\nadjList.remove(vet);\n// \u904d\u5386\u5176\u4ed6\u9876\u70b9\u7684\u94fe\u8868\uff0c\u5220\u9664\u6240\u6709\u5305\u542b vet \u7684\u8fb9\nadjList.forEach((key, value) {\nvalue.remove(vet);\n});\n}\n/* \u6253\u5370\u90bb\u63a5\u8868 */\nvoid printAdjList() {\nprint(\"\u90bb\u63a5\u8868 =\");\nadjList.forEach((key, value) {\nList&lt;int&gt; tmp = [];\nfor (Vertex vertex in value) {\ntmp.add(vertex.val);\n}\nprint(\"${key.val}: $tmp,\");\n});\n}\n}\n</code></pre>"},{"location":"chapter_graph/graph_operations/#923","title":"9.2.3. \u00a0 \u6548\u7387\u5bf9\u6bd4","text":"<p>\u8bbe\u56fe\u4e2d\u5171\u6709 \\(n\\) \u4e2a\u9876\u70b9\u548c \\(m\\) \u6761\u8fb9\uff0c\u4e0b\u8868\u4e3a\u90bb\u63a5\u77e9\u9635\u548c\u90bb\u63a5\u8868\u7684\u65f6\u95f4\u548c\u7a7a\u95f4\u6548\u7387\u5bf9\u6bd4\u3002</p> \u90bb\u63a5\u77e9\u9635 \u90bb\u63a5\u8868\uff08\u94fe\u8868\uff09 \u90bb\u63a5\u8868\uff08\u54c8\u5e0c\u8868\uff09 \u5224\u65ad\u662f\u5426\u90bb\u63a5 \\(O(1)\\) \\(O(m)\\) \\(O(1)\\) \u6dfb\u52a0\u8fb9 \\(O(1)\\) \\(O(1)\\) \\(O(1)\\) \u5220\u9664\u8fb9 \\(O(1)\\) \\(O(m)\\) \\(O(1)\\) \u6dfb\u52a0\u9876\u70b9 \\(O(n)\\) \\(O(1)\\) \\(O(1)\\) \u5220\u9664\u9876\u70b9 \\(O(n^2)\\) \\(O(n + m)\\) \\(O(n)\\) \u5185\u5b58\u7a7a\u95f4\u5360\u7528 \\(O(n^2)\\) \\(O(n + m)\\) \\(O(n + m)\\) <p>\u89c2\u5bdf\u4e0a\u8868\uff0c\u4f3c\u4e4e\u90bb\u63a5\u8868\uff08\u54c8\u5e0c\u8868\uff09\u7684\u65f6\u95f4\u4e0e\u7a7a\u95f4\u6548\u7387\u6700\u4f18\u3002\u4f46\u5b9e\u9645\u4e0a\uff0c\u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u64cd\u4f5c\u8fb9\u7684\u6548\u7387\u66f4\u9ad8\uff0c\u53ea\u9700\u8981\u4e00\u6b21\u6570\u7ec4\u8bbf\u95ee\u6216\u8d4b\u503c\u64cd\u4f5c\u5373\u53ef\u3002\u7efc\u5408\u6765\u770b\uff0c\u90bb\u63a5\u77e9\u9635\u4f53\u73b0\u4e86\u201c\u4ee5\u7a7a\u95f4\u6362\u65f6\u95f4\u201d\u7684\u539f\u5219\uff0c\u800c\u90bb\u63a5\u8868\u4f53\u73b0\u4e86\u201c\u4ee5\u65f6\u95f4\u6362\u7a7a\u95f4\u201d\u7684\u539f\u5219\u3002</p>"},{"location":"chapter_graph/graph_traversal/","title":"9.3. \u00a0 \u56fe\u7684\u904d\u5386","text":"<p>\u56fe\u4e0e\u6811\u7684\u5173\u7cfb</p> <p>\u6811\u4ee3\u8868\u7684\u662f\u201c\u4e00\u5bf9\u591a\u201d\u7684\u5173\u7cfb\uff0c\u800c\u56fe\u5219\u5177\u6709\u66f4\u9ad8\u7684\u81ea\u7531\u5ea6\uff0c\u53ef\u4ee5\u8868\u793a\u4efb\u610f\u7684\u201c\u591a\u5bf9\u591a\u201d\u5173\u7cfb\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u53ef\u4ee5\u628a\u6811\u770b\u4f5c\u662f\u56fe\u7684\u4e00\u79cd\u7279\u4f8b\u3002\u663e\u7136\uff0c\u6811\u7684\u904d\u5386\u64cd\u4f5c\u4e5f\u662f\u56fe\u7684\u904d\u5386\u64cd\u4f5c\u7684\u4e00\u79cd\u7279\u4f8b\uff0c\u5efa\u8bae\u4f60\u5728\u5b66\u4e60\u672c\u7ae0\u8282\u65f6\u878d\u4f1a\u8d2f\u901a\u4e24\u8005\u7684\u6982\u5ff5\u4e0e\u5b9e\u73b0\u65b9\u6cd5\u3002</p> <p>\u300c\u56fe\u300d\u548c\u300c\u6811\u300d\u90fd\u662f\u975e\u7ebf\u6027\u6570\u636e\u7ed3\u6784\uff0c\u90fd\u9700\u8981\u4f7f\u7528\u300c\u641c\u7d22\u7b97\u6cd5\u300d\u6765\u5b9e\u73b0\u904d\u5386\u64cd\u4f5c\u3002</p> <p>\u4e0e\u6811\u7c7b\u4f3c\uff0c\u56fe\u7684\u904d\u5386\u65b9\u5f0f\u4e5f\u53ef\u5206\u4e3a\u4e24\u79cd\uff0c\u5373\u300c\u5e7f\u5ea6\u4f18\u5148\u904d\u5386 Breadth-First Traversal\u300d\u548c\u300c\u6df1\u5ea6\u4f18\u5148\u904d\u5386 Depth-First Traversal\u300d\uff0c\u4e5f\u79f0\u4e3a\u300c\u5e7f\u5ea6\u4f18\u5148\u641c\u7d22 Breadth-First Search\u300d\u548c\u300c\u6df1\u5ea6\u4f18\u5148\u641c\u7d22 Depth-First Search\u300d\uff0c\u7b80\u79f0 BFS \u548c DFS\u3002</p>"},{"location":"chapter_graph/graph_traversal/#931","title":"9.3.1. \u00a0 \u5e7f\u5ea6\u4f18\u5148\u904d\u5386","text":"<p>\u5e7f\u5ea6\u4f18\u5148\u904d\u5386\u662f\u4e00\u79cd\u7531\u8fd1\u53ca\u8fdc\u7684\u904d\u5386\u65b9\u5f0f\uff0c\u4ece\u8ddd\u79bb\u6700\u8fd1\u7684\u9876\u70b9\u5f00\u59cb\u8bbf\u95ee\uff0c\u5e76\u4e00\u5c42\u5c42\u5411\u5916\u6269\u5f20\u3002\u5177\u4f53\u6765\u8bf4\uff0c\u4ece\u67d0\u4e2a\u9876\u70b9\u51fa\u53d1\uff0c\u5148\u904d\u5386\u8be5\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\uff0c\u7136\u540e\u904d\u5386\u4e0b\u4e00\u4e2a\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\uff0c\u4ee5\u6b64\u7c7b\u63a8\uff0c\u76f4\u81f3\u6240\u6709\u9876\u70b9\u8bbf\u95ee\u5b8c\u6bd5\u3002</p> <p></p> <p> Fig. \u56fe\u7684\u5e7f\u5ea6\u4f18\u5148\u904d\u5386 </p>"},{"location":"chapter_graph/graph_traversal/#_1","title":"\u7b97\u6cd5\u5b9e\u73b0","text":"<p>BFS \u901a\u5e38\u501f\u52a9\u300c\u961f\u5217\u300d\u6765\u5b9e\u73b0\u3002\u961f\u5217\u5177\u6709\u201c\u5148\u5165\u5148\u51fa\u201d\u7684\u6027\u8d28\uff0c\u8fd9\u4e0e BFS \u7684\u201c\u7531\u8fd1\u53ca\u8fdc\u201d\u7684\u601d\u60f3\u5f02\u66f2\u540c\u5de5\u3002</p> <ol> <li>\u5c06\u904d\u5386\u8d77\u59cb\u9876\u70b9 <code>startVet</code> \u52a0\u5165\u961f\u5217\uff0c\u5e76\u5f00\u542f\u5faa\u73af\uff1b</li> <li>\u5728\u5faa\u73af\u7684\u6bcf\u8f6e\u8fed\u4ee3\u4e2d\uff0c\u5f39\u51fa\u961f\u9996\u9876\u70b9\u5e76\u8bb0\u5f55\u8bbf\u95ee\uff0c\u7136\u540e\u5c06\u8be5\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\u52a0\u5165\u5230\u961f\u5217\u5c3e\u90e8\uff1b</li> <li>\u5faa\u73af\u6b65\u9aa4 <code>2.</code> \uff0c\u76f4\u5230\u6240\u6709\u9876\u70b9\u88ab\u8bbf\u95ee\u5b8c\u6210\u540e\u7ed3\u675f\uff1b</li> </ol> <p>\u4e3a\u4e86\u9632\u6b62\u91cd\u590d\u904d\u5386\u9876\u70b9\uff0c\u6211\u4eec\u9700\u8981\u501f\u52a9\u4e00\u4e2a\u54c8\u5e0c\u8868 <code>visited</code> \u6765\u8bb0\u5f55\u54ea\u4e9b\u8282\u70b9\u5df2\u88ab\u8bbf\u95ee\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart graph_bfs.java<pre><code>/* \u5e7f\u5ea6\u4f18\u5148\u904d\u5386 BFS */\n// \u4f7f\u7528\u90bb\u63a5\u8868\u6765\u8868\u793a\u56fe\uff0c\u4ee5\u4fbf\u83b7\u53d6\u6307\u5b9a\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nList&lt;Vertex&gt; graphBFS(GraphAdjList graph, Vertex startVet) {\n// \u9876\u70b9\u904d\u5386\u5e8f\u5217\nList&lt;Vertex&gt; res = new ArrayList&lt;&gt;();\n// \u54c8\u5e0c\u8868\uff0c\u7528\u4e8e\u8bb0\u5f55\u5df2\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9\nSet&lt;Vertex&gt; visited = new HashSet&lt;&gt;() {{ add(startVet); }};\n// \u961f\u5217\u7528\u4e8e\u5b9e\u73b0 BFS\nQueue&lt;Vertex&gt; que = new LinkedList&lt;&gt;() {{ offer(startVet); }};\n// \u4ee5\u9876\u70b9 vet \u4e3a\u8d77\u70b9\uff0c\u5faa\u73af\u76f4\u81f3\u8bbf\u95ee\u5b8c\u6240\u6709\u9876\u70b9\nwhile (!que.isEmpty()) {\nVertex vet = que.poll(); // \u961f\u9996\u9876\u70b9\u51fa\u961f\nres.add(vet);            // \u8bb0\u5f55\u8bbf\u95ee\u9876\u70b9\n// \u904d\u5386\u8be5\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nfor (Vertex adjVet : graph.adjList.get(vet)) {\nif (visited.contains(adjVet))\ncontinue;        // \u8df3\u8fc7\u5df2\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9\nque.offer(adjVet);   // \u53ea\u5165\u961f\u672a\u8bbf\u95ee\u7684\u9876\u70b9\nvisited.add(adjVet); // \u6807\u8bb0\u8be5\u9876\u70b9\u5df2\u88ab\u8bbf\u95ee\n}\n}\n// \u8fd4\u56de\u9876\u70b9\u904d\u5386\u5e8f\u5217\nreturn res;\n}\n</code></pre> graph_bfs.cpp<pre><code>/* \u5e7f\u5ea6\u4f18\u5148\u904d\u5386 BFS */\n// \u4f7f\u7528\u90bb\u63a5\u8868\u6765\u8868\u793a\u56fe\uff0c\u4ee5\u4fbf\u83b7\u53d6\u6307\u5b9a\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nvector&lt;Vertex *&gt; graphBFS(GraphAdjList &amp;graph, Vertex *startVet) {\n// \u9876\u70b9\u904d\u5386\u5e8f\u5217\nvector&lt;Vertex *&gt; res;\n// \u54c8\u5e0c\u8868\uff0c\u7528\u4e8e\u8bb0\u5f55\u5df2\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9\nunordered_set&lt;Vertex *&gt; visited = {startVet};\n// \u961f\u5217\u7528\u4e8e\u5b9e\u73b0 BFS\nqueue&lt;Vertex *&gt; que;\nque.push(startVet);\n// \u4ee5\u9876\u70b9 vet \u4e3a\u8d77\u70b9\uff0c\u5faa\u73af\u76f4\u81f3\u8bbf\u95ee\u5b8c\u6240\u6709\u9876\u70b9\nwhile (!que.empty()) {\nVertex *vet = que.front();\nque.pop();          // \u961f\u9996\u9876\u70b9\u51fa\u961f\nres.push_back(vet); // \u8bb0\u5f55\u8bbf\u95ee\u9876\u70b9\n// \u904d\u5386\u8be5\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nfor (auto adjVet : graph.adjList[vet]) {\nif (visited.count(adjVet))\ncontinue;            // \u8df3\u8fc7\u5df2\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9\nque.push(adjVet);        // \u53ea\u5165\u961f\u672a\u8bbf\u95ee\u7684\u9876\u70b9\nvisited.emplace(adjVet); // \u6807\u8bb0\u8be5\u9876\u70b9\u5df2\u88ab\u8bbf\u95ee\n}\n}\n// \u8fd4\u56de\u9876\u70b9\u904d\u5386\u5e8f\u5217\nreturn res;\n}\n</code></pre> graph_bfs.py<pre><code>def graph_bfs(graph: GraphAdjList, start_vet: Vertex) -&gt; list[Vertex]:\n\"\"\"\u5e7f\u5ea6\u4f18\u5148\u904d\u5386 BFS\"\"\"\n# \u4f7f\u7528\u90bb\u63a5\u8868\u6765\u8868\u793a\u56fe\uff0c\u4ee5\u4fbf\u83b7\u53d6\u6307\u5b9a\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\n# \u9876\u70b9\u904d\u5386\u5e8f\u5217\nres = []\n# \u54c8\u5e0c\u8868\uff0c\u7528\u4e8e\u8bb0\u5f55\u5df2\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9\nvisited = set[Vertex]([start_vet])\n# \u961f\u5217\u7528\u4e8e\u5b9e\u73b0 BFS\nque = deque[Vertex]([start_vet])\n# \u4ee5\u9876\u70b9 vet \u4e3a\u8d77\u70b9\uff0c\u5faa\u73af\u76f4\u81f3\u8bbf\u95ee\u5b8c\u6240\u6709\u9876\u70b9\nwhile len(que) &gt; 0:\nvet = que.popleft()  # \u961f\u9996\u9876\u70b9\u51fa\u961f\nres.append(vet)  # \u8bb0\u5f55\u8bbf\u95ee\u9876\u70b9\n# \u904d\u5386\u8be5\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nfor adj_vet in graph.adj_list[vet]:\nif adj_vet in visited:\ncontinue  # \u8df3\u8fc7\u5df2\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9\nque.append(adj_vet)  # \u53ea\u5165\u961f\u672a\u8bbf\u95ee\u7684\u9876\u70b9\nvisited.add(adj_vet)  # \u6807\u8bb0\u8be5\u9876\u70b9\u5df2\u88ab\u8bbf\u95ee\n# \u8fd4\u56de\u9876\u70b9\u904d\u5386\u5e8f\u5217\nreturn res\n</code></pre> graph_bfs.go<pre><code>/* \u5e7f\u5ea6\u4f18\u5148\u904d\u5386 BFS */\n// \u4f7f\u7528\u90bb\u63a5\u8868\u6765\u8868\u793a\u56fe\uff0c\u4ee5\u4fbf\u83b7\u53d6\u6307\u5b9a\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nfunc graphBFS(g *graphAdjList, startVet Vertex) []Vertex {\n// \u9876\u70b9\u904d\u5386\u5e8f\u5217\nres := make([]Vertex, 0)\n// \u54c8\u5e0c\u8868\uff0c\u7528\u4e8e\u8bb0\u5f55\u5df2\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9\nvisited := make(map[Vertex]struct{})\nvisited[startVet] = struct{}{}\n// \u961f\u5217\u7528\u4e8e\u5b9e\u73b0 BFS, \u4f7f\u7528\u5207\u7247\u6a21\u62df\u961f\u5217\nqueue := make([]Vertex, 0)\nqueue = append(queue, startVet)\n// \u4ee5\u9876\u70b9 vet \u4e3a\u8d77\u70b9\uff0c\u5faa\u73af\u76f4\u81f3\u8bbf\u95ee\u5b8c\u6240\u6709\u9876\u70b9\nfor len(queue) &gt; 0 {\n// \u961f\u9996\u9876\u70b9\u51fa\u961f\nvet := queue[0]\nqueue = queue[1:]\n// \u8bb0\u5f55\u8bbf\u95ee\u9876\u70b9\nres = append(res, vet)\n// \u904d\u5386\u8be5\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nfor _, adjVet := range g.adjList[vet] {\n_, isExist := visited[adjVet]\n// \u53ea\u5165\u961f\u672a\u8bbf\u95ee\u7684\u9876\u70b9\nif !isExist {\nqueue = append(queue, adjVet)\nvisited[adjVet] = struct{}{}\n}\n}\n}\n// \u8fd4\u56de\u9876\u70b9\u904d\u5386\u5e8f\u5217\nreturn res\n}\n</code></pre> graph_bfs.js<pre><code>/* \u5e7f\u5ea6\u4f18\u5148\u904d\u5386 BFS */\n// \u4f7f\u7528\u90bb\u63a5\u8868\u6765\u8868\u793a\u56fe\uff0c\u4ee5\u4fbf\u83b7\u53d6\u6307\u5b9a\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nfunction graphBFS(graph, startVet) {\n// \u9876\u70b9\u904d\u5386\u5e8f\u5217\nconst res = [];\n// \u54c8\u5e0c\u8868\uff0c\u7528\u4e8e\u8bb0\u5f55\u5df2\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9\nconst visited = new Set();\nvisited.add(startVet);\n// \u961f\u5217\u7528\u4e8e\u5b9e\u73b0 BFS\nconst que = [startVet];\n// \u4ee5\u9876\u70b9 vet \u4e3a\u8d77\u70b9\uff0c\u5faa\u73af\u76f4\u81f3\u8bbf\u95ee\u5b8c\u6240\u6709\u9876\u70b9\nwhile (que.length) {\nconst vet = que.shift(); // \u961f\u9996\u9876\u70b9\u51fa\u961f\nres.push(vet); // \u8bb0\u5f55\u8bbf\u95ee\u9876\u70b9\n// \u904d\u5386\u8be5\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nfor (const adjVet of graph.adjList.get(vet) ?? []) {\nif (visited.has(adjVet)) {\ncontinue; // \u8df3\u8fc7\u5df2\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9\n}\nque.push(adjVet); // \u53ea\u5165\u961f\u672a\u8bbf\u95ee\u7684\u9876\u70b9\nvisited.add(adjVet); // \u6807\u8bb0\u8be5\u9876\u70b9\u5df2\u88ab\u8bbf\u95ee\n}\n}\n// \u8fd4\u56de\u9876\u70b9\u904d\u5386\u5e8f\u5217\nreturn res;\n}\n</code></pre> graph_bfs.ts<pre><code>/* \u5e7f\u5ea6\u4f18\u5148\u904d\u5386 BFS */\n// \u4f7f\u7528\u90bb\u63a5\u8868\u6765\u8868\u793a\u56fe\uff0c\u4ee5\u4fbf\u83b7\u53d6\u6307\u5b9a\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nfunction graphBFS(graph: GraphAdjList, startVet: Vertex): Vertex[] {\n// \u9876\u70b9\u904d\u5386\u5e8f\u5217\nconst res: Vertex[] = [];\n// \u54c8\u5e0c\u8868\uff0c\u7528\u4e8e\u8bb0\u5f55\u5df2\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9\nconst visited: Set&lt;Vertex&gt; = new Set();\nvisited.add(startVet);\n// \u961f\u5217\u7528\u4e8e\u5b9e\u73b0 BFS\nconst que = [startVet];\n// \u4ee5\u9876\u70b9 vet \u4e3a\u8d77\u70b9\uff0c\u5faa\u73af\u76f4\u81f3\u8bbf\u95ee\u5b8c\u6240\u6709\u9876\u70b9\nwhile (que.length) {\nconst vet = que.shift(); // \u961f\u9996\u9876\u70b9\u51fa\u961f\nres.push(vet); // \u8bb0\u5f55\u8bbf\u95ee\u9876\u70b9\n// \u904d\u5386\u8be5\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nfor (const adjVet of graph.adjList.get(vet) ?? []) {\nif (visited.has(adjVet)) {\ncontinue; // \u8df3\u8fc7\u5df2\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9\n}\nque.push(adjVet); // \u53ea\u5165\u961f\u672a\u8bbf\u95ee\nvisited.add(adjVet); // \u6807\u8bb0\u8be5\u9876\u70b9\u5df2\u88ab\u8bbf\u95ee\n}\n}\n// \u8fd4\u56de\u9876\u70b9\u904d\u5386\u5e8f\u5217\nreturn res;\n}\n</code></pre> graph_bfs.c<pre><code>[class]{}-[func]{graphBFS}\n</code></pre> graph_bfs.cs<pre><code>/* \u5e7f\u5ea6\u4f18\u5148\u904d\u5386 BFS */\n// \u4f7f\u7528\u90bb\u63a5\u8868\u6765\u8868\u793a\u56fe\uff0c\u4ee5\u4fbf\u83b7\u53d6\u6307\u5b9a\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nList&lt;Vertex&gt; graphBFS(GraphAdjList graph, Vertex startVet) {\n// \u9876\u70b9\u904d\u5386\u5e8f\u5217\nList&lt;Vertex&gt; res = new List&lt;Vertex&gt;();\n// \u54c8\u5e0c\u8868\uff0c\u7528\u4e8e\u8bb0\u5f55\u5df2\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9\nHashSet&lt;Vertex&gt; visited = new HashSet&lt;Vertex&gt;() { startVet };\n// \u961f\u5217\u7528\u4e8e\u5b9e\u73b0 BFS\nQueue&lt;Vertex&gt; que = new Queue&lt;Vertex&gt;();\nque.Enqueue(startVet);\n// \u4ee5\u9876\u70b9 vet \u4e3a\u8d77\u70b9\uff0c\u5faa\u73af\u76f4\u81f3\u8bbf\u95ee\u5b8c\u6240\u6709\u9876\u70b9\nwhile (que.Count &gt; 0) {\nVertex vet = que.Dequeue(); // \u961f\u9996\u9876\u70b9\u51fa\u961f\nres.Add(vet);               // \u8bb0\u5f55\u8bbf\u95ee\u9876\u70b9\nforeach (Vertex adjVet in graph.adjList[vet]) {\nif (visited.Contains(adjVet)) {\ncontinue;          // \u8df3\u8fc7\u5df2\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9\n}\nque.Enqueue(adjVet);   // \u53ea\u5165\u961f\u672a\u8bbf\u95ee\u7684\u9876\u70b9\nvisited.Add(adjVet);   // \u6807\u8bb0\u8be5\u9876\u70b9\u5df2\u88ab\u8bbf\u95ee\n}\n}\n// \u8fd4\u56de\u9876\u70b9\u904d\u5386\u5e8f\u5217\nreturn res;\n}\n</code></pre> graph_bfs.swift<pre><code>/* \u5e7f\u5ea6\u4f18\u5148\u904d\u5386 BFS */\n// \u4f7f\u7528\u90bb\u63a5\u8868\u6765\u8868\u793a\u56fe\uff0c\u4ee5\u4fbf\u83b7\u53d6\u6307\u5b9a\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nfunc graphBFS(graph: GraphAdjList, startVet: Vertex) -&gt; [Vertex] {\n// \u9876\u70b9\u904d\u5386\u5e8f\u5217\nvar res: [Vertex] = []\n// \u54c8\u5e0c\u8868\uff0c\u7528\u4e8e\u8bb0\u5f55\u5df2\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9\nvar visited: Set&lt;Vertex&gt; = [startVet]\n// \u961f\u5217\u7528\u4e8e\u5b9e\u73b0 BFS\nvar que: [Vertex] = [startVet]\n// \u4ee5\u9876\u70b9 vet \u4e3a\u8d77\u70b9\uff0c\u5faa\u73af\u76f4\u81f3\u8bbf\u95ee\u5b8c\u6240\u6709\u9876\u70b9\nwhile !que.isEmpty {\nlet vet = que.removeFirst() // \u961f\u9996\u9876\u70b9\u51fa\u961f\nres.append(vet) // \u8bb0\u5f55\u8bbf\u95ee\u9876\u70b9\n// \u904d\u5386\u8be5\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nfor adjVet in graph.adjList[vet] ?? [] {\nif visited.contains(adjVet) {\ncontinue // \u8df3\u8fc7\u5df2\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9\n}\nque.append(adjVet) // \u53ea\u5165\u961f\u672a\u8bbf\u95ee\u7684\u9876\u70b9\nvisited.insert(adjVet) // \u6807\u8bb0\u8be5\u9876\u70b9\u5df2\u88ab\u8bbf\u95ee\n}\n}\n// \u8fd4\u56de\u9876\u70b9\u904d\u5386\u5e8f\u5217\nreturn res\n}\n</code></pre> graph_bfs.zig<pre><code>[class]{}-[func]{graphBFS}\n</code></pre> graph_bfs.dart<pre><code>/* \u5e7f\u5ea6\u4f18\u5148\u904d\u5386 BFS */\nList&lt;Vertex&gt; graphBFS(GraphAdjList graph, Vertex startVet) {\n// \u4f7f\u7528\u90bb\u63a5\u8868\u6765\u8868\u793a\u56fe\uff0c\u4ee5\u4fbf\u83b7\u53d6\u6307\u5b9a\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\n// \u9876\u70b9\u904d\u5386\u5e8f\u5217\nList&lt;Vertex&gt; res = [];\n// \u54c8\u5e0c\u8868\uff0c\u7528\u4e8e\u8bb0\u5f55\u5df2\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9\nSet&lt;Vertex&gt; visited = {};\nvisited.add(startVet);\n// \u961f\u5217\u7528\u4e8e\u5b9e\u73b0 BFS\nQueue&lt;Vertex&gt; que = Queue();\nque.add(startVet);\n// \u4ee5\u9876\u70b9 vet \u4e3a\u8d77\u70b9\uff0c\u5faa\u73af\u76f4\u81f3\u8bbf\u95ee\u5b8c\u6240\u6709\u9876\u70b9\nwhile (que.isNotEmpty) {\nVertex vet = que.removeFirst(); // \u961f\u9996\u9876\u70b9\u51fa\u961f\nres.add(vet); // \u8bb0\u5f55\u8bbf\u95ee\u9876\u70b9\n// \u904d\u5386\u8be5\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nfor (Vertex adjVet in graph.adjList[vet]!) {\nif (visited.contains(adjVet)) {\ncontinue; // \u8df3\u8fc7\u5df2\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9\n}\nque.add(adjVet); // \u53ea\u5165\u961f\u672a\u8bbf\u95ee\u7684\u9876\u70b9\nvisited.add(adjVet); // \u6807\u8bb0\u8be5\u9876\u70b9\u5df2\u88ab\u8bbf\u95ee\n}\n}\n// \u8fd4\u56de\u9876\u70b9\u904d\u5386\u5e8f\u5217\nreturn res;\n}\n</code></pre> <p>\u4ee3\u7801\u76f8\u5bf9\u62bd\u8c61\uff0c\u5efa\u8bae\u5bf9\u7167\u4ee5\u4e0b\u52a8\u753b\u56fe\u793a\u6765\u52a0\u6df1\u7406\u89e3\u3002</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt;&lt;11&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p>\u5e7f\u5ea6\u4f18\u5148\u904d\u5386\u7684\u5e8f\u5217\u662f\u5426\u552f\u4e00\uff1f</p> <p>\u4e0d\u552f\u4e00\u3002\u5e7f\u5ea6\u4f18\u5148\u904d\u5386\u53ea\u8981\u6c42\u6309\u201c\u7531\u8fd1\u53ca\u8fdc\u201d\u7684\u987a\u5e8f\u904d\u5386\uff0c\u800c\u591a\u4e2a\u76f8\u540c\u8ddd\u79bb\u7684\u9876\u70b9\u7684\u904d\u5386\u987a\u5e8f\u662f\u5141\u8bb8\u88ab\u4efb\u610f\u6253\u4e71\u7684\u3002\u4ee5\u4e0a\u56fe\u4e3a\u4f8b\uff0c\u9876\u70b9 \\(1\\) , \\(3\\) \u7684\u8bbf\u95ee\u987a\u5e8f\u53ef\u4ee5\u4ea4\u6362\u3001\u9876\u70b9 \\(2\\) , \\(4\\) , \\(6\\) \u7684\u8bbf\u95ee\u987a\u5e8f\u4e5f\u53ef\u4ee5\u4efb\u610f\u4ea4\u6362\u3002</p>"},{"location":"chapter_graph/graph_traversal/#_2","title":"\u590d\u6742\u5ea6\u5206\u6790","text":"<p>\u65f6\u95f4\u590d\u6742\u5ea6\uff1a \u6240\u6709\u9876\u70b9\u90fd\u4f1a\u5165\u961f\u5e76\u51fa\u961f\u4e00\u6b21\uff0c\u4f7f\u7528 \\(O(|V|)\\) \u65f6\u95f4\uff1b\u5728\u904d\u5386\u90bb\u63a5\u9876\u70b9\u7684\u8fc7\u7a0b\u4e2d\uff0c\u7531\u4e8e\u662f\u65e0\u5411\u56fe\uff0c\u56e0\u6b64\u6240\u6709\u8fb9\u90fd\u4f1a\u88ab\u8bbf\u95ee \\(2\\) \u6b21\uff0c\u4f7f\u7528 \\(O(2|E|)\\) \u65f6\u95f4\uff1b\u603b\u4f53\u4f7f\u7528 \\(O(|V| + |E|)\\) \u65f6\u95f4\u3002</p> <p>\u7a7a\u95f4\u590d\u6742\u5ea6\uff1a \u5217\u8868 <code>res</code> \uff0c\u54c8\u5e0c\u8868 <code>visited</code> \uff0c\u961f\u5217 <code>que</code> \u4e2d\u7684\u9876\u70b9\u6570\u91cf\u6700\u591a\u4e3a \\(|V|\\) \uff0c\u4f7f\u7528 \\(O(|V|)\\) \u7a7a\u95f4\u3002</p>"},{"location":"chapter_graph/graph_traversal/#932","title":"9.3.2. \u00a0 \u6df1\u5ea6\u4f18\u5148\u904d\u5386","text":"<p>\u6df1\u5ea6\u4f18\u5148\u904d\u5386\u662f\u4e00\u79cd\u4f18\u5148\u8d70\u5230\u5e95\u3001\u65e0\u8def\u53ef\u8d70\u518d\u56de\u5934\u7684\u904d\u5386\u65b9\u5f0f\u3002\u5177\u4f53\u5730\uff0c\u4ece\u67d0\u4e2a\u9876\u70b9\u51fa\u53d1\uff0c\u8bbf\u95ee\u5f53\u524d\u9876\u70b9\u7684\u67d0\u4e2a\u90bb\u63a5\u9876\u70b9\uff0c\u76f4\u5230\u8d70\u5230\u5c3d\u5934\u65f6\u8fd4\u56de\uff0c\u518d\u7ee7\u7eed\u8d70\u5230\u5c3d\u5934\u5e76\u8fd4\u56de\uff0c\u4ee5\u6b64\u7c7b\u63a8\uff0c\u76f4\u81f3\u6240\u6709\u9876\u70b9\u904d\u5386\u5b8c\u6210\u3002</p> <p></p> <p> Fig. \u56fe\u7684\u6df1\u5ea6\u4f18\u5148\u904d\u5386 </p>"},{"location":"chapter_graph/graph_traversal/#_3","title":"\u7b97\u6cd5\u5b9e\u73b0","text":"<p>\u8fd9\u79cd\u201c\u8d70\u5230\u5c3d\u5934 + \u56de\u6eaf\u201d\u7684\u7b97\u6cd5\u5f62\u5f0f\u901a\u5e38\u57fa\u4e8e\u9012\u5f52\u6765\u5b9e\u73b0\u3002\u4e0e BFS \u7c7b\u4f3c\uff0c\u5728 DFS \u4e2d\u6211\u4eec\u4e5f\u9700\u8981\u501f\u52a9\u4e00\u4e2a\u54c8\u5e0c\u8868 <code>visited</code> \u6765\u8bb0\u5f55\u5df2\u88ab\u8bbf\u95ee\u7684\u9876\u70b9\uff0c\u4ee5\u907f\u514d\u91cd\u590d\u8bbf\u95ee\u9876\u70b9\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart graph_dfs.java<pre><code>/* \u6df1\u5ea6\u4f18\u5148\u904d\u5386 DFS \u8f85\u52a9\u51fd\u6570 */\nvoid dfs(GraphAdjList graph, Set&lt;Vertex&gt; visited, List&lt;Vertex&gt; res, Vertex vet) {\nres.add(vet);     // \u8bb0\u5f55\u8bbf\u95ee\u9876\u70b9\nvisited.add(vet); // \u6807\u8bb0\u8be5\u9876\u70b9\u5df2\u88ab\u8bbf\u95ee\n// \u904d\u5386\u8be5\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nfor (Vertex adjVet : graph.adjList.get(vet)) {\nif (visited.contains(adjVet))\ncontinue; // \u8df3\u8fc7\u5df2\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9\n// \u9012\u5f52\u8bbf\u95ee\u90bb\u63a5\u9876\u70b9\ndfs(graph, visited, res, adjVet);\n}\n}\n/* \u6df1\u5ea6\u4f18\u5148\u904d\u5386 DFS */\n// \u4f7f\u7528\u90bb\u63a5\u8868\u6765\u8868\u793a\u56fe\uff0c\u4ee5\u4fbf\u83b7\u53d6\u6307\u5b9a\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nList&lt;Vertex&gt; graphDFS(GraphAdjList graph, Vertex startVet) {\n// \u9876\u70b9\u904d\u5386\u5e8f\u5217\nList&lt;Vertex&gt; res = new ArrayList&lt;&gt;();\n// \u54c8\u5e0c\u8868\uff0c\u7528\u4e8e\u8bb0\u5f55\u5df2\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9\nSet&lt;Vertex&gt; visited = new HashSet&lt;&gt;();\ndfs(graph, visited, res, startVet);\nreturn res;\n}\n</code></pre> graph_dfs.cpp<pre><code>/* \u6df1\u5ea6\u4f18\u5148\u904d\u5386 DFS \u8f85\u52a9\u51fd\u6570 */\nvoid dfs(GraphAdjList &amp;graph, unordered_set&lt;Vertex *&gt; &amp;visited, vector&lt;Vertex *&gt; &amp;res, Vertex *vet) {\nres.push_back(vet);   // \u8bb0\u5f55\u8bbf\u95ee\u9876\u70b9\nvisited.emplace(vet); // \u6807\u8bb0\u8be5\u9876\u70b9\u5df2\u88ab\u8bbf\u95ee\n// \u904d\u5386\u8be5\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nfor (Vertex *adjVet : graph.adjList[vet]) {\nif (visited.count(adjVet))\ncontinue; // \u8df3\u8fc7\u5df2\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9\n// \u9012\u5f52\u8bbf\u95ee\u90bb\u63a5\u9876\u70b9\ndfs(graph, visited, res, adjVet);\n}\n}\n/* \u6df1\u5ea6\u4f18\u5148\u904d\u5386 DFS */\n// \u4f7f\u7528\u90bb\u63a5\u8868\u6765\u8868\u793a\u56fe\uff0c\u4ee5\u4fbf\u83b7\u53d6\u6307\u5b9a\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nvector&lt;Vertex *&gt; graphDFS(GraphAdjList &amp;graph, Vertex *startVet) {\n// \u9876\u70b9\u904d\u5386\u5e8f\u5217\nvector&lt;Vertex *&gt; res;\n// \u54c8\u5e0c\u8868\uff0c\u7528\u4e8e\u8bb0\u5f55\u5df2\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9\nunordered_set&lt;Vertex *&gt; visited;\ndfs(graph, visited, res, startVet);\nreturn res;\n}\n</code></pre> graph_dfs.py<pre><code>def dfs(graph: GraphAdjList, visited: set[Vertex], res: list[Vertex], vet: Vertex):\n\"\"\"\u6df1\u5ea6\u4f18\u5148\u904d\u5386 DFS \u8f85\u52a9\u51fd\u6570\"\"\"\nres.append(vet)  # \u8bb0\u5f55\u8bbf\u95ee\u9876\u70b9\nvisited.add(vet)  # \u6807\u8bb0\u8be5\u9876\u70b9\u5df2\u88ab\u8bbf\u95ee\n# \u904d\u5386\u8be5\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nfor adjVet in graph.adj_list[vet]:\nif adjVet in visited:\ncontinue  # \u8df3\u8fc7\u5df2\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9\n# \u9012\u5f52\u8bbf\u95ee\u90bb\u63a5\u9876\u70b9\ndfs(graph, visited, res, adjVet)\ndef graph_dfs(graph: GraphAdjList, start_vet: Vertex) -&gt; list[Vertex]:\n\"\"\"\u6df1\u5ea6\u4f18\u5148\u904d\u5386 DFS\"\"\"\n# \u9876\u70b9\u904d\u5386\u5e8f\u5217\nres = []\n# \u54c8\u5e0c\u8868\uff0c\u7528\u4e8e\u8bb0\u5f55\u5df2\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9\nvisited = set[Vertex]()\ndfs(graph, visited, res, start_vet)\nreturn res\n</code></pre> graph_dfs.go<pre><code>/* \u6df1\u5ea6\u4f18\u5148\u904d\u5386 DFS \u8f85\u52a9\u51fd\u6570 */\nfunc dfs(g *graphAdjList, visited map[Vertex]struct{}, res *[]Vertex, vet Vertex) {\n// append \u64cd\u4f5c\u4f1a\u8fd4\u56de\u65b0\u7684\u7684\u5f15\u7528\uff0c\u5fc5\u987b\u8ba9\u539f\u5f15\u7528\u91cd\u65b0\u8d4b\u503c\u4e3a\u65b0slice\u7684\u5f15\u7528\n*res = append(*res, vet)\nvisited[vet] = struct{}{}\n// \u904d\u5386\u8be5\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nfor _, adjVet := range g.adjList[vet] {\n_, isExist := visited[adjVet]\n// \u9012\u5f52\u8bbf\u95ee\u90bb\u63a5\u9876\u70b9\nif !isExist {\ndfs(g, visited, res, adjVet)\n}\n}\n}\n/* \u6df1\u5ea6\u4f18\u5148\u904d\u5386 DFS */\n// \u4f7f\u7528\u90bb\u63a5\u8868\u6765\u8868\u793a\u56fe\uff0c\u4ee5\u4fbf\u83b7\u53d6\u6307\u5b9a\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nfunc graphDFS(g *graphAdjList, startVet Vertex) []Vertex {\n// \u9876\u70b9\u904d\u5386\u5e8f\u5217\nres := make([]Vertex, 0)\n// \u54c8\u5e0c\u8868\uff0c\u7528\u4e8e\u8bb0\u5f55\u5df2\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9\nvisited := make(map[Vertex]struct{})\ndfs(g, visited, &amp;res, startVet)\n// \u8fd4\u56de\u9876\u70b9\u904d\u5386\u5e8f\u5217\nreturn res\n}\n</code></pre> graph_dfs.js<pre><code>/* \u6df1\u5ea6\u4f18\u5148\u904d\u5386 DFS */\n// \u4f7f\u7528\u90bb\u63a5\u8868\u6765\u8868\u793a\u56fe\uff0c\u4ee5\u4fbf\u83b7\u53d6\u6307\u5b9a\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nfunction dfs(graph, visited, res, vet) {\nres.push(vet); // \u8bb0\u5f55\u8bbf\u95ee\u9876\u70b9\nvisited.add(vet); // \u6807\u8bb0\u8be5\u9876\u70b9\u5df2\u88ab\u8bbf\u95ee\n// \u904d\u5386\u8be5\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nfor (const adjVet of graph.adjList.get(vet)) {\nif (visited.has(adjVet)) {\ncontinue; // \u8df3\u8fc7\u5df2\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9\n}\n// \u9012\u5f52\u8bbf\u95ee\u90bb\u63a5\u9876\u70b9\ndfs(graph, visited, res, adjVet);\n}\n}\n/* \u6df1\u5ea6\u4f18\u5148\u904d\u5386 DFS */\n// \u4f7f\u7528\u90bb\u63a5\u8868\u6765\u8868\u793a\u56fe\uff0c\u4ee5\u4fbf\u83b7\u53d6\u6307\u5b9a\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nfunction graphDFS(graph, startVet) {\n// \u9876\u70b9\u904d\u5386\u5e8f\u5217\nconst res = [];\n// \u54c8\u5e0c\u8868\uff0c\u7528\u4e8e\u8bb0\u5f55\u5df2\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9\nconst visited = new Set();\ndfs(graph, visited, res, startVet);\nreturn res;\n}\n</code></pre> graph_dfs.ts<pre><code>/* \u6df1\u5ea6\u4f18\u5148\u904d\u5386 DFS \u8f85\u52a9\u51fd\u6570 */\nfunction dfs(\ngraph: GraphAdjList,\nvisited: Set&lt;Vertex&gt;,\nres: Vertex[],\nvet: Vertex\n): void {\nres.push(vet); // \u8bb0\u5f55\u8bbf\u95ee\u9876\u70b9\nvisited.add(vet); // \u6807\u8bb0\u8be5\u9876\u70b9\u5df2\u88ab\u8bbf\u95ee\n// \u904d\u5386\u8be5\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nfor (const adjVet of graph.adjList.get(vet)) {\nif (visited.has(adjVet)) {\ncontinue; // \u8df3\u8fc7\u5df2\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9\n}\n// \u9012\u5f52\u8bbf\u95ee\u90bb\u63a5\u9876\u70b9\ndfs(graph, visited, res, adjVet);\n}\n}\n/* \u6df1\u5ea6\u4f18\u5148\u904d\u5386 DFS */\n// \u4f7f\u7528\u90bb\u63a5\u8868\u6765\u8868\u793a\u56fe\uff0c\u4ee5\u4fbf\u83b7\u53d6\u6307\u5b9a\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nfunction graphDFS(graph: GraphAdjList, startVet: Vertex): Vertex[] {\n// \u9876\u70b9\u904d\u5386\u5e8f\u5217\nconst res: Vertex[] = [];\n// \u54c8\u5e0c\u8868\uff0c\u7528\u4e8e\u8bb0\u5f55\u5df2\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9\nconst visited: Set&lt;Vertex&gt; = new Set();\ndfs(graph, visited, res, startVet);\nreturn res;\n}\n</code></pre> graph_dfs.c<pre><code>[class]{}-[func]{dfs}\n[class]{}-[func]{graphDFS}\n</code></pre> graph_dfs.cs<pre><code>/* \u6df1\u5ea6\u4f18\u5148\u904d\u5386 DFS \u8f85\u52a9\u51fd\u6570 */\nvoid dfs(GraphAdjList graph, HashSet&lt;Vertex&gt; visited, List&lt;Vertex&gt; res, Vertex vet) {\nres.Add(vet);     // \u8bb0\u5f55\u8bbf\u95ee\u9876\u70b9\nvisited.Add(vet); // \u6807\u8bb0\u8be5\u9876\u70b9\u5df2\u88ab\u8bbf\u95ee\n// \u904d\u5386\u8be5\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nforeach (Vertex adjVet in graph.adjList[vet]) {\nif (visited.Contains(adjVet)) {\ncontinue; // \u8df3\u8fc7\u5df2\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9                             \n}\n// \u9012\u5f52\u8bbf\u95ee\u90bb\u63a5\u9876\u70b9\ndfs(graph, visited, res, adjVet);\n}\n}\n/* \u6df1\u5ea6\u4f18\u5148\u904d\u5386 DFS */\n// \u4f7f\u7528\u90bb\u63a5\u8868\u6765\u8868\u793a\u56fe\uff0c\u4ee5\u4fbf\u83b7\u53d6\u6307\u5b9a\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nList&lt;Vertex&gt; graphDFS(GraphAdjList graph, Vertex startVet) {\n// \u9876\u70b9\u904d\u5386\u5e8f\u5217\nList&lt;Vertex&gt; res = new List&lt;Vertex&gt;();\n// \u54c8\u5e0c\u8868\uff0c\u7528\u4e8e\u8bb0\u5f55\u5df2\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9\nHashSet&lt;Vertex&gt; visited = new HashSet&lt;Vertex&gt;();\ndfs(graph, visited, res, startVet);\nreturn res;\n}\n</code></pre> graph_dfs.swift<pre><code>/* \u6df1\u5ea6\u4f18\u5148\u904d\u5386 DFS \u8f85\u52a9\u51fd\u6570 */\nfunc dfs(graph: GraphAdjList, visited: inout Set&lt;Vertex&gt;, res: inout [Vertex], vet: Vertex) {\nres.append(vet) // \u8bb0\u5f55\u8bbf\u95ee\u9876\u70b9\nvisited.insert(vet) // \u6807\u8bb0\u8be5\u9876\u70b9\u5df2\u88ab\u8bbf\u95ee\n// \u904d\u5386\u8be5\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nfor adjVet in graph.adjList[vet] ?? [] {\nif visited.contains(adjVet) {\ncontinue // \u8df3\u8fc7\u5df2\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9\n}\n// \u9012\u5f52\u8bbf\u95ee\u90bb\u63a5\u9876\u70b9\ndfs(graph: graph, visited: &amp;visited, res: &amp;res, vet: adjVet)\n}\n}\n/* \u6df1\u5ea6\u4f18\u5148\u904d\u5386 DFS */\n// \u4f7f\u7528\u90bb\u63a5\u8868\u6765\u8868\u793a\u56fe\uff0c\u4ee5\u4fbf\u83b7\u53d6\u6307\u5b9a\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nfunc graphDFS(graph: GraphAdjList, startVet: Vertex) -&gt; [Vertex] {\n// \u9876\u70b9\u904d\u5386\u5e8f\u5217\nvar res: [Vertex] = []\n// \u54c8\u5e0c\u8868\uff0c\u7528\u4e8e\u8bb0\u5f55\u5df2\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9\nvar visited: Set&lt;Vertex&gt; = []\ndfs(graph: graph, visited: &amp;visited, res: &amp;res, vet: startVet)\nreturn res\n}\n</code></pre> graph_dfs.zig<pre><code>[class]{}-[func]{dfs}\n[class]{}-[func]{graphDFS}\n</code></pre> graph_dfs.dart<pre><code>/* \u6df1\u5ea6\u4f18\u5148\u904d\u5386 DFS \u8f85\u52a9\u51fd\u6570 */\nvoid dfs(\nGraphAdjList graph,\nSet&lt;Vertex&gt; visited,\nList&lt;Vertex&gt; res,\nVertex vet,\n) {\nres.add(vet); // \u8bb0\u5f55\u8bbf\u95ee\u9876\u70b9\nvisited.add(vet); // \u6807\u8bb0\u8be5\u9876\u70b9\u5df2\u88ab\u8bbf\u95ee\n// \u904d\u5386\u8be5\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nfor (Vertex adjVet in graph.adjList[vet]!) {\nif (visited.contains(adjVet)) {\ncontinue; // \u8df3\u8fc7\u5df2\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9\n}\n// \u9012\u5f52\u8bbf\u95ee\u90bb\u63a5\u9876\u70b9\ndfs(graph, visited, res, adjVet);\n}\n}\n/* \u6df1\u5ea6\u4f18\u5148\u904d\u5386 DFS */\nList&lt;Vertex&gt; graphDFS(GraphAdjList graph, Vertex startVet) {\n// \u9876\u70b9\u904d\u5386\u5e8f\u5217\nList&lt;Vertex&gt; res = [];\n// \u54c8\u5e0c\u8868\uff0c\u7528\u4e8e\u8bb0\u5f55\u5df2\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9\nSet&lt;Vertex&gt; visited = {};\ndfs(graph, visited, res, startVet);\nreturn res;\n}\n</code></pre> <p>\u6df1\u5ea6\u4f18\u5148\u904d\u5386\u7684\u7b97\u6cd5\u6d41\u7a0b\u5982\u4e0b\u56fe\u6240\u793a\uff0c\u5176\u4e2d\uff1a</p> <ul> <li>\u76f4\u865a\u7ebf\u4ee3\u8868\u5411\u4e0b\u9012\u63a8\uff0c\u8868\u793a\u5f00\u542f\u4e86\u4e00\u4e2a\u65b0\u7684\u9012\u5f52\u65b9\u6cd5\u6765\u8bbf\u95ee\u65b0\u9876\u70b9\uff1b</li> <li>\u66f2\u865a\u7ebf\u4ee3\u8868\u5411\u4e0a\u56de\u6eaf\uff0c\u8868\u793a\u6b64\u9012\u5f52\u65b9\u6cd5\u5df2\u7ecf\u8fd4\u56de\uff0c\u56de\u6eaf\u5230\u4e86\u5f00\u542f\u6b64\u9012\u5f52\u65b9\u6cd5\u7684\u4f4d\u7f6e\uff1b</li> </ul> <p>\u4e3a\u4e86\u52a0\u6df1\u7406\u89e3\uff0c\u5efa\u8bae\u5c06\u56fe\u793a\u4e0e\u4ee3\u7801\u7ed3\u5408\u8d77\u6765\uff0c\u5728\u8111\u4e2d\uff08\u6216\u8005\u7528\u7b14\u753b\u4e0b\u6765\uff09\u6a21\u62df\u6574\u4e2a DFS \u8fc7\u7a0b\uff0c\u5305\u62ec\u6bcf\u4e2a\u9012\u5f52\u65b9\u6cd5\u4f55\u65f6\u5f00\u542f\u3001\u4f55\u65f6\u8fd4\u56de\u3002</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt;&lt;11&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p>\u6df1\u5ea6\u4f18\u5148\u904d\u5386\u7684\u5e8f\u5217\u662f\u5426\u552f\u4e00\uff1f</p> <p>\u4e0e\u5e7f\u5ea6\u4f18\u5148\u904d\u5386\u7c7b\u4f3c\uff0c\u6df1\u5ea6\u4f18\u5148\u904d\u5386\u5e8f\u5217\u7684\u987a\u5e8f\u4e5f\u4e0d\u662f\u552f\u4e00\u7684\u3002\u7ed9\u5b9a\u67d0\u9876\u70b9\uff0c\u5148\u5f80\u54ea\u4e2a\u65b9\u5411\u63a2\u7d22\u90fd\u53ef\u4ee5\uff0c\u5373\u90bb\u63a5\u9876\u70b9\u7684\u987a\u5e8f\u53ef\u4ee5\u4efb\u610f\u6253\u4e71\uff0c\u90fd\u662f\u6df1\u5ea6\u4f18\u5148\u904d\u5386\u3002</p> <p>\u4ee5\u6811\u7684\u904d\u5386\u4e3a\u4f8b\uff0c\u201c\u6839 \\(\\rightarrow\\) \u5de6 \\(\\rightarrow\\) \u53f3\u201d\u3001\u201c\u5de6 \\(\\rightarrow\\) \u6839 \\(\\rightarrow\\) \u53f3\u201d\u3001\u201c\u5de6 \\(\\rightarrow\\) \u53f3 \\(\\rightarrow\\) \u6839\u201d\u5206\u522b\u5bf9\u5e94\u524d\u5e8f\u3001\u4e2d\u5e8f\u3001\u540e\u5e8f\u904d\u5386\uff0c\u5b83\u4eec\u5c55\u793a\u4e86\u4e09\u79cd\u4e0d\u540c\u7684\u904d\u5386\u4f18\u5148\u7ea7\uff0c\u7136\u800c\u8fd9\u4e09\u8005\u90fd\u5c5e\u4e8e\u6df1\u5ea6\u4f18\u5148\u904d\u5386\u3002</p>"},{"location":"chapter_graph/graph_traversal/#_4","title":"\u590d\u6742\u5ea6\u5206\u6790","text":"<p>\u65f6\u95f4\u590d\u6742\u5ea6\uff1a \u6240\u6709\u9876\u70b9\u90fd\u4f1a\u88ab\u8bbf\u95ee \\(1\\) \u6b21\uff0c\u4f7f\u7528 \\(O(|V|)\\) \u65f6\u95f4\uff1b\u6240\u6709\u8fb9\u90fd\u4f1a\u88ab\u8bbf\u95ee \\(2\\) \u6b21\uff0c\u4f7f\u7528 \\(O(2|E|)\\) \u65f6\u95f4\uff1b\u603b\u4f53\u4f7f\u7528 \\(O(|V| + |E|)\\) \u65f6\u95f4\u3002</p> <p>\u7a7a\u95f4\u590d\u6742\u5ea6\uff1a \u5217\u8868 <code>res</code> \uff0c\u54c8\u5e0c\u8868 <code>visited</code> \u9876\u70b9\u6570\u91cf\u6700\u591a\u4e3a \\(|V|\\) \uff0c\u9012\u5f52\u6df1\u5ea6\u6700\u5927\u4e3a \\(|V|\\) \uff0c\u56e0\u6b64\u4f7f\u7528 \\(O(|V|)\\) \u7a7a\u95f4\u3002</p>"},{"location":"chapter_graph/summary/","title":"9.4. \u00a0 \u5c0f\u7ed3","text":"<ul> <li>\u56fe\u7531\u9876\u70b9\u548c\u8fb9\u7ec4\u6210\uff0c\u53ef\u4ee5\u88ab\u8868\u793a\u4e3a\u4e00\u7ec4\u9876\u70b9\u548c\u4e00\u7ec4\u8fb9\u6784\u6210\u7684\u96c6\u5408\u3002</li> <li>\u76f8\u8f83\u4e8e\u7ebf\u6027\u5173\u7cfb\uff08\u94fe\u8868\uff09\u548c\u5206\u6cbb\u5173\u7cfb\uff08\u6811\uff09\uff0c\u7f51\u7edc\u5173\u7cfb\uff08\u56fe\uff09\u5177\u6709\u66f4\u9ad8\u7684\u81ea\u7531\u5ea6\uff0c\u56e0\u800c\u66f4\u4e3a\u590d\u6742\u3002</li> <li>\u6709\u5411\u56fe\u7684\u8fb9\u5177\u6709\u65b9\u5411\u6027\uff0c\u8fde\u901a\u56fe\u4e2d\u7684\u4efb\u610f\u9876\u70b9\u5747\u53ef\u8fbe\uff0c\u6709\u6743\u56fe\u7684\u6bcf\u6761\u8fb9\u90fd\u5305\u542b\u6743\u91cd\u53d8\u91cf\u3002</li> <li>\u90bb\u63a5\u77e9\u9635\u5229\u7528\u77e9\u9635\u6765\u8868\u793a\u56fe\uff0c\u6bcf\u4e00\u884c\uff08\u5217\uff09\u4ee3\u8868\u4e00\u4e2a\u9876\u70b9\uff0c\u77e9\u9635\u5143\u7d20\u4ee3\u8868\u8fb9\uff0c\u7528 \\(1\\) \u6216 \\(0\\) \u8868\u793a\u4e24\u4e2a\u9876\u70b9\u4e4b\u95f4\u6709\u8fb9\u6216\u65e0\u8fb9\u3002\u90bb\u63a5\u77e9\u9635\u5728\u589e\u5220\u67e5\u64cd\u4f5c\u4e0a\u6548\u7387\u5f88\u9ad8\uff0c\u4f46\u7a7a\u95f4\u5360\u7528\u8f83\u591a\u3002</li> <li>\u90bb\u63a5\u8868\u4f7f\u7528\u591a\u4e2a\u94fe\u8868\u6765\u8868\u793a\u56fe\uff0c\u7b2c \\(i\\) \u6761\u94fe\u8868\u5bf9\u5e94\u9876\u70b9 \\(i\\) \uff0c\u5176\u4e2d\u5b58\u50a8\u4e86\u8be5\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\u3002\u90bb\u63a5\u8868\u76f8\u5bf9\u4e8e\u90bb\u63a5\u77e9\u9635\u66f4\u52a0\u8282\u7701\u7a7a\u95f4\uff0c\u4f46\u7531\u4e8e\u9700\u8981\u904d\u5386\u94fe\u8868\u6765\u67e5\u627e\u8fb9\uff0c\u65f6\u95f4\u6548\u7387\u8f83\u4f4e\u3002</li> <li>\u5f53\u90bb\u63a5\u8868\u4e2d\u7684\u94fe\u8868\u8fc7\u957f\u65f6\uff0c\u53ef\u4ee5\u5c06\u5176\u8f6c\u6362\u4e3a\u7ea2\u9ed1\u6811\u6216\u54c8\u5e0c\u8868\uff0c\u4ece\u800c\u63d0\u5347\u67e5\u8be2\u6548\u7387\u3002</li> <li>\u4ece\u7b97\u6cd5\u601d\u60f3\u89d2\u5ea6\u5206\u6790\uff0c\u90bb\u63a5\u77e9\u9635\u4f53\u73b0\u201c\u4ee5\u7a7a\u95f4\u6362\u65f6\u95f4\u201d\uff0c\u90bb\u63a5\u8868\u4f53\u73b0\u201c\u4ee5\u65f6\u95f4\u6362\u7a7a\u95f4\u201d\u3002</li> <li>\u56fe\u53ef\u7528\u4e8e\u5efa\u6a21\u5404\u7c7b\u73b0\u5b9e\u7cfb\u7edf\uff0c\u5982\u793e\u4ea4\u7f51\u7edc\u3001\u5730\u94c1\u7ebf\u8def\u7b49\u3002</li> <li>\u6811\u662f\u56fe\u7684\u4e00\u79cd\u7279\u4f8b\uff0c\u6811\u7684\u904d\u5386\u4e5f\u662f\u56fe\u7684\u904d\u5386\u7684\u4e00\u79cd\u7279\u4f8b\u3002</li> <li>\u56fe\u7684\u5e7f\u5ea6\u4f18\u5148\u904d\u5386\u662f\u4e00\u79cd\u7531\u8fd1\u53ca\u8fdc\u3001\u5c42\u5c42\u6269\u5f20\u7684\u641c\u7d22\u65b9\u5f0f\uff0c\u901a\u5e38\u501f\u52a9\u961f\u5217\u5b9e\u73b0\u3002</li> <li>\u56fe\u7684\u6df1\u5ea6\u4f18\u5148\u904d\u5386\u662f\u4e00\u79cd\u4f18\u5148\u8d70\u5230\u5e95\u3001\u65e0\u8def\u53ef\u8d70\u65f6\u518d\u56de\u6eaf\u7684\u641c\u7d22\u65b9\u5f0f\uff0c\u5e38\u57fa\u4e8e\u9012\u5f52\u6765\u5b9e\u73b0\u3002</li> </ul>"},{"location":"chapter_graph/summary/#941-q-a","title":"9.4.1. \u00a0 Q &amp; A","text":"<p>\u8def\u5f84\u7684\u5b9a\u4e49\u662f\u9876\u70b9\u5e8f\u5217\u8fd8\u662f\u8fb9\u5e8f\u5217\uff1f</p> <p>\u7ef4\u57fa\u767e\u79d1\u4e0a\u4e0d\u540c\u8bed\u8a00\u7248\u672c\u7684\u5b9a\u4e49\u4e0d\u4e00\u81f4\uff1a\u82f1\u6587\u7248\u662f\u201c\u8def\u5f84\u662f\u4e00\u4e2a\u8fb9\u5e8f\u5217\u201d\uff0c\u800c\u4e2d\u6587\u7248\u662f\u201c\u8def\u5f84\u662f\u4e00\u4e2a\u9876\u70b9\u5e8f\u5217\u201d\u3002\u4ee5\u4e0b\u662f\u82f1\u6587\u7248\u539f\u6587\uff1aIn graph theory, a path in a graph is a finite or infinite sequence of edges which joins a sequence of vertices. \u5728\u672c\u6587\u4e2d\uff0c\u8def\u5f84\u88ab\u8ba4\u4e3a\u662f\u4e00\u4e2a\u8fb9\u5e8f\u5217\uff0c\u800c\u4e0d\u662f\u4e00\u4e2a\u9876\u70b9\u5e8f\u5217\u3002\u8fd9\u662f\u56e0\u4e3a\u4e24\u4e2a\u9876\u70b9\u4e4b\u95f4\u53ef\u80fd\u5b58\u5728\u591a\u6761\u8fb9\u8fde\u63a5\uff0c\u6b64\u65f6\u6bcf\u6761\u8fb9\u90fd\u5bf9\u5e94\u4e00\u6761\u8def\u5f84\u3002</p> <p>\u975e\u8fde\u901a\u56fe\u4e2d\uff0c\u662f\u5426\u4f1a\u6709\u65e0\u6cd5\u904d\u5386\u5230\u7684\u70b9\uff1f</p> <p>\u5728\u975e\u8fde\u901a\u56fe\u4e2d\uff0c\u4ece\u67d0\u4e2a\u9876\u70b9\u51fa\u53d1\uff0c\u81f3\u5c11\u6709\u4e00\u4e2a\u9876\u70b9\u65e0\u6cd5\u5230\u8fbe\u3002\u904d\u5386\u975e\u8fde\u901a\u56fe\u9700\u8981\u8bbe\u7f6e\u591a\u4e2a\u8d77\u70b9\uff0c\u4ee5\u904d\u5386\u5230\u56fe\u7684\u6240\u6709\u8fde\u901a\u5206\u91cf\u3002</p> <p>\u5728\u90bb\u63a5\u8868\u4e2d\uff0c\u201c\u4e0e\u8be5\u9876\u70b9\u76f8\u8fde\u7684\u6240\u6709\u9876\u70b9\u201d\u7684\u9876\u70b9\u987a\u5e8f\u662f\u5426\u6709\u8981\u6c42\uff1f</p> <p>\u53ef\u4ee5\u662f\u4efb\u610f\u987a\u5e8f\u3002\u4f46\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u53ef\u80fd\u4f1a\u9700\u8981\u6309\u7167\u6307\u5b9a\u89c4\u5219\u6765\u6392\u5e8f\uff0c\u6bd4\u5982\u6309\u7167\u9876\u70b9\u6dfb\u52a0\u7684\u6b21\u5e8f\u3001\u6216\u8005\u6309\u7167\u9876\u70b9\u503c\u5927\u5c0f\u7684\u987a\u5e8f\u7b49\u7b49\uff0c\u8fd9\u6837\u53ef\u4ee5\u6709\u52a9\u4e8e\u5feb\u901f\u67e5\u627e\u201c\u5e26\u6709\u67d0\u79cd\u6781\u503c\u201d\u7684\u9876\u70b9\u3002</p>"},{"location":"chapter_hashing/","title":"6. \u00a0 \u6563\u5217\u8868","text":""},{"location":"chapter_hashing/hash_collision/","title":"6.2. \u00a0 \u54c8\u5e0c\u51b2\u7a81","text":"<p>\u5728\u7406\u60f3\u60c5\u51b5\u4e0b\uff0c\u54c8\u5e0c\u51fd\u6570\u4e3a\u6bcf\u4e2a\u8f93\u5165\u751f\u6210\u552f\u4e00\u7684\u8f93\u51fa\uff0c\u5b9e\u73b0 key \u548c\u6570\u7ec4\u7d22\u5f15\u7684\u4e00\u4e00\u5bf9\u5e94\u3002\u4f46\u5b9e\u9645\u4e0a\uff0c\u54c8\u5e0c\u51fd\u6570\u7684\u8f93\u5165\u7a7a\u95f4\u901a\u5e38\u8fdc\u5927\u4e8e\u8f93\u51fa\u7a7a\u95f4\uff0c\u56e0\u6b64\u591a\u4e2a\u8f93\u5165\u4ea7\u751f\u76f8\u540c\u8f93\u51fa\u7684\u60c5\u51b5\u662f\u4e0d\u53ef\u907f\u514d\u7684\u3002\u4f8b\u5982\uff0c\u8f93\u5165\u7a7a\u95f4\u4e3a\u5168\u4f53\u6574\u6570\uff0c\u8f93\u51fa\u7a7a\u95f4\u4e3a\u6570\u7ec4\u5bb9\u91cf\u5927\u5c0f\uff0c\u5219\u5fc5\u7136\u6709\u591a\u4e2a\u6574\u6570\u6620\u5c04\u81f3\u540c\u4e00\u6570\u7ec4\u7d22\u5f15\u3002</p> <p>\u8fd9\u79cd\u591a\u4e2a\u8f93\u5165\u5bf9\u5e94\u540c\u4e00\u8f93\u51fa\u7d22\u5f15\u7684\u73b0\u8c61\u88ab\u79f0\u4e3a\u300c\u54c8\u5e0c\u51b2\u7a81 Hash Collision\u300d\u3002\u54c8\u5e0c\u51b2\u7a81\u4f1a\u5bfc\u81f4\u67e5\u8be2\u7ed3\u679c\u9519\u8bef\uff0c\u4e25\u91cd\u5f71\u54cd\u54c8\u5e0c\u8868\u7684\u53ef\u7528\u6027\u3002\u54c8\u5e0c\u51b2\u7a81\u7684\u89e3\u51b3\u65b9\u6cd5\u4e3b\u8981\u6709\u4e24\u79cd\uff1a</p> <ul> <li>\u6269\u5927\u54c8\u5e0c\u8868\u5bb9\u91cf\uff1a\u54c8\u5e0c\u8868\u5bb9\u91cf\u8d8a\u5927\uff0c\u952e\u503c\u5bf9\u805a\u96c6\u7684\u6982\u7387\u5c31\u8d8a\u4f4e\u3002\u6781\u7aef\u60c5\u51b5\u4e0b\uff0c\u5f53\u8f93\u5165\u7a7a\u95f4\u548c\u8f93\u51fa\u7a7a\u95f4\u5927\u5c0f\u76f8\u7b49\u65f6\uff0c\u54c8\u5e0c\u8868\u7b49\u540c\u4e8e\u6570\u7ec4\uff0c\u6bcf\u4e2a key \u90fd\u5bf9\u5e94\u552f\u4e00\u7684\u6570\u7ec4\u7d22\u5f15\u3002</li> <li>\u4f18\u5316\u54c8\u5e0c\u8868\u7ed3\u6784\uff1a\u5e38\u7528\u65b9\u6cd5\u5305\u62ec\u94fe\u5f0f\u5730\u5740\u548c\u5f00\u653e\u5bfb\u5740\u3002</li> </ul>"},{"location":"chapter_hashing/hash_collision/#621","title":"6.2.1. \u00a0 \u54c8\u5e0c\u8868\u6269\u5bb9","text":"<p>\u54c8\u5e0c\u51fd\u6570\u7684\u6700\u540e\u4e00\u6b65\u901a\u5e38\u662f\u5bf9\u6876\u6570\u91cf \\(n\\) \u53d6\u4f59\uff0c\u4f5c\u7528\u662f\u5c06\u54c8\u5e0c\u503c\u6620\u5c04\u5230\u6876\u7d22\u5f15\u8303\u56f4\uff0c\u4ece\u800c\u5c06 key \u653e\u5165\u5bf9\u5e94\u7684\u6876\u4e2d\u3002\u5f53\u54c8\u5e0c\u8868\u5bb9\u91cf\u8d8a\u5927\uff08\u5373 \\(n\\) \u8d8a\u5927\uff09\u65f6\uff0c\u591a\u4e2a key \u88ab\u5206\u914d\u5230\u540c\u4e00\u4e2a\u6876\u4e2d\u7684\u6982\u7387\u5c31\u8d8a\u4f4e\uff0c\u51b2\u7a81\u5c31\u8d8a\u5c11\u3002</p> <p>\u56e0\u6b64\uff0c\u5f53\u54c8\u5e0c\u8868\u5185\u7684\u51b2\u7a81\u603b\u4f53\u8f83\u4e3a\u4e25\u91cd\u65f6\uff0c\u7f16\u7a0b\u8bed\u8a00\u901a\u5e38\u901a\u8fc7\u6269\u5bb9\u54c8\u5e0c\u8868\u6765\u7f13\u89e3\u51b2\u7a81\u3002\u7c7b\u4f3c\u4e8e\u6570\u7ec4\u6269\u5bb9\uff0c\u54c8\u5e0c\u8868\u6269\u5bb9\u9700\u5c06\u6240\u6709\u952e\u503c\u5bf9\u4ece\u539f\u54c8\u5e0c\u8868\u8fc1\u79fb\u81f3\u65b0\u54c8\u5e0c\u8868\uff0c\u5f00\u9500\u8f83\u5927\u3002</p> <p>\u7f16\u7a0b\u8bed\u8a00\u901a\u5e38\u4f7f\u7528\u300c\u8d1f\u8f7d\u56e0\u5b50 Load Factor\u300d\u6765\u8861\u91cf\u54c8\u5e0c\u51b2\u7a81\u7684\u4e25\u91cd\u7a0b\u5ea6\uff0c\u5b9a\u4e49\u4e3a\u54c8\u5e0c\u8868\u4e2d\u5143\u7d20\u6570\u91cf\u9664\u4ee5\u6876\u6570\u91cf\uff0c\u5e38\u4f5c\u4e3a\u54c8\u5e0c\u8868\u6269\u5bb9\u7684\u89e6\u53d1\u6761\u4ef6\u3002\u5728 Java \u4e2d\uff0c\u5f53\u8d1f\u8f7d\u56e0\u5b50\u8d85\u8fc7 \\(0.75\\) \u65f6\uff0c\u7cfb\u7edf\u4f1a\u5c06 HashMap \u5bb9\u91cf\u6269\u5c55\u4e3a\u539f\u5148\u7684 \\(2\\) \u500d\u3002</p>"},{"location":"chapter_hashing/hash_collision/#622","title":"6.2.2. \u00a0 \u94fe\u5f0f\u5730\u5740","text":"<p>\u5728\u539f\u59cb\u54c8\u5e0c\u8868\u4e2d\uff0c\u6bcf\u4e2a\u6876\u4ec5\u80fd\u5b58\u50a8\u4e00\u4e2a\u952e\u503c\u5bf9\u3002\u300c\u94fe\u5f0f\u5730\u5740 Separate Chaining\u300d\u5c06\u5355\u4e2a\u5143\u7d20\u8f6c\u6362\u4e3a\u94fe\u8868\uff0c\u5c06\u952e\u503c\u5bf9\u4f5c\u4e3a\u94fe\u8868\u8282\u70b9\uff0c\u5c06\u6240\u6709\u53d1\u751f\u51b2\u7a81\u7684\u952e\u503c\u5bf9\u90fd\u5b58\u50a8\u5728\u540c\u4e00\u94fe\u8868\u4e2d\u3002</p> <p></p> <p> Fig. \u94fe\u5f0f\u5730\u5740\u54c8\u5e0c\u8868 </p> <p>\u94fe\u5f0f\u5730\u5740\u4e0b\uff0c\u54c8\u5e0c\u8868\u7684\u64cd\u4f5c\u65b9\u6cd5\u5305\u62ec\uff1a</p> <ul> <li>\u67e5\u8be2\u5143\u7d20\uff1a\u8f93\u5165 key \uff0c\u7ecf\u8fc7\u54c8\u5e0c\u51fd\u6570\u5f97\u5230\u6570\u7ec4\u7d22\u5f15\uff0c\u5373\u53ef\u8bbf\u95ee\u94fe\u8868\u5934\u8282\u70b9\uff0c\u7136\u540e\u904d\u5386\u94fe\u8868\u5e76\u5bf9\u6bd4 key \u4ee5\u67e5\u627e\u76ee\u6807\u952e\u503c\u5bf9\u3002</li> <li>\u6dfb\u52a0\u5143\u7d20\uff1a\u5148\u901a\u8fc7\u54c8\u5e0c\u51fd\u6570\u8bbf\u95ee\u94fe\u8868\u5934\u8282\u70b9\uff0c\u7136\u540e\u5c06\u8282\u70b9\uff08\u5373\u952e\u503c\u5bf9\uff09\u6dfb\u52a0\u5230\u94fe\u8868\u4e2d\u3002</li> <li>\u5220\u9664\u5143\u7d20\uff1a\u6839\u636e\u54c8\u5e0c\u51fd\u6570\u7684\u7ed3\u679c\u8bbf\u95ee\u94fe\u8868\u5934\u90e8\uff0c\u63a5\u7740\u904d\u5386\u94fe\u8868\u4ee5\u67e5\u627e\u76ee\u6807\u8282\u70b9\uff0c\u5e76\u5c06\u5176\u5220\u9664\u3002</li> </ul> <p>\u5c3d\u7ba1\u94fe\u5f0f\u5730\u5740\u6cd5\u89e3\u51b3\u4e86\u54c8\u5e0c\u51b2\u7a81\u95ee\u9898\uff0c\u4f46\u4ecd\u5b58\u5728\u4e00\u4e9b\u5c40\u9650\u6027\uff0c\u5305\u62ec\uff1a</p> <ul> <li>\u5360\u7528\u7a7a\u95f4\u589e\u5927\uff0c\u7531\u4e8e\u94fe\u8868\u6216\u4e8c\u53c9\u6811\u5305\u542b\u8282\u70b9\u6307\u9488\uff0c\u76f8\u6bd4\u6570\u7ec4\u66f4\u52a0\u8017\u8d39\u5185\u5b58\u7a7a\u95f4\uff1b</li> <li>\u67e5\u8be2\u6548\u7387\u964d\u4f4e\uff0c\u56e0\u4e3a\u9700\u8981\u7ebf\u6027\u904d\u5386\u94fe\u8868\u6765\u67e5\u627e\u5bf9\u5e94\u5143\u7d20\uff1b</li> </ul> <p>\u4ee5\u4e0b\u7ed9\u51fa\u4e86\u94fe\u5f0f\u5730\u5740\u54c8\u5e0c\u8868\u7684\u7b80\u5355\u5b9e\u73b0\uff0c\u9700\u8981\u6ce8\u610f\uff1a</p> <ul> <li>\u4e3a\u4e86\u4f7f\u5f97\u4ee3\u7801\u5c3d\u91cf\u7b80\u77ed\uff0c\u6211\u4eec\u4f7f\u7528\u5217\u8868\uff08\u52a8\u6001\u6570\u7ec4\uff09\u4ee3\u66ff\u94fe\u8868\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u54c8\u5e0c\u8868\uff08\u6570\u7ec4\uff09\u5305\u542b\u591a\u4e2a\u6876\uff0c\u6bcf\u4e2a\u6876\u90fd\u662f\u4e00\u4e2a\u5217\u8868\u3002</li> <li>\u4ee5\u4e0b\u4ee3\u7801\u5b9e\u73b0\u4e86\u54c8\u5e0c\u8868\u6269\u5bb9\u65b9\u6cd5\u3002\u5177\u4f53\u6765\u770b\uff0c\u5f53\u8d1f\u8f7d\u56e0\u5b50\u8d85\u8fc7 \\(0.75\\) \u65f6\uff0c\u6211\u4eec\u5c06\u54c8\u5e0c\u8868\u6269\u5bb9\u81f3 \\(2\\) \u500d\u3002</li> </ul> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart hash_map_chaining.java<pre><code>/* \u952e\u503c\u5bf9 */\nclass Pair {\npublic int key;\npublic String val;\npublic Pair(int key, String val) {\nthis.key = key;\nthis.val = val;\n}\n}\n/* \u94fe\u5f0f\u5730\u5740\u54c8\u5e0c\u8868 */\nclass HashMapChaining {\nint size; // \u952e\u503c\u5bf9\u6570\u91cf\nint capacity; // \u54c8\u5e0c\u8868\u5bb9\u91cf\ndouble loadThres; // \u89e6\u53d1\u6269\u5bb9\u7684\u8d1f\u8f7d\u56e0\u5b50\u9608\u503c\nint extendRatio; // \u6269\u5bb9\u500d\u6570\nList&lt;List&lt;Pair&gt;&gt; buckets; // \u6876\u6570\u7ec4\n/* \u6784\u9020\u65b9\u6cd5 */\npublic HashMapChaining() {\nsize = 0;\ncapacity = 4;\nloadThres = 2 / 3.0;\nextendRatio = 2;\nbuckets = new ArrayList&lt;&gt;(capacity);\nfor (int i = 0; i &lt; capacity; i++) {\nbuckets.add(new ArrayList&lt;&gt;());\n}\n}\n/* \u54c8\u5e0c\u51fd\u6570 */\nint hashFunc(int key) {\nreturn key % capacity;\n}\n/* \u8d1f\u8f7d\u56e0\u5b50 */\ndouble loadFactor() {\nreturn (double) size / capacity;\n}\n/* \u67e5\u8be2\u64cd\u4f5c */\nString get(int key) {\nint index = hashFunc(key);\nList&lt;Pair&gt; bucket = buckets.get(index);\n// \u904d\u5386\u6876\uff0c\u82e5\u627e\u5230 key \u5219\u8fd4\u56de\u5bf9\u5e94 val\nfor (Pair pair : bucket) {\nif (pair.key == key) {\nreturn pair.val;\n}\n}\n// \u82e5\u672a\u627e\u5230 key \u5219\u8fd4\u56de null\nreturn null;\n}\n/* \u6dfb\u52a0\u64cd\u4f5c */\nvoid put(int key, String val) {\n// \u5f53\u8d1f\u8f7d\u56e0\u5b50\u8d85\u8fc7\u9608\u503c\u65f6\uff0c\u6267\u884c\u6269\u5bb9\nif (loadFactor() &gt; loadThres) {\nextend();\n}\nint index = hashFunc(key);\nList&lt;Pair&gt; bucket = buckets.get(index);\n// \u904d\u5386\u6876\uff0c\u82e5\u9047\u5230\u6307\u5b9a key \uff0c\u5219\u66f4\u65b0\u5bf9\u5e94 val \u5e76\u8fd4\u56de\nfor (Pair pair : bucket) {\nif (pair.key == key) {\npair.val = val;\nreturn;\n}\n}\n// \u82e5\u65e0\u8be5 key \uff0c\u5219\u5c06\u952e\u503c\u5bf9\u6dfb\u52a0\u81f3\u5c3e\u90e8\nPair pair = new Pair(key, val);\nbucket.add(pair);\nsize++;\n}\n/* \u5220\u9664\u64cd\u4f5c */\nvoid remove(int key) {\nint index = hashFunc(key);\nList&lt;Pair&gt; bucket = buckets.get(index);\n// \u904d\u5386\u6876\uff0c\u4ece\u4e2d\u5220\u9664\u952e\u503c\u5bf9\nfor (Pair pair : bucket) {\nif (pair.key == key)\nbucket.remove(pair);\n}\nsize--;\n}\n/* \u6269\u5bb9\u54c8\u5e0c\u8868 */\nvoid extend() {\n// \u6682\u5b58\u539f\u54c8\u5e0c\u8868\nList&lt;List&lt;Pair&gt;&gt; bucketsTmp = buckets;\n// \u521d\u59cb\u5316\u6269\u5bb9\u540e\u7684\u65b0\u54c8\u5e0c\u8868\ncapacity *= extendRatio;\nbuckets = new ArrayList&lt;&gt;(capacity);\nfor (int i = 0; i &lt; capacity; i++) {\nbuckets.add(new ArrayList&lt;&gt;());\n}\nsize = 0;\n// \u5c06\u952e\u503c\u5bf9\u4ece\u539f\u54c8\u5e0c\u8868\u642c\u8fd0\u81f3\u65b0\u54c8\u5e0c\u8868\nfor (List&lt;Pair&gt; bucket : bucketsTmp) {\nfor (Pair pair : bucket) {\nput(pair.key, pair.val);\n}\n}\n}\n/* \u6253\u5370\u54c8\u5e0c\u8868 */\nvoid print() {\nfor (List&lt;Pair&gt; bucket : buckets) {\nList&lt;String&gt; res = new ArrayList&lt;&gt;();\nfor (Pair pair : bucket) {\nres.add(pair.key + \" -&gt; \" + pair.val);\n}\nSystem.out.println(res);\n}\n}\n}\n</code></pre> hash_map_chaining.cpp<pre><code>/* \u952e\u503c\u5bf9 */\nstruct Pair {\npublic:\nint key;\nstring val;\nPair(int key, string val) {\nthis-&gt;key = key;\nthis-&gt;val = val;\n}\n};\n/* \u94fe\u5f0f\u5730\u5740\u54c8\u5e0c\u8868 */\nclass HashMapChaining {\nprivate:\nint size;                       // \u952e\u503c\u5bf9\u6570\u91cf\nint capacity;                   // \u54c8\u5e0c\u8868\u5bb9\u91cf\ndouble loadThres;               // \u89e6\u53d1\u6269\u5bb9\u7684\u8d1f\u8f7d\u56e0\u5b50\u9608\u503c\nint extendRatio;                // \u6269\u5bb9\u500d\u6570\nvector&lt;vector&lt;Pair *&gt;&gt; buckets; // \u6876\u6570\u7ec4\npublic:\n/* \u6784\u9020\u65b9\u6cd5 */\nHashMapChaining() : size(0), capacity(4), loadThres(2.0 / 3), extendRatio(2) {\nbuckets.resize(capacity);\n}\n/* \u54c8\u5e0c\u51fd\u6570 */\nint hashFunc(int key) {\nreturn key % capacity;\n}\n/* \u8d1f\u8f7d\u56e0\u5b50 */\ndouble loadFactor() {\nreturn (double)size / (double)capacity;\n}\n/* \u67e5\u8be2\u64cd\u4f5c */\nstring get(int key) {\nint index = hashFunc(key);\n// \u904d\u5386\u6876\uff0c\u82e5\u627e\u5230 key \u5219\u8fd4\u56de\u5bf9\u5e94 val\nfor (Pair *pair : buckets[index]) {\nif (pair-&gt;key == key) {\nreturn pair-&gt;val;\n}\n}\n// \u82e5\u672a\u627e\u5230 key \u5219\u8fd4\u56de nullptr\nreturn nullptr;\n}\n/* \u6dfb\u52a0\u64cd\u4f5c */\nvoid put(int key, string val) {\n// \u5f53\u8d1f\u8f7d\u56e0\u5b50\u8d85\u8fc7\u9608\u503c\u65f6\uff0c\u6267\u884c\u6269\u5bb9\nif (loadFactor() &gt; loadThres) {\nextend();\n}\nint index = hashFunc(key);\n// \u904d\u5386\u6876\uff0c\u82e5\u9047\u5230\u6307\u5b9a key \uff0c\u5219\u66f4\u65b0\u5bf9\u5e94 val \u5e76\u8fd4\u56de\nfor (Pair *pair : buckets[index]) {\nif (pair-&gt;key == key) {\npair-&gt;val = val;\nreturn;\n}\n}\n// \u82e5\u65e0\u8be5 key \uff0c\u5219\u5c06\u952e\u503c\u5bf9\u6dfb\u52a0\u81f3\u5c3e\u90e8\nbuckets[index].push_back(new Pair(key, val));\nsize++;\n}\n/* \u5220\u9664\u64cd\u4f5c */\nvoid remove(int key) {\nint index = hashFunc(key);\nauto &amp;bucket = buckets[index];\n// \u904d\u5386\u6876\uff0c\u4ece\u4e2d\u5220\u9664\u952e\u503c\u5bf9\nfor (int i = 0; i &lt; bucket.size(); i++) {\nif (bucket[i]-&gt;key == key) {\nPair *tmp = bucket[i];\nbucket.erase(bucket.begin() + i); // \u4ece\u4e2d\u5220\u9664\u952e\u503c\u5bf9\ndelete tmp;                       // \u91ca\u653e\u5185\u5b58\nsize--;\nreturn;\n}\n}\n}\n/* \u6269\u5bb9\u54c8\u5e0c\u8868 */\nvoid extend() {\n// \u6682\u5b58\u539f\u54c8\u5e0c\u8868\nvector&lt;vector&lt;Pair *&gt;&gt; bucketsTmp = buckets;\n// \u521d\u59cb\u5316\u6269\u5bb9\u540e\u7684\u65b0\u54c8\u5e0c\u8868\ncapacity *= extendRatio;\nbuckets.clear();\nbuckets.resize(capacity);\nsize = 0;\n// \u5c06\u952e\u503c\u5bf9\u4ece\u539f\u54c8\u5e0c\u8868\u642c\u8fd0\u81f3\u65b0\u54c8\u5e0c\u8868\nfor (auto &amp;bucket : bucketsTmp) {\nfor (Pair *pair : bucket) {\nput(pair-&gt;key, pair-&gt;val);\n}\n}\n}\n/* \u6253\u5370\u54c8\u5e0c\u8868 */\nvoid print() {\nfor (auto &amp;bucket : buckets) {\ncout &lt;&lt; \"[\";\nfor (Pair *pair : bucket) {\ncout &lt;&lt; pair-&gt;key &lt;&lt; \" -&gt; \" &lt;&lt; pair-&gt;val &lt;&lt; \", \";\n}\ncout &lt;&lt; \"]\\n\";\n}\n}\n};\n</code></pre> hash_map_chaining.py<pre><code>class Pair:\n\"\"\"\u952e\u503c\u5bf9\"\"\"\ndef __init__(self, key: int, val: str):\nself.key = key\nself.val = val\nclass HashMapChaining:\n\"\"\"\u94fe\u5f0f\u5730\u5740\u54c8\u5e0c\u8868\"\"\"\ndef __init__(self):\n\"\"\"\u6784\u9020\u65b9\u6cd5\"\"\"\nself.size = 0  # \u952e\u503c\u5bf9\u6570\u91cf\nself.capacity = 4  # \u54c8\u5e0c\u8868\u5bb9\u91cf\nself.load_thres = 2 / 3  # \u89e6\u53d1\u6269\u5bb9\u7684\u8d1f\u8f7d\u56e0\u5b50\u9608\u503c\nself.extend_ratio = 2  # \u6269\u5bb9\u500d\u6570\nself.buckets = [[] for _ in range(self.capacity)]  # \u6876\u6570\u7ec4\ndef hash_func(self, key: int) -&gt; int:\n\"\"\"\u54c8\u5e0c\u51fd\u6570\"\"\"\nreturn key % self.capacity\ndef load_factor(self) -&gt; float:\n\"\"\"\u8d1f\u8f7d\u56e0\u5b50\"\"\"\nreturn self.size / self.capacity\ndef get(self, key: int) -&gt; str:\n\"\"\"\u67e5\u8be2\u64cd\u4f5c\"\"\"\nindex = self.hash_func(key)\nbucket = self.buckets[index]\n# \u904d\u5386\u6876\uff0c\u82e5\u627e\u5230 key \u5219\u8fd4\u56de\u5bf9\u5e94 val\nfor pair in bucket:\nif pair.key == key:\nreturn pair.val\n# \u82e5\u672a\u627e\u5230 key \u5219\u8fd4\u56de None\nreturn None\ndef put(self, key: int, val: str):\n\"\"\"\u6dfb\u52a0\u64cd\u4f5c\"\"\"\n# \u5f53\u8d1f\u8f7d\u56e0\u5b50\u8d85\u8fc7\u9608\u503c\u65f6\uff0c\u6267\u884c\u6269\u5bb9\nif self.load_factor() &gt; self.load_thres:\nself.extend()\nindex = self.hash_func(key)\nbucket = self.buckets[index]\n# \u904d\u5386\u6876\uff0c\u82e5\u9047\u5230\u6307\u5b9a key \uff0c\u5219\u66f4\u65b0\u5bf9\u5e94 val \u5e76\u8fd4\u56de\nfor pair in bucket:\nif pair.key == key:\npair.val = val\nreturn\n# \u82e5\u65e0\u8be5 key \uff0c\u5219\u5c06\u952e\u503c\u5bf9\u6dfb\u52a0\u81f3\u5c3e\u90e8\npair = Pair(key, val)\nbucket.append(pair)\nself.size += 1\ndef remove(self, key: int):\n\"\"\"\u5220\u9664\u64cd\u4f5c\"\"\"\nindex = self.hash_func(key)\nbucket = self.buckets[index]\n# \u904d\u5386\u6876\uff0c\u4ece\u4e2d\u5220\u9664\u952e\u503c\u5bf9\nfor pair in bucket:\nif pair.key == key:\nbucket.remove(pair)\nself.size -= 1\nreturn\ndef extend(self):\n\"\"\"\u6269\u5bb9\u54c8\u5e0c\u8868\"\"\"\n# \u6682\u5b58\u539f\u54c8\u5e0c\u8868\nbuckets = self.buckets\n# \u521d\u59cb\u5316\u6269\u5bb9\u540e\u7684\u65b0\u54c8\u5e0c\u8868\nself.capacity *= self.extend_ratio\nself.buckets = [[] for _ in range(self.capacity)]\nself.size = 0\n# \u5c06\u952e\u503c\u5bf9\u4ece\u539f\u54c8\u5e0c\u8868\u642c\u8fd0\u81f3\u65b0\u54c8\u5e0c\u8868\nfor bucket in buckets:\nfor pair in bucket:\nself.put(pair.key, pair.val)\ndef print(self):\n\"\"\"\u6253\u5370\u54c8\u5e0c\u8868\"\"\"\nfor bucket in self.buckets:\nres = []\nfor pair in bucket:\nres.append(str(pair.key) + \" -&gt; \" + pair.val)\nprint(res)\n</code></pre> hash_map_chaining.go<pre><code>[class]{pair}-[func]{}\n[class]{hashMapChaining}-[func]{}\n</code></pre> hash_map_chaining.js<pre><code>[class]{Pair}-[func]{}\n[class]{HashMapChaining}-[func]{}\n</code></pre> hash_map_chaining.ts<pre><code>[class]{Pair}-[func]{}\n[class]{HashMapChaining}-[func]{}\n</code></pre> hash_map_chaining.c<pre><code>[class]{pair}-[func]{}\n[class]{hashMapChaining}-[func]{}\n</code></pre> hash_map_chaining.cs<pre><code>[class]{Pair}-[func]{}\n[class]{HashMapChaining}-[func]{}\n</code></pre> hash_map_chaining.swift<pre><code>[class]{Pair}-[func]{}\n[class]{HashMapChaining}-[func]{}\n</code></pre> hash_map_chaining.zig<pre><code>[class]{Pair}-[func]{}\n[class]{HashMapChaining}-[func]{}\n</code></pre> hash_map_chaining.dart<pre><code>[class]{Pair}-[func]{}\n[class]{HashMapChaining}-[func]{}\n</code></pre> <p>Tip</p> <p>\u4e3a\u4e86\u63d0\u9ad8\u6548\u7387\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u94fe\u8868\u8f6c\u6362\u4e3a\u300cAVL \u6811\u300d\u6216\u300c\u7ea2\u9ed1\u6811\u300d\uff0c\u4ece\u800c\u5c06\u67e5\u8be2\u64cd\u4f5c\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4f18\u5316\u81f3 \\(O(\\log n)\\) \u3002</p>"},{"location":"chapter_hashing/hash_collision/#623","title":"6.2.3. \u00a0 \u5f00\u653e\u5bfb\u5740","text":"<p>\u300c\u5f00\u653e\u5bfb\u5740 Open Addressing\u300d\u4e0d\u5f15\u5165\u989d\u5916\u7684\u6570\u636e\u7ed3\u6784\uff0c\u800c\u662f\u901a\u8fc7\u201c\u591a\u6b21\u63a2\u6d4b\u201d\u6765\u89e3\u51b3\u54c8\u5e0c\u51b2\u7a81\uff0c\u63a2\u6d4b\u65b9\u5f0f\u4e3b\u8981\u5305\u62ec\u7ebf\u6027\u63a2\u6d4b\u3001\u5e73\u65b9\u63a2\u6d4b\u3001\u591a\u6b21\u54c8\u5e0c\u3002</p>"},{"location":"chapter_hashing/hash_collision/#_1","title":"\u7ebf\u6027\u63a2\u6d4b","text":"<p>\u7ebf\u6027\u63a2\u6d4b\u91c7\u7528\u56fa\u5b9a\u6b65\u957f\u7684\u7ebf\u6027\u67e5\u627e\u6765\u89e3\u51b3\u54c8\u5e0c\u51b2\u7a81\u3002</p> <ul> <li>\u63d2\u5165\u5143\u7d20\uff1a\u901a\u8fc7\u54c8\u5e0c\u51fd\u6570\u8ba1\u7b97\u6570\u7ec4\u7d22\u5f15\uff0c\u82e5\u53d1\u73b0\u6876\u5185\u5df2\u6709\u5143\u7d20\uff0c\u5219\u4ece\u51b2\u7a81\u4f4d\u7f6e\u5411\u540e\u7ebf\u6027\u904d\u5386\uff08\u6b65\u957f\u901a\u5e38\u4e3a \\(1\\) \uff09\uff0c\u76f4\u81f3\u627e\u5230\u7a7a\u4f4d\uff0c\u5c06\u5143\u7d20\u63d2\u5165\u5176\u4e2d\u3002</li> <li>\u67e5\u627e\u5143\u7d20\uff1a\u82e5\u53d1\u73b0\u54c8\u5e0c\u51b2\u7a81\uff0c\u5219\u4f7f\u7528\u76f8\u540c\u6b65\u957f\u5411\u540e\u7ebf\u6027\u904d\u5386\uff0c\u76f4\u5230\u627e\u5230\u5bf9\u5e94\u5143\u7d20\uff0c\u8fd4\u56de value \u5373\u53ef\uff1b\u6216\u8005\u82e5\u9047\u5230\u7a7a\u4f4d\uff0c\u8bf4\u660e\u76ee\u6807\u952e\u503c\u5bf9\u4e0d\u5728\u54c8\u5e0c\u8868\u4e2d\uff0c\u8fd4\u56de \\(\\text{None}\\) \u3002</li> </ul> <p></p> <p> Fig. \u7ebf\u6027\u63a2\u6d4b </p> <p>\u7136\u800c\uff0c\u7ebf\u6027\u63a2\u6d4b\u5b58\u5728\u4ee5\u4e0b\u7f3a\u9677\uff1a</p> <ul> <li>\u4e0d\u80fd\u76f4\u63a5\u5220\u9664\u5143\u7d20\u3002\u5220\u9664\u5143\u7d20\u4f1a\u5728\u6570\u7ec4\u5185\u4ea7\u751f\u4e00\u4e2a\u7a7a\u4f4d\uff0c\u67e5\u627e\u5176\u4ed6\u5143\u7d20\u65f6\uff0c\u8be5\u7a7a\u4f4d\u53ef\u80fd\u5bfc\u81f4\u7a0b\u5e8f\u8bef\u5224\u5143\u7d20\u4e0d\u5b58\u5728\u3002\u56e0\u6b64\uff0c\u9700\u8981\u501f\u52a9\u4e00\u4e2a\u6807\u5fd7\u4f4d\u6765\u6807\u8bb0\u5df2\u5220\u9664\u5143\u7d20\u3002</li> <li>\u5bb9\u6613\u4ea7\u751f\u805a\u96c6\u3002\u6570\u7ec4\u5185\u8fde\u7eed\u88ab\u5360\u7528\u4f4d\u7f6e\u8d8a\u957f\uff0c\u8fd9\u4e9b\u8fde\u7eed\u4f4d\u7f6e\u53d1\u751f\u54c8\u5e0c\u51b2\u7a81\u7684\u53ef\u80fd\u6027\u8d8a\u5927\uff0c\u8fdb\u4e00\u6b65\u4fc3\u4f7f\u8fd9\u4e00\u4f4d\u7f6e\u7684\u201c\u805a\u5806\u751f\u957f\u201d\uff0c\u6700\u7ec8\u5bfc\u81f4\u589e\u5220\u67e5\u6539\u64cd\u4f5c\u6548\u7387\u964d\u4f4e\u3002</li> </ul> <p>\u5982\u4ee5\u4e0b\u4ee3\u7801\u6240\u793a\uff0c\u4e3a\u5f00\u653e\u5bfb\u5740\uff08\u7ebf\u6027\u63a2\u6d4b\uff09\u54c8\u5e0c\u8868\u7684\u7b80\u5355\u5b9e\u73b0\uff0c\u91cd\u70b9\u5305\u62ec\uff1a</p> <ul> <li>\u6211\u4eec\u4f7f\u7528\u4e00\u4e2a\u56fa\u5b9a\u7684\u952e\u503c\u5bf9\u5b9e\u4f8b <code>removed</code> \u6765\u6807\u8bb0\u5df2\u5220\u9664\u5143\u7d20\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u5f53\u4e00\u4e2a\u6876\u4e3a \\(\\text{None}\\) \u6216 <code>removed</code> \u65f6\uff0c\u8fd9\u4e2a\u6876\u90fd\u662f\u7a7a\u7684\uff0c\u53ef\u7528\u4e8e\u653e\u7f6e\u952e\u503c\u5bf9\u3002</li> <li>\u88ab\u6807\u8bb0\u4e3a\u5df2\u5220\u9664\u7684\u7a7a\u95f4\u662f\u53ef\u4ee5\u518d\u6b21\u88ab\u4f7f\u7528\u7684\u3002\u5f53\u63d2\u5165\u5143\u7d20\u65f6\uff0c\u82e5\u901a\u8fc7\u54c8\u5e0c\u51fd\u6570\u627e\u5230\u4e86\u88ab\u6807\u8bb0\u4e3a\u5df2\u5220\u9664\u7684\u7d22\u5f15\uff0c\u5219\u53ef\u5c06\u8be5\u5143\u7d20\u653e\u7f6e\u5230\u8be5\u7d22\u5f15\u3002</li> <li>\u5728\u7ebf\u6027\u63a2\u6d4b\u65f6\uff0c\u6211\u4eec\u4ece\u5f53\u524d\u7d22\u5f15 <code>index</code> \u5411\u540e\u904d\u5386\uff1b\u800c\u5f53\u8d8a\u8fc7\u6570\u7ec4\u5c3e\u90e8\u65f6\uff0c\u9700\u8981\u56de\u5230\u5934\u90e8\u7ee7\u7eed\u904d\u5386\u3002</li> </ul> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart hash_map_open_addressing.java<pre><code>/* \u952e\u503c\u5bf9 */\nclass Pair {\npublic int key;\npublic String val;\npublic Pair(int key, String val) {\nthis.key = key;\nthis.val = val;\n}\n}\n/* \u5f00\u653e\u5bfb\u5740\u54c8\u5e0c\u8868 */\nclass HashMapOpenAddressing {\nprivate int size; // \u952e\u503c\u5bf9\u6570\u91cf\nprivate int capacity; // \u54c8\u5e0c\u8868\u5bb9\u91cf\nprivate double loadThres; // \u89e6\u53d1\u6269\u5bb9\u7684\u8d1f\u8f7d\u56e0\u5b50\u9608\u503c\nprivate int extendRatio; // \u6269\u5bb9\u500d\u6570\nprivate Pair[] buckets; // \u6876\u6570\u7ec4\nprivate Pair removed; // \u5220\u9664\u6807\u8bb0\n/* \u6784\u9020\u65b9\u6cd5 */\npublic HashMapOpenAddressing() {\nsize = 0;\ncapacity = 4;\nloadThres = 2.0 / 3.0;\nextendRatio = 2;\nbuckets = new Pair[capacity];\nremoved = new Pair(-1, \"-1\");\n}\n/* \u54c8\u5e0c\u51fd\u6570 */\npublic int hashFunc(int key) {\nreturn key % capacity;\n}\n/* \u8d1f\u8f7d\u56e0\u5b50 */\npublic double loadFactor() {\nreturn (double) size / capacity;\n}\n/* \u67e5\u8be2\u64cd\u4f5c */\npublic String get(int key) {\nint index = hashFunc(key);\n// \u7ebf\u6027\u63a2\u6d4b\uff0c\u4ece index \u5f00\u59cb\u5411\u540e\u904d\u5386\nfor (int i = 0; i &lt; capacity; i++) {\n// \u8ba1\u7b97\u6876\u7d22\u5f15\uff0c\u8d8a\u8fc7\u5c3e\u90e8\u8fd4\u56de\u5934\u90e8\nint j = (index + i) % capacity;\n// \u82e5\u9047\u5230\u7a7a\u6876\uff0c\u8bf4\u660e\u65e0\u6b64 key \uff0c\u5219\u8fd4\u56de null\nif (buckets[j] == null)\nreturn null;\n// \u82e5\u9047\u5230\u6307\u5b9a key \uff0c\u5219\u8fd4\u56de\u5bf9\u5e94 val\nif (buckets[j].key == key &amp;&amp; buckets[j] != removed)\nreturn buckets[j].val;\n}\nreturn null;\n}\n/* \u6dfb\u52a0\u64cd\u4f5c */\npublic void put(int key, String val) {\n// \u5f53\u8d1f\u8f7d\u56e0\u5b50\u8d85\u8fc7\u9608\u503c\u65f6\uff0c\u6267\u884c\u6269\u5bb9\nif (loadFactor() &gt; loadThres) {\nextend();\n}\nint index = hashFunc(key);\n// \u7ebf\u6027\u63a2\u6d4b\uff0c\u4ece index \u5f00\u59cb\u5411\u540e\u904d\u5386\nfor (int i = 0; i &lt; capacity; i++) {\n// \u8ba1\u7b97\u6876\u7d22\u5f15\uff0c\u8d8a\u8fc7\u5c3e\u90e8\u8fd4\u56de\u5934\u90e8\nint j = (index + i) % capacity;\n// \u82e5\u9047\u5230\u7a7a\u6876\u3001\u6216\u5e26\u6709\u5220\u9664\u6807\u8bb0\u7684\u6876\uff0c\u5219\u5c06\u952e\u503c\u5bf9\u653e\u5165\u8be5\u6876\nif (buckets[j] == null || buckets[j] == removed) {\nbuckets[j] = new Pair(key, val);\nsize += 1;\nreturn;\n}\n// \u82e5\u9047\u5230\u6307\u5b9a key \uff0c\u5219\u66f4\u65b0\u5bf9\u5e94 val\nif (buckets[j].key == key) {\nbuckets[j].val = val;\nreturn;\n}\n}\n}\n/* \u5220\u9664\u64cd\u4f5c */\npublic void remove(int key) {\nint index = hashFunc(key);\n// \u7ebf\u6027\u63a2\u6d4b\uff0c\u4ece index \u5f00\u59cb\u5411\u540e\u904d\u5386\nfor (int i = 0; i &lt; capacity; i++) {\n// \u8ba1\u7b97\u6876\u7d22\u5f15\uff0c\u8d8a\u8fc7\u5c3e\u90e8\u8fd4\u56de\u5934\u90e8\nint j = (index + i) % capacity;\n// \u82e5\u9047\u5230\u7a7a\u6876\uff0c\u8bf4\u660e\u65e0\u6b64 key \uff0c\u5219\u76f4\u63a5\u8fd4\u56de\nif (buckets[j] == null) {\nreturn;\n}\n// \u82e5\u9047\u5230\u6307\u5b9a key \uff0c\u5219\u6807\u8bb0\u5220\u9664\u5e76\u8fd4\u56de\nif (buckets[j].key == key) {\nbuckets[j] = removed;\nsize -= 1;\nreturn;\n}\n}\n}\n/* \u6269\u5bb9\u54c8\u5e0c\u8868 */\npublic void extend() {\n// \u6682\u5b58\u539f\u54c8\u5e0c\u8868\nPair[] bucketsTmp = buckets;\n// \u521d\u59cb\u5316\u6269\u5bb9\u540e\u7684\u65b0\u54c8\u5e0c\u8868\ncapacity *= extendRatio;\nbuckets = new Pair[capacity];\nsize = 0;\n// \u5c06\u952e\u503c\u5bf9\u4ece\u539f\u54c8\u5e0c\u8868\u642c\u8fd0\u81f3\u65b0\u54c8\u5e0c\u8868\nfor (Pair pair : bucketsTmp) {\nif (pair != null &amp;&amp; pair != removed) {\nput(pair.key, pair.val);\n}\n}\n}\n/* \u6253\u5370\u54c8\u5e0c\u8868 */\npublic void print() {\nfor (Pair pair : buckets) {\nif (pair != null) {\nSystem.out.println(pair.key + \" -&gt; \" + pair.val);\n} else {\nSystem.out.println(\"null\");\n}\n}\n}\n}\n</code></pre> hash_map_open_addressing.cpp<pre><code>/* \u952e\u503c\u5bf9 */\nstruct Pair {\nint key;\nstring val;\nPair(int k, string v) : key(k), val(v) {\n}\n};\n/* \u5f00\u653e\u5bfb\u5740\u54c8\u5e0c\u8868 */\nclass HashMapOpenAddressing {\nprivate:\nint size;               // \u952e\u503c\u5bf9\u6570\u91cf\nint capacity;           // \u54c8\u5e0c\u8868\u5bb9\u91cf\ndouble loadThres;       // \u89e6\u53d1\u6269\u5bb9\u7684\u8d1f\u8f7d\u56e0\u5b50\u9608\u503c\nint extendRatio;        // \u6269\u5bb9\u500d\u6570\nvector&lt;Pair *&gt; buckets; // \u6876\u6570\u7ec4\nPair *removed;          // \u5220\u9664\u6807\u8bb0\npublic:\n/* \u6784\u9020\u65b9\u6cd5 */\nHashMapOpenAddressing() {\n// \u6784\u9020\u65b9\u6cd5\nsize = 0;\ncapacity = 4;\nloadThres = 2.0 / 3.0;\nextendRatio = 2;\nbuckets = vector&lt;Pair *&gt;(capacity, nullptr);\nremoved = new Pair(-1, \"-1\");\n}\n/* \u54c8\u5e0c\u51fd\u6570 */\nint hashFunc(int key) {\nreturn key % capacity;\n}\n/* \u8d1f\u8f7d\u56e0\u5b50 */\ndouble loadFactor() {\nreturn static_cast&lt;double&gt;(size) / capacity;\n}\n/* \u67e5\u8be2\u64cd\u4f5c */\nstring get(int key) {\nint index = hashFunc(key);\n// \u7ebf\u6027\u63a2\u6d4b\uff0c\u4ece index \u5f00\u59cb\u5411\u540e\u904d\u5386\nfor (int i = 0; i &lt; capacity; i++) {\n// \u8ba1\u7b97\u6876\u7d22\u5f15\uff0c\u8d8a\u8fc7\u5c3e\u90e8\u8fd4\u56de\u5934\u90e8\nint j = (index + i) % capacity;\n// \u82e5\u9047\u5230\u7a7a\u6876\uff0c\u8bf4\u660e\u65e0\u6b64 key \uff0c\u5219\u8fd4\u56de nullptr\nif (buckets[j] == nullptr)\nreturn nullptr;\n// \u82e5\u9047\u5230\u6307\u5b9a key \uff0c\u5219\u8fd4\u56de\u5bf9\u5e94 val\nif (buckets[j]-&gt;key == key &amp;&amp; buckets[j] != removed)\nreturn buckets[j]-&gt;val;\n}\nreturn nullptr;\n}\n/* \u6dfb\u52a0\u64cd\u4f5c */\nvoid put(int key, string val) {\n// \u5f53\u8d1f\u8f7d\u56e0\u5b50\u8d85\u8fc7\u9608\u503c\u65f6\uff0c\u6267\u884c\u6269\u5bb9\nif (loadFactor() &gt; loadThres)\nextend();\nint index = hashFunc(key);\n// \u7ebf\u6027\u63a2\u6d4b\uff0c\u4ece index \u5f00\u59cb\u5411\u540e\u904d\u5386\nfor (int i = 0; i &lt; capacity; i++) {\n// \u8ba1\u7b97\u6876\u7d22\u5f15\uff0c\u8d8a\u8fc7\u5c3e\u90e8\u8fd4\u56de\u5934\u90e8\nint j = (index + i) % capacity;\n// \u82e5\u9047\u5230\u7a7a\u6876\u3001\u6216\u5e26\u6709\u5220\u9664\u6807\u8bb0\u7684\u6876\uff0c\u5219\u5c06\u952e\u503c\u5bf9\u653e\u5165\u8be5\u6876\nif (buckets[j] == nullptr || buckets[j] == removed) {\nbuckets[j] = new Pair(key, val);\nsize += 1;\nreturn;\n}\n// \u82e5\u9047\u5230\u6307\u5b9a key \uff0c\u5219\u66f4\u65b0\u5bf9\u5e94 val\nif (buckets[j]-&gt;key == key) {\nbuckets[j]-&gt;val = val;\nreturn;\n}\n}\n}\n/* \u5220\u9664\u64cd\u4f5c */\nvoid remove(int key) {\nint index = hashFunc(key);\n// \u7ebf\u6027\u63a2\u6d4b\uff0c\u4ece index \u5f00\u59cb\u5411\u540e\u904d\u5386\nfor (int i = 0; i &lt; capacity; i++) {\n// \u8ba1\u7b97\u6876\u7d22\u5f15\uff0c\u8d8a\u8fc7\u5c3e\u90e8\u8fd4\u56de\u5934\u90e8\nint j = (index + i) % capacity;\n// \u82e5\u9047\u5230\u7a7a\u6876\uff0c\u8bf4\u660e\u65e0\u6b64 key \uff0c\u5219\u76f4\u63a5\u8fd4\u56de\nif (buckets[j] == nullptr)\nreturn;\n// \u82e5\u9047\u5230\u6307\u5b9a key \uff0c\u5219\u6807\u8bb0\u5220\u9664\u5e76\u8fd4\u56de\nif (buckets[j]-&gt;key == key) {\ndelete buckets[j]; // \u91ca\u653e\u5185\u5b58\nbuckets[j] = removed;\nsize -= 1;\nreturn;\n}\n}\n}\n/* \u6269\u5bb9\u54c8\u5e0c\u8868 */\nvoid extend() {\n// \u6682\u5b58\u539f\u54c8\u5e0c\u8868\nvector&lt;Pair *&gt; bucketsTmp = buckets;\n// \u521d\u59cb\u5316\u6269\u5bb9\u540e\u7684\u65b0\u54c8\u5e0c\u8868\ncapacity *= extendRatio;\nbuckets = vector&lt;Pair *&gt;(capacity, nullptr);\nsize = 0;\n// \u5c06\u952e\u503c\u5bf9\u4ece\u539f\u54c8\u5e0c\u8868\u642c\u8fd0\u81f3\u65b0\u54c8\u5e0c\u8868\nfor (Pair *pair : bucketsTmp) {\nif (pair != nullptr &amp;&amp; pair != removed) {\nput(pair-&gt;key, pair-&gt;val);\n}\n}\n}\n/* \u6253\u5370\u54c8\u5e0c\u8868 */\nvoid print() {\nfor (auto &amp;pair : buckets) {\nif (pair != nullptr) {\ncout &lt;&lt; pair-&gt;key &lt;&lt; \" -&gt; \" &lt;&lt; pair-&gt;val &lt;&lt; endl;\n} else {\ncout &lt;&lt; \"nullptr\" &lt;&lt; endl;\n}\n}\n}\n};\n</code></pre> hash_map_open_addressing.py<pre><code>class Pair:\n\"\"\"\u952e\u503c\u5bf9\"\"\"\ndef __init__(self, key: int, val: str):\nself.key = key\nself.val = val\nclass HashMapOpenAddressing:\n\"\"\"\u5f00\u653e\u5bfb\u5740\u54c8\u5e0c\u8868\"\"\"\ndef __init__(self):\n\"\"\"\u6784\u9020\u65b9\u6cd5\"\"\"\nself.size = 0  # \u952e\u503c\u5bf9\u6570\u91cf\nself.capacity = 4  # \u54c8\u5e0c\u8868\u5bb9\u91cf\nself.load_thres = 2 / 3  # \u89e6\u53d1\u6269\u5bb9\u7684\u8d1f\u8f7d\u56e0\u5b50\u9608\u503c\nself.extend_ratio = 2  # \u6269\u5bb9\u500d\u6570\nself.buckets: list[Pair | None] = [None] * self.capacity  # \u6876\u6570\u7ec4\nself.removed = Pair(-1, \"-1\")  # \u5220\u9664\u6807\u8bb0\ndef hash_func(self, key: int) -&gt; int:\n\"\"\"\u54c8\u5e0c\u51fd\u6570\"\"\"\nreturn key % self.capacity\ndef load_factor(self) -&gt; float:\n\"\"\"\u8d1f\u8f7d\u56e0\u5b50\"\"\"\nreturn self.size / self.capacity\ndef get(self, key: int) -&gt; str:\n\"\"\"\u67e5\u8be2\u64cd\u4f5c\"\"\"\nindex = self.hash_func(key)\n# \u7ebf\u6027\u63a2\u6d4b\uff0c\u4ece index \u5f00\u59cb\u5411\u540e\u904d\u5386\nfor i in range(self.capacity):\n# \u8ba1\u7b97\u6876\u7d22\u5f15\uff0c\u8d8a\u8fc7\u5c3e\u90e8\u8fd4\u56de\u5934\u90e8\nj = (index + i) % self.capacity\n# \u82e5\u9047\u5230\u7a7a\u6876\uff0c\u8bf4\u660e\u65e0\u6b64 key \uff0c\u5219\u8fd4\u56de None\nif self.buckets[j] is None:\nreturn None\n# \u82e5\u9047\u5230\u6307\u5b9a key \uff0c\u5219\u8fd4\u56de\u5bf9\u5e94 val\nif self.buckets[j].key == key and self.buckets[j] != self.removed:\nreturn self.buckets[j].val\ndef put(self, key: int, val: str):\n\"\"\"\u6dfb\u52a0\u64cd\u4f5c\"\"\"\n# \u5f53\u8d1f\u8f7d\u56e0\u5b50\u8d85\u8fc7\u9608\u503c\u65f6\uff0c\u6267\u884c\u6269\u5bb9\nif self.load_factor() &gt; self.load_thres:\nself.extend()\nindex = self.hash_func(key)\n# \u7ebf\u6027\u63a2\u6d4b\uff0c\u4ece index \u5f00\u59cb\u5411\u540e\u904d\u5386\nfor i in range(self.capacity):\n# \u8ba1\u7b97\u6876\u7d22\u5f15\uff0c\u8d8a\u8fc7\u5c3e\u90e8\u8fd4\u56de\u5934\u90e8\nj = (index + i) % self.capacity\n# \u82e5\u9047\u5230\u7a7a\u6876\u3001\u6216\u5e26\u6709\u5220\u9664\u6807\u8bb0\u7684\u6876\uff0c\u5219\u5c06\u952e\u503c\u5bf9\u653e\u5165\u8be5\u6876\nif self.buckets[j] in [None, self.removed]:\nself.buckets[j] = Pair(key, val)\nself.size += 1\nreturn\n# \u82e5\u9047\u5230\u6307\u5b9a key \uff0c\u5219\u66f4\u65b0\u5bf9\u5e94 val\nif self.buckets[j].key == key:\nself.buckets[j].val = val\nreturn\ndef remove(self, key: int):\n\"\"\"\u5220\u9664\u64cd\u4f5c\"\"\"\nindex = self.hash_func(key)\n# \u7ebf\u6027\u63a2\u6d4b\uff0c\u4ece index \u5f00\u59cb\u5411\u540e\u904d\u5386\nfor i in range(self.capacity):\n# \u8ba1\u7b97\u6876\u7d22\u5f15\uff0c\u8d8a\u8fc7\u5c3e\u90e8\u8fd4\u56de\u5934\u90e8\nj = (index + i) % self.capacity\n# \u82e5\u9047\u5230\u7a7a\u6876\uff0c\u8bf4\u660e\u65e0\u6b64 key \uff0c\u5219\u76f4\u63a5\u8fd4\u56de\nif self.buckets[j] is None:\nreturn\n# \u82e5\u9047\u5230\u6307\u5b9a key \uff0c\u5219\u6807\u8bb0\u5220\u9664\u5e76\u8fd4\u56de\nif self.buckets[j].key == key:\nself.buckets[j] = self.removed\nself.size -= 1\nreturn\ndef extend(self):\n\"\"\"\u6269\u5bb9\u54c8\u5e0c\u8868\"\"\"\n# \u6682\u5b58\u539f\u54c8\u5e0c\u8868\nbuckets_tmp = self.buckets\n# \u521d\u59cb\u5316\u6269\u5bb9\u540e\u7684\u65b0\u54c8\u5e0c\u8868\nself.capacity *= self.extend_ratio\nself.buckets = [None] * self.capacity\nself.size = 0\n# \u5c06\u952e\u503c\u5bf9\u4ece\u539f\u54c8\u5e0c\u8868\u642c\u8fd0\u81f3\u65b0\u54c8\u5e0c\u8868\nfor pair in buckets_tmp:\nif pair not in [None, self.removed]:\nself.put(pair.key, pair.val)\ndef print(self) -&gt; None:\n\"\"\"\u6253\u5370\u54c8\u5e0c\u8868\"\"\"\nfor pair in self.buckets:\nif pair is not None:\nprint(pair.key, \"-&gt;\", pair.val)\nelse:\nprint(\"None\")\n</code></pre> hash_map_open_addressing.go<pre><code>[class]{pair}-[func]{}\n[class]{hashMapOpenAddressing}-[func]{}\n</code></pre> hash_map_open_addressing.js<pre><code>[class]{Pair}-[func]{}\n[class]{HashMapOpenAddressing}-[func]{}\n</code></pre> hash_map_open_addressing.ts<pre><code>[class]{Pair}-[func]{}\n[class]{HashMapOpenAddressing}-[func]{}\n</code></pre> hash_map_open_addressing.c<pre><code>[class]{pair}-[func]{}\n[class]{hashMapOpenAddressing}-[func]{}\n</code></pre> hash_map_open_addressing.cs<pre><code>[class]{Pair}-[func]{}\n[class]{HashMapOpenAddressing}-[func]{}\n</code></pre> hash_map_open_addressing.swift<pre><code>[class]{Pair}-[func]{}\n[class]{HashMapOpenAddressing}-[func]{}\n</code></pre> hash_map_open_addressing.zig<pre><code>[class]{Pair}-[func]{}\n[class]{HashMapOpenAddressing}-[func]{}\n</code></pre> hash_map_open_addressing.dart<pre><code>[class]{Pair}-[func]{}\n[class]{HashMapOpenAddressing}-[func]{}\n</code></pre>"},{"location":"chapter_hashing/hash_collision/#_2","title":"\u591a\u6b21\u54c8\u5e0c","text":"<p>\u987e\u540d\u601d\u4e49\uff0c\u591a\u6b21\u54c8\u5e0c\u65b9\u6cd5\u662f\u4f7f\u7528\u591a\u4e2a\u54c8\u5e0c\u51fd\u6570 \\(f_1(x)\\) , \\(f_2(x)\\) , \\(f_3(x)\\) , \\(\\cdots\\) \u8fdb\u884c\u63a2\u6d4b\u3002</p> <ul> <li>\u63d2\u5165\u5143\u7d20\uff1a\u82e5\u54c8\u5e0c\u51fd\u6570 \\(f_1(x)\\) \u51fa\u73b0\u51b2\u7a81\uff0c\u5219\u5c1d\u8bd5 \\(f_2(x)\\) \uff0c\u4ee5\u6b64\u7c7b\u63a8\uff0c\u76f4\u5230\u627e\u5230\u7a7a\u4f4d\u540e\u63d2\u5165\u5143\u7d20\u3002</li> <li>\u67e5\u627e\u5143\u7d20\uff1a\u5728\u76f8\u540c\u7684\u54c8\u5e0c\u51fd\u6570\u987a\u5e8f\u4e0b\u8fdb\u884c\u67e5\u627e\uff0c\u76f4\u5230\u627e\u5230\u76ee\u6807\u5143\u7d20\u65f6\u8fd4\u56de\uff1b\u6216\u9047\u5230\u7a7a\u4f4d\u6216\u5df2\u5c1d\u8bd5\u6240\u6709\u54c8\u5e0c\u51fd\u6570\uff0c\u8bf4\u660e\u54c8\u5e0c\u8868\u4e2d\u4e0d\u5b58\u5728\u8be5\u5143\u7d20\uff0c\u5219\u8fd4\u56de \\(\\text{None}\\) \u3002</li> </ul> <p>\u4e0e\u7ebf\u6027\u63a2\u6d4b\u76f8\u6bd4\uff0c\u591a\u6b21\u54c8\u5e0c\u65b9\u6cd5\u4e0d\u6613\u4ea7\u751f\u805a\u96c6\uff0c\u4f46\u591a\u4e2a\u54c8\u5e0c\u51fd\u6570\u4f1a\u589e\u52a0\u989d\u5916\u7684\u8ba1\u7b97\u91cf\u3002</p> <p>\u7f16\u7a0b\u8bed\u8a00\u7684\u9009\u62e9</p> <p>Java \u91c7\u7528\u94fe\u5f0f\u5730\u5740\u3002\u81ea JDK 1.8 \u4ee5\u6765\uff0c\u5f53 HashMap \u5185\u6570\u7ec4\u957f\u5ea6\u8fbe\u5230 64 \u4e14\u94fe\u8868\u957f\u5ea6\u8fbe\u5230 8 \u65f6\uff0c\u94fe\u8868\u4f1a\u88ab\u8f6c\u6362\u4e3a\u7ea2\u9ed1\u6811\u4ee5\u63d0\u5347\u67e5\u627e\u6027\u80fd\u3002</p> <p>Python \u91c7\u7528\u5f00\u653e\u5bfb\u5740\u3002\u5b57\u5178 dict \u4f7f\u7528\u4f2a\u968f\u673a\u6570\u8fdb\u884c\u63a2\u6d4b\u3002</p> <p>Golang \u91c7\u7528\u94fe\u5f0f\u5730\u5740\u3002Go \u89c4\u5b9a\u6bcf\u4e2a\u6876\u6700\u591a\u5b58\u50a8 8 \u4e2a\u952e\u503c\u5bf9\uff0c\u8d85\u51fa\u5bb9\u91cf\u5219\u8fde\u63a5\u4e00\u4e2a\u6ea2\u51fa\u6876\uff1b\u5f53\u6ea2\u51fa\u6876\u8fc7\u591a\u65f6\uff0c\u4f1a\u6267\u884c\u4e00\u6b21\u7279\u6b8a\u7684\u7b49\u91cf\u6269\u5bb9\u64cd\u4f5c\uff0c\u4ee5\u786e\u4fdd\u6027\u80fd\u3002</p>"},{"location":"chapter_hashing/hash_map/","title":"6.1. \u00a0 \u54c8\u5e0c\u8868","text":"<p>\u54c8\u5e0c\u8868\u901a\u8fc7\u5efa\u7acb\u300c\u952e key\u300d\u4e0e\u300c\u503c value\u300d\u4e4b\u95f4\u7684\u6620\u5c04\uff0c\u5b9e\u73b0\u9ad8\u6548\u7684\u5143\u7d20\u67e5\u8be2\u3002\u5177\u4f53\u800c\u8a00\uff0c\u6211\u4eec\u5411\u54c8\u5e0c\u8868\u8f93\u5165\u4e00\u4e2a key\uff0c\u5219\u53ef\u4ee5\u5728 \\(O(1)\\) \u65f6\u95f4\u5185\u83b7\u53d6\u5bf9\u5e94\u7684 value \u3002</p> <p>\u4ee5\u4e00\u4e2a\u5305\u542b \\(n\\) \u4e2a\u5b66\u751f\u7684\u6570\u636e\u5e93\u4e3a\u4f8b\uff0c\u6bcf\u4e2a\u5b66\u751f\u90fd\u6709\u201c\u59d3\u540d <code>name</code>\u201d\u548c\u201c\u5b66\u53f7 <code>id</code>\u201d\u4e24\u9879\u6570\u636e\u3002\u5047\u5982\u6211\u4eec\u5e0c\u671b\u5b9e\u73b0\u67e5\u8be2\u529f\u80fd\uff0c\u4f8b\u5982\u201c\u8f93\u5165\u4e00\u4e2a\u5b66\u53f7\uff0c\u8fd4\u56de\u5bf9\u5e94\u7684\u59d3\u540d\u201d\uff0c\u5219\u53ef\u4ee5\u91c7\u7528\u54c8\u5e0c\u8868\u6765\u5b9e\u73b0\u3002</p> <p></p> <p> Fig. \u54c8\u5e0c\u8868\u7684\u62bd\u8c61\u8868\u793a </p> <p>\u9664\u54c8\u5e0c\u8868\u5916\uff0c\u6211\u4eec\u8fd8\u53ef\u4ee5\u4f7f\u7528\u6570\u7ec4\u6216\u94fe\u8868\u5b9e\u73b0\u5143\u7d20\u67e5\u8be2\uff0c\u5176\u4e2d\uff1a</p> <ul> <li>\u67e5\u8be2\u5143\u7d20\u9700\u8981\u904d\u5386\u6240\u6709\u5143\u7d20\uff0c\u4f7f\u7528 \\(O(n)\\) \u65f6\u95f4\uff1b</li> <li>\u6dfb\u52a0\u5143\u7d20\u4ec5\u9700\u6dfb\u52a0\u81f3\u5c3e\u90e8\u5373\u53ef\uff0c\u4f7f\u7528 \\(O(1)\\) \u65f6\u95f4\uff1b</li> <li>\u5220\u9664\u5143\u7d20\u9700\u8981\u5148\u67e5\u8be2\u518d\u5220\u9664\uff0c\u4f7f\u7528 \\(O(n)\\) \u65f6\u95f4\uff1b</li> </ul> <p>\u7136\u800c\uff0c\u5728\u54c8\u5e0c\u8868\u4e2d\u8fdb\u884c\u589e\u5220\u67e5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u90fd\u662f \\(O(1)\\) \u3002\u54c8\u5e0c\u8868\u5168\u9762\u80dc\u51fa\uff01\u56e0\u6b64\uff0c\u54c8\u5e0c\u8868\u5e38\u7528\u4e8e\u5bf9\u67e5\u627e\u6548\u7387\u8981\u6c42\u8f83\u9ad8\u7684\u573a\u666f\u3002</p> \u6570\u7ec4 \u94fe\u8868 \u54c8\u5e0c\u8868 \u67e5\u627e\u5143\u7d20 \\(O(n)\\) \\(O(n)\\) \\(O(1)\\) \u6dfb\u52a0\u5143\u7d20 \\(O(1)\\) \\(O(1)\\) \\(O(1)\\) \u5220\u9664\u5143\u7d20 \\(O(n)\\) \\(O(n)\\) \\(O(1)\\)"},{"location":"chapter_hashing/hash_map/#611","title":"6.1.1. \u00a0 \u54c8\u5e0c\u8868\u5e38\u7528\u64cd\u4f5c","text":"<p>\u54c8\u5e0c\u8868\u7684\u57fa\u672c\u64cd\u4f5c\u5305\u62ec \u521d\u59cb\u5316\u3001\u67e5\u8be2\u64cd\u4f5c\u3001\u6dfb\u52a0\u4e0e\u5220\u9664\u952e\u503c\u5bf9\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart hash_map.java<pre><code>/* \u521d\u59cb\u5316\u54c8\u5e0c\u8868 */\nMap&lt;Integer, String&gt; map = new HashMap&lt;&gt;();\n/* \u6dfb\u52a0\u64cd\u4f5c */\n// \u5728\u54c8\u5e0c\u8868\u4e2d\u6dfb\u52a0\u952e\u503c\u5bf9 (key, value)\nmap.put(12836, \"\u5c0f\u54c8\");   map.put(15937, \"\u5c0f\u5570\");   map.put(16750, \"\u5c0f\u7b97\");   map.put(13276, \"\u5c0f\u6cd5\");\nmap.put(10583, \"\u5c0f\u9e2d\");\n/* \u67e5\u8be2\u64cd\u4f5c */\n// \u5411\u54c8\u5e0c\u8868\u8f93\u5165\u952e key \uff0c\u5f97\u5230\u503c value\nString name = map.get(15937);\n/* \u5220\u9664\u64cd\u4f5c */\n// \u5728\u54c8\u5e0c\u8868\u4e2d\u5220\u9664\u952e\u503c\u5bf9 (key, value)\nmap.remove(10583);\n</code></pre> hash_map.cpp<pre><code>/* \u521d\u59cb\u5316\u54c8\u5e0c\u8868 */\nunordered_map&lt;int, string&gt; map;\n/* \u6dfb\u52a0\u64cd\u4f5c */\n// \u5728\u54c8\u5e0c\u8868\u4e2d\u6dfb\u52a0\u952e\u503c\u5bf9 (key, value)\nmap[12836] = \"\u5c0f\u54c8\";\nmap[15937] = \"\u5c0f\u5570\";\nmap[16750] = \"\u5c0f\u7b97\";\nmap[13276] = \"\u5c0f\u6cd5\";\nmap[10583] = \"\u5c0f\u9e2d\";\n/* \u67e5\u8be2\u64cd\u4f5c */\n// \u5411\u54c8\u5e0c\u8868\u8f93\u5165\u952e key \uff0c\u5f97\u5230\u503c value\nstring name = map[15937];\n/* \u5220\u9664\u64cd\u4f5c */\n// \u5728\u54c8\u5e0c\u8868\u4e2d\u5220\u9664\u952e\u503c\u5bf9 (key, value)\nmap.erase(10583);\n</code></pre> hash_map.py<pre><code># \u521d\u59cb\u5316\u54c8\u5e0c\u8868\nmapp: Dict = {}\n# \u6dfb\u52a0\u64cd\u4f5c\n# \u5728\u54c8\u5e0c\u8868\u4e2d\u6dfb\u52a0\u952e\u503c\u5bf9 (key, value)\nmapp[12836] = \"\u5c0f\u54c8\"\nmapp[15937] = \"\u5c0f\u5570\"\nmapp[16750] = \"\u5c0f\u7b97\"\nmapp[13276] = \"\u5c0f\u6cd5\"\nmapp[10583] = \"\u5c0f\u9e2d\"\n# \u67e5\u8be2\u64cd\u4f5c\n# \u5411\u54c8\u5e0c\u8868\u8f93\u5165\u952e key \uff0c\u5f97\u5230\u503c value\nname: str = mapp[15937]\n# \u5220\u9664\u64cd\u4f5c\n# \u5728\u54c8\u5e0c\u8868\u4e2d\u5220\u9664\u952e\u503c\u5bf9 (key, value)\nmapp.pop(10583)\n</code></pre> hash_map.go<pre><code>/* \u521d\u59cb\u5316\u54c8\u5e0c\u8868 */\nmapp := make(map[int]string)\n/* \u6dfb\u52a0\u64cd\u4f5c */\n// \u5728\u54c8\u5e0c\u8868\u4e2d\u6dfb\u52a0\u952e\u503c\u5bf9 (key, value)\nmapp[12836] = \"\u5c0f\u54c8\"\nmapp[15937] = \"\u5c0f\u5570\"\nmapp[16750] = \"\u5c0f\u7b97\"\nmapp[13276] = \"\u5c0f\u6cd5\"\nmapp[10583] = \"\u5c0f\u9e2d\"\n/* \u67e5\u8be2\u64cd\u4f5c */\n// \u5411\u54c8\u5e0c\u8868\u8f93\u5165\u952e key \uff0c\u5f97\u5230\u503c value\nname := mapp[15937]\n/* \u5220\u9664\u64cd\u4f5c */\n// \u5728\u54c8\u5e0c\u8868\u4e2d\u5220\u9664\u952e\u503c\u5bf9 (key, value)\ndelete(mapp, 10583)\n</code></pre> hash_map.js<pre><code>/* \u521d\u59cb\u5316\u54c8\u5e0c\u8868 */\nconst map = new ArrayHashMap();\n/* \u6dfb\u52a0\u64cd\u4f5c */\n// \u5728\u54c8\u5e0c\u8868\u4e2d\u6dfb\u52a0\u952e\u503c\u5bf9 (key, value)\nmap.set(12836, '\u5c0f\u54c8');\nmap.set(15937, '\u5c0f\u5570');\nmap.set(16750, '\u5c0f\u7b97');\nmap.set(13276, '\u5c0f\u6cd5');\nmap.set(10583, '\u5c0f\u9e2d');\n/* \u67e5\u8be2\u64cd\u4f5c */\n// \u5411\u54c8\u5e0c\u8868\u8f93\u5165\u952e key \uff0c\u5f97\u5230\u503c value\nlet name = map.get(15937);\n/* \u5220\u9664\u64cd\u4f5c */\n// \u5728\u54c8\u5e0c\u8868\u4e2d\u5220\u9664\u952e\u503c\u5bf9 (key, value)\nmap.delete(10583);\n</code></pre> hash_map.ts<pre><code>/* \u521d\u59cb\u5316\u54c8\u5e0c\u8868 */\nconst map = new Map&lt;number, string&gt;();\n/* \u6dfb\u52a0\u64cd\u4f5c */\n// \u5728\u54c8\u5e0c\u8868\u4e2d\u6dfb\u52a0\u952e\u503c\u5bf9 (key, value)\nmap.set(12836, '\u5c0f\u54c8');\nmap.set(15937, '\u5c0f\u5570');\nmap.set(16750, '\u5c0f\u7b97');\nmap.set(13276, '\u5c0f\u6cd5');\nmap.set(10583, '\u5c0f\u9e2d');\nconsole.info('\\n\u6dfb\u52a0\u5b8c\u6210\u540e\uff0c\u54c8\u5e0c\u8868\u4e3a\\nKey -&gt; Value');\nconsole.info(map);\n/* \u67e5\u8be2\u64cd\u4f5c */\n// \u5411\u54c8\u5e0c\u8868\u8f93\u5165\u952e key \uff0c\u5f97\u5230\u503c value\nlet name = map.get(15937);\nconsole.info('\\n\u8f93\u5165\u5b66\u53f7 15937 \uff0c\u67e5\u8be2\u5230\u59d3\u540d ' + name);\n/* \u5220\u9664\u64cd\u4f5c */\n// \u5728\u54c8\u5e0c\u8868\u4e2d\u5220\u9664\u952e\u503c\u5bf9 (key, value)\nmap.delete(10583);\nconsole.info('\\n\u5220\u9664 10583 \u540e\uff0c\u54c8\u5e0c\u8868\u4e3a\\nKey -&gt; Value');\nconsole.info(map);\n</code></pre> hash_map.c<pre><code>// C \u672a\u63d0\u4f9b\u5185\u7f6e\u54c8\u5e0c\u8868\n</code></pre> hash_map.cs<pre><code>/* \u521d\u59cb\u5316\u54c8\u5e0c\u8868 */\nDictionary&lt;int, String&gt; map = new ();\n/* \u6dfb\u52a0\u64cd\u4f5c */\n// \u5728\u54c8\u5e0c\u8868\u4e2d\u6dfb\u52a0\u952e\u503c\u5bf9 (key, value)\nmap.Add(12836, \"\u5c0f\u54c8\");\nmap.Add(15937, \"\u5c0f\u5570\");\nmap.Add(16750, \"\u5c0f\u7b97\");\nmap.Add(13276, \"\u5c0f\u6cd5\");\nmap.Add(10583, \"\u5c0f\u9e2d\");\n/* \u67e5\u8be2\u64cd\u4f5c */\n// \u5411\u54c8\u5e0c\u8868\u8f93\u5165\u952e key \uff0c\u5f97\u5230\u503c value\nString name = map[15937];\n/* \u5220\u9664\u64cd\u4f5c */\n// \u5728\u54c8\u5e0c\u8868\u4e2d\u5220\u9664\u952e\u503c\u5bf9 (key, value)\nmap.Remove(10583);\n</code></pre> hash_map.swift<pre><code>/* \u521d\u59cb\u5316\u54c8\u5e0c\u8868 */\nvar map: [Int: String] = [:]\n/* \u6dfb\u52a0\u64cd\u4f5c */\n// \u5728\u54c8\u5e0c\u8868\u4e2d\u6dfb\u52a0\u952e\u503c\u5bf9 (key, value)\nmap[12836] = \"\u5c0f\u54c8\"\nmap[15937] = \"\u5c0f\u5570\"\nmap[16750] = \"\u5c0f\u7b97\"\nmap[13276] = \"\u5c0f\u6cd5\"\nmap[10583] = \"\u5c0f\u9e2d\"\n/* \u67e5\u8be2\u64cd\u4f5c */\n// \u5411\u54c8\u5e0c\u8868\u8f93\u5165\u952e key \uff0c\u5f97\u5230\u503c value\nlet name = map[15937]!\n/* \u5220\u9664\u64cd\u4f5c */\n// \u5728\u54c8\u5e0c\u8868\u4e2d\u5220\u9664\u952e\u503c\u5bf9 (key, value)\nmap.removeValue(forKey: 10583)\n</code></pre> hash_map.zig<pre><code>\n</code></pre> hash_map.dart<pre><code>/* \u521d\u59cb\u5316\u54c8\u5e0c\u8868 */\nMap&lt;int, String&gt; map = {};\n/* \u6dfb\u52a0\u64cd\u4f5c */\n// \u5728\u54c8\u5e0c\u8868\u4e2d\u6dfb\u52a0\u952e\u503c\u5bf9 (key, value)\nmap[12836] = \"\u5c0f\u54c8\";\nmap[15937] = \"\u5c0f\u5570\";\nmap[16750] = \"\u5c0f\u7b97\";\nmap[13276] = \"\u5c0f\u6cd5\";\nmap[10583] = \"\u5c0f\u9e2d\";\n/* \u67e5\u8be2\u64cd\u4f5c */\n// \u5411\u54c8\u5e0c\u8868\u8f93\u5165\u952e key \uff0c\u5f97\u5230\u503c value\nString name = map[15937];\n/* \u5220\u9664\u64cd\u4f5c */\n// \u5728\u54c8\u5e0c\u8868\u4e2d\u5220\u9664\u952e\u503c\u5bf9 (key, value)\nmap.remove(10583);\n</code></pre> <p>\u904d\u5386\u54c8\u5e0c\u8868\u6709\u4e09\u79cd\u65b9\u5f0f\uff0c\u5373 \u904d\u5386\u952e\u503c\u5bf9\u3001\u904d\u5386\u952e\u3001\u904d\u5386\u503c\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart hash_map.java<pre><code>/* \u904d\u5386\u54c8\u5e0c\u8868 */\n// \u904d\u5386\u952e\u503c\u5bf9 key-&gt;value\nfor (Map.Entry &lt;Integer, String&gt; kv: map.entrySet()) {\nSystem.out.println(kv.getKey() + \" -&gt; \" + kv.getValue());\n}\n// \u5355\u72ec\u904d\u5386\u952e key\nfor (int key: map.keySet()) {\nSystem.out.println(key);\n}\n// \u5355\u72ec\u904d\u5386\u503c value\nfor (String val: map.values()) {\nSystem.out.println(val);\n}\n</code></pre> hash_map.cpp<pre><code>/* \u904d\u5386\u54c8\u5e0c\u8868 */\n// \u904d\u5386\u952e\u503c\u5bf9 key-&gt;value\nfor (auto kv: map) {\ncout &lt;&lt; kv.first &lt;&lt; \" -&gt; \" &lt;&lt; kv.second &lt;&lt; endl;\n}\n// \u5355\u72ec\u904d\u5386\u952e key\nfor (auto key: map) {\ncout &lt;&lt; key.first &lt;&lt; endl;\n}\n// \u5355\u72ec\u904d\u5386\u503c value\nfor (auto val: map) {\ncout &lt;&lt; val.second &lt;&lt; endl;\n}\n</code></pre> hash_map.py<pre><code># \u904d\u5386\u54c8\u5e0c\u8868\n# \u904d\u5386\u952e\u503c\u5bf9 key-&gt;value\nfor key, value in mapp.items():\nprint(key, \"-&gt;\", value)\n# \u5355\u72ec\u904d\u5386\u952e key\nfor key in mapp.keys():\nprint(key)\n# \u5355\u72ec\u904d\u5386\u503c value\nfor value in mapp.values():\nprint(value)\n</code></pre> hash_map_test.go<pre><code>/* \u904d\u5386\u54c8\u5e0c\u8868 */\n// \u904d\u5386\u952e\u503c\u5bf9 key-&gt;value\nfor key, value := range mapp {\nfmt.Println(key, \"-&gt;\", value)\n}\n// \u5355\u72ec\u904d\u5386\u952e key\nfor key := range mapp {\nfmt.Println(key)\n}\n// \u5355\u72ec\u904d\u5386\u503c value\nfor _, value := range mapp {\nfmt.Println(value)\n}\n</code></pre> hash_map.js<pre><code>/* \u904d\u5386\u54c8\u5e0c\u8868 */\nconsole.info('\\n\u904d\u5386\u952e\u503c\u5bf9 Key-&gt;Value');\nfor (const [k, v] of map.entries()) {\nconsole.info(k + ' -&gt; ' + v);\n}\nconsole.info('\\n\u5355\u72ec\u904d\u5386\u952e Key');\nfor (const k of map.keys()) {\nconsole.info(k);\n}\nconsole.info('\\n\u5355\u72ec\u904d\u5386\u503c Value');\nfor (const v of map.values()) {\nconsole.info(v);\n}\n</code></pre> hash_map.ts<pre><code>/* \u904d\u5386\u54c8\u5e0c\u8868 */\nconsole.info('\\n\u904d\u5386\u952e\u503c\u5bf9 Key-&gt;Value');\nfor (const [k, v] of map.entries()) {\nconsole.info(k + ' -&gt; ' + v);\n}\nconsole.info('\\n\u5355\u72ec\u904d\u5386\u952e Key');\nfor (const k of map.keys()) {\nconsole.info(k);\n}\nconsole.info('\\n\u5355\u72ec\u904d\u5386\u503c Value');\nfor (const v of map.values()) {\nconsole.info(v);\n}\n</code></pre> hash_map.c<pre><code>// C \u672a\u63d0\u4f9b\u5185\u7f6e\u54c8\u5e0c\u8868\n</code></pre> hash_map.cs<pre><code>/* \u904d\u5386\u54c8\u5e0c\u8868 */\n// \u904d\u5386\u952e\u503c\u5bf9 Key-&gt;Value\nforeach (var kv in map)\n{\nConsole.WriteLine(kv.Key + \" -&gt; \" + kv.Value);\n}\n// \u5355\u72ec\u904d\u5386\u952e key\nforeach (int key in map.Keys)\n{\nConsole.WriteLine(key);\n}\n// \u5355\u72ec\u904d\u5386\u503c value\nforeach (String val in map.Values)\n{\nConsole.WriteLine(val);\n}\n</code></pre> hash_map.swift<pre><code>/* \u904d\u5386\u54c8\u5e0c\u8868 */\n// \u904d\u5386\u952e\u503c\u5bf9 Key-&gt;Value\nfor (key, value) in map {\nprint(\"\\(key) -&gt; \\(value)\")\n}\n// \u5355\u72ec\u904d\u5386\u952e Key\nfor key in map.keys {\nprint(key)\n}\n// \u5355\u72ec\u904d\u5386\u503c Value\nfor value in map.values {\nprint(value)\n}\n</code></pre> hash_map.zig<pre><code>\n</code></pre> hash_map.dart<pre><code>/* \u904d\u5386\u54c8\u5e0c\u8868 */\n// \u904d\u5386\u952e\u503c\u5bf9 Key-&gt;Value\nmap.forEach((key, value) {\nprint('$key -&gt; $value');\n});\n// \u5355\u72ec\u904d\u5386\u952e Key\nmap.keys.forEach((key) {\nprint(key);\n});\n// \u5355\u72ec\u904d\u5386\u503c Value\nmap.values.forEach((value) {\nprint(value);\n});\n</code></pre>"},{"location":"chapter_hashing/hash_map/#612","title":"6.1.2. \u00a0 \u54c8\u5e0c\u51fd\u6570","text":"<p>\u54c8\u5e0c\u8868\u7684\u5e95\u5c42\u5b9e\u73b0\u4e3a\u6570\u7ec4\uff0c\u540c\u65f6\u53ef\u80fd\u5305\u542b\u94fe\u8868\u3001\u4e8c\u53c9\u6811\uff08\u7ea2\u9ed1\u6811\uff09\u7b49\u6570\u636e\u7ed3\u6784\uff0c\u4ee5\u63d0\u9ad8\u67e5\u8be2\u6027\u80fd\uff08\u5c06\u5728\u4e0b\u8282\u8ba8\u8bba\uff09\u3002</p> <p>\u9996\u5148\u8003\u8651\u6700\u7b80\u5355\u7684\u60c5\u51b5\uff0c\u4ec5\u4f7f\u7528\u4e00\u4e2a\u6570\u7ec4\u6765\u5b9e\u73b0\u54c8\u5e0c\u8868\u3002\u901a\u5e38\uff0c\u6211\u4eec\u5c06\u6570\u7ec4\u4e2d\u7684\u6bcf\u4e2a\u7a7a\u4f4d\u79f0\u4e3a\u300c\u6876 Bucket\u300d\uff0c\u7528\u4e8e\u5b58\u50a8\u952e\u503c\u5bf9\u3002</p> <p>\u6211\u4eec\u5c06\u952e\u503c\u5bf9 key, value \u5c01\u88c5\u6210\u4e00\u4e2a\u7c7b <code>Pair</code> \uff0c\u5e76\u5c06\u6240\u6709 <code>Pair</code> \u653e\u5165\u6570\u7ec4\u4e2d\u3002\u8fd9\u6837\uff0c\u6570\u7ec4\u4e2d\u7684\u6bcf\u4e2a <code>Pair</code> \u90fd\u5177\u6709\u552f\u4e00\u7684\u7d22\u5f15\u3002\u4e3a\u4e86\u5efa\u7acb key \u548c\u7d22\u5f15\u4e4b\u95f4\u7684\u6620\u5c04\u5173\u7cfb\uff0c\u6211\u4eec\u9700\u8981\u4f7f\u7528\u300c\u54c8\u5e0c\u51fd\u6570 Hash Function\u300d\u3002</p> <p>\u8bbe\u54c8\u5e0c\u8868\u7684\u6570\u7ec4\u4e3a <code>buckets</code> \uff0c\u54c8\u5e0c\u51fd\u6570\u4e3a <code>f(x)</code> \uff0c\u90a3\u4e48\u67e5\u8be2\u64cd\u4f5c\u7684\u6b65\u9aa4\u5982\u4e0b\uff1a</p> <ol> <li>\u8f93\u5165 <code>key</code> \uff0c\u901a\u8fc7\u54c8\u5e0c\u51fd\u6570\u8ba1\u7b97\u51fa\u7d22\u5f15 <code>index</code> \uff0c\u5373 <code>index = f(key)</code> \uff1b</li> <li>\u901a\u8fc7\u7d22\u5f15\u5728\u6570\u7ec4\u4e2d\u8bbf\u95ee\u5230\u952e\u503c\u5bf9 <code>pair</code> \uff0c\u5373 <code>pair = buckets[index]</code> \uff0c\u7136\u540e\u4ece <code>pair</code> \u4e2d\u83b7\u53d6\u5bf9\u5e94\u7684 <code>value</code> \uff1b</li> </ol> <p>\u4ee5\u5b66\u751f\u6570\u636e <code>key \u5b66\u53f7 -&gt; value \u59d3\u540d</code> \u4e3a\u4f8b\uff0c\u6211\u4eec\u53ef\u4ee5\u8bbe\u8ba1\u5982\u4e0b\u54c8\u5e0c\u51fd\u6570\uff1a</p> \\[ f(x) = x \\bmod {100} \\] <p>\u5176\u4e2d \\(\\bmod\\) \u8868\u793a\u53d6\u4f59\u8fd0\u7b97\u3002</p> <p></p> <p> Fig. \u54c8\u5e0c\u51fd\u6570\u5de5\u4f5c\u539f\u7406 </p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart array_hash_map.java<pre><code>/* \u952e\u503c\u5bf9 */\nclass Pair {\npublic int key;\npublic String val;\npublic Pair(int key, String val) {\nthis.key = key;\nthis.val = val;\n}\n}\n/* \u57fa\u4e8e\u6570\u7ec4\u7b80\u6613\u5b9e\u73b0\u7684\u54c8\u5e0c\u8868 */\nclass ArrayHashMap {\nprivate List&lt;Pair&gt; buckets;\npublic ArrayHashMap() {\n// \u521d\u59cb\u5316\u6570\u7ec4\uff0c\u5305\u542b 100 \u4e2a\u6876\nbuckets = new ArrayList&lt;&gt;();\nfor (int i = 0; i &lt; 100; i++) {\nbuckets.add(null);\n}\n}\n/* \u54c8\u5e0c\u51fd\u6570 */\nprivate int hashFunc(int key) {\nint index = key % 100;\nreturn index;\n}\n/* \u67e5\u8be2\u64cd\u4f5c */\npublic String get(int key) {\nint index = hashFunc(key);\nPair pair = buckets.get(index);\nif (pair == null)\nreturn null;\nreturn pair.val;\n}\n/* \u6dfb\u52a0\u64cd\u4f5c */\npublic void put(int key, String val) {\nPair pair = new Pair(key, val);\nint index = hashFunc(key);\nbuckets.set(index, pair);\n}\n/* \u5220\u9664\u64cd\u4f5c */\npublic void remove(int key) {\nint index = hashFunc(key);\n// \u7f6e\u4e3a null \uff0c\u4ee3\u8868\u5220\u9664\nbuckets.set(index, null);\n}\n/* \u83b7\u53d6\u6240\u6709\u952e\u503c\u5bf9 */\npublic List&lt;Pair&gt; pairSet() {\nList&lt;Pair&gt; pairSet = new ArrayList&lt;&gt;();\nfor (Pair pair : buckets) {\nif (pair != null)\npairSet.add(pair);\n}\nreturn pairSet;\n}\n/* \u83b7\u53d6\u6240\u6709\u952e */\npublic List&lt;Integer&gt; keySet() {\nList&lt;Integer&gt; keySet = new ArrayList&lt;&gt;();\nfor (Pair pair : buckets) {\nif (pair != null)\nkeySet.add(pair.key);\n}\nreturn keySet;\n}\n/* \u83b7\u53d6\u6240\u6709\u503c */\npublic List&lt;String&gt; valueSet() {\nList&lt;String&gt; valueSet = new ArrayList&lt;&gt;();\nfor (Pair pair : buckets) {\nif (pair != null)\nvalueSet.add(pair.val);\n}\nreturn valueSet;\n}\n/* \u6253\u5370\u54c8\u5e0c\u8868 */\npublic void print() {\nfor (Pair kv : pairSet()) {\nSystem.out.println(kv.key + \" -&gt; \" + kv.val);\n}\n}\n}\n</code></pre> array_hash_map.cpp<pre><code>/* \u952e\u503c\u5bf9 */\nstruct Pair {\npublic:\nint key;\nstring val;\nPair(int key, string val) {\nthis-&gt;key = key;\nthis-&gt;val = val;\n}\n};\n/* \u57fa\u4e8e\u6570\u7ec4\u7b80\u6613\u5b9e\u73b0\u7684\u54c8\u5e0c\u8868 */\nclass ArrayHashMap {\nprivate:\nvector&lt;Pair *&gt; buckets;\npublic:\nArrayHashMap() {\n// \u521d\u59cb\u5316\u6570\u7ec4\uff0c\u5305\u542b 100 \u4e2a\u6876\nbuckets = vector&lt;Pair *&gt;(100);\n}\n~ArrayHashMap() {\n// \u91ca\u653e\u5185\u5b58\nfor (const auto &amp;bucket : buckets) {\ndelete bucket;\n}\nbuckets.clear();\n}\n/* \u54c8\u5e0c\u51fd\u6570 */\nint hashFunc(int key) {\nint index = key % 100;\nreturn index;\n}\n/* \u67e5\u8be2\u64cd\u4f5c */\nstring get(int key) {\nint index = hashFunc(key);\nPair *pair = buckets[index];\nif (pair == nullptr)\nreturn nullptr;\nreturn pair-&gt;val;\n}\n/* \u6dfb\u52a0\u64cd\u4f5c */\nvoid put(int key, string val) {\nPair *pair = new Pair(key, val);\nint index = hashFunc(key);\nbuckets[index] = pair;\n}\n/* \u5220\u9664\u64cd\u4f5c */\nvoid remove(int key) {\nint index = hashFunc(key);\n// \u91ca\u653e\u5185\u5b58\u5e76\u7f6e\u4e3a nullptr\ndelete buckets[index];\nbuckets[index] = nullptr;\n}\n/* \u83b7\u53d6\u6240\u6709\u952e\u503c\u5bf9 */\nvector&lt;Pair *&gt; pairSet() {\nvector&lt;Pair *&gt; pairSet;\nfor (Pair *pair : buckets) {\nif (pair != nullptr) {\npairSet.push_back(pair);\n}\n}\nreturn pairSet;\n}\n/* \u83b7\u53d6\u6240\u6709\u952e */\nvector&lt;int&gt; keySet() {\nvector&lt;int&gt; keySet;\nfor (Pair *pair : buckets) {\nif (pair != nullptr) {\nkeySet.push_back(pair-&gt;key);\n}\n}\nreturn keySet;\n}\n/* \u83b7\u53d6\u6240\u6709\u503c */\nvector&lt;string&gt; valueSet() {\nvector&lt;string&gt; valueSet;\nfor (Pair *pair : buckets) {\nif (pair != nullptr) {\nvalueSet.push_back(pair-&gt;val);\n}\n}\nreturn valueSet;\n}\n/* \u6253\u5370\u54c8\u5e0c\u8868 */\nvoid print() {\nfor (Pair *kv : pairSet()) {\ncout &lt;&lt; kv-&gt;key &lt;&lt; \" -&gt; \" &lt;&lt; kv-&gt;val &lt;&lt; endl;\n}\n}\n};\n</code></pre> array_hash_map.py<pre><code>class Pair:\n\"\"\"\u952e\u503c\u5bf9\"\"\"\ndef __init__(self, key: int, val: str):\nself.key = key\nself.val = val\nclass ArrayHashMap:\n\"\"\"\u57fa\u4e8e\u6570\u7ec4\u7b80\u6613\u5b9e\u73b0\u7684\u54c8\u5e0c\u8868\"\"\"\ndef __init__(self):\n\"\"\"\u6784\u9020\u65b9\u6cd5\"\"\"\n# \u521d\u59cb\u5316\u6570\u7ec4\uff0c\u5305\u542b 100 \u4e2a\u6876\nself.buckets: list[Pair | None] = [None] * 100\ndef hash_func(self, key: int) -&gt; int:\n\"\"\"\u54c8\u5e0c\u51fd\u6570\"\"\"\nindex = key % 100\nreturn index\ndef get(self, key: int) -&gt; str:\n\"\"\"\u67e5\u8be2\u64cd\u4f5c\"\"\"\nindex: int = self.hash_func(key)\npair: Pair = self.buckets[index]\nif pair is None:\nreturn None\nreturn pair.val\ndef put(self, key: int, val: str):\n\"\"\"\u6dfb\u52a0\u64cd\u4f5c\"\"\"\npair = Pair(key, val)\nindex: int = self.hash_func(key)\nself.buckets[index] = pair\ndef remove(self, key: int):\n\"\"\"\u5220\u9664\u64cd\u4f5c\"\"\"\nindex: int = self.hash_func(key)\n# \u7f6e\u4e3a None \uff0c\u4ee3\u8868\u5220\u9664\nself.buckets[index] = None\ndef entry_set(self) -&gt; list[Pair]:\n\"\"\"\u83b7\u53d6\u6240\u6709\u952e\u503c\u5bf9\"\"\"\nresult: list[Pair] = []\nfor pair in self.buckets:\nif pair is not None:\nresult.append(pair)\nreturn result\ndef key_set(self) -&gt; list[int]:\n\"\"\"\u83b7\u53d6\u6240\u6709\u952e\"\"\"\nresult = []\nfor pair in self.buckets:\nif pair is not None:\nresult.append(pair.key)\nreturn result\ndef value_set(self) -&gt; list[str]:\n\"\"\"\u83b7\u53d6\u6240\u6709\u503c\"\"\"\nresult = []\nfor pair in self.buckets:\nif pair is not None:\nresult.append(pair.val)\nreturn result\ndef print(self):\n\"\"\"\u6253\u5370\u54c8\u5e0c\u8868\"\"\"\nfor pair in self.buckets:\nif pair is not None:\nprint(pair.key, \"-&gt;\", pair.val)\n</code></pre> array_hash_map.go<pre><code>/* \u952e\u503c\u5bf9 */\ntype pair struct {\nkey int\nval string\n}\n/* \u57fa\u4e8e\u6570\u7ec4\u7b80\u6613\u5b9e\u73b0\u7684\u54c8\u5e0c\u8868 */\ntype arrayHashMap struct {\nbuckets []*pair\n}\n/* \u521d\u59cb\u5316\u54c8\u5e0c\u8868 */\nfunc newArrayHashMap() *arrayHashMap {\n// \u521d\u59cb\u5316\u6570\u7ec4\uff0c\u5305\u542b 100 \u4e2a\u6876\nbuckets := make([]*pair, 100)\nreturn &amp;arrayHashMap{buckets: buckets}\n}\n/* \u54c8\u5e0c\u51fd\u6570 */\nfunc (a *arrayHashMap) hashFunc(key int) int {\nindex := key % 100\nreturn index\n}\n/* \u67e5\u8be2\u64cd\u4f5c */\nfunc (a *arrayHashMap) get(key int) string {\nindex := a.hashFunc(key)\npair := a.buckets[index]\nif pair == nil {\nreturn \"Not Found\"\n}\nreturn pair.val\n}\n/* \u6dfb\u52a0\u64cd\u4f5c */\nfunc (a *arrayHashMap) put(key int, val string) {\npair := &amp;pair{key: key, val: val}\nindex := a.hashFunc(key)\na.buckets[index] = pair\n}\n/* \u5220\u9664\u64cd\u4f5c */\nfunc (a *arrayHashMap) remove(key int) {\nindex := a.hashFunc(key)\n// \u7f6e\u4e3a nil \uff0c\u4ee3\u8868\u5220\u9664\na.buckets[index] = nil\n}\n/* \u83b7\u53d6\u6240\u6709\u952e\u5bf9 */\nfunc (a *arrayHashMap) pairSet() []*pair {\nvar pairs []*pair\nfor _, pair := range a.buckets {\nif pair != nil {\npairs = append(pairs, pair)\n}\n}\nreturn pairs\n}\n/* \u83b7\u53d6\u6240\u6709\u952e */\nfunc (a *arrayHashMap) keySet() []int {\nvar keys []int\nfor _, pair := range a.buckets {\nif pair != nil {\nkeys = append(keys, pair.key)\n}\n}\nreturn keys\n}\n/* \u83b7\u53d6\u6240\u6709\u503c */\nfunc (a *arrayHashMap) valueSet() []string {\nvar values []string\nfor _, pair := range a.buckets {\nif pair != nil {\nvalues = append(values, pair.val)\n}\n}\nreturn values\n}\n/* \u6253\u5370\u54c8\u5e0c\u8868 */\nfunc (a *arrayHashMap) print() {\nfor _, pair := range a.buckets {\nif pair != nil {\nfmt.Println(pair.key, \"-&gt;\", pair.val)\n}\n}\n}\n</code></pre> array_hash_map.js<pre><code>/* \u952e\u503c\u5bf9 Number -&gt; String */\nclass Pair {\nconstructor(key, val) {\nthis.key = key;\nthis.val = val;\n}\n}\n/* \u57fa\u4e8e\u6570\u7ec4\u7b80\u6613\u5b9e\u73b0\u7684\u54c8\u5e0c\u8868 */\nclass ArrayHashMap {\n#buckets;\nconstructor() {\n// \u521d\u59cb\u5316\u6570\u7ec4\uff0c\u5305\u542b 100 \u4e2a\u6876\nthis.#buckets = new Array(100).fill(null);\n}\n/* \u54c8\u5e0c\u51fd\u6570 */\n#hashFunc(key) {\nreturn key % 100;\n}\n/* \u67e5\u8be2\u64cd\u4f5c */\nget(key) {\nlet index = this.#hashFunc(key);\nlet pair = this.#buckets[index];\nif (pair === null) return null;\nreturn pair.val;\n}\n/* \u6dfb\u52a0\u64cd\u4f5c */\nset(key, val) {\nlet index = this.#hashFunc(key);\nthis.#buckets[index] = new Pair(key, val);\n}\n/* \u5220\u9664\u64cd\u4f5c */\ndelete(key) {\nlet index = this.#hashFunc(key);\n// \u7f6e\u4e3a null \uff0c\u4ee3\u8868\u5220\u9664\nthis.#buckets[index] = null;\n}\n/* \u83b7\u53d6\u6240\u6709\u952e\u503c\u5bf9 */\nentries() {\nlet arr = [];\nfor (let i = 0; i &lt; this.#buckets.length; i++) {\nif (this.#buckets[i]) {\narr.push(this.#buckets[i]);\n}\n}\nreturn arr;\n}\n/* \u83b7\u53d6\u6240\u6709\u952e */\nkeys() {\nlet arr = [];\nfor (let i = 0; i &lt; this.#buckets.length; i++) {\nif (this.#buckets[i]) {\narr.push(this.#buckets[i]?.key);\n}\n}\nreturn arr;\n}\n/* \u83b7\u53d6\u6240\u6709\u503c */\nvalues() {\nlet arr = [];\nfor (let i = 0; i &lt; this.#buckets.length; i++) {\nif (this.#buckets[i]) {\narr.push(this.#buckets[i]?.val);\n}\n}\nreturn arr;\n}\n/* \u6253\u5370\u54c8\u5e0c\u8868 */\nprint() {\nlet pairSet = this.entries();\nfor (const pair of pairSet) {\nif (!pair) continue;\nconsole.info(`${pair.key} -&gt; ${pair.val}`);\n}\n}\n}\n</code></pre> array_hash_map.ts<pre><code>/* \u952e\u503c\u5bf9 Number -&gt; String */\nclass Pair {\npublic key: number;\npublic val: string;\nconstructor(key: number, val: string) {\nthis.key = key;\nthis.val = val;\n}\n}\n/* \u57fa\u4e8e\u6570\u7ec4\u7b80\u6613\u5b9e\u73b0\u7684\u54c8\u5e0c\u8868 */\nclass ArrayHashMap {\nprivate readonly buckets: (Pair | null)[];\nconstructor() {\n// \u521d\u59cb\u5316\u6570\u7ec4\uff0c\u5305\u542b 100 \u4e2a\u6876\nthis.buckets = new Array(100).fill(null);\n}\n/* \u54c8\u5e0c\u51fd\u6570 */\nprivate hashFunc(key: number): number {\nreturn key % 100;\n}\n/* \u67e5\u8be2\u64cd\u4f5c */\npublic get(key: number): string | null {\nlet index = this.hashFunc(key);\nlet pair = this.buckets[index];\nif (pair === null) return null;\nreturn pair.val;\n}\n/* \u6dfb\u52a0\u64cd\u4f5c */\npublic set(key: number, val: string) {\nlet index = this.hashFunc(key);\nthis.buckets[index] = new Pair(key, val);\n}\n/* \u5220\u9664\u64cd\u4f5c */\npublic delete(key: number) {\nlet index = this.hashFunc(key);\n// \u7f6e\u4e3a null \uff0c\u4ee3\u8868\u5220\u9664\nthis.buckets[index] = null;\n}\n/* \u83b7\u53d6\u6240\u6709\u952e\u503c\u5bf9 */\npublic entries(): (Pair | null)[] {\nlet arr: (Pair | null)[] = [];\nfor (let i = 0; i &lt; this.buckets.length; i++) {\nif (this.buckets[i]) {\narr.push(this.buckets[i]);\n}\n}\nreturn arr;\n}\n/* \u83b7\u53d6\u6240\u6709\u952e */\npublic keys(): (number | undefined)[] {\nlet arr: (number | undefined)[] = [];\nfor (let i = 0; i &lt; this.buckets.length; i++) {\nif (this.buckets[i]) {\narr.push(this.buckets[i]?.key);\n}\n}\nreturn arr;\n}\n/* \u83b7\u53d6\u6240\u6709\u503c */\npublic values(): (string | undefined)[] {\nlet arr: (string | undefined)[] = [];\nfor (let i = 0; i &lt; this.buckets.length; i++) {\nif (this.buckets[i]) {\narr.push(this.buckets[i]?.val);\n}\n}\nreturn arr;\n}\n/* \u6253\u5370\u54c8\u5e0c\u8868 */\npublic print() {\nlet pairSet = this.entries();\nfor (const pair of pairSet) {\nif (!pair) continue;\nconsole.info(`${pair.key} -&gt; ${pair.val}`);\n}\n}\n}\n</code></pre> array_hash_map.c<pre><code>/* \u952e\u503c\u5bf9 int-&gt;string */\nstruct pair {\nint key;\nchar *val;\n};\ntypedef struct pair pair;\n[class]{arrayHashMap}-[func]{}\n</code></pre> array_hash_map.cs<pre><code>/* \u952e\u503c\u5bf9 int-&gt;string */\nclass Pair {\npublic int key;\npublic string val;\npublic Pair(int key, string val) {\nthis.key = key;\nthis.val = val;\n}\n}\n/* \u57fa\u4e8e\u6570\u7ec4\u7b80\u6613\u5b9e\u73b0\u7684\u54c8\u5e0c\u8868 */\nclass ArrayHashMap {\nprivate List&lt;Pair?&gt; buckets;\npublic ArrayHashMap() {\n// \u521d\u59cb\u5316\u6570\u7ec4\uff0c\u5305\u542b 100 \u4e2a\u6876\nbuckets = new();\nfor (int i = 0; i &lt; 100; i++) {\nbuckets.Add(null);\n}\n}\n/* \u54c8\u5e0c\u51fd\u6570 */\nprivate int hashFunc(int key) {\nint index = key % 100;\nreturn index;\n}\n/* \u67e5\u8be2\u64cd\u4f5c */\npublic string? get(int key) {\nint index = hashFunc(key);\nPair? pair = buckets[index];\nif (pair == null) return null;\nreturn pair.val;\n}\n/* \u6dfb\u52a0\u64cd\u4f5c */\npublic void put(int key, string val) {\nPair pair = new Pair(key, val);\nint index = hashFunc(key);\nbuckets[index] = pair;\n}\n/* \u5220\u9664\u64cd\u4f5c */\npublic void remove(int key) {\nint index = hashFunc(key);\n// \u7f6e\u4e3a null \uff0c\u4ee3\u8868\u5220\u9664\nbuckets[index] = null;\n}\n/* \u83b7\u53d6\u6240\u6709\u952e\u503c\u5bf9 */\npublic List&lt;Pair&gt; pairSet() {\nList&lt;Pair&gt; pairSet = new();\nforeach (Pair? pair in buckets) {\nif (pair != null)\npairSet.Add(pair);\n}\nreturn pairSet;\n}\n/* \u83b7\u53d6\u6240\u6709\u952e */\npublic List&lt;int&gt; keySet() {\nList&lt;int&gt; keySet = new();\nforeach (Pair? pair in buckets) {\nif (pair != null)\nkeySet.Add(pair.key);\n}\nreturn keySet;\n}\n/* \u83b7\u53d6\u6240\u6709\u503c */\npublic List&lt;string&gt; valueSet() {\nList&lt;string&gt; valueSet = new();\nforeach (Pair? pair in buckets) {\nif (pair != null)\nvalueSet.Add(pair.val);\n}\nreturn valueSet;\n}\n/* \u6253\u5370\u54c8\u5e0c\u8868 */\npublic void print() {\nforeach (Pair kv in pairSet()) {\nConsole.WriteLine(kv.key + \" -&gt; \" + kv.val);\n}\n}\n}\n</code></pre> array_hash_map.swift<pre><code>/* \u952e\u503c\u5bf9 */\nclass Pair {\nvar key: Int\nvar val: String\ninit(key: Int, val: String) {\nself.key = key\nself.val = val\n}\n}\n/* \u57fa\u4e8e\u6570\u7ec4\u7b80\u6613\u5b9e\u73b0\u7684\u54c8\u5e0c\u8868 */\nclass ArrayHashMap {\nprivate var buckets: [Pair?] = []\ninit() {\n// \u521d\u59cb\u5316\u6570\u7ec4\uff0c\u5305\u542b 100 \u4e2a\u6876\nfor _ in 0 ..&lt; 100 {\nbuckets.append(nil)\n}\n}\n/* \u54c8\u5e0c\u51fd\u6570 */\nprivate func hashFunc(key: Int) -&gt; Int {\nlet index = key % 100\nreturn index\n}\n/* \u67e5\u8be2\u64cd\u4f5c */\nfunc get(key: Int) -&gt; String? {\nlet index = hashFunc(key: key)\nlet pair = buckets[index]\nreturn pair?.val\n}\n/* \u6dfb\u52a0\u64cd\u4f5c */\nfunc put(key: Int, val: String) {\nlet pair = Pair(key: key, val: val)\nlet index = hashFunc(key: key)\nbuckets[index] = pair\n}\n/* \u5220\u9664\u64cd\u4f5c */\nfunc remove(key: Int) {\nlet index = hashFunc(key: key)\n// \u7f6e\u4e3a nil \uff0c\u4ee3\u8868\u5220\u9664\nbuckets[index] = nil\n}\n/* \u83b7\u53d6\u6240\u6709\u952e\u503c\u5bf9 */\nfunc pairSet() -&gt; [Pair] {\nvar pairSet: [Pair] = []\nfor pair in buckets {\nif let pair = pair {\npairSet.append(pair)\n}\n}\nreturn pairSet\n}\n/* \u83b7\u53d6\u6240\u6709\u952e */\nfunc keySet() -&gt; [Int] {\nvar keySet: [Int] = []\nfor pair in buckets {\nif let pair = pair {\nkeySet.append(pair.key)\n}\n}\nreturn keySet\n}\n/* \u83b7\u53d6\u6240\u6709\u503c */\nfunc valueSet() -&gt; [String] {\nvar valueSet: [String] = []\nfor pair in buckets {\nif let pair = pair {\nvalueSet.append(pair.val)\n}\n}\nreturn valueSet\n}\n/* \u6253\u5370\u54c8\u5e0c\u8868 */\nfunc print() {\nfor pair in pairSet() {\nSwift.print(\"\\(pair.key) -&gt; \\(pair.val)\")\n}\n}\n}\n</code></pre> array_hash_map.zig<pre><code>// \u952e\u503c\u5bf9\nconst Pair = struct {\nkey: usize = undefined,\nval: []const u8 = undefined,\npub fn init(key: usize, val: []const u8) Pair {\nreturn Pair {\n.key = key,\n.val = val,\n};\n}\n};\n// \u57fa\u4e8e\u6570\u7ec4\u7b80\u6613\u5b9e\u73b0\u7684\u54c8\u5e0c\u8868\nfn ArrayHashMap(comptime T: type) type {\nreturn struct {\nbuckets: ?std.ArrayList(?T) = null,\nmem_allocator: std.mem.Allocator = undefined,\nconst Self = @This();\n// \u6784\u9020\u65b9\u6cd5\npub fn init(self: *Self, allocator: std.mem.Allocator) !void {\nself.mem_allocator = allocator;\n// \u521d\u59cb\u5316\u6570\u7ec4\uff0c\u5305\u542b 100 \u4e2a\u6876\nself.buckets = std.ArrayList(?T).init(self.mem_allocator);\nvar i: i32 = 0;\nwhile (i &lt; 100) : (i += 1) {\ntry self.buckets.?.append(null);\n}\n}\n// \u6790\u6784\u65b9\u6cd5\npub fn deinit(self: *Self) void {\nif (self.buckets != null) self.buckets.?.deinit();\n}\n// \u54c8\u5e0c\u51fd\u6570\nfn hashFunc(key: usize) usize {\nvar index = key % 100;\nreturn index;\n}\n// \u67e5\u8be2\u64cd\u4f5c\npub fn get(self: *Self, key: usize) []const u8 {\nvar index = hashFunc(key);\nvar pair = self.buckets.?.items[index];\nreturn pair.?.val;\n}\n// \u6dfb\u52a0\u64cd\u4f5c\npub fn put(self: *Self, key: usize, val: []const u8) !void {\nvar pair = Pair.init(key, val);\nvar index = hashFunc(key);\nself.buckets.?.items[index] = pair;\n}\n// \u5220\u9664\u64cd\u4f5c\npub fn remove(self: *Self, key: usize) !void {\nvar index = hashFunc(key);\n// \u7f6e\u4e3a null \uff0c\u4ee3\u8868\u5220\u9664\nself.buckets.?.items[index] = null;\n}       // \u83b7\u53d6\u6240\u6709\u952e\u503c\u5bf9\npub fn pairSet(self: *Self) !*std.ArrayList(T) {\nvar entry_set = std.ArrayList(T).init(self.mem_allocator);\nfor (self.buckets.?.items) |item| {\nif (item == null) continue;\ntry entry_set.append(item.?);\n}\nreturn &amp;entry_set;\n}  // \u83b7\u53d6\u6240\u6709\u952e\npub fn keySet(self: *Self) !*std.ArrayList(usize) {\nvar key_set = std.ArrayList(usize).init(self.mem_allocator);\nfor (self.buckets.?.items) |item| {\nif (item == null) continue;\ntry key_set.append(item.?.key);\n}\nreturn &amp;key_set;\n}  // \u83b7\u53d6\u6240\u6709\u503c\npub fn valueSet(self: *Self) !*std.ArrayList([]const u8) {\nvar value_set = std.ArrayList([]const u8).init(self.mem_allocator);\nfor (self.buckets.?.items) |item| {\nif (item == null) continue;\ntry value_set.append(item.?.val);\n}\nreturn &amp;value_set;\n}\n// \u6253\u5370\u54c8\u5e0c\u8868\npub fn print(self: *Self) !void {\nvar entry_set = try self.pairSet();\ndefer entry_set.deinit();\nfor (entry_set.items) |item| {\nstd.debug.print(\"{} -&gt; {s}\\n\", .{item.key, item.val});\n}\n}\n};\n}\n</code></pre> array_hash_map.dart<pre><code>/* \u952e\u503c\u5bf9 */\nclass Pair {\nint key;\nString val;\nPair(this.key, this.val);\n}\n/* \u57fa\u4e8e\u6570\u7ec4\u7b80\u6613\u5b9e\u73b0\u7684\u54c8\u5e0c\u8868 */\nclass ArrayHashMap {\nlate List&lt;Pair?&gt; _buckets;\nArrayHashMap() {\n// \u521d\u59cb\u5316\u6570\u7ec4\uff0c\u5305\u542b 100 \u4e2a\u6876\n_buckets = List.filled(100, null);\n}\n/* \u54c8\u5e0c\u51fd\u6570 */\nint _hashFunc(int key) {\nfinal int index = key % 100;\nreturn index;\n}\n/* \u67e5\u8be2\u64cd\u4f5c */\nString? get(int key) {\nfinal int index = _hashFunc(key);\nfinal Pair? pair = _buckets[index];\nif (pair == null) {\nreturn null;\n}\nreturn pair.val;\n}\n/* \u6dfb\u52a0\u64cd\u4f5c */\nvoid put(int key, String val) {\nfinal Pair pair = Pair(key, val);\nfinal int index = _hashFunc(key);\n_buckets[index] = pair;\n}\n/* \u5220\u9664\u64cd\u4f5c */\nvoid remove(int key) {\nfinal int index = _hashFunc(key);\n_buckets[index] = null;\n}\n/* \u83b7\u53d6\u6240\u6709\u952e\u503c\u5bf9 */\nList&lt;Pair&gt; pairSet() {\nList&lt;Pair&gt; pairSet = [];\nfor (final Pair? pair in _buckets) {\nif (pair != null) {\npairSet.add(pair);\n}\n}\nreturn pairSet;\n}\n/* \u83b7\u53d6\u6240\u6709\u952e */\nList&lt;int&gt; keySet() {\nList&lt;int&gt; keySet = [];\nfor (final Pair? pair in _buckets) {\nif (pair != null) {\nkeySet.add(pair.key);\n}\n}\nreturn keySet;\n}\n/* \u83b7\u53d6\u6240\u6709\u503c */\nList&lt;String&gt; values() {\nList&lt;String&gt; valueSet = [];\nfor (final Pair? pair in _buckets) {\nif (pair != null) {\nvalueSet.add(pair.val);\n}\n}\nreturn valueSet;\n}\n/* \u6253\u5370\u54c8\u5e0c\u8868 */\nvoid printHashMap() {\nfor (final Pair kv in pairSet()) {\nprint(\"${kv.key} -&gt; ${kv.val}\");\n}\n}\n}\n</code></pre>"},{"location":"chapter_hashing/hash_map/#613","title":"6.1.3. \u00a0 \u54c8\u5e0c\u51b2\u7a81","text":"<p>\u7ec6\u5fc3\u7684\u4f60\u53ef\u80fd\u5df2\u7ecf\u6ce8\u610f\u5230\uff0c\u5728\u67d0\u4e9b\u60c5\u51b5\u4e0b\uff0c\u54c8\u5e0c\u51fd\u6570 \\(f(x) = x \\bmod 100\\) \u53ef\u80fd\u65e0\u6cd5\u6b63\u5e38\u5de5\u4f5c\u3002\u5177\u4f53\u6765\u8bf4\uff0c\u5f53\u8f93\u5165\u7684 key \u540e\u4e24\u4f4d\u76f8\u540c\u65f6\uff0c\u54c8\u5e0c\u51fd\u6570\u7684\u8ba1\u7b97\u7ed3\u679c\u4e5f\u4f1a\u76f8\u540c\uff0c\u4ece\u800c\u6307\u5411\u540c\u4e00\u4e2a value \u3002\u4f8b\u5982\uff0c\u67e5\u8be2\u5b66\u53f7\u4e3a \\(12836\\) \u548c \\(20336\\) \u7684\u4e24\u4e2a\u5b66\u751f\u65f6\uff0c\u6211\u4eec\u5f97\u5230\uff1a</p> \\[ f(12836) = f(20336) = 36 \\] <p>\u8fd9\u4e24\u4e2a\u5b66\u53f7\u6307\u5411\u4e86\u540c\u4e00\u4e2a\u59d3\u540d\uff0c\u8fd9\u663e\u7136\u662f\u9519\u8bef\u7684\u3002\u6211\u4eec\u628a\u8fd9\u79cd\u60c5\u51b5\u79f0\u4e3a\u300c\u54c8\u5e0c\u51b2\u7a81 Hash Collision\u300d\u3002\u5728\u540e\u7eed\u7ae0\u8282\u4e2d\uff0c\u6211\u4eec\u5c06\u8ba8\u8bba\u5982\u4f55\u89e3\u51b3\u54c8\u5e0c\u51b2\u7a81\u7684\u95ee\u9898\u3002</p> <p></p> <p> Fig. \u54c8\u5e0c\u51b2\u7a81\u793a\u4f8b </p> <p>\u7efc\u4e0a\u6240\u8ff0\uff0c\u4e00\u4e2a\u4f18\u79c0\u7684\u54c8\u5e0c\u51fd\u6570\u5e94\u5177\u5907\u4ee5\u4e0b\u7279\u6027\uff1a</p> <ul> <li>\u5c3d\u53ef\u80fd\u51cf\u5c11\u54c8\u5e0c\u51b2\u7a81\u7684\u53d1\u751f\uff1b</li> <li>\u67e5\u8be2\u6548\u7387\u9ad8\u4e14\u7a33\u5b9a\uff0c\u80fd\u591f\u5728\u7edd\u5927\u591a\u6570\u60c5\u51b5\u4e0b\u8fbe\u5230 \\(O(1)\\) \u65f6\u95f4\u590d\u6742\u5ea6\uff1b</li> <li>\u8f83\u9ad8\u7684\u7a7a\u95f4\u5229\u7528\u7387\uff0c\u5373\u4f7f\u201c\u952e\u503c\u5bf9\u5360\u7528\u7a7a\u95f4 / \u54c8\u5e0c\u8868\u603b\u5360\u7528\u7a7a\u95f4\u201d\u6bd4\u4f8b\u6700\u5927\u5316\uff1b</li> </ul>"},{"location":"chapter_hashing/summary/","title":"6.3. \u00a0 \u5c0f\u7ed3","text":"<ul> <li>\u54c8\u5e0c\u8868\u80fd\u591f\u5728 \\(O(1)\\) \u65f6\u95f4\u5185\u5c06\u952e key \u6620\u5c04\u5230\u503c value\uff0c\u6548\u7387\u975e\u5e38\u9ad8\u3002</li> <li>\u5e38\u89c1\u7684\u54c8\u5e0c\u8868\u64cd\u4f5c\u5305\u62ec\u67e5\u8be2\u3001\u6dfb\u52a0\u4e0e\u5220\u9664\u952e\u503c\u5bf9\u3001\u904d\u5386\u952e\u503c\u5bf9\u7b49\u3002</li> <li>\u54c8\u5e0c\u51fd\u6570\u5c06 key \u6620\u5c04\u4e3a\u6570\u7ec4\u7d22\u5f15\uff08\u6876\u7d22\u5f15\uff09\uff0c\u4ece\u800c\u8bbf\u95ee\u5bf9\u5e94\u7684\u503c value \u3002</li> <li>\u4e24\u4e2a\u4e0d\u540c\u7684 key \u53ef\u80fd\u5728\u7ecf\u8fc7\u54c8\u5e0c\u51fd\u6570\u540e\u5f97\u5230\u76f8\u540c\u7684\u7d22\u5f15\uff0c\u5bfc\u81f4\u67e5\u8be2\u7ed3\u679c\u51fa\u9519\uff0c\u8fd9\u79cd\u73b0\u8c61\u88ab\u79f0\u4e3a\u54c8\u5e0c\u51b2\u7a81\u3002</li> <li>\u7f13\u89e3\u54c8\u5e0c\u51b2\u7a81\u7684\u65b9\u6cd5\u4e3b\u8981\u6709\u6269\u5bb9\u54c8\u5e0c\u8868\u548c\u4f18\u5316\u54c8\u5e0c\u8868\u7684\u8868\u793a\u65b9\u6cd5\u3002</li> <li>\u8d1f\u8f7d\u56e0\u5b50\u5b9a\u4e49\u4e3a\u54c8\u5e0c\u8868\u4e2d\u5143\u7d20\u6570\u91cf\u9664\u4ee5\u6876\u6570\u91cf\uff0c\u53cd\u6620\u4e86\u54c8\u5e0c\u51b2\u7a81\u7684\u4e25\u91cd\u7a0b\u5ea6\uff0c\u5e38\u7528\u4f5c\u89e6\u53d1\u54c8\u5e0c\u8868\u6269\u5bb9\u7684\u6761\u4ef6\u3002\u4e0e\u6570\u7ec4\u6269\u5bb9\u7c7b\u4f3c\uff0c\u54c8\u5e0c\u8868\u6269\u5bb9\u64cd\u4f5c\u4e5f\u4f1a\u4ea7\u751f\u8f83\u5927\u7684\u5f00\u9500\u3002</li> <li>\u94fe\u5f0f\u5730\u5740\u901a\u8fc7\u5c06\u5355\u4e2a\u5143\u7d20\u8f6c\u5316\u4e3a\u94fe\u8868\uff0c\u5c06\u6240\u6709\u51b2\u7a81\u5143\u7d20\u5b58\u50a8\u5728\u540c\u4e00\u4e2a\u94fe\u8868\u4e2d\uff0c\u4ece\u800c\u89e3\u51b3\u54c8\u5e0c\u51b2\u7a81\u3002\u7136\u800c\uff0c\u8fc7\u957f\u7684\u94fe\u8868\u4f1a\u964d\u4f4e\u67e5\u8be2\u6548\u7387\uff0c\u53ef\u4ee5\u901a\u8fc7\u5c06\u94fe\u8868\u8f6c\u6362\u4e3a AVL \u6811\u6216\u7ea2\u9ed1\u6811\u6765\u6539\u5584\u3002</li> <li>\u5f00\u653e\u5bfb\u5740\u901a\u8fc7\u591a\u6b21\u63a2\u6d4b\u6765\u89e3\u51b3\u54c8\u5e0c\u51b2\u7a81\u3002\u7ebf\u6027\u63a2\u6d4b\u4f7f\u7528\u56fa\u5b9a\u6b65\u957f\uff0c\u7f3a\u70b9\u662f\u4e0d\u80fd\u5220\u9664\u5143\u7d20\u4e14\u5bb9\u6613\u4ea7\u751f\u805a\u96c6\u3002\u591a\u6b21\u54c8\u5e0c\u4f7f\u7528\u591a\u4e2a\u54c8\u5e0c\u51fd\u6570\u8fdb\u884c\u63a2\u6d4b\uff0c\u76f8\u5bf9\u7ebf\u6027\u63a2\u6d4b\u4e0d\u6613\u4ea7\u751f\u805a\u96c6\uff0c\u4f46\u591a\u4e2a\u54c8\u5e0c\u51fd\u6570\u589e\u52a0\u4e86\u8ba1\u7b97\u91cf\u3002</li> <li>\u4e0d\u540c\u7f16\u7a0b\u8bed\u8a00\u91c7\u53d6\u4e86\u4e0d\u540c\u7684\u54c8\u5e0c\u8868\u5b9e\u73b0\u7b56\u7565\u3002\u4f8b\u5982\uff0cJava \u7684 HashMap \u4f7f\u7528\u94fe\u5f0f\u5730\u5740\uff0c\u800c Python \u7684 Dict \u91c7\u7528\u5f00\u653e\u5bfb\u5740\u3002</li> </ul>"},{"location":"chapter_heap/","title":"8. \u00a0 \u5806","text":""},{"location":"chapter_heap/build_heap/","title":"8.2. \u00a0 \u5efa\u5806\u64cd\u4f5c","text":"<p>\u5982\u679c\u6211\u4eec\u60f3\u8981\u6839\u636e\u8f93\u5165\u5217\u8868\u751f\u6210\u4e00\u4e2a\u5806\uff0c\u8fd9\u4e2a\u8fc7\u7a0b\u88ab\u79f0\u4e3a\u300c\u5efa\u5806\u300d\u3002</p>"},{"location":"chapter_heap/build_heap/#821","title":"8.2.1. \u00a0 \u501f\u52a9\u5165\u5806\u65b9\u6cd5\u5b9e\u73b0","text":"<p>\u6700\u76f4\u63a5\u7684\u65b9\u6cd5\u662f\u501f\u52a9\u201c\u5143\u7d20\u5165\u5806\u64cd\u4f5c\u201d\u5b9e\u73b0\uff0c\u9996\u5148\u521b\u5efa\u4e00\u4e2a\u7a7a\u5806\uff0c\u7136\u540e\u5c06\u5217\u8868\u5143\u7d20\u4f9d\u6b21\u6dfb\u52a0\u5230\u5806\u4e2d\u3002</p> <p>\u8bbe\u5143\u7d20\u6570\u91cf\u4e3a \\(n\\) \uff0c\u5219\u6700\u540e\u4e00\u4e2a\u5143\u7d20\u5165\u5806\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(\\log n)\\) \u3002\u5728\u4f9d\u6b21\u6dfb\u52a0\u5143\u7d20\u65f6\uff0c\u5806\u7684\u5e73\u5747\u957f\u5ea6\u4e3a \\(\\frac{n}{2}\\) \uff0c\u56e0\u6b64\u8be5\u65b9\u6cd5\u7684\u603b\u4f53\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(n \\log n)\\) \u3002</p>"},{"location":"chapter_heap/build_heap/#822","title":"8.2.2. \u00a0 \u57fa\u4e8e\u5806\u5316\u64cd\u4f5c\u5b9e\u73b0","text":"<p>\u6709\u8da3\u7684\u662f\uff0c\u5b58\u5728\u4e00\u79cd\u66f4\u9ad8\u6548\u7684\u5efa\u5806\u65b9\u6cd5\uff0c\u5176\u65f6\u95f4\u590d\u6742\u5ea6\u4ec5\u4e3a \\(O(n)\\) \u3002\u6211\u4eec\u5148\u5c06\u5217\u8868\u6240\u6709\u5143\u7d20\u539f\u5c01\u4e0d\u52a8\u6dfb\u52a0\u5230\u5806\u4e2d\uff0c\u7136\u540e\u8fed\u4ee3\u5730\u5bf9\u5404\u4e2a\u8282\u70b9\u6267\u884c\u201c\u4ece\u9876\u81f3\u5e95\u5806\u5316\u201d\u3002\u5f53\u7136\uff0c\u6211\u4eec\u4e0d\u9700\u8981\u5bf9\u53f6\u8282\u70b9\u6267\u884c\u5806\u5316\u64cd\u4f5c\uff0c\u56e0\u4e3a\u5b83\u4eec\u6ca1\u6709\u5b50\u8282\u70b9\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart my_heap.java<pre><code>/* \u6784\u9020\u65b9\u6cd5\uff0c\u6839\u636e\u8f93\u5165\u5217\u8868\u5efa\u5806 */\nMaxHeap(List&lt;Integer&gt; nums) {\n// \u5c06\u5217\u8868\u5143\u7d20\u539f\u5c01\u4e0d\u52a8\u6dfb\u52a0\u8fdb\u5806\nmaxHeap = new ArrayList&lt;&gt;(nums);\n// \u5806\u5316\u9664\u53f6\u8282\u70b9\u4ee5\u5916\u7684\u5176\u4ed6\u6240\u6709\u8282\u70b9\nfor (int i = parent(size() - 1); i &gt;= 0; i--) {\nsiftDown(i);\n}\n}\n</code></pre> my_heap.cpp<pre><code>/* \u6784\u9020\u65b9\u6cd5\uff0c\u6839\u636e\u8f93\u5165\u5217\u8868\u5efa\u5806 */\nMaxHeap(vector&lt;int&gt; nums) {\n// \u5c06\u5217\u8868\u5143\u7d20\u539f\u5c01\u4e0d\u52a8\u6dfb\u52a0\u8fdb\u5806\nmaxHeap = nums;\n// \u5806\u5316\u9664\u53f6\u8282\u70b9\u4ee5\u5916\u7684\u5176\u4ed6\u6240\u6709\u8282\u70b9\nfor (int i = parent(size() - 1); i &gt;= 0; i--) {\nsiftDown(i);\n}\n}\n</code></pre> my_heap.py<pre><code>def __init__(self, nums: list[int]):\n\"\"\"\u6784\u9020\u65b9\u6cd5\uff0c\u6839\u636e\u8f93\u5165\u5217\u8868\u5efa\u5806\"\"\"\n# \u5c06\u5217\u8868\u5143\u7d20\u539f\u5c01\u4e0d\u52a8\u6dfb\u52a0\u8fdb\u5806\nself.max_heap = nums\n# \u5806\u5316\u9664\u53f6\u8282\u70b9\u4ee5\u5916\u7684\u5176\u4ed6\u6240\u6709\u8282\u70b9\nfor i in range(self.parent(self.size() - 1), -1, -1):\nself.sift_down(i)\n</code></pre> my_heap.go<pre><code>/* \u6784\u9020\u65b9\u6cd5\uff0c\u6839\u636e\u5207\u7247\u5efa\u5806 */\nfunc newMaxHeap(nums []any) *maxHeap {\n// \u5c06\u5217\u8868\u5143\u7d20\u539f\u5c01\u4e0d\u52a8\u6dfb\u52a0\u8fdb\u5806\nh := &amp;maxHeap{data: nums}\nfor i := len(h.data) - 1; i &gt;= 0; i-- {\n// \u5806\u5316\u9664\u53f6\u8282\u70b9\u4ee5\u5916\u7684\u5176\u4ed6\u6240\u6709\u8282\u70b9\nh.siftDown(i)\n}\nreturn h\n}\n</code></pre> my_heap.js<pre><code>/* \u6784\u9020\u65b9\u6cd5\uff0c\u5efa\u7acb\u7a7a\u5806\u6216\u6839\u636e\u8f93\u5165\u5217\u8868\u5efa\u5806 */\nconstructor(nums) {\n// \u5c06\u5217\u8868\u5143\u7d20\u539f\u5c01\u4e0d\u52a8\u6dfb\u52a0\u8fdb\u5806\nthis.#maxHeap = nums === undefined ? [] : [...nums];\n// \u5806\u5316\u9664\u53f6\u8282\u70b9\u4ee5\u5916\u7684\u5176\u4ed6\u6240\u6709\u8282\u70b9\nfor (let i = this.#parent(this.size() - 1); i &gt;= 0; i--) {\nthis.#siftDown(i);\n}\n}\n</code></pre> my_heap.ts<pre><code>/* \u6784\u9020\u65b9\u6cd5\uff0c\u5efa\u7acb\u7a7a\u5806\u6216\u6839\u636e\u8f93\u5165\u5217\u8868\u5efa\u5806 */\nconstructor(nums?: number[]) {\n// \u5c06\u5217\u8868\u5143\u7d20\u539f\u5c01\u4e0d\u52a8\u6dfb\u52a0\u8fdb\u5806\nthis.maxHeap = nums === undefined ? [] : [...nums];\n// \u5806\u5316\u9664\u53f6\u8282\u70b9\u4ee5\u5916\u7684\u5176\u4ed6\u6240\u6709\u8282\u70b9\nfor (let i = this.parent(this.size() - 1); i &gt;= 0; i--) {\nthis.siftDown(i);\n}\n}\n</code></pre> my_heap.c<pre><code>/* \u6784\u9020\u51fd\u6570\uff0c\u6839\u636e\u5207\u7247\u5efa\u5806 */\nmaxHeap *newMaxHeap(int nums[], int size) {\n// \u6240\u6709\u5143\u7d20\u5165\u5806\nmaxHeap *h = (maxHeap *)malloc(sizeof(maxHeap));\nh-&gt;size = size;\nmemcpy(h-&gt;data, nums, size * sizeof(int));\nfor (int i = size - 1; i &gt;= 0; i--) {\n// \u5806\u5316\u9664\u53f6\u8282\u70b9\u4ee5\u5916\u7684\u5176\u4ed6\u6240\u6709\u8282\u70b9\nsiftDown(h, i);\n}\nreturn h;\n}\n</code></pre> my_heap.cs<pre><code>/* \u6784\u9020\u51fd\u6570\uff0c\u6839\u636e\u8f93\u5165\u5217\u8868\u5efa\u5806 */\nMaxHeap(IEnumerable&lt;int&gt; nums) {\n// \u5c06\u5217\u8868\u5143\u7d20\u539f\u5c01\u4e0d\u52a8\u6dfb\u52a0\u8fdb\u5806\nmaxHeap = new List&lt;int&gt;(nums);\n// \u5806\u5316\u9664\u53f6\u8282\u70b9\u4ee5\u5916\u7684\u5176\u4ed6\u6240\u6709\u8282\u70b9\nvar size = parent(this.size() - 1);\nfor (int i = size; i &gt;= 0; i--) {\nsiftDown(i);\n}\n}\n</code></pre> my_heap.swift<pre><code>/* \u6784\u9020\u65b9\u6cd5\uff0c\u6839\u636e\u8f93\u5165\u5217\u8868\u5efa\u5806 */\ninit(nums: [Int]) {\n// \u5c06\u5217\u8868\u5143\u7d20\u539f\u5c01\u4e0d\u52a8\u6dfb\u52a0\u8fdb\u5806\nmaxHeap = nums\n// \u5806\u5316\u9664\u53f6\u8282\u70b9\u4ee5\u5916\u7684\u5176\u4ed6\u6240\u6709\u8282\u70b9\nfor i in stride(from: parent(i: size() - 1), through: 0, by: -1) {\nsiftDown(i: i)\n}\n}\n</code></pre> my_heap.zig<pre><code>// \u6784\u9020\u65b9\u6cd5\uff0c\u6839\u636e\u8f93\u5165\u5217\u8868\u5efa\u5806\nfn init(self: *Self, allocator: std.mem.Allocator, nums: []const T) !void {\nif (self.max_heap != null) return;\nself.max_heap = std.ArrayList(T).init(allocator);\n// \u5c06\u5217\u8868\u5143\u7d20\u539f\u5c01\u4e0d\u52a8\u6dfb\u52a0\u8fdb\u5806\ntry self.max_heap.?.appendSlice(nums);\n// \u5806\u5316\u9664\u53f6\u8282\u70b9\u4ee5\u5916\u7684\u5176\u4ed6\u6240\u6709\u8282\u70b9\nvar i: usize = parent(self.size() - 1) + 1;\nwhile (i &gt; 0) : (i -= 1) {\ntry self.siftDown(i - 1);\n}\n}\n</code></pre> my_heap.dart<pre><code>/* \u6784\u9020\u65b9\u6cd5\uff0c\u6839\u636e\u8f93\u5165\u5217\u8868\u5efa\u5806 */\nMaxHeap(List&lt;int&gt; nums) {\n// \u5c06\u5217\u8868\u5143\u7d20\u539f\u5c01\u4e0d\u52a8\u6dfb\u52a0\u8fdb\u5806\n_maxHeap = nums;\n// \u5806\u5316\u9664\u53f6\u8282\u70b9\u4ee5\u5916\u7684\u5176\u4ed6\u6240\u6709\u8282\u70b9\nfor (int i = _parent(size() - 1); i &gt;= 0; i--) {\n_siftDown(i);\n}\n}\n</code></pre>"},{"location":"chapter_heap/build_heap/#823","title":"8.2.3. \u00a0 \u590d\u6742\u5ea6\u5206\u6790","text":"<p>\u4e3a\u4ec0\u4e48\u7b2c\u4e8c\u79cd\u5efa\u5806\u65b9\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u662f \\(O(n)\\) \uff1f\u6211\u4eec\u6765\u5c55\u5f00\u63a8\u7b97\u4e00\u4e0b\u3002</p> <ul> <li>\u5b8c\u5168\u4e8c\u53c9\u6811\u4e2d\uff0c\u8bbe\u8282\u70b9\u603b\u6570\u4e3a \\(n\\) \uff0c\u5219\u53f6\u8282\u70b9\u6570\u91cf\u4e3a \\((n + 1) / 2\\) \uff0c\u5176\u4e2d \\(/\\) \u4e3a\u5411\u4e0b\u6574\u9664\u3002\u56e0\u6b64\uff0c\u5728\u6392\u9664\u53f6\u8282\u70b9\u540e\uff0c\u9700\u8981\u5806\u5316\u7684\u8282\u70b9\u6570\u91cf\u4e3a \\((n - 1)/2\\) \uff0c\u590d\u6742\u5ea6\u4e3a \\(O(n)\\) \uff1b</li> <li>\u5728\u4ece\u9876\u81f3\u5e95\u5806\u5316\u7684\u8fc7\u7a0b\u4e2d\uff0c\u6bcf\u4e2a\u8282\u70b9\u6700\u591a\u5806\u5316\u5230\u53f6\u8282\u70b9\uff0c\u56e0\u6b64\u6700\u5927\u8fed\u4ee3\u6b21\u6570\u4e3a\u4e8c\u53c9\u6811\u9ad8\u5ea6 \\(O(\\log n)\\) \uff1b</li> </ul> <p>\u5c06\u4e0a\u8ff0\u4e24\u8005\u76f8\u4e58\uff0c\u53ef\u5f97\u5230\u5efa\u5806\u8fc7\u7a0b\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(n \\log n)\\) \u3002\u7136\u800c\uff0c\u8fd9\u4e2a\u4f30\u7b97\u7ed3\u679c\u5e76\u4e0d\u51c6\u786e\uff0c\u56e0\u4e3a\u6211\u4eec\u6ca1\u6709\u8003\u8651\u5230\u4e8c\u53c9\u6811\u5e95\u5c42\u8282\u70b9\u6570\u91cf\u8fdc\u591a\u4e8e\u9876\u5c42\u8282\u70b9\u7684\u7279\u6027\u3002</p> <p>\u63a5\u4e0b\u6765\u6211\u4eec\u6765\u8fdb\u884c\u66f4\u4e3a\u8be6\u7ec6\u7684\u8ba1\u7b97\u3002\u4e3a\u4e86\u51cf\u5c0f\u8ba1\u7b97\u96be\u5ea6\uff0c\u6211\u4eec\u5047\u8bbe\u6811\u662f\u4e00\u4e2a\u201c\u5b8c\u7f8e\u4e8c\u53c9\u6811\u201d\uff0c\u8be5\u5047\u8bbe\u4e0d\u4f1a\u5f71\u54cd\u8ba1\u7b97\u7ed3\u679c\u7684\u6b63\u786e\u6027\u3002\u8bbe\u4e8c\u53c9\u6811\uff08\u5373\u5806\uff09\u8282\u70b9\u6570\u91cf\u4e3a \\(n\\) \uff0c\u6811\u9ad8\u5ea6\u4e3a \\(h\\) \u3002\u4e0a\u6587\u63d0\u5230\uff0c\u8282\u70b9\u5806\u5316\u6700\u5927\u8fed\u4ee3\u6b21\u6570\u7b49\u4e8e\u8be5\u8282\u70b9\u5230\u53f6\u8282\u70b9\u7684\u8ddd\u79bb\uff0c\u800c\u8be5\u8ddd\u79bb\u6b63\u662f\u201c\u8282\u70b9\u9ad8\u5ea6\u201d\u3002</p> <p></p> <p> Fig. \u5b8c\u7f8e\u4e8c\u53c9\u6811\u7684\u5404\u5c42\u8282\u70b9\u6570\u91cf </p> <p>\u56e0\u6b64\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u5404\u5c42\u7684\u201c\u8282\u70b9\u6570\u91cf \\(\\times\\) \u8282\u70b9\u9ad8\u5ea6\u201d\u6c42\u548c\uff0c\u4ece\u800c\u5f97\u5230\u6240\u6709\u8282\u70b9\u7684\u5806\u5316\u8fed\u4ee3\u6b21\u6570\u7684\u603b\u548c\u3002</p> \\[ T(h) = 2^0h + 2^1(h-1) + 2^2(h-2) + \\cdots + 2^{(h-1)}\\times1 \\] <p>\u5316\u7b80\u4e0a\u5f0f\u9700\u8981\u501f\u52a9\u4e2d\u5b66\u7684\u6570\u5217\u77e5\u8bc6\uff0c\u5148\u5bf9 \\(T(h)\\) \u4e58\u4ee5 \\(2\\) \uff0c\u5f97\u5230</p> \\[ \\begin{aligned} T(h) &amp; = 2^0h + 2^1(h-1) + 2^2(h-2) + \\cdots + 2^{h-1}\\times1 \\newline 2 T(h) &amp; = 2^1h + 2^2(h-1) + 2^3(h-2) + \\cdots + 2^{h}\\times1 \\newline \\end{aligned} \\] <p>\u4f7f\u7528\u9519\u4f4d\u76f8\u51cf\u6cd5\uff0c\u4ee4\u4e0b\u5f0f \\(2 T(h)\\) \u51cf\u53bb\u4e0a\u5f0f \\(T(h)\\) \uff0c\u53ef\u5f97</p> \\[ 2T(h) - T(h) = T(h) = -2^0h + 2^1 + 2^2 + \\cdots + 2^{h-1} + 2^h \\] <p>\u89c2\u5bdf\u4e0a\u5f0f\uff0c\u53d1\u73b0 \\(T(h)\\) \u662f\u4e00\u4e2a\u7b49\u6bd4\u6570\u5217\uff0c\u53ef\u76f4\u63a5\u4f7f\u7528\u6c42\u548c\u516c\u5f0f\uff0c\u5f97\u5230\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a</p> \\[ \\begin{aligned} T(h) &amp; = 2 \\frac{1 - 2^h}{1 - 2} - h \\newline &amp; = 2^{h+1} - h \\newline &amp; = O(2^h) \\end{aligned} \\] <p>\u8fdb\u4e00\u6b65\u5730\uff0c\u9ad8\u5ea6\u4e3a \\(h\\) \u7684\u5b8c\u7f8e\u4e8c\u53c9\u6811\u7684\u8282\u70b9\u6570\u91cf\u4e3a \\(n = 2^{h+1} - 1\\) \uff0c\u6613\u5f97\u590d\u6742\u5ea6\u4e3a \\(O(2^h) = O(n)\\) \u3002\u4ee5\u4e0a\u63a8\u7b97\u8868\u660e\uff0c\u8f93\u5165\u5217\u8868\u5e76\u5efa\u5806\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(n)\\) \uff0c\u975e\u5e38\u9ad8\u6548\u3002</p>"},{"location":"chapter_heap/heap/","title":"8.1. \u00a0 \u5806","text":"<p>\u300c\u5806 Heap\u300d\u662f\u4e00\u79cd\u6ee1\u8db3\u7279\u5b9a\u6761\u4ef6\u7684\u5b8c\u5168\u4e8c\u53c9\u6811\uff0c\u53ef\u5206\u4e3a\u4e24\u79cd\u7c7b\u578b\uff1a</p> <ul> <li>\u300c\u5927\u9876\u5806 Max Heap\u300d\uff0c\u4efb\u610f\u8282\u70b9\u7684\u503c \\(\\geq\\) \u5176\u5b50\u8282\u70b9\u7684\u503c\uff1b</li> <li>\u300c\u5c0f\u9876\u5806 Min Heap\u300d\uff0c\u4efb\u610f\u8282\u70b9\u7684\u503c \\(\\leq\\) \u5176\u5b50\u8282\u70b9\u7684\u503c\uff1b</li> </ul> <p></p> <p> Fig. \u5c0f\u9876\u5806\u4e0e\u5927\u9876\u5806 </p> <p>\u5806\u4f5c\u4e3a\u5b8c\u5168\u4e8c\u53c9\u6811\u7684\u4e00\u4e2a\u7279\u4f8b\uff0c\u5177\u6709\u4ee5\u4e0b\u7279\u6027\uff1a</p> <ul> <li>\u6700\u5e95\u5c42\u8282\u70b9\u9760\u5de6\u586b\u5145\uff0c\u5176\u4ed6\u5c42\u7684\u8282\u70b9\u90fd\u88ab\u586b\u6ee1\u3002</li> <li>\u6211\u4eec\u5c06\u4e8c\u53c9\u6811\u7684\u6839\u8282\u70b9\u79f0\u4e3a\u300c\u5806\u9876\u300d\uff0c\u5c06\u5e95\u5c42\u6700\u9760\u53f3\u7684\u8282\u70b9\u79f0\u4e3a\u300c\u5806\u5e95\u300d\u3002</li> <li>\u5bf9\u4e8e\u5927\u9876\u5806\uff08\u5c0f\u9876\u5806\uff09\uff0c\u5806\u9876\u5143\u7d20\uff08\u5373\u6839\u8282\u70b9\uff09\u7684\u503c\u5206\u522b\u662f\u6700\u5927\uff08\u6700\u5c0f\uff09\u7684\u3002</li> </ul>"},{"location":"chapter_heap/heap/#811","title":"8.1.1. \u00a0 \u5806\u5e38\u7528\u64cd\u4f5c","text":"<p>\u9700\u8981\u6307\u51fa\u7684\u662f\uff0c\u8bb8\u591a\u7f16\u7a0b\u8bed\u8a00\u63d0\u4f9b\u7684\u662f\u300c\u4f18\u5148\u961f\u5217 Priority Queue\u300d\uff0c\u8fd9\u662f\u4e00\u79cd\u62bd\u8c61\u6570\u636e\u7ed3\u6784\uff0c\u5b9a\u4e49\u4e3a\u5177\u6709\u4f18\u5148\u7ea7\u6392\u5e8f\u7684\u961f\u5217\u3002</p> <p>\u5b9e\u9645\u4e0a\uff0c\u5806\u901a\u5e38\u7528\u4f5c\u5b9e\u73b0\u4f18\u5148\u961f\u5217\uff0c\u5927\u9876\u5806\u76f8\u5f53\u4e8e\u5143\u7d20\u6309\u4ece\u5927\u5230\u5c0f\u987a\u5e8f\u51fa\u961f\u7684\u4f18\u5148\u961f\u5217\u3002\u4ece\u4f7f\u7528\u89d2\u5ea6\u6765\u770b\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u300c\u4f18\u5148\u961f\u5217\u300d\u548c\u300c\u5806\u300d\u770b\u4f5c\u7b49\u4ef7\u7684\u6570\u636e\u7ed3\u6784\u3002\u56e0\u6b64\uff0c\u672c\u4e66\u5bf9\u4e24\u8005\u4e0d\u505a\u7279\u522b\u533a\u5206\uff0c\u7edf\u4e00\u4f7f\u7528\u300c\u5806\u300d\u6765\u547d\u540d\u3002</p> <p>\u5806\u7684\u5e38\u7528\u64cd\u4f5c\u89c1\u4e0b\u8868\uff0c\u65b9\u6cd5\u540d\u9700\u8981\u6839\u636e\u7f16\u7a0b\u8bed\u8a00\u6765\u786e\u5b9a\u3002</p> \u65b9\u6cd5\u540d \u63cf\u8ff0 \u65f6\u95f4\u590d\u6742\u5ea6 push() \u5143\u7d20\u5165\u5806 \\(O(\\log n)\\) pop() \u5806\u9876\u5143\u7d20\u51fa\u5806 \\(O(\\log n)\\) peek() \u8bbf\u95ee\u5806\u9876\u5143\u7d20\uff08\u5927 / \u5c0f\u9876\u5806\u5206\u522b\u4e3a\u6700\u5927 / \u5c0f\u503c\uff09 \\(O(1)\\) size() \u83b7\u53d6\u5806\u7684\u5143\u7d20\u6570\u91cf \\(O(1)\\) isEmpty() \u5224\u65ad\u5806\u662f\u5426\u4e3a\u7a7a \\(O(1)\\) <p>\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u6211\u4eec\u53ef\u4ee5\u76f4\u63a5\u4f7f\u7528\u7f16\u7a0b\u8bed\u8a00\u63d0\u4f9b\u7684\u5806\u7c7b\uff08\u6216\u4f18\u5148\u961f\u5217\u7c7b\uff09\u3002</p> <p>Tip</p> <p>\u7c7b\u4f3c\u4e8e\u6392\u5e8f\u7b97\u6cd5\u4e2d\u7684\u201c\u4ece\u5c0f\u5230\u5927\u6392\u5217\u201d\u548c\u201c\u4ece\u5927\u5230\u5c0f\u6392\u5217\u201d\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u4fee\u6539 Comparator \u6765\u5b9e\u73b0\u201c\u5c0f\u9876\u5806\u201d\u4e0e\u201c\u5927\u9876\u5806\u201d\u4e4b\u95f4\u7684\u8f6c\u6362\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart heap.java<pre><code>/* \u521d\u59cb\u5316\u5806 */\n// \u521d\u59cb\u5316\u5c0f\u9876\u5806\nQueue&lt;Integer&gt; minHeap = new PriorityQueue&lt;&gt;();\n// \u521d\u59cb\u5316\u5927\u9876\u5806\uff08\u4f7f\u7528 lambda \u8868\u8fbe\u5f0f\u4fee\u6539 Comparator \u5373\u53ef\uff09\nQueue&lt;Integer&gt; maxHeap = new PriorityQueue&lt;&gt;((a, b) -&gt; b - a);\n/* \u5143\u7d20\u5165\u5806 */\nmaxHeap.offer(1);\nmaxHeap.offer(3);\nmaxHeap.offer(2);\nmaxHeap.offer(5);\nmaxHeap.offer(4);\n/* \u83b7\u53d6\u5806\u9876\u5143\u7d20 */\nint peek = maxHeap.peek(); // 5\n/* \u5806\u9876\u5143\u7d20\u51fa\u5806 */\n// \u51fa\u5806\u5143\u7d20\u4f1a\u5f62\u6210\u4e00\u4e2a\u4ece\u5927\u5230\u5c0f\u7684\u5e8f\u5217\npeek = heap.poll();  // 5\npeek = heap.poll();  // 4\npeek = heap.poll();  // 3\npeek = heap.poll();  // 2\npeek = heap.poll();  // 1\n/* \u83b7\u53d6\u5806\u5927\u5c0f */\nint size = maxHeap.size();\n/* \u5224\u65ad\u5806\u662f\u5426\u4e3a\u7a7a */\nboolean isEmpty = maxHeap.isEmpty();\n/* \u8f93\u5165\u5217\u8868\u5e76\u5efa\u5806 */\nminHeap = new PriorityQueue&lt;&gt;(Arrays.asList(1, 3, 2, 5, 4));\n</code></pre> heap.cpp<pre><code>/* \u521d\u59cb\u5316\u5806 */\n// \u521d\u59cb\u5316\u5c0f\u9876\u5806\npriority_queue&lt;int, vector&lt;int&gt;, greater&lt;int&gt;&gt; minHeap;\n// \u521d\u59cb\u5316\u5927\u9876\u5806\npriority_queue&lt;int, vector&lt;int&gt;, less&lt;int&gt;&gt; maxHeap;\n/* \u5143\u7d20\u5165\u5806 */\nmaxHeap.push(1);\nmaxHeap.push(3);\nmaxHeap.push(2);\nmaxHeap.push(5);\nmaxHeap.push(4);\n/* \u83b7\u53d6\u5806\u9876\u5143\u7d20 */\nint peek = maxHeap.top(); // 5\n/* \u5806\u9876\u5143\u7d20\u51fa\u5806 */\n// \u51fa\u5806\u5143\u7d20\u4f1a\u5f62\u6210\u4e00\u4e2a\u4ece\u5927\u5230\u5c0f\u7684\u5e8f\u5217\nmaxHeap.pop(); // 5\nmaxHeap.pop(); // 4\nmaxHeap.pop(); // 3\nmaxHeap.pop(); // 2\nmaxHeap.pop(); // 1\n/* \u83b7\u53d6\u5806\u5927\u5c0f */\nint size = maxHeap.size();\n/* \u5224\u65ad\u5806\u662f\u5426\u4e3a\u7a7a */\nbool isEmpty = maxHeap.empty();\n/* \u8f93\u5165\u5217\u8868\u5e76\u5efa\u5806 */\nvector&lt;int&gt; input{1, 3, 2, 5, 4};\npriority_queue&lt;int, vector&lt;int&gt;, greater&lt;int&gt;&gt; minHeap(input.begin(), input.end());\n</code></pre> heap.py<pre><code># \u521d\u59cb\u5316\u5c0f\u9876\u5806\nmin_heap, flag = [], 1\n# \u521d\u59cb\u5316\u5927\u9876\u5806\nmax_heap, flag = [], -1\n# Python \u7684 heapq \u6a21\u5757\u9ed8\u8ba4\u5b9e\u73b0\u5c0f\u9876\u5806\n# \u8003\u8651\u5c06\u201c\u5143\u7d20\u53d6\u8d1f\u201d\u540e\u518d\u5165\u5806\uff0c\u8fd9\u6837\u5c31\u53ef\u4ee5\u5c06\u5927\u5c0f\u5173\u7cfb\u98a0\u5012\uff0c\u4ece\u800c\u5b9e\u73b0\u5927\u9876\u5806\n# \u5728\u672c\u793a\u4f8b\u4e2d\uff0cflag = 1 \u65f6\u5bf9\u5e94\u5c0f\u9876\u5806\uff0cflag = -1 \u65f6\u5bf9\u5e94\u5927\u9876\u5806\n# \u5143\u7d20\u5165\u5806\nheapq.heappush(max_heap, flag * 1)\nheapq.heappush(max_heap, flag * 3)\nheapq.heappush(max_heap, flag * 2)\nheapq.heappush(max_heap, flag * 5)\nheapq.heappush(max_heap, flag * 4)\n# \u83b7\u53d6\u5806\u9876\u5143\u7d20\npeek: int = flag * max_heap[0] # 5\n# \u5806\u9876\u5143\u7d20\u51fa\u5806\n# \u51fa\u5806\u5143\u7d20\u4f1a\u5f62\u6210\u4e00\u4e2a\u4ece\u5927\u5230\u5c0f\u7684\u5e8f\u5217\nval = flag * heapq.heappop(max_heap) # 5\nval = flag * heapq.heappop(max_heap) # 4\nval = flag * heapq.heappop(max_heap) # 3\nval = flag * heapq.heappop(max_heap) # 2\nval = flag * heapq.heappop(max_heap) # 1\n# \u83b7\u53d6\u5806\u5927\u5c0f\nsize: int = len(max_heap)\n# \u5224\u65ad\u5806\u662f\u5426\u4e3a\u7a7a\nis_empty: bool = not max_heap\n# \u8f93\u5165\u5217\u8868\u5e76\u5efa\u5806\nmin_heap: List[int] = [1, 3, 2, 5, 4]\nheapq.heapify(min_heap)\n</code></pre> heap.go<pre><code>// Go \u8bed\u8a00\u4e2d\u53ef\u4ee5\u901a\u8fc7\u5b9e\u73b0 heap.Interface \u6765\u6784\u5efa\u6574\u6570\u5927\u9876\u5806\n// \u5b9e\u73b0 heap.Interface \u9700\u8981\u540c\u65f6\u5b9e\u73b0 sort.Interface\ntype intHeap []any\n// Push heap.Interface \u7684\u65b9\u6cd5\uff0c\u5b9e\u73b0\u63a8\u5165\u5143\u7d20\u5230\u5806\nfunc (h *intHeap) Push(x any) {\n// Push \u548c Pop \u4f7f\u7528 pointer receiver \u4f5c\u4e3a\u53c2\u6570\n// \u56e0\u4e3a\u5b83\u4eec\u4e0d\u4ec5\u4f1a\u5bf9\u5207\u7247\u7684\u5185\u5bb9\u8fdb\u884c\u8c03\u6574\uff0c\u8fd8\u4f1a\u4fee\u6539\u5207\u7247\u7684\u957f\u5ea6\u3002\n*h = append(*h, x.(int))\n}\n// Pop heap.Interface \u7684\u65b9\u6cd5\uff0c\u5b9e\u73b0\u5f39\u51fa\u5806\u9876\u5143\u7d20\nfunc (h *intHeap) Pop() any {\n// \u5f85\u51fa\u5806\u5143\u7d20\u5b58\u653e\u5728\u6700\u540e\nlast := (*h)[len(*h)-1]\n*h = (*h)[:len(*h)-1]\nreturn last\n}\n// Len sort.Interface \u7684\u65b9\u6cd5\nfunc (h *intHeap) Len() int {\nreturn len(*h)\n}\n// Less sort.Interface \u7684\u65b9\u6cd5\nfunc (h *intHeap) Less(i, j int) bool {\n// \u5982\u679c\u5b9e\u73b0\u5c0f\u9876\u5806\uff0c\u5219\u9700\u8981\u8c03\u6574\u4e3a\u5c0f\u4e8e\u53f7\nreturn (*h)[i].(int) &gt; (*h)[j].(int)\n}\n// Swap sort.Interface \u7684\u65b9\u6cd5\nfunc (h *intHeap) Swap(i, j int) {\n(*h)[i], (*h)[j] = (*h)[j], (*h)[i]\n}\n// Top \u83b7\u53d6\u5806\u9876\u5143\u7d20\nfunc (h *intHeap) Top() any {\nreturn (*h)[0]\n}\n/* Driver Code */\nfunc TestHeap(t *testing.T) {\n/* \u521d\u59cb\u5316\u5806 */\n// \u521d\u59cb\u5316\u5927\u9876\u5806\nmaxHeap := &amp;intHeap{}\nheap.Init(maxHeap)\n/* \u5143\u7d20\u5165\u5806 */\n// \u8c03\u7528 heap.Interface \u7684\u65b9\u6cd5\uff0c\u6765\u6dfb\u52a0\u5143\u7d20\nheap.Push(maxHeap, 1)\nheap.Push(maxHeap, 3)\nheap.Push(maxHeap, 2)\nheap.Push(maxHeap, 4)\nheap.Push(maxHeap, 5)\n/* \u83b7\u53d6\u5806\u9876\u5143\u7d20 */\ntop := maxHeap.Top()\nfmt.Printf(\"\u5806\u9876\u5143\u7d20\u4e3a %d\\n\", top)\n/* \u5806\u9876\u5143\u7d20\u51fa\u5806 */\n// \u8c03\u7528 heap.Interface \u7684\u65b9\u6cd5\uff0c\u6765\u79fb\u9664\u5143\u7d20\nheap.Pop(maxHeap) // 5\nheap.Pop(maxHeap) // 4\nheap.Pop(maxHeap) // 3\nheap.Pop(maxHeap) // 2\nheap.Pop(maxHeap) // 1\n/* \u83b7\u53d6\u5806\u5927\u5c0f */\nsize := len(*maxHeap)\nfmt.Printf(\"\u5806\u5143\u7d20\u6570\u91cf\u4e3a %d\\n\", size)\n/* \u5224\u65ad\u5806\u662f\u5426\u4e3a\u7a7a */\nisEmpty := len(*maxHeap) == 0\nfmt.Printf(\"\u5806\u662f\u5426\u4e3a\u7a7a %t\\n\", isEmpty)\n}\n</code></pre> heap.js<pre><code>// JavaScript \u672a\u63d0\u4f9b\u5185\u7f6e Heap \u7c7b\n</code></pre> heap.ts<pre><code>// TypeScript \u672a\u63d0\u4f9b\u5185\u7f6e Heap \u7c7b\n</code></pre> heap.c<pre><code>// C \u672a\u63d0\u4f9b\u5185\u7f6e Heap \u7c7b\n</code></pre> heap.cs<pre><code>/* \u521d\u59cb\u5316\u5806 */\n// \u521d\u59cb\u5316\u5c0f\u9876\u5806\nPriorityQueue&lt;int, int&gt; minHeap = new PriorityQueue&lt;int, int&gt;();\n// \u521d\u59cb\u5316\u5927\u9876\u5806\uff08\u4f7f\u7528 lambda \u8868\u8fbe\u5f0f\u4fee\u6539 Comparator \u5373\u53ef\uff09\nPriorityQueue&lt;int, int&gt; maxHeap = new PriorityQueue&lt;int, int&gt;(Comparer&lt;int&gt;.Create((x, y) =&gt; y - x));\n/* \u5143\u7d20\u5165\u5806 */\nmaxHeap.Enqueue(1, 1);\nmaxHeap.Enqueue(3, 3);\nmaxHeap.Enqueue(2, 2);\nmaxHeap.Enqueue(5, 5);\nmaxHeap.Enqueue(4, 4);\n/* \u83b7\u53d6\u5806\u9876\u5143\u7d20 */\nint peek = maxHeap.Peek();//5\n/* \u5806\u9876\u5143\u7d20\u51fa\u5806 */\n// \u51fa\u5806\u5143\u7d20\u4f1a\u5f62\u6210\u4e00\u4e2a\u4ece\u5927\u5230\u5c0f\u7684\u5e8f\u5217\npeek = maxHeap.Dequeue();  // 5\npeek = maxHeap.Dequeue();  // 4\npeek = maxHeap.Dequeue();  // 3\npeek = maxHeap.Dequeue();  // 2\npeek = maxHeap.Dequeue();  // 1\n/* \u83b7\u53d6\u5806\u5927\u5c0f */\nint size = maxHeap.Count;\n/* \u5224\u65ad\u5806\u662f\u5426\u4e3a\u7a7a */\nbool isEmpty = maxHeap.Count == 0;\n/* \u8f93\u5165\u5217\u8868\u5e76\u5efa\u5806 */\nminHeap = new PriorityQueue&lt;int, int&gt;(new List&lt;(int, int)&gt; { (1, 1), (3, 3), (2, 2), (5, 5), (4, 4), });\n</code></pre> heap.swift<pre><code>// Swift \u672a\u63d0\u4f9b\u5185\u7f6e Heap \u7c7b\n</code></pre> heap.zig<pre><code>\n</code></pre> heap.dart<pre><code>// Dart \u672a\u63d0\u4f9b\u5185\u7f6e Heap \u7c7b\n</code></pre>"},{"location":"chapter_heap/heap/#812","title":"8.1.2. \u00a0 \u5806\u7684\u5b9e\u73b0","text":"<p>\u4e0b\u6587\u5b9e\u73b0\u7684\u662f\u5927\u9876\u5806\u3002\u82e5\u8981\u5c06\u5176\u8f6c\u6362\u4e3a\u5c0f\u9876\u5806\uff0c\u53ea\u9700\u5c06\u6240\u6709\u5927\u5c0f\u903b\u8f91\u5224\u65ad\u53d6\u9006\uff08\u4f8b\u5982\uff0c\u5c06 \\(\\geq\\) \u66ff\u6362\u4e3a \\(\\leq\\) \uff09\u3002\u611f\u5174\u8da3\u7684\u8bfb\u8005\u53ef\u4ee5\u81ea\u884c\u5b9e\u73b0\u3002</p>"},{"location":"chapter_heap/heap/#_1","title":"\u5806\u7684\u5b58\u50a8\u4e0e\u8868\u793a","text":"<p>\u6211\u4eec\u5728\u4e8c\u53c9\u6811\u7ae0\u8282\u4e2d\u5b66\u4e60\u5230\uff0c\u5b8c\u5168\u4e8c\u53c9\u6811\u975e\u5e38\u9002\u5408\u7528\u6570\u7ec4\u6765\u8868\u793a\u3002\u7531\u4e8e\u5806\u6b63\u662f\u4e00\u79cd\u5b8c\u5168\u4e8c\u53c9\u6811\uff0c\u6211\u4eec\u5c06\u91c7\u7528\u6570\u7ec4\u6765\u5b58\u50a8\u5806\u3002</p> <p>\u5f53\u4f7f\u7528\u6570\u7ec4\u8868\u793a\u4e8c\u53c9\u6811\u65f6\uff0c\u5143\u7d20\u4ee3\u8868\u8282\u70b9\u503c\uff0c\u7d22\u5f15\u4ee3\u8868\u8282\u70b9\u5728\u4e8c\u53c9\u6811\u4e2d\u7684\u4f4d\u7f6e\u3002\u8282\u70b9\u6307\u9488\u901a\u8fc7\u7d22\u5f15\u6620\u5c04\u516c\u5f0f\u6765\u5b9e\u73b0\u3002</p> <p>\u5177\u4f53\u800c\u8a00\uff0c\u7ed9\u5b9a\u7d22\u5f15 \\(i\\) \uff0c\u5176\u5de6\u5b50\u8282\u70b9\u7d22\u5f15\u4e3a \\(2i + 1\\) \uff0c\u53f3\u5b50\u8282\u70b9\u7d22\u5f15\u4e3a \\(2i + 2\\) \uff0c\u7236\u8282\u70b9\u7d22\u5f15\u4e3a \\((i - 1) / 2\\)\uff08\u5411\u4e0b\u53d6\u6574\uff09\u3002\u5f53\u7d22\u5f15\u8d8a\u754c\u65f6\uff0c\u8868\u793a\u7a7a\u8282\u70b9\u6216\u8282\u70b9\u4e0d\u5b58\u5728\u3002</p> <p></p> <p> Fig. \u5806\u7684\u8868\u793a\u4e0e\u5b58\u50a8 </p> <p>\u6211\u4eec\u53ef\u4ee5\u5c06\u7d22\u5f15\u6620\u5c04\u516c\u5f0f\u5c01\u88c5\u6210\u51fd\u6570\uff0c\u65b9\u4fbf\u540e\u7eed\u4f7f\u7528\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart my_heap.java<pre><code>/* \u83b7\u53d6\u5de6\u5b50\u8282\u70b9\u7d22\u5f15 */\nint left(int i) {\nreturn 2 * i + 1;\n}\n/* \u83b7\u53d6\u53f3\u5b50\u8282\u70b9\u7d22\u5f15 */\nint right(int i) {\nreturn 2 * i + 2;\n}\n/* \u83b7\u53d6\u7236\u8282\u70b9\u7d22\u5f15 */\nint parent(int i) {\nreturn (i - 1) / 2; // \u5411\u4e0b\u6574\u9664\n}\n</code></pre> my_heap.cpp<pre><code>/* \u83b7\u53d6\u5de6\u5b50\u8282\u70b9\u7d22\u5f15 */\nint left(int i) {\nreturn 2 * i + 1;\n}\n/* \u83b7\u53d6\u53f3\u5b50\u8282\u70b9\u7d22\u5f15 */\nint right(int i) {\nreturn 2 * i + 2;\n}\n/* \u83b7\u53d6\u7236\u8282\u70b9\u7d22\u5f15 */\nint parent(int i) {\nreturn (i - 1) / 2; // \u5411\u4e0b\u53d6\u6574\n}\n</code></pre> my_heap.py<pre><code>def left(self, i: int) -&gt; int:\n\"\"\"\u83b7\u53d6\u5de6\u5b50\u8282\u70b9\u7d22\u5f15\"\"\"\nreturn 2 * i + 1\ndef right(self, i: int) -&gt; int:\n\"\"\"\u83b7\u53d6\u53f3\u5b50\u8282\u70b9\u7d22\u5f15\"\"\"\nreturn 2 * i + 2\ndef parent(self, i: int) -&gt; int:\n\"\"\"\u83b7\u53d6\u7236\u8282\u70b9\u7d22\u5f15\"\"\"\nreturn (i - 1) // 2  # \u5411\u4e0b\u6574\u9664\n</code></pre> my_heap.go<pre><code>/* \u83b7\u53d6\u5de6\u5b50\u8282\u70b9\u7d22\u5f15 */\nfunc (h *maxHeap) left(i int) int {\nreturn 2*i + 1\n}\n/* \u83b7\u53d6\u53f3\u5b50\u8282\u70b9\u7d22\u5f15 */\nfunc (h *maxHeap) right(i int) int {\nreturn 2*i + 2\n}\n/* \u83b7\u53d6\u7236\u8282\u70b9\u7d22\u5f15 */\nfunc (h *maxHeap) parent(i int) int {\n// \u5411\u4e0b\u6574\u9664\nreturn (i - 1) / 2\n}\n</code></pre> my_heap.js<pre><code>/* \u83b7\u53d6\u5de6\u5b50\u8282\u70b9\u7d22\u5f15 */\n#left(i) {\nreturn 2 * i + 1;\n}\n/* \u83b7\u53d6\u53f3\u5b50\u8282\u70b9\u7d22\u5f15 */\n#right(i) {\nreturn 2 * i + 2;\n}\n/* \u83b7\u53d6\u7236\u8282\u70b9\u7d22\u5f15 */\n#parent(i) {\nreturn Math.floor((i - 1) / 2); // \u5411\u4e0b\u6574\u9664\n}\n</code></pre> my_heap.ts<pre><code>/* \u83b7\u53d6\u5de6\u5b50\u8282\u70b9\u7d22\u5f15 */\nleft(i: number): number {\nreturn 2 * i + 1;\n}\n/* \u83b7\u53d6\u53f3\u5b50\u8282\u70b9\u7d22\u5f15 */\nright(i: number): number {\nreturn 2 * i + 2;\n}\n/* \u83b7\u53d6\u7236\u8282\u70b9\u7d22\u5f15 */\nparent(i: number): number {\nreturn Math.floor((i - 1) / 2); // \u5411\u4e0b\u6574\u9664\n}\n</code></pre> my_heap.c<pre><code>/* \u83b7\u53d6\u5de6\u5b50\u8282\u70b9\u7d22\u5f15 */\nint left(maxHeap *h, int i) {\nreturn 2 * i + 1;\n}\n/* \u83b7\u53d6\u53f3\u5b50\u8282\u70b9\u7d22\u5f15 */\nint right(maxHeap *h, int i) {\nreturn 2 * i + 2;\n}\n/* \u83b7\u53d6\u7236\u8282\u70b9\u7d22\u5f15 */\nint parent(maxHeap *h, int i) {\nreturn (i - 1) / 2;\n}\n</code></pre> my_heap.cs<pre><code>/* \u83b7\u53d6\u5de6\u5b50\u8282\u70b9\u7d22\u5f15 */\nint left(int i) {\nreturn 2 * i + 1;\n}\n/* \u83b7\u53d6\u53f3\u5b50\u8282\u70b9\u7d22\u5f15 */\nint right(int i) {\nreturn 2 * i + 2;\n}\n/* \u83b7\u53d6\u7236\u8282\u70b9\u7d22\u5f15 */\nint parent(int i) {\nreturn (i - 1) / 2; // \u5411\u4e0b\u6574\u9664\n}\n</code></pre> my_heap.swift<pre><code>/* \u83b7\u53d6\u5de6\u5b50\u8282\u70b9\u7d22\u5f15 */\nfunc left(i: Int) -&gt; Int {\n2 * i + 1\n}\n/* \u83b7\u53d6\u53f3\u5b50\u8282\u70b9\u7d22\u5f15 */\nfunc right(i: Int) -&gt; Int {\n2 * i + 2\n}\n/* \u83b7\u53d6\u7236\u8282\u70b9\u7d22\u5f15 */\nfunc parent(i: Int) -&gt; Int {\n(i - 1) / 2 // \u5411\u4e0b\u6574\u9664\n}\n</code></pre> my_heap.zig<pre><code>// \u83b7\u53d6\u5de6\u5b50\u8282\u70b9\u7d22\u5f15\nfn left(i: usize) usize {\nreturn 2 * i + 1;\n}\n// \u83b7\u53d6\u53f3\u5b50\u8282\u70b9\u7d22\u5f15\nfn right(i: usize) usize {\nreturn 2 * i + 2;\n}\n// \u83b7\u53d6\u7236\u8282\u70b9\u7d22\u5f15\nfn parent(i: usize) usize {\n// return (i - 1) / 2; // \u5411\u4e0b\u6574\u9664\nreturn @divFloor(i - 1, 2);\n}\n</code></pre> my_heap.dart<pre><code>/* \u83b7\u53d6\u5de6\u5b50\u8282\u70b9\u7d22\u5f15 */\nint _left(int i) {\nreturn 2 * i + 1;\n}\n/* \u83b7\u53d6\u53f3\u5b50\u8282\u70b9\u7d22\u5f15 */\nint _right(int i) {\nreturn 2 * i + 2;\n}\n/* \u83b7\u53d6\u7236\u8282\u70b9\u7d22\u5f15 */\nint _parent(int i) {\nreturn (i - 1) ~/ 2; // \u5411\u4e0b\u6574\u9664\n}\n</code></pre>"},{"location":"chapter_heap/heap/#_2","title":"\u8bbf\u95ee\u5806\u9876\u5143\u7d20","text":"<p>\u5806\u9876\u5143\u7d20\u5373\u4e3a\u4e8c\u53c9\u6811\u7684\u6839\u8282\u70b9\uff0c\u4e5f\u5c31\u662f\u5217\u8868\u7684\u9996\u4e2a\u5143\u7d20\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart my_heap.java<pre><code>/* \u8bbf\u95ee\u5806\u9876\u5143\u7d20 */\nint peek() {\nreturn maxHeap.get(0);\n}\n</code></pre> my_heap.cpp<pre><code>/* \u8bbf\u95ee\u5806\u9876\u5143\u7d20 */\nint peek() {\nreturn maxHeap[0];\n}\n</code></pre> my_heap.py<pre><code>def peek(self) -&gt; int:\n\"\"\"\u8bbf\u95ee\u5806\u9876\u5143\u7d20\"\"\"\nreturn self.max_heap[0]\n</code></pre> my_heap.go<pre><code>/* \u8bbf\u95ee\u5806\u9876\u5143\u7d20 */\nfunc (h *maxHeap) peek() any {\nreturn h.data[0]\n}\n</code></pre> my_heap.js<pre><code>/* \u8bbf\u95ee\u5806\u9876\u5143\u7d20 */\npeek() {\nreturn this.#maxHeap[0];\n}\n</code></pre> my_heap.ts<pre><code>/* \u8bbf\u95ee\u5806\u9876\u5143\u7d20 */\npeek(): number {\nreturn this.maxHeap[0];\n}\n</code></pre> my_heap.c<pre><code>/* \u8bbf\u95ee\u5806\u9876\u5143\u7d20 */\nint peek(maxHeap *h) {\nreturn h-&gt;data[0];\n}\n</code></pre> my_heap.cs<pre><code>/* \u8bbf\u95ee\u5806\u9876\u5143\u7d20 */\nint peek() {\nreturn maxHeap[0];\n}\n</code></pre> my_heap.swift<pre><code>/* \u8bbf\u95ee\u5806\u9876\u5143\u7d20 */\nfunc peek() -&gt; Int {\nmaxHeap[0]\n}\n</code></pre> my_heap.zig<pre><code>// \u8bbf\u95ee\u5806\u9876\u5143\u7d20\nfn peek(self: *Self) T {\nreturn self.max_heap.?.items[0];\n}  </code></pre> my_heap.dart<pre><code>/* \u8bbf\u95ee\u5806\u9876\u5143\u7d20 */\nint peek() {\nreturn _maxHeap[0];\n}\n</code></pre>"},{"location":"chapter_heap/heap/#_3","title":"\u5143\u7d20\u5165\u5806","text":"<p>\u7ed9\u5b9a\u5143\u7d20 <code>val</code> \uff0c\u6211\u4eec\u9996\u5148\u5c06\u5176\u6dfb\u52a0\u5230\u5806\u5e95\u3002\u6dfb\u52a0\u4e4b\u540e\uff0c\u7531\u4e8e val \u53ef\u80fd\u5927\u4e8e\u5806\u4e2d\u5176\u4ed6\u5143\u7d20\uff0c\u5806\u7684\u6210\u7acb\u6761\u4ef6\u53ef\u80fd\u5df2\u88ab\u7834\u574f\u3002\u56e0\u6b64\uff0c\u9700\u8981\u4fee\u590d\u4ece\u63d2\u5165\u8282\u70b9\u5230\u6839\u8282\u70b9\u7684\u8def\u5f84\u4e0a\u7684\u5404\u4e2a\u8282\u70b9\uff0c\u8fd9\u4e2a\u64cd\u4f5c\u88ab\u79f0\u4e3a\u300c\u5806\u5316 Heapify\u300d\u3002</p> <p>\u8003\u8651\u4ece\u5165\u5806\u8282\u70b9\u5f00\u59cb\uff0c\u4ece\u5e95\u81f3\u9876\u6267\u884c\u5806\u5316\u3002\u5177\u4f53\u6765\u8bf4\uff0c\u6211\u4eec\u6bd4\u8f83\u63d2\u5165\u8282\u70b9\u4e0e\u5176\u7236\u8282\u70b9\u7684\u503c\uff0c\u5982\u679c\u63d2\u5165\u8282\u70b9\u66f4\u5927\uff0c\u5219\u5c06\u5b83\u4eec\u4ea4\u6362\u3002\u7136\u540e\u7ee7\u7eed\u6267\u884c\u6b64\u64cd\u4f5c\uff0c\u4ece\u5e95\u81f3\u9876\u4fee\u590d\u5806\u4e2d\u7684\u5404\u4e2a\u8282\u70b9\uff0c\u76f4\u81f3\u8d8a\u8fc7\u6839\u8282\u70b9\u6216\u9047\u5230\u65e0\u9700\u4ea4\u6362\u7684\u8282\u70b9\u65f6\u7ed3\u675f\u3002</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p>\u8bbe\u8282\u70b9\u603b\u6570\u4e3a \\(n\\) \uff0c\u5219\u6811\u7684\u9ad8\u5ea6\u4e3a \\(O(\\log n)\\) \u3002\u7531\u6b64\u53ef\u77e5\uff0c\u5806\u5316\u64cd\u4f5c\u7684\u5faa\u73af\u8f6e\u6570\u6700\u591a\u4e3a \\(O(\\log n)\\) \uff0c\u5143\u7d20\u5165\u5806\u64cd\u4f5c\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(\\log n)\\) \u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart my_heap.java<pre><code>/* \u5143\u7d20\u5165\u5806 */\nvoid push(int val) {\n// \u6dfb\u52a0\u8282\u70b9\nmaxHeap.add(val);\n// \u4ece\u5e95\u81f3\u9876\u5806\u5316\nsiftUp(size() - 1);\n}\n/* \u4ece\u8282\u70b9 i \u5f00\u59cb\uff0c\u4ece\u5e95\u81f3\u9876\u5806\u5316 */\nvoid siftUp(int i) {\nwhile (true) {\n// \u83b7\u53d6\u8282\u70b9 i \u7684\u7236\u8282\u70b9\nint p = parent(i);\n// \u5f53\u201c\u8d8a\u8fc7\u6839\u8282\u70b9\u201d\u6216\u201c\u8282\u70b9\u65e0\u9700\u4fee\u590d\u201d\u65f6\uff0c\u7ed3\u675f\u5806\u5316\nif (p &lt; 0 || maxHeap.get(i) &lt;= maxHeap.get(p))\nbreak;\n// \u4ea4\u6362\u4e24\u8282\u70b9\nswap(i, p);\n// \u5faa\u73af\u5411\u4e0a\u5806\u5316\ni = p;\n}\n}\n</code></pre> my_heap.cpp<pre><code>/* \u5143\u7d20\u5165\u5806 */\nvoid push(int val) {\n// \u6dfb\u52a0\u8282\u70b9\nmaxHeap.push_back(val);\n// \u4ece\u5e95\u81f3\u9876\u5806\u5316\nsiftUp(size() - 1);\n}\n/* \u4ece\u8282\u70b9 i \u5f00\u59cb\uff0c\u4ece\u5e95\u81f3\u9876\u5806\u5316 */\nvoid siftUp(int i) {\nwhile (true) {\n// \u83b7\u53d6\u8282\u70b9 i \u7684\u7236\u8282\u70b9\nint p = parent(i);\n// \u5f53\u201c\u8d8a\u8fc7\u6839\u8282\u70b9\u201d\u6216\u201c\u8282\u70b9\u65e0\u9700\u4fee\u590d\u201d\u65f6\uff0c\u7ed3\u675f\u5806\u5316\nif (p &lt; 0 || maxHeap[i] &lt;= maxHeap[p])\nbreak;\n// \u4ea4\u6362\u4e24\u8282\u70b9\nswap(maxHeap[i], maxHeap[p]);\n// \u5faa\u73af\u5411\u4e0a\u5806\u5316\ni = p;\n}\n}\n</code></pre> my_heap.py<pre><code>def push(self, val: int):\n\"\"\"\u5143\u7d20\u5165\u5806\"\"\"\n# \u6dfb\u52a0\u8282\u70b9\nself.max_heap.append(val)\n# \u4ece\u5e95\u81f3\u9876\u5806\u5316\nself.sift_up(self.size() - 1)\ndef sift_up(self, i: int):\n\"\"\"\u4ece\u8282\u70b9 i \u5f00\u59cb\uff0c\u4ece\u5e95\u81f3\u9876\u5806\u5316\"\"\"\nwhile True:\n# \u83b7\u53d6\u8282\u70b9 i \u7684\u7236\u8282\u70b9\np = self.parent(i)\n# \u5f53\u201c\u8d8a\u8fc7\u6839\u8282\u70b9\u201d\u6216\u201c\u8282\u70b9\u65e0\u9700\u4fee\u590d\u201d\u65f6\uff0c\u7ed3\u675f\u5806\u5316\nif p &lt; 0 or self.max_heap[i] &lt;= self.max_heap[p]:\nbreak\n# \u4ea4\u6362\u4e24\u8282\u70b9\nself.swap(i, p)\n# \u5faa\u73af\u5411\u4e0a\u5806\u5316\ni = p\n</code></pre> my_heap.go<pre><code>/* \u5143\u7d20\u5165\u5806 */\nfunc (h *maxHeap) push(val any) {\n// \u6dfb\u52a0\u8282\u70b9\nh.data = append(h.data, val)\n// \u4ece\u5e95\u81f3\u9876\u5806\u5316\nh.siftUp(len(h.data) - 1)\n}\n/* \u4ece\u8282\u70b9 i \u5f00\u59cb\uff0c\u4ece\u5e95\u81f3\u9876\u5806\u5316 */\nfunc (h *maxHeap) siftUp(i int) {\nfor true {\n// \u83b7\u53d6\u8282\u70b9 i \u7684\u7236\u8282\u70b9\np := h.parent(i)\n// \u5f53\u201c\u8d8a\u8fc7\u6839\u8282\u70b9\u201d\u6216\u201c\u8282\u70b9\u65e0\u9700\u4fee\u590d\u201d\u65f6\uff0c\u7ed3\u675f\u5806\u5316\nif p &lt; 0 || h.data[i].(int) &lt;= h.data[p].(int) {\nbreak\n}\n// \u4ea4\u6362\u4e24\u8282\u70b9\nh.swap(i, p)\n// \u5faa\u73af\u5411\u4e0a\u5806\u5316\ni = p\n}\n}\n</code></pre> my_heap.js<pre><code>/* \u5143\u7d20\u5165\u5806 */\npush(val) {\n// \u6dfb\u52a0\u8282\u70b9\nthis.#maxHeap.push(val);\n// \u4ece\u5e95\u81f3\u9876\u5806\u5316\nthis.#siftUp(this.size() - 1);\n}\n/* \u4ece\u8282\u70b9 i \u5f00\u59cb\uff0c\u4ece\u5e95\u81f3\u9876\u5806\u5316 */\n#siftUp(i) {\nwhile (true) {\n// \u83b7\u53d6\u8282\u70b9 i \u7684\u7236\u8282\u70b9\nconst p = this.#parent(i);\n// \u5f53\u201c\u8d8a\u8fc7\u6839\u8282\u70b9\u201d\u6216\u201c\u8282\u70b9\u65e0\u9700\u4fee\u590d\u201d\u65f6\uff0c\u7ed3\u675f\u5806\u5316\nif (p &lt; 0 || this.#maxHeap[i] &lt;= this.#maxHeap[p]) break;\n// \u4ea4\u6362\u4e24\u8282\u70b9\nthis.#swap(i, p);\n// \u5faa\u73af\u5411\u4e0a\u5806\u5316\ni = p;\n}\n}\n</code></pre> my_heap.ts<pre><code>/* \u5143\u7d20\u5165\u5806 */\npush(val: number): void {\n// \u6dfb\u52a0\u8282\u70b9\nthis.maxHeap.push(val);\n// \u4ece\u5e95\u81f3\u9876\u5806\u5316\nthis.siftUp(this.size() - 1);\n}\n/* \u4ece\u8282\u70b9 i \u5f00\u59cb\uff0c\u4ece\u5e95\u81f3\u9876\u5806\u5316 */\nsiftUp(i: number): void {\nwhile (true) {\n// \u83b7\u53d6\u8282\u70b9 i \u7684\u7236\u8282\u70b9\nconst p = this.parent(i);\n// \u5f53\u201c\u8d8a\u8fc7\u6839\u8282\u70b9\u201d\u6216\u201c\u8282\u70b9\u65e0\u9700\u4fee\u590d\u201d\u65f6\uff0c\u7ed3\u675f\u5806\u5316\nif (p &lt; 0 || this.maxHeap[i] &lt;= this.maxHeap[p]) break;\n// \u4ea4\u6362\u4e24\u8282\u70b9\nthis.swap(i, p);\n// \u5faa\u73af\u5411\u4e0a\u5806\u5316\ni = p;\n}\n}\n</code></pre> my_heap.c<pre><code>/* \u5143\u7d20\u5165\u5806 */\nvoid push(maxHeap *h, int val) {\n// \u9ed8\u8ba4\u60c5\u51b5\u4e0b\uff0c\u4e0d\u5e94\u8be5\u6dfb\u52a0\u8fd9\u4e48\u591a\u8282\u70b9\nif (h-&gt;size == MAX_SIZE) {\nprintf(\"heap is full!\");\nreturn;\n}\n// \u6dfb\u52a0\u8282\u70b9\nh-&gt;data[h-&gt;size] = val;\nh-&gt;size++;\n// \u4ece\u5e95\u81f3\u9876\u5806\u5316\nsiftUp(h, h-&gt;size - 1);\n}\n/* \u4ece\u8282\u70b9 i \u5f00\u59cb\uff0c\u4ece\u5e95\u81f3\u9876\u5806\u5316 */\nvoid siftUp(maxHeap *h, int i) {\nwhile (true) {\n// \u83b7\u53d6\u8282\u70b9 i \u7684\u7236\u8282\u70b9\nint p = parent(h, i);\n// \u5f53\u201c\u8d8a\u8fc7\u6839\u8282\u70b9\u201d\u6216\u201c\u8282\u70b9\u65e0\u9700\u4fee\u590d\u201d\u65f6\uff0c\u7ed3\u675f\u5806\u5316\nif (p &lt; 0 || h-&gt;data[i] &lt;= h-&gt;data[p]) {\nbreak;\n}\n// \u4ea4\u6362\u4e24\u8282\u70b9\nswap(h, i, p);\n// \u5faa\u73af\u5411\u4e0a\u5806\u5316\ni = p;\n}\n}\n</code></pre> my_heap.cs<pre><code>/* \u5143\u7d20\u5165\u5806 */\nvoid push(int val) {\n// \u6dfb\u52a0\u8282\u70b9\nmaxHeap.Add(val);\n// \u4ece\u5e95\u81f3\u9876\u5806\u5316\nsiftUp(size() - 1);\n}\n/* \u4ece\u8282\u70b9 i \u5f00\u59cb\uff0c\u4ece\u5e95\u81f3\u9876\u5806\u5316 */\nvoid siftUp(int i) {\nwhile (true) {\n// \u83b7\u53d6\u8282\u70b9 i \u7684\u7236\u8282\u70b9\nint p = parent(i);\n// \u82e5\u201c\u8d8a\u8fc7\u6839\u8282\u70b9\u201d\u6216\u201c\u8282\u70b9\u65e0\u9700\u4fee\u590d\u201d\uff0c\u5219\u7ed3\u675f\u5806\u5316\nif (p &lt; 0 || maxHeap[i] &lt;= maxHeap[p])\nbreak;\n// \u4ea4\u6362\u4e24\u8282\u70b9\nswap(i, p);\n// \u5faa\u73af\u5411\u4e0a\u5806\u5316\ni = p;\n}\n}\n</code></pre> my_heap.swift<pre><code>/* \u5143\u7d20\u5165\u5806 */\nfunc push(val: Int) {\n// \u6dfb\u52a0\u8282\u70b9\nmaxHeap.append(val)\n// \u4ece\u5e95\u81f3\u9876\u5806\u5316\nsiftUp(i: size() - 1)\n}\n/* \u4ece\u8282\u70b9 i \u5f00\u59cb\uff0c\u4ece\u5e95\u81f3\u9876\u5806\u5316 */\nfunc siftUp(i: Int) {\nvar i = i\nwhile true {\n// \u83b7\u53d6\u8282\u70b9 i \u7684\u7236\u8282\u70b9\nlet p = parent(i: i)\n// \u5f53\u201c\u8d8a\u8fc7\u6839\u8282\u70b9\u201d\u6216\u201c\u8282\u70b9\u65e0\u9700\u4fee\u590d\u201d\u65f6\uff0c\u7ed3\u675f\u5806\u5316\nif p &lt; 0 || maxHeap[i] &lt;= maxHeap[p] {\nbreak\n}\n// \u4ea4\u6362\u4e24\u8282\u70b9\nswap(i: i, j: p)\n// \u5faa\u73af\u5411\u4e0a\u5806\u5316\ni = p\n}\n}\n</code></pre> my_heap.zig<pre><code>// \u5143\u7d20\u5165\u5806\nfn push(self: *Self, val: T) !void {\n// \u6dfb\u52a0\u8282\u70b9\ntry self.max_heap.?.append(val);\n// \u4ece\u5e95\u81f3\u9876\u5806\u5316\ntry self.siftUp(self.size() - 1);\n}  // \u4ece\u8282\u70b9 i \u5f00\u59cb\uff0c\u4ece\u5e95\u81f3\u9876\u5806\u5316\nfn siftUp(self: *Self, i_: usize) !void {\nvar i = i_;\nwhile (true) {\n// \u83b7\u53d6\u8282\u70b9 i \u7684\u7236\u8282\u70b9\nvar p = parent(i);\n// \u5f53\u201c\u8d8a\u8fc7\u6839\u8282\u70b9\u201d\u6216\u201c\u8282\u70b9\u65e0\u9700\u4fee\u590d\u201d\u65f6\uff0c\u7ed3\u675f\u5806\u5316\nif (p &lt; 0 or self.max_heap.?.items[i] &lt;= self.max_heap.?.items[p]) break;\n// \u4ea4\u6362\u4e24\u8282\u70b9\ntry self.swap(i, p);\n// \u5faa\u73af\u5411\u4e0a\u5806\u5316\ni = p;\n}\n}\n</code></pre> my_heap.dart<pre><code>/* \u5143\u7d20\u5165\u5806 */\nvoid push(int val) {\n// \u6dfb\u52a0\u8282\u70b9\n_maxHeap.add(val);\n// \u4ece\u5e95\u81f3\u9876\u5806\u5316\n_siftUp(size() - 1);\n}\n[class]{MaxHeap}-[func]{siftUp}\n</code></pre>"},{"location":"chapter_heap/heap/#_4","title":"\u5806\u9876\u5143\u7d20\u51fa\u5806","text":"<p>\u5806\u9876\u5143\u7d20\u662f\u4e8c\u53c9\u6811\u7684\u6839\u8282\u70b9\uff0c\u5373\u5217\u8868\u9996\u5143\u7d20\u3002\u5982\u679c\u6211\u4eec\u76f4\u63a5\u4ece\u5217\u8868\u4e2d\u5220\u9664\u9996\u5143\u7d20\uff0c\u90a3\u4e48\u4e8c\u53c9\u6811\u4e2d\u6240\u6709\u8282\u70b9\u7684\u7d22\u5f15\u90fd\u4f1a\u53d1\u751f\u53d8\u5316\uff0c\u8fd9\u5c06\u4f7f\u5f97\u540e\u7eed\u4f7f\u7528\u5806\u5316\u4fee\u590d\u53d8\u5f97\u56f0\u96be\u3002\u4e3a\u4e86\u5c3d\u91cf\u51cf\u5c11\u5143\u7d20\u7d22\u5f15\u7684\u53d8\u52a8\uff0c\u6211\u4eec\u91c7\u53d6\u4ee5\u4e0b\u64cd\u4f5c\u6b65\u9aa4\uff1a</p> <ol> <li>\u4ea4\u6362\u5806\u9876\u5143\u7d20\u4e0e\u5806\u5e95\u5143\u7d20\uff08\u5373\u4ea4\u6362\u6839\u8282\u70b9\u4e0e\u6700\u53f3\u53f6\u8282\u70b9\uff09\uff1b</li> <li>\u4ea4\u6362\u5b8c\u6210\u540e\uff0c\u5c06\u5806\u5e95\u4ece\u5217\u8868\u4e2d\u5220\u9664\uff08\u6ce8\u610f\uff0c\u7531\u4e8e\u5df2\u7ecf\u4ea4\u6362\uff0c\u5b9e\u9645\u4e0a\u5220\u9664\u7684\u662f\u539f\u6765\u7684\u5806\u9876\u5143\u7d20\uff09\uff1b</li> <li>\u4ece\u6839\u8282\u70b9\u5f00\u59cb\uff0c\u4ece\u9876\u81f3\u5e95\u6267\u884c\u5806\u5316\uff1b</li> </ol> <p>\u987e\u540d\u601d\u4e49\uff0c\u4ece\u9876\u81f3\u5e95\u5806\u5316\u7684\u64cd\u4f5c\u65b9\u5411\u4e0e\u4ece\u5e95\u81f3\u9876\u5806\u5316\u76f8\u53cd\uff0c\u6211\u4eec\u5c06\u6839\u8282\u70b9\u7684\u503c\u4e0e\u5176\u4e24\u4e2a\u5b50\u8282\u70b9\u7684\u503c\u8fdb\u884c\u6bd4\u8f83\uff0c\u5c06\u6700\u5927\u7684\u5b50\u8282\u70b9\u4e0e\u6839\u8282\u70b9\u4ea4\u6362\uff1b\u7136\u540e\u5faa\u73af\u6267\u884c\u6b64\u64cd\u4f5c\uff0c\u76f4\u5230\u8d8a\u8fc7\u53f6\u8282\u70b9\u6216\u9047\u5230\u65e0\u9700\u4ea4\u6362\u7684\u8282\u70b9\u65f6\u7ed3\u675f\u3002</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p>\u4e0e\u5143\u7d20\u5165\u5806\u64cd\u4f5c\u76f8\u4f3c\uff0c\u5806\u9876\u5143\u7d20\u51fa\u5806\u64cd\u4f5c\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e5f\u4e3a \\(O(\\log n)\\) \u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart my_heap.java<pre><code>/* \u5143\u7d20\u51fa\u5806 */\nint pop() {\n// \u5224\u7a7a\u5904\u7406\nif (isEmpty())\nthrow new IndexOutOfBoundsException();\n// \u4ea4\u6362\u6839\u8282\u70b9\u4e0e\u6700\u53f3\u53f6\u8282\u70b9\uff08\u5373\u4ea4\u6362\u9996\u5143\u7d20\u4e0e\u5c3e\u5143\u7d20\uff09\nswap(0, size() - 1);\n// \u5220\u9664\u8282\u70b9\nint val = maxHeap.remove(size() - 1);\n// \u4ece\u9876\u81f3\u5e95\u5806\u5316\nsiftDown(0);\n// \u8fd4\u56de\u5806\u9876\u5143\u7d20\nreturn val;\n}\n/* \u4ece\u8282\u70b9 i \u5f00\u59cb\uff0c\u4ece\u9876\u81f3\u5e95\u5806\u5316 */\nvoid siftDown(int i) {\nwhile (true) {\n// \u5224\u65ad\u8282\u70b9 i, l, r \u4e2d\u503c\u6700\u5927\u7684\u8282\u70b9\uff0c\u8bb0\u4e3a ma\nint l = left(i), r = right(i), ma = i;\nif (l &lt; size() &amp;&amp; maxHeap.get(l) &gt; maxHeap.get(ma))\nma = l;\nif (r &lt; size() &amp;&amp; maxHeap.get(r) &gt; maxHeap.get(ma))\nma = r;\n// \u82e5\u8282\u70b9 i \u6700\u5927\u6216\u7d22\u5f15 l, r \u8d8a\u754c\uff0c\u5219\u65e0\u9700\u7ee7\u7eed\u5806\u5316\uff0c\u8df3\u51fa\nif (ma == i)\nbreak;\n// \u4ea4\u6362\u4e24\u8282\u70b9\nswap(i, ma);\n// \u5faa\u73af\u5411\u4e0b\u5806\u5316\ni = ma;\n}\n}\n</code></pre> my_heap.cpp<pre><code>/* \u5143\u7d20\u51fa\u5806 */\nvoid pop() {\n// \u5224\u7a7a\u5904\u7406\nif (empty()) {\nthrow out_of_range(\"\u5806\u4e3a\u7a7a\");\n}\n// \u4ea4\u6362\u6839\u8282\u70b9\u4e0e\u6700\u53f3\u53f6\u8282\u70b9\uff08\u5373\u4ea4\u6362\u9996\u5143\u7d20\u4e0e\u5c3e\u5143\u7d20\uff09\nswap(maxHeap[0], maxHeap[size() - 1]);\n// \u5220\u9664\u8282\u70b9\nmaxHeap.pop_back();\n// \u4ece\u9876\u81f3\u5e95\u5806\u5316\nsiftDown(0);\n}\n/* \u4ece\u8282\u70b9 i \u5f00\u59cb\uff0c\u4ece\u9876\u81f3\u5e95\u5806\u5316 */\nvoid siftDown(int i) {\nwhile (true) {\n// \u5224\u65ad\u8282\u70b9 i, l, r \u4e2d\u503c\u6700\u5927\u7684\u8282\u70b9\uff0c\u8bb0\u4e3a ma\nint l = left(i), r = right(i), ma = i;\n// \u82e5\u8282\u70b9 i \u6700\u5927\u6216\u7d22\u5f15 l, r \u8d8a\u754c\uff0c\u5219\u65e0\u9700\u7ee7\u7eed\u5806\u5316\uff0c\u8df3\u51fa\nif (l &lt; size() &amp;&amp; maxHeap[l] &gt; maxHeap[ma])\nma = l;\nif (r &lt; size() &amp;&amp; maxHeap[r] &gt; maxHeap[ma])\nma = r;\n// \u82e5\u8282\u70b9 i \u6700\u5927\u6216\u7d22\u5f15 l, r \u8d8a\u754c\uff0c\u5219\u65e0\u9700\u7ee7\u7eed\u5806\u5316\uff0c\u8df3\u51fa\nif (ma == i)\nbreak;\nswap(maxHeap[i], maxHeap[ma]);\n// \u5faa\u73af\u5411\u4e0b\u5806\u5316\ni = ma;\n}\n}\n</code></pre> my_heap.py<pre><code>def pop(self) -&gt; int:\n\"\"\"\u5143\u7d20\u51fa\u5806\"\"\"\n# \u5224\u7a7a\u5904\u7406\nif self.is_empty():\nraise IndexError(\"\u5806\u4e3a\u7a7a\")\n# \u4ea4\u6362\u6839\u8282\u70b9\u4e0e\u6700\u53f3\u53f6\u8282\u70b9\uff08\u5373\u4ea4\u6362\u9996\u5143\u7d20\u4e0e\u5c3e\u5143\u7d20\uff09\nself.swap(0, self.size() - 1)\n# \u5220\u9664\u8282\u70b9\nval = self.max_heap.pop()\n# \u4ece\u9876\u81f3\u5e95\u5806\u5316\nself.sift_down(0)\n# \u8fd4\u56de\u5806\u9876\u5143\u7d20\nreturn val\ndef sift_down(self, i: int):\n\"\"\"\u4ece\u8282\u70b9 i \u5f00\u59cb\uff0c\u4ece\u9876\u81f3\u5e95\u5806\u5316\"\"\"\nwhile True:\n# \u5224\u65ad\u8282\u70b9 i, l, r \u4e2d\u503c\u6700\u5927\u7684\u8282\u70b9\uff0c\u8bb0\u4e3a ma\nl, r, ma = self.left(i), self.right(i), i\nif l &lt; self.size() and self.max_heap[l] &gt; self.max_heap[ma]:\nma = l\nif r &lt; self.size() and self.max_heap[r] &gt; self.max_heap[ma]:\nma = r\n# \u82e5\u8282\u70b9 i \u6700\u5927\u6216\u7d22\u5f15 l, r \u8d8a\u754c\uff0c\u5219\u65e0\u9700\u7ee7\u7eed\u5806\u5316\uff0c\u8df3\u51fa\nif ma == i:\nbreak\n# \u4ea4\u6362\u4e24\u8282\u70b9\nself.swap(i, ma)\n# \u5faa\u73af\u5411\u4e0b\u5806\u5316\ni = ma\n</code></pre> my_heap.go<pre><code>/* \u5143\u7d20\u51fa\u5806 */\nfunc (h *maxHeap) pop() any {\n// \u5224\u7a7a\u5904\u7406\nif h.isEmpty() {\nfmt.Println(\"error\")\nreturn nil\n}\n// \u4ea4\u6362\u6839\u8282\u70b9\u4e0e\u6700\u53f3\u53f6\u8282\u70b9\uff08\u5373\u4ea4\u6362\u9996\u5143\u7d20\u4e0e\u5c3e\u5143\u7d20\uff09\nh.swap(0, h.size()-1)\n// \u5220\u9664\u8282\u70b9\nval := h.data[len(h.data)-1]\nh.data = h.data[:len(h.data)-1]\n// \u4ece\u9876\u81f3\u5e95\u5806\u5316\nh.siftDown(0)\n// \u8fd4\u56de\u5806\u9876\u5143\u7d20\nreturn val\n}\n/* \u4ece\u8282\u70b9 i \u5f00\u59cb\uff0c\u4ece\u9876\u81f3\u5e95\u5806\u5316 */\nfunc (h *maxHeap) siftDown(i int) {\nfor true {\n// \u5224\u65ad\u8282\u70b9 i, l, r \u4e2d\u503c\u6700\u5927\u7684\u8282\u70b9\uff0c\u8bb0\u4e3a max\nl, r, max := h.left(i), h.right(i), i\nif l &lt; h.size() &amp;&amp; h.data[l].(int) &gt; h.data[max].(int) {\nmax = l\n}\nif r &lt; h.size() &amp;&amp; h.data[r].(int) &gt; h.data[max].(int) {\nmax = r\n}\n// \u82e5\u8282\u70b9 i \u6700\u5927\u6216\u7d22\u5f15 l, r \u8d8a\u754c\uff0c\u5219\u65e0\u9700\u7ee7\u7eed\u5806\u5316\uff0c\u8df3\u51fa\nif max == i {\nbreak\n}\n// \u4ea4\u6362\u4e24\u8282\u70b9\nh.swap(i, max)\n// \u5faa\u73af\u5411\u4e0b\u5806\u5316\ni = max\n}\n}\n</code></pre> my_heap.js<pre><code>/* \u5143\u7d20\u51fa\u5806 */\npop() {\n// \u5224\u7a7a\u5904\u7406\nif (this.isEmpty()) throw new Error('\u5806\u4e3a\u7a7a');\n// \u4ea4\u6362\u6839\u8282\u70b9\u4e0e\u6700\u53f3\u53f6\u8282\u70b9\uff08\u5373\u4ea4\u6362\u9996\u5143\u7d20\u4e0e\u5c3e\u5143\u7d20\uff09\nthis.#swap(0, this.size() - 1);\n// \u5220\u9664\u8282\u70b9\nconst val = this.#maxHeap.pop();\n// \u4ece\u9876\u81f3\u5e95\u5806\u5316\nthis.#siftDown(0);\n// \u8fd4\u56de\u5806\u9876\u5143\u7d20\nreturn val;\n}\n/* \u4ece\u8282\u70b9 i \u5f00\u59cb\uff0c\u4ece\u9876\u81f3\u5e95\u5806\u5316 */\n#siftDown(i) {\nwhile (true) {\n// \u5224\u65ad\u8282\u70b9 i, l, r \u4e2d\u503c\u6700\u5927\u7684\u8282\u70b9\uff0c\u8bb0\u4e3a ma\nconst l = this.#left(i),\nr = this.#right(i);\nlet ma = i;\nif (l &lt; this.size() &amp;&amp; this.#maxHeap[l] &gt; this.#maxHeap[ma]) ma = l;\nif (r &lt; this.size() &amp;&amp; this.#maxHeap[r] &gt; this.#maxHeap[ma]) ma = r;\n// \u82e5\u8282\u70b9 i \u6700\u5927\u6216\u7d22\u5f15 l, r \u8d8a\u754c\uff0c\u5219\u65e0\u9700\u7ee7\u7eed\u5806\u5316\uff0c\u8df3\u51fa\nif (ma == i) break;\n// \u4ea4\u6362\u4e24\u8282\u70b9\nthis.#swap(i, ma);\n// \u5faa\u73af\u5411\u4e0b\u5806\u5316\ni = ma;\n}\n}\n</code></pre> my_heap.ts<pre><code>/* \u5143\u7d20\u51fa\u5806 */\npop(): number {\n// \u5224\u7a7a\u5904\u7406\nif (this.isEmpty()) throw new RangeError('Heap is empty.');\n// \u4ea4\u6362\u6839\u8282\u70b9\u4e0e\u6700\u53f3\u53f6\u8282\u70b9\uff08\u5373\u4ea4\u6362\u9996\u5143\u7d20\u4e0e\u5c3e\u5143\u7d20\uff09\nthis.swap(0, this.size() - 1);\n// \u5220\u9664\u8282\u70b9\nconst val = this.maxHeap.pop();\n// \u4ece\u9876\u81f3\u5e95\u5806\u5316\nthis.siftDown(0);\n// \u8fd4\u56de\u5806\u9876\u5143\u7d20\nreturn val;\n}\n/* \u4ece\u8282\u70b9 i \u5f00\u59cb\uff0c\u4ece\u9876\u81f3\u5e95\u5806\u5316 */\nsiftDown(i: number): void {\nwhile (true) {\n// \u5224\u65ad\u8282\u70b9 i, l, r \u4e2d\u503c\u6700\u5927\u7684\u8282\u70b9\uff0c\u8bb0\u4e3a ma\nconst l = this.left(i),\nr = this.right(i);\nlet ma = i;\nif (l &lt; this.size() &amp;&amp; this.maxHeap[l] &gt; this.maxHeap[ma]) ma = l;\nif (r &lt; this.size() &amp;&amp; this.maxHeap[r] &gt; this.maxHeap[ma]) ma = r;\n// \u82e5\u8282\u70b9 i \u6700\u5927\u6216\u7d22\u5f15 l, r \u8d8a\u754c\uff0c\u5219\u65e0\u9700\u7ee7\u7eed\u5806\u5316\uff0c\u8df3\u51fa\nif (ma == i) break;\n// \u4ea4\u6362\u4e24\u8282\u70b9\nthis.swap(i, ma);\n// \u5faa\u73af\u5411\u4e0b\u5806\u5316\ni = ma;\n}\n}\n</code></pre> my_heap.c<pre><code>/* \u5143\u7d20\u51fa\u5806 */\nint pop(maxHeap *h) {\n// \u5224\u7a7a\u5904\u7406\nif (isEmpty(h)) {\nprintf(\"heap is empty!\");\nreturn INT_MAX;\n}\n// \u4ea4\u6362\u6839\u8282\u70b9\u4e0e\u6700\u53f3\u53f6\u8282\u70b9\uff08\u5373\u4ea4\u6362\u9996\u5143\u7d20\u4e0e\u5c3e\u5143\u7d20\uff09\nswap(h, 0, size(h) - 1);\n// \u5220\u9664\u8282\u70b9\nint val = h-&gt;data[h-&gt;size - 1];\nh-&gt;size--;\n// \u4ece\u9876\u81f3\u5e95\u5806\u5316\nsiftDown(h, 0);\n// \u8fd4\u56de\u5806\u9876\u5143\u7d20\nreturn val;\n}\n/* \u4ece\u8282\u70b9 i \u5f00\u59cb\uff0c\u4ece\u9876\u81f3\u5e95\u5806\u5316 */\nvoid siftDown(maxHeap *h, int i) {\nwhile (true) {\n// \u5224\u65ad\u8282\u70b9 i, l, r \u4e2d\u503c\u6700\u5927\u7684\u8282\u70b9\uff0c\u8bb0\u4e3a max\nint l = left(h, i);\nint r = right(h, i);\nint max = i;\nif (l &lt; size(h) &amp;&amp; h-&gt;data[l] &gt; h-&gt;data[max]) {\nmax = l;\n}\nif (r &lt; size(h) &amp;&amp; h-&gt;data[r] &gt; h-&gt;data[max]) {\nmax = r;\n}\n// \u82e5\u8282\u70b9 i \u6700\u5927\u6216\u7d22\u5f15 l, r \u8d8a\u754c\uff0c\u5219\u65e0\u9700\u7ee7\u7eed\u5806\u5316\uff0c\u8df3\u51fa\nif (max == i) {\nbreak;\n}\n// \u4ea4\u6362\u4e24\u8282\u70b9\nswap(h, i, max);\n// \u5faa\u73af\u5411\u4e0b\u5806\u5316\ni = max;\n}\n}\n</code></pre> my_heap.cs<pre><code>/* \u5143\u7d20\u51fa\u5806 */\nint pop() {\n// \u5224\u7a7a\u5904\u7406\nif (isEmpty())\nthrow new IndexOutOfRangeException();\n// \u4ea4\u6362\u6839\u8282\u70b9\u4e0e\u6700\u53f3\u53f6\u8282\u70b9\uff08\u5373\u4ea4\u6362\u9996\u5143\u7d20\u4e0e\u5c3e\u5143\u7d20\uff09\nswap(0, size() - 1);\n// \u5220\u9664\u8282\u70b9\nint val = maxHeap.Last();\nmaxHeap.RemoveAt(size() - 1);\n// \u4ece\u9876\u81f3\u5e95\u5806\u5316\nsiftDown(0);\n// \u8fd4\u56de\u5806\u9876\u5143\u7d20\nreturn val;\n}\n/* \u4ece\u8282\u70b9 i \u5f00\u59cb\uff0c\u4ece\u9876\u81f3\u5e95\u5806\u5316 */\nvoid siftDown(int i) {\nwhile (true) {\n// \u5224\u65ad\u8282\u70b9 i, l, r \u4e2d\u503c\u6700\u5927\u7684\u8282\u70b9\uff0c\u8bb0\u4e3a ma\nint l = left(i), r = right(i), ma = i;\nif (l &lt; size() &amp;&amp; maxHeap[l] &gt; maxHeap[ma])\nma = l;\nif (r &lt; size() &amp;&amp; maxHeap[r] &gt; maxHeap[ma])\nma = r;\n// \u82e5\u201c\u8282\u70b9 i \u6700\u5927\u201d\u6216\u201c\u8d8a\u8fc7\u53f6\u8282\u70b9\u201d\uff0c\u5219\u7ed3\u675f\u5806\u5316\nif (ma == i) break;\n// \u4ea4\u6362\u4e24\u8282\u70b9\nswap(i, ma);\n// \u5faa\u73af\u5411\u4e0b\u5806\u5316\ni = ma;\n}\n}\n</code></pre> my_heap.swift<pre><code>/* \u5143\u7d20\u51fa\u5806 */\nfunc pop() -&gt; Int {\n// \u5224\u7a7a\u5904\u7406\nif isEmpty() {\nfatalError(\"\u5806\u4e3a\u7a7a\")\n}\n// \u4ea4\u6362\u6839\u8282\u70b9\u4e0e\u6700\u53f3\u53f6\u8282\u70b9\uff08\u5373\u4ea4\u6362\u9996\u5143\u7d20\u4e0e\u5c3e\u5143\u7d20\uff09\nswap(i: 0, j: size() - 1)\n// \u5220\u9664\u8282\u70b9\nlet val = maxHeap.remove(at: size() - 1)\n// \u4ece\u9876\u81f3\u5e95\u5806\u5316\nsiftDown(i: 0)\n// \u8fd4\u56de\u5806\u9876\u5143\u7d20\nreturn val\n}\n/* \u4ece\u8282\u70b9 i \u5f00\u59cb\uff0c\u4ece\u9876\u81f3\u5e95\u5806\u5316 */\nfunc siftDown(i: Int) {\nvar i = i\nwhile true {\n// \u5224\u65ad\u8282\u70b9 i, l, r \u4e2d\u503c\u6700\u5927\u7684\u8282\u70b9\uff0c\u8bb0\u4e3a ma\nlet l = left(i: i)\nlet r = right(i: i)\nvar ma = i\nif l &lt; size(), maxHeap[l] &gt; maxHeap[ma] {\nma = l\n}\nif r &lt; size(), maxHeap[r] &gt; maxHeap[ma] {\nma = r\n}\n// \u82e5\u8282\u70b9 i \u6700\u5927\u6216\u7d22\u5f15 l, r \u8d8a\u754c\uff0c\u5219\u65e0\u9700\u7ee7\u7eed\u5806\u5316\uff0c\u8df3\u51fa\nif ma == i {\nbreak\n}\n// \u4ea4\u6362\u4e24\u8282\u70b9\nswap(i: i, j: ma)\n// \u5faa\u73af\u5411\u4e0b\u5806\u5316\ni = ma\n}\n}\n</code></pre> my_heap.zig<pre><code>// \u5143\u7d20\u51fa\u5806\nfn pop(self: *Self) !T {\n// \u5224\u65ad\u5904\u7406\nif (self.isEmpty()) unreachable;\n// \u4ea4\u6362\u6839\u8282\u70b9\u4e0e\u6700\u53f3\u53f6\u8282\u70b9\uff08\u5373\u4ea4\u6362\u9996\u5143\u7d20\u4e0e\u5c3e\u5143\u7d20\uff09\ntry self.swap(0, self.size() - 1);\n// \u5220\u9664\u8282\u70b9\nvar val = self.max_heap.?.pop();\n// \u4ece\u9876\u81f3\u5e95\u5806\u5316\ntry self.siftDown(0);\n// \u8fd4\u56de\u5806\u9876\u5143\u7d20\nreturn val;\n} // \u4ece\u8282\u70b9 i \u5f00\u59cb\uff0c\u4ece\u9876\u81f3\u5e95\u5806\u5316\nfn siftDown(self: *Self, i_: usize) !void {\nvar i = i_;\nwhile (true) {\n// \u5224\u65ad\u8282\u70b9 i, l, r \u4e2d\u503c\u6700\u5927\u7684\u8282\u70b9\uff0c\u8bb0\u4e3a ma\nvar l = left(i);\nvar r = right(i);\nvar ma = i;\nif (l &lt; self.size() and self.max_heap.?.items[l] &gt; self.max_heap.?.items[ma]) ma = l;\nif (r &lt; self.size() and self.max_heap.?.items[r] &gt; self.max_heap.?.items[ma]) ma = r;\n// \u82e5\u8282\u70b9 i \u6700\u5927\u6216\u7d22\u5f15 l, r \u8d8a\u754c\uff0c\u5219\u65e0\u9700\u7ee7\u7eed\u5806\u5316\uff0c\u8df3\u51fa\nif (ma == i) break;\n// \u4ea4\u6362\u4e24\u8282\u70b9\ntry self.swap(i, ma);\n// \u5faa\u73af\u5411\u4e0b\u5806\u5316\ni = ma;\n}\n}\n</code></pre> my_heap.dart<pre><code>/* \u5143\u7d20\u51fa\u5806 */\nint pop() {\n// \u5224\u7a7a\u5904\u7406\nif (isEmpty()) throw Exception('\u5806\u4e3a\u7a7a');\n// \u4ea4\u6362\u6839\u8282\u70b9\u4e0e\u6700\u53f3\u53f6\u8282\u70b9\uff08\u5373\u4ea4\u6362\u9996\u5143\u7d20\u4e0e\u5c3e\u5143\u7d20\uff09\n_swap(0, size() - 1);\n// \u5220\u9664\u8282\u70b9\nint val = _maxHeap.removeLast();\n// \u4ece\u9876\u81f3\u5e95\u5806\u5316\n_siftDown(0);\n// \u8fd4\u56de\u5806\u9876\u5143\u7d20\nreturn val;\n}\n[class]{MaxHeap}-[func]{siftDown}\n</code></pre>"},{"location":"chapter_heap/heap/#813","title":"8.1.3. \u00a0 \u5806\u5e38\u89c1\u5e94\u7528","text":"<ul> <li>\u4f18\u5148\u961f\u5217\uff1a\u5806\u901a\u5e38\u4f5c\u4e3a\u5b9e\u73b0\u4f18\u5148\u961f\u5217\u7684\u9996\u9009\u6570\u636e\u7ed3\u6784\uff0c\u5176\u5165\u961f\u548c\u51fa\u961f\u64cd\u4f5c\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u5747\u4e3a \\(O(\\log n)\\) \uff0c\u800c\u5efa\u961f\u64cd\u4f5c\u4e3a \\(O(n)\\) \uff0c\u8fd9\u4e9b\u64cd\u4f5c\u90fd\u975e\u5e38\u9ad8\u6548\u3002</li> <li>\u5806\u6392\u5e8f\uff1a\u7ed9\u5b9a\u4e00\u7ec4\u6570\u636e\uff0c\u6211\u4eec\u53ef\u4ee5\u7528\u5b83\u4eec\u5efa\u7acb\u4e00\u4e2a\u5806\uff0c\u7136\u540e\u4e0d\u65ad\u5730\u6267\u884c\u5143\u7d20\u51fa\u5806\u64cd\u4f5c\uff0c\u4ece\u800c\u5f97\u5230\u6709\u5e8f\u6570\u636e\u3002\u7136\u800c\uff0c\u6211\u4eec\u901a\u5e38\u4f1a\u4f7f\u7528\u4e00\u79cd\u66f4\u4f18\u96c5\u7684\u65b9\u5f0f\u5b9e\u73b0\u5806\u6392\u5e8f\uff0c\u8be6\u89c1\u540e\u7eed\u7684\u5806\u6392\u5e8f\u7ae0\u8282\u3002</li> <li>\u83b7\u53d6\u6700\u5927\u7684 \\(k\\) \u4e2a\u5143\u7d20\uff1a\u8fd9\u662f\u4e00\u4e2a\u7ecf\u5178\u7684\u7b97\u6cd5\u95ee\u9898\uff0c\u540c\u65f6\u4e5f\u662f\u4e00\u79cd\u5178\u578b\u5e94\u7528\uff0c\u4f8b\u5982\u9009\u62e9\u70ed\u5ea6\u524d 10 \u7684\u65b0\u95fb\u4f5c\u4e3a\u5fae\u535a\u70ed\u641c\uff0c\u9009\u53d6\u9500\u91cf\u524d 10 \u7684\u5546\u54c1\u7b49\u3002</li> </ul>"},{"location":"chapter_heap/summary/","title":"8.4. \u00a0 \u5c0f\u7ed3","text":"<ul> <li>\u5806\u662f\u4e00\u68f5\u5b8c\u5168\u4e8c\u53c9\u6811\uff0c\u6839\u636e\u6210\u7acb\u6761\u4ef6\u53ef\u5206\u4e3a\u5927\u9876\u5806\u548c\u5c0f\u9876\u5806\u3002\u5927\uff08\u5c0f\uff09\u9876\u5806\u7684\u5806\u9876\u5143\u7d20\u662f\u6700\u5927\uff08\u5c0f\uff09\u7684\u3002</li> <li>\u4f18\u5148\u961f\u5217\u7684\u5b9a\u4e49\u662f\u5177\u6709\u51fa\u961f\u4f18\u5148\u7ea7\u7684\u961f\u5217\uff0c\u901a\u5e38\u4f7f\u7528\u5806\u6765\u5b9e\u73b0\u3002</li> <li>\u5806\u7684\u5e38\u7528\u64cd\u4f5c\u53ca\u5176\u5bf9\u5e94\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u5305\u62ec\uff1a\u5143\u7d20\u5165\u5806 \\(O(\\log n)\\) \u3001\u5806\u9876\u5143\u7d20\u51fa\u5806 \\(O(\\log n)\\) \u548c\u8bbf\u95ee\u5806\u9876\u5143\u7d20 \\(O(1)\\) \u7b49\u3002</li> <li>\u5b8c\u5168\u4e8c\u53c9\u6811\u975e\u5e38\u9002\u5408\u7528\u6570\u7ec4\u8868\u793a\uff0c\u56e0\u6b64\u6211\u4eec\u901a\u5e38\u4f7f\u7528\u6570\u7ec4\u6765\u5b58\u50a8\u5806\u3002</li> <li>\u5806\u5316\u64cd\u4f5c\u7528\u4e8e\u7ef4\u62a4\u5806\u7684\u6027\u8d28\uff0c\u5728\u5165\u5806\u548c\u51fa\u5806\u64cd\u4f5c\u4e2d\u90fd\u4f1a\u7528\u5230\u3002</li> <li>\u8f93\u5165 \\(n\\) \u4e2a\u5143\u7d20\u5e76\u5efa\u5806\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u53ef\u4ee5\u4f18\u5316\u81f3 \\(O(n)\\) \uff0c\u975e\u5e38\u9ad8\u6548\u3002</li> </ul>"},{"location":"chapter_heap/top_k/","title":"8.3. \u00a0 Top-K \u95ee\u9898","text":"<p>Question</p> <p>\u7ed9\u5b9a\u4e00\u4e2a\u957f\u5ea6\u4e3a \\(n\\) \u65e0\u5e8f\u6570\u7ec4 <code>nums</code> \uff0c\u8bf7\u8fd4\u56de\u6570\u7ec4\u4e2d\u524d \\(k\\) \u5927\u7684\u5143\u7d20\u3002</p> <p>\u5bf9\u4e8e\u8be5\u95ee\u9898\uff0c\u6211\u4eec\u5148\u4ecb\u7ecd\u4e24\u79cd\u601d\u8def\u6bd4\u8f83\u76f4\u63a5\u7684\u89e3\u6cd5\uff0c\u518d\u4ecb\u7ecd\u6548\u7387\u66f4\u9ad8\u7684\u5806\u89e3\u6cd5\u3002</p>"},{"location":"chapter_heap/top_k/#831","title":"8.3.1. \u00a0 \u65b9\u6cd5\u4e00\uff1a\u904d\u5386\u9009\u62e9","text":"<p>\u6211\u4eec\u53ef\u4ee5\u8fdb\u884c \\(k\\) \u8f6e\u904d\u5386\uff0c\u5206\u522b\u5728\u6bcf\u8f6e\u4e2d\u63d0\u53d6\u7b2c \\(1\\) , \\(2\\) , \\(\\cdots\\) , \\(k\\) \u5927\u7684\u5143\u7d20\uff0c\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(nk)\\) \u3002</p> <p>\u8be5\u65b9\u6cd5\u53ea\u9002\u7528\u4e8e \\(k \\ll n\\) \u7684\u60c5\u51b5\uff0c\u56e0\u4e3a\u5f53 \\(k\\) \u4e0e \\(n\\) \u6bd4\u8f83\u63a5\u8fd1\u65f6\uff0c\u5176\u65f6\u95f4\u590d\u6742\u5ea6\u8d8b\u5411\u4e8e \\(O(n^2)\\) \uff0c\u975e\u5e38\u8017\u65f6\u3002</p> <p></p> <p> Fig. \u904d\u5386\u5bfb\u627e\u6700\u5927\u7684 k \u4e2a\u5143\u7d20 </p> <p>Tip</p> <p>\u5f53 \\(k = n\\) \u65f6\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\u4ece\u5927\u5230\u5c0f\u7684\u5e8f\u5217\uff0c\u7b49\u4ef7\u4e8e\u300c\u9009\u62e9\u6392\u5e8f\u300d\u7b97\u6cd5\u3002 </p>"},{"location":"chapter_heap/top_k/#832","title":"8.3.2. \u00a0 \u65b9\u6cd5\u4e8c\uff1a\u6392\u5e8f","text":"<p>\u6211\u4eec\u53ef\u4ee5\u5bf9\u6570\u7ec4 <code>nums</code> \u8fdb\u884c\u6392\u5e8f\uff0c\u5e76\u8fd4\u56de\u6700\u53f3\u8fb9\u7684 \\(k\\) \u4e2a\u5143\u7d20\uff0c\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(n \\log n)\\) \u3002</p> <p>\u663e\u7136\uff0c\u8be5\u65b9\u6cd5\u201c\u8d85\u989d\u201d\u5b8c\u6210\u4efb\u52a1\u4e86\uff0c\u56e0\u4e3a\u6211\u4eec\u53ea\u9700\u8981\u627e\u51fa\u6700\u5927\u7684 \\(k\\) \u4e2a\u5143\u7d20\u5373\u53ef\uff0c\u800c\u4e0d\u9700\u8981\u6392\u5e8f\u5176\u4ed6\u5143\u7d20\u3002</p> <p></p> <p> Fig. \u6392\u5e8f\u5bfb\u627e\u6700\u5927\u7684 k \u4e2a\u5143\u7d20 </p>"},{"location":"chapter_heap/top_k/#833","title":"8.3.3. \u00a0 \u65b9\u6cd5\u4e09\uff1a\u5806","text":"<p>\u6211\u4eec\u53ef\u4ee5\u57fa\u4e8e\u5806\u66f4\u52a0\u9ad8\u6548\u5730\u89e3\u51b3 Top-K \u95ee\u9898\uff0c\u6d41\u7a0b\u5982\u4e0b\uff1a</p> <ol> <li>\u521d\u59cb\u5316\u4e00\u4e2a\u5c0f\u9876\u5806\uff0c\u5176\u5806\u9876\u5143\u7d20\u6700\u5c0f\uff1b</li> <li>\u5148\u5c06\u6570\u7ec4\u7684\u524d \\(k\\) \u4e2a\u5143\u7d20\u4f9d\u6b21\u5165\u5806\uff1b</li> <li>\u4ece\u7b2c \\(k + 1\\) \u4e2a\u5143\u7d20\u5f00\u59cb\uff0c\u82e5\u5f53\u524d\u5143\u7d20\u5927\u4e8e\u5806\u9876\u5143\u7d20\uff0c\u5219\u5c06\u5806\u9876\u5143\u7d20\u51fa\u5806\uff0c\u5e76\u5c06\u5f53\u524d\u5143\u7d20\u5165\u5806\uff1b</li> <li>\u904d\u5386\u5b8c\u6210\u540e\uff0c\u5806\u4e2d\u4fdd\u5b58\u7684\u5c31\u662f\u6700\u5927\u7684 \\(k\\) \u4e2a\u5143\u7d20\uff1b</li> </ol> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p>\u603b\u5171\u6267\u884c\u4e86 \\(n\\) \u8f6e\u5165\u5806\u548c\u51fa\u5806\uff0c\u5806\u7684\u6700\u5927\u957f\u5ea6\u4e3a \\(k\\) \uff0c\u56e0\u6b64\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(n \\log k)\\) \u3002\u8be5\u65b9\u6cd5\u7684\u6548\u7387\u5f88\u9ad8\uff0c\u5f53 \\(k\\) \u8f83\u5c0f\u65f6\uff0c\u65f6\u95f4\u590d\u6742\u5ea6\u8d8b\u5411 \\(O(n)\\) \uff1b\u5f53 \\(k\\) \u8f83\u5927\u65f6\uff0c\u65f6\u95f4\u590d\u6742\u5ea6\u4e0d\u4f1a\u8d85\u8fc7 \\(O(n \\log n)\\) \u3002</p> <p>\u53e6\u5916\uff0c\u8be5\u65b9\u6cd5\u9002\u7528\u4e8e\u52a8\u6001\u6570\u636e\u6d41\u7684\u4f7f\u7528\u573a\u666f\u3002\u5728\u4e0d\u65ad\u52a0\u5165\u6570\u636e\u65f6\uff0c\u6211\u4eec\u53ef\u4ee5\u6301\u7eed\u7ef4\u62a4\u5806\u5185\u7684\u5143\u7d20\uff0c\u4ece\u800c\u5b9e\u73b0\u6700\u5927 \\(k\\) \u4e2a\u5143\u7d20\u7684\u52a8\u6001\u66f4\u65b0\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart top_k.java<pre><code>/* \u57fa\u4e8e\u5806\u67e5\u627e\u6570\u7ec4\u4e2d\u6700\u5927\u7684 k \u4e2a\u5143\u7d20 */\nQueue&lt;Integer&gt; topKHeap(int[] nums, int k) {\nQueue&lt;Integer&gt; heap = new PriorityQueue&lt;Integer&gt;();\n// \u5c06\u6570\u7ec4\u7684\u524d k \u4e2a\u5143\u7d20\u5165\u5806\nfor (int i = 0; i &lt; k; i++) {\nheap.add(nums[i]);\n}\n// \u4ece\u7b2c k+1 \u4e2a\u5143\u7d20\u5f00\u59cb\uff0c\u4fdd\u6301\u5806\u7684\u957f\u5ea6\u4e3a k\nfor (int i = k; i &lt; nums.length; i++) {\n// \u82e5\u5f53\u524d\u5143\u7d20\u5927\u4e8e\u5806\u9876\u5143\u7d20\uff0c\u5219\u5c06\u5806\u9876\u5143\u7d20\u51fa\u5806\u3001\u5f53\u524d\u5143\u7d20\u5165\u5806\nif (nums[i] &gt; heap.peek()) {\nheap.poll();\nheap.add(nums[i]);\n}\n}\nreturn heap;\n}\n</code></pre> top_k.cpp<pre><code>/* \u57fa\u4e8e\u5806\u67e5\u627e\u6570\u7ec4\u4e2d\u6700\u5927\u7684 k \u4e2a\u5143\u7d20 */\npriority_queue&lt;int, vector&lt;int&gt;, greater&lt;int&gt;&gt; topKHeap(vector&lt;int&gt; &amp;nums, int k) {\npriority_queue&lt;int, vector&lt;int&gt;, greater&lt;int&gt;&gt; heap;\n// \u5c06\u6570\u7ec4\u7684\u524d k \u4e2a\u5143\u7d20\u5165\u5806\nfor (int i = 0; i &lt; k; i++) {\nheap.push(nums[i]);\n}\n// \u4ece\u7b2c k+1 \u4e2a\u5143\u7d20\u5f00\u59cb\uff0c\u4fdd\u6301\u5806\u7684\u957f\u5ea6\u4e3a k\nfor (int i = k; i &lt; nums.size(); i++) {\n// \u82e5\u5f53\u524d\u5143\u7d20\u5927\u4e8e\u5806\u9876\u5143\u7d20\uff0c\u5219\u5c06\u5806\u9876\u5143\u7d20\u51fa\u5806\u3001\u5f53\u524d\u5143\u7d20\u5165\u5806\nif (nums[i] &gt; heap.top()) {\nheap.pop();\nheap.push(nums[i]);\n}\n}\nreturn heap;\n}\n</code></pre> top_k.py<pre><code>def top_k_heap(nums: list[int], k: int) -&gt; list[int]:\n\"\"\"\u57fa\u4e8e\u5806\u67e5\u627e\u6570\u7ec4\u4e2d\u6700\u5927\u7684 k \u4e2a\u5143\u7d20\"\"\"\nheap = []\n# \u5c06\u6570\u7ec4\u7684\u524d k \u4e2a\u5143\u7d20\u5165\u5806\nfor i in range(k):\nheapq.heappush(heap, nums[i])\n# \u4ece\u7b2c k+1 \u4e2a\u5143\u7d20\u5f00\u59cb\uff0c\u4fdd\u6301\u5806\u7684\u957f\u5ea6\u4e3a k\nfor i in range(k, len(nums)):\n# \u82e5\u5f53\u524d\u5143\u7d20\u5927\u4e8e\u5806\u9876\u5143\u7d20\uff0c\u5219\u5c06\u5806\u9876\u5143\u7d20\u51fa\u5806\u3001\u5f53\u524d\u5143\u7d20\u5165\u5806\nif nums[i] &gt; heap[0]:\nheapq.heappop(heap)\nheapq.heappush(heap, nums[i])\nreturn heap\n</code></pre> top_k.go<pre><code>[class]{maxHeap}-[func]{topKHeap}\n</code></pre> top_k.js<pre><code>[class]{}-[func]{topKHeap}\n</code></pre> top_k.ts<pre><code>[class]{}-[func]{topKHeap}\n</code></pre> top_k.c<pre><code>[class]{maxHeap}-[func]{topKHeap}\n</code></pre> top_k.cs<pre><code>[class]{top_k}-[func]{topKHeap}\n</code></pre> top_k.swift<pre><code>[class]{}-[func]{topKHeap}\n</code></pre> top_k.zig<pre><code>[class]{}-[func]{topKHeap}\n</code></pre> top_k.dart<pre><code>[class]{}-[func]{top_k_heap}\n</code></pre>"},{"location":"chapter_introduction/","title":"1. \u00a0 \u5f15\u8a00","text":""},{"location":"chapter_introduction/algorithms_are_everywhere/","title":"1.1. \u00a0 \u7b97\u6cd5\u65e0\u5904\u4e0d\u5728","text":"<p>\u5f53\u6211\u4eec\u542c\u5230\u201c\u7b97\u6cd5\u201d\u8fd9\u4e2a\u8bcd\u65f6\uff0c\u5f88\u81ea\u7136\u5730\u4f1a\u60f3\u5230\u6570\u5b66\u3002\u7136\u800c\u5b9e\u9645\u4e0a\uff0c\u8bb8\u591a\u7b97\u6cd5\u5e76\u4e0d\u6d89\u53ca\u590d\u6742\u6570\u5b66\uff0c\u800c\u662f\u66f4\u591a\u5730\u4f9d\u8d56\u4e8e\u57fa\u672c\u903b\u8f91\uff0c\u8fd9\u4e9b\u903b\u8f91\u5728\u6211\u4eec\u7684\u65e5\u5e38\u751f\u6d3b\u4e2d\u5904\u5904\u53ef\u89c1\u3002</p> <p>\u5728\u6b63\u5f0f\u63a2\u8ba8\u7b97\u6cd5\u4e4b\u524d\uff0c\u6709\u4e00\u4e2a\u6709\u8da3\u7684\u4e8b\u5b9e\u503c\u5f97\u5206\u4eab\uff1a\u5b9e\u9645\u4e0a\uff0c\u4f60\u5df2\u7ecf\u5b66\u4f1a\u4e86\u8bb8\u591a\u7b97\u6cd5\uff0c\u5e76\u4e60\u60ef\u5c06\u4ed6\u4eec\u5e94\u7528\u5230\u65e5\u5e38\u751f\u6d3b\u4e2d\u4e86\u3002\u4e0b\u9762\uff0c\u6211\u5c06\u4e3e\u4e24\u4e2a\u5177\u4f53\u4f8b\u5b50\u6765\u8bc1\u5b9e\u8fd9\u4e00\u70b9\u3002</p> <p>\u4f8b\u4e00\uff1a\u7ec4\u88c5\u79ef\u6728\u3002\u4e00\u5957\u79ef\u6728\uff0c\u9664\u4e86\u5305\u542b\u8bb8\u591a\u96f6\u4ef6\u4e4b\u5916\uff0c\u8fd8\u9644\u6709\u8be6\u7ec6\u7684\u7ec4\u88c5\u8bf4\u660e\u4e66\u3002\u6211\u4eec\u6309\u7167\u8bf4\u660e\u4e66\u4e00\u6b65\u6b65\u64cd\u4f5c\uff0c\u5c31\u80fd\u7ec4\u88c5\u51fa\u7cbe\u7f8e\u7684\u79ef\u6728\u6a21\u578b\u3002</p> <p>\u4ece\u6570\u636e\u7ed3\u6784\u4e0e\u7b97\u6cd5\u7684\u89d2\u5ea6\u6765\u770b\uff0c\u79ef\u6728\u7684\u5404\u79cd\u5f62\u72b6\u548c\u8fde\u63a5\u65b9\u5f0f\u4ee3\u8868\u6570\u636e\u7ed3\u6784\uff0c\u800c\u7ec4\u88c5\u8bf4\u660e\u4e66\u4e0a\u7684\u4e00\u7cfb\u5217\u6b65\u9aa4\u5219\u662f\u7b97\u6cd5\u3002</p> <p></p> <p> Fig. \u62fc\u88c5\u79ef\u6728 </p> <p>\u4f8b\u4e8c\uff1a\u67e5\u9605\u5b57\u5178\u3002\u5728\u5b57\u5178\u91cc\uff0c\u6bcf\u4e2a\u6c49\u5b57\u90fd\u5bf9\u5e94\u4e00\u4e2a\u62fc\u97f3\uff0c\u800c\u5b57\u5178\u662f\u6309\u7167\u62fc\u97f3\u7684\u82f1\u6587\u5b57\u6bcd\u987a\u5e8f\u6392\u5217\u7684\u3002\u5047\u8bbe\u6211\u4eec\u9700\u8981\u67e5\u627e\u4e00\u4e2a\u62fc\u97f3\u9996\u5b57\u6bcd\u4e3a \\(r\\) \u7684\u5b57\uff0c\u901a\u5e38\u4f1a\u8fd9\u6837\u64cd\u4f5c\uff1a</p> <ol> <li>\u7ffb\u5f00\u5b57\u5178\u7ea6\u4e00\u534a\u7684\u9875\u6570\uff0c\u67e5\u770b\u8be5\u9875\u9996\u5b57\u6bcd\u662f\u4ec0\u4e48\uff08\u5047\u8bbe\u4e3a \\(m\\) \uff09\uff1b</li> <li>\u7531\u4e8e\u5728\u82f1\u6587\u5b57\u6bcd\u8868\u4e2d \\(r\\) \u4f4d\u4e8e \\(m\\) \u4e4b\u540e\uff0c\u6240\u4ee5\u6392\u9664\u5b57\u5178\u524d\u534a\u90e8\u5206\uff0c\u67e5\u627e\u8303\u56f4\u7f29\u5c0f\u5230\u540e\u534a\u90e8\u5206\uff1b</li> <li>\u4e0d\u65ad\u91cd\u590d\u6b65\u9aa4 1-2 \uff0c\u76f4\u81f3\u627e\u5230\u62fc\u97f3\u9996\u5b57\u6bcd\u4e3a \\(r\\) \u7684\u9875\u7801\u4e3a\u6b62\u3002</li> </ol> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p>\u67e5\u9605\u5b57\u5178\u8fd9\u4e2a\u5c0f\u5b66\u751f\u5fc5\u5907\u6280\u80fd\uff0c\u5b9e\u9645\u4e0a\u5c31\u662f\u8457\u540d\u7684\u300c\u4e8c\u5206\u67e5\u627e\u300d\u3002\u4ece\u6570\u636e\u7ed3\u6784\u7684\u89d2\u5ea6\uff0c\u6211\u4eec\u53ef\u4ee5\u628a\u5b57\u5178\u89c6\u4e3a\u4e00\u4e2a\u5df2\u6392\u5e8f\u7684\u300c\u6570\u7ec4\u300d\uff1b\u4ece\u7b97\u6cd5\u7684\u89d2\u5ea6\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u4e0a\u8ff0\u67e5\u5b57\u5178\u7684\u4e00\u7cfb\u5217\u64cd\u4f5c\u770b\u4f5c\u662f\u300c\u4e8c\u5206\u67e5\u627e\u300d\u7b97\u6cd5\u3002</p> <p>\u5c0f\u5230\u70f9\u996a\u4e00\u9053\u83dc\uff0c\u5927\u5230\u661f\u9645\u822a\u884c\uff0c\u51e0\u4e4e\u6240\u6709\u95ee\u9898\u7684\u89e3\u51b3\u90fd\u79bb\u4e0d\u5f00\u7b97\u6cd5\u3002\u8ba1\u7b97\u673a\u7684\u51fa\u73b0\u4f7f\u6211\u4eec\u80fd\u591f\u901a\u8fc7\u7f16\u7a0b\u5c06\u6570\u636e\u7ed3\u6784\u5b58\u50a8\u5728\u5185\u5b58\u4e2d\uff0c\u540c\u65f6\u7f16\u5199\u4ee3\u7801\u8c03\u7528 CPU \u548c GPU \u6267\u884c\u7b97\u6cd5\u3002\u8fd9\u6837\u4e00\u6765\uff0c\u6211\u4eec\u5c31\u80fd\u628a\u751f\u6d3b\u4e2d\u7684\u95ee\u9898\u8f6c\u79fb\u5230\u8ba1\u7b97\u673a\u4e0a\uff0c\u4ee5\u66f4\u9ad8\u6548\u7684\u65b9\u5f0f\u89e3\u51b3\u5404\u79cd\u590d\u6742\u95ee\u9898\u3002</p> <p>Tip</p> <p>\u9605\u8bfb\u81f3\u6b64\uff0c\u5982\u679c\u4f60\u5bf9\u6570\u636e\u7ed3\u6784\u3001\u7b97\u6cd5\u3001\u6570\u7ec4\u548c\u4e8c\u5206\u67e5\u627e\u7b49\u6982\u5ff5\u4ecd\u611f\u5230\u4e00\u77e5\u534a\u89e3\uff0c\u90a3\u4e48\u592a\u597d\u4e86\uff01\u56e0\u4e3a\u8fd9\u6b63\u662f\u672c\u4e66\u5b58\u5728\u7684\u610f\u4e49\u3002\u63a5\u4e0b\u6765\uff0c\u8fd9\u672c\u4e66\u5c06\u4e00\u6b65\u6b65\u5f15\u5bfc\u4f60\u6df1\u5165\u6570\u636e\u7ed3\u6784\u4e0e\u7b97\u6cd5\u7684\u77e5\u8bc6\u6bbf\u5802\u3002</p>"},{"location":"chapter_introduction/summary/","title":"1.3. \u00a0 \u5c0f\u7ed3","text":"<ul> <li>\u7b97\u6cd5\u5728\u65e5\u5e38\u751f\u6d3b\u4e2d\u65e0\u5904\u4e0d\u5728\uff0c\u5e76\u4e0d\u662f\u9065\u4e0d\u53ef\u53ca\u7684\u9ad8\u6df1\u77e5\u8bc6\u3002\u5b9e\u9645\u4e0a\uff0c\u6211\u4eec\u5df2\u7ecf\u5728\u4e0d\u77e5\u4e0d\u89c9\u4e2d\u5b66\u4e60\u4e86\u8bb8\u591a\u201c\u7b97\u6cd5\u201d\uff0c\u7528\u4ee5\u89e3\u51b3\u751f\u6d3b\u4e2d\u7684\u5927\u5c0f\u95ee\u9898\u3002</li> <li>\u67e5\u9605\u5b57\u5178\u7684\u539f\u7406\u4e0e\u4e8c\u5206\u67e5\u627e\u7b97\u6cd5\u76f8\u4e00\u81f4\u3002\u4e8c\u5206\u67e5\u627e\u4f53\u73b0\u4e86\u5206\u800c\u6cbb\u4e4b\u7684\u91cd\u8981\u7b97\u6cd5\u601d\u60f3\u3002</li> <li>\u7b97\u6cd5\u662f\u5728\u6709\u9650\u65f6\u95f4\u5185\u89e3\u51b3\u7279\u5b9a\u95ee\u9898\u7684\u4e00\u7ec4\u6307\u4ee4\u6216\u64cd\u4f5c\u6b65\u9aa4\uff0c\u800c\u6570\u636e\u7ed3\u6784\u662f\u8ba1\u7b97\u673a\u4e2d\u7ec4\u7ec7\u548c\u5b58\u50a8\u6570\u636e\u7684\u65b9\u5f0f\u3002</li> <li>\u6570\u636e\u7ed3\u6784\u4e0e\u7b97\u6cd5\u7d27\u5bc6\u76f8\u8fde\u3002\u6570\u636e\u7ed3\u6784\u662f\u7b97\u6cd5\u7684\u57fa\u77f3\uff0c\u800c\u7b97\u6cd5\u5219\u662f\u53d1\u6325\u6570\u636e\u7ed3\u6784\u4f5c\u7528\u7684\u821e\u53f0\u3002</li> <li>\u4e50\u9ad8\u79ef\u6728\u5bf9\u5e94\u4e8e\u6570\u636e\uff0c\u79ef\u6728\u5f62\u72b6\u548c\u8fde\u63a5\u65b9\u5f0f\u4ee3\u8868\u6570\u636e\u7ed3\u6784\uff0c\u62fc\u88c5\u79ef\u6728\u7684\u6b65\u9aa4\u5219\u5bf9\u5e94\u7b97\u6cd5\u3002</li> </ul>"},{"location":"chapter_introduction/what_is_dsa/","title":"1.2. \u00a0 \u7b97\u6cd5\u662f\u4ec0\u4e48","text":""},{"location":"chapter_introduction/what_is_dsa/#121","title":"1.2.1. \u00a0 \u7b97\u6cd5\u5b9a\u4e49","text":"<p>\u300c\u7b97\u6cd5 Algorithm\u300d\u662f\u5728\u6709\u9650\u65f6\u95f4\u5185\u89e3\u51b3\u7279\u5b9a\u95ee\u9898\u7684\u4e00\u7ec4\u6307\u4ee4\u6216\u64cd\u4f5c\u6b65\u9aa4\u3002\u7b97\u6cd5\u5177\u6709\u4ee5\u4e0b\u7279\u6027\uff1a</p> <ul> <li>\u95ee\u9898\u662f\u660e\u786e\u7684\uff0c\u5177\u6709\u6e05\u6670\u7684\u8f93\u5165\u548c\u8f93\u51fa\u5b9a\u4e49\u3002</li> <li>\u89e3\u5177\u6709\u786e\u5b9a\u6027\uff0c\u5373\u7ed9\u5b9a\u76f8\u540c\u7684\u8f93\u5165\u65f6\uff0c\u8f93\u51fa\u59cb\u7ec8\u76f8\u540c\u3002</li> <li>\u5177\u6709\u53ef\u884c\u6027\uff0c\u5728\u6709\u9650\u6b65\u9aa4\u3001\u65f6\u95f4\u548c\u5185\u5b58\u7a7a\u95f4\u4e0b\u53ef\u5b8c\u6210\u3002</li> </ul>"},{"location":"chapter_introduction/what_is_dsa/#122","title":"1.2.2. \u00a0 \u6570\u636e\u7ed3\u6784\u5b9a\u4e49","text":"<p>\u300c\u6570\u636e\u7ed3\u6784 Data Structure\u300d\u662f\u8ba1\u7b97\u673a\u4e2d\u7ec4\u7ec7\u548c\u5b58\u50a8\u6570\u636e\u7684\u65b9\u5f0f\u3002\u4e3a\u4e86\u63d0\u9ad8\u6570\u636e\u5b58\u50a8\u548c\u64cd\u4f5c\u6027\u80fd\uff0c\u6570\u636e\u7ed3\u6784\u7684\u8bbe\u8ba1\u76ee\u6807\u5305\u62ec\uff1a</p> <ul> <li>\u7a7a\u95f4\u5360\u7528\u5c3d\u91cf\u51cf\u5c11\uff0c\u8282\u7701\u8ba1\u7b97\u673a\u5185\u5b58\u3002</li> <li>\u6570\u636e\u64cd\u4f5c\u5c3d\u53ef\u80fd\u5feb\u901f\uff0c\u6db5\u76d6\u6570\u636e\u8bbf\u95ee\u3001\u6dfb\u52a0\u3001\u5220\u9664\u3001\u66f4\u65b0\u7b49\u3002</li> <li>\u63d0\u4f9b\u7b80\u6d01\u7684\u6570\u636e\u8868\u793a\u548c\u903b\u8f91\u4fe1\u606f\uff0c\u4ee5\u5229\u4e8e\u7b97\u6cd5\u9ad8\u6548\u8fd0\u884c\u3002</li> </ul> <p>\u6570\u636e\u7ed3\u6784\u8bbe\u8ba1\u662f\u4e00\u4e2a\u5145\u6ee1\u6743\u8861\u7684\u8fc7\u7a0b\uff0c\u8fd9\u610f\u5473\u7740\u8981\u5728\u67d0\u65b9\u9762\u53d6\u5f97\u4f18\u52bf\uff0c\u5f80\u5f80\u9700\u8981\u5728\u53e6\u4e00\u65b9\u9762\u4f5c\u51fa\u59a5\u534f\u3002\u4f8b\u5982\uff0c\u94fe\u8868\u76f8\u8f83\u4e8e\u6570\u7ec4\uff0c\u5728\u6570\u636e\u6dfb\u52a0\u548c\u5220\u9664\u64cd\u4f5c\u4e0a\u66f4\u52a0\u4fbf\u6377\uff0c\u4f46\u727a\u7272\u4e86\u6570\u636e\u8bbf\u95ee\u901f\u5ea6\uff1b\u56fe\u76f8\u8f83\u4e8e\u94fe\u8868\uff0c\u63d0\u4f9b\u4e86\u66f4\u4e30\u5bcc\u7684\u903b\u8f91\u4fe1\u606f\uff0c\u4f46\u9700\u8981\u5360\u7528\u66f4\u5927\u7684\u5185\u5b58\u7a7a\u95f4\u3002</p>"},{"location":"chapter_introduction/what_is_dsa/#123","title":"1.2.3. \u00a0 \u6570\u636e\u7ed3\u6784\u4e0e\u7b97\u6cd5\u7684\u5173\u7cfb","text":"<p>\u300c\u6570\u636e\u7ed3\u6784\u300d\u4e0e\u300c\u7b97\u6cd5\u300d\u9ad8\u5ea6\u76f8\u5173\u4e14\u7d27\u5bc6\u7ed3\u5408\uff0c\u5177\u4f53\u8868\u73b0\u5728\uff1a</p> <ul> <li>\u6570\u636e\u7ed3\u6784\u662f\u7b97\u6cd5\u7684\u57fa\u77f3\u3002\u6570\u636e\u7ed3\u6784\u4e3a\u7b97\u6cd5\u63d0\u4f9b\u4e86\u7ed3\u6784\u5316\u5b58\u50a8\u7684\u6570\u636e\uff0c\u4ee5\u53ca\u7528\u4e8e\u64cd\u4f5c\u6570\u636e\u7684\u65b9\u6cd5\u3002</li> <li>\u7b97\u6cd5\u662f\u6570\u636e\u7ed3\u6784\u53d1\u6325\u7684\u821e\u53f0\u3002\u6570\u636e\u7ed3\u6784\u672c\u8eab\u4ec5\u5b58\u50a8\u6570\u636e\u4fe1\u606f\uff0c\u901a\u8fc7\u7ed3\u5408\u7b97\u6cd5\u624d\u80fd\u89e3\u51b3\u7279\u5b9a\u95ee\u9898\u3002</li> <li>\u7279\u5b9a\u7b97\u6cd5\u901a\u5e38\u6709\u5bf9\u5e94\u6700\u4f18\u7684\u6570\u636e\u7ed3\u6784\u3002\u7b97\u6cd5\u901a\u5e38\u53ef\u4ee5\u57fa\u4e8e\u4e0d\u540c\u7684\u6570\u636e\u7ed3\u6784\u8fdb\u884c\u5b9e\u73b0\uff0c\u4f46\u6700\u7ec8\u6267\u884c\u6548\u7387\u53ef\u80fd\u76f8\u5dee\u5f88\u5927\u3002</li> </ul> <p></p> <p> Fig. \u6570\u636e\u7ed3\u6784\u4e0e\u7b97\u6cd5\u7684\u5173\u7cfb </p> <p>\u7c7b\u6bd4\u300cLEGO \u4e50\u9ad8\u300d\u548c\u300c\u6570\u636e\u7ed3\u6784\u4e0e\u7b97\u6cd5\u300d\uff0c\u5219\u5bf9\u5e94\u5173\u7cfb\u5982\u4e0b\u8868\u6240\u793a\u3002</p> \u6570\u636e\u7ed3\u6784\u4e0e\u7b97\u6cd5 LEGO \u4e50\u9ad8 \u8f93\u5165\u6570\u636e \u672a\u62fc\u88c5\u7684\u79ef\u6728 \u6570\u636e\u7ed3\u6784 \u79ef\u6728\u7ec4\u7ec7\u5f62\u5f0f\uff0c\u5305\u62ec\u5f62\u72b6\u3001\u5927\u5c0f\u3001\u8fde\u63a5\u65b9\u5f0f\u7b49 \u7b97\u6cd5 \u628a\u79ef\u6728\u62fc\u6210\u76ee\u6807\u5f62\u6001\u7684\u4e00\u7cfb\u5217\u64cd\u4f5c\u6b65\u9aa4 \u8f93\u51fa\u6570\u636e \u79ef\u6728\u6a21\u578b <p>\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u6570\u636e\u7ed3\u6784\u4e0e\u7b97\u6cd5\u72ec\u7acb\u4e8e\u7f16\u7a0b\u8bed\u8a00\u3002\u6b63\u56e0\u5982\u6b64\uff0c\u672c\u4e66\u5f97\u4ee5\u63d0\u4f9b\u591a\u79cd\u7f16\u7a0b\u8bed\u8a00\u7684\u5b9e\u73b0\u3002</p> <p>\u7ea6\u5b9a\u4fd7\u6210\u7684\u7b80\u79f0</p> <p>\u5728\u5b9e\u9645\u8ba8\u8bba\u65f6\uff0c\u6211\u4eec\u901a\u5e38\u4f1a\u5c06\u300c\u6570\u636e\u7ed3\u6784\u4e0e\u7b97\u6cd5\u300d\u7b80\u79f0\u4e3a\u300c\u7b97\u6cd5\u300d\u3002\u4f8b\u5982\uff0c\u4f17\u6240\u5468\u77e5\u7684 LeetCode \u7b97\u6cd5\u9898\u76ee\uff0c\u5b9e\u9645\u4e0a\u540c\u65f6\u8003\u5bdf\u4e86\u6570\u636e\u7ed3\u6784\u548c\u7b97\u6cd5\u4e24\u65b9\u9762\u7684\u77e5\u8bc6\u3002</p>"},{"location":"chapter_preface/","title":"0. \u00a0 \u5199\u5728\u524d\u9762","text":""},{"location":"chapter_preface/about_the_book/","title":"0.1. \u00a0 \u5173\u4e8e\u672c\u4e66","text":"<p>\u672c\u9879\u76ee\u65e8\u5728\u521b\u5efa\u4e00\u672c\u5f00\u6e90\u514d\u8d39\u3001\u65b0\u624b\u53cb\u597d\u7684\u6570\u636e\u7ed3\u6784\u4e0e\u7b97\u6cd5\u5165\u95e8\u6559\u7a0b\u3002</p> <ul> <li>\u5168\u4e66\u91c7\u7528\u52a8\u753b\u56fe\u89e3\uff0c\u7ed3\u6784\u5316\u5730\u8bb2\u89e3\u6570\u636e\u7ed3\u6784\u4e0e\u7b97\u6cd5\u77e5\u8bc6\uff0c\u5185\u5bb9\u6e05\u6670\u6613\u61c2\u3001\u5b66\u4e60\u66f2\u7ebf\u5e73\u6ed1\uff1b</li> <li>\u7b97\u6cd5\u6e90\u4ee3\u7801\u7686\u53ef\u4e00\u952e\u8fd0\u884c\uff0c\u652f\u6301 Java, C++, Python, Go, JS, TS, C#, Swift, Zig \u7b49\u8bed\u8a00\uff1b</li> <li>\u9f13\u52b1\u8bfb\u8005\u5728\u7ae0\u8282\u8ba8\u8bba\u533a\u4e92\u5e2e\u4e92\u52a9\u3001\u5171\u540c\u8fdb\u6b65\uff0c\u63d0\u95ee\u4e0e\u8bc4\u8bba\u901a\u5e38\u53ef\u5728\u4e24\u65e5\u5185\u5f97\u5230\u56de\u590d\uff1b</li> </ul>"},{"location":"chapter_preface/about_the_book/#011","title":"0.1.1. \u00a0 \u8bfb\u8005\u5bf9\u8c61","text":"<p>\u82e5\u60a8\u662f\u300c\u7b97\u6cd5\u521d\u5b66\u8005\u300d\uff0c\u4ece\u672a\u63a5\u89e6\u8fc7\u7b97\u6cd5\uff0c\u6216\u8005\u5df2\u7ecf\u6709\u4e00\u4e9b\u5237\u9898\u7ecf\u9a8c\uff0c\u5bf9\u6570\u636e\u7ed3\u6784\u4e0e\u7b97\u6cd5\u6709\u6a21\u7cca\u7684\u8ba4\u8bc6\uff0c\u5728\u4f1a\u4e0e\u4e0d\u4f1a\u4e4b\u95f4\u53cd\u590d\u6a2a\u8df3\uff0c\u90a3\u4e48\u8fd9\u672c\u4e66\u6b63\u662f\u4e3a\u60a8\u91cf\u8eab\u5b9a\u5236\uff01</p> <p>\u5982\u679c\u60a8\u662f\u300c\u7b97\u6cd5\u8001\u624b\u300d\uff0c\u5df2\u7ecf\u79ef\u7d2f\u4e00\u5b9a\u5237\u9898\u91cf\uff0c\u719f\u6089\u5927\u90e8\u5206\u9898\u578b\uff0c\u90a3\u4e48\u672c\u4e66\u53ef\u52a9\u60a8\u56de\u987e\u4e0e\u68b3\u7406\u7b97\u6cd5\u77e5\u8bc6\u4f53\u7cfb\uff0c\u4ed3\u5e93\u6e90\u4ee3\u7801\u53ef\u4ee5\u88ab\u5f53\u4f5c\u201c\u5237\u9898\u5de5\u5177\u5e93\u201d\u6216\u201c\u7b97\u6cd5\u5b57\u5178\u201d\u6765\u4f7f\u7528\u3002</p> <p>\u82e5\u60a8\u662f\u300c\u7b97\u6cd5\u4e13\u5bb6\u300d\uff0c\u6211\u4eec\u671f\u5f85\u6536\u5230\u60a8\u7684\u5b9d\u8d35\u5efa\u8bae\uff0c\u6216\u8005\u4e00\u8d77\u53c2\u4e0e\u521b\u4f5c\u3002</p> <p>\u524d\u7f6e\u6761\u4ef6</p> <p>\u60a8\u9700\u8981\u81f3\u5c11\u5177\u5907\u4efb\u4e00\u8bed\u8a00\u7684\u7f16\u7a0b\u57fa\u7840\uff0c\u80fd\u591f\u9605\u8bfb\u548c\u7f16\u5199\u7b80\u5355\u4ee3\u7801\u3002</p>"},{"location":"chapter_preface/about_the_book/#012","title":"0.1.2. \u00a0 \u5185\u5bb9\u7ed3\u6784","text":"<p>\u672c\u4e66\u4e3b\u8981\u5185\u5bb9\u5305\u62ec\uff1a</p> <ul> <li>\u590d\u6742\u5ea6\u5206\u6790\uff1a\u6570\u636e\u7ed3\u6784\u4e0e\u7b97\u6cd5\u7684\u8bc4\u4ef7\u7ef4\u5ea6\u3001\u7b97\u6cd5\u6548\u7387\u7684\u8bc4\u4f30\u65b9\u6cd5\u3002\u65f6\u95f4\u590d\u6742\u5ea6\u3001\u7a7a\u95f4\u590d\u6742\u5ea6\uff0c\u5305\u62ec\u63a8\u7b97\u65b9\u6cd5\u3001\u5e38\u89c1\u7c7b\u578b\u3001\u793a\u4f8b\u7b49\u3002</li> <li>\u6570\u636e\u7ed3\u6784\uff1a\u5e38\u89c1\u57fa\u672c\u6570\u636e\u7c7b\u578b\uff0c\u6570\u636e\u5728\u5185\u5b58\u4e2d\u7684\u5b58\u50a8\u5f62\u5f0f\u3001\u6570\u636e\u7ed3\u6784\u7684\u5206\u7c7b\u65b9\u6cd5\u3002\u6d89\u53ca\u6570\u7ec4\u3001\u94fe\u8868\u3001\u6808\u3001\u961f\u5217\u3001\u6563\u5217\u8868\u3001\u6811\u3001\u5806\u3001\u56fe\u7b49\u6570\u636e\u7ed3\u6784\uff0c\u5185\u5bb9\u5305\u62ec\u5b9a\u4e49\u3001\u4f18\u7f3a\u70b9\u3001\u5e38\u7528\u64cd\u4f5c\u3001\u5e38\u89c1\u7c7b\u578b\u3001\u5178\u578b\u5e94\u7528\u3001\u5b9e\u73b0\u65b9\u6cd5\u7b49\u3002</li> <li>\u7b97\u6cd5\uff1a\u67e5\u627e\u7b97\u6cd5\u3001\u6392\u5e8f\u7b97\u6cd5\u3001\u641c\u7d22\u4e0e\u56de\u6eaf\u3001\u52a8\u6001\u89c4\u5212\u3001\u5206\u6cbb\u7b97\u6cd5\u7b49\uff0c\u5185\u5bb9\u6db5\u76d6\u5b9a\u4e49\u3001\u5e94\u7528\u573a\u666f\u3001\u4f18\u7f3a\u70b9\u3001\u65f6\u7a7a\u6548\u7387\u3001\u5b9e\u73b0\u65b9\u6cd5\u3001\u793a\u4f8b\u9898\u76ee\u7b49\u3002</li> </ul> <p></p> <p> Fig. Hello \u7b97\u6cd5\u5185\u5bb9\u7ed3\u6784 </p>"},{"location":"chapter_preface/about_the_book/#013","title":"0.1.3. \u00a0 \u81f4\u8c22","text":"<p>\u5728\u672c\u4e66\u7684\u521b\u4f5c\u8fc7\u7a0b\u4e2d\uff0c\u6211\u5f97\u5230\u4e86\u8bb8\u591a\u4eba\u7684\u5e2e\u52a9\uff0c\u5305\u62ec\u4f46\u4e0d\u9650\u4e8e\uff1a</p> <ul> <li>\u611f\u8c22\u6211\u5728\u516c\u53f8\u7684\u5bfc\u5e08\u674e\u6c50\u535a\u58eb\uff0c\u5728\u6df1\u5165\u4ea4\u8c08\u4e2d\u60a8\u9f13\u52b1\u6211\u201c\u884c\u52a8\u8d77\u6765\u201d\uff0c\u575a\u5b9a\u4e86\u6211\u5199\u8fd9\u672c\u4e66\u7684\u51b3\u5fc3\u3002</li> <li>\u611f\u8c22\u6211\u7684\u5973\u670b\u53cb\u6ce1\u6ce1\u4f5c\u4e3a\u672c\u4e66\u7684\u9996\u4f4d\u8bfb\u8005\uff0c\u4ece\u7b97\u6cd5\u5c0f\u767d\u7684\u89d2\u5ea6\u63d0\u51fa\u8bb8\u591a\u5b9d\u8d35\u5efa\u8bae\uff0c\u4f7f\u5f97\u672c\u4e66\u66f4\u9002\u5408\u65b0\u624b\u9605\u8bfb\u3002</li> <li>\u611f\u8c22\u817e\u5b9d\u3001\u7426\u5b9d\u3001\u98de\u5b9d\u4e3a\u672c\u4e66\u8d77\u4e86\u4e00\u4e2a\u5bcc\u6709\u521b\u610f\u7684\u540d\u5b57\uff0c\u5524\u8d77\u5927\u5bb6\u5199\u4e0b\u7b2c\u4e00\u884c\u4ee3\u7801 \"Hello World!\" \u7684\u7f8e\u597d\u56de\u5fc6\u3002</li> <li>\u611f\u8c22\u82cf\u6f7c\u4e3a\u672c\u4e66\u8bbe\u8ba1\u4e86\u7cbe\u7f8e\u7684\u5c01\u9762\u548c LOGO\uff0c\u5e76\u5728\u6211\u7684\u5f3a\u8feb\u75c7\u4e0b\u591a\u6b21\u8010\u5fc3\u4fee\u6539\u3002</li> <li>\u611f\u8c22 @squidfunk \u63d0\u4f9b\u7684\u5199\u4f5c\u6392\u7248\u5efa\u8bae\uff0c\u4ee5\u53ca\u6770\u51fa\u7684\u5f00\u6e90\u9879\u76ee Material-for-MkDocs \u3002</li> </ul> <p>\u5728\u5199\u4f5c\u8fc7\u7a0b\u4e2d\uff0c\u6211\u9605\u8bfb\u4e86\u8bb8\u591a\u5173\u4e8e\u6570\u636e\u7ed3\u6784\u4e0e\u7b97\u6cd5\u7684\u6559\u6750\u548c\u6587\u7ae0\u3002\u8fd9\u4e9b\u4f5c\u54c1\u4e3a\u672c\u4e66\u63d0\u4f9b\u4e86\u4f18\u79c0\u7684\u8303\u672c\uff0c\u786e\u4fdd\u4e86\u672c\u4e66\u5185\u5bb9\u7684\u51c6\u786e\u6027\u4e0e\u54c1\u8d28\u3002\u5728\u6b64\u611f\u8c22\u6240\u6709\u8001\u5e08\u548c\u524d\u8f88\u4eec\u7684\u6770\u51fa\u8d21\u732e\uff01</p> <p>\u672c\u4e66\u5021\u5bfc\u624b\u8111\u5e76\u7528\u7684\u5b66\u4e60\u65b9\u5f0f\uff0c\u5728\u8fd9\u4e00\u70b9\u4e0a\u6df1\u53d7\u300a\u52a8\u624b\u5b66\u6df1\u5ea6\u5b66\u4e60\u300b\u7684\u542f\u53d1\u3002\u5728\u6b64\u5411\u5404\u4f4d\u8bfb\u8005\u5f3a\u70c8\u63a8\u8350\u8fd9\u672c\u4f18\u79c0\u8457\u4f5c\u3002</p> <p>\u8877\u5fc3\u611f\u8c22\u6211\u7684\u7236\u6bcd\uff0c\u6b63\u662f\u4f60\u4eec\u4e00\u76f4\u4ee5\u6765\u7684\u652f\u6301\u4e0e\u9f13\u52b1\uff0c\u8ba9\u6211\u6709\u673a\u4f1a\u505a\u8fd9\u4e9b\u5bcc\u6709\u8da3\u5473\u7684\u4e8b\u3002</p>"},{"location":"chapter_preface/suggestions/","title":"0.2. \u00a0 \u5982\u4f55\u4f7f\u7528\u672c\u4e66","text":"<p>Tip</p> <p>\u4e3a\u4e86\u83b7\u5f97\u6700\u4f73\u7684\u9605\u8bfb\u4f53\u9a8c\uff0c\u5efa\u8bae\u60a8\u901a\u8bfb\u672c\u8282\u5185\u5bb9\u3002</p>"},{"location":"chapter_preface/suggestions/#021","title":"0.2.1. \u00a0 \u884c\u6587\u98ce\u683c\u7ea6\u5b9a","text":"<p>\u6807\u9898\u540e\u6807\u6ce8 <code>*</code> \u7684\u662f\u9009\u8bfb\u7ae0\u8282\uff0c\u5185\u5bb9\u76f8\u5bf9\u56f0\u96be\u3002\u5982\u679c\u4f60\u7684\u65f6\u95f4\u6709\u9650\uff0c\u5efa\u8bae\u53ef\u4ee5\u5148\u8df3\u8fc7\u3002</p> <p>\u6587\u7ae0\u4e2d\u7684\u91cd\u8981\u540d\u8bcd\u4f1a\u7528 <code>\u300c \u300d</code> \u62ec\u53f7\u6807\u6ce8\uff0c\u4f8b\u5982 <code>\u300c\u6570\u7ec4 Array\u300d</code> \u3002\u8bf7\u52a1\u5fc5\u8bb0\u4f4f\u8fd9\u4e9b\u540d\u8bcd\uff0c\u5305\u62ec\u82f1\u6587\u7ffb\u8bd1\uff0c\u4ee5\u4fbf\u540e\u7eed\u9605\u8bfb\u6587\u732e\u65f6\u4f7f\u7528\u3002</p> <p>\u52a0\u7c97\u7684\u6587\u5b57 \u8868\u793a\u91cd\u70b9\u5185\u5bb9\u6216\u603b\u7ed3\u6027\u8bed\u53e5\uff0c\u8fd9\u7c7b\u6587\u5b57\u503c\u5f97\u7279\u522b\u5173\u6ce8\u3002</p> <p>\u4e13\u6709\u540d\u8bcd\u548c\u6709\u7279\u6307\u542b\u4e49\u7684\u8bcd\u53e5\u4f1a\u4f7f\u7528 <code>\u201c\u53cc\u5f15\u53f7\u201d</code> \u6807\u6ce8\uff0c\u4ee5\u907f\u514d\u6b67\u4e49\u3002</p> <p>\u672c\u4e66\u90e8\u5206\u653e\u5f03\u4e86\u7f16\u7a0b\u8bed\u8a00\u7684\u6ce8\u91ca\u89c4\u8303\uff0c\u4ee5\u6362\u53d6\u66f4\u52a0\u7d27\u51d1\u7684\u5185\u5bb9\u6392\u7248\u3002\u6ce8\u91ca\u4e3b\u8981\u5206\u4e3a\u4e09\u79cd\u7c7b\u578b\uff1a\u6807\u9898\u6ce8\u91ca\u3001\u5185\u5bb9\u6ce8\u91ca\u3001\u591a\u884c\u6ce8\u91ca\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart <pre><code>/* \u6807\u9898\u6ce8\u91ca\uff0c\u7528\u4e8e\u6807\u6ce8\u51fd\u6570\u3001\u7c7b\u3001\u6d4b\u8bd5\u6837\u4f8b\u7b49 */\n// \u5185\u5bb9\u6ce8\u91ca\uff0c\u7528\u4e8e\u8be6\u89e3\u4ee3\u7801\n/**\n * \u591a\u884c\n * \u6ce8\u91ca\n */\n</code></pre> <pre><code>/* \u6807\u9898\u6ce8\u91ca\uff0c\u7528\u4e8e\u6807\u6ce8\u51fd\u6570\u3001\u7c7b\u3001\u6d4b\u8bd5\u6837\u4f8b\u7b49 */\n// \u5185\u5bb9\u6ce8\u91ca\uff0c\u7528\u4e8e\u8be6\u89e3\u4ee3\u7801\n/**\n * \u591a\u884c\n * \u6ce8\u91ca\n */\n</code></pre> <pre><code>\"\"\"\u6807\u9898\u6ce8\u91ca\uff0c\u7528\u4e8e\u6807\u6ce8\u51fd\u6570\u3001\u7c7b\u3001\u6d4b\u8bd5\u6837\u4f8b\u7b49\"\"\"\n# \u5185\u5bb9\u6ce8\u91ca\uff0c\u7528\u4e8e\u8be6\u89e3\u4ee3\u7801\n\"\"\"\n\u591a\u884c\n\u6ce8\u91ca\n\"\"\"\n</code></pre> <pre><code>/* \u6807\u9898\u6ce8\u91ca\uff0c\u7528\u4e8e\u6807\u6ce8\u51fd\u6570\u3001\u7c7b\u3001\u6d4b\u8bd5\u6837\u4f8b\u7b49 */\n// \u5185\u5bb9\u6ce8\u91ca\uff0c\u7528\u4e8e\u8be6\u89e3\u4ee3\u7801\n/**\n * \u591a\u884c\n * \u6ce8\u91ca\n */\n</code></pre> <pre><code>/* \u6807\u9898\u6ce8\u91ca\uff0c\u7528\u4e8e\u6807\u6ce8\u51fd\u6570\u3001\u7c7b\u3001\u6d4b\u8bd5\u6837\u4f8b\u7b49 */\n// \u5185\u5bb9\u6ce8\u91ca\uff0c\u7528\u4e8e\u8be6\u89e3\u4ee3\u7801\n/**\n * \u591a\u884c\n * \u6ce8\u91ca\n */\n</code></pre> <pre><code>/* \u6807\u9898\u6ce8\u91ca\uff0c\u7528\u4e8e\u6807\u6ce8\u51fd\u6570\u3001\u7c7b\u3001\u6d4b\u8bd5\u6837\u4f8b\u7b49 */\n// \u5185\u5bb9\u6ce8\u91ca\uff0c\u7528\u4e8e\u8be6\u89e3\u4ee3\u7801\n/**\n * \u591a\u884c\n * \u6ce8\u91ca\n */\n</code></pre> <pre><code>/* \u6807\u9898\u6ce8\u91ca\uff0c\u7528\u4e8e\u6807\u6ce8\u51fd\u6570\u3001\u7c7b\u3001\u6d4b\u8bd5\u6837\u4f8b\u7b49 */\n// \u5185\u5bb9\u6ce8\u91ca\uff0c\u7528\u4e8e\u8be6\u89e3\u4ee3\u7801\n/**\n * \u591a\u884c\n * \u6ce8\u91ca\n */\n</code></pre> <pre><code>/* \u6807\u9898\u6ce8\u91ca\uff0c\u7528\u4e8e\u6807\u6ce8\u51fd\u6570\u3001\u7c7b\u3001\u6d4b\u8bd5\u6837\u4f8b\u7b49 */\n// \u5185\u5bb9\u6ce8\u91ca\uff0c\u7528\u4e8e\u8be6\u89e3\u4ee3\u7801\n/**\n * \u591a\u884c\n * \u6ce8\u91ca\n */\n</code></pre> <pre><code>/* \u6807\u9898\u6ce8\u91ca\uff0c\u7528\u4e8e\u6807\u6ce8\u51fd\u6570\u3001\u7c7b\u3001\u6d4b\u8bd5\u6837\u4f8b\u7b49 */\n// \u5185\u5bb9\u6ce8\u91ca\uff0c\u7528\u4e8e\u8be6\u89e3\u4ee3\u7801\n/**\n * \u591a\u884c\n * \u6ce8\u91ca\n */\n</code></pre> <pre><code>// \u6807\u9898\u6ce8\u91ca\uff0c\u7528\u4e8e\u6807\u6ce8\u51fd\u6570\u3001\u7c7b\u3001\u6d4b\u8bd5\u6837\u4f8b\u7b49\n// \u5185\u5bb9\u6ce8\u91ca\uff0c\u7528\u4e8e\u8be6\u89e3\u4ee3\u7801\n// \u591a\u884c\n// \u6ce8\u91ca\n</code></pre> <pre><code>/* \u6807\u9898\u6ce8\u91ca\uff0c\u7528\u4e8e\u6807\u6ce8\u51fd\u6570\u3001\u7c7b\u3001\u6d4b\u8bd5\u6837\u4f8b\u7b49 */\n// \u5185\u5bb9\u6ce8\u91ca\uff0c\u7528\u4e8e\u8be6\u89e3\u4ee3\u7801\n/**\n * \u591a\u884c\n * \u6ce8\u91ca\n */\n</code></pre>"},{"location":"chapter_preface/suggestions/#022","title":"0.2.2. \u00a0 \u5728\u52a8\u753b\u56fe\u89e3\u4e2d\u9ad8\u6548\u5b66\u4e60","text":"<p>\u76f8\u8f83\u4e8e\u6587\u5b57\uff0c\u89c6\u9891\u548c\u56fe\u7247\u5177\u6709\u66f4\u9ad8\u7684\u4fe1\u606f\u5bc6\u5ea6\u548c\u7ed3\u6784\u5316\u7a0b\u5ea6\uff0c\u56e0\u6b64\u66f4\u6613\u4e8e\u7406\u89e3\u3002\u5728\u672c\u4e66\u4e2d\uff0c\u91cd\u70b9\u548c\u96be\u70b9\u77e5\u8bc6\u5c06\u4e3b\u8981\u901a\u8fc7\u52a8\u753b\u548c\u56fe\u89e3\u5f62\u5f0f\u5c55\u793a\uff0c\u800c\u6587\u5b57\u5219\u4f5c\u4e3a\u52a8\u753b\u548c\u56fe\u7247\u7684\u89e3\u91ca\u4e0e\u8865\u5145\u3002</p> <p>\u5728\u9605\u8bfb\u672c\u4e66\u65f6\uff0c\u5982\u679c\u53d1\u73b0\u67d0\u6bb5\u5185\u5bb9\u63d0\u4f9b\u4e86\u52a8\u753b\u6216\u56fe\u89e3\uff0c\u5efa\u8bae\u4ee5\u56fe\u4e3a\u4e3b\u7ebf\uff0c\u4ee5\u6587\u5b57\uff08\u901a\u5e38\u4f4d\u4e8e\u56fe\u50cf\u4e0a\u65b9\uff09\u4e3a\u8f85\uff0c\u7efc\u5408\u4e24\u8005\u6765\u7406\u89e3\u5185\u5bb9\u3002</p> <p></p> <p> Fig. \u52a8\u753b\u56fe\u89e3\u793a\u4f8b </p>"},{"location":"chapter_preface/suggestions/#023","title":"0.2.3. \u00a0 \u5728\u4ee3\u7801\u5b9e\u8df5\u4e2d\u52a0\u6df1\u7406\u89e3","text":"<p>\u672c\u4e66\u7684\u914d\u5957\u4ee3\u7801\u6258\u7ba1\u5728GitHub \u4ed3\u5e93\uff0c\u6e90\u4ee3\u7801\u5305\u542b\u8be6\u7ec6\u6ce8\u91ca\uff0c\u5e76\u9644\u6709\u6d4b\u8bd5\u6837\u4f8b\uff0c\u53ef\u76f4\u63a5\u8fd0\u884c\u3002</p> <p>\u5982\u679c\u5b66\u4e60\u65f6\u95f4\u6709\u9650\uff0c\u5efa\u8bae\u4f60\u81f3\u5c11\u901a\u8bfb\u5e76\u8fd0\u884c\u6240\u6709\u4ee3\u7801\u3002\u5982\u679c\u65f6\u95f4\u5145\u88d5\uff0c\u5efa\u8bae\u53c2\u7167\u4ee3\u7801\u81ea\u884c\u6572\u4e00\u904d\u3002\u4e0e\u4ec5\u9605\u8bfb\u4ee3\u7801\u76f8\u6bd4\uff0c\u7f16\u5199\u4ee3\u7801\u7684\u8fc7\u7a0b\u5f80\u5f80\u80fd\u5e26\u6765\u66f4\u591a\u6536\u83b7\u3002</p> <p></p> <p> Fig. \u8fd0\u884c\u4ee3\u7801\u793a\u4f8b </p> <p>\u7b2c\u4e00\u6b65\uff1a\u5b89\u88c5\u672c\u5730\u7f16\u7a0b\u73af\u5883\u3002\u8bf7\u53c2\u7167\u9644\u5f55\u6559\u7a0b\u8fdb\u884c\u5b89\u88c5\uff0c\u5982\u679c\u5df2\u5b89\u88c5\u5219\u53ef\u8df3\u8fc7\u6b64\u6b65\u9aa4\u3002</p> <p>\u7b2c\u4e8c\u6b65\uff1a\u4e0b\u8f7d\u4ee3\u7801\u4ed3\u3002\u5982\u679c\u5df2\u7ecf\u5b89\u88c5 Git \uff0c\u53ef\u4ee5\u901a\u8fc7\u4ee5\u4e0b\u547d\u4ee4\u514b\u9686\u672c\u4ed3\u5e93\u3002</p> <pre><code>git clone https://github.com/krahets/hello-algo.git\n</code></pre> <p>\u5f53\u7136\uff0c\u4f60\u4e5f\u53ef\u4ee5\u70b9\u51fb\u201cDownload ZIP\u201d\u76f4\u63a5\u4e0b\u8f7d\u4ee3\u7801\u538b\u7f29\u5305\uff0c\u7136\u540e\u5728\u672c\u5730\u89e3\u538b\u5373\u53ef\u3002</p> <p></p> <p> Fig. \u514b\u9686\u4ed3\u5e93\u4e0e\u4e0b\u8f7d\u4ee3\u7801 </p> <p>\u7b2c\u4e09\u6b65\uff1a\u8fd0\u884c\u6e90\u4ee3\u7801\u3002\u5982\u679c\u4ee3\u7801\u5757\u9876\u90e8\u6807\u6709\u6587\u4ef6\u540d\u79f0\uff0c\u5219\u53ef\u4ee5\u5728\u4ed3\u5e93\u7684 <code>codes</code> \u6587\u4ef6\u5939\u4e2d\u627e\u5230\u76f8\u5e94\u7684\u6e90\u4ee3\u7801\u6587\u4ef6\u3002\u6e90\u4ee3\u7801\u6587\u4ef6\u5c06\u5e2e\u52a9\u4f60\u8282\u7701\u4e0d\u5fc5\u8981\u7684\u8c03\u8bd5\u65f6\u95f4\uff0c\u8ba9\u4f60\u80fd\u591f\u4e13\u6ce8\u4e8e\u5b66\u4e60\u5185\u5bb9\u3002</p> <p></p> <p> Fig. \u4ee3\u7801\u5757\u4e0e\u5bf9\u5e94\u7684\u6e90\u4ee3\u7801\u6587\u4ef6 </p>"},{"location":"chapter_preface/suggestions/#024","title":"0.2.4. \u00a0 \u5728\u63d0\u95ee\u8ba8\u8bba\u4e2d\u5171\u540c\u6210\u957f","text":"<p>\u9605\u8bfb\u672c\u4e66\u65f6\uff0c\u8bf7\u4e0d\u8981\u201c\u60ef\u7740\u201d\u90a3\u4e9b\u6ca1\u5b66\u660e\u767d\u7684\u77e5\u8bc6\u70b9\u3002\u6b22\u8fce\u5728\u8bc4\u8bba\u533a\u63d0\u51fa\u4f60\u7684\u95ee\u9898\uff0c\u6211\u548c\u5176\u4ed6\u5c0f\u4f19\u4f34\u4eec\u5c06\u7aed\u8bda\u4e3a\u4f60\u89e3\u7b54\uff0c\u4e00\u822c\u60c5\u51b5\u4e0b\u53ef\u5728\u4e24\u5929\u5185\u5f97\u5230\u56de\u590d\u3002</p> <p>\u540c\u65f6\uff0c\u4e5f\u5e0c\u671b\u60a8\u80fd\u5728\u8bc4\u8bba\u533a\u591a\u82b1\u4e9b\u65f6\u95f4\u3002\u4e00\u65b9\u9762\uff0c\u60a8\u53ef\u4ee5\u4e86\u89e3\u5927\u5bb6\u9047\u5230\u7684\u95ee\u9898\uff0c\u4ece\u800c\u67e5\u6f0f\u8865\u7f3a\uff0c\u8fd9\u5c06\u6709\u52a9\u4e8e\u6fc0\u53d1\u66f4\u6df1\u5165\u7684\u601d\u8003\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u5e0c\u671b\u60a8\u80fd\u6177\u6168\u5730\u56de\u7b54\u5176\u4ed6\u5c0f\u4f19\u4f34\u7684\u95ee\u9898\u3001\u5206\u4eab\u60a8\u7684\u89c1\u89e3\uff0c\u8ba9\u5927\u5bb6\u5171\u540c\u5b66\u4e60\u548c\u8fdb\u6b65\u3002</p> <p></p> <p> Fig. \u8bc4\u8bba\u533a\u793a\u4f8b </p>"},{"location":"chapter_preface/suggestions/#025","title":"0.2.5. \u00a0 \u7b97\u6cd5\u5b66\u4e60\u8def\u7ebf","text":"<p>\u4ece\u603b\u4f53\u4e0a\u770b\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u5b66\u4e60\u6570\u636e\u7ed3\u6784\u4e0e\u7b97\u6cd5\u7684\u8fc7\u7a0b\u5212\u5206\u4e3a\u4e09\u4e2a\u9636\u6bb5\uff1a</p> <ol> <li>\u7b97\u6cd5\u5165\u95e8\u3002\u6211\u4eec\u9700\u8981\u719f\u6089\u5404\u79cd\u6570\u636e\u7ed3\u6784\u7684\u7279\u70b9\u548c\u7528\u6cd5\uff0c\u5b66\u4e60\u4e0d\u540c\u7b97\u6cd5\u7684\u539f\u7406\u3001\u6d41\u7a0b\u3001\u7528\u9014\u548c\u6548\u7387\u7b49\u65b9\u9762\u5185\u5bb9\u3002</li> <li>\u5237\u7b97\u6cd5\u9898\u3002\u5efa\u8bae\u4ece\u70ed\u95e8\u9898\u76ee\u5f00\u5237\uff0c\u5982\u5251\u6307 Offer\u548cLeetCode Hot 100\uff0c\u5148\u79ef\u7d2f\u81f3\u5c11 100 \u9053\u9898\u76ee\uff0c\u719f\u6089\u4e3b\u6d41\u7684\u7b97\u6cd5\u95ee\u9898\u3002\u521d\u6b21\u5237\u9898\u65f6\uff0c\u201c\u77e5\u8bc6\u9057\u5fd8\u201d\u53ef\u80fd\u662f\u4e00\u4e2a\u6311\u6218\uff0c\u4f46\u8bf7\u653e\u5fc3\uff0c\u8fd9\u662f\u5f88\u6b63\u5e38\u7684\u3002\u6211\u4eec\u53ef\u4ee5\u6309\u7167\u201c\u827e\u5bbe\u6d69\u65af\u9057\u5fd8\u66f2\u7ebf\u201d\u6765\u590d\u4e60\u9898\u76ee\uff0c\u901a\u5e38\u5728\u8fdb\u884c 3-5 \u8f6e\u7684\u91cd\u590d\u540e\uff0c\u5c31\u80fd\u5c06\u5176\u7262\u8bb0\u5728\u5fc3\u3002</li> <li>\u642d\u5efa\u77e5\u8bc6\u4f53\u7cfb\u3002\u5728\u5b66\u4e60\u65b9\u9762\uff0c\u6211\u4eec\u53ef\u4ee5\u9605\u8bfb\u7b97\u6cd5\u4e13\u680f\u6587\u7ae0\u3001\u89e3\u9898\u6846\u67b6\u548c\u7b97\u6cd5\u6559\u6750\uff0c\u4ee5\u4e0d\u65ad\u4e30\u5bcc\u77e5\u8bc6\u4f53\u7cfb\u3002\u5728\u5237\u9898\u65b9\u9762\uff0c\u53ef\u4ee5\u5c1d\u8bd5\u91c7\u7528\u8fdb\u9636\u5237\u9898\u7b56\u7565\uff0c\u5982\u6309\u4e13\u9898\u5206\u7c7b\u3001\u4e00\u9898\u591a\u89e3\u3001\u4e00\u89e3\u591a\u9898\u7b49\uff0c\u76f8\u5173\u7684\u5237\u9898\u5fc3\u5f97\u53ef\u4ee5\u5728\u5404\u4e2a\u793e\u533a\u627e\u5230\u3002</li> </ol> <p>\u4f5c\u4e3a\u4e00\u672c\u5165\u95e8\u6559\u7a0b\uff0c\u672c\u4e66\u5185\u5bb9\u4e3b\u8981\u6db5\u76d6\u201c\u7b2c\u4e00\u9636\u6bb5\u201d\uff0c\u65e8\u5728\u5e2e\u52a9\u4f60\u66f4\u9ad8\u6548\u5730\u5c55\u5f00\u7b2c\u4e8c\u548c\u7b2c\u4e09\u9636\u6bb5\u7684\u5b66\u4e60\u3002</p> <p></p> <p> Fig. \u7b97\u6cd5\u5b66\u4e60\u8def\u7ebf </p>"},{"location":"chapter_preface/summary/","title":"0.3. \u00a0 \u5c0f\u7ed3","text":"<ul> <li>\u672c\u4e66\u7684\u4e3b\u8981\u53d7\u4f17\u662f\u7b97\u6cd5\u521d\u5b66\u8005\u3002\u5982\u679c\u5df2\u6709\u4e00\u5b9a\u57fa\u7840\uff0c\u672c\u4e66\u80fd\u5e2e\u52a9\u60a8\u7cfb\u7edf\u56de\u987e\u7b97\u6cd5\u77e5\u8bc6\uff0c\u4e66\u5185\u6e90\u4ee3\u7801\u4e5f\u53ef\u4f5c\u4e3a\u201c\u5237\u9898\u5de5\u5177\u5e93\u201d\u4f7f\u7528\u3002</li> <li>\u4e66\u4e2d\u5185\u5bb9\u4e3b\u8981\u5305\u62ec\u590d\u6742\u5ea6\u5206\u6790\u3001\u6570\u636e\u7ed3\u6784\u3001\u7b97\u6cd5\u4e09\u90e8\u5206\uff0c\u6db5\u76d6\u4e86\u8be5\u9886\u57df\u7684\u5927\u90e8\u5206\u4e3b\u9898\u3002</li> <li>\u5bf9\u4e8e\u7b97\u6cd5\u65b0\u624b\uff0c\u5728\u521d\u5b66\u9636\u6bb5\u9605\u8bfb\u4e00\u672c\u5165\u95e8\u4e66\u7c4d\u81f3\u5173\u91cd\u8981\uff0c\u53ef\u4ee5\u5c11\u8d70\u8bb8\u591a\u5f2f\u8def\u3002</li> <li>\u4e66\u5185\u7684\u52a8\u753b\u548c\u56fe\u89e3\u901a\u5e38\u7528\u4e8e\u4ecb\u7ecd\u91cd\u70b9\u548c\u96be\u70b9\u77e5\u8bc6\u3002\u9605\u8bfb\u672c\u4e66\u65f6\uff0c\u5e94\u7ed9\u4e88\u8fd9\u4e9b\u5185\u5bb9\u66f4\u591a\u5173\u6ce8\u3002</li> <li>\u5b9e\u8df5\u4e43\u5b66\u4e60\u7f16\u7a0b\u4e4b\u6700\u4f73\u9014\u5f84\u3002\u5f3a\u70c8\u5efa\u8bae\u8fd0\u884c\u6e90\u4ee3\u7801\u5e76\u4eb2\u81ea\u6572\u6253\u4ee3\u7801\u3002</li> <li>\u672c\u4e66\u7f51\u9875\u7248\u7684\u6bcf\u4e2a\u7ae0\u8282\u90fd\u8bbe\u6709\u8ba8\u8bba\u533a\uff0c\u6b22\u8fce\u968f\u65f6\u5206\u4eab\u4f60\u7684\u7591\u60d1\u4e0e\u89c1\u89e3\u3002</li> </ul>"},{"location":"chapter_reference/","title":"\u53c2\u8003\u6587\u732e","text":"<p>[1] Thomas H. Cormen, et al. Introduction to Algorithms (3rd Edition).</p> <p>[2] Aditya Bhargava. Grokking Algorithms: An Illustrated Guide for Programmers and Other Curious People (1st Edition).</p> <p>[3] \u4e25\u851a\u654f. \u6570\u636e\u7ed3\u6784\uff08C \u8bed\u8a00\u7248\uff09.</p> <p>[4] \u9093\u4fca\u8f89. \u6570\u636e\u7ed3\u6784\uff08C++ \u8bed\u8a00\u7248\uff0c\u7b2c\u4e09\u7248\uff09.</p> <p>[5] \u9a6c\u514b \u827e\u4f26 \u7ef4\u65af\u8457\uff0c\u9648\u8d8a\u8bd1. \u6570\u636e\u7ed3\u6784\u4e0e\u7b97\u6cd5\u5206\u6790\uff1aJava\u8bed\u8a00\u63cf\u8ff0\uff08\u7b2c\u4e09\u7248\uff09.</p> <p>[6] \u7a0b\u6770. \u5927\u8bdd\u6570\u636e\u7ed3\u6784.</p> <p>[7] \u738b\u4e89. \u6570\u636e\u7ed3\u6784\u4e0e\u7b97\u6cd5\u4e4b\u7f8e.</p> <p>[8] Gayle Laakmann McDowell. Cracking the Coding Interview: 189 Programming Questions and Solutions (6th Edition). </p> <p>[9] Aston Zhang, et al. Dive into Deep Learning.</p>"},{"location":"chapter_searching/","title":"10. \u00a0 \u641c\u7d22","text":""},{"location":"chapter_searching/binary_search/","title":"10.1. \u00a0 \u4e8c\u5206\u67e5\u627e","text":"<p>\u300c\u4e8c\u5206\u67e5\u627e Binary Search\u300d\u662f\u4e00\u79cd\u57fa\u4e8e\u5206\u6cbb\u601d\u60f3\u7684\u9ad8\u6548\u641c\u7d22\u7b97\u6cd5\u3002\u5b83\u5229\u7528\u6570\u636e\u7684\u6709\u5e8f\u6027\uff0c\u6bcf\u8f6e\u51cf\u5c11\u4e00\u534a\u641c\u7d22\u8303\u56f4\uff0c\u76f4\u81f3\u627e\u5230\u76ee\u6807\u5143\u7d20\u6216\u641c\u7d22\u533a\u95f4\u4e3a\u7a7a\u4e3a\u6b62\u3002</p> <p>Question</p> <p>\u7ed9\u5b9a\u4e00\u4e2a\u957f\u5ea6\u4e3a \\(n\\) \u7684\u6570\u7ec4 <code>nums</code> \uff0c\u5143\u7d20\u6309\u4ece\u5c0f\u5230\u5927\u7684\u987a\u5e8f\u6392\u5217\uff0c\u6570\u7ec4\u4e0d\u5305\u542b\u91cd\u590d\u5143\u7d20\u3002\u8bf7\u67e5\u627e\u5e76\u8fd4\u56de\u5143\u7d20 <code>target</code> \u5728\u8be5\u6570\u7ec4\u4e2d\u7684\u7d22\u5f15\u3002\u82e5\u6570\u7ec4\u4e0d\u5305\u542b\u8be5\u5143\u7d20\uff0c\u5219\u8fd4\u56de \\(-1\\) \u3002</p> <p>\u5bf9\u4e8e\u4e0a\u8ff0\u95ee\u9898\uff0c\u6211\u4eec\u5148\u521d\u59cb\u5316\u6307\u9488 \\(i = 0\\) \u548c \\(j = n - 1\\) \uff0c\u5206\u522b\u6307\u5411\u6570\u7ec4\u9996\u5143\u7d20\u548c\u5c3e\u5143\u7d20\uff0c\u4ee3\u8868\u641c\u7d22\u533a\u95f4 \\([0, n - 1]\\) \u3002\u5176\u4e2d\uff0c\u4e2d\u62ec\u53f7\u8868\u793a\u201c\u95ed\u533a\u95f4\u201d\uff0c\u5373\u5305\u542b\u8fb9\u754c\u503c\u672c\u8eab\u3002</p> <p>\u63a5\u4e0b\u6765\uff0c\u5faa\u73af\u6267\u884c\u4ee5\u4e0b\u4e24\u4e2a\u6b65\u9aa4\uff1a</p> <ol> <li>\u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 \\(m = \\lfloor {(i + j) / 2} \\rfloor\\) \uff0c\u5176\u4e2d \\(\\lfloor \\space \\rfloor\\) \u8868\u793a\u5411\u4e0b\u53d6\u6574\u64cd\u4f5c\u3002</li> <li>\u5224\u65ad <code>nums[m]</code> \u548c <code>target</code> \u7684\u5927\u5c0f\u5173\u7cfb\uff0c\u5206\u4e3a\u4e09\u79cd\u60c5\u51b5\uff1a<ol> <li>\u5f53 <code>nums[m] &lt; target</code> \u65f6\uff0c\u8bf4\u660e <code>target</code> \u5728\u533a\u95f4 \\([m + 1, j]\\) \u4e2d\uff0c\u56e0\u6b64\u6267\u884c \\(i = m + 1\\) \uff1b</li> <li>\u5f53 <code>nums[m] &gt; target</code> \u65f6\uff0c\u8bf4\u660e <code>target</code> \u5728\u533a\u95f4 \\([i, m - 1]\\) \u4e2d\uff0c\u56e0\u6b64\u6267\u884c \\(j = m - 1\\) \uff1b</li> <li>\u5f53 <code>nums[m] = target</code> \u65f6\uff0c\u8bf4\u660e\u627e\u5230 <code>target</code> \uff0c\u56e0\u6b64\u8fd4\u56de\u7d22\u5f15 \\(m\\) \uff1b</li> </ol> </li> </ol> <p>\u82e5\u6570\u7ec4\u4e0d\u5305\u542b\u76ee\u6807\u5143\u7d20\uff0c\u641c\u7d22\u533a\u95f4\u6700\u7ec8\u4f1a\u7f29\u5c0f\u4e3a\u7a7a\u3002\u6b64\u65f6\u8fd4\u56de \\(-1\\) \u3002</p> &lt;0&gt;&lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p>\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u7531\u4e8e \\(i\\) \u548c \\(j\\) \u90fd\u662f <code>int</code> \u7c7b\u578b\uff0c\u56e0\u6b64 \\(i + j\\) \u53ef\u80fd\u4f1a\u8d85\u51fa <code>int</code> \u7c7b\u578b\u7684\u53d6\u503c\u8303\u56f4\u3002\u4e3a\u4e86\u907f\u514d\u5927\u6570\u8d8a\u754c\uff0c\u6211\u4eec\u901a\u5e38\u91c7\u7528\u516c\u5f0f \\(m = \\lfloor {i + (j - i) / 2} \\rfloor\\) \u6765\u8ba1\u7b97\u4e2d\u70b9\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart binary_search.java<pre><code>/* \u4e8c\u5206\u67e5\u627e\uff08\u53cc\u95ed\u533a\u95f4\uff09 */\nint binarySearch(int[] nums, int target) {\n// \u521d\u59cb\u5316\u53cc\u95ed\u533a\u95f4 [0, n-1] \uff0c\u5373 i, j \u5206\u522b\u6307\u5411\u6570\u7ec4\u9996\u5143\u7d20\u3001\u5c3e\u5143\u7d20\nint i = 0, j = nums.length - 1;\n// \u5faa\u73af\uff0c\u5f53\u641c\u7d22\u533a\u95f4\u4e3a\u7a7a\u65f6\u8df3\u51fa\uff08\u5f53 i &gt; j \u65f6\u4e3a\u7a7a\uff09\nwhile (i &lt;= j) {\nint m = i + (j - i) / 2; // \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nif (nums[m] &lt; target) // \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [m+1, j] \u4e2d\ni = m + 1;\nelse if (nums[m] &gt; target) // \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [i, m-1] \u4e2d\nj = m - 1;\nelse // \u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de\u5176\u7d22\u5f15\nreturn m;\n}\n// \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\nreturn -1;\n}\n</code></pre> binary_search.cpp<pre><code>/* \u4e8c\u5206\u67e5\u627e\uff08\u53cc\u95ed\u533a\u95f4\uff09 */\nint binarySearch(vector&lt;int&gt; &amp;nums, int target) {\n// \u521d\u59cb\u5316\u53cc\u95ed\u533a\u95f4 [0, n-1] \uff0c\u5373 i, j \u5206\u522b\u6307\u5411\u6570\u7ec4\u9996\u5143\u7d20\u3001\u5c3e\u5143\u7d20\nint i = 0, j = nums.size() - 1;\n// \u5faa\u73af\uff0c\u5f53\u641c\u7d22\u533a\u95f4\u4e3a\u7a7a\u65f6\u8df3\u51fa\uff08\u5f53 i &gt; j \u65f6\u4e3a\u7a7a\uff09\nwhile (i &lt;= j) {\nint m = i + (j - i) / 2; // \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nif (nums[m] &lt; target)    // \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [m+1, j] \u4e2d\ni = m + 1;\nelse if (nums[m] &gt; target) // \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [i, m-1] \u4e2d\nj = m - 1;\nelse // \u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de\u5176\u7d22\u5f15\nreturn m;\n}\n// \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\nreturn -1;\n}\n</code></pre> binary_search.py<pre><code>def binary_search(nums: list[int], target: int) -&gt; int:\n\"\"\"\u4e8c\u5206\u67e5\u627e\uff08\u53cc\u95ed\u533a\u95f4\uff09\"\"\"\n# \u521d\u59cb\u5316\u53cc\u95ed\u533a\u95f4 [0, n-1] \uff0c\u5373 i, j \u5206\u522b\u6307\u5411\u6570\u7ec4\u9996\u5143\u7d20\u3001\u5c3e\u5143\u7d20\ni, j = 0, len(nums) - 1\n# \u5faa\u73af\uff0c\u5f53\u641c\u7d22\u533a\u95f4\u4e3a\u7a7a\u65f6\u8df3\u51fa\uff08\u5f53 i &gt; j \u65f6\u4e3a\u7a7a\uff09\nwhile i &lt;= j:\n# \u7406\u8bba\u4e0a Python \u7684\u6570\u5b57\u53ef\u4ee5\u65e0\u9650\u5927\uff08\u53d6\u51b3\u4e8e\u5185\u5b58\u5927\u5c0f\uff09\uff0c\u65e0\u9700\u8003\u8651\u5927\u6570\u8d8a\u754c\u95ee\u9898\nm = (i + j) // 2  # \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nif nums[m] &lt; target:\ni = m + 1  # \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [m+1, j] \u4e2d\nelif nums[m] &gt; target:\nj = m - 1  # \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [i, m-1] \u4e2d\nelse:\nreturn m  # \u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de\u5176\u7d22\u5f15\nreturn -1  # \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\n</code></pre> binary_search.go<pre><code>/* \u4e8c\u5206\u67e5\u627e\uff08\u53cc\u95ed\u533a\u95f4\uff09 */\nfunc binarySearch(nums []int, target int) int {\n// \u521d\u59cb\u5316\u53cc\u95ed\u533a\u95f4 [0, n-1] \uff0c\u5373 i, j \u5206\u522b\u6307\u5411\u6570\u7ec4\u9996\u5143\u7d20\u3001\u5c3e\u5143\u7d20\ni, j := 0, len(nums)-1\n// \u5faa\u73af\uff0c\u5f53\u641c\u7d22\u533a\u95f4\u4e3a\u7a7a\u65f6\u8df3\u51fa\uff08\u5f53 i &gt; j \u65f6\u4e3a\u7a7a\uff09\nfor i &lt;= j {\nm := i + (j-i)/2      // \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nif nums[m] &lt; target { // \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [m+1, j] \u4e2d\ni = m + 1\n} else if nums[m] &gt; target { // \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [i, m-1] \u4e2d\nj = m - 1\n} else { // \u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de\u5176\u7d22\u5f15\nreturn m\n}\n}\n// \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\nreturn -1\n}\n</code></pre> binary_search.js<pre><code>/* \u4e8c\u5206\u67e5\u627e\uff08\u53cc\u95ed\u533a\u95f4\uff09 */\nfunction binarySearch(nums, target) {\n// \u521d\u59cb\u5316\u53cc\u95ed\u533a\u95f4 [0, n-1] \uff0c\u5373 i, j \u5206\u522b\u6307\u5411\u6570\u7ec4\u9996\u5143\u7d20\u3001\u5c3e\u5143\u7d20\nlet i = 0,\nj = nums.length - 1;\n// \u5faa\u73af\uff0c\u5f53\u641c\u7d22\u533a\u95f4\u4e3a\u7a7a\u65f6\u8df3\u51fa\uff08\u5f53 i &gt; j \u65f6\u4e3a\u7a7a\uff09\nwhile (i &lt;= j) {\n// \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m \uff0c\u4f7f\u7528 parseInt() \u5411\u4e0b\u53d6\u6574\nconst m = parseInt(i + (j - i) / 2);\nif (nums[m] &lt; target)\n// \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [m+1, j] \u4e2d\ni = m + 1;\nelse if (nums[m] &gt; target)\n// \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [i, m-1] \u4e2d\nj = m - 1;\nelse return m; // \u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de\u5176\u7d22\u5f15\n}\n// \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\nreturn -1;\n}\n</code></pre> binary_search.ts<pre><code>/* \u4e8c\u5206\u67e5\u627e\uff08\u53cc\u95ed\u533a\u95f4\uff09 */\nfunction binarySearch(nums: number[], target: number): number {\n// \u521d\u59cb\u5316\u53cc\u95ed\u533a\u95f4 [0, n-1] \uff0c\u5373 i, j \u5206\u522b\u6307\u5411\u6570\u7ec4\u9996\u5143\u7d20\u3001\u5c3e\u5143\u7d20\nlet i = 0,\nj = nums.length - 1;\n// \u5faa\u73af\uff0c\u5f53\u641c\u7d22\u533a\u95f4\u4e3a\u7a7a\u65f6\u8df3\u51fa\uff08\u5f53 i &gt; j \u65f6\u4e3a\u7a7a\uff09\nwhile (i &lt;= j) {\n// \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nconst m = Math.floor(i + (j - i) / 2);\nif (nums[m] &lt; target) {\n// \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [m+1, j] \u4e2d\ni = m + 1;\n} else if (nums[m] &gt; target) {\n// \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [i, m-1] \u4e2d\nj = m - 1;\n} else {\n// \u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de\u5176\u7d22\u5f15\nreturn m;\n}\n}\nreturn -1; // \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\n}\n</code></pre> binary_search.c<pre><code>/* \u4e8c\u5206\u67e5\u627e\uff08\u53cc\u95ed\u533a\u95f4\uff09 */\nint binarySearch(int *nums, int len, int target) {\n// \u521d\u59cb\u5316\u53cc\u95ed\u533a\u95f4 [0, n-1] \uff0c\u5373 i, j \u5206\u522b\u6307\u5411\u6570\u7ec4\u9996\u5143\u7d20\u3001\u5c3e\u5143\u7d20\nint i = 0, j = len - 1;\n// \u5faa\u73af\uff0c\u5f53\u641c\u7d22\u533a\u95f4\u4e3a\u7a7a\u65f6\u8df3\u51fa\uff08\u5f53 i &gt; j \u65f6\u4e3a\u7a7a\uff09\nwhile (i &lt;= j) {\nint m = i + (j - i) / 2; // \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nif (nums[m] &lt; target)    // \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [m+1, j] \u4e2d\ni = m + 1;\nelse if (nums[m] &gt; target) // \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [i, m-1] \u4e2d\nj = m - 1;\nelse // \u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de\u5176\u7d22\u5f15\nreturn m;\n}\n// \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\nreturn -1;\n}\n</code></pre> binary_search.cs<pre><code>/* \u4e8c\u5206\u67e5\u627e\uff08\u53cc\u95ed\u533a\u95f4\uff09 */\nint binarySearch(int[] nums, int target) {\n// \u521d\u59cb\u5316\u53cc\u95ed\u533a\u95f4 [0, n-1] \uff0c\u5373 i, j \u5206\u522b\u6307\u5411\u6570\u7ec4\u9996\u5143\u7d20\u3001\u5c3e\u5143\u7d20\nint i = 0, j = nums.Length - 1;\n// \u5faa\u73af\uff0c\u5f53\u641c\u7d22\u533a\u95f4\u4e3a\u7a7a\u65f6\u8df3\u51fa\uff08\u5f53 i &gt; j \u65f6\u4e3a\u7a7a\uff09\nwhile (i &lt;= j) {\nint m = i + (j - i) / 2;   // \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nif (nums[m] &lt; target)      // \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [m+1, j] \u4e2d\ni = m + 1;\nelse if (nums[m] &gt; target) // \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [i, m-1] \u4e2d\nj = m - 1;\nelse                       // \u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de\u5176\u7d22\u5f15\nreturn m;\n}\n// \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\nreturn -1;\n}\n</code></pre> binary_search.swift<pre><code>/* \u4e8c\u5206\u67e5\u627e\uff08\u53cc\u95ed\u533a\u95f4\uff09 */\nfunc binarySearch(nums: [Int], target: Int) -&gt; Int {\n// \u521d\u59cb\u5316\u53cc\u95ed\u533a\u95f4 [0, n-1] \uff0c\u5373 i, j \u5206\u522b\u6307\u5411\u6570\u7ec4\u9996\u5143\u7d20\u3001\u5c3e\u5143\u7d20\nvar i = 0\nvar j = nums.count - 1\n// \u5faa\u73af\uff0c\u5f53\u641c\u7d22\u533a\u95f4\u4e3a\u7a7a\u65f6\u8df3\u51fa\uff08\u5f53 i &gt; j \u65f6\u4e3a\u7a7a\uff09\nwhile i &lt;= j {\nlet m = i + (j - i) / 2 // \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nif nums[m] &lt; target { // \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [m+1, j] \u4e2d\ni = m + 1\n} else if nums[m] &gt; target { // \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [i, m-1] \u4e2d\nj = m - 1\n} else { // \u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de\u5176\u7d22\u5f15\nreturn m\n}\n}\n// \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\nreturn -1\n}\n</code></pre> binary_search.zig<pre><code>// \u4e8c\u5206\u67e5\u627e\uff08\u53cc\u95ed\u533a\u95f4\uff09\nfn binarySearch(comptime T: type, nums: std.ArrayList(T), target: T) T {\n// \u521d\u59cb\u5316\u53cc\u95ed\u533a\u95f4 [0, n-1] \uff0c\u5373 i, j \u5206\u522b\u6307\u5411\u6570\u7ec4\u9996\u5143\u7d20\u3001\u5c3e\u5143\u7d20\nvar i: usize = 0;\nvar j: usize = nums.items.len - 1;\n// \u5faa\u73af\uff0c\u5f53\u641c\u7d22\u533a\u95f4\u4e3a\u7a7a\u65f6\u8df3\u51fa\uff08\u5f53 i &gt; j \u65f6\u4e3a\u7a7a\uff09\nwhile (i &lt;= j) {\nvar m = i + (j - i) / 2;                // \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nif (nums.items[m] &lt; target) {           // \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [m+1, j] \u4e2d\ni = m + 1;\n} else if (nums.items[m] &gt; target) {    // \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [i, m-1] \u4e2d\nj = m - 1;\n} else {                                // \u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de\u5176\u7d22\u5f15\nreturn @intCast(T, m);\n}\n}\n// \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\nreturn -1;\n}\n</code></pre> binary_search.dart<pre><code>/* \u4e8c\u5206\u67e5\u627e\uff08\u53cc\u95ed\u533a\u95f4\uff09 */\nint binarySearch(List&lt;int&gt; nums, int target) {\n// \u521d\u59cb\u5316\u53cc\u95ed\u533a\u95f4 [0, n-1] \uff0c\u5373 i, j \u5206\u522b\u6307\u5411\u6570\u7ec4\u9996\u5143\u7d20\u3001\u5c3e\u5143\u7d20\nint i = 0, j = nums.length - 1;\n// \u5faa\u73af\uff0c\u5f53\u641c\u7d22\u533a\u95f4\u4e3a\u7a7a\u65f6\u8df3\u51fa\uff08\u5f53 i &gt; j \u65f6\u4e3a\u7a7a\uff09\nwhile (i &lt;= j) {\nint m = i + (j - i) ~/ 2; // \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nif (nums[m] &lt; target) {\n// \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [m+1, j] \u4e2d\ni = m + 1;\n} else if (nums[m] &gt; target) {\n// \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [i, m-1] \u4e2d\nj = m - 1;\n} else {\n// \u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de\u5176\u7d22\u5f15\nreturn m;\n}\n}\n// \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\nreturn -1;\n}\n</code></pre> <p>\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(\\log n)\\) \u3002\u6bcf\u8f6e\u7f29\u5c0f\u4e00\u534a\u533a\u95f4\uff0c\u56e0\u6b64\u4e8c\u5206\u5faa\u73af\u6b21\u6570\u4e3a \\(\\log_2 n\\) \u3002</p> <p>\u7a7a\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(1)\\)  \u3002\u6307\u9488 <code>i</code> , <code>j</code> \u4f7f\u7528\u5e38\u6570\u5927\u5c0f\u7a7a\u95f4\u3002</p>"},{"location":"chapter_searching/binary_search/#1011","title":"10.1.1. \u00a0 \u533a\u95f4\u8868\u793a\u65b9\u6cd5","text":"<p>\u9664\u4e86\u4e0a\u8ff0\u7684\u53cc\u95ed\u533a\u95f4\u5916\uff0c\u5e38\u89c1\u7684\u533a\u95f4\u8868\u793a\u8fd8\u6709\u201c\u5de6\u95ed\u53f3\u5f00\u201d\u533a\u95f4\uff0c\u5b9a\u4e49\u4e3a \\([0, n)\\) \uff0c\u5373\u5de6\u8fb9\u754c\u5305\u542b\u81ea\u8eab\uff0c\u53f3\u8fb9\u754c\u4e0d\u5305\u542b\u81ea\u8eab\u3002\u5728\u8be5\u8868\u793a\u4e0b\uff0c\u533a\u95f4 \\([i, j]\\) \u5728 \\(i = j\\) \u65f6\u4e3a\u7a7a\u3002</p> <p>\u6211\u4eec\u53ef\u4ee5\u57fa\u4e8e\u8be5\u8868\u793a\u5b9e\u73b0\u5177\u6709\u76f8\u540c\u529f\u80fd\u7684\u4e8c\u5206\u67e5\u627e\u7b97\u6cd5\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart binary_search.java<pre><code>/* \u4e8c\u5206\u67e5\u627e\uff08\u5de6\u95ed\u53f3\u5f00\uff09 */\nint binarySearchLCRO(int[] nums, int target) {\n// \u521d\u59cb\u5316\u5de6\u95ed\u53f3\u5f00 [0, n) \uff0c\u5373 i, j \u5206\u522b\u6307\u5411\u6570\u7ec4\u9996\u5143\u7d20\u3001\u5c3e\u5143\u7d20+1\nint i = 0, j = nums.length;\n// \u5faa\u73af\uff0c\u5f53\u641c\u7d22\u533a\u95f4\u4e3a\u7a7a\u65f6\u8df3\u51fa\uff08\u5f53 i = j \u65f6\u4e3a\u7a7a\uff09\nwhile (i &lt; j) {\nint m = i + (j - i) / 2; // \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nif (nums[m] &lt; target) // \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [m+1, j) \u4e2d\ni = m + 1;\nelse if (nums[m] &gt; target) // \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [i, m) \u4e2d\nj = m;\nelse // \u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de\u5176\u7d22\u5f15\nreturn m;\n}\n// \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\nreturn -1;\n}\n</code></pre> binary_search.cpp<pre><code>/* \u4e8c\u5206\u67e5\u627e\uff08\u5de6\u95ed\u53f3\u5f00\uff09 */\nint binarySearchLCRO(vector&lt;int&gt; &amp;nums, int target) {\n// \u521d\u59cb\u5316\u5de6\u95ed\u53f3\u5f00 [0, n) \uff0c\u5373 i, j \u5206\u522b\u6307\u5411\u6570\u7ec4\u9996\u5143\u7d20\u3001\u5c3e\u5143\u7d20+1\nint i = 0, j = nums.size();\n// \u5faa\u73af\uff0c\u5f53\u641c\u7d22\u533a\u95f4\u4e3a\u7a7a\u65f6\u8df3\u51fa\uff08\u5f53 i = j \u65f6\u4e3a\u7a7a\uff09\nwhile (i &lt; j) {\nint m = i + (j - i) / 2; // \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nif (nums[m] &lt; target)    // \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [m+1, j) \u4e2d\ni = m + 1;\nelse if (nums[m] &gt; target) // \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [i, m) \u4e2d\nj = m;\nelse // \u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de\u5176\u7d22\u5f15\nreturn m;\n}\n// \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\nreturn -1;\n}\n</code></pre> binary_search.py<pre><code>def binary_search_lcro(nums: list[int], target: int) -&gt; int:\n\"\"\"\u4e8c\u5206\u67e5\u627e\uff08\u5de6\u95ed\u53f3\u5f00\uff09\"\"\"\n# \u521d\u59cb\u5316\u5de6\u95ed\u53f3\u5f00 [0, n) \uff0c\u5373 i, j \u5206\u522b\u6307\u5411\u6570\u7ec4\u9996\u5143\u7d20\u3001\u5c3e\u5143\u7d20+1\ni, j = 0, len(nums)\n# \u5faa\u73af\uff0c\u5f53\u641c\u7d22\u533a\u95f4\u4e3a\u7a7a\u65f6\u8df3\u51fa\uff08\u5f53 i = j \u65f6\u4e3a\u7a7a\uff09\nwhile i &lt; j:\nm = (i + j) // 2  # \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nif nums[m] &lt; target:\ni = m + 1  # \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [m+1, j) \u4e2d\nelif nums[m] &gt; target:\nj = m  # \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [i, m) \u4e2d\nelse:\nreturn m  # \u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de\u5176\u7d22\u5f15\nreturn -1  # \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\n</code></pre> binary_search.go<pre><code>/* \u4e8c\u5206\u67e5\u627e\uff08\u5de6\u95ed\u53f3\u5f00\uff09 */\nfunc binarySearchLCRO(nums []int, target int) int {\n// \u521d\u59cb\u5316\u5de6\u95ed\u53f3\u5f00 [0, n) \uff0c\u5373 i, j \u5206\u522b\u6307\u5411\u6570\u7ec4\u9996\u5143\u7d20\u3001\u5c3e\u5143\u7d20+1\ni, j := 0, len(nums)\n// \u5faa\u73af\uff0c\u5f53\u641c\u7d22\u533a\u95f4\u4e3a\u7a7a\u65f6\u8df3\u51fa\uff08\u5f53 i = j \u65f6\u4e3a\u7a7a\uff09\nfor i &lt; j {\nm := i + (j-i)/2      // \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nif nums[m] &lt; target { // \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [m+1, j) \u4e2d\ni = m + 1\n} else if nums[m] &gt; target { // \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [i, m) \u4e2d\nj = m\n} else { // \u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de\u5176\u7d22\u5f15\nreturn m\n}\n}\n// \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\nreturn -1\n}\n</code></pre> binary_search.js<pre><code>/* \u4e8c\u5206\u67e5\u627e\uff08\u5de6\u95ed\u53f3\u5f00\uff09 */\nfunction binarySearchLCRO(nums, target) {\n// \u521d\u59cb\u5316\u5de6\u95ed\u53f3\u5f00 [0, n) \uff0c\u5373 i, j \u5206\u522b\u6307\u5411\u6570\u7ec4\u9996\u5143\u7d20\u3001\u5c3e\u5143\u7d20+1\nlet i = 0,\nj = nums.length;\n// \u5faa\u73af\uff0c\u5f53\u641c\u7d22\u533a\u95f4\u4e3a\u7a7a\u65f6\u8df3\u51fa\uff08\u5f53 i = j \u65f6\u4e3a\u7a7a\uff09\nwhile (i &lt; j) {\n// \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m \uff0c\u4f7f\u7528 parseInt() \u5411\u4e0b\u53d6\u6574\nconst m = parseInt(i + (j - i) / 2);\nif (nums[m] &lt; target)\n// \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [m+1, j) \u4e2d\ni = m + 1;\nelse if (nums[m] &gt; target)\n// \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [i, m) \u4e2d\nj = m;\n// \u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de\u5176\u7d22\u5f15\nelse return m;\n}\n// \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\nreturn -1;\n}\n</code></pre> binary_search.ts<pre><code>/* \u4e8c\u5206\u67e5\u627e\uff08\u5de6\u95ed\u53f3\u5f00\uff09 */\nfunction binarySearchLCRO(nums: number[], target: number): number {\n// \u521d\u59cb\u5316\u5de6\u95ed\u53f3\u5f00 [0, n) \uff0c\u5373 i, j \u5206\u522b\u6307\u5411\u6570\u7ec4\u9996\u5143\u7d20\u3001\u5c3e\u5143\u7d20+1\nlet i = 0,\nj = nums.length;\n// \u5faa\u73af\uff0c\u5f53\u641c\u7d22\u533a\u95f4\u4e3a\u7a7a\u65f6\u8df3\u51fa\uff08\u5f53 i = j \u65f6\u4e3a\u7a7a\uff09\nwhile (i &lt; j) {\n// \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nconst m = Math.floor(i + (j - i) / 2);\nif (nums[m] &lt; target) {\n// \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [m+1, j) \u4e2d\ni = m + 1;\n} else if (nums[m] &gt; target) {\n// \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [i, m) \u4e2d\nj = m;\n} else {\n// \u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de\u5176\u7d22\u5f15\nreturn m;\n}\n}\nreturn -1; // \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\n}\n</code></pre> binary_search.c<pre><code>/* \u4e8c\u5206\u67e5\u627e\uff08\u5de6\u95ed\u53f3\u5f00\uff09 */\nint binarySearchLCRO(int *nums, int len, int target) {\n// \u521d\u59cb\u5316\u5de6\u95ed\u53f3\u5f00 [0, n) \uff0c\u5373 i, j \u5206\u522b\u6307\u5411\u6570\u7ec4\u9996\u5143\u7d20\u3001\u5c3e\u5143\u7d20+1\nint i = 0, j = len;\n// \u5faa\u73af\uff0c\u5f53\u641c\u7d22\u533a\u95f4\u4e3a\u7a7a\u65f6\u8df3\u51fa\uff08\u5f53 i = j \u65f6\u4e3a\u7a7a\uff09\nwhile (i &lt; j) {\nint m = i + (j - i) / 2; // \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nif (nums[m] &lt; target)    // \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [m+1, j) \u4e2d\ni = m + 1;\nelse if (nums[m] &gt; target) // \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [i, m) \u4e2d\nj = m;\nelse // \u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de\u5176\u7d22\u5f15\nreturn m;\n}\n// \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\nreturn -1;\n}\n</code></pre> binary_search.cs<pre><code>/* \u4e8c\u5206\u67e5\u627e\uff08\u5de6\u95ed\u53f3\u5f00\uff09 */\nint binarySearchLCRO(int[] nums, int target) {\n// \u521d\u59cb\u5316\u5de6\u95ed\u53f3\u5f00 [0, n) \uff0c\u5373 i, j \u5206\u522b\u6307\u5411\u6570\u7ec4\u9996\u5143\u7d20\u3001\u5c3e\u5143\u7d20+1\nint i = 0, j = nums.Length;\n// \u5faa\u73af\uff0c\u5f53\u641c\u7d22\u533a\u95f4\u4e3a\u7a7a\u65f6\u8df3\u51fa\uff08\u5f53 i = j \u65f6\u4e3a\u7a7a\uff09\nwhile (i &lt; j) {\nint m = i + (j - i) / 2;   // \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nif (nums[m] &lt; target)      // \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [m+1, j) \u4e2d\ni = m + 1;\nelse if (nums[m] &gt; target) // \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [i, m) \u4e2d\nj = m;\nelse                       // \u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de\u5176\u7d22\u5f15\nreturn m;\n}\n// \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\nreturn -1;\n}\n</code></pre> binary_search.swift<pre><code>/* \u4e8c\u5206\u67e5\u627e\uff08\u5de6\u95ed\u53f3\u5f00\uff09 */\nfunc binarySearchLCRO(nums: [Int], target: Int) -&gt; Int {\n// \u521d\u59cb\u5316\u5de6\u95ed\u53f3\u5f00 [0, n) \uff0c\u5373 i, j \u5206\u522b\u6307\u5411\u6570\u7ec4\u9996\u5143\u7d20\u3001\u5c3e\u5143\u7d20+1\nvar i = 0\nvar j = nums.count\n// \u5faa\u73af\uff0c\u5f53\u641c\u7d22\u533a\u95f4\u4e3a\u7a7a\u65f6\u8df3\u51fa\uff08\u5f53 i = j \u65f6\u4e3a\u7a7a\uff09\nwhile i &lt; j {\nlet m = i + (j - i) / 2 // \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nif nums[m] &lt; target { // \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [m+1, j) \u4e2d\ni = m + 1\n} else if nums[m] &gt; target { // \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [i, m) \u4e2d\nj = m\n} else { // \u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de\u5176\u7d22\u5f15\nreturn m\n}\n}\n// \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\nreturn -1\n}\n</code></pre> binary_search.zig<pre><code>// \u4e8c\u5206\u67e5\u627e\uff08\u5de6\u95ed\u53f3\u5f00\uff09\nfn binarySearchLCRO(comptime T: type, nums: std.ArrayList(T), target: T) T {\n// \u521d\u59cb\u5316\u5de6\u95ed\u53f3\u5f00 [0, n) \uff0c\u5373 i, j \u5206\u522b\u6307\u5411\u6570\u7ec4\u9996\u5143\u7d20\u3001\u5c3e\u5143\u7d20+1\nvar i: usize = 0;\nvar j: usize = nums.items.len;\n// \u5faa\u73af\uff0c\u5f53\u641c\u7d22\u533a\u95f4\u4e3a\u7a7a\u65f6\u8df3\u51fa\uff08\u5f53 i = j \u65f6\u4e3a\u7a7a\uff09\nwhile (i &lt;= j) {\nvar m = i + (j - i) / 2;                // \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nif (nums.items[m] &lt; target) {           // \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [m+1, j) \u4e2d\ni = m + 1;\n} else if (nums.items[m] &gt; target) {    // \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [i, m) \u4e2d\nj = m;\n} else {                                // \u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de\u5176\u7d22\u5f15\nreturn @intCast(T, m);\n}\n}\n// \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\nreturn -1;\n}\n</code></pre> binary_search.dart<pre><code>/* \u4e8c\u5206\u67e5\u627e\uff08\u5de6\u95ed\u53f3\u5f00\u533a\u95f4\uff09 */\nint binarySearchLCRO(List&lt;int&gt; nums, int target) {\n// \u521d\u59cb\u5316\u5de6\u95ed\u53f3\u5f00 [0, n) \uff0c\u5373 i, j \u5206\u522b\u6307\u5411\u6570\u7ec4\u9996\u5143\u7d20\u3001\u5c3e\u5143\u7d20+1\nint i = 0, j = nums.length;\n// \u5faa\u73af\uff0c\u5f53\u641c\u7d22\u533a\u95f4\u4e3a\u7a7a\u65f6\u8df3\u51fa\uff08\u5f53 i = j \u65f6\u4e3a\u7a7a\uff09\nwhile (i &lt; j) {\nint m = i + (j - i) ~/ 2; // \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nif (nums[m] &lt; target) {\n// \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [m+1, j) \u4e2d\ni = m + 1;\n} else if (nums[m] &gt; target) {\n// \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [i, m) \u4e2d\nj = m;\n} else {\n// \u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de\u5176\u7d22\u5f15\nreturn m;\n}\n}\n// \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\nreturn -1;\n}\n</code></pre> <p>\u5982\u4e0b\u56fe\u6240\u793a\uff0c\u5728\u4e24\u79cd\u533a\u95f4\u8868\u793a\u4e0b\uff0c\u4e8c\u5206\u67e5\u627e\u7b97\u6cd5\u7684\u521d\u59cb\u5316\u3001\u5faa\u73af\u6761\u4ef6\u548c\u7f29\u5c0f\u533a\u95f4\u64cd\u4f5c\u7686\u6709\u6240\u4e0d\u540c\u3002</p> <p>\u5728\u201c\u53cc\u95ed\u533a\u95f4\u201d\u8868\u793a\u6cd5\u4e2d\uff0c\u7531\u4e8e\u5de6\u53f3\u8fb9\u754c\u90fd\u88ab\u5b9a\u4e49\u4e3a\u95ed\u533a\u95f4\uff0c\u56e0\u6b64\u6307\u9488 \\(i\\) \u548c \\(j\\) \u7f29\u5c0f\u533a\u95f4\u64cd\u4f5c\u4e5f\u662f\u5bf9\u79f0\u7684\u3002\u8fd9\u6837\u66f4\u4e0d\u5bb9\u6613\u51fa\u9519\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u901a\u5e38\u91c7\u7528\u201c\u53cc\u95ed\u533a\u95f4\u201d\u7684\u5199\u6cd5\u3002</p> <p></p> <p> Fig. \u4e24\u79cd\u533a\u95f4\u5b9a\u4e49 </p>"},{"location":"chapter_searching/binary_search/#1012","title":"10.1.2. \u00a0 \u4f18\u70b9\u4e0e\u5c40\u9650\u6027","text":"<p>\u4e8c\u5206\u67e5\u627e\u5728\u65f6\u95f4\u548c\u7a7a\u95f4\u65b9\u9762\u90fd\u6709\u8f83\u597d\u7684\u6027\u80fd\uff1a</p> <ul> <li>\u4e8c\u5206\u67e5\u627e\u7684\u65f6\u95f4\u6548\u7387\u9ad8\u3002\u5728\u5927\u6570\u636e\u91cf\u4e0b\uff0c\u5bf9\u6570\u9636\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u5177\u6709\u663e\u8457\u4f18\u52bf\u3002\u4f8b\u5982\uff0c\u5f53\u6570\u636e\u5927\u5c0f \\(n = 2^{20}\\) \u65f6\uff0c\u7ebf\u6027\u67e5\u627e\u9700\u8981 \\(2^{20} = 1048576\\) \u8f6e\u5faa\u73af\uff0c\u800c\u4e8c\u5206\u67e5\u627e\u4ec5\u9700 \\(\\log_2 2^{20} = 20\\) \u8f6e\u5faa\u73af\u3002</li> <li>\u4e8c\u5206\u67e5\u627e\u65e0\u9700\u989d\u5916\u7a7a\u95f4\u3002\u76f8\u8f83\u4e8e\u9700\u8981\u501f\u52a9\u989d\u5916\u7a7a\u95f4\u7684\u641c\u7d22\u7b97\u6cd5\uff08\u4f8b\u5982\u54c8\u5e0c\u67e5\u627e\uff09\uff0c\u4e8c\u5206\u67e5\u627e\u66f4\u52a0\u8282\u7701\u7a7a\u95f4\u3002</li> </ul> <p>\u7136\u800c\uff0c\u4e8c\u5206\u67e5\u627e\u5e76\u975e\u9002\u7528\u4e8e\u6240\u6709\u60c5\u51b5\uff0c\u539f\u56e0\u5982\u4e0b\uff1a</p> <ul> <li>\u4e8c\u5206\u67e5\u627e\u4ec5\u9002\u7528\u4e8e\u6709\u5e8f\u6570\u636e\u3002\u82e5\u8f93\u5165\u6570\u636e\u65e0\u5e8f\uff0c\u4e3a\u4e86\u4f7f\u7528\u4e8c\u5206\u67e5\u627e\u800c\u4e13\u95e8\u8fdb\u884c\u6392\u5e8f\uff0c\u5f97\u4e0d\u507f\u5931\u3002\u56e0\u4e3a\u6392\u5e8f\u7b97\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u901a\u5e38\u4e3a \\(O(n \\log n)\\) \uff0c\u6bd4\u7ebf\u6027\u67e5\u627e\u548c\u4e8c\u5206\u67e5\u627e\u90fd\u66f4\u9ad8\u3002\u5bf9\u4e8e\u9891\u7e41\u63d2\u5165\u5143\u7d20\u7684\u573a\u666f\uff0c\u4e3a\u4fdd\u6301\u6570\u7ec4\u6709\u5e8f\u6027\uff0c\u9700\u8981\u5c06\u5143\u7d20\u63d2\u5165\u5230\u7279\u5b9a\u4f4d\u7f6e\uff0c\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(n)\\) \uff0c\u4e5f\u662f\u975e\u5e38\u6602\u8d35\u7684\u3002</li> <li>\u4e8c\u5206\u67e5\u627e\u4ec5\u9002\u7528\u4e8e\u6570\u7ec4\u3002\u4e8c\u5206\u67e5\u627e\u9700\u8981\u8df3\u8dc3\u5f0f\uff08\u975e\u8fde\u7eed\u5730\uff09\u8bbf\u95ee\u5143\u7d20\uff0c\u800c\u5728\u94fe\u8868\u4e2d\u6267\u884c\u8df3\u8dc3\u5f0f\u8bbf\u95ee\u7684\u6548\u7387\u8f83\u4f4e\uff0c\u56e0\u6b64\u4e0d\u9002\u5408\u5e94\u7528\u5728\u94fe\u8868\u6216\u57fa\u4e8e\u94fe\u8868\u5b9e\u73b0\u7684\u6570\u636e\u7ed3\u6784\u3002</li> <li>\u5c0f\u6570\u636e\u91cf\u4e0b\uff0c\u7ebf\u6027\u67e5\u627e\u6027\u80fd\u66f4\u4f73\u3002\u5728\u7ebf\u6027\u67e5\u627e\u4e2d\uff0c\u6bcf\u8f6e\u53ea\u9700\u8981 1 \u6b21\u5224\u65ad\u64cd\u4f5c\uff1b\u800c\u5728\u4e8c\u5206\u67e5\u627e\u4e2d\uff0c\u9700\u8981 1 \u6b21\u52a0\u6cd5\u30011 \u6b21\u9664\u6cd5\u30011 ~ 3 \u6b21\u5224\u65ad\u64cd\u4f5c\u30011 \u6b21\u52a0\u6cd5\uff08\u51cf\u6cd5\uff09\uff0c\u5171 4 ~ 6 \u4e2a\u5355\u5143\u64cd\u4f5c\uff1b\u56e0\u6b64\uff0c\u5f53\u6570\u636e\u91cf \\(n\\) \u8f83\u5c0f\u65f6\uff0c\u7ebf\u6027\u67e5\u627e\u53cd\u800c\u6bd4\u4e8c\u5206\u67e5\u627e\u66f4\u5feb\u3002</li> </ul>"},{"location":"chapter_searching/binary_search_edge/","title":"10.2. \u00a0 \u4e8c\u5206\u67e5\u627e\u8fb9\u754c","text":"<p>\u5728\u4e0a\u4e00\u8282\u4e2d\uff0c\u9898\u76ee\u89c4\u5b9a\u6570\u7ec4\u4e2d\u6240\u6709\u5143\u7d20\u90fd\u662f\u552f\u4e00\u7684\u3002\u5982\u679c\u76ee\u6807\u5143\u7d20\u5728\u6570\u7ec4\u4e2d\u591a\u6b21\u51fa\u73b0\uff0c\u4e0a\u8282\u4ecb\u7ecd\u7684\u65b9\u6cd5\u53ea\u80fd\u4fdd\u8bc1\u8fd4\u56de\u5176\u4e2d\u4e00\u4e2a\u76ee\u6807\u5143\u7d20\u7684\u7d22\u5f15\uff0c\u800c\u65e0\u6cd5\u786e\u5b9a\u8be5\u7d22\u5f15\u7684\u5de6\u8fb9\u548c\u53f3\u8fb9\u8fd8\u6709\u591a\u5c11\u76ee\u6807\u5143\u7d20\u3002</p> <p>Question</p> <p>\u7ed9\u5b9a\u4e00\u4e2a\u957f\u5ea6\u4e3a \\(n\\) \u7684\u6709\u5e8f\u6570\u7ec4 <code>nums</code> \uff0c\u6570\u7ec4\u53ef\u80fd\u5305\u542b\u91cd\u590d\u5143\u7d20\u3002\u8bf7\u67e5\u627e\u5e76\u8fd4\u56de\u5143\u7d20 <code>target</code> \u5728\u6570\u7ec4\u4e2d\u9996\u6b21\u51fa\u73b0\u7684\u7d22\u5f15\u3002\u82e5\u6570\u7ec4\u4e2d\u4e0d\u5305\u542b\u8be5\u5143\u7d20\uff0c\u5219\u8fd4\u56de \\(-1\\) \u3002</p>"},{"location":"chapter_searching/binary_search_edge/#1021","title":"10.2.1. \u00a0 \u7b80\u5355\u65b9\u6cd5","text":"<p>\u4e3a\u4e86\u67e5\u627e\u6570\u7ec4\u4e2d\u6700\u5de6\u8fb9\u7684 <code>target</code> \uff0c\u6211\u4eec\u53ef\u4ee5\u5206\u4e3a\u4e24\u6b65\uff1a</p> <ol> <li>\u8fdb\u884c\u4e8c\u5206\u67e5\u627e\uff0c\u5b9a\u4f4d\u5230\u4efb\u610f\u4e00\u4e2a <code>target</code> \u7684\u7d22\u5f15\uff0c\u8bb0\u4e3a \\(k\\) \uff1b</li> <li>\u4ee5\u7d22\u5f15 \\(k\\) \u4e3a\u8d77\u59cb\u70b9\uff0c\u5411\u5de6\u8fdb\u884c\u7ebf\u6027\u904d\u5386\uff0c\u627e\u5230\u6700\u5de6\u8fb9\u7684 <code>target</code> \u8fd4\u56de\u5373\u53ef\u3002</li> </ol> <p></p> <p> Fig. \u7ebf\u6027\u67e5\u627e\u6700\u5de6\u8fb9\u7684\u5143\u7d20 </p> <p>\u8fd9\u4e2a\u65b9\u6cd5\u867d\u7136\u6709\u6548\uff0c\u4f46\u7531\u4e8e\u5305\u542b\u7ebf\u6027\u67e5\u627e\uff0c\u5176\u65f6\u95f4\u590d\u6742\u5ea6\u53ef\u80fd\u4f1a\u52a3\u5316\u81f3 \\(O(n)\\) \u3002</p>"},{"location":"chapter_searching/binary_search_edge/#1022","title":"10.2.2. \u00a0 \u4e8c\u5206\u65b9\u6cd5","text":"<p>\u5b9e\u9645\u4e0a\uff0c\u6211\u4eec\u53ef\u4ee5\u4ec5\u901a\u8fc7\u4e8c\u5206\u67e5\u627e\u89e3\u51b3\u4ee5\u4e0a\u95ee\u9898\u3002\u6574\u4f53\u7b97\u6cd5\u6d41\u7a0b\u4e0d\u53d8\uff0c\u5148\u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 \\(m\\) \uff0c\u518d\u5224\u65ad <code>target</code> \u548c <code>nums[m]</code> \u5927\u5c0f\u5173\u7cfb\uff1a</p> <ul> <li>\u5f53 <code>nums[m] &lt; target</code> \u6216 <code>nums[m] &gt; target</code> \u65f6\uff0c\u8bf4\u660e\u8fd8\u6ca1\u6709\u627e\u5230 <code>target</code> \uff0c\u56e0\u6b64\u91c7\u53d6\u4e0e\u4e0a\u8282\u4ee3\u7801\u76f8\u540c\u7684\u7f29\u5c0f\u533a\u95f4\u64cd\u4f5c\uff0c\u4ece\u800c\u4f7f\u6307\u9488 \\(i\\) \u548c \\(j\\) \u5411 <code>target</code> \u9760\u8fd1\u3002</li> <li>\u5f53 <code>nums[m] == target</code> \u65f6\uff0c\u8bf4\u660e\u201c\u5c0f\u4e8e <code>target</code> \u7684\u5143\u7d20\u201d\u5728\u533a\u95f4 \\([i, m - 1]\\) \u4e2d\uff0c\u56e0\u6b64\u91c7\u7528 \\(j = m - 1\\) \u6765\u7f29\u5c0f\u533a\u95f4\uff0c\u4ece\u800c\u4f7f\u6307\u9488 \\(j\\) \u5411\u5c0f\u4e8e <code>target</code> \u7684\u5143\u7d20\u9760\u8fd1\u3002</li> </ul> <p>\u4e8c\u5206\u67e5\u627e\u5b8c\u6210\u540e\uff0c\\(i\\) \u6307\u5411\u6700\u5de6\u8fb9\u7684 <code>target</code> \uff0c\\(j\\) \u6307\u5411\u9996\u4e2a\u5c0f\u4e8e <code>target</code> \u7684\u5143\u7d20\uff0c\u56e0\u6b64\u8fd4\u56de\u7d22\u5f15 \\(i\\) \u5373\u53ef\u3002</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p>\u6ce8\u610f\uff0c\u6570\u7ec4\u53ef\u80fd\u4e0d\u5305\u542b\u76ee\u6807\u5143\u7d20 <code>target</code> \u3002\u56e0\u6b64\u5728\u51fd\u6570\u8fd4\u56de\u524d\uff0c\u6211\u4eec\u9700\u8981\u5148\u5224\u65ad <code>nums[i]</code> \u4e0e <code>target</code> \u662f\u5426\u76f8\u7b49\uff0c\u4ee5\u53ca\u7d22\u5f15 \\(i\\) \u662f\u5426\u8d8a\u754c\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart binary_search_edge.java<pre><code>/* \u4e8c\u5206\u67e5\u627e\u6700\u5de6\u4e00\u4e2a\u5143\u7d20 */\nint binarySearchLeftEdge(int[] nums, int target) {\nint i = 0, j = nums.length - 1; // \u521d\u59cb\u5316\u53cc\u95ed\u533a\u95f4 [0, n-1]\nwhile (i &lt;= j) {\nint m = i + (j - i) / 2; // \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nif (nums[m] &lt; target)\ni = m + 1; // target \u5728\u533a\u95f4 [m+1, j] \u4e2d\nelse if (nums[m] &gt; target)\nj = m - 1; // target \u5728\u533a\u95f4 [i, m-1] \u4e2d\nelse\nj = m - 1; // \u9996\u4e2a\u5c0f\u4e8e target \u7684\u5143\u7d20\u5728\u533a\u95f4 [i, m-1] \u4e2d\n}\nif (i == nums.length || nums[i] != target)\nreturn -1; // \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\nreturn i;\n}\n</code></pre> binary_search_edge.cpp<pre><code>/* \u4e8c\u5206\u67e5\u627e\u6700\u5de6\u4e00\u4e2a\u5143\u7d20 */\nint binarySearchLeftEdge(vector&lt;int&gt; &amp;nums, int target) {\nint i = 0, j = nums.size() - 1; // \u521d\u59cb\u5316\u53cc\u95ed\u533a\u95f4 [0, n-1]\nwhile (i &lt;= j) {\nint m = i + (j - i) / 2; // \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nif (nums[m] &lt; target)\ni = m + 1; // target \u5728\u533a\u95f4 [m+1, j] \u4e2d\nelse if (nums[m] &gt; target)\nj = m - 1; // target \u5728\u533a\u95f4 [i, m-1] \u4e2d\nelse\nj = m - 1; // \u9996\u4e2a\u5c0f\u4e8e target \u7684\u5143\u7d20\u5728\u533a\u95f4 [i, m-1] \u4e2d\n}\nif (i == nums.size() || nums[i] != target)\nreturn -1; // \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\nreturn i;\n}\n</code></pre> binary_search_edge.py<pre><code>def binary_search_left_edge(nums: list[int], target: int) -&gt; int:\n\"\"\"\u4e8c\u5206\u67e5\u627e\u6700\u5de6\u4e00\u4e2a\u5143\u7d20\"\"\"\ni, j = 0, len(nums) - 1  # \u521d\u59cb\u5316\u53cc\u95ed\u533a\u95f4 [0, n-1]\nwhile i &lt;= j:\nm = (i + j) // 2  # \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nif nums[m] &lt; target:\ni = m + 1  # target \u5728\u533a\u95f4 [m+1, j] \u4e2d\nelif nums[m] &gt; target:\nj = m - 1  # target \u5728\u533a\u95f4 [i, m-1] \u4e2d\nelse:\nj = m - 1  # \u9996\u4e2a\u5c0f\u4e8e target \u7684\u5143\u7d20\u5728\u533a\u95f4 [i, m-1] \u4e2d\nif i == len(nums) or nums[i] != target:\nreturn -1  # \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\nreturn i\n</code></pre> binary_search_edge.go<pre><code>/* \u4e8c\u5206\u67e5\u627e\u6700\u5de6\u4e00\u4e2a\u5143\u7d20 */\nfunc binarySearchLeftEdge(nums []int, target int) int {\n// \u521d\u59cb\u5316\u53cc\u95ed\u533a\u95f4 [0, n-1]\ni, j := 0, len(nums)-1\nfor i &lt;= j {\n// \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nm := i + (j-i)/2\nif nums[m] &lt; target {\n// target \u5728\u533a\u95f4 [m+1, j] \u4e2d\ni = m + 1\n} else if nums[m] &gt; target {\n// target \u5728\u533a\u95f4 [i, m-1] \u4e2d\nj = m - 1\n} else {\n// \u9996\u4e2a\u5c0f\u4e8e target \u7684\u5143\u7d20\u5728\u533a\u95f4 [i, m-1] \u4e2d\nj = m - 1\n}\n}\nif i == len(nums) || nums[i] != target {\n// \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\nreturn -1\n}\nreturn i\n}\n</code></pre> binary_search_edge.js<pre><code>/* \u4e8c\u5206\u67e5\u627e\u6700\u5de6\u4e00\u4e2a\u5143\u7d20 */\nfunction binarySearchLeftEdge(nums, target) {\nlet i = 0,\nj = nums.length - 1; // \u521d\u59cb\u5316\u53cc\u95ed\u533a\u95f4 [0, n-1]\nwhile (i &lt;= j) {\nlet m = Math.floor((i + j) / 2); // \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nif (nums[m] &lt; target) {\ni = m + 1; // target \u5728\u533a\u95f4 [m+1, j] \u4e2d\n} else if (nums[m] &gt; target) {\nj = m - 1; // target \u5728\u533a\u95f4 [i, m-1] \u4e2d\n} else {\nj = m - 1; // \u9996\u4e2a\u5c0f\u4e8e target \u7684\u5143\u7d20\u5728\u533a\u95f4 [i, m-1] \u4e2d\n}\n}\nif (i == nums.length || nums[i] != target) {\nreturn -1; // \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\n}\nreturn i;\n}\n</code></pre> binary_search_edge.ts<pre><code>/* \u4e8c\u5206\u67e5\u627e\u6700\u5de6\u4e00\u4e2a\u5143\u7d20 */\nfunction binarySearchLeftEdge(nums: number[], target: number): number {\nlet i = 0, j = nums.length - 1;  // \u521d\u59cb\u5316\u53cc\u95ed\u533a\u95f4 [0, n-1]\nwhile (i &lt;= j) {\nlet m = Math.floor((i + j) / 2);  // \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nif (nums[m] &lt; target) {\ni = m + 1;  // target \u5728\u533a\u95f4 [m+1, j] \u4e2d\n} else if (nums[m] &gt; target) {\nj = m - 1;  // target \u5728\u533a\u95f4 [i, m-1] \u4e2d\n} else {\nj = m - 1;  // \u9996\u4e2a\u5c0f\u4e8e target \u7684\u5143\u7d20\u5728\u533a\u95f4 [i, m-1] \u4e2d\n}\n}\nif (i == nums.length || nums[i] != target) {\nreturn -1;  // \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\n}\nreturn i;\n}\n</code></pre> binary_search_edge.c<pre><code>/* \u4e8c\u5206\u67e5\u627e\u6700\u5de6\u4e00\u4e2a\u5143\u7d20 */\nint binarySearchLeftEdge(int *nums, int size, int target) {\nint i = 0, j = size - 1; // \u521d\u59cb\u5316\u53cc\u95ed\u533a\u95f4 [0, n-1]\nwhile (i &lt;= j) {\nint m = i + (j - i) / 2; // \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nif (nums[m] &lt; target)\ni = m + 1; // target \u5728\u533a\u95f4 [m+1, j] \u4e2d\nelse if (nums[m] &gt; target)\nj = m - 1; // target \u5728\u533a\u95f4 [i, m-1] \u4e2d\nelse\nj = m - 1; // \u9996\u4e2a\u5c0f\u4e8e target \u7684\u5143\u7d20\u5728\u533a\u95f4 [i, m-1] \u4e2d\n}\nif (i == size || nums[i] != target)\nreturn -1; // \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\nreturn i;\n}\n</code></pre> binary_search_edge.cs<pre><code>/* \u4e8c\u5206\u67e5\u627e\u6700\u5de6\u4e00\u4e2a\u5143\u7d20 */\nint binarySearchLeftEdge(int[] nums, int target) {\nint i = 0, j = nums.Length - 1; // \u521d\u59cb\u5316\u53cc\u95ed\u533a\u95f4 [0, n-1]\nwhile (i &lt;= j) {\nint m = i + (j - i) / 2; // \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nif (nums[m] &lt; target)\ni = m + 1; // target \u5728\u533a\u95f4 [m+1, j] \u4e2d\nelse if (nums[m] &gt; target)\nj = m - 1; // target \u5728\u533a\u95f4 [i, m-1] \u4e2d\nelse\nj = m - 1; // \u9996\u4e2a\u5c0f\u4e8e target \u7684\u5143\u7d20\u5728\u533a\u95f4 [i, m-1] \u4e2d\n}\nif (i == nums.Length || nums[i] != target)\nreturn -1; // \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\nreturn i;\n}\n</code></pre> binary_search_edge.swift<pre><code>/* \u4e8c\u5206\u67e5\u627e\u6700\u5de6\u4e00\u4e2a\u5143\u7d20 */\nfunc binarySearchLeftEdge(nums: [Int], target: Int) -&gt; Int {\n// \u521d\u59cb\u5316\u53cc\u95ed\u533a\u95f4 [0, n-1]\nvar i = 0\nvar j = nums.count - 1\nwhile i &lt;= j {\nlet m = i + (j - 1) / 2 // \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nif nums[m] &lt; target {\ni = m + 1 // target \u5728\u533a\u95f4 [m+1, j] \u4e2d\n} else if nums[m] &gt; target {\nj = m - 1 // target \u5728\u533a\u95f4 [i, m-1] \u4e2d\n} else {\nj = m - 1 // \u9996\u4e2a\u5c0f\u4e8e target \u7684\u5143\u7d20\u5728\u533a\u95f4 [i, m-1] \u4e2d\n}\n}\nif i == nums.count || nums[i] != target {\nreturn -1 // \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\n}\nreturn i\n}\n</code></pre> binary_search_edge.zig<pre><code>[class]{}-[func]{binarySearchLeftEdge}\n</code></pre> binary_search_edge.dart<pre><code>/* \u4e8c\u5206\u67e5\u627e\u6700\u5de6\u4e00\u4e2a\u5143\u7d20 */\nint binarySearchLeftEdge(List&lt;int&gt; nums, int target) {\nint i = 0, j = nums.length - 1; // \u521d\u59cb\u5316\u53cc\u95ed\u533a\u95f4 [0, n-1]\nwhile (i &lt;= j) {\nint m = i + (j - i) ~/ 2; // \u8ba1\u7b97\u4e2d\u95f4\u7d22\u5f15 m\nif (nums[m] &lt; target)\ni = m + 1; // target \u5728\u533a\u95f4 [m+1, j] \u4e2d\nelse if (nums[m] &gt; target)\nj = m - 1; // target \u5728\u533a\u95f4 [i, m-1] \u4e2d\nelse\nj = m - 1; // \u9996\u4e2a\u5c0f\u4e8e target \u7684\u5143\u7d20\u5728\u533a\u95f4 [i, m-1] \u4e2d\n}\nif (i == nums.length || nums[i] != target) return -1; // \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\nreturn i;\n}\n</code></pre>"},{"location":"chapter_searching/binary_search_edge/#1023","title":"10.2.3. \u00a0 \u67e5\u627e\u53f3\u8fb9\u754c","text":"<p>\u7c7b\u4f3c\u5730\uff0c\u6211\u4eec\u4e5f\u53ef\u4ee5\u4e8c\u5206\u67e5\u627e\u6700\u53f3\u8fb9\u7684 <code>target</code> \u3002\u5f53 <code>nums[m] == target</code> \u65f6\uff0c\u8bf4\u660e\u5927\u4e8e <code>target</code> \u7684\u5143\u7d20\u5728\u533a\u95f4 \\([m + 1, j]\\) \u4e2d\uff0c\u56e0\u6b64\u6267\u884c <code>i = m + 1</code> \uff0c\u4f7f\u5f97\u6307\u9488 \\(i\\) \u5411\u5927\u4e8e <code>target</code> \u7684\u5143\u7d20\u9760\u8fd1\u3002</p> <p>\u5b8c\u6210\u4e8c\u5206\u540e\uff0c\\(i\\) \u6307\u5411\u9996\u4e2a\u5927\u4e8e <code>target</code> \u7684\u5143\u7d20\uff0c\\(j\\) \u6307\u5411\u6700\u53f3\u8fb9\u7684 <code>target</code> \uff0c\u56e0\u6b64\u8fd4\u56de\u7d22\u5f15 \\(j\\) \u5373\u53ef\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart binary_search_edge.java<pre><code>/* \u4e8c\u5206\u67e5\u627e\u6700\u53f3\u4e00\u4e2a\u5143\u7d20 */\nint binarySearchRightEdge(int[] nums, int target) {\nint i = 0, j = nums.length - 1; // \u521d\u59cb\u5316\u53cc\u95ed\u533a\u95f4 [0, n-1]\nwhile (i &lt;= j) {\nint m = i + (j - i) / 2; // \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nif (nums[m] &lt; target)\ni = m + 1; // target \u5728\u533a\u95f4 [m+1, j] \u4e2d\nelse if (nums[m] &gt; target)\nj = m - 1; // target \u5728\u533a\u95f4 [i, m-1] \u4e2d\nelse\ni = m + 1; // \u9996\u4e2a\u5927\u4e8e target \u7684\u5143\u7d20\u5728\u533a\u95f4 [m+1, j] \u4e2d\n}\nif (j &lt; 0 || nums[j] != target)\nreturn -1; // \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\nreturn j;\n}\n</code></pre> binary_search_edge.cpp<pre><code>/* \u4e8c\u5206\u67e5\u627e\u6700\u53f3\u4e00\u4e2a\u5143\u7d20 */\nint binarySearchRightEdge(vector&lt;int&gt; &amp;nums, int target) {\nint i = 0, j = nums.size() - 1; // \u521d\u59cb\u5316\u53cc\u95ed\u533a\u95f4 [0, n-1]\nwhile (i &lt;= j) {\nint m = i + (j - i) / 2; // \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nif (nums[m] &lt; target)\ni = m + 1; // target \u5728\u533a\u95f4 [m+1, j] \u4e2d\nelse if (nums[m] &gt; target)\nj = m - 1; // target \u5728\u533a\u95f4 [i, m-1] \u4e2d\nelse\ni = m + 1; // \u9996\u4e2a\u5927\u4e8e target \u7684\u5143\u7d20\u5728\u533a\u95f4 [m+1, j] \u4e2d\n}\nif (j &lt; 0 || nums[j] != target)\nreturn -1; // \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\nreturn j;\n}\n</code></pre> binary_search_edge.py<pre><code>def binary_search_right_edge(nums: list[int], target: int) -&gt; int:\n\"\"\"\u4e8c\u5206\u67e5\u627e\u6700\u53f3\u4e00\u4e2a\u5143\u7d20\"\"\"\ni, j = 0, len(nums) - 1  # \u521d\u59cb\u5316\u53cc\u95ed\u533a\u95f4 [0, n-1]\nwhile i &lt;= j:\nm = (i + j) // 2  # \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nif nums[m] &lt; target:\ni = m + 1  # target \u5728\u533a\u95f4 [m+1, j] \u4e2d\nelif nums[m] &gt; target:\nj = m - 1  # target \u5728\u533a\u95f4 [i, m-1] \u4e2d\nelse:\ni = m + 1  # \u9996\u4e2a\u5927\u4e8e target \u7684\u5143\u7d20\u5728\u533a\u95f4 [m+1, j] \u4e2d\nif j == len(nums) or nums[j] != target:\nreturn -1  # \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\nreturn j\n</code></pre> binary_search_edge.go<pre><code>/* \u4e8c\u5206\u67e5\u627e\u6700\u53f3\u4e00\u4e2a\u5143\u7d20 */\nfunc binarySearchRightEdge(nums []int, target int) int {\n// \u521d\u59cb\u5316\u53cc\u95ed\u533a\u95f4 [0, n-1]\ni, j := 0, len(nums)-1\nfor i &lt;= j {\n// \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nm := i + (j-i)/2\nif nums[m] &lt; target {\n// target \u5728\u533a\u95f4 [m+1, j] \u4e2d\ni = m + 1\n} else if nums[m] &gt; target {\n// target \u5728\u533a\u95f4 [i, m-1] \u4e2d\nj = m - 1\n} else {\n// \u9996\u4e2a\u5927\u4e8e target \u7684\u5143\u7d20\u5728\u533a\u95f4 [m+1, j] \u4e2d\ni = m + 1\n}\n}\nif j &lt; 0 || nums[j] != target {\n// \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\nreturn -1\n}\nreturn j\n}\n</code></pre> binary_search_edge.js<pre><code>/* \u4e8c\u5206\u67e5\u627e\u6700\u53f3\u4e00\u4e2a\u5143\u7d20 */\nfunction binarySearchRightEdge(nums, target) {\nlet i = 0,\nj = nums.length - 1; // \u521d\u59cb\u5316\u53cc\u95ed\u533a\u95f4 [0, n-1]\nwhile (i &lt;= j) {\nlet m = Math.floor((i + j) / 2); // \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nif (nums[m] &lt; target) {\ni = m + 1; // target \u5728\u533a\u95f4 [m+1, j] \u4e2d\n} else if (nums[m] &gt; target) {\nj = m - 1; // target \u5728\u533a\u95f4 [i, m-1] \u4e2d\n} else {\ni = m + 1; // \u9996\u4e2a\u5927\u4e8e target \u7684\u5143\u7d20\u5728\u533a\u95f4 [m+1, j] \u4e2d\n}\n}\nif (j == nums.length || nums[j] != target) {\nreturn -1; // \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\n}\nreturn j;\n}\n</code></pre> binary_search_edge.ts<pre><code>/* \u4e8c\u5206\u67e5\u627e\u6700\u53f3\u4e00\u4e2a\u5143\u7d20 */\nfunction binarySearchRightEdge(nums: number[], target: number): number {\nlet i = 0, j = nums.length - 1;  // \u521d\u59cb\u5316\u53cc\u95ed\u533a\u95f4 [0, n-1]\nwhile (i &lt;= j) {\nlet m = Math.floor((i + j) / 2);  // \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nif (nums[m] &lt; target) {\ni = m + 1;  // target \u5728\u533a\u95f4 [m+1, j] \u4e2d\n} else if (nums[m] &gt; target) {\nj = m - 1;  // target \u5728\u533a\u95f4 [i, m-1] \u4e2d\n} else {\ni = m + 1;  // \u9996\u4e2a\u5927\u4e8e target \u7684\u5143\u7d20\u5728\u533a\u95f4 [m+1, j] \u4e2d\n}\n}\nif (j == nums.length || nums[j] != target) {\nreturn -1;  // \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\n}\nreturn j;\n}\n</code></pre> binary_search_edge.c<pre><code>/* \u4e8c\u5206\u67e5\u627e\u6700\u53f3\u4e00\u4e2a\u5143\u7d20 */\nint binarySearchRightEdge(int *nums, int size, int target) {\nint i = 0, j = size - 1; // \u521d\u59cb\u5316\u53cc\u95ed\u533a\u95f4 [0, n-1]\nwhile (i &lt;= j) {\nint m = i + (j - i) / 2; // \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nif (nums[m] &lt; target)\ni = m + 1; // target \u5728\u533a\u95f4 [m+1, j] \u4e2d\nelse if (nums[m] &gt; target)\nj = m - 1; // target \u5728\u533a\u95f4 [i, m-1] \u4e2d\nelse\ni = m + 1; // \u9996\u4e2a\u5927\u4e8e target \u7684\u5143\u7d20\u5728\u533a\u95f4 [m+1, j] \u4e2d\n}\nif (j &lt; 0 || nums[j] != target)\nreturn -1; // \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\nreturn j;\n}\n</code></pre> binary_search_edge.cs<pre><code>/* \u4e8c\u5206\u67e5\u627e\u6700\u53f3\u4e00\u4e2a\u5143\u7d20 */\nint binarySearchRightEdge(int[] nums, int target) {\nint i = 0, j = nums.Length - 1; // \u521d\u59cb\u5316\u53cc\u95ed\u533a\u95f4 [0, n-1]\nwhile (i &lt;= j) {\nint m = i + (j - i) / 2; // \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nif (nums[m] &lt; target)\ni = m + 1; // target \u5728\u533a\u95f4 [m+1, j] \u4e2d\nelse if (nums[m] &gt; target)\nj = m - 1; // target \u5728\u533a\u95f4 [i, m-1] \u4e2d\nelse\ni = m + 1; // \u9996\u4e2a\u5927\u4e8e target \u7684\u5143\u7d20\u5728\u533a\u95f4 [m+1, j] \u4e2d\n}\nif (j &lt; 0 || nums[j] != target)\nreturn -1; // \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\nreturn j;\n}\n</code></pre> binary_search_edge.swift<pre><code>/* \u4e8c\u5206\u67e5\u627e\u6700\u53f3\u4e00\u4e2a\u5143\u7d20 */\nfunc binarySearchRightEdge(nums: [Int], target: Int) -&gt; Int {\n// \u521d\u59cb\u5316\u53cc\u95ed\u533a\u95f4 [0, n-1]\nvar i = 0\nvar j = nums.count - 1\nwhile i &lt;= j {\nlet m = i + (j - i) / 2 // \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nif nums[m] &lt; target {\ni = m + 1 // target \u5728\u533a\u95f4 [m+1, j] \u4e2d\n} else if nums[m] &gt; target {\nj = m - 1 // target \u5728\u533a\u95f4 [i, m-1] \u4e2d\n} else {\ni = m + 1 // \u9996\u4e2a\u5927\u4e8e target \u7684\u5143\u7d20\u5728\u533a\u95f4 [m+1, j] \u4e2d\n}\n}\nif j &lt; 0 || nums[j] != target {\nreturn -1 // \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\n}\nreturn j\n}\n</code></pre> binary_search_edge.zig<pre><code>[class]{}-[func]{binarySearchRightEdge}\n</code></pre> binary_search_edge.dart<pre><code>/* \u4e8c\u5206\u67e5\u627e\u6700\u53f3\u4e00\u4e2a\u5143\u7d20 */\nint binarySearchRightEdge(List&lt;int&gt; nums, int target) {\nint i = 0, j = nums.length - 1; // \u521d\u59cb\u5316\u53cc\u95ed\u533a\u95f4 [0, n-1]\nwhile (i &lt;= j) {\nint m = i + (j - i) ~/ 2; // \u8ba1\u7b97\u4e2d\u95f4\u7d22\u5f15 m\nif (nums[m] &lt; target)\ni = m + 1; // target \u5728\u533a\u95f4 [m+1, j] \u4e2d\nelse if (nums[m] &gt; target)\nj = m - 1; // target \u5728\u533a\u95f4 [i, m-1] \u4e2d\nelse\ni = m + 1; // \u9996\u4e2a\u5927\u4e8e target \u7684\u5143\u7d20\u5728\u533a\u95f4 [m+1, j] \u4e2d\n}\nif (j &lt; 0 || nums[j] != target) return -1; // \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\nreturn j;\n}\n</code></pre> <p>\u89c2\u5bdf\u4e0b\u56fe\uff0c\u641c\u7d22\u6700\u53f3\u8fb9\u5143\u7d20\u65f6\u6307\u9488 \\(j\\) \u7684\u4f5c\u7528\u4e0e\u641c\u7d22\u6700\u5de6\u8fb9\u5143\u7d20\u65f6\u6307\u9488 \\(i\\) \u7684\u4f5c\u7528\u4e00\u81f4\uff0c\u53cd\u4e4b\u4ea6\u7136\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u641c\u7d22\u6700\u5de6\u8fb9\u5143\u7d20\u548c\u6700\u53f3\u8fb9\u5143\u7d20\u7684\u5b9e\u73b0\u662f\u955c\u50cf\u5bf9\u79f0\u7684\u3002</p> <p></p> <p> Fig. \u67e5\u627e\u6700\u5de6\u8fb9\u548c\u6700\u53f3\u8fb9\u5143\u7d20\u7684\u5bf9\u79f0\u6027 </p> <p>Tip</p> <p>\u4ee5\u4e0a\u4ee3\u7801\u91c7\u53d6\u7684\u90fd\u662f\u201c\u53cc\u95ed\u533a\u95f4\u201d\u5199\u6cd5\u3002\u6709\u5174\u8da3\u7684\u8bfb\u8005\u53ef\u4ee5\u81ea\u884c\u5b9e\u73b0\u201c\u5de6\u95ed\u53f3\u5f00\u201d\u5199\u6cd5\u3002</p>"},{"location":"chapter_searching/replace_linear_by_hashing/","title":"10.3. \u00a0 \u54c8\u5e0c\u4f18\u5316\u7b56\u7565","text":"<p>\u5728\u7b97\u6cd5\u9898\u4e2d\uff0c\u6211\u4eec\u5e38\u901a\u8fc7\u5c06\u7ebf\u6027\u67e5\u627e\u66ff\u6362\u4e3a\u54c8\u5e0c\u67e5\u627e\u6765\u964d\u4f4e\u7b97\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u3002\u6211\u4eec\u501f\u52a9\u4e00\u4e2a\u7b97\u6cd5\u9898\u6765\u52a0\u6df1\u7406\u89e3\u3002</p> <p>Question</p> <p>\u7ed9\u5b9a\u4e00\u4e2a\u6574\u6570\u6570\u7ec4 <code>nums</code> \u548c\u4e00\u4e2a\u76ee\u6807\u5143\u7d20 <code>target</code> \uff0c\u8bf7\u5728\u6570\u7ec4\u4e2d\u641c\u7d22\u201c\u548c\u201d\u4e3a <code>target</code> \u7684\u4e24\u4e2a\u5143\u7d20\uff0c\u5e76\u8fd4\u56de\u5b83\u4eec\u7684\u6570\u7ec4\u7d22\u5f15\u3002\u8fd4\u56de\u4efb\u610f\u4e00\u4e2a\u89e3\u5373\u53ef\u3002</p>"},{"location":"chapter_searching/replace_linear_by_hashing/#1031","title":"10.3.1. \u00a0 \u7ebf\u6027\u67e5\u627e\uff1a\u4ee5\u65f6\u95f4\u6362\u7a7a\u95f4","text":"<p>\u8003\u8651\u76f4\u63a5\u904d\u5386\u6240\u6709\u53ef\u80fd\u7684\u7ec4\u5408\u3002\u5f00\u542f\u4e00\u4e2a\u4e24\u5c42\u5faa\u73af\uff0c\u5728\u6bcf\u8f6e\u4e2d\u5224\u65ad\u4e24\u4e2a\u6574\u6570\u7684\u548c\u662f\u5426\u4e3a <code>target</code> \uff0c\u82e5\u662f\uff0c\u5219\u8fd4\u56de\u5b83\u4eec\u7684\u7d22\u5f15\u3002</p> <p></p> <p> Fig. \u7ebf\u6027\u67e5\u627e\u6c42\u89e3\u4e24\u6570\u4e4b\u548c </p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart two_sum.java<pre><code>/* \u65b9\u6cd5\u4e00\uff1a\u66b4\u529b\u679a\u4e3e */\nint[] twoSumBruteForce(int[] nums, int target) {\nint size = nums.length;\n// \u4e24\u5c42\u5faa\u73af\uff0c\u65f6\u95f4\u590d\u6742\u5ea6 O(n^2)\nfor (int i = 0; i &lt; size - 1; i++) {\nfor (int j = i + 1; j &lt; size; j++) {\nif (nums[i] + nums[j] == target)\nreturn new int[] { i, j };\n}\n}\nreturn new int[0];\n}\n</code></pre> two_sum.cpp<pre><code>/* \u65b9\u6cd5\u4e00\uff1a\u66b4\u529b\u679a\u4e3e */\nvector&lt;int&gt; twoSumBruteForce(vector&lt;int&gt; &amp;nums, int target) {\nint size = nums.size();\n// \u4e24\u5c42\u5faa\u73af\uff0c\u65f6\u95f4\u590d\u6742\u5ea6 O(n^2)\nfor (int i = 0; i &lt; size - 1; i++) {\nfor (int j = i + 1; j &lt; size; j++) {\nif (nums[i] + nums[j] == target)\nreturn {i, j};\n}\n}\nreturn {};\n}\n</code></pre> two_sum.py<pre><code>def two_sum_brute_force(nums: list[int], target: int) -&gt; list[int]:\n\"\"\"\u65b9\u6cd5\u4e00\uff1a\u66b4\u529b\u679a\u4e3e\"\"\"\n# \u4e24\u5c42\u5faa\u73af\uff0c\u65f6\u95f4\u590d\u6742\u5ea6 O(n^2)\nfor i in range(len(nums) - 1):\nfor j in range(i + 1, len(nums)):\nif nums[i] + nums[j] == target:\nreturn [i, j]\nreturn []\n</code></pre> two_sum.go<pre><code>/* \u65b9\u6cd5\u4e00\uff1a\u66b4\u529b\u679a\u4e3e */\nfunc twoSumBruteForce(nums []int, target int) []int {\nsize := len(nums)\n// \u4e24\u5c42\u5faa\u73af\uff0c\u65f6\u95f4\u590d\u6742\u5ea6 O(n^2)\nfor i := 0; i &lt; size-1; i++ {\nfor j := i + 1; i &lt; size; j++ {\nif nums[i]+nums[j] == target {\nreturn []int{i, j}\n}\n}\n}\nreturn nil\n}\n</code></pre> two_sum.js<pre><code>/* \u65b9\u6cd5\u4e00\uff1a\u66b4\u529b\u679a\u4e3e */\nfunction twoSumBruteForce(nums, target) {\nconst n = nums.length;\n// \u4e24\u5c42\u5faa\u73af\uff0c\u65f6\u95f4\u590d\u6742\u5ea6 O(n^2)\nfor (let i = 0; i &lt; n; i++) {\nfor (let j = i + 1; j &lt; n; j++) {\nif (nums[i] + nums[j] === target) {\nreturn [i, j];\n}\n}\n}\nreturn [];\n}\n</code></pre> two_sum.ts<pre><code>/* \u65b9\u6cd5\u4e00\uff1a\u66b4\u529b\u679a\u4e3e */\nfunction twoSumBruteForce(nums: number[], target: number): number[] {\nconst n = nums.length;\n// \u4e24\u5c42\u5faa\u73af\uff0c\u65f6\u95f4\u590d\u6742\u5ea6 O(n^2)\nfor (let i = 0; i &lt; n; i++) {\nfor (let j = i + 1; j &lt; n; j++) {\nif (nums[i] + nums[j] === target) {\nreturn [i, j];\n}\n}\n}\nreturn [];\n}\n</code></pre> two_sum.c<pre><code>/* \u65b9\u6cd5\u4e00\uff1a\u66b4\u529b\u679a\u4e3e */\nint *twoSumBruteForce(int *nums, int numsSize, int target, int *returnSize) {\nfor (int i = 0; i &lt; numsSize; ++i) {\nfor (int j = i + 1; j &lt; numsSize; ++j) {\nif (nums[i] + nums[j] == target) {\nint *res = malloc(sizeof(int) * 2);\nres[0] = i, res[1] = j;\n*returnSize = 2;\nreturn res;\n}\n}\n}\n*returnSize = 0;\nreturn NULL;\n}\n</code></pre> two_sum.cs<pre><code>/* \u65b9\u6cd5\u4e00\uff1a\u66b4\u529b\u679a\u4e3e */\nint[] twoSumBruteForce(int[] nums, int target) {\nint size = nums.Length;\n// \u4e24\u5c42\u5faa\u73af\uff0c\u65f6\u95f4\u590d\u6742\u5ea6 O(n^2)\nfor (int i = 0; i &lt; size - 1; i++) {\nfor (int j = i + 1; j &lt; size; j++) {\nif (nums[i] + nums[j] == target)\nreturn new int[] { i, j };\n}\n}\nreturn new int[0];\n}\n</code></pre> two_sum.swift<pre><code>/* \u65b9\u6cd5\u4e00\uff1a\u66b4\u529b\u679a\u4e3e */\nfunc twoSumBruteForce(nums: [Int], target: Int) -&gt; [Int] {\n// \u4e24\u5c42\u5faa\u73af\uff0c\u65f6\u95f4\u590d\u6742\u5ea6 O(n^2)\nfor i in nums.indices.dropLast() {\nfor j in nums.indices.dropFirst(i + 1) {\nif nums[i] + nums[j] == target {\nreturn [i, j]\n}\n}\n}\nreturn [0]\n}\n</code></pre> two_sum.zig<pre><code>// \u65b9\u6cd5\u4e00\uff1a\u66b4\u529b\u679a\u4e3e\nfn twoSumBruteForce(nums: []i32, target: i32) ?[2]i32 {\nvar size: usize = nums.len;\nvar i: usize = 0;\n// \u4e24\u5c42\u5faa\u73af\uff0c\u65f6\u95f4\u590d\u6742\u5ea6 O(n^2)\nwhile (i &lt; size - 1) : (i += 1) {\nvar j = i + 1;\nwhile (j &lt; size) : (j += 1) {\nif (nums[i] + nums[j] == target) {\nreturn [_]i32{@intCast(i32, i), @intCast(i32, j)};\n}\n}\n}\nreturn null;\n}\n</code></pre> two_sum.dart<pre><code>/* \u65b9\u6cd5\u4e00\uff1a \u66b4\u529b\u679a\u4e3e */\nList&lt;int&gt; twoSumBruteForce(List&lt;int&gt; nums, int target) {\nint size = nums.length;\nfor (var i = 0; i &lt; size - 1; i++) {\nfor (var j = i + 1; j &lt; size; j++) {\nif (nums[i] + nums[j] == target) return [i, j];\n}\n}\nreturn [0];\n}\n</code></pre> <p>\u6b64\u65b9\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(n^2)\\) \uff0c\u7a7a\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(1)\\) \uff0c\u5728\u5927\u6570\u636e\u91cf\u4e0b\u975e\u5e38\u8017\u65f6\u3002</p>"},{"location":"chapter_searching/replace_linear_by_hashing/#1032","title":"10.3.2. \u00a0 \u54c8\u5e0c\u67e5\u627e\uff1a\u4ee5\u7a7a\u95f4\u6362\u65f6\u95f4","text":"<p>\u8003\u8651\u501f\u52a9\u4e00\u4e2a\u54c8\u5e0c\u8868\uff0c\u952e\u503c\u5bf9\u5206\u522b\u4e3a\u6570\u7ec4\u5143\u7d20\u548c\u5143\u7d20\u7d22\u5f15\u3002\u5faa\u73af\u904d\u5386\u6570\u7ec4\uff0c\u6bcf\u8f6e\u6267\u884c\uff1a</p> <ol> <li>\u5224\u65ad\u6570\u5b57 <code>target - nums[i]</code> \u662f\u5426\u5728\u54c8\u5e0c\u8868\u4e2d\uff0c\u82e5\u662f\u5219\u76f4\u63a5\u8fd4\u56de\u8fd9\u4e24\u4e2a\u5143\u7d20\u7684\u7d22\u5f15\uff1b</li> <li>\u5c06\u952e\u503c\u5bf9 <code>nums[i]</code> \u548c\u7d22\u5f15 <code>i</code> \u6dfb\u52a0\u8fdb\u54c8\u5e0c\u8868\uff1b</li> </ol> &lt;1&gt;&lt;2&gt;&lt;3&gt; <p></p> <p></p> <p></p> <p>\u5b9e\u73b0\u4ee3\u7801\u5982\u4e0b\u6240\u793a\uff0c\u4ec5\u9700\u5355\u5c42\u5faa\u73af\u5373\u53ef\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart two_sum.java<pre><code>/* \u65b9\u6cd5\u4e8c\uff1a\u8f85\u52a9\u54c8\u5e0c\u8868 */\nint[] twoSumHashTable(int[] nums, int target) {\nint size = nums.length;\n// \u8f85\u52a9\u54c8\u5e0c\u8868\uff0c\u7a7a\u95f4\u590d\u6742\u5ea6 O(n)\nMap&lt;Integer, Integer&gt; dic = new HashMap&lt;&gt;();\n// \u5355\u5c42\u5faa\u73af\uff0c\u65f6\u95f4\u590d\u6742\u5ea6 O(n)\nfor (int i = 0; i &lt; size; i++) {\nif (dic.containsKey(target - nums[i])) {\nreturn new int[] { dic.get(target - nums[i]), i };\n}\ndic.put(nums[i], i);\n}\nreturn new int[0];\n}\n</code></pre> two_sum.cpp<pre><code>/* \u65b9\u6cd5\u4e8c\uff1a\u8f85\u52a9\u54c8\u5e0c\u8868 */\nvector&lt;int&gt; twoSumHashTable(vector&lt;int&gt; &amp;nums, int target) {\nint size = nums.size();\n// \u8f85\u52a9\u54c8\u5e0c\u8868\uff0c\u7a7a\u95f4\u590d\u6742\u5ea6 O(n)\nunordered_map&lt;int, int&gt; dic;\n// \u5355\u5c42\u5faa\u73af\uff0c\u65f6\u95f4\u590d\u6742\u5ea6 O(n)\nfor (int i = 0; i &lt; size; i++) {\nif (dic.find(target - nums[i]) != dic.end()) {\nreturn {dic[target - nums[i]], i};\n}\ndic.emplace(nums[i], i);\n}\nreturn {};\n}\n</code></pre> two_sum.py<pre><code>def two_sum_hash_table(nums: list[int], target: int) -&gt; list[int]:\n\"\"\"\u65b9\u6cd5\u4e8c\uff1a\u8f85\u52a9\u54c8\u5e0c\u8868\"\"\"\n# \u8f85\u52a9\u54c8\u5e0c\u8868\uff0c\u7a7a\u95f4\u590d\u6742\u5ea6 O(n)\ndic = {}\n# \u5355\u5c42\u5faa\u73af\uff0c\u65f6\u95f4\u590d\u6742\u5ea6 O(n)\nfor i in range(len(nums)):\nif target - nums[i] in dic:\nreturn [dic[target - nums[i]], i]\ndic[nums[i]] = i\nreturn []\n</code></pre> two_sum.go<pre><code>/* \u65b9\u6cd5\u4e8c\uff1a\u8f85\u52a9\u54c8\u5e0c\u8868 */\nfunc twoSumHashTable(nums []int, target int) []int {\n// \u8f85\u52a9\u54c8\u5e0c\u8868\uff0c\u7a7a\u95f4\u590d\u6742\u5ea6 O(n)\nhashTable := map[int]int{}\n// \u5355\u5c42\u5faa\u73af\uff0c\u65f6\u95f4\u590d\u6742\u5ea6 O(n)\nfor idx, val := range nums {\nif preIdx, ok := hashTable[target-val]; ok {\nreturn []int{preIdx, idx}\n}\nhashTable[val] = idx\n}\nreturn nil\n}\n</code></pre> two_sum.js<pre><code>/* \u65b9\u6cd5\u4e8c\uff1a\u8f85\u52a9\u54c8\u5e0c\u8868 */\nfunction twoSumHashTable(nums, target) {\n// \u8f85\u52a9\u54c8\u5e0c\u8868\uff0c\u7a7a\u95f4\u590d\u6742\u5ea6 O(n)\nlet m = {};\n// \u5355\u5c42\u5faa\u73af\uff0c\u65f6\u95f4\u590d\u6742\u5ea6 O(n)\nfor (let i = 0; i &lt; nums.length; i++) {\nif (m[nums[i]] !== undefined) {\nreturn [m[nums[i]], i];\n} else {\nm[target - nums[i]] = i;\n}\n}\nreturn [];\n}\n</code></pre> two_sum.ts<pre><code>/* \u65b9\u6cd5\u4e8c\uff1a\u8f85\u52a9\u54c8\u5e0c\u8868 */\nfunction twoSumHashTable(nums: number[], target: number): number[] {\n// \u8f85\u52a9\u54c8\u5e0c\u8868\uff0c\u7a7a\u95f4\u590d\u6742\u5ea6 O(n)\nlet m: Map&lt;number, number&gt; = new Map();\n// \u5355\u5c42\u5faa\u73af\uff0c\u65f6\u95f4\u590d\u6742\u5ea6 O(n)\nfor (let i = 0; i &lt; nums.length; i++) {\nlet index = m.get(nums[i]);\nif (index !== undefined) {\nreturn [index, i];\n} else {\nm.set(target - nums[i], i);\n}\n}\nreturn [];\n}\n</code></pre> two_sum.c<pre><code>/* \u54c8\u5e0c\u8868 */\nstruct hashTable {\nint key;\nint val;\nUT_hash_handle hh; // \u57fa\u4e8e uthash.h \u5b9e\u73b0\n};\ntypedef struct hashTable hashTable;\n/* \u54c8\u5e0c\u8868\u67e5\u8be2 */\nhashTable *find(hashTable *h, int key) {\nhashTable *tmp;\nHASH_FIND_INT(h, &amp;key, tmp);\nreturn tmp;\n}\n/* \u54c8\u5e0c\u8868\u5143\u7d20\u63d2\u5165 */\nvoid insert(hashTable *h, int key, int val) {\nhashTable *t = find(h, key);\nif (t == NULL) {\nhashTable *tmp = malloc(sizeof(hashTable));\ntmp-&gt;key = key, tmp-&gt;val = val;\nHASH_ADD_INT(h, key, tmp);\n} else {\nt-&gt;val = val;\n}\n}\n/* \u65b9\u6cd5\u4e8c\uff1a\u8f85\u52a9\u54c8\u5e0c\u8868 */\nint *twoSumHashTable(int *nums, int numsSize, int target, int *returnSize) {\nhashTable *hashtable = NULL;\nfor (int i = 0; i &lt; numsSize; i++) {\nhashTable *t = find(hashtable, target - nums[i]);\nif (t != NULL) {\nint *res = malloc(sizeof(int) * 2);\nres[0] = t-&gt;val, res[1] = i;\n*returnSize = 2;\nreturn res;\n}\ninsert(hashtable, nums[i], i);\n}\n*returnSize = 0;\nreturn NULL;\n}\n</code></pre> two_sum.cs<pre><code>/* \u65b9\u6cd5\u4e8c\uff1a\u8f85\u52a9\u54c8\u5e0c\u8868 */\nint[] twoSumHashTable(int[] nums, int target) {\nint size = nums.Length;\n// \u8f85\u52a9\u54c8\u5e0c\u8868\uff0c\u7a7a\u95f4\u590d\u6742\u5ea6 O(n)\nDictionary&lt;int, int&gt; dic = new();\n// \u5355\u5c42\u5faa\u73af\uff0c\u65f6\u95f4\u590d\u6742\u5ea6 O(n)\nfor (int i = 0; i &lt; size; i++) {\nif (dic.ContainsKey(target - nums[i])) {\nreturn new int[] { dic[target - nums[i]], i };\n}\ndic.Add(nums[i], i);\n}\nreturn new int[0];\n}\n</code></pre> two_sum.swift<pre><code>/* \u65b9\u6cd5\u4e8c\uff1a\u8f85\u52a9\u54c8\u5e0c\u8868 */\nfunc twoSumHashTable(nums: [Int], target: Int) -&gt; [Int] {\n// \u8f85\u52a9\u54c8\u5e0c\u8868\uff0c\u7a7a\u95f4\u590d\u6742\u5ea6 O(n)\nvar dic: [Int: Int] = [:]\n// \u5355\u5c42\u5faa\u73af\uff0c\u65f6\u95f4\u590d\u6742\u5ea6 O(n)\nfor i in nums.indices {\nif let j = dic[target - nums[i]] {\nreturn [j, i]\n}\ndic[nums[i]] = i\n}\nreturn [0]\n}\n</code></pre> two_sum.zig<pre><code>// \u65b9\u6cd5\u4e8c\uff1a\u8f85\u52a9\u54c8\u5e0c\u8868\nfn twoSumHashTable(nums: []i32, target: i32) !?[2]i32 {\nvar size: usize = nums.len;\n// \u8f85\u52a9\u54c8\u5e0c\u8868\uff0c\u7a7a\u95f4\u590d\u6742\u5ea6 O(n)\nvar dic = std.AutoHashMap(i32, i32).init(std.heap.page_allocator);\ndefer dic.deinit();\nvar i: usize = 0;\n// \u5355\u5c42\u5faa\u73af\uff0c\u65f6\u95f4\u590d\u6742\u5ea6 O(n)\nwhile (i &lt; size) : (i += 1) {\nif (dic.contains(target - nums[i])) {\nreturn [_]i32{dic.get(target - nums[i]).?, @intCast(i32, i)};\n}\ntry dic.put(nums[i], @intCast(i32, i));\n}\nreturn null;\n}\n</code></pre> two_sum.dart<pre><code>/* \u65b9\u6cd5\u4e8c\uff1a \u8f85\u52a9\u54c8\u5e0c\u8868 */\nList&lt;int&gt; twoSumHashTable(List&lt;int&gt; nums, int target) {\nint size = nums.length;\nMap&lt;int, int&gt; dic = HashMap();\nfor (var i = 0; i &lt; size; i++) {\nif (dic.containsKey(target - nums[i])) {\nreturn [dic[target - nums[i]]!, i];\n}\ndic.putIfAbsent(nums[i], () =&gt; i);\n}\nreturn [0];\n}\n</code></pre> <p>\u6b64\u65b9\u6cd5\u901a\u8fc7\u54c8\u5e0c\u67e5\u627e\u5c06\u65f6\u95f4\u590d\u6742\u5ea6\u4ece \\(O(n^2)\\) \u964d\u4f4e\u81f3 \\(O(n)\\) \uff0c\u5927\u5e45\u63d0\u5347\u8fd0\u884c\u6548\u7387\u3002</p> <p>\u7531\u4e8e\u9700\u8981\u7ef4\u62a4\u4e00\u4e2a\u989d\u5916\u7684\u54c8\u5e0c\u8868\uff0c\u56e0\u6b64\u7a7a\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(n)\\) \u3002\u5c3d\u7ba1\u5982\u6b64\uff0c\u8be5\u65b9\u6cd5\u7684\u6574\u4f53\u65f6\u7a7a\u6548\u7387\u66f4\u4e3a\u5747\u8861\uff0c\u56e0\u6b64\u5b83\u662f\u672c\u9898\u7684\u6700\u4f18\u89e3\u6cd5\u3002</p>"},{"location":"chapter_searching/searching_algorithm_revisited/","title":"10.4. \u00a0 \u91cd\u8bc6\u641c\u7d22\u7b97\u6cd5","text":"<p>\u300c\u641c\u7d22\u7b97\u6cd5 Searching Algorithm\u300d\u7528\u4e8e\u5728\u6570\u636e\u7ed3\u6784\uff08\u4f8b\u5982\u6570\u7ec4\u3001\u94fe\u8868\u3001\u6811\u6216\u56fe\uff09\u4e2d\u641c\u7d22\u4e00\u4e2a\u6216\u4e00\u7ec4\u6ee1\u8db3\u7279\u5b9a\u6761\u4ef6\u7684\u5143\u7d20\u3002</p> <p>\u6839\u636e\u5b9e\u73b0\u601d\u8def\uff0c\u641c\u7d22\u7b97\u6cd5\u603b\u4f53\u53ef\u5206\u4e3a\u4e24\u79cd\uff1a</p> <ul> <li>\u901a\u8fc7\u904d\u5386\u6570\u636e\u7ed3\u6784\u6765\u5b9a\u4f4d\u76ee\u6807\u5143\u7d20\uff0c\u4f8b\u5982\u6570\u7ec4\u3001\u94fe\u8868\u3001\u6811\u548c\u56fe\u7684\u904d\u5386\u7b49\u3002</li> <li>\u5229\u7528\u6570\u636e\u7ec4\u7ec7\u7ed3\u6784\u6216\u6570\u636e\u5305\u542b\u7684\u5148\u9a8c\u4fe1\u606f\uff0c\u5b9e\u73b0\u9ad8\u6548\u5143\u7d20\u67e5\u627e\uff0c\u4f8b\u5982\u4e8c\u5206\u67e5\u627e\u3001\u54c8\u5e0c\u67e5\u627e\u548c\u4e8c\u53c9\u641c\u7d22\u6811\u67e5\u627e\u7b49\u3002</li> </ul> <p>\u4e0d\u96be\u53d1\u73b0\uff0c\u8fd9\u4e9b\u77e5\u8bc6\u70b9\u90fd\u5df2\u5728\u524d\u9762\u7684\u7ae0\u8282\u4e2d\u4ecb\u7ecd\u8fc7\uff0c\u56e0\u6b64\u641c\u7d22\u7b97\u6cd5\u5bf9\u4e8e\u6211\u4eec\u6765\u8bf4\u5e76\u4e0d\u964c\u751f\u3002\u5728\u672c\u8282\u4e2d\uff0c\u6211\u4eec\u5c06\u4ece\u66f4\u52a0\u7cfb\u7edf\u7684\u89c6\u89d2\u5207\u5165\uff0c\u91cd\u65b0\u5ba1\u89c6\u641c\u7d22\u7b97\u6cd5\u3002</p>"},{"location":"chapter_searching/searching_algorithm_revisited/#1041","title":"10.4.1. \u00a0 \u66b4\u529b\u641c\u7d22","text":"<p>\u66b4\u529b\u641c\u7d22\u901a\u8fc7\u904d\u5386\u6570\u636e\u7ed3\u6784\u7684\u6bcf\u4e2a\u5143\u7d20\u6765\u5b9a\u4f4d\u76ee\u6807\u5143\u7d20\u3002</p> <ul> <li>\u300c\u7ebf\u6027\u641c\u7d22\u300d\u9002\u7528\u4e8e\u6570\u7ec4\u548c\u94fe\u8868\u7b49\u7ebf\u6027\u6570\u636e\u7ed3\u6784\u3002\u5b83\u4ece\u6570\u636e\u7ed3\u6784\u7684\u4e00\u7aef\u5f00\u59cb\uff0c\u9010\u4e2a\u8bbf\u95ee\u5143\u7d20\uff0c\u76f4\u5230\u627e\u5230\u76ee\u6807\u5143\u7d20\u6216\u5230\u8fbe\u53e6\u4e00\u7aef\u4ecd\u6ca1\u6709\u627e\u5230\u76ee\u6807\u5143\u7d20\u4e3a\u6b62\u3002</li> <li>\u300c\u5e7f\u5ea6\u4f18\u5148\u641c\u7d22\u300d\u548c\u300c\u6df1\u5ea6\u4f18\u5148\u641c\u7d22\u300d\u662f\u56fe\u548c\u6811\u7684\u4e24\u79cd\u904d\u5386\u7b56\u7565\u3002\u5e7f\u5ea6\u4f18\u5148\u641c\u7d22\u4ece\u521d\u59cb\u8282\u70b9\u5f00\u59cb\u9010\u5c42\u641c\u7d22\uff0c\u7531\u8fd1\u53ca\u8fdc\u5730\u8bbf\u95ee\u5404\u4e2a\u8282\u70b9\u3002\u6df1\u5ea6\u4f18\u5148\u641c\u7d22\u662f\u4ece\u521d\u59cb\u8282\u70b9\u5f00\u59cb\uff0c\u6cbf\u7740\u4e00\u6761\u8def\u5f84\u8d70\u5230\u5934\u4e3a\u6b62\uff0c\u518d\u56de\u6eaf\u5e76\u5c1d\u8bd5\u5176\u4ed6\u8def\u5f84\uff0c\u76f4\u5230\u904d\u5386\u5b8c\u6574\u4e2a\u6570\u636e\u7ed3\u6784\u3002</li> </ul> <p>\u66b4\u529b\u641c\u7d22\u7684\u4f18\u70b9\u662f\u7b80\u5355\u4e14\u901a\u7528\u6027\u597d\uff0c\u65e0\u9700\u5bf9\u6570\u636e\u505a\u9884\u5904\u7406\u548c\u501f\u52a9\u989d\u5916\u7684\u6570\u636e\u7ed3\u6784\u3002</p> <p>\u7136\u800c\uff0c\u6b64\u7c7b\u7b97\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(n)\\) \uff0c\u5176\u4e2d \\(n\\) \u4e3a\u5143\u7d20\u6570\u91cf\uff0c\u56e0\u6b64\u5728\u6570\u636e\u91cf\u8f83\u5927\u7684\u60c5\u51b5\u4e0b\u6027\u80fd\u8f83\u5dee\u3002</p>"},{"location":"chapter_searching/searching_algorithm_revisited/#1042","title":"10.4.2. \u00a0 \u81ea\u9002\u5e94\u641c\u7d22","text":"<p>\u81ea\u9002\u5e94\u641c\u7d22\u5229\u7528\u6570\u636e\u7684\u7279\u6709\u5c5e\u6027\uff08\u4f8b\u5982\u6709\u5e8f\u6027\uff09\u6765\u4f18\u5316\u641c\u7d22\u8fc7\u7a0b\uff0c\u4ece\u800c\u66f4\u9ad8\u6548\u5730\u5b9a\u4f4d\u76ee\u6807\u5143\u7d20\u3002</p> <ul> <li>\u300c\u4e8c\u5206\u67e5\u627e\u300d\u5229\u7528\u6570\u636e\u7684\u6709\u5e8f\u6027\u5b9e\u73b0\u9ad8\u6548\u67e5\u627e\uff0c\u4ec5\u9002\u7528\u4e8e\u6570\u7ec4\u3002</li> <li>\u300c\u54c8\u5e0c\u67e5\u627e\u300d\u5229\u7528\u54c8\u5e0c\u8868\u5c06\u641c\u7d22\u6570\u636e\u548c\u76ee\u6807\u6570\u636e\u5efa\u7acb\u4e3a\u952e\u503c\u5bf9\u6620\u5c04\uff0c\u4ece\u800c\u5b9e\u73b0\u67e5\u8be2\u64cd\u4f5c\u3002</li> <li>\u300c\u6811\u67e5\u627e\u300d\u5728\u7279\u5b9a\u7684\u6811\u7ed3\u6784\uff08\u4f8b\u5982\u4e8c\u53c9\u641c\u7d22\u6811\uff09\u4e2d\uff0c\u57fa\u4e8e\u6bd4\u8f83\u8282\u70b9\u503c\u6765\u5feb\u901f\u6392\u9664\u8282\u70b9\uff0c\u4ece\u800c\u5b9a\u4f4d\u76ee\u6807\u5143\u7d20\u3002</li> </ul> <p>\u6b64\u7c7b\u7b97\u6cd5\u7684\u4f18\u70b9\u662f\u6548\u7387\u9ad8\uff0c\u65f6\u95f4\u590d\u6742\u5ea6\u53ef\u8fbe\u5230 \\(O(\\log n)\\) \u751a\u81f3 \\(O(1)\\) \u3002</p> <p>\u7136\u800c\uff0c\u4f7f\u7528\u8fd9\u4e9b\u7b97\u6cd5\u5f80\u5f80\u9700\u8981\u5bf9\u6570\u636e\u8fdb\u884c\u9884\u5904\u7406\u3002\u4f8b\u5982\uff0c\u4e8c\u5206\u67e5\u627e\u9700\u8981\u9884\u5148\u5bf9\u6570\u7ec4\u8fdb\u884c\u6392\u5e8f\uff0c\u54c8\u5e0c\u67e5\u627e\u548c\u6811\u67e5\u627e\u90fd\u9700\u8981\u501f\u52a9\u989d\u5916\u7684\u6570\u636e\u7ed3\u6784\uff0c\u7ef4\u62a4\u8fd9\u4e9b\u6570\u636e\u7ed3\u6784\u4e5f\u9700\u8981\u989d\u5916\u7684\u65f6\u95f4\u548c\u7a7a\u95f4\u5f00\u652f\u3002</p> <p>Note</p> <p>\u81ea\u9002\u5e94\u641c\u7d22\u7b97\u6cd5\u5e38\u88ab\u79f0\u4e3a\u67e5\u627e\u7b97\u6cd5\uff0c\u4e3b\u8981\u5173\u6ce8\u5728\u7279\u5b9a\u6570\u636e\u7ed3\u6784\u4e2d\u5feb\u901f\u68c0\u7d22\u76ee\u6807\u5143\u7d20\u3002</p>"},{"location":"chapter_searching/searching_algorithm_revisited/#1043","title":"10.4.3. \u00a0 \u641c\u7d22\u65b9\u6cd5\u9009\u53d6","text":"<p>\u7ed9\u5b9a\u5927\u5c0f\u4e3a \\(n\\) \u7684\u4e00\u7ec4\u6570\u636e\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u7ebf\u6027\u641c\u7d22\u3001\u4e8c\u5206\u67e5\u627e\u3001\u6811\u67e5\u627e\u3001\u54c8\u5e0c\u67e5\u627e\u7b49\u591a\u79cd\u65b9\u6cd5\u5728\u8be5\u6570\u636e\u4e2d\u641c\u7d22\u76ee\u6807\u5143\u7d20\u3002\u5404\u4e2a\u65b9\u6cd5\u7684\u5de5\u4f5c\u539f\u7406\u5982\u4e0b\u56fe\u6240\u793a\u3002</p> <p></p> <p> Fig. \u591a\u79cd\u641c\u7d22\u7b56\u7565 </p> <p>\u4e0a\u8ff0\u51e0\u79cd\u65b9\u6cd5\u7684\u64cd\u4f5c\u6548\u7387\u4e0e\u7279\u6027\u5982\u4e0b\u8868\u6240\u793a\u3002</p> \u7ebf\u6027\u641c\u7d22 \u4e8c\u5206\u67e5\u627e \u6811\u67e5\u627e \u54c8\u5e0c\u67e5\u627e \u67e5\u627e\u5143\u7d20 \\(O(n)\\) \\(O(\\log n)\\) \\(O(\\log n)\\) \\(O(1)\\) \u63d2\u5165\u5143\u7d20 \\(O(1)\\) \\(O(n)\\) \\(O(\\log n)\\) \\(O(1)\\) \u5220\u9664\u5143\u7d20 \\(O(n)\\) \\(O(n)\\) \\(O(\\log n)\\) \\(O(1)\\) \u989d\u5916\u7a7a\u95f4 \\(O(1)\\) \\(O(1)\\) \\(O(n)\\) \\(O(n)\\) \u6570\u636e\u9884\u5904\u7406 / \u6392\u5e8f \\(O(n \\log n)\\) \u5efa\u6811 \\(O(n \\log n)\\) \u5efa\u54c8\u5e0c\u8868 \\(O(n)\\) \u6570\u636e\u662f\u5426\u6709\u5e8f \u65e0\u5e8f \u6709\u5e8f \u6709\u5e8f \u65e0\u5e8f <p>\u9664\u4e86\u4ee5\u4e0a\u8868\u683c\u5185\u5bb9\uff0c\u641c\u7d22\u7b97\u6cd5\u7684\u9009\u62e9\u8fd8\u53d6\u51b3\u4e8e\u6570\u636e\u4f53\u91cf\u3001\u641c\u7d22\u6027\u80fd\u8981\u6c42\u3001\u6570\u636e\u67e5\u8be2\u4e0e\u66f4\u65b0\u9891\u7387\u7b49\u3002</p> <p>\u7ebf\u6027\u641c\u7d22</p> <ul> <li>\u901a\u7528\u6027\u8f83\u597d\uff0c\u65e0\u9700\u4efb\u4f55\u6570\u636e\u9884\u5904\u7406\u64cd\u4f5c\u3002\u5047\u5982\u6211\u4eec\u4ec5\u9700\u67e5\u8be2\u4e00\u6b21\u6570\u636e\uff0c\u90a3\u4e48\u5176\u4ed6\u4e09\u79cd\u65b9\u6cd5\u7684\u6570\u636e\u9884\u5904\u7406\u7684\u65f6\u95f4\u6bd4\u7ebf\u6027\u641c\u7d22\u7684\u65f6\u95f4\u8fd8\u8981\u66f4\u957f\u3002</li> <li>\u9002\u7528\u4e8e\u4f53\u91cf\u8f83\u5c0f\u7684\u6570\u636e\uff0c\u6b64\u60c5\u51b5\u4e0b\u65f6\u95f4\u590d\u6742\u5ea6\u5bf9\u6548\u7387\u5f71\u54cd\u8f83\u5c0f\u3002</li> <li>\u9002\u7528\u4e8e\u6570\u636e\u66f4\u65b0\u9891\u7387\u8f83\u9ad8\u7684\u573a\u666f\uff0c\u56e0\u4e3a\u8be5\u65b9\u6cd5\u4e0d\u9700\u8981\u5bf9\u6570\u636e\u8fdb\u884c\u4efb\u4f55\u989d\u5916\u7ef4\u62a4\u3002</li> </ul> <p>\u4e8c\u5206\u67e5\u627e</p> <ul> <li>\u9002\u7528\u4e8e\u5927\u6570\u636e\u91cf\u7684\u60c5\u51b5\uff0c\u6548\u7387\u8868\u73b0\u7a33\u5b9a\uff0c\u6700\u5dee\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(\\log n)\\) \u3002</li> <li>\u6570\u636e\u91cf\u4e0d\u80fd\u8fc7\u5927\uff0c\u56e0\u4e3a\u5b58\u50a8\u6570\u7ec4\u9700\u8981\u8fde\u7eed\u7684\u5185\u5b58\u7a7a\u95f4\u3002</li> <li>\u4e0d\u9002\u7528\u4e8e\u9ad8\u9891\u589e\u5220\u6570\u636e\u7684\u573a\u666f\uff0c\u56e0\u4e3a\u7ef4\u62a4\u6709\u5e8f\u6570\u7ec4\u7684\u5f00\u9500\u8f83\u5927\u3002</li> </ul> <p>\u54c8\u5e0c\u67e5\u627e</p> <ul> <li>\u9002\u5408\u5bf9\u67e5\u8be2\u6027\u80fd\u8981\u6c42\u5f88\u9ad8\u7684\u573a\u666f\uff0c\u5e73\u5747\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(1)\\) \u3002</li> <li>\u4e0d\u9002\u5408\u9700\u8981\u6709\u5e8f\u6570\u636e\u6216\u8303\u56f4\u67e5\u627e\u7684\u573a\u666f\uff0c\u56e0\u4e3a\u54c8\u5e0c\u8868\u65e0\u6cd5\u7ef4\u62a4\u6570\u636e\u7684\u6709\u5e8f\u6027\u3002</li> <li>\u5bf9\u54c8\u5e0c\u51fd\u6570\u548c\u54c8\u5e0c\u51b2\u7a81\u5904\u7406\u7b56\u7565\u7684\u4f9d\u8d56\u6027\u8f83\u9ad8\uff0c\u5177\u6709\u8f83\u5927\u7684\u6027\u80fd\u52a3\u5316\u98ce\u9669\u3002</li> <li>\u4e0d\u9002\u5408\u6570\u636e\u91cf\u8fc7\u5927\u7684\u60c5\u51b5\uff0c\u56e0\u4e3a\u54c8\u5e0c\u8868\u9700\u8981\u989d\u5916\u7a7a\u95f4\u6765\u6700\u5927\u7a0b\u5ea6\u5730\u51cf\u5c11\u51b2\u7a81\uff0c\u4ece\u800c\u63d0\u4f9b\u826f\u597d\u7684\u67e5\u8be2\u6027\u80fd\u3002</li> </ul> <p>\u6811\u67e5\u627e</p> <ul> <li>\u9002\u7528\u4e8e\u6d77\u91cf\u6570\u636e\uff0c\u56e0\u4e3a\u6811\u8282\u70b9\u5728\u5185\u5b58\u4e2d\u662f\u79bb\u6563\u5b58\u50a8\u7684\u3002</li> <li>\u9002\u5408\u9700\u8981\u7ef4\u62a4\u6709\u5e8f\u6570\u636e\u6216\u8303\u56f4\u67e5\u627e\u7684\u573a\u666f\u3002</li> <li>\u5728\u6301\u7eed\u589e\u5220\u8282\u70b9\u7684\u8fc7\u7a0b\u4e2d\uff0c\u4e8c\u53c9\u641c\u7d22\u6811\u53ef\u80fd\u4ea7\u751f\u503e\u659c\uff0c\u65f6\u95f4\u590d\u6742\u5ea6\u52a3\u5316\u81f3 \\(O(n)\\) \u3002</li> <li>\u82e5\u4f7f\u7528 AVL \u6811\u6216\u7ea2\u9ed1\u6811\uff0c\u5219\u5404\u9879\u64cd\u4f5c\u53ef\u5728 \\(O(\\log n)\\) \u6548\u7387\u4e0b\u7a33\u5b9a\u8fd0\u884c\uff0c\u4f46\u7ef4\u62a4\u6811\u5e73\u8861\u7684\u64cd\u4f5c\u4f1a\u589e\u52a0\u989d\u5916\u5f00\u9500\u3002</li> </ul>"},{"location":"chapter_searching/summary/","title":"10.5. \u00a0 \u5c0f\u7ed3","text":"<ul> <li>\u4e8c\u5206\u67e5\u627e\u4f9d\u8d56\u4e8e\u6570\u636e\u7684\u6709\u5e8f\u6027\uff0c\u901a\u8fc7\u5faa\u73af\u9010\u6b65\u7f29\u51cf\u4e00\u534a\u641c\u7d22\u533a\u95f4\u6765\u5b9e\u73b0\u67e5\u627e\u3002\u5b83\u8981\u6c42\u8f93\u5165\u6570\u636e\u6709\u5e8f\uff0c\u4e14\u4ec5\u9002\u7528\u4e8e\u6570\u7ec4\u6216\u57fa\u4e8e\u6570\u7ec4\u5b9e\u73b0\u7684\u6570\u636e\u7ed3\u6784\u3002</li> <li>\u66b4\u529b\u641c\u7d22\u901a\u8fc7\u904d\u5386\u6570\u636e\u7ed3\u6784\u6765\u5b9a\u4f4d\u6570\u636e\u3002\u7ebf\u6027\u641c\u7d22\u9002\u7528\u4e8e\u6570\u7ec4\u548c\u94fe\u8868\uff0c\u5e7f\u5ea6\u4f18\u5148\u641c\u7d22\u548c\u6df1\u5ea6\u4f18\u5148\u641c\u7d22\u9002\u7528\u4e8e\u56fe\u548c\u6811\u3002\u6b64\u7c7b\u7b97\u6cd5\u901a\u7528\u6027\u597d\uff0c\u65e0\u9700\u5bf9\u6570\u636e\u9884\u5904\u7406\uff0c\u4f46\u65f6\u95f4\u590d\u6742\u5ea6 \\(O(n)\\) \u8f83\u9ad8\u3002</li> <li>\u54c8\u5e0c\u67e5\u627e\u3001\u6811\u67e5\u627e\u548c\u4e8c\u5206\u67e5\u627e\u5c5e\u4e8e\u9ad8\u6548\u641c\u7d22\u65b9\u6cd5\uff0c\u53ef\u5728\u7279\u5b9a\u6570\u636e\u7ed3\u6784\u4e2d\u5feb\u901f\u5b9a\u4f4d\u76ee\u6807\u5143\u7d20\u3002\u6b64\u7c7b\u7b97\u6cd5\u6548\u7387\u9ad8\uff0c\u65f6\u95f4\u590d\u6742\u5ea6\u53ef\u8fbe \\(O(\\log n)\\) \u751a\u81f3 \\(O(1)\\) \uff0c\u4f46\u901a\u5e38\u9700\u8981\u501f\u52a9\u989d\u5916\u6570\u636e\u7ed3\u6784\u3002</li> <li>\u5b9e\u9645\u4e2d\uff0c\u6211\u4eec\u9700\u8981\u5bf9\u6570\u636e\u4f53\u91cf\u3001\u641c\u7d22\u6027\u80fd\u8981\u6c42\u3001\u6570\u636e\u67e5\u8be2\u548c\u66f4\u65b0\u9891\u7387\u7b49\u56e0\u7d20\u8fdb\u884c\u5177\u4f53\u5206\u6790\uff0c\u4ece\u800c\u9009\u62e9\u5408\u9002\u7684\u641c\u7d22\u65b9\u6cd5\u3002</li> <li>\u7ebf\u6027\u641c\u7d22\u9002\u7528\u4e8e\u5c0f\u578b\u6216\u9891\u7e41\u66f4\u65b0\u7684\u6570\u636e\uff1b\u4e8c\u5206\u67e5\u627e\u9002\u7528\u4e8e\u5927\u578b\u3001\u6392\u5e8f\u7684\u6570\u636e\uff1b\u54c8\u5e0c\u67e5\u627e\u9002\u5408\u5bf9\u67e5\u8be2\u6548\u7387\u8981\u6c42\u8f83\u9ad8\u4e14\u65e0\u9700\u8303\u56f4\u67e5\u8be2\u7684\u6570\u636e\uff1b\u6811\u67e5\u627e\u9002\u7528\u4e8e\u9700\u8981\u7ef4\u62a4\u987a\u5e8f\u548c\u652f\u6301\u8303\u56f4\u67e5\u8be2\u7684\u5927\u578b\u52a8\u6001\u6570\u636e\u3002</li> <li>\u7528\u54c8\u5e0c\u67e5\u627e\u66ff\u6362\u7ebf\u6027\u67e5\u627e\u662f\u4e00\u79cd\u5e38\u7528\u7684\u4f18\u5316\u8fd0\u884c\u65f6\u95f4\u7684\u7b56\u7565\uff0c\u53ef\u5c06\u65f6\u95f4\u590d\u6742\u5ea6\u4ece \\(O(n)\\) \u964d\u4f4e\u81f3 \\(O(1)\\) \u3002 </li> </ul>"},{"location":"chapter_sorting/","title":"11. \u00a0 \u6392\u5e8f","text":""},{"location":"chapter_sorting/bubble_sort/","title":"11.3. \u00a0 \u5192\u6ce1\u6392\u5e8f","text":"<p>\u300c\u5192\u6ce1\u6392\u5e8f Bubble Sort\u300d\u901a\u8fc7\u8fde\u7eed\u5730\u6bd4\u8f83\u4e0e\u4ea4\u6362\u76f8\u90bb\u5143\u7d20\u5b9e\u73b0\u6392\u5e8f\u3002\u8fd9\u4e2a\u8fc7\u7a0b\u5c31\u50cf\u6c14\u6ce1\u4ece\u5e95\u90e8\u5347\u5230\u9876\u90e8\u4e00\u6837\uff0c\u56e0\u6b64\u5f97\u540d\u5192\u6ce1\u6392\u5e8f\u3002</p> <p>\u6211\u4eec\u53ef\u4ee5\u5229\u7528\u5143\u7d20\u4ea4\u6362\u64cd\u4f5c\u6a21\u62df\u4e0a\u8ff0\u8fc7\u7a0b\uff1a\u4ece\u6570\u7ec4\u6700\u5de6\u7aef\u5f00\u59cb\u5411\u53f3\u904d\u5386\uff0c\u4f9d\u6b21\u6bd4\u8f83\u76f8\u90bb\u5143\u7d20\u5927\u5c0f\uff0c\u5982\u679c\u201c\u5de6\u5143\u7d20 &gt; \u53f3\u5143\u7d20\u201d\u5c31\u4ea4\u6362\u5b83\u4fe9\u3002\u904d\u5386\u5b8c\u6210\u540e\uff0c\u6700\u5927\u7684\u5143\u7d20\u4f1a\u88ab\u79fb\u52a8\u5230\u6570\u7ec4\u7684\u6700\u53f3\u7aef\u3002</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p>"},{"location":"chapter_sorting/bubble_sort/#1131","title":"11.3.1. \u00a0 \u7b97\u6cd5\u6d41\u7a0b","text":"<p>\u8bbe\u6570\u7ec4\u7684\u957f\u5ea6\u4e3a \\(n\\) \uff0c\u5192\u6ce1\u6392\u5e8f\u7684\u6b65\u9aa4\u4e3a\uff1a</p> <ol> <li>\u9996\u5148\uff0c\u5bf9 \\(n\\) \u4e2a\u5143\u7d20\u6267\u884c\u201c\u5192\u6ce1\u201d\uff0c\u5c06\u6570\u7ec4\u7684\u6700\u5927\u5143\u7d20\u4ea4\u6362\u81f3\u6b63\u786e\u4f4d\u7f6e\uff0c</li> <li>\u63a5\u4e0b\u6765\uff0c\u5bf9\u5269\u4f59 \\(n - 1\\) \u4e2a\u5143\u7d20\u6267\u884c\u201c\u5192\u6ce1\u201d\uff0c\u5c06\u7b2c\u4e8c\u5927\u5143\u7d20\u4ea4\u6362\u81f3\u6b63\u786e\u4f4d\u7f6e\u3002</li> <li>\u4ee5\u6b64\u7c7b\u63a8\uff0c\u7ecf\u8fc7 \\(n - 1\\) \u8f6e\u201c\u5192\u6ce1\u201d\u540e\uff0c\u524d \\(n - 1\\) \u5927\u7684\u5143\u7d20\u90fd\u88ab\u4ea4\u6362\u81f3\u6b63\u786e\u4f4d\u7f6e\u3002</li> <li>\u4ec5\u5269\u7684\u4e00\u4e2a\u5143\u7d20\u5fc5\u5b9a\u662f\u6700\u5c0f\u5143\u7d20\uff0c\u65e0\u9700\u6392\u5e8f\uff0c\u56e0\u6b64\u6570\u7ec4\u6392\u5e8f\u5b8c\u6210\u3002</li> </ol> <p></p> <p> Fig. \u5192\u6ce1\u6392\u5e8f\u6d41\u7a0b </p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart bubble_sort.java<pre><code>/* \u5192\u6ce1\u6392\u5e8f */\nvoid bubbleSort(int[] nums) {\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [0, i]\nfor (int i = nums.length - 1; i &gt; 0; i--) {\n// \u5185\u5faa\u73af\uff1a\u5c06\u672a\u6392\u5e8f\u533a\u95f4 [0, i] \u4e2d\u7684\u6700\u5927\u5143\u7d20\u4ea4\u6362\u81f3\u8be5\u533a\u95f4\u7684\u6700\u53f3\u7aef \nfor (int j = 0; j &lt; i; j++) {\nif (nums[j] &gt; nums[j + 1]) {\n// \u4ea4\u6362 nums[j] \u4e0e nums[j + 1]\nint tmp = nums[j];\nnums[j] = nums[j + 1];\nnums[j + 1] = tmp;\n}\n}\n}\n}\n</code></pre> bubble_sort.cpp<pre><code>/* \u5192\u6ce1\u6392\u5e8f */\nvoid bubbleSort(vector&lt;int&gt; &amp;nums) {\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [0, i]\nfor (int i = nums.size() - 1; i &gt; 0; i--) {\n// \u5185\u5faa\u73af\uff1a\u5c06\u672a\u6392\u5e8f\u533a\u95f4 [0, i] \u4e2d\u7684\u6700\u5927\u5143\u7d20\u4ea4\u6362\u81f3\u8be5\u533a\u95f4\u7684\u6700\u53f3\u7aef \nfor (int j = 0; j &lt; i; j++) {\nif (nums[j] &gt; nums[j + 1]) {\n// \u4ea4\u6362 nums[j] \u4e0e nums[j + 1]\n// \u8fd9\u91cc\u4f7f\u7528\u4e86 std::swap() \u51fd\u6570\nswap(nums[j], nums[j + 1]);\n}\n}\n}\n}\n</code></pre> bubble_sort.py<pre><code>def bubble_sort(nums: list[int]) -&gt; None:\n\"\"\"\u5192\u6ce1\u6392\u5e8f\"\"\"\nn = len(nums)\n# \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [0, i]\nfor i in range(n - 1, 0, -1):\n# \u5185\u5faa\u73af\uff1a\u5c06\u672a\u6392\u5e8f\u533a\u95f4 [0, i] \u4e2d\u7684\u6700\u5927\u5143\u7d20\u4ea4\u6362\u81f3\u8be5\u533a\u95f4\u7684\u6700\u53f3\u7aef \nfor j in range(i):\nif nums[j] &gt; nums[j + 1]:\n# \u4ea4\u6362 nums[j] \u4e0e nums[j + 1]\nnums[j], nums[j + 1] = nums[j + 1], nums[j]\n</code></pre> bubble_sort.go<pre><code>/* \u5192\u6ce1\u6392\u5e8f */\nfunc bubbleSort(nums []int) {\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [0, i]\nfor i := len(nums) - 1; i &gt; 0; i-- {\n// \u5185\u5faa\u73af\uff1a\u5c06\u672a\u6392\u5e8f\u533a\u95f4 [0, i] \u4e2d\u7684\u6700\u5927\u5143\u7d20\u4ea4\u6362\u81f3\u8be5\u533a\u95f4\u7684\u6700\u53f3\u7aef\nfor j := 0; j &lt; i; j++ {\nif nums[j] &gt; nums[j+1] {\n// \u4ea4\u6362 nums[j] \u4e0e nums[j + 1]\nnums[j], nums[j+1] = nums[j+1], nums[j]\n}\n}\n}\n}\n</code></pre> bubble_sort.js<pre><code>/* \u5192\u6ce1\u6392\u5e8f */\nfunction bubbleSort(nums) {\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [0, i]\nfor (let i = nums.length - 1; i &gt; 0; i--) {\n// \u5185\u5faa\u73af\uff1a\u5c06\u672a\u6392\u5e8f\u533a\u95f4 [0, i] \u4e2d\u7684\u6700\u5927\u5143\u7d20\u4ea4\u6362\u81f3\u8be5\u533a\u95f4\u7684\u6700\u53f3\u7aef \nfor (let j = 0; j &lt; i; j++) {\nif (nums[j] &gt; nums[j + 1]) {\n// \u4ea4\u6362 nums[j] \u4e0e nums[j + 1]\nlet tmp = nums[j];\nnums[j] = nums[j + 1];\nnums[j + 1] = tmp;\n}\n}\n}\n}\n</code></pre> bubble_sort.ts<pre><code>/* \u5192\u6ce1\u6392\u5e8f */\nfunction bubbleSort(nums: number[]): void {\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [0, i]\nfor (let i = nums.length - 1; i &gt; 0; i--) {\n// \u5185\u5faa\u73af\uff1a\u5c06\u672a\u6392\u5e8f\u533a\u95f4 [0, i] \u4e2d\u7684\u6700\u5927\u5143\u7d20\u4ea4\u6362\u81f3\u8be5\u533a\u95f4\u7684\u6700\u53f3\u7aef \nfor (let j = 0; j &lt; i; j++) {\nif (nums[j] &gt; nums[j + 1]) {\n// \u4ea4\u6362 nums[j] \u4e0e nums[j + 1]\nlet tmp = nums[j];\nnums[j] = nums[j + 1];\nnums[j + 1] = tmp;\n}\n}\n}\n}\n</code></pre> bubble_sort.c<pre><code>/* \u5192\u6ce1\u6392\u5e8f */\nvoid bubbleSort(int nums[], int size) {\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [0, i]\nfor (int i = 0; i &lt; size - 1; i++) {\n// \u5185\u5faa\u73af\uff1a\u5c06\u672a\u6392\u5e8f\u533a\u95f4 [0, i] \u4e2d\u7684\u6700\u5927\u5143\u7d20\u4ea4\u6362\u81f3\u8be5\u533a\u95f4\u7684\u6700\u53f3\u7aef \nfor (int j = 0; j &lt; size - 1 - i; j++) {\nif (nums[j] &gt; nums[j + 1]) {\nint temp = nums[j];\nnums[j] = nums[j + 1];\nnums[j + 1] = temp;\n}\n}\n}\n}\n</code></pre> bubble_sort.cs<pre><code>/* \u5192\u6ce1\u6392\u5e8f */\nvoid bubbleSort(int[] nums) {\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [0, i]\nfor (int i = nums.Length - 1; i &gt; 0; i--) {\n// \u5185\u5faa\u73af\uff1a\u5c06\u672a\u6392\u5e8f\u533a\u95f4 [0, i] \u4e2d\u7684\u6700\u5927\u5143\u7d20\u4ea4\u6362\u81f3\u8be5\u533a\u95f4\u7684\u6700\u53f3\u7aef \nfor (int j = 0; j &lt; i; j++) {\nif (nums[j] &gt; nums[j + 1]) {\n// \u4ea4\u6362 nums[j] \u4e0e nums[j + 1]\nint tmp = nums[j];\nnums[j] = nums[j + 1];\nnums[j + 1] = tmp;\n}\n}\n}\n}\n</code></pre> bubble_sort.swift<pre><code>/* \u5192\u6ce1\u6392\u5e8f */\nfunc bubbleSort(nums: inout [Int]) {\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [0, i]\nfor i in stride(from: nums.count - 1, to: 0, by: -1) {\n// \u5185\u5faa\u73af\uff1a\u5c06\u672a\u6392\u5e8f\u533a\u95f4 [0, i] \u4e2d\u7684\u6700\u5927\u5143\u7d20\u4ea4\u6362\u81f3\u8be5\u533a\u95f4\u7684\u6700\u53f3\u7aef \nfor j in stride(from: 0, to: i, by: 1) {\nif nums[j] &gt; nums[j + 1] {\n// \u4ea4\u6362 nums[j] \u4e0e nums[j + 1]\nlet tmp = nums[j]\nnums[j] = nums[j + 1]\nnums[j + 1] = tmp\n}\n}\n}\n}\n</code></pre> bubble_sort.zig<pre><code>// \u5192\u6ce1\u6392\u5e8f\nfn bubbleSort(nums: []i32) void {\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [0, i]\nvar i: usize = nums.len - 1;\nwhile (i &gt; 0) : (i -= 1) {\nvar j: usize = 0;\n// \u5185\u5faa\u73af\uff1a\u5c06\u672a\u6392\u5e8f\u533a\u95f4 [0, i] \u4e2d\u7684\u6700\u5927\u5143\u7d20\u4ea4\u6362\u81f3\u8be5\u533a\u95f4\u7684\u6700\u53f3\u7aef \nwhile (j &lt; i) : (j += 1) {\nif (nums[j] &gt; nums[j + 1]) {\n// \u4ea4\u6362 nums[j] \u4e0e nums[j + 1]\nvar tmp = nums[j];\nnums[j] = nums[j + 1];\nnums[j + 1] = tmp;\n}\n}\n}\n}\n</code></pre> bubble_sort.dart<pre><code>/* \u5192\u6ce1\u6392\u5e8f */\nvoid bubbleSort(List&lt;int&gt; nums) {\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [0, i]\nfor (int i = nums.length - 1; i &gt; 0; i--) {\n// \u5185\u5faa\u73af\uff1a\u5c06\u672a\u6392\u5e8f\u533a\u95f4 [0, i] \u4e2d\u7684\u6700\u5927\u5143\u7d20\u4ea4\u6362\u81f3\u8be5\u533a\u95f4\u7684\u6700\u53f3\u7aef \nfor (int j = 0; j &lt; i; j++) {\nif (nums[j] &gt; nums[j + 1]) {\n// \u4ea4\u6362 nums[j] \u4e0e nums[j + 1]\nint tmp = nums[j];\nnums[j] = nums[j + 1];\nnums[j + 1] = tmp;\n}\n}\n}\n}\n</code></pre>"},{"location":"chapter_sorting/bubble_sort/#1132","title":"11.3.2. \u00a0 \u6548\u7387\u4f18\u5316","text":"<p>\u6211\u4eec\u53d1\u73b0\uff0c\u5982\u679c\u67d0\u8f6e\u201c\u5192\u6ce1\u201d\u4e2d\u6ca1\u6709\u6267\u884c\u4efb\u4f55\u4ea4\u6362\u64cd\u4f5c\uff0c\u8bf4\u660e\u6570\u7ec4\u5df2\u7ecf\u5b8c\u6210\u6392\u5e8f\uff0c\u53ef\u76f4\u63a5\u8fd4\u56de\u7ed3\u679c\u3002\u56e0\u6b64\uff0c\u53ef\u4ee5\u589e\u52a0\u4e00\u4e2a\u6807\u5fd7\u4f4d <code>flag</code> \u6765\u76d1\u6d4b\u8fd9\u79cd\u60c5\u51b5\uff0c\u4e00\u65e6\u51fa\u73b0\u5c31\u7acb\u5373\u8fd4\u56de\u3002</p> <p>\u7ecf\u8fc7\u4f18\u5316\uff0c\u5192\u6ce1\u6392\u5e8f\u7684\u6700\u5dee\u548c\u5e73\u5747\u65f6\u95f4\u590d\u6742\u5ea6\u4ecd\u4e3a \\(O(n^2)\\) \uff1b\u4f46\u5f53\u8f93\u5165\u6570\u7ec4\u5b8c\u5168\u6709\u5e8f\u65f6\uff0c\u53ef\u8fbe\u5230\u6700\u4f73\u65f6\u95f4\u590d\u6742\u5ea6 \\(O(n)\\) \u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart bubble_sort.java<pre><code>/* \u5192\u6ce1\u6392\u5e8f\uff08\u6807\u5fd7\u4f18\u5316\uff09 */\nvoid bubbleSortWithFlag(int[] nums) {\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [0, i]\nfor (int i = nums.length - 1; i &gt; 0; i--) {\nboolean flag = false; // \u521d\u59cb\u5316\u6807\u5fd7\u4f4d\n// \u5185\u5faa\u73af\uff1a\u5c06\u672a\u6392\u5e8f\u533a\u95f4 [0, i] \u4e2d\u7684\u6700\u5927\u5143\u7d20\u4ea4\u6362\u81f3\u8be5\u533a\u95f4\u7684\u6700\u53f3\u7aef \nfor (int j = 0; j &lt; i; j++) {\nif (nums[j] &gt; nums[j + 1]) {\n// \u4ea4\u6362 nums[j] \u4e0e nums[j + 1]\nint tmp = nums[j];\nnums[j] = nums[j + 1];\nnums[j + 1] = tmp;\nflag = true; // \u8bb0\u5f55\u4ea4\u6362\u5143\u7d20\n}\n}\nif (!flag)\nbreak; // \u6b64\u8f6e\u5192\u6ce1\u672a\u4ea4\u6362\u4efb\u4f55\u5143\u7d20\uff0c\u76f4\u63a5\u8df3\u51fa\n}\n}\n</code></pre> bubble_sort.cpp<pre><code>/* \u5192\u6ce1\u6392\u5e8f\uff08\u6807\u5fd7\u4f18\u5316\uff09*/\nvoid bubbleSortWithFlag(vector&lt;int&gt; &amp;nums) {\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [0, i]\nfor (int i = nums.size() - 1; i &gt; 0; i--) {\nbool flag = false; // \u521d\u59cb\u5316\u6807\u5fd7\u4f4d\n// \u5185\u5faa\u73af\uff1a\u5c06\u672a\u6392\u5e8f\u533a\u95f4 [0, i] \u4e2d\u7684\u6700\u5927\u5143\u7d20\u4ea4\u6362\u81f3\u8be5\u533a\u95f4\u7684\u6700\u53f3\u7aef \nfor (int j = 0; j &lt; i; j++) {\nif (nums[j] &gt; nums[j + 1]) {\n// \u4ea4\u6362 nums[j] \u4e0e nums[j + 1]\n// \u8fd9\u91cc\u4f7f\u7528\u4e86 std::swap() \u51fd\u6570\nswap(nums[j], nums[j + 1]);\nflag = true; // \u8bb0\u5f55\u4ea4\u6362\u5143\u7d20\n}\n}\nif (!flag)\nbreak; // \u6b64\u8f6e\u5192\u6ce1\u672a\u4ea4\u6362\u4efb\u4f55\u5143\u7d20\uff0c\u76f4\u63a5\u8df3\u51fa\n}\n}\n</code></pre> bubble_sort.py<pre><code>def bubble_sort_with_flag(nums: list[int]) -&gt; None:\n\"\"\"\u5192\u6ce1\u6392\u5e8f\uff08\u6807\u5fd7\u4f18\u5316\uff09\"\"\"\nn = len(nums)\n# \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [0, i]\nfor i in range(n - 1, 0, -1):\nflag = False  # \u521d\u59cb\u5316\u6807\u5fd7\u4f4d\n# \u5185\u5faa\u73af\uff1a\u5c06\u672a\u6392\u5e8f\u533a\u95f4 [0, i] \u4e2d\u7684\u6700\u5927\u5143\u7d20\u4ea4\u6362\u81f3\u8be5\u533a\u95f4\u7684\u6700\u53f3\u7aef \nfor j in range(i):\nif nums[j] &gt; nums[j + 1]:\n# \u4ea4\u6362 nums[j] \u4e0e nums[j + 1]\nnums[j], nums[j + 1] = nums[j + 1], nums[j]\nflag = True  # \u8bb0\u5f55\u4ea4\u6362\u5143\u7d20\nif not flag:\nbreak  # \u6b64\u8f6e\u5192\u6ce1\u672a\u4ea4\u6362\u4efb\u4f55\u5143\u7d20\uff0c\u76f4\u63a5\u8df3\u51fa\n</code></pre> bubble_sort.go<pre><code>/* \u5192\u6ce1\u6392\u5e8f\uff08\u6807\u5fd7\u4f18\u5316\uff09*/\nfunc bubbleSortWithFlag(nums []int) {\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [0, i]\nfor i := len(nums) - 1; i &gt; 0; i-- {\nflag := false // \u521d\u59cb\u5316\u6807\u5fd7\u4f4d\n// \u5185\u5faa\u73af\uff1a\u5c06\u672a\u6392\u5e8f\u533a\u95f4 [0, i] \u4e2d\u7684\u6700\u5927\u5143\u7d20\u4ea4\u6362\u81f3\u8be5\u533a\u95f4\u7684\u6700\u53f3\u7aef\nfor j := 0; j &lt; i; j++ {\nif nums[j] &gt; nums[j+1] {\n// \u4ea4\u6362 nums[j] \u4e0e nums[j + 1]\nnums[j], nums[j+1] = nums[j+1], nums[j]\nflag = true // \u8bb0\u5f55\u4ea4\u6362\u5143\u7d20\n}\n}\nif flag == false { // \u6b64\u8f6e\u5192\u6ce1\u672a\u4ea4\u6362\u4efb\u4f55\u5143\u7d20\uff0c\u76f4\u63a5\u8df3\u51fa\nbreak\n}\n}\n}\n</code></pre> bubble_sort.js<pre><code>/* \u5192\u6ce1\u6392\u5e8f\uff08\u6807\u5fd7\u4f18\u5316\uff09*/\nfunction bubbleSortWithFlag(nums) {\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [0, i]\nfor (let i = nums.length - 1; i &gt; 0; i--) {\nlet flag = false; // \u521d\u59cb\u5316\u6807\u5fd7\u4f4d\n// \u5185\u5faa\u73af\uff1a\u5c06\u672a\u6392\u5e8f\u533a\u95f4 [0, i] \u4e2d\u7684\u6700\u5927\u5143\u7d20\u4ea4\u6362\u81f3\u8be5\u533a\u95f4\u7684\u6700\u53f3\u7aef \nfor (let j = 0; j &lt; i; j++) {\nif (nums[j] &gt; nums[j + 1]) {\n// \u4ea4\u6362 nums[j] \u4e0e nums[j + 1]\nlet tmp = nums[j];\nnums[j] = nums[j + 1];\nnums[j + 1] = tmp;\nflag = true; // \u8bb0\u5f55\u4ea4\u6362\u5143\u7d20\n}\n}\nif (!flag) break; // \u6b64\u8f6e\u5192\u6ce1\u672a\u4ea4\u6362\u4efb\u4f55\u5143\u7d20\uff0c\u76f4\u63a5\u8df3\u51fa\n}\n}\n</code></pre> bubble_sort.ts<pre><code>/* \u5192\u6ce1\u6392\u5e8f\uff08\u6807\u5fd7\u4f18\u5316\uff09*/\nfunction bubbleSortWithFlag(nums: number[]): void {\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [0, i]\nfor (let i = nums.length - 1; i &gt; 0; i--) {\nlet flag = false; // \u521d\u59cb\u5316\u6807\u5fd7\u4f4d\n// \u5185\u5faa\u73af\uff1a\u5c06\u672a\u6392\u5e8f\u533a\u95f4 [0, i] \u4e2d\u7684\u6700\u5927\u5143\u7d20\u4ea4\u6362\u81f3\u8be5\u533a\u95f4\u7684\u6700\u53f3\u7aef \nfor (let j = 0; j &lt; i; j++) {\nif (nums[j] &gt; nums[j + 1]) {\n// \u4ea4\u6362 nums[j] \u4e0e nums[j + 1]\nlet tmp = nums[j];\nnums[j] = nums[j + 1];\nnums[j + 1] = tmp;\nflag = true; // \u8bb0\u5f55\u4ea4\u6362\u5143\u7d20\n}\n}\nif (!flag) break; // \u6b64\u8f6e\u5192\u6ce1\u672a\u4ea4\u6362\u4efb\u4f55\u5143\u7d20\uff0c\u76f4\u63a5\u8df3\u51fa\n}\n}\n</code></pre> bubble_sort.c<pre><code>/* \u5192\u6ce1\u6392\u5e8f\uff08\u6807\u5fd7\u4f18\u5316\uff09*/\nvoid bubbleSortWithFlag(int nums[], int size) {\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [0, i]\nfor (int i = 0; i &lt; size - 1; i++) {\nbool flag = false;\n// \u5185\u5faa\u73af\uff1a\u5c06\u672a\u6392\u5e8f\u533a\u95f4 [0, i] \u4e2d\u7684\u6700\u5927\u5143\u7d20\u4ea4\u6362\u81f3\u8be5\u533a\u95f4\u7684\u6700\u53f3\u7aef \nfor (int j = 0; j &lt; size - 1 - i; j++) {\nif (nums[j] &gt; nums[j + 1]) {\nint temp = nums[j];\nnums[j] = nums[j + 1];\nnums[j + 1] = temp;\nflag = true;\n}\n}\nif (!flag)\nbreak;\n}\n}\n</code></pre> bubble_sort.cs<pre><code>/* \u5192\u6ce1\u6392\u5e8f\uff08\u6807\u5fd7\u4f18\u5316\uff09*/\nvoid bubbleSortWithFlag(int[] nums) {\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [0, i]\nfor (int i = nums.Length - 1; i &gt; 0; i--) {\nbool flag = false; // \u521d\u59cb\u5316\u6807\u5fd7\u4f4d\n// \u5185\u5faa\u73af\uff1a\u5c06\u672a\u6392\u5e8f\u533a\u95f4 [0, i] \u4e2d\u7684\u6700\u5927\u5143\u7d20\u4ea4\u6362\u81f3\u8be5\u533a\u95f4\u7684\u6700\u53f3\u7aef \nfor (int j = 0; j &lt; i; j++) {\nif (nums[j] &gt; nums[j + 1]) {\n// \u4ea4\u6362 nums[j] \u4e0e nums[j + 1]\nint tmp = nums[j];\nnums[j] = nums[j + 1];\nnums[j + 1] = tmp;\nflag = true;  // \u8bb0\u5f55\u4ea4\u6362\u5143\u7d20\n}\n}\nif (!flag) break;     // \u6b64\u8f6e\u5192\u6ce1\u672a\u4ea4\u6362\u4efb\u4f55\u5143\u7d20\uff0c\u76f4\u63a5\u8df3\u51fa\n}\n}\n</code></pre> bubble_sort.swift<pre><code>/* \u5192\u6ce1\u6392\u5e8f\uff08\u6807\u5fd7\u4f18\u5316\uff09*/\nfunc bubbleSortWithFlag(nums: inout [Int]) {\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [0, i]\nfor i in stride(from: nums.count - 1, to: 0, by: -1) {\nvar flag = false // \u521d\u59cb\u5316\u6807\u5fd7\u4f4d\nfor j in stride(from: 0, to: i, by: 1) {\nif nums[j] &gt; nums[j + 1] {\n// \u4ea4\u6362 nums[j] \u4e0e nums[j + 1]\nlet tmp = nums[j]\nnums[j] = nums[j + 1]\nnums[j + 1] = tmp\nflag = true // \u8bb0\u5f55\u4ea4\u6362\u5143\u7d20\n}\n}\nif !flag { // \u6b64\u8f6e\u5192\u6ce1\u672a\u4ea4\u6362\u4efb\u4f55\u5143\u7d20\uff0c\u76f4\u63a5\u8df3\u51fa\nbreak\n}\n}\n}\n</code></pre> bubble_sort.zig<pre><code>// \u5192\u6ce1\u6392\u5e8f\uff08\u6807\u5fd7\u4f18\u5316\uff09\nfn bubbleSortWithFlag(nums: []i32) void {\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [0, i]\nvar i: usize = nums.len - 1;\nwhile (i &gt; 0) : (i -= 1) {\nvar flag = false;   // \u521d\u59cb\u5316\u6807\u5fd7\u4f4d\nvar j: usize = 0;\n// \u5185\u5faa\u73af\uff1a\u5c06\u672a\u6392\u5e8f\u533a\u95f4 [0, i] \u4e2d\u7684\u6700\u5927\u5143\u7d20\u4ea4\u6362\u81f3\u8be5\u533a\u95f4\u7684\u6700\u53f3\u7aef \nwhile (j &lt; i) : (j += 1) {\nif (nums[j] &gt; nums[j + 1]) {\n// \u4ea4\u6362 nums[j] \u4e0e nums[j + 1]\nvar tmp = nums[j];\nnums[j] = nums[j + 1];\nnums[j + 1] = tmp;\nflag = true;\n}\n}\nif (!flag) break;   // \u6b64\u8f6e\u5192\u6ce1\u672a\u4ea4\u6362\u4efb\u4f55\u5143\u7d20\uff0c\u76f4\u63a5\u8df3\u51fa\n}\n}\n</code></pre> bubble_sort.dart<pre><code>/* \u5192\u6ce1\u6392\u5e8f\uff08\u6807\u5fd7\u4f18\u5316\uff09*/\nvoid bubbleSortWithFlag(List&lt;int&gt; nums) {\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [0, i]\nfor (int i = nums.length - 1; i &gt; 0; i--) {\nbool flag = false; // \u521d\u59cb\u5316\u6807\u5fd7\u4f4d\n// \u5185\u5faa\u73af\uff1a\u5c06\u672a\u6392\u5e8f\u533a\u95f4 [0, i] \u4e2d\u7684\u6700\u5927\u5143\u7d20\u4ea4\u6362\u81f3\u8be5\u533a\u95f4\u7684\u6700\u53f3\u7aef \nfor (int j = 0; j &lt; i; j++) {\nif (nums[j] &gt; nums[j + 1]) {\n// \u4ea4\u6362 nums[j] \u4e0e nums[j + 1]\nint tmp = nums[j];\nnums[j] = nums[j + 1];\nnums[j + 1] = tmp;\nflag = true; // \u8bb0\u5f55\u4ea4\u6362\u5143\u7d20\n}\n}\nif (!flag) break; // \u6b64\u8f6e\u5192\u6ce1\u672a\u4ea4\u6362\u4efb\u4f55\u5143\u7d20\uff0c\u76f4\u63a5\u8df3\u51fa\n}\n}\n</code></pre>"},{"location":"chapter_sorting/bubble_sort/#1133","title":"11.3.3. \u00a0 \u7b97\u6cd5\u7279\u6027","text":"<ul> <li>\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(n^2)\\) \u3001\u81ea\u9002\u5e94\u6392\u5e8f \uff1a\u5404\u8f6e\u201c\u5192\u6ce1\u201d\u904d\u5386\u7684\u6570\u7ec4\u957f\u5ea6\u4f9d\u6b21\u4e3a \\(n - 1\\) , \\(n - 2\\) , \\(\\cdots\\) , \\(2\\) , \\(1\\) \uff0c\u603b\u548c\u4e3a \\(\\frac{(n - 1) n}{2}\\) \u3002\u5728\u5f15\u5165 <code>flag</code> \u4f18\u5316\u540e\uff0c\u6700\u4f73\u65f6\u95f4\u590d\u6742\u5ea6\u53ef\u8fbe\u5230 \\(O(n)\\) \u3002</li> <li>\u7a7a\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(1)\\) \u3001\u539f\u5730\u6392\u5e8f\uff1a\u6307\u9488 \\(i\\) , \\(j\\) \u4f7f\u7528\u5e38\u6570\u5927\u5c0f\u7684\u989d\u5916\u7a7a\u95f4\u3002</li> <li>\u7a33\u5b9a\u6392\u5e8f\uff1a\u7531\u4e8e\u5728\u201c\u5192\u6ce1\u201d\u4e2d\u9047\u5230\u76f8\u7b49\u5143\u7d20\u4e0d\u4ea4\u6362\u3002</li> </ul>"},{"location":"chapter_sorting/bucket_sort/","title":"11.8. \u00a0 \u6876\u6392\u5e8f","text":"<p>\u524d\u8ff0\u7684\u51e0\u79cd\u6392\u5e8f\u7b97\u6cd5\u90fd\u5c5e\u4e8e\u201c\u57fa\u4e8e\u6bd4\u8f83\u7684\u6392\u5e8f\u7b97\u6cd5\u201d\uff0c\u5b83\u4eec\u901a\u8fc7\u6bd4\u8f83\u5143\u7d20\u95f4\u7684\u5927\u5c0f\u6765\u5b9e\u73b0\u6392\u5e8f\u3002\u6b64\u7c7b\u6392\u5e8f\u7b97\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u65e0\u6cd5\u8d85\u8d8a \\(O(n \\log n)\\) \u3002\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u5c06\u63a2\u8ba8\u51e0\u79cd\u201c\u975e\u6bd4\u8f83\u6392\u5e8f\u7b97\u6cd5\u201d\uff0c\u5b83\u4eec\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u53ef\u4ee5\u8fbe\u5230\u7ebf\u6027\u6c34\u5e73\u3002</p> <p>\u300c\u6876\u6392\u5e8f Bucket Sort\u300d\u662f\u5206\u6cbb\u601d\u60f3\u7684\u4e00\u4e2a\u5178\u578b\u5e94\u7528\u3002\u5b83\u901a\u8fc7\u8bbe\u7f6e\u4e00\u4e9b\u5177\u6709\u5927\u5c0f\u987a\u5e8f\u7684\u6876\uff0c\u6bcf\u4e2a\u6876\u5bf9\u5e94\u4e00\u4e2a\u6570\u636e\u8303\u56f4\uff0c\u5c06\u6570\u636e\u5e73\u5747\u5206\u914d\u5230\u5404\u4e2a\u6876\u4e2d\uff1b\u7136\u540e\uff0c\u5728\u6bcf\u4e2a\u6876\u5185\u90e8\u5206\u522b\u6267\u884c\u6392\u5e8f\uff1b\u6700\u7ec8\u6309\u7167\u6876\u7684\u987a\u5e8f\u5c06\u6240\u6709\u6570\u636e\u5408\u5e76\u3002</p>"},{"location":"chapter_sorting/bucket_sort/#1181","title":"11.8.1. \u00a0 \u7b97\u6cd5\u6d41\u7a0b","text":"<p>\u8003\u8651\u4e00\u4e2a\u957f\u5ea6\u4e3a \\(n\\) \u7684\u6570\u7ec4\uff0c\u5143\u7d20\u662f\u8303\u56f4 \\([0, 1)\\) \u7684\u6d6e\u70b9\u6570\u3002\u6876\u6392\u5e8f\u7684\u6d41\u7a0b\u5982\u4e0b\uff1a</p> <ol> <li>\u521d\u59cb\u5316 \\(k\\) \u4e2a\u6876\uff0c\u5c06 \\(n\\) \u4e2a\u5143\u7d20\u5206\u914d\u5230 \\(k\\) \u4e2a\u6876\u4e2d\uff1b</li> <li>\u5bf9\u6bcf\u4e2a\u6876\u5206\u522b\u6267\u884c\u6392\u5e8f\uff08\u672c\u6587\u91c7\u7528\u7f16\u7a0b\u8bed\u8a00\u7684\u5185\u7f6e\u6392\u5e8f\u51fd\u6570\uff09\uff1b</li> <li>\u6309\u7167\u6876\u7684\u4ece\u5c0f\u5230\u5927\u7684\u987a\u5e8f\uff0c\u5408\u5e76\u7ed3\u679c\uff1b</li> </ol> <p></p> <p> Fig. \u6876\u6392\u5e8f\u7b97\u6cd5\u6d41\u7a0b </p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart bucket_sort.java<pre><code>/* \u6876\u6392\u5e8f */\nvoid bucketSort(float[] nums) {\n// \u521d\u59cb\u5316 k = n/2 \u4e2a\u6876\uff0c\u9884\u671f\u5411\u6bcf\u4e2a\u6876\u5206\u914d 2 \u4e2a\u5143\u7d20\nint k = nums.length / 2;\nList&lt;List&lt;Float&gt;&gt; buckets = new ArrayList&lt;&gt;();\nfor (int i = 0; i &lt; k; i++) {\nbuckets.add(new ArrayList&lt;&gt;());\n}\n// 1. \u5c06\u6570\u7ec4\u5143\u7d20\u5206\u914d\u5230\u5404\u4e2a\u6876\u4e2d\nfor (float num : nums) {\n// \u8f93\u5165\u6570\u636e\u8303\u56f4 [0, 1)\uff0c\u4f7f\u7528 num * k \u6620\u5c04\u5230\u7d22\u5f15\u8303\u56f4 [0, k-1]\nint i = (int) (num * k);\n// \u5c06 num \u6dfb\u52a0\u8fdb\u6876 i\nbuckets.get(i).add(num);\n}\n// 2. \u5bf9\u5404\u4e2a\u6876\u6267\u884c\u6392\u5e8f\nfor (List&lt;Float&gt; bucket : buckets) {\n// \u4f7f\u7528\u5185\u7f6e\u6392\u5e8f\u51fd\u6570\uff0c\u4e5f\u53ef\u4ee5\u66ff\u6362\u6210\u5176\u4ed6\u6392\u5e8f\u7b97\u6cd5\nCollections.sort(bucket);\n}\n// 3. \u904d\u5386\u6876\u5408\u5e76\u7ed3\u679c\nint i = 0;\nfor (List&lt;Float&gt; bucket : buckets) {\nfor (float num : bucket) {\nnums[i++] = num;\n}\n}\n}\n</code></pre> bucket_sort.cpp<pre><code>/* \u6876\u6392\u5e8f */\nvoid bucketSort(vector&lt;float&gt; &amp;nums) {\n// \u521d\u59cb\u5316 k = n/2 \u4e2a\u6876\uff0c\u9884\u671f\u5411\u6bcf\u4e2a\u6876\u5206\u914d 2 \u4e2a\u5143\u7d20\nint k = nums.size() / 2;\nvector&lt;vector&lt;float&gt;&gt; buckets(k);\n// 1. \u5c06\u6570\u7ec4\u5143\u7d20\u5206\u914d\u5230\u5404\u4e2a\u6876\u4e2d\nfor (float num : nums) {\n// \u8f93\u5165\u6570\u636e\u8303\u56f4 [0, 1)\uff0c\u4f7f\u7528 num * k \u6620\u5c04\u5230\u7d22\u5f15\u8303\u56f4 [0, k-1]\nint i = num * k;\n// \u5c06 num \u6dfb\u52a0\u8fdb\u6876 bucket_idx\nbuckets[i].push_back(num);\n}\n// 2. \u5bf9\u5404\u4e2a\u6876\u6267\u884c\u6392\u5e8f\nfor (vector&lt;float&gt; &amp;bucket : buckets) {\n// \u4f7f\u7528\u5185\u7f6e\u6392\u5e8f\u51fd\u6570\uff0c\u4e5f\u53ef\u4ee5\u66ff\u6362\u6210\u5176\u4ed6\u6392\u5e8f\u7b97\u6cd5\nsort(bucket.begin(), bucket.end());\n}\n// 3. \u904d\u5386\u6876\u5408\u5e76\u7ed3\u679c\nint i = 0;\nfor (vector&lt;float&gt; &amp;bucket : buckets) {\nfor (float num : bucket) {\nnums[i++] = num;\n}\n}\n}\n</code></pre> bucket_sort.py<pre><code>def bucket_sort(nums: list[float]) -&gt; None:\n\"\"\"\u6876\u6392\u5e8f\"\"\"\n# \u521d\u59cb\u5316 k = n/2 \u4e2a\u6876\uff0c\u9884\u671f\u5411\u6bcf\u4e2a\u6876\u5206\u914d 2 \u4e2a\u5143\u7d20\nk = len(nums) // 2\nbuckets = [[] for _ in range(k)]\n# 1. \u5c06\u6570\u7ec4\u5143\u7d20\u5206\u914d\u5230\u5404\u4e2a\u6876\u4e2d\nfor num in nums:\n# \u8f93\u5165\u6570\u636e\u8303\u56f4 [0, 1)\uff0c\u4f7f\u7528 num * k \u6620\u5c04\u5230\u7d22\u5f15\u8303\u56f4 [0, k-1]\ni = int(num * k)\n# \u5c06 num \u6dfb\u52a0\u8fdb\u6876 i\nbuckets[i].append(num)\n# 2. \u5bf9\u5404\u4e2a\u6876\u6267\u884c\u6392\u5e8f5\nfor bucket in buckets:\n# \u4f7f\u7528\u5185\u7f6e\u6392\u5e8f\u51fd\u6570\uff0c\u4e5f\u53ef\u4ee5\u66ff\u6362\u6210\u5176\u4ed6\u6392\u5e8f\u7b97\u6cd5\nbucket.sort()\n# 3. \u904d\u5386\u6876\u5408\u5e76\u7ed3\u679c\ni = 0\nfor bucket in buckets:\nfor num in bucket:\nnums[i] = num\ni += 1\n</code></pre> bucket_sort.go<pre><code>/* \u6876\u6392\u5e8f */\nfunc bucketSort(nums []float64) {\n// \u521d\u59cb\u5316 k = n/2 \u4e2a\u6876\uff0c\u9884\u671f\u5411\u6bcf\u4e2a\u6876\u5206\u914d 2 \u4e2a\u5143\u7d20\nk := len(nums) / 2\nbuckets := make([][]float64, k)\nfor i := 0; i &lt; k; i++ {\nbuckets[i] = make([]float64, 0)\n}\n// 1. \u5c06\u6570\u7ec4\u5143\u7d20\u5206\u914d\u5230\u5404\u4e2a\u6876\u4e2d\nfor _, num := range nums {\n// \u8f93\u5165\u6570\u636e\u8303\u56f4 [0, 1)\uff0c\u4f7f\u7528 num * k \u6620\u5c04\u5230\u7d22\u5f15\u8303\u56f4 [0, k-1]\ni := int(num * float64(k))\n// \u5c06 num \u6dfb\u52a0\u8fdb\u6876 i\nbuckets[i] = append(buckets[i], num)\n}\n// 2. \u5bf9\u5404\u4e2a\u6876\u6267\u884c\u6392\u5e8f\nfor i := 0; i &lt; k; i++ {\n// \u4f7f\u7528\u5185\u7f6e\u5207\u7247\u6392\u5e8f\u51fd\u6570\uff0c\u4e5f\u53ef\u4ee5\u66ff\u6362\u6210\u5176\u4ed6\u6392\u5e8f\u7b97\u6cd5\nsort.Float64s(buckets[i])\n}\n// 3. \u904d\u5386\u6876\u5408\u5e76\u7ed3\u679c\ni := 0\nfor _, bucket := range buckets {\nfor _, num := range bucket {\nnums[i] = num\ni++\n}\n}\n}\n</code></pre> bucket_sort.js<pre><code>/* \u6876\u6392\u5e8f */\nfunction bucketSort(nums) {\n// \u521d\u59cb\u5316 k = n/2 \u4e2a\u6876\uff0c\u9884\u671f\u5411\u6bcf\u4e2a\u6876\u5206\u914d 2 \u4e2a\u5143\u7d20\nconst k = nums.length / 2;\nconst buckets = [];\nfor (let i = 0; i &lt; k; i++) {\nbuckets.push([]);\n}\n// 1. \u5c06\u6570\u7ec4\u5143\u7d20\u5206\u914d\u5230\u5404\u4e2a\u6876\u4e2d\nfor (const num of nums) {\n// \u8f93\u5165\u6570\u636e\u8303\u56f4 [0, 1)\uff0c\u4f7f\u7528 num * k \u6620\u5c04\u5230\u7d22\u5f15\u8303\u56f4 [0, k-1]\nconst i = Math.floor(num * k);\n// \u5c06 num \u6dfb\u52a0\u8fdb\u6876 i\nbuckets[i].push(num);\n}\n// 2. \u5bf9\u5404\u4e2a\u6876\u6267\u884c\u6392\u5e8f\nfor (const bucket of buckets) {\n// \u4f7f\u7528\u5185\u7f6e\u6392\u5e8f\u51fd\u6570\uff0c\u4e5f\u53ef\u4ee5\u66ff\u6362\u6210\u5176\u4ed6\u6392\u5e8f\u7b97\u6cd5\nbucket.sort((a, b) =&gt; a - b);\n}\n// 3. \u904d\u5386\u6876\u5408\u5e76\u7ed3\u679c\nlet i = 0;\nfor (const bucket of buckets) {\nfor (const num of bucket) {\nnums[i++] = num;\n}\n}\n}\n</code></pre> bucket_sort.ts<pre><code>/* \u6876\u6392\u5e8f */\nfunction bucketSort(nums: number[]): void {\n// \u521d\u59cb\u5316 k = n/2 \u4e2a\u6876\uff0c\u9884\u671f\u5411\u6bcf\u4e2a\u6876\u5206\u914d 2 \u4e2a\u5143\u7d20\nconst k = nums.length / 2;\nconst buckets: number[][] = [];\nfor (let i = 0; i &lt; k; i++) {\nbuckets.push([]);\n}\n// 1. \u5c06\u6570\u7ec4\u5143\u7d20\u5206\u914d\u5230\u5404\u4e2a\u6876\u4e2d\nfor (const num of nums) {\n// \u8f93\u5165\u6570\u636e\u8303\u56f4 [0, 1)\uff0c\u4f7f\u7528 num * k \u6620\u5c04\u5230\u7d22\u5f15\u8303\u56f4 [0, k-1]\nconst i = Math.floor(num * k);\n// \u5c06 num \u6dfb\u52a0\u8fdb\u6876 i\nbuckets[i].push(num);\n}\n// 2. \u5bf9\u5404\u4e2a\u6876\u6267\u884c\u6392\u5e8f\nfor (const bucket of buckets) {\n// \u4f7f\u7528\u5185\u7f6e\u6392\u5e8f\u51fd\u6570\uff0c\u4e5f\u53ef\u4ee5\u66ff\u6362\u6210\u5176\u4ed6\u6392\u5e8f\u7b97\u6cd5\nbucket.sort((a, b) =&gt; a - b);\n}\n// 3. \u904d\u5386\u6876\u5408\u5e76\u7ed3\u679c\nlet i = 0;\nfor (const bucket of buckets) {\nfor (const num of bucket) {\nnums[i++] = num;\n}\n}\n}\n</code></pre> bucket_sort.c<pre><code>/* \u6876\u6392\u5e8f */\nvoid bucketSort(float nums[], int size) {\n// \u521d\u59cb\u5316 k = n/2 \u4e2a\u6876\uff0c\u9884\u671f\u5411\u6bcf\u4e2a\u6876\u5206\u914d 2 \u4e2a\u5143\u7d20\nint k = size / 2;\nfloat **buckets = calloc(k, sizeof(float *));\nfor (int i = 0; i &lt; k; i++) {\n// \u6bcf\u4e2a\u6876\u6700\u591a\u53ef\u4ee5\u5206\u914d k \u4e2a\u5143\u7d20\nbuckets[i] = calloc(ARRAY_SIZE, sizeof(float));\n}\n// 1. \u5c06\u6570\u7ec4\u5143\u7d20\u5206\u914d\u5230\u5404\u4e2a\u6876\u4e2d\nfor (int i = 0; i &lt; size; i++) {\n// \u8f93\u5165\u6570\u636e\u8303\u56f4 [0, 1)\uff0c\u4f7f\u7528 num * k \u6620\u5c04\u5230\u7d22\u5f15\u8303\u56f4 [0, k-1]\nint bucket_idx = nums[i] * k;\nint j = 0;\n// \u5982\u679c\u6876\u4e2d\u6709\u6570\u636e\u4e14\u6570\u636e\u5c0f\u4e8e\u5f53\u524d\u503c nums[i], \u8981\u5c06\u5176\u653e\u5230\u5f53\u524d\u6876\u7684\u540e\u9762\uff0c\u76f8\u5f53\u4e8e cpp \u4e2d\u7684 push_back\nwhile (buckets[bucket_idx][j] &gt; 0 &amp;&amp; buckets[bucket_idx][j] &lt; nums[i]) {\nj++;\n}\nfloat temp = nums[i];\nwhile (j &lt; ARRAY_SIZE &amp;&amp; buckets[bucket_idx][j] &gt; 0) {\nswap(&amp;temp, &amp;buckets[bucket_idx][j]);\nj++;\n}\nbuckets[bucket_idx][j] = temp;\n}\n// 2. \u5bf9\u5404\u4e2a\u6876\u6267\u884c\u6392\u5e8f\nfor (int i = 0; i &lt; k; i++) {\nqsort(buckets[i], ARRAY_SIZE, sizeof(float), compare_float);\n}\n// 3. \u904d\u5386\u6876\u5408\u5e76\u7ed3\u679c\nfor (int i = 0, j = 0; j &lt; k; j++) {\nfor (int l = 0; l &lt; ARRAY_SIZE; l++) {\nif (buckets[j][l] &gt; 0) {\nnums[i++] = buckets[j][l];\n}\n}\n}\n// \u91ca\u653e\u4e0a\u8ff0\u5206\u914d\u7684\u5185\u5b58\nfor (int i = 0; i &lt; k; i++) {\nfree(buckets[i]);\n}\nfree(buckets);\n}\n</code></pre> bucket_sort.cs<pre><code>/* \u6876\u6392\u5e8f */\nvoid bucketSort(float[] nums) {\n// \u521d\u59cb\u5316 k = n/2 \u4e2a\u6876\uff0c\u9884\u671f\u5411\u6bcf\u4e2a\u6876\u5206\u914d 2 \u4e2a\u5143\u7d20\nint k = nums.Length / 2;\nList&lt;List&lt;float&gt;&gt; buckets = new List&lt;List&lt;float&gt;&gt;();\nfor (int i = 0; i &lt; k; i++) {\nbuckets.Add(new List&lt;float&gt;());\n}\n// 1. \u5c06\u6570\u7ec4\u5143\u7d20\u5206\u914d\u5230\u5404\u4e2a\u6876\u4e2d\nforeach (float num in nums) {\n// \u8f93\u5165\u6570\u636e\u8303\u56f4 [0, 1)\uff0c\u4f7f\u7528 num * k \u6620\u5c04\u5230\u7d22\u5f15\u8303\u56f4 [0, k-1]\nint i = (int) (num * k);\n// \u5c06 num \u6dfb\u52a0\u8fdb\u6876 i\nbuckets[i].Add(num);\n}\n// 2. \u5bf9\u5404\u4e2a\u6876\u6267\u884c\u6392\u5e8f\nforeach (List&lt;float&gt; bucket in buckets) {\n// \u4f7f\u7528\u5185\u7f6e\u6392\u5e8f\u51fd\u6570\uff0c\u4e5f\u53ef\u4ee5\u66ff\u6362\u6210\u5176\u4ed6\u6392\u5e8f\u7b97\u6cd5\nbucket.Sort();\n}\n// 3. \u904d\u5386\u6876\u5408\u5e76\u7ed3\u679c\nint j = 0;\nforeach (List&lt;float&gt; bucket in buckets) {\nforeach (float num in bucket) {\nnums[j++] = num;\n}\n}\n}\n</code></pre> bucket_sort.swift<pre><code>/* \u6876\u6392\u5e8f */\nfunc bucketSort(nums: inout [Double]) {\n// \u521d\u59cb\u5316 k = n/2 \u4e2a\u6876\uff0c\u9884\u671f\u5411\u6bcf\u4e2a\u6876\u5206\u914d 2 \u4e2a\u5143\u7d20\nlet k = nums.count / 2\nvar buckets = (0 ..&lt; k).map { _ in [Double]() }\n// 1. \u5c06\u6570\u7ec4\u5143\u7d20\u5206\u914d\u5230\u5404\u4e2a\u6876\u4e2d\nfor num in nums {\n// \u8f93\u5165\u6570\u636e\u8303\u56f4 [0, 1)\uff0c\u4f7f\u7528 num * k \u6620\u5c04\u5230\u7d22\u5f15\u8303\u56f4 [0, k-1]\nlet i = Int(num * k)\n// \u5c06 num \u6dfb\u52a0\u8fdb\u6876 i\nbuckets[i].append(num)\n}\n// 2. \u5bf9\u5404\u4e2a\u6876\u6267\u884c\u6392\u5e8f\nfor i in buckets.indices {\n// \u4f7f\u7528\u5185\u7f6e\u6392\u5e8f\u51fd\u6570\uff0c\u4e5f\u53ef\u4ee5\u66ff\u6362\u6210\u5176\u4ed6\u6392\u5e8f\u7b97\u6cd5\nbuckets[i].sort()\n}\n// 3. \u904d\u5386\u6876\u5408\u5e76\u7ed3\u679c\nvar i = nums.startIndex\nfor bucket in buckets {\nfor num in bucket {\nnums[i] = num\nnums.formIndex(after: &amp;i)\n}\n}\n}\n</code></pre> bucket_sort.zig<pre><code>[class]{}-[func]{bucketSort}\n</code></pre> bucket_sort.dart<pre><code>/* \u6876\u6392\u5e8f */\nvoid bucketSort(List&lt;double&gt; nums) {\n// \u521d\u59cb\u5316 k = n/2 \u4e2a\u6876\uff0c\u9884\u671f\u5411\u6bcf\u4e2a\u6876\u5206\u914d 2 \u4e2a\u5143\u7d20\nint k = nums.length ~/ 2;\nList&lt;List&lt;double&gt;&gt; buckets = List.generate(k, (index) =&gt; []);\n// 1. \u5c06\u6570\u7ec4\u5143\u7d20\u5206\u914d\u5230\u5404\u4e2a\u6876\u4e2d\nfor (double num in nums) {\n// \u8f93\u5165\u6570\u636e\u8303\u56f4 [0, 1)\uff0c\u4f7f\u7528 num * k \u6620\u5c04\u5230\u7d22\u5f15\u8303\u56f4 [0, k-1]\nint i = (num * k).toInt();\n// \u5c06 num \u6dfb\u52a0\u8fdb\u6876 bucket_idx\nbuckets[i].add(num);\n}\n// 2. \u5bf9\u5404\u4e2a\u6876\u6267\u884c\u6392\u5e8f\nfor (List&lt;double&gt; bucket in buckets) {\nbucket.sort();\n}\n// 3. \u904d\u5386\u6876\u5408\u5e76\u7ed3\u679c\nint i = 0;\nfor (List&lt;double&gt; bucket in buckets) {\nfor (double num in bucket) {\nnums[i++] = num;\n}\n}\n}\n</code></pre> <p>\u6876\u6392\u5e8f\u7684\u9002\u7528\u573a\u666f\u662f\u4ec0\u4e48\uff1f</p> <p>\u6876\u6392\u5e8f\u9002\u7528\u4e8e\u5904\u7406\u4f53\u91cf\u5f88\u5927\u7684\u6570\u636e\u3002\u4f8b\u5982\uff0c\u8f93\u5165\u6570\u636e\u5305\u542b 100 \u4e07\u4e2a\u5143\u7d20\uff0c\u7531\u4e8e\u7a7a\u95f4\u9650\u5236\uff0c\u7cfb\u7edf\u5185\u5b58\u65e0\u6cd5\u4e00\u6b21\u6027\u52a0\u8f7d\u6240\u6709\u6570\u636e\u3002\u6b64\u65f6\uff0c\u53ef\u4ee5\u5c06\u6570\u636e\u5206\u6210 1000 \u4e2a\u6876\uff0c\u7136\u540e\u5206\u522b\u5bf9\u6bcf\u4e2a\u6876\u8fdb\u884c\u6392\u5e8f\uff0c\u6700\u540e\u5c06\u7ed3\u679c\u5408\u5e76\u3002</p>"},{"location":"chapter_sorting/bucket_sort/#1182","title":"11.8.2. \u00a0 \u7b97\u6cd5\u7279\u6027","text":"<ul> <li>\u65f6\u95f4\u590d\u6742\u5ea6 \\(O(n + k)\\) \uff1a\u5047\u8bbe\u5143\u7d20\u5728\u5404\u4e2a\u6876\u5185\u5e73\u5747\u5206\u5e03\uff0c\u90a3\u4e48\u6bcf\u4e2a\u6876\u5185\u7684\u5143\u7d20\u6570\u91cf\u4e3a \\(\\frac{n}{k}\\) \u3002\u5047\u8bbe\u6392\u5e8f\u5355\u4e2a\u6876\u4f7f\u7528 \\(O(\\frac{n}{k} \\log\\frac{n}{k})\\) \u65f6\u95f4\uff0c\u5219\u6392\u5e8f\u6240\u6709\u6876\u4f7f\u7528 \\(O(n \\log\\frac{n}{k})\\) \u65f6\u95f4\u3002\u5f53\u6876\u6570\u91cf \\(k\\) \u6bd4\u8f83\u5927\u65f6\uff0c\u65f6\u95f4\u590d\u6742\u5ea6\u5219\u8d8b\u5411\u4e8e \\(O(n)\\) \u3002\u5408\u5e76\u7ed3\u679c\u65f6\u9700\u8981\u904d\u5386 \\(n\\) \u4e2a\u6876\uff0c\u82b1\u8d39 \\(O(k)\\) \u65f6\u95f4\u3002</li> <li>\u81ea\u9002\u5e94\u6392\u5e8f\uff1a\u5728\u6700\u574f\u60c5\u51b5\u4e0b\uff0c\u6240\u6709\u6570\u636e\u88ab\u5206\u914d\u5230\u4e00\u4e2a\u6876\u4e2d\uff0c\u4e14\u6392\u5e8f\u8be5\u6876\u4f7f\u7528 \\(O(n^2)\\) \u65f6\u95f4\u3002</li> <li>\u7a7a\u95f4\u590d\u6742\u5ea6 \\(O(n + k)\\) \u3001\u975e\u539f\u5730\u6392\u5e8f \uff1a\u9700\u8981\u501f\u52a9 \\(k\\) \u4e2a\u6876\u548c\u603b\u5171 \\(n\\) \u4e2a\u5143\u7d20\u7684\u989d\u5916\u7a7a\u95f4\u3002</li> <li>\u6876\u6392\u5e8f\u662f\u5426\u7a33\u5b9a\u53d6\u51b3\u4e8e\u6392\u5e8f\u6876\u5185\u5143\u7d20\u7684\u7b97\u6cd5\u662f\u5426\u7a33\u5b9a\u3002</li> </ul>"},{"location":"chapter_sorting/bucket_sort/#1183","title":"11.8.3. \u00a0 \u5982\u4f55\u5b9e\u73b0\u5e73\u5747\u5206\u914d","text":"<p>\u6876\u6392\u5e8f\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u7406\u8bba\u4e0a\u53ef\u4ee5\u8fbe\u5230 \\(O(n)\\) \uff0c\u5173\u952e\u5728\u4e8e\u5c06\u5143\u7d20\u5747\u5300\u5206\u914d\u5230\u5404\u4e2a\u6876\u4e2d\uff0c\u56e0\u4e3a\u5b9e\u9645\u6570\u636e\u5f80\u5f80\u4e0d\u662f\u5747\u5300\u5206\u5e03\u7684\u3002\u4f8b\u5982\uff0c\u6211\u4eec\u60f3\u8981\u5c06\u6dd8\u5b9d\u4e0a\u7684\u6240\u6709\u5546\u54c1\u6309\u4ef7\u683c\u8303\u56f4\u5e73\u5747\u5206\u914d\u5230 10 \u4e2a\u6876\u4e2d\uff0c\u4f46\u5546\u54c1\u4ef7\u683c\u5206\u5e03\u4e0d\u5747\uff0c\u4f4e\u4e8e 100 \u5143\u7684\u975e\u5e38\u591a\uff0c\u9ad8\u4e8e 1000 \u5143\u7684\u975e\u5e38\u5c11\u3002\u82e5\u5c06\u4ef7\u683c\u533a\u95f4\u5e73\u5747\u5212\u5206\u4e3a 10 \u4efd\uff0c\u5404\u4e2a\u6876\u4e2d\u7684\u5546\u54c1\u6570\u91cf\u5dee\u8ddd\u4f1a\u975e\u5e38\u5927\u3002</p> <p>\u4e3a\u5b9e\u73b0\u5e73\u5747\u5206\u914d\uff0c\u6211\u4eec\u53ef\u4ee5\u5148\u8bbe\u5b9a\u4e00\u4e2a\u5927\u81f4\u7684\u5206\u754c\u7ebf\uff0c\u5c06\u6570\u636e\u7c97\u7565\u5730\u5206\u5230 3 \u4e2a\u6876\u4e2d\u3002\u5206\u914d\u5b8c\u6bd5\u540e\uff0c\u518d\u5c06\u5546\u54c1\u8f83\u591a\u7684\u6876\u7ee7\u7eed\u5212\u5206\u4e3a 3 \u4e2a\u6876\uff0c\u76f4\u81f3\u6240\u6709\u6876\u4e2d\u7684\u5143\u7d20\u6570\u91cf\u5927\u81f4\u76f8\u7b49\u3002\u8fd9\u79cd\u65b9\u6cd5\u672c\u8d28\u4e0a\u662f\u521b\u5efa\u4e00\u4e2a\u9012\u5f52\u6811\uff0c\u4f7f\u53f6\u8282\u70b9\u7684\u503c\u5c3d\u53ef\u80fd\u5e73\u5747\u3002\u5f53\u7136\uff0c\u4e0d\u4e00\u5b9a\u8981\u6bcf\u8f6e\u5c06\u6570\u636e\u5212\u5206\u4e3a 3 \u4e2a\u6876\uff0c\u5177\u4f53\u5212\u5206\u65b9\u5f0f\u53ef\u6839\u636e\u6570\u636e\u7279\u70b9\u7075\u6d3b\u9009\u62e9\u3002</p> <p></p> <p> Fig. \u9012\u5f52\u5212\u5206\u6876 </p> <p>\u5982\u679c\u6211\u4eec\u63d0\u524d\u77e5\u9053\u5546\u54c1\u4ef7\u683c\u7684\u6982\u7387\u5206\u5e03\uff0c\u5219\u53ef\u4ee5\u6839\u636e\u6570\u636e\u6982\u7387\u5206\u5e03\u8bbe\u7f6e\u6bcf\u4e2a\u6876\u7684\u4ef7\u683c\u5206\u754c\u7ebf\u3002\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u6570\u636e\u5206\u5e03\u5e76\u4e0d\u4e00\u5b9a\u9700\u8981\u7279\u610f\u7edf\u8ba1\uff0c\u4e5f\u53ef\u4ee5\u6839\u636e\u6570\u636e\u7279\u70b9\u91c7\u7528\u67d0\u79cd\u6982\u7387\u6a21\u578b\u8fdb\u884c\u8fd1\u4f3c\u3002\u5982\u4e0b\u56fe\u6240\u793a\uff0c\u6211\u4eec\u5047\u8bbe\u5546\u54c1\u4ef7\u683c\u670d\u4ece\u6b63\u6001\u5206\u5e03\uff0c\u8fd9\u6837\u5c31\u53ef\u4ee5\u5408\u7406\u5730\u8bbe\u5b9a\u4ef7\u683c\u533a\u95f4\uff0c\u4ece\u800c\u5c06\u5546\u54c1\u5e73\u5747\u5206\u914d\u5230\u5404\u4e2a\u6876\u4e2d\u3002</p> <p></p> <p> Fig. \u6839\u636e\u6982\u7387\u5206\u5e03\u5212\u5206\u6876 </p>"},{"location":"chapter_sorting/counting_sort/","title":"11.9. \u00a0 \u8ba1\u6570\u6392\u5e8f","text":"<p>\u300c\u8ba1\u6570\u6392\u5e8f Counting Sort\u300d\u901a\u8fc7\u7edf\u8ba1\u5143\u7d20\u6570\u91cf\u6765\u5b9e\u73b0\u6392\u5e8f\uff0c\u901a\u5e38\u5e94\u7528\u4e8e\u6574\u6570\u6570\u7ec4\u3002</p>"},{"location":"chapter_sorting/counting_sort/#1191","title":"11.9.1. \u00a0 \u7b80\u5355\u5b9e\u73b0","text":"<p>\u5148\u6765\u770b\u4e00\u4e2a\u7b80\u5355\u7684\u4f8b\u5b50\u3002\u7ed9\u5b9a\u4e00\u4e2a\u957f\u5ea6\u4e3a \\(n\\) \u7684\u6570\u7ec4 <code>nums</code> \uff0c\u5176\u4e2d\u7684\u5143\u7d20\u90fd\u662f\u201c\u975e\u8d1f\u6574\u6570\u201d\u3002\u8ba1\u6570\u6392\u5e8f\u7684\u6574\u4f53\u6d41\u7a0b\u5982\u4e0b\uff1a</p> <ol> <li>\u904d\u5386\u6570\u7ec4\uff0c\u627e\u51fa\u6570\u7ec4\u4e2d\u7684\u6700\u5927\u6570\u5b57\uff0c\u8bb0\u4e3a \\(m\\) \uff0c\u7136\u540e\u521b\u5efa\u4e00\u4e2a\u957f\u5ea6\u4e3a \\(m + 1\\) \u7684\u8f85\u52a9\u6570\u7ec4 <code>counter</code> \uff1b</li> <li>\u501f\u52a9 <code>counter</code> \u7edf\u8ba1 <code>nums</code> \u4e2d\u5404\u6570\u5b57\u7684\u51fa\u73b0\u6b21\u6570\uff0c\u5176\u4e2d <code>counter[num]</code> \u5bf9\u5e94\u6570\u5b57 <code>num</code> \u7684\u51fa\u73b0\u6b21\u6570\u3002\u7edf\u8ba1\u65b9\u6cd5\u5f88\u7b80\u5355\uff0c\u53ea\u9700\u904d\u5386 <code>nums</code>\uff08\u8bbe\u5f53\u524d\u6570\u5b57\u4e3a <code>num</code>\uff09\uff0c\u6bcf\u8f6e\u5c06 <code>counter[num]</code> \u589e\u52a0 \\(1\\) \u5373\u53ef\u3002</li> <li>\u7531\u4e8e <code>counter</code> \u7684\u5404\u4e2a\u7d22\u5f15\u5929\u7136\u6709\u5e8f\uff0c\u56e0\u6b64\u76f8\u5f53\u4e8e\u6240\u6709\u6570\u5b57\u5df2\u7ecf\u88ab\u6392\u5e8f\u597d\u4e86\u3002\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u904d\u5386 <code>counter</code> \uff0c\u6839\u636e\u5404\u6570\u5b57\u7684\u51fa\u73b0\u6b21\u6570\uff0c\u5c06\u5b83\u4eec\u6309\u4ece\u5c0f\u5230\u5927\u7684\u987a\u5e8f\u586b\u5165 <code>nums</code> \u5373\u53ef\u3002</li> </ol> <p></p> <p> Fig. \u8ba1\u6570\u6392\u5e8f\u6d41\u7a0b </p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart counting_sort.java<pre><code>/* \u8ba1\u6570\u6392\u5e8f */\n// \u7b80\u5355\u5b9e\u73b0\uff0c\u65e0\u6cd5\u7528\u4e8e\u6392\u5e8f\u5bf9\u8c61\nvoid countingSortNaive(int[] nums) {\n// 1. \u7edf\u8ba1\u6570\u7ec4\u6700\u5927\u5143\u7d20 m\nint m = 0;\nfor (int num : nums) {\nm = Math.max(m, num);\n}\n// 2. \u7edf\u8ba1\u5404\u6570\u5b57\u7684\u51fa\u73b0\u6b21\u6570\n// counter[num] \u4ee3\u8868 num \u7684\u51fa\u73b0\u6b21\u6570\nint[] counter = new int[m + 1];\nfor (int num : nums) {\ncounter[num]++;\n}\n// 3. \u904d\u5386 counter \uff0c\u5c06\u5404\u5143\u7d20\u586b\u5165\u539f\u6570\u7ec4 nums\nint i = 0;\nfor (int num = 0; num &lt; m + 1; num++) {\nfor (int j = 0; j &lt; counter[num]; j++, i++) {\nnums[i] = num;\n}\n}\n}\n</code></pre> counting_sort.cpp<pre><code>/* \u8ba1\u6570\u6392\u5e8f */\n// \u7b80\u5355\u5b9e\u73b0\uff0c\u65e0\u6cd5\u7528\u4e8e\u6392\u5e8f\u5bf9\u8c61\nvoid countingSortNaive(vector&lt;int&gt; &amp;nums) {\n// 1. \u7edf\u8ba1\u6570\u7ec4\u6700\u5927\u5143\u7d20 m\nint m = 0;\nfor (int num : nums) {\nm = max(m, num);\n}\n// 2. \u7edf\u8ba1\u5404\u6570\u5b57\u7684\u51fa\u73b0\u6b21\u6570\n// counter[num] \u4ee3\u8868 num \u7684\u51fa\u73b0\u6b21\u6570\nvector&lt;int&gt; counter(m + 1, 0);\nfor (int num : nums) {\ncounter[num]++;\n}\n// 3. \u904d\u5386 counter \uff0c\u5c06\u5404\u5143\u7d20\u586b\u5165\u539f\u6570\u7ec4 nums\nint i = 0;\nfor (int num = 0; num &lt; m + 1; num++) {\nfor (int j = 0; j &lt; counter[num]; j++, i++) {\nnums[i] = num;\n}\n}\n}\n</code></pre> counting_sort.py<pre><code>def counting_sort_naive(nums: list[int]) -&gt; None:\n\"\"\"\u8ba1\u6570\u6392\u5e8f\"\"\"\n# \u7b80\u5355\u5b9e\u73b0\uff0c\u65e0\u6cd5\u7528\u4e8e\u6392\u5e8f\u5bf9\u8c61\n# 1. \u7edf\u8ba1\u6570\u7ec4\u6700\u5927\u5143\u7d20 m\nm = 0\nfor num in nums:\nm = max(m, num)\n# 2. \u7edf\u8ba1\u5404\u6570\u5b57\u7684\u51fa\u73b0\u6b21\u6570\n# counter[num] \u4ee3\u8868 num \u7684\u51fa\u73b0\u6b21\u6570\ncounter = [0] * (m + 1)\nfor num in nums:\ncounter[num] += 1\n# 3. \u904d\u5386 counter \uff0c\u5c06\u5404\u5143\u7d20\u586b\u5165\u539f\u6570\u7ec4 nums\ni = 0\nfor num in range(m + 1):\nfor _ in range(counter[num]):\nnums[i] = num\ni += 1\n</code></pre> counting_sort.go<pre><code>/* \u8ba1\u6570\u6392\u5e8f */\n// \u7b80\u5355\u5b9e\u73b0\uff0c\u65e0\u6cd5\u7528\u4e8e\u6392\u5e8f\u5bf9\u8c61\nfunc countingSortNaive(nums []int) {\n// 1. \u7edf\u8ba1\u6570\u7ec4\u6700\u5927\u5143\u7d20 m\nm := 0\nfor _, num := range nums {\nif num &gt; m {\nm = num\n}\n}\n// 2. \u7edf\u8ba1\u5404\u6570\u5b57\u7684\u51fa\u73b0\u6b21\u6570\n// counter[num] \u4ee3\u8868 num \u7684\u51fa\u73b0\u6b21\u6570\ncounter := make([]int, m+1)\nfor _, num := range nums {\ncounter[num]++\n}\n// 3. \u904d\u5386 counter \uff0c\u5c06\u5404\u5143\u7d20\u586b\u5165\u539f\u6570\u7ec4 nums\nfor i, num := 0, 0; num &lt; m+1; num++ {\nfor j := 0; j &lt; counter[num]; j++ {\nnums[i] = num\ni++\n}\n}\n}\n</code></pre> counting_sort.js<pre><code>/* \u8ba1\u6570\u6392\u5e8f */\n// \u7b80\u5355\u5b9e\u73b0\uff0c\u65e0\u6cd5\u7528\u4e8e\u6392\u5e8f\u5bf9\u8c61\nfunction countingSortNaive(nums) {\n// 1. \u7edf\u8ba1\u6570\u7ec4\u6700\u5927\u5143\u7d20 m\nlet m = 0;\nfor (const num of nums) {\nm = Math.max(m, num);\n}\n// 2. \u7edf\u8ba1\u5404\u6570\u5b57\u7684\u51fa\u73b0\u6b21\u6570\n// counter[num] \u4ee3\u8868 num \u7684\u51fa\u73b0\u6b21\u6570\nconst counter = new Array(m + 1).fill(0);\nfor (const num of nums) {\ncounter[num]++;\n}\n// 3. \u904d\u5386 counter \uff0c\u5c06\u5404\u5143\u7d20\u586b\u5165\u539f\u6570\u7ec4 nums\nlet i = 0;\nfor (let num = 0; num &lt; m + 1; num++) {\nfor (let j = 0; j &lt; counter[num]; j++, i++) {\nnums[i] = num;\n}\n}\n}\n</code></pre> counting_sort.ts<pre><code>/* \u8ba1\u6570\u6392\u5e8f */\n// \u7b80\u5355\u5b9e\u73b0\uff0c\u65e0\u6cd5\u7528\u4e8e\u6392\u5e8f\u5bf9\u8c61\nfunction countingSortNaive(nums: number[]): void {\n// 1. \u7edf\u8ba1\u6570\u7ec4\u6700\u5927\u5143\u7d20 m\nlet m = 0;\nfor (const num of nums) {\nm = Math.max(m, num);\n}\n// 2. \u7edf\u8ba1\u5404\u6570\u5b57\u7684\u51fa\u73b0\u6b21\u6570\n// counter[num] \u4ee3\u8868 num \u7684\u51fa\u73b0\u6b21\u6570\nconst counter: number[] = new Array&lt;number&gt;(m + 1).fill(0);\nfor (const num of nums) {\ncounter[num]++;\n}\n// 3. \u904d\u5386 counter \uff0c\u5c06\u5404\u5143\u7d20\u586b\u5165\u539f\u6570\u7ec4 nums\nlet i = 0;\nfor (let num = 0; num &lt; m + 1; num++) {\nfor (let j = 0; j &lt; counter[num]; j++, i++) {\nnums[i] = num;\n}\n}\n}\n</code></pre> counting_sort.c<pre><code>/* \u8ba1\u6570\u6392\u5e8f */\n// \u7b80\u5355\u5b9e\u73b0\uff0c\u65e0\u6cd5\u7528\u4e8e\u6392\u5e8f\u5bf9\u8c61\nvoid countingSortNaive(int nums[], int size) {\n// 1. \u7edf\u8ba1\u6570\u7ec4\u6700\u5927\u5143\u7d20 m\nint m = 0;\nfor (int i = 0; i &lt; size; i++) {\nif (nums[i] &gt; m) {\nm = nums[i];\n}\n}\n// 2. \u7edf\u8ba1\u5404\u6570\u5b57\u7684\u51fa\u73b0\u6b21\u6570\n// counter[num] \u4ee3\u8868 num \u7684\u51fa\u73b0\u6b21\u6570\nint *counter = malloc(sizeof(int) * m);\nfor (int i = 0; i &lt; size; i++) {\ncounter[nums[i]]++;\n}\n// 3. \u904d\u5386 counter \uff0c\u5c06\u5404\u5143\u7d20\u586b\u5165\u539f\u6570\u7ec4 nums\nint i = 0;\nfor (int num = 0; num &lt; m + 1; num++) {\nfor (int j = 0; j &lt; counter[num]; j++, i++) {\nnums[i] = num;\n}\n}\n}\n</code></pre> counting_sort.cs<pre><code>/* \u8ba1\u6570\u6392\u5e8f */\n// \u7b80\u5355\u5b9e\u73b0\uff0c\u65e0\u6cd5\u7528\u4e8e\u6392\u5e8f\u5bf9\u8c61\nvoid countingSortNaive(int[] nums) {\n// 1. \u7edf\u8ba1\u6570\u7ec4\u6700\u5927\u5143\u7d20 m\nint m = 0;\nforeach (int num in nums) {\nm = Math.Max(m, num);\n}\n// 2. \u7edf\u8ba1\u5404\u6570\u5b57\u7684\u51fa\u73b0\u6b21\u6570\n// counter[num] \u4ee3\u8868 num \u7684\u51fa\u73b0\u6b21\u6570\nint[] counter = new int[m + 1];\nforeach (int num in nums) {\ncounter[num]++;\n}\n// 3. \u904d\u5386 counter \uff0c\u5c06\u5404\u5143\u7d20\u586b\u5165\u539f\u6570\u7ec4 nums\nint i = 0;\nfor (int num = 0; num &lt; m + 1; num++) {\nfor (int j = 0; j &lt; counter[num]; j++, i++) {\nnums[i] = num;\n}\n}\n}\n</code></pre> counting_sort.swift<pre><code>/* \u8ba1\u6570\u6392\u5e8f */\n// \u7b80\u5355\u5b9e\u73b0\uff0c\u65e0\u6cd5\u7528\u4e8e\u6392\u5e8f\u5bf9\u8c61\nfunc countingSortNaive(nums: inout [Int]) {\n// 1. \u7edf\u8ba1\u6570\u7ec4\u6700\u5927\u5143\u7d20 m\nlet m = nums.max()!\n// 2. \u7edf\u8ba1\u5404\u6570\u5b57\u7684\u51fa\u73b0\u6b21\u6570\n// counter[num] \u4ee3\u8868 num \u7684\u51fa\u73b0\u6b21\u6570\nvar counter = Array(repeating: 0, count: m + 1)\nfor num in nums {\ncounter[num] += 1\n}\n// 3. \u904d\u5386 counter \uff0c\u5c06\u5404\u5143\u7d20\u586b\u5165\u539f\u6570\u7ec4 nums\nvar i = 0\nfor num in stride(from: 0, to: m + 1, by: 1) {\nfor _ in stride(from: 0, to: counter[num], by: 1) {\nnums[i] = num\ni += 1\n}\n}\n}\n</code></pre> counting_sort.zig<pre><code>[class]{}-[func]{countingSortNaive}\n</code></pre> counting_sort.dart<pre><code>/* \u8ba1\u6570\u6392\u5e8f */\n// \u7b80\u5355\u5b9e\u73b0\uff0c\u65e0\u6cd5\u7528\u4e8e\u6392\u5e8f\u5bf9\u8c61\nvoid countingSortNaive(List&lt;int&gt; nums) {\n// 1. \u7edf\u8ba1\u6570\u7ec4\u6700\u5927\u5143\u7d20 m\nint m = 0;\nfor (int num in nums) {\nm = max(m, num);\n}\n// 2. \u7edf\u8ba1\u5404\u6570\u5b57\u7684\u51fa\u73b0\u6b21\u6570\n// counter[num] \u4ee3\u8868 num \u7684\u51fa\u73b0\u6b21\u6570\nList&lt;int&gt; counter = List.filled(m + 1, 0);\nfor (int num in nums) {\ncounter[num]++;\n}\n// 3. \u904d\u5386 counter \uff0c\u5c06\u5404\u5143\u7d20\u586b\u5165\u539f\u6570\u7ec4 nums\nint i = 0;\nfor (int num = 0; num &lt; m + 1; num++) {\nfor (int j = 0; j &lt; counter[num]; j++, i++) {\nnums[i] = num;\n}\n}\n}\n</code></pre> <p>\u8ba1\u6570\u6392\u5e8f\u4e0e\u6876\u6392\u5e8f\u7684\u8054\u7cfb</p> <p>\u4ece\u6876\u6392\u5e8f\u7684\u89d2\u5ea6\u770b\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u8ba1\u6570\u6392\u5e8f\u4e2d\u7684\u8ba1\u6570\u6570\u7ec4 <code>counter</code> \u7684\u6bcf\u4e2a\u7d22\u5f15\u89c6\u4e3a\u4e00\u4e2a\u6876\uff0c\u5c06\u7edf\u8ba1\u6570\u91cf\u7684\u8fc7\u7a0b\u770b\u4f5c\u662f\u5c06\u5404\u4e2a\u5143\u7d20\u5206\u914d\u5230\u5bf9\u5e94\u7684\u6876\u4e2d\u3002\u672c\u8d28\u4e0a\uff0c\u8ba1\u6570\u6392\u5e8f\u662f\u6876\u6392\u5e8f\u5728\u6574\u578b\u6570\u636e\u4e0b\u7684\u4e00\u4e2a\u7279\u4f8b\u3002</p>"},{"location":"chapter_sorting/counting_sort/#1192","title":"11.9.2. \u00a0 \u5b8c\u6574\u5b9e\u73b0","text":"<p>\u7ec6\u5fc3\u7684\u540c\u5b66\u53ef\u80fd\u53d1\u73b0\uff0c\u5982\u679c\u8f93\u5165\u6570\u636e\u662f\u5bf9\u8c61\uff0c\u4e0a\u8ff0\u6b65\u9aa4 <code>3.</code> \u5c31\u5931\u6548\u4e86\u3002\u4f8b\u5982\uff0c\u8f93\u5165\u6570\u636e\u662f\u5546\u54c1\u5bf9\u8c61\uff0c\u6211\u4eec\u60f3\u8981\u6309\u7167\u5546\u54c1\u4ef7\u683c\uff08\u7c7b\u7684\u6210\u5458\u53d8\u91cf\uff09\u5bf9\u5546\u54c1\u8fdb\u884c\u6392\u5e8f\uff0c\u800c\u4e0a\u8ff0\u7b97\u6cd5\u53ea\u80fd\u7ed9\u51fa\u4ef7\u683c\u7684\u6392\u5e8f\u7ed3\u679c\u3002</p> <p>\u90a3\u4e48\u5982\u4f55\u624d\u80fd\u5f97\u5230\u539f\u6570\u636e\u7684\u6392\u5e8f\u7ed3\u679c\u5462\uff1f\u6211\u4eec\u9996\u5148\u8ba1\u7b97 <code>counter</code> \u7684\u300c\u524d\u7f00\u548c\u300d\u3002\u987e\u540d\u601d\u4e49\uff0c\u7d22\u5f15 <code>i</code> \u5904\u7684\u524d\u7f00\u548c <code>prefix[i]</code> \u7b49\u4e8e\u6570\u7ec4\u524d <code>i</code> \u4e2a\u5143\u7d20\u4e4b\u548c\uff0c\u5373</p> \\[ \\text{prefix}[i] = \\sum_{j=0}^i \\text{counter[j]} \\] <p>\u524d\u7f00\u548c\u5177\u6709\u660e\u786e\u7684\u610f\u4e49\uff0c<code>prefix[num] - 1</code> \u4ee3\u8868\u5143\u7d20 <code>num</code> \u5728\u7ed3\u679c\u6570\u7ec4 <code>res</code> \u4e2d\u6700\u540e\u4e00\u6b21\u51fa\u73b0\u7684\u7d22\u5f15\u3002\u8fd9\u4e2a\u4fe1\u606f\u975e\u5e38\u5173\u952e\uff0c\u56e0\u4e3a\u5b83\u544a\u8bc9\u6211\u4eec\u5404\u4e2a\u5143\u7d20\u5e94\u8be5\u51fa\u73b0\u5728\u7ed3\u679c\u6570\u7ec4\u7684\u54ea\u4e2a\u4f4d\u7f6e\u3002\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u5012\u5e8f\u904d\u5386\u539f\u6570\u7ec4 <code>nums</code> \u7684\u6bcf\u4e2a\u5143\u7d20 <code>num</code> \uff0c\u5728\u6bcf\u8f6e\u8fed\u4ee3\u4e2d\u6267\u884c\uff1a</p> <ol> <li>\u5c06 <code>num</code> \u586b\u5165\u6570\u7ec4 <code>res</code> \u7684\u7d22\u5f15 <code>prefix[num] - 1</code> \u5904\uff1b</li> <li>\u4ee4\u524d\u7f00\u548c <code>prefix[num]</code> \u51cf\u5c0f \\(1\\) \uff0c\u4ece\u800c\u5f97\u5230\u4e0b\u6b21\u653e\u7f6e <code>num</code> \u7684\u7d22\u5f15\uff1b</li> </ol> <p>\u904d\u5386\u5b8c\u6210\u540e\uff0c\u6570\u7ec4 <code>res</code> \u4e2d\u5c31\u662f\u6392\u5e8f\u597d\u7684\u7ed3\u679c\uff0c\u6700\u540e\u4f7f\u7528 <code>res</code> \u8986\u76d6\u539f\u6570\u7ec4 <code>nums</code> \u5373\u53ef\u3002</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p>\u8ba1\u6570\u6392\u5e8f\u7684\u5b9e\u73b0\u4ee3\u7801\u5982\u4e0b\u6240\u793a\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart counting_sort.java<pre><code>/* \u8ba1\u6570\u6392\u5e8f */\n// \u5b8c\u6574\u5b9e\u73b0\uff0c\u53ef\u6392\u5e8f\u5bf9\u8c61\uff0c\u5e76\u4e14\u662f\u7a33\u5b9a\u6392\u5e8f\nvoid countingSort(int[] nums) {\n// 1. \u7edf\u8ba1\u6570\u7ec4\u6700\u5927\u5143\u7d20 m\nint m = 0;\nfor (int num : nums) {\nm = Math.max(m, num);\n}\n// 2. \u7edf\u8ba1\u5404\u6570\u5b57\u7684\u51fa\u73b0\u6b21\u6570\n// counter[num] \u4ee3\u8868 num \u7684\u51fa\u73b0\u6b21\u6570\nint[] counter = new int[m + 1];\nfor (int num : nums) {\ncounter[num]++;\n}\n// 3. \u6c42 counter \u7684\u524d\u7f00\u548c\uff0c\u5c06\u201c\u51fa\u73b0\u6b21\u6570\u201d\u8f6c\u6362\u4e3a\u201c\u5c3e\u7d22\u5f15\u201d\n// \u5373 counter[num]-1 \u662f num \u5728 res \u4e2d\u6700\u540e\u4e00\u6b21\u51fa\u73b0\u7684\u7d22\u5f15\nfor (int i = 0; i &lt; m; i++) {\ncounter[i + 1] += counter[i];\n}\n// 4. \u5012\u5e8f\u904d\u5386 nums \uff0c\u5c06\u5404\u5143\u7d20\u586b\u5165\u7ed3\u679c\u6570\u7ec4 res\n// \u521d\u59cb\u5316\u6570\u7ec4 res \u7528\u4e8e\u8bb0\u5f55\u7ed3\u679c\nint n = nums.length;\nint[] res = new int[n];\nfor (int i = n - 1; i &gt;= 0; i--) {\nint num = nums[i];\nres[counter[num] - 1] = num; // \u5c06 num \u653e\u7f6e\u5230\u5bf9\u5e94\u7d22\u5f15\u5904\ncounter[num]--; // \u4ee4\u524d\u7f00\u548c\u81ea\u51cf 1 \uff0c\u5f97\u5230\u4e0b\u6b21\u653e\u7f6e num \u7684\u7d22\u5f15\n}\n// \u4f7f\u7528\u7ed3\u679c\u6570\u7ec4 res \u8986\u76d6\u539f\u6570\u7ec4 nums\nfor (int i = 0; i &lt; n; i++) {\nnums[i] = res[i];\n}\n}\n</code></pre> counting_sort.cpp<pre><code>/* \u8ba1\u6570\u6392\u5e8f */\n// \u5b8c\u6574\u5b9e\u73b0\uff0c\u53ef\u6392\u5e8f\u5bf9\u8c61\uff0c\u5e76\u4e14\u662f\u7a33\u5b9a\u6392\u5e8f\nvoid countingSort(vector&lt;int&gt; &amp;nums) {\n// 1. \u7edf\u8ba1\u6570\u7ec4\u6700\u5927\u5143\u7d20 m\nint m = 0;\nfor (int num : nums) {\nm = max(m, num);\n}\n// 2. \u7edf\u8ba1\u5404\u6570\u5b57\u7684\u51fa\u73b0\u6b21\u6570\n// counter[num] \u4ee3\u8868 num \u7684\u51fa\u73b0\u6b21\u6570\nvector&lt;int&gt; counter(m + 1, 0);\nfor (int num : nums) {\ncounter[num]++;\n}\n// 3. \u6c42 counter \u7684\u524d\u7f00\u548c\uff0c\u5c06\u201c\u51fa\u73b0\u6b21\u6570\u201d\u8f6c\u6362\u4e3a\u201c\u5c3e\u7d22\u5f15\u201d\n// \u5373 counter[num]-1 \u662f num \u5728 res \u4e2d\u6700\u540e\u4e00\u6b21\u51fa\u73b0\u7684\u7d22\u5f15\nfor (int i = 0; i &lt; m; i++) {\ncounter[i + 1] += counter[i];\n}\n// 4. \u5012\u5e8f\u904d\u5386 nums \uff0c\u5c06\u5404\u5143\u7d20\u586b\u5165\u7ed3\u679c\u6570\u7ec4 res\n// \u521d\u59cb\u5316\u6570\u7ec4 res \u7528\u4e8e\u8bb0\u5f55\u7ed3\u679c\nint n = nums.size();\nvector&lt;int&gt; res(n);\nfor (int i = n - 1; i &gt;= 0; i--) {\nint num = nums[i];\nres[counter[num] - 1] = num; // \u5c06 num \u653e\u7f6e\u5230\u5bf9\u5e94\u7d22\u5f15\u5904\ncounter[num]--;              // \u4ee4\u524d\u7f00\u548c\u81ea\u51cf 1 \uff0c\u5f97\u5230\u4e0b\u6b21\u653e\u7f6e num \u7684\u7d22\u5f15\n}\n// \u4f7f\u7528\u7ed3\u679c\u6570\u7ec4 res \u8986\u76d6\u539f\u6570\u7ec4 nums\nnums = res;\n}\n</code></pre> counting_sort.py<pre><code>def counting_sort(nums: list[int]) -&gt; None:\n\"\"\"\u8ba1\u6570\u6392\u5e8f\"\"\"\n# \u5b8c\u6574\u5b9e\u73b0\uff0c\u53ef\u6392\u5e8f\u5bf9\u8c61\uff0c\u5e76\u4e14\u662f\u7a33\u5b9a\u6392\u5e8f\n# 1. \u7edf\u8ba1\u6570\u7ec4\u6700\u5927\u5143\u7d20 m\nm = max(nums)\n# 2. \u7edf\u8ba1\u5404\u6570\u5b57\u7684\u51fa\u73b0\u6b21\u6570\n# counter[num] \u4ee3\u8868 num \u7684\u51fa\u73b0\u6b21\u6570\ncounter = [0] * (m + 1)\nfor num in nums:\ncounter[num] += 1\n# 3. \u6c42 counter \u7684\u524d\u7f00\u548c\uff0c\u5c06\u201c\u51fa\u73b0\u6b21\u6570\u201d\u8f6c\u6362\u4e3a\u201c\u5c3e\u7d22\u5f15\u201d\n# \u5373 counter[num]-1 \u662f num \u5728 res \u4e2d\u6700\u540e\u4e00\u6b21\u51fa\u73b0\u7684\u7d22\u5f15\nfor i in range(m):\ncounter[i + 1] += counter[i]\n# 4. \u5012\u5e8f\u904d\u5386 nums \uff0c\u5c06\u5404\u5143\u7d20\u586b\u5165\u7ed3\u679c\u6570\u7ec4 res\n# \u521d\u59cb\u5316\u6570\u7ec4 res \u7528\u4e8e\u8bb0\u5f55\u7ed3\u679c\nn = len(nums)\nres = [0] * n\nfor i in range(n - 1, -1, -1):\nnum = nums[i]\nres[counter[num] - 1] = num  # \u5c06 num \u653e\u7f6e\u5230\u5bf9\u5e94\u7d22\u5f15\u5904\ncounter[num] -= 1  # \u4ee4\u524d\u7f00\u548c\u81ea\u51cf 1 \uff0c\u5f97\u5230\u4e0b\u6b21\u653e\u7f6e num \u7684\u7d22\u5f15\n# \u4f7f\u7528\u7ed3\u679c\u6570\u7ec4 res \u8986\u76d6\u539f\u6570\u7ec4 nums\nfor i in range(n):\nnums[i] = res[i]\n</code></pre> counting_sort.go<pre><code>/* \u8ba1\u6570\u6392\u5e8f */\n// \u5b8c\u6574\u5b9e\u73b0\uff0c\u53ef\u6392\u5e8f\u5bf9\u8c61\uff0c\u5e76\u4e14\u662f\u7a33\u5b9a\u6392\u5e8f\nfunc countingSort(nums []int) {\n// 1. \u7edf\u8ba1\u6570\u7ec4\u6700\u5927\u5143\u7d20 m\nm := 0\nfor _, num := range nums {\nif num &gt; m {\nm = num\n}\n}\n// 2. \u7edf\u8ba1\u5404\u6570\u5b57\u7684\u51fa\u73b0\u6b21\u6570\n// counter[num] \u4ee3\u8868 num \u7684\u51fa\u73b0\u6b21\u6570\ncounter := make([]int, m+1)\nfor _, num := range nums {\ncounter[num]++\n}\n// 3. \u6c42 counter \u7684\u524d\u7f00\u548c\uff0c\u5c06\u201c\u51fa\u73b0\u6b21\u6570\u201d\u8f6c\u6362\u4e3a\u201c\u5c3e\u7d22\u5f15\u201d\n// \u5373 counter[num]-1 \u662f num \u5728 res \u4e2d\u6700\u540e\u4e00\u6b21\u51fa\u73b0\u7684\u7d22\u5f15\nfor i := 0; i &lt; m; i++ {\ncounter[i+1] += counter[i]\n}\n// 4. \u5012\u5e8f\u904d\u5386 nums \uff0c\u5c06\u5404\u5143\u7d20\u586b\u5165\u7ed3\u679c\u6570\u7ec4 res\n// \u521d\u59cb\u5316\u6570\u7ec4 res \u7528\u4e8e\u8bb0\u5f55\u7ed3\u679c\nn := len(nums)\nres := make([]int, n)\nfor i := n - 1; i &gt;= 0; i-- {\nnum := nums[i]\n// \u5c06 num \u653e\u7f6e\u5230\u5bf9\u5e94\u7d22\u5f15\u5904\nres[counter[num]-1] = num\n// \u4ee4\u524d\u7f00\u548c\u81ea\u51cf 1 \uff0c\u5f97\u5230\u4e0b\u6b21\u653e\u7f6e num \u7684\u7d22\u5f15\ncounter[num]--\n}\n// \u4f7f\u7528\u7ed3\u679c\u6570\u7ec4 res \u8986\u76d6\u539f\u6570\u7ec4 nums\ncopy(nums, res)\n}\n</code></pre> counting_sort.js<pre><code>/* \u8ba1\u6570\u6392\u5e8f */\n// \u5b8c\u6574\u5b9e\u73b0\uff0c\u53ef\u6392\u5e8f\u5bf9\u8c61\uff0c\u5e76\u4e14\u662f\u7a33\u5b9a\u6392\u5e8f\nfunction countingSort(nums) {\n// 1. \u7edf\u8ba1\u6570\u7ec4\u6700\u5927\u5143\u7d20 m\nlet m = 0;\nfor (const num of nums) {\nm = Math.max(m, num);\n}\n// 2. \u7edf\u8ba1\u5404\u6570\u5b57\u7684\u51fa\u73b0\u6b21\u6570\n// counter[num] \u4ee3\u8868 num \u7684\u51fa\u73b0\u6b21\u6570\nconst counter = new Array(m + 1).fill(0);\nfor (const num of nums) {\ncounter[num]++;\n}\n// 3. \u6c42 counter \u7684\u524d\u7f00\u548c\uff0c\u5c06\u201c\u51fa\u73b0\u6b21\u6570\u201d\u8f6c\u6362\u4e3a\u201c\u5c3e\u7d22\u5f15\u201d\n// \u5373 counter[num]-1 \u662f num \u5728 res \u4e2d\u6700\u540e\u4e00\u6b21\u51fa\u73b0\u7684\u7d22\u5f15\nfor (let i = 0; i &lt; m; i++) {\ncounter[i + 1] += counter[i];\n}\n// 4. \u5012\u5e8f\u904d\u5386 nums \uff0c\u5c06\u5404\u5143\u7d20\u586b\u5165\u7ed3\u679c\u6570\u7ec4 res\n// \u521d\u59cb\u5316\u6570\u7ec4 res \u7528\u4e8e\u8bb0\u5f55\u7ed3\u679c\nconst n = nums.length;\nconst res = new Array(n);\nfor (let i = n - 1; i &gt;= 0; i--) {\nconst num = nums[i];\nres[counter[num] - 1] = num; // \u5c06 num \u653e\u7f6e\u5230\u5bf9\u5e94\u7d22\u5f15\u5904\ncounter[num]--; // \u4ee4\u524d\u7f00\u548c\u81ea\u51cf 1 \uff0c\u5f97\u5230\u4e0b\u6b21\u653e\u7f6e num \u7684\u7d22\u5f15\n}\n// \u4f7f\u7528\u7ed3\u679c\u6570\u7ec4 res \u8986\u76d6\u539f\u6570\u7ec4 nums\nfor (let i = 0; i &lt; n; i++) {\nnums[i] = res[i];\n}\n}\n</code></pre> counting_sort.ts<pre><code>/* \u8ba1\u6570\u6392\u5e8f */\n// \u5b8c\u6574\u5b9e\u73b0\uff0c\u53ef\u6392\u5e8f\u5bf9\u8c61\uff0c\u5e76\u4e14\u662f\u7a33\u5b9a\u6392\u5e8f\nfunction countingSort(nums: number[]): void {\n// 1. \u7edf\u8ba1\u6570\u7ec4\u6700\u5927\u5143\u7d20 m\nlet m = 0;\nfor (const num of nums) {\nm = Math.max(m, num);\n}\n// 2. \u7edf\u8ba1\u5404\u6570\u5b57\u7684\u51fa\u73b0\u6b21\u6570\n// counter[num] \u4ee3\u8868 num \u7684\u51fa\u73b0\u6b21\u6570\nconst counter: number[] = new Array&lt;number&gt;(m + 1).fill(0);\nfor (const num of nums) {\ncounter[num]++;\n}\n// 3. \u6c42 counter \u7684\u524d\u7f00\u548c\uff0c\u5c06\u201c\u51fa\u73b0\u6b21\u6570\u201d\u8f6c\u6362\u4e3a\u201c\u5c3e\u7d22\u5f15\u201d\n// \u5373 counter[num]-1 \u662f num \u5728 res \u4e2d\u6700\u540e\u4e00\u6b21\u51fa\u73b0\u7684\u7d22\u5f15\nfor (let i = 0; i &lt; m; i++) {\ncounter[i + 1] += counter[i];\n}\n// 4. \u5012\u5e8f\u904d\u5386 nums \uff0c\u5c06\u5404\u5143\u7d20\u586b\u5165\u7ed3\u679c\u6570\u7ec4 res\n// \u521d\u59cb\u5316\u6570\u7ec4 res \u7528\u4e8e\u8bb0\u5f55\u7ed3\u679c\nconst n = nums.length;\nconst res: number[] = new Array&lt;number&gt;(n);\nfor (let i = n - 1; i &gt;= 0; i--) {\nconst num = nums[i];\nres[counter[num] - 1] = num; // \u5c06 num \u653e\u7f6e\u5230\u5bf9\u5e94\u7d22\u5f15\u5904\ncounter[num]--; // \u4ee4\u524d\u7f00\u548c\u81ea\u51cf 1 \uff0c\u5f97\u5230\u4e0b\u6b21\u653e\u7f6e num \u7684\u7d22\u5f15\n}\n// \u4f7f\u7528\u7ed3\u679c\u6570\u7ec4 res \u8986\u76d6\u539f\u6570\u7ec4 nums\nfor (let i = 0; i &lt; n; i++) {\nnums[i] = res[i];\n}\n}\n</code></pre> counting_sort.c<pre><code>/* \u8ba1\u6570\u6392\u5e8f */\n// \u5b8c\u6574\u5b9e\u73b0\uff0c\u53ef\u6392\u5e8f\u5bf9\u8c61\uff0c\u5e76\u4e14\u662f\u7a33\u5b9a\u6392\u5e8f\nvoid countingSort(int nums[], int size) {\n// 1. \u7edf\u8ba1\u6570\u7ec4\u6700\u5927\u5143\u7d20 m\nint m = 0;\nfor (int i = 0; i &lt; size; i++) {\nif (nums[i] &gt; m) {\nm = nums[i];\n}\n}\n// 2. \u7edf\u8ba1\u5404\u6570\u5b57\u7684\u51fa\u73b0\u6b21\u6570\n// counter[num] \u4ee3\u8868 num \u7684\u51fa\u73b0\u6b21\u6570\nint *counter = malloc(sizeof(int) * m);\nfor (int i = 0; i &lt; size; i++) {\ncounter[nums[i]]++;\n}\n// 3. \u6c42 counter \u7684\u524d\u7f00\u548c\uff0c\u5c06\u201c\u51fa\u73b0\u6b21\u6570\u201d\u8f6c\u6362\u4e3a\u201c\u5c3e\u7d22\u5f15\u201d\n// \u5373 counter[num]-1 \u662f num \u5728 res \u4e2d\u6700\u540e\u4e00\u6b21\u51fa\u73b0\u7684\u7d22\u5f15\nfor (int i = 0; i &lt; m; i++) {\ncounter[i + 1] += counter[i];\n}\n// 4. \u5012\u5e8f\u904d\u5386 nums \uff0c\u5c06\u5404\u5143\u7d20\u586b\u5165\u7ed3\u679c\u6570\u7ec4 res\n// \u521d\u59cb\u5316\u6570\u7ec4 res \u7528\u4e8e\u8bb0\u5f55\u7ed3\u679c\nint *res = malloc(sizeof(int) * size);\nfor (int i = size - 1; i &gt;= 0; i--) {\nint num = nums[i];\nres[counter[num] - 1] = num; // \u5c06 num \u653e\u7f6e\u5230\u5bf9\u5e94\u7d22\u5f15\u5904\ncounter[num]--;              // \u4ee4\u524d\u7f00\u548c\u81ea\u51cf 1 \uff0c\u5f97\u5230\u4e0b\u6b21\u653e\u7f6e num \u7684\u7d22\u5f15\n}\n// \u4f7f\u7528\u7ed3\u679c\u6570\u7ec4 res \u8986\u76d6\u539f\u6570\u7ec4 nums\nmemcpy(nums, res, size * sizeof(int));\n}\n</code></pre> counting_sort.cs<pre><code>/* \u8ba1\u6570\u6392\u5e8f */\n// \u5b8c\u6574\u5b9e\u73b0\uff0c\u53ef\u6392\u5e8f\u5bf9\u8c61\uff0c\u5e76\u4e14\u662f\u7a33\u5b9a\u6392\u5e8f\nvoid countingSort(int[] nums) {\n// 1. \u7edf\u8ba1\u6570\u7ec4\u6700\u5927\u5143\u7d20 m\nint m = 0;\nforeach (int num in nums) {\nm = Math.Max(m, num);\n}\n// 2. \u7edf\u8ba1\u5404\u6570\u5b57\u7684\u51fa\u73b0\u6b21\u6570\n// counter[num] \u4ee3\u8868 num \u7684\u51fa\u73b0\u6b21\u6570\nint[] counter = new int[m + 1];\nforeach (int num in nums) {\ncounter[num]++;\n}\n// 3. \u6c42 counter \u7684\u524d\u7f00\u548c\uff0c\u5c06\u201c\u51fa\u73b0\u6b21\u6570\u201d\u8f6c\u6362\u4e3a\u201c\u5c3e\u7d22\u5f15\u201d\n// \u5373 counter[num]-1 \u662f num \u5728 res \u4e2d\u6700\u540e\u4e00\u6b21\u51fa\u73b0\u7684\u7d22\u5f15\nfor (int i = 0; i &lt; m; i++) {\ncounter[i + 1] += counter[i];\n}\n// 4. \u5012\u5e8f\u904d\u5386 nums \uff0c\u5c06\u5404\u5143\u7d20\u586b\u5165\u7ed3\u679c\u6570\u7ec4 res\n// \u521d\u59cb\u5316\u6570\u7ec4 res \u7528\u4e8e\u8bb0\u5f55\u7ed3\u679c\nint n = nums.Length;\nint[] res = new int[n];\nfor (int i = n - 1; i &gt;= 0; i--) {\nint num = nums[i];\nres[counter[num] - 1] = num; // \u5c06 num \u653e\u7f6e\u5230\u5bf9\u5e94\u7d22\u5f15\u5904\ncounter[num]--; // \u4ee4\u524d\u7f00\u548c\u81ea\u51cf 1 \uff0c\u5f97\u5230\u4e0b\u6b21\u653e\u7f6e num \u7684\u7d22\u5f15\n}\n// \u4f7f\u7528\u7ed3\u679c\u6570\u7ec4 res \u8986\u76d6\u539f\u6570\u7ec4 nums\nfor (int i = 0; i &lt; n; i++) {\nnums[i] = res[i];\n}\n}\n</code></pre> counting_sort.swift<pre><code>/* \u8ba1\u6570\u6392\u5e8f */\n// \u5b8c\u6574\u5b9e\u73b0\uff0c\u53ef\u6392\u5e8f\u5bf9\u8c61\uff0c\u5e76\u4e14\u662f\u7a33\u5b9a\u6392\u5e8f\nfunc countingSort(nums: inout [Int]) {\n// 1. \u7edf\u8ba1\u6570\u7ec4\u6700\u5927\u5143\u7d20 m\nlet m = nums.max()!\n// 2. \u7edf\u8ba1\u5404\u6570\u5b57\u7684\u51fa\u73b0\u6b21\u6570\n// counter[num] \u4ee3\u8868 num \u7684\u51fa\u73b0\u6b21\u6570\nvar counter = Array(repeating: 0, count: m + 1)\nfor num in nums {\ncounter[num] += 1\n}\n// 3. \u6c42 counter \u7684\u524d\u7f00\u548c\uff0c\u5c06\u201c\u51fa\u73b0\u6b21\u6570\u201d\u8f6c\u6362\u4e3a\u201c\u5c3e\u7d22\u5f15\u201d\n// \u5373 counter[num]-1 \u662f num \u5728 res \u4e2d\u6700\u540e\u4e00\u6b21\u51fa\u73b0\u7684\u7d22\u5f15\nfor i in stride(from: 0, to: m, by: 1) {\ncounter[i + 1] += counter[i]\n}\n// 4. \u5012\u5e8f\u904d\u5386 nums \uff0c\u5c06\u5404\u5143\u7d20\u586b\u5165\u7ed3\u679c\u6570\u7ec4 res\n// \u521d\u59cb\u5316\u6570\u7ec4 res \u7528\u4e8e\u8bb0\u5f55\u7ed3\u679c\nvar res = Array(repeating: 0, count: nums.count)\nfor i in stride(from: nums.count - 1, through: 0, by: -1) {\nlet num = nums[i]\nres[counter[num] - 1] = num // \u5c06 num \u653e\u7f6e\u5230\u5bf9\u5e94\u7d22\u5f15\u5904\ncounter[num] -= 1 // \u4ee4\u524d\u7f00\u548c\u81ea\u51cf 1 \uff0c\u5f97\u5230\u4e0b\u6b21\u653e\u7f6e num \u7684\u7d22\u5f15\n}\n// \u4f7f\u7528\u7ed3\u679c\u6570\u7ec4 res \u8986\u76d6\u539f\u6570\u7ec4 nums\nfor i in stride(from: 0, to: nums.count, by: 1) {\nnums[i] = res[i]\n}\n}\n</code></pre> counting_sort.zig<pre><code>[class]{}-[func]{countingSort}\n</code></pre> counting_sort.dart<pre><code>/* \u8ba1\u6570\u6392\u5e8f */\n// \u5b8c\u6574\u5b9e\u73b0\uff0c\u53ef\u6392\u5e8f\u5bf9\u8c61\uff0c\u5e76\u4e14\u662f\u7a33\u5b9a\u6392\u5e8f\nvoid countingSort(List&lt;int&gt; nums) {\n// 1. \u7edf\u8ba1\u6570\u7ec4\u6700\u5927\u5143\u7d20 m\nint m = 0;\nfor (int num in nums) {\nm = max(m, num);\n}\n// 2. \u7edf\u8ba1\u5404\u6570\u5b57\u7684\u51fa\u73b0\u6b21\u6570\n// counter[num] \u4ee3\u8868 num \u7684\u51fa\u73b0\u6b21\u6570\nList&lt;int&gt; counter = List.filled(m + 1, 0);\nfor (int num in nums) {\ncounter[num]++;\n}\n// 3. \u6c42 counter \u7684\u524d\u7f00\u548c\uff0c\u5c06\u201c\u51fa\u73b0\u6b21\u6570\u201d\u8f6c\u6362\u4e3a\u201c\u5c3e\u7d22\u5f15\u201d\n// \u5373 counter[num]-1 \u662f num \u5728 res \u4e2d\u6700\u540e\u4e00\u6b21\u51fa\u73b0\u7684\u7d22\u5f15\nfor (int i = 0; i &lt; m; i++) {\ncounter[i + 1] += counter[i];\n}\n// 4. \u5012\u5e8f\u904d\u5386 nums \uff0c\u5c06\u5404\u5143\u7d20\u586b\u5165\u7ed3\u679c\u6570\u7ec4 res\n// \u521d\u59cb\u5316\u6570\u7ec4 res \u7528\u4e8e\u8bb0\u5f55\u7ed3\u679c\nint n = nums.length;\nList&lt;int&gt; res = List.filled(n, 0);\nfor (int i = n - 1; i &gt;= 0; i--) {\nint num = nums[i];\nres[counter[num] - 1] = num; // \u5c06 num \u653e\u7f6e\u5230\u5bf9\u5e94\u7d22\u5f15\u5904\ncounter[num]--;              // \u4ee4\u524d\u7f00\u548c\u81ea\u51cf 1 \uff0c\u5f97\u5230\u4e0b\u6b21\u653e\u7f6e num \u7684\u7d22\u5f15\n}\n// \u4f7f\u7528\u7ed3\u679c\u6570\u7ec4 res \u8986\u76d6\u539f\u6570\u7ec4 nums\nnums.setAll(0, res);\n}\n</code></pre>"},{"location":"chapter_sorting/counting_sort/#1193","title":"11.9.3. \u00a0 \u7b97\u6cd5\u7279\u6027","text":"<ul> <li>\u65f6\u95f4\u590d\u6742\u5ea6 \\(O(n + m)\\) \uff1a\u6d89\u53ca\u904d\u5386 <code>nums</code> \u548c\u904d\u5386 <code>counter</code> \uff0c\u90fd\u4f7f\u7528\u7ebf\u6027\u65f6\u95f4\u3002\u4e00\u822c\u60c5\u51b5\u4e0b \\(n \\gg m\\) \uff0c\u65f6\u95f4\u590d\u6742\u5ea6\u8d8b\u4e8e \\(O(n)\\) \u3002</li> <li>\u7a7a\u95f4\u590d\u6742\u5ea6 \\(O(n + m)\\) \u3001\u975e\u539f\u5730\u6392\u5e8f \uff1a\u501f\u52a9\u4e86\u957f\u5ea6\u5206\u522b\u4e3a \\(n\\) \u548c \\(m\\) \u7684\u6570\u7ec4 <code>res</code> \u548c <code>counter</code> \u3002</li> <li>\u7a33\u5b9a\u6392\u5e8f\uff1a\u7531\u4e8e\u5411 <code>res</code> \u4e2d\u586b\u5145\u5143\u7d20\u7684\u987a\u5e8f\u662f\u201c\u4ece\u53f3\u5411\u5de6\u201d\u7684\uff0c\u56e0\u6b64\u5012\u5e8f\u904d\u5386 <code>nums</code> \u53ef\u4ee5\u907f\u514d\u6539\u53d8\u76f8\u7b49\u5143\u7d20\u4e4b\u95f4\u7684\u76f8\u5bf9\u4f4d\u7f6e\uff0c\u4ece\u800c\u5b9e\u73b0\u7a33\u5b9a\u6392\u5e8f\u3002\u5b9e\u9645\u4e0a\uff0c\u6b63\u5e8f\u904d\u5386 <code>nums</code> \u4e5f\u53ef\u4ee5\u5f97\u5230\u6b63\u786e\u7684\u6392\u5e8f\u7ed3\u679c\uff0c\u4f46\u7ed3\u679c\u662f\u975e\u7a33\u5b9a\u7684\u3002</li> </ul>"},{"location":"chapter_sorting/counting_sort/#1194","title":"11.9.4. \u00a0 \u5c40\u9650\u6027","text":"<p>\u770b\u5230\u8fd9\u91cc\uff0c\u4f60\u4e5f\u8bb8\u4f1a\u89c9\u5f97\u8ba1\u6570\u6392\u5e8f\u975e\u5e38\u5de7\u5999\uff0c\u4ec5\u901a\u8fc7\u7edf\u8ba1\u6570\u91cf\u5c31\u53ef\u4ee5\u5b9e\u73b0\u9ad8\u6548\u7684\u6392\u5e8f\u5de5\u4f5c\u3002\u7136\u800c\uff0c\u4f7f\u7528\u8ba1\u6570\u6392\u5e8f\u7684\u524d\u7f6e\u6761\u4ef6\u76f8\u5bf9\u8f83\u4e3a\u4e25\u683c\u3002</p> <p>\u8ba1\u6570\u6392\u5e8f\u53ea\u9002\u7528\u4e8e\u975e\u8d1f\u6574\u6570\u3002\u82e5\u60f3\u8981\u5c06\u5176\u7528\u4e8e\u5176\u4ed6\u7c7b\u578b\u7684\u6570\u636e\uff0c\u9700\u8981\u786e\u4fdd\u8fd9\u4e9b\u6570\u636e\u53ef\u4ee5\u88ab\u8f6c\u6362\u4e3a\u975e\u8d1f\u6574\u6570\uff0c\u5e76\u4e14\u5728\u8f6c\u6362\u8fc7\u7a0b\u4e2d\u4e0d\u80fd\u6539\u53d8\u5404\u4e2a\u5143\u7d20\u4e4b\u95f4\u7684\u76f8\u5bf9\u5927\u5c0f\u5173\u7cfb\u3002\u4f8b\u5982\uff0c\u5bf9\u4e8e\u5305\u542b\u8d1f\u6570\u7684\u6574\u6570\u6570\u7ec4\uff0c\u53ef\u4ee5\u5148\u7ed9\u6240\u6709\u6570\u5b57\u52a0\u4e0a\u4e00\u4e2a\u5e38\u6570\uff0c\u5c06\u5168\u90e8\u6570\u5b57\u8f6c\u5316\u4e3a\u6b63\u6570\uff0c\u6392\u5e8f\u5b8c\u6210\u540e\u518d\u8f6c\u6362\u56de\u53bb\u5373\u53ef\u3002</p> <p>\u8ba1\u6570\u6392\u5e8f\u9002\u7528\u4e8e\u6570\u636e\u91cf\u5927\u4f46\u6570\u636e\u8303\u56f4\u8f83\u5c0f\u7684\u60c5\u51b5\u3002\u6bd4\u5982\uff0c\u5728\u4e0a\u8ff0\u793a\u4f8b\u4e2d \\(m\\) \u4e0d\u80fd\u592a\u5927\uff0c\u5426\u5219\u4f1a\u5360\u7528\u8fc7\u591a\u7a7a\u95f4\u3002\u800c\u5f53 \\(n \\ll m\\) \u65f6\uff0c\u8ba1\u6570\u6392\u5e8f\u4f7f\u7528 \\(O(m)\\) \u65f6\u95f4\uff0c\u53ef\u80fd\u6bd4 \\(O(n \\log n)\\) \u7684\u6392\u5e8f\u7b97\u6cd5\u8fd8\u8981\u6162\u3002</p>"},{"location":"chapter_sorting/heap_sort/","title":"11.7. \u00a0 \u5806\u6392\u5e8f","text":"<p>Tip</p> <p>\u9605\u8bfb\u672c\u8282\u524d\uff0c\u8bf7\u786e\u4fdd\u5df2\u5b66\u5b8c\u300c\u5806\u300d\u7ae0\u8282\u3002</p> <p>\u300c\u5806\u6392\u5e8f Heap Sort\u300d\u662f\u4e00\u79cd\u57fa\u4e8e\u5806\u6570\u636e\u7ed3\u6784\u5b9e\u73b0\u7684\u9ad8\u6548\u6392\u5e8f\u7b97\u6cd5\u3002\u6211\u4eec\u53ef\u4ee5\u5229\u7528\u5df2\u7ecf\u5b66\u8fc7\u7684\u201c\u5efa\u5806\u64cd\u4f5c\u201d\u548c\u201c\u5143\u7d20\u51fa\u5806\u64cd\u4f5c\u201d\u5b9e\u73b0\u5806\u6392\u5e8f\uff1a</p> <ol> <li>\u8f93\u5165\u6570\u7ec4\u5e76\u5efa\u7acb\u5c0f\u9876\u5806\uff0c\u6b64\u65f6\u6700\u5c0f\u5143\u7d20\u4f4d\u4e8e\u5806\u9876\u3002</li> <li>\u4e0d\u65ad\u6267\u884c\u51fa\u5806\u64cd\u4f5c\uff0c\u4f9d\u6b21\u8bb0\u5f55\u51fa\u5806\u5143\u7d20\uff0c\u5373\u53ef\u5f97\u5230\u4ece\u5c0f\u5230\u5927\u6392\u5e8f\u7684\u5e8f\u5217\u3002</li> </ol> <p>\u4ee5\u4e0a\u65b9\u6cd5\u867d\u7136\u53ef\u884c\uff0c\u4f46\u9700\u8981\u501f\u52a9\u4e00\u4e2a\u989d\u5916\u6570\u7ec4\u6765\u4fdd\u5b58\u5f39\u51fa\u7684\u5143\u7d20\uff0c\u6bd4\u8f83\u6d6a\u8d39\u7a7a\u95f4\u3002\u5728\u5b9e\u9645\u4e2d\uff0c\u6211\u4eec\u901a\u5e38\u4f7f\u7528\u4e00\u79cd\u66f4\u52a0\u4f18\u96c5\u7684\u5b9e\u73b0\u65b9\u5f0f\u3002</p>"},{"location":"chapter_sorting/heap_sort/#1171","title":"11.7.1. \u00a0 \u7b97\u6cd5\u6d41\u7a0b","text":"<p>\u8bbe\u6570\u7ec4\u7684\u957f\u5ea6\u4e3a \\(n\\) \uff0c\u5806\u6392\u5e8f\u7684\u6d41\u7a0b\u5982\u4e0b\uff1a</p> <ol> <li>\u8f93\u5165\u6570\u7ec4\u5e76\u5efa\u7acb\u5927\u9876\u5806\u3002\u5b8c\u6210\u540e\uff0c\u6700\u5927\u5143\u7d20\u4f4d\u4e8e\u5806\u9876\u3002</li> <li>\u5c06\u5806\u9876\u5143\u7d20\uff08\u7b2c\u4e00\u4e2a\u5143\u7d20\uff09\u4e0e\u5806\u5e95\u5143\u7d20\uff08\u6700\u540e\u4e00\u4e2a\u5143\u7d20\uff09\u4ea4\u6362\u3002\u5b8c\u6210\u4ea4\u6362\u540e\uff0c\u5806\u7684\u957f\u5ea6\u51cf \\(1\\) \uff0c\u5df2\u6392\u5e8f\u5143\u7d20\u6570\u91cf\u52a0 \\(1\\) \u3002</li> <li>\u4ece\u5806\u9876\u5143\u7d20\u5f00\u59cb\uff0c\u4ece\u9876\u5230\u5e95\u6267\u884c\u5806\u5316\u64cd\u4f5c\uff08Sift Down\uff09\u3002\u5b8c\u6210\u5806\u5316\u540e\uff0c\u5806\u7684\u6027\u8d28\u5f97\u5230\u4fee\u590d\u3002</li> <li>\u5faa\u73af\u6267\u884c\u7b2c <code>2.</code> \u548c <code>3.</code> \u6b65\u3002\u5faa\u73af \\(n - 1\\) \u8f6e\u540e\uff0c\u5373\u53ef\u5b8c\u6210\u6570\u7ec4\u6392\u5e8f\u3002</li> </ol> <p>\u5b9e\u9645\u4e0a\uff0c\u5143\u7d20\u51fa\u5806\u64cd\u4f5c\u4e2d\u4e5f\u5305\u542b\u7b2c <code>2.</code> \u548c <code>3.</code> \u6b65\uff0c\u53ea\u662f\u591a\u4e86\u4e00\u4e2a\u5f39\u51fa\u5143\u7d20\u7684\u6b65\u9aa4\u3002</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt;&lt;11&gt;&lt;12&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p>\u5728\u4ee3\u7801\u5b9e\u73b0\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528\u4e86\u4e0e\u5806\u7ae0\u8282\u76f8\u540c\u7684\u4ece\u9876\u81f3\u5e95\u5806\u5316\uff08Sift Down\uff09\u7684\u51fd\u6570\u3002\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u7531\u4e8e\u5806\u7684\u957f\u5ea6\u4f1a\u968f\u7740\u63d0\u53d6\u6700\u5927\u5143\u7d20\u800c\u51cf\u5c0f\uff0c\u56e0\u6b64\u6211\u4eec\u9700\u8981\u7ed9 Sift Down \u51fd\u6570\u6dfb\u52a0\u4e00\u4e2a\u957f\u5ea6\u53c2\u6570 \\(n\\) \uff0c\u7528\u4e8e\u6307\u5b9a\u5806\u7684\u5f53\u524d\u6709\u6548\u957f\u5ea6\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart heap_sort.java<pre><code>/* \u5806\u7684\u957f\u5ea6\u4e3a n \uff0c\u4ece\u8282\u70b9 i \u5f00\u59cb\uff0c\u4ece\u9876\u81f3\u5e95\u5806\u5316 */\nvoid siftDown(int[] nums, int n, int i) {\nwhile (true) {\n// \u5224\u65ad\u8282\u70b9 i, l, r \u4e2d\u503c\u6700\u5927\u7684\u8282\u70b9\uff0c\u8bb0\u4e3a ma\nint l = 2 * i + 1;\nint r = 2 * i + 2;\nint ma = i;\nif (l &lt; n &amp;&amp; nums[l] &gt; nums[ma])\nma = l;\nif (r &lt; n &amp;&amp; nums[r] &gt; nums[ma])\nma = r;\n// \u82e5\u8282\u70b9 i \u6700\u5927\u6216\u7d22\u5f15 l, r \u8d8a\u754c\uff0c\u5219\u65e0\u9700\u7ee7\u7eed\u5806\u5316\uff0c\u8df3\u51fa\nif (ma == i)\nbreak;\n// \u4ea4\u6362\u4e24\u8282\u70b9\nint temp = nums[i];\nnums[i] = nums[ma];\nnums[ma] = temp;\n// \u5faa\u73af\u5411\u4e0b\u5806\u5316\ni = ma;\n}\n}\n/* \u5806\u6392\u5e8f */\nvoid heapSort(int[] nums) {\n// \u5efa\u5806\u64cd\u4f5c\uff1a\u5806\u5316\u9664\u53f6\u8282\u70b9\u4ee5\u5916\u7684\u5176\u4ed6\u6240\u6709\u8282\u70b9\nfor (int i = nums.length / 2 - 1; i &gt;= 0; i--) {\nsiftDown(nums, nums.length, i);\n}\n// \u4ece\u5806\u4e2d\u63d0\u53d6\u6700\u5927\u5143\u7d20\uff0c\u5faa\u73af n-1 \u8f6e\nfor (int i = nums.length - 1; i &gt; 0; i--) {\n// \u4ea4\u6362\u6839\u8282\u70b9\u4e0e\u6700\u53f3\u53f6\u8282\u70b9\uff08\u5373\u4ea4\u6362\u9996\u5143\u7d20\u4e0e\u5c3e\u5143\u7d20\uff09\nint tmp = nums[0];\nnums[0] = nums[i];\nnums[i] = tmp;\n// \u4ee5\u6839\u8282\u70b9\u4e3a\u8d77\u70b9\uff0c\u4ece\u9876\u81f3\u5e95\u8fdb\u884c\u5806\u5316\nsiftDown(nums, i, 0);\n}\n}\n</code></pre> heap_sort.cpp<pre><code>/* \u5806\u7684\u957f\u5ea6\u4e3a n \uff0c\u4ece\u8282\u70b9 i \u5f00\u59cb\uff0c\u4ece\u9876\u81f3\u5e95\u5806\u5316 */\nvoid siftDown(vector&lt;int&gt; &amp;nums, int n, int i) {\nwhile (true) {\n// \u5224\u65ad\u8282\u70b9 i, l, r \u4e2d\u503c\u6700\u5927\u7684\u8282\u70b9\uff0c\u8bb0\u4e3a ma\nint l = 2 * i + 1;\nint r = 2 * i + 2;\nint ma = i;\nif (l &lt; n &amp;&amp; nums[l] &gt; nums[ma])\nma = l;\nif (r &lt; n &amp;&amp; nums[r] &gt; nums[ma])\nma = r;\n// \u82e5\u8282\u70b9 i \u6700\u5927\u6216\u7d22\u5f15 l, r \u8d8a\u754c\uff0c\u5219\u65e0\u9700\u7ee7\u7eed\u5806\u5316\uff0c\u8df3\u51fa\nif (ma == i) {\nbreak;\n}\n// \u4ea4\u6362\u4e24\u8282\u70b9\nswap(nums[i], nums[ma]);\n// \u5faa\u73af\u5411\u4e0b\u5806\u5316\ni = ma;\n}\n}\n/* \u5806\u6392\u5e8f */\nvoid heapSort(vector&lt;int&gt; &amp;nums) {\n// \u5efa\u5806\u64cd\u4f5c\uff1a\u5806\u5316\u9664\u53f6\u8282\u70b9\u4ee5\u5916\u7684\u5176\u4ed6\u6240\u6709\u8282\u70b9\nfor (int i = nums.size() / 2 - 1; i &gt;= 0; --i) {\nsiftDown(nums, nums.size(), i);\n}\n// \u4ece\u5806\u4e2d\u63d0\u53d6\u6700\u5927\u5143\u7d20\uff0c\u5faa\u73af n-1 \u8f6e\nfor (int i = nums.size() - 1; i &gt; 0; --i) {\n// \u4ea4\u6362\u6839\u8282\u70b9\u4e0e\u6700\u53f3\u53f6\u8282\u70b9\uff08\u5373\u4ea4\u6362\u9996\u5143\u7d20\u4e0e\u5c3e\u5143\u7d20\uff09\nswap(nums[0], nums[i]);\n// \u4ee5\u6839\u8282\u70b9\u4e3a\u8d77\u70b9\uff0c\u4ece\u9876\u81f3\u5e95\u8fdb\u884c\u5806\u5316\nsiftDown(nums, i, 0);\n}\n}\n</code></pre> heap_sort.py<pre><code>def sift_down(nums: list[int], n: int, i: int):\n\"\"\"\u5806\u7684\u957f\u5ea6\u4e3a n \uff0c\u4ece\u8282\u70b9 i \u5f00\u59cb\uff0c\u4ece\u9876\u81f3\u5e95\u5806\u5316\"\"\"\nwhile True:\n# \u5224\u65ad\u8282\u70b9 i, l, r \u4e2d\u503c\u6700\u5927\u7684\u8282\u70b9\uff0c\u8bb0\u4e3a ma\nl = 2 * i + 1\nr = 2 * i + 2\nma = i\nif l &lt; n and nums[l] &gt; nums[ma]:\nma = l\nif r &lt; n and nums[r] &gt; nums[ma]:\nma = r\n# \u82e5\u8282\u70b9 i \u6700\u5927\u6216\u7d22\u5f15 l, r \u8d8a\u754c\uff0c\u5219\u65e0\u9700\u7ee7\u7eed\u5806\u5316\uff0c\u8df3\u51fa\nif ma == i:\nbreak\n# \u4ea4\u6362\u4e24\u8282\u70b9\nnums[i], nums[ma] = nums[ma], nums[i]\n# \u5faa\u73af\u5411\u4e0b\u5806\u5316\ni = ma\ndef heap_sort(nums: list[int]):\n\"\"\"\u5806\u6392\u5e8f\"\"\"\n# \u5efa\u5806\u64cd\u4f5c\uff1a\u5806\u5316\u9664\u53f6\u8282\u70b9\u4ee5\u5916\u7684\u5176\u4ed6\u6240\u6709\u8282\u70b9\nfor i in range(len(nums) // 2 - 1, -1, -1):\nsift_down(nums, len(nums), i)\n# \u4ece\u5806\u4e2d\u63d0\u53d6\u6700\u5927\u5143\u7d20\uff0c\u5faa\u73af n-1 \u8f6e\nfor i in range(len(nums) - 1, 0, -1):\n# \u4ea4\u6362\u6839\u8282\u70b9\u4e0e\u6700\u53f3\u53f6\u8282\u70b9\uff08\u5373\u4ea4\u6362\u9996\u5143\u7d20\u4e0e\u5c3e\u5143\u7d20\uff09\nnums[0], nums[i] = nums[i], nums[0]\n# \u4ee5\u6839\u8282\u70b9\u4e3a\u8d77\u70b9\uff0c\u4ece\u9876\u81f3\u5e95\u8fdb\u884c\u5806\u5316\nsift_down(nums, i, 0)\n</code></pre> heap_sort.go<pre><code>/* \u5806\u7684\u957f\u5ea6\u4e3a n \uff0c\u4ece\u8282\u70b9 i \u5f00\u59cb\uff0c\u4ece\u9876\u81f3\u5e95\u5806\u5316 */\nfunc siftDown(nums *[]int, n, i int) {\nfor true {\n// \u5224\u65ad\u8282\u70b9 i, l, r \u4e2d\u503c\u6700\u5927\u7684\u8282\u70b9\uff0c\u8bb0\u4e3a ma\nl := 2*i + 1\nr := 2*i + 2\nma := i\nif l &lt; n &amp;&amp; (*nums)[l] &gt; (*nums)[ma] {\nma = l\n}\nif r &lt; n &amp;&amp; (*nums)[r] &gt; (*nums)[ma] {\nma = r\n}\n// \u82e5\u8282\u70b9 i \u6700\u5927\u6216\u7d22\u5f15 l, r \u8d8a\u754c\uff0c\u5219\u65e0\u9700\u7ee7\u7eed\u5806\u5316\uff0c\u8df3\u51fa\nif ma == i {\nbreak\n}\n// \u4ea4\u6362\u4e24\u8282\u70b9\n(*nums)[i], (*nums)[ma] = (*nums)[ma], (*nums)[i]\n// \u5faa\u73af\u5411\u4e0b\u5806\u5316\ni = ma\n}\n}\n/* \u5806\u6392\u5e8f */\nfunc heapSort(nums *[]int) {\n// \u5efa\u5806\u64cd\u4f5c\uff1a\u5806\u5316\u9664\u53f6\u8282\u70b9\u4ee5\u5916\u7684\u5176\u4ed6\u6240\u6709\u8282\u70b9\nfor i := len(*nums)/2 - 1; i &gt;= 0; i-- {\nsiftDown(nums, len(*nums), i)\n}\n// \u4ece\u5806\u4e2d\u63d0\u53d6\u6700\u5927\u5143\u7d20\uff0c\u5faa\u73af n-1 \u8f6e\nfor i := len(*nums) - 1; i &gt; 0; i-- {\n// \u4ea4\u6362\u6839\u8282\u70b9\u4e0e\u6700\u53f3\u53f6\u8282\u70b9\uff08\u5373\u4ea4\u6362\u9996\u5143\u7d20\u4e0e\u5c3e\u5143\u7d20\uff09\n(*nums)[0], (*nums)[i] = (*nums)[i], (*nums)[0]\n// \u4ee5\u6839\u8282\u70b9\u4e3a\u8d77\u70b9\uff0c\u4ece\u9876\u81f3\u5e95\u8fdb\u884c\u5806\u5316\nsiftDown(nums, i, 0)\n}\n}\n</code></pre> heap_sort.js<pre><code>/* \u5806\u7684\u957f\u5ea6\u4e3a n \uff0c\u4ece\u8282\u70b9 i \u5f00\u59cb\uff0c\u4ece\u9876\u81f3\u5e95\u5806\u5316 */\nfunction siftDown(nums, n, i) {\nwhile (true) {\n// \u5224\u65ad\u8282\u70b9 i, l, r \u4e2d\u503c\u6700\u5927\u7684\u8282\u70b9\uff0c\u8bb0\u4e3a ma\nlet l = 2 * i + 1;\nlet r = 2 * i + 2;\nlet ma = i;\nif (l &lt; n &amp;&amp; nums[l] &gt; nums[ma]) {\nma = l;\n}\nif (r &lt; n &amp;&amp; nums[r] &gt; nums[ma]) {\nma = r;\n}\n// \u82e5\u8282\u70b9 i \u6700\u5927\u6216\u7d22\u5f15 l, r \u8d8a\u754c\uff0c\u5219\u65e0\u9700\u7ee7\u7eed\u5806\u5316\uff0c\u8df3\u51fa\nif (ma === i) {\nbreak;\n}\n// \u4ea4\u6362\u4e24\u8282\u70b9\n[nums[i], nums[ma]] = [nums[ma], nums[i]];\n// \u5faa\u73af\u5411\u4e0b\u5806\u5316\ni = ma;\n}\n}\n/* \u5806\u6392\u5e8f */\nfunction heapSort(nums) {\n// \u5efa\u5806\u64cd\u4f5c\uff1a\u5806\u5316\u9664\u53f6\u8282\u70b9\u4ee5\u5916\u7684\u5176\u4ed6\u6240\u6709\u8282\u70b9\nfor (let i = Math.floor(nums.length / 2) - 1; i &gt;= 0; i--) {\nsiftDown(nums, nums.length, i);\n}\n// \u4ece\u5806\u4e2d\u63d0\u53d6\u6700\u5927\u5143\u7d20\uff0c\u5faa\u73af n-1 \u8f6e\nfor (let i = nums.length - 1; i &gt; 0; i--) {\n// \u4ea4\u6362\u6839\u8282\u70b9\u4e0e\u6700\u53f3\u53f6\u8282\u70b9\uff08\u5373\u4ea4\u6362\u9996\u5143\u7d20\u4e0e\u5c3e\u5143\u7d20\uff09\n[nums[0], nums[i]] = [nums[i], nums[0]];\n// \u4ee5\u6839\u8282\u70b9\u4e3a\u8d77\u70b9\uff0c\u4ece\u9876\u81f3\u5e95\u8fdb\u884c\u5806\u5316\nsiftDown(nums, i, 0);\n}\n}\n</code></pre> heap_sort.ts<pre><code>/* \u5806\u7684\u957f\u5ea6\u4e3a n \uff0c\u4ece\u8282\u70b9 i \u5f00\u59cb\uff0c\u4ece\u9876\u81f3\u5e95\u5806\u5316 */\nfunction siftDown(nums: number[], n: number, i: number): void {\nwhile (true) {\n// \u5224\u65ad\u8282\u70b9 i, l, r \u4e2d\u503c\u6700\u5927\u7684\u8282\u70b9\uff0c\u8bb0\u4e3a ma\nlet l = 2 * i + 1;\nlet r = 2 * i + 2;\nlet ma = i;\nif (l &lt; n &amp;&amp; nums[l] &gt; nums[ma]) {\nma = l;\n}\nif (r &lt; n &amp;&amp; nums[r] &gt; nums[ma]) {\nma = r;\n}\n// \u82e5\u8282\u70b9 i \u6700\u5927\u6216\u7d22\u5f15 l, r \u8d8a\u754c\uff0c\u5219\u65e0\u9700\u7ee7\u7eed\u5806\u5316\uff0c\u8df3\u51fa\nif (ma === i) {\nbreak;\n}\n// \u4ea4\u6362\u4e24\u8282\u70b9\n[nums[i], nums[ma]] = [nums[ma], nums[i]];\n// \u5faa\u73af\u5411\u4e0b\u5806\u5316\ni = ma;\n}\n}\n/* \u5806\u6392\u5e8f */\nfunction heapSort(nums: number[]): void {\n// \u5efa\u5806\u64cd\u4f5c\uff1a\u5806\u5316\u9664\u53f6\u8282\u70b9\u4ee5\u5916\u7684\u5176\u4ed6\u6240\u6709\u8282\u70b9\nfor (let i = Math.floor(nums.length / 2) - 1; i &gt;= 0; i--) {\nsiftDown(nums, nums.length, i);\n}\n// \u4ece\u5806\u4e2d\u63d0\u53d6\u6700\u5927\u5143\u7d20\uff0c\u5faa\u73af n-1 \u8f6e\nfor (let i = nums.length - 1; i &gt; 0; i--) {\n// \u4ea4\u6362\u6839\u8282\u70b9\u4e0e\u6700\u53f3\u53f6\u8282\u70b9\uff08\u5373\u4ea4\u6362\u9996\u5143\u7d20\u4e0e\u5c3e\u5143\u7d20\uff09\n[nums[0], nums[i]] = [nums[i], nums[0]];\n// \u4ee5\u6839\u8282\u70b9\u4e3a\u8d77\u70b9\uff0c\u4ece\u9876\u81f3\u5e95\u8fdb\u884c\u5806\u5316\nsiftDown(nums, i, 0);\n}\n}\n</code></pre> heap_sort.c<pre><code>/* \u5806\u7684\u957f\u5ea6\u4e3a n \uff0c\u4ece\u8282\u70b9 i \u5f00\u59cb\uff0c\u4ece\u9876\u81f3\u5e95\u5806\u5316 */\nvoid siftDown(int nums[], int n, int i) {\nwhile (1) {\n// \u5224\u65ad\u8282\u70b9 i, l, r \u4e2d\u503c\u6700\u5927\u7684\u8282\u70b9\uff0c\u8bb0\u4e3a ma\nint l = 2 * i + 1;\nint r = 2 * i + 2;\nint ma = i;\nif (l &lt; n &amp;&amp; nums[l] &gt; nums[ma])\nma = l;\nif (r &lt; n &amp;&amp; nums[r] &gt; nums[ma])\nma = r;\n// \u82e5\u8282\u70b9 i \u6700\u5927\u6216\u7d22\u5f15 l, r \u8d8a\u754c\uff0c\u5219\u65e0\u9700\u7ee7\u7eed\u5806\u5316\uff0c\u8df3\u51fa\nif (ma == i) {\nbreak;\n}\n// \u4ea4\u6362\u4e24\u8282\u70b9\nint temp = nums[i];\nnums[i] = nums[ma];\nnums[ma] = temp;\n// \u5faa\u73af\u5411\u4e0b\u5806\u5316\ni = ma;\n}\n}\n/* \u5806\u6392\u5e8f */\nvoid heapSort(int nums[], int n) {\n// \u5efa\u5806\u64cd\u4f5c\uff1a\u5806\u5316\u9664\u53f6\u8282\u70b9\u4ee5\u5916\u7684\u5176\u4ed6\u6240\u6709\u8282\u70b9\nfor (int i = n / 2 - 1; i &gt;= 0; --i) {\nsiftDown(nums, n, i);\n}\n// \u4ece\u5806\u4e2d\u63d0\u53d6\u6700\u5927\u5143\u7d20\uff0c\u5faa\u73af n-1 \u8f6e\nfor (int i = n - 1; i &gt; 0; --i) {\n// \u4ea4\u6362\u6839\u8282\u70b9\u4e0e\u6700\u53f3\u53f6\u8282\u70b9\uff08\u5373\u4ea4\u6362\u9996\u5143\u7d20\u4e0e\u5c3e\u5143\u7d20\uff09\nint tmp = nums[0];\nnums[0] = nums[i];\nnums[i] = tmp;\n// \u4ee5\u6839\u8282\u70b9\u4e3a\u8d77\u70b9\uff0c\u4ece\u9876\u81f3\u5e95\u8fdb\u884c\u5806\u5316\nsiftDown(nums, i, 0);\n}\n}\n</code></pre> heap_sort.cs<pre><code>/* \u5806\u7684\u957f\u5ea6\u4e3a n \uff0c\u4ece\u8282\u70b9 i \u5f00\u59cb\uff0c\u4ece\u9876\u81f3\u5e95\u5806\u5316 */\nvoid siftDown(int[] nums, int n, int i) {\nwhile (true) {\n// \u5224\u65ad\u8282\u70b9 i, l, r \u4e2d\u503c\u6700\u5927\u7684\u8282\u70b9\uff0c\u8bb0\u4e3a ma\nint l = 2 * i + 1;\nint r = 2 * i + 2;\nint ma = i;\nif (l &lt; n &amp;&amp; nums[l] &gt; nums[ma])\nma = l;\nif (r &lt; n &amp;&amp; nums[r] &gt; nums[ma])\nma = r;\n// \u82e5\u8282\u70b9 i \u6700\u5927\u6216\u7d22\u5f15 l, r \u8d8a\u754c\uff0c\u5219\u65e0\u9700\u7ee7\u7eed\u5806\u5316\uff0c\u8df3\u51fa\nif (ma == i)\nbreak;\n// \u4ea4\u6362\u4e24\u8282\u70b9\n(nums[ma], nums[i]) = (nums[i], nums[ma]);\n// \u5faa\u73af\u5411\u4e0b\u5806\u5316\ni = ma;\n}\n}\n/* \u5806\u6392\u5e8f */\nvoid heapSort(int[] nums) {\n// \u5efa\u5806\u64cd\u4f5c\uff1a\u5806\u5316\u9664\u53f6\u8282\u70b9\u4ee5\u5916\u7684\u5176\u4ed6\u6240\u6709\u8282\u70b9\nfor (int i = nums.Length / 2 - 1; i &gt;= 0; i--) {\nsiftDown(nums, nums.Length, i);\n}\n// \u4ece\u5806\u4e2d\u63d0\u53d6\u6700\u5927\u5143\u7d20\uff0c\u5faa\u73af n-1 \u8f6e\nfor (int i = nums.Length - 1; i &gt; 0; i--) {\n// \u4ea4\u6362\u6839\u8282\u70b9\u4e0e\u6700\u53f3\u53f6\u8282\u70b9\uff08\u5373\u4ea4\u6362\u9996\u5143\u7d20\u4e0e\u5c3e\u5143\u7d20\uff09\n(nums[i], nums[0]) = (nums[0], nums[i]);\n// \u4ee5\u6839\u8282\u70b9\u4e3a\u8d77\u70b9\uff0c\u4ece\u9876\u81f3\u5e95\u8fdb\u884c\u5806\u5316\nsiftDown(nums, i, 0);\n}\n}\n</code></pre> heap_sort.swift<pre><code>/* \u5806\u7684\u957f\u5ea6\u4e3a n \uff0c\u4ece\u8282\u70b9 i \u5f00\u59cb\uff0c\u4ece\u9876\u81f3\u5e95\u5806\u5316 */\nfunc siftDown(nums: inout [Int], n: Int, i: Int) {\nvar i = i\nwhile true {\n// \u5224\u65ad\u8282\u70b9 i, l, r \u4e2d\u503c\u6700\u5927\u7684\u8282\u70b9\uff0c\u8bb0\u4e3a ma\nlet l = 2 * i + 1\nlet r = 2 * i + 2\nvar ma = i\nif l &lt; n, nums[l] &gt; nums[ma] {\nma = l\n}\nif r &lt; n, nums[r] &gt; nums[ma] {\nma = r\n}\n// \u82e5\u8282\u70b9 i \u6700\u5927\u6216\u7d22\u5f15 l, r \u8d8a\u754c\uff0c\u5219\u65e0\u9700\u7ee7\u7eed\u5806\u5316\uff0c\u8df3\u51fa\nif ma == i {\nbreak\n}\n// \u4ea4\u6362\u4e24\u8282\u70b9\nnums.swapAt(i, ma)\n// \u5faa\u73af\u5411\u4e0b\u5806\u5316\ni = ma\n}\n}\n/* \u5806\u6392\u5e8f */\nfunc heapSort(nums: inout [Int]) {\n// \u5efa\u5806\u64cd\u4f5c\uff1a\u5806\u5316\u9664\u53f6\u8282\u70b9\u4ee5\u5916\u7684\u5176\u4ed6\u6240\u6709\u8282\u70b9\nfor i in stride(from: nums.count / 2 - 1, through: 0, by: -1) {\nsiftDown(nums: &amp;nums, n: nums.count, i: i)\n}\n// \u4ece\u5806\u4e2d\u63d0\u53d6\u6700\u5927\u5143\u7d20\uff0c\u5faa\u73af n-1 \u8f6e\nfor i in stride(from: nums.count - 1, to: 0, by: -1) {\n// \u4ea4\u6362\u6839\u8282\u70b9\u4e0e\u6700\u53f3\u53f6\u8282\u70b9\uff08\u5373\u4ea4\u6362\u9996\u5143\u7d20\u4e0e\u5c3e\u5143\u7d20\uff09\nnums.swapAt(0, i)\n// \u4ee5\u6839\u8282\u70b9\u4e3a\u8d77\u70b9\uff0c\u4ece\u9876\u81f3\u5e95\u8fdb\u884c\u5806\u5316\nsiftDown(nums: &amp;nums, n: i, i: 0)\n}\n}\n</code></pre> heap_sort.zig<pre><code>[class]{}-[func]{siftDown}\n[class]{}-[func]{heapSort}\n</code></pre> heap_sort.dart<pre><code>/* \u5806\u7684\u957f\u5ea6\u4e3a n \uff0c\u4ece\u8282\u70b9 i \u5f00\u59cb\uff0c\u4ece\u9876\u81f3\u5e95\u5806\u5316 */\nvoid siftDown(List&lt;int&gt; nums, int n, int i) {\nwhile (true) {\n// \u5224\u65ad\u8282\u70b9 i, l, r \u4e2d\u503c\u6700\u5927\u7684\u8282\u70b9\uff0c\u8bb0\u4e3a ma\nint l = 2 * i + 1;\nint r = 2 * i + 2;\nint ma = i;\nif (l &lt; n &amp;&amp; nums[l] &gt; nums[ma]) ma = l;\nif (r &lt; n &amp;&amp; nums[r] &gt; nums[ma]) ma = r;\n// \u82e5\u8282\u70b9 i \u6700\u5927\u6216\u7d22\u5f15 l, r \u8d8a\u754c\uff0c\u5219\u65e0\u9700\u7ee7\u7eed\u5806\u5316\uff0c\u8df3\u51fa\nif (ma == i) break;\n// \u4ea4\u6362\u4e24\u8282\u70b9\nint temp = nums[i];\nnums[i] = nums[ma];\nnums[ma] = temp;\n// \u5faa\u73af\u5411\u4e0b\u5806\u5316\ni = ma;\n}\n}\n/* \u5806\u6392\u5e8f */\nvoid heapSort(List&lt;int&gt; nums) {\n// \u5efa\u5806\u64cd\u4f5c\uff1a\u5806\u5316\u9664\u53f6\u8282\u70b9\u4ee5\u5916\u7684\u5176\u4ed6\u6240\u6709\u8282\u70b9\nfor (int i = nums.length ~/ 2 - 1; i &gt;= 0; i--) {\nsiftDown(nums, nums.length, i);\n}\n// \u4ece\u5806\u4e2d\u63d0\u53d6\u6700\u5927\u5143\u7d20\uff0c\u5faa\u73af n-1 \u8f6e\nfor (int i = nums.length - 1; i &gt; 0; i--) {\n// \u4ea4\u6362\u6839\u8282\u70b9\u4e0e\u6700\u53f3\u53f6\u8282\u70b9\uff08\u5373\u4ea4\u6362\u9996\u5143\u7d20\u4e0e\u5c3e\u5143\u7d20\uff09\nint tmp = nums[0];\nnums[0] = nums[i];\nnums[i] = tmp;\n// \u4ee5\u6839\u8282\u70b9\u4e3a\u8d77\u70b9\uff0c\u4ece\u9876\u81f3\u5e95\u8fdb\u884c\u5806\u5316\nsiftDown(nums, i, 0);\n}\n}\n</code></pre>"},{"location":"chapter_sorting/heap_sort/#1172","title":"11.7.2. \u00a0 \u7b97\u6cd5\u7279\u6027","text":"<ul> <li>\u65f6\u95f4\u590d\u6742\u5ea6 \\(O(n \\log n)\\) \u3001\u975e\u81ea\u9002\u5e94\u6392\u5e8f \uff1a\u5efa\u5806\u64cd\u4f5c\u4f7f\u7528 \\(O(n)\\) \u65f6\u95f4\u3002\u4ece\u5806\u4e2d\u63d0\u53d6\u6700\u5927\u5143\u7d20\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(\\log n)\\) \uff0c\u5171\u5faa\u73af \\(n - 1\\) \u8f6e\u3002</li> <li>\u7a7a\u95f4\u590d\u6742\u5ea6 \\(O(1)\\) \u3001\u539f\u5730\u6392\u5e8f \uff1a\u51e0\u4e2a\u6307\u9488\u53d8\u91cf\u4f7f\u7528 \\(O(1)\\) \u7a7a\u95f4\u3002\u5143\u7d20\u4ea4\u6362\u548c\u5806\u5316\u64cd\u4f5c\u90fd\u662f\u5728\u539f\u6570\u7ec4\u4e0a\u8fdb\u884c\u7684\u3002</li> <li>\u975e\u7a33\u5b9a\u6392\u5e8f\uff1a\u5728\u4ea4\u6362\u5806\u9876\u5143\u7d20\u548c\u5806\u5e95\u5143\u7d20\u65f6\uff0c\u76f8\u7b49\u5143\u7d20\u7684\u76f8\u5bf9\u4f4d\u7f6e\u53ef\u80fd\u53d1\u751f\u53d8\u5316\u3002</li> </ul>"},{"location":"chapter_sorting/insertion_sort/","title":"11.4. \u00a0 \u63d2\u5165\u6392\u5e8f","text":"<p>\u300c\u63d2\u5165\u6392\u5e8f Insertion Sort\u300d\u662f\u4e00\u79cd\u7b80\u5355\u7684\u6392\u5e8f\u7b97\u6cd5\uff0c\u5b83\u7684\u5de5\u4f5c\u539f\u7406\u4e0e\u624b\u52a8\u6574\u7406\u4e00\u526f\u724c\u7684\u8fc7\u7a0b\u975e\u5e38\u76f8\u4f3c\u3002</p> <p>\u5177\u4f53\u6765\u8bf4\uff0c\u6211\u4eec\u5728\u672a\u6392\u5e8f\u533a\u95f4\u9009\u62e9\u4e00\u4e2a\u57fa\u51c6\u5143\u7d20\uff0c\u5c06\u8be5\u5143\u7d20\u4e0e\u5176\u5de6\u4fa7\u5df2\u6392\u5e8f\u533a\u95f4\u7684\u5143\u7d20\u9010\u4e00\u6bd4\u8f83\u5927\u5c0f\uff0c\u5e76\u5c06\u8be5\u5143\u7d20\u63d2\u5165\u5230\u6b63\u786e\u7684\u4f4d\u7f6e\u3002</p> <p>\u56de\u5fc6\u6570\u7ec4\u7684\u5143\u7d20\u63d2\u5165\u64cd\u4f5c\uff0c\u8bbe\u57fa\u51c6\u5143\u7d20\u4e3a <code>base</code> \uff0c\u6211\u4eec\u9700\u8981\u5c06\u4ece\u76ee\u6807\u7d22\u5f15\u5230 <code>base</code> \u4e4b\u95f4\u7684\u6240\u6709\u5143\u7d20\u5411\u53f3\u79fb\u52a8\u4e00\u4f4d\uff0c\u7136\u540e\u518d\u5c06 <code>base</code> \u8d4b\u503c\u7ed9\u76ee\u6807\u7d22\u5f15\u3002</p> <p></p> <p> Fig. \u5355\u6b21\u63d2\u5165\u64cd\u4f5c </p>"},{"location":"chapter_sorting/insertion_sort/#1141","title":"11.4.1. \u00a0 \u7b97\u6cd5\u6d41\u7a0b","text":"<p>\u63d2\u5165\u6392\u5e8f\u7684\u6574\u4f53\u6d41\u7a0b\u5982\u4e0b\uff1a</p> <ol> <li>\u521d\u59cb\u72b6\u6001\u4e0b\uff0c\u6570\u7ec4\u7684\u7b2c 1 \u4e2a\u5143\u7d20\u5df2\u5b8c\u6210\u6392\u5e8f\u3002</li> <li>\u9009\u53d6\u6570\u7ec4\u7684\u7b2c 2 \u4e2a\u5143\u7d20\u4f5c\u4e3a <code>base</code> \uff0c\u5c06\u5176\u63d2\u5165\u5230\u6b63\u786e\u4f4d\u7f6e\u540e\uff0c\u6570\u7ec4\u7684\u524d 2 \u4e2a\u5143\u7d20\u5df2\u6392\u5e8f\u3002</li> <li>\u9009\u53d6\u7b2c 3 \u4e2a\u5143\u7d20\u4f5c\u4e3a <code>base</code> \uff0c\u5c06\u5176\u63d2\u5165\u5230\u6b63\u786e\u4f4d\u7f6e\u540e\uff0c\u6570\u7ec4\u7684\u524d 3 \u4e2a\u5143\u7d20\u5df2\u6392\u5e8f\u3002</li> <li>\u4ee5\u6b64\u7c7b\u63a8\uff0c\u5728\u6700\u540e\u4e00\u8f6e\u4e2d\uff0c\u9009\u53d6\u6700\u540e\u4e00\u4e2a\u5143\u7d20\u4f5c\u4e3a <code>base</code> \uff0c\u5c06\u5176\u63d2\u5165\u5230\u6b63\u786e\u4f4d\u7f6e\u540e\uff0c\u6240\u6709\u5143\u7d20\u5747\u5df2\u6392\u5e8f\u3002</li> </ol> <p></p> <p> Fig. \u63d2\u5165\u6392\u5e8f\u6d41\u7a0b </p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart insertion_sort.java<pre><code>/* \u63d2\u5165\u6392\u5e8f */\nvoid insertionSort(int[] nums) {\n// \u5916\u5faa\u73af\uff1a\u5df2\u6392\u5e8f\u5143\u7d20\u6570\u91cf\u4e3a 1, 2, ..., n\nfor (int i = 1; i &lt; nums.length; i++) {\nint base = nums[i], j = i - 1;\n// \u5185\u5faa\u73af\uff1a\u5c06 base \u63d2\u5165\u5230\u5df2\u6392\u5e8f\u90e8\u5206\u7684\u6b63\u786e\u4f4d\u7f6e\nwhile (j &gt;= 0 &amp;&amp; nums[j] &gt; base) {\nnums[j + 1] = nums[j]; // \u5c06 nums[j] \u5411\u53f3\u79fb\u52a8\u4e00\u4f4d\nj--;\n}\nnums[j + 1] = base;        // \u5c06 base \u8d4b\u503c\u5230\u6b63\u786e\u4f4d\u7f6e\n}\n}\n</code></pre> insertion_sort.cpp<pre><code>/* \u63d2\u5165\u6392\u5e8f */\nvoid insertionSort(vector&lt;int&gt; &amp;nums) {\n// \u5916\u5faa\u73af\uff1a\u5df2\u6392\u5e8f\u5143\u7d20\u6570\u91cf\u4e3a 1, 2, ..., n\nfor (int i = 1; i &lt; nums.size(); i++) {\nint base = nums[i], j = i - 1;\n// \u5185\u5faa\u73af\uff1a\u5c06 base \u63d2\u5165\u5230\u5df2\u6392\u5e8f\u90e8\u5206\u7684\u6b63\u786e\u4f4d\u7f6e\nwhile (j &gt;= 0 &amp;&amp; nums[j] &gt; base) {\nnums[j + 1] = nums[j]; // \u5c06 nums[j] \u5411\u53f3\u79fb\u52a8\u4e00\u4f4d\nj--;\n}\nnums[j + 1] = base; // \u5c06 base \u8d4b\u503c\u5230\u6b63\u786e\u4f4d\u7f6e\n}\n}\n</code></pre> insertion_sort.py<pre><code>def insertion_sort(nums: list[int]) -&gt; None:\n\"\"\"\u63d2\u5165\u6392\u5e8f\"\"\"\n# \u5916\u5faa\u73af\uff1a\u5df2\u6392\u5e8f\u533a\u95f4\u4e3a [0, i-1]\nfor i in range(1, len(nums)):\nbase = nums[i]\nj = i - 1\n# \u5185\u5faa\u73af\uff1a\u5c06 base \u63d2\u5165\u5230\u5df2\u6392\u5e8f\u533a\u95f4 [0, i-1] \u4e2d\u7684\u6b63\u786e\u4f4d\u7f6e\nwhile j &gt;= 0 and nums[j] &gt; base:\nnums[j + 1] = nums[j]  # \u5c06 nums[j] \u5411\u53f3\u79fb\u52a8\u4e00\u4f4d\nj -= 1\nnums[j + 1] = base  # \u5c06 base \u8d4b\u503c\u5230\u6b63\u786e\u4f4d\u7f6e\n</code></pre> insertion_sort.go<pre><code>/* \u63d2\u5165\u6392\u5e8f */\nfunc insertionSort(nums []int) {\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [0, i]\nfor i := 1; i &lt; len(nums); i++ {\nbase := nums[i]\nj := i - 1\n// \u5185\u5faa\u73af\uff1a\u5c06 base \u63d2\u5165\u5230\u5df2\u6392\u5e8f\u90e8\u5206\u7684\u6b63\u786e\u4f4d\u7f6e\nfor j &gt;= 0 &amp;&amp; nums[j] &gt; base {\nnums[j+1] = nums[j] // \u5c06 nums[j] \u5411\u53f3\u79fb\u52a8\u4e00\u4f4d\nj--\n}\nnums[j+1] = base // \u5c06 base \u8d4b\u503c\u5230\u6b63\u786e\u4f4d\u7f6e\n}\n}\n</code></pre> insertion_sort.js<pre><code>/* \u63d2\u5165\u6392\u5e8f */\nfunction insertionSort(nums) {\n// \u5916\u5faa\u73af\uff1a\u5df2\u6392\u5e8f\u5143\u7d20\u6570\u91cf\u4e3a 1, 2, ..., n\nfor (let i = 1; i &lt; nums.length; i++) {\nlet base = nums[i],\nj = i - 1;\n// \u5185\u5faa\u73af\uff1a\u5c06 base \u63d2\u5165\u5230\u5df2\u6392\u5e8f\u90e8\u5206\u7684\u6b63\u786e\u4f4d\u7f6e\nwhile (j &gt;= 0 &amp;&amp; nums[j] &gt; base) {\nnums[j + 1] = nums[j]; // \u5c06 nums[j] \u5411\u53f3\u79fb\u52a8\u4e00\u4f4d\nj--;\n}\nnums[j + 1] = base; // \u5c06 base \u8d4b\u503c\u5230\u6b63\u786e\u4f4d\u7f6e\n}\n}\n</code></pre> insertion_sort.ts<pre><code>/* \u63d2\u5165\u6392\u5e8f */\nfunction insertionSort(nums: number[]): void {\n// \u5916\u5faa\u73af\uff1a\u5df2\u6392\u5e8f\u5143\u7d20\u6570\u91cf\u4e3a 1, 2, ..., n\nfor (let i = 1; i &lt; nums.length; i++) {\nconst base = nums[i];\nlet j = i - 1;\n// \u5185\u5faa\u73af\uff1a\u5c06 base \u63d2\u5165\u5230\u5df2\u6392\u5e8f\u90e8\u5206\u7684\u6b63\u786e\u4f4d\u7f6e\nwhile (j &gt;= 0 &amp;&amp; nums[j] &gt; base) {\nnums[j + 1] = nums[j]; // \u5c06 nums[j] \u5411\u53f3\u79fb\u52a8\u4e00\u4f4d\nj--;\n}\nnums[j + 1] = base; // \u5c06 base \u8d4b\u503c\u5230\u6b63\u786e\u4f4d\u7f6e\n}\n}\n</code></pre> insertion_sort.c<pre><code>/* \u63d2\u5165\u6392\u5e8f */\nvoid insertionSort(int nums[], int size) {\n// \u5916\u5faa\u73af\uff1a\u5df2\u6392\u5e8f\u5143\u7d20\u6570\u91cf\u4e3a 1, 2, ..., n\nfor (int i = 1; i &lt; size; i++) {\nint base = nums[i], j = i - 1;\n// \u5185\u5faa\u73af\uff1a\u5c06 base \u63d2\u5165\u5230\u5df2\u6392\u5e8f\u90e8\u5206\u7684\u6b63\u786e\u4f4d\u7f6e\nwhile (j &gt;= 0 &amp;&amp; nums[j] &gt; base) {\n// \u5c06 nums[j] \u5411\u53f3\u79fb\u52a8\u4e00\u4f4d\nnums[j + 1] = nums[j];\nj--;\n}\n// \u5c06 base \u8d4b\u503c\u5230\u6b63\u786e\u4f4d\u7f6e\nnums[j + 1] = base;\n}\n}\n</code></pre> insertion_sort.cs<pre><code>/* \u63d2\u5165\u6392\u5e8f */\nvoid insertionSort(int[] nums) {\n// \u5916\u5faa\u73af\uff1a\u5df2\u6392\u5e8f\u5143\u7d20\u6570\u91cf\u4e3a 1, 2, ..., n\nfor (int i = 1; i &lt; nums.Length; i++) {\nint bas = nums[i], j = i - 1;\n// \u5185\u5faa\u73af\uff1a\u5c06 base \u63d2\u5165\u5230\u5df2\u6392\u5e8f\u90e8\u5206\u7684\u6b63\u786e\u4f4d\u7f6e\nwhile (j &gt;= 0 &amp;&amp; nums[j] &gt; bas) {\nnums[j + 1] = nums[j]; // \u5c06 nums[j] \u5411\u53f3\u79fb\u52a8\u4e00\u4f4d\nj--;\n}\nnums[j + 1] = bas;         // \u5c06 base \u8d4b\u503c\u5230\u6b63\u786e\u4f4d\u7f6e\n}\n}\n</code></pre> insertion_sort.swift<pre><code>/* \u63d2\u5165\u6392\u5e8f */\nfunc insertionSort(nums: inout [Int]) {\n// \u5916\u5faa\u73af\uff1a\u5df2\u6392\u5e8f\u5143\u7d20\u6570\u91cf\u4e3a 1, 2, ..., n\nfor i in stride(from: 1, to: nums.count, by: 1) {\nlet base = nums[i]\nvar j = i - 1\n// \u5185\u5faa\u73af\uff1a\u5c06 base \u63d2\u5165\u5230\u5df2\u6392\u5e8f\u90e8\u5206\u7684\u6b63\u786e\u4f4d\u7f6e\nwhile j &gt;= 0, nums[j] &gt; base {\nnums[j + 1] = nums[j] // \u5c06 nums[j] \u5411\u53f3\u79fb\u52a8\u4e00\u4f4d\nj -= 1\n}\nnums[j + 1] = base // \u5c06 base \u8d4b\u503c\u5230\u6b63\u786e\u4f4d\u7f6e\n}\n}\n</code></pre> insertion_sort.zig<pre><code>// \u63d2\u5165\u6392\u5e8f\nfn insertionSort(nums: []i32) void {\n// \u5916\u5faa\u73af\uff1a\u5df2\u6392\u5e8f\u5143\u7d20\u6570\u91cf\u4e3a 1, 2, ..., n\nvar i: usize = 1;\nwhile (i &lt; nums.len) : (i += 1) {\nvar base = nums[i];\nvar j: usize = i;\n// \u5185\u5faa\u73af\uff1a\u5c06 base \u63d2\u5165\u5230\u5df2\u6392\u5e8f\u90e8\u5206\u7684\u6b63\u786e\u4f4d\u7f6e\nwhile (j &gt;= 1 and nums[j - 1] &gt; base) : (j -= 1) {\nnums[j] = nums[j - 1];  // \u5c06 nums[j] \u5411\u53f3\u79fb\u52a8\u4e00\u4f4d\n}\nnums[j] = base;             // \u5c06 base \u8d4b\u503c\u5230\u6b63\u786e\u4f4d\u7f6e\n}\n}\n</code></pre> insertion_sort.dart<pre><code>/* \u63d2\u5165\u6392\u5e8f */\nvoid insertionSort(List&lt;int&gt; nums) {\n// \u5916\u5faa\u73af\uff1a\u5df2\u6392\u5e8f\u5143\u7d20\u6570\u91cf\u4e3a 1, 2, ..., n\nfor (int i = 1; i &lt; nums.length; i++) {\nint base = nums[i], j = i - 1;\n// \u5185\u5faa\u73af\uff1a\u5c06 base \u63d2\u5165\u5230\u5df2\u6392\u5e8f\u90e8\u5206\u7684\u6b63\u786e\u4f4d\u7f6e\nwhile (j &gt;= 0 &amp;&amp; nums[j] &gt; base) {\nnums[j + 1] = nums[j]; // \u5c06 nums[j] \u5411\u53f3\u79fb\u52a8\u4e00\u4f4d\nj--;\n}\nnums[j + 1] = base; // \u5c06 base \u8d4b\u503c\u5230\u6b63\u786e\u4f4d\u7f6e\n}\n}\n</code></pre>"},{"location":"chapter_sorting/insertion_sort/#1142","title":"11.4.2. \u00a0 \u7b97\u6cd5\u7279\u6027","text":"<ul> <li>\u65f6\u95f4\u590d\u6742\u5ea6 \\(O(n^2)\\) \u3001\u81ea\u9002\u5e94\u6392\u5e8f \uff1a\u6700\u5dee\u60c5\u51b5\u4e0b\uff0c\u6bcf\u6b21\u63d2\u5165\u64cd\u4f5c\u5206\u522b\u9700\u8981\u5faa\u73af \\(n - 1\\) , \\(n-2\\) , \\(\\cdots\\) , \\(2\\) , \\(1\\) \u6b21\uff0c\u6c42\u548c\u5f97\u5230 \\(\\frac{(n - 1) n}{2}\\) \uff0c\u56e0\u6b64\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(n^2)\\) \u3002\u5728\u9047\u5230\u6709\u5e8f\u6570\u636e\u65f6\uff0c\u63d2\u5165\u64cd\u4f5c\u4f1a\u63d0\u524d\u7ec8\u6b62\u3002\u5f53\u8f93\u5165\u6570\u7ec4\u5b8c\u5168\u6709\u5e8f\u65f6\uff0c\u63d2\u5165\u6392\u5e8f\u8fbe\u5230\u6700\u4f73\u65f6\u95f4\u590d\u6742\u5ea6 \\(O(n)\\) \u3002</li> <li>\u7a7a\u95f4\u590d\u6742\u5ea6 \\(O(1)\\) \u3001\u539f\u5730\u6392\u5e8f \uff1a\u6307\u9488 \\(i\\) , \\(j\\) \u4f7f\u7528\u5e38\u6570\u5927\u5c0f\u7684\u989d\u5916\u7a7a\u95f4\u3002</li> <li>\u7a33\u5b9a\u6392\u5e8f\uff1a\u5728\u63d2\u5165\u64cd\u4f5c\u8fc7\u7a0b\u4e2d\uff0c\u6211\u4eec\u4f1a\u5c06\u5143\u7d20\u63d2\u5165\u5230\u76f8\u7b49\u5143\u7d20\u7684\u53f3\u4fa7\uff0c\u4e0d\u4f1a\u6539\u53d8\u5b83\u4eec\u7684\u987a\u5e8f\u3002</li> </ul>"},{"location":"chapter_sorting/insertion_sort/#1143","title":"11.4.3. \u00a0 \u63d2\u5165\u6392\u5e8f\u4f18\u52bf","text":"<p>\u63d2\u5165\u6392\u5e8f\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(n^2)\\) \uff0c\u800c\u6211\u4eec\u5373\u5c06\u5b66\u4e60\u7684\u5feb\u901f\u6392\u5e8f\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(n \\log n)\\) \u3002\u5c3d\u7ba1\u63d2\u5165\u6392\u5e8f\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u76f8\u6bd4\u5feb\u901f\u6392\u5e8f\u66f4\u9ad8\uff0c\u4f46\u5728\u6570\u636e\u91cf\u8f83\u5c0f\u7684\u60c5\u51b5\u4e0b\uff0c\u63d2\u5165\u6392\u5e8f\u901a\u5e38\u66f4\u5feb\u3002</p> <p>\u8fd9\u4e2a\u7ed3\u8bba\u4e0e\u7ebf\u6027\u67e5\u627e\u548c\u4e8c\u5206\u67e5\u627e\u7684\u9002\u7528\u60c5\u51b5\u7684\u7ed3\u8bba\u7c7b\u4f3c\u3002\u5feb\u901f\u6392\u5e8f\u8fd9\u7c7b \\(O(n \\log n)\\) \u7684\u7b97\u6cd5\u5c5e\u4e8e\u57fa\u4e8e\u5206\u6cbb\u7684\u6392\u5e8f\u7b97\u6cd5\uff0c\u5f80\u5f80\u5305\u542b\u66f4\u591a\u5355\u5143\u8ba1\u7b97\u64cd\u4f5c\u3002\u800c\u5728\u6570\u636e\u91cf\u8f83\u5c0f\u65f6\uff0c\\(n^2\\) \u548c \\(n \\log n\\) \u7684\u6570\u503c\u6bd4\u8f83\u63a5\u8fd1\uff0c\u590d\u6742\u5ea6\u4e0d\u5360\u4e3b\u5bfc\u4f5c\u7528\uff1b\u6bcf\u8f6e\u4e2d\u7684\u5355\u5143\u8ba1\u7b97\u64cd\u4f5c\u6570\u91cf\u8d77\u5230\u51b3\u5b9a\u6027\u56e0\u7d20\u3002</p> <p>\u5b9e\u9645\u4e0a\uff0c\u8bb8\u591a\u7f16\u7a0b\u8bed\u8a00\uff08\u4f8b\u5982 Java\uff09\u7684\u5185\u7f6e\u6392\u5e8f\u51fd\u6570\u90fd\u91c7\u7528\u4e86\u63d2\u5165\u6392\u5e8f\uff0c\u5927\u81f4\u601d\u8def\u4e3a\uff1a\u5bf9\u4e8e\u957f\u6570\u7ec4\uff0c\u91c7\u7528\u57fa\u4e8e\u5206\u6cbb\u7684\u6392\u5e8f\u7b97\u6cd5\uff0c\u4f8b\u5982\u5feb\u901f\u6392\u5e8f\uff1b\u5bf9\u4e8e\u77ed\u6570\u7ec4\uff0c\u76f4\u63a5\u4f7f\u7528\u63d2\u5165\u6392\u5e8f\u3002</p> <p>\u867d\u7136\u5192\u6ce1\u6392\u5e8f\u3001\u9009\u62e9\u6392\u5e8f\u548c\u63d2\u5165\u6392\u5e8f\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u90fd\u4e3a \\(O(n^2)\\) \uff0c\u4f46\u5728\u5b9e\u9645\u60c5\u51b5\u4e2d\uff0c\u63d2\u5165\u6392\u5e8f\u7684\u4f7f\u7528\u9891\u7387\u663e\u8457\u9ad8\u4e8e\u5192\u6ce1\u6392\u5e8f\u548c\u9009\u62e9\u6392\u5e8f\u3002\u8fd9\u662f\u56e0\u4e3a\uff1a</p> <ul> <li>\u5192\u6ce1\u6392\u5e8f\u57fa\u4e8e\u5143\u7d20\u4ea4\u6362\u5b9e\u73b0\uff0c\u9700\u8981\u501f\u52a9\u4e00\u4e2a\u4e34\u65f6\u53d8\u91cf\uff0c\u5171\u6d89\u53ca 3 \u4e2a\u5355\u5143\u64cd\u4f5c\uff1b\u63d2\u5165\u6392\u5e8f\u57fa\u4e8e\u5143\u7d20\u8d4b\u503c\u5b9e\u73b0\uff0c\u4ec5\u9700 1 \u4e2a\u5355\u5143\u64cd\u4f5c\u3002\u56e0\u6b64\uff0c\u5192\u6ce1\u6392\u5e8f\u7684\u8ba1\u7b97\u5f00\u9500\u901a\u5e38\u6bd4\u63d2\u5165\u6392\u5e8f\u66f4\u9ad8\u3002</li> <li>\u9009\u62e9\u6392\u5e8f\u5728\u4efb\u4f55\u60c5\u51b5\u4e0b\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u90fd\u4e3a \\(O(n^2)\\) \u3002\u5982\u679c\u7ed9\u5b9a\u4e00\u7ec4\u90e8\u5206\u6709\u5e8f\u7684\u6570\u636e\uff0c\u63d2\u5165\u6392\u5e8f\u901a\u5e38\u6bd4\u9009\u62e9\u6392\u5e8f\u6548\u7387\u66f4\u9ad8\u3002</li> <li>\u9009\u62e9\u6392\u5e8f\u4e0d\u7a33\u5b9a\uff0c\u65e0\u6cd5\u5e94\u7528\u4e8e\u591a\u7ea7\u6392\u5e8f\u3002</li> </ul>"},{"location":"chapter_sorting/merge_sort/","title":"11.6. \u00a0 \u5f52\u5e76\u6392\u5e8f","text":"<p>\u300c\u5f52\u5e76\u6392\u5e8f Merge Sort\u300d\u57fa\u4e8e\u5206\u6cbb\u601d\u60f3\u5b9e\u73b0\u6392\u5e8f\uff0c\u5305\u542b\u201c\u5212\u5206\u201d\u548c\u201c\u5408\u5e76\u201d\u4e24\u4e2a\u9636\u6bb5\uff1a</p> <ol> <li>\u5212\u5206\u9636\u6bb5\uff1a\u901a\u8fc7\u9012\u5f52\u4e0d\u65ad\u5730\u5c06\u6570\u7ec4\u4ece\u4e2d\u70b9\u5904\u5206\u5f00\uff0c\u5c06\u957f\u6570\u7ec4\u7684\u6392\u5e8f\u95ee\u9898\u8f6c\u6362\u4e3a\u77ed\u6570\u7ec4\u7684\u6392\u5e8f\u95ee\u9898\uff1b</li> <li>\u5408\u5e76\u9636\u6bb5\uff1a\u5f53\u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a 1 \u65f6\u7ec8\u6b62\u5212\u5206\uff0c\u5f00\u59cb\u5408\u5e76\uff0c\u6301\u7eed\u5730\u5c06\u5de6\u53f3\u4e24\u4e2a\u8f83\u77ed\u7684\u6709\u5e8f\u6570\u7ec4\u5408\u5e76\u4e3a\u4e00\u4e2a\u8f83\u957f\u7684\u6709\u5e8f\u6570\u7ec4\uff0c\u76f4\u81f3\u7ed3\u675f\uff1b</li> </ol> <p></p> <p> Fig. \u5f52\u5e76\u6392\u5e8f\u7684\u5212\u5206\u4e0e\u5408\u5e76\u9636\u6bb5 </p>"},{"location":"chapter_sorting/merge_sort/#1161","title":"11.6.1. \u00a0 \u7b97\u6cd5\u6d41\u7a0b","text":"<p>\u201c\u5212\u5206\u9636\u6bb5\u201d\u4ece\u9876\u81f3\u5e95\u9012\u5f52\u5730\u5c06\u6570\u7ec4\u4ece\u4e2d\u70b9\u5207\u4e3a\u4e24\u4e2a\u5b50\u6570\u7ec4\uff0c\u76f4\u81f3\u957f\u5ea6\u4e3a 1 \uff1b</p> <ol> <li>\u8ba1\u7b97\u6570\u7ec4\u4e2d\u70b9 <code>mid</code> \uff0c\u9012\u5f52\u5212\u5206\u5de6\u5b50\u6570\u7ec4\uff08\u533a\u95f4 <code>[left, mid]</code> \uff09\u548c\u53f3\u5b50\u6570\u7ec4\uff08\u533a\u95f4 <code>[mid + 1, right]</code> \uff09\uff1b</li> <li>\u9012\u5f52\u6267\u884c\u6b65\u9aa4 <code>1.</code> \uff0c\u76f4\u81f3\u5b50\u6570\u7ec4\u533a\u95f4\u957f\u5ea6\u4e3a 1 \u65f6\uff0c\u7ec8\u6b62\u9012\u5f52\u5212\u5206\uff1b</li> </ol> <p>\u201c\u5408\u5e76\u9636\u6bb5\u201d\u4ece\u5e95\u81f3\u9876\u5730\u5c06\u5de6\u5b50\u6570\u7ec4\u548c\u53f3\u5b50\u6570\u7ec4\u5408\u5e76\u4e3a\u4e00\u4e2a\u6709\u5e8f\u6570\u7ec4\u3002\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u4ece\u957f\u5ea6\u4e3a 1 \u7684\u5b50\u6570\u7ec4\u5f00\u59cb\u5408\u5e76\uff0c\u5408\u5e76\u9636\u6bb5\u4e2d\u7684\u6bcf\u4e2a\u5b50\u6570\u7ec4\u90fd\u662f\u6709\u5e8f\u7684\u3002</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p>\u89c2\u5bdf\u53d1\u73b0\uff0c\u5f52\u5e76\u6392\u5e8f\u7684\u9012\u5f52\u987a\u5e8f\u4e0e\u4e8c\u53c9\u6811\u7684\u540e\u5e8f\u904d\u5386\u76f8\u540c\uff0c\u5177\u4f53\u6765\u770b\uff1a</p> <ul> <li>\u540e\u5e8f\u904d\u5386\uff1a\u5148\u9012\u5f52\u5de6\u5b50\u6811\uff0c\u518d\u9012\u5f52\u53f3\u5b50\u6811\uff0c\u6700\u540e\u5904\u7406\u6839\u8282\u70b9\u3002</li> <li>\u5f52\u5e76\u6392\u5e8f\uff1a\u5148\u9012\u5f52\u5de6\u5b50\u6570\u7ec4\uff0c\u518d\u9012\u5f52\u53f3\u5b50\u6570\u7ec4\uff0c\u6700\u540e\u5904\u7406\u5408\u5e76\u3002</li> </ul> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart merge_sort.java<pre><code>/* \u5408\u5e76\u5de6\u5b50\u6570\u7ec4\u548c\u53f3\u5b50\u6570\u7ec4 */\n// \u5de6\u5b50\u6570\u7ec4\u533a\u95f4 [left, mid]\n// \u53f3\u5b50\u6570\u7ec4\u533a\u95f4 [mid + 1, right]\nvoid merge(int[] nums, int left, int mid, int right) {\n// \u521d\u59cb\u5316\u8f85\u52a9\u6570\u7ec4\nint[] tmp = Arrays.copyOfRange(nums, left, right + 1);\n// \u5de6\u5b50\u6570\u7ec4\u7684\u8d77\u59cb\u7d22\u5f15\u548c\u7ed3\u675f\u7d22\u5f15\nint leftStart = left - left, leftEnd = mid - left;\n// \u53f3\u5b50\u6570\u7ec4\u7684\u8d77\u59cb\u7d22\u5f15\u548c\u7ed3\u675f\u7d22\u5f15\nint rightStart = mid + 1 - left, rightEnd = right - left;\n// i, j \u5206\u522b\u6307\u5411\u5de6\u5b50\u6570\u7ec4\u3001\u53f3\u5b50\u6570\u7ec4\u7684\u9996\u5143\u7d20\nint i = leftStart, j = rightStart;\n// \u901a\u8fc7\u8986\u76d6\u539f\u6570\u7ec4 nums \u6765\u5408\u5e76\u5de6\u5b50\u6570\u7ec4\u548c\u53f3\u5b50\u6570\u7ec4\nfor (int k = left; k &lt;= right; k++) {\n// \u82e5\u201c\u5de6\u5b50\u6570\u7ec4\u5df2\u5168\u90e8\u5408\u5e76\u5b8c\u201d\uff0c\u5219\u9009\u53d6\u53f3\u5b50\u6570\u7ec4\u5143\u7d20\uff0c\u5e76\u4e14 j++\nif (i &gt; leftEnd)\nnums[k] = tmp[j++];\n// \u5426\u5219\uff0c\u82e5\u201c\u53f3\u5b50\u6570\u7ec4\u5df2\u5168\u90e8\u5408\u5e76\u5b8c\u201d\u6216\u201c\u5de6\u5b50\u6570\u7ec4\u5143\u7d20 &lt;= \u53f3\u5b50\u6570\u7ec4\u5143\u7d20\u201d\uff0c\u5219\u9009\u53d6\u5de6\u5b50\u6570\u7ec4\u5143\u7d20\uff0c\u5e76\u4e14 i++\nelse if (j &gt; rightEnd || tmp[i] &lt;= tmp[j])\nnums[k] = tmp[i++];\n// \u5426\u5219\uff0c\u82e5\u201c\u5de6\u53f3\u5b50\u6570\u7ec4\u90fd\u672a\u5168\u90e8\u5408\u5e76\u5b8c\u201d\u4e14\u201c\u5de6\u5b50\u6570\u7ec4\u5143\u7d20 &gt; \u53f3\u5b50\u6570\u7ec4\u5143\u7d20\u201d\uff0c\u5219\u9009\u53d6\u53f3\u5b50\u6570\u7ec4\u5143\u7d20\uff0c\u5e76\u4e14 j++\nelse\nnums[k] = tmp[j++];\n}\n}\n/* \u5f52\u5e76\u6392\u5e8f */\nvoid mergeSort(int[] nums, int left, int right) {\n// \u7ec8\u6b62\u6761\u4ef6\nif (left &gt;= right)\nreturn;                      // \u5f53\u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a 1 \u65f6\u7ec8\u6b62\u9012\u5f52\n// \u5212\u5206\u9636\u6bb5\nint mid = (left + right) / 2;    // \u8ba1\u7b97\u4e2d\u70b9\nmergeSort(nums, left, mid);      // \u9012\u5f52\u5de6\u5b50\u6570\u7ec4\nmergeSort(nums, mid + 1, right); // \u9012\u5f52\u53f3\u5b50\u6570\u7ec4\n// \u5408\u5e76\u9636\u6bb5\nmerge(nums, left, mid, right);\n}\n</code></pre> merge_sort.cpp<pre><code>/* \u5408\u5e76\u5de6\u5b50\u6570\u7ec4\u548c\u53f3\u5b50\u6570\u7ec4 */\n// \u5de6\u5b50\u6570\u7ec4\u533a\u95f4 [left, mid]\n// \u53f3\u5b50\u6570\u7ec4\u533a\u95f4 [mid + 1, right]\nvoid merge(vector&lt;int&gt; &amp;nums, int left, int mid, int right) {\n// \u521d\u59cb\u5316\u8f85\u52a9\u6570\u7ec4\nvector&lt;int&gt; tmp(nums.begin() + left, nums.begin() + right + 1);\n// \u5de6\u5b50\u6570\u7ec4\u7684\u8d77\u59cb\u7d22\u5f15\u548c\u7ed3\u675f\u7d22\u5f15\nint leftStart = left - left, leftEnd = mid - left;\n// \u53f3\u5b50\u6570\u7ec4\u7684\u8d77\u59cb\u7d22\u5f15\u548c\u7ed3\u675f\u7d22\u5f15\nint rightStart = mid + 1 - left, rightEnd = right - left;\n// i, j \u5206\u522b\u6307\u5411\u5de6\u5b50\u6570\u7ec4\u3001\u53f3\u5b50\u6570\u7ec4\u7684\u9996\u5143\u7d20\nint i = leftStart, j = rightStart;\n// \u901a\u8fc7\u8986\u76d6\u539f\u6570\u7ec4 nums \u6765\u5408\u5e76\u5de6\u5b50\u6570\u7ec4\u548c\u53f3\u5b50\u6570\u7ec4\nfor (int k = left; k &lt;= right; k++) {\n// \u82e5\u201c\u5de6\u5b50\u6570\u7ec4\u5df2\u5168\u90e8\u5408\u5e76\u5b8c\u201d\uff0c\u5219\u9009\u53d6\u53f3\u5b50\u6570\u7ec4\u5143\u7d20\uff0c\u5e76\u4e14 j++\nif (i &gt; leftEnd)\nnums[k] = tmp[j++];\n// \u5426\u5219\uff0c\u82e5\u201c\u53f3\u5b50\u6570\u7ec4\u5df2\u5168\u90e8\u5408\u5e76\u5b8c\u201d\u6216\u201c\u5de6\u5b50\u6570\u7ec4\u5143\u7d20 &lt;= \u53f3\u5b50\u6570\u7ec4\u5143\u7d20\u201d\uff0c\u5219\u9009\u53d6\u5de6\u5b50\u6570\u7ec4\u5143\u7d20\uff0c\u5e76\u4e14 i++\nelse if (j &gt; rightEnd || tmp[i] &lt;= tmp[j])\nnums[k] = tmp[i++];\n// \u5426\u5219\uff0c\u82e5\u201c\u5de6\u53f3\u5b50\u6570\u7ec4\u90fd\u672a\u5168\u90e8\u5408\u5e76\u5b8c\u201d\u4e14\u201c\u5de6\u5b50\u6570\u7ec4\u5143\u7d20 &gt; \u53f3\u5b50\u6570\u7ec4\u5143\u7d20\u201d\uff0c\u5219\u9009\u53d6\u53f3\u5b50\u6570\u7ec4\u5143\u7d20\uff0c\u5e76\u4e14 j++\nelse\nnums[k] = tmp[j++];\n}\n}\n/* \u5f52\u5e76\u6392\u5e8f */\nvoid mergeSort(vector&lt;int&gt; &amp;nums, int left, int right) {\n// \u7ec8\u6b62\u6761\u4ef6\nif (left &gt;= right)\nreturn; // \u5f53\u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a 1 \u65f6\u7ec8\u6b62\u9012\u5f52\n// \u5212\u5206\u9636\u6bb5\nint mid = (left + right) / 2;    // \u8ba1\u7b97\u4e2d\u70b9\nmergeSort(nums, left, mid);      // \u9012\u5f52\u5de6\u5b50\u6570\u7ec4\nmergeSort(nums, mid + 1, right); // \u9012\u5f52\u53f3\u5b50\u6570\u7ec4\n// \u5408\u5e76\u9636\u6bb5\nmerge(nums, left, mid, right);\n}\n</code></pre> merge_sort.py<pre><code>def merge(nums: list[int], left: int, mid: int, right: int) -&gt; None:\n\"\"\"\u5408\u5e76\u5de6\u5b50\u6570\u7ec4\u548c\u53f3\u5b50\u6570\u7ec4\"\"\"\n# \u5de6\u5b50\u6570\u7ec4\u533a\u95f4 [left, mid]\n# \u53f3\u5b50\u6570\u7ec4\u533a\u95f4 [mid + 1, right]\n# \u521d\u59cb\u5316\u8f85\u52a9\u6570\u7ec4\ntmp = list(nums[left : right + 1])\n# \u5de6\u5b50\u6570\u7ec4\u7684\u8d77\u59cb\u7d22\u5f15\u548c\u7ed3\u675f\u7d22\u5f15\nleft_start = 0\nleft_end = mid - left\n# \u53f3\u5b50\u6570\u7ec4\u7684\u8d77\u59cb\u7d22\u5f15\u548c\u7ed3\u675f\u7d22\u5f15\nright_start = mid + 1 - left\nright_end = right - left\n# i, j \u5206\u522b\u6307\u5411\u5de6\u5b50\u6570\u7ec4\u3001\u53f3\u5b50\u6570\u7ec4\u7684\u9996\u5143\u7d20\ni = left_start\nj = right_start\n# \u901a\u8fc7\u8986\u76d6\u539f\u6570\u7ec4 nums \u6765\u5408\u5e76\u5de6\u5b50\u6570\u7ec4\u548c\u53f3\u5b50\u6570\u7ec4\nfor k in range(left, right + 1):\n# \u82e5\u201c\u5de6\u5b50\u6570\u7ec4\u5df2\u5168\u90e8\u5408\u5e76\u5b8c\u201d\uff0c\u5219\u9009\u53d6\u53f3\u5b50\u6570\u7ec4\u5143\u7d20\uff0c\u5e76\u4e14 j++\nif i &gt; left_end:\nnums[k] = tmp[j]\nj += 1\n# \u5426\u5219\uff0c\u82e5\u201c\u53f3\u5b50\u6570\u7ec4\u5df2\u5168\u90e8\u5408\u5e76\u5b8c\u201d\u6216\u201c\u5de6\u5b50\u6570\u7ec4\u5143\u7d20 &lt;= \u53f3\u5b50\u6570\u7ec4\u5143\u7d20\u201d\uff0c\u5219\u9009\u53d6\u5de6\u5b50\u6570\u7ec4\u5143\u7d20\uff0c\u5e76\u4e14 i++\nelif j &gt; right_end or tmp[i] &lt;= tmp[j]:\nnums[k] = tmp[i]\ni += 1\n# \u5426\u5219\uff0c\u82e5\u201c\u5de6\u53f3\u5b50\u6570\u7ec4\u90fd\u672a\u5168\u90e8\u5408\u5e76\u5b8c\u201d\u4e14\u201c\u5de6\u5b50\u6570\u7ec4\u5143\u7d20 &gt; \u53f3\u5b50\u6570\u7ec4\u5143\u7d20\u201d\uff0c\u5219\u9009\u53d6\u53f3\u5b50\u6570\u7ec4\u5143\u7d20\uff0c\u5e76\u4e14 j++\nelse:\nnums[k] = tmp[j]\nj += 1\ndef merge_sort(nums: list[int], left: int, right: int) -&gt; None:\n\"\"\"\u5f52\u5e76\u6392\u5e8f\"\"\"\n# \u7ec8\u6b62\u6761\u4ef6\nif left &gt;= right:\nreturn  # \u5f53\u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a 1 \u65f6\u7ec8\u6b62\u9012\u5f52\n# \u5212\u5206\u9636\u6bb5\nmid = (left + right) // 2  # \u8ba1\u7b97\u4e2d\u70b9\nmerge_sort(nums, left, mid)  # \u9012\u5f52\u5de6\u5b50\u6570\u7ec4\nmerge_sort(nums, mid + 1, right)  # \u9012\u5f52\u53f3\u5b50\u6570\u7ec4\n# \u5408\u5e76\u9636\u6bb5\nmerge(nums, left, mid, right)\n</code></pre> merge_sort.go<pre><code>/* \u5408\u5e76\u5de6\u5b50\u6570\u7ec4\u548c\u53f3\u5b50\u6570\u7ec4 */\n// \u5de6\u5b50\u6570\u7ec4\u533a\u95f4 [left, mid]\n// \u53f3\u5b50\u6570\u7ec4\u533a\u95f4 [mid + 1, right]\nfunc merge(nums []int, left, mid, right int) {\n// \u521d\u59cb\u5316\u8f85\u52a9\u6570\u7ec4 \u501f\u52a9 copy \u6a21\u5757\ntmp := make([]int, right-left+1)\nfor i := left; i &lt;= right; i++ {\ntmp[i-left] = nums[i]\n}\n// \u5de6\u5b50\u6570\u7ec4\u7684\u8d77\u59cb\u7d22\u5f15\u548c\u7ed3\u675f\u7d22\u5f15\nleftStart, leftEnd := left-left, mid-left\n// \u53f3\u5b50\u6570\u7ec4\u7684\u8d77\u59cb\u7d22\u5f15\u548c\u7ed3\u675f\u7d22\u5f15\nrightStart, rightEnd := mid+1-left, right-left\n// i, j \u5206\u522b\u6307\u5411\u5de6\u5b50\u6570\u7ec4\u3001\u53f3\u5b50\u6570\u7ec4\u7684\u9996\u5143\u7d20\ni, j := leftStart, rightStart\n// \u901a\u8fc7\u8986\u76d6\u539f\u6570\u7ec4 nums \u6765\u5408\u5e76\u5de6\u5b50\u6570\u7ec4\u548c\u53f3\u5b50\u6570\u7ec4\nfor k := left; k &lt;= right; k++ {\n// \u82e5\u201c\u5de6\u5b50\u6570\u7ec4\u5df2\u5168\u90e8\u5408\u5e76\u5b8c\u201d\uff0c\u5219\u9009\u53d6\u53f3\u5b50\u6570\u7ec4\u5143\u7d20\uff0c\u5e76\u4e14 j++\nif i &gt; leftEnd {\nnums[k] = tmp[j]\nj++\n// \u5426\u5219\uff0c\u82e5\u201c\u53f3\u5b50\u6570\u7ec4\u5df2\u5168\u90e8\u5408\u5e76\u5b8c\u201d\u6216\u201c\u5de6\u5b50\u6570\u7ec4\u5143\u7d20 &lt;= \u53f3\u5b50\u6570\u7ec4\u5143\u7d20\u201d\uff0c\u5219\u9009\u53d6\u5de6\u5b50\u6570\u7ec4\u5143\u7d20\uff0c\u5e76\u4e14 i++\n} else if j &gt; rightEnd || tmp[i] &lt;= tmp[j] {\nnums[k] = tmp[i]\ni++\n// \u5426\u5219\uff0c\u82e5\u201c\u5de6\u53f3\u5b50\u6570\u7ec4\u90fd\u672a\u5168\u90e8\u5408\u5e76\u5b8c\u201d\u4e14\u201c\u5de6\u5b50\u6570\u7ec4\u5143\u7d20 &gt; \u53f3\u5b50\u6570\u7ec4\u5143\u7d20\u201d\uff0c\u5219\u9009\u53d6\u53f3\u5b50\u6570\u7ec4\u5143\u7d20\uff0c\u5e76\u4e14 j++\n} else {\nnums[k] = tmp[j]\nj++\n}\n}\n}\n/* \u5f52\u5e76\u6392\u5e8f */\nfunc mergeSort(nums []int, left, right int) {\n// \u7ec8\u6b62\u6761\u4ef6\nif left &gt;= right {\nreturn\n}\n// \u5212\u5206\u9636\u6bb5\nmid := (left + right) / 2\nmergeSort(nums, left, mid)\nmergeSort(nums, mid+1, right)\n// \u5408\u5e76\u9636\u6bb5\nmerge(nums, left, mid, right)\n}\n</code></pre> merge_sort.js<pre><code>/* \u5408\u5e76\u5de6\u5b50\u6570\u7ec4\u548c\u53f3\u5b50\u6570\u7ec4 */\n// \u5de6\u5b50\u6570\u7ec4\u533a\u95f4 [left, mid]\n// \u53f3\u5b50\u6570\u7ec4\u533a\u95f4 [mid + 1, right]\nfunction merge(nums, left, mid, right) {\n// \u521d\u59cb\u5316\u8f85\u52a9\u6570\u7ec4\nlet tmp = nums.slice(left, right + 1);\n// \u5de6\u5b50\u6570\u7ec4\u7684\u8d77\u59cb\u7d22\u5f15\u548c\u7ed3\u675f\u7d22\u5f15\nlet leftStart = left - left,\nleftEnd = mid - left;\n// \u53f3\u5b50\u6570\u7ec4\u7684\u8d77\u59cb\u7d22\u5f15\u548c\u7ed3\u675f\u7d22\u5f15\nlet rightStart = mid + 1 - left,\nrightEnd = right - left;\n// i, j \u5206\u522b\u6307\u5411\u5de6\u5b50\u6570\u7ec4\u3001\u53f3\u5b50\u6570\u7ec4\u7684\u9996\u5143\u7d20\nlet i = leftStart,\nj = rightStart;\n// \u901a\u8fc7\u8986\u76d6\u539f\u6570\u7ec4 nums \u6765\u5408\u5e76\u5de6\u5b50\u6570\u7ec4\u548c\u53f3\u5b50\u6570\u7ec4\nfor (let k = left; k &lt;= right; k++) {\nif (i &gt; leftEnd) {\n// \u82e5\u201c\u5de6\u5b50\u6570\u7ec4\u5df2\u5168\u90e8\u5408\u5e76\u5b8c\u201d\uff0c\u5219\u9009\u53d6\u53f3\u5b50\u6570\u7ec4\u5143\u7d20\uff0c\u5e76\u4e14 j++\nnums[k] = tmp[j++];\n} else if (j &gt; rightEnd || tmp[i] &lt;= tmp[j]) {\n// \u5426\u5219\uff0c\u82e5\u201c\u53f3\u5b50\u6570\u7ec4\u5df2\u5168\u90e8\u5408\u5e76\u5b8c\u201d\u6216\u201c\u5de6\u5b50\u6570\u7ec4\u5143\u7d20 &lt;= \u53f3\u5b50\u6570\u7ec4\u5143\u7d20\u201d\uff0c\u5219\u9009\u53d6\u5de6\u5b50\u6570\u7ec4\u5143\u7d20\uff0c\u5e76\u4e14 i++\nnums[k] = tmp[i++];\n} else {\n// \u5426\u5219\uff0c\u82e5\u201c\u5de6\u53f3\u5b50\u6570\u7ec4\u90fd\u672a\u5168\u90e8\u5408\u5e76\u5b8c\u201d\u4e14\u201c\u5de6\u5b50\u6570\u7ec4\u5143\u7d20 &gt; \u53f3\u5b50\u6570\u7ec4\u5143\u7d20\u201d\uff0c\u5219\u9009\u53d6\u53f3\u5b50\u6570\u7ec4\u5143\u7d20\uff0c\u5e76\u4e14 j++\nnums[k] = tmp[j++];\n}\n}\n}\n/* \u5f52\u5e76\u6392\u5e8f */\nfunction mergeSort(nums, left, right) {\n// \u7ec8\u6b62\u6761\u4ef6\nif (left &gt;= right) return; // \u5f53\u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a 1 \u65f6\u7ec8\u6b62\u9012\u5f52\n// \u5212\u5206\u9636\u6bb5\nlet mid = Math.floor((left + right) / 2); // \u8ba1\u7b97\u4e2d\u70b9\nmergeSort(nums, left, mid); // \u9012\u5f52\u5de6\u5b50\u6570\u7ec4\nmergeSort(nums, mid + 1, right); // \u9012\u5f52\u53f3\u5b50\u6570\u7ec4\n// \u5408\u5e76\u9636\u6bb5\nmerge(nums, left, mid, right);\n}\n</code></pre> merge_sort.ts<pre><code>/* \u5408\u5e76\u5de6\u5b50\u6570\u7ec4\u548c\u53f3\u5b50\u6570\u7ec4 */\n// \u5de6\u5b50\u6570\u7ec4\u533a\u95f4 [left, mid]\n// \u53f3\u5b50\u6570\u7ec4\u533a\u95f4 [mid + 1, right]\nfunction merge(nums: number[], left: number, mid: number, right: number): void {\n// \u521d\u59cb\u5316\u8f85\u52a9\u6570\u7ec4\nlet tmp = nums.slice(left, right + 1);\n// \u5de6\u5b50\u6570\u7ec4\u7684\u8d77\u59cb\u7d22\u5f15\u548c\u7ed3\u675f\u7d22\u5f15\nlet leftStart = left - left,\nleftEnd = mid - left;\n// \u53f3\u5b50\u6570\u7ec4\u7684\u8d77\u59cb\u7d22\u5f15\u548c\u7ed3\u675f\u7d22\u5f15\nlet rightStart = mid + 1 - left,\nrightEnd = right - left;\n// i, j \u5206\u522b\u6307\u5411\u5de6\u5b50\u6570\u7ec4\u3001\u53f3\u5b50\u6570\u7ec4\u7684\u9996\u5143\u7d20\nlet i = leftStart,\nj = rightStart;\n// \u901a\u8fc7\u8986\u76d6\u539f\u6570\u7ec4 nums \u6765\u5408\u5e76\u5de6\u5b50\u6570\u7ec4\u548c\u53f3\u5b50\u6570\u7ec4\nfor (let k = left; k &lt;= right; k++) {\nif (i &gt; leftEnd) {\n// \u82e5\u201c\u5de6\u5b50\u6570\u7ec4\u5df2\u5168\u90e8\u5408\u5e76\u5b8c\u201d\uff0c\u5219\u9009\u53d6\u53f3\u5b50\u6570\u7ec4\u5143\u7d20\uff0c\u5e76\u4e14 j++\nnums[k] = tmp[j++];\n// \u5426\u5219\uff0c\u82e5\u201c\u53f3\u5b50\u6570\u7ec4\u5df2\u5168\u90e8\u5408\u5e76\u5b8c\u201d\u6216\u201c\u5de6\u5b50\u6570\u7ec4\u5143\u7d20 &lt;= \u53f3\u5b50\u6570\u7ec4\u5143\u7d20\u201d\uff0c\u5219\u9009\u53d6\u5de6\u5b50\u6570\u7ec4\u5143\u7d20\uff0c\u5e76\u4e14 i++\n} else if (j &gt; rightEnd || tmp[i] &lt;= tmp[j]) {\nnums[k] = tmp[i++];\n// \u5426\u5219\uff0c\u82e5\u201c\u5de6\u53f3\u5b50\u6570\u7ec4\u90fd\u672a\u5168\u90e8\u5408\u5e76\u5b8c\u201d\u4e14\u201c\u5de6\u5b50\u6570\u7ec4\u5143\u7d20 &gt; \u53f3\u5b50\u6570\u7ec4\u5143\u7d20\u201d\uff0c\u5219\u9009\u53d6\u53f3\u5b50\u6570\u7ec4\u5143\u7d20\uff0c\u5e76\u4e14 j++\n} else {\nnums[k] = tmp[j++];\n}\n}\n}\n/* \u5f52\u5e76\u6392\u5e8f */\nfunction mergeSort(nums: number[], left: number, right: number): void {\n// \u7ec8\u6b62\u6761\u4ef6\nif (left &gt;= right) return; // \u5f53\u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a 1 \u65f6\u7ec8\u6b62\u9012\u5f52\n// \u5212\u5206\u9636\u6bb5\nlet mid = Math.floor((left + right) / 2); // \u8ba1\u7b97\u4e2d\u70b9\nmergeSort(nums, left, mid); // \u9012\u5f52\u5de6\u5b50\u6570\u7ec4\nmergeSort(nums, mid + 1, right); // \u9012\u5f52\u53f3\u5b50\u6570\u7ec4\n// \u5408\u5e76\u9636\u6bb5\nmerge(nums, left, mid, right);\n}\n</code></pre> merge_sort.c<pre><code>/* \u5408\u5e76\u5de6\u5b50\u6570\u7ec4\u548c\u53f3\u5b50\u6570\u7ec4 */\n// \u5de6\u5b50\u6570\u7ec4\u533a\u95f4 [left, mid]\n// \u53f3\u5b50\u6570\u7ec4\u533a\u95f4 [mid + 1, right]\nvoid merge(int *nums, int left, int mid, int right) {\nint index;\n// \u521d\u59cb\u5316\u8f85\u52a9\u6570\u7ec4\nint tmp[right + 1 - left];\nfor (index = left; index &lt; right + 1; index++) {\ntmp[index - left] = nums[index];\n}\n// \u5de6\u5b50\u6570\u7ec4\u7684\u8d77\u59cb\u7d22\u5f15\u548c\u7ed3\u675f\u7d22\u5f15\nint leftStart = left - left, leftEnd = mid - left;\n// \u53f3\u5b50\u6570\u7ec4\u7684\u8d77\u59cb\u7d22\u5f15\u548c\u7ed3\u675f\u7d22\u5f15\nint rightStart = mid + 1 - left, rightEnd = right - left;\n// i, j \u5206\u522b\u6307\u5411\u5de6\u5b50\u6570\u7ec4\u3001\u53f3\u5b50\u6570\u7ec4\u7684\u9996\u5143\u7d20\nint i = leftStart, j = rightStart;\n// \u901a\u8fc7\u8986\u76d6\u539f\u6570\u7ec4 nums \u6765\u5408\u5e76\u5de6\u5b50\u6570\u7ec4\u548c\u53f3\u5b50\u6570\u7ec4\nfor (int k = left; k &lt;= right; k++) {\n// \u82e5\u201c\u5de6\u5b50\u6570\u7ec4\u5df2\u5168\u90e8\u5408\u5e76\u5b8c\u201d\uff0c\u5219\u9009\u53d6\u53f3\u5b50\u6570\u7ec4\u5143\u7d20\uff0c\u5e76\u4e14 j++\nif (i &gt; leftEnd)\nnums[k] = tmp[j++];\n// \u5426\u5219\uff0c\u82e5\u201c\u53f3\u5b50\u6570\u7ec4\u5df2\u5168\u90e8\u5408\u5e76\u5b8c\u201d\u6216\u201c\u5de6\u5b50\u6570\u7ec4\u5143\u7d20 &lt;= \u53f3\u5b50\u6570\u7ec4\u5143\u7d20\u201d\uff0c\u5219\u9009\u53d6\u5de6\u5b50\u6570\u7ec4\u5143\u7d20\uff0c\u5e76\u4e14 i++\nelse if (j &gt; rightEnd || tmp[i] &lt;= tmp[j])\nnums[k] = tmp[i++];\n// \u5426\u5219\uff0c\u82e5\u201c\u5de6\u53f3\u5b50\u6570\u7ec4\u90fd\u672a\u5168\u90e8\u5408\u5e76\u5b8c\u201d\u4e14\u201c\u5de6\u5b50\u6570\u7ec4\u5143\u7d20 &gt; \u53f3\u5b50\u6570\u7ec4\u5143\u7d20\u201d\uff0c\u5219\u9009\u53d6\u53f3\u5b50\u6570\u7ec4\u5143\u7d20\uff0c\u5e76\u4e14 j++\nelse\nnums[k] = tmp[j++];\n}\n}\n/* \u5f52\u5e76\u6392\u5e8f */\nvoid mergeSort(int *nums, int left, int right) {\n// \u7ec8\u6b62\u6761\u4ef6\nif (left &gt;= right)\nreturn; // \u5f53\u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a 1 \u65f6\u7ec8\u6b62\u9012\u5f52\n// \u5212\u5206\u9636\u6bb5\nint mid = (left + right) / 2;    // \u8ba1\u7b97\u4e2d\u70b9\nmergeSort(nums, left, mid);      // \u9012\u5f52\u5de6\u5b50\u6570\u7ec4\nmergeSort(nums, mid + 1, right); // \u9012\u5f52\u53f3\u5b50\u6570\u7ec4\n// \u5408\u5e76\u9636\u6bb5\nmerge(nums, left, mid, right);\n}\n</code></pre> merge_sort.cs<pre><code>/* \u5408\u5e76\u5de6\u5b50\u6570\u7ec4\u548c\u53f3\u5b50\u6570\u7ec4 */\n// \u5de6\u5b50\u6570\u7ec4\u533a\u95f4 [left, mid]\n// \u53f3\u5b50\u6570\u7ec4\u533a\u95f4 [mid + 1, right]\nvoid merge(int[] nums, int left, int mid, int right) {\n// \u521d\u59cb\u5316\u8f85\u52a9\u6570\u7ec4\nint[] tmp = nums[left..(right + 1)];\n// \u5de6\u5b50\u6570\u7ec4\u7684\u8d77\u59cb\u7d22\u5f15\u548c\u7ed3\u675f\u7d22\u5f15  \nint leftStart = left - left, leftEnd = mid - left;\n// \u53f3\u5b50\u6570\u7ec4\u7684\u8d77\u59cb\u7d22\u5f15\u548c\u7ed3\u675f\u7d22\u5f15       \nint rightStart = mid + 1 - left, rightEnd = right - left;\n// i, j \u5206\u522b\u6307\u5411\u5de6\u5b50\u6570\u7ec4\u3001\u53f3\u5b50\u6570\u7ec4\u7684\u9996\u5143\u7d20\nint i = leftStart, j = rightStart;\n// \u901a\u8fc7\u8986\u76d6\u539f\u6570\u7ec4 nums \u6765\u5408\u5e76\u5de6\u5b50\u6570\u7ec4\u548c\u53f3\u5b50\u6570\u7ec4\nfor (int k = left; k &lt;= right; k++) {\n// \u82e5\u201c\u5de6\u5b50\u6570\u7ec4\u5df2\u5168\u90e8\u5408\u5e76\u5b8c\u201d\uff0c\u5219\u9009\u53d6\u53f3\u5b50\u6570\u7ec4\u5143\u7d20\uff0c\u5e76\u4e14 j++\nif (i &gt; leftEnd)\nnums[k] = tmp[j++];\n// \u5426\u5219\uff0c\u82e5\u201c\u53f3\u5b50\u6570\u7ec4\u5df2\u5168\u90e8\u5408\u5e76\u5b8c\u201d\u6216\u201c\u5de6\u5b50\u6570\u7ec4\u5143\u7d20 &lt;= \u53f3\u5b50\u6570\u7ec4\u5143\u7d20\u201d\uff0c\u5219\u9009\u53d6\u5de6\u5b50\u6570\u7ec4\u5143\u7d20\uff0c\u5e76\u4e14 i++\nelse if (j &gt; rightEnd || tmp[i] &lt;= tmp[j])\nnums[k] = tmp[i++];\n// \u5426\u5219\uff0c\u82e5\u201c\u5de6\u53f3\u5b50\u6570\u7ec4\u90fd\u672a\u5168\u90e8\u5408\u5e76\u5b8c\u201d\u4e14\u201c\u5de6\u5b50\u6570\u7ec4\u5143\u7d20 &gt; \u53f3\u5b50\u6570\u7ec4\u5143\u7d20\u201d\uff0c\u5219\u9009\u53d6\u53f3\u5b50\u6570\u7ec4\u5143\u7d20\uff0c\u5e76\u4e14 j++\nelse\nnums[k] = tmp[j++];\n}\n}\n/* \u5f52\u5e76\u6392\u5e8f */\nvoid mergeSort(int[] nums, int left, int right) {\n// \u7ec8\u6b62\u6761\u4ef6\nif (left &gt;= right) return;       // \u5f53\u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a 1 \u65f6\u7ec8\u6b62\u9012\u5f52\n// \u5212\u5206\u9636\u6bb5\nint mid = (left + right) / 2;    // \u8ba1\u7b97\u4e2d\u70b9\nmergeSort(nums, left, mid);      // \u9012\u5f52\u5de6\u5b50\u6570\u7ec4\nmergeSort(nums, mid + 1, right); // \u9012\u5f52\u53f3\u5b50\u6570\u7ec4\n// \u5408\u5e76\u9636\u6bb5\nmerge(nums, left, mid, right);\n}\n</code></pre> merge_sort.swift<pre><code>/* \u5408\u5e76\u5de6\u5b50\u6570\u7ec4\u548c\u53f3\u5b50\u6570\u7ec4 */\n// \u5de6\u5b50\u6570\u7ec4\u533a\u95f4 [left, mid]\n// \u53f3\u5b50\u6570\u7ec4\u533a\u95f4 [mid + 1, right]\nfunc merge(nums: inout [Int], left: Int, mid: Int, right: Int) {\n// \u521d\u59cb\u5316\u8f85\u52a9\u6570\u7ec4\nlet tmp = Array(nums[left ..&lt; (right + 1)])\n// \u5de6\u5b50\u6570\u7ec4\u7684\u8d77\u59cb\u7d22\u5f15\u548c\u7ed3\u675f\u7d22\u5f15\nlet leftStart = left - left\nlet leftEnd = mid - left\n// \u53f3\u5b50\u6570\u7ec4\u7684\u8d77\u59cb\u7d22\u5f15\u548c\u7ed3\u675f\u7d22\u5f15\nlet rightStart = mid + 1 - left\nlet rightEnd = right - left\n// i, j \u5206\u522b\u6307\u5411\u5de6\u5b50\u6570\u7ec4\u3001\u53f3\u5b50\u6570\u7ec4\u7684\u9996\u5143\u7d20\nvar i = leftStart\nvar j = rightStart\n// \u901a\u8fc7\u8986\u76d6\u539f\u6570\u7ec4 nums \u6765\u5408\u5e76\u5de6\u5b50\u6570\u7ec4\u548c\u53f3\u5b50\u6570\u7ec4\nfor k in left ... right {\n// \u82e5\u201c\u5de6\u5b50\u6570\u7ec4\u5df2\u5168\u90e8\u5408\u5e76\u5b8c\u201d\uff0c\u5219\u9009\u53d6\u53f3\u5b50\u6570\u7ec4\u5143\u7d20\uff0c\u5e76\u4e14 j++\nif i &gt; leftEnd {\nnums[k] = tmp[j]\nj += 1\n}\n// \u5426\u5219\uff0c\u82e5\u201c\u53f3\u5b50\u6570\u7ec4\u5df2\u5168\u90e8\u5408\u5e76\u5b8c\u201d\u6216\u201c\u5de6\u5b50\u6570\u7ec4\u5143\u7d20 &lt;= \u53f3\u5b50\u6570\u7ec4\u5143\u7d20\u201d\uff0c\u5219\u9009\u53d6\u5de6\u5b50\u6570\u7ec4\u5143\u7d20\uff0c\u5e76\u4e14 i++\nelse if j &gt; rightEnd || tmp[i] &lt;= tmp[j] {\nnums[k] = tmp[i]\ni += 1\n}\n// \u5426\u5219\uff0c\u82e5\u201c\u5de6\u53f3\u5b50\u6570\u7ec4\u90fd\u672a\u5168\u90e8\u5408\u5e76\u5b8c\u201d\u4e14\u201c\u5de6\u5b50\u6570\u7ec4\u5143\u7d20 &gt; \u53f3\u5b50\u6570\u7ec4\u5143\u7d20\u201d\uff0c\u5219\u9009\u53d6\u53f3\u5b50\u6570\u7ec4\u5143\u7d20\uff0c\u5e76\u4e14 j++\nelse {\nnums[k] = tmp[j]\nj += 1\n}\n}\n}\n/* \u5f52\u5e76\u6392\u5e8f */\nfunc mergeSort(nums: inout [Int], left: Int, right: Int) {\n// \u7ec8\u6b62\u6761\u4ef6\nif left &gt;= right { // \u5f53\u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a 1 \u65f6\u7ec8\u6b62\u9012\u5f52\nreturn\n}\n// \u5212\u5206\u9636\u6bb5\nlet mid = (left + right) / 2 // \u8ba1\u7b97\u4e2d\u70b9\nmergeSort(nums: &amp;nums, left: left, right: mid) // \u9012\u5f52\u5de6\u5b50\u6570\u7ec4\nmergeSort(nums: &amp;nums, left: mid + 1, right: right) // \u9012\u5f52\u53f3\u5b50\u6570\u7ec4\n// \u5408\u5e76\u9636\u6bb5\nmerge(nums: &amp;nums, left: left, mid: mid, right: right)\n}\n</code></pre> merge_sort.zig<pre><code>// \u5408\u5e76\u5de6\u5b50\u6570\u7ec4\u548c\u53f3\u5b50\u6570\u7ec4\n// \u5de6\u5b50\u6570\u7ec4\u533a\u95f4 [left, mid]\n// \u53f3\u5b50\u6570\u7ec4\u533a\u95f4 [mid + 1, right]\nfn merge(nums: []i32, left: usize, mid: usize, right: usize) !void {\n// \u521d\u59cb\u5316\u8f85\u52a9\u6570\u7ec4\nvar mem_arena = std.heap.ArenaAllocator.init(std.heap.page_allocator);\ndefer mem_arena.deinit();\nconst mem_allocator = mem_arena.allocator();\nvar tmp = try mem_allocator.alloc(i32, right + 1 - left);\nstd.mem.copy(i32, tmp, nums[left..right+1]);\n// \u5de6\u5b50\u6570\u7ec4\u7684\u8d77\u59cb\u7d22\u5f15\u548c\u7ed3\u675f\u7d22\u5f15  \nvar leftStart = left - left;\nvar leftEnd = mid - left;\n// \u53f3\u5b50\u6570\u7ec4\u7684\u8d77\u59cb\u7d22\u5f15\u548c\u7ed3\u675f\u7d22\u5f15       \nvar rightStart = mid + 1 - left;\nvar rightEnd = right - left;\n// i, j \u5206\u522b\u6307\u5411\u5de6\u5b50\u6570\u7ec4\u3001\u53f3\u5b50\u6570\u7ec4\u7684\u9996\u5143\u7d20\nvar i = leftStart;\nvar j = rightStart;\n// \u901a\u8fc7\u8986\u76d6\u539f\u6570\u7ec4 nums \u6765\u5408\u5e76\u5de6\u5b50\u6570\u7ec4\u548c\u53f3\u5b50\u6570\u7ec4\nvar k = left;\nwhile (k &lt;= right) : (k += 1) {\n// \u82e5\u201c\u5de6\u5b50\u6570\u7ec4\u5df2\u5168\u90e8\u5408\u5e76\u5b8c\u201d\uff0c\u5219\u9009\u53d6\u53f3\u5b50\u6570\u7ec4\u5143\u7d20\uff0c\u5e76\u4e14 j++\nif (i &gt; leftEnd) {\nnums[k] = tmp[j];\nj += 1;\n// \u5426\u5219\uff0c\u82e5\u201c\u53f3\u5b50\u6570\u7ec4\u5df2\u5168\u90e8\u5408\u5e76\u5b8c\u201d\u6216\u201c\u5de6\u5b50\u6570\u7ec4\u5143\u7d20 &lt;= \u53f3\u5b50\u6570\u7ec4\u5143\u7d20\u201d\uff0c\u5219\u9009\u53d6\u5de6\u5b50\u6570\u7ec4\u5143\u7d20\uff0c\u5e76\u4e14 i++\n} else if  (j &gt; rightEnd or tmp[i] &lt;= tmp[j]) {\nnums[k] = tmp[i];\ni += 1;\n// \u5426\u5219\uff0c\u82e5\u201c\u5de6\u53f3\u5b50\u6570\u7ec4\u90fd\u672a\u5168\u90e8\u5408\u5e76\u5b8c\u201d\u4e14\u201c\u5de6\u5b50\u6570\u7ec4\u5143\u7d20 &gt; \u53f3\u5b50\u6570\u7ec4\u5143\u7d20\u201d\uff0c\u5219\u9009\u53d6\u53f3\u5b50\u6570\u7ec4\u5143\u7d20\uff0c\u5e76\u4e14 j++\n} else {\nnums[k] = tmp[j];\nj += 1;\n}\n}\n}\n// \u5f52\u5e76\u6392\u5e8f\nfn mergeSort(nums: []i32, left: usize, right: usize) !void {\n// \u7ec8\u6b62\u6761\u4ef6\nif (left &gt;= right) return;              // \u5f53\u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a 1 \u65f6\u7ec8\u6b62\u9012\u5f52\n// \u5212\u5206\u9636\u6bb5\nvar mid = (left + right) / 2;           // \u8ba1\u7b97\u4e2d\u70b9\ntry mergeSort(nums, left, mid);         // \u9012\u5f52\u5de6\u5b50\u6570\u7ec4\ntry mergeSort(nums, mid + 1, right);    // \u9012\u5f52\u53f3\u5b50\u6570\u7ec4\n// \u5408\u5e76\u9636\u6bb5\ntry merge(nums, left, mid, right);\n}\n</code></pre> merge_sort.dart<pre><code>/* \u5408\u5e76\u5de6\u5b50\u6570\u7ec4\u548c\u53f3\u5b50\u6570\u7ec4 */\n// \u5de6\u5b50\u6570\u7ec4\u533a\u95f4 [left, mid]\n// \u53f3\u5b50\u6570\u7ec4\u533a\u95f4 [mid + 1, right]\nvoid merge(List&lt;int&gt; nums, int left, int mid, int right) {\n// \u521d\u59cb\u5316\u8f85\u52a9\u6570\u7ec4\nList&lt;int&gt; tmp = nums.sublist(left, right + 1);\n// \u5de6\u5b50\u6570\u7ec4\u7684\u8d77\u59cb\u7d22\u5f15\u548c\u7ed3\u675f\u7d22\u5f15\nint leftStart = left - left, leftEnd = mid - left;\n// \u53f3\u5b50\u6570\u7ec4\u7684\u8d77\u59cb\u7d22\u5f15\u548c\u7ed3\u675f\u7d22\u5f15\nint rightStart = mid + 1 - left, rightEnd = right - left;\n// i, j \u5206\u522b\u6307\u5411\u5de6\u5b50\u6570\u7ec4\u3001\u53f3\u5b50\u6570\u7ec4\u7684\u9996\u5143\u7d20\nint i = leftStart, j = rightStart;\n// \u901a\u8fc7\u8986\u76d6\u539f\u6570\u7ec4 nums \u6765\u5408\u5e76\u5de6\u5b50\u6570\u7ec4\u548c\u53f3\u5b50\u6570\u7ec4\nfor (int k = left; k &lt;= right; k++) {\n// \u82e5\u201c\u5de6\u5b50\u6570\u7ec4\u5df2\u5168\u90e8\u5408\u5e76\u5b8c\u201d\uff0c\u5219\u9009\u53d6\u53f3\u5b50\u6570\u7ec4\u5143\u7d20\uff0c\u5e76\u4e14 j++\nif (i &gt; leftEnd)\nnums[k] = tmp[j++];\n// \u5426\u5219\uff0c\u82e5\u201c\u53f3\u5b50\u6570\u7ec4\u5df2\u5168\u90e8\u5408\u5e76\u5b8c\u201d\u6216\u201c\u5de6\u5b50\u6570\u7ec4\u5143\u7d20 &lt;= \u53f3\u5b50\u6570\u7ec4\u5143\u7d20\u201d\uff0c\u5219\u9009\u53d6\u5de6\u5b50\u6570\u7ec4\u5143\u7d20\uff0c\u5e76\u4e14 i++\nelse if (j &gt; rightEnd || tmp[i] &lt;= tmp[j])\nnums[k] = tmp[i++];\n// \u5426\u5219\uff0c\u82e5\u201c\u5de6\u53f3\u5b50\u6570\u7ec4\u90fd\u672a\u5168\u90e8\u5408\u5e76\u5b8c\u201d\u4e14\u201c\u5de6\u5b50\u6570\u7ec4\u5143\u7d20 &gt; \u53f3\u5b50\u6570\u7ec4\u5143\u7d20\u201d\uff0c\u5219\u9009\u53d6\u53f3\u5b50\u6570\u7ec4\u5143\u7d20\uff0c\u5e76\u4e14 j++\nelse\nnums[k] = tmp[j++];\n}\n}\n/* \u5f52\u5e76\u6392\u5e8f */\nvoid mergeSort(List&lt;int&gt; nums, int left, int right) {\n// \u7ec8\u6b62\u6761\u4ef6\nif (left &gt;= right) return; // \u5f53\u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a 1 \u65f6\u7ec8\u6b62\u9012\u5f52\n// \u5212\u5206\u9636\u6bb5\nint mid = (left + right) ~/ 2; // \u8ba1\u7b97\u4e2d\u70b9\nmergeSort(nums, left, mid); // \u9012\u5f52\u5de6\u5b50\u6570\u7ec4\nmergeSort(nums, mid + 1, right); // \u9012\u5f52\u53f3\u5b50\u6570\u7ec4\n// \u5408\u5e76\u9636\u6bb5\nmerge(nums, left, mid, right);\n}\n</code></pre> <p>\u5408\u5e76\u65b9\u6cd5 <code>merge()</code> \u4ee3\u7801\u4e2d\u7684\u96be\u70b9\u5305\u62ec\uff1a</p> <ul> <li>\u5728\u9605\u8bfb\u4ee3\u7801\u65f6\uff0c\u9700\u8981\u7279\u522b\u6ce8\u610f\u5404\u4e2a\u53d8\u91cf\u7684\u542b\u4e49\u3002<code>nums</code> \u7684\u5f85\u5408\u5e76\u533a\u95f4\u4e3a <code>[left, right]</code> \uff0c\u4f46\u7531\u4e8e <code>tmp</code> \u4ec5\u590d\u5236\u4e86 <code>nums</code> \u8be5\u533a\u95f4\u7684\u5143\u7d20\uff0c\u56e0\u6b64 <code>tmp</code> \u5bf9\u5e94\u533a\u95f4\u4e3a <code>[0, right - left]</code> \u3002</li> <li>\u5728\u6bd4\u8f83 <code>tmp[i]</code> \u548c <code>tmp[j]</code> \u7684\u5927\u5c0f\u65f6\uff0c\u8fd8\u9700\u8003\u8651\u5b50\u6570\u7ec4\u904d\u5386\u5b8c\u6210\u540e\u7684\u7d22\u5f15\u8d8a\u754c\u95ee\u9898\uff0c\u5373 <code>i &gt; leftEnd</code> \u548c <code>j &gt; rightEnd</code> \u7684\u60c5\u51b5\u3002\u7d22\u5f15\u8d8a\u754c\u7684\u4f18\u5148\u7ea7\u662f\u6700\u9ad8\u7684\uff0c\u5982\u679c\u5de6\u5b50\u6570\u7ec4\u5df2\u7ecf\u88ab\u5408\u5e76\u5b8c\u4e86\uff0c\u90a3\u4e48\u4e0d\u9700\u8981\u7ee7\u7eed\u6bd4\u8f83\uff0c\u76f4\u63a5\u5408\u5e76\u53f3\u5b50\u6570\u7ec4\u5143\u7d20\u5373\u53ef\u3002</li> </ul>"},{"location":"chapter_sorting/merge_sort/#1162","title":"11.6.2. \u00a0 \u7b97\u6cd5\u7279\u6027","text":"<ul> <li>\u65f6\u95f4\u590d\u6742\u5ea6 \\(O(n \\log n)\\) \u3001\u975e\u81ea\u9002\u5e94\u6392\u5e8f \uff1a\u5212\u5206\u4ea7\u751f\u9ad8\u5ea6\u4e3a \\(\\log n\\) \u7684\u9012\u5f52\u6811\uff0c\u6bcf\u5c42\u5408\u5e76\u7684\u603b\u64cd\u4f5c\u6570\u91cf\u4e3a \\(n\\) \uff0c\u56e0\u6b64\u603b\u4f53\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(n \\log n)\\) \u3002</li> <li>\u7a7a\u95f4\u590d\u6742\u5ea6 \\(O(n)\\) \u3001\u975e\u539f\u5730\u6392\u5e8f \uff1a\u9012\u5f52\u6df1\u5ea6\u4e3a \\(\\log n\\) \uff0c\u4f7f\u7528 \\(O(\\log n)\\) \u5927\u5c0f\u7684\u6808\u5e27\u7a7a\u95f4\u3002\u5408\u5e76\u64cd\u4f5c\u9700\u8981\u501f\u52a9\u8f85\u52a9\u6570\u7ec4\u5b9e\u73b0\uff0c\u4f7f\u7528 \\(O(n)\\) \u5927\u5c0f\u7684\u989d\u5916\u7a7a\u95f4\u3002</li> <li>\u7a33\u5b9a\u6392\u5e8f\uff1a\u5728\u5408\u5e76\u8fc7\u7a0b\u4e2d\uff0c\u76f8\u7b49\u5143\u7d20\u7684\u6b21\u5e8f\u4fdd\u6301\u4e0d\u53d8\u3002</li> </ul>"},{"location":"chapter_sorting/merge_sort/#1163","title":"11.6.3. \u00a0 \u94fe\u8868\u6392\u5e8f *","text":"<p>\u5f52\u5e76\u6392\u5e8f\u5728\u6392\u5e8f\u94fe\u8868\u65f6\u5177\u6709\u663e\u8457\u4f18\u52bf\uff0c\u7a7a\u95f4\u590d\u6742\u5ea6\u53ef\u4ee5\u4f18\u5316\u81f3 \\(O(1)\\) \uff0c\u539f\u56e0\u5982\u4e0b\uff1a</p> <ul> <li>\u7531\u4e8e\u94fe\u8868\u4ec5\u9700\u6539\u53d8\u6307\u9488\u5c31\u53ef\u5b9e\u73b0\u8282\u70b9\u7684\u589e\u5220\u64cd\u4f5c\uff0c\u56e0\u6b64\u5408\u5e76\u9636\u6bb5\uff08\u5c06\u4e24\u4e2a\u77ed\u6709\u5e8f\u94fe\u8868\u5408\u5e76\u4e3a\u4e00\u4e2a\u957f\u6709\u5e8f\u94fe\u8868\uff09\u65e0\u9700\u521b\u5efa\u8f85\u52a9\u94fe\u8868\u3002</li> <li>\u901a\u8fc7\u4f7f\u7528\u201c\u8fed\u4ee3\u5212\u5206\u201d\u66ff\u4ee3\u201c\u9012\u5f52\u5212\u5206\u201d\uff0c\u53ef\u7701\u53bb\u9012\u5f52\u4f7f\u7528\u7684\u6808\u5e27\u7a7a\u95f4\uff1b</li> </ul> <p>\u5177\u4f53\u5b9e\u73b0\u7ec6\u8282\u6bd4\u8f83\u590d\u6742\uff0c\u6709\u5174\u8da3\u7684\u540c\u5b66\u53ef\u4ee5\u67e5\u9605\u76f8\u5173\u8d44\u6599\u8fdb\u884c\u5b66\u4e60\u3002</p>"},{"location":"chapter_sorting/quick_sort/","title":"11.5. \u00a0 \u5feb\u901f\u6392\u5e8f","text":"<p>\u300c\u5feb\u901f\u6392\u5e8f Quick Sort\u300d\u662f\u4e00\u79cd\u57fa\u4e8e\u5206\u6cbb\u601d\u60f3\u7684\u6392\u5e8f\u7b97\u6cd5\uff0c\u8fd0\u884c\u9ad8\u6548\uff0c\u5e94\u7528\u5e7f\u6cdb\u3002</p> <p>\u5feb\u901f\u6392\u5e8f\u7684\u6838\u5fc3\u64cd\u4f5c\u662f\u300c\u54e8\u5175\u5212\u5206\u300d\uff0c\u5176\u76ee\u6807\u662f\uff1a\u9009\u62e9\u6570\u7ec4\u4e2d\u7684\u67d0\u4e2a\u5143\u7d20\u4f5c\u4e3a\u201c\u57fa\u51c6\u6570\u201d\uff0c\u5c06\u6240\u6709\u5c0f\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\u79fb\u5230\u5176\u5de6\u4fa7\uff0c\u800c\u5927\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\u79fb\u5230\u5176\u53f3\u4fa7\u3002\u5177\u4f53\u6765\u8bf4\uff0c\u54e8\u5175\u5212\u5206\u7684\u6d41\u7a0b\u4e3a\uff1a</p> <ol> <li>\u9009\u53d6\u6570\u7ec4\u6700\u5de6\u7aef\u5143\u7d20\u4f5c\u4e3a\u57fa\u51c6\u6570\uff0c\u521d\u59cb\u5316\u4e24\u4e2a\u6307\u9488 <code>i</code> \u548c <code>j</code> \u5206\u522b\u6307\u5411\u6570\u7ec4\u7684\u4e24\u7aef\uff1b</li> <li>\u8bbe\u7f6e\u4e00\u4e2a\u5faa\u73af\uff0c\u5728\u6bcf\u8f6e\u4e2d\u4f7f\u7528 <code>i</code>\uff08<code>j</code>\uff09\u5206\u522b\u5bfb\u627e\u7b2c\u4e00\u4e2a\u6bd4\u57fa\u51c6\u6570\u5927\uff08\u5c0f\uff09\u7684\u5143\u7d20\uff0c\u7136\u540e\u4ea4\u6362\u8fd9\u4e24\u4e2a\u5143\u7d20\uff1b</li> <li>\u5faa\u73af\u6267\u884c\u6b65\u9aa4 <code>2.</code> \uff0c\u76f4\u5230 <code>i</code> \u548c <code>j</code> \u76f8\u9047\u65f6\u505c\u6b62\uff0c\u6700\u540e\u5c06\u57fa\u51c6\u6570\u4ea4\u6362\u81f3\u4e24\u4e2a\u5b50\u6570\u7ec4\u7684\u5206\u754c\u7ebf\uff1b</li> </ol> <p>\u54e8\u5175\u5212\u5206\u5b8c\u6210\u540e\uff0c\u539f\u6570\u7ec4\u88ab\u5212\u5206\u6210\u4e09\u90e8\u5206\uff1a\u5de6\u5b50\u6570\u7ec4\u3001\u57fa\u51c6\u6570\u3001\u53f3\u5b50\u6570\u7ec4\uff0c\u4e14\u6ee1\u8db3\u201c\u5de6\u5b50\u6570\u7ec4\u4efb\u610f\u5143\u7d20 \\(\\leq\\) \u57fa\u51c6\u6570 \\(\\leq\\) \u53f3\u5b50\u6570\u7ec4\u4efb\u610f\u5143\u7d20\u201d\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u63a5\u4e0b\u6765\u53ea\u9700\u5bf9\u8fd9\u4e24\u4e2a\u5b50\u6570\u7ec4\u8fdb\u884c\u6392\u5e8f\u3002</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p>\u5feb\u901f\u6392\u5e8f\u7684\u5206\u6cbb\u601d\u60f3</p> <p>\u54e8\u5175\u5212\u5206\u7684\u5b9e\u8d28\u662f\u5c06\u4e00\u4e2a\u8f83\u957f\u6570\u7ec4\u7684\u6392\u5e8f\u95ee\u9898\u7b80\u5316\u4e3a\u4e24\u4e2a\u8f83\u77ed\u6570\u7ec4\u7684\u6392\u5e8f\u95ee\u9898\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart quick_sort.java<pre><code>/* \u5143\u7d20\u4ea4\u6362 */\nvoid swap(int[] nums, int i, int j) {\nint tmp = nums[i];\nnums[i] = nums[j];\nnums[j] = tmp;\n}\n/* \u54e8\u5175\u5212\u5206 */\nint partition(int[] nums, int left, int right) {\n// \u4ee5 nums[left] \u4f5c\u4e3a\u57fa\u51c6\u6570\nint i = left, j = right;\nwhile (i &lt; j) {\nwhile (i &lt; j &amp;&amp; nums[j] &gt;= nums[left])\nj--;          // \u4ece\u53f3\u5411\u5de6\u627e\u9996\u4e2a\u5c0f\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\nwhile (i &lt; j &amp;&amp; nums[i] &lt;= nums[left])\ni++;          // \u4ece\u5de6\u5411\u53f3\u627e\u9996\u4e2a\u5927\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\nswap(nums, i, j); // \u4ea4\u6362\u8fd9\u4e24\u4e2a\u5143\u7d20\n}\nswap(nums, i, left);  // \u5c06\u57fa\u51c6\u6570\u4ea4\u6362\u81f3\u4e24\u5b50\u6570\u7ec4\u7684\u5206\u754c\u7ebf\nreturn i;             // \u8fd4\u56de\u57fa\u51c6\u6570\u7684\u7d22\u5f15\n}\n</code></pre> quick_sort.cpp<pre><code>/* \u5143\u7d20\u4ea4\u6362 */\nvoid swap(vector&lt;int&gt; &amp;nums, int i, int j) {\nint tmp = nums[i];\nnums[i] = nums[j];\nnums[j] = tmp;\n}\n/* \u54e8\u5175\u5212\u5206 */\nint partition(vector&lt;int&gt; &amp;nums, int left, int right) {\n// \u4ee5 nums[left] \u4f5c\u4e3a\u57fa\u51c6\u6570\nint i = left, j = right;\nwhile (i &lt; j) {\nwhile (i &lt; j &amp;&amp; nums[j] &gt;= nums[left])\nj--; // \u4ece\u53f3\u5411\u5de6\u627e\u9996\u4e2a\u5c0f\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\nwhile (i &lt; j &amp;&amp; nums[i] &lt;= nums[left])\ni++;          // \u4ece\u5de6\u5411\u53f3\u627e\u9996\u4e2a\u5927\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\nswap(nums, i, j); // \u4ea4\u6362\u8fd9\u4e24\u4e2a\u5143\u7d20\n}\nswap(nums, i, left); // \u5c06\u57fa\u51c6\u6570\u4ea4\u6362\u81f3\u4e24\u5b50\u6570\u7ec4\u7684\u5206\u754c\u7ebf\nreturn i;            // \u8fd4\u56de\u57fa\u51c6\u6570\u7684\u7d22\u5f15\n}\n</code></pre> quick_sort.py<pre><code>def partition(self, nums: list[int], left: int, right: int) -&gt; int:\n\"\"\"\u54e8\u5175\u5212\u5206\"\"\"\n# \u4ee5 nums[left] \u4f5c\u4e3a\u57fa\u51c6\u6570\ni, j = left, right\nwhile i &lt; j:\nwhile i &lt; j and nums[j] &gt;= nums[left]:\nj -= 1  # \u4ece\u53f3\u5411\u5de6\u627e\u9996\u4e2a\u5c0f\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\nwhile i &lt; j and nums[i] &lt;= nums[left]:\ni += 1  # \u4ece\u5de6\u5411\u53f3\u627e\u9996\u4e2a\u5927\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\n# \u5143\u7d20\u4ea4\u6362\nnums[i], nums[j] = nums[j], nums[i]\n# \u5c06\u57fa\u51c6\u6570\u4ea4\u6362\u81f3\u4e24\u5b50\u6570\u7ec4\u7684\u5206\u754c\u7ebf\nnums[i], nums[left] = nums[left], nums[i]\nreturn i  # \u8fd4\u56de\u57fa\u51c6\u6570\u7684\u7d22\u5f15\n</code></pre> quick_sort.go<pre><code>/* \u54e8\u5175\u5212\u5206 */\nfunc (q *quickSort) partition(nums []int, left, right int) int {\n// \u4ee5 nums[left] \u4f5c\u4e3a\u57fa\u51c6\u6570\ni, j := left, right\nfor i &lt; j {\nfor i &lt; j &amp;&amp; nums[j] &gt;= nums[left] {\nj-- // \u4ece\u53f3\u5411\u5de6\u627e\u9996\u4e2a\u5c0f\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\n}\nfor i &lt; j &amp;&amp; nums[i] &lt;= nums[left] {\ni++ // \u4ece\u5de6\u5411\u53f3\u627e\u9996\u4e2a\u5927\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\n}\n// \u5143\u7d20\u4ea4\u6362\nnums[i], nums[j] = nums[j], nums[i]\n}\n// \u5c06\u57fa\u51c6\u6570\u4ea4\u6362\u81f3\u4e24\u5b50\u6570\u7ec4\u7684\u5206\u754c\u7ebf\nnums[i], nums[left] = nums[left], nums[i]\nreturn i // \u8fd4\u56de\u57fa\u51c6\u6570\u7684\u7d22\u5f15\n}\n</code></pre> quick_sort.js<pre><code>/* \u5143\u7d20\u4ea4\u6362 */\nswap(nums, i, j) {\nlet tmp = nums[i];\nnums[i] = nums[j];\nnums[j] = tmp;\n}\n/* \u54e8\u5175\u5212\u5206 */\npartition(nums, left, right) {\n// \u4ee5 nums[left] \u4f5c\u4e3a\u57fa\u51c6\u6570\nlet i = left,\nj = right;\nwhile (i &lt; j) {\nwhile (i &lt; j &amp;&amp; nums[j] &gt;= nums[left]) {\nj -= 1; // \u4ece\u53f3\u5411\u5de6\u627e\u9996\u4e2a\u5c0f\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\n}\nwhile (i &lt; j &amp;&amp; nums[i] &lt;= nums[left]) {\ni += 1; // \u4ece\u5de6\u5411\u53f3\u627e\u9996\u4e2a\u5927\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\n}\n// \u5143\u7d20\u4ea4\u6362\nthis.swap(nums, i, j); // \u4ea4\u6362\u8fd9\u4e24\u4e2a\u5143\u7d20\n}\nthis.swap(nums, i, left); // \u5c06\u57fa\u51c6\u6570\u4ea4\u6362\u81f3\u4e24\u5b50\u6570\u7ec4\u7684\u5206\u754c\u7ebf\nreturn i; // \u8fd4\u56de\u57fa\u51c6\u6570\u7684\u7d22\u5f15\n}\n</code></pre> quick_sort.ts<pre><code>/* \u5143\u7d20\u4ea4\u6362 */\nswap(nums: number[], i: number, j: number): void {\nlet tmp = nums[i];\nnums[i] = nums[j];\nnums[j] = tmp;\n}\n/* \u54e8\u5175\u5212\u5206 */\npartition(nums: number[], left: number, right: number): number {\n// \u4ee5 nums[left] \u4f5c\u4e3a\u57fa\u51c6\u6570\nlet i = left,\nj = right;\nwhile (i &lt; j) {\nwhile (i &lt; j &amp;&amp; nums[j] &gt;= nums[left]) {\nj -= 1; // \u4ece\u53f3\u5411\u5de6\u627e\u9996\u4e2a\u5c0f\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\n}\nwhile (i &lt; j &amp;&amp; nums[i] &lt;= nums[left]) {\ni += 1; // \u4ece\u5de6\u5411\u53f3\u627e\u9996\u4e2a\u5927\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\n}\n// \u5143\u7d20\u4ea4\u6362\nthis.swap(nums, i, j); // \u4ea4\u6362\u8fd9\u4e24\u4e2a\u5143\u7d20\n}\nthis.swap(nums, i, left); // \u5c06\u57fa\u51c6\u6570\u4ea4\u6362\u81f3\u4e24\u5b50\u6570\u7ec4\u7684\u5206\u754c\u7ebf\nreturn i; // \u8fd4\u56de\u57fa\u51c6\u6570\u7684\u7d22\u5f15\n}\n</code></pre> quick_sort.c<pre><code>/* \u5143\u7d20\u4ea4\u6362 */\nvoid swap(int nums[], int i, int j) {\nint tmp = nums[i];\nnums[i] = nums[j];\nnums[j] = tmp;\n}\n/* \u5feb\u901f\u6392\u5e8f\u7c7b */\n// \u5feb\u901f\u6392\u5e8f\u7c7b-\u54e8\u5175\u5212\u5206\nint partition(int nums[], int left, int right) {\n// \u4ee5 nums[left] \u4f5c\u4e3a\u57fa\u51c6\u6570\nint i = left, j = right;\nwhile (i &lt; j) {\nwhile (i &lt; j &amp;&amp; nums[j] &gt;= nums[left]) {\n// \u4ece\u53f3\u5411\u5de6\u627e\u9996\u4e2a\u5c0f\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\nj--;\n}\nwhile (i &lt; j &amp;&amp; nums[i] &lt;= nums[left]) {\n// \u4ece\u5de6\u5411\u53f3\u627e\u9996\u4e2a\u5927\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\ni++;\n}\n// \u4ea4\u6362\u8fd9\u4e24\u4e2a\u5143\u7d20\nswap(nums, i, j);\n}\n// \u5c06\u57fa\u51c6\u6570\u4ea4\u6362\u81f3\u4e24\u5b50\u6570\u7ec4\u7684\u5206\u754c\u7ebf\nswap(nums, i, left);\n// \u8fd4\u56de\u57fa\u51c6\u6570\u7684\u7d22\u5f15\nreturn i;\n}\n</code></pre> quick_sort.cs<pre><code>/* \u5143\u7d20\u4ea4\u6362 */\nvoid swap(int[] nums, int i, int j) {\nint tmp = nums[i];\nnums[i] = nums[j];\nnums[j] = tmp;\n}\n/* \u54e8\u5175\u5212\u5206 */\nint partition(int[] nums, int left, int right) {\n// \u4ee5 nums[left] \u4f5c\u4e3a\u57fa\u51c6\u6570\nint i = left, j = right;\nwhile (i &lt; j) {\nwhile (i &lt; j &amp;&amp; nums[j] &gt;= nums[left])\nj--;          // \u4ece\u53f3\u5411\u5de6\u627e\u9996\u4e2a\u5c0f\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\nwhile (i &lt; j &amp;&amp; nums[i] &lt;= nums[left])\ni++;          // \u4ece\u5de6\u5411\u53f3\u627e\u9996\u4e2a\u5927\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\nswap(nums, i, j); // \u4ea4\u6362\u8fd9\u4e24\u4e2a\u5143\u7d20\n}\nswap(nums, i, left);  // \u5c06\u57fa\u51c6\u6570\u4ea4\u6362\u81f3\u4e24\u5b50\u6570\u7ec4\u7684\u5206\u754c\u7ebf\nreturn i;             // \u8fd4\u56de\u57fa\u51c6\u6570\u7684\u7d22\u5f15\n}\n</code></pre> quick_sort.swift<pre><code>/* \u5143\u7d20\u4ea4\u6362 */\nfunc swap(nums: inout [Int], i: Int, j: Int) {\nlet tmp = nums[i]\nnums[i] = nums[j]\nnums[j] = tmp\n}\n/* \u54e8\u5175\u5212\u5206 */\nfunc partition(nums: inout [Int], left: Int, right: Int) -&gt; Int {\n// \u4ee5 nums[left] \u4f5c\u4e3a\u57fa\u51c6\u6570\nvar i = left\nvar j = right\nwhile i &lt; j {\nwhile i &lt; j, nums[j] &gt;= nums[left] {\nj -= 1 // \u4ece\u53f3\u5411\u5de6\u627e\u9996\u4e2a\u5c0f\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\n}\nwhile i &lt; j, nums[i] &lt;= nums[left] {\ni += 1 // \u4ece\u5de6\u5411\u53f3\u627e\u9996\u4e2a\u5927\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\n}\nswap(nums: &amp;nums, i: i, j: j) // \u4ea4\u6362\u8fd9\u4e24\u4e2a\u5143\u7d20\n}\nswap(nums: &amp;nums, i: i, j: left) // \u5c06\u57fa\u51c6\u6570\u4ea4\u6362\u81f3\u4e24\u5b50\u6570\u7ec4\u7684\u5206\u754c\u7ebf\nreturn i // \u8fd4\u56de\u57fa\u51c6\u6570\u7684\u7d22\u5f15\n}\n</code></pre> quick_sort.zig<pre><code>// \u5143\u7d20\u4ea4\u6362\nfn swap(nums: []i32, i: usize, j: usize) void {\nvar tmp = nums[i];\nnums[i] = nums[j];\nnums[j] = tmp;\n}\n// \u54e8\u5175\u5212\u5206\nfn partition(nums: []i32, left: usize, right: usize) usize {\n// \u4ee5 nums[left] \u4f5c\u4e3a\u57fa\u51c6\u6570\nvar i = left;\nvar j = right;\nwhile (i &lt; j) {\nwhile (i &lt; j and nums[j] &gt;= nums[left]) j -= 1; // \u4ece\u53f3\u5411\u5de6\u627e\u9996\u4e2a\u5c0f\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\nwhile (i &lt; j and nums[i] &lt;= nums[left]) i += 1; // \u4ece\u5de6\u5411\u53f3\u627e\u9996\u4e2a\u5927\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\nswap(nums, i, j);   // \u4ea4\u6362\u8fd9\u4e24\u4e2a\u5143\u7d20\n}\nswap(nums, i, left);    // \u5c06\u57fa\u51c6\u6570\u4ea4\u6362\u81f3\u4e24\u5b50\u6570\u7ec4\u7684\u5206\u754c\u7ebf\nreturn i;               // \u8fd4\u56de\u57fa\u51c6\u6570\u7684\u7d22\u5f15\n}\n</code></pre> quick_sort.dart<pre><code>/* \u5143\u7d20\u4ea4\u6362 */\nvoid _swap(List&lt;int&gt; nums, int i, int j) {\nint tmp = nums[i];\nnums[i] = nums[j];\nnums[j] = tmp;\n}\n/* \u54e8\u5175\u5212\u5206 */\nint _partition(List&lt;int&gt; nums, int left, int right) {\n// \u4ee5 nums[left] \u4f5c\u4e3a\u57fa\u51c6\u6570\nint i = left, j = right;\nwhile (i &lt; j) {\nwhile (i &lt; j &amp;&amp; nums[j] &gt;= nums[left]) j--; // \u4ece\u53f3\u5411\u5de6\u627e\u9996\u4e2a\u5c0f\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\nwhile (i &lt; j &amp;&amp; nums[i] &lt;= nums[left]) i++; // \u4ece\u5de6\u5411\u53f3\u627e\u9996\u4e2a\u5927\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\n_swap(nums, i, j); // \u4ea4\u6362\u8fd9\u4e24\u4e2a\u5143\u7d20\n}\n_swap(nums, i, left); // \u5c06\u57fa\u51c6\u6570\u4ea4\u6362\u81f3\u4e24\u5b50\u6570\u7ec4\u7684\u5206\u754c\u7ebf\nreturn i; // \u8fd4\u56de\u57fa\u51c6\u6570\u7684\u7d22\u5f15\n}\n</code></pre>"},{"location":"chapter_sorting/quick_sort/#1151","title":"11.5.1. \u00a0 \u7b97\u6cd5\u6d41\u7a0b","text":"<ol> <li>\u9996\u5148\uff0c\u5bf9\u539f\u6570\u7ec4\u6267\u884c\u4e00\u6b21\u300c\u54e8\u5175\u5212\u5206\u300d\uff0c\u5f97\u5230\u672a\u6392\u5e8f\u7684\u5de6\u5b50\u6570\u7ec4\u548c\u53f3\u5b50\u6570\u7ec4\uff1b</li> <li>\u7136\u540e\uff0c\u5bf9\u5de6\u5b50\u6570\u7ec4\u548c\u53f3\u5b50\u6570\u7ec4\u5206\u522b\u9012\u5f52\u6267\u884c\u300c\u54e8\u5175\u5212\u5206\u300d\uff1b</li> <li>\u6301\u7eed\u9012\u5f52\uff0c\u76f4\u81f3\u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a 1 \u65f6\u7ec8\u6b62\uff0c\u4ece\u800c\u5b8c\u6210\u6574\u4e2a\u6570\u7ec4\u7684\u6392\u5e8f\uff1b</li> </ol> <p> Fig. \u5feb\u901f\u6392\u5e8f\u6d41\u7a0b </p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart quick_sort.java<pre><code>/* \u5feb\u901f\u6392\u5e8f */\nvoid quickSort(int[] nums, int left, int right) {\n// \u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a 1 \u65f6\u7ec8\u6b62\u9012\u5f52\nif (left &gt;= right)\nreturn;\n// \u54e8\u5175\u5212\u5206\nint pivot = partition(nums, left, right);\n// \u9012\u5f52\u5de6\u5b50\u6570\u7ec4\u3001\u53f3\u5b50\u6570\u7ec4\nquickSort(nums, left, pivot - 1);\nquickSort(nums, pivot + 1, right);\n}\n</code></pre> quick_sort.cpp<pre><code>/* \u5feb\u901f\u6392\u5e8f */\nvoid quickSort(vector&lt;int&gt; &amp;nums, int left, int right) {\n// \u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a 1 \u65f6\u7ec8\u6b62\u9012\u5f52\nif (left &gt;= right)\nreturn;\n// \u54e8\u5175\u5212\u5206\nint pivot = partition(nums, left, right);\n// \u9012\u5f52\u5de6\u5b50\u6570\u7ec4\u3001\u53f3\u5b50\u6570\u7ec4\nquickSort(nums, left, pivot - 1);\nquickSort(nums, pivot + 1, right);\n}\n</code></pre> quick_sort.py<pre><code>def quick_sort(self, nums: list[int], left: int, right: int) -&gt; None:\n\"\"\"\u5feb\u901f\u6392\u5e8f\"\"\"\n# \u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a 1 \u65f6\u7ec8\u6b62\u9012\u5f52\nif left &gt;= right:\nreturn\n# \u54e8\u5175\u5212\u5206\npivot = self.partition(nums, left, right)\n# \u9012\u5f52\u5de6\u5b50\u6570\u7ec4\u3001\u53f3\u5b50\u6570\u7ec4\nself.quick_sort(nums, left, pivot - 1)\nself.quick_sort(nums, pivot + 1, right)\n</code></pre> quick_sort.go<pre><code>/* \u5feb\u901f\u6392\u5e8f */\nfunc (q *quickSort) quickSort(nums []int, left, right int) {\n// \u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a 1 \u65f6\u7ec8\u6b62\u9012\u5f52\nif left &gt;= right {\nreturn\n}\n// \u54e8\u5175\u5212\u5206\npivot := q.partition(nums, left, right)\n// \u9012\u5f52\u5de6\u5b50\u6570\u7ec4\u3001\u53f3\u5b50\u6570\u7ec4\nq.quickSort(nums, left, pivot-1)\nq.quickSort(nums, pivot+1, right)\n}\n</code></pre> quick_sort.js<pre><code>/* \u5feb\u901f\u6392\u5e8f */\nquickSort(nums, left, right) {\n// \u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a 1 \u65f6\u7ec8\u6b62\u9012\u5f52\nif (left &gt;= right) return;\n// \u54e8\u5175\u5212\u5206\nconst pivot = this.partition(nums, left, right);\n// \u9012\u5f52\u5de6\u5b50\u6570\u7ec4\u3001\u53f3\u5b50\u6570\u7ec4\nthis.quickSort(nums, left, pivot - 1);\nthis.quickSort(nums, pivot + 1, right);\n}\n</code></pre> quick_sort.ts<pre><code>/* \u5feb\u901f\u6392\u5e8f */\nquickSort(nums: number[], left: number, right: number): void {\n// \u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a 1 \u65f6\u7ec8\u6b62\u9012\u5f52\nif (left &gt;= right) {\nreturn;\n}\n// \u54e8\u5175\u5212\u5206\nconst pivot = this.partition(nums, left, right);\n// \u9012\u5f52\u5de6\u5b50\u6570\u7ec4\u3001\u53f3\u5b50\u6570\u7ec4\nthis.quickSort(nums, left, pivot - 1);\nthis.quickSort(nums, pivot + 1, right);\n}\n</code></pre> quick_sort.c<pre><code>/* \u5feb\u901f\u6392\u5e8f\u7c7b */\n// \u5feb\u901f\u6392\u5e8f\u7c7b-\u54e8\u5175\u5212\u5206\nint partition(int nums[], int left, int right) {\n// \u4ee5 nums[left] \u4f5c\u4e3a\u57fa\u51c6\u6570\nint i = left, j = right;\nwhile (i &lt; j) {\nwhile (i &lt; j &amp;&amp; nums[j] &gt;= nums[left]) {\n// \u4ece\u53f3\u5411\u5de6\u627e\u9996\u4e2a\u5c0f\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\nj--;\n}\nwhile (i &lt; j &amp;&amp; nums[i] &lt;= nums[left]) {\n// \u4ece\u5de6\u5411\u53f3\u627e\u9996\u4e2a\u5927\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\ni++;\n}\n// \u4ea4\u6362\u8fd9\u4e24\u4e2a\u5143\u7d20\nswap(nums, i, j);\n}\n// \u5c06\u57fa\u51c6\u6570\u4ea4\u6362\u81f3\u4e24\u5b50\u6570\u7ec4\u7684\u5206\u754c\u7ebf\nswap(nums, i, left);\n// \u8fd4\u56de\u57fa\u51c6\u6570\u7684\u7d22\u5f15\nreturn i;\n}\n// \u5feb\u901f\u6392\u5e8f\u7c7b-\u5feb\u901f\u6392\u5e8f\nvoid quickSort(int nums[], int left, int right) {\n// \u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a 1 \u65f6\u7ec8\u6b62\u9012\u5f52\nif (left &gt;= right) {\nreturn;\n}\n// \u54e8\u5175\u5212\u5206\nint pivot = partition(nums, left, right);\n// \u9012\u5f52\u5de6\u5b50\u6570\u7ec4\u3001\u53f3\u5b50\u6570\u7ec4\nquickSort(nums, left, pivot - 1);\nquickSort(nums, pivot + 1, right);\n}\n</code></pre> quick_sort.cs<pre><code>/* \u5feb\u901f\u6392\u5e8f */\nvoid quickSort(int[] nums, int left, int right) {\n// \u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a 1 \u65f6\u7ec8\u6b62\u9012\u5f52\nif (left &gt;= right)\nreturn;\n// \u54e8\u5175\u5212\u5206\nint pivot = partition(nums, left, right);\n// \u9012\u5f52\u5de6\u5b50\u6570\u7ec4\u3001\u53f3\u5b50\u6570\u7ec4\nquickSort(nums, left, pivot - 1);\nquickSort(nums, pivot + 1, right);\n}\n</code></pre> quick_sort.swift<pre><code>/* \u5feb\u901f\u6392\u5e8f */\nfunc quickSort(nums: inout [Int], left: Int, right: Int) {\n// \u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a 1 \u65f6\u7ec8\u6b62\u9012\u5f52\nif left &gt;= right {\nreturn\n}\n// \u54e8\u5175\u5212\u5206\nlet pivot = partition(nums: &amp;nums, left: left, right: right)\n// \u9012\u5f52\u5de6\u5b50\u6570\u7ec4\u3001\u53f3\u5b50\u6570\u7ec4\nquickSort(nums: &amp;nums, left: left, right: pivot - 1)\nquickSort(nums: &amp;nums, left: pivot + 1, right: right)\n}\n</code></pre> quick_sort.zig<pre><code>// \u5feb\u901f\u6392\u5e8f\nfn quickSort(nums: []i32, left: usize, right: usize) void {\n// \u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a 1 \u65f6\u7ec8\u6b62\u9012\u5f52\nif (left &gt;= right) return;\n// \u54e8\u5175\u5212\u5206\nvar pivot = partition(nums, left, right);\n// \u9012\u5f52\u5de6\u5b50\u6570\u7ec4\u3001\u53f3\u5b50\u6570\u7ec4\nquickSort(nums, left, pivot - 1);\nquickSort(nums, pivot + 1, right);\n}\n</code></pre> quick_sort.dart<pre><code>/* \u5feb\u901f\u6392\u5e8f */\nvoid quickSort(List&lt;int&gt; nums, int left, int right) {\n// \u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a 1 \u65f6\u7ec8\u6b62\u9012\u5f52\nif (left &gt;= right) return;\n// \u54e8\u5175\u5212\u5206\nint pivot = _partition(nums, left, right);\n// \u9012\u5f52\u5de6\u5b50\u6570\u7ec4\u3001\u53f3\u5b50\u6570\u7ec4\nquickSort(nums, left, pivot - 1);\nquickSort(nums, pivot + 1, right);\n}\n</code></pre>"},{"location":"chapter_sorting/quick_sort/#1152","title":"11.5.2. \u00a0 \u7b97\u6cd5\u7279\u6027","text":"<ul> <li>\u65f6\u95f4\u590d\u6742\u5ea6 \\(O(n \\log n)\\) \u3001\u81ea\u9002\u5e94\u6392\u5e8f \uff1a\u5728\u5e73\u5747\u60c5\u51b5\u4e0b\uff0c\u54e8\u5175\u5212\u5206\u7684\u9012\u5f52\u5c42\u6570\u4e3a \\(\\log n\\) \uff0c\u6bcf\u5c42\u4e2d\u7684\u603b\u5faa\u73af\u6570\u4e3a \\(n\\) \uff0c\u603b\u4f53\u4f7f\u7528 \\(O(n \\log n)\\) \u65f6\u95f4\u3002\u5728\u6700\u5dee\u60c5\u51b5\u4e0b\uff0c\u6bcf\u8f6e\u54e8\u5175\u5212\u5206\u64cd\u4f5c\u90fd\u5c06\u957f\u5ea6\u4e3a \\(n\\) \u7684\u6570\u7ec4\u5212\u5206\u4e3a\u957f\u5ea6\u4e3a \\(0\\) \u548c \\(n - 1\\) \u7684\u4e24\u4e2a\u5b50\u6570\u7ec4\uff0c\u6b64\u65f6\u9012\u5f52\u5c42\u6570\u8fbe\u5230 \\(n\\) \u5c42\uff0c\u6bcf\u5c42\u4e2d\u7684\u5faa\u73af\u6570\u4e3a \\(n\\) \uff0c\u603b\u4f53\u4f7f\u7528 \\(O(n^2)\\) \u65f6\u95f4\u3002</li> <li>\u7a7a\u95f4\u590d\u6742\u5ea6 \\(O(n)\\) \u3001\u539f\u5730\u6392\u5e8f \uff1a\u5728\u8f93\u5165\u6570\u7ec4\u5b8c\u5168\u5012\u5e8f\u7684\u60c5\u51b5\u4e0b\uff0c\u8fbe\u5230\u6700\u5dee\u9012\u5f52\u6df1\u5ea6 \\(n\\) \uff0c\u4f7f\u7528 \\(O(n)\\) \u6808\u5e27\u7a7a\u95f4\u3002\u6392\u5e8f\u64cd\u4f5c\u662f\u5728\u539f\u6570\u7ec4\u4e0a\u8fdb\u884c\u7684\uff0c\u672a\u501f\u52a9\u989d\u5916\u6570\u7ec4\u3002</li> <li>\u975e\u7a33\u5b9a\u6392\u5e8f\uff1a\u5728\u54e8\u5175\u5212\u5206\u7684\u6700\u540e\u4e00\u6b65\uff0c\u57fa\u51c6\u6570\u53ef\u80fd\u4f1a\u88ab\u4ea4\u6362\u81f3\u76f8\u7b49\u5143\u7d20\u7684\u53f3\u4fa7\u3002</li> </ul>"},{"location":"chapter_sorting/quick_sort/#1153","title":"11.5.3. \u00a0 \u5feb\u6392\u4e3a\u4ec0\u4e48\u5feb\uff1f","text":"<p>\u4ece\u540d\u79f0\u4e0a\u5c31\u80fd\u770b\u51fa\uff0c\u5feb\u901f\u6392\u5e8f\u5728\u6548\u7387\u65b9\u9762\u5e94\u8be5\u5177\u6709\u4e00\u5b9a\u7684\u4f18\u52bf\u3002\u5c3d\u7ba1\u5feb\u901f\u6392\u5e8f\u7684\u5e73\u5747\u65f6\u95f4\u590d\u6742\u5ea6\u4e0e\u300c\u5f52\u5e76\u6392\u5e8f\u300d\u548c\u300c\u5806\u6392\u5e8f\u300d\u76f8\u540c\uff0c\u4f46\u901a\u5e38\u5feb\u901f\u6392\u5e8f\u7684\u6548\u7387\u66f4\u9ad8\uff0c\u539f\u56e0\u5982\u4e0b\uff1a</p> <ul> <li>\u51fa\u73b0\u6700\u5dee\u60c5\u51b5\u7684\u6982\u7387\u5f88\u4f4e\uff1a\u867d\u7136\u5feb\u901f\u6392\u5e8f\u7684\u6700\u5dee\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(n^2)\\) \uff0c\u6ca1\u6709\u5f52\u5e76\u6392\u5e8f\u7a33\u5b9a\uff0c\u4f46\u5728\u7edd\u5927\u591a\u6570\u60c5\u51b5\u4e0b\uff0c\u5feb\u901f\u6392\u5e8f\u80fd\u5728 \\(O(n \\log n)\\) \u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e0b\u8fd0\u884c\u3002</li> <li>\u7f13\u5b58\u4f7f\u7528\u6548\u7387\u9ad8\uff1a\u5728\u6267\u884c\u54e8\u5175\u5212\u5206\u64cd\u4f5c\u65f6\uff0c\u7cfb\u7edf\u53ef\u5c06\u6574\u4e2a\u5b50\u6570\u7ec4\u52a0\u8f7d\u5230\u7f13\u5b58\uff0c\u56e0\u6b64\u8bbf\u95ee\u5143\u7d20\u7684\u6548\u7387\u8f83\u9ad8\u3002\u800c\u50cf\u300c\u5806\u6392\u5e8f\u300d\u8fd9\u7c7b\u7b97\u6cd5\u9700\u8981\u8df3\u8dc3\u5f0f\u8bbf\u95ee\u5143\u7d20\uff0c\u4ece\u800c\u7f3a\u4e4f\u8fd9\u4e00\u7279\u6027\u3002</li> <li>\u590d\u6742\u5ea6\u7684\u5e38\u6570\u7cfb\u6570\u4f4e\uff1a\u5728\u4e0a\u8ff0\u4e09\u79cd\u7b97\u6cd5\u4e2d\uff0c\u5feb\u901f\u6392\u5e8f\u7684\u6bd4\u8f83\u3001\u8d4b\u503c\u3001\u4ea4\u6362\u7b49\u64cd\u4f5c\u7684\u603b\u6570\u91cf\u6700\u5c11\u3002\u8fd9\u4e0e\u300c\u63d2\u5165\u6392\u5e8f\u300d\u6bd4\u300c\u5192\u6ce1\u6392\u5e8f\u300d\u66f4\u5feb\u7684\u539f\u56e0\u7c7b\u4f3c\u3002</li> </ul>"},{"location":"chapter_sorting/quick_sort/#1154","title":"11.5.4. \u00a0 \u57fa\u51c6\u6570\u4f18\u5316","text":"<p>\u5feb\u901f\u6392\u5e8f\u5728\u67d0\u4e9b\u8f93\u5165\u4e0b\u7684\u65f6\u95f4\u6548\u7387\u53ef\u80fd\u964d\u4f4e\u3002\u4e3e\u4e00\u4e2a\u6781\u7aef\u4f8b\u5b50\uff0c\u5047\u8bbe\u8f93\u5165\u6570\u7ec4\u662f\u5b8c\u5168\u5012\u5e8f\u7684\uff0c\u7531\u4e8e\u6211\u4eec\u9009\u62e9\u6700\u5de6\u7aef\u5143\u7d20\u4f5c\u4e3a\u57fa\u51c6\u6570\uff0c\u90a3\u4e48\u5728\u54e8\u5175\u5212\u5206\u5b8c\u6210\u540e\uff0c\u57fa\u51c6\u6570\u88ab\u4ea4\u6362\u81f3\u6570\u7ec4\u6700\u53f3\u7aef\uff0c\u5bfc\u81f4\u5de6\u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a \\(n - 1\\) \u3001\u53f3\u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a \\(0\\) \u3002\u5982\u6b64\u9012\u5f52\u4e0b\u53bb\uff0c\u6bcf\u8f6e\u54e8\u5175\u5212\u5206\u540e\u7684\u53f3\u5b50\u6570\u7ec4\u957f\u5ea6\u90fd\u4e3a \\(0\\) \uff0c\u5206\u6cbb\u7b56\u7565\u5931\u6548\uff0c\u5feb\u901f\u6392\u5e8f\u9000\u5316\u4e3a\u300c\u5192\u6ce1\u6392\u5e8f\u300d\u3002</p> <p>\u4e3a\u4e86\u5c3d\u91cf\u907f\u514d\u8fd9\u79cd\u60c5\u51b5\u53d1\u751f\uff0c\u6211\u4eec\u53ef\u4ee5\u4f18\u5316\u54e8\u5175\u5212\u5206\u4e2d\u7684\u57fa\u51c6\u6570\u7684\u9009\u53d6\u7b56\u7565\u3002\u4f8b\u5982\uff0c\u6211\u4eec\u53ef\u4ee5\u968f\u673a\u9009\u53d6\u4e00\u4e2a\u5143\u7d20\u4f5c\u4e3a\u57fa\u51c6\u6570\u3002\u7136\u800c\uff0c\u5982\u679c\u8fd0\u6c14\u4e0d\u4f73\uff0c\u6bcf\u6b21\u90fd\u9009\u5230\u4e0d\u7406\u60f3\u7684\u57fa\u51c6\u6570\uff0c\u6548\u7387\u4ecd\u7136\u4e0d\u5c3d\u5982\u4eba\u610f\u3002</p> <p>\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u7f16\u7a0b\u8bed\u8a00\u901a\u5e38\u751f\u6210\u7684\u662f\u201c\u4f2a\u968f\u673a\u6570\u201d\u3002\u5982\u679c\u6211\u4eec\u9488\u5bf9\u4f2a\u968f\u673a\u6570\u5e8f\u5217\u6784\u5efa\u4e00\u4e2a\u7279\u5b9a\u7684\u6d4b\u8bd5\u6837\u4f8b\uff0c\u90a3\u4e48\u5feb\u901f\u6392\u5e8f\u7684\u6548\u7387\u4ecd\u7136\u53ef\u80fd\u52a3\u5316\u3002</p> <p>\u4e3a\u4e86\u8fdb\u4e00\u6b65\u6539\u8fdb\uff0c\u6211\u4eec\u53ef\u4ee5\u5728\u6570\u7ec4\u4e2d\u9009\u53d6\u4e09\u4e2a\u5019\u9009\u5143\u7d20\uff08\u901a\u5e38\u4e3a\u6570\u7ec4\u7684\u9996\u3001\u5c3e\u3001\u4e2d\u70b9\u5143\u7d20\uff09\uff0c\u5e76\u5c06\u8fd9\u4e09\u4e2a\u5019\u9009\u5143\u7d20\u7684\u4e2d\u4f4d\u6570\u4f5c\u4e3a\u57fa\u51c6\u6570\u3002\u8fd9\u6837\u4e00\u6765\uff0c\u57fa\u51c6\u6570\u201c\u65e2\u4e0d\u592a\u5c0f\u4e5f\u4e0d\u592a\u5927\u201d\u7684\u6982\u7387\u5c06\u5927\u5e45\u63d0\u5347\u3002\u5f53\u7136\uff0c\u6211\u4eec\u8fd8\u53ef\u4ee5\u9009\u53d6\u66f4\u591a\u5019\u9009\u5143\u7d20\uff0c\u4ee5\u8fdb\u4e00\u6b65\u63d0\u9ad8\u7b97\u6cd5\u7684\u7a33\u5065\u6027\u3002\u91c7\u7528\u8fd9\u79cd\u65b9\u6cd5\u540e\uff0c\u65f6\u95f4\u590d\u6742\u5ea6\u52a3\u5316\u81f3 \\(O(n^2)\\) \u7684\u6982\u7387\u5927\u5927\u964d\u4f4e\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart quick_sort.java<pre><code>/* \u9009\u53d6\u4e09\u4e2a\u5143\u7d20\u7684\u4e2d\u4f4d\u6570 */\nint medianThree(int[] nums, int left, int mid, int right) {\n// \u6b64\u5904\u4f7f\u7528\u5f02\u6216\u8fd0\u7b97\u6765\u7b80\u5316\u4ee3\u7801\n// \u5f02\u6216\u89c4\u5219\u4e3a 0 ^ 0 = 1 ^ 1 = 0, 0 ^ 1 = 1 ^ 0 = 1\nif ((nums[left] &lt; nums[mid]) ^ (nums[left] &lt; nums[right]))\nreturn left;\nelse if ((nums[mid] &lt; nums[left]) ^ (nums[mid] &lt; nums[right]))\nreturn mid;\nelse\nreturn right;\n}\n/* \u54e8\u5175\u5212\u5206\uff08\u4e09\u6570\u53d6\u4e2d\u503c\uff09 */\nint partition(int[] nums, int left, int right) {\n// \u9009\u53d6\u4e09\u4e2a\u5019\u9009\u5143\u7d20\u7684\u4e2d\u4f4d\u6570\nint med = medianThree(nums, left, (left + right) / 2, right);\n// \u5c06\u4e2d\u4f4d\u6570\u4ea4\u6362\u81f3\u6570\u7ec4\u6700\u5de6\u7aef\nswap(nums, left, med);\n// \u4ee5 nums[left] \u4f5c\u4e3a\u57fa\u51c6\u6570\nint i = left, j = right;\nwhile (i &lt; j) {\nwhile (i &lt; j &amp;&amp; nums[j] &gt;= nums[left])\nj--;          // \u4ece\u53f3\u5411\u5de6\u627e\u9996\u4e2a\u5c0f\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\nwhile (i &lt; j &amp;&amp; nums[i] &lt;= nums[left])\ni++;          // \u4ece\u5de6\u5411\u53f3\u627e\u9996\u4e2a\u5927\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\nswap(nums, i, j); // \u4ea4\u6362\u8fd9\u4e24\u4e2a\u5143\u7d20\n}\nswap(nums, i, left);  // \u5c06\u57fa\u51c6\u6570\u4ea4\u6362\u81f3\u4e24\u5b50\u6570\u7ec4\u7684\u5206\u754c\u7ebf\nreturn i;             // \u8fd4\u56de\u57fa\u51c6\u6570\u7684\u7d22\u5f15\n}\n</code></pre> quick_sort.cpp<pre><code>/* \u9009\u53d6\u4e09\u4e2a\u5143\u7d20\u7684\u4e2d\u4f4d\u6570 */\nint medianThree(vector&lt;int&gt; &amp;nums, int left, int mid, int right) {\n// \u6b64\u5904\u4f7f\u7528\u5f02\u6216\u8fd0\u7b97\u6765\u7b80\u5316\u4ee3\u7801\n// \u5f02\u6216\u89c4\u5219\u4e3a 0 ^ 0 = 1 ^ 1 = 0, 0 ^ 1 = 1 ^ 0 = 1\nif ((nums[left] &lt; nums[mid]) ^ (nums[left] &lt; nums[right]))\nreturn left;\nelse if ((nums[mid] &lt; nums[left]) ^ (nums[mid] &lt; nums[right]))\nreturn mid;\nelse\nreturn right;\n}\n/* \u54e8\u5175\u5212\u5206\uff08\u4e09\u6570\u53d6\u4e2d\u503c\uff09 */\nint partition(vector&lt;int&gt; &amp;nums, int left, int right) {\n// \u9009\u53d6\u4e09\u4e2a\u5019\u9009\u5143\u7d20\u7684\u4e2d\u4f4d\u6570\nint med = medianThree(nums, left, (left + right) / 2, right);\n// \u5c06\u4e2d\u4f4d\u6570\u4ea4\u6362\u81f3\u6570\u7ec4\u6700\u5de6\u7aef\nswap(nums, left, med);\n// \u4ee5 nums[left] \u4f5c\u4e3a\u57fa\u51c6\u6570\nint i = left, j = right;\nwhile (i &lt; j) {\nwhile (i &lt; j &amp;&amp; nums[j] &gt;= nums[left])\nj--; // \u4ece\u53f3\u5411\u5de6\u627e\u9996\u4e2a\u5c0f\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\nwhile (i &lt; j &amp;&amp; nums[i] &lt;= nums[left])\ni++;          // \u4ece\u5de6\u5411\u53f3\u627e\u9996\u4e2a\u5927\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\nswap(nums, i, j); // \u4ea4\u6362\u8fd9\u4e24\u4e2a\u5143\u7d20\n}\nswap(nums, i, left); // \u5c06\u57fa\u51c6\u6570\u4ea4\u6362\u81f3\u4e24\u5b50\u6570\u7ec4\u7684\u5206\u754c\u7ebf\nreturn i;            // \u8fd4\u56de\u57fa\u51c6\u6570\u7684\u7d22\u5f15\n}\n</code></pre> quick_sort.py<pre><code>def median_three(self, nums: list[int], left: int, mid: int, right: int) -&gt; int:\n\"\"\"\u9009\u53d6\u4e09\u4e2a\u5143\u7d20\u7684\u4e2d\u4f4d\u6570\"\"\"\n# \u6b64\u5904\u4f7f\u7528\u5f02\u6216\u8fd0\u7b97\u6765\u7b80\u5316\u4ee3\u7801\n# \u5f02\u6216\u89c4\u5219\u4e3a 0 ^ 0 = 1 ^ 1 = 0, 0 ^ 1 = 1 ^ 0 = 1\nif (nums[left] &lt; nums[mid]) ^ (nums[left] &lt; nums[right]):\nreturn left\nelif (nums[mid] &lt; nums[left]) ^ (nums[mid] &lt; nums[right]):\nreturn mid\nreturn right\ndef partition(self, nums: list[int], left: int, right: int) -&gt; int:\n\"\"\"\u54e8\u5175\u5212\u5206\uff08\u4e09\u6570\u53d6\u4e2d\u503c\uff09\"\"\"\n# \u4ee5 nums[left] \u4f5c\u4e3a\u57fa\u51c6\u6570\nmed = self.median_three(nums, left, (left + right) // 2, right)\n# \u5c06\u4e2d\u4f4d\u6570\u4ea4\u6362\u81f3\u6570\u7ec4\u6700\u5de6\u7aef\nnums[left], nums[med] = nums[med], nums[left]\n# \u4ee5 nums[left] \u4f5c\u4e3a\u57fa\u51c6\u6570\ni, j = left, right\nwhile i &lt; j:\nwhile i &lt; j and nums[j] &gt;= nums[left]:\nj -= 1  # \u4ece\u53f3\u5411\u5de6\u627e\u9996\u4e2a\u5c0f\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\nwhile i &lt; j and nums[i] &lt;= nums[left]:\ni += 1  # \u4ece\u5de6\u5411\u53f3\u627e\u9996\u4e2a\u5927\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\n# \u5143\u7d20\u4ea4\u6362\nnums[i], nums[j] = nums[j], nums[i]\n# \u5c06\u57fa\u51c6\u6570\u4ea4\u6362\u81f3\u4e24\u5b50\u6570\u7ec4\u7684\u5206\u754c\u7ebf\nnums[i], nums[left] = nums[left], nums[i]\nreturn i  # \u8fd4\u56de\u57fa\u51c6\u6570\u7684\u7d22\u5f15\n</code></pre> quick_sort.go<pre><code>/* \u9009\u53d6\u4e09\u4e2a\u5143\u7d20\u7684\u4e2d\u4f4d\u6570 */\nfunc (q *quickSortMedian) medianThree(nums []int, left, mid, right int) int {\n// \u6b64\u5904\u4f7f\u7528\u5f02\u6216\u8fd0\u7b97\u6765\u7b80\u5316\u4ee3\u7801\uff08!= \u5728\u8fd9\u91cc\u8d77\u5230\u5f02\u6216\u7684\u4f5c\u7528\uff09\n// \u5f02\u6216\u89c4\u5219\u4e3a 0 ^ 0 = 1 ^ 1 = 0, 0 ^ 1 = 1 ^ 0 = 1\nif (nums[left] &lt; nums[mid]) != (nums[left] &lt; nums[right]) {\nreturn left\n} else if (nums[mid] &lt; nums[left]) != (nums[mid] &lt; nums[right]) {\nreturn mid\n}\nreturn right\n}\n/* \u54e8\u5175\u5212\u5206\uff08\u4e09\u6570\u53d6\u4e2d\u503c\uff09*/\nfunc (q *quickSortMedian) partition(nums []int, left, right int) int {\n// \u4ee5 nums[left] \u4f5c\u4e3a\u57fa\u51c6\u6570\nmed := q.medianThree(nums, left, (left+right)/2, right)\n// \u5c06\u4e2d\u4f4d\u6570\u4ea4\u6362\u81f3\u6570\u7ec4\u6700\u5de6\u7aef\nnums[left], nums[med] = nums[med], nums[left]\n// \u4ee5 nums[left] \u4f5c\u4e3a\u57fa\u51c6\u6570\ni, j := left, right\nfor i &lt; j {\nfor i &lt; j &amp;&amp; nums[j] &gt;= nums[left] {\nj-- //\u4ece\u53f3\u5411\u5de6\u627e\u9996\u4e2a\u5c0f\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\n}\nfor i &lt; j &amp;&amp; nums[i] &lt;= nums[left] {\ni++ //\u4ece\u5de6\u5411\u53f3\u627e\u9996\u4e2a\u5927\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\n}\n//\u5143\u7d20\u4ea4\u6362\nnums[i], nums[j] = nums[j], nums[i]\n}\n//\u5c06\u57fa\u51c6\u6570\u4ea4\u6362\u81f3\u4e24\u5b50\u6570\u7ec4\u7684\u5206\u754c\u7ebf\nnums[i], nums[left] = nums[left], nums[i]\nreturn i //\u8fd4\u56de\u57fa\u51c6\u6570\u7684\u7d22\u5f15\n}\n</code></pre> quick_sort.js<pre><code>/* \u9009\u53d6\u4e09\u4e2a\u5143\u7d20\u7684\u4e2d\u4f4d\u6570 */\nmedianThree(nums, left, mid, right) {\n// \u6b64\u5904\u4f7f\u7528\u5f02\u6216\u8fd0\u7b97\u6765\u7b80\u5316\u4ee3\u7801\n// \u5f02\u6216\u89c4\u5219\u4e3a 0 ^ 0 = 1 ^ 1 = 0, 0 ^ 1 = 1 ^ 0 = 1\nif ((nums[left] &lt; nums[mid]) ^ (nums[left] &lt; nums[right])) return left;\nelse if ((nums[mid] &lt; nums[left]) ^ (nums[mid] &lt; nums[right]))\nreturn mid;\nelse return right;\n}\n/* \u54e8\u5175\u5212\u5206\uff08\u4e09\u6570\u53d6\u4e2d\u503c\uff09 */\npartition(nums, left, right) {\n// \u9009\u53d6\u4e09\u4e2a\u5019\u9009\u5143\u7d20\u7684\u4e2d\u4f4d\u6570\nlet med = this.medianThree(\nnums,\nleft,\nMath.floor((left + right) / 2),\nright\n);\n// \u5c06\u4e2d\u4f4d\u6570\u4ea4\u6362\u81f3\u6570\u7ec4\u6700\u5de6\u7aef\nthis.swap(nums, left, med);\n// \u4ee5 nums[left] \u4f5c\u4e3a\u57fa\u51c6\u6570\nlet i = left,\nj = right;\nwhile (i &lt; j) {\nwhile (i &lt; j &amp;&amp; nums[j] &gt;= nums[left]) j--; // \u4ece\u53f3\u5411\u5de6\u627e\u9996\u4e2a\u5c0f\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\nwhile (i &lt; j &amp;&amp; nums[i] &lt;= nums[left]) i++; // \u4ece\u5de6\u5411\u53f3\u627e\u9996\u4e2a\u5927\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\nthis.swap(nums, i, j); // \u4ea4\u6362\u8fd9\u4e24\u4e2a\u5143\u7d20\n}\nthis.swap(nums, i, left); // \u5c06\u57fa\u51c6\u6570\u4ea4\u6362\u81f3\u4e24\u5b50\u6570\u7ec4\u7684\u5206\u754c\u7ebf\nreturn i; // \u8fd4\u56de\u57fa\u51c6\u6570\u7684\u7d22\u5f15\n}\n</code></pre> quick_sort.ts<pre><code>/* \u9009\u53d6\u4e09\u4e2a\u5143\u7d20\u7684\u4e2d\u4f4d\u6570 */\nmedianThree(\nnums: number[],\nleft: number,\nmid: number,\nright: number\n): number {\n// \u6b64\u5904\u4f7f\u7528\u5f02\u6216\u8fd0\u7b97\u6765\u7b80\u5316\u4ee3\u7801\n// \u5f02\u6216\u89c4\u5219\u4e3a 0 ^ 0 = 1 ^ 1 = 0, 0 ^ 1 = 1 ^ 0 = 1\nif (Number(nums[left] &lt; nums[mid]) ^ Number(nums[left] &lt; nums[right])) {\nreturn left;\n} else if (\nNumber(nums[mid] &lt; nums[left]) ^ Number(nums[mid] &lt; nums[right])\n) {\nreturn mid;\n} else {\nreturn right;\n}\n}\n/* \u54e8\u5175\u5212\u5206\uff08\u4e09\u6570\u53d6\u4e2d\u503c\uff09 */\npartition(nums: number[], left: number, right: number): number {\n// \u9009\u53d6\u4e09\u4e2a\u5019\u9009\u5143\u7d20\u7684\u4e2d\u4f4d\u6570\nlet med = this.medianThree(\nnums,\nleft,\nMath.floor((left + right) / 2),\nright\n);\n// \u5c06\u4e2d\u4f4d\u6570\u4ea4\u6362\u81f3\u6570\u7ec4\u6700\u5de6\u7aef\nthis.swap(nums, left, med);\n// \u4ee5 nums[left] \u4f5c\u4e3a\u57fa\u51c6\u6570\nlet i = left,\nj = right;\nwhile (i &lt; j) {\nwhile (i &lt; j &amp;&amp; nums[j] &gt;= nums[left]) {\nj--; // \u4ece\u53f3\u5411\u5de6\u627e\u9996\u4e2a\u5c0f\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\n}\nwhile (i &lt; j &amp;&amp; nums[i] &lt;= nums[left]) {\ni++; // \u4ece\u5de6\u5411\u53f3\u627e\u9996\u4e2a\u5927\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\n}\nthis.swap(nums, i, j); // \u4ea4\u6362\u8fd9\u4e24\u4e2a\u5143\u7d20\n}\nthis.swap(nums, i, left); // \u5c06\u57fa\u51c6\u6570\u4ea4\u6362\u81f3\u4e24\u5b50\u6570\u7ec4\u7684\u5206\u754c\u7ebf\nreturn i; // \u8fd4\u56de\u57fa\u51c6\u6570\u7684\u7d22\u5f15\n}\n</code></pre> quick_sort.c<pre><code>/* \u5feb\u901f\u6392\u5e8f\u7c7b\uff08\u4e2d\u4f4d\u57fa\u51c6\u6570\u4f18\u5316\uff09 */\n// \u9009\u53d6\u4e09\u4e2a\u5143\u7d20\u7684\u4e2d\u4f4d\u6570\nint medianThree(int nums[], int left, int mid, int right) {\n// \u6b64\u5904\u4f7f\u7528\u5f02\u6216\u8fd0\u7b97\u6765\u7b80\u5316\u4ee3\u7801\n// \u5f02\u6216\u89c4\u5219\u4e3a 0 ^ 0 = 1 ^ 1 = 0, 0 ^ 1 = 1 ^ 0 = 1\nif ((nums[left] &lt; nums[mid]) ^ (nums[left] &lt; nums[right]))\nreturn left;\nelse if ((nums[mid] &lt; nums[left]) ^ (nums[mid] &lt; nums[right]))\nreturn mid;\nelse\nreturn right;\n}\n/* \u5feb\u901f\u6392\u5e8f\u7c7b\uff08\u4e2d\u4f4d\u57fa\u51c6\u6570\u4f18\u5316\uff09 */\n// \u9009\u53d6\u4e09\u4e2a\u5143\u7d20\u7684\u4e2d\u4f4d\u6570\nint medianThree(int nums[], int left, int mid, int right) {\n// \u6b64\u5904\u4f7f\u7528\u5f02\u6216\u8fd0\u7b97\u6765\u7b80\u5316\u4ee3\u7801\n// \u5f02\u6216\u89c4\u5219\u4e3a 0 ^ 0 = 1 ^ 1 = 0, 0 ^ 1 = 1 ^ 0 = 1\nif ((nums[left] &lt; nums[mid]) ^ (nums[left] &lt; nums[right]))\nreturn left;\nelse if ((nums[mid] &lt; nums[left]) ^ (nums[mid] &lt; nums[right]))\nreturn mid;\nelse\nreturn right;\n}\n// \u54e8\u5175\u5212\u5206\uff08\u4e09\u6570\u53d6\u4e2d\u503c\uff09\nint partitionMedian(int nums[], int left, int right) {\n// \u9009\u53d6\u4e09\u4e2a\u5019\u9009\u5143\u7d20\u7684\u4e2d\u4f4d\u6570\nint med = medianThree(nums, left, (left + right) / 2, right);\n// \u5c06\u4e2d\u4f4d\u6570\u4ea4\u6362\u81f3\u6570\u7ec4\u6700\u5de6\u7aef\nswap(nums, left, med);\n// \u4ee5 nums[left] \u4f5c\u4e3a\u57fa\u51c6\u6570\nint i = left, j = right;\nwhile (i &lt; j) {\nwhile (i &lt; j &amp;&amp; nums[j] &gt;= nums[left])\nj--; // \u4ece\u53f3\u5411\u5de6\u627e\u9996\u4e2a\u5c0f\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\nwhile (i &lt; j &amp;&amp; nums[i] &lt;= nums[left])\ni++;          // \u4ece\u5de6\u5411\u53f3\u627e\u9996\u4e2a\u5927\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\nswap(nums, i, j); // \u4ea4\u6362\u8fd9\u4e24\u4e2a\u5143\u7d20\n}\nswap(nums, i, left); // \u5c06\u57fa\u51c6\u6570\u4ea4\u6362\u81f3\u4e24\u5b50\u6570\u7ec4\u7684\u5206\u754c\u7ebf\nreturn i;            // \u8fd4\u56de\u57fa\u51c6\u6570\u7684\u7d22\u5f15\n}\n</code></pre> quick_sort.cs<pre><code>/* \u9009\u53d6\u4e09\u4e2a\u5143\u7d20\u7684\u4e2d\u4f4d\u6570 */\nint medianThree(int[] nums, int left, int mid, int right) {\n// \u6b64\u5904\u4f7f\u7528\u5f02\u6216\u8fd0\u7b97\u6765\u7b80\u5316\u4ee3\u7801\n// \u5f02\u6216\u89c4\u5219\u4e3a 0 ^ 0 = 1 ^ 1 = 0, 0 ^ 1 = 1 ^ 0 = 1\nif ((nums[left] &lt; nums[mid]) ^ (nums[left] &lt; nums[right]))\nreturn left;\nelse if ((nums[mid] &lt; nums[left]) ^ (nums[mid] &lt; nums[right]))\nreturn mid;\nelse\nreturn right;\n}\n/* \u54e8\u5175\u5212\u5206\uff08\u4e09\u6570\u53d6\u4e2d\u503c\uff09 */\nint partition(int[] nums, int left, int right) {\n// \u9009\u53d6\u4e09\u4e2a\u5019\u9009\u5143\u7d20\u7684\u4e2d\u4f4d\u6570\nint med = medianThree(nums, left, (left + right) / 2, right);\n// \u5c06\u4e2d\u4f4d\u6570\u4ea4\u6362\u81f3\u6570\u7ec4\u6700\u5de6\u7aef\nswap(nums, left, med);\n// \u4ee5 nums[left] \u4f5c\u4e3a\u57fa\u51c6\u6570\nint i = left, j = right;\nwhile (i &lt; j) {\nwhile (i &lt; j &amp;&amp; nums[j] &gt;= nums[left])\nj--;          // \u4ece\u53f3\u5411\u5de6\u627e\u9996\u4e2a\u5c0f\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\nwhile (i &lt; j &amp;&amp; nums[i] &lt;= nums[left])\ni++;          // \u4ece\u5de6\u5411\u53f3\u627e\u9996\u4e2a\u5927\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\nswap(nums, i, j); // \u4ea4\u6362\u8fd9\u4e24\u4e2a\u5143\u7d20\n}\nswap(nums, i, left);  // \u5c06\u57fa\u51c6\u6570\u4ea4\u6362\u81f3\u4e24\u5b50\u6570\u7ec4\u7684\u5206\u754c\u7ebf\nreturn i;             // \u8fd4\u56de\u57fa\u51c6\u6570\u7684\u7d22\u5f15\n}\n</code></pre> quick_sort.swift<pre><code>/* \u9009\u53d6\u4e09\u4e2a\u5143\u7d20\u7684\u4e2d\u4f4d\u6570 */\nfunc medianThree(nums: [Int], left: Int, mid: Int, right: Int) -&gt; Int {\nif (nums[left] &lt; nums[mid]) != (nums[left] &lt; nums[right]) {\nreturn left\n} else if (nums[mid] &lt; nums[left]) != (nums[mid] &lt; nums[right]) {\nreturn mid\n} else {\nreturn right\n}\n}\n/* \u54e8\u5175\u5212\u5206\uff08\u4e09\u6570\u53d6\u4e2d\u503c\uff09 */\nfunc partitionMedian(nums: inout [Int], left: Int, right: Int) -&gt; Int {\n// \u9009\u53d6\u4e09\u4e2a\u5019\u9009\u5143\u7d20\u7684\u4e2d\u4f4d\u6570\nlet med = medianThree(nums: nums, left: left, mid: (left + right) / 2, right: right)\n// \u5c06\u4e2d\u4f4d\u6570\u4ea4\u6362\u81f3\u6570\u7ec4\u6700\u5de6\u7aef\nswap(nums: &amp;nums, i: left, j: med)\nreturn partition(nums: &amp;nums, left: left, right: right)\n}\n</code></pre> quick_sort.zig<pre><code>// \u9009\u53d6\u4e09\u4e2a\u5143\u7d20\u7684\u4e2d\u4f4d\u6570\nfn medianThree(nums: []i32, left: usize, mid: usize, right: usize) usize {\n// \u6b64\u5904\u4f7f\u7528\u5f02\u6216\u8fd0\u7b97\u6765\u7b80\u5316\u4ee3\u7801\n// \u5f02\u6216\u89c4\u5219\u4e3a 0 ^ 0 = 1 ^ 1 = 0, 0 ^ 1 = 1 ^ 0 = 1\nif ((nums[left] &lt; nums[mid]) != (nums[left] &lt; nums[right])) {\nreturn left;\n} else if ((nums[mid] &lt; nums[left]) != (nums[mid] &lt; nums[right])) {\nreturn mid;\n} else {\nreturn right;\n}\n}\n// \u54e8\u5175\u5212\u5206\uff08\u4e09\u6570\u53d6\u4e2d\u503c\uff09\nfn partition(nums: []i32, left: usize, right: usize) usize {\n// \u9009\u53d6\u4e09\u4e2a\u5019\u9009\u5143\u7d20\u7684\u4e2d\u4f4d\u6570\nvar med = medianThree(nums, left, (left + right) / 2, right);\n// \u5c06\u4e2d\u4f4d\u6570\u4ea4\u6362\u81f3\u6570\u7ec4\u6700\u5de6\u7aef\nswap(nums, left, med);\n// \u4ee5 nums[left] \u4f5c\u4e3a\u57fa\u51c6\u6570\nvar i = left;\nvar j = right;\nwhile (i &lt; j) {\nwhile (i &lt; j and nums[j] &gt;= nums[left]) j -= 1; // \u4ece\u53f3\u5411\u5de6\u627e\u9996\u4e2a\u5c0f\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\nwhile (i &lt; j and nums[i] &lt;= nums[left]) i += 1; // \u4ece\u5de6\u5411\u53f3\u627e\u9996\u4e2a\u5927\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\nswap(nums, i, j);   // \u4ea4\u6362\u8fd9\u4e24\u4e2a\u5143\u7d20\n}\nswap(nums, i, left);    // \u5c06\u57fa\u51c6\u6570\u4ea4\u6362\u81f3\u4e24\u5b50\u6570\u7ec4\u7684\u5206\u754c\u7ebf\nreturn i;               // \u8fd4\u56de\u57fa\u51c6\u6570\u7684\u7d22\u5f15\n}\n</code></pre> quick_sort.dart<pre><code>/* \u9009\u53d6\u4e09\u4e2a\u5143\u7d20\u7684\u4e2d\u4f4d\u6570 */\nint _medianThree(List&lt;int&gt; nums, int left, int mid, int right) {\n// \u6b64\u5904\u4f7f\u7528\u5f02\u6216\u8fd0\u7b97\u6765\u7b80\u5316\u4ee3\u7801\n// \u5f02\u6216\u89c4\u5219\u4e3a 0 ^ 0 = 1 ^ 1 = 0, 0 ^ 1 = 1 ^ 0 = 1\nif ((nums[left] &lt; nums[mid]) ^ (nums[left] &lt; nums[right]))\nreturn left;\nelse if ((nums[mid] &lt; nums[left]) ^ (nums[mid] &lt; nums[right]))\nreturn mid;\nelse\nreturn right;\n}\n/* \u54e8\u5175\u5212\u5206\uff08\u4e09\u6570\u53d6\u4e2d\u503c\uff09 */\nint _partition(List&lt;int&gt; nums, int left, int right) {\n// \u9009\u53d6\u4e09\u4e2a\u5019\u9009\u5143\u7d20\u7684\u4e2d\u4f4d\u6570\nint med = _medianThree(nums, left, (left + right) ~/ 2, right);\n// \u5c06\u4e2d\u4f4d\u6570\u4ea4\u6362\u81f3\u6570\u7ec4\u6700\u5de6\u7aef\n_swap(nums, left, med);\n// \u4ee5 nums[left] \u4f5c\u4e3a\u57fa\u51c6\u6570\nint i = left, j = right;\nwhile (i &lt; j) {\nwhile (i &lt; j &amp;&amp; nums[j] &gt;= nums[left]) j--; // \u4ece\u53f3\u5411\u5de6\u627e\u9996\u4e2a\u5c0f\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\nwhile (i &lt; j &amp;&amp; nums[i] &lt;= nums[left]) i++; // \u4ece\u5de6\u5411\u53f3\u627e\u9996\u4e2a\u5927\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\n_swap(nums, i, j); // \u4ea4\u6362\u8fd9\u4e24\u4e2a\u5143\u7d20\n}\n_swap(nums, i, left); // \u5c06\u57fa\u51c6\u6570\u4ea4\u6362\u81f3\u4e24\u5b50\u6570\u7ec4\u7684\u5206\u754c\u7ebf\nreturn i; // \u8fd4\u56de\u57fa\u51c6\u6570\u7684\u7d22\u5f15\n}\n</code></pre>"},{"location":"chapter_sorting/quick_sort/#1155","title":"11.5.5. \u00a0 \u5c3e\u9012\u5f52\u4f18\u5316","text":"<p>\u5728\u67d0\u4e9b\u8f93\u5165\u4e0b\uff0c\u5feb\u901f\u6392\u5e8f\u53ef\u80fd\u5360\u7528\u7a7a\u95f4\u8f83\u591a\u3002\u4ee5\u5b8c\u5168\u5012\u5e8f\u7684\u8f93\u5165\u6570\u7ec4\u4e3a\u4f8b\uff0c\u7531\u4e8e\u6bcf\u8f6e\u54e8\u5175\u5212\u5206\u540e\u53f3\u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a \\(0\\) \uff0c\u9012\u5f52\u6811\u7684\u9ad8\u5ea6\u4f1a\u8fbe\u5230 \\(n - 1\\) \uff0c\u6b64\u65f6\u9700\u8981\u5360\u7528 \\(O(n)\\) \u5927\u5c0f\u7684\u6808\u5e27\u7a7a\u95f4\u3002</p> <p>\u4e3a\u4e86\u9632\u6b62\u6808\u5e27\u7a7a\u95f4\u7684\u7d2f\u79ef\uff0c\u6211\u4eec\u53ef\u4ee5\u5728\u6bcf\u8f6e\u54e8\u5175\u6392\u5e8f\u5b8c\u6210\u540e\uff0c\u6bd4\u8f83\u4e24\u4e2a\u5b50\u6570\u7ec4\u7684\u957f\u5ea6\uff0c\u4ec5\u5bf9\u8f83\u77ed\u7684\u5b50\u6570\u7ec4\u8fdb\u884c\u9012\u5f52\u3002\u7531\u4e8e\u8f83\u77ed\u5b50\u6570\u7ec4\u7684\u957f\u5ea6\u4e0d\u4f1a\u8d85\u8fc7 \\(\\frac{n}{2}\\) \uff0c\u56e0\u6b64\u8fd9\u79cd\u65b9\u6cd5\u80fd\u786e\u4fdd\u9012\u5f52\u6df1\u5ea6\u4e0d\u8d85\u8fc7 \\(\\log n\\) \uff0c\u4ece\u800c\u5c06\u6700\u5dee\u7a7a\u95f4\u590d\u6742\u5ea6\u4f18\u5316\u81f3 \\(O(\\log n)\\) \u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart quick_sort.java<pre><code>/* \u5feb\u901f\u6392\u5e8f\uff08\u5c3e\u9012\u5f52\u4f18\u5316\uff09 */\nvoid quickSort(int[] nums, int left, int right) {\n// \u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a 1 \u65f6\u7ec8\u6b62\nwhile (left &lt; right) {\n// \u54e8\u5175\u5212\u5206\u64cd\u4f5c\nint pivot = partition(nums, left, right);\n// \u5bf9\u4e24\u4e2a\u5b50\u6570\u7ec4\u4e2d\u8f83\u77ed\u7684\u90a3\u4e2a\u6267\u884c\u5feb\u6392\nif (pivot - left &lt; right - pivot) {\nquickSort(nums, left, pivot - 1); // \u9012\u5f52\u6392\u5e8f\u5de6\u5b50\u6570\u7ec4\nleft = pivot + 1; // \u5269\u4f59\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [pivot + 1, right]\n} else {\nquickSort(nums, pivot + 1, right); // \u9012\u5f52\u6392\u5e8f\u53f3\u5b50\u6570\u7ec4\nright = pivot - 1; // \u5269\u4f59\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [left, pivot - 1]\n}\n}\n}\n</code></pre> quick_sort.cpp<pre><code>/* \u5feb\u901f\u6392\u5e8f\uff08\u5c3e\u9012\u5f52\u4f18\u5316\uff09 */\nvoid quickSort(vector&lt;int&gt; &amp;nums, int left, int right) {\n// \u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a 1 \u65f6\u7ec8\u6b62\nwhile (left &lt; right) {\n// \u54e8\u5175\u5212\u5206\u64cd\u4f5c\nint pivot = partition(nums, left, right);\n// \u5bf9\u4e24\u4e2a\u5b50\u6570\u7ec4\u4e2d\u8f83\u77ed\u7684\u90a3\u4e2a\u6267\u884c\u5feb\u6392\nif (pivot - left &lt; right - pivot) {\nquickSort(nums, left, pivot - 1); // \u9012\u5f52\u6392\u5e8f\u5de6\u5b50\u6570\u7ec4\nleft = pivot + 1;                 // \u5269\u4f59\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [pivot + 1, right]\n} else {\nquickSort(nums, pivot + 1, right); // \u9012\u5f52\u6392\u5e8f\u53f3\u5b50\u6570\u7ec4\nright = pivot - 1;                 // \u5269\u4f59\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [left, pivot - 1]\n}\n}\n}\n</code></pre> quick_sort.py<pre><code>def quick_sort(self, nums: list[int], left: int, right: int) -&gt; None:\n\"\"\"\u5feb\u901f\u6392\u5e8f\uff08\u5c3e\u9012\u5f52\u4f18\u5316\uff09\"\"\"\n# \u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a 1 \u65f6\u7ec8\u6b62\nwhile left &lt; right:\n# \u54e8\u5175\u5212\u5206\u64cd\u4f5c\npivot = self.partition(nums, left, right)\n# \u5bf9\u4e24\u4e2a\u5b50\u6570\u7ec4\u4e2d\u8f83\u77ed\u7684\u90a3\u4e2a\u6267\u884c\u5feb\u6392\nif pivot - left &lt; right - pivot:\nself.quick_sort(nums, left, pivot - 1)  # \u9012\u5f52\u6392\u5e8f\u5de6\u5b50\u6570\u7ec4\nleft = pivot + 1  # \u5269\u4f59\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [pivot + 1, right]\nelse:\nself.quick_sort(nums, pivot + 1, right)  # \u9012\u5f52\u6392\u5e8f\u53f3\u5b50\u6570\u7ec4\nright = pivot - 1  # \u5269\u4f59\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [left, pivot - 1]\n</code></pre> quick_sort.go<pre><code>/* \u5feb\u901f\u6392\u5e8f\uff08\u5c3e\u9012\u5f52\u4f18\u5316\uff09*/\nfunc (q *quickSortTailCall) quickSort(nums []int, left, right int) {\n// \u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a 1 \u65f6\u7ec8\u6b62\nfor left &lt; right {\n// \u54e8\u5175\u5212\u5206\u64cd\u4f5c\npivot := q.partition(nums, left, right)\n// \u5bf9\u4e24\u4e2a\u5b50\u6570\u7ec4\u4e2d\u8f83\u77ed\u7684\u90a3\u4e2a\u6267\u884c\u5feb\u6392\nif pivot-left &lt; right-pivot {\nq.quickSort(nums, left, pivot-1) // \u9012\u5f52\u6392\u5e8f\u5de6\u5b50\u6570\u7ec4\nleft = pivot + 1                 // \u5269\u4f59\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [pivot + 1, right]\n} else {\nq.quickSort(nums, pivot+1, right) // \u9012\u5f52\u6392\u5e8f\u53f3\u5b50\u6570\u7ec4\nright = pivot - 1                 // \u5269\u4f59\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [left, pivot - 1]\n}\n}\n}\n</code></pre> quick_sort.js<pre><code>/* \u5feb\u901f\u6392\u5e8f\uff08\u5c3e\u9012\u5f52\u4f18\u5316\uff09 */\nquickSort(nums, left, right) {\n// \u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a 1 \u65f6\u7ec8\u6b62\nwhile (left &lt; right) {\n// \u54e8\u5175\u5212\u5206\u64cd\u4f5c\nlet pivot = this.partition(nums, left, right);\n// \u5bf9\u4e24\u4e2a\u5b50\u6570\u7ec4\u4e2d\u8f83\u77ed\u7684\u90a3\u4e2a\u6267\u884c\u5feb\u6392\nif (pivot - left &lt; right - pivot) {\nthis.quickSort(nums, left, pivot - 1); // \u9012\u5f52\u6392\u5e8f\u5de6\u5b50\u6570\u7ec4\nleft = pivot + 1; // \u5269\u4f59\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [pivot + 1, right]\n} else {\nthis.quickSort(nums, pivot + 1, right); // \u9012\u5f52\u6392\u5e8f\u53f3\u5b50\u6570\u7ec4\nright = pivot - 1; // \u5269\u4f59\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [left, pivot - 1]\n}\n}\n}\n</code></pre> quick_sort.ts<pre><code>/* \u5feb\u901f\u6392\u5e8f\uff08\u5c3e\u9012\u5f52\u4f18\u5316\uff09 */\nquickSort(nums: number[], left: number, right: number): void {\n// \u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a 1 \u65f6\u7ec8\u6b62\nwhile (left &lt; right) {\n// \u54e8\u5175\u5212\u5206\u64cd\u4f5c\nlet pivot = this.partition(nums, left, right);\n// \u5bf9\u4e24\u4e2a\u5b50\u6570\u7ec4\u4e2d\u8f83\u77ed\u7684\u90a3\u4e2a\u6267\u884c\u5feb\u6392\nif (pivot - left &lt; right - pivot) {\nthis.quickSort(nums, left, pivot - 1); // \u9012\u5f52\u6392\u5e8f\u5de6\u5b50\u6570\u7ec4\nleft = pivot + 1; // \u5269\u4f59\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [pivot + 1, right]\n} else {\nthis.quickSort(nums, pivot + 1, right); // \u9012\u5f52\u6392\u5e8f\u53f3\u5b50\u6570\u7ec4\nright = pivot - 1; // \u5269\u4f59\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [left, pivot - 1]\n}\n}\n}\n</code></pre> quick_sort.c<pre><code>/* \u5feb\u901f\u6392\u5e8f\u7c7b\uff08\u5c3e\u9012\u5f52\u4f18\u5316\uff09 */\n// \u5feb\u901f\u6392\u5e8f\uff08\u5c3e\u9012\u5f52\u4f18\u5316\uff09\nvoid quickSortTailCall(int nums[], int left, int right) {\n// \u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a 1 \u65f6\u7ec8\u6b62\nwhile (left &lt; right) {\n// \u54e8\u5175\u5212\u5206\u64cd\u4f5c\nint pivot = partition(nums, left, right);\n// \u5bf9\u4e24\u4e2a\u5b50\u6570\u7ec4\u4e2d\u8f83\u77ed\u7684\u90a3\u4e2a\u6267\u884c\u5feb\u6392\nif (pivot - left &lt; right - pivot) {\nquickSortTailCall(nums, left, pivot - 1); // \u9012\u5f52\u6392\u5e8f\u5de6\u5b50\u6570\u7ec4\nleft = pivot + 1;                         // \u5269\u4f59\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [pivot + 1, right]\n} else {\nquickSortTailCall(nums, pivot + 1, right); // \u9012\u5f52\u6392\u5e8f\u53f3\u5b50\u6570\u7ec4\nright = pivot - 1;                         // \u5269\u4f59\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [left, pivot - 1]\n}\n}\n}\n</code></pre> quick_sort.cs<pre><code>/* \u5feb\u901f\u6392\u5e8f\uff08\u5c3e\u9012\u5f52\u4f18\u5316\uff09 */\nvoid quickSort(int[] nums, int left, int right) {\n// \u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a 1 \u65f6\u7ec8\u6b62\nwhile (left &lt; right) {\n// \u54e8\u5175\u5212\u5206\u64cd\u4f5c\nint pivot = partition(nums, left, right);\n// \u5bf9\u4e24\u4e2a\u5b50\u6570\u7ec4\u4e2d\u8f83\u77ed\u7684\u90a3\u4e2a\u6267\u884c\u5feb\u6392\nif (pivot - left &lt; right - pivot) {\nquickSort(nums, left, pivot - 1);  // \u9012\u5f52\u6392\u5e8f\u5de6\u5b50\u6570\u7ec4\nleft = pivot + 1;  // \u5269\u4f59\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [pivot + 1, right]\n} else {\nquickSort(nums, pivot + 1, right); // \u9012\u5f52\u6392\u5e8f\u53f3\u5b50\u6570\u7ec4\nright = pivot - 1; // \u5269\u4f59\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [left, pivot - 1]\n}\n}\n}\n</code></pre> quick_sort.swift<pre><code>/* \u5feb\u901f\u6392\u5e8f\uff08\u5c3e\u9012\u5f52\u4f18\u5316\uff09 */\nfunc quickSortTailCall(nums: inout [Int], left: Int, right: Int) {\nvar left = left\nvar right = right\n// \u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a 1 \u65f6\u7ec8\u6b62\nwhile left &lt; right {\n// \u54e8\u5175\u5212\u5206\u64cd\u4f5c\nlet pivot = partition(nums: &amp;nums, left: left, right: right)\n// \u5bf9\u4e24\u4e2a\u5b50\u6570\u7ec4\u4e2d\u8f83\u77ed\u7684\u90a3\u4e2a\u6267\u884c\u5feb\u6392\nif (pivot - left) &lt; (right - pivot) {\nquickSortTailCall(nums: &amp;nums, left: left, right: pivot - 1) // \u9012\u5f52\u6392\u5e8f\u5de6\u5b50\u6570\u7ec4\nleft = pivot + 1 // \u5269\u4f59\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [pivot + 1, right]\n} else {\nquickSortTailCall(nums: &amp;nums, left: pivot + 1, right: right) // \u9012\u5f52\u6392\u5e8f\u53f3\u5b50\u6570\u7ec4\nright = pivot - 1 // \u5269\u4f59\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [left, pivot - 1]\n}\n}\n}\n</code></pre> quick_sort.zig<pre><code>// \u5feb\u901f\u6392\u5e8f\uff08\u5c3e\u9012\u5f52\u4f18\u5316\uff09\nfn quickSort(nums: []i32, left_: usize, right_: usize) void {\nvar left = left_;\nvar right = right_;\n// \u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a 1 \u65f6\u7ec8\u6b62\u9012\u5f52\nwhile (left &lt; right) {\n// \u54e8\u5175\u5212\u5206\u64cd\u4f5c\nvar pivot = partition(nums, left, right);\n// \u5bf9\u4e24\u4e2a\u5b50\u6570\u7ec4\u4e2d\u8f83\u77ed\u7684\u90a3\u4e2a\u6267\u884c\u5feb\u6392\nif (pivot - left &lt; right - pivot) {\nquickSort(nums, left, pivot - 1);   // \u9012\u5f52\u6392\u5e8f\u5de6\u5b50\u6570\u7ec4\nleft = pivot + 1;                   // \u5269\u4f59\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [pivot + 1, right]\n} else {\nquickSort(nums, pivot + 1, right);  // \u9012\u5f52\u6392\u5e8f\u53f3\u5b50\u6570\u7ec4\nright = pivot - 1;                  // \u5269\u4f59\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [left, pivot - 1]\n}\n}\n}\n</code></pre> quick_sort.dart<pre><code>/* \u5feb\u901f\u6392\u5e8f\uff08\u5c3e\u9012\u5f52\u4f18\u5316\uff09 */\nvoid quickSort(List&lt;int&gt; nums, int left, int right) {\n// \u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a 1 \u65f6\u7ec8\u6b62\nwhile (left &lt; right) {\n// \u54e8\u5175\u5212\u5206\u64cd\u4f5c\nint pivot = _partition(nums, left, right);\n// \u5bf9\u4e24\u4e2a\u5b50\u6570\u7ec4\u4e2d\u8f83\u77ed\u7684\u90a3\u4e2a\u6267\u884c\u5feb\u6392\nif (pivot - left &lt; right - pivot) {\nquickSort(nums, left, pivot - 1); // \u9012\u5f52\u6392\u5e8f\u5de6\u5b50\u6570\u7ec4\nleft = pivot + 1; // \u5269\u4f59\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [pivot + 1, right]\n} else {\nquickSort(nums, pivot + 1, right); // \u9012\u5f52\u6392\u5e8f\u53f3\u5b50\u6570\u7ec4\nright = pivot - 1; // \u5269\u4f59\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [left, pivot - 1]\n}\n}\n}\n</code></pre>"},{"location":"chapter_sorting/radix_sort/","title":"11.10. \u00a0 \u57fa\u6570\u6392\u5e8f","text":"<p>\u4e0a\u4e00\u8282\u6211\u4eec\u4ecb\u7ecd\u4e86\u8ba1\u6570\u6392\u5e8f\uff0c\u5b83\u9002\u7528\u4e8e\u6570\u636e\u91cf \\(n\\) \u8f83\u5927\u4f46\u6570\u636e\u8303\u56f4 \\(m\\) \u8f83\u5c0f\u7684\u60c5\u51b5\u3002\u5047\u8bbe\u6211\u4eec\u9700\u8981\u5bf9 \\(n = 10^6\\) \u4e2a\u5b66\u53f7\u8fdb\u884c\u6392\u5e8f\uff0c\u800c\u5b66\u53f7\u662f\u4e00\u4e2a \\(8\\) \u4f4d\u6570\u5b57\uff0c\u8fd9\u610f\u5473\u7740\u6570\u636e\u8303\u56f4 \\(m = 10^8\\) \u975e\u5e38\u5927\uff0c\u4f7f\u7528\u8ba1\u6570\u6392\u5e8f\u9700\u8981\u5206\u914d\u5927\u91cf\u5185\u5b58\u7a7a\u95f4\uff0c\u800c\u57fa\u6570\u6392\u5e8f\u53ef\u4ee5\u907f\u514d\u8fd9\u79cd\u60c5\u51b5\u3002</p> <p>\u300c\u57fa\u6570\u6392\u5e8f Radix Sort\u300d\u7684\u6838\u5fc3\u601d\u60f3\u4e0e\u8ba1\u6570\u6392\u5e8f\u4e00\u81f4\uff0c\u4e5f\u901a\u8fc7\u7edf\u8ba1\u4e2a\u6570\u6765\u5b9e\u73b0\u6392\u5e8f\u3002\u5728\u6b64\u57fa\u7840\u4e0a\uff0c\u57fa\u6570\u6392\u5e8f\u5229\u7528\u6570\u5b57\u5404\u4f4d\u4e4b\u95f4\u7684\u9012\u8fdb\u5173\u7cfb\uff0c\u4f9d\u6b21\u5bf9\u6bcf\u4e00\u4f4d\u8fdb\u884c\u6392\u5e8f\uff0c\u4ece\u800c\u5f97\u5230\u6700\u7ec8\u7684\u6392\u5e8f\u7ed3\u679c\u3002</p>"},{"location":"chapter_sorting/radix_sort/#11101","title":"11.10.1. \u00a0 \u7b97\u6cd5\u6d41\u7a0b","text":"<p>\u4ee5\u5b66\u53f7\u6570\u636e\u4e3a\u4f8b\uff0c\u5047\u8bbe\u6570\u5b57\u7684\u6700\u4f4e\u4f4d\u662f\u7b2c \\(1\\) \u4f4d\uff0c\u6700\u9ad8\u4f4d\u662f\u7b2c \\(8\\) \u4f4d\uff0c\u57fa\u6570\u6392\u5e8f\u7684\u6b65\u9aa4\u5982\u4e0b\uff1a</p> <ol> <li>\u521d\u59cb\u5316\u4f4d\u6570 \\(k = 1\\) \uff1b</li> <li>\u5bf9\u5b66\u53f7\u7684\u7b2c \\(k\\) \u4f4d\u6267\u884c\u300c\u8ba1\u6570\u6392\u5e8f\u300d\u3002\u5b8c\u6210\u540e\uff0c\u6570\u636e\u4f1a\u6839\u636e\u7b2c \\(k\\) \u4f4d\u4ece\u5c0f\u5230\u5927\u6392\u5e8f\uff1b</li> <li>\u5c06 \\(k\\) \u589e\u52a0 \\(1\\) \uff0c\u7136\u540e\u8fd4\u56de\u6b65\u9aa4 <code>2.</code> \u7ee7\u7eed\u8fed\u4ee3\uff0c\u76f4\u5230\u6240\u6709\u4f4d\u90fd\u6392\u5e8f\u5b8c\u6210\u540e\u7ed3\u675f\uff1b</li> </ol> <p></p> <p> Fig. \u57fa\u6570\u6392\u5e8f\u7b97\u6cd5\u6d41\u7a0b </p> <p>\u4e0b\u9762\u6765\u5256\u6790\u4ee3\u7801\u5b9e\u73b0\u3002\u5bf9\u4e8e\u4e00\u4e2a \\(d\\) \u8fdb\u5236\u7684\u6570\u5b57 \\(x\\) \uff0c\u8981\u83b7\u53d6\u5176\u7b2c \\(k\\) \u4f4d \\(x_k\\) \uff0c\u53ef\u4ee5\u4f7f\u7528\u4ee5\u4e0b\u8ba1\u7b97\u516c\u5f0f\uff1a</p> \\[ x_k = \\lfloor\\frac{x}{d^{k-1}}\\rfloor \\bmod d \\] <p>\u5176\u4e2d \\(\\lfloor a \\rfloor\\) \u8868\u793a\u5bf9\u6d6e\u70b9\u6570 \\(a\\) \u5411\u4e0b\u53d6\u6574\uff0c\u800c \\(\\bmod \\space d\\) \u8868\u793a\u5bf9 \\(d\\) \u53d6\u4f59\u3002\u5bf9\u4e8e\u5b66\u53f7\u6570\u636e\uff0c\\(d = 10\\) \u4e14 \\(k \\in [1, 8]\\) \u3002</p> <p>\u6b64\u5916\uff0c\u6211\u4eec\u9700\u8981\u5c0f\u5e45\u6539\u52a8\u8ba1\u6570\u6392\u5e8f\u4ee3\u7801\uff0c\u4f7f\u4e4b\u53ef\u4ee5\u6839\u636e\u6570\u5b57\u7684\u7b2c \\(k\\) \u4f4d\u8fdb\u884c\u6392\u5e8f\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart radix_sort.java<pre><code>/* \u83b7\u53d6\u5143\u7d20 num \u7684\u7b2c k \u4f4d\uff0c\u5176\u4e2d exp = 10^(k-1) */\nint digit(int num, int exp) {\n// \u4f20\u5165 exp \u800c\u975e k \u53ef\u4ee5\u907f\u514d\u5728\u6b64\u91cd\u590d\u6267\u884c\u6602\u8d35\u7684\u6b21\u65b9\u8ba1\u7b97\nreturn (num / exp) % 10;\n}\n/* \u8ba1\u6570\u6392\u5e8f\uff08\u6839\u636e nums \u7b2c k \u4f4d\u6392\u5e8f\uff09 */\nvoid countingSortDigit(int[] nums, int exp) {\n// \u5341\u8fdb\u5236\u7684\u4f4d\u8303\u56f4\u4e3a 0~9 \uff0c\u56e0\u6b64\u9700\u8981\u957f\u5ea6\u4e3a 10 \u7684\u6876\nint[] counter = new int[10];\nint n = nums.length;\n// \u7edf\u8ba1 0~9 \u5404\u6570\u5b57\u7684\u51fa\u73b0\u6b21\u6570\nfor (int i = 0; i &lt; n; i++) {\nint d = digit(nums[i], exp); // \u83b7\u53d6 nums[i] \u7b2c k \u4f4d\uff0c\u8bb0\u4e3a d\ncounter[d]++;                // \u7edf\u8ba1\u6570\u5b57 d \u7684\u51fa\u73b0\u6b21\u6570\n}\n// \u6c42\u524d\u7f00\u548c\uff0c\u5c06\u201c\u51fa\u73b0\u4e2a\u6570\u201d\u8f6c\u6362\u4e3a\u201c\u6570\u7ec4\u7d22\u5f15\u201d\nfor (int i = 1; i &lt; 10; i++) {\ncounter[i] += counter[i - 1];\n}\n// \u5012\u5e8f\u904d\u5386\uff0c\u6839\u636e\u6876\u5185\u7edf\u8ba1\u7ed3\u679c\uff0c\u5c06\u5404\u5143\u7d20\u586b\u5165 res\nint[] res = new int[n];\nfor (int i = n - 1; i &gt;= 0; i--) {\nint d = digit(nums[i], exp);\nint j = counter[d] - 1; // \u83b7\u53d6 d \u5728\u6570\u7ec4\u4e2d\u7684\u7d22\u5f15 j\nres[j] = nums[i];       // \u5c06\u5f53\u524d\u5143\u7d20\u586b\u5165\u7d22\u5f15 j\ncounter[d]--;           // \u5c06 d \u7684\u6570\u91cf\u51cf 1\n}\n// \u4f7f\u7528\u7ed3\u679c\u8986\u76d6\u539f\u6570\u7ec4 nums\nfor (int i = 0; i &lt; n; i++)\nnums[i] = res[i];\n}\n/* \u57fa\u6570\u6392\u5e8f */\nvoid radixSort(int[] nums) {\n// \u83b7\u53d6\u6570\u7ec4\u7684\u6700\u5927\u5143\u7d20\uff0c\u7528\u4e8e\u5224\u65ad\u6700\u5927\u4f4d\u6570\nint m = Integer.MIN_VALUE;\nfor (int num : nums)\nif (num &gt; m)\nm = num;\n// \u6309\u7167\u4ece\u4f4e\u4f4d\u5230\u9ad8\u4f4d\u7684\u987a\u5e8f\u904d\u5386\nfor (int exp = 1; exp &lt;= m; exp *= 10)\n// \u5bf9\u6570\u7ec4\u5143\u7d20\u7684\u7b2c k \u4f4d\u6267\u884c\u8ba1\u6570\u6392\u5e8f\n// k = 1 -&gt; exp = 1\n// k = 2 -&gt; exp = 10\n// \u5373 exp = 10^(k-1)\ncountingSortDigit(nums, exp);\n}\n</code></pre> radix_sort.cpp<pre><code>/* \u83b7\u53d6\u5143\u7d20 num \u7684\u7b2c k \u4f4d\uff0c\u5176\u4e2d exp = 10^(k-1) */\nint digit(int num, int exp) {\n// \u4f20\u5165 exp \u800c\u975e k \u53ef\u4ee5\u907f\u514d\u5728\u6b64\u91cd\u590d\u6267\u884c\u6602\u8d35\u7684\u6b21\u65b9\u8ba1\u7b97\nreturn (num / exp) % 10;\n}\n/* \u8ba1\u6570\u6392\u5e8f\uff08\u6839\u636e nums \u7b2c k \u4f4d\u6392\u5e8f\uff09 */\nvoid countingSortDigit(vector&lt;int&gt; &amp;nums, int exp) {\n// \u5341\u8fdb\u5236\u7684\u4f4d\u8303\u56f4\u4e3a 0~9 \uff0c\u56e0\u6b64\u9700\u8981\u957f\u5ea6\u4e3a 10 \u7684\u6876\nvector&lt;int&gt; counter(10, 0);\nint n = nums.size();\n// \u7edf\u8ba1 0~9 \u5404\u6570\u5b57\u7684\u51fa\u73b0\u6b21\u6570\nfor (int i = 0; i &lt; n; i++) {\nint d = digit(nums[i], exp); // \u83b7\u53d6 nums[i] \u7b2c k \u4f4d\uff0c\u8bb0\u4e3a d\ncounter[d]++;                // \u7edf\u8ba1\u6570\u5b57 d \u7684\u51fa\u73b0\u6b21\u6570\n}\n// \u6c42\u524d\u7f00\u548c\uff0c\u5c06\u201c\u51fa\u73b0\u4e2a\u6570\u201d\u8f6c\u6362\u4e3a\u201c\u6570\u7ec4\u7d22\u5f15\u201d\nfor (int i = 1; i &lt; 10; i++) {\ncounter[i] += counter[i - 1];\n}\n// \u5012\u5e8f\u904d\u5386\uff0c\u6839\u636e\u6876\u5185\u7edf\u8ba1\u7ed3\u679c\uff0c\u5c06\u5404\u5143\u7d20\u586b\u5165 res\nvector&lt;int&gt; res(n, 0);\nfor (int i = n - 1; i &gt;= 0; i--) {\nint d = digit(nums[i], exp);\nint j = counter[d] - 1; // \u83b7\u53d6 d \u5728\u6570\u7ec4\u4e2d\u7684\u7d22\u5f15 j\nres[j] = nums[i];       // \u5c06\u5f53\u524d\u5143\u7d20\u586b\u5165\u7d22\u5f15 j\ncounter[d]--;           // \u5c06 d \u7684\u6570\u91cf\u51cf 1\n}\n// \u4f7f\u7528\u7ed3\u679c\u8986\u76d6\u539f\u6570\u7ec4 nums\nfor (int i = 0; i &lt; n; i++)\nnums[i] = res[i];\n}\n/* \u57fa\u6570\u6392\u5e8f */\nvoid radixSort(vector&lt;int&gt; &amp;nums) {\n// \u83b7\u53d6\u6570\u7ec4\u7684\u6700\u5927\u5143\u7d20\uff0c\u7528\u4e8e\u5224\u65ad\u6700\u5927\u4f4d\u6570\nint m = *max_element(nums.begin(), nums.end());\n// \u6309\u7167\u4ece\u4f4e\u4f4d\u5230\u9ad8\u4f4d\u7684\u987a\u5e8f\u904d\u5386\nfor (int exp = 1; exp &lt;= m; exp *= 10)\n// \u5bf9\u6570\u7ec4\u5143\u7d20\u7684\u7b2c k \u4f4d\u6267\u884c\u8ba1\u6570\u6392\u5e8f\n// k = 1 -&gt; exp = 1\n// k = 2 -&gt; exp = 10\n// \u5373 exp = 10^(k-1)\ncountingSortDigit(nums, exp);\n}\n</code></pre> radix_sort.py<pre><code>def digit(num: int, exp: int) -&gt; int:\n\"\"\"\u83b7\u53d6\u5143\u7d20 num \u7684\u7b2c k \u4f4d\uff0c\u5176\u4e2d exp = 10^(k-1)\"\"\"\n# \u4f20\u5165 exp \u800c\u975e k \u53ef\u4ee5\u907f\u514d\u5728\u6b64\u91cd\u590d\u6267\u884c\u6602\u8d35\u7684\u6b21\u65b9\u8ba1\u7b97\nreturn (num // exp) % 10\ndef counting_sort_digit(nums: list[int], exp: int) -&gt; None:\n\"\"\"\u8ba1\u6570\u6392\u5e8f\uff08\u6839\u636e nums \u7b2c k \u4f4d\u6392\u5e8f\uff09\"\"\"\n# \u5341\u8fdb\u5236\u7684\u4f4d\u8303\u56f4\u4e3a 0~9 \uff0c\u56e0\u6b64\u9700\u8981\u957f\u5ea6\u4e3a 10 \u7684\u6876\ncounter = [0] * 10\nn = len(nums)\n# \u7edf\u8ba1 0~9 \u5404\u6570\u5b57\u7684\u51fa\u73b0\u6b21\u6570\nfor i in range(n):\nd = digit(nums[i], exp)  # \u83b7\u53d6 nums[i] \u7b2c k \u4f4d\uff0c\u8bb0\u4e3a d\ncounter[d] += 1  # \u7edf\u8ba1\u6570\u5b57 d \u7684\u51fa\u73b0\u6b21\u6570\n# \u6c42\u524d\u7f00\u548c\uff0c\u5c06\u201c\u51fa\u73b0\u4e2a\u6570\u201d\u8f6c\u6362\u4e3a\u201c\u6570\u7ec4\u7d22\u5f15\u201d\nfor i in range(1, 10):\ncounter[i] += counter[i - 1]\n# \u5012\u5e8f\u904d\u5386\uff0c\u6839\u636e\u6876\u5185\u7edf\u8ba1\u7ed3\u679c\uff0c\u5c06\u5404\u5143\u7d20\u586b\u5165 res\nres = [0] * n\nfor i in range(n - 1, -1, -1):\nd = digit(nums[i], exp)\nj = counter[d] - 1  # \u83b7\u53d6 d \u5728\u6570\u7ec4\u4e2d\u7684\u7d22\u5f15 j\nres[j] = nums[i]  # \u5c06\u5f53\u524d\u5143\u7d20\u586b\u5165\u7d22\u5f15 j\ncounter[d] -= 1  # \u5c06 d \u7684\u6570\u91cf\u51cf 1\n# \u4f7f\u7528\u7ed3\u679c\u8986\u76d6\u539f\u6570\u7ec4 nums\nfor i in range(n):\nnums[i] = res[i]\ndef radix_sort(nums: list[int]) -&gt; None:\n\"\"\"\u57fa\u6570\u6392\u5e8f\"\"\"\n# \u83b7\u53d6\u6570\u7ec4\u7684\u6700\u5927\u5143\u7d20\uff0c\u7528\u4e8e\u5224\u65ad\u6700\u5927\u4f4d\u6570\nm = max(nums)\n# \u6309\u7167\u4ece\u4f4e\u4f4d\u5230\u9ad8\u4f4d\u7684\u987a\u5e8f\u904d\u5386\nexp = 1\nwhile exp &lt;= m:\n# \u5bf9\u6570\u7ec4\u5143\u7d20\u7684\u7b2c k \u4f4d\u6267\u884c\u8ba1\u6570\u6392\u5e8f\n# k = 1 -&gt; exp = 1\n# k = 2 -&gt; exp = 10\n# \u5373 exp = 10^(k-1)\ncounting_sort_digit(nums, exp)\nexp *= 10\n</code></pre> radix_sort.go<pre><code>/* \u83b7\u53d6\u5143\u7d20 num \u7684\u7b2c k \u4f4d\uff0c\u5176\u4e2d exp = 10^(k-1) */\nfunc digit(num, exp int) int {\n// \u4f20\u5165 exp \u800c\u975e k \u53ef\u4ee5\u907f\u514d\u5728\u6b64\u91cd\u590d\u6267\u884c\u6602\u8d35\u7684\u6b21\u65b9\u8ba1\u7b97\nreturn (num / exp) % 10\n}\n/* \u8ba1\u6570\u6392\u5e8f\uff08\u6839\u636e nums \u7b2c k \u4f4d\u6392\u5e8f\uff09 */\nfunc countingSortDigit(nums []int, exp int) {\n// \u5341\u8fdb\u5236\u7684\u4f4d\u8303\u56f4\u4e3a 0~9 \uff0c\u56e0\u6b64\u9700\u8981\u957f\u5ea6\u4e3a 10 \u7684\u6876\ncounter := make([]int, 10)\nn := len(nums)\n// \u7edf\u8ba1 0~9 \u5404\u6570\u5b57\u7684\u51fa\u73b0\u6b21\u6570\nfor i := 0; i &lt; n; i++ {\nd := digit(nums[i], exp) // \u83b7\u53d6 nums[i] \u7b2c k \u4f4d\uff0c\u8bb0\u4e3a d\ncounter[d]++             // \u7edf\u8ba1\u6570\u5b57 d \u7684\u51fa\u73b0\u6b21\u6570\n}\n// \u6c42\u524d\u7f00\u548c\uff0c\u5c06\u201c\u51fa\u73b0\u4e2a\u6570\u201d\u8f6c\u6362\u4e3a\u201c\u6570\u7ec4\u7d22\u5f15\u201d\nfor i := 1; i &lt; 10; i++ {\ncounter[i] += counter[i-1]\n}\n// \u5012\u5e8f\u904d\u5386\uff0c\u6839\u636e\u6876\u5185\u7edf\u8ba1\u7ed3\u679c\uff0c\u5c06\u5404\u5143\u7d20\u586b\u5165 res\nres := make([]int, n)\nfor i := n - 1; i &gt;= 0; i-- {\nd := digit(nums[i], exp)\nj := counter[d] - 1 // \u83b7\u53d6 d \u5728\u6570\u7ec4\u4e2d\u7684\u7d22\u5f15 j\nres[j] = nums[i]    // \u5c06\u5f53\u524d\u5143\u7d20\u586b\u5165\u7d22\u5f15 j\ncounter[d]--        // \u5c06 d \u7684\u6570\u91cf\u51cf 1\n}\n// \u4f7f\u7528\u7ed3\u679c\u8986\u76d6\u539f\u6570\u7ec4 nums\nfor i := 0; i &lt; n; i++ {\nnums[i] = res[i]\n}\n}\n/* \u57fa\u6570\u6392\u5e8f */\nfunc radixSort(nums []int) {\n// \u83b7\u53d6\u6570\u7ec4\u7684\u6700\u5927\u5143\u7d20\uff0c\u7528\u4e8e\u5224\u65ad\u6700\u5927\u4f4d\u6570\nmax := math.MinInt\nfor _, num := range nums {\nif num &gt; max {\nmax = num\n}\n}\n// \u6309\u7167\u4ece\u4f4e\u4f4d\u5230\u9ad8\u4f4d\u7684\u987a\u5e8f\u904d\u5386\nfor exp := 1; max &gt;= exp; exp *= 10 {\n// \u5bf9\u6570\u7ec4\u5143\u7d20\u7684\u7b2c k \u4f4d\u6267\u884c\u8ba1\u6570\u6392\u5e8f\n// k = 1 -&gt; exp = 1\n// k = 2 -&gt; exp = 10\n// \u5373 exp = 10^(k-1)\ncountingSortDigit(nums, exp)\n}\n}\n</code></pre> radix_sort.js<pre><code>/* \u83b7\u53d6\u5143\u7d20 num \u7684\u7b2c k \u4f4d\uff0c\u5176\u4e2d exp = 10^(k-1) */\nfunction digit(num, exp) {\n// \u4f20\u5165 exp \u800c\u975e k \u53ef\u4ee5\u907f\u514d\u5728\u6b64\u91cd\u590d\u6267\u884c\u6602\u8d35\u7684\u6b21\u65b9\u8ba1\u7b97\nreturn Math.floor(num / exp) % 10;\n}\n/* \u8ba1\u6570\u6392\u5e8f\uff08\u6839\u636e nums \u7b2c k \u4f4d\u6392\u5e8f\uff09 */\nfunction countingSortDigit(nums, exp) {\n// \u5341\u8fdb\u5236\u7684\u4f4d\u8303\u56f4\u4e3a 0~9 \uff0c\u56e0\u6b64\u9700\u8981\u957f\u5ea6\u4e3a 10 \u7684\u6876\nconst counter = new Array(10).fill(0);\nconst n = nums.length;\n// \u7edf\u8ba1 0~9 \u5404\u6570\u5b57\u7684\u51fa\u73b0\u6b21\u6570\nfor (let i = 0; i &lt; n; i++) {\nconst d = digit(nums[i], exp); // \u83b7\u53d6 nums[i] \u7b2c k \u4f4d\uff0c\u8bb0\u4e3a d\ncounter[d]++; // \u7edf\u8ba1\u6570\u5b57 d \u7684\u51fa\u73b0\u6b21\u6570\n}\n// \u6c42\u524d\u7f00\u548c\uff0c\u5c06\u201c\u51fa\u73b0\u4e2a\u6570\u201d\u8f6c\u6362\u4e3a\u201c\u6570\u7ec4\u7d22\u5f15\u201d\nfor (let i = 1; i &lt; 10; i++) {\ncounter[i] += counter[i - 1];\n}\n// \u5012\u5e8f\u904d\u5386\uff0c\u6839\u636e\u6876\u5185\u7edf\u8ba1\u7ed3\u679c\uff0c\u5c06\u5404\u5143\u7d20\u586b\u5165 res\nconst res = new Array(n).fill(0);\nfor (let i = n - 1; i &gt;= 0; i--) {\nconst d = digit(nums[i], exp);\nconst j = counter[d] - 1; // \u83b7\u53d6 d \u5728\u6570\u7ec4\u4e2d\u7684\u7d22\u5f15 j\nres[j] = nums[i]; // \u5c06\u5f53\u524d\u5143\u7d20\u586b\u5165\u7d22\u5f15 j\ncounter[d]--; // \u5c06 d \u7684\u6570\u91cf\u51cf 1\n}\n// \u4f7f\u7528\u7ed3\u679c\u8986\u76d6\u539f\u6570\u7ec4 nums\nfor (let i = 0; i &lt; n; i++) {\nnums[i] = res[i];\n}\n}\n/* \u57fa\u6570\u6392\u5e8f */\nfunction radixSort(nums) {\n// \u83b7\u53d6\u6570\u7ec4\u7684\u6700\u5927\u5143\u7d20\uff0c\u7528\u4e8e\u5224\u65ad\u6700\u5927\u4f4d\u6570\nlet m = Number.MIN_VALUE;\nfor (const num of nums) {\nif (num &gt; m) {\nm = num;\n}\n}\n// \u6309\u7167\u4ece\u4f4e\u4f4d\u5230\u9ad8\u4f4d\u7684\u987a\u5e8f\u904d\u5386\nfor (let exp = 1; exp &lt;= m; exp *= 10) {\n// \u5bf9\u6570\u7ec4\u5143\u7d20\u7684\u7b2c k \u4f4d\u6267\u884c\u8ba1\u6570\u6392\u5e8f\n// k = 1 -&gt; exp = 1\n// k = 2 -&gt; exp = 10\n// \u5373 exp = 10^(k-1)\ncountingSortDigit(nums, exp);\n}\n}\n</code></pre> radix_sort.ts<pre><code>/* \u83b7\u53d6\u5143\u7d20 num \u7684\u7b2c k \u4f4d\uff0c\u5176\u4e2d exp = 10^(k-1) */\nfunction digit(num: number, exp: number): number {\n// \u4f20\u5165 exp \u800c\u975e k \u53ef\u4ee5\u907f\u514d\u5728\u6b64\u91cd\u590d\u6267\u884c\u6602\u8d35\u7684\u6b21\u65b9\u8ba1\u7b97\nreturn Math.floor(num / exp) % 10;\n}\n/* \u8ba1\u6570\u6392\u5e8f\uff08\u6839\u636e nums \u7b2c k \u4f4d\u6392\u5e8f\uff09 */\nfunction countingSortDigit(nums: number[], exp: number): void {\n// \u5341\u8fdb\u5236\u7684\u4f4d\u8303\u56f4\u4e3a 0~9 \uff0c\u56e0\u6b64\u9700\u8981\u957f\u5ea6\u4e3a 10 \u7684\u6876\nconst counter = new Array(10).fill(0);\nconst n = nums.length;\n// \u7edf\u8ba1 0~9 \u5404\u6570\u5b57\u7684\u51fa\u73b0\u6b21\u6570\nfor (let i = 0; i &lt; n; i++) {\nconst d = digit(nums[i], exp); // \u83b7\u53d6 nums[i] \u7b2c k \u4f4d\uff0c\u8bb0\u4e3a d\ncounter[d]++; // \u7edf\u8ba1\u6570\u5b57 d \u7684\u51fa\u73b0\u6b21\u6570\n}\n// \u6c42\u524d\u7f00\u548c\uff0c\u5c06\u201c\u51fa\u73b0\u4e2a\u6570\u201d\u8f6c\u6362\u4e3a\u201c\u6570\u7ec4\u7d22\u5f15\u201d\nfor (let i = 1; i &lt; 10; i++) {\ncounter[i] += counter[i - 1];\n}\n// \u5012\u5e8f\u904d\u5386\uff0c\u6839\u636e\u6876\u5185\u7edf\u8ba1\u7ed3\u679c\uff0c\u5c06\u5404\u5143\u7d20\u586b\u5165 res\nconst res = new Array(n).fill(0);\nfor (let i = n - 1; i &gt;= 0; i--) {\nconst d = digit(nums[i], exp);\nconst j = counter[d] - 1; // \u83b7\u53d6 d \u5728\u6570\u7ec4\u4e2d\u7684\u7d22\u5f15 j\nres[j] = nums[i]; // \u5c06\u5f53\u524d\u5143\u7d20\u586b\u5165\u7d22\u5f15 j\ncounter[d]--; // \u5c06 d \u7684\u6570\u91cf\u51cf 1\n}\n// \u4f7f\u7528\u7ed3\u679c\u8986\u76d6\u539f\u6570\u7ec4 nums\nfor (let i = 0; i &lt; n; i++) {\nnums[i] = res[i];\n}\n}\n/* \u57fa\u6570\u6392\u5e8f */\nfunction radixSort(nums: number[]): void {\n// \u83b7\u53d6\u6570\u7ec4\u7684\u6700\u5927\u5143\u7d20\uff0c\u7528\u4e8e\u5224\u65ad\u6700\u5927\u4f4d\u6570\nlet m = Number.MIN_VALUE;\nfor (const num of nums) {\nif (num &gt; m) {\nm = num;\n}\n}\n// \u6309\u7167\u4ece\u4f4e\u4f4d\u5230\u9ad8\u4f4d\u7684\u987a\u5e8f\u904d\u5386\nfor (let exp = 1; exp &lt;= m; exp *= 10) {\n// \u5bf9\u6570\u7ec4\u5143\u7d20\u7684\u7b2c k \u4f4d\u6267\u884c\u8ba1\u6570\u6392\u5e8f\n// k = 1 -&gt; exp = 1\n// k = 2 -&gt; exp = 10\n// \u5373 exp = 10^(k-1)\ncountingSortDigit(nums, exp);\n}\n}\n</code></pre> radix_sort.c<pre><code>/* \u83b7\u53d6\u5143\u7d20 num \u7684\u7b2c k \u4f4d\uff0c\u5176\u4e2d exp = 10^(k-1) */\nint digit(int num, int exp) {\n// \u4f20\u5165 exp \u800c\u975e k \u53ef\u4ee5\u907f\u514d\u5728\u6b64\u91cd\u590d\u6267\u884c\u6602\u8d35\u7684\u6b21\u65b9\u8ba1\u7b97\nreturn (num / exp) % 10;\n}\n/* \u8ba1\u6570\u6392\u5e8f\uff08\u6839\u636e nums \u7b2c k \u4f4d\u6392\u5e8f\uff09 */\nvoid countingSortDigit(int nums[], int size, int exp) {\n// \u5341\u8fdb\u5236\u7684\u4f4d\u8303\u56f4\u4e3a 0~9 \uff0c\u56e0\u6b64\u9700\u8981\u957f\u5ea6\u4e3a 10 \u7684\u6876\nint *counter = (int *)malloc((sizeof(int) * 10));\n// \u7edf\u8ba1 0~9 \u5404\u6570\u5b57\u7684\u51fa\u73b0\u6b21\u6570\nfor (int i = 0; i &lt; size; i++) {\n// \u83b7\u53d6 nums[i] \u7b2c k \u4f4d\uff0c\u8bb0\u4e3a d\nint d = digit(nums[i], exp);\n// \u7edf\u8ba1\u6570\u5b57 d \u7684\u51fa\u73b0\u6b21\u6570\ncounter[d]++;\n}\n// \u6c42\u524d\u7f00\u548c\uff0c\u5c06\u201c\u51fa\u73b0\u4e2a\u6570\u201d\u8f6c\u6362\u4e3a\u201c\u6570\u7ec4\u7d22\u5f15\u201d\nfor (int i = 1; i &lt; 10; i++) {\ncounter[i] += counter[i - 1];\n}\n// \u5012\u5e8f\u904d\u5386\uff0c\u6839\u636e\u6876\u5185\u7edf\u8ba1\u7ed3\u679c\uff0c\u5c06\u5404\u5143\u7d20\u586b\u5165 res\nint *res = (int *)malloc(sizeof(int) * size);\nfor (int i = size - 1; i &gt;= 0; i--) {\nint d = digit(nums[i], exp);\nint j = counter[d] - 1; // \u83b7\u53d6 d \u5728\u6570\u7ec4\u4e2d\u7684\u7d22\u5f15 j\nres[j] = nums[i];       // \u5c06\u5f53\u524d\u5143\u7d20\u586b\u5165\u7d22\u5f15 j\ncounter[d]--;           // \u5c06 d \u7684\u6570\u91cf\u51cf 1\n}\n// \u4f7f\u7528\u7ed3\u679c\u8986\u76d6\u539f\u6570\u7ec4 nums\nfor (int i = 0; i &lt; size; i++) {\nnums[i] = res[i];\n}\n}\n/* \u57fa\u6570\u6392\u5e8f */\nvoid radixSort(int nums[], int size) {\n// \u83b7\u53d6\u6570\u7ec4\u7684\u6700\u5927\u5143\u7d20\uff0c\u7528\u4e8e\u5224\u65ad\u6700\u5927\u4f4d\u6570\nint max = INT32_MIN;\nfor (size_t i = 0; i &lt; size - 1; i++) {\nif (nums[i] &gt; max) {\nmax = nums[i];\n}\n}\n// \u6309\u7167\u4ece\u4f4e\u4f4d\u5230\u9ad8\u4f4d\u7684\u987a\u5e8f\u904d\u5386\nfor (int exp = 1; max &gt;= exp; exp *= 10)\n// \u5bf9\u6570\u7ec4\u5143\u7d20\u7684\u7b2c k \u4f4d\u6267\u884c\u8ba1\u6570\u6392\u5e8f\n// k = 1 -&gt; exp = 1\n// k = 2 -&gt; exp = 10\n// \u5373 exp = 10^(k-1)\ncountingSortDigit(nums, size, exp);\n}\n</code></pre> radix_sort.cs<pre><code>/* \u83b7\u53d6\u5143\u7d20 num \u7684\u7b2c k \u4f4d\uff0c\u5176\u4e2d exp = 10^(k-1) */\nint digit(int num, int exp) {\n// \u4f20\u5165 exp \u800c\u975e k \u53ef\u4ee5\u907f\u514d\u5728\u6b64\u91cd\u590d\u6267\u884c\u6602\u8d35\u7684\u6b21\u65b9\u8ba1\u7b97\nreturn (num / exp) % 10;\n}\n/* \u8ba1\u6570\u6392\u5e8f\uff08\u6839\u636e nums \u7b2c k \u4f4d\u6392\u5e8f\uff09 */\nvoid countingSortDigit(int[] nums, int exp) {\n// \u5341\u8fdb\u5236\u7684\u4f4d\u8303\u56f4\u4e3a 0~9 \uff0c\u56e0\u6b64\u9700\u8981\u957f\u5ea6\u4e3a 10 \u7684\u6876\nint[] counter = new int[10];\nint n = nums.Length;\n// \u7edf\u8ba1 0~9 \u5404\u6570\u5b57\u7684\u51fa\u73b0\u6b21\u6570\nfor (int i = 0; i &lt; n; i++) {\nint d = digit(nums[i], exp); // \u83b7\u53d6 nums[i] \u7b2c k \u4f4d\uff0c\u8bb0\u4e3a d\ncounter[d]++;                // \u7edf\u8ba1\u6570\u5b57 d \u7684\u51fa\u73b0\u6b21\u6570\n}\n// \u6c42\u524d\u7f00\u548c\uff0c\u5c06\u201c\u51fa\u73b0\u4e2a\u6570\u201d\u8f6c\u6362\u4e3a\u201c\u6570\u7ec4\u7d22\u5f15\u201d\nfor (int i = 1; i &lt; 10; i++) {\ncounter[i] += counter[i - 1];\n}\n// \u5012\u5e8f\u904d\u5386\uff0c\u6839\u636e\u6876\u5185\u7edf\u8ba1\u7ed3\u679c\uff0c\u5c06\u5404\u5143\u7d20\u586b\u5165 res\nint[] res = new int[n];\nfor (int i = n - 1; i &gt;= 0; i--) {\nint d = digit(nums[i], exp);\nint j = counter[d] - 1; // \u83b7\u53d6 d \u5728\u6570\u7ec4\u4e2d\u7684\u7d22\u5f15 j\nres[j] = nums[i];       // \u5c06\u5f53\u524d\u5143\u7d20\u586b\u5165\u7d22\u5f15 j\ncounter[d]--;           // \u5c06 d \u7684\u6570\u91cf\u51cf 1\n}\n// \u4f7f\u7528\u7ed3\u679c\u8986\u76d6\u539f\u6570\u7ec4 nums\nfor (int i = 0; i &lt; n; i++) {\nnums[i] = res[i];\n}\n}\n/* \u57fa\u6570\u6392\u5e8f */\nvoid radixSort(int[] nums) {\n// \u83b7\u53d6\u6570\u7ec4\u7684\u6700\u5927\u5143\u7d20\uff0c\u7528\u4e8e\u5224\u65ad\u6700\u5927\u4f4d\u6570\nint m = int.MinValue;\nforeach (int num in nums) {\nif (num &gt; m) m = num;\n}\n// \u6309\u7167\u4ece\u4f4e\u4f4d\u5230\u9ad8\u4f4d\u7684\u987a\u5e8f\u904d\u5386\nfor (int exp = 1; exp &lt;= m; exp *= 10) {\n// \u5bf9\u6570\u7ec4\u5143\u7d20\u7684\u7b2c k \u4f4d\u6267\u884c\u8ba1\u6570\u6392\u5e8f\n// k = 1 -&gt; exp = 1\n// k = 2 -&gt; exp = 10\n// \u5373 exp = 10^(k-1)\ncountingSortDigit(nums, exp);\n}\n}\n</code></pre> radix_sort.swift<pre><code>/* \u83b7\u53d6\u5143\u7d20 num \u7684\u7b2c k \u4f4d\uff0c\u5176\u4e2d exp = 10^(k-1) */\nfunc digit(num: Int, exp: Int) -&gt; Int {\n// \u4f20\u5165 exp \u800c\u975e k \u53ef\u4ee5\u907f\u514d\u5728\u6b64\u91cd\u590d\u6267\u884c\u6602\u8d35\u7684\u6b21\u65b9\u8ba1\u7b97\n(num / exp) % 10\n}\n/* \u8ba1\u6570\u6392\u5e8f\uff08\u6839\u636e nums \u7b2c k \u4f4d\u6392\u5e8f\uff09 */\nfunc countingSortDigit(nums: inout [Int], exp: Int) {\n// \u5341\u8fdb\u5236\u7684\u4f4d\u8303\u56f4\u4e3a 0~9 \uff0c\u56e0\u6b64\u9700\u8981\u957f\u5ea6\u4e3a 10 \u7684\u6876\nvar counter = Array(repeating: 0, count: 10)\nlet n = nums.count\n// \u7edf\u8ba1 0~9 \u5404\u6570\u5b57\u7684\u51fa\u73b0\u6b21\u6570\nfor i in nums.indices {\nlet d = digit(num: nums[i], exp: exp) // \u83b7\u53d6 nums[i] \u7b2c k \u4f4d\uff0c\u8bb0\u4e3a d\ncounter[d] += 1 // \u7edf\u8ba1\u6570\u5b57 d \u7684\u51fa\u73b0\u6b21\u6570\n}\n// \u6c42\u524d\u7f00\u548c\uff0c\u5c06\u201c\u51fa\u73b0\u4e2a\u6570\u201d\u8f6c\u6362\u4e3a\u201c\u6570\u7ec4\u7d22\u5f15\u201d\nfor i in 1 ..&lt; 10 {\ncounter[i] += counter[i - 1]\n}\n// \u5012\u5e8f\u904d\u5386\uff0c\u6839\u636e\u6876\u5185\u7edf\u8ba1\u7ed3\u679c\uff0c\u5c06\u5404\u5143\u7d20\u586b\u5165 res\nvar res = Array(repeating: 0, count: n)\nfor i in stride(from: n - 1, through: 0, by: -1) {\nlet d = digit(num: nums[i], exp: exp)\nlet j = counter[d] - 1 // \u83b7\u53d6 d \u5728\u6570\u7ec4\u4e2d\u7684\u7d22\u5f15 j\nres[j] = nums[i] // \u5c06\u5f53\u524d\u5143\u7d20\u586b\u5165\u7d22\u5f15 j\ncounter[d] -= 1 // \u5c06 d \u7684\u6570\u91cf\u51cf 1\n}\n// \u4f7f\u7528\u7ed3\u679c\u8986\u76d6\u539f\u6570\u7ec4 nums\nfor i in nums.indices {\nnums[i] = res[i]\n}\n}\n/* \u57fa\u6570\u6392\u5e8f */\nfunc radixSort(nums: inout [Int]) {\n// \u83b7\u53d6\u6570\u7ec4\u7684\u6700\u5927\u5143\u7d20\uff0c\u7528\u4e8e\u5224\u65ad\u6700\u5927\u4f4d\u6570\nvar m = Int.min\nfor num in nums {\nif num &gt; m {\nm = num\n}\n}\n// \u6309\u7167\u4ece\u4f4e\u4f4d\u5230\u9ad8\u4f4d\u7684\u987a\u5e8f\u904d\u5386\nfor exp in sequence(first: 1, next: { m &gt;= ($0 * 10) ? $0 * 10 : nil }) {\n// \u5bf9\u6570\u7ec4\u5143\u7d20\u7684\u7b2c k \u4f4d\u6267\u884c\u8ba1\u6570\u6392\u5e8f\n// k = 1 -&gt; exp = 1\n// k = 2 -&gt; exp = 10\n// \u5373 exp = 10^(k-1)\ncountingSortDigit(nums: &amp;nums, exp: exp)\n}\n}\n</code></pre> radix_sort.zig<pre><code>// \u83b7\u53d6\u5143\u7d20 num \u7684\u7b2c k \u4f4d\uff0c\u5176\u4e2d exp = 10^(k-1)\nfn digit(num: i32, exp: i32) i32 {\n// \u4f20\u5165 exp \u800c\u975e k \u53ef\u4ee5\u907f\u514d\u5728\u6b64\u91cd\u590d\u6267\u884c\u6602\u8d35\u7684\u6b21\u65b9\u8ba1\u7b97\nreturn @mod(@divFloor(num, exp), 10);\n}\n// \u8ba1\u6570\u6392\u5e8f\uff08\u6839\u636e nums \u7b2c k \u4f4d\u6392\u5e8f\uff09\nfn countingSortDigit(nums: []i32, exp: i32) !void {\n// \u5341\u8fdb\u5236\u7684\u4f4d\u8303\u56f4\u4e3a 0~9 \uff0c\u56e0\u6b64\u9700\u8981\u957f\u5ea6\u4e3a 10 \u7684\u6876\nvar mem_arena = std.heap.ArenaAllocator.init(std.heap.page_allocator);\n// defer mem_arena.deinit();\nconst mem_allocator = mem_arena.allocator();\nvar counter = try mem_allocator.alloc(usize, 10);\nstd.mem.set(usize, counter, 0);\nvar n = nums.len;\n// \u7edf\u8ba1 0~9 \u5404\u6570\u5b57\u7684\u51fa\u73b0\u6b21\u6570\nfor (nums) |num| {\nvar d = @bitCast(u32, digit(num, exp)); // \u83b7\u53d6 nums[i] \u7b2c k \u4f4d\uff0c\u8bb0\u4e3a d\ncounter[d] += 1; // \u7edf\u8ba1\u6570\u5b57 d \u7684\u51fa\u73b0\u6b21\u6570\n}\n// \u6c42\u524d\u7f00\u548c\uff0c\u5c06\u201c\u51fa\u73b0\u4e2a\u6570\u201d\u8f6c\u6362\u4e3a\u201c\u6570\u7ec4\u7d22\u5f15\u201d\nvar i: usize = 1;\nwhile (i &lt; 10) : (i += 1) {\ncounter[i] += counter[i - 1];\n}\n// \u5012\u5e8f\u904d\u5386\uff0c\u6839\u636e\u6876\u5185\u7edf\u8ba1\u7ed3\u679c\uff0c\u5c06\u5404\u5143\u7d20\u586b\u5165 res\nvar res = try mem_allocator.alloc(i32, n);\ni = n - 1;\nwhile (i &gt;= 0) : (i -= 1) {\nvar d = @bitCast(u32, digit(nums[i], exp));\nvar j = counter[d] - 1; // \u83b7\u53d6 d \u5728\u6570\u7ec4\u4e2d\u7684\u7d22\u5f15 j\nres[j] = nums[i];       // \u5c06\u5f53\u524d\u5143\u7d20\u586b\u5165\u7d22\u5f15 j\ncounter[d] -= 1;        // \u5c06 d \u7684\u6570\u91cf\u51cf 1\nif (i == 0) break;\n}\n// \u4f7f\u7528\u7ed3\u679c\u8986\u76d6\u539f\u6570\u7ec4 nums\ni = 0;\nwhile (i &lt; n) : (i += 1) {\nnums[i] = res[i];\n}\n}\n// \u57fa\u6570\u6392\u5e8f\nfn radixSort(nums: []i32) !void {\n// \u83b7\u53d6\u6570\u7ec4\u7684\u6700\u5927\u5143\u7d20\uff0c\u7528\u4e8e\u5224\u65ad\u6700\u5927\u4f4d\u6570\nvar m: i32 = std.math.minInt(i32);\nfor (nums) |num| {\nif (num &gt; m) m = num;\n}\n// \u6309\u7167\u4ece\u4f4e\u4f4d\u5230\u9ad8\u4f4d\u7684\u987a\u5e8f\u904d\u5386\nvar exp: i32 = 1;\nwhile (exp &lt;= m) : (exp *= 10) {\n// \u5bf9\u6570\u7ec4\u5143\u7d20\u7684\u7b2c k \u4f4d\u6267\u884c\u8ba1\u6570\u6392\u5e8f\n// k = 1 -&gt; exp = 1\n// k = 2 -&gt; exp = 10\n// \u5373 exp = 10^(k-1)\ntry countingSortDigit(nums, exp);    }\n} </code></pre> radix_sort.dart<pre><code>/* \u83b7\u53d6\u5143\u7d20 num \u7684\u7b2c k \u4f4d\uff0c\u5176\u4e2d exp = 10^(k-1) */\nint digit(int num, int exp) {\n// \u4f20\u5165 exp \u800c\u975e k \u53ef\u4ee5\u907f\u514d\u5728\u6b64\u91cd\u590d\u6267\u884c\u6602\u8d35\u7684\u6b21\u65b9\u8ba1\u7b97\nreturn (num ~/ exp) % 10;\n}\n/* \u8ba1\u6570\u6392\u5e8f\uff08\u6839\u636e nums \u7b2c k \u4f4d\u6392\u5e8f\uff09 */\nvoid countingSortDigit(List&lt;int&gt; nums, int exp) {\n// \u5341\u8fdb\u5236\u7684\u4f4d\u8303\u56f4\u4e3a 0~9 \uff0c\u56e0\u6b64\u9700\u8981\u957f\u5ea6\u4e3a 10 \u7684\u6876\nList&lt;int&gt; counter = List&lt;int&gt;.filled(10, 0);\nint n = nums.length;\n// \u7edf\u8ba1 0~9 \u5404\u6570\u5b57\u7684\u51fa\u73b0\u6b21\u6570\nfor (int i = 0; i &lt; n; i++) {\nint d = digit(nums[i], exp); // \u83b7\u53d6 nums[i] \u7b2c k \u4f4d\uff0c\u8bb0\u4e3a d\ncounter[d]++; // \u7edf\u8ba1\u6570\u5b57 d \u7684\u51fa\u73b0\u6b21\u6570\n}\n// \u6c42\u524d\u7f00\u548c\uff0c\u5c06\u201c\u51fa\u73b0\u4e2a\u6570\u201d\u8f6c\u6362\u4e3a\u201c\u6570\u7ec4\u7d22\u5f15\u201d\nfor (int i = 1; i &lt; 10; i++) {\ncounter[i] += counter[i - 1];\n}\n// \u5012\u5e8f\u904d\u5386\uff0c\u6839\u636e\u6876\u5185\u7edf\u8ba1\u7ed3\u679c\uff0c\u5c06\u5404\u5143\u7d20\u586b\u5165 res\nList&lt;int&gt; res = List&lt;int&gt;.filled(n, 0);\nfor (int i = n - 1; i &gt;= 0; i--) {\nint d = digit(nums[i], exp);\nint j = counter[d] - 1; // \u83b7\u53d6 d \u5728\u6570\u7ec4\u4e2d\u7684\u7d22\u5f15 j\nres[j] = nums[i]; // \u5c06\u5f53\u524d\u5143\u7d20\u586b\u5165\u7d22\u5f15 j\ncounter[d]--; // \u5c06 d \u7684\u6570\u91cf\u51cf 1\n}\n// \u4f7f\u7528\u7ed3\u679c\u8986\u76d6\u539f\u6570\u7ec4 nums\nfor (int i = 0; i &lt; n; i++) nums[i] = res[i];\n}\n/* \u57fa\u6570\u6392\u5e8f */\nvoid radixSort(List&lt;int&gt; nums) {\n// \u83b7\u53d6\u6570\u7ec4\u7684\u6700\u5927\u5143\u7d20\uff0c\u7528\u4e8e\u5224\u65ad\u6700\u5927\u4f4d\u6570\n// dart \u4e2d int \u7684\u957f\u5ea6\u662f 64 \u4f4d\u7684\nint m = -1 &lt;&lt; 63; for (int num in nums) if (num &gt; m) m = num;\n// \u6309\u7167\u4ece\u4f4e\u4f4d\u5230\u9ad8\u4f4d\u7684\u987a\u5e8f\u904d\u5386\nfor (int exp = 1; exp &lt;= m; exp *= 10)\n// \u5bf9\u6570\u7ec4\u5143\u7d20\u7684\u7b2c k \u4f4d\u6267\u884c\u8ba1\u6570\u6392\u5e8f\n// k = 1 -&gt; exp = 1\n// k = 2 -&gt; exp = 10\n// \u5373 exp = 10^(k-1)\ncountingSortDigit(nums, exp);\n}\n</code></pre> <p>\u4e3a\u4ec0\u4e48\u4ece\u6700\u4f4e\u4f4d\u5f00\u59cb\u6392\u5e8f\uff1f</p> <p>\u5728\u8fde\u7eed\u7684\u6392\u5e8f\u8f6e\u6b21\u4e2d\uff0c\u540e\u4e00\u8f6e\u6392\u5e8f\u4f1a\u8986\u76d6\u524d\u4e00\u8f6e\u6392\u5e8f\u7684\u7ed3\u679c\u3002\u4e3e\u4f8b\u6765\u8bf4\uff0c\u5982\u679c\u7b2c\u4e00\u8f6e\u6392\u5e8f\u7ed3\u679c \\(a &lt; b\\) \uff0c\u800c\u7b2c\u4e8c\u8f6e\u6392\u5e8f\u7ed3\u679c \\(a &gt; b\\) \uff0c\u90a3\u4e48\u7b2c\u4e8c\u8f6e\u7684\u7ed3\u679c\u5c06\u53d6\u4ee3\u7b2c\u4e00\u8f6e\u7684\u7ed3\u679c\u3002\u7531\u4e8e\u6570\u5b57\u7684\u9ad8\u4f4d\u4f18\u5148\u7ea7\u9ad8\u4e8e\u4f4e\u4f4d\uff0c\u6211\u4eec\u5e94\u8be5\u5148\u6392\u5e8f\u4f4e\u4f4d\u518d\u6392\u5e8f\u9ad8\u4f4d\u3002</p>"},{"location":"chapter_sorting/radix_sort/#11102","title":"11.10.2. \u00a0 \u7b97\u6cd5\u7279\u6027","text":"<p>\u76f8\u8f83\u4e8e\u8ba1\u6570\u6392\u5e8f\uff0c\u57fa\u6570\u6392\u5e8f\u9002\u7528\u4e8e\u6570\u503c\u8303\u56f4\u8f83\u5927\u7684\u60c5\u51b5\uff0c\u4f46\u524d\u63d0\u662f\u6570\u636e\u5fc5\u987b\u53ef\u4ee5\u8868\u793a\u4e3a\u56fa\u5b9a\u4f4d\u6570\u7684\u683c\u5f0f\uff0c\u4e14\u4f4d\u6570\u4e0d\u80fd\u8fc7\u5927\u3002\u4f8b\u5982\uff0c\u6d6e\u70b9\u6570\u4e0d\u9002\u5408\u4f7f\u7528\u57fa\u6570\u6392\u5e8f\uff0c\u56e0\u4e3a\u5176\u4f4d\u6570 \\(k\\) \u8fc7\u5927\uff0c\u53ef\u80fd\u5bfc\u81f4\u65f6\u95f4\u590d\u6742\u5ea6 \\(O(nk) \\gg O(n^2)\\) \u3002</p> <ul> <li>\u65f6\u95f4\u590d\u6742\u5ea6 \\(O(nk)\\) \uff1a\u8bbe\u6570\u636e\u91cf\u4e3a \\(n\\) \u3001\u6570\u636e\u4e3a \\(d\\) \u8fdb\u5236\u3001\u6700\u5927\u4f4d\u6570\u4e3a \\(k\\) \uff0c\u5219\u5bf9\u67d0\u4e00\u4f4d\u6267\u884c\u8ba1\u6570\u6392\u5e8f\u4f7f\u7528 \\(O(n + d)\\) \u65f6\u95f4\uff0c\u6392\u5e8f\u6240\u6709 \\(k\\) \u4f4d\u4f7f\u7528 \\(O((n + d)k)\\) \u65f6\u95f4\u3002\u901a\u5e38\u60c5\u51b5\u4e0b\uff0c\\(d\\) \u548c \\(k\\) \u90fd\u76f8\u5bf9\u8f83\u5c0f\uff0c\u65f6\u95f4\u590d\u6742\u5ea6\u8d8b\u5411 \\(O(n)\\) \u3002</li> <li>\u7a7a\u95f4\u590d\u6742\u5ea6 \\(O(n + d)\\) \u3001\u975e\u539f\u5730\u6392\u5e8f \uff1a\u4e0e\u8ba1\u6570\u6392\u5e8f\u76f8\u540c\uff0c\u57fa\u6570\u6392\u5e8f\u9700\u8981\u501f\u52a9\u957f\u5ea6\u4e3a \\(n\\) \u548c \\(d\\) \u7684\u6570\u7ec4 <code>res</code> \u548c <code>counter</code> \u3002</li> <li>\u7a33\u5b9a\u6392\u5e8f\uff1a\u4e0e\u8ba1\u6570\u6392\u5e8f\u76f8\u540c\u3002</li> </ul>"},{"location":"chapter_sorting/selection_sort/","title":"11.2. \u00a0 \u9009\u62e9\u6392\u5e8f","text":"<p>\u300c\u9009\u62e9\u6392\u5e8f Selection Sort\u300d\u7684\u5de5\u4f5c\u539f\u7406\u975e\u5e38\u76f4\u63a5\uff1a\u5f00\u542f\u4e00\u4e2a\u5faa\u73af\uff0c\u6bcf\u8f6e\u4ece\u672a\u6392\u5e8f\u533a\u95f4\u9009\u62e9\u6700\u5c0f\u7684\u5143\u7d20\uff0c\u5c06\u5176\u653e\u5230\u5df2\u6392\u5e8f\u533a\u95f4\u7684\u672b\u5c3e\u3002</p> <p>\u8bbe\u6570\u7ec4\u7684\u957f\u5ea6\u4e3a \\(n\\) \uff0c\u9009\u62e9\u6392\u5e8f\u7684\u7b97\u6cd5\u6d41\u7a0b\u5982\u4e0b\uff1a</p> <ol> <li>\u521d\u59cb\u72b6\u6001\u4e0b\uff0c\u6240\u6709\u5143\u7d20\u672a\u6392\u5e8f\uff0c\u5373\u672a\u6392\u5e8f\uff08\u7d22\u5f15\uff09\u533a\u95f4\u4e3a \\([0, n-1]\\) \u3002</li> <li>\u9009\u53d6\u533a\u95f4 \\([0, n-1]\\) \u4e2d\u7684\u6700\u5c0f\u5143\u7d20\uff0c\u5c06\u5176\u4e0e\u7d22\u5f15 \\(0\\) \u5904\u5143\u7d20\u4ea4\u6362\u3002\u5b8c\u6210\u540e\uff0c\u6570\u7ec4\u524d 1 \u4e2a\u5143\u7d20\u5df2\u6392\u5e8f\u3002</li> <li>\u9009\u53d6\u533a\u95f4 \\([1, n-1]\\) \u4e2d\u7684\u6700\u5c0f\u5143\u7d20\uff0c\u5c06\u5176\u4e0e\u7d22\u5f15 \\(1\\) \u5904\u5143\u7d20\u4ea4\u6362\u3002\u5b8c\u6210\u540e\uff0c\u6570\u7ec4\u524d 2 \u4e2a\u5143\u7d20\u5df2\u6392\u5e8f\u3002</li> <li>\u4ee5\u6b64\u7c7b\u63a8\u3002\u7ecf\u8fc7 \\(n - 1\\) \u8f6e\u9009\u62e9\u4e0e\u4ea4\u6362\u540e\uff0c\u6570\u7ec4\u524d \\(n - 1\\) \u4e2a\u5143\u7d20\u5df2\u6392\u5e8f\u3002</li> <li>\u4ec5\u5269\u7684\u4e00\u4e2a\u5143\u7d20\u5fc5\u5b9a\u662f\u6700\u5927\u5143\u7d20\uff0c\u65e0\u9700\u6392\u5e8f\uff0c\u56e0\u6b64\u6570\u7ec4\u6392\u5e8f\u5b8c\u6210\u3002</li> </ol> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt;&lt;11&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p>\u5728\u4ee3\u7801\u4e2d\uff0c\u6211\u4eec\u7528 \\(k\\) \u6765\u8bb0\u5f55\u672a\u6392\u5e8f\u533a\u95f4\u5185\u7684\u6700\u5c0f\u5143\u7d20\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart selection_sort.java<pre><code>/* \u9009\u62e9\u6392\u5e8f */\nvoid selectionSort(int[] nums) {\nint n = nums.length;\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [i, n-1]\nfor (int i = 0; i &lt; n - 1; i++) {\n// \u5185\u5faa\u73af\uff1a\u627e\u5230\u672a\u6392\u5e8f\u533a\u95f4\u5185\u7684\u6700\u5c0f\u5143\u7d20\nint k = i;\nfor (int j = i + 1; j &lt; n; j++) {\nif (nums[j] &lt; nums[k])\nk = j; // \u8bb0\u5f55\u6700\u5c0f\u5143\u7d20\u7684\u7d22\u5f15\n}\n// \u5c06\u8be5\u6700\u5c0f\u5143\u7d20\u4e0e\u672a\u6392\u5e8f\u533a\u95f4\u7684\u9996\u4e2a\u5143\u7d20\u4ea4\u6362\nint temp = nums[i];\nnums[i] = nums[k];\nnums[k] = temp;\n}\n}\n</code></pre> selection_sort.cpp<pre><code>/* \u9009\u62e9\u6392\u5e8f */\nvoid selectionSort(vector&lt;int&gt; &amp;nums) {\nint n = nums.size();\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [i, n-1]\nfor (int i = 0; i &lt; n - 1; i++) {\n// \u5185\u5faa\u73af\uff1a\u627e\u5230\u672a\u6392\u5e8f\u533a\u95f4\u5185\u7684\u6700\u5c0f\u5143\u7d20\nint k = i;\nfor (int j = i + 1; j &lt; n; j++) {\nif (nums[j] &lt; nums[k])\nk = j; // \u8bb0\u5f55\u6700\u5c0f\u5143\u7d20\u7684\u7d22\u5f15\n}\n// \u5c06\u8be5\u6700\u5c0f\u5143\u7d20\u4e0e\u672a\u6392\u5e8f\u533a\u95f4\u7684\u9996\u4e2a\u5143\u7d20\u4ea4\u6362\nswap(nums[i], nums[k]);\n}\n}\n</code></pre> selection_sort.py<pre><code>def selection_sort(nums: list[int]):\n\"\"\"\u9009\u62e9\u6392\u5e8f\"\"\"\nn = len(nums)\n# \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [i, n-1]\nfor i in range(n - 1):\n# \u5185\u5faa\u73af\uff1a\u627e\u5230\u672a\u6392\u5e8f\u533a\u95f4\u5185\u7684\u6700\u5c0f\u5143\u7d20\nk = i\nfor j in range(i + 1, n):\nif nums[j] &lt; nums[k]:\nk = j  # \u8bb0\u5f55\u6700\u5c0f\u5143\u7d20\u7684\u7d22\u5f15\n# \u5c06\u8be5\u6700\u5c0f\u5143\u7d20\u4e0e\u672a\u6392\u5e8f\u533a\u95f4\u7684\u9996\u4e2a\u5143\u7d20\u4ea4\u6362\nnums[i], nums[k] = nums[k], nums[i]\n</code></pre> selection_sort.go<pre><code>/* \u9009\u62e9\u6392\u5e8f */\nfunc selectionSort(nums []int) {\nn := len(nums)\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [i, n-1]\nfor i := 0; i &lt; n-1; i++ {\n// \u5185\u5faa\u73af\uff1a\u627e\u5230\u672a\u6392\u5e8f\u533a\u95f4\u5185\u7684\u6700\u5c0f\u5143\u7d20\nk := i\nfor j := i + 1; j &lt; n; j++ {\nif nums[j] &lt; nums[k] {\n// \u8bb0\u5f55\u6700\u5c0f\u5143\u7d20\u7684\u7d22\u5f15\nk = j\n}\n}\n// \u5c06\u8be5\u6700\u5c0f\u5143\u7d20\u4e0e\u672a\u6392\u5e8f\u533a\u95f4\u7684\u9996\u4e2a\u5143\u7d20\u4ea4\u6362\nnums[i], nums[k] = nums[k], nums[i]\n}\n}\n</code></pre> selection_sort.js<pre><code>/* \u9009\u62e9\u6392\u5e8f */\nfunction selectionSort(nums) {\nlet n = nums.length;\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [i, n-1]\nfor (let i = 0; i &lt; n - 1; i++) {\n// \u5185\u5faa\u73af\uff1a\u627e\u5230\u672a\u6392\u5e8f\u533a\u95f4\u5185\u7684\u6700\u5c0f\u5143\u7d20\nlet k = i;\nfor (let j = i + 1; j &lt; n; j++) {\nif (nums[j] &lt; nums[k]) {\nk = j; // \u8bb0\u5f55\u6700\u5c0f\u5143\u7d20\u7684\u7d22\u5f15\n}\n}\n// \u5c06\u8be5\u6700\u5c0f\u5143\u7d20\u4e0e\u672a\u6392\u5e8f\u533a\u95f4\u7684\u9996\u4e2a\u5143\u7d20\u4ea4\u6362\n[nums[i], nums[k]] = [nums[k], nums[i]];\n}\n}\n</code></pre> selection_sort.ts<pre><code>/* \u9009\u62e9\u6392\u5e8f */\nfunction selectionSort(nums: number[]): void {\nlet n = nums.length;\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [i, n-1]\nfor (let i = 0; i &lt; n - 1; i++) {\n// \u5185\u5faa\u73af\uff1a\u627e\u5230\u672a\u6392\u5e8f\u533a\u95f4\u5185\u7684\u6700\u5c0f\u5143\u7d20\nlet k = i;\nfor (let j = i + 1; j &lt; n; j++) {\nif (nums[j] &lt; nums[k]) {\nk = j; // \u8bb0\u5f55\u6700\u5c0f\u5143\u7d20\u7684\u7d22\u5f15\n}\n}\n// \u5c06\u8be5\u6700\u5c0f\u5143\u7d20\u4e0e\u672a\u6392\u5e8f\u533a\u95f4\u7684\u9996\u4e2a\u5143\u7d20\u4ea4\u6362\n[nums[i], nums[k]] = [nums[k], nums[i]];\n}\n}\n</code></pre> selection_sort.c<pre><code>/* \u9009\u62e9\u6392\u5e8f */\nvoid selectionSort(int nums[], int n) {\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [i, n-1]\nfor (int i = 0; i &lt; n - 1; i++) {\n// \u5185\u5faa\u73af\uff1a\u627e\u5230\u672a\u6392\u5e8f\u533a\u95f4\u5185\u7684\u6700\u5c0f\u5143\u7d20\nint k = i;\nfor (int j = i + 1; j &lt; n; j++) {\nif (nums[j] &lt; nums[k])\nk = j;  // \u8bb0\u5f55\u6700\u5c0f\u5143\u7d20\u7684\u7d22\u5f15\n}\n// \u5c06\u8be5\u6700\u5c0f\u5143\u7d20\u4e0e\u672a\u6392\u5e8f\u533a\u95f4\u7684\u9996\u4e2a\u5143\u7d20\u4ea4\u6362\nint temp = nums[i];\nnums[i] = nums[k];\nnums[k] = temp;\n}\n}\n</code></pre> selection_sort.cs<pre><code>/* \u9009\u62e9\u6392\u5e8f */\nvoid selectionSort(int[] nums) {\nint n = nums.Length;\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [i, n-1]\nfor (int i = 0; i &lt; n - 1; i++) {\n// \u5185\u5faa\u73af\uff1a\u627e\u5230\u672a\u6392\u5e8f\u533a\u95f4\u5185\u7684\u6700\u5c0f\u5143\u7d20\nint k = i;\nfor (int j = i + 1; j &lt; n; j++) {\nif (nums[j] &lt; nums[k])\nk = j; // \u8bb0\u5f55\u6700\u5c0f\u5143\u7d20\u7684\u7d22\u5f15\n}\n// \u5c06\u8be5\u6700\u5c0f\u5143\u7d20\u4e0e\u672a\u6392\u5e8f\u533a\u95f4\u7684\u9996\u4e2a\u5143\u7d20\u4ea4\u6362\n(nums[k], nums[i]) = (nums[i], nums[k]);\n}\n}\n</code></pre> selection_sort.swift<pre><code>/* \u9009\u62e9\u6392\u5e8f */\nfunc selectionSort(nums: inout [Int]) {\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [i, n-1]\nfor i in nums.indices.dropLast() {\n// \u5185\u5faa\u73af\uff1a\u627e\u5230\u672a\u6392\u5e8f\u533a\u95f4\u5185\u7684\u6700\u5c0f\u5143\u7d20\nvar k = i\nfor j in nums.indices.dropFirst(i + 1) {\nif nums[j] &lt; nums[k] {\nk = j // \u8bb0\u5f55\u6700\u5c0f\u5143\u7d20\u7684\u7d22\u5f15\n}\n}\n// \u5c06\u8be5\u6700\u5c0f\u5143\u7d20\u4e0e\u672a\u6392\u5e8f\u533a\u95f4\u7684\u9996\u4e2a\u5143\u7d20\u4ea4\u6362\nnums.swapAt(i, k)\n}\n}\n</code></pre> selection_sort.zig<pre><code>[class]{}-[func]{selectionSort}\n</code></pre> selection_sort.dart<pre><code>/* \u9009\u62e9\u6392\u5e8f */\nvoid selectionSort(List&lt;int&gt; nums) {\nint n = nums.length;\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [i, n-1]\nfor (int i = 0; i &lt; n - 1; i++) {\n// \u5185\u5faa\u73af\uff1a\u627e\u5230\u672a\u6392\u5e8f\u533a\u95f4\u5185\u7684\u6700\u5c0f\u5143\u7d20\nint k = i;\nfor (int j = i + 1; j &lt; n; j++) {\nif (nums[j] &lt; nums[k]) k = j; // \u8bb0\u5f55\u6700\u5c0f\u5143\u7d20\u7684\u7d22\u5f15\n}\n// \u5c06\u8be5\u6700\u5c0f\u5143\u7d20\u4e0e\u672a\u6392\u5e8f\u533a\u95f4\u7684\u9996\u4e2a\u5143\u7d20\u4ea4\u6362\nint temp = nums[i];\nnums[i] = nums[k];\nnums[k] = temp;\n}\n}\n</code></pre>"},{"location":"chapter_sorting/selection_sort/#1121","title":"11.2.1. \u00a0 \u7b97\u6cd5\u7279\u6027","text":"<ul> <li>\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(n^2)\\) \u3001\u975e\u81ea\u9002\u5e94\u6392\u5e8f\uff1a\u5916\u5faa\u73af\u5171 \\(n - 1\\) \u8f6e\uff0c\u7b2c\u4e00\u8f6e\u7684\u672a\u6392\u5e8f\u533a\u95f4\u957f\u5ea6\u4e3a \\(n\\) \uff0c\u6700\u540e\u4e00\u8f6e\u7684\u672a\u6392\u5e8f\u533a\u95f4\u957f\u5ea6\u4e3a \\(2\\) \uff0c\u5373\u5404\u8f6e\u5916\u5faa\u73af\u5206\u522b\u5305\u542b \\(n\\) , \\(n - 1\\) , \\(\\cdots\\) , \\(2\\) \u8f6e\u5185\u5faa\u73af\uff0c\u6c42\u548c\u4e3a \\(\\frac{(n - 1)(n + 2)}{2}\\) \u3002</li> <li>\u7a7a\u95f4\u590d\u6742\u5ea6 \\(O(1)\\) \u3001\u539f\u5730\u6392\u5e8f\uff1a\u6307\u9488 \\(i\\) , \\(j\\) \u4f7f\u7528\u5e38\u6570\u5927\u5c0f\u7684\u989d\u5916\u7a7a\u95f4\u3002</li> <li>\u975e\u7a33\u5b9a\u6392\u5e8f\uff1a\u5728\u4ea4\u6362\u5143\u7d20\u65f6\uff0c\u6709\u53ef\u80fd\u5c06 <code>nums[i]</code> \u4ea4\u6362\u81f3\u5176\u76f8\u7b49\u5143\u7d20\u7684\u53f3\u8fb9\uff0c\u5bfc\u81f4\u4e24\u8005\u7684\u76f8\u5bf9\u987a\u5e8f\u53d1\u751f\u6539\u53d8\u3002</li> </ul> <p> Fig. \u9009\u62e9\u6392\u5e8f\u975e\u7a33\u5b9a\u793a\u4f8b </p>"},{"location":"chapter_sorting/sorting_algorithm/","title":"11.1. \u00a0 \u6392\u5e8f\u7b97\u6cd5","text":"<p>\u300c\u6392\u5e8f\u7b97\u6cd5 Sorting Algorithm\u300d\u7528\u4e8e\u5bf9\u4e00\u7ec4\u6570\u636e\u6309\u7167\u7279\u5b9a\u987a\u5e8f\u8fdb\u884c\u6392\u5217\u3002\u6392\u5e8f\u7b97\u6cd5\u6709\u7740\u5e7f\u6cdb\u7684\u5e94\u7528\uff0c\u56e0\u4e3a\u6709\u5e8f\u6570\u636e\u901a\u5e38\u80fd\u591f\u88ab\u66f4\u6709\u6548\u5730\u67e5\u627e\u3001\u5206\u6790\u548c\u5904\u7406\u3002</p> <p>\u5728\u6392\u5e8f\u7b97\u6cd5\u4e2d\uff0c\u6570\u636e\u7c7b\u578b\u53ef\u4ee5\u662f\u6574\u6570\u3001\u6d6e\u70b9\u6570\u3001\u5b57\u7b26\u6216\u5b57\u7b26\u4e32\u7b49\uff1b\u987a\u5e8f\u7684\u5224\u65ad\u89c4\u5219\u53ef\u6839\u636e\u9700\u6c42\u8bbe\u5b9a\uff0c\u5982\u6570\u5b57\u5927\u5c0f\u3001\u5b57\u7b26 ASCII \u7801\u987a\u5e8f\u6216\u81ea\u5b9a\u4e49\u89c4\u5219\u3002</p> <p></p> <p> Fig. \u6570\u636e\u7c7b\u578b\u548c\u5224\u65ad\u89c4\u5219\u793a\u4f8b </p>"},{"location":"chapter_sorting/sorting_algorithm/#1111","title":"11.1.1. \u00a0 \u8bc4\u4ef7\u7ef4\u5ea6","text":"<p>\u8fd0\u884c\u6548\u7387\uff1a\u6211\u4eec\u671f\u671b\u6392\u5e8f\u7b97\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u5c3d\u91cf\u4f4e\uff0c\u4e14\u603b\u4f53\u64cd\u4f5c\u6570\u91cf\u8f83\u5c11\uff08\u5373\u65f6\u95f4\u590d\u6742\u5ea6\u4e2d\u7684\u5e38\u6570\u9879\u964d\u4f4e\uff09\u3002\u5bf9\u4e8e\u5927\u6570\u636e\u91cf\u60c5\u51b5\uff0c\u8fd0\u884c\u6548\u7387\u663e\u5f97\u5c24\u4e3a\u91cd\u8981\u3002</p> <p>\u5c31\u5730\u6027\uff1a\u987e\u540d\u601d\u4e49\uff0c\u300c\u539f\u5730\u6392\u5e8f\u300d\u901a\u8fc7\u5728\u539f\u6570\u7ec4\u4e0a\u76f4\u63a5\u64cd\u4f5c\u5b9e\u73b0\u6392\u5e8f\uff0c\u65e0\u9700\u501f\u52a9\u989d\u5916\u7684\u8f85\u52a9\u6570\u7ec4\uff0c\u4ece\u800c\u8282\u7701\u5185\u5b58\u3002\u901a\u5e38\u60c5\u51b5\u4e0b\uff0c\u539f\u5730\u6392\u5e8f\u7684\u6570\u636e\u642c\u8fd0\u64cd\u4f5c\u8f83\u5c11\uff0c\u8fd0\u884c\u901f\u5ea6\u4e5f\u66f4\u5feb\u3002</p> <p>\u7a33\u5b9a\u6027\uff1a\u300c\u7a33\u5b9a\u6392\u5e8f\u300d\u5728\u5b8c\u6210\u6392\u5e8f\u540e\uff0c\u76f8\u7b49\u5143\u7d20\u5728\u6570\u7ec4\u4e2d\u7684\u76f8\u5bf9\u987a\u5e8f\u4e0d\u53d1\u751f\u6539\u53d8\u3002\u7a33\u5b9a\u6392\u5e8f\u662f\u4f18\u826f\u7279\u6027\uff0c\u4e5f\u662f\u591a\u7ea7\u6392\u5e8f\u573a\u666f\u7684\u5fc5\u8981\u6761\u4ef6\u3002</p> <p>\u5047\u8bbe\u6211\u4eec\u6709\u4e00\u4e2a\u5b58\u50a8\u5b66\u751f\u4fe1\u606f\u7684\u8868\u683c\uff0c\u7b2c 1, 2 \u5217\u5206\u522b\u662f\u59d3\u540d\u548c\u5e74\u9f84\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u300c\u975e\u7a33\u5b9a\u6392\u5e8f\u300d\u53ef\u80fd\u5bfc\u81f4\u8f93\u5165\u6570\u636e\u7684\u6709\u5e8f\u6027\u4e27\u5931\u3002</p> <pre><code># \u8f93\u5165\u6570\u636e\u662f\u6309\u7167\u59d3\u540d\u6392\u5e8f\u597d\u7684\n# (name, age)\n('A', 19)\n('B', 18)\n('C', 21)\n('D', 19)\n('E', 23)\n# \u5047\u8bbe\u4f7f\u7528\u975e\u7a33\u5b9a\u6392\u5e8f\u7b97\u6cd5\u6309\u5e74\u9f84\u6392\u5e8f\u5217\u8868\uff0c\n# \u7ed3\u679c\u4e2d ('D', 19) \u548c ('A', 19) \u7684\u76f8\u5bf9\u4f4d\u7f6e\u6539\u53d8\uff0c\n# \u8f93\u5165\u6570\u636e\u6309\u59d3\u540d\u6392\u5e8f\u7684\u6027\u8d28\u4e22\u5931\n('B', 18)\n('D', 19)\n('A', 19)\n('C', 21)\n('E', 23)\n</code></pre> <p>\u81ea\u9002\u5e94\u6027\uff1a\u300c\u81ea\u9002\u5e94\u6392\u5e8f\u300d\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4f1a\u53d7\u8f93\u5165\u6570\u636e\u7684\u5f71\u54cd\uff0c\u5373\u6700\u4f73\u3001\u6700\u5dee\u3001\u5e73\u5747\u65f6\u95f4\u590d\u6742\u5ea6\u5e76\u4e0d\u5b8c\u5168\u76f8\u7b49\u3002</p> <p>\u81ea\u9002\u5e94\u6027\u9700\u8981\u6839\u636e\u5177\u4f53\u60c5\u51b5\u6765\u8bc4\u4f30\u3002\u5982\u679c\u6700\u5dee\u65f6\u95f4\u590d\u6742\u5ea6\u5dee\u4e8e\u5e73\u5747\u65f6\u95f4\u590d\u6742\u5ea6\uff0c\u8bf4\u660e\u6392\u5e8f\u7b97\u6cd5\u5728\u67d0\u4e9b\u6570\u636e\u4e0b\u6027\u80fd\u53ef\u80fd\u52a3\u5316\uff0c\u56e0\u6b64\u88ab\u89c6\u4e3a\u8d1f\u9762\u5c5e\u6027\uff1b\u800c\u5982\u679c\u6700\u4f73\u65f6\u95f4\u590d\u6742\u5ea6\u4f18\u4e8e\u5e73\u5747\u65f6\u95f4\u590d\u6742\u5ea6\uff0c\u5219\u88ab\u89c6\u4e3a\u6b63\u9762\u5c5e\u6027\u3002</p> <p>\u662f\u5426\u57fa\u4e8e\u6bd4\u8f83\uff1a\u300c\u57fa\u4e8e\u6bd4\u8f83\u7684\u6392\u5e8f\u300d\u4f9d\u8d56\u4e8e\u6bd4\u8f83\u8fd0\u7b97\u7b26\uff08\\(&lt;\\) , \\(=\\) , \\(&gt;\\)\uff09\u6765\u5224\u65ad\u5143\u7d20\u7684\u76f8\u5bf9\u987a\u5e8f\uff0c\u4ece\u800c\u6392\u5e8f\u6574\u4e2a\u6570\u7ec4\uff0c\u7406\u8bba\u6700\u4f18\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(n \\log n)\\) \u3002\u800c\u300c\u975e\u6bd4\u8f83\u6392\u5e8f\u300d\u4e0d\u4f7f\u7528\u6bd4\u8f83\u8fd0\u7b97\u7b26\uff0c\u65f6\u95f4\u590d\u6742\u5ea6\u53ef\u8fbe \\(O(n)\\) \uff0c\u4f46\u5176\u901a\u7528\u6027\u76f8\u5bf9\u8f83\u5dee\u3002</p>"},{"location":"chapter_sorting/sorting_algorithm/#1112","title":"11.1.2. \u00a0 \u7406\u60f3\u6392\u5e8f\u7b97\u6cd5","text":"<p>\u8fd0\u884c\u5feb\u3001\u539f\u5730\u3001\u7a33\u5b9a\u3001\u6b63\u5411\u81ea\u9002\u5e94\u3001\u901a\u7528\u6027\u597d\u3002\u663e\u7136\uff0c\u8fc4\u4eca\u4e3a\u6b62\u5c1a\u672a\u53d1\u73b0\u517c\u5177\u4ee5\u4e0a\u6240\u6709\u7279\u6027\u7684\u6392\u5e8f\u7b97\u6cd5\u3002\u56e0\u6b64\uff0c\u5728\u9009\u62e9\u6392\u5e8f\u7b97\u6cd5\u65f6\uff0c\u9700\u8981\u6839\u636e\u5177\u4f53\u7684\u6570\u636e\u7279\u70b9\u548c\u95ee\u9898\u9700\u6c42\u6765\u51b3\u5b9a\u3002</p> <p>\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u5c06\u5171\u540c\u5b66\u4e60\u5404\u79cd\u6392\u5e8f\u7b97\u6cd5\uff0c\u5e76\u57fa\u4e8e\u4e0a\u8ff0\u8bc4\u4ef7\u7ef4\u5ea6\u5bf9\u5404\u4e2a\u6392\u5e8f\u7b97\u6cd5\u7684\u4f18\u7f3a\u70b9\u8fdb\u884c\u5206\u6790\u3002</p>"},{"location":"chapter_sorting/summary/","title":"11.11. \u00a0 \u5c0f\u7ed3","text":"<ul> <li>\u5192\u6ce1\u6392\u5e8f\u901a\u8fc7\u4ea4\u6362\u76f8\u90bb\u5143\u7d20\u6765\u5b9e\u73b0\u6392\u5e8f\u3002\u901a\u8fc7\u6dfb\u52a0\u4e00\u4e2a\u6807\u5fd7\u4f4d\u6765\u5b9e\u73b0\u63d0\u524d\u8fd4\u56de\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u5192\u6ce1\u6392\u5e8f\u7684\u6700\u4f73\u65f6\u95f4\u590d\u6742\u5ea6\u4f18\u5316\u5230 \\(O(n)\\) \u3002</li> <li>\u63d2\u5165\u6392\u5e8f\u6bcf\u8f6e\u5c06\u672a\u6392\u5e8f\u533a\u95f4\u5185\u7684\u5143\u7d20\u63d2\u5165\u5230\u5df2\u6392\u5e8f\u533a\u95f4\u7684\u6b63\u786e\u4f4d\u7f6e\uff0c\u4ece\u800c\u5b8c\u6210\u6392\u5e8f\u3002\u867d\u7136\u63d2\u5165\u6392\u5e8f\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(n^2)\\) \uff0c\u4f46\u7531\u4e8e\u5355\u5143\u64cd\u4f5c\u76f8\u5bf9\u8f83\u5c11\uff0c\u5b83\u5728\u5c0f\u6570\u636e\u91cf\u7684\u6392\u5e8f\u4efb\u52a1\u4e2d\u975e\u5e38\u53d7\u6b22\u8fce\u3002</li> <li>\u5feb\u901f\u6392\u5e8f\u57fa\u4e8e\u54e8\u5175\u5212\u5206\u64cd\u4f5c\u5b9e\u73b0\u6392\u5e8f\u3002\u5728\u54e8\u5175\u5212\u5206\u4e2d\uff0c\u6709\u53ef\u80fd\u6bcf\u6b21\u90fd\u9009\u53d6\u5230\u6700\u5dee\u7684\u57fa\u51c6\u6570\uff0c\u5bfc\u81f4\u65f6\u95f4\u590d\u6742\u5ea6\u52a3\u5316\u81f3 \\(O(n^2)\\) \u3002\u5f15\u5165\u4e2d\u4f4d\u6570\u57fa\u51c6\u6570\u6216\u968f\u673a\u57fa\u51c6\u6570\u53ef\u4ee5\u964d\u4f4e\u8fd9\u79cd\u52a3\u5316\u7684\u6982\u7387\u3002\u5c3e\u9012\u5f52\u65b9\u6cd5\u53ef\u4ee5\u6709\u6548\u5730\u51cf\u5c11\u9012\u5f52\u6df1\u5ea6\uff0c\u5c06\u7a7a\u95f4\u590d\u6742\u5ea6\u4f18\u5316\u5230 \\(O(\\log n)\\) \u3002</li> <li>\u5f52\u5e76\u6392\u5e8f\u5305\u62ec\u5212\u5206\u548c\u5408\u5e76\u4e24\u4e2a\u9636\u6bb5\uff0c\u5178\u578b\u5730\u4f53\u73b0\u4e86\u5206\u6cbb\u7b56\u7565\u3002\u5728\u5f52\u5e76\u6392\u5e8f\u4e2d\uff0c\u6392\u5e8f\u6570\u7ec4\u9700\u8981\u521b\u5efa\u8f85\u52a9\u6570\u7ec4\uff0c\u7a7a\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(n)\\) \uff1b\u7136\u800c\u6392\u5e8f\u94fe\u8868\u7684\u7a7a\u95f4\u590d\u6742\u5ea6\u53ef\u4ee5\u4f18\u5316\u81f3 \\(O(1)\\) \u3002</li> <li>\u6876\u6392\u5e8f\u5305\u542b\u4e09\u4e2a\u6b65\u9aa4\uff1a\u6570\u636e\u5206\u6876\u3001\u6876\u5185\u6392\u5e8f\u548c\u5408\u5e76\u7ed3\u679c\u3002\u5b83\u540c\u6837\u4f53\u73b0\u4e86\u5206\u6cbb\u7b56\u7565\uff0c\u9002\u7528\u4e8e\u6570\u636e\u4f53\u91cf\u5f88\u5927\u7684\u60c5\u51b5\u3002\u6876\u6392\u5e8f\u7684\u5173\u952e\u5728\u4e8e\u5bf9\u6570\u636e\u8fdb\u884c\u5e73\u5747\u5206\u914d\u3002</li> <li>\u8ba1\u6570\u6392\u5e8f\u662f\u6876\u6392\u5e8f\u7684\u4e00\u4e2a\u7279\u4f8b\uff0c\u5b83\u901a\u8fc7\u7edf\u8ba1\u6570\u636e\u51fa\u73b0\u7684\u6b21\u6570\u6765\u5b9e\u73b0\u6392\u5e8f\u3002\u8ba1\u6570\u6392\u5e8f\u9002\u7528\u4e8e\u6570\u636e\u91cf\u5927\u4f46\u6570\u636e\u8303\u56f4\u6709\u9650\u7684\u60c5\u51b5\uff0c\u5e76\u4e14\u8981\u6c42\u6570\u636e\u80fd\u591f\u8f6c\u6362\u4e3a\u6b63\u6574\u6570\u3002</li> <li>\u57fa\u6570\u6392\u5e8f\u901a\u8fc7\u9010\u4f4d\u6392\u5e8f\u6765\u5b9e\u73b0\u6570\u636e\u6392\u5e8f\uff0c\u8981\u6c42\u6570\u636e\u80fd\u591f\u8868\u793a\u4e3a\u56fa\u5b9a\u4f4d\u6570\u7684\u6570\u5b57\u3002</li> </ul> <p> Fig. \u6392\u5e8f\u7b97\u6cd5\u5bf9\u6bd4 </p> <ul> <li>\u603b\u7684\u6765\u8bf4\uff0c\u6211\u4eec\u5e0c\u671b\u627e\u5230\u4e00\u79cd\u6392\u5e8f\u7b97\u6cd5\uff0c\u5177\u6709\u9ad8\u6548\u7387\u3001\u7a33\u5b9a\u3001\u539f\u5730\u4ee5\u53ca\u6b63\u5411\u81ea\u9002\u5e94\u6027\u7b49\u4f18\u70b9\u3002\u7136\u800c\uff0c\u6b63\u5982\u5176\u4ed6\u6570\u636e\u7ed3\u6784\u548c\u7b97\u6cd5\u4e00\u6837\uff0c\u6ca1\u6709\u4e00\u79cd\u6392\u5e8f\u7b97\u6cd5\u80fd\u591f\u540c\u65f6\u6ee1\u8db3\u6240\u6709\u8fd9\u4e9b\u6761\u4ef6\u3002\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u6211\u4eec\u9700\u8981\u6839\u636e\u6570\u636e\u7684\u7279\u6027\u6765\u9009\u62e9\u5408\u9002\u7684\u6392\u5e8f\u7b97\u6cd5\u3002</li> </ul>"},{"location":"chapter_sorting/summary/#11111-q-a","title":"11.11.1. \u00a0 Q &amp; A","text":"<p>\u54e8\u5175\u5212\u5206\u4e2d\u201c\u4ece\u53f3\u5f80\u5de6\u67e5\u627e\u201d\u4e0e\u201c\u4ece\u5de6\u5f80\u53f3\u67e5\u627e\u201d\u7684\u987a\u5e8f\u53ef\u4ee5\u4ea4\u6362\u5417\uff1f</p> <p>\u4e0d\u884c\uff0c\u5f53\u6211\u4eec\u4ee5\u6700\u5de6\u7aef\u5143\u7d20\u4e3a\u57fa\u51c6\u6570\u65f6\uff0c\u5fc5\u987b\u5148\u201c\u4ece\u53f3\u5f80\u5de6\u67e5\u627e\u201d\u518d\u201c\u4ece\u5de6\u5f80\u53f3\u67e5\u627e\u201d\u3002\u8fd9\u4e2a\u7ed3\u8bba\u6709\u4e9b\u53cd\u76f4\u89c9\uff0c\u6211\u4eec\u6765\u5256\u6790\u4e00\u4e0b\u539f\u56e0\u3002</p> <p>\u54e8\u5175\u5212\u5206 <code>partition()</code> \u7684\u6700\u540e\u4e00\u6b65\u662f\u4ea4\u6362 <code>nums[left]</code> \u548c <code>nums[i]</code> \u3002\u5b8c\u6210\u4ea4\u6362\u540e\uff0c\u57fa\u51c6\u6570\u5de6\u8fb9\u7684\u5143\u7d20\u90fd <code>&lt;=</code> \u57fa\u51c6\u6570\uff0c\u8fd9\u5c31\u8981\u6c42\u6700\u540e\u4e00\u6b65\u4ea4\u6362\u524d <code>nums[left] &gt;= nums[i]</code> \u5fc5\u987b\u6210\u7acb\u3002\u5047\u8bbe\u6211\u4eec\u5148\u201c\u4ece\u5de6\u5f80\u53f3\u67e5\u627e\u201d\uff0c\u90a3\u4e48\u5982\u679c\u627e\u4e0d\u5230\u6bd4\u57fa\u51c6\u6570\u66f4\u5c0f\u7684\u5143\u7d20\uff0c\u5219\u4f1a\u5728 <code>i == j</code> \u65f6\u8df3\u51fa\u5faa\u73af\uff0c\u6b64\u65f6\u53ef\u80fd <code>nums[j] == nums[i] &gt; nums[left]</code>\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u6b64\u65f6\u6700\u540e\u4e00\u6b65\u4ea4\u6362\u64cd\u4f5c\u4f1a\u628a\u4e00\u4e2a\u6bd4\u57fa\u51c6\u6570\u66f4\u5927\u7684\u5143\u7d20\u4ea4\u6362\u81f3\u6570\u7ec4\u6700\u5de6\u7aef\uff0c\u5bfc\u81f4\u54e8\u5175\u5212\u5206\u5931\u8d25\u3002</p> <p>\u4e3e\u4e2a\u4f8b\u5b50\uff0c\u7ed9\u5b9a\u6570\u7ec4 <code>[0, 0, 0, 0, 1]</code> \uff0c\u5982\u679c\u5148\u201c\u4ece\u5de6\u5411\u53f3\u67e5\u627e\u201d\uff0c\u54e8\u5175\u5212\u5206\u540e\u6570\u7ec4\u4e3a <code>[1, 0, 0, 0, 0]</code> \uff0c\u8fd9\u4e2a\u7ed3\u679c\u662f\u4e0d\u6b63\u786e\u7684\u3002</p> <p>\u518d\u6df1\u5165\u601d\u8003\u4e00\u4e0b\uff0c\u5982\u679c\u6211\u4eec\u9009\u62e9 <code>nums[right]</code> \u4e3a\u57fa\u51c6\u6570\uff0c\u90a3\u4e48\u6b63\u597d\u53cd\u8fc7\u6765\uff0c\u5fc5\u987b\u5148\u201c\u4ece\u5de6\u5f80\u53f3\u67e5\u627e\u201d\u3002</p>"},{"location":"chapter_stack_and_queue/","title":"5. \u00a0 \u6808\u4e0e\u961f\u5217","text":""},{"location":"chapter_stack_and_queue/deque/","title":"5.3. \u00a0 \u53cc\u5411\u961f\u5217","text":"<p>\u5bf9\u4e8e\u961f\u5217\uff0c\u6211\u4eec\u4ec5\u80fd\u5728\u5934\u90e8\u5220\u9664\u6216\u5728\u5c3e\u90e8\u6dfb\u52a0\u5143\u7d20\u3002\u7136\u800c\uff0c\u300c\u53cc\u5411\u961f\u5217 Deque\u300d\u63d0\u4f9b\u4e86\u66f4\u9ad8\u7684\u7075\u6d3b\u6027\uff0c\u5141\u8bb8\u5728\u5934\u90e8\u548c\u5c3e\u90e8\u6267\u884c\u5143\u7d20\u7684\u6dfb\u52a0\u6216\u5220\u9664\u64cd\u4f5c\u3002</p> <p></p> <p> Fig. \u53cc\u5411\u961f\u5217\u7684\u64cd\u4f5c </p>"},{"location":"chapter_stack_and_queue/deque/#531","title":"5.3.1. \u00a0 \u53cc\u5411\u961f\u5217\u5e38\u7528\u64cd\u4f5c","text":"<p>\u53cc\u5411\u961f\u5217\u7684\u5e38\u7528\u64cd\u4f5c\u5982\u4e0b\u8868\u6240\u793a\uff0c\u5177\u4f53\u7684\u65b9\u6cd5\u540d\u79f0\u9700\u8981\u6839\u636e\u6240\u4f7f\u7528\u7684\u7f16\u7a0b\u8bed\u8a00\u6765\u786e\u5b9a\u3002</p> \u65b9\u6cd5\u540d \u63cf\u8ff0 \u65f6\u95f4\u590d\u6742\u5ea6 pushFirst() \u5c06\u5143\u7d20\u6dfb\u52a0\u81f3\u961f\u9996 \\(O(1)\\) pushLast() \u5c06\u5143\u7d20\u6dfb\u52a0\u81f3\u961f\u5c3e \\(O(1)\\) popFirst() \u5220\u9664\u961f\u9996\u5143\u7d20 \\(O(1)\\) popLast() \u5220\u9664\u961f\u5c3e\u5143\u7d20 \\(O(1)\\) peekFirst() \u8bbf\u95ee\u961f\u9996\u5143\u7d20 \\(O(1)\\) peekLast() \u8bbf\u95ee\u961f\u5c3e\u5143\u7d20 \\(O(1)\\) <p>\u540c\u6837\u5730\uff0c\u6211\u4eec\u53ef\u4ee5\u76f4\u63a5\u4f7f\u7528\u7f16\u7a0b\u8bed\u8a00\u4e2d\u5df2\u5b9e\u73b0\u7684\u53cc\u5411\u961f\u5217\u7c7b\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart deque.java<pre><code>/* \u521d\u59cb\u5316\u53cc\u5411\u961f\u5217 */\nDeque&lt;Integer&gt; deque = new LinkedList&lt;&gt;();\n/* \u5143\u7d20\u5165\u961f */\ndeque.offerLast(2);   // \u6dfb\u52a0\u81f3\u961f\u5c3e\ndeque.offerLast(5);\ndeque.offerLast(4);\ndeque.offerFirst(3);  // \u6dfb\u52a0\u81f3\u961f\u9996\ndeque.offerFirst(1);\n/* \u8bbf\u95ee\u5143\u7d20 */\nint peekFirst = deque.peekFirst();  // \u961f\u9996\u5143\u7d20\nint peekLast = deque.peekLast();    // \u961f\u5c3e\u5143\u7d20\n/* \u5143\u7d20\u51fa\u961f */\nint popFirst = deque.pollFirst();  // \u961f\u9996\u5143\u7d20\u51fa\u961f\nint popLast = deque.pollLast();    // \u961f\u5c3e\u5143\u7d20\u51fa\u961f\n/* \u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6 */\nint size = deque.size();\n/* \u5224\u65ad\u53cc\u5411\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nboolean isEmpty = deque.isEmpty();\n</code></pre> deque.cpp<pre><code>/* \u521d\u59cb\u5316\u53cc\u5411\u961f\u5217 */\ndeque&lt;int&gt; deque;\n/* \u5143\u7d20\u5165\u961f */\ndeque.push_back(2);   // \u6dfb\u52a0\u81f3\u961f\u5c3e\ndeque.push_back(5);\ndeque.push_back(4);\ndeque.push_front(3);  // \u6dfb\u52a0\u81f3\u961f\u9996\ndeque.push_front(1);\n/* \u8bbf\u95ee\u5143\u7d20 */\nint front = deque.front(); // \u961f\u9996\u5143\u7d20\nint back = deque.back();   // \u961f\u5c3e\u5143\u7d20\n/* \u5143\u7d20\u51fa\u961f */\ndeque.pop_front();  // \u961f\u9996\u5143\u7d20\u51fa\u961f\ndeque.pop_back();   // \u961f\u5c3e\u5143\u7d20\u51fa\u961f\n/* \u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6 */\nint size = deque.size();\n/* \u5224\u65ad\u53cc\u5411\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nbool empty = deque.empty();\n</code></pre> deque.py<pre><code># \u521d\u59cb\u5316\u53cc\u5411\u961f\u5217\ndeque: Deque[int] = collections.deque()\n# \u5143\u7d20\u5165\u961f\ndeque.append(2)      # \u6dfb\u52a0\u81f3\u961f\u5c3e\ndeque.append(5)\ndeque.append(4)\ndeque.appendleft(3)  # \u6dfb\u52a0\u81f3\u961f\u9996\ndeque.appendleft(1)\n# \u8bbf\u95ee\u5143\u7d20\nfront: int = deque[0]  # \u961f\u9996\u5143\u7d20\nrear: int = deque[-1]  # \u961f\u5c3e\u5143\u7d20\n# \u5143\u7d20\u51fa\u961f\npop_front: int = deque.popleft()  # \u961f\u9996\u5143\u7d20\u51fa\u961f\npop_rear: int = deque.pop()       # \u961f\u5c3e\u5143\u7d20\u51fa\u961f\n# \u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6\nsize: int = len(deque)\n# \u5224\u65ad\u53cc\u5411\u961f\u5217\u662f\u5426\u4e3a\u7a7a\nis_empty: bool = len(deque) == 0\n</code></pre> deque_test.go<pre><code>/* \u521d\u59cb\u5316\u53cc\u5411\u961f\u5217 */\n// \u5728 Go \u4e2d\uff0c\u5c06 list \u4f5c\u4e3a\u53cc\u5411\u961f\u5217\u4f7f\u7528\ndeque := list.New()\n/* \u5143\u7d20\u5165\u961f */\ndeque.PushBack(2)      // \u6dfb\u52a0\u81f3\u961f\u5c3e\ndeque.PushBack(5)\ndeque.PushBack(4)\ndeque.PushFront(3)     // \u6dfb\u52a0\u81f3\u961f\u9996\ndeque.PushFront(1)\n/* \u8bbf\u95ee\u5143\u7d20 */\nfront := deque.Front() // \u961f\u9996\u5143\u7d20\nrear := deque.Back()   // \u961f\u5c3e\u5143\u7d20\n/* \u5143\u7d20\u51fa\u961f */\ndeque.Remove(front)    // \u961f\u9996\u5143\u7d20\u51fa\u961f\ndeque.Remove(rear)     // \u961f\u5c3e\u5143\u7d20\u51fa\u961f\n/* \u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6 */\nsize := deque.Len()\n/* \u5224\u65ad\u53cc\u5411\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nisEmpty := deque.Len() == 0\n</code></pre> deque.js<pre><code>/* \u521d\u59cb\u5316\u53cc\u5411\u961f\u5217 */\n// JavaScript \u6ca1\u6709\u5185\u7f6e\u7684\u53cc\u7aef\u961f\u5217\uff0c\u53ea\u80fd\u628a Array \u5f53\u4f5c\u53cc\u7aef\u961f\u5217\u6765\u4f7f\u7528\nconst deque = [];\n/* \u5143\u7d20\u5165\u961f */\ndeque.push(2);\ndeque.push(5);\ndeque.push(4);\n// \u8bf7\u6ce8\u610f\uff0c\u7531\u4e8e\u662f\u6570\u7ec4\uff0cunshift() \u65b9\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a O(n)\ndeque.unshift(3);\ndeque.unshift(1);\nconsole.log(\"\u53cc\u5411\u961f\u5217 deque = \", deque);\n/* \u8bbf\u95ee\u5143\u7d20 */\nconst peekFirst = deque[0];\nconsole.log(\"\u961f\u9996\u5143\u7d20 peekFirst = \" + peekFirst);\nconst peekLast = deque[deque.length - 1];\nconsole.log(\"\u961f\u5c3e\u5143\u7d20 peekLast = \" + peekLast);\n/* \u5143\u7d20\u51fa\u961f */\n// \u8bf7\u6ce8\u610f\uff0c\u7531\u4e8e\u662f\u6570\u7ec4\uff0cshift() \u65b9\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a O(n)\nconst popFront = deque.shift();\nconsole.log(\"\u961f\u9996\u51fa\u961f\u5143\u7d20 popFront = \" + popFront + \"\uff0c\u961f\u9996\u51fa\u961f\u540e deque = \" + deque);\nconst popBack = deque.pop();\nconsole.log(\"\u961f\u5c3e\u51fa\u961f\u5143\u7d20 popBack = \" + popBack + \"\uff0c\u961f\u5c3e\u51fa\u961f\u540e deque = \" + deque);\n/* \u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6 */\nconst size = deque.length;\nconsole.log(\"\u53cc\u5411\u961f\u5217\u957f\u5ea6 size = \" + size);\n/* \u5224\u65ad\u53cc\u5411\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nconst isEmpty = size === 0;\nconsole.log(\"\u53cc\u5411\u961f\u5217\u662f\u5426\u4e3a\u7a7a = \" + isEmpty);\n</code></pre> deque.ts<pre><code>/* \u521d\u59cb\u5316\u53cc\u5411\u961f\u5217 */\n// TypeScript \u6ca1\u6709\u5185\u7f6e\u7684\u53cc\u7aef\u961f\u5217\uff0c\u53ea\u80fd\u628a Array \u5f53\u4f5c\u53cc\u7aef\u961f\u5217\u6765\u4f7f\u7528\nconst deque: number[] = [];\n/* \u5143\u7d20\u5165\u961f */\ndeque.push(2);\ndeque.push(5);\ndeque.push(4);\n// \u8bf7\u6ce8\u610f\uff0c\u7531\u4e8e\u662f\u6570\u7ec4\uff0cunshift() \u65b9\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a O(n)\ndeque.unshift(3);\ndeque.unshift(1);\nconsole.log(\"\u53cc\u5411\u961f\u5217 deque = \", deque);\n/* \u8bbf\u95ee\u5143\u7d20 */\nconst peekFirst: number = deque[0];\nconsole.log(\"\u961f\u9996\u5143\u7d20 peekFirst = \" + peekFirst);\nconst peekLast: number = deque[deque.length - 1];\nconsole.log(\"\u961f\u5c3e\u5143\u7d20 peekLast = \" + peekLast);\n/* \u5143\u7d20\u51fa\u961f */\n// \u8bf7\u6ce8\u610f\uff0c\u7531\u4e8e\u662f\u6570\u7ec4\uff0cshift() \u65b9\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a O(n)\nconst popFront: number = deque.shift() as number;\nconsole.log(\"\u961f\u9996\u51fa\u961f\u5143\u7d20 popFront = \" + popFront + \"\uff0c\u961f\u9996\u51fa\u961f\u540e deque = \" + deque);\nconst popBack: number = deque.pop() as number;\nconsole.log(\"\u961f\u5c3e\u51fa\u961f\u5143\u7d20 popBack = \" + popBack + \"\uff0c\u961f\u5c3e\u51fa\u961f\u540e deque = \" + deque);\n/* \u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6 */\nconst size: number = deque.length;\nconsole.log(\"\u53cc\u5411\u961f\u5217\u957f\u5ea6 size = \" + size);\n/* \u5224\u65ad\u53cc\u5411\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nconst isEmpty: boolean = size === 0;\nconsole.log(\"\u53cc\u5411\u961f\u5217\u662f\u5426\u4e3a\u7a7a = \" + isEmpty);\n</code></pre> deque.c<pre><code>// C \u672a\u63d0\u4f9b\u5185\u7f6e\u53cc\u5411\u961f\u5217\n</code></pre> deque.cs<pre><code>/* \u521d\u59cb\u5316\u53cc\u5411\u961f\u5217 */\n// \u5728 C# \u4e2d\uff0c\u5c06\u94fe\u8868 LinkedList \u770b\u4f5c\u53cc\u5411\u961f\u5217\u6765\u4f7f\u7528\nLinkedList&lt;int&gt; deque = new LinkedList&lt;int&gt;();\n/* \u5143\u7d20\u5165\u961f */\ndeque.AddLast(2);   // \u6dfb\u52a0\u81f3\u961f\u5c3e\ndeque.AddLast(5);\ndeque.AddLast(4);\ndeque.AddFirst(3);  // \u6dfb\u52a0\u81f3\u961f\u9996\ndeque.AddFirst(1);\n/* \u8bbf\u95ee\u5143\u7d20 */\nint peekFirst = deque.First.Value;  // \u961f\u9996\u5143\u7d20\nint peekLast = deque.Last.Value;    // \u961f\u5c3e\u5143\u7d20\n/* \u5143\u7d20\u51fa\u961f */\ndeque.RemoveFirst();  // \u961f\u9996\u5143\u7d20\u51fa\u961f\ndeque.RemoveLast();   // \u961f\u5c3e\u5143\u7d20\u51fa\u961f\n/* \u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6 */\nint size = deque.Count;\n/* \u5224\u65ad\u53cc\u5411\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nbool isEmpty = deque.Count == 0;\n</code></pre> deque.swift<pre><code>/* \u521d\u59cb\u5316\u53cc\u5411\u961f\u5217 */\n// Swift \u6ca1\u6709\u5185\u7f6e\u7684\u53cc\u5411\u961f\u5217\u7c7b\uff0c\u53ef\u4ee5\u628a Array \u5f53\u4f5c\u53cc\u5411\u961f\u5217\u6765\u4f7f\u7528\nvar deque: [Int] = []\n/* \u5143\u7d20\u5165\u961f */\ndeque.append(2) // \u6dfb\u52a0\u81f3\u961f\u5c3e\ndeque.append(5)\ndeque.append(4)\ndeque.insert(3, at: 0) // \u6dfb\u52a0\u81f3\u961f\u9996\ndeque.insert(1, at: 0)\n/* \u8bbf\u95ee\u5143\u7d20 */\nlet peekFirst = deque.first! // \u961f\u9996\u5143\u7d20\nlet peekLast = deque.last! // \u961f\u5c3e\u5143\u7d20\n/* \u5143\u7d20\u51fa\u961f */\n// \u4f7f\u7528 Array \u6a21\u62df\u65f6 popFirst \u7684\u590d\u6742\u5ea6\u4e3a O(n)\nlet popFirst = deque.removeFirst() // \u961f\u9996\u5143\u7d20\u51fa\u961f\nlet popLast = deque.removeLast() // \u961f\u5c3e\u5143\u7d20\u51fa\u961f\n/* \u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6 */\nlet size = deque.count\n/* \u5224\u65ad\u53cc\u5411\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nlet isEmpty = deque.isEmpty\n</code></pre> deque.zig<pre><code>\n</code></pre> deque.dart<pre><code>/* \u521d\u59cb\u5316\u53cc\u5411\u961f\u5217 */\n// \u5728 Dart \u4e2d\uff0cQueue \u88ab\u5b9a\u4e49\u4e3a\u53cc\u5411\u961f\u5217\nQueue&lt;int&gt; deque = Queue&lt;int&gt;();\n/* \u5143\u7d20\u5165\u961f */\ndeque.addLast(2);  // \u6dfb\u52a0\u81f3\u961f\u5c3e\ndeque.addLast(5);\ndeque.addLast(4);\ndeque.addFirst(3); // \u6dfb\u52a0\u81f3\u961f\u9996\ndeque.addFirst(1);\n/* \u8bbf\u95ee\u5143\u7d20 */\nint peekFirst = deque.first; // \u961f\u9996\u5143\u7d20\nint peekLast = deque.last;   // \u961f\u5c3e\u5143\u7d20\n/* \u5143\u7d20\u51fa\u961f */\nint popFirst = deque.removeFirst(); // \u961f\u9996\u5143\u7d20\u51fa\u961f\nint popLast = deque.removeLast();   // \u961f\u5c3e\u5143\u7d20\u51fa\u961f\n/* \u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6 */\nint size = deque.length;\n/* \u5224\u65ad\u53cc\u5411\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nbool isEmpty = deque.isEmpty;W\n</code></pre>"},{"location":"chapter_stack_and_queue/deque/#532","title":"5.3.2. \u00a0 \u53cc\u5411\u961f\u5217\u5b9e\u73b0 *","text":"<p>\u53cc\u5411\u961f\u5217\u7684\u5b9e\u73b0\u4e0e\u961f\u5217\u7c7b\u4f3c\uff0c\u53ef\u4ee5\u9009\u62e9\u94fe\u8868\u6216\u6570\u7ec4\u4f5c\u4e3a\u5e95\u5c42\u6570\u636e\u7ed3\u6784\u3002</p>"},{"location":"chapter_stack_and_queue/deque/#_1","title":"\u57fa\u4e8e\u53cc\u5411\u94fe\u8868\u7684\u5b9e\u73b0","text":"<p>\u56de\u987e\u4e0a\u4e00\u8282\u5185\u5bb9\uff0c\u6211\u4eec\u4f7f\u7528\u666e\u901a\u5355\u5411\u94fe\u8868\u6765\u5b9e\u73b0\u961f\u5217\uff0c\u56e0\u4e3a\u5b83\u53ef\u4ee5\u65b9\u4fbf\u5730\u5220\u9664\u5934\u8282\u70b9\uff08\u5bf9\u5e94\u51fa\u961f\u64cd\u4f5c\uff09\u548c\u5728\u5c3e\u8282\u70b9\u540e\u6dfb\u52a0\u65b0\u8282\u70b9\uff08\u5bf9\u5e94\u5165\u961f\u64cd\u4f5c\uff09\u3002</p> <p>\u5bf9\u4e8e\u53cc\u5411\u961f\u5217\u800c\u8a00\uff0c\u5934\u90e8\u548c\u5c3e\u90e8\u90fd\u53ef\u4ee5\u6267\u884c\u5165\u961f\u548c\u51fa\u961f\u64cd\u4f5c\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u53cc\u5411\u961f\u5217\u9700\u8981\u5b9e\u73b0\u53e6\u4e00\u4e2a\u5bf9\u79f0\u65b9\u5411\u7684\u64cd\u4f5c\u3002\u4e3a\u6b64\uff0c\u6211\u4eec\u91c7\u7528\u300c\u53cc\u5411\u94fe\u8868\u300d\u4f5c\u4e3a\u53cc\u5411\u961f\u5217\u7684\u5e95\u5c42\u6570\u636e\u7ed3\u6784\u3002</p> <p>\u6211\u4eec\u5c06\u53cc\u5411\u94fe\u8868\u7684\u5934\u8282\u70b9\u548c\u5c3e\u8282\u70b9\u89c6\u4e3a\u53cc\u5411\u961f\u5217\u7684\u961f\u9996\u548c\u961f\u5c3e\uff0c\u540c\u65f6\u5b9e\u73b0\u5728\u4e24\u7aef\u6dfb\u52a0\u548c\u5220\u9664\u8282\u70b9\u7684\u529f\u80fd\u3002</p> LinkedListDequepushLast()pushFirst()popLast()popFirst() <p></p> <p></p> <p></p> <p></p> <p></p> <p>\u4ee5\u4e0b\u662f\u5177\u4f53\u5b9e\u73b0\u4ee3\u7801\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart linkedlist_deque.java<pre><code>/* \u53cc\u5411\u94fe\u8868\u8282\u70b9 */\nclass ListNode {\nint val; // \u8282\u70b9\u503c\nListNode next; // \u540e\u7ee7\u8282\u70b9\u5f15\u7528\uff08\u6307\u9488\uff09\nListNode prev; // \u524d\u9a71\u8282\u70b9\u5f15\u7528\uff08\u6307\u9488\uff09\nListNode(int val) {\nthis.val = val;\nprev = next = null;\n}\n}\n/* \u57fa\u4e8e\u53cc\u5411\u94fe\u8868\u5b9e\u73b0\u7684\u53cc\u5411\u961f\u5217 */\nclass LinkedListDeque {\nprivate ListNode front, rear; // \u5934\u8282\u70b9 front \uff0c\u5c3e\u8282\u70b9 rear\nprivate int queSize = 0; // \u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6\npublic LinkedListDeque() {\nfront = rear = null;\n}\n/* \u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6 */\npublic int size() {\nreturn queSize;\n}\n/* \u5224\u65ad\u53cc\u5411\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\npublic boolean isEmpty() {\nreturn size() == 0;\n}\n/* \u5165\u961f\u64cd\u4f5c */\nprivate void push(int num, boolean isFront) {\nListNode node = new ListNode(num);\n// \u82e5\u94fe\u8868\u4e3a\u7a7a\uff0c\u5219\u4ee4 front, rear \u90fd\u6307\u5411 node\nif (isEmpty())\nfront = rear = node;\n// \u961f\u9996\u5165\u961f\u64cd\u4f5c\nelse if (isFront) {\n// \u5c06 node \u6dfb\u52a0\u81f3\u94fe\u8868\u5934\u90e8\nfront.prev = node;\nnode.next = front;\nfront = node; // \u66f4\u65b0\u5934\u8282\u70b9\n// \u961f\u5c3e\u5165\u961f\u64cd\u4f5c\n} else {\n// \u5c06 node \u6dfb\u52a0\u81f3\u94fe\u8868\u5c3e\u90e8\nrear.next = node;\nnode.prev = rear;\nrear = node; // \u66f4\u65b0\u5c3e\u8282\u70b9\n}\nqueSize++; // \u66f4\u65b0\u961f\u5217\u957f\u5ea6\n}\n/* \u961f\u9996\u5165\u961f */\npublic void pushFirst(int num) {\npush(num, true);\n}\n/* \u961f\u5c3e\u5165\u961f */\npublic void pushLast(int num) {\npush(num, false);\n}\n/* \u51fa\u961f\u64cd\u4f5c */\nprivate Integer pop(boolean isFront) {\n// \u82e5\u961f\u5217\u4e3a\u7a7a\uff0c\u76f4\u63a5\u8fd4\u56de null\nif (isEmpty())\nreturn null;\nint val;\n// \u961f\u9996\u51fa\u961f\u64cd\u4f5c\nif (isFront) {\nval = front.val; // \u6682\u5b58\u5934\u8282\u70b9\u503c\n// \u5220\u9664\u5934\u8282\u70b9\nListNode fNext = front.next;\nif (fNext != null) {\nfNext.prev = null;\nfront.next = null;\n}\nfront = fNext; // \u66f4\u65b0\u5934\u8282\u70b9\n// \u961f\u5c3e\u51fa\u961f\u64cd\u4f5c\n} else {\nval = rear.val; // \u6682\u5b58\u5c3e\u8282\u70b9\u503c\n// \u5220\u9664\u5c3e\u8282\u70b9\nListNode rPrev = rear.prev;\nif (rPrev != null) {\nrPrev.next = null;\nrear.prev = null;\n}\nrear = rPrev; // \u66f4\u65b0\u5c3e\u8282\u70b9\n}\nqueSize--; // \u66f4\u65b0\u961f\u5217\u957f\u5ea6\nreturn val;\n}\n/* \u961f\u9996\u51fa\u961f */\npublic Integer popFirst() {\nreturn pop(true);\n}\n/* \u961f\u5c3e\u51fa\u961f */\npublic Integer popLast() {\nreturn pop(false);\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\npublic Integer peekFirst() {\nreturn isEmpty() ? null : front.val;\n}\n/* \u8bbf\u95ee\u961f\u5c3e\u5143\u7d20 */\npublic Integer peekLast() {\nreturn isEmpty() ? null : rear.val;\n}\n/* \u8fd4\u56de\u6570\u7ec4\u7528\u4e8e\u6253\u5370 */\npublic int[] toArray() {\nListNode node = front;\nint[] res = new int[size()];\nfor (int i = 0; i &lt; res.length; i++) {\nres[i] = node.val;\nnode = node.next;\n}\nreturn res;\n}\n}\n</code></pre> linkedlist_deque.cpp<pre><code>/* \u53cc\u5411\u94fe\u8868\u8282\u70b9 */\nstruct DoublyListNode {\nint val;              // \u8282\u70b9\u503c\nDoublyListNode *next; // \u540e\u7ee7\u8282\u70b9\u6307\u9488\nDoublyListNode *prev; // \u524d\u9a71\u8282\u70b9\u6307\u9488\nDoublyListNode(int val) : val(val), prev(nullptr), next(nullptr) {\n}\n};\n/* \u57fa\u4e8e\u53cc\u5411\u94fe\u8868\u5b9e\u73b0\u7684\u53cc\u5411\u961f\u5217 */\nclass LinkedListDeque {\nprivate:\nDoublyListNode *front, *rear; // \u5934\u8282\u70b9 front \uff0c\u5c3e\u8282\u70b9 rear\nint queSize = 0;              // \u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6\npublic:\n/* \u6784\u9020\u65b9\u6cd5 */\nLinkedListDeque() : front(nullptr), rear(nullptr) {\n}\n/* \u6790\u6784\u65b9\u6cd5 */\n~LinkedListDeque() {\n// \u904d\u5386\u94fe\u8868\u5220\u9664\u8282\u70b9\uff0c\u91ca\u653e\u5185\u5b58\nDoublyListNode *pre, *cur = front;\nwhile (cur != nullptr) {\npre = cur;\ncur = cur-&gt;next;\ndelete pre;\n}\n}\n/* \u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6 */\nint size() {\nreturn queSize;\n}\n/* \u5224\u65ad\u53cc\u5411\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nbool isEmpty() {\nreturn size() == 0;\n}\n/* \u5165\u961f\u64cd\u4f5c */\nvoid push(int num, bool isFront) {\nDoublyListNode *node = new DoublyListNode(num);\n// \u82e5\u94fe\u8868\u4e3a\u7a7a\uff0c\u5219\u4ee4 front, rear \u90fd\u6307\u5411 node\nif (isEmpty())\nfront = rear = node;\n// \u961f\u9996\u5165\u961f\u64cd\u4f5c\nelse if (isFront) {\n// \u5c06 node \u6dfb\u52a0\u81f3\u94fe\u8868\u5934\u90e8\nfront-&gt;prev = node;\nnode-&gt;next = front;\nfront = node; // \u66f4\u65b0\u5934\u8282\u70b9\n// \u961f\u5c3e\u5165\u961f\u64cd\u4f5c\n} else {\n// \u5c06 node \u6dfb\u52a0\u81f3\u94fe\u8868\u5c3e\u90e8\nrear-&gt;next = node;\nnode-&gt;prev = rear;\nrear = node; // \u66f4\u65b0\u5c3e\u8282\u70b9\n}\nqueSize++; // \u66f4\u65b0\u961f\u5217\u957f\u5ea6\n}\n/* \u961f\u9996\u5165\u961f */\nvoid pushFirst(int num) {\npush(num, true);\n}\n/* \u961f\u5c3e\u5165\u961f */\nvoid pushLast(int num) {\npush(num, false);\n}\n/* \u51fa\u961f\u64cd\u4f5c */\nint pop(bool isFront) {\n// \u82e5\u961f\u5217\u4e3a\u7a7a\uff0c\u76f4\u63a5\u8fd4\u56de -1\nif (isEmpty())\nreturn -1;\nint val;\n// \u961f\u9996\u51fa\u961f\u64cd\u4f5c\nif (isFront) {\nval = front-&gt;val; // \u6682\u5b58\u5934\u8282\u70b9\u503c\n// \u5220\u9664\u5934\u8282\u70b9\nDoublyListNode *fNext = front-&gt;next;\nif (fNext != nullptr) {\nfNext-&gt;prev = nullptr;\nfront-&gt;next = nullptr;\ndelete front;\n}\nfront = fNext; // \u66f4\u65b0\u5934\u8282\u70b9\n// \u961f\u5c3e\u51fa\u961f\u64cd\u4f5c\n} else {\nval = rear-&gt;val; // \u6682\u5b58\u5c3e\u8282\u70b9\u503c\n// \u5220\u9664\u5c3e\u8282\u70b9\nDoublyListNode *rPrev = rear-&gt;prev;\nif (rPrev != nullptr) {\nrPrev-&gt;next = nullptr;\nrear-&gt;prev = nullptr;\ndelete rear;\n}\nrear = rPrev; // \u66f4\u65b0\u5c3e\u8282\u70b9\n}\nqueSize--; // \u66f4\u65b0\u961f\u5217\u957f\u5ea6\nreturn val;\n}\n/* \u961f\u9996\u51fa\u961f */\nint popFirst() {\nreturn pop(true);\n}\n/* \u961f\u5c3e\u51fa\u961f */\nint popLast() {\nreturn pop(false);\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\nint peekFirst() {\nreturn isEmpty() ? -1 : front-&gt;val;\n}\n/* \u8bbf\u95ee\u961f\u5c3e\u5143\u7d20 */\nint peekLast() {\nreturn isEmpty() ? -1 : rear-&gt;val;\n}\n/* \u8fd4\u56de\u6570\u7ec4\u7528\u4e8e\u6253\u5370 */\nvector&lt;int&gt; toVector() {\nDoublyListNode *node = front;\nvector&lt;int&gt; res(size());\nfor (int i = 0; i &lt; res.size(); i++) {\nres[i] = node-&gt;val;\nnode = node-&gt;next;\n}\nreturn res;\n}\n};\n</code></pre> linkedlist_deque.py<pre><code>class ListNode:\n\"\"\"\u53cc\u5411\u94fe\u8868\u8282\u70b9\"\"\"\ndef __init__(self, val: int) -&gt; None:\n\"\"\"\u6784\u9020\u65b9\u6cd5\"\"\"\nself.val: int = val\nself.next: ListNode | None = None  # \u540e\u7ee7\u8282\u70b9\u5f15\u7528\uff08\u6307\u9488\uff09\nself.prev: ListNode | None = None  # \u524d\u9a71\u8282\u70b9\u5f15\u7528\uff08\u6307\u9488\uff09\nclass LinkedListDeque:\n\"\"\"\u57fa\u4e8e\u53cc\u5411\u94fe\u8868\u5b9e\u73b0\u7684\u53cc\u5411\u961f\u5217\"\"\"\ndef __init__(self) -&gt; None:\n\"\"\"\u6784\u9020\u65b9\u6cd5\"\"\"\nself.front: ListNode | None = None  # \u5934\u8282\u70b9 front\nself.rear: ListNode | None = None  # \u5c3e\u8282\u70b9 rear\nself.__size: int = 0  # \u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6\ndef size(self) -&gt; int:\n\"\"\"\u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6\"\"\"\nreturn self.__size\ndef is_empty(self) -&gt; bool:\n\"\"\"\u5224\u65ad\u53cc\u5411\u961f\u5217\u662f\u5426\u4e3a\u7a7a\"\"\"\nreturn self.size() == 0\ndef push(self, num: int, is_front: bool) -&gt; None:\n\"\"\"\u5165\u961f\u64cd\u4f5c\"\"\"\nnode = ListNode(num)\n# \u82e5\u94fe\u8868\u4e3a\u7a7a\uff0c\u5219\u4ee4 front, rear \u90fd\u6307\u5411 node\nif self.is_empty():\nself.front = self.rear = node\n# \u961f\u9996\u5165\u961f\u64cd\u4f5c\nelif is_front:\n# \u5c06 node \u6dfb\u52a0\u81f3\u94fe\u8868\u5934\u90e8\nself.front.prev = node\nnode.next = self.front\nself.front = node  # \u66f4\u65b0\u5934\u8282\u70b9\n# \u961f\u5c3e\u5165\u961f\u64cd\u4f5c\nelse:\n# \u5c06 node \u6dfb\u52a0\u81f3\u94fe\u8868\u5c3e\u90e8\nself.rear.next = node\nnode.prev = self.rear\nself.rear = node  # \u66f4\u65b0\u5c3e\u8282\u70b9\nself.__size += 1  # \u66f4\u65b0\u961f\u5217\u957f\u5ea6\ndef push_first(self, num: int) -&gt; None:\n\"\"\"\u961f\u9996\u5165\u961f\"\"\"\nself.push(num, True)\ndef push_last(self, num: int) -&gt; None:\n\"\"\"\u961f\u5c3e\u5165\u961f\"\"\"\nself.push(num, False)\ndef pop(self, is_front: bool) -&gt; int:\n\"\"\"\u51fa\u961f\u64cd\u4f5c\"\"\"\n# \u82e5\u961f\u5217\u4e3a\u7a7a\uff0c\u76f4\u63a5\u8fd4\u56de None\nif self.is_empty():\nreturn None\n# \u961f\u9996\u51fa\u961f\u64cd\u4f5c\nif is_front:\nval: int = self.front.val  # \u6682\u5b58\u5934\u8282\u70b9\u503c\n# \u5220\u9664\u5934\u8282\u70b9\nfnext: ListNode | None = self.front.next\nif fnext != None:\nfnext.prev = None\nself.front.next = None\nself.front = fnext  # \u66f4\u65b0\u5934\u8282\u70b9\n# \u961f\u5c3e\u51fa\u961f\u64cd\u4f5c\nelse:\nval: int = self.rear.val  # \u6682\u5b58\u5c3e\u8282\u70b9\u503c\n# \u5220\u9664\u5c3e\u8282\u70b9\nrprev: ListNode | None = self.rear.prev\nif rprev != None:\nrprev.next = None\nself.rear.prev = None\nself.rear = rprev  # \u66f4\u65b0\u5c3e\u8282\u70b9\nself.__size -= 1  # \u66f4\u65b0\u961f\u5217\u957f\u5ea6\nreturn val\ndef pop_first(self) -&gt; int:\n\"\"\"\u961f\u9996\u51fa\u961f\"\"\"\nreturn self.pop(True)\ndef pop_last(self) -&gt; int:\n\"\"\"\u961f\u5c3e\u51fa\u961f\"\"\"\nreturn self.pop(False)\ndef peek_first(self) -&gt; int:\n\"\"\"\u8bbf\u95ee\u961f\u9996\u5143\u7d20\"\"\"\nreturn None if self.is_empty() else self.front.val\ndef peek_last(self) -&gt; int:\n\"\"\"\u8bbf\u95ee\u961f\u5c3e\u5143\u7d20\"\"\"\nreturn None if self.is_empty() else self.rear.val\ndef to_array(self) -&gt; list[int]:\n\"\"\"\u8fd4\u56de\u6570\u7ec4\u7528\u4e8e\u6253\u5370\"\"\"\nnode = self.front\nres = [0] * self.size()\nfor i in range(self.size()):\nres[i] = node.val\nnode = node.next\nreturn res\n</code></pre> linkedlist_deque.go<pre><code>/* \u57fa\u4e8e\u53cc\u5411\u94fe\u8868\u5b9e\u73b0\u7684\u53cc\u5411\u961f\u5217 */\ntype linkedListDeque struct {\n// \u4f7f\u7528\u5185\u7f6e\u5305 list\ndata *list.List\n}\n/* \u521d\u59cb\u5316\u53cc\u7aef\u961f\u5217 */\nfunc newLinkedListDeque() *linkedListDeque {\nreturn &amp;linkedListDeque{\ndata: list.New(),\n}\n}\n/* \u961f\u9996\u5143\u7d20\u5165\u961f */\nfunc (s *linkedListDeque) pushFirst(value any) {\ns.data.PushFront(value)\n}\n/* \u961f\u5c3e\u5143\u7d20\u5165\u961f */\nfunc (s *linkedListDeque) pushLast(value any) {\ns.data.PushBack(value)\n}\n/* \u961f\u9996\u5143\u7d20\u51fa\u961f */\nfunc (s *linkedListDeque) popFirst() any {\nif s.isEmpty() {\nreturn nil\n}\ne := s.data.Front()\ns.data.Remove(e)\nreturn e.Value\n}\n/* \u961f\u5c3e\u5143\u7d20\u51fa\u961f */\nfunc (s *linkedListDeque) popLast() any {\nif s.isEmpty() {\nreturn nil\n}\ne := s.data.Back()\ns.data.Remove(e)\nreturn e.Value\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\nfunc (s *linkedListDeque) peekFirst() any {\nif s.isEmpty() {\nreturn nil\n}\ne := s.data.Front()\nreturn e.Value\n}\n/* \u8bbf\u95ee\u961f\u5c3e\u5143\u7d20 */\nfunc (s *linkedListDeque) peekLast() any {\nif s.isEmpty() {\nreturn nil\n}\ne := s.data.Back()\nreturn e.Value\n}\n/* \u83b7\u53d6\u961f\u5217\u7684\u957f\u5ea6 */\nfunc (s *linkedListDeque) size() int {\nreturn s.data.Len()\n}\n/* \u5224\u65ad\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nfunc (s *linkedListDeque) isEmpty() bool {\nreturn s.data.Len() == 0\n}\n/* \u83b7\u53d6 List \u7528\u4e8e\u6253\u5370 */\nfunc (s *linkedListDeque) toList() *list.List {\nreturn s.data\n}\n</code></pre> linkedlist_deque.js<pre><code>/* \u53cc\u5411\u94fe\u8868\u8282\u70b9 */\nclass ListNode {\nprev; // \u524d\u9a71\u8282\u70b9\u5f15\u7528 (\u6307\u9488)\nnext; // \u540e\u7ee7\u8282\u70b9\u5f15\u7528 (\u6307\u9488)\nval; // \u8282\u70b9\u503c\nconstructor(val) {\nthis.val = val;\nthis.next = null;\nthis.prev = null;\n}\n}\n/* \u57fa\u4e8e\u53cc\u5411\u94fe\u8868\u5b9e\u73b0\u7684\u53cc\u5411\u961f\u5217 */\nclass LinkedListDeque {\n#front; // \u5934\u8282\u70b9 front\n#rear; // \u5c3e\u8282\u70b9 rear\n#queSize; // \u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6\nconstructor() {\nthis.#front = null;\nthis.#rear = null;\nthis.#queSize = 0;\n}\n/* \u961f\u5c3e\u5165\u961f\u64cd\u4f5c */\npushLast(val) {\nconst node = new ListNode(val);\n// \u82e5\u94fe\u8868\u4e3a\u7a7a\uff0c\u5219\u4ee4 front, rear \u90fd\u6307\u5411 node\nif (this.#queSize === 0) {\nthis.#front = node;\nthis.#rear = node;\n} else {\n// \u5c06 node \u6dfb\u52a0\u81f3\u94fe\u8868\u5c3e\u90e8\nthis.#rear.next = node;\nnode.prev = this.#rear;\nthis.#rear = node; // \u66f4\u65b0\u5c3e\u8282\u70b9\n}\nthis.#queSize++;\n}\n/* \u961f\u9996\u5165\u961f\u64cd\u4f5c */\npushFirst(val) {\nconst node = new ListNode(val);\n// \u82e5\u94fe\u8868\u4e3a\u7a7a\uff0c\u5219\u4ee4 front, rear \u90fd\u6307\u5411 node\nif (this.#queSize === 0) {\nthis.#front = node;\nthis.#rear = node;\n} else {\n// \u5c06 node \u6dfb\u52a0\u81f3\u94fe\u8868\u5934\u90e8\nthis.#front.prev = node;\nnode.next = this.#front;\nthis.#front = node; // \u66f4\u65b0\u5934\u8282\u70b9\n}\nthis.#queSize++;\n}\n/* \u961f\u5c3e\u51fa\u961f\u64cd\u4f5c */\npopLast() {\nif (this.#queSize === 0) {\nreturn null;\n}\nconst value = this.#rear.val; // \u5b58\u50a8\u5c3e\u8282\u70b9\u503c\n// \u5220\u9664\u5c3e\u8282\u70b9\nlet temp = this.#rear.prev;\nif (temp !== null) {\ntemp.next = null;\nthis.#rear.prev = null;\n}\nthis.#rear = temp; // \u66f4\u65b0\u5c3e\u8282\u70b9\nthis.#queSize--;\nreturn value;\n}\n/* \u961f\u9996\u51fa\u961f\u64cd\u4f5c */\npopFirst() {\nif (this.#queSize === 0) {\nreturn null;\n}\nconst value = this.#front.val; // \u5b58\u50a8\u5c3e\u8282\u70b9\u503c\n// \u5220\u9664\u5934\u8282\u70b9\nlet temp = this.#front.next;\nif (temp !== null) {\ntemp.prev = null;\nthis.#front.next = null;\n}\nthis.#front = temp; // \u66f4\u65b0\u5934\u8282\u70b9\nthis.#queSize--;\nreturn value;\n}\n/* \u8bbf\u95ee\u961f\u5c3e\u5143\u7d20 */\npeekLast() {\nreturn this.#queSize === 0 ? null : this.#rear.val;\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\npeekFirst() {\nreturn this.#queSize === 0 ? null : this.#front.val;\n}\n/* \u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6 */\nsize() {\nreturn this.#queSize;\n}\n/* \u5224\u65ad\u53cc\u5411\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nisEmpty() {\nreturn this.#queSize === 0;\n}\n/* \u6253\u5370\u53cc\u5411\u961f\u5217 */\nprint() {\nconst arr = [];\nlet temp = this.#front;\nwhile (temp !== null) {\narr.push(temp.val);\ntemp = temp.next;\n}\nconsole.log('[' + arr.join(', ') + ']');\n}\n}\n</code></pre> linkedlist_deque.ts<pre><code>/* \u53cc\u5411\u94fe\u8868\u8282\u70b9 */\nclass ListNode {\nprev: ListNode; // \u524d\u9a71\u8282\u70b9\u5f15\u7528 (\u6307\u9488)\nnext: ListNode; // \u540e\u7ee7\u8282\u70b9\u5f15\u7528 (\u6307\u9488)\nval: number; // \u8282\u70b9\u503c\nconstructor(val: number) {\nthis.val = val;\nthis.next = null;\nthis.prev = null;\n}\n}\n/* \u57fa\u4e8e\u53cc\u5411\u94fe\u8868\u5b9e\u73b0\u7684\u53cc\u5411\u961f\u5217 */\nclass LinkedListDeque {\nprivate front: ListNode; // \u5934\u8282\u70b9 front\nprivate rear: ListNode; // \u5c3e\u8282\u70b9 rear\nprivate queSize: number; // \u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6\nconstructor() {\nthis.front = null;\nthis.rear = null;\nthis.queSize = 0;\n}\n/* \u961f\u5c3e\u5165\u961f\u64cd\u4f5c */\npushLast(val: number): void {\nconst node: ListNode = new ListNode(val);\n// \u82e5\u94fe\u8868\u4e3a\u7a7a\uff0c\u5219\u4ee4 front, rear \u90fd\u6307\u5411 node\nif (this.queSize === 0) {\nthis.front = node;\nthis.rear = node;\n} else {\n// \u5c06 node \u6dfb\u52a0\u81f3\u94fe\u8868\u5c3e\u90e8\nthis.rear.next = node;\nnode.prev = this.rear;\nthis.rear = node; // \u66f4\u65b0\u5c3e\u8282\u70b9\n}\nthis.queSize++;\n}\n/* \u961f\u9996\u5165\u961f\u64cd\u4f5c */\npushFirst(val: number): void {\nconst node: ListNode = new ListNode(val);\n// \u82e5\u94fe\u8868\u4e3a\u7a7a\uff0c\u5219\u4ee4 front, rear \u90fd\u6307\u5411 node\nif (this.queSize === 0) {\nthis.front = node;\nthis.rear = node;\n} else {\n// \u5c06 node \u6dfb\u52a0\u81f3\u94fe\u8868\u5934\u90e8\nthis.front.prev = node;\nnode.next = this.front;\nthis.front = node; // \u66f4\u65b0\u5934\u8282\u70b9\n}\nthis.queSize++;\n}\n/* \u961f\u5c3e\u51fa\u961f\u64cd\u4f5c */\npopLast(): number {\nif (this.queSize === 0) {\nreturn null;\n}\nconst value: number = this.rear.val; // \u5b58\u50a8\u5c3e\u8282\u70b9\u503c\n// \u5220\u9664\u5c3e\u8282\u70b9\nlet temp: ListNode = this.rear.prev;\nif (temp !== null) {\ntemp.next = null;\nthis.rear.prev = null;\n}\nthis.rear = temp; // \u66f4\u65b0\u5c3e\u8282\u70b9\nthis.queSize--;\nreturn value;\n}\n/* \u961f\u9996\u51fa\u961f\u64cd\u4f5c */\npopFirst(): number {\nif (this.queSize === 0) {\nreturn null;\n}\nconst value: number = this.front.val; // \u5b58\u50a8\u5c3e\u8282\u70b9\u503c\n// \u5220\u9664\u5934\u8282\u70b9\nlet temp: ListNode = this.front.next;\nif (temp !== null) {\ntemp.prev = null;\nthis.front.next = null;\n}\nthis.front = temp; // \u66f4\u65b0\u5934\u8282\u70b9\nthis.queSize--;\nreturn value;\n}\n/* \u8bbf\u95ee\u961f\u5c3e\u5143\u7d20 */\npeekLast(): number {\nreturn this.queSize === 0 ? null : this.rear.val;\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\npeekFirst(): number {\nreturn this.queSize === 0 ? null : this.front.val;\n}\n/* \u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6 */\nsize(): number {\nreturn this.queSize;\n}\n/* \u5224\u65ad\u53cc\u5411\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nisEmpty(): boolean {\nreturn this.queSize === 0;\n}\n/* \u6253\u5370\u53cc\u5411\u961f\u5217 */\nprint(): void {\nconst arr: number[] = [];\nlet temp: ListNode = this.front;\nwhile (temp !== null) {\narr.push(temp.val);\ntemp = temp.next;\n}\nconsole.log('[' + arr.join(', ') + ']');\n}\n}\n</code></pre> linkedlist_deque.c<pre><code>/* \u53cc\u5411\u94fe\u8868\u8282\u70b9 */\nstruct doublyListNode {\nint val;                     // \u8282\u70b9\u503c\nstruct doublyListNode *next; // \u540e\u7ee7\u8282\u70b9\nstruct doublyListNode *prev; // \u524d\u9a71\u8282\u70b9\n};\ntypedef struct doublyListNode doublyListNode;\n/* \u6784\u9020\u51fd\u6570 */\ndoublyListNode *newDoublyListNode(int num) {\ndoublyListNode *new = (doublyListNode *)malloc(sizeof(doublyListNode));\nnew-&gt;val = num;\nnew-&gt;next = NULL;\nnew-&gt;prev = NULL;\nreturn new;\n}\n/* \u6790\u6784\u51fd\u6570 */\nvoid delDoublyListNode(doublyListNode *node) {\nfree(node);\n}\n/* \u57fa\u4e8e\u53cc\u5411\u94fe\u8868\u5b9e\u73b0\u7684\u53cc\u5411\u961f\u5217 */\nstruct linkedListDeque {\ndoublyListNode *front, *rear; // \u5934\u8282\u70b9 front \uff0c\u5c3e\u8282\u70b9 rear\nint queSize;                  // \u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6\n};\ntypedef struct linkedListDeque linkedListDeque;\n/* \u6784\u9020\u51fd\u6570 */\nlinkedListDeque *newLinkedListDeque() {\nlinkedListDeque *deque = (linkedListDeque *)malloc(sizeof(linkedListDeque));\ndeque-&gt;front = NULL;\ndeque-&gt;rear = NULL;\ndeque-&gt;queSize = 0;\nreturn deque;\n}\n/* \u6790\u6784\u51fd\u6570 */\nvoid delLinkedListdeque(linkedListDeque *deque) {\n// \u91ca\u653e\u6240\u6709\u8282\u70b9\nfor (int i = 0; i &lt; deque-&gt;queSize &amp;&amp; deque-&gt;front != NULL; i++) {\ndoublyListNode *tmp = deque-&gt;front;\ndeque-&gt;front = deque-&gt;front-&gt;next;\nfree(tmp);\n}\n// \u91ca\u653e deque \u7ed3\u6784\u4f53\nfree(deque);\n}\n/* \u83b7\u53d6\u961f\u5217\u7684\u957f\u5ea6 */\nint size(linkedListDeque *deque) {\nreturn deque-&gt;queSize;\n}\n/* \u5224\u65ad\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nbool empty(linkedListDeque *deque) {\nreturn (size(deque) == 0);\n}\n/* \u5165\u961f */\nvoid push(linkedListDeque *deque, int num, bool isFront) {\ndoublyListNode *node = newDoublyListNode(num);\n// \u82e5\u94fe\u8868\u4e3a\u7a7a\uff0c\u5219\u4ee4 front, rear \u90fd\u6307\u5411node\nif (empty(deque)) {\ndeque-&gt;front = deque-&gt;rear = node;\n}\n// \u961f\u9996\u5165\u961f\u64cd\u4f5c\nelse if (isFront) {\n// \u5c06 node \u6dfb\u52a0\u81f3\u94fe\u8868\u5934\u90e8\ndeque-&gt;front-&gt;prev = node;\nnode-&gt;next = deque-&gt;front;\ndeque-&gt;front = node; // \u66f4\u65b0\u5934\u8282\u70b9\n}\n// \u5bf9\u5c3e\u5165\u961f\u64cd\u4f5c\nelse {\n// \u5c06 node \u6dfb\u52a0\u81f3\u94fe\u8868\u5c3e\u90e8\ndeque-&gt;rear-&gt;next = node;\nnode-&gt;prev = deque-&gt;rear;\ndeque-&gt;rear = node;\n}\ndeque-&gt;queSize++; // \u66f4\u65b0\u961f\u5217\u957f\u5ea6\n}\n/* \u961f\u9996\u5165\u961f */\nvoid pushFirst(linkedListDeque *deque, int num) {\npush(deque, num, true);\n}\n/* \u961f\u5c3e\u5165\u961f */\nvoid pushLast(linkedListDeque *deque, int num) {\npush(deque, num, false);\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\nint peekFirst(linkedListDeque *deque) {\nassert(size(deque) &amp;&amp; deque-&gt;front);\nreturn deque-&gt;front-&gt;val;\n}\n/* \u8bbf\u95ee\u961f\u5c3e\u5143\u7d20 */\nint peekLast(linkedListDeque *deque) {\nassert(size(deque) &amp;&amp; deque-&gt;rear);\nreturn deque-&gt;rear-&gt;val;\n}\n/* \u51fa\u961f */\nint pop(linkedListDeque *deque, bool isFront) {\nif (empty(deque))\nreturn -1;\nint val;\n// \u961f\u9996\u51fa\u961f\u64cd\u4f5c\nif (isFront) {\nval = peekFirst(deque); // \u6682\u5b58\u5934\u8282\u70b9\u503c\ndoublyListNode *fNext = deque-&gt;front-&gt;next;\nif (fNext) {\nfNext-&gt;prev = NULL;\ndeque-&gt;front-&gt;next = NULL;\ndelDoublyListNode(deque-&gt;front);\n}\ndeque-&gt;front = fNext; // \u66f4\u65b0\u5934\u8282\u70b9\n}\n// \u961f\u5c3e\u51fa\u961f\u64cd\u4f5c\nelse {\nval = peekLast(deque); // \u6682\u5b58\u5c3e\u8282\u70b9\u503c\ndoublyListNode *rPrev = deque-&gt;rear-&gt;prev;\nif (rPrev) {\nrPrev-&gt;next = NULL;\ndeque-&gt;rear-&gt;prev = NULL;\ndelDoublyListNode(deque-&gt;rear);\n}\ndeque-&gt;rear = rPrev; // \u66f4\u65b0\u5c3e\u8282\u70b9\n}\ndeque-&gt;queSize--; // \u66f4\u65b0\u961f\u5217\u957f\u5ea6\nreturn val;\n}\n/* \u961f\u9996\u51fa\u961f */\nint popFirst(linkedListDeque *deque) {\nreturn pop(deque, true);\n}\n/* \u961f\u5c3e\u51fa\u961f */\nint popLast(linkedListDeque *deque) {\nreturn pop(deque, false);\n}\n/* \u6253\u5370\u961f\u5217 */\nvoid printLinkedListDeque(linkedListDeque *deque) {\nint arr[deque-&gt;queSize];\n// \u62f7\u8d1d\u94fe\u8868\u4e2d\u7684\u6570\u636e\u5230\u6570\u7ec4\nint i;\ndoublyListNode *node;\nfor (i = 0, node = deque-&gt;front; i &lt; deque-&gt;queSize; i++) {\narr[i] = node-&gt;val;\nnode = node-&gt;next;\n}\nprintArray(arr, deque-&gt;queSize);\n}\n</code></pre> linkedlist_deque.cs<pre><code>/* \u53cc\u5411\u94fe\u8868\u8282\u70b9 */\nclass ListNode {\npublic int val;       // \u8282\u70b9\u503c\npublic ListNode? next; // \u540e\u7ee7\u8282\u70b9\u5f15\u7528\uff08\u6307\u9488\uff09\npublic ListNode? prev; // \u524d\u9a71\u8282\u70b9\u5f15\u7528\uff08\u6307\u9488\uff09\npublic ListNode(int val) {\nthis.val = val;\nprev = null;\nnext = null;\n}\n}\n/* \u57fa\u4e8e\u53cc\u5411\u94fe\u8868\u5b9e\u73b0\u7684\u53cc\u5411\u961f\u5217 */\nclass LinkedListDeque {\nprivate ListNode? front, rear; // \u5934\u8282\u70b9 front, \u5c3e\u8282\u70b9 rear\nprivate int queSize = 0;      // \u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6\npublic LinkedListDeque() {\nfront = null;\nrear = null;\n}\n/* \u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6 */\npublic int size() {\nreturn queSize;\n}\n/* \u5224\u65ad\u53cc\u5411\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\npublic bool isEmpty() {\nreturn size() == 0;\n}\n/* \u5165\u961f\u64cd\u4f5c */\nprivate void push(int num, bool isFront) {\nListNode node = new ListNode(num);\n// \u82e5\u94fe\u8868\u4e3a\u7a7a\uff0c\u5219\u4ee4 front, rear \u90fd\u6307\u5411 node\nif (isEmpty()) {\nfront = node;\nrear = node;\n}\n// \u961f\u9996\u5165\u961f\u64cd\u4f5c\nelse if (isFront) {\n// \u5c06 node \u6dfb\u52a0\u81f3\u94fe\u8868\u5934\u90e8\nfront.prev = node;\nnode.next = front;\nfront = node; // \u66f4\u65b0\u5934\u8282\u70b9                           \n}\n// \u961f\u5c3e\u5165\u961f\u64cd\u4f5c\nelse {\n// \u5c06 node \u6dfb\u52a0\u81f3\u94fe\u8868\u5c3e\u90e8\nrear.next = node;\nnode.prev = rear;\nrear = node;  // \u66f4\u65b0\u5c3e\u8282\u70b9\n}\nqueSize++; // \u66f4\u65b0\u961f\u5217\u957f\u5ea6\n}\n/* \u961f\u9996\u5165\u961f */\npublic void pushFirst(int num) {\npush(num, true);\n}\n/* \u961f\u5c3e\u5165\u961f */\npublic void pushLast(int num) {\npush(num, false);\n}\n/* \u51fa\u961f\u64cd\u4f5c */\nprivate int? pop(bool isFront) {\n// \u82e5\u961f\u5217\u4e3a\u7a7a\uff0c\u76f4\u63a5\u8fd4\u56de null\nif (isEmpty()) {\nreturn null;\n}\nint val;\n// \u961f\u9996\u51fa\u961f\u64cd\u4f5c\nif (isFront) {\nval = front.val; // \u6682\u5b58\u5934\u8282\u70b9\u503c\n// \u5220\u9664\u5934\u8282\u70b9\nListNode fNext = front.next;\nif (fNext != null) {\nfNext.prev = null;\nfront.next = null;\n}\nfront = fNext;   // \u66f4\u65b0\u5934\u8282\u70b9\n}\n// \u961f\u5c3e\u51fa\u961f\u64cd\u4f5c\nelse {\nval = rear.val;  // \u6682\u5b58\u5c3e\u8282\u70b9\u503c\n// \u5220\u9664\u5c3e\u8282\u70b9\nListNode rPrev = rear.prev;\nif (rPrev != null) {\nrPrev.next = null;\nrear.prev = null;\n}\nrear = rPrev;    // \u66f4\u65b0\u5c3e\u8282\u70b9\n}\nqueSize--; // \u66f4\u65b0\u961f\u5217\u957f\u5ea6\nreturn val;\n}\n/* \u961f\u9996\u51fa\u961f */\npublic int? popFirst() {\nreturn pop(true);\n}\n/* \u961f\u5c3e\u51fa\u961f */\npublic int? popLast() {\nreturn pop(false);\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\npublic int? peekFirst() {\nreturn isEmpty() ? null : front.val;\n}\n/* \u8bbf\u95ee\u961f\u5c3e\u5143\u7d20 */\npublic int? peekLast() {\nreturn isEmpty() ? null : rear.val;\n}\n/* \u8fd4\u56de\u6570\u7ec4\u7528\u4e8e\u6253\u5370 */\npublic int[] toArray() {\nListNode node = front;\nint[] res = new int[size()];\nfor (int i = 0; i &lt; res.Length; i++) {\nres[i] = node.val;\nnode = node.next;\n}\nreturn res;\n}\n}\n</code></pre> linkedlist_deque.swift<pre><code>/* \u53cc\u5411\u94fe\u8868\u8282\u70b9 */\nclass ListNode {\nvar val: Int // \u8282\u70b9\u503c\nvar next: ListNode? // \u540e\u7ee7\u8282\u70b9\u5f15\u7528\uff08\u6307\u9488\uff09\nvar prev: ListNode? // \u524d\u9a71\u8282\u70b9\u5f15\u7528\uff08\u6307\u9488\uff09\ninit(val: Int) {\nself.val = val\n}\n}\n/* \u57fa\u4e8e\u53cc\u5411\u94fe\u8868\u5b9e\u73b0\u7684\u53cc\u5411\u961f\u5217 */\nclass LinkedListDeque {\nprivate var front: ListNode? // \u5934\u8282\u70b9 front\nprivate var rear: ListNode? // \u5c3e\u8282\u70b9 rear\nprivate var queSize: Int // \u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6\ninit() {\nqueSize = 0\n}\n/* \u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6 */\nfunc size() -&gt; Int {\nqueSize\n}\n/* \u5224\u65ad\u53cc\u5411\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nfunc isEmpty() -&gt; Bool {\nsize() == 0\n}\n/* \u5165\u961f\u64cd\u4f5c */\nprivate func push(num: Int, isFront: Bool) {\nlet node = ListNode(val: num)\n// \u82e5\u94fe\u8868\u4e3a\u7a7a\uff0c\u5219\u4ee4 front, rear \u90fd\u6307\u5411 node\nif isEmpty() {\nfront = node\nrear = node\n}\n// \u961f\u9996\u5165\u961f\u64cd\u4f5c\nelse if isFront {\n// \u5c06 node \u6dfb\u52a0\u81f3\u94fe\u8868\u5934\u90e8\nfront?.prev = node\nnode.next = front\nfront = node // \u66f4\u65b0\u5934\u8282\u70b9\n}\n// \u961f\u5c3e\u5165\u961f\u64cd\u4f5c\nelse {\n// \u5c06 node \u6dfb\u52a0\u81f3\u94fe\u8868\u5c3e\u90e8\nrear?.next = node\nnode.prev = rear\nrear = node // \u66f4\u65b0\u5c3e\u8282\u70b9\n}\nqueSize += 1 // \u66f4\u65b0\u961f\u5217\u957f\u5ea6\n}\n/* \u961f\u9996\u5165\u961f */\nfunc pushFirst(num: Int) {\npush(num: num, isFront: true)\n}\n/* \u961f\u5c3e\u5165\u961f */\nfunc pushLast(num: Int) {\npush(num: num, isFront: false)\n}\n/* \u51fa\u961f\u64cd\u4f5c */\nprivate func pop(isFront: Bool) -&gt; Int {\nif isEmpty() {\nfatalError(\"\u53cc\u5411\u961f\u5217\u4e3a\u7a7a\")\n}\nlet val: Int\n// \u961f\u9996\u51fa\u961f\u64cd\u4f5c\nif isFront {\nval = front!.val // \u6682\u5b58\u5934\u8282\u70b9\u503c\n// \u5220\u9664\u5934\u8282\u70b9\nlet fNext = front?.next\nif fNext != nil {\nfNext?.prev = nil\nfront?.next = nil\n}\nfront = fNext // \u66f4\u65b0\u5934\u8282\u70b9\n}\n// \u961f\u5c3e\u51fa\u961f\u64cd\u4f5c\nelse {\nval = rear!.val // \u6682\u5b58\u5c3e\u8282\u70b9\u503c\n// \u5220\u9664\u5c3e\u8282\u70b9\nlet rPrev = rear?.prev\nif rPrev != nil {\nrPrev?.next = nil\nrear?.prev = nil\n}\nrear = rPrev // \u66f4\u65b0\u5c3e\u8282\u70b9\n}\nqueSize -= 1 // \u66f4\u65b0\u961f\u5217\u957f\u5ea6\nreturn val\n}\n/* \u961f\u9996\u51fa\u961f */\nfunc popFirst() -&gt; Int {\npop(isFront: true)\n}\n/* \u961f\u5c3e\u51fa\u961f */\nfunc popLast() -&gt; Int {\npop(isFront: false)\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\nfunc peekFirst() -&gt; Int? {\nisEmpty() ? nil : front?.val\n}\n/* \u8bbf\u95ee\u961f\u5c3e\u5143\u7d20 */\nfunc peekLast() -&gt; Int? {\nisEmpty() ? nil : rear?.val\n}\n/* \u8fd4\u56de\u6570\u7ec4\u7528\u4e8e\u6253\u5370 */\nfunc toArray() -&gt; [Int] {\nvar node = front\nvar res = Array(repeating: 0, count: size())\nfor i in res.indices {\nres[i] = node!.val\nnode = node?.next\n}\nreturn res\n}\n}\n</code></pre> linkedlist_deque.zig<pre><code>// \u53cc\u5411\u94fe\u8868\u8282\u70b9\nfn ListNode(comptime T: type) type {\nreturn struct {\nconst Self = @This();\nval: T = undefined,     // \u8282\u70b9\u503c\nnext: ?*Self = null,    // \u540e\u7ee7\u8282\u70b9\u5f15\u7528\uff08\u6307\u9488\uff09\nprev: ?*Self = null,    // \u524d\u9a71\u8282\u70b9\u5f15\u7528\uff08\u6307\u9488\uff09\n// Initialize a list node with specific value\npub fn init(self: *Self, x: i32) void {\nself.val = x;\nself.next = null;\nself.prev = null;\n}\n};\n}\n// \u57fa\u4e8e\u53cc\u5411\u94fe\u8868\u5b9e\u73b0\u7684\u53cc\u5411\u961f\u5217\nfn LinkedListDeque(comptime T: type) type {\nreturn struct {\nconst Self = @This();\nfront: ?*ListNode(T) = null,                    // \u5934\u8282\u70b9 front\nrear: ?*ListNode(T) = null,                     // \u5c3e\u8282\u70b9 rear\nque_size: usize = 0,                             // \u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6\nmem_arena: ?std.heap.ArenaAllocator = null,\nmem_allocator: std.mem.Allocator = undefined,   // \u5185\u5b58\u5206\u914d\u5668\n// \u6784\u9020\u65b9\u6cd5\uff08\u5206\u914d\u5185\u5b58+\u521d\u59cb\u5316\u961f\u5217\uff09\npub fn init(self: *Self, allocator: std.mem.Allocator) !void {\nif (self.mem_arena == null) {\nself.mem_arena = std.heap.ArenaAllocator.init(allocator);\nself.mem_allocator = self.mem_arena.?.allocator();\n}\nself.front = null;\nself.rear = null;\nself.que_size = 0;\n}\n// \u6790\u6784\u65b9\u6cd5\uff08\u91ca\u653e\u5185\u5b58\uff09\npub fn deinit(self: *Self) void {\nif (self.mem_arena == null) return;\nself.mem_arena.?.deinit();\n}\n// \u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6\npub fn size(self: *Self) usize {\nreturn self.que_size;\n}\n// \u5224\u65ad\u53cc\u5411\u961f\u5217\u662f\u5426\u4e3a\u7a7a\npub fn isEmpty(self: *Self) bool {\nreturn self.size() == 0;\n}\n// \u5165\u961f\u64cd\u4f5c\npub fn push(self: *Self, num: T, is_front: bool) !void {\nvar node = try self.mem_allocator.create(ListNode(T));\nnode.init(num);\n// \u82e5\u94fe\u8868\u4e3a\u7a7a\uff0c\u5219\u4ee4 front, rear \u90fd\u6307\u5411 node\nif (self.isEmpty()) {\nself.front = node;\nself.rear = node;\n// \u961f\u9996\u5165\u961f\u64cd\u4f5c\n} else if (is_front) {\n// \u5c06 node \u6dfb\u52a0\u81f3\u94fe\u8868\u5934\u90e8\nself.front.?.prev = node;\nnode.next = self.front;\nself.front = node;  // \u66f4\u65b0\u5934\u8282\u70b9\n// \u961f\u5c3e\u5165\u961f\u64cd\u4f5c\n} else {\n// \u5c06 node \u6dfb\u52a0\u81f3\u94fe\u8868\u5c3e\u90e8\nself.rear.?.next = node;\nnode.prev = self.rear;\nself.rear = node;   // \u66f4\u65b0\u5c3e\u8282\u70b9\n}\nself.que_size += 1;      // \u66f4\u65b0\u961f\u5217\u957f\u5ea6\n} // \u961f\u9996\u5165\u961f\npub fn pushFirst(self: *Self, num: T) !void {\ntry self.push(num, true);\n} // \u961f\u5c3e\u5165\u961f\npub fn pushLast(self: *Self, num: T) !void {\ntry self.push(num, false);\n} // \u51fa\u961f\u64cd\u4f5c\npub fn pop(self: *Self, is_front: bool) T {\nif (self.isEmpty()) @panic(\"\u53cc\u5411\u961f\u5217\u4e3a\u7a7a\");\nvar val: T = undefined;\n// \u961f\u9996\u51fa\u961f\u64cd\u4f5c\nif (is_front) {\nval = self.front.?.val;     // \u6682\u5b58\u5934\u8282\u70b9\u503c\n// \u5220\u9664\u5934\u8282\u70b9\nvar fNext = self.front.?.next;\nif (fNext != null) {\nfNext.?.prev = null;\nself.front.?.next = null;\n}\nself.front = fNext;         // \u66f4\u65b0\u5934\u8282\u70b9\n// \u961f\u5c3e\u51fa\u961f\u64cd\u4f5c\n} else {\nval = self.rear.?.val;      // \u6682\u5b58\u5c3e\u8282\u70b9\u503c\n// \u5220\u9664\u5c3e\u8282\u70b9\nvar rPrev = self.rear.?.prev;\nif (rPrev != null) {\nrPrev.?.next = null;\nself.rear.?.prev = null;\n}\nself.rear = rPrev;          // \u66f4\u65b0\u5c3e\u8282\u70b9\n}\nself.que_size -= 1;              // \u66f4\u65b0\u961f\u5217\u957f\u5ea6\nreturn val;\n} // \u961f\u9996\u51fa\u961f\npub fn popFirst(self: *Self) T {\nreturn self.pop(true);\n} // \u961f\u5c3e\u51fa\u961f\npub fn popLast(self: *Self) T {\nreturn self.pop(false);\n} // \u8bbf\u95ee\u961f\u9996\u5143\u7d20\npub fn peekFirst(self: *Self) T {\nif (self.isEmpty()) @panic(\"\u53cc\u5411\u961f\u5217\u4e3a\u7a7a\");\nreturn self.front.?.val;\n}  // \u8bbf\u95ee\u961f\u5c3e\u5143\u7d20\npub fn peekLast(self: *Self) T {\nif (self.isEmpty()) @panic(\"\u53cc\u5411\u961f\u5217\u4e3a\u7a7a\");\nreturn self.rear.?.val;\n}\n// \u8fd4\u56de\u6570\u7ec4\u7528\u4e8e\u6253\u5370\npub fn toArray(self: *Self) ![]T {\nvar node = self.front;\nvar res = try self.mem_allocator.alloc(T, self.size());\nstd.mem.set(T, res, @as(T, 0));\nvar i: usize = 0;\nwhile (i &lt; res.len) : (i += 1) {\nres[i] = node.?.val;\nnode = node.?.next;\n}\nreturn res;\n}\n};\n}\n</code></pre> linkedlist_deque.dart<pre><code>/* \u53cc\u5411\u94fe\u8868\u8282\u70b9 */\nclass ListNode {\nint val; // \u8282\u70b9\u503c\nListNode? next; // \u540e\u7ee7\u8282\u70b9\u5f15\u7528\uff08\u6307\u9488\uff09\nListNode? prev; // \u524d\u9a71\u8282\u70b9\u5f15\u7528\uff08\u6307\u9488\uff09\nListNode(this.val, {this.next, this.prev});\n}\n/* \u57fa\u4e8e\u53cc\u5411\u94fe\u8868\u5b9e\u73b0\u7684\u53cc\u5411\u5bf9\u5217 */\nclass LinkedListDeque {\nlate ListNode? _front; // \u5934\u8282\u70b9 _front\nlate ListNode? _rear; // \u5c3e\u8282\u70b9 _rear\nint _queSize = 0; // \u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6\nLinkedListDeque() {\nthis._front = null;\nthis._rear = null;\n}\n/* \u83b7\u53d6\u53cc\u5411\u961f\u5217\u957f\u5ea6 */\nint size() {\nreturn this._queSize;\n}\n/* \u5224\u65ad\u53cc\u5411\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nbool isEmpty() {\nreturn size() == 0;\n}\n/* \u5165\u961f\u64cd\u4f5c */\nvoid push(int num, bool isFront) {\nfinal ListNode node = ListNode(num);\nif (isEmpty()) {\n// \u82e5\u94fe\u8868\u4e3a\u7a7a\uff0c\u5219\u4ee4 _front\uff0c_rear \u90fd\u6307\u5411 node\n_front = _rear = node;\n} else if (isFront) {\n// \u961f\u9996\u5165\u961f\u64cd\u4f5c\n// \u5c06 node \u6dfb\u52a0\u81f3\u94fe\u8868\u5934\u90e8\n_front!.prev = node;\nnode.next = _front;\n_front = node; // \u66f4\u65b0\u5934\u8282\u70b9\n} else {\n// \u961f\u5c3e\u5165\u961f\u64cd\u4f5c\n// \u5c06 node \u6dfb\u52a0\u81f3\u94fe\u8868\u5c3e\u90e8\n_rear!.next = node;\nnode.prev = _rear;\n_rear = node; // \u66f4\u65b0\u5c3e\u8282\u70b9\n}\n_queSize++; // \u66f4\u65b0\u961f\u5217\u957f\u5ea6\n}\n/* \u961f\u9996\u5165\u961f */\nvoid pushFirst(int num) {\npush(num, true);\n}\n/* \u961f\u5c3e\u5165\u961f */\nvoid pushLast(int num) {\npush(num, false);\n}\n/* \u51fa\u961f\u64cd\u4f5c */\nint? pop(bool isFront) {\n// \u82e5\u961f\u5217\u4e3a\u7a7a\uff0c\u76f4\u63a5\u8fd4\u56de null\nif (isEmpty()) {\nreturn null;\n}\nfinal int val;\nif (isFront) {\n// \u961f\u9996\u51fa\u961f\u64cd\u4f5c\nval = _front!.val; // \u6682\u5b58\u5934\u8282\u70b9\u503c\n// \u5220\u9664\u5934\u8282\u70b9\nListNode? fNext = _front!.next;\nif (fNext != null) {\nfNext.prev = null;\n_front!.next = null;\n}\n_front = fNext; // \u66f4\u65b0\u5934\u8282\u70b9\n} else {\n// \u961f\u5c3e\u51fa\u961f\u64cd\u4f5c\nval = _rear!.val; // \u6682\u5b58\u5c3e\u8282\u70b9\u503c\n// \u5220\u9664\u5c3e\u8282\u70b9\nListNode? rPrev = _rear!.prev;\nif (rPrev != null) {\nrPrev.next = null;\n_rear!.prev = null;\n}\n_rear = rPrev; // \u66f4\u65b0\u5c3e\u8282\u70b9\n}\n_queSize--; // \u66f4\u65b0\u961f\u5217\u957f\u5ea6\nreturn val;\n}\n/* \u961f\u9996\u51fa\u961f */\nint? popFirst() {\nreturn pop(true);\n}\n/* \u961f\u5c3e\u51fa\u961f */\nint? popLast() {\nreturn pop(false);\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\nint? peekFirst() {\nreturn _front?.val;\n}\n/* \u8bbf\u95ee\u961f\u5c3e\u5143\u7d20 */\nint? peekLast() {\nreturn _rear?.val;\n}\n/* \u8fd4\u56de\u6570\u7ec4\u7528\u4e8e\u6253\u5370 */\nList&lt;int&gt; toArray() {\nListNode? node = _front;\nfinal List&lt;int&gt; res = [];\nfor (int i = 0; i &lt; _queSize; i++) {\nres.add(node!.val);\nnode = node.next;\n}\nreturn res;\n}\n}\n</code></pre>"},{"location":"chapter_stack_and_queue/deque/#_2","title":"\u57fa\u4e8e\u6570\u7ec4\u7684\u5b9e\u73b0","text":"<p>\u4e0e\u57fa\u4e8e\u6570\u7ec4\u5b9e\u73b0\u961f\u5217\u7c7b\u4f3c\uff0c\u6211\u4eec\u4e5f\u53ef\u4ee5\u4f7f\u7528\u73af\u5f62\u6570\u7ec4\u6765\u5b9e\u73b0\u53cc\u5411\u961f\u5217\u3002\u5728\u961f\u5217\u7684\u5b9e\u73b0\u57fa\u7840\u4e0a\uff0c\u4ec5\u9700\u589e\u52a0\u201c\u961f\u9996\u5165\u961f\u201d\u548c\u201c\u961f\u5c3e\u51fa\u961f\u201d\u7684\u65b9\u6cd5\u3002</p> ArrayDequepushLast()pushFirst()popLast()popFirst() <p></p> <p></p> <p></p> <p></p> <p></p> <p>\u4ee5\u4e0b\u662f\u5177\u4f53\u5b9e\u73b0\u4ee3\u7801\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart array_deque.java<pre><code>/* \u57fa\u4e8e\u73af\u5f62\u6570\u7ec4\u5b9e\u73b0\u7684\u53cc\u5411\u961f\u5217 */\nclass ArrayDeque {\nprivate int[] nums; // \u7528\u4e8e\u5b58\u50a8\u53cc\u5411\u961f\u5217\u5143\u7d20\u7684\u6570\u7ec4\nprivate int front; // \u961f\u9996\u6307\u9488\uff0c\u6307\u5411\u961f\u9996\u5143\u7d20\nprivate int queSize; // \u53cc\u5411\u961f\u5217\u957f\u5ea6\n/* \u6784\u9020\u65b9\u6cd5 */\npublic ArrayDeque(int capacity) {\nthis.nums = new int[capacity];\nfront = queSize = 0;\n}\n/* \u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u5bb9\u91cf */\npublic int capacity() {\nreturn nums.length;\n}\n/* \u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6 */\npublic int size() {\nreturn queSize;\n}\n/* \u5224\u65ad\u53cc\u5411\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\npublic boolean isEmpty() {\nreturn queSize == 0;\n}\n/* \u8ba1\u7b97\u73af\u5f62\u6570\u7ec4\u7d22\u5f15 */\nprivate int index(int i) {\n// \u901a\u8fc7\u53d6\u4f59\u64cd\u4f5c\u5b9e\u73b0\u6570\u7ec4\u9996\u5c3e\u76f8\u8fde\n// \u5f53 i \u8d8a\u8fc7\u6570\u7ec4\u5c3e\u90e8\u540e\uff0c\u56de\u5230\u5934\u90e8\n// \u5f53 i \u8d8a\u8fc7\u6570\u7ec4\u5934\u90e8\u540e\uff0c\u56de\u5230\u5c3e\u90e8\nreturn (i + capacity()) % capacity();\n}\n/* \u961f\u9996\u5165\u961f */\npublic void pushFirst(int num) {\nif (queSize == capacity()) {\nSystem.out.println(\"\u53cc\u5411\u961f\u5217\u5df2\u6ee1\");\nreturn;\n}\n// \u961f\u9996\u6307\u9488\u5411\u5de6\u79fb\u52a8\u4e00\u4f4d\n// \u901a\u8fc7\u53d6\u4f59\u64cd\u4f5c\uff0c\u5b9e\u73b0 front \u8d8a\u8fc7\u6570\u7ec4\u5934\u90e8\u540e\u56de\u5230\u5c3e\u90e8\nfront = index(front - 1);\n// \u5c06 num \u6dfb\u52a0\u81f3\u961f\u9996\nnums[front] = num;\nqueSize++;\n}\n/* \u961f\u5c3e\u5165\u961f */\npublic void pushLast(int num) {\nif (queSize == capacity()) {\nSystem.out.println(\"\u53cc\u5411\u961f\u5217\u5df2\u6ee1\");\nreturn;\n}\n// \u8ba1\u7b97\u5c3e\u6307\u9488\uff0c\u6307\u5411\u961f\u5c3e\u7d22\u5f15 + 1\nint rear = index(front + queSize);\n// \u5c06 num \u6dfb\u52a0\u81f3\u961f\u5c3e\nnums[rear] = num;\nqueSize++;\n}\n/* \u961f\u9996\u51fa\u961f */\npublic int popFirst() {\nint num = peekFirst();\n// \u961f\u9996\u6307\u9488\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\nfront = index(front + 1);\nqueSize--;\nreturn num;\n}\n/* \u961f\u5c3e\u51fa\u961f */\npublic int popLast() {\nint num = peekLast();\nqueSize--;\nreturn num;\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\npublic int peekFirst() {\nif (isEmpty())\nthrow new IndexOutOfBoundsException();\nreturn nums[front];\n}\n/* \u8bbf\u95ee\u961f\u5c3e\u5143\u7d20 */\npublic int peekLast() {\nif (isEmpty())\nthrow new IndexOutOfBoundsException();\n// \u8ba1\u7b97\u5c3e\u5143\u7d20\u7d22\u5f15\nint last = index(front + queSize - 1);\nreturn nums[last];\n}\n/* \u8fd4\u56de\u6570\u7ec4\u7528\u4e8e\u6253\u5370 */\npublic int[] toArray() {\n// \u4ec5\u8f6c\u6362\u6709\u6548\u957f\u5ea6\u8303\u56f4\u5185\u7684\u5217\u8868\u5143\u7d20\nint[] res = new int[queSize];\nfor (int i = 0, j = front; i &lt; queSize; i++, j++) {\nres[i] = nums[index(j)];\n}\nreturn res;\n}\n}\n</code></pre> array_deque.cpp<pre><code>/* \u57fa\u4e8e\u73af\u5f62\u6570\u7ec4\u5b9e\u73b0\u7684\u53cc\u5411\u961f\u5217 */\nclass ArrayDeque {\nprivate:\nvector&lt;int&gt; nums; // \u7528\u4e8e\u5b58\u50a8\u53cc\u5411\u961f\u5217\u5143\u7d20\u7684\u6570\u7ec4\nint front;        // \u961f\u9996\u6307\u9488\uff0c\u6307\u5411\u961f\u9996\u5143\u7d20\nint queSize;      // \u53cc\u5411\u961f\u5217\u957f\u5ea6\npublic:\n/* \u6784\u9020\u65b9\u6cd5 */\nArrayDeque(int capacity) {\nnums.resize(capacity);\nfront = queSize = 0;\n}\n/* \u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u5bb9\u91cf */\nint capacity() {\nreturn nums.size();\n}\n/* \u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6 */\nint size() {\nreturn queSize;\n}\n/* \u5224\u65ad\u53cc\u5411\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nbool isEmpty() {\nreturn queSize == 0;\n}\n/* \u8ba1\u7b97\u73af\u5f62\u6570\u7ec4\u7d22\u5f15 */\nint index(int i) {\n// \u901a\u8fc7\u53d6\u4f59\u64cd\u4f5c\u5b9e\u73b0\u6570\u7ec4\u9996\u5c3e\u76f8\u8fde\n// \u5f53 i \u8d8a\u8fc7\u6570\u7ec4\u5c3e\u90e8\u540e\uff0c\u56de\u5230\u5934\u90e8\n// \u5f53 i \u8d8a\u8fc7\u6570\u7ec4\u5934\u90e8\u540e\uff0c\u56de\u5230\u5c3e\u90e8\nreturn (i + capacity()) % capacity();\n}\n/* \u961f\u9996\u5165\u961f */\nvoid pushFirst(int num) {\nif (queSize == capacity()) {\ncout &lt;&lt; \"\u53cc\u5411\u961f\u5217\u5df2\u6ee1\" &lt;&lt; endl;\nreturn;\n}\n// \u961f\u9996\u6307\u9488\u5411\u5de6\u79fb\u52a8\u4e00\u4f4d\n// \u901a\u8fc7\u53d6\u4f59\u64cd\u4f5c\uff0c\u5b9e\u73b0 front \u8d8a\u8fc7\u6570\u7ec4\u5934\u90e8\u540e\u56de\u5230\u5c3e\u90e8\nfront = index(front - 1);\n// \u5c06 num \u6dfb\u52a0\u81f3\u961f\u9996\nnums[front] = num;\nqueSize++;\n}\n/* \u961f\u5c3e\u5165\u961f */\nvoid pushLast(int num) {\nif (queSize == capacity()) {\ncout &lt;&lt; \"\u53cc\u5411\u961f\u5217\u5df2\u6ee1\" &lt;&lt; endl;\nreturn;\n}\n// \u8ba1\u7b97\u5c3e\u6307\u9488\uff0c\u6307\u5411\u961f\u5c3e\u7d22\u5f15 + 1\nint rear = index(front + queSize);\n// \u5c06 num \u6dfb\u52a0\u81f3\u961f\u5c3e\nnums[rear] = num;\nqueSize++;\n}\n/* \u961f\u9996\u51fa\u961f */\nint popFirst() {\nint num = peekFirst();\n// \u961f\u9996\u6307\u9488\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\nfront = index(front + 1);\nqueSize--;\nreturn num;\n}\n/* \u961f\u5c3e\u51fa\u961f */\nint popLast() {\nint num = peekLast();\nqueSize--;\nreturn num;\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\nint peekFirst() {\nif (isEmpty())\nthrow out_of_range(\"\u53cc\u5411\u961f\u5217\u4e3a\u7a7a\");\nreturn nums[front];\n}\n/* \u8bbf\u95ee\u961f\u5c3e\u5143\u7d20 */\nint peekLast() {\nif (isEmpty())\nthrow out_of_range(\"\u53cc\u5411\u961f\u5217\u4e3a\u7a7a\");\n// \u8ba1\u7b97\u5c3e\u5143\u7d20\u7d22\u5f15\nint last = index(front + queSize - 1);\nreturn nums[last];\n}\n/* \u8fd4\u56de\u6570\u7ec4\u7528\u4e8e\u6253\u5370 */\nvector&lt;int&gt; toVector() {\n// \u4ec5\u8f6c\u6362\u6709\u6548\u957f\u5ea6\u8303\u56f4\u5185\u7684\u5217\u8868\u5143\u7d20\nvector&lt;int&gt; res(queSize);\nfor (int i = 0, j = front; i &lt; queSize; i++, j++) {\nres[i] = nums[index(j)];\n}\nreturn res;\n}\n};\n</code></pre> array_deque.py<pre><code>class ArrayDeque:\n\"\"\"\u57fa\u4e8e\u73af\u5f62\u6570\u7ec4\u5b9e\u73b0\u7684\u53cc\u5411\u961f\u5217\"\"\"\ndef __init__(self, capacity: int) -&gt; None:\n\"\"\"\u6784\u9020\u65b9\u6cd5\"\"\"\nself.__nums: list[int] = [0] * capacity\nself.__front: int = 0\nself.__size: int = 0\ndef capacity(self) -&gt; int:\n\"\"\"\u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u5bb9\u91cf\"\"\"\nreturn len(self.__nums)\ndef size(self) -&gt; int:\n\"\"\"\u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6\"\"\"\nreturn self.__size\ndef is_empty(self) -&gt; bool:\n\"\"\"\u5224\u65ad\u53cc\u5411\u961f\u5217\u662f\u5426\u4e3a\u7a7a\"\"\"\nreturn self.__size == 0\ndef index(self, i: int) -&gt; int:\n\"\"\"\u8ba1\u7b97\u73af\u5f62\u6570\u7ec4\u7d22\u5f15\"\"\"\n# \u901a\u8fc7\u53d6\u4f59\u64cd\u4f5c\u5b9e\u73b0\u6570\u7ec4\u9996\u5c3e\u76f8\u8fde\n# \u5f53 i \u8d8a\u8fc7\u6570\u7ec4\u5c3e\u90e8\u540e\uff0c\u56de\u5230\u5934\u90e8\n# \u5f53 i \u8d8a\u8fc7\u6570\u7ec4\u5934\u90e8\u540e\uff0c\u56de\u5230\u5c3e\u90e8\nreturn (i + self.capacity()) % self.capacity()\ndef push_first(self, num: int) -&gt; None:\n\"\"\"\u961f\u9996\u5165\u961f\"\"\"\nif self.__size == self.capacity():\nprint(\"\u53cc\u5411\u961f\u5217\u5df2\u6ee1\")\nreturn\n# \u961f\u9996\u6307\u9488\u5411\u5de6\u79fb\u52a8\u4e00\u4f4d\n# \u901a\u8fc7\u53d6\u4f59\u64cd\u4f5c\uff0c\u5b9e\u73b0 front \u8d8a\u8fc7\u6570\u7ec4\u5934\u90e8\u540e\u56de\u5230\u5c3e\u90e8\nself.__front = self.index(self.__front - 1)\n# \u5c06 num \u6dfb\u52a0\u81f3\u961f\u9996\nself.__nums[self.__front] = num\nself.__size += 1\ndef push_last(self, num: int) -&gt; None:\n\"\"\"\u961f\u5c3e\u5165\u961f\"\"\"\nif self.__size == self.capacity():\nprint(\"\u53cc\u5411\u961f\u5217\u5df2\u6ee1\")\nreturn\n# \u8ba1\u7b97\u5c3e\u6307\u9488\uff0c\u6307\u5411\u961f\u5c3e\u7d22\u5f15 + 1\nrear = self.index(self.__front + self.__size)\n# \u5c06 num \u6dfb\u52a0\u81f3\u961f\u5c3e\nself.__nums[rear] = num\nself.__size += 1\ndef pop_first(self) -&gt; int:\n\"\"\"\u961f\u9996\u51fa\u961f\"\"\"\nnum = self.peek_first()\n# \u961f\u9996\u6307\u9488\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\nself.__front = self.index(self.__front + 1)\nself.__size -= 1\nreturn num\ndef pop_last(self) -&gt; int:\n\"\"\"\u961f\u5c3e\u51fa\u961f\"\"\"\nnum = self.peek_last()\nself.__size -= 1\nreturn num\ndef peek_first(self) -&gt; int:\n\"\"\"\u8bbf\u95ee\u961f\u9996\u5143\u7d20\"\"\"\nif self.is_empty():\nraise IndexError(\"\u53cc\u5411\u961f\u5217\u4e3a\u7a7a\")\nreturn self.__nums[self.__front]\ndef peek_last(self) -&gt; int:\n\"\"\"\u8bbf\u95ee\u961f\u5c3e\u5143\u7d20\"\"\"\nif self.is_empty():\nraise IndexError(\"\u53cc\u5411\u961f\u5217\u4e3a\u7a7a\")\n# \u8ba1\u7b97\u5c3e\u5143\u7d20\u7d22\u5f15\nlast = self.index(self.__front + self.__size - 1)\nreturn self.__nums[last]\ndef to_array(self) -&gt; list[int]:\n\"\"\"\u8fd4\u56de\u6570\u7ec4\u7528\u4e8e\u6253\u5370\"\"\"\n# \u4ec5\u8f6c\u6362\u6709\u6548\u957f\u5ea6\u8303\u56f4\u5185\u7684\u5217\u8868\u5143\u7d20\nres = []\nfor i in range(self.__size):\nres.append(self.__nums[self.index(self.__front + i)])\nreturn res\n</code></pre> array_deque.go<pre><code>/* \u57fa\u4e8e\u73af\u5f62\u6570\u7ec4\u5b9e\u73b0\u7684\u53cc\u5411\u961f\u5217 */\ntype arrayDeque struct {\nnums        []int // \u7528\u4e8e\u5b58\u50a8\u53cc\u5411\u961f\u5217\u5143\u7d20\u7684\u6570\u7ec4\nfront       int   // \u961f\u9996\u6307\u9488\uff0c\u6307\u5411\u961f\u9996\u5143\u7d20\nqueSize     int   // \u53cc\u5411\u961f\u5217\u957f\u5ea6\nqueCapacity int   // \u961f\u5217\u5bb9\u91cf\uff08\u5373\u6700\u5927\u5bb9\u7eb3\u5143\u7d20\u6570\u91cf\uff09\n}\n/* \u521d\u59cb\u5316\u961f\u5217 */\nfunc newArrayDeque(queCapacity int) *arrayDeque {\nreturn &amp;arrayDeque{\nnums:        make([]int, queCapacity),\nqueCapacity: queCapacity,\nfront:       0,\nqueSize:     0,\n}\n}\n/* \u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6 */\nfunc (q *arrayDeque) size() int {\nreturn q.queSize\n}\n/* \u5224\u65ad\u53cc\u5411\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nfunc (q *arrayDeque) isEmpty() bool {\nreturn q.queSize == 0\n}\n/* \u8ba1\u7b97\u73af\u5f62\u6570\u7ec4\u7d22\u5f15 */\nfunc (q *arrayDeque) index(i int) int {\n// \u901a\u8fc7\u53d6\u4f59\u64cd\u4f5c\u5b9e\u73b0\u6570\u7ec4\u9996\u5c3e\u76f8\u8fde\n// \u5f53 i \u8d8a\u8fc7\u6570\u7ec4\u5c3e\u90e8\u540e\uff0c\u56de\u5230\u5934\u90e8\n// \u5f53 i \u8d8a\u8fc7\u6570\u7ec4\u5934\u90e8\u540e\uff0c\u56de\u5230\u5c3e\u90e8\nreturn (i + q.queCapacity) % q.queCapacity\n}\n/* \u961f\u9996\u5165\u961f */\nfunc (q *arrayDeque) pushFirst(num int) {\nif q.queSize == q.queCapacity {\nfmt.Println(\"\u53cc\u5411\u961f\u5217\u5df2\u6ee1\")\nreturn\n}\n// \u961f\u9996\u6307\u9488\u5411\u5de6\u79fb\u52a8\u4e00\u4f4d\n// \u901a\u8fc7\u53d6\u4f59\u64cd\u4f5c\uff0c\u5b9e\u73b0 front \u8d8a\u8fc7\u6570\u7ec4\u5934\u90e8\u540e\u56de\u5230\u5c3e\u90e8\nq.front = q.index(q.front - 1)\n// \u5c06 num \u6dfb\u52a0\u81f3\u961f\u9996\nq.nums[q.front] = num\nq.queSize++\n}\n/* \u961f\u5c3e\u5165\u961f */\nfunc (q *arrayDeque) pushLast(num int) {\nif q.queSize == q.queCapacity {\nfmt.Println(\"\u53cc\u5411\u961f\u5217\u5df2\u6ee1\")\nreturn\n}\n// \u8ba1\u7b97\u5c3e\u6307\u9488\uff0c\u6307\u5411\u961f\u5c3e\u7d22\u5f15 + 1\nrear := q.index(q.front + q.queSize)\n// \u5c06 num \u6dfb\u52a0\u81f3\u961f\u9996\nq.nums[rear] = num\nq.queSize++\n}\n/* \u961f\u9996\u51fa\u961f */\nfunc (q *arrayDeque) popFirst() any {\nnum := q.peekFirst()\n// \u961f\u9996\u6307\u9488\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\nq.front = q.index(q.front + 1)\nq.queSize--\nreturn num\n}\n/* \u961f\u5c3e\u51fa\u961f */\nfunc (q *arrayDeque) popLast() any {\nnum := q.peekLast()\nq.queSize--\nreturn num\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\nfunc (q *arrayDeque) peekFirst() any {\nif q.isEmpty() {\nreturn nil\n}\nreturn q.nums[q.front]\n}\n/* \u8bbf\u95ee\u961f\u5c3e\u5143\u7d20 */\nfunc (q *arrayDeque) peekLast() any {\nif q.isEmpty() {\nreturn nil\n}\n// \u8ba1\u7b97\u5c3e\u5143\u7d20\u7d22\u5f15\nlast := q.index(q.front + q.queSize - 1)\nreturn q.nums[last]\n}\n/* \u83b7\u53d6 Slice \u7528\u4e8e\u6253\u5370 */\nfunc (q *arrayDeque) toSlice() []int {\n// \u4ec5\u8f6c\u6362\u6709\u6548\u957f\u5ea6\u8303\u56f4\u5185\u7684\u5217\u8868\u5143\u7d20\nres := make([]int, q.queSize)\nfor i, j := 0, q.front; i &lt; q.queSize; i++ {\nres[i] = q.nums[q.index(j)]\nj++\n}\nreturn res\n}\n</code></pre> array_deque.js<pre><code>/* \u57fa\u4e8e\u73af\u5f62\u6570\u7ec4\u5b9e\u73b0\u7684\u53cc\u5411\u961f\u5217 */\nclass ArrayDeque {\n#nums; // \u7528\u4e8e\u5b58\u50a8\u53cc\u5411\u961f\u5217\u5143\u7d20\u7684\u6570\u7ec4\n#front; // \u961f\u9996\u6307\u9488\uff0c\u6307\u5411\u961f\u9996\u5143\u7d20\n#queSize; // \u53cc\u5411\u961f\u5217\u957f\u5ea6\n/* \u6784\u9020\u65b9\u6cd5 */\nconstructor(capacity) {\nthis.#nums = new Array(capacity);\nthis.#front = 0;\nthis.#queSize = 0;\n}\n/* \u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u5bb9\u91cf */\ncapacity() {\nreturn this.#nums.length;\n}\n/* \u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6 */\nsize() {\nreturn this.#queSize;\n}\n/* \u5224\u65ad\u53cc\u5411\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nisEmpty() {\nreturn this.#queSize === 0;\n}\n/* \u8ba1\u7b97\u73af\u5f62\u6570\u7ec4\u7d22\u5f15 */\nindex(i) {\n// \u901a\u8fc7\u53d6\u4f59\u64cd\u4f5c\u5b9e\u73b0\u6570\u7ec4\u9996\u5c3e\u76f8\u8fde\n// \u5f53 i \u8d8a\u8fc7\u6570\u7ec4\u5c3e\u90e8\u540e\uff0c\u56de\u5230\u5934\u90e8\n// \u5f53 i \u8d8a\u8fc7\u6570\u7ec4\u5934\u90e8\u540e\uff0c\u56de\u5230\u5c3e\u90e8\nreturn (i + this.capacity()) % this.capacity();\n}\n/* \u961f\u9996\u5165\u961f */\npushFirst(num) {\nif (this.#queSize === this.capacity()) {\nconsole.log('\u53cc\u5411\u961f\u5217\u5df2\u6ee1');\nreturn;\n}\n// \u961f\u9996\u6307\u9488\u5411\u5de6\u79fb\u52a8\u4e00\u4f4d\n// \u901a\u8fc7\u53d6\u4f59\u64cd\u4f5c\uff0c\u5b9e\u73b0 front \u8d8a\u8fc7\u6570\u7ec4\u5934\u90e8\u540e\u56de\u5230\u5c3e\u90e8\nthis.#front = this.index(this.#front - 1);\n// \u5c06 num \u6dfb\u52a0\u81f3\u961f\u9996\nthis.#nums[this.#front] = num;\nthis.#queSize++;\n}\n/* \u961f\u5c3e\u5165\u961f */\npushLast(num) {\nif (this.#queSize === this.capacity()) {\nconsole.log('\u53cc\u5411\u961f\u5217\u5df2\u6ee1');\nreturn;\n}\n// \u8ba1\u7b97\u5c3e\u6307\u9488\uff0c\u6307\u5411\u961f\u5c3e\u7d22\u5f15 + 1\nconst rear = this.index(this.#front + this.#queSize);\n// \u5c06 num \u6dfb\u52a0\u81f3\u961f\u5c3e\nthis.#nums[rear] = num;\nthis.#queSize++;\n}\n/* \u961f\u9996\u51fa\u961f */\npopFirst() {\nconst num = this.peekFirst();\n// \u961f\u9996\u6307\u9488\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\nthis.#front = this.index(this.#front + 1);\nthis.#queSize--;\nreturn num;\n}\n/* \u961f\u5c3e\u51fa\u961f */\npopLast() {\nconst num = this.peekLast();\nthis.#queSize--;\nreturn num;\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\npeekFirst() {\nif (this.isEmpty()) throw new Error('The Deque Is Empty.');\nreturn this.#nums[this.#front];\n}\n/* \u8bbf\u95ee\u961f\u5c3e\u5143\u7d20 */\npeekLast() {\nif (this.isEmpty()) throw new Error('The Deque Is Empty.');\n// \u8ba1\u7b97\u5c3e\u5143\u7d20\u7d22\u5f15\nconst last = this.index(this.#front + this.#queSize - 1);\nreturn this.#nums[last];\n}\n/* \u8fd4\u56de\u6570\u7ec4\u7528\u4e8e\u6253\u5370 */\ntoArray() {\n// \u4ec5\u8f6c\u6362\u6709\u6548\u957f\u5ea6\u8303\u56f4\u5185\u7684\u5217\u8868\u5143\u7d20\nconst res = [];\nfor (let i = 0, j = this.#front; i &lt; this.#queSize; i++, j++) {\nres[i] = this.#nums[this.index(j)];\n}\nreturn res;\n}\n}\n</code></pre> array_deque.ts<pre><code>/* \u57fa\u4e8e\u73af\u5f62\u6570\u7ec4\u5b9e\u73b0\u7684\u53cc\u5411\u961f\u5217 */\nclass ArrayDeque {\nprivate nums: number[]; // \u7528\u4e8e\u5b58\u50a8\u53cc\u5411\u961f\u5217\u5143\u7d20\u7684\u6570\u7ec4\nprivate front: number; // \u961f\u9996\u6307\u9488\uff0c\u6307\u5411\u961f\u9996\u5143\u7d20\nprivate queSize: number; // \u53cc\u5411\u961f\u5217\u957f\u5ea6\n/* \u6784\u9020\u65b9\u6cd5 */\nconstructor(capacity: number) {\nthis.nums = new Array(capacity);\nthis.front = 0;\nthis.queSize = 0;\n}\n/* \u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u5bb9\u91cf */\ncapacity(): number {\nreturn this.nums.length;\n}\n/* \u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6 */\nsize(): number {\nreturn this.queSize;\n}\n/* \u5224\u65ad\u53cc\u5411\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nisEmpty(): boolean {\nreturn this.queSize === 0;\n}\n/* \u8ba1\u7b97\u73af\u5f62\u6570\u7ec4\u7d22\u5f15 */\nindex(i: number): number {\n// \u901a\u8fc7\u53d6\u4f59\u64cd\u4f5c\u5b9e\u73b0\u6570\u7ec4\u9996\u5c3e\u76f8\u8fde\n// \u5f53 i \u8d8a\u8fc7\u6570\u7ec4\u5c3e\u90e8\u540e\uff0c\u56de\u5230\u5934\u90e8\n// \u5f53 i \u8d8a\u8fc7\u6570\u7ec4\u5934\u90e8\u540e\uff0c\u56de\u5230\u5c3e\u90e8\nreturn (i + this.capacity()) % this.capacity();\n}\n/* \u961f\u9996\u5165\u961f */\npushFirst(num: number): void {\nif (this.queSize === this.capacity()) {\nconsole.log('\u53cc\u5411\u961f\u5217\u5df2\u6ee1');\nreturn;\n}\n// \u961f\u9996\u6307\u9488\u5411\u5de6\u79fb\u52a8\u4e00\u4f4d\n// \u901a\u8fc7\u53d6\u4f59\u64cd\u4f5c\uff0c\u5b9e\u73b0 front \u8d8a\u8fc7\u6570\u7ec4\u5934\u90e8\u540e\u56de\u5230\u5c3e\u90e8\nthis.front = this.index(this.front - 1);\n// \u5c06 num \u6dfb\u52a0\u81f3\u961f\u9996\nthis.nums[this.front] = num;\nthis.queSize++;\n}\n/* \u961f\u5c3e\u5165\u961f */\npushLast(num: number): void {\nif (this.queSize === this.capacity()) {\nconsole.log('\u53cc\u5411\u961f\u5217\u5df2\u6ee1');\nreturn;\n}\n// \u8ba1\u7b97\u5c3e\u6307\u9488\uff0c\u6307\u5411\u961f\u5c3e\u7d22\u5f15 + 1\nconst rear: number = this.index(this.front + this.queSize);\n// \u5c06 num \u6dfb\u52a0\u81f3\u961f\u5c3e\nthis.nums[rear] = num;\nthis.queSize++;\n}\n/* \u961f\u9996\u51fa\u961f */\npopFirst(): number {\nconst num: number = this.peekFirst();\n// \u961f\u9996\u6307\u9488\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\nthis.front = this.index(this.front + 1);\nthis.queSize--;\nreturn num;\n}\n/* \u961f\u5c3e\u51fa\u961f */\npopLast(): number {\nconst num: number = this.peekLast();\nthis.queSize--;\nreturn num;\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\npeekFirst(): number {\nif (this.isEmpty()) throw new Error('The Deque Is Empty.');\nreturn this.nums[this.front];\n}\n/* \u8bbf\u95ee\u961f\u5c3e\u5143\u7d20 */\npeekLast(): number {\nif (this.isEmpty()) throw new Error('The Deque Is Empty.');\n// \u8ba1\u7b97\u5c3e\u5143\u7d20\u7d22\u5f15\nconst last = this.index(this.front + this.queSize - 1);\nreturn this.nums[last];\n}\n/* \u8fd4\u56de\u6570\u7ec4\u7528\u4e8e\u6253\u5370 */\ntoArray(): number[] {\n// \u4ec5\u8f6c\u6362\u6709\u6548\u957f\u5ea6\u8303\u56f4\u5185\u7684\u5217\u8868\u5143\u7d20\nconst res: number[] = [];\nfor (let i = 0, j = this.front; i &lt; this.queSize; i++, j++) {\nres[i] = this.nums[this.index(j)];\n}\nreturn res;\n}\n}\n</code></pre> array_deque.c<pre><code>/* \u57fa\u4e8e\u73af\u5f62\u6570\u7ec4\u5b9e\u73b0\u7684\u53cc\u5411\u961f\u5217 */\nstruct arrayDeque {\nint *nums;       // \u7528\u4e8e\u5b58\u50a8\u961f\u5217\u5143\u7d20\u7684\u6570\u7ec4\nint front;       // \u961f\u9996\u6307\u9488\uff0c\u6307\u5411\u961f\u9996\u5143\u7d20\nint queSize;     // \u5c3e\u6307\u9488\uff0c\u6307\u5411\u961f\u5c3e + 1\nint queCapacity; // \u961f\u5217\u5bb9\u91cf\n};\ntypedef struct arrayDeque arrayDeque;\n/* \u6784\u9020\u51fd\u6570 */\narrayDeque *newArrayDeque(int capacity) {\narrayDeque *deque = (arrayDeque *)malloc(sizeof(arrayDeque));\n// \u521d\u59cb\u5316\u6570\u7ec4\ndeque-&gt;queCapacity = capacity;\ndeque-&gt;nums = (int *)malloc(sizeof(int) * deque-&gt;queCapacity);\ndeque-&gt;front = deque-&gt;queSize = 0;\nreturn deque;\n}\n/* \u6790\u6784\u51fd\u6570 */\nvoid delArrayDeque(arrayDeque *deque) {\nfree(deque-&gt;nums);\ndeque-&gt;queCapacity = 0;\n}\n/* \u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u5bb9\u91cf */\nint capacity(arrayDeque *deque) {\nreturn deque-&gt;queCapacity;\n}\n/* \u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6 */\nint size(arrayDeque *deque) {\nreturn deque-&gt;queSize;\n}\n/* \u5224\u65ad\u53cc\u5411\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nbool empty(arrayDeque *deque) {\nreturn deque-&gt;queSize == 0;\n}\n/* \u8ba1\u7b97\u73af\u5f62\u6570\u7ec4\u7d22\u5f15 */\nint dequeIndex(arrayDeque *deque, int i) {\n// \u901a\u8fc7\u53d6\u4f59\u64cd\u4f5c\u5b9e\u73b0\u6570\u7ec4\u9996\u5c3e\u76f8\u8fde\n// \u5f53 i \u8d8a\u8fc7\u6570\u7ec4\u5c3e\u90e8\u65f6\uff0c\u56de\u5230\u5934\u90e8\n// \u5f53 i \u8d8a\u8fc7\u6570\u7ec4\u5934\u90e8\u540e\uff0c\u56de\u5230\u5c3e\u90e8\nreturn ((i + capacity(deque)) % capacity(deque));\n}\n/* \u961f\u9996\u5165\u961f */\nvoid pushFirst(arrayDeque *deque, int num) {\nif (deque-&gt;queSize == capacity(deque)) {\nprintf(\"\u53cc\u5411\u961f\u5217\u5df2\u6ee1\\r\\n\");\nreturn;\n}\n// \u961f\u9996\u6307\u9488\u5411\u5de6\u79fb\u52a8\u4e00\u4f4d\n// \u901a\u8fc7\u53d6\u4f59\u64cd\u4f5c\uff0c\u5b9e\u73b0 front \u8d8a\u8fc7\u6570\u7ec4\u5934\u90e8\u56de\u5230\u5c3e\u90e8\ndeque-&gt;front = dequeIndex(deque, deque-&gt;front - 1);\n// \u5c06 num \u6dfb\u52a0\u5230\u961f\u9996\ndeque-&gt;nums[deque-&gt;front] = num;\ndeque-&gt;queSize++;\n}\n/* \u961f\u5c3e\u5165\u961f */\nvoid pushLast(arrayDeque *deque, int num) {\nif (deque-&gt;queSize == capacity(deque)) {\nprintf(\"\u53cc\u5411\u961f\u5217\u5df2\u6ee1\\r\\n\");\nreturn;\n}\n// \u8ba1\u7b97\u5c3e\u6307\u9488\uff0c\u6307\u5411\u961f\u5c3e\u7d22\u5f15 + 1\nint rear = dequeIndex(deque, deque-&gt;front + deque-&gt;queSize);\n// \u5c06 num \u6dfb\u52a0\u81f3\u961f\u5c3e\ndeque-&gt;nums[rear] = num;\ndeque-&gt;queSize++;\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\nint peekFirst(arrayDeque *deque) {\n// \u8bbf\u95ee\u5f02\u5e38\uff1a\u53cc\u5411\u961f\u5217\u4e3a\u7a7a\nassert(empty(deque) == 0);\nreturn deque-&gt;nums[deque-&gt;front];\n}\n/* \u8bbf\u95ee\u961f\u5c3e\u5143\u7d20 */\nint peekLast(arrayDeque *deque) {\n// \u8bbf\u95ee\u5f02\u5e38\uff1a\u53cc\u5411\u961f\u5217\u4e3a\u7a7a\nassert(empty(deque) == 0);\nint last = dequeIndex(deque, deque-&gt;front + deque-&gt;queSize - 1);\nreturn deque-&gt;nums[last];\n}\n/* \u961f\u9996\u51fa\u961f */\nint popFirst(arrayDeque *deque) {\nint num = peekFirst(deque);\n// \u961f\u9996\u6307\u9488\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\ndeque-&gt;front = dequeIndex(deque, deque-&gt;front + 1);\ndeque-&gt;queSize--;\nreturn num;\n}\n/* \u961f\u5c3e\u51fa\u961f */\nint popLast(arrayDeque *deque) {\nint num = peekLast(deque);\ndeque-&gt;queSize--;\nreturn num;\n}\n/* \u6253\u5370\u961f\u5217 */\nvoid printArrayDeque(arrayDeque *deque) {\nint arr[deque-&gt;queSize];\n// \u62f7\u8d1d\nfor (int i = 0, j = deque-&gt;front; i &lt; deque-&gt;queSize; i++, j++) {\narr[i] = deque-&gt;nums[j % deque-&gt;queCapacity];\n}\nprintArray(arr, deque-&gt;queSize);\n}\n</code></pre> array_deque.cs<pre><code>/* \u57fa\u4e8e\u73af\u5f62\u6570\u7ec4\u5b9e\u73b0\u7684\u53cc\u5411\u961f\u5217 */\nclass ArrayDeque {\nprivate readonly int[] nums;  // \u7528\u4e8e\u5b58\u50a8\u53cc\u5411\u961f\u5217\u5143\u7d20\u7684\u6570\u7ec4\nprivate int front;   // \u961f\u9996\u6307\u9488\uff0c\u6307\u5411\u961f\u9996\u5143\u7d20\nprivate int queSize; // \u53cc\u5411\u961f\u5217\u957f\u5ea6\n/* \u6784\u9020\u65b9\u6cd5 */\npublic ArrayDeque(int capacity) {\nthis.nums = new int[capacity];\nfront = queSize = 0;\n}\n/* \u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u5bb9\u91cf */\npublic int capacity() {\nreturn nums.Length;\n}\n/* \u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6 */\npublic int size() {\nreturn queSize;\n}\n/* \u5224\u65ad\u53cc\u5411\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\npublic bool isEmpty() {\nreturn queSize == 0;\n}\n/* \u8ba1\u7b97\u73af\u5f62\u6570\u7ec4\u7d22\u5f15 */\nprivate int index(int i) {\n// \u901a\u8fc7\u53d6\u4f59\u64cd\u4f5c\u5b9e\u73b0\u6570\u7ec4\u9996\u5c3e\u76f8\u8fde\n// \u5f53 i \u8d8a\u8fc7\u6570\u7ec4\u5c3e\u90e8\u540e\uff0c\u56de\u5230\u5934\u90e8\n// \u5f53 i \u8d8a\u8fc7\u6570\u7ec4\u5934\u90e8\u540e\uff0c\u56de\u5230\u5c3e\u90e8\nreturn (i + capacity()) % capacity();\n}\n/* \u961f\u9996\u5165\u961f */\npublic void pushFirst(int num) {\nif (queSize == capacity()) {\nConsole.WriteLine(\"\u53cc\u5411\u961f\u5217\u5df2\u6ee1\");\nreturn;\n}\n// \u961f\u9996\u6307\u9488\u5411\u5de6\u79fb\u52a8\u4e00\u4f4d\n// \u901a\u8fc7\u53d6\u4f59\u64cd\u4f5c\uff0c\u5b9e\u73b0 front \u8d8a\u8fc7\u6570\u7ec4\u5934\u90e8\u540e\u56de\u5230\u5c3e\u90e8\nfront = index(front - 1);\n// \u5c06 num \u6dfb\u52a0\u81f3\u961f\u9996\nnums[front] = num;\nqueSize++;\n}\n/* \u961f\u5c3e\u5165\u961f */\npublic void pushLast(int num) {\nif (queSize == capacity()) {\nConsole.WriteLine(\"\u53cc\u5411\u961f\u5217\u5df2\u6ee1\");\nreturn;\n}\n// \u8ba1\u7b97\u5c3e\u6307\u9488\uff0c\u6307\u5411\u961f\u5c3e\u7d22\u5f15 + 1\nint rear = index(front + queSize);\n// \u5c06 num \u6dfb\u52a0\u81f3\u961f\u5c3e\nnums[rear] = num;\nqueSize++;\n}\n/* \u961f\u9996\u51fa\u961f */\npublic int popFirst() {\nint num = peekFirst();\n// \u961f\u9996\u6307\u9488\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\nfront = index(front + 1);\nqueSize--;\nreturn num;\n}\n/* \u961f\u5c3e\u51fa\u961f */\npublic int popLast() {\nint num = peekLast();\nqueSize--;\nreturn num;\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\npublic int peekFirst() {\nif (isEmpty()) {\nthrow new InvalidOperationException();\n}\nreturn nums[front];\n}\n/* \u8bbf\u95ee\u961f\u5c3e\u5143\u7d20 */\npublic int peekLast() {\nif (isEmpty()) {\nthrow new InvalidOperationException();\n}\n// \u8ba1\u7b97\u5c3e\u5143\u7d20\u7d22\u5f15\nint last = index(front + queSize - 1);\nreturn nums[last];\n}\n/* \u8fd4\u56de\u6570\u7ec4\u7528\u4e8e\u6253\u5370 */\npublic int[] toArray() {\n// \u4ec5\u8f6c\u6362\u6709\u6548\u957f\u5ea6\u8303\u56f4\u5185\u7684\u5217\u8868\u5143\u7d20\nint[] res = new int[queSize];\nfor (int i = 0, j = front; i &lt; queSize; i++, j++) {\nres[i] = nums[index(j)];\n}\nreturn res;\n}\n}\n</code></pre> array_deque.swift<pre><code>/* \u57fa\u4e8e\u73af\u5f62\u6570\u7ec4\u5b9e\u73b0\u7684\u53cc\u5411\u961f\u5217 */\nclass ArrayDeque {\nprivate var nums: [Int] // \u7528\u4e8e\u5b58\u50a8\u53cc\u5411\u961f\u5217\u5143\u7d20\u7684\u6570\u7ec4\nprivate var front: Int // \u961f\u9996\u6307\u9488\uff0c\u6307\u5411\u961f\u9996\u5143\u7d20\nprivate var queSize: Int // \u53cc\u5411\u961f\u5217\u957f\u5ea6\n/* \u6784\u9020\u65b9\u6cd5 */\ninit(capacity: Int) {\nnums = Array(repeating: 0, count: capacity)\nfront = 0\nqueSize = 0\n}\n/* \u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u5bb9\u91cf */\nfunc capacity() -&gt; Int {\nnums.count\n}\n/* \u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6 */\nfunc size() -&gt; Int {\nqueSize\n}\n/* \u5224\u65ad\u53cc\u5411\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nfunc isEmpty() -&gt; Bool {\nsize() == 0\n}\n/* \u8ba1\u7b97\u73af\u5f62\u6570\u7ec4\u7d22\u5f15 */\nprivate func index(i: Int) -&gt; Int {\n// \u901a\u8fc7\u53d6\u4f59\u64cd\u4f5c\u5b9e\u73b0\u6570\u7ec4\u9996\u5c3e\u76f8\u8fde\n// \u5f53 i \u8d8a\u8fc7\u6570\u7ec4\u5c3e\u90e8\u540e\uff0c\u56de\u5230\u5934\u90e8\n// \u5f53 i \u8d8a\u8fc7\u6570\u7ec4\u5934\u90e8\u540e\uff0c\u56de\u5230\u5c3e\u90e8\n(i + capacity()) % capacity()\n}\n/* \u961f\u9996\u5165\u961f */\nfunc pushFirst(num: Int) {\nif size() == capacity() {\nprint(\"\u53cc\u5411\u961f\u5217\u5df2\u6ee1\")\nreturn\n}\n// \u961f\u9996\u6307\u9488\u5411\u5de6\u79fb\u52a8\u4e00\u4f4d\n// \u901a\u8fc7\u53d6\u4f59\u64cd\u4f5c\uff0c\u5b9e\u73b0 front \u8d8a\u8fc7\u6570\u7ec4\u5934\u90e8\u540e\u56de\u5230\u5c3e\u90e8\nfront = index(i: front - 1)\n// \u5c06 num \u6dfb\u52a0\u81f3\u961f\u9996\nnums[front] = num\nqueSize += 1\n}\n/* \u961f\u5c3e\u5165\u961f */\nfunc pushLast(num: Int) {\nif size() == capacity() {\nprint(\"\u53cc\u5411\u961f\u5217\u5df2\u6ee1\")\nreturn\n}\n// \u8ba1\u7b97\u5c3e\u6307\u9488\uff0c\u6307\u5411\u961f\u5c3e\u7d22\u5f15 + 1\nlet rear = index(i: front + size())\n// \u5c06 num \u6dfb\u52a0\u81f3\u961f\u5c3e\nnums[rear] = num\nqueSize += 1\n}\n/* \u961f\u9996\u51fa\u961f */\nfunc popFirst() -&gt; Int {\nlet num = peekFirst()\n// \u961f\u9996\u6307\u9488\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\nfront = index(i: front + 1)\nqueSize -= 1\nreturn num\n}\n/* \u961f\u5c3e\u51fa\u961f */\nfunc popLast() -&gt; Int {\nlet num = peekLast()\nqueSize -= 1\nreturn num\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\nfunc peekFirst() -&gt; Int {\nif isEmpty() {\nfatalError(\"\u53cc\u5411\u961f\u5217\u4e3a\u7a7a\")\n}\nreturn nums[front]\n}\n/* \u8bbf\u95ee\u961f\u5c3e\u5143\u7d20 */\nfunc peekLast() -&gt; Int {\nif isEmpty() {\nfatalError(\"\u53cc\u5411\u961f\u5217\u4e3a\u7a7a\")\n}\n// \u8ba1\u7b97\u5c3e\u5143\u7d20\u7d22\u5f15\nlet last = index(i: front + size() - 1)\nreturn nums[last]\n}\n/* \u8fd4\u56de\u6570\u7ec4\u7528\u4e8e\u6253\u5370 */\nfunc toArray() -&gt; [Int] {\n// \u4ec5\u8f6c\u6362\u6709\u6548\u957f\u5ea6\u8303\u56f4\u5185\u7684\u5217\u8868\u5143\u7d20\nvar res = Array(repeating: 0, count: size())\nfor (i, j) in sequence(first: (0, front), next: { $0 &lt; self.size() - 1 ? ($0 + 1, $1 + 1) : nil }) {\nres[i] = nums[index(i: j)]\n}\nreturn res\n}\n}\n</code></pre> array_deque.zig<pre><code>[class]{ArrayDeque}-[func]{}\n</code></pre> array_deque.dart<pre><code>/* \u57fa\u4e8e\u73af\u5f62\u6570\u7ec4\u5b9e\u73b0\u7684\u53cc\u5411\u961f\u5217 */\nclass ArrayDeque {\nlate List&lt;int&gt; _nums; // \u7528\u4e8e\u5b58\u50a8\u53cc\u5411\u961f\u5217\u5143\u7d20\u7684\u6570\u7ec4\nlate int _front; // \u961f\u9996\u6307\u9488\uff0c\u6307\u5411\u961f\u9996\u5143\u7d20\nlate int _queSize; // \u53cc\u5411\u961f\u5217\u957f\u5ea6\n/* \u6784\u9020\u65b9\u6cd5 */\nArrayDeque(int capacity) {\nthis._nums = List.filled(capacity, 0);\nthis._front = this._queSize = 0;\n}\n/* \u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u5bb9\u91cf */\nint capacity() {\nreturn _nums.length;\n}\n/* \u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6 */\nint size() {\nreturn _queSize;\n}\n/* \u5224\u65ad\u53cc\u5411\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nbool isEmpty() {\nreturn _queSize == 0;\n}\n/* \u8ba1\u7b97\u73af\u5f62\u6570\u7ec4\u7d22\u5f15 */\nint index(int i) {\n// \u901a\u8fc7\u53d6\u4f59\u64cd\u4f5c\u5b9e\u73b0\u6570\u7ec4\u9996\u5c3e\u76f8\u8fde\n// \u5f53 i \u8d8a\u8fc7\u6570\u7ec4\u5c3e\u90e8\u540e\uff0c\u56de\u5230\u5934\u90e8\n// \u5f53 i \u8d8a\u8fc7\u6570\u7ec4\u5934\u90e8\u540e\uff0c\u56de\u5230\u5c3e\u90e8\nreturn (i + capacity()) % capacity();\n}\n/* \u961f\u9996\u5165\u961f */\nvoid pushFirst(int num) {\nif (_queSize == capacity()) {\nthrow Exception(\"\u53cc\u5411\u961f\u5217\u5df2\u6ee1\");\n}\n// \u961f\u9996\u6307\u9488\u5411\u5de6\u79fb\u52a8\u4e00\u4f4d\n// \u901a\u8fc7\u53d6\u4f59\u64cd\u4f5c\uff0c\u5b9e\u73b0 _front \u8d8a\u8fc7\u6570\u7ec4\u5934\u90e8\u540e\u56de\u5230\u5c3e\u90e8\n_front = index(_front - 1);\n// \u5c06 num \u6dfb\u52a0\u81f3\u961f\u9996\n_nums[_front] = num;\n_queSize++;\n}\n/* \u961f\u5c3e\u5165\u961f */\nvoid pushLast(int num) {\nif (_queSize == capacity()) {\nthrow Exception(\"\u53cc\u5411\u961f\u5217\u5df2\u6ee1\");\n}\n// \u8ba1\u7b97\u5c3e\u6307\u9488\uff0c\u6307\u5411\u961f\u5c3e\u7d22\u5f15 + 1\nint rear = index(_front + _queSize);\n// \u5c06 num \u6dfb\u52a0\u81f3\u961f\u5c3e\n_nums[rear] = num;\n_queSize++;\n}\n/* \u961f\u9996\u51fa\u961f */\nint popFirst() {\nint num = peekFirst();\n// \u961f\u9996\u6307\u9488\u5411\u53f3\u79fb\u52a8\u4e00\u4f4d\n_front = index(_front + 1);\n_queSize--;\nreturn num;\n}\n/* \u961f\u5c3e\u51fa\u961f */\nint popLast() {\nint num = peekLast();\n_queSize--;\nreturn num;\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\nint peekFirst() {\nif (isEmpty()) {\nthrow Exception(\"\u53cc\u5411\u961f\u5217\u4e3a\u7a7a\");\n}\nreturn _nums[_front];\n}\n/* \u8bbf\u95ee\u961f\u5c3e\u5143\u7d20 */\nint peekLast() {\nif (isEmpty()) {\nthrow Exception(\"\u53cc\u5411\u961f\u5217\u4e3a\u7a7a\");\n}\n// \u8ba1\u7b97\u5c3e\u5143\u7d20\u7d22\u5f15\nint last = index(_front + _queSize - 1);\nreturn _nums[last];\n}\n/* \u8fd4\u56de\u6570\u7ec4\u7528\u4e8e\u6253\u5370 */\nList&lt;int&gt; toArray() {\n// \u4ec5\u8f6c\u6362\u6709\u6548\u957f\u5ea6\u8303\u56f4\u5185\u7684\u5217\u8868\u5143\u7d20\nList&lt;int&gt; res = List.filled(_queSize, 0);\nfor (int i = 0, j = _front; i &lt; _queSize; i++, j++) {\nres[i] = _nums[index(j)];\n}\nreturn res;\n}\n}\n</code></pre>"},{"location":"chapter_stack_and_queue/deque/#533","title":"5.3.3. \u00a0 \u53cc\u5411\u961f\u5217\u5e94\u7528","text":"<p>\u53cc\u5411\u961f\u5217\u517c\u5177\u6808\u4e0e\u961f\u5217\u7684\u903b\u8f91\uff0c\u56e0\u6b64\u5b83\u53ef\u4ee5\u5b9e\u73b0\u8fd9\u4e24\u8005\u7684\u6240\u6709\u5e94\u7528\u573a\u666f\uff0c\u540c\u65f6\u63d0\u4f9b\u66f4\u9ad8\u7684\u81ea\u7531\u5ea6\u3002</p> <p>\u6211\u4eec\u77e5\u9053\uff0c\u8f6f\u4ef6\u7684\u201c\u64a4\u9500\u201d\u529f\u80fd\u901a\u5e38\u4f7f\u7528\u6808\u6765\u5b9e\u73b0\uff1a\u7cfb\u7edf\u5c06\u6bcf\u6b21\u66f4\u6539\u64cd\u4f5c <code>push</code> \u5230\u6808\u4e2d\uff0c\u7136\u540e\u901a\u8fc7 <code>pop</code> \u5b9e\u73b0\u64a4\u9500\u3002\u7136\u800c\uff0c\u8003\u8651\u5230\u7cfb\u7edf\u8d44\u6e90\u7684\u9650\u5236\uff0c\u8f6f\u4ef6\u901a\u5e38\u4f1a\u9650\u5236\u64a4\u9500\u7684\u6b65\u6570\uff08\u4f8b\u5982\u4ec5\u5141\u8bb8\u4fdd\u5b58 \\(50\\) \u6b65\uff09\u3002\u5f53\u6808\u7684\u957f\u5ea6\u8d85\u8fc7 \\(50\\) \u65f6\uff0c\u8f6f\u4ef6\u9700\u8981\u5728\u6808\u5e95\uff08\u5373\u961f\u9996\uff09\u6267\u884c\u5220\u9664\u64cd\u4f5c\u3002\u4f46\u6808\u65e0\u6cd5\u5b9e\u73b0\u8be5\u529f\u80fd\uff0c\u6b64\u65f6\u5c31\u9700\u8981\u4f7f\u7528\u53cc\u5411\u961f\u5217\u6765\u66ff\u4ee3\u6808\u3002\u8bf7\u6ce8\u610f\uff0c\u201c\u64a4\u9500\u201d\u7684\u6838\u5fc3\u903b\u8f91\u4ecd\u7136\u9075\u5faa\u6808\u7684\u5148\u5165\u540e\u51fa\u539f\u5219\uff0c\u53ea\u662f\u53cc\u5411\u961f\u5217\u80fd\u591f\u66f4\u52a0\u7075\u6d3b\u5730\u5b9e\u73b0\u4e00\u4e9b\u989d\u5916\u903b\u8f91\u3002</p>"},{"location":"chapter_stack_and_queue/queue/","title":"5.2. \u00a0 \u961f\u5217","text":"<p>\u300c\u961f\u5217 Queue\u300d\u662f\u4e00\u79cd\u9075\u5faa\u5148\u5165\u5148\u51fa\uff08First In, First Out\uff09\u89c4\u5219\u7684\u7ebf\u6027\u6570\u636e\u7ed3\u6784\u3002\u987e\u540d\u601d\u4e49\uff0c\u961f\u5217\u6a21\u62df\u4e86\u6392\u961f\u73b0\u8c61\uff0c\u5373\u65b0\u6765\u7684\u4eba\u4e0d\u65ad\u52a0\u5165\u961f\u5217\u7684\u5c3e\u90e8\uff0c\u800c\u4f4d\u4e8e\u961f\u5217\u5934\u90e8\u7684\u4eba\u9010\u4e2a\u79bb\u5f00\u3002</p> <p>\u6211\u4eec\u628a\u961f\u5217\u7684\u5934\u90e8\u79f0\u4e3a\u300c\u961f\u9996\u300d\uff0c\u5c3e\u90e8\u79f0\u4e3a\u300c\u961f\u5c3e\u300d\uff0c\u628a\u5c06\u5143\u7d20\u52a0\u5165\u961f\u5c3e\u7684\u64cd\u4f5c\u79f0\u4e3a\u300c\u5165\u961f\u300d\uff0c\u5220\u9664\u961f\u9996\u5143\u7d20\u7684\u64cd\u4f5c\u79f0\u4e3a\u300c\u51fa\u961f\u300d\u3002</p> <p></p> <p> Fig. \u961f\u5217\u7684\u5148\u5165\u5148\u51fa\u89c4\u5219 </p>"},{"location":"chapter_stack_and_queue/queue/#521","title":"5.2.1. \u00a0 \u961f\u5217\u5e38\u7528\u64cd\u4f5c","text":"<p>\u961f\u5217\u7684\u5e38\u89c1\u64cd\u4f5c\u5982\u4e0b\u8868\u6240\u793a\u3002\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u4e0d\u540c\u7f16\u7a0b\u8bed\u8a00\u7684\u65b9\u6cd5\u540d\u79f0\u53ef\u80fd\u4f1a\u6709\u6240\u4e0d\u540c\u3002\u6211\u4eec\u5728\u6b64\u91c7\u7528\u4e0e\u6808\u76f8\u540c\u7684\u65b9\u6cd5\u547d\u540d\u3002</p> \u65b9\u6cd5\u540d \u63cf\u8ff0 \u65f6\u95f4\u590d\u6742\u5ea6 push() \u5143\u7d20\u5165\u961f\uff0c\u5373\u5c06\u5143\u7d20\u6dfb\u52a0\u81f3\u961f\u5c3e \\(O(1)\\) pop() \u961f\u9996\u5143\u7d20\u51fa\u961f \\(O(1)\\) peek() \u8bbf\u95ee\u961f\u9996\u5143\u7d20 \\(O(1)\\) <p>\u6211\u4eec\u53ef\u4ee5\u76f4\u63a5\u4f7f\u7528\u7f16\u7a0b\u8bed\u8a00\u4e2d\u73b0\u6210\u7684\u961f\u5217\u7c7b\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart queue.java<pre><code>/* \u521d\u59cb\u5316\u961f\u5217 */\nQueue&lt;Integer&gt; queue = new LinkedList&lt;&gt;();\n/* \u5143\u7d20\u5165\u961f */\nqueue.offer(1);\nqueue.offer(3);\nqueue.offer(2);\nqueue.offer(5);\nqueue.offer(4);\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\nint peek = queue.peek();\n/* \u5143\u7d20\u51fa\u961f */\nint pop = queue.poll();\n/* \u83b7\u53d6\u961f\u5217\u7684\u957f\u5ea6 */\nint size = queue.size();\n/* \u5224\u65ad\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nboolean isEmpty = queue.isEmpty();\n</code></pre> queue.cpp<pre><code>/* \u521d\u59cb\u5316\u961f\u5217 */\nqueue&lt;int&gt; queue;\n/* \u5143\u7d20\u5165\u961f */\nqueue.push(1);\nqueue.push(3);\nqueue.push(2);\nqueue.push(5);\nqueue.push(4);\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\nint front = queue.front();\n/* \u5143\u7d20\u51fa\u961f */\nqueue.pop();\n/* \u83b7\u53d6\u961f\u5217\u7684\u957f\u5ea6 */\nint size = queue.size();\n/* \u5224\u65ad\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nbool empty = queue.empty();\n</code></pre> queue.py<pre><code># \u521d\u59cb\u5316\u961f\u5217\n# \u5728 Python \u4e2d\uff0c\u6211\u4eec\u4e00\u822c\u5c06\u53cc\u5411\u961f\u5217\u7c7b deque \u770b\u4f5c\u961f\u5217\u4f7f\u7528\n# \u867d\u7136 queue.Queue() \u662f\u7eaf\u6b63\u7684\u961f\u5217\u7c7b\uff0c\u4f46\u4e0d\u592a\u597d\u7528\uff0c\u56e0\u6b64\u4e0d\u5efa\u8bae\nque: Deque[int] = collections.deque()\n# \u5143\u7d20\u5165\u961f\nque.append(1)\nque.append(3)\nque.append(2)\nque.append(5)\nque.append(4)\n# \u8bbf\u95ee\u961f\u9996\u5143\u7d20\nfront: int = que[0];\n# \u5143\u7d20\u51fa\u961f\npop: int = que.popleft()\n# \u83b7\u53d6\u961f\u5217\u7684\u957f\u5ea6\nsize: int = len(que)\n# \u5224\u65ad\u961f\u5217\u662f\u5426\u4e3a\u7a7a\nis_empty: bool = len(que) == 0\n</code></pre> queue_test.go<pre><code>/* \u521d\u59cb\u5316\u961f\u5217 */\n// \u5728 Go \u4e2d\uff0c\u5c06 list \u4f5c\u4e3a\u961f\u5217\u6765\u4f7f\u7528\nqueue := list.New()\n/* \u5143\u7d20\u5165\u961f */\nqueue.PushBack(1)\nqueue.PushBack(3)\nqueue.PushBack(2)\nqueue.PushBack(5)\nqueue.PushBack(4)\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\npeek := queue.Front()\n/* \u5143\u7d20\u51fa\u961f */\npop := queue.Front()\nqueue.Remove(pop)\n/* \u83b7\u53d6\u961f\u5217\u7684\u957f\u5ea6 */\nsize := queue.Len()\n/* \u5224\u65ad\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nisEmpty := queue.Len() == 0\n</code></pre> queue.js<pre><code>/* \u521d\u59cb\u5316\u961f\u5217 */\n// JavaScript \u6ca1\u6709\u5185\u7f6e\u7684\u961f\u5217\uff0c\u53ef\u4ee5\u628a Array \u5f53\u4f5c\u961f\u5217\u6765\u4f7f\u7528\nconst queue = [];\n/* \u5143\u7d20\u5165\u961f */\nqueue.push(1);\nqueue.push(3);\nqueue.push(2);\nqueue.push(5);\nqueue.push(4);\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\nconst peek = queue[0];\n/* \u5143\u7d20\u51fa\u961f */\n// \u5e95\u5c42\u662f\u6570\u7ec4\uff0c\u56e0\u6b64 shift() \u65b9\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a O(n)\nconst pop = queue.shift();\n/* \u83b7\u53d6\u961f\u5217\u7684\u957f\u5ea6 */\nconst size = queue.length;\n/* \u5224\u65ad\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nconst empty = queue.length === 0;\n</code></pre> queue.ts<pre><code>/* \u521d\u59cb\u5316\u961f\u5217 */\n// TypeScript \u6ca1\u6709\u5185\u7f6e\u7684\u961f\u5217\uff0c\u53ef\u4ee5\u628a Array \u5f53\u4f5c\u961f\u5217\u6765\u4f7f\u7528 \nconst queue: number[] = [];\n/* \u5143\u7d20\u5165\u961f */\nqueue.push(1);\nqueue.push(3);\nqueue.push(2);\nqueue.push(5);\nqueue.push(4);\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\nconst peek = queue[0];\n/* \u5143\u7d20\u51fa\u961f */\n// \u5e95\u5c42\u662f\u6570\u7ec4\uff0c\u56e0\u6b64 shift() \u65b9\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a O(n)\nconst pop = queue.shift();\n/* \u83b7\u53d6\u961f\u5217\u7684\u957f\u5ea6 */\nconst size = queue.length;\n/* \u5224\u65ad\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nconst empty = queue.length === 0;\n</code></pre> queue.c<pre><code>// C \u672a\u63d0\u4f9b\u5185\u7f6e\u961f\u5217\n</code></pre> queue.cs<pre><code>/* \u521d\u59cb\u5316\u961f\u5217 */\nQueue&lt;int&gt; queue = new();\n/* \u5143\u7d20\u5165\u961f */\nqueue.Enqueue(1);\nqueue.Enqueue(3);\nqueue.Enqueue(2);\nqueue.Enqueue(5);\nqueue.Enqueue(4);\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\nint peek = queue.Peek();\n/* \u5143\u7d20\u51fa\u961f */\nint pop = queue.Dequeue();\n/* \u83b7\u53d6\u961f\u5217\u7684\u957f\u5ea6 */\nint size = queue.Count();\n/* \u5224\u65ad\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nbool isEmpty = queue.Count() == 0;\n</code></pre> queue.swift<pre><code>/* \u521d\u59cb\u5316\u961f\u5217 */\n// Swift \u6ca1\u6709\u5185\u7f6e\u7684\u961f\u5217\u7c7b\uff0c\u53ef\u4ee5\u628a Array \u5f53\u4f5c\u961f\u5217\u6765\u4f7f\u7528\nvar queue: [Int] = []\n/* \u5143\u7d20\u5165\u961f */\nqueue.append(1)\nqueue.append(3)\nqueue.append(2)\nqueue.append(5)\nqueue.append(4)\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\nlet peek = queue.first!\n/* \u5143\u7d20\u51fa\u961f */\n// \u7531\u4e8e\u662f\u6570\u7ec4\uff0c\u56e0\u6b64 removeFirst \u7684\u590d\u6742\u5ea6\u4e3a O(n)\nlet pool = queue.removeFirst()\n/* \u83b7\u53d6\u961f\u5217\u7684\u957f\u5ea6 */\nlet size = queue.count\n/* \u5224\u65ad\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nlet isEmpty = queue.isEmpty\n</code></pre> queue.zig<pre><code>\n</code></pre> queue.dart<pre><code>/* \u521d\u59cb\u5316\u961f\u5217 */\n// \u5728 Dart \u4e2d\uff0c\u961f\u5217\u7c7b Qeque \u662f\u53cc\u5411\u961f\u5217\uff0c\u4e5f\u53ef\u4f5c\u4e3a\u961f\u5217\u4f7f\u7528\nQueue&lt;int&gt; queue = Queue();\n/* \u5143\u7d20\u5165\u961f */\nqueue.add(1);\nqueue.add(3);\nqueue.add(2);\nqueue.add(5);\nqueue.add(4);\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\nint peek = queue.first;\n/* \u5143\u7d20\u51fa\u961f */\nint pop = queue.removeFirst();\n/* \u83b7\u53d6\u961f\u5217\u7684\u957f\u5ea6 */\nint size = queue.length;\n/* \u5224\u65ad\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nbool isEmpty = queue.isEmpty;\n</code></pre>"},{"location":"chapter_stack_and_queue/queue/#522","title":"5.2.2. \u00a0 \u961f\u5217\u5b9e\u73b0","text":"<p>\u4e3a\u4e86\u5b9e\u73b0\u961f\u5217\uff0c\u6211\u4eec\u9700\u8981\u4e00\u79cd\u6570\u636e\u7ed3\u6784\uff0c\u53ef\u4ee5\u5728\u4e00\u7aef\u6dfb\u52a0\u5143\u7d20\uff0c\u5e76\u5728\u53e6\u4e00\u7aef\u5220\u9664\u5143\u7d20\u3002\u56e0\u6b64\uff0c\u94fe\u8868\u548c\u6570\u7ec4\u90fd\u53ef\u4ee5\u7528\u6765\u5b9e\u73b0\u961f\u5217\u3002</p>"},{"location":"chapter_stack_and_queue/queue/#_1","title":"\u57fa\u4e8e\u94fe\u8868\u7684\u5b9e\u73b0","text":"<p>\u5bf9\u4e8e\u94fe\u8868\u5b9e\u73b0\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u94fe\u8868\u7684\u300c\u5934\u8282\u70b9\u300d\u548c\u300c\u5c3e\u8282\u70b9\u300d\u5206\u522b\u89c6\u4e3a\u961f\u9996\u548c\u961f\u5c3e\uff0c\u89c4\u5b9a\u961f\u5c3e\u4ec5\u53ef\u6dfb\u52a0\u8282\u70b9\uff0c\u800c\u961f\u9996\u4ec5\u53ef\u5220\u9664\u8282\u70b9\u3002</p> LinkedListQueuepush()pop() <p></p> <p></p> <p></p> <p>\u4ee5\u4e0b\u662f\u7528\u94fe\u8868\u5b9e\u73b0\u961f\u5217\u7684\u793a\u4f8b\u4ee3\u7801\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart linkedlist_queue.java<pre><code>/* \u57fa\u4e8e\u94fe\u8868\u5b9e\u73b0\u7684\u961f\u5217 */\nclass LinkedListQueue {\nprivate ListNode front, rear; // \u5934\u8282\u70b9 front \uff0c\u5c3e\u8282\u70b9 rear\nprivate int queSize = 0;\npublic LinkedListQueue() {\nfront = null;\nrear = null;\n}\n/* \u83b7\u53d6\u961f\u5217\u7684\u957f\u5ea6 */\npublic int size() {\nreturn queSize;\n}\n/* \u5224\u65ad\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\npublic boolean isEmpty() {\nreturn size() == 0;\n}\n/* \u5165\u961f */\npublic void push(int num) {\n// \u5c3e\u8282\u70b9\u540e\u6dfb\u52a0 num\nListNode node = new ListNode(num);\n// \u5982\u679c\u961f\u5217\u4e3a\u7a7a\uff0c\u5219\u4ee4\u5934\u3001\u5c3e\u8282\u70b9\u90fd\u6307\u5411\u8be5\u8282\u70b9\nif (front == null) {\nfront = node;\nrear = node;\n// \u5982\u679c\u961f\u5217\u4e0d\u4e3a\u7a7a\uff0c\u5219\u5c06\u8be5\u8282\u70b9\u6dfb\u52a0\u5230\u5c3e\u8282\u70b9\u540e\n} else {\nrear.next = node;\nrear = node;\n}\nqueSize++;\n}\n/* \u51fa\u961f */\npublic int pop() {\nint num = peek();\n// \u5220\u9664\u5934\u8282\u70b9\nfront = front.next;\nqueSize--;\nreturn num;\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\npublic int peek() {\nif (size() == 0)\nthrow new IndexOutOfBoundsException();\nreturn front.val;\n}\n/* \u5c06\u94fe\u8868\u8f6c\u5316\u4e3a Array \u5e76\u8fd4\u56de */\npublic int[] toArray() {\nListNode node = front;\nint[] res = new int[size()];\nfor (int i = 0; i &lt; res.length; i++) {\nres[i] = node.val;\nnode = node.next;\n}\nreturn res;\n}\n}\n</code></pre> linkedlist_queue.cpp<pre><code>/* \u57fa\u4e8e\u94fe\u8868\u5b9e\u73b0\u7684\u961f\u5217 */\nclass LinkedListQueue {\nprivate:\nListNode *front, *rear; // \u5934\u8282\u70b9 front \uff0c\u5c3e\u8282\u70b9 rear\nint queSize;\npublic:\nLinkedListQueue() {\nfront = nullptr;\nrear = nullptr;\nqueSize = 0;\n}\n~LinkedListQueue() {\n// \u904d\u5386\u94fe\u8868\u5220\u9664\u8282\u70b9\uff0c\u91ca\u653e\u5185\u5b58\nfreeMemoryLinkedList(front);\n}\n/* \u83b7\u53d6\u961f\u5217\u7684\u957f\u5ea6 */\nint size() {\nreturn queSize;\n}\n/* \u5224\u65ad\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nbool empty() {\nreturn queSize == 0;\n}\n/* \u5165\u961f */\nvoid push(int num) {\n// \u5c3e\u8282\u70b9\u540e\u6dfb\u52a0 num\nListNode *node = new ListNode(num);\n// \u5982\u679c\u961f\u5217\u4e3a\u7a7a\uff0c\u5219\u4ee4\u5934\u3001\u5c3e\u8282\u70b9\u90fd\u6307\u5411\u8be5\u8282\u70b9\nif (front == nullptr) {\nfront = node;\nrear = node;\n}\n// \u5982\u679c\u961f\u5217\u4e0d\u4e3a\u7a7a\uff0c\u5219\u5c06\u8be5\u8282\u70b9\u6dfb\u52a0\u5230\u5c3e\u8282\u70b9\u540e\nelse {\nrear-&gt;next = node;\nrear = node;\n}\nqueSize++;\n}\n/* \u51fa\u961f */\nvoid pop() {\nint num = peek();\n// \u5220\u9664\u5934\u8282\u70b9\nListNode *tmp = front;\nfront = front-&gt;next;\n// \u91ca\u653e\u5185\u5b58\ndelete tmp;\nqueSize--;\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\nint peek() {\nif (size() == 0)\nthrow out_of_range(\"\u961f\u5217\u4e3a\u7a7a\");\nreturn front-&gt;val;\n}\n/* \u5c06\u94fe\u8868\u8f6c\u5316\u4e3a Vector \u5e76\u8fd4\u56de */\nvector&lt;int&gt; toVector() {\nListNode *node = front;\nvector&lt;int&gt; res(size());\nfor (int i = 0; i &lt; res.size(); i++) {\nres[i] = node-&gt;val;\nnode = node-&gt;next;\n}\nreturn res;\n}\n};\n</code></pre> linkedlist_queue.py<pre><code>class LinkedListQueue:\n\"\"\"\u57fa\u4e8e\u94fe\u8868\u5b9e\u73b0\u7684\u961f\u5217\"\"\"\ndef __init__(self):\n\"\"\"\u6784\u9020\u65b9\u6cd5\"\"\"\nself.__front: ListNode | None = None  # \u5934\u8282\u70b9 front\nself.__rear: ListNode | None = None  # \u5c3e\u8282\u70b9 rear\nself.__size: int = 0\ndef size(self) -&gt; int:\n\"\"\"\u83b7\u53d6\u961f\u5217\u7684\u957f\u5ea6\"\"\"\nreturn self.__size\ndef is_empty(self) -&gt; bool:\n\"\"\"\u5224\u65ad\u961f\u5217\u662f\u5426\u4e3a\u7a7a\"\"\"\nreturn not self.__front\ndef push(self, num: int) -&gt; None:\n\"\"\"\u5165\u961f\"\"\"\n# \u5c3e\u8282\u70b9\u540e\u6dfb\u52a0 num\nnode = ListNode(num)\n# \u5982\u679c\u961f\u5217\u4e3a\u7a7a\uff0c\u5219\u4ee4\u5934\u3001\u5c3e\u8282\u70b9\u90fd\u6307\u5411\u8be5\u8282\u70b9\nif self.__front is None:\nself.__front = node\nself.__rear = node\n# \u5982\u679c\u961f\u5217\u4e0d\u4e3a\u7a7a\uff0c\u5219\u5c06\u8be5\u8282\u70b9\u6dfb\u52a0\u5230\u5c3e\u8282\u70b9\u540e\nelse:\nself.__rear.next = node\nself.__rear = node\nself.__size += 1\ndef pop(self) -&gt; int:\n\"\"\"\u51fa\u961f\"\"\"\nnum = self.peek()\n# \u5220\u9664\u5934\u8282\u70b9\nself.__front = self.__front.next\nself.__size -= 1\nreturn num\ndef peek(self) -&gt; int:\n\"\"\"\u8bbf\u95ee\u961f\u9996\u5143\u7d20\"\"\"\nif self.size() == 0:\nprint(\"\u961f\u5217\u4e3a\u7a7a\")\nreturn False\nreturn self.__front.val\ndef to_list(self) -&gt; list[int]:\n\"\"\"\u8f6c\u5316\u4e3a\u5217\u8868\u7528\u4e8e\u6253\u5370\"\"\"\nqueue = []\ntemp = self.__front\nwhile temp:\nqueue.append(temp.val)\ntemp = temp.next\nreturn queue\n</code></pre> linkedlist_queue.go<pre><code>/* \u57fa\u4e8e\u94fe\u8868\u5b9e\u73b0\u7684\u961f\u5217 */\ntype linkedListQueue struct {\n// \u4f7f\u7528\u5185\u7f6e\u5305 list \u6765\u5b9e\u73b0\u961f\u5217\ndata *list.List\n}\n/* \u521d\u59cb\u5316\u961f\u5217 */\nfunc newLinkedListQueue() *linkedListQueue {\nreturn &amp;linkedListQueue{\ndata: list.New(),\n}\n}\n/* \u5165\u961f */\nfunc (s *linkedListQueue) push(value any) {\ns.data.PushBack(value)\n}\n/* \u51fa\u961f */\nfunc (s *linkedListQueue) pop() any {\nif s.isEmpty() {\nreturn nil\n}\ne := s.data.Front()\ns.data.Remove(e)\nreturn e.Value\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\nfunc (s *linkedListQueue) peek() any {\nif s.isEmpty() {\nreturn nil\n}\ne := s.data.Front()\nreturn e.Value\n}\n/* \u83b7\u53d6\u961f\u5217\u7684\u957f\u5ea6 */\nfunc (s *linkedListQueue) size() int {\nreturn s.data.Len()\n}\n/* \u5224\u65ad\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nfunc (s *linkedListQueue) isEmpty() bool {\nreturn s.data.Len() == 0\n}\n/* \u83b7\u53d6 List \u7528\u4e8e\u6253\u5370 */\nfunc (s *linkedListQueue) toList() *list.List {\nreturn s.data\n}\n</code></pre> linkedlist_queue.js<pre><code>/* \u57fa\u4e8e\u94fe\u8868\u5b9e\u73b0\u7684\u961f\u5217 */\nclass LinkedListQueue {\n#front; // \u5934\u8282\u70b9 #front\n#rear; // \u5c3e\u8282\u70b9 #rear\n#queSize = 0;\nconstructor() {\nthis.#front = null;\nthis.#rear = null;\n}\n/* \u83b7\u53d6\u961f\u5217\u7684\u957f\u5ea6 */\nget size() {\nreturn this.#queSize;\n}\n/* \u5224\u65ad\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nisEmpty() {\nreturn this.size === 0;\n}\n/* \u5165\u961f */\npush(num) {\n// \u5c3e\u8282\u70b9\u540e\u6dfb\u52a0 num\nconst node = new ListNode(num);\n// \u5982\u679c\u961f\u5217\u4e3a\u7a7a\uff0c\u5219\u4ee4\u5934\u3001\u5c3e\u8282\u70b9\u90fd\u6307\u5411\u8be5\u8282\u70b9\nif (!this.#front) {\nthis.#front = node;\nthis.#rear = node;\n// \u5982\u679c\u961f\u5217\u4e0d\u4e3a\u7a7a\uff0c\u5219\u5c06\u8be5\u8282\u70b9\u6dfb\u52a0\u5230\u5c3e\u8282\u70b9\u540e\n} else {\nthis.#rear.next = node;\nthis.#rear = node;\n}\nthis.#queSize++;\n}\n/* \u51fa\u961f */\npop() {\nconst num = this.peek();\n// \u5220\u9664\u5934\u8282\u70b9\nthis.#front = this.#front.next;\nthis.#queSize--;\nreturn num;\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\npeek() {\nif (this.size === 0) throw new Error('\u961f\u5217\u4e3a\u7a7a');\nreturn this.#front.val;\n}\n/* \u5c06\u94fe\u8868\u8f6c\u5316\u4e3a Array \u5e76\u8fd4\u56de */\ntoArray() {\nlet node = this.#front;\nconst res = new Array(this.size);\nfor (let i = 0; i &lt; res.length; i++) {\nres[i] = node.val;\nnode = node.next;\n}\nreturn res;\n}\n}\n</code></pre> linkedlist_queue.ts<pre><code>/* \u57fa\u4e8e\u94fe\u8868\u5b9e\u73b0\u7684\u961f\u5217 */\nclass LinkedListQueue {\nprivate front: ListNode | null; // \u5934\u8282\u70b9 front\nprivate rear: ListNode | null; // \u5c3e\u8282\u70b9 rear\nprivate queSize: number = 0;\nconstructor() {\nthis.front = null;\nthis.rear = null;\n}\n/* \u83b7\u53d6\u961f\u5217\u7684\u957f\u5ea6 */\nget size(): number {\nreturn this.queSize;\n}\n/* \u5224\u65ad\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nisEmpty(): boolean {\nreturn this.size === 0;\n}\n/* \u5165\u961f */\npush(num: number): void {\n// \u5c3e\u8282\u70b9\u540e\u6dfb\u52a0 num\nconst node = new ListNode(num);\n// \u5982\u679c\u961f\u5217\u4e3a\u7a7a\uff0c\u5219\u4ee4\u5934\u3001\u5c3e\u8282\u70b9\u90fd\u6307\u5411\u8be5\u8282\u70b9\nif (!this.front) {\nthis.front = node;\nthis.rear = node;\n// \u5982\u679c\u961f\u5217\u4e0d\u4e3a\u7a7a\uff0c\u5219\u5c06\u8be5\u8282\u70b9\u6dfb\u52a0\u5230\u5c3e\u8282\u70b9\u540e\n} else {\nthis.rear!.next = node;\nthis.rear = node;\n}\nthis.queSize++;\n}\n/* \u51fa\u961f */\npop(): number {\nconst num = this.peek();\nif (!this.front) throw new Error('\u961f\u5217\u4e3a\u7a7a');\n// \u5220\u9664\u5934\u8282\u70b9\nthis.front = this.front.next;\nthis.queSize--;\nreturn num;\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\npeek(): number {\nif (this.size === 0) throw new Error('\u961f\u5217\u4e3a\u7a7a');\nreturn this.front!.val;\n}\n/* \u5c06\u94fe\u8868\u8f6c\u5316\u4e3a Array \u5e76\u8fd4\u56de */\ntoArray(): number[] {\nlet node = this.front;\nconst res = new Array&lt;number&gt;(this.size);\nfor (let i = 0; i &lt; res.length; i++) {\nres[i] = node!.val;\nnode = node!.next;\n}\nreturn res;\n}\n}\n</code></pre> linkedlist_queue.c<pre><code>/* \u57fa\u4e8e\u94fe\u8868\u5b9e\u73b0\u7684\u961f\u5217 */\nstruct linkedListQueue {\nListNode *front, *rear;\nint queSize;\n};\ntypedef struct linkedListQueue linkedListQueue;\n/* \u6784\u9020\u51fd\u6570 */\nlinkedListQueue *newLinkedListQueue() {\nlinkedListQueue *queue = (linkedListQueue *)malloc(sizeof(linkedListQueue));\nqueue-&gt;front = NULL;\nqueue-&gt;rear = NULL;\nqueue-&gt;queSize = 0;\nreturn queue;\n}\n/* \u6790\u6784\u51fd\u6570 */\nvoid delLinkedListQueue(linkedListQueue *queue) {\n// \u91ca\u653e\u6240\u6709\u8282\u70b9\nfor (int i = 0; i &lt; queue-&gt;queSize &amp;&amp; queue-&gt;front != NULL; i++) {\nListNode *tmp = queue-&gt;front;\nqueue-&gt;front = queue-&gt;front-&gt;next;\nfree(tmp);\n}\n// \u91ca\u653e queue \u7ed3\u6784\u4f53\nfree(queue);\n}\n/* \u83b7\u53d6\u961f\u5217\u7684\u957f\u5ea6 */\nint size(linkedListQueue *queue) {\nreturn queue-&gt;queSize;\n}\n/* \u5224\u65ad\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nbool empty(linkedListQueue *queue) {\nreturn (size(queue) == 0);\n}\n/* \u5165\u961f */\nvoid push(linkedListQueue *queue, int num) {\n// \u5c3e\u8282\u70b9\u5904\u6dfb\u52a0 node\nListNode *node = newListNode(num);\n// \u5982\u679c\u961f\u5217\u4e3a\u7a7a\uff0c\u5219\u4ee4\u5934\u3001\u5c3e\u8282\u70b9\u90fd\u6307\u5411\u8be5\u8282\u70b9\nif (queue-&gt;front == NULL) {\nqueue-&gt;front = node;\nqueue-&gt;rear = node;\n}\n// \u5982\u679c\u961f\u5217\u4e0d\u4e3a\u7a7a\uff0c\u5219\u5c06\u8be5\u8282\u70b9\u6dfb\u52a0\u5230\u5c3e\u8282\u70b9\u540e\nelse {\nqueue-&gt;rear-&gt;next = node;\nqueue-&gt;rear = node;\n}\nqueue-&gt;queSize++;\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\nint peek(linkedListQueue *queue) {\nassert(size(queue) &amp;&amp; queue-&gt;front);\nreturn queue-&gt;front-&gt;val;\n}\n/* \u51fa\u961f */\nvoid pop(linkedListQueue *queue) {\nint num = peek(queue);\nListNode *tmp = queue-&gt;front;\nqueue-&gt;front = queue-&gt;front-&gt;next;\nfree(tmp);\nqueue-&gt;queSize--;\n}\n/* \u6253\u5370\u961f\u5217 */\nvoid printLinkedListQueue(linkedListQueue *queue) {\nint arr[queue-&gt;queSize];\n// \u62f7\u8d1d\u94fe\u8868\u4e2d\u7684\u6570\u636e\u5230\u6570\u7ec4\nint i;\nListNode *node;\nfor (i = 0, node = queue-&gt;front; i &lt; queue-&gt;queSize &amp;&amp; queue-&gt;front != queue-&gt;rear; i++) {\narr[i] = node-&gt;val;\nnode = node-&gt;next;\n}\nprintArray(arr, queue-&gt;queSize);\n}\n</code></pre> linkedlist_queue.cs<pre><code>/* \u57fa\u4e8e\u94fe\u8868\u5b9e\u73b0\u7684\u961f\u5217 */\nclass LinkedListQueue {\nprivate ListNode? front, rear;  // \u5934\u8282\u70b9 front \uff0c\u5c3e\u8282\u70b9 rear \nprivate int queSize = 0;\npublic LinkedListQueue() {\nfront = null;\nrear = null;\n}\n/* \u83b7\u53d6\u961f\u5217\u7684\u957f\u5ea6 */\npublic int size() {\nreturn queSize;\n}\n/* \u5224\u65ad\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\npublic bool isEmpty() {\nreturn size() == 0;\n}\n/* \u5165\u961f */\npublic void push(int num) {\n// \u5c3e\u8282\u70b9\u540e\u6dfb\u52a0 num\nListNode node = new ListNode(num);\n// \u5982\u679c\u961f\u5217\u4e3a\u7a7a\uff0c\u5219\u4ee4\u5934\u3001\u5c3e\u8282\u70b9\u90fd\u6307\u5411\u8be5\u8282\u70b9\nif (front == null) {\nfront = node;\nrear = node;\n// \u5982\u679c\u961f\u5217\u4e0d\u4e3a\u7a7a\uff0c\u5219\u5c06\u8be5\u8282\u70b9\u6dfb\u52a0\u5230\u5c3e\u8282\u70b9\u540e\n} else if (rear != null) {\nrear.next = node;\nrear = node;\n}\nqueSize++;\n}\n/* \u51fa\u961f */\npublic int pop() {\nint num = peek();\n// \u5220\u9664\u5934\u8282\u70b9\nfront = front?.next;\nqueSize--;\nreturn num;\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\npublic int peek() {\nif (size() == 0 || front == null)\nthrow new Exception();\nreturn front.val;\n}\n/* \u5c06\u94fe\u8868\u8f6c\u5316\u4e3a Array \u5e76\u8fd4\u56de */\npublic int[] toArray() {\nif (front == null)\nreturn Array.Empty&lt;int&gt;();\nListNode node = front;\nint[] res = new int[size()];\nfor (int i = 0; i &lt; res.Length; i++) {\nres[i] = node.val;\nnode = node.next;\n}\nreturn res;\n}\n}\n</code></pre> linkedlist_queue.swift<pre><code>/* \u57fa\u4e8e\u94fe\u8868\u5b9e\u73b0\u7684\u961f\u5217 */\nclass LinkedListQueue {\nprivate var front: ListNode? // \u5934\u8282\u70b9\nprivate var rear: ListNode? // \u5c3e\u8282\u70b9\nprivate var _size = 0\ninit() {}\n/* \u83b7\u53d6\u961f\u5217\u7684\u957f\u5ea6 */\nfunc size() -&gt; Int {\n_size\n}\n/* \u5224\u65ad\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nfunc isEmpty() -&gt; Bool {\nsize() == 0\n}\n/* \u5165\u961f */\nfunc push(num: Int) {\n// \u5c3e\u8282\u70b9\u540e\u6dfb\u52a0 num\nlet node = ListNode(x: num)\n// \u5982\u679c\u961f\u5217\u4e3a\u7a7a\uff0c\u5219\u4ee4\u5934\u3001\u5c3e\u8282\u70b9\u90fd\u6307\u5411\u8be5\u8282\u70b9\nif front == nil {\nfront = node\nrear = node\n}\n// \u5982\u679c\u961f\u5217\u4e0d\u4e3a\u7a7a\uff0c\u5219\u5c06\u8be5\u8282\u70b9\u6dfb\u52a0\u5230\u5c3e\u8282\u70b9\u540e\nelse {\nrear?.next = node\nrear = node\n}\n_size += 1\n}\n/* \u51fa\u961f */\n@discardableResult\nfunc pop() -&gt; Int {\nlet num = peek()\n// \u5220\u9664\u5934\u8282\u70b9\nfront = front?.next\n_size -= 1\nreturn num\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\nfunc peek() -&gt; Int {\nif isEmpty() {\nfatalError(\"\u961f\u5217\u4e3a\u7a7a\")\n}\nreturn front!.val\n}\n/* \u5c06\u94fe\u8868\u8f6c\u5316\u4e3a Array \u5e76\u8fd4\u56de */\nfunc toArray() -&gt; [Int] {\nvar node = front\nvar res = Array(repeating: 0, count: size())\nfor i in res.indices {\nres[i] = node!.val\nnode = node?.next\n}\nreturn res\n}\n}\n</code></pre> linkedlist_queue.zig<pre><code>// \u57fa\u4e8e\u94fe\u8868\u5b9e\u73b0\u7684\u961f\u5217\nfn LinkedListQueue(comptime T: type) type {\nreturn struct {\nconst Self = @This();\nfront: ?*inc.ListNode(T) = null,                // \u5934\u8282\u70b9 front\nrear: ?*inc.ListNode(T) = null,                 // \u5c3e\u8282\u70b9 rear\nque_size: usize = 0,                             // \u961f\u5217\u7684\u957f\u5ea6\nmem_arena: ?std.heap.ArenaAllocator = null,\nmem_allocator: std.mem.Allocator = undefined,   // \u5185\u5b58\u5206\u914d\u5668\n// \u6784\u9020\u65b9\u6cd5\uff08\u5206\u914d\u5185\u5b58+\u521d\u59cb\u5316\u961f\u5217\uff09\npub fn init(self: *Self, allocator: std.mem.Allocator) !void {\nif (self.mem_arena == null) {\nself.mem_arena = std.heap.ArenaAllocator.init(allocator);\nself.mem_allocator = self.mem_arena.?.allocator();\n}\nself.front = null;\nself.rear = null;\nself.que_size = 0;\n}\n// \u6790\u6784\u65b9\u6cd5\uff08\u91ca\u653e\u5185\u5b58\uff09\npub fn deinit(self: *Self) void {\nif (self.mem_arena == null) return;\nself.mem_arena.?.deinit();\n}\n// \u83b7\u53d6\u961f\u5217\u7684\u957f\u5ea6\npub fn size(self: *Self) usize {\nreturn self.que_size;\n}\n// \u5224\u65ad\u961f\u5217\u662f\u5426\u4e3a\u7a7a\npub fn isEmpty(self: *Self) bool {\nreturn self.size() == 0;\n}\n// \u8bbf\u95ee\u961f\u9996\u5143\u7d20\npub fn peek(self: *Self) T {\nif (self.size() == 0) @panic(\"\u961f\u5217\u4e3a\u7a7a\");\nreturn self.front.?.val;\n}  // \u5165\u961f\npub fn push(self: *Self, num: T) !void {\n// \u5c3e\u8282\u70b9\u540e\u6dfb\u52a0 num\nvar node = try self.mem_allocator.create(inc.ListNode(T));\nnode.init(num);\n// \u5982\u679c\u961f\u5217\u4e3a\u7a7a\uff0c\u5219\u4ee4\u5934\u3001\u5c3e\u8282\u70b9\u90fd\u6307\u5411\u8be5\u8282\u70b9\nif (self.front == null) {\nself.front = node;\nself.rear = node;\n// \u5982\u679c\u961f\u5217\u4e0d\u4e3a\u7a7a\uff0c\u5219\u5c06\u8be5\u8282\u70b9\u6dfb\u52a0\u5230\u5c3e\u8282\u70b9\u540e\n} else {\nself.rear.?.next = node;\nself.rear = node;\n}\nself.que_size += 1;\n} // \u51fa\u961f\npub fn pop(self: *Self) T {\nvar num = self.peek();\n// \u5220\u9664\u5934\u8282\u70b9\nself.front = self.front.?.next;\nself.que_size -= 1;\nreturn num;\n} // \u5c06\u94fe\u8868\u8f6c\u6362\u4e3a\u6570\u7ec4\npub fn toArray(self: *Self) ![]T {\nvar node = self.front;\nvar res = try self.mem_allocator.alloc(T, self.size());\nstd.mem.set(T, res, @as(T, 0));\nvar i: usize = 0;\nwhile (i &lt; res.len) : (i += 1) {\nres[i] = node.?.val;\nnode = node.?.next;\n}\nreturn res;\n}\n};\n}\n</code></pre> linkedlist_queue.dart<pre><code>/* \u57fa\u4e8e\u94fe\u8868\u5b9e\u73b0\u7684\u961f\u5217 */\nclass LinkedListQueue {\nListNode? _front; // \u5934\u8282\u70b9 _front\nListNode? _rear; // \u5c3e\u8282\u70b9 _rear\nint _queSize = 0; // \u961f\u5217\u957f\u5ea6\nLinkedListQueue() {\n_front = null;\n_rear = null;\n}\n/* \u83b7\u53d6\u961f\u5217\u7684\u957f\u5ea6 */\nint size() {\nreturn _queSize;\n}\n/* \u5224\u65ad\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nbool isEmpty() {\nreturn _queSize == 0;\n}\n/* \u5165\u961f */\nvoid push(int num) {\n// \u5c3e\u8282\u70b9\u540e\u6dfb\u52a0 num\nfinal node = ListNode(num);\n// \u5982\u679c\u961f\u5217\u4e3a\u7a7a\uff0c\u5219\u4ee4\u5934\u3001\u5c3e\u8282\u70b9\u90fd\u6307\u5411\u8be5\u8282\u70b9\nif (_front == null) {\n_front = node;\n_rear = node;\n} else {\n// \u5982\u679c\u961f\u5217\u4e0d\u4e3a\u7a7a\uff0c\u5219\u5c06\u8be5\u8282\u70b9\u6dfb\u52a0\u5230\u5c3e\u8282\u70b9\u540e\n_rear!.next = node;\n_rear = node;\n}\n_queSize++;\n}\n/* \u51fa\u961f */\nint pop() {\nfinal int num = peek();\n// \u5220\u9664\u5934\u8282\u70b9\n_front = _front!.next;\n_queSize--;\nreturn num;\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\nint peek() {\nif (_queSize == 0) {\nthrow Exception('\u961f\u5217\u4e3a\u7a7a');\n}\nreturn _front!.val;\n}\n/* \u5c06\u94fe\u8868\u8f6c\u5316\u4e3a Array \u5e76\u8fd4\u56de */\nList&lt;int&gt; toArray() {\nListNode? node = _front;\nfinal List&lt;int&gt; queue = [];\nwhile (node != null) {\nqueue.add(node.val);\nnode = node.next;\n}\nreturn queue;\n}\n}\n</code></pre>"},{"location":"chapter_stack_and_queue/queue/#_2","title":"\u57fa\u4e8e\u6570\u7ec4\u7684\u5b9e\u73b0","text":"<p>\u7531\u4e8e\u6570\u7ec4\u5220\u9664\u9996\u5143\u7d20\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(n)\\) \uff0c\u8fd9\u4f1a\u5bfc\u81f4\u51fa\u961f\u64cd\u4f5c\u6548\u7387\u8f83\u4f4e\u3002\u7136\u800c\uff0c\u6211\u4eec\u53ef\u4ee5\u91c7\u7528\u4ee5\u4e0b\u5de7\u5999\u65b9\u6cd5\u6765\u907f\u514d\u8fd9\u4e2a\u95ee\u9898\u3002</p> <p>\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u4e00\u4e2a\u53d8\u91cf <code>front</code> \u6307\u5411\u961f\u9996\u5143\u7d20\u7684\u7d22\u5f15\uff0c\u5e76\u7ef4\u62a4\u4e00\u4e2a\u53d8\u91cf <code>queSize</code> \u7528\u4e8e\u8bb0\u5f55\u961f\u5217\u957f\u5ea6\u3002\u5b9a\u4e49 <code>rear = front + queSize</code> \uff0c\u8fd9\u4e2a\u516c\u5f0f\u8ba1\u7b97\u51fa\u7684 <code>rear</code> \u6307\u5411\u961f\u5c3e\u5143\u7d20\u4e4b\u540e\u7684\u4e0b\u4e00\u4e2a\u4f4d\u7f6e\u3002</p> <p>\u57fa\u4e8e\u6b64\u8bbe\u8ba1\uff0c\u6570\u7ec4\u4e2d\u5305\u542b\u5143\u7d20\u7684\u6709\u6548\u533a\u95f4\u4e3a [front, rear - 1]\uff0c\u8fdb\u800c\uff1a</p> <ul> <li>\u5bf9\u4e8e\u5165\u961f\u64cd\u4f5c\uff0c\u5c06\u8f93\u5165\u5143\u7d20\u8d4b\u503c\u7ed9 <code>rear</code> \u7d22\u5f15\u5904\uff0c\u5e76\u5c06 <code>queSize</code> \u589e\u52a0 1 \uff1b</li> <li>\u5bf9\u4e8e\u51fa\u961f\u64cd\u4f5c\uff0c\u53ea\u9700\u5c06 <code>front</code> \u589e\u52a0 1 \uff0c\u5e76\u5c06 <code>queSize</code> \u51cf\u5c11 1 \uff1b</li> </ul> <p>\u53ef\u4ee5\u770b\u5230\uff0c\u5165\u961f\u548c\u51fa\u961f\u64cd\u4f5c\u90fd\u53ea\u9700\u8fdb\u884c\u4e00\u6b21\u64cd\u4f5c\uff0c\u65f6\u95f4\u590d\u6742\u5ea6\u5747\u4e3a \\(O(1)\\) \u3002</p> ArrayQueuepush()pop() <p></p> <p></p> <p></p> <p>\u4f60\u53ef\u80fd\u4f1a\u53d1\u73b0\u4e00\u4e2a\u95ee\u9898\uff1a\u5728\u4e0d\u65ad\u8fdb\u884c\u5165\u961f\u548c\u51fa\u961f\u7684\u8fc7\u7a0b\u4e2d\uff0c<code>front</code> \u548c <code>rear</code> \u90fd\u5728\u5411\u53f3\u79fb\u52a8\uff0c\u5f53\u5b83\u4eec\u5230\u8fbe\u6570\u7ec4\u5c3e\u90e8\u65f6\u5c31\u65e0\u6cd5\u7ee7\u7eed\u79fb\u52a8\u4e86\u3002\u4e3a\u89e3\u51b3\u6b64\u95ee\u9898\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u6570\u7ec4\u89c6\u4e3a\u9996\u5c3e\u76f8\u63a5\u7684\u300c\u73af\u5f62\u6570\u7ec4\u300d\u3002</p> <p>\u5bf9\u4e8e\u73af\u5f62\u6570\u7ec4\uff0c\u6211\u4eec\u9700\u8981\u8ba9 <code>front</code> \u6216 <code>rear</code> \u5728\u8d8a\u8fc7\u6570\u7ec4\u5c3e\u90e8\u65f6\uff0c\u76f4\u63a5\u56de\u5230\u6570\u7ec4\u5934\u90e8\u7ee7\u7eed\u904d\u5386\u3002\u8fd9\u79cd\u5468\u671f\u6027\u89c4\u5f8b\u53ef\u4ee5\u901a\u8fc7\u201c\u53d6\u4f59\u64cd\u4f5c\u201d\u6765\u5b9e\u73b0\uff0c\u4ee3\u7801\u5982\u4e0b\u6240\u793a\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart array_queue.java<pre><code>/* \u57fa\u4e8e\u73af\u5f62\u6570\u7ec4\u5b9e\u73b0\u7684\u961f\u5217 */\nclass ArrayQueue {\nprivate int[] nums; // \u7528\u4e8e\u5b58\u50a8\u961f\u5217\u5143\u7d20\u7684\u6570\u7ec4\nprivate int front; // \u961f\u9996\u6307\u9488\uff0c\u6307\u5411\u961f\u9996\u5143\u7d20\nprivate int queSize; // \u961f\u5217\u957f\u5ea6\npublic ArrayQueue(int capacity) {\nnums = new int[capacity];\nfront = queSize = 0;\n}\n/* \u83b7\u53d6\u961f\u5217\u7684\u5bb9\u91cf */\npublic int capacity() {\nreturn nums.length;\n}\n/* \u83b7\u53d6\u961f\u5217\u7684\u957f\u5ea6 */\npublic int size() {\nreturn queSize;\n}\n/* \u5224\u65ad\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\npublic boolean isEmpty() {\nreturn queSize == 0;\n}\n/* \u5165\u961f */\npublic void push(int num) {\nif (queSize == capacity()) {\nSystem.out.println(\"\u961f\u5217\u5df2\u6ee1\");\nreturn;\n}\n// \u8ba1\u7b97\u5c3e\u6307\u9488\uff0c\u6307\u5411\u961f\u5c3e\u7d22\u5f15 + 1\n// \u901a\u8fc7\u53d6\u4f59\u64cd\u4f5c\uff0c\u5b9e\u73b0 rear \u8d8a\u8fc7\u6570\u7ec4\u5c3e\u90e8\u540e\u56de\u5230\u5934\u90e8\nint rear = (front + queSize) % capacity();\n// \u5c06 num \u6dfb\u52a0\u81f3\u961f\u5c3e\nnums[rear] = num;\nqueSize++;\n}\n/* \u51fa\u961f */\npublic int pop() {\nint num = peek();\n// \u961f\u9996\u6307\u9488\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\uff0c\u82e5\u8d8a\u8fc7\u5c3e\u90e8\u5219\u8fd4\u56de\u5230\u6570\u7ec4\u5934\u90e8\nfront = (front + 1) % capacity();\nqueSize--;\nreturn num;\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\npublic int peek() {\nif (isEmpty())\nthrow new IndexOutOfBoundsException();\nreturn nums[front];\n}\n/* \u8fd4\u56de\u6570\u7ec4 */\npublic int[] toArray() {\n// \u4ec5\u8f6c\u6362\u6709\u6548\u957f\u5ea6\u8303\u56f4\u5185\u7684\u5217\u8868\u5143\u7d20\nint[] res = new int[queSize];\nfor (int i = 0, j = front; i &lt; queSize; i++, j++) {\nres[i] = nums[j % capacity()];\n}\nreturn res;\n}\n}\n</code></pre> array_queue.cpp<pre><code>/* \u57fa\u4e8e\u73af\u5f62\u6570\u7ec4\u5b9e\u73b0\u7684\u961f\u5217 */\nclass ArrayQueue {\nprivate:\nint *nums;       // \u7528\u4e8e\u5b58\u50a8\u961f\u5217\u5143\u7d20\u7684\u6570\u7ec4\nint front;       // \u961f\u9996\u6307\u9488\uff0c\u6307\u5411\u961f\u9996\u5143\u7d20\nint queSize;     // \u961f\u5217\u957f\u5ea6\nint queCapacity; // \u961f\u5217\u5bb9\u91cf\npublic:\nArrayQueue(int capacity) {\n// \u521d\u59cb\u5316\u6570\u7ec4\nnums = new int[capacity];\nqueCapacity = capacity;\nfront = queSize = 0;\n}\n~ArrayQueue() {\ndelete[] nums;\n}\n/* \u83b7\u53d6\u961f\u5217\u7684\u5bb9\u91cf */\nint capacity() {\nreturn queCapacity;\n}\n/* \u83b7\u53d6\u961f\u5217\u7684\u957f\u5ea6 */\nint size() {\nreturn queSize;\n}\n/* \u5224\u65ad\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nbool empty() {\nreturn size() == 0;\n}\n/* \u5165\u961f */\nvoid push(int num) {\nif (queSize == queCapacity) {\ncout &lt;&lt; \"\u961f\u5217\u5df2\u6ee1\" &lt;&lt; endl;\nreturn;\n}\n// \u8ba1\u7b97\u961f\u5c3e\u6307\u9488\uff0c\u6307\u5411\u961f\u5c3e\u7d22\u5f15 + 1\n// \u901a\u8fc7\u53d6\u4f59\u64cd\u4f5c\uff0c\u5b9e\u73b0 rear \u8d8a\u8fc7\u6570\u7ec4\u5c3e\u90e8\u540e\u56de\u5230\u5934\u90e8\nint rear = (front + queSize) % queCapacity;\n// \u5c06 num \u6dfb\u52a0\u81f3\u961f\u5c3e\nnums[rear] = num;\nqueSize++;\n}\n/* \u51fa\u961f */\nvoid pop() {\nint num = peek();\n// \u961f\u9996\u6307\u9488\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\uff0c\u82e5\u8d8a\u8fc7\u5c3e\u90e8\u5219\u8fd4\u56de\u5230\u6570\u7ec4\u5934\u90e8\nfront = (front + 1) % queCapacity;\nqueSize--;\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\nint peek() {\nif (empty())\nthrow out_of_range(\"\u961f\u5217\u4e3a\u7a7a\");\nreturn nums[front];\n}\n/* \u5c06\u6570\u7ec4\u8f6c\u5316\u4e3a Vector \u5e76\u8fd4\u56de */\nvector&lt;int&gt; toVector() {\n// \u4ec5\u8f6c\u6362\u6709\u6548\u957f\u5ea6\u8303\u56f4\u5185\u7684\u5217\u8868\u5143\u7d20\nvector&lt;int&gt; arr(queSize);\nfor (int i = 0, j = front; i &lt; queSize; i++, j++) {\narr[i] = nums[j % queCapacity];\n}\nreturn arr;\n}\n};\n</code></pre> array_queue.py<pre><code>class ArrayQueue:\n\"\"\"\u57fa\u4e8e\u73af\u5f62\u6570\u7ec4\u5b9e\u73b0\u7684\u961f\u5217\"\"\"\ndef __init__(self, size: int) -&gt; None:\n\"\"\"\u6784\u9020\u65b9\u6cd5\"\"\"\nself.__nums: list[int] = [0] * size  # \u7528\u4e8e\u5b58\u50a8\u961f\u5217\u5143\u7d20\u7684\u6570\u7ec4\nself.__front: int = 0  # \u961f\u9996\u6307\u9488\uff0c\u6307\u5411\u961f\u9996\u5143\u7d20\nself.__size: int = 0  # \u961f\u5217\u957f\u5ea6\ndef capacity(self) -&gt; int:\n\"\"\"\u83b7\u53d6\u961f\u5217\u7684\u5bb9\u91cf\"\"\"\nreturn len(self.__nums)\ndef size(self) -&gt; int:\n\"\"\"\u83b7\u53d6\u961f\u5217\u7684\u957f\u5ea6\"\"\"\nreturn self.__size\ndef is_empty(self) -&gt; bool:\n\"\"\"\u5224\u65ad\u961f\u5217\u662f\u5426\u4e3a\u7a7a\"\"\"\nreturn self.__size == 0\ndef push(self, num: int) -&gt; None:\n\"\"\"\u5165\u961f\"\"\"\nif self.__size == self.capacity():\nraise IndexError(\"\u961f\u5217\u5df2\u6ee1\")\n# \u8ba1\u7b97\u5c3e\u6307\u9488\uff0c\u6307\u5411\u961f\u5c3e\u7d22\u5f15 + 1\n# \u901a\u8fc7\u53d6\u4f59\u64cd\u4f5c\uff0c\u5b9e\u73b0 rear \u8d8a\u8fc7\u6570\u7ec4\u5c3e\u90e8\u540e\u56de\u5230\u5934\u90e8F\nrear: int = (self.__front + self.__size) % self.capacity()\n# \u5c06 num \u6dfb\u52a0\u81f3\u961f\u5c3e\nself.__nums[rear] = num\nself.__size += 1\ndef pop(self) -&gt; int:\n\"\"\"\u51fa\u961f\"\"\"\nnum: int = self.peek()\n# \u961f\u9996\u6307\u9488\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\uff0c\u82e5\u8d8a\u8fc7\u5c3e\u90e8\u5219\u8fd4\u56de\u5230\u6570\u7ec4\u5934\u90e8\nself.__front = (self.__front + 1) % self.capacity()\nself.__size -= 1\nreturn num\ndef peek(self) -&gt; int:\n\"\"\"\u8bbf\u95ee\u961f\u9996\u5143\u7d20\"\"\"\nif self.is_empty():\nraise IndexError(\"\u961f\u5217\u4e3a\u7a7a\")\nreturn self.__nums[self.__front]\ndef to_list(self) -&gt; list[int]:\n\"\"\"\u8fd4\u56de\u5217\u8868\u7528\u4e8e\u6253\u5370\"\"\"\nres = [0] * self.size()\nj: int = self.__front\nfor i in range(self.size()):\nres[i] = self.__nums[(j % self.capacity())]\nj += 1\nreturn res\n</code></pre> array_queue.go<pre><code>/* \u57fa\u4e8e\u73af\u5f62\u6570\u7ec4\u5b9e\u73b0\u7684\u961f\u5217 */\ntype arrayQueue struct {\nnums        []int // \u7528\u4e8e\u5b58\u50a8\u961f\u5217\u5143\u7d20\u7684\u6570\u7ec4\nfront       int   // \u961f\u9996\u6307\u9488\uff0c\u6307\u5411\u961f\u9996\u5143\u7d20\nqueSize     int   // \u961f\u5217\u957f\u5ea6\nqueCapacity int   // \u961f\u5217\u5bb9\u91cf\uff08\u5373\u6700\u5927\u5bb9\u7eb3\u5143\u7d20\u6570\u91cf\uff09\n}\n/* \u521d\u59cb\u5316\u961f\u5217 */\nfunc newArrayQueue(queCapacity int) *arrayQueue {\nreturn &amp;arrayQueue{\nnums:        make([]int, queCapacity),\nqueCapacity: queCapacity,\nfront:       0,\nqueSize:     0,\n}\n}\n/* \u83b7\u53d6\u961f\u5217\u7684\u957f\u5ea6 */\nfunc (q *arrayQueue) size() int {\nreturn q.queSize\n}\n/* \u5224\u65ad\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nfunc (q *arrayQueue) isEmpty() bool {\nreturn q.queSize == 0\n}\n/* \u5165\u961f */\nfunc (q *arrayQueue) push(num int) {\n// \u5f53 rear == queCapacity \u8868\u793a\u961f\u5217\u5df2\u6ee1\nif q.queSize == q.queCapacity {\nreturn\n}\n// \u8ba1\u7b97\u5c3e\u6307\u9488\uff0c\u6307\u5411\u961f\u5c3e\u7d22\u5f15 + 1\n// \u901a\u8fc7\u53d6\u4f59\u64cd\u4f5c\uff0c\u5b9e\u73b0 rear \u8d8a\u8fc7\u6570\u7ec4\u5c3e\u90e8\u540e\u56de\u5230\u5934\u90e8\nrear := (q.front + q.queSize) % q.queCapacity\n// \u5c06 num \u6dfb\u52a0\u81f3\u961f\u5c3e\nq.nums[rear] = num\nq.queSize++\n}\n/* \u51fa\u961f */\nfunc (q *arrayQueue) pop() any {\nnum := q.peek()\n// \u961f\u9996\u6307\u9488\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\uff0c\u82e5\u8d8a\u8fc7\u5c3e\u90e8\u5219\u8fd4\u56de\u5230\u6570\u7ec4\u5934\u90e8\nq.front = (q.front + 1) % q.queCapacity\nq.queSize--\nreturn num\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\nfunc (q *arrayQueue) peek() any {\nif q.isEmpty() {\nreturn nil\n}\nreturn q.nums[q.front]\n}\n/* \u83b7\u53d6 Slice \u7528\u4e8e\u6253\u5370 */\nfunc (q *arrayQueue) toSlice() []int {\nrear := (q.front + q.queSize)\nif rear &gt;= q.queCapacity {\nrear %= q.queCapacity\nreturn append(q.nums[q.front:], q.nums[:rear]...)\n}\nreturn q.nums[q.front:rear]\n}\n</code></pre> array_queue.js<pre><code>/* \u57fa\u4e8e\u73af\u5f62\u6570\u7ec4\u5b9e\u73b0\u7684\u961f\u5217 */\nclass ArrayQueue {\n#nums; // \u7528\u4e8e\u5b58\u50a8\u961f\u5217\u5143\u7d20\u7684\u6570\u7ec4\n#front = 0; // \u961f\u9996\u6307\u9488\uff0c\u6307\u5411\u961f\u9996\u5143\u7d20\n#queSize = 0; // \u961f\u5217\u957f\u5ea6\nconstructor(capacity) {\nthis.#nums = new Array(capacity);\n}\n/* \u83b7\u53d6\u961f\u5217\u7684\u5bb9\u91cf */\nget capacity() {\nreturn this.#nums.length;\n}\n/* \u83b7\u53d6\u961f\u5217\u7684\u957f\u5ea6 */\nget size() {\nreturn this.#queSize;\n}\n/* \u5224\u65ad\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nempty() {\nreturn this.#queSize == 0;\n}\n/* \u5165\u961f */\npush(num) {\nif (this.size == this.capacity) {\nconsole.log('\u961f\u5217\u5df2\u6ee1');\nreturn;\n}\n// \u8ba1\u7b97\u5c3e\u6307\u9488\uff0c\u6307\u5411\u961f\u5c3e\u7d22\u5f15 + 1\n// \u901a\u8fc7\u53d6\u4f59\u64cd\u4f5c\uff0c\u5b9e\u73b0 rear \u8d8a\u8fc7\u6570\u7ec4\u5c3e\u90e8\u540e\u56de\u5230\u5934\u90e8\nconst rear = (this.#front + this.size) % this.capacity;\n// \u5c06 num \u6dfb\u52a0\u81f3\u961f\u5c3e\nthis.#nums[rear] = num;\nthis.#queSize++;\n}\n/* \u51fa\u961f */\npop() {\nconst num = this.peek();\n// \u961f\u9996\u6307\u9488\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\uff0c\u82e5\u8d8a\u8fc7\u5c3e\u90e8\u5219\u8fd4\u56de\u5230\u6570\u7ec4\u5934\u90e8\nthis.#front = (this.#front + 1) % this.capacity;\nthis.#queSize--;\nreturn num;\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\npeek() {\nif (this.empty()) throw new Error('\u961f\u5217\u4e3a\u7a7a');\nreturn this.#nums[this.#front];\n}\n/* \u8fd4\u56de Array */\ntoArray() {\n// \u4ec5\u8f6c\u6362\u6709\u6548\u957f\u5ea6\u8303\u56f4\u5185\u7684\u5217\u8868\u5143\u7d20\nconst arr = new Array(this.size);\nfor (let i = 0, j = this.#front; i &lt; this.size; i++, j++) {\narr[i] = this.#nums[j % this.capacity];\n}\nreturn arr;\n}\n}\n</code></pre> array_queue.ts<pre><code>/* \u57fa\u4e8e\u73af\u5f62\u6570\u7ec4\u5b9e\u73b0\u7684\u961f\u5217 */\nclass ArrayQueue {\nprivate nums: number[]; // \u7528\u4e8e\u5b58\u50a8\u961f\u5217\u5143\u7d20\u7684\u6570\u7ec4\nprivate front: number; // \u961f\u9996\u6307\u9488\uff0c\u6307\u5411\u961f\u9996\u5143\u7d20\nprivate queSize: number; // \u961f\u5217\u957f\u5ea6\nconstructor(capacity: number) {\nthis.nums = new Array(capacity);\nthis.front = this.queSize = 0;\n}\n/* \u83b7\u53d6\u961f\u5217\u7684\u5bb9\u91cf */\nget capacity(): number {\nreturn this.nums.length;\n}\n/* \u83b7\u53d6\u961f\u5217\u7684\u957f\u5ea6 */\nget size(): number {\nreturn this.queSize;\n}\n/* \u5224\u65ad\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nempty(): boolean {\nreturn this.queSize == 0;\n}\n/* \u5165\u961f */\npush(num: number): void {\nif (this.size == this.capacity) {\nconsole.log('\u961f\u5217\u5df2\u6ee1');\nreturn;\n}\n// \u8ba1\u7b97\u5c3e\u6307\u9488\uff0c\u6307\u5411\u961f\u5c3e\u7d22\u5f15 + 1\n// \u901a\u8fc7\u53d6\u4f59\u64cd\u4f5c\uff0c\u5b9e\u73b0 rear \u8d8a\u8fc7\u6570\u7ec4\u5c3e\u90e8\u540e\u56de\u5230\u5934\u90e8\nconst rear = (this.front + this.queSize) % this.capacity;\n// \u5c06 num \u6dfb\u52a0\u81f3\u961f\u5c3e\nthis.nums[rear] = num;\nthis.queSize++;\n}\n/* \u51fa\u961f */\npop(): number {\nconst num = this.peek();\n// \u961f\u9996\u6307\u9488\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\uff0c\u82e5\u8d8a\u8fc7\u5c3e\u90e8\u5219\u8fd4\u56de\u5230\u6570\u7ec4\u5934\u90e8\nthis.front = (this.front + 1) % this.capacity;\nthis.queSize--;\nreturn num;\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\npeek(): number {\nif (this.empty()) throw new Error('\u961f\u5217\u4e3a\u7a7a');\nreturn this.nums[this.front];\n}\n/* \u8fd4\u56de Array */\ntoArray(): number[] {\n// \u4ec5\u8f6c\u6362\u6709\u6548\u957f\u5ea6\u8303\u56f4\u5185\u7684\u5217\u8868\u5143\u7d20\nconst arr = new Array(this.size);\nfor (let i = 0, j = this.front; i &lt; this.size; i++, j++) {\narr[i] = this.nums[j % this.capacity];\n}\nreturn arr;\n}\n}\n</code></pre> array_queue.c<pre><code>/* \u57fa\u4e8e\u73af\u5f62\u6570\u7ec4\u5b9e\u73b0\u7684\u961f\u5217 */\nstruct arrayQueue {\nint *nums;       // \u7528\u4e8e\u5b58\u50a8\u961f\u5217\u5143\u7d20\u7684\u6570\u7ec4\nint front;       // \u961f\u9996\u6307\u9488\uff0c\u6307\u5411\u961f\u9996\u5143\u7d20\nint queSize;     // \u5c3e\u6307\u9488\uff0c\u6307\u5411\u961f\u5c3e + 1\nint queCapacity; // \u961f\u5217\u5bb9\u91cf\n};\ntypedef struct arrayQueue arrayQueue;\n/* \u6784\u9020\u51fd\u6570 */\narrayQueue *newArrayQueue(int capacity) {\narrayQueue *queue = (arrayQueue *)malloc(sizeof(arrayQueue));\n// \u521d\u59cb\u5316\u6570\u7ec4\nqueue-&gt;queCapacity = capacity;\nqueue-&gt;nums = (int *)malloc(sizeof(int) * queue-&gt;queCapacity);\nqueue-&gt;front = queue-&gt;queSize = 0;\nreturn queue;\n}\n/* \u6790\u6784\u51fd\u6570 */\nvoid delArrayQueue(arrayQueue *queue) {\nfree(queue-&gt;nums);\nqueue-&gt;queCapacity = 0;\n}\n/* \u83b7\u53d6\u961f\u5217\u7684\u5bb9\u91cf */\nint capacity(arrayQueue *queue) {\nreturn queue-&gt;queCapacity;\n}\n/* \u83b7\u53d6\u961f\u5217\u7684\u957f\u5ea6 */\nint size(arrayQueue *queue) {\nreturn queue-&gt;queSize;\n}\n/* \u5224\u65ad\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nbool empty(arrayQueue *queue) {\nreturn queue-&gt;queSize == 0;\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\nint peek(arrayQueue *queue) {\nassert(size(queue) != 0);\nreturn queue-&gt;nums[queue-&gt;front];\n}\n/* \u5165\u961f */\nvoid push(arrayQueue *queue, int num) {\nif (size(queue) == capacity(queue)) {\nprintf(\"\u961f\u5217\u5df2\u6ee1\\r\\n\");\nreturn;\n}\n// \u8ba1\u7b97\u961f\u5c3e\u6307\u9488\uff0c\u6307\u5411\u961f\u5c3e\u7d22\u5f15 + 1\n// \u901a\u8fc7\u53d6\u4f59\u64cd\u4f5c\uff0c\u5b9e\u73b0 rear \u8d8a\u8fc7\u6570\u7ec4\u5c3e\u90e8\u540e\u56de\u5230\u5934\u90e8\nint rear = (queue-&gt;front + queue-&gt;queSize) % queue-&gt;queCapacity;\n// \u5c06 num \u6dfb\u52a0\u81f3\u961f\u5c3e\nqueue-&gt;nums[rear] = num;\nqueue-&gt;queSize++;\n}\n/* \u51fa\u961f */\nvoid pop(arrayQueue *queue) {\nint num = peek(queue);\n// \u961f\u9996\u6307\u9488\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\uff0c\u82e5\u8d8a\u8fc7\u5c3e\u90e8\u5219\u8fd4\u56de\u5230\u6570\u7ec4\u5934\u90e8\nqueue-&gt;front = (queue-&gt;front + 1) % queue-&gt;queCapacity;\nqueue-&gt;queSize--;\n}\n/* \u6253\u5370\u961f\u5217 */\nvoid printArrayQueue(arrayQueue *queue) {\nint arr[queue-&gt;queSize];\n// \u62f7\u8d1d\nfor (int i = 0, j = queue-&gt;front; i &lt; queue-&gt;queSize; i++, j++) {\narr[i] = queue-&gt;nums[j % queue-&gt;queCapacity];\n}\nprintArray(arr, queue-&gt;queSize);\n}\n</code></pre> array_queue.cs<pre><code>/* \u57fa\u4e8e\u73af\u5f62\u6570\u7ec4\u5b9e\u73b0\u7684\u961f\u5217 */\nclass ArrayQueue {\nprivate int[] nums;  // \u7528\u4e8e\u5b58\u50a8\u961f\u5217\u5143\u7d20\u7684\u6570\u7ec4\nprivate int front;   // \u961f\u9996\u6307\u9488\uff0c\u6307\u5411\u961f\u9996\u5143\u7d20\nprivate int queSize; // \u961f\u5217\u957f\u5ea6\npublic ArrayQueue(int capacity) {\nnums = new int[capacity];\nfront = queSize = 0;\n}\n/* \u83b7\u53d6\u961f\u5217\u7684\u5bb9\u91cf */\npublic int capacity() {\nreturn nums.Length;\n}\n/* \u83b7\u53d6\u961f\u5217\u7684\u957f\u5ea6 */\npublic int size() {\nreturn queSize;\n}\n/* \u5224\u65ad\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\npublic bool isEmpty() {\nreturn queSize == 0;\n}\n/* \u5165\u961f */\npublic void push(int num) {\nif (queSize == capacity()) {\nConsole.WriteLine(\"\u961f\u5217\u5df2\u6ee1\");\nreturn;\n}\n// \u8ba1\u7b97\u5c3e\u6307\u9488\uff0c\u6307\u5411\u961f\u5c3e\u7d22\u5f15 + 1\n// \u901a\u8fc7\u53d6\u4f59\u64cd\u4f5c\uff0c\u5b9e\u73b0 rear \u8d8a\u8fc7\u6570\u7ec4\u5c3e\u90e8\u540e\u56de\u5230\u5934\u90e8\nint rear = (front + queSize) % capacity();\n// \u5c06 num \u6dfb\u52a0\u81f3\u961f\u5c3e\nnums[rear] = num;\nqueSize++;\n}\n/* \u51fa\u961f */\npublic int pop() {\nint num = peek();\n// \u961f\u9996\u6307\u9488\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\uff0c\u82e5\u8d8a\u8fc7\u5c3e\u90e8\u5219\u8fd4\u56de\u5230\u6570\u7ec4\u5934\u90e8\nfront = (front + 1) % capacity();\nqueSize--;\nreturn num;\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\npublic int peek() {\nif (isEmpty())\nthrow new Exception();\nreturn nums[front];\n}\n/* \u8fd4\u56de\u6570\u7ec4 */\npublic int[] toArray() {\n// \u4ec5\u8f6c\u6362\u6709\u6548\u957f\u5ea6\u8303\u56f4\u5185\u7684\u5217\u8868\u5143\u7d20\nint[] res = new int[queSize];\nfor (int i = 0, j = front; i &lt; queSize; i++, j++) {\nres[i] = nums[j % this.capacity()];\n}\nreturn res;\n}\n}\n</code></pre> array_queue.swift<pre><code>/* \u57fa\u4e8e\u73af\u5f62\u6570\u7ec4\u5b9e\u73b0\u7684\u961f\u5217 */\nclass ArrayQueue {\nprivate var nums: [Int] // \u7528\u4e8e\u5b58\u50a8\u961f\u5217\u5143\u7d20\u7684\u6570\u7ec4\nprivate var front = 0 // \u961f\u9996\u6307\u9488\uff0c\u6307\u5411\u961f\u9996\u5143\u7d20\nprivate var queSize = 0 // \u961f\u5217\u957f\u5ea6\ninit(capacity: Int) {\n// \u521d\u59cb\u5316\u6570\u7ec4\nnums = Array(repeating: 0, count: capacity)\n}\n/* \u83b7\u53d6\u961f\u5217\u7684\u5bb9\u91cf */\nfunc capacity() -&gt; Int {\nnums.count\n}\n/* \u83b7\u53d6\u961f\u5217\u7684\u957f\u5ea6 */\nfunc size() -&gt; Int {\nqueSize\n}\n/* \u5224\u65ad\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nfunc isEmpty() -&gt; Bool {\nqueSize == 0\n}\n/* \u5165\u961f */\nfunc push(num: Int) {\nif size() == capacity() {\nprint(\"\u961f\u5217\u5df2\u6ee1\")\nreturn\n}\n// \u8ba1\u7b97\u5c3e\u6307\u9488\uff0c\u6307\u5411\u961f\u5c3e\u7d22\u5f15 + 1\n// \u901a\u8fc7\u53d6\u4f59\u64cd\u4f5c\uff0c\u5b9e\u73b0 rear \u8d8a\u8fc7\u6570\u7ec4\u5c3e\u90e8\u540e\u56de\u5230\u5934\u90e8\nlet rear = (front + queSize) % capacity()\n// \u5c06 num \u6dfb\u52a0\u81f3\u961f\u5c3e\nnums[rear] = num\nqueSize += 1\n}\n/* \u51fa\u961f */\n@discardableResult\nfunc pop() -&gt; Int {\nlet num = peek()\n// \u961f\u9996\u6307\u9488\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\uff0c\u82e5\u8d8a\u8fc7\u5c3e\u90e8\u5219\u8fd4\u56de\u5230\u6570\u7ec4\u5934\u90e8\nfront = (front + 1) % capacity()\nqueSize -= 1\nreturn num\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\nfunc peek() -&gt; Int {\nif isEmpty() {\nfatalError(\"\u961f\u5217\u4e3a\u7a7a\")\n}\nreturn nums[front]\n}\n/* \u8fd4\u56de\u6570\u7ec4 */\nfunc toArray() -&gt; [Int] {\n// \u4ec5\u8f6c\u6362\u6709\u6548\u957f\u5ea6\u8303\u56f4\u5185\u7684\u5217\u8868\u5143\u7d20\nvar res = Array(repeating: 0, count: queSize)\nfor (i, j) in sequence(first: (0, front), next: { $0 &lt; self.queSize - 1 ? ($0 + 1, $1 + 1) : nil }) {\nres[i] = nums[j % capacity()]\n}\nreturn res\n}\n}\n</code></pre> array_queue.zig<pre><code>// \u57fa\u4e8e\u73af\u5f62\u6570\u7ec4\u5b9e\u73b0\u7684\u961f\u5217\nfn ArrayQueue(comptime T: type) type {\nreturn struct {\nconst Self = @This();\nnums: []T = undefined,                          // \u7528\u4e8e\u5b58\u50a8\u961f\u5217\u5143\u7d20\u7684\u6570\u7ec4     \ncap: usize = 0,                                 // \u961f\u5217\u5bb9\u91cf\nfront: usize = 0,                               // \u961f\u9996\u6307\u9488\uff0c\u6307\u5411\u961f\u9996\u5143\u7d20\nque_size: usize = 0,                             // \u5c3e\u6307\u9488\uff0c\u6307\u5411\u961f\u5c3e + 1\nmem_arena: ?std.heap.ArenaAllocator = null,\nmem_allocator: std.mem.Allocator = undefined,   // \u5185\u5b58\u5206\u914d\u5668\n// \u6784\u9020\u65b9\u6cd5\uff08\u5206\u914d\u5185\u5b58+\u521d\u59cb\u5316\u6570\u7ec4\uff09\npub fn init(self: *Self, allocator: std.mem.Allocator, cap: usize) !void {\nif (self.mem_arena == null) {\nself.mem_arena = std.heap.ArenaAllocator.init(allocator);\nself.mem_allocator = self.mem_arena.?.allocator();\n}\nself.cap = cap;\nself.nums = try self.mem_allocator.alloc(T, self.cap);\nstd.mem.set(T, self.nums, @as(T, 0));\n}\n// \u6790\u6784\u65b9\u6cd5\uff08\u91ca\u653e\u5185\u5b58\uff09\npub fn deinit(self: *Self) void {\nif (self.mem_arena == null) return;\nself.mem_arena.?.deinit();\n}\n// \u83b7\u53d6\u961f\u5217\u7684\u5bb9\u91cf\npub fn capacity(self: *Self) usize {\nreturn self.cap;\n}\n// \u83b7\u53d6\u961f\u5217\u7684\u957f\u5ea6\npub fn size(self: *Self) usize {\nreturn self.que_size;\n}\n// \u5224\u65ad\u961f\u5217\u662f\u5426\u4e3a\u7a7a\npub fn isEmpty(self: *Self) bool {\nreturn self.que_size == 0;\n}\n// \u5165\u961f\npub fn push(self: *Self, num: T) !void {\nif (self.size() == self.capacity()) {\nstd.debug.print(\"\u961f\u5217\u5df2\u6ee1\\n\", .{});\nreturn;\n}\n// \u8ba1\u7b97\u5c3e\u6307\u9488\uff0c\u6307\u5411\u961f\u5c3e\u7d22\u5f15 + 1\n// \u901a\u8fc7\u53d6\u4f59\u64cd\u4f5c\uff0c\u5b9e\u73b0 rear \u8d8a\u8fc7\u6570\u7ec4\u5c3e\u90e8\u540e\u56de\u5230\u5934\u90e8\nvar rear = (self.front + self.que_size) % self.capacity();\n// \u5c06 num \u6dfb\u52a0\u81f3\u961f\u5c3e\nself.nums[rear] = num;\nself.que_size += 1;\n} // \u51fa\u961f\npub fn pop(self: *Self) T {\nvar num = self.peek();\n// \u961f\u9996\u6307\u9488\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\uff0c\u82e5\u8d8a\u8fc7\u5c3e\u90e8\u5219\u8fd4\u56de\u5230\u6570\u7ec4\u5934\u90e8\nself.front = (self.front + 1) % self.capacity();\nself.que_size -= 1;\nreturn num;\n} // \u8bbf\u95ee\u961f\u9996\u5143\u7d20\npub fn peek(self: *Self) T {\nif (self.isEmpty()) @panic(\"\u961f\u5217\u4e3a\u7a7a\");\nreturn self.nums[self.front];\n} // \u8fd4\u56de\u6570\u7ec4\npub fn toArray(self: *Self) ![]T {\n// \u4ec5\u8f6c\u6362\u6709\u6548\u957f\u5ea6\u8303\u56f4\u5185\u7684\u5217\u8868\u5143\u7d20\nvar res = try self.mem_allocator.alloc(T, self.size());\nstd.mem.set(T, res, @as(T, 0));\nvar i: usize = 0;\nvar j: usize = self.front;\nwhile (i &lt; self.size()) : ({ i += 1; j += 1; }) {\nres[i] = self.nums[j % self.capacity()];\n}\nreturn res;\n}\n};\n}\n</code></pre> array_queue.dart<pre><code>/* \u57fa\u4e8e\u73af\u5f62\u6570\u7ec4\u5b9e\u73b0\u7684\u961f\u5217 */\nclass ArrayQueue {\nlate List&lt;int&gt; _nums; // \u7528\u4e8e\u50a8\u5b58\u961f\u5217\u5143\u7d20\u7684\u6570\u7ec4\nlate int _front; // \u961f\u9996\u6307\u9488\uff0c\u6307\u5411\u961f\u9996\u5143\u7d20\nlate int _queSize; // \u961f\u5217\u957f\u5ea6\nArrayQueue(int capacity) {\n_nums = List.filled(capacity, 0);\n_front = _queSize = 0;\n}\n/* \u83b7\u53d6\u961f\u5217\u7684\u5bb9\u91cf */\nint capaCity() {\nreturn _nums.length;\n}\n/* \u83b7\u53d6\u961f\u5217\u7684\u957f\u5ea6 */\nint size() {\nreturn _queSize;\n}\n/* \u5224\u65ad\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nbool isEmpty() {\nreturn _queSize == 0;\n}\n/* \u5165\u961f */\nvoid push(int num) {\nif (_queSize == capaCity()) {\nthrow Exception(\"\u961f\u5217\u5df2\u6ee1\");\n}\n// \u8ba1\u7b97\u5c3e\u6307\u9488\uff0c\u6307\u5411\u961f\u5c3e\u7d22\u5f15 + 1\n// \u901a\u8fc7\u53d6\u4f59\u64cd\u4f5c\uff0c\u5b9e\u73b0 rear \u8d8a\u8fc7\u6570\u7ec4\u5c3e\u90e8\u540e\u56de\u5230\u5934\u90e8\nint rear = (_front + _queSize) % capaCity();\n// \u5c06 num \u6dfb\u52a0\u81f3\u961f\u5c3e\n_nums[rear] = num;\n_queSize++;\n}\n/* \u51fa\u961f */\nint pop() {\nint num = peek();\n// \u961f\u9996\u6307\u9488\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\uff0c\u82e5\u8d8a\u8fc7\u5c3e\u90e8\u5219\u8fd4\u56de\u5230\u6570\u7ec4\u5934\u90e8\n_front = (_front + 1) % capaCity();\n_queSize--;\nreturn num;\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\nint peek() {\nif (isEmpty()) {\nthrow Exception(\"\u961f\u5217\u4e3a\u7a7a\");\n}\nreturn _nums[_front];\n}\n/* \u8fd4\u56de Array */\nList&lt;int&gt; toArray() {\n// \u4ec5\u8f6c\u6362\u6709\u6548\u957f\u5ea6\u8303\u56f4\u5185\u7684\u5217\u8868\u5143\u7d20\nfinal List&lt;int&gt; res = List.filled(_queSize, 0);\nfor (int i = 0, j = _front; i &lt; _queSize; i++, j++) {\nres[i] = _nums[j % capaCity()];\n}\nreturn res;\n}\n}\n</code></pre> <p>\u4ee5\u4e0a\u5b9e\u73b0\u7684\u961f\u5217\u4ecd\u7136\u5177\u6709\u5c40\u9650\u6027\uff0c\u5373\u5176\u957f\u5ea6\u4e0d\u53ef\u53d8\u3002\u7136\u800c\uff0c\u8fd9\u4e2a\u95ee\u9898\u4e0d\u96be\u89e3\u51b3\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u6570\u7ec4\u66ff\u6362\u4e3a\u52a8\u6001\u6570\u7ec4\uff0c\u4ece\u800c\u5f15\u5165\u6269\u5bb9\u673a\u5236\u3002\u6709\u5174\u8da3\u7684\u540c\u5b66\u53ef\u4ee5\u5c1d\u8bd5\u81ea\u884c\u5b9e\u73b0\u3002</p> <p>\u4e24\u79cd\u5b9e\u73b0\u7684\u5bf9\u6bd4\u7ed3\u8bba\u4e0e\u6808\u4e00\u81f4\uff0c\u5728\u6b64\u4e0d\u518d\u8d58\u8ff0\u3002</p>"},{"location":"chapter_stack_and_queue/queue/#523","title":"5.2.3. \u00a0 \u961f\u5217\u5178\u578b\u5e94\u7528","text":"<ul> <li>\u6dd8\u5b9d\u8ba2\u5355\u3002\u8d2d\u7269\u8005\u4e0b\u5355\u540e\uff0c\u8ba2\u5355\u5c06\u52a0\u5165\u961f\u5217\u4e2d\uff0c\u7cfb\u7edf\u968f\u540e\u4f1a\u6839\u636e\u987a\u5e8f\u4f9d\u6b21\u5904\u7406\u961f\u5217\u4e2d\u7684\u8ba2\u5355\u3002\u5728\u53cc\u5341\u4e00\u671f\u95f4\uff0c\u77ed\u65f6\u95f4\u5185\u4f1a\u4ea7\u751f\u6d77\u91cf\u8ba2\u5355\uff0c\u9ad8\u5e76\u53d1\u6210\u4e3a\u5de5\u7a0b\u5e08\u4eec\u9700\u8981\u91cd\u70b9\u653b\u514b\u7684\u95ee\u9898\u3002</li> <li>\u5404\u7c7b\u5f85\u529e\u4e8b\u9879\u3002\u4efb\u4f55\u9700\u8981\u5b9e\u73b0\u201c\u5148\u6765\u540e\u5230\u201d\u529f\u80fd\u7684\u573a\u666f\uff0c\u4f8b\u5982\u6253\u5370\u673a\u7684\u4efb\u52a1\u961f\u5217\u3001\u9910\u5385\u7684\u51fa\u9910\u961f\u5217\u7b49\u3002\u961f\u5217\u5728\u8fd9\u4e9b\u573a\u666f\u4e2d\u53ef\u4ee5\u6709\u6548\u5730\u7ef4\u62a4\u5904\u7406\u987a\u5e8f\u3002</li> </ul>"},{"location":"chapter_stack_and_queue/stack/","title":"5.1. \u00a0 \u6808","text":"<p>\u300c\u6808 Stack\u300d\u662f\u4e00\u79cd\u9075\u5faa\u5148\u5165\u540e\u51fa\uff08First In, Last Out\uff09\u539f\u5219\u7684\u7ebf\u6027\u6570\u636e\u7ed3\u6784\u3002</p> <p>\u6211\u4eec\u53ef\u4ee5\u5c06\u6808\u7c7b\u6bd4\u4e3a\u684c\u9762\u4e0a\u7684\u4e00\u645e\u76d8\u5b50\uff0c\u5982\u679c\u9700\u8981\u62ff\u51fa\u5e95\u90e8\u7684\u76d8\u5b50\uff0c\u5219\u9700\u8981\u5148\u5c06\u4e0a\u9762\u7684\u76d8\u5b50\u4f9d\u6b21\u53d6\u51fa\u3002\u6211\u4eec\u5c06\u76d8\u5b50\u66ff\u6362\u4e3a\u5404\u79cd\u7c7b\u578b\u7684\u5143\u7d20\uff08\u5982\u6574\u6570\u3001\u5b57\u7b26\u3001\u5bf9\u8c61\u7b49\uff09\uff0c\u5c31\u5f97\u5230\u4e86\u6808\u6570\u636e\u7ed3\u6784\u3002</p> <p>\u5728\u6808\u4e2d\uff0c\u6211\u4eec\u628a\u5806\u53e0\u5143\u7d20\u7684\u9876\u90e8\u79f0\u4e3a\u300c\u6808\u9876\u300d\uff0c\u5e95\u90e8\u79f0\u4e3a\u300c\u6808\u5e95\u300d\u3002\u5c06\u628a\u5143\u7d20\u6dfb\u52a0\u5230\u6808\u9876\u7684\u64cd\u4f5c\u53eb\u505a\u300c\u5165\u6808\u300d\uff0c\u800c\u5220\u9664\u6808\u9876\u5143\u7d20\u7684\u64cd\u4f5c\u53eb\u505a\u300c\u51fa\u6808\u300d\u3002</p> <p></p> <p> Fig. \u6808\u7684\u5148\u5165\u540e\u51fa\u89c4\u5219 </p>"},{"location":"chapter_stack_and_queue/stack/#511","title":"5.1.1. \u00a0 \u6808\u5e38\u7528\u64cd\u4f5c","text":"<p>\u6808\u7684\u5e38\u7528\u64cd\u4f5c\u5982\u4e0b\u8868\u6240\u793a\uff0c\u5177\u4f53\u7684\u65b9\u6cd5\u540d\u9700\u8981\u6839\u636e\u6240\u4f7f\u7528\u7684\u7f16\u7a0b\u8bed\u8a00\u6765\u786e\u5b9a\u3002\u5728\u6b64\uff0c\u6211\u4eec\u4ee5\u5e38\u89c1\u7684 <code>push()</code> , <code>pop()</code> , <code>peek()</code> \u547d\u540d\u4e3a\u4f8b\u3002</p> \u65b9\u6cd5 \u63cf\u8ff0 \u65f6\u95f4\u590d\u6742\u5ea6 push() \u5143\u7d20\u5165\u6808\uff08\u6dfb\u52a0\u81f3\u6808\u9876\uff09 \\(O(1)\\) pop() \u6808\u9876\u5143\u7d20\u51fa\u6808 \\(O(1)\\) peek() \u8bbf\u95ee\u6808\u9876\u5143\u7d20 \\(O(1)\\) <p>\u901a\u5e38\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u53ef\u4ee5\u76f4\u63a5\u4f7f\u7528\u7f16\u7a0b\u8bed\u8a00\u5185\u7f6e\u7684\u6808\u7c7b\u3002\u7136\u800c\uff0c\u67d0\u4e9b\u8bed\u8a00\u53ef\u80fd\u6ca1\u6709\u4e13\u95e8\u63d0\u4f9b\u6808\u7c7b\uff0c\u8fd9\u65f6\u6211\u4eec\u53ef\u4ee5\u5c06\u8be5\u8bed\u8a00\u7684\u300c\u6570\u7ec4\u300d\u6216\u300c\u94fe\u8868\u300d\u89c6\u4f5c\u6808\u6765\u4f7f\u7528\uff0c\u5e76\u901a\u8fc7\u201c\u8111\u8865\u201d\u6765\u5ffd\u7565\u4e0e\u6808\u65e0\u5173\u7684\u64cd\u4f5c\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart stack.java<pre><code>/* \u521d\u59cb\u5316\u6808 */\nStack&lt;Integer&gt; stack = new Stack&lt;&gt;();\n/* \u5143\u7d20\u5165\u6808 */\nstack.push(1);\nstack.push(3);\nstack.push(2);\nstack.push(5);\nstack.push(4);\n/* \u8bbf\u95ee\u6808\u9876\u5143\u7d20 */\nint peek = stack.peek();\n/* \u5143\u7d20\u51fa\u6808 */\nint pop = stack.pop();\n/* \u83b7\u53d6\u6808\u7684\u957f\u5ea6 */\nint size = stack.size();\n/* \u5224\u65ad\u662f\u5426\u4e3a\u7a7a */\nboolean isEmpty = stack.isEmpty();\n</code></pre> stack.cpp<pre><code>/* \u521d\u59cb\u5316\u6808 */\nstack&lt;int&gt; stack;\n/* \u5143\u7d20\u5165\u6808 */\nstack.push(1);\nstack.push(3);\nstack.push(2);\nstack.push(5);\nstack.push(4);\n/* \u8bbf\u95ee\u6808\u9876\u5143\u7d20 */\nint top = stack.top();\n/* \u5143\u7d20\u51fa\u6808 */\nstack.pop(); // \u65e0\u8fd4\u56de\u503c\n/* \u83b7\u53d6\u6808\u7684\u957f\u5ea6 */\nint size = stack.size();\n/* \u5224\u65ad\u662f\u5426\u4e3a\u7a7a */\nbool empty = stack.empty();\n</code></pre> stack.py<pre><code># \u521d\u59cb\u5316\u6808\n# Python \u6ca1\u6709\u5185\u7f6e\u7684\u6808\u7c7b\uff0c\u53ef\u4ee5\u628a List \u5f53\u4f5c\u6808\u6765\u4f7f\u7528 \nstack: List[int] = []\n# \u5143\u7d20\u5165\u6808\nstack.append(1)\nstack.append(3)\nstack.append(2)\nstack.append(5)\nstack.append(4)\n# \u8bbf\u95ee\u6808\u9876\u5143\u7d20\npeek: int = stack[-1]\n# \u5143\u7d20\u51fa\u6808\npop: int = stack.pop()\n# \u83b7\u53d6\u6808\u7684\u957f\u5ea6\nsize: int = len(stack)\n# \u5224\u65ad\u662f\u5426\u4e3a\u7a7a\nis_empty: bool = len(stack) == 0\n</code></pre> stack_test.go<pre><code>/* \u521d\u59cb\u5316\u6808 */\n// \u5728 Go \u4e2d\uff0c\u63a8\u8350\u5c06 Slice \u5f53\u4f5c\u6808\u6765\u4f7f\u7528\nvar stack []int\n/* \u5143\u7d20\u5165\u6808 */\nstack = append(stack, 1)\nstack = append(stack, 3)\nstack = append(stack, 2)\nstack = append(stack, 5)\nstack = append(stack, 4)\n/* \u8bbf\u95ee\u6808\u9876\u5143\u7d20 */\npeek := stack[len(stack)-1]\n/* \u5143\u7d20\u51fa\u6808 */\npop := stack[len(stack)-1]\nstack = stack[:len(stack)-1]\n/* \u83b7\u53d6\u6808\u7684\u957f\u5ea6 */\nsize := len(stack)\n/* \u5224\u65ad\u662f\u5426\u4e3a\u7a7a */\nisEmpty := len(stack) == 0\n</code></pre> stack.js<pre><code>/* \u521d\u59cb\u5316\u6808 */\n// Javascript \u6ca1\u6709\u5185\u7f6e\u7684\u6808\u7c7b\uff0c\u53ef\u4ee5\u628a Array \u5f53\u4f5c\u6808\u6765\u4f7f\u7528 \nconst stack = [];\n/* \u5143\u7d20\u5165\u6808 */\nstack.push(1);\nstack.push(3);\nstack.push(2);\nstack.push(5);\nstack.push(4);\n/* \u8bbf\u95ee\u6808\u9876\u5143\u7d20 */\nconst peek = stack[stack.length-1];\n/* \u5143\u7d20\u51fa\u6808 */\nconst pop = stack.pop();\n/* \u83b7\u53d6\u6808\u7684\u957f\u5ea6 */\nconst size = stack.length;\n/* \u5224\u65ad\u662f\u5426\u4e3a\u7a7a */\nconst is_empty = stack.length === 0;\n</code></pre> stack.ts<pre><code>/* \u521d\u59cb\u5316\u6808 */\n// Typescript \u6ca1\u6709\u5185\u7f6e\u7684\u6808\u7c7b\uff0c\u53ef\u4ee5\u628a Array \u5f53\u4f5c\u6808\u6765\u4f7f\u7528 \nconst stack: number[] = [];\n/* \u5143\u7d20\u5165\u6808 */\nstack.push(1);\nstack.push(3);\nstack.push(2);\nstack.push(5);\nstack.push(4);\n/* \u8bbf\u95ee\u6808\u9876\u5143\u7d20 */\nconst peek = stack[stack.length - 1];\n/* \u5143\u7d20\u51fa\u6808 */\nconst pop = stack.pop();\n/* \u83b7\u53d6\u6808\u7684\u957f\u5ea6 */\nconst size = stack.length;\n/* \u5224\u65ad\u662f\u5426\u4e3a\u7a7a */\nconst is_empty = stack.length === 0;\n</code></pre> stack.c<pre><code>// C \u672a\u63d0\u4f9b\u5185\u7f6e\u6808\n</code></pre> stack.cs<pre><code>/* \u521d\u59cb\u5316\u6808 */\nStack&lt;int&gt; stack = new ();\n/* \u5143\u7d20\u5165\u6808 */\nstack.Push(1);\nstack.Push(3);\nstack.Push(2);\nstack.Push(5);\nstack.Push(4);\n/* \u8bbf\u95ee\u6808\u9876\u5143\u7d20 */\nint peek = stack.Peek();\n/* \u5143\u7d20\u51fa\u6808 */\nint pop = stack.Pop();\n/* \u83b7\u53d6\u6808\u7684\u957f\u5ea6 */\nint size = stack.Count();\n/* \u5224\u65ad\u662f\u5426\u4e3a\u7a7a */\nbool isEmpty = stack.Count()==0;\n</code></pre> stack.swift<pre><code>/* \u521d\u59cb\u5316\u6808 */\n// Swift \u6ca1\u6709\u5185\u7f6e\u7684\u6808\u7c7b\uff0c\u53ef\u4ee5\u628a Array \u5f53\u4f5c\u6808\u6765\u4f7f\u7528\nvar stack: [Int] = []\n/* \u5143\u7d20\u5165\u6808 */\nstack.append(1)\nstack.append(3)\nstack.append(2)\nstack.append(5)\nstack.append(4)\n/* \u8bbf\u95ee\u6808\u9876\u5143\u7d20 */\nlet peek = stack.last!\n/* \u5143\u7d20\u51fa\u6808 */\nlet pop = stack.removeLast()\n/* \u83b7\u53d6\u6808\u7684\u957f\u5ea6 */\nlet size = stack.count\n/* \u5224\u65ad\u662f\u5426\u4e3a\u7a7a */\nlet isEmpty = stack.isEmpty\n</code></pre> stack.zig<pre><code>\n</code></pre> stack.dart<pre><code>/* \u521d\u59cb\u5316\u6808 */\n// Dart \u6ca1\u6709\u5185\u7f6e\u7684\u6808\u7c7b\uff0c\u53ef\u4ee5\u628a List \u5f53\u4f5c\u6808\u6765\u4f7f\u7528\nList&lt;int&gt; stack = [];\n/* \u5143\u7d20\u5165\u6808 */\nstack.add(1);\nstack.add(3);\nstack.add(2);\nstack.add(5);\nstack.add(4);\n/* \u8bbf\u95ee\u6808\u9876\u5143\u7d20 */\nint peek = stack.last;\n/* \u5143\u7d20\u51fa\u6808 */\nint pop = stack.removeLast();\n/* \u83b7\u53d6\u6808\u7684\u957f\u5ea6 */\nint size = stack.length;\n/* \u5224\u65ad\u662f\u5426\u4e3a\u7a7a */\nbool isEmpty = stack.isEmpty;\n</code></pre>"},{"location":"chapter_stack_and_queue/stack/#512","title":"5.1.2. \u00a0 \u6808\u7684\u5b9e\u73b0","text":"<p>\u4e3a\u4e86\u6df1\u5165\u4e86\u89e3\u6808\u7684\u8fd0\u884c\u673a\u5236\uff0c\u6211\u4eec\u6765\u5c1d\u8bd5\u81ea\u5df1\u5b9e\u73b0\u4e00\u4e2a\u6808\u7c7b\u3002</p> <p>\u6808\u9075\u5faa\u5148\u5165\u540e\u51fa\u7684\u539f\u5219\uff0c\u56e0\u6b64\u6211\u4eec\u53ea\u80fd\u5728\u6808\u9876\u6dfb\u52a0\u6216\u5220\u9664\u5143\u7d20\u3002\u7136\u800c\uff0c\u6570\u7ec4\u548c\u94fe\u8868\u90fd\u53ef\u4ee5\u5728\u4efb\u610f\u4f4d\u7f6e\u6dfb\u52a0\u548c\u5220\u9664\u5143\u7d20\uff0c\u56e0\u6b64\u6808\u53ef\u4ee5\u88ab\u89c6\u4e3a\u4e00\u79cd\u53d7\u9650\u5236\u7684\u6570\u7ec4\u6216\u94fe\u8868\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u6211\u4eec\u53ef\u4ee5\u201c\u5c4f\u853d\u201d\u6570\u7ec4\u6216\u94fe\u8868\u7684\u90e8\u5206\u65e0\u5173\u64cd\u4f5c\uff0c\u4f7f\u5176\u5bf9\u5916\u8868\u73b0\u7684\u903b\u8f91\u7b26\u5408\u6808\u7684\u7279\u6027\u3002</p>"},{"location":"chapter_stack_and_queue/stack/#_1","title":"\u57fa\u4e8e\u94fe\u8868\u7684\u5b9e\u73b0","text":"<p>\u4f7f\u7528\u94fe\u8868\u6765\u5b9e\u73b0\u6808\u65f6\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u94fe\u8868\u7684\u5934\u8282\u70b9\u89c6\u4e3a\u6808\u9876\uff0c\u5c3e\u8282\u70b9\u89c6\u4e3a\u6808\u5e95\u3002</p> <p>\u5bf9\u4e8e\u5165\u6808\u64cd\u4f5c\uff0c\u6211\u4eec\u53ea\u9700\u5c06\u5143\u7d20\u63d2\u5165\u94fe\u8868\u5934\u90e8\uff0c\u8fd9\u79cd\u8282\u70b9\u63d2\u5165\u65b9\u6cd5\u88ab\u79f0\u4e3a\u201c\u5934\u63d2\u6cd5\u201d\u3002\u800c\u5bf9\u4e8e\u51fa\u6808\u64cd\u4f5c\uff0c\u53ea\u9700\u5c06\u5934\u8282\u70b9\u4ece\u94fe\u8868\u4e2d\u5220\u9664\u5373\u53ef\u3002</p> LinkedListStackpush()pop() <p></p> <p></p> <p></p> <p>\u4ee5\u4e0b\u662f\u57fa\u4e8e\u94fe\u8868\u5b9e\u73b0\u6808\u7684\u793a\u4f8b\u4ee3\u7801\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart linkedlist_stack.java<pre><code>/* \u57fa\u4e8e\u94fe\u8868\u5b9e\u73b0\u7684\u6808 */\nclass LinkedListStack {\nprivate ListNode stackPeek; // \u5c06\u5934\u8282\u70b9\u4f5c\u4e3a\u6808\u9876\nprivate int stkSize = 0; // \u6808\u7684\u957f\u5ea6\npublic LinkedListStack() {\nstackPeek = null;\n}\n/* \u83b7\u53d6\u6808\u7684\u957f\u5ea6 */\npublic int size() {\nreturn stkSize;\n}\n/* \u5224\u65ad\u6808\u662f\u5426\u4e3a\u7a7a */\npublic boolean isEmpty() {\nreturn size() == 0;\n}\n/* \u5165\u6808 */\npublic void push(int num) {\nListNode node = new ListNode(num);\nnode.next = stackPeek;\nstackPeek = node;\nstkSize++;\n}\n/* \u51fa\u6808 */\npublic int pop() {\nint num = peek();\nstackPeek = stackPeek.next;\nstkSize--;\nreturn num;\n}\n/* \u8bbf\u95ee\u6808\u9876\u5143\u7d20 */\npublic int peek() {\nif (size() == 0)\nthrow new IndexOutOfBoundsException();\nreturn stackPeek.val;\n}\n/* \u5c06 List \u8f6c\u5316\u4e3a Array \u5e76\u8fd4\u56de */\npublic int[] toArray() {\nListNode node = stackPeek;\nint[] res = new int[size()];\nfor (int i = res.length - 1; i &gt;= 0; i--) {\nres[i] = node.val;\nnode = node.next;\n}\nreturn res;\n}\n}\n</code></pre> linkedlist_stack.cpp<pre><code>/* \u57fa\u4e8e\u94fe\u8868\u5b9e\u73b0\u7684\u6808 */\nclass LinkedListStack {\nprivate:\nListNode *stackTop; // \u5c06\u5934\u8282\u70b9\u4f5c\u4e3a\u6808\u9876\nint stkSize;        // \u6808\u7684\u957f\u5ea6\npublic:\nLinkedListStack() {\nstackTop = nullptr;\nstkSize = 0;\n}\n~LinkedListStack() {\n// \u904d\u5386\u94fe\u8868\u5220\u9664\u8282\u70b9\uff0c\u91ca\u653e\u5185\u5b58\nfreeMemoryLinkedList(stackTop);\n}\n/* \u83b7\u53d6\u6808\u7684\u957f\u5ea6 */\nint size() {\nreturn stkSize;\n}\n/* \u5224\u65ad\u6808\u662f\u5426\u4e3a\u7a7a */\nbool empty() {\nreturn size() == 0;\n}\n/* \u5165\u6808 */\nvoid push(int num) {\nListNode *node = new ListNode(num);\nnode-&gt;next = stackTop;\nstackTop = node;\nstkSize++;\n}\n/* \u51fa\u6808 */\nvoid pop() {\nint num = top();\nListNode *tmp = stackTop;\nstackTop = stackTop-&gt;next;\n// \u91ca\u653e\u5185\u5b58\ndelete tmp;\nstkSize--;\n}\n/* \u8bbf\u95ee\u6808\u9876\u5143\u7d20 */\nint top() {\nif (size() == 0)\nthrow out_of_range(\"\u6808\u4e3a\u7a7a\");\nreturn stackTop-&gt;val;\n}\n/* \u5c06 List \u8f6c\u5316\u4e3a Array \u5e76\u8fd4\u56de */\nvector&lt;int&gt; toVector() {\nListNode *node = stackTop;\nvector&lt;int&gt; res(size());\nfor (int i = res.size() - 1; i &gt;= 0; i--) {\nres[i] = node-&gt;val;\nnode = node-&gt;next;\n}\nreturn res;\n}\n};\n</code></pre> linkedlist_stack.py<pre><code>class LinkedListStack:\n\"\"\"\u57fa\u4e8e\u94fe\u8868\u5b9e\u73b0\u7684\u6808\"\"\"\ndef __init__(self):\n\"\"\"\u6784\u9020\u65b9\u6cd5\"\"\"\nself.__peek: ListNode | None = None\nself.__size: int = 0\ndef size(self) -&gt; int:\n\"\"\"\u83b7\u53d6\u6808\u7684\u957f\u5ea6\"\"\"\nreturn self.__size\ndef is_empty(self) -&gt; bool:\n\"\"\"\u5224\u65ad\u6808\u662f\u5426\u4e3a\u7a7a\"\"\"\nreturn not self.__peek\ndef push(self, val: int) -&gt; None:\n\"\"\"\u5165\u6808\"\"\"\nnode = ListNode(val)\nnode.next = self.__peek\nself.__peek = node\nself.__size += 1\ndef pop(self) -&gt; int:\n\"\"\"\u51fa\u6808\"\"\"\nnum: int = self.peek()\nself.__peek = self.__peek.next\nself.__size -= 1\nreturn num\ndef peek(self) -&gt; int:\n\"\"\"\u8bbf\u95ee\u6808\u9876\u5143\u7d20\"\"\"\n# \u5224\u7a7a\u5904\u7406\nif not self.__peek:\nreturn None\nreturn self.__peek.val\ndef to_list(self) -&gt; list[int]:\n\"\"\"\u8f6c\u5316\u4e3a\u5217\u8868\u7528\u4e8e\u6253\u5370\"\"\"\narr = []\nnode = self.__peek\nwhile node:\narr.append(node.val)\nnode = node.next\narr.reverse()\nreturn arr\n</code></pre> linkedlist_stack.go<pre><code>/* \u57fa\u4e8e\u94fe\u8868\u5b9e\u73b0\u7684\u6808 */\ntype linkedListStack struct {\n// \u4f7f\u7528\u5185\u7f6e\u5305 list \u6765\u5b9e\u73b0\u6808\ndata *list.List\n}\n/* \u521d\u59cb\u5316\u6808 */\nfunc newLinkedListStack() *linkedListStack {\nreturn &amp;linkedListStack{\ndata: list.New(),\n}\n}\n/* \u5165\u6808 */\nfunc (s *linkedListStack) push(value int) {\ns.data.PushBack(value)\n}\n/* \u51fa\u6808 */\nfunc (s *linkedListStack) pop() any {\nif s.isEmpty() {\nreturn nil\n}\ne := s.data.Back()\ns.data.Remove(e)\nreturn e.Value\n}\n/* \u8bbf\u95ee\u6808\u9876\u5143\u7d20 */\nfunc (s *linkedListStack) peek() any {\nif s.isEmpty() {\nreturn nil\n}\ne := s.data.Back()\nreturn e.Value\n}\n/* \u83b7\u53d6\u6808\u7684\u957f\u5ea6 */\nfunc (s *linkedListStack) size() int {\nreturn s.data.Len()\n}\n/* \u5224\u65ad\u6808\u662f\u5426\u4e3a\u7a7a */\nfunc (s *linkedListStack) isEmpty() bool {\nreturn s.data.Len() == 0\n}\n/* \u83b7\u53d6 List \u7528\u4e8e\u6253\u5370 */\nfunc (s *linkedListStack) toList() *list.List {\nreturn s.data\n}\n</code></pre> linkedlist_stack.js<pre><code>/* \u57fa\u4e8e\u94fe\u8868\u5b9e\u73b0\u7684\u6808 */\nclass LinkedListStack {\n#stackPeek; // \u5c06\u5934\u8282\u70b9\u4f5c\u4e3a\u6808\u9876\n#stkSize = 0; // \u6808\u7684\u957f\u5ea6\nconstructor() {\nthis.#stackPeek = null;\n}\n/* \u83b7\u53d6\u6808\u7684\u957f\u5ea6 */\nget size() {\nreturn this.#stkSize;\n}\n/* \u5224\u65ad\u6808\u662f\u5426\u4e3a\u7a7a */\nisEmpty() {\nreturn this.size == 0;\n}\n/* \u5165\u6808 */\npush(num) {\nconst node = new ListNode(num);\nnode.next = this.#stackPeek;\nthis.#stackPeek = node;\nthis.#stkSize++;\n}\n/* \u51fa\u6808 */\npop() {\nconst num = this.peek();\nthis.#stackPeek = this.#stackPeek.next;\nthis.#stkSize--;\nreturn num;\n}\n/* \u8bbf\u95ee\u6808\u9876\u5143\u7d20 */\npeek() {\nif (!this.#stackPeek) throw new Error('\u6808\u4e3a\u7a7a');\nreturn this.#stackPeek.val;\n}\n/* \u5c06\u94fe\u8868\u8f6c\u5316\u4e3a Array \u5e76\u8fd4\u56de */\ntoArray() {\nlet node = this.#stackPeek;\nconst res = new Array(this.size);\nfor (let i = res.length - 1; i &gt;= 0; i--) {\nres[i] = node.val;\nnode = node.next;\n}\nreturn res;\n}\n}\n</code></pre> linkedlist_stack.ts<pre><code>/* \u57fa\u4e8e\u94fe\u8868\u5b9e\u73b0\u7684\u6808 */\nclass LinkedListStack {\nprivate stackPeek: ListNode | null; // \u5c06\u5934\u8282\u70b9\u4f5c\u4e3a\u6808\u9876\nprivate stkSize: number = 0; // \u6808\u7684\u957f\u5ea6\nconstructor() {\nthis.stackPeek = null;\n}\n/* \u83b7\u53d6\u6808\u7684\u957f\u5ea6 */\nget size(): number {\nreturn this.stkSize;\n}\n/* \u5224\u65ad\u6808\u662f\u5426\u4e3a\u7a7a */\nisEmpty(): boolean {\nreturn this.size == 0;\n}\n/* \u5165\u6808 */\npush(num: number): void {\nconst node = new ListNode(num);\nnode.next = this.stackPeek;\nthis.stackPeek = node;\nthis.stkSize++;\n}\n/* \u51fa\u6808 */\npop(): number {\nconst num = this.peek();\nif (!this.stackPeek) throw new Error('\u6808\u4e3a\u7a7a');\nthis.stackPeek = this.stackPeek.next;\nthis.stkSize--;\nreturn num;\n}\n/* \u8bbf\u95ee\u6808\u9876\u5143\u7d20 */\npeek(): number {\nif (!this.stackPeek) throw new Error('\u6808\u4e3a\u7a7a');\nreturn this.stackPeek.val;\n}\n/* \u5c06\u94fe\u8868\u8f6c\u5316\u4e3a Array \u5e76\u8fd4\u56de */\ntoArray(): number[] {\nlet node = this.stackPeek;\nconst res = new Array&lt;number&gt;(this.size);\nfor (let i = res.length - 1; i &gt;= 0; i--) {\nres[i] = node!.val;\nnode = node!.next;\n}\nreturn res;\n}\n}\n</code></pre> linkedlist_stack.c<pre><code>/* \u57fa\u4e8e\u94fe\u8868\u5b9e\u73b0\u7684\u6808 */\nstruct linkedListStack {\nListNode *top; // \u5c06\u5934\u8282\u70b9\u4f5c\u4e3a\u6808\u9876\nint size;      // \u6808\u7684\u957f\u5ea6\n};\ntypedef struct linkedListStack linkedListStack;\n/* \u6784\u9020\u51fd\u6570 */\nlinkedListStack *newLinkedListStack() {\nlinkedListStack *s = malloc(sizeof(linkedListStack));\ns-&gt;top = NULL;\ns-&gt;size = 0;\nreturn s;\n}\n/* \u6790\u6784\u51fd\u6570 */\nvoid delLinkedListStack(linkedListStack *s) {\nwhile (s-&gt;top) {\nListNode *n = s-&gt;top-&gt;next;\nfree(s-&gt;top);\ns-&gt;top = n;\n}\nfree(s);\n}\n/* \u83b7\u53d6\u6808\u7684\u957f\u5ea6 */\nint size(linkedListStack *s) {\nassert(s);\nreturn s-&gt;size;\n}\n/* \u5224\u65ad\u6808\u662f\u5426\u4e3a\u7a7a */\nbool isEmpty(linkedListStack *s) {\nassert(s);\nreturn size(s) == 0;\n}\n/* \u8bbf\u95ee\u6808\u9876\u5143\u7d20 */\nint peek(linkedListStack *s) {\nassert(s);\nassert(size(s) != 0);\nreturn s-&gt;top-&gt;val;\n}\n/* \u5165\u6808 */\nvoid push(linkedListStack *s, int num) {\nassert(s);\nListNode *node = (ListNode *)malloc(sizeof(ListNode));\nnode-&gt;next = s-&gt;top; // \u66f4\u65b0\u65b0\u52a0\u8282\u70b9\u6307\u9488\u57df\nnode-&gt;val = num;     // \u66f4\u65b0\u65b0\u52a0\u8282\u70b9\u6570\u636e\u57df\ns-&gt;top = node;       // \u66f4\u65b0\u6808\u9876\ns-&gt;size++;           // \u66f4\u65b0\u6808\u5927\u5c0f\n}\n/* \u51fa\u6808 */\nint pop(linkedListStack *s) {\nif (s-&gt;size == 0) {\nprintf(\"stack is empty.\\n\");\nreturn INT_MAX;\n}\nassert(s);\nint val = peek(s);\nListNode *tmp = s-&gt;top;\ns-&gt;top = s-&gt;top-&gt;next;\n// \u91ca\u653e\u5185\u5b58\nfree(tmp);\ns-&gt;size--;\nreturn val;\n}\n</code></pre> linkedlist_stack.cs<pre><code>/* \u57fa\u4e8e\u94fe\u8868\u5b9e\u73b0\u7684\u6808 */\nclass LinkedListStack {\nprivate ListNode? stackPeek;  // \u5c06\u5934\u8282\u70b9\u4f5c\u4e3a\u6808\u9876\nprivate int stkSize = 0;   // \u6808\u7684\u957f\u5ea6\npublic LinkedListStack() {\nstackPeek = null;\n}\n/* \u83b7\u53d6\u6808\u7684\u957f\u5ea6 */\npublic int size() {\nreturn stkSize;\n}\n/* \u5224\u65ad\u6808\u662f\u5426\u4e3a\u7a7a */\npublic bool isEmpty() {\nreturn size() == 0;\n}\n/* \u5165\u6808 */\npublic void push(int num) {\nListNode node = new ListNode(num);\nnode.next = stackPeek;\nstackPeek = node;\nstkSize++;\n}\n/* \u51fa\u6808 */\npublic int pop() {\nif (stackPeek == null)\nthrow new Exception();\nint num = peek();\nstackPeek = stackPeek.next;\nstkSize--;\nreturn num;\n}\n/* \u8bbf\u95ee\u6808\u9876\u5143\u7d20 */\npublic int peek() {\nif (size() == 0 || stackPeek == null)\nthrow new Exception();\nreturn stackPeek.val;\n}\n/* \u5c06 List \u8f6c\u5316\u4e3a Array \u5e76\u8fd4\u56de */\npublic int[] toArray() {\nif (stackPeek == null)\nreturn Array.Empty&lt;int&gt;();\nListNode node = stackPeek;\nint[] res = new int[size()];\nfor (int i = res.Length - 1; i &gt;= 0; i--) {\nres[i] = node.val;\nnode = node.next;\n}\nreturn res;\n}\n}\n</code></pre> linkedlist_stack.swift<pre><code>/* \u57fa\u4e8e\u94fe\u8868\u5b9e\u73b0\u7684\u6808 */\nclass LinkedListStack {\nprivate var _peek: ListNode? // \u5c06\u5934\u8282\u70b9\u4f5c\u4e3a\u6808\u9876\nprivate var _size = 0 // \u6808\u7684\u957f\u5ea6\ninit() {}\n/* \u83b7\u53d6\u6808\u7684\u957f\u5ea6 */\nfunc size() -&gt; Int {\n_size\n}\n/* \u5224\u65ad\u6808\u662f\u5426\u4e3a\u7a7a */\nfunc isEmpty() -&gt; Bool {\nsize() == 0\n}\n/* \u5165\u6808 */\nfunc push(num: Int) {\nlet node = ListNode(x: num)\nnode.next = _peek\n_peek = node\n_size += 1\n}\n/* \u51fa\u6808 */\n@discardableResult\nfunc pop() -&gt; Int {\nlet num = peek()\n_peek = _peek?.next\n_size -= 1\nreturn num\n}\n/* \u8bbf\u95ee\u6808\u9876\u5143\u7d20 */\nfunc peek() -&gt; Int {\nif isEmpty() {\nfatalError(\"\u6808\u4e3a\u7a7a\")\n}\nreturn _peek!.val\n}\n/* \u5c06 List \u8f6c\u5316\u4e3a Array \u5e76\u8fd4\u56de */\nfunc toArray() -&gt; [Int] {\nvar node = _peek\nvar res = Array(repeating: 0, count: _size)\nfor i in sequence(first: res.count - 1, next: { $0 &gt;= 0 + 1 ? $0 - 1 : nil }) {\nres[i] = node!.val\nnode = node?.next\n}\nreturn res\n}\n}\n</code></pre> linkedlist_stack.zig<pre><code>// \u57fa\u4e8e\u94fe\u8868\u5b9e\u73b0\u7684\u6808\nfn LinkedListStack(comptime T: type) type {\nreturn struct {\nconst Self = @This();\nstack_top: ?*inc.ListNode(T) = null,             // \u5c06\u5934\u8282\u70b9\u4f5c\u4e3a\u6808\u9876\nstk_size: usize = 0,                             // \u6808\u7684\u957f\u5ea6\nmem_arena: ?std.heap.ArenaAllocator = null,\nmem_allocator: std.mem.Allocator = undefined,   // \u5185\u5b58\u5206\u914d\u5668\n// \u6784\u9020\u65b9\u6cd5\uff08\u5206\u914d\u5185\u5b58+\u521d\u59cb\u5316\u6808\uff09\npub fn init(self: *Self, allocator: std.mem.Allocator) !void {\nif (self.mem_arena == null) {\nself.mem_arena = std.heap.ArenaAllocator.init(allocator);\nself.mem_allocator = self.mem_arena.?.allocator();\n}\nself.stack_top = null;\nself.stk_size = 0;\n}\n// \u6790\u6784\u65b9\u6cd5\uff08\u91ca\u653e\u5185\u5b58\uff09\npub fn deinit(self: *Self) void {\nif (self.mem_arena == null) return;\nself.mem_arena.?.deinit();\n}\n// \u83b7\u53d6\u6808\u7684\u957f\u5ea6\npub fn size(self: *Self) usize {\nreturn self.stk_size;\n}\n// \u5224\u65ad\u6808\u662f\u5426\u4e3a\u7a7a\npub fn isEmpty(self: *Self) bool {\nreturn self.size() == 0;\n}\n// \u8bbf\u95ee\u6808\u9876\u5143\u7d20\npub fn peek(self: *Self) T {\nif (self.size() == 0) @panic(\"\u6808\u4e3a\u7a7a\");\nreturn self.stack_top.?.val;\n}  // \u5165\u6808\npub fn push(self: *Self, num: T) !void {\nvar node = try self.mem_allocator.create(inc.ListNode(T));\nnode.init(num);\nnode.next = self.stack_top;\nself.stack_top = node;\nself.stk_size += 1;\n} // \u51fa\u6808\npub fn pop(self: *Self) T {\nvar num = self.peek();\nself.stack_top = self.stack_top.?.next;\nself.stk_size -= 1;\nreturn num;\n} // \u5c06\u6808\u8f6c\u6362\u4e3a\u6570\u7ec4\npub fn toArray(self: *Self) ![]T {\nvar node = self.stack_top;\nvar res = try self.mem_allocator.alloc(T, self.size());\nstd.mem.set(T, res, @as(T, 0));\nvar i: usize = 0;\nwhile (i &lt; res.len) : (i += 1) {\nres[res.len - i - 1] = node.?.val;\nnode = node.?.next;\n}\nreturn res;\n}\n};\n}\n</code></pre> linkedlist_stack.dart<pre><code>/* \u57fa\u4e8e\u94fe\u8868\u7c7b\u5b9e\u73b0\u7684\u6808 */\nclass LinkedListStack {\nListNode? _stackPeek; // \u5c06\u5934\u8282\u70b9\u4f5c\u4e3a\u6808\u9876\nint _stkSize = 0; // \u6808\u7684\u957f\u5ea6\nLinkedListStack() {\n_stackPeek = null;\n}\n/* \u83b7\u53d6\u6808\u7684\u957f\u5ea6 */\nint size() {\nreturn _stkSize;\n}\n/* \u5224\u65ad\u6808\u662f\u5426\u4e3a\u7a7a */\nbool isEmpty() {\nreturn _stkSize == 0;\n}\n/* \u5165\u6808 */\nvoid push(int num) {\nfinal ListNode node = ListNode(num);\nnode.next = _stackPeek;\n_stackPeek = node;\n_stkSize++;\n}\n/* \u51fa\u6808 */\nint pop() {\nfinal int num = peek();\n_stackPeek = _stackPeek!.next;\n_stkSize--;\nreturn num;\n}\n/* \u8bbf\u95ee\u6808\u9876\u5143\u7d20 */\nint peek() {\nif (_stackPeek == null) {\nthrow Exception(\"\u6808\u4e3a\u7a7a\");\n}\nreturn _stackPeek!.val;\n}\n/* \u5c06\u94fe\u8868\u8f6c\u5316\u4e3a List \u5e76\u8fd4\u56de */\nList&lt;int&gt; toList() {\nListNode? node = _stackPeek;\nList&lt;int&gt; list = [];\nwhile (node != null) {\nlist.add(node.val);\nnode = node.next;\n}\nlist = list.reversed.toList();\nreturn list;\n}\n}\n</code></pre>"},{"location":"chapter_stack_and_queue/stack/#_2","title":"\u57fa\u4e8e\u6570\u7ec4\u7684\u5b9e\u73b0","text":"<p>\u5728\u57fa\u4e8e\u300c\u6570\u7ec4\u300d\u5b9e\u73b0\u6808\u65f6\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u6570\u7ec4\u7684\u5c3e\u90e8\u4f5c\u4e3a\u6808\u9876\u3002\u5728\u8fd9\u6837\u7684\u8bbe\u8ba1\u4e0b\uff0c\u5165\u6808\u4e0e\u51fa\u6808\u64cd\u4f5c\u5c31\u5206\u522b\u5bf9\u5e94\u5728\u6570\u7ec4\u5c3e\u90e8\u6dfb\u52a0\u5143\u7d20\u4e0e\u5220\u9664\u5143\u7d20\uff0c\u65f6\u95f4\u590d\u6742\u5ea6\u90fd\u4e3a \\(O(1)\\) \u3002</p> ArrayStackpush()pop() <p></p> <p></p> <p></p> <p>\u7531\u4e8e\u5165\u6808\u7684\u5143\u7d20\u53ef\u80fd\u4f1a\u6e90\u6e90\u4e0d\u65ad\u5730\u589e\u52a0\uff0c\u56e0\u6b64\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u52a8\u6001\u6570\u7ec4\uff0c\u8fd9\u6837\u5c31\u65e0\u9700\u81ea\u884c\u5904\u7406\u6570\u7ec4\u6269\u5bb9\u95ee\u9898\u3002\u4ee5\u4e0b\u4e3a\u793a\u4f8b\u4ee3\u7801\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart array_stack.java<pre><code>/* \u57fa\u4e8e\u6570\u7ec4\u5b9e\u73b0\u7684\u6808 */\nclass ArrayStack {\nprivate ArrayList&lt;Integer&gt; stack;\npublic ArrayStack() {\n// \u521d\u59cb\u5316\u5217\u8868\uff08\u52a8\u6001\u6570\u7ec4\uff09\nstack = new ArrayList&lt;&gt;();\n}\n/* \u83b7\u53d6\u6808\u7684\u957f\u5ea6 */\npublic int size() {\nreturn stack.size();\n}\n/* \u5224\u65ad\u6808\u662f\u5426\u4e3a\u7a7a */\npublic boolean isEmpty() {\nreturn size() == 0;\n}\n/* \u5165\u6808 */\npublic void push(int num) {\nstack.add(num);\n}\n/* \u51fa\u6808 */\npublic int pop() {\nif (isEmpty())\nthrow new IndexOutOfBoundsException();\nreturn stack.remove(size() - 1);\n}\n/* \u8bbf\u95ee\u6808\u9876\u5143\u7d20 */\npublic int peek() {\nif (isEmpty())\nthrow new IndexOutOfBoundsException();\nreturn stack.get(size() - 1);\n}\n/* \u5c06 List \u8f6c\u5316\u4e3a Array \u5e76\u8fd4\u56de */\npublic Object[] toArray() {\nreturn stack.toArray();\n}\n}\n</code></pre> array_stack.cpp<pre><code>/* \u57fa\u4e8e\u6570\u7ec4\u5b9e\u73b0\u7684\u6808 */\nclass ArrayStack {\nprivate:\nvector&lt;int&gt; stack;\npublic:\n/* \u83b7\u53d6\u6808\u7684\u957f\u5ea6 */\nint size() {\nreturn stack.size();\n}\n/* \u5224\u65ad\u6808\u662f\u5426\u4e3a\u7a7a */\nbool empty() {\nreturn stack.empty();\n}\n/* \u5165\u6808 */\nvoid push(int num) {\nstack.push_back(num);\n}\n/* \u51fa\u6808 */\nvoid pop() {\nint oldTop = top();\nstack.pop_back();\n}\n/* \u8bbf\u95ee\u6808\u9876\u5143\u7d20 */\nint top() {\nif (empty())\nthrow out_of_range(\"\u6808\u4e3a\u7a7a\");\nreturn stack.back();\n}\n/* \u8fd4\u56de Vector */\nvector&lt;int&gt; toVector() {\nreturn stack;\n}\n};\n</code></pre> array_stack.py<pre><code>class ArrayStack:\n\"\"\"\u57fa\u4e8e\u6570\u7ec4\u5b9e\u73b0\u7684\u6808\"\"\"\ndef __init__(self) -&gt; None:\n\"\"\"\u6784\u9020\u65b9\u6cd5\"\"\"\nself.__stack: list[int] = []\ndef size(self) -&gt; int:\n\"\"\"\u83b7\u53d6\u6808\u7684\u957f\u5ea6\"\"\"\nreturn len(self.__stack)\ndef is_empty(self) -&gt; bool:\n\"\"\"\u5224\u65ad\u6808\u662f\u5426\u4e3a\u7a7a\"\"\"\nreturn self.__stack == []\ndef push(self, item: int) -&gt; None:\n\"\"\"\u5165\u6808\"\"\"\nself.__stack.append(item)\ndef pop(self) -&gt; int:\n\"\"\"\u51fa\u6808\"\"\"\nif self.is_empty():\nraise IndexError(\"\u6808\u4e3a\u7a7a\")\nreturn self.__stack.pop()\ndef peek(self) -&gt; int:\n\"\"\"\u8bbf\u95ee\u6808\u9876\u5143\u7d20\"\"\"\nif self.is_empty():\nraise IndexError(\"\u6808\u4e3a\u7a7a\")\nreturn self.__stack[-1]\ndef to_list(self) -&gt; list[int]:\n\"\"\"\u8fd4\u56de\u5217\u8868\u7528\u4e8e\u6253\u5370\"\"\"\nreturn self.__stack\n</code></pre> array_stack.go<pre><code>/* \u57fa\u4e8e\u6570\u7ec4\u5b9e\u73b0\u7684\u6808 */\ntype arrayStack struct {\ndata []int // \u6570\u636e\n}\n/* \u521d\u59cb\u5316\u6808 */\nfunc newArrayStack() *arrayStack {\nreturn &amp;arrayStack{\n// \u8bbe\u7f6e\u6808\u7684\u957f\u5ea6\u4e3a 0\uff0c\u5bb9\u91cf\u4e3a 16\ndata: make([]int, 0, 16),\n}\n}\n/* \u6808\u7684\u957f\u5ea6 */\nfunc (s *arrayStack) size() int {\nreturn len(s.data)\n}\n/* \u6808\u662f\u5426\u4e3a\u7a7a */\nfunc (s *arrayStack) isEmpty() bool {\nreturn s.size() == 0\n}\n/* \u5165\u6808 */\nfunc (s *arrayStack) push(v int) {\n// \u5207\u7247\u4f1a\u81ea\u52a8\u6269\u5bb9\ns.data = append(s.data, v)\n}\n/* \u51fa\u6808 */\nfunc (s *arrayStack) pop() any {\nval := s.peek()\ns.data = s.data[:len(s.data)-1]\nreturn val\n}\n/* \u83b7\u53d6\u6808\u9876\u5143\u7d20 */\nfunc (s *arrayStack) peek() any {\nif s.isEmpty() {\nreturn nil\n}\nval := s.data[len(s.data)-1]\nreturn val\n}\n/* \u83b7\u53d6 Slice \u7528\u4e8e\u6253\u5370 */\nfunc (s *arrayStack) toSlice() []int {\nreturn s.data\n}\n</code></pre> array_stack.js<pre><code>/* \u57fa\u4e8e\u6570\u7ec4\u5b9e\u73b0\u7684\u6808 */\nclass ArrayStack {\n#stack;\nconstructor() {\nthis.#stack = [];\n}\n/* \u83b7\u53d6\u6808\u7684\u957f\u5ea6 */\nget size() {\nreturn this.#stack.length;\n}\n/* \u5224\u65ad\u6808\u662f\u5426\u4e3a\u7a7a */\nempty() {\nreturn this.#stack.length === 0;\n}\n/* \u5165\u6808 */\npush(num) {\nthis.#stack.push(num);\n}\n/* \u51fa\u6808 */\npop() {\nif (this.empty()) throw new Error('\u6808\u4e3a\u7a7a');\nreturn this.#stack.pop();\n}\n/* \u8bbf\u95ee\u6808\u9876\u5143\u7d20 */\ntop() {\nif (this.empty()) throw new Error('\u6808\u4e3a\u7a7a');\nreturn this.#stack[this.#stack.length - 1];\n}\n/* \u8fd4\u56de Array */\ntoArray() {\nreturn this.#stack;\n}\n}\n</code></pre> array_stack.ts<pre><code>/* \u57fa\u4e8e\u6570\u7ec4\u5b9e\u73b0\u7684\u6808 */\nclass ArrayStack {\nprivate stack: number[];\nconstructor() {\nthis.stack = [];\n}\n/* \u83b7\u53d6\u6808\u7684\u957f\u5ea6 */\nget size(): number {\nreturn this.stack.length;\n}\n/* \u5224\u65ad\u6808\u662f\u5426\u4e3a\u7a7a */\nempty(): boolean {\nreturn this.stack.length === 0;\n}\n/* \u5165\u6808 */\npush(num: number): void {\nthis.stack.push(num);\n}\n/* \u51fa\u6808 */\npop(): number | undefined {\nif (this.empty()) throw new Error('\u6808\u4e3a\u7a7a');\nreturn this.stack.pop();\n}\n/* \u8bbf\u95ee\u6808\u9876\u5143\u7d20 */\ntop(): number | undefined {\nif (this.empty()) throw new Error('\u6808\u4e3a\u7a7a');\nreturn this.stack[this.stack.length - 1];\n}\n/* \u8fd4\u56de Array */\ntoArray() {\nreturn this.stack;\n}\n}\n</code></pre> array_stack.c<pre><code>/* \u57fa\u4e8e\u6570\u7ec4\u5b9e\u73b0\u7684\u6808 */\nstruct arrayStack {\nint *data;\nint size;\n};\ntypedef struct arrayStack arrayStack;\n/* \u6784\u9020\u51fd\u6570 */\narrayStack *newArrayStack() {\narrayStack *s = malloc(sizeof(arrayStack));\n// \u521d\u59cb\u5316\u4e00\u4e2a\u5927\u5bb9\u91cf\uff0c\u907f\u514d\u6269\u5bb9\ns-&gt;data = malloc(sizeof(int) * MAX_SIZE);\ns-&gt;size = 0;\nreturn s;\n}\n/* \u83b7\u53d6\u6808\u7684\u957f\u5ea6 */\nint size(arrayStack *s) {\nreturn s-&gt;size;\n}\n/* \u5224\u65ad\u6808\u662f\u5426\u4e3a\u7a7a */\nbool isEmpty(arrayStack *s) {\nreturn s-&gt;size == 0;\n}\n/* \u5165\u6808 */\nvoid push(arrayStack *s, int num) {\nif (s-&gt;size == MAX_SIZE) {\nprintf(\"stack is full.\\n\");\nreturn;\n}\ns-&gt;data[s-&gt;size] = num;\ns-&gt;size++;\n}\n/* \u8bbf\u95ee\u6808\u9876\u5143\u7d20 */\nint peek(arrayStack *s) {\nif (s-&gt;size == 0) {\nprintf(\"stack is empty.\\n\");\nreturn INT_MAX;\n}\nreturn s-&gt;data[s-&gt;size - 1];\n}\n/* \u51fa\u6808 */\nint pop(arrayStack *s) {\nif (s-&gt;size == 0) {\nprintf(\"stack is empty.\\n\");\nreturn INT_MAX;\n}\nint val = peek(s);\ns-&gt;size--;\nreturn val;\n}\n</code></pre> array_stack.cs<pre><code>/* \u57fa\u4e8e\u6570\u7ec4\u5b9e\u73b0\u7684\u6808 */\nclass ArrayStack {\nprivate List&lt;int&gt; stack;\npublic ArrayStack() {\n// \u521d\u59cb\u5316\u5217\u8868\uff08\u52a8\u6001\u6570\u7ec4\uff09\nstack = new();\n}\n/* \u83b7\u53d6\u6808\u7684\u957f\u5ea6 */\npublic int size() {\nreturn stack.Count();\n}\n/* \u5224\u65ad\u6808\u662f\u5426\u4e3a\u7a7a */\npublic bool isEmpty() {\nreturn size() == 0;\n}\n/* \u5165\u6808 */\npublic void push(int num) {\nstack.Add(num);\n}\n/* \u51fa\u6808 */\npublic int pop() {\nif (isEmpty())\nthrow new Exception();\nvar val = peek();\nstack.RemoveAt(size() - 1);\nreturn val;\n}\n/* \u8bbf\u95ee\u6808\u9876\u5143\u7d20 */\npublic int peek() {\nif (isEmpty())\nthrow new Exception();\nreturn stack[size() - 1];\n}\n/* \u5c06 List \u8f6c\u5316\u4e3a Array \u5e76\u8fd4\u56de */\npublic int[] toArray() {\nreturn stack.ToArray();\n}\n}\n</code></pre> array_stack.swift<pre><code>/* \u57fa\u4e8e\u6570\u7ec4\u5b9e\u73b0\u7684\u6808 */\nclass ArrayStack {\nprivate var stack: [Int]\ninit() {\n// \u521d\u59cb\u5316\u5217\u8868\uff08\u52a8\u6001\u6570\u7ec4\uff09\nstack = []\n}\n/* \u83b7\u53d6\u6808\u7684\u957f\u5ea6 */\nfunc size() -&gt; Int {\nstack.count\n}\n/* \u5224\u65ad\u6808\u662f\u5426\u4e3a\u7a7a */\nfunc isEmpty() -&gt; Bool {\nstack.isEmpty\n}\n/* \u5165\u6808 */\nfunc push(num: Int) {\nstack.append(num)\n}\n/* \u51fa\u6808 */\n@discardableResult\nfunc pop() -&gt; Int {\nif isEmpty() {\nfatalError(\"\u6808\u4e3a\u7a7a\")\n}\nreturn stack.removeLast()\n}\n/* \u8bbf\u95ee\u6808\u9876\u5143\u7d20 */\nfunc peek() -&gt; Int {\nif isEmpty() {\nfatalError(\"\u6808\u4e3a\u7a7a\")\n}\nreturn stack.last!\n}\n/* \u5c06 List \u8f6c\u5316\u4e3a Array \u5e76\u8fd4\u56de */\nfunc toArray() -&gt; [Int] {\nstack\n}\n}\n</code></pre> array_stack.zig<pre><code>// \u57fa\u4e8e\u6570\u7ec4\u5b9e\u73b0\u7684\u6808\nfn ArrayStack(comptime T: type) type {\nreturn struct {\nconst Self = @This();\nstack: ?std.ArrayList(T) = null,     // \u6784\u9020\u65b9\u6cd5\uff08\u5206\u914d\u5185\u5b58+\u521d\u59cb\u5316\u6808\uff09\npub fn init(self: *Self, allocator: std.mem.Allocator) void {\nif (self.stack == null) {\nself.stack = std.ArrayList(T).init(allocator);\n}\n}\n// \u6790\u6784\u65b9\u6cd5\uff08\u91ca\u653e\u5185\u5b58\uff09\npub fn deinit(self: *Self) void {\nif (self.stack == null) return;\nself.stack.?.deinit();\n}\n// \u83b7\u53d6\u6808\u7684\u957f\u5ea6\npub fn size(self: *Self) usize {\nreturn self.stack.?.items.len;\n}\n// \u5224\u65ad\u6808\u662f\u5426\u4e3a\u7a7a\npub fn isEmpty(self: *Self) bool {\nreturn self.size() == 0;\n}\n// \u8bbf\u95ee\u6808\u9876\u5143\u7d20\npub fn peek(self: *Self) T {\nif (self.isEmpty()) @panic(\"\u6808\u4e3a\u7a7a\");\nreturn self.stack.?.items[self.size() - 1];\n}  // \u5165\u6808\npub fn push(self: *Self, num: T) !void {\ntry self.stack.?.append(num);\n} // \u51fa\u6808\npub fn pop(self: *Self) T {\nvar num = self.stack.?.pop();\nreturn num;\n} // \u8fd4\u56de ArrayList\npub fn toList(self: *Self) std.ArrayList(T) {\nreturn self.stack.?;\n}\n};\n}\n</code></pre> array_stack.dart<pre><code>/* \u57fa\u4e8e\u6570\u7ec4\u5b9e\u73b0\u7684\u6808 */\nclass ArrayStack {\nlate List&lt;int&gt; _stack;\nArrayStack() {\n_stack = [];\n}\n/* \u83b7\u53d6\u6808\u7684\u957f\u5ea6 */\nint size() {\nreturn _stack.length;\n}\n/* \u5224\u65ad\u6808\u662f\u5426\u4e3a\u7a7a */\nbool isEmpty() {\nreturn _stack.isEmpty;\n}\n/* \u5165\u6808 */\nvoid push(int num) {\n_stack.add(num);\n}\n/* \u51fa\u6808 */\nint pop() {\nif (isEmpty()) {\nthrow Exception(\"\u6808\u4e3a\u7a7a\");\n}\nreturn _stack.removeLast();\n}\n/* \u8bbf\u95ee\u6808\u9876\u5143\u7d20 */\nint peek() {\nif (isEmpty()) {\nthrow Exception(\"\u6808\u4e3a\u7a7a\");\n}\nreturn _stack.last;\n}\n/* \u5c06\u6808\u8f6c\u5316\u4e3a Array \u5e76\u8fd4\u56de */\nList&lt;int&gt; toArray() =&gt; _stack;\n}\n</code></pre>"},{"location":"chapter_stack_and_queue/stack/#513","title":"5.1.3. \u00a0 \u4e24\u79cd\u5b9e\u73b0\u5bf9\u6bd4","text":""},{"location":"chapter_stack_and_queue/stack/#_3","title":"\u652f\u6301\u64cd\u4f5c","text":"<p>\u4e24\u79cd\u5b9e\u73b0\u90fd\u652f\u6301\u6808\u5b9a\u4e49\u4e2d\u7684\u5404\u9879\u64cd\u4f5c\u3002\u6570\u7ec4\u5b9e\u73b0\u989d\u5916\u652f\u6301\u968f\u673a\u8bbf\u95ee\uff0c\u4f46\u8fd9\u5df2\u8d85\u51fa\u4e86\u6808\u7684\u5b9a\u4e49\u8303\u7574\uff0c\u56e0\u6b64\u4e00\u822c\u4e0d\u4f1a\u7528\u5230\u3002</p>"},{"location":"chapter_stack_and_queue/stack/#_4","title":"\u65f6\u95f4\u6548\u7387","text":"<p>\u5728\u57fa\u4e8e\u6570\u7ec4\u7684\u5b9e\u73b0\u4e2d\uff0c\u5165\u6808\u548c\u51fa\u6808\u64cd\u4f5c\u90fd\u662f\u5728\u9884\u5148\u5206\u914d\u597d\u7684\u8fde\u7eed\u5185\u5b58\u4e2d\u8fdb\u884c\uff0c\u5177\u6709\u5f88\u597d\u7684\u7f13\u5b58\u672c\u5730\u6027\uff0c\u56e0\u6b64\u6548\u7387\u8f83\u9ad8\u3002\u7136\u800c\uff0c\u5982\u679c\u5165\u6808\u65f6\u8d85\u51fa\u6570\u7ec4\u5bb9\u91cf\uff0c\u4f1a\u89e6\u53d1\u6269\u5bb9\u673a\u5236\uff0c\u5bfc\u81f4\u8be5\u6b21\u5165\u6808\u64cd\u4f5c\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u53d8\u4e3a \\(O(n)\\) \u3002</p> <p>\u5728\u94fe\u8868\u5b9e\u73b0\u4e2d\uff0c\u94fe\u8868\u7684\u6269\u5bb9\u975e\u5e38\u7075\u6d3b\uff0c\u4e0d\u5b58\u5728\u4e0a\u8ff0\u6570\u7ec4\u6269\u5bb9\u65f6\u6548\u7387\u964d\u4f4e\u7684\u95ee\u9898\u3002\u4f46\u662f\uff0c\u5165\u6808\u64cd\u4f5c\u9700\u8981\u521d\u59cb\u5316\u8282\u70b9\u5bf9\u8c61\u5e76\u4fee\u6539\u6307\u9488\uff0c\u56e0\u6b64\u6548\u7387\u76f8\u5bf9\u8f83\u4f4e\u3002\u4e0d\u8fc7\uff0c\u5982\u679c\u5165\u6808\u5143\u7d20\u672c\u8eab\u5c31\u662f\u8282\u70b9\u5bf9\u8c61\uff0c\u90a3\u4e48\u53ef\u4ee5\u7701\u53bb\u521d\u59cb\u5316\u6b65\u9aa4\uff0c\u4ece\u800c\u63d0\u9ad8\u6548\u7387\u3002</p> <p>\u7efc\u4e0a\u6240\u8ff0\uff0c\u5f53\u5165\u6808\u4e0e\u51fa\u6808\u64cd\u4f5c\u7684\u5143\u7d20\u662f\u57fa\u672c\u6570\u636e\u7c7b\u578b\uff08\u5982 <code>int</code> , <code>double</code> \uff09\u65f6\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u51fa\u4ee5\u4e0b\u7ed3\u8bba\uff1a</p> <ul> <li>\u57fa\u4e8e\u6570\u7ec4\u5b9e\u73b0\u7684\u6808\u5728\u89e6\u53d1\u6269\u5bb9\u65f6\u6548\u7387\u4f1a\u964d\u4f4e\uff0c\u4f46\u7531\u4e8e\u6269\u5bb9\u662f\u4f4e\u9891\u64cd\u4f5c\uff0c\u56e0\u6b64\u5e73\u5747\u6548\u7387\u66f4\u9ad8\uff1b</li> <li>\u57fa\u4e8e\u94fe\u8868\u5b9e\u73b0\u7684\u6808\u53ef\u4ee5\u63d0\u4f9b\u66f4\u52a0\u7a33\u5b9a\u7684\u6548\u7387\u8868\u73b0\uff1b</li> </ul>"},{"location":"chapter_stack_and_queue/stack/#_5","title":"\u7a7a\u95f4\u6548\u7387","text":"<p>\u5728\u521d\u59cb\u5316\u5217\u8868\u65f6\uff0c\u7cfb\u7edf\u4f1a\u4e3a\u5217\u8868\u5206\u914d\u201c\u521d\u59cb\u5bb9\u91cf\u201d\uff0c\u8be5\u5bb9\u91cf\u53ef\u80fd\u8d85\u8fc7\u5b9e\u9645\u9700\u6c42\u3002\u5e76\u4e14\uff0c\u6269\u5bb9\u673a\u5236\u901a\u5e38\u662f\u6309\u7167\u7279\u5b9a\u500d\u7387\uff08\u4f8b\u5982 2 \u500d\uff09\u8fdb\u884c\u6269\u5bb9\uff0c\u6269\u5bb9\u540e\u7684\u5bb9\u91cf\u4e5f\u53ef\u80fd\u8d85\u51fa\u5b9e\u9645\u9700\u6c42\u3002\u56e0\u6b64\uff0c\u57fa\u4e8e\u6570\u7ec4\u5b9e\u73b0\u7684\u6808\u53ef\u80fd\u9020\u6210\u4e00\u5b9a\u7684\u7a7a\u95f4\u6d6a\u8d39\u3002</p> <p>\u7136\u800c\uff0c\u7531\u4e8e\u94fe\u8868\u8282\u70b9\u9700\u8981\u989d\u5916\u5b58\u50a8\u6307\u9488\uff0c\u56e0\u6b64\u94fe\u8868\u8282\u70b9\u5360\u7528\u7684\u7a7a\u95f4\u76f8\u5bf9\u8f83\u5927\u3002</p> <p>\u7efc\u4e0a\uff0c\u6211\u4eec\u4e0d\u80fd\u7b80\u5355\u5730\u786e\u5b9a\u54ea\u79cd\u5b9e\u73b0\u66f4\u52a0\u8282\u7701\u5185\u5b58\uff0c\u9700\u8981\u9488\u5bf9\u5177\u4f53\u60c5\u51b5\u8fdb\u884c\u5206\u6790\u3002</p>"},{"location":"chapter_stack_and_queue/stack/#514","title":"5.1.4. \u00a0 \u6808\u5178\u578b\u5e94\u7528","text":"<ul> <li>\u6d4f\u89c8\u5668\u4e2d\u7684\u540e\u9000\u4e0e\u524d\u8fdb\u3001\u8f6f\u4ef6\u4e2d\u7684\u64a4\u9500\u4e0e\u53cd\u64a4\u9500\u3002\u6bcf\u5f53\u6211\u4eec\u6253\u5f00\u65b0\u7684\u7f51\u9875\uff0c\u6d4f\u89c8\u5668\u5c31\u4f1a\u5c06\u4e0a\u4e00\u4e2a\u7f51\u9875\u6267\u884c\u5165\u6808\uff0c\u8fd9\u6837\u6211\u4eec\u5c31\u53ef\u4ee5\u901a\u8fc7\u300c\u540e\u9000\u300d\u64cd\u4f5c\u56de\u5230\u4e0a\u4e00\u9875\u9762\u3002\u540e\u9000\u64cd\u4f5c\u5b9e\u9645\u4e0a\u662f\u5728\u6267\u884c\u51fa\u6808\u3002\u5982\u679c\u8981\u540c\u65f6\u652f\u6301\u540e\u9000\u548c\u524d\u8fdb\uff0c\u90a3\u4e48\u9700\u8981\u4e24\u4e2a\u6808\u6765\u914d\u5408\u5b9e\u73b0\u3002</li> <li>\u7a0b\u5e8f\u5185\u5b58\u7ba1\u7406\u3002\u6bcf\u6b21\u8c03\u7528\u51fd\u6570\u65f6\uff0c\u7cfb\u7edf\u90fd\u4f1a\u5728\u6808\u9876\u6dfb\u52a0\u4e00\u4e2a\u6808\u5e27\uff0c\u7528\u4e8e\u8bb0\u5f55\u51fd\u6570\u7684\u4e0a\u4e0b\u6587\u4fe1\u606f\u3002\u5728\u9012\u5f52\u51fd\u6570\u4e2d\uff0c\u5411\u4e0b\u9012\u63a8\u9636\u6bb5\u4f1a\u4e0d\u65ad\u6267\u884c\u5165\u6808\u64cd\u4f5c\uff0c\u800c\u5411\u4e0a\u56de\u6eaf\u9636\u6bb5\u5219\u4f1a\u6267\u884c\u51fa\u6808\u64cd\u4f5c\u3002</li> </ul>"},{"location":"chapter_stack_and_queue/summary/","title":"5.4. \u00a0 \u5c0f\u7ed3","text":"<ul> <li>\u6808\u662f\u4e00\u79cd\u9075\u5faa\u5148\u5165\u540e\u51fa\u539f\u5219\u7684\u6570\u636e\u7ed3\u6784\uff0c\u53ef\u901a\u8fc7\u6570\u7ec4\u6216\u94fe\u8868\u6765\u5b9e\u73b0\u3002</li> <li>\u4ece\u65f6\u95f4\u6548\u7387\u89d2\u5ea6\u770b\uff0c\u6808\u7684\u6570\u7ec4\u5b9e\u73b0\u5177\u6709\u8f83\u9ad8\u7684\u5e73\u5747\u6548\u7387\uff0c\u4f46\u5728\u6269\u5bb9\u8fc7\u7a0b\u4e2d\uff0c\u5355\u6b21\u5165\u6808\u64cd\u4f5c\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4f1a\u964d\u4f4e\u81f3 \\(O(n)\\) \u3002\u76f8\u6bd4\u4e4b\u4e0b\uff0c\u57fa\u4e8e\u94fe\u8868\u5b9e\u73b0\u7684\u6808\u5177\u6709\u66f4\u4e3a\u7a33\u5b9a\u7684\u6548\u7387\u8868\u73b0\u3002</li> <li>\u5728\u7a7a\u95f4\u6548\u7387\u65b9\u9762\uff0c\u6808\u7684\u6570\u7ec4\u5b9e\u73b0\u53ef\u80fd\u5bfc\u81f4\u4e00\u5b9a\u7a0b\u5ea6\u7684\u7a7a\u95f4\u6d6a\u8d39\u3002\u4f46\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u94fe\u8868\u8282\u70b9\u6240\u5360\u7528\u7684\u5185\u5b58\u7a7a\u95f4\u6bd4\u6570\u7ec4\u5143\u7d20\u66f4\u5927\u3002</li> <li>\u961f\u5217\u662f\u4e00\u79cd\u9075\u5faa\u5148\u5165\u5148\u51fa\u539f\u5219\u7684\u6570\u636e\u7ed3\u6784\uff0c\u540c\u6837\u53ef\u4ee5\u901a\u8fc7\u6570\u7ec4\u6216\u94fe\u8868\u6765\u5b9e\u73b0\u3002\u5728\u65f6\u95f4\u6548\u7387\u548c\u7a7a\u95f4\u6548\u7387\u7684\u5bf9\u6bd4\u4e0a\uff0c\u961f\u5217\u7684\u7ed3\u8bba\u4e0e\u524d\u8ff0\u6808\u7684\u7ed3\u8bba\u76f8\u4f3c\u3002</li> <li>\u53cc\u5411\u961f\u5217\u662f\u4e00\u79cd\u5177\u6709\u66f4\u9ad8\u81ea\u7531\u5ea6\u7684\u961f\u5217\uff0c\u5b83\u5141\u8bb8\u5728\u4e24\u7aef\u8fdb\u884c\u5143\u7d20\u7684\u6dfb\u52a0\u548c\u5220\u9664\u64cd\u4f5c\u3002</li> </ul>"},{"location":"chapter_stack_and_queue/summary/#541-q-a","title":"5.4.1. \u00a0 Q &amp; A","text":"<p>\u6d4f\u89c8\u5668\u7684\u524d\u8fdb\u540e\u9000\u662f\u5426\u662f\u53cc\u5411\u94fe\u8868\u5b9e\u73b0\uff1f</p> <p>\u6d4f\u89c8\u5668\u7684\u524d\u8fdb\u540e\u9000\u529f\u80fd\u672c\u8d28\u4e0a\u662f\u201c\u6808\u201d\u7684\u4f53\u73b0\u3002\u5f53\u7528\u6237\u8bbf\u95ee\u4e00\u4e2a\u65b0\u9875\u9762\u65f6\uff0c\u8be5\u9875\u9762\u4f1a\u88ab\u6dfb\u52a0\u5230\u6808\u9876\uff1b\u5f53\u7528\u6237\u70b9\u51fb\u540e\u9000\u6309\u94ae\u65f6\uff0c\u8be5\u9875\u9762\u4f1a\u4ece\u6808\u9876\u5f39\u51fa\u3002\u4f7f\u7528\u53cc\u5411\u961f\u5217\u53ef\u4ee5\u65b9\u4fbf\u5b9e\u73b0\u4e00\u4e9b\u989d\u5916\u64cd\u4f5c\uff0c\u8fd9\u4e2a\u5728\u53cc\u5411\u961f\u5217\u7ae0\u8282\u6709\u63d0\u5230\u3002</p> <p>\u5728\u51fa\u6808\u540e\uff0c\u662f\u5426\u9700\u8981\u91ca\u653e\u51fa\u6808\u8282\u70b9\u7684\u5185\u5b58\uff1f</p> <p>\u5982\u679c\u540e\u7eed\u4ecd\u9700\u8981\u4f7f\u7528\u5f39\u51fa\u8282\u70b9\uff0c\u5219\u4e0d\u9700\u8981\u91ca\u653e\u5185\u5b58\u3002\u82e5\u4e4b\u540e\u4e0d\u9700\u8981\u7528\u5230\uff0c<code>Java</code> \u548c <code>Python</code> \u7b49\u8bed\u8a00\u62e5\u6709\u81ea\u52a8\u5783\u573e\u56de\u6536\u673a\u5236\uff0c\u56e0\u6b64\u4e0d\u9700\u8981\u624b\u52a8\u91ca\u653e\u5185\u5b58\uff1b\u5728 <code>C</code> \u548c <code>C++</code> \u4e2d\u9700\u8981\u624b\u52a8\u91ca\u653e\u5185\u5b58\u3002</p> <p>\u53cc\u5411\u961f\u5217\u50cf\u662f\u4e24\u4e2a\u6808\u62fc\u63a5\u5728\u4e86\u4e00\u8d77\uff0c\u5b83\u7684\u7528\u9014\u662f\u4ec0\u4e48\uff1f</p> <p>\u53cc\u5411\u961f\u5217\u5c31\u50cf\u662f\u6808\u548c\u961f\u5217\u7684\u7ec4\u5408\uff0c\u6216\u8005\u662f\u4e24\u4e2a\u6808\u62fc\u5728\u4e86\u4e00\u8d77\u3002\u5b83\u8868\u73b0\u7684\u662f\u6808 + \u961f\u5217\u7684\u903b\u8f91\uff0c\u56e0\u6b64\u53ef\u4ee5\u5b9e\u73b0\u6808\u4e0e\u961f\u5217\u7684\u6240\u6709\u5e94\u7528\uff0c\u5e76\u4e14\u66f4\u52a0\u7075\u6d3b\u3002</p>"},{"location":"chapter_tree/","title":"7. \u00a0 \u6811","text":""},{"location":"chapter_tree/array_representation_of_tree/","title":"7.3. \u00a0 \u4e8c\u53c9\u6811\u6570\u7ec4\u8868\u793a","text":"<p>\u5728\u94fe\u8868\u8868\u793a\u4e0b\uff0c\u4e8c\u53c9\u6811\u7684\u5b58\u50a8\u5355\u5143\u4e3a\u8282\u70b9 <code>TreeNode</code> \uff0c\u8282\u70b9\u4e4b\u95f4\u901a\u8fc7\u6307\u9488\u76f8\u8fde\u63a5\u3002\u5728\u4e0a\u8282\u4e2d\uff0c\u6211\u4eec\u5b66\u4e60\u4e86\u5728\u94fe\u8868\u8868\u793a\u4e0b\u7684\u4e8c\u53c9\u6811\u7684\u5404\u9879\u57fa\u672c\u64cd\u4f5c\u3002</p> <p>\u90a3\u4e48\uff0c\u80fd\u5426\u7528\u300c\u6570\u7ec4\u300d\u6765\u8868\u793a\u4e8c\u53c9\u6811\u5462\uff1f\u7b54\u6848\u662f\u80af\u5b9a\u7684\u3002</p>"},{"location":"chapter_tree/array_representation_of_tree/#731","title":"7.3.1. \u00a0 \u8868\u793a\u5b8c\u7f8e\u4e8c\u53c9\u6811","text":"<p>\u5148\u5206\u6790\u4e00\u4e2a\u7b80\u5355\u6848\u4f8b\uff0c\u7ed9\u5b9a\u4e00\u4e2a\u5b8c\u7f8e\u4e8c\u53c9\u6811\uff0c\u6211\u4eec\u5c06\u8282\u70b9\u6309\u7167\u5c42\u5e8f\u904d\u5386\u7684\u987a\u5e8f\u7f16\u53f7\uff08\u4ece \\(0\\) \u5f00\u59cb\uff09\uff0c\u6b64\u65f6\u6bcf\u4e2a\u8282\u70b9\u90fd\u5bf9\u5e94\u552f\u4e00\u7684\u7d22\u5f15\u3002</p> <p>\u6839\u636e\u5c42\u5e8f\u904d\u5386\u7684\u7279\u6027\uff0c\u6211\u4eec\u53ef\u4ee5\u63a8\u5bfc\u51fa\u7236\u8282\u70b9\u7d22\u5f15\u4e0e\u5b50\u8282\u70b9\u7d22\u5f15\u4e4b\u95f4\u7684\u201c\u6620\u5c04\u516c\u5f0f\u201d\uff1a\u82e5\u8282\u70b9\u7684\u7d22\u5f15\u4e3a \\(i\\) \uff0c\u5219\u8be5\u8282\u70b9\u7684\u5de6\u5b50\u8282\u70b9\u7d22\u5f15\u4e3a \\(2i + 1\\) \uff0c\u53f3\u5b50\u8282\u70b9\u7d22\u5f15\u4e3a \\(2i + 2\\) \u3002</p> <p></p> <p> Fig. \u5b8c\u7f8e\u4e8c\u53c9\u6811\u7684\u6570\u7ec4\u8868\u793a </p> <p>\u6620\u5c04\u516c\u5f0f\u7684\u4f5c\u7528\u76f8\u5f53\u4e8e\u94fe\u8868\u4e2d\u7684\u6307\u9488\u3002\u5982\u679c\u6211\u4eec\u5c06\u8282\u70b9\u6309\u7167\u5c42\u5e8f\u904d\u5386\u7684\u987a\u5e8f\u5b58\u50a8\u5728\u4e00\u4e2a\u6570\u7ec4\u4e2d\uff0c\u90a3\u4e48\u5bf9\u4e8e\u6570\u7ec4\u4e2d\u7684\u4efb\u610f\u8282\u70b9\uff0c\u6211\u4eec\u90fd\u53ef\u4ee5\u901a\u8fc7\u6620\u5c04\u516c\u5f0f\u6765\u8bbf\u95ee\u5176\u5b50\u8282\u70b9\u3002</p>"},{"location":"chapter_tree/array_representation_of_tree/#732","title":"7.3.2. \u00a0 \u8868\u793a\u4efb\u610f\u4e8c\u53c9\u6811","text":"<p>\u7136\u800c\uff0c\u5b8c\u7f8e\u4e8c\u53c9\u6811\u53ea\u662f\u4e00\u4e2a\u7279\u4f8b\u3002\u5728\u4e8c\u53c9\u6811\u7684\u4e2d\u95f4\u5c42\uff0c\u901a\u5e38\u5b58\u5728\u8bb8\u591a \\(\\text{null}\\) \uff0c\u800c\u5c42\u5e8f\u904d\u5386\u5e8f\u5217\u5e76\u4e0d\u5305\u542b\u8fd9\u4e9b \\(\\text{null}\\) \u3002\u6211\u4eec\u65e0\u6cd5\u4ec5\u51ed\u8be5\u5e8f\u5217\u6765\u63a8\u6d4b \\(\\text{null}\\) \u7684\u6570\u91cf\u548c\u5206\u5e03\u4f4d\u7f6e\uff0c\u8fd9\u610f\u5473\u7740\u5b58\u5728\u591a\u79cd\u4e8c\u53c9\u6811\u7ed3\u6784\u90fd\u7b26\u5408\u8be5\u5c42\u5e8f\u904d\u5386\u5e8f\u5217\u3002\u663e\u7136\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u4e0a\u8ff0\u7684\u6570\u7ec4\u8868\u793a\u65b9\u6cd5\u5df2\u7ecf\u5931\u6548\u3002</p> <p></p> <p> Fig. \u5c42\u5e8f\u904d\u5386\u5e8f\u5217\u5bf9\u5e94\u591a\u79cd\u4e8c\u53c9\u6811\u53ef\u80fd\u6027 </p> <p>\u4e3a\u4e86\u89e3\u51b3\u6b64\u95ee\u9898\uff0c\u6211\u4eec\u53ef\u4ee5\u8003\u8651\u5728\u5c42\u5e8f\u904d\u5386\u5e8f\u5217\u4e2d\u663e\u5f0f\u5730\u5199\u51fa\u6240\u6709 \\(\\text{null}\\)\u3002\u5982\u4e0b\u56fe\u6240\u793a\uff0c\u8fd9\u6837\u5904\u7406\u540e\uff0c\u5c42\u5e8f\u904d\u5386\u5e8f\u5217\u5c31\u53ef\u4ee5\u552f\u4e00\u8868\u793a\u4e8c\u53c9\u6811\u4e86\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart <pre><code>/* \u4e8c\u53c9\u6811\u7684\u6570\u7ec4\u8868\u793a */\n// \u4f7f\u7528 int \u7684\u5305\u88c5\u7c7b Integer \uff0c\u5c31\u53ef\u4ee5\u4f7f\u7528 null \u6765\u6807\u8bb0\u7a7a\u4f4d\nInteger[] tree = { 1, 2, 3, 4, null, 6, 7, 8, 9, null, null, 12, null, null, 15 };\n</code></pre> <pre><code>/* \u4e8c\u53c9\u6811\u7684\u6570\u7ec4\u8868\u793a */\n// \u4f7f\u7528 int \u6700\u5927\u503c\u6807\u8bb0\u7a7a\u4f4d\uff0c\u56e0\u6b64\u8981\u6c42\u8282\u70b9\u503c\u4e0d\u80fd\u4e3a INT_MAX\nvector&lt;int&gt; tree = {1, 2, 3, 4, INT_MAX, 6, 7, 8, 9, INT_MAX, INT_MAX, 12, INT_MAX, INT_MAX, 15};\n</code></pre> <pre><code># \u4e8c\u53c9\u6811\u7684\u6570\u7ec4\u8868\u793a\n# \u76f4\u63a5\u4f7f\u7528 None \u6765\u8868\u793a\u7a7a\u4f4d\ntree = [1, 2, 3, 4, None, 6, 7, 8, 9, None, None, 12, None, None, 15]\n</code></pre> <pre><code>/* \u4e8c\u53c9\u6811\u7684\u6570\u7ec4\u8868\u793a */\n// \u4f7f\u7528 any \u7c7b\u578b\u7684\u5207\u7247, \u5c31\u53ef\u4ee5\u4f7f\u7528 nil \u6765\u6807\u8bb0\u7a7a\u4f4d\ntree := []any{1, 2, 3, 4, nil, 6, 7, 8, 9, nil, nil, 12, nil, nil, 15}\n</code></pre> <pre><code>/* \u4e8c\u53c9\u6811\u7684\u6570\u7ec4\u8868\u793a */\n// \u76f4\u63a5\u4f7f\u7528 null \u6765\u8868\u793a\u7a7a\u4f4d\nlet tree = [1, 2, 3, 4, null, 6, 7, 8, 9, null, null, 12, null, null, 15];\n</code></pre> <pre><code>/* \u4e8c\u53c9\u6811\u7684\u6570\u7ec4\u8868\u793a */\n// \u76f4\u63a5\u4f7f\u7528 null \u6765\u8868\u793a\u7a7a\u4f4d\nlet tree: (number | null)[] = [1, 2, 3, 4, null, 6, 7, 8, 9, null, null, 12, null, null, 15];\n</code></pre> <pre><code>/* \u4e8c\u53c9\u6811\u7684\u6570\u7ec4\u8868\u793a */\n// \u4f7f\u7528 int \u6700\u5927\u503c\u6807\u8bb0\u7a7a\u4f4d\uff0c\u56e0\u6b64\u8981\u6c42\u8282\u70b9\u503c\u4e0d\u80fd\u4e3a INT_MAX\nint tree[] = {1, 2, 3, 4, INT_MAX, 6, 7, 8, 9, INT_MAX, INT_MAX, 12, INT_MAX, INT_MAX, 15};\n</code></pre> <pre><code>/* \u4e8c\u53c9\u6811\u7684\u6570\u7ec4\u8868\u793a */\n// \u4f7f\u7528 int? \u53ef\u7a7a\u7c7b\u578b \uff0c\u5c31\u53ef\u4ee5\u4f7f\u7528 null \u6765\u6807\u8bb0\u7a7a\u4f4d\nint?[] tree = { 1, 2, 3, 4, null, 6, 7, 8, 9, null, null, 12, null, null, 15 };\n</code></pre> <pre><code>/* \u4e8c\u53c9\u6811\u7684\u6570\u7ec4\u8868\u793a */\n// \u4f7f\u7528 Int? \u53ef\u7a7a\u7c7b\u578b \uff0c\u5c31\u53ef\u4ee5\u4f7f\u7528 nil \u6765\u6807\u8bb0\u7a7a\u4f4d\nlet tree: [Int?] = [1, 2, 3, 4, nil, 6, 7, 8, 9, nil, nil, 12, nil, nil, 15]\n</code></pre> <pre><code>\n</code></pre> <pre><code>/* \u4e8c\u53c9\u6811\u7684\u6570\u7ec4\u8868\u793a */\n// \u4f7f\u7528 int? \u53ef\u7a7a\u7c7b\u578b \uff0c\u5c31\u53ef\u4ee5\u4f7f\u7528 null \u6765\u6807\u8bb0\u7a7a\u4f4d\nList&lt;int?&gt; tree = [1, 2, 3, 4, null, 6, 7, 8, 9, null, null, 12, null, null, 15];\n</code></pre> <p></p> <p> Fig. \u4efb\u610f\u7c7b\u578b\u4e8c\u53c9\u6811\u7684\u6570\u7ec4\u8868\u793a </p>"},{"location":"chapter_tree/array_representation_of_tree/#733","title":"7.3.3. \u00a0 \u4f18\u52bf\u4e0e\u5c40\u9650\u6027","text":"<p>\u4e8c\u53c9\u6811\u7684\u6570\u7ec4\u8868\u793a\u5b58\u5728\u4ee5\u4e0b\u4f18\u70b9\uff1a</p> <ul> <li>\u6570\u7ec4\u5b58\u50a8\u5728\u8fde\u7eed\u7684\u5185\u5b58\u7a7a\u95f4\u4e2d\uff0c\u7f13\u5b58\u53cb\u597d\uff0c\u8bbf\u95ee\u4e0e\u904d\u5386\u901f\u5ea6\u8f83\u5feb\uff1b</li> <li>\u4e0d\u9700\u8981\u5b58\u50a8\u6307\u9488\uff0c\u6bd4\u8f83\u8282\u7701\u7a7a\u95f4\uff1b</li> <li>\u5141\u8bb8\u968f\u673a\u8bbf\u95ee\u8282\u70b9\uff1b</li> </ul> <p>\u7136\u800c\uff0c\u6570\u7ec4\u8868\u793a\u4e5f\u5177\u6709\u4e00\u4e9b\u5c40\u9650\u6027\uff1a</p> <ul> <li>\u6570\u7ec4\u5b58\u50a8\u9700\u8981\u8fde\u7eed\u5185\u5b58\u7a7a\u95f4\uff0c\u56e0\u6b64\u4e0d\u9002\u5408\u5b58\u50a8\u6570\u636e\u91cf\u8fc7\u5927\u7684\u6811\u3002</li> <li>\u589e\u5220\u8282\u70b9\u9700\u8981\u901a\u8fc7\u6570\u7ec4\u63d2\u5165\u4e0e\u5220\u9664\u64cd\u4f5c\u5b9e\u73b0\uff0c\u6548\u7387\u8f83\u4f4e\uff1b</li> <li>\u5f53\u4e8c\u53c9\u6811\u4e2d\u5b58\u5728\u5927\u91cf \\(\\text{null}\\) \u65f6\uff0c\u6570\u7ec4\u4e2d\u5305\u542b\u7684\u8282\u70b9\u6570\u636e\u6bd4\u91cd\u8f83\u4f4e\uff0c\u7a7a\u95f4\u5229\u7528\u7387\u8f83\u4f4e\u3002</li> </ul> <p>\u5b8c\u5168\u4e8c\u53c9\u6811\u975e\u5e38\u9002\u5408\u4f7f\u7528\u6570\u7ec4\u6765\u8868\u793a\u3002\u56de\u987e\u5b8c\u5168\u4e8c\u53c9\u6811\u7684\u5b9a\u4e49\uff0c\\(\\text{null}\\) \u53ea\u51fa\u73b0\u5728\u6700\u5e95\u5c42\u4e14\u9760\u53f3\u7684\u4f4d\u7f6e\uff0c\u8fd9\u610f\u5473\u7740\u6240\u6709 \\(\\text{null}\\) \u4e00\u5b9a\u51fa\u73b0\u5728\u5c42\u5e8f\u904d\u5386\u5e8f\u5217\u7684\u672b\u5c3e\u3002\u56e0\u6b64\uff0c\u5728\u4f7f\u7528\u6570\u7ec4\u8868\u793a\u5b8c\u5168\u4e8c\u53c9\u6811\u65f6\uff0c\u53ef\u4ee5\u7701\u7565\u5b58\u50a8\u6240\u6709 \\(\\text{null}\\) \u3002</p> <p></p> <p> Fig. \u5b8c\u5168\u4e8c\u53c9\u6811\u7684\u6570\u7ec4\u8868\u793a </p>"},{"location":"chapter_tree/avl_tree/","title":"7.5. \u00a0 AVL \u6811 *","text":"<p>\u5728\u4e8c\u53c9\u641c\u7d22\u6811\u7ae0\u8282\u4e2d\uff0c\u6211\u4eec\u63d0\u5230\u4e86\u5728\u591a\u6b21\u63d2\u5165\u548c\u5220\u9664\u64cd\u4f5c\u540e\uff0c\u4e8c\u53c9\u641c\u7d22\u6811\u53ef\u80fd\u9000\u5316\u4e3a\u94fe\u8868\u3002\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u6240\u6709\u64cd\u4f5c\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u5c06\u4ece \\(O(\\log n)\\) \u6076\u5316\u4e3a \\(O(n)\\)\u3002</p> <p>\u5982\u4e0b\u56fe\u6240\u793a\uff0c\u7ecf\u8fc7\u4e24\u6b21\u5220\u9664\u8282\u70b9\u64cd\u4f5c\uff0c\u8fd9\u4e2a\u4e8c\u53c9\u641c\u7d22\u6811\u4fbf\u4f1a\u9000\u5316\u4e3a\u94fe\u8868\u3002</p> <p></p> <p> Fig. AVL \u6811\u5728\u5220\u9664\u8282\u70b9\u540e\u53d1\u751f\u9000\u5316 </p> <p>\u518d\u4f8b\u5982\uff0c\u5728\u4ee5\u4e0b\u5b8c\u7f8e\u4e8c\u53c9\u6811\u4e2d\u63d2\u5165\u4e24\u4e2a\u8282\u70b9\u540e\uff0c\u6811\u5c06\u4e25\u91cd\u5411\u5de6\u503e\u659c\uff0c\u67e5\u627e\u64cd\u4f5c\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e5f\u968f\u4e4b\u6076\u5316\u3002</p> <p></p> <p> Fig. AVL \u6811\u5728\u63d2\u5165\u8282\u70b9\u540e\u53d1\u751f\u9000\u5316 </p> <p>G. M. Adelson-Velsky \u548c E. M. Landis \u5728\u5176 1962 \u5e74\u53d1\u8868\u7684\u8bba\u6587 \"An algorithm for the organization of information\" \u4e2d\u63d0\u51fa\u4e86\u300cAVL \u6811\u300d\u3002\u8bba\u6587\u4e2d\u8be6\u7ec6\u63cf\u8ff0\u4e86\u4e00\u7cfb\u5217\u64cd\u4f5c\uff0c\u786e\u4fdd\u5728\u6301\u7eed\u6dfb\u52a0\u548c\u5220\u9664\u8282\u70b9\u540e\uff0cAVL \u6811\u4e0d\u4f1a\u9000\u5316\uff0c\u4ece\u800c\u4f7f\u5f97\u5404\u79cd\u64cd\u4f5c\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4fdd\u6301\u5728 \\(O(\\log n)\\) \u7ea7\u522b\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u5728\u9700\u8981\u9891\u7e41\u8fdb\u884c\u589e\u5220\u67e5\u6539\u64cd\u4f5c\u7684\u573a\u666f\u4e2d\uff0cAVL \u6811\u80fd\u59cb\u7ec8\u4fdd\u6301\u9ad8\u6548\u7684\u6570\u636e\u64cd\u4f5c\u6027\u80fd\uff0c\u5177\u6709\u5f88\u597d\u7684\u5e94\u7528\u4ef7\u503c\u3002</p>"},{"location":"chapter_tree/avl_tree/#751-avl","title":"7.5.1. \u00a0 AVL \u6811\u5e38\u89c1\u672f\u8bed","text":"<p>\u300cAVL \u6811\u300d\u65e2\u662f\u4e8c\u53c9\u641c\u7d22\u6811\u4e5f\u662f\u5e73\u8861\u4e8c\u53c9\u6811\uff0c\u540c\u65f6\u6ee1\u8db3\u8fd9\u4e24\u7c7b\u4e8c\u53c9\u6811\u7684\u6240\u6709\u6027\u8d28\uff0c\u56e0\u6b64\u4e5f\u88ab\u79f0\u4e3a\u300c\u5e73\u8861\u4e8c\u53c9\u641c\u7d22\u6811\u300d\u3002</p>"},{"location":"chapter_tree/avl_tree/#_1","title":"\u8282\u70b9\u9ad8\u5ea6","text":"<p>\u5728\u64cd\u4f5c AVL \u6811\u65f6\uff0c\u6211\u4eec\u9700\u8981\u83b7\u53d6\u8282\u70b9\u7684\u9ad8\u5ea6\uff0c\u56e0\u6b64\u9700\u8981\u4e3a AVL \u6811\u7684\u8282\u70b9\u7c7b\u6dfb\u52a0 <code>height</code> \u53d8\u91cf\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart <pre><code>/* AVL \u6811\u8282\u70b9\u7c7b */\nclass TreeNode {\npublic int val;        // \u8282\u70b9\u503c\npublic int height;     // \u8282\u70b9\u9ad8\u5ea6\npublic TreeNode left;  // \u5de6\u5b50\u8282\u70b9\npublic TreeNode right; // \u53f3\u5b50\u8282\u70b9\npublic TreeNode(int x) { val = x; }\n}\n</code></pre> <pre><code>/* AVL \u6811\u8282\u70b9\u7c7b */\nstruct TreeNode {\nint val{};          // \u8282\u70b9\u503c\nint height = 0;     // \u8282\u70b9\u9ad8\u5ea6\nTreeNode *left{};   // \u5de6\u5b50\u8282\u70b9\nTreeNode *right{};  // \u53f3\u5b50\u8282\u70b9\nTreeNode() = default;\nexplicit TreeNode(int x) : val(x){}\n};\n</code></pre> <pre><code>class TreeNode:\n\"\"\"AVL \u6811\u8282\u70b9\u7c7b\"\"\"\ndef __init__(self, val: int):\nself.val: int = val                    # \u8282\u70b9\u503c\nself.height: int = 0                   # \u8282\u70b9\u9ad8\u5ea6\nself.left: Optional[TreeNode] = None   # \u5de6\u5b50\u8282\u70b9\u5f15\u7528\nself.right: Optional[TreeNode] = None  # \u53f3\u5b50\u8282\u70b9\u5f15\u7528\n</code></pre> <pre><code>/* AVL \u6811\u8282\u70b9\u7ed3\u6784\u4f53 */\ntype TreeNode struct {\nVal    int       // \u8282\u70b9\u503c\nHeight int       // \u8282\u70b9\u9ad8\u5ea6\nLeft   *TreeNode // \u5de6\u5b50\u8282\u70b9\u5f15\u7528\nRight  *TreeNode // \u53f3\u5b50\u8282\u70b9\u5f15\u7528\n}\n</code></pre> <pre><code>/* AVL \u6811\u8282\u70b9\u7c7b */\nclass TreeNode {\nval; // \u8282\u70b9\u503c\nheight; //\u8282\u70b9\u9ad8\u5ea6\nleft; // \u5de6\u5b50\u8282\u70b9\u6307\u9488\nright; // \u53f3\u5b50\u8282\u70b9\u6307\u9488\nconstructor(val, left, right, height) {\nthis.val = val === undefined ? 0 : val;\nthis.height = height === undefined ? 0 : height;\nthis.left = left === undefined ? null : left;\nthis.right = right === undefined ? null : right;\n}\n}\n</code></pre> <pre><code>/* AVL \u6811\u8282\u70b9\u7c7b */\nclass TreeNode {\nval: number;            // \u8282\u70b9\u503c\nheight: number;         // \u8282\u70b9\u9ad8\u5ea6\nleft: TreeNode | null;  // \u5de6\u5b50\u8282\u70b9\u6307\u9488\nright: TreeNode | null; // \u53f3\u5b50\u8282\u70b9\u6307\u9488\nconstructor(val?: number, height?: number, left?: TreeNode | null, right?: TreeNode | null) {\nthis.val = val === undefined ? 0 : val;\nthis.height = height === undefined ? 0 : height; this.left = left === undefined ? null : left; this.right = right === undefined ? null : right; }\n}\n</code></pre> <pre><code>/* AVL \u6811\u8282\u70b9\u7ed3\u6784\u4f53 */\nstruct TreeNode {\nint val;\nint height;\nstruct TreeNode *left;\nstruct TreeNode *right;\n};\ntypedef struct TreeNode TreeNode;\n/* \u6784\u9020\u51fd\u6570 */\nTreeNode *newTreeNode(int val) {\nTreeNode *node;\nnode = (TreeNode *)malloc(sizeof(TreeNode));\nnode-&gt;val = val;\nnode-&gt;height = 0;\nnode-&gt;left = NULL;\nnode-&gt;right = NULL;\nreturn node;\n}\n</code></pre> <pre><code>/* AVL \u6811\u8282\u70b9\u7c7b */\nclass TreeNode {\npublic int val;          // \u8282\u70b9\u503c\npublic int height;       // \u8282\u70b9\u9ad8\u5ea6\npublic TreeNode? left;   // \u5de6\u5b50\u8282\u70b9\npublic TreeNode? right;  // \u53f3\u5b50\u8282\u70b9\npublic TreeNode(int x) { val = x; }\n}\n</code></pre> <pre><code>/* AVL \u6811\u8282\u70b9\u7c7b */\nclass TreeNode {\nvar val: Int // \u8282\u70b9\u503c\nvar height: Int // \u8282\u70b9\u9ad8\u5ea6\nvar left: TreeNode? // \u5de6\u5b50\u8282\u70b9\nvar right: TreeNode? // \u53f3\u5b50\u8282\u70b9\ninit(x: Int) {\nval = x\nheight = 0\n}\n}\n</code></pre> <pre><code>\n</code></pre> <pre><code>/* AVL \u6811\u8282\u70b9\u7c7b */\nclass TreeNode {\nint val;         // \u8282\u70b9\u503c\nint height;      // \u8282\u70b9\u9ad8\u5ea6\nTreeNode? left;  // \u5de6\u5b50\u8282\u70b9\nTreeNode? right; // \u53f3\u5b50\u8282\u70b9\nTreeNode(this.val, [this.height = 0, this.left, this.right]);\n}\n</code></pre> <p>\u300c\u8282\u70b9\u9ad8\u5ea6\u300d\u662f\u6307\u4ece\u8be5\u8282\u70b9\u5230\u6700\u8fdc\u53f6\u8282\u70b9\u7684\u8ddd\u79bb\uff0c\u5373\u6240\u7ecf\u8fc7\u7684\u201c\u8fb9\u201d\u7684\u6570\u91cf\u3002\u9700\u8981\u7279\u522b\u6ce8\u610f\u7684\u662f\uff0c\u53f6\u8282\u70b9\u7684\u9ad8\u5ea6\u4e3a 0 \uff0c\u800c\u7a7a\u8282\u70b9\u7684\u9ad8\u5ea6\u4e3a -1 \u3002\u6211\u4eec\u5c06\u521b\u5efa\u4e24\u4e2a\u5de5\u5177\u51fd\u6570\uff0c\u5206\u522b\u7528\u4e8e\u83b7\u53d6\u548c\u66f4\u65b0\u8282\u70b9\u7684\u9ad8\u5ea6\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart avl_tree.java<pre><code>/* \u83b7\u53d6\u8282\u70b9\u9ad8\u5ea6 */\nint height(TreeNode node) {\n// \u7a7a\u8282\u70b9\u9ad8\u5ea6\u4e3a -1 \uff0c\u53f6\u8282\u70b9\u9ad8\u5ea6\u4e3a 0\nreturn node == null ? -1 : node.height;\n}\n/* \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6 */\nvoid updateHeight(TreeNode node) {\n// \u8282\u70b9\u9ad8\u5ea6\u7b49\u4e8e\u6700\u9ad8\u5b50\u6811\u9ad8\u5ea6 + 1\nnode.height = Math.max(height(node.left), height(node.right)) + 1;\n}\n</code></pre> avl_tree.cpp<pre><code>/* \u83b7\u53d6\u8282\u70b9\u9ad8\u5ea6 */\nint height(TreeNode *node) {\n// \u7a7a\u8282\u70b9\u9ad8\u5ea6\u4e3a -1 \uff0c\u53f6\u8282\u70b9\u9ad8\u5ea6\u4e3a 0\nreturn node == nullptr ? -1 : node-&gt;height;\n}\n/* \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6 */\nvoid updateHeight(TreeNode *node) {\n// \u8282\u70b9\u9ad8\u5ea6\u7b49\u4e8e\u6700\u9ad8\u5b50\u6811\u9ad8\u5ea6 + 1\nnode-&gt;height = max(height(node-&gt;left), height(node-&gt;right)) + 1;\n}\n</code></pre> avl_tree.py<pre><code>def height(self, node: TreeNode | None) -&gt; int:\n\"\"\"\u83b7\u53d6\u8282\u70b9\u9ad8\u5ea6\"\"\"\n# \u7a7a\u8282\u70b9\u9ad8\u5ea6\u4e3a -1 \uff0c\u53f6\u8282\u70b9\u9ad8\u5ea6\u4e3a 0\nif node is not None:\nreturn node.height\nreturn -1\ndef __update_height(self, node: TreeNode | None):\n\"\"\"\u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\"\"\"\n# \u8282\u70b9\u9ad8\u5ea6\u7b49\u4e8e\u6700\u9ad8\u5b50\u6811\u9ad8\u5ea6 + 1\nnode.height = max([self.height(node.left), self.height(node.right)]) + 1\n</code></pre> avl_tree.go<pre><code>/* \u83b7\u53d6\u8282\u70b9\u9ad8\u5ea6 */\nfunc (t *aVLTree) height(node *TreeNode) int {\n// \u7a7a\u8282\u70b9\u9ad8\u5ea6\u4e3a -1 \uff0c\u53f6\u8282\u70b9\u9ad8\u5ea6\u4e3a 0\nif node != nil {\nreturn node.Height\n}\nreturn -1\n}\n/* \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6 */\nfunc (t *aVLTree) updateHeight(node *TreeNode) {\nlh := t.height(node.Left)\nrh := t.height(node.Right)\n// \u8282\u70b9\u9ad8\u5ea6\u7b49\u4e8e\u6700\u9ad8\u5b50\u6811\u9ad8\u5ea6 + 1\nif lh &gt; rh {\nnode.Height = lh + 1\n} else {\nnode.Height = rh + 1\n}\n}\n</code></pre> avl_tree.js<pre><code>/* \u83b7\u53d6\u8282\u70b9\u9ad8\u5ea6 */\nheight(node) {\n// \u7a7a\u8282\u70b9\u9ad8\u5ea6\u4e3a -1 \uff0c\u53f6\u8282\u70b9\u9ad8\u5ea6\u4e3a 0\nreturn node === null ? -1 : node.height;\n}\n/* \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6 */\n#updateHeight(node) {\n// \u8282\u70b9\u9ad8\u5ea6\u7b49\u4e8e\u6700\u9ad8\u5b50\u6811\u9ad8\u5ea6 + 1\nnode.height =\nMath.max(this.height(node.left), this.height(node.right)) + 1;\n}\n</code></pre> avl_tree.ts<pre><code>/* \u83b7\u53d6\u8282\u70b9\u9ad8\u5ea6 */\nheight(node: TreeNode): number {\n// \u7a7a\u8282\u70b9\u9ad8\u5ea6\u4e3a -1 \uff0c\u53f6\u8282\u70b9\u9ad8\u5ea6\u4e3a 0\nreturn node === null ? -1 : node.height;\n}\n/* \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6 */\nupdateHeight(node: TreeNode): void {\n// \u8282\u70b9\u9ad8\u5ea6\u7b49\u4e8e\u6700\u9ad8\u5b50\u6811\u9ad8\u5ea6 + 1\nnode.height =\nMath.max(this.height(node.left), this.height(node.right)) + 1;\n}\n</code></pre> avl_tree.c<pre><code>/* \u83b7\u53d6\u8282\u70b9\u9ad8\u5ea6 */\nint height(TreeNode *node) {\n// \u7a7a\u8282\u70b9\u9ad8\u5ea6\u4e3a -1 \uff0c\u53f6\u8282\u70b9\u9ad8\u5ea6\u4e3a 0\nif (node != NULL) {\nreturn node-&gt;height;\n}\nreturn -1;\n}\n/* \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6 */\nvoid updateHeight(TreeNode *node) {\nint lh = height(node-&gt;left);\nint rh = height(node-&gt;right);\n// \u8282\u70b9\u9ad8\u5ea6\u7b49\u4e8e\u6700\u9ad8\u5b50\u6811\u9ad8\u5ea6 + 1\nif (lh &gt; rh) {\nnode-&gt;height = lh + 1;\n} else {\nnode-&gt;height = rh + 1;\n}\n}\n</code></pre> avl_tree.cs<pre><code>/* \u83b7\u53d6\u8282\u70b9\u9ad8\u5ea6 */\nint height(TreeNode? node) {\n// \u7a7a\u8282\u70b9\u9ad8\u5ea6\u4e3a -1 \uff0c\u53f6\u8282\u70b9\u9ad8\u5ea6\u4e3a 0\nreturn node == null ? -1 : node.height;\n}\n/* \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6 */\nvoid updateHeight(TreeNode node) {\n// \u8282\u70b9\u9ad8\u5ea6\u7b49\u4e8e\u6700\u9ad8\u5b50\u6811\u9ad8\u5ea6 + 1\nnode.height = Math.Max(height(node.left), height(node.right)) + 1;\n}\n</code></pre> avl_tree.swift<pre><code>/* \u83b7\u53d6\u8282\u70b9\u9ad8\u5ea6 */\nfunc height(node: TreeNode?) -&gt; Int {\n// \u7a7a\u8282\u70b9\u9ad8\u5ea6\u4e3a -1 \uff0c\u53f6\u8282\u70b9\u9ad8\u5ea6\u4e3a 0\nnode == nil ? -1 : node!.height\n}\n/* \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6 */\nfunc updateHeight(node: TreeNode?) {\n// \u8282\u70b9\u9ad8\u5ea6\u7b49\u4e8e\u6700\u9ad8\u5b50\u6811\u9ad8\u5ea6 + 1\nnode?.height = max(height(node: node?.left), height(node: node?.right)) + 1\n}\n</code></pre> avl_tree.zig<pre><code>// \u83b7\u53d6\u8282\u70b9\u9ad8\u5ea6\nfn height(self: *Self, node: ?*inc.TreeNode(T)) i32 {\n_ = self;\n// \u7a7a\u8282\u70b9\u9ad8\u5ea6\u4e3a -1 \uff0c\u53f6\u8282\u70b9\u9ad8\u5ea6\u4e3a 0\nreturn if (node == null) -1 else node.?.height;\n}\n// \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\nfn updateHeight(self: *Self, node: ?*inc.TreeNode(T)) void {\n// \u8282\u70b9\u9ad8\u5ea6\u7b49\u4e8e\u6700\u9ad8\u5b50\u6811\u9ad8\u5ea6 + 1\nnode.?.height = std.math.max(self.height(node.?.left), self.height(node.?.right)) + 1;\n}\n</code></pre> avl_tree.dart<pre><code>/* \u83b7\u53d6\u8282\u70b9\u9ad8\u5ea6 */\nint height(TreeNode? node) {\nreturn node == null ? -1 : node.height;\n}\n/* \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6 */\nvoid updateHeight(TreeNode? node) {\n// \u8282\u70b9\u9ad8\u5ea6\u7b49\u4e8e\u6700\u9ad8\u5b50\u6811\u9ad8\u5ea6 + 1\nnode!.height = max(height(node.left), height(node.right)) + 1;\n}\n</code></pre>"},{"location":"chapter_tree/avl_tree/#_2","title":"\u8282\u70b9\u5e73\u8861\u56e0\u5b50","text":"<p>\u8282\u70b9\u7684\u300c\u5e73\u8861\u56e0\u5b50 Balance Factor\u300d\u5b9a\u4e49\u4e3a\u8282\u70b9\u5de6\u5b50\u6811\u7684\u9ad8\u5ea6\u51cf\u53bb\u53f3\u5b50\u6811\u7684\u9ad8\u5ea6\uff0c\u540c\u65f6\u89c4\u5b9a\u7a7a\u8282\u70b9\u7684\u5e73\u8861\u56e0\u5b50\u4e3a 0 \u3002\u6211\u4eec\u540c\u6837\u5c06\u83b7\u53d6\u8282\u70b9\u5e73\u8861\u56e0\u5b50\u7684\u529f\u80fd\u5c01\u88c5\u6210\u51fd\u6570\uff0c\u65b9\u4fbf\u540e\u7eed\u4f7f\u7528\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart avl_tree.java<pre><code>/* \u83b7\u53d6\u5e73\u8861\u56e0\u5b50 */\nint balanceFactor(TreeNode node) {\n// \u7a7a\u8282\u70b9\u5e73\u8861\u56e0\u5b50\u4e3a 0\nif (node == null)\nreturn 0;\n// \u8282\u70b9\u5e73\u8861\u56e0\u5b50 = \u5de6\u5b50\u6811\u9ad8\u5ea6 - \u53f3\u5b50\u6811\u9ad8\u5ea6\nreturn height(node.left) - height(node.right);\n}\n</code></pre> avl_tree.cpp<pre><code>/* \u83b7\u53d6\u5e73\u8861\u56e0\u5b50 */\nint balanceFactor(TreeNode *node) {\n// \u7a7a\u8282\u70b9\u5e73\u8861\u56e0\u5b50\u4e3a 0\nif (node == nullptr)\nreturn 0;\n// \u8282\u70b9\u5e73\u8861\u56e0\u5b50 = \u5de6\u5b50\u6811\u9ad8\u5ea6 - \u53f3\u5b50\u6811\u9ad8\u5ea6\nreturn height(node-&gt;left) - height(node-&gt;right);\n}\n</code></pre> avl_tree.py<pre><code>def balance_factor(self, node: TreeNode | None) -&gt; int:\n\"\"\"\u83b7\u53d6\u5e73\u8861\u56e0\u5b50\"\"\"\n# \u7a7a\u8282\u70b9\u5e73\u8861\u56e0\u5b50\u4e3a 0\nif node is None:\nreturn 0\n# \u8282\u70b9\u5e73\u8861\u56e0\u5b50 = \u5de6\u5b50\u6811\u9ad8\u5ea6 - \u53f3\u5b50\u6811\u9ad8\u5ea6\nreturn self.height(node.left) - self.height(node.right)\n</code></pre> avl_tree.go<pre><code>/* \u83b7\u53d6\u5e73\u8861\u56e0\u5b50 */\nfunc (t *aVLTree) balanceFactor(node *TreeNode) int {\n// \u7a7a\u8282\u70b9\u5e73\u8861\u56e0\u5b50\u4e3a 0\nif node == nil {\nreturn 0\n}\n// \u8282\u70b9\u5e73\u8861\u56e0\u5b50 = \u5de6\u5b50\u6811\u9ad8\u5ea6 - \u53f3\u5b50\u6811\u9ad8\u5ea6\nreturn t.height(node.Left) - t.height(node.Right)\n}\n</code></pre> avl_tree.js<pre><code>/* \u83b7\u53d6\u5e73\u8861\u56e0\u5b50 */\nbalanceFactor(node) {\n// \u7a7a\u8282\u70b9\u5e73\u8861\u56e0\u5b50\u4e3a 0\nif (node === null) return 0;\n// \u8282\u70b9\u5e73\u8861\u56e0\u5b50 = \u5de6\u5b50\u6811\u9ad8\u5ea6 - \u53f3\u5b50\u6811\u9ad8\u5ea6\nreturn this.height(node.left) - this.height(node.right);\n}\n</code></pre> avl_tree.ts<pre><code>/* \u83b7\u53d6\u5e73\u8861\u56e0\u5b50 */\nbalanceFactor(node: TreeNode): number {\n// \u7a7a\u8282\u70b9\u5e73\u8861\u56e0\u5b50\u4e3a 0\nif (node === null) return 0;\n// \u8282\u70b9\u5e73\u8861\u56e0\u5b50 = \u5de6\u5b50\u6811\u9ad8\u5ea6 - \u53f3\u5b50\u6811\u9ad8\u5ea6\nreturn this.height(node.left) - this.height(node.right);\n}\n</code></pre> avl_tree.c<pre><code>/* \u83b7\u53d6\u5e73\u8861\u56e0\u5b50 */\nint balanceFactor(TreeNode *node) {\n// \u7a7a\u8282\u70b9\u5e73\u8861\u56e0\u5b50\u4e3a 0\nif (node == NULL) {\nreturn 0;\n}\n// \u8282\u70b9\u5e73\u8861\u56e0\u5b50 = \u5de6\u5b50\u6811\u9ad8\u5ea6 - \u53f3\u5b50\u6811\u9ad8\u5ea6\nreturn height(node-&gt;left) - height(node-&gt;right);\n}\n</code></pre> avl_tree.cs<pre><code>/* \u83b7\u53d6\u5e73\u8861\u56e0\u5b50 */\nint balanceFactor(TreeNode? node) {\n// \u7a7a\u8282\u70b9\u5e73\u8861\u56e0\u5b50\u4e3a 0\nif (node == null) return 0;\n// \u8282\u70b9\u5e73\u8861\u56e0\u5b50 = \u5de6\u5b50\u6811\u9ad8\u5ea6 - \u53f3\u5b50\u6811\u9ad8\u5ea6\nreturn height(node.left) - height(node.right);\n}\n</code></pre> avl_tree.swift<pre><code>/* \u83b7\u53d6\u5e73\u8861\u56e0\u5b50 */\nfunc balanceFactor(node: TreeNode?) -&gt; Int {\n// \u7a7a\u8282\u70b9\u5e73\u8861\u56e0\u5b50\u4e3a 0\nguard let node = node else { return 0 }\n// \u8282\u70b9\u5e73\u8861\u56e0\u5b50 = \u5de6\u5b50\u6811\u9ad8\u5ea6 - \u53f3\u5b50\u6811\u9ad8\u5ea6\nreturn height(node: node.left) - height(node: node.right)\n}\n</code></pre> avl_tree.zig<pre><code>// \u83b7\u53d6\u5e73\u8861\u56e0\u5b50\nfn balanceFactor(self: *Self, node: ?*inc.TreeNode(T)) i32 {\n// \u7a7a\u8282\u70b9\u5e73\u8861\u56e0\u5b50\u4e3a 0\nif (node == null) return 0;\n// \u8282\u70b9\u5e73\u8861\u56e0\u5b50 = \u5de6\u5b50\u6811\u9ad8\u5ea6 - \u53f3\u5b50\u6811\u9ad8\u5ea6\nreturn self.height(node.?.left) - self.height(node.?.right);\n}\n</code></pre> avl_tree.dart<pre><code>/* \u83b7\u53d6\u5e73\u8861\u56e0\u5b50 */\nint balanceFactor(TreeNode? node) {\n// \u7a7a\u8282\u70b9\u5e73\u8861\u56e0\u5b50\u4e3a 0\nif (node == null) return 0;\n// \u8282\u70b9\u5e73\u8861\u56e0\u5b50 = \u5de6\u5b50\u6811\u9ad8\u5ea6 - \u53f3\u5b50\u6811\u9ad8\u5ea6\nreturn height(node.left) - height(node.right);\n}\n</code></pre> <p>Note</p> <p>\u8bbe\u5e73\u8861\u56e0\u5b50\u4e3a \\(f\\) \uff0c\u5219\u4e00\u68f5 AVL \u6811\u7684\u4efb\u610f\u8282\u70b9\u7684\u5e73\u8861\u56e0\u5b50\u7686\u6ee1\u8db3 \\(-1 \\le f \\le 1\\) \u3002</p>"},{"location":"chapter_tree/avl_tree/#752-avl","title":"7.5.2. \u00a0 AVL \u6811\u65cb\u8f6c","text":"<p>AVL \u6811\u7684\u7279\u70b9\u5728\u4e8e\u300c\u65cb\u8f6c Rotation\u300d\u64cd\u4f5c\uff0c\u5b83\u80fd\u591f\u5728\u4e0d\u5f71\u54cd\u4e8c\u53c9\u6811\u7684\u4e2d\u5e8f\u904d\u5386\u5e8f\u5217\u7684\u524d\u63d0\u4e0b\uff0c\u4f7f\u5931\u8861\u8282\u70b9\u91cd\u65b0\u6062\u590d\u5e73\u8861\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u65cb\u8f6c\u64cd\u4f5c\u65e2\u80fd\u4fdd\u6301\u6811\u7684\u300c\u4e8c\u53c9\u641c\u7d22\u6811\u300d\u5c5e\u6027\uff0c\u4e5f\u80fd\u4f7f\u6811\u91cd\u65b0\u53d8\u4e3a\u300c\u5e73\u8861\u4e8c\u53c9\u6811\u300d\u3002</p> <p>\u6211\u4eec\u5c06\u5e73\u8861\u56e0\u5b50\u7edd\u5bf9\u503c \\(&gt; 1\\) \u7684\u8282\u70b9\u79f0\u4e3a\u300c\u5931\u8861\u8282\u70b9\u300d\u3002\u6839\u636e\u8282\u70b9\u5931\u8861\u60c5\u51b5\u7684\u4e0d\u540c\uff0c\u65cb\u8f6c\u64cd\u4f5c\u5206\u4e3a\u56db\u79cd\uff1a\u53f3\u65cb\u3001\u5de6\u65cb\u3001\u5148\u53f3\u65cb\u540e\u5de6\u65cb\u3001\u5148\u5de6\u65cb\u540e\u53f3\u65cb\u3002\u4e0b\u9762\u6211\u4eec\u5c06\u8be6\u7ec6\u4ecb\u7ecd\u8fd9\u4e9b\u65cb\u8f6c\u64cd\u4f5c\u3002</p>"},{"location":"chapter_tree/avl_tree/#_3","title":"\u53f3\u65cb","text":"<p>\u5982\u4e0b\u56fe\u6240\u793a\uff0c\u8282\u70b9\u4e0b\u65b9\u4e3a\u5e73\u8861\u56e0\u5b50\u3002\u4ece\u5e95\u81f3\u9876\u770b\uff0c\u4e8c\u53c9\u6811\u4e2d\u9996\u4e2a\u5931\u8861\u8282\u70b9\u662f\u201c\u8282\u70b9 3\u201d\u3002\u6211\u4eec\u5173\u6ce8\u4ee5\u8be5\u5931\u8861\u8282\u70b9\u4e3a\u6839\u8282\u70b9\u7684\u5b50\u6811\uff0c\u5c06\u8be5\u8282\u70b9\u8bb0\u4e3a <code>node</code> \uff0c\u5176\u5de6\u5b50\u8282\u70b9\u8bb0\u4e3a <code>child</code> \uff0c\u6267\u884c\u300c\u53f3\u65cb\u300d\u64cd\u4f5c\u3002\u5b8c\u6210\u53f3\u65cb\u540e\uff0c\u5b50\u6811\u5df2\u7ecf\u6062\u590d\u5e73\u8861\uff0c\u5e76\u4e14\u4ecd\u7136\u4fdd\u6301\u4e8c\u53c9\u641c\u7d22\u6811\u7684\u7279\u6027\u3002</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt; <p></p> <p></p> <p></p> <p></p> <p>\u6b64\u5916\uff0c\u5982\u679c\u8282\u70b9 <code>child</code> \u672c\u8eab\u6709\u53f3\u5b50\u8282\u70b9\uff08\u8bb0\u4e3a <code>grandChild</code> \uff09\uff0c\u5219\u9700\u8981\u5728\u300c\u53f3\u65cb\u300d\u4e2d\u6dfb\u52a0\u4e00\u6b65\uff1a\u5c06 <code>grandChild</code> \u4f5c\u4e3a <code>node</code> \u7684\u5de6\u5b50\u8282\u70b9\u3002</p> <p></p> <p> Fig. \u6709 grandChild \u7684\u53f3\u65cb\u64cd\u4f5c </p> <p>\u201c\u5411\u53f3\u65cb\u8f6c\u201d\u662f\u4e00\u79cd\u5f62\u8c61\u5316\u7684\u8bf4\u6cd5\uff0c\u5b9e\u9645\u4e0a\u9700\u8981\u901a\u8fc7\u4fee\u6539\u8282\u70b9\u6307\u9488\u6765\u5b9e\u73b0\uff0c\u4ee3\u7801\u5982\u4e0b\u6240\u793a\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart avl_tree.java<pre><code>/* \u53f3\u65cb\u64cd\u4f5c */\nTreeNode rightRotate(TreeNode node) {\nTreeNode child = node.left;\nTreeNode grandChild = child.right;\n// \u4ee5 child \u4e3a\u539f\u70b9\uff0c\u5c06 node \u5411\u53f3\u65cb\u8f6c\nchild.right = node;\nnode.left = grandChild;\n// \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\nupdateHeight(node);\nupdateHeight(child);\n// \u8fd4\u56de\u65cb\u8f6c\u540e\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn child;\n}\n</code></pre> avl_tree.cpp<pre><code>/* \u53f3\u65cb\u64cd\u4f5c */\nTreeNode *rightRotate(TreeNode *node) {\nTreeNode *child = node-&gt;left;\nTreeNode *grandChild = child-&gt;right;\n// \u4ee5 child \u4e3a\u539f\u70b9\uff0c\u5c06 node \u5411\u53f3\u65cb\u8f6c\nchild-&gt;right = node;\nnode-&gt;left = grandChild;\n// \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\nupdateHeight(node);\nupdateHeight(child);\n// \u8fd4\u56de\u65cb\u8f6c\u540e\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn child;\n}\n</code></pre> avl_tree.py<pre><code>def __right_rotate(self, node: TreeNode | None) -&gt; TreeNode | None:\n\"\"\"\u53f3\u65cb\u64cd\u4f5c\"\"\"\nchild = node.left\ngrand_child = child.right\n# \u4ee5 child \u4e3a\u539f\u70b9\uff0c\u5c06 node \u5411\u53f3\u65cb\u8f6c\nchild.right = node\nnode.left = grand_child\n# \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\nself.__update_height(node)\nself.__update_height(child)\n# \u8fd4\u56de\u65cb\u8f6c\u540e\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn child\n</code></pre> avl_tree.go<pre><code>/* \u53f3\u65cb\u64cd\u4f5c */\nfunc (t *aVLTree) rightRotate(node *TreeNode) *TreeNode {\nchild := node.Left\ngrandChild := child.Right\n// \u4ee5 child \u4e3a\u539f\u70b9\uff0c\u5c06 node \u5411\u53f3\u65cb\u8f6c\nchild.Right = node\nnode.Left = grandChild\n// \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\nt.updateHeight(node)\nt.updateHeight(child)\n// \u8fd4\u56de\u65cb\u8f6c\u540e\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn child\n}\n</code></pre> avl_tree.js<pre><code>/* \u53f3\u65cb\u64cd\u4f5c */\n#rightRotate(node) {\nconst child = node.left;\nconst grandChild = child.right;\n// \u4ee5 child \u4e3a\u539f\u70b9\uff0c\u5c06 node \u5411\u53f3\u65cb\u8f6c\nchild.right = node;\nnode.left = grandChild;\n// \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\nthis.#updateHeight(node);\nthis.#updateHeight(child);\n// \u8fd4\u56de\u65cb\u8f6c\u540e\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn child;\n}\n</code></pre> avl_tree.ts<pre><code>/* \u53f3\u65cb\u64cd\u4f5c */\nrightRotate(node: TreeNode): TreeNode {\nconst child = node.left;\nconst grandChild = child.right;\n// \u4ee5 child \u4e3a\u539f\u70b9\uff0c\u5c06 node \u5411\u53f3\u65cb\u8f6c\nchild.right = node;\nnode.left = grandChild;\n// \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\nthis.updateHeight(node);\nthis.updateHeight(child);\n// \u8fd4\u56de\u65cb\u8f6c\u540e\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn child;\n}\n</code></pre> avl_tree.c<pre><code>/* \u53f3\u65cb\u64cd\u4f5c */\nTreeNode *rightRotate(TreeNode *node) {\nTreeNode *child, *grandChild;\nchild = node-&gt;left;\ngrandChild = child-&gt;right;\n// \u4ee5 child \u4e3a\u539f\u70b9\uff0c\u5c06 node \u5411\u53f3\u65cb\u8f6c\nchild-&gt;right = node;\nnode-&gt;left = grandChild;\n// \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\nupdateHeight(node);\nupdateHeight(child);\n// \u8fd4\u56de\u65cb\u8f6c\u540e\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn child;\n}\n</code></pre> avl_tree.cs<pre><code>/* \u53f3\u65cb\u64cd\u4f5c */\nTreeNode? rightRotate(TreeNode? node) {\nTreeNode? child = node.left;\nTreeNode? grandChild = child?.right;\n// \u4ee5 child \u4e3a\u539f\u70b9\uff0c\u5c06 node \u5411\u53f3\u65cb\u8f6c\nchild.right = node;\nnode.left = grandChild;\n// \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\nupdateHeight(node);\nupdateHeight(child);\n// \u8fd4\u56de\u65cb\u8f6c\u540e\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn child;\n}\n</code></pre> avl_tree.swift<pre><code>/* \u53f3\u65cb\u64cd\u4f5c */\nfunc rightRotate(node: TreeNode?) -&gt; TreeNode? {\nlet child = node?.left\nlet grandChild = child?.right\n// \u4ee5 child \u4e3a\u539f\u70b9\uff0c\u5c06 node \u5411\u53f3\u65cb\u8f6c\nchild?.right = node\nnode?.left = grandChild\n// \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\nupdateHeight(node: node)\nupdateHeight(node: child)\n// \u8fd4\u56de\u65cb\u8f6c\u540e\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn child\n}\n</code></pre> avl_tree.zig<pre><code>// \u53f3\u65cb\u64cd\u4f5c\nfn rightRotate(self: *Self, node: ?*inc.TreeNode(T)) ?*inc.TreeNode(T) {\nvar child = node.?.left;\nvar grandChild = child.?.right;\n// \u4ee5 child \u4e3a\u539f\u70b9\uff0c\u5c06 node \u5411\u53f3\u65cb\u8f6c\nchild.?.right = node;\nnode.?.left = grandChild;\n// \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\nself.updateHeight(node);\nself.updateHeight(child);\n// \u8fd4\u56de\u65cb\u8f6c\u540e\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn child;\n}\n</code></pre> avl_tree.dart<pre><code>/* \u53f3\u65cb\u64cd\u4f5c */\nTreeNode? rightRotate(TreeNode? node) {\nTreeNode? child = node!.left;\nTreeNode? grandChild = child!.right;\n// \u4ee5 child \u4e3a\u539f\u70b9\uff0c\u5c06 node \u5411\u53f3\u65cb\u8f6c\nchild.right = node;\nnode.left = grandChild;\n// \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\nupdateHeight(node);\nupdateHeight(child);\n// \u8fd4\u56de\u65cb\u8f6c\u540e\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn child;\n}\n</code></pre>"},{"location":"chapter_tree/avl_tree/#_4","title":"\u5de6\u65cb","text":"<p>\u76f8\u5e94\u7684\uff0c\u5982\u679c\u8003\u8651\u4e0a\u8ff0\u5931\u8861\u4e8c\u53c9\u6811\u7684\u201c\u955c\u50cf\u201d\uff0c\u5219\u9700\u8981\u6267\u884c\u300c\u5de6\u65cb\u300d\u64cd\u4f5c\u3002</p> <p></p> <p> Fig. \u5de6\u65cb\u64cd\u4f5c </p> <p>\u540c\u7406\uff0c\u82e5\u8282\u70b9 <code>child</code> \u672c\u8eab\u6709\u5de6\u5b50\u8282\u70b9\uff08\u8bb0\u4e3a <code>grandChild</code> \uff09\uff0c\u5219\u9700\u8981\u5728\u300c\u5de6\u65cb\u300d\u4e2d\u6dfb\u52a0\u4e00\u6b65\uff1a\u5c06 <code>grandChild</code> \u4f5c\u4e3a <code>node</code> \u7684\u53f3\u5b50\u8282\u70b9\u3002</p> <p></p> <p> Fig. \u6709 grandChild \u7684\u5de6\u65cb\u64cd\u4f5c </p> <p>\u53ef\u4ee5\u89c2\u5bdf\u5230\uff0c\u53f3\u65cb\u548c\u5de6\u65cb\u64cd\u4f5c\u5728\u903b\u8f91\u4e0a\u662f\u955c\u50cf\u5bf9\u79f0\u7684\uff0c\u5b83\u4eec\u5206\u522b\u89e3\u51b3\u7684\u4e24\u79cd\u5931\u8861\u60c5\u51b5\u4e5f\u662f\u5bf9\u79f0\u7684\u3002\u57fa\u4e8e\u5bf9\u79f0\u6027\uff0c\u6211\u4eec\u53ef\u4ee5\u8f7b\u677e\u5730\u4ece\u53f3\u65cb\u7684\u4ee3\u7801\u63a8\u5bfc\u51fa\u5de6\u65cb\u7684\u4ee3\u7801\u3002\u5177\u4f53\u5730\uff0c\u53ea\u9700\u5c06\u300c\u53f3\u65cb\u300d\u4ee3\u7801\u4e2d\u7684\u628a\u6240\u6709\u7684 <code>left</code> \u66ff\u6362\u4e3a <code>right</code> \uff0c\u5c06\u6240\u6709\u7684 <code>right</code> \u66ff\u6362\u4e3a <code>left</code> \uff0c\u5373\u53ef\u5f97\u5230\u300c\u5de6\u65cb\u300d\u4ee3\u7801\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart avl_tree.java<pre><code>/* \u5de6\u65cb\u64cd\u4f5c */\nTreeNode leftRotate(TreeNode node) {\nTreeNode child = node.right;\nTreeNode grandChild = child.left;\n// \u4ee5 child \u4e3a\u539f\u70b9\uff0c\u5c06 node \u5411\u5de6\u65cb\u8f6c\nchild.left = node;\nnode.right = grandChild;\n// \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\nupdateHeight(node);\nupdateHeight(child);\n// \u8fd4\u56de\u65cb\u8f6c\u540e\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn child;\n}\n</code></pre> avl_tree.cpp<pre><code>/* \u5de6\u65cb\u64cd\u4f5c */\nTreeNode *leftRotate(TreeNode *node) {\nTreeNode *child = node-&gt;right;\nTreeNode *grandChild = child-&gt;left;\n// \u4ee5 child \u4e3a\u539f\u70b9\uff0c\u5c06 node \u5411\u5de6\u65cb\u8f6c\nchild-&gt;left = node;\nnode-&gt;right = grandChild;\n// \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\nupdateHeight(node);\nupdateHeight(child);\n// \u8fd4\u56de\u65cb\u8f6c\u540e\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn child;\n}\n</code></pre> avl_tree.py<pre><code>def __left_rotate(self, node: TreeNode | None) -&gt; TreeNode | None:\n\"\"\"\u5de6\u65cb\u64cd\u4f5c\"\"\"\nchild = node.right\ngrand_child = child.left\n# \u4ee5 child \u4e3a\u539f\u70b9\uff0c\u5c06 node \u5411\u5de6\u65cb\u8f6c\nchild.left = node\nnode.right = grand_child\n# \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\nself.__update_height(node)\nself.__update_height(child)\n# \u8fd4\u56de\u65cb\u8f6c\u540e\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn child\n</code></pre> avl_tree.go<pre><code>/* \u5de6\u65cb\u64cd\u4f5c */\nfunc (t *aVLTree) leftRotate(node *TreeNode) *TreeNode {\nchild := node.Right\ngrandChild := child.Left\n// \u4ee5 child \u4e3a\u539f\u70b9\uff0c\u5c06 node \u5411\u5de6\u65cb\u8f6c\nchild.Left = node\nnode.Right = grandChild\n// \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\nt.updateHeight(node)\nt.updateHeight(child)\n// \u8fd4\u56de\u65cb\u8f6c\u540e\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn child\n}\n</code></pre> avl_tree.js<pre><code>/* \u5de6\u65cb\u64cd\u4f5c */\n#leftRotate(node) {\nconst child = node.right;\nconst grandChild = child.left;\n// \u4ee5 child \u4e3a\u539f\u70b9\uff0c\u5c06 node \u5411\u5de6\u65cb\u8f6c\nchild.left = node;\nnode.right = grandChild;\n// \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\nthis.#updateHeight(node);\nthis.#updateHeight(child);\n// \u8fd4\u56de\u65cb\u8f6c\u540e\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn child;\n}\n</code></pre> avl_tree.ts<pre><code>/* \u5de6\u65cb\u64cd\u4f5c */\nleftRotate(node: TreeNode): TreeNode {\nconst child = node.right;\nconst grandChild = child.left;\n// \u4ee5 child \u4e3a\u539f\u70b9\uff0c\u5c06 node \u5411\u5de6\u65cb\u8f6c\nchild.left = node;\nnode.right = grandChild;\n// \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\nthis.updateHeight(node);\nthis.updateHeight(child);\n// \u8fd4\u56de\u65cb\u8f6c\u540e\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn child;\n}\n</code></pre> avl_tree.c<pre><code>/* \u5de6\u65cb\u64cd\u4f5c */\nTreeNode *leftRotate(TreeNode *node) {\nTreeNode *child, *grandChild;\nchild = node-&gt;right;\ngrandChild = child-&gt;left;\n// \u4ee5 child \u4e3a\u539f\u70b9\uff0c\u5c06 node \u5411\u5de6\u65cb\u8f6c\nchild-&gt;left = node;\nnode-&gt;right = grandChild;\n// \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\nupdateHeight(node);\nupdateHeight(child);\n// \u8fd4\u56de\u65cb\u8f6c\u540e\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn child;\n}\n</code></pre> avl_tree.cs<pre><code>/* \u5de6\u65cb\u64cd\u4f5c */\nTreeNode? leftRotate(TreeNode? node) {\nTreeNode? child = node.right;\nTreeNode? grandChild = child?.left;\n// \u4ee5 child \u4e3a\u539f\u70b9\uff0c\u5c06 node \u5411\u5de6\u65cb\u8f6c\nchild.left = node;\nnode.right = grandChild;\n// \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\nupdateHeight(node);\nupdateHeight(child);\n// \u8fd4\u56de\u65cb\u8f6c\u540e\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn child;\n}\n</code></pre> avl_tree.swift<pre><code>/* \u5de6\u65cb\u64cd\u4f5c */\nfunc leftRotate(node: TreeNode?) -&gt; TreeNode? {\nlet child = node?.right\nlet grandChild = child?.left\n// \u4ee5 child \u4e3a\u539f\u70b9\uff0c\u5c06 node \u5411\u5de6\u65cb\u8f6c\nchild?.left = node\nnode?.right = grandChild\n// \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\nupdateHeight(node: node)\nupdateHeight(node: child)\n// \u8fd4\u56de\u65cb\u8f6c\u540e\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn child\n}\n</code></pre> avl_tree.zig<pre><code>// \u5de6\u65cb\u64cd\u4f5c\nfn leftRotate(self: *Self, node: ?*inc.TreeNode(T)) ?*inc.TreeNode(T) {\nvar child = node.?.right;\nvar grandChild = child.?.left;\n// \u4ee5 child \u4e3a\u539f\u70b9\uff0c\u5c06 node \u5411\u5de6\u65cb\u8f6c\nchild.?.left = node;\nnode.?.right = grandChild;\n// \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\nself.updateHeight(node);\nself.updateHeight(child);\n// \u8fd4\u56de\u65cb\u8f6c\u540e\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn child;\n}\n</code></pre> avl_tree.dart<pre><code>/* \u5de6\u65cb\u64cd\u4f5c */\nTreeNode? leftRotate(TreeNode? node) {\nTreeNode? child = node!.right;\nTreeNode? grandChild = child!.left;\n// \u4ee5 child \u4e3a\u539f\u70b9\uff0c\u5c06 node \u5411\u5de6\u65cb\u8f6c\nchild.left = node;\nnode.right = grandChild;\n// \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\nupdateHeight(node);\nupdateHeight(child);\n// \u8fd4\u56de\u65cb\u8f6c\u540e\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn child;\n}\n</code></pre>"},{"location":"chapter_tree/avl_tree/#_5","title":"\u5148\u5de6\u65cb\u540e\u53f3\u65cb","text":"<p>\u5bf9\u4e8e\u4e0b\u56fe\u4e2d\u7684\u5931\u8861\u8282\u70b9 3\uff0c\u4ec5\u4f7f\u7528\u5de6\u65cb\u6216\u53f3\u65cb\u90fd\u65e0\u6cd5\u4f7f\u5b50\u6811\u6062\u590d\u5e73\u8861\u3002\u6b64\u65f6\u9700\u8981\u5148\u5de6\u65cb\u540e\u53f3\u65cb\uff0c\u5373\u5148\u5bf9 <code>child</code> \u6267\u884c\u300c\u5de6\u65cb\u300d\uff0c\u518d\u5bf9 <code>node</code> \u6267\u884c\u300c\u53f3\u65cb\u300d\u3002</p> <p></p> <p> Fig. \u5148\u5de6\u65cb\u540e\u53f3\u65cb </p>"},{"location":"chapter_tree/avl_tree/#_6","title":"\u5148\u53f3\u65cb\u540e\u5de6\u65cb","text":"<p>\u540c\u7406\uff0c\u5bf9\u4e8e\u4e0a\u8ff0\u5931\u8861\u4e8c\u53c9\u6811\u7684\u955c\u50cf\u60c5\u51b5\uff0c\u9700\u8981\u5148\u53f3\u65cb\u540e\u5de6\u65cb\uff0c\u5373\u5148\u5bf9 <code>child</code> \u6267\u884c\u300c\u53f3\u65cb\u300d\uff0c\u7136\u540e\u5bf9 <code>node</code> \u6267\u884c\u300c\u5de6\u65cb\u300d\u3002</p> <p></p> <p> Fig. \u5148\u53f3\u65cb\u540e\u5de6\u65cb </p>"},{"location":"chapter_tree/avl_tree/#_7","title":"\u65cb\u8f6c\u7684\u9009\u62e9","text":"<p>\u4e0b\u56fe\u5c55\u793a\u7684\u56db\u79cd\u5931\u8861\u60c5\u51b5\u4e0e\u4e0a\u8ff0\u6848\u4f8b\u9010\u4e2a\u5bf9\u5e94\uff0c\u5206\u522b\u9700\u8981\u91c7\u7528\u53f3\u65cb\u3001\u5de6\u65cb\u3001\u5148\u53f3\u540e\u5de6\u3001\u5148\u5de6\u540e\u53f3\u7684\u65cb\u8f6c\u64cd\u4f5c\u3002</p> <p></p> <p> Fig. AVL \u6811\u7684\u56db\u79cd\u65cb\u8f6c\u60c5\u51b5 </p> <p>\u5728\u4ee3\u7801\u4e2d\uff0c\u6211\u4eec\u901a\u8fc7\u5224\u65ad\u5931\u8861\u8282\u70b9\u7684\u5e73\u8861\u56e0\u5b50\u4ee5\u53ca\u8f83\u9ad8\u4e00\u4fa7\u5b50\u8282\u70b9\u7684\u5e73\u8861\u56e0\u5b50\u7684\u6b63\u8d1f\u53f7\uff0c\u6765\u786e\u5b9a\u5931\u8861\u8282\u70b9\u5c5e\u4e8e\u4e0a\u56fe\u4e2d\u7684\u54ea\u79cd\u60c5\u51b5\u3002</p> \u5931\u8861\u8282\u70b9\u7684\u5e73\u8861\u56e0\u5b50 \u5b50\u8282\u70b9\u7684\u5e73\u8861\u56e0\u5b50 \u5e94\u91c7\u7528\u7684\u65cb\u8f6c\u65b9\u6cd5 \\(&gt;0\\) \uff08\u5373\u5de6\u504f\u6811\uff09 \\(\\geq 0\\) \u53f3\u65cb \\(&gt;0\\) \uff08\u5373\u5de6\u504f\u6811\uff09 \\(&lt;0\\) \u5148\u5de6\u65cb\u540e\u53f3\u65cb \\(&lt;0\\) \uff08\u5373\u53f3\u504f\u6811\uff09 \\(\\leq 0\\) \u5de6\u65cb \\(&lt;0\\) \uff08\u5373\u53f3\u504f\u6811\uff09 \\(&gt;0\\) \u5148\u53f3\u65cb\u540e\u5de6\u65cb <p>\u4e3a\u4e86\u4fbf\u4e8e\u4f7f\u7528\uff0c\u6211\u4eec\u5c06\u65cb\u8f6c\u64cd\u4f5c\u5c01\u88c5\u6210\u4e00\u4e2a\u51fd\u6570\u3002\u6709\u4e86\u8fd9\u4e2a\u51fd\u6570\uff0c\u6211\u4eec\u5c31\u80fd\u5bf9\u5404\u79cd\u5931\u8861\u60c5\u51b5\u8fdb\u884c\u65cb\u8f6c\uff0c\u4f7f\u5931\u8861\u8282\u70b9\u91cd\u65b0\u6062\u590d\u5e73\u8861\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart avl_tree.java<pre><code>/* \u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u8be5\u5b50\u6811\u91cd\u65b0\u6062\u590d\u5e73\u8861 */\nTreeNode rotate(TreeNode node) {\n// \u83b7\u53d6\u8282\u70b9 node \u7684\u5e73\u8861\u56e0\u5b50\nint balanceFactor = balanceFactor(node);\n// \u5de6\u504f\u6811\nif (balanceFactor &gt; 1) {\nif (balanceFactor(node.left) &gt;= 0) {\n// \u53f3\u65cb\nreturn rightRotate(node);\n} else {\n// \u5148\u5de6\u65cb\u540e\u53f3\u65cb\nnode.left = leftRotate(node.left);\nreturn rightRotate(node);\n}\n}\n// \u53f3\u504f\u6811\nif (balanceFactor &lt; -1) {\nif (balanceFactor(node.right) &lt;= 0) {\n// \u5de6\u65cb\nreturn leftRotate(node);\n} else {\n// \u5148\u53f3\u65cb\u540e\u5de6\u65cb\nnode.right = rightRotate(node.right);\nreturn leftRotate(node);\n}\n}\n// \u5e73\u8861\u6811\uff0c\u65e0\u9700\u65cb\u8f6c\uff0c\u76f4\u63a5\u8fd4\u56de\nreturn node;\n}\n</code></pre> avl_tree.cpp<pre><code>/* \u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u8be5\u5b50\u6811\u91cd\u65b0\u6062\u590d\u5e73\u8861 */\nTreeNode *rotate(TreeNode *node) {\n// \u83b7\u53d6\u8282\u70b9 node \u7684\u5e73\u8861\u56e0\u5b50\nint _balanceFactor = balanceFactor(node);\n// \u5de6\u504f\u6811\nif (_balanceFactor &gt; 1) {\nif (balanceFactor(node-&gt;left) &gt;= 0) {\n// \u53f3\u65cb\nreturn rightRotate(node);\n} else {\n// \u5148\u5de6\u65cb\u540e\u53f3\u65cb\nnode-&gt;left = leftRotate(node-&gt;left);\nreturn rightRotate(node);\n}\n}\n// \u53f3\u504f\u6811\nif (_balanceFactor &lt; -1) {\nif (balanceFactor(node-&gt;right) &lt;= 0) {\n// \u5de6\u65cb\nreturn leftRotate(node);\n} else {\n// \u5148\u53f3\u65cb\u540e\u5de6\u65cb\nnode-&gt;right = rightRotate(node-&gt;right);\nreturn leftRotate(node);\n}\n}\n// \u5e73\u8861\u6811\uff0c\u65e0\u9700\u65cb\u8f6c\uff0c\u76f4\u63a5\u8fd4\u56de\nreturn node;\n}\n</code></pre> avl_tree.py<pre><code>def __rotate(self, node: TreeNode | None) -&gt; TreeNode | None:\n\"\"\"\u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u8be5\u5b50\u6811\u91cd\u65b0\u6062\u590d\u5e73\u8861\"\"\"\n# \u83b7\u53d6\u8282\u70b9 node \u7684\u5e73\u8861\u56e0\u5b50\nbalance_factor = self.balance_factor(node)\n# \u5de6\u504f\u6811\nif balance_factor &gt; 1:\nif self.balance_factor(node.left) &gt;= 0:\n# \u53f3\u65cb\nreturn self.__right_rotate(node)\nelse:\n# \u5148\u5de6\u65cb\u540e\u53f3\u65cb\nnode.left = self.__left_rotate(node.left)\nreturn self.__right_rotate(node)\n# \u53f3\u504f\u6811\nelif balance_factor &lt; -1:\nif self.balance_factor(node.right) &lt;= 0:\n# \u5de6\u65cb\nreturn self.__left_rotate(node)\nelse:\n# \u5148\u53f3\u65cb\u540e\u5de6\u65cb\nnode.right = self.__right_rotate(node.right)\nreturn self.__left_rotate(node)\n# \u5e73\u8861\u6811\uff0c\u65e0\u9700\u65cb\u8f6c\uff0c\u76f4\u63a5\u8fd4\u56de\nreturn node\n</code></pre> avl_tree.go<pre><code>/* \u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u8be5\u5b50\u6811\u91cd\u65b0\u6062\u590d\u5e73\u8861 */\nfunc (t *aVLTree) rotate(node *TreeNode) *TreeNode {\n// \u83b7\u53d6\u8282\u70b9 node \u7684\u5e73\u8861\u56e0\u5b50\n// Go \u63a8\u8350\u77ed\u53d8\u91cf\uff0c\u8fd9\u91cc bf \u6307\u4ee3 t.balanceFactor\nbf := t.balanceFactor(node)\n// \u5de6\u504f\u6811\nif bf &gt; 1 {\nif t.balanceFactor(node.Left) &gt;= 0 {\n// \u53f3\u65cb\nreturn t.rightRotate(node)\n} else {\n// \u5148\u5de6\u65cb\u540e\u53f3\u65cb\nnode.Left = t.leftRotate(node.Left)\nreturn t.rightRotate(node)\n}\n}\n// \u53f3\u504f\u6811\nif bf &lt; -1 {\nif t.balanceFactor(node.Right) &lt;= 0 {\n// \u5de6\u65cb\nreturn t.leftRotate(node)\n} else {\n// \u5148\u53f3\u65cb\u540e\u5de6\u65cb\nnode.Right = t.rightRotate(node.Right)\nreturn t.leftRotate(node)\n}\n}\n// \u5e73\u8861\u6811\uff0c\u65e0\u9700\u65cb\u8f6c\uff0c\u76f4\u63a5\u8fd4\u56de\nreturn node\n}\n</code></pre> avl_tree.js<pre><code>/* \u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u8be5\u5b50\u6811\u91cd\u65b0\u6062\u590d\u5e73\u8861 */\n#rotate(node) {\n// \u83b7\u53d6\u8282\u70b9 node \u7684\u5e73\u8861\u56e0\u5b50\nconst balanceFactor = this.balanceFactor(node);\n// \u5de6\u504f\u6811\nif (balanceFactor &gt; 1) {\nif (this.balanceFactor(node.left) &gt;= 0) {\n// \u53f3\u65cb\nreturn this.#rightRotate(node);\n} else {\n// \u5148\u5de6\u65cb\u540e\u53f3\u65cb\nnode.left = this.#leftRotate(node.left);\nreturn this.#rightRotate(node);\n}\n}\n// \u53f3\u504f\u6811\nif (balanceFactor &lt; -1) {\nif (this.balanceFactor(node.right) &lt;= 0) {\n// \u5de6\u65cb\nreturn this.#leftRotate(node);\n} else {\n// \u5148\u53f3\u65cb\u540e\u5de6\u65cb\nnode.right = this.#rightRotate(node.right);\nreturn this.#leftRotate(node);\n}\n}\n// \u5e73\u8861\u6811\uff0c\u65e0\u9700\u65cb\u8f6c\uff0c\u76f4\u63a5\u8fd4\u56de\nreturn node;\n}\n</code></pre> avl_tree.ts<pre><code>/* \u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u8be5\u5b50\u6811\u91cd\u65b0\u6062\u590d\u5e73\u8861 */\nrotate(node: TreeNode): TreeNode {\n// \u83b7\u53d6\u8282\u70b9 node \u7684\u5e73\u8861\u56e0\u5b50\nconst balanceFactor = this.balanceFactor(node);\n// \u5de6\u504f\u6811\nif (balanceFactor &gt; 1) {\nif (this.balanceFactor(node.left) &gt;= 0) {\n// \u53f3\u65cb\nreturn this.rightRotate(node);\n} else {\n// \u5148\u5de6\u65cb\u540e\u53f3\u65cb\nnode.left = this.leftRotate(node.left);\nreturn this.rightRotate(node);\n}\n}\n// \u53f3\u504f\u6811\nif (balanceFactor &lt; -1) {\nif (this.balanceFactor(node.right) &lt;= 0) {\n// \u5de6\u65cb\nreturn this.leftRotate(node);\n} else {\n// \u5148\u53f3\u65cb\u540e\u5de6\u65cb\nnode.right = this.rightRotate(node.right);\nreturn this.leftRotate(node);\n}\n}\n// \u5e73\u8861\u6811\uff0c\u65e0\u9700\u65cb\u8f6c\uff0c\u76f4\u63a5\u8fd4\u56de\nreturn node;\n}\n</code></pre> avl_tree.c<pre><code>/* \u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u8be5\u5b50\u6811\u91cd\u65b0\u6062\u590d\u5e73\u8861 */\nTreeNode *rotate(TreeNode *node) {\n// \u83b7\u53d6\u8282\u70b9 node \u7684\u5e73\u8861\u56e0\u5b50\nint bf = balanceFactor(node);\n// \u5de6\u504f\u6811\nif (bf &gt; 1) {\nif (balanceFactor(node-&gt;left) &gt;= 0) {\n// \u53f3\u65cb\nreturn rightRotate(node);\n} else {\n// \u5148\u5de6\u65cb\u540e\u53f3\u65cb\nnode-&gt;left = leftRotate(node-&gt;left);\nreturn rightRotate(node);\n}\n}\n// \u53f3\u504f\u6811\nif (bf &lt; -1) {\nif (balanceFactor(node-&gt;right) &lt;= 0) {\n// \u5de6\u65cb\nreturn leftRotate(node);\n} else {\n// \u5148\u53f3\u65cb\u540e\u5de6\u65cb\nnode-&gt;right = rightRotate(node-&gt;right);\nreturn leftRotate(node);\n}\n}\n// \u5e73\u8861\u6811\uff0c\u65e0\u9700\u65cb\u8f6c\uff0c\u76f4\u63a5\u8fd4\u56de\nreturn node;\n}\n</code></pre> avl_tree.cs<pre><code>/* \u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u8be5\u5b50\u6811\u91cd\u65b0\u6062\u590d\u5e73\u8861 */\nTreeNode? rotate(TreeNode? node) {\n// \u83b7\u53d6\u8282\u70b9 node \u7684\u5e73\u8861\u56e0\u5b50\nint balanceFactorInt = balanceFactor(node);\n// \u5de6\u504f\u6811\nif (balanceFactorInt &gt; 1) {\nif (balanceFactor(node.left) &gt;= 0) {\n// \u53f3\u65cb\nreturn rightRotate(node);\n} else {\n// \u5148\u5de6\u65cb\u540e\u53f3\u65cb\nnode.left = leftRotate(node?.left);\nreturn rightRotate(node);\n}\n}\n// \u53f3\u504f\u6811\nif (balanceFactorInt &lt; -1) {\nif (balanceFactor(node.right) &lt;= 0) {\n// \u5de6\u65cb\nreturn leftRotate(node);\n} else {\n// \u5148\u53f3\u65cb\u540e\u5de6\u65cb\nnode.right = rightRotate(node?.right);\nreturn leftRotate(node);\n}\n}\n// \u5e73\u8861\u6811\uff0c\u65e0\u9700\u65cb\u8f6c\uff0c\u76f4\u63a5\u8fd4\u56de\nreturn node;\n}\n</code></pre> avl_tree.swift<pre><code>/* \u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u8be5\u5b50\u6811\u91cd\u65b0\u6062\u590d\u5e73\u8861 */\nfunc rotate(node: TreeNode?) -&gt; TreeNode? {\n// \u83b7\u53d6\u8282\u70b9 node \u7684\u5e73\u8861\u56e0\u5b50\nlet balanceFactor = balanceFactor(node: node)\n// \u5de6\u504f\u6811\nif balanceFactor &gt; 1 {\nif self.balanceFactor(node: node?.left) &gt;= 0 {\n// \u53f3\u65cb\nreturn rightRotate(node: node)\n} else {\n// \u5148\u5de6\u65cb\u540e\u53f3\u65cb\nnode?.left = leftRotate(node: node?.left)\nreturn rightRotate(node: node)\n}\n}\n// \u53f3\u504f\u6811\nif balanceFactor &lt; -1 {\nif self.balanceFactor(node: node?.right) &lt;= 0 {\n// \u5de6\u65cb\nreturn leftRotate(node: node)\n} else {\n// \u5148\u53f3\u65cb\u540e\u5de6\u65cb\nnode?.right = rightRotate(node: node?.right)\nreturn leftRotate(node: node)\n}\n}\n// \u5e73\u8861\u6811\uff0c\u65e0\u9700\u65cb\u8f6c\uff0c\u76f4\u63a5\u8fd4\u56de\nreturn node\n}\n</code></pre> avl_tree.zig<pre><code>// \u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u8be5\u5b50\u6811\u91cd\u65b0\u6062\u590d\u5e73\u8861\nfn rotate(self: *Self, node: ?*inc.TreeNode(T)) ?*inc.TreeNode(T) {\n// \u83b7\u53d6\u8282\u70b9 node \u7684\u5e73\u8861\u56e0\u5b50\nvar balance_factor = self.balanceFactor(node);\n// \u5de6\u504f\u6811\nif (balance_factor &gt; 1) {\nif (self.balanceFactor(node.?.left) &gt;= 0) {\n// \u53f3\u65cb\nreturn self.rightRotate(node);\n} else {\n// \u5148\u5de6\u65cb\u540e\u53f3\u65cb\nnode.?.left = self.leftRotate(node.?.left);\nreturn self.rightRotate(node);\n}\n}\n// \u53f3\u504f\u6811\nif (balance_factor &lt; -1) {\nif (self.balanceFactor(node.?.right) &lt;= 0) {\n// \u5de6\u65cb\nreturn self.leftRotate(node);\n} else {\n// \u5148\u53f3\u65cb\u540e\u5de6\u65cb\nnode.?.right = self.rightRotate(node.?.right);\nreturn self.leftRotate(node);\n}\n}\n// \u5e73\u8861\u6811\uff0c\u65e0\u9700\u65cb\u8f6c\uff0c\u76f4\u63a5\u8fd4\u56de\nreturn node;\n}\n</code></pre> avl_tree.dart<pre><code>/* \u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u8be5\u5b50\u6811\u91cd\u65b0\u6062\u590d\u5e73\u8861 */\nTreeNode? rotate(TreeNode? node) {\n// \u83b7\u53d6\u8282\u70b9 node \u7684\u5e73\u8861\u56e0\u5b50\nint factor = balanceFactor(node);\n// \u5de6\u504f\u6811\nif (factor &gt; 1) {\nif (balanceFactor(node!.left) &gt;= 0) {\n// \u53f3\u65cb\nreturn rightRotate(node);\n} else {\n// \u5148\u5de6\u65cb\u540e\u53f3\u65cb\nnode.left = leftRotate(node.left);\nreturn rightRotate(node);\n}\n}\n// \u53f3\u504f\u6811\nif (factor &lt; -1) {\nif (balanceFactor(node!.right) &lt;= 0) {\n// \u5de6\u65cb\nreturn leftRotate(node);\n} else {\n// \u5148\u53f3\u65cb\u540e\u5de6\u65cb\nnode.right = rightRotate(node.right);\nreturn leftRotate(node);\n}\n}\n// \u5e73\u8861\u6811\uff0c\u65e0\u9700\u65cb\u8f6c\uff0c\u76f4\u63a5\u8fd4\u56de\nreturn node;\n}\n</code></pre>"},{"location":"chapter_tree/avl_tree/#753-avl","title":"7.5.3. \u00a0 AVL \u6811\u5e38\u7528\u64cd\u4f5c","text":""},{"location":"chapter_tree/avl_tree/#_8","title":"\u63d2\u5165\u8282\u70b9","text":"<p>\u300cAVL \u6811\u300d\u7684\u8282\u70b9\u63d2\u5165\u64cd\u4f5c\u4e0e\u300c\u4e8c\u53c9\u641c\u7d22\u6811\u300d\u5728\u4e3b\u4f53\u4e0a\u7c7b\u4f3c\u3002\u552f\u4e00\u7684\u533a\u522b\u5728\u4e8e\uff0c\u5728 AVL \u6811\u4e2d\u63d2\u5165\u8282\u70b9\u540e\uff0c\u4ece\u8be5\u8282\u70b9\u5230\u6839\u8282\u70b9\u7684\u8def\u5f84\u4e0a\u53ef\u80fd\u4f1a\u51fa\u73b0\u4e00\u7cfb\u5217\u5931\u8861\u8282\u70b9\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u9700\u8981\u4ece\u8fd9\u4e2a\u8282\u70b9\u5f00\u59cb\uff0c\u81ea\u5e95\u5411\u4e0a\u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u6240\u6709\u5931\u8861\u8282\u70b9\u6062\u590d\u5e73\u8861\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart avl_tree.java<pre><code>/* \u63d2\u5165\u8282\u70b9 */\nvoid insert(int val) {\nroot = insertHelper(root, val);\n}\n/* \u9012\u5f52\u63d2\u5165\u8282\u70b9\uff08\u8f85\u52a9\u65b9\u6cd5\uff09 */\nTreeNode insertHelper(TreeNode node, int val) {\nif (node == null)\nreturn new TreeNode(val);\n/* 1. \u67e5\u627e\u63d2\u5165\u4f4d\u7f6e\uff0c\u5e76\u63d2\u5165\u8282\u70b9 */\nif (val &lt; node.val)\nnode.left = insertHelper(node.left, val);\nelse if (val &gt; node.val)\nnode.right = insertHelper(node.right, val);\nelse\nreturn node; // \u91cd\u590d\u8282\u70b9\u4e0d\u63d2\u5165\uff0c\u76f4\u63a5\u8fd4\u56de\nupdateHeight(node); // \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\n/* 2. \u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u8be5\u5b50\u6811\u91cd\u65b0\u6062\u590d\u5e73\u8861 */\nnode = rotate(node);\n// \u8fd4\u56de\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn node;\n}\n</code></pre> avl_tree.cpp<pre><code>/* \u63d2\u5165\u8282\u70b9 */\nvoid insert(int val) {\nroot = insertHelper(root, val);\n}\n/* \u9012\u5f52\u63d2\u5165\u8282\u70b9\uff08\u8f85\u52a9\u65b9\u6cd5\uff09 */\nTreeNode *insertHelper(TreeNode *node, int val) {\nif (node == nullptr)\nreturn new TreeNode(val);\n/* 1. \u67e5\u627e\u63d2\u5165\u4f4d\u7f6e\uff0c\u5e76\u63d2\u5165\u8282\u70b9 */\nif (val &lt; node-&gt;val)\nnode-&gt;left = insertHelper(node-&gt;left, val);\nelse if (val &gt; node-&gt;val)\nnode-&gt;right = insertHelper(node-&gt;right, val);\nelse\nreturn node;    // \u91cd\u590d\u8282\u70b9\u4e0d\u63d2\u5165\uff0c\u76f4\u63a5\u8fd4\u56de\nupdateHeight(node); // \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\n/* 2. \u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u8be5\u5b50\u6811\u91cd\u65b0\u6062\u590d\u5e73\u8861 */\nnode = rotate(node);\n// \u8fd4\u56de\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn node;\n}\n</code></pre> avl_tree.py<pre><code>def insert(self, val) -&gt; None:\n\"\"\"\u63d2\u5165\u8282\u70b9\"\"\"\nself.__root = self.__insert_helper(self.__root, val)\ndef __insert_helper(self, node: TreeNode | None, val: int) -&gt; TreeNode:\n\"\"\"\u9012\u5f52\u63d2\u5165\u8282\u70b9\uff08\u8f85\u52a9\u65b9\u6cd5\uff09\"\"\"\nif node is None:\nreturn TreeNode(val)\n# 1. \u67e5\u627e\u63d2\u5165\u4f4d\u7f6e\uff0c\u5e76\u63d2\u5165\u8282\u70b9\nif val &lt; node.val:\nnode.left = self.__insert_helper(node.left, val)\nelif val &gt; node.val:\nnode.right = self.__insert_helper(node.right, val)\nelse:\n# \u91cd\u590d\u8282\u70b9\u4e0d\u63d2\u5165\uff0c\u76f4\u63a5\u8fd4\u56de\nreturn node\n# \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\nself.__update_height(node)\n# 2. \u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u8be5\u5b50\u6811\u91cd\u65b0\u6062\u590d\u5e73\u8861\nreturn self.__rotate(node)\n</code></pre> avl_tree.go<pre><code>/* \u63d2\u5165\u8282\u70b9 */\nfunc (t *aVLTree) insert(val int) {\nt.root = t.insertHelper(t.root, val)\n}\n/* \u9012\u5f52\u63d2\u5165\u8282\u70b9\uff08\u8f85\u52a9\u65b9\u6cd5\uff09 */\nfunc (t *aVLTree) insertHelper(node *TreeNode, val int) *TreeNode {\nif node == nil {\nreturn NewTreeNode(val)\n}\n/* 1. \u67e5\u627e\u63d2\u5165\u4f4d\u7f6e\uff0c\u5e76\u63d2\u5165\u8282\u70b9 */\nif val &lt; node.Val {\nnode.Left = t.insertHelper(node.Left, val)\n} else if val &gt; node.Val {\nnode.Right = t.insertHelper(node.Right, val)\n} else {\n// \u91cd\u590d\u8282\u70b9\u4e0d\u63d2\u5165\uff0c\u76f4\u63a5\u8fd4\u56de\nreturn node\n}\n// \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\nt.updateHeight(node)\n/* 2. \u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u8be5\u5b50\u6811\u91cd\u65b0\u6062\u590d\u5e73\u8861 */\nnode = t.rotate(node)\n// \u8fd4\u56de\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn node\n}\n</code></pre> avl_tree.js<pre><code>/* \u63d2\u5165\u8282\u70b9 */\ninsert(val) {\nthis.root = this.#insertHelper(this.root, val);\n}\n/* \u9012\u5f52\u63d2\u5165\u8282\u70b9\uff08\u8f85\u52a9\u65b9\u6cd5\uff09 */\n#insertHelper(node, val) {\nif (node === null) return new TreeNode(val);\n/* 1. \u67e5\u627e\u63d2\u5165\u4f4d\u7f6e\uff0c\u5e76\u63d2\u5165\u8282\u70b9 */\nif (val &lt; node.val) node.left = this.#insertHelper(node.left, val);\nelse if (val &gt; node.val)\nnode.right = this.#insertHelper(node.right, val);\nelse return node; // \u91cd\u590d\u8282\u70b9\u4e0d\u63d2\u5165\uff0c\u76f4\u63a5\u8fd4\u56de\nthis.#updateHeight(node); // \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\n/* 2. \u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u8be5\u5b50\u6811\u91cd\u65b0\u6062\u590d\u5e73\u8861 */\nnode = this.#rotate(node);\n// \u8fd4\u56de\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn node;\n}\n</code></pre> avl_tree.ts<pre><code>/* \u63d2\u5165\u8282\u70b9 */\ninsert(val: number): void {\nthis.root = this.insertHelper(this.root, val);\n}\n/* \u9012\u5f52\u63d2\u5165\u8282\u70b9\uff08\u8f85\u52a9\u65b9\u6cd5\uff09 */\ninsertHelper(node: TreeNode, val: number): TreeNode {\nif (node === null) return new TreeNode(val);\n/* 1. \u67e5\u627e\u63d2\u5165\u4f4d\u7f6e\uff0c\u5e76\u63d2\u5165\u8282\u70b9 */\nif (val &lt; node.val) {\nnode.left = this.insertHelper(node.left, val);\n} else if (val &gt; node.val) {\nnode.right = this.insertHelper(node.right, val);\n} else {\nreturn node; // \u91cd\u590d\u8282\u70b9\u4e0d\u63d2\u5165\uff0c\u76f4\u63a5\u8fd4\u56de\n}\nthis.updateHeight(node); // \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\n/* 2. \u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u8be5\u5b50\u6811\u91cd\u65b0\u6062\u590d\u5e73\u8861 */\nnode = this.rotate(node);\n// \u8fd4\u56de\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn node;\n}\n</code></pre> avl_tree.c<pre><code>/* \u63d2\u5165\u8282\u70b9 */\nvoid insert(aVLTree *tree, int val) {\ntree-&gt;root = insertHelper(tree-&gt;root, val);\n}\n/* \u9012\u5f52\u63d2\u5165\u8282\u70b9\uff08\u8f85\u52a9\u65b9\u6cd5\uff09 */\nTreeNode *insertHelper(TreeNode *node, int val) {\nif (node == NULL) {\nreturn newTreeNode(val);\n}\n/* 1. \u67e5\u627e\u63d2\u5165\u4f4d\u7f6e\uff0c\u5e76\u63d2\u5165\u8282\u70b9 */\nif (val &lt; node-&gt;val) {\nnode-&gt;left = insertHelper(node-&gt;left, val);\n} else if (val &gt; node-&gt;val) {\nnode-&gt;right = insertHelper(node-&gt;right, val);\n} else {\n// \u91cd\u590d\u8282\u70b9\u4e0d\u63d2\u5165\uff0c\u76f4\u63a5\u8fd4\u56de\nreturn node;\n}\n// \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\nupdateHeight(node);\n/* 2. \u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u8be5\u5b50\u6811\u91cd\u65b0\u6062\u590d\u5e73\u8861 */\nnode = rotate(node);\n// \u8fd4\u56de\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn node;\n}\n</code></pre> avl_tree.cs<pre><code>/* \u63d2\u5165\u8282\u70b9 */\nvoid insert(int val) {\nroot = insertHelper(root, val);\n}\n/* \u9012\u5f52\u63d2\u5165\u8282\u70b9\uff08\u8f85\u52a9\u65b9\u6cd5\uff09 */\nTreeNode? insertHelper(TreeNode? node, int val) {\nif (node == null) return new TreeNode(val);\n/* 1. \u67e5\u627e\u63d2\u5165\u4f4d\u7f6e\uff0c\u5e76\u63d2\u5165\u8282\u70b9 */\nif (val &lt; node.val)\nnode.left = insertHelper(node.left, val);\nelse if (val &gt; node.val)\nnode.right = insertHelper(node.right, val);\nelse\nreturn node;     // \u91cd\u590d\u8282\u70b9\u4e0d\u63d2\u5165\uff0c\u76f4\u63a5\u8fd4\u56de\nupdateHeight(node);  // \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\n/* 2. \u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u8be5\u5b50\u6811\u91cd\u65b0\u6062\u590d\u5e73\u8861 */\nnode = rotate(node);\n// \u8fd4\u56de\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn node;\n}\n</code></pre> avl_tree.swift<pre><code>/* \u63d2\u5165\u8282\u70b9 */\n@discardableResult\nfunc insert(val: Int) {\nroot = insertHelper(node: root, val: val)\n}\n/* \u9012\u5f52\u63d2\u5165\u8282\u70b9\uff08\u8f85\u52a9\u65b9\u6cd5\uff09 */\nfunc insertHelper(node: TreeNode?, val: Int) -&gt; TreeNode? {\nvar node = node\nif node == nil {\nreturn TreeNode(x: val)\n}\n/* 1. \u67e5\u627e\u63d2\u5165\u4f4d\u7f6e\uff0c\u5e76\u63d2\u5165\u8282\u70b9 */\nif val &lt; node!.val {\nnode?.left = insertHelper(node: node?.left, val: val)\n} else if val &gt; node!.val {\nnode?.right = insertHelper(node: node?.right, val: val)\n} else {\nreturn node // \u91cd\u590d\u8282\u70b9\u4e0d\u63d2\u5165\uff0c\u76f4\u63a5\u8fd4\u56de\n}\nupdateHeight(node: node) // \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\n/* 2. \u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u8be5\u5b50\u6811\u91cd\u65b0\u6062\u590d\u5e73\u8861 */\nnode = rotate(node: node)\n// \u8fd4\u56de\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn node\n}\n</code></pre> avl_tree.zig<pre><code>// \u63d2\u5165\u8282\u70b9\nfn insert(self: *Self, val: T) void {\nself.root = try self.insertHelper(self.root, val);\n}\n// \u9012\u5f52\u63d2\u5165\u8282\u70b9\uff08\u8f85\u52a9\u65b9\u6cd5\uff09\nfn insertHelper(self: *Self, node_: ?*inc.TreeNode(T), val: T) !?*inc.TreeNode(T) {\nvar node = node_;\nif (node == null) {\nvar tmp_node = try self.mem_allocator.create(inc.TreeNode(T));\ntmp_node.init(val);\nreturn tmp_node;\n}\n// 1. \u67e5\u627e\u63d2\u5165\u4f4d\u7f6e\uff0c\u5e76\u63d2\u5165\u8282\u70b9\nif (val &lt; node.?.val) {\nnode.?.left = try self.insertHelper(node.?.left, val);\n} else if (val &gt; node.?.val) {\nnode.?.right = try self.insertHelper(node.?.right, val);\n} else {\nreturn node;            // \u91cd\u590d\u8282\u70b9\u4e0d\u63d2\u5165\uff0c\u76f4\u63a5\u8fd4\u56de\n}\nself.updateHeight(node);    // \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\n// 2. \u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u8be5\u5b50\u6811\u91cd\u65b0\u6062\u590d\u5e73\u8861\nnode = self.rotate(node);\n// \u8fd4\u56de\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn node;\n}\n</code></pre> avl_tree.dart<pre><code>/* \u63d2\u5165\u8282\u70b9 */\nvoid insert(int val) {\nroot = insertHelper(root, val);\n}\n/* \u9012\u5f52\u63d2\u5165\u8282\u70b9\uff08\u8f85\u52a9\u65b9\u6cd5\uff09 */\nTreeNode? insertHelper(TreeNode? node, int val) {\nif (node == null) return TreeNode(val);\n/* 1. \u67e5\u627e\u63d2\u5165\u4f4d\u7f6e\uff0c\u5e76\u63d2\u5165\u8282\u70b9 */\nif (val &lt; node.val)\nnode.left = insertHelper(node.left, val);\nelse if (val &gt; node.val)\nnode.right = insertHelper(node.right, val);\nelse\nreturn node; // \u91cd\u590d\u8282\u70b9\u4e0d\u63d2\u5165\uff0c\u76f4\u63a5\u8fd4\u56de\nupdateHeight(node); // \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\n/* 2. \u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u8be5\u5b50\u6811\u91cd\u65b0\u6062\u590d\u5e73\u8861 */\nnode = rotate(node);\n// \u8fd4\u56de\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn node;\n}\n</code></pre>"},{"location":"chapter_tree/avl_tree/#_9","title":"\u5220\u9664\u8282\u70b9","text":"<p>\u7c7b\u4f3c\u5730\uff0c\u5728\u4e8c\u53c9\u641c\u7d22\u6811\u7684\u5220\u9664\u8282\u70b9\u65b9\u6cd5\u7684\u57fa\u7840\u4e0a\uff0c\u9700\u8981\u4ece\u5e95\u81f3\u9876\u5730\u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u6240\u6709\u5931\u8861\u8282\u70b9\u6062\u590d\u5e73\u8861\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart avl_tree.java<pre><code>/* \u5220\u9664\u8282\u70b9 */\nvoid remove(int val) {\nroot = removeHelper(root, val);\n}\n/* \u9012\u5f52\u5220\u9664\u8282\u70b9\uff08\u8f85\u52a9\u65b9\u6cd5\uff09 */\nTreeNode removeHelper(TreeNode node, int val) {\nif (node == null)\nreturn null;\n/* 1. \u67e5\u627e\u8282\u70b9\uff0c\u5e76\u5220\u9664\u4e4b */\nif (val &lt; node.val)\nnode.left = removeHelper(node.left, val);\nelse if (val &gt; node.val)\nnode.right = removeHelper(node.right, val);\nelse {\nif (node.left == null || node.right == null) {\nTreeNode child = node.left != null ? node.left : node.right;\n// \u5b50\u8282\u70b9\u6570\u91cf = 0 \uff0c\u76f4\u63a5\u5220\u9664 node \u5e76\u8fd4\u56de\nif (child == null)\nreturn null;\n// \u5b50\u8282\u70b9\u6570\u91cf = 1 \uff0c\u76f4\u63a5\u5220\u9664 node\nelse\nnode = child;\n} else {\n// \u5b50\u8282\u70b9\u6570\u91cf = 2 \uff0c\u5219\u5c06\u4e2d\u5e8f\u904d\u5386\u7684\u4e0b\u4e2a\u8282\u70b9\u5220\u9664\uff0c\u5e76\u7528\u8be5\u8282\u70b9\u66ff\u6362\u5f53\u524d\u8282\u70b9\nTreeNode temp = node.right;\nwhile (temp.left != null) {\ntemp = temp.left;\n}\nnode.right = removeHelper(node.right, temp.val);\nnode.val = temp.val;\n}\n}\nupdateHeight(node); // \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\n/* 2. \u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u8be5\u5b50\u6811\u91cd\u65b0\u6062\u590d\u5e73\u8861 */\nnode = rotate(node);\n// \u8fd4\u56de\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn node;\n}\n</code></pre> avl_tree.cpp<pre><code>/* \u5220\u9664\u8282\u70b9 */\nvoid remove(int val) {\nroot = removeHelper(root, val);\n}\n/* \u9012\u5f52\u5220\u9664\u8282\u70b9\uff08\u8f85\u52a9\u65b9\u6cd5\uff09 */\nTreeNode *removeHelper(TreeNode *node, int val) {\nif (node == nullptr)\nreturn nullptr;\n/* 1. \u67e5\u627e\u8282\u70b9\uff0c\u5e76\u5220\u9664\u4e4b */\nif (val &lt; node-&gt;val)\nnode-&gt;left = removeHelper(node-&gt;left, val);\nelse if (val &gt; node-&gt;val)\nnode-&gt;right = removeHelper(node-&gt;right, val);\nelse {\nif (node-&gt;left == nullptr || node-&gt;right == nullptr) {\nTreeNode *child = node-&gt;left != nullptr ? node-&gt;left : node-&gt;right;\n// \u5b50\u8282\u70b9\u6570\u91cf = 0 \uff0c\u76f4\u63a5\u5220\u9664 node \u5e76\u8fd4\u56de\nif (child == nullptr) {\ndelete node;\nreturn nullptr;\n}\n// \u5b50\u8282\u70b9\u6570\u91cf = 1 \uff0c\u76f4\u63a5\u5220\u9664 node\nelse {\ndelete node;\nnode = child;\n}\n} else {\n// \u5b50\u8282\u70b9\u6570\u91cf = 2 \uff0c\u5219\u5c06\u4e2d\u5e8f\u904d\u5386\u7684\u4e0b\u4e2a\u8282\u70b9\u5220\u9664\uff0c\u5e76\u7528\u8be5\u8282\u70b9\u66ff\u6362\u5f53\u524d\u8282\u70b9\nTreeNode *temp = node-&gt;right;\nwhile (temp-&gt;left != nullptr) {\ntemp = temp-&gt;left;\n}\nint tempVal = temp-&gt;val;\nnode-&gt;right = removeHelper(node-&gt;right, temp-&gt;val);\nnode-&gt;val = tempVal;\n}\n}\nupdateHeight(node); // \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\n/* 2. \u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u8be5\u5b50\u6811\u91cd\u65b0\u6062\u590d\u5e73\u8861 */\nnode = rotate(node);\n// \u8fd4\u56de\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn node;\n}\n</code></pre> avl_tree.py<pre><code>def remove(self, val: int) -&gt; None:\n\"\"\"\u5220\u9664\u8282\u70b9\"\"\"\nself.__root = self.__remove_helper(self.__root, val)\ndef __remove_helper(self, node: TreeNode | None, val: int) -&gt; TreeNode | None:\n\"\"\"\u9012\u5f52\u5220\u9664\u8282\u70b9\uff08\u8f85\u52a9\u65b9\u6cd5\uff09\"\"\"\nif node is None:\nreturn None\n# 1. \u67e5\u627e\u8282\u70b9\uff0c\u5e76\u5220\u9664\u4e4b\nif val &lt; node.val:\nnode.left = self.__remove_helper(node.left, val)\nelif val &gt; node.val:\nnode.right = self.__remove_helper(node.right, val)\nelse:\nif node.left is None or node.right is None:\nchild = node.left or node.right\n# \u5b50\u8282\u70b9\u6570\u91cf = 0 \uff0c\u76f4\u63a5\u5220\u9664 node \u5e76\u8fd4\u56de\nif child is None:\nreturn None\n# \u5b50\u8282\u70b9\u6570\u91cf = 1 \uff0c\u76f4\u63a5\u5220\u9664 node\nelse:\nnode = child\nelse:\n# \u5b50\u8282\u70b9\u6570\u91cf = 2 \uff0c\u5219\u5c06\u4e2d\u5e8f\u904d\u5386\u7684\u4e0b\u4e2a\u8282\u70b9\u5220\u9664\uff0c\u5e76\u7528\u8be5\u8282\u70b9\u66ff\u6362\u5f53\u524d\u8282\u70b9\ntemp = node.right\nwhile temp.left is not None:\ntemp = temp.left\nnode.right = self.__remove_helper(node.right, temp.val)\nnode.val = temp.val\n# \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\nself.__update_height(node)\n# 2. \u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u8be5\u5b50\u6811\u91cd\u65b0\u6062\u590d\u5e73\u8861\nreturn self.__rotate(node)\n</code></pre> avl_tree.go<pre><code>/* \u5220\u9664\u8282\u70b9 */\nfunc (t *aVLTree) remove(val int) {\nt.root = t.removeHelper(t.root, val)\n}\n/* \u9012\u5f52\u5220\u9664\u8282\u70b9\uff08\u8f85\u52a9\u65b9\u6cd5\uff09 */\nfunc (t *aVLTree) removeHelper(node *TreeNode, val int) *TreeNode {\nif node == nil {\nreturn nil\n}\n/* 1. \u67e5\u627e\u8282\u70b9\uff0c\u5e76\u5220\u9664\u4e4b */\nif val &lt; node.Val {\nnode.Left = t.removeHelper(node.Left, val)\n} else if val &gt; node.Val {\nnode.Right = t.removeHelper(node.Right, val)\n} else {\nif node.Left == nil || node.Right == nil {\nchild := node.Left\nif node.Right != nil {\nchild = node.Right\n}\nif child == nil {\n// \u5b50\u8282\u70b9\u6570\u91cf = 0 \uff0c\u76f4\u63a5\u5220\u9664 node \u5e76\u8fd4\u56de\nreturn nil\n} else {\n// \u5b50\u8282\u70b9\u6570\u91cf = 1 \uff0c\u76f4\u63a5\u5220\u9664 node\nnode = child\n}\n} else {\n// \u5b50\u8282\u70b9\u6570\u91cf = 2 \uff0c\u5219\u5c06\u4e2d\u5e8f\u904d\u5386\u7684\u4e0b\u4e2a\u8282\u70b9\u5220\u9664\uff0c\u5e76\u7528\u8be5\u8282\u70b9\u66ff\u6362\u5f53\u524d\u8282\u70b9\ntemp := node.Right\nfor temp.Left != nil {\ntemp = temp.Left\n}\nnode.Right = t.removeHelper(node.Right, temp.Val)\nnode.Val = temp.Val\n}\n}\n// \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\nt.updateHeight(node)\n/* 2. \u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u8be5\u5b50\u6811\u91cd\u65b0\u6062\u590d\u5e73\u8861 */\nnode = t.rotate(node)\n// \u8fd4\u56de\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn node\n}\n</code></pre> avl_tree.js<pre><code>/* \u5220\u9664\u8282\u70b9 */\nremove(val) {\nthis.root = this.#removeHelper(this.root, val);\n}\n/* \u9012\u5f52\u5220\u9664\u8282\u70b9\uff08\u8f85\u52a9\u65b9\u6cd5\uff09 */\n#removeHelper(node, val) {\nif (node === null) return null;\n/* 1. \u67e5\u627e\u8282\u70b9\uff0c\u5e76\u5220\u9664\u4e4b */\nif (val &lt; node.val) node.left = this.#removeHelper(node.left, val);\nelse if (val &gt; node.val)\nnode.right = this.#removeHelper(node.right, val);\nelse {\nif (node.left === null || node.right === null) {\nconst child = node.left !== null ? node.left : node.right;\n// \u5b50\u8282\u70b9\u6570\u91cf = 0 \uff0c\u76f4\u63a5\u5220\u9664 node \u5e76\u8fd4\u56de\nif (child === null) return null;\n// \u5b50\u8282\u70b9\u6570\u91cf = 1 \uff0c\u76f4\u63a5\u5220\u9664 node\nelse node = child;\n} else {\n// \u5b50\u8282\u70b9\u6570\u91cf = 2 \uff0c\u5219\u5c06\u4e2d\u5e8f\u904d\u5386\u7684\u4e0b\u4e2a\u8282\u70b9\u5220\u9664\uff0c\u5e76\u7528\u8be5\u8282\u70b9\u66ff\u6362\u5f53\u524d\u8282\u70b9\nlet temp = node.right;\nwhile (temp.left !== null) {\ntemp = temp.left;\n}\nnode.right = this.#removeHelper(node.right, temp.val);\nnode.val = temp.val;\n}\n}\nthis.#updateHeight(node); // \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\n/* 2. \u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u8be5\u5b50\u6811\u91cd\u65b0\u6062\u590d\u5e73\u8861 */\nnode = this.#rotate(node);\n// \u8fd4\u56de\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn node;\n}\n</code></pre> avl_tree.ts<pre><code>/* \u5220\u9664\u8282\u70b9 */\nremove(val: number): void {\nthis.root = this.removeHelper(this.root, val);\n}\n/* \u9012\u5f52\u5220\u9664\u8282\u70b9\uff08\u8f85\u52a9\u65b9\u6cd5\uff09 */\nremoveHelper(node: TreeNode, val: number): TreeNode {\nif (node === null) return null;\n/* 1. \u67e5\u627e\u8282\u70b9\uff0c\u5e76\u5220\u9664\u4e4b */\nif (val &lt; node.val) {\nnode.left = this.removeHelper(node.left, val);\n} else if (val &gt; node.val) {\nnode.right = this.removeHelper(node.right, val);\n} else {\nif (node.left === null || node.right === null) {\nconst child = node.left !== null ? node.left : node.right;\n// \u5b50\u8282\u70b9\u6570\u91cf = 0 \uff0c\u76f4\u63a5\u5220\u9664 node \u5e76\u8fd4\u56de\nif (child === null) {\nreturn null;\n} else {\n// \u5b50\u8282\u70b9\u6570\u91cf = 1 \uff0c\u76f4\u63a5\u5220\u9664 node\nnode = child;\n}\n} else {\n// \u5b50\u8282\u70b9\u6570\u91cf = 2 \uff0c\u5219\u5c06\u4e2d\u5e8f\u904d\u5386\u7684\u4e0b\u4e2a\u8282\u70b9\u5220\u9664\uff0c\u5e76\u7528\u8be5\u8282\u70b9\u66ff\u6362\u5f53\u524d\u8282\u70b9\nlet temp = node.right;\nwhile (temp.left !== null) {\ntemp = temp.left;\n}\nnode.right = this.removeHelper(node.right, temp.val);\nnode.val = temp.val;\n}\n}\nthis.updateHeight(node); // \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\n/* 2. \u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u8be5\u5b50\u6811\u91cd\u65b0\u6062\u590d\u5e73\u8861 */\nnode = this.rotate(node);\n// \u8fd4\u56de\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn node;\n}\n</code></pre> avl_tree.c<pre><code>/* \u5220\u9664\u8282\u70b9 */\n// \u7531\u4e8e\u5f15\u5165\u4e86 stdio.h \uff0c\u6b64\u5904\u65e0\u6cd5\u4f7f\u7528 remove \u5173\u952e\u8bcd\nvoid removeNode(aVLTree *tree, int val) {\nTreeNode *root = removeHelper(tree-&gt;root, val);\n}\n/* \u9012\u5f52\u5220\u9664\u8282\u70b9\uff08\u8f85\u52a9\u65b9\u6cd5\uff09 */\nTreeNode *removeHelper(TreeNode *node, int val) {\nTreeNode *child, *grandChild;\nif (node == NULL) {\nreturn NULL;\n}\n/* 1. \u67e5\u627e\u8282\u70b9\uff0c\u5e76\u5220\u9664\u4e4b */\nif (val &lt; node-&gt;val) {\nnode-&gt;left = removeHelper(node-&gt;left, val);\n} else if (val &gt; node-&gt;val) {\nnode-&gt;right = removeHelper(node-&gt;right, val);\n} else {\nif (node-&gt;left == NULL || node-&gt;right == NULL) {\nchild = node-&gt;left;\nif (node-&gt;right != NULL) {\nchild = node-&gt;right;\n}\n// \u5b50\u8282\u70b9\u6570\u91cf = 0 \uff0c\u76f4\u63a5\u5220\u9664 node \u5e76\u8fd4\u56de\nif (child == NULL) {\nreturn NULL;\n} else {\n// \u5b50\u8282\u70b9\u6570\u91cf = 1 \uff0c\u76f4\u63a5\u5220\u9664 node\nnode = child;\n}\n} else {\n// \u5b50\u8282\u70b9\u6570\u91cf = 2 \uff0c\u5219\u5c06\u4e2d\u5e8f\u904d\u5386\u7684\u4e0b\u4e2a\u8282\u70b9\u5220\u9664\uff0c\u5e76\u7528\u8be5\u8282\u70b9\u66ff\u6362\u5f53\u524d\u8282\u70b9\nTreeNode *temp = node-&gt;right;\nwhile (temp-&gt;left != NULL) {\ntemp = temp-&gt;left;\n}\nint tempVal = temp-&gt;val;\nnode-&gt;right = removeHelper(node-&gt;right, temp-&gt;val);\nnode-&gt;val = tempVal;\n}\n}\n// \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\nupdateHeight(node);\n/* 2. \u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u8be5\u5b50\u6811\u91cd\u65b0\u6062\u590d\u5e73\u8861 */\nnode = rotate(node);\n// \u8fd4\u56de\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn node;\n}\n</code></pre> avl_tree.cs<pre><code>/* \u5220\u9664\u8282\u70b9 */\nvoid remove(int val) {\nroot = removeHelper(root, val);\n}\n/* \u9012\u5f52\u5220\u9664\u8282\u70b9\uff08\u8f85\u52a9\u65b9\u6cd5\uff09 */\nTreeNode? removeHelper(TreeNode? node, int val) {\nif (node == null) return null;\n/* 1. \u67e5\u627e\u8282\u70b9\uff0c\u5e76\u5220\u9664\u4e4b */\nif (val &lt; node.val)\nnode.left = removeHelper(node.left, val);\nelse if (val &gt; node.val)\nnode.right = removeHelper(node.right, val);\nelse {\nif (node.left == null || node.right == null) {\nTreeNode? child = node.left != null ? node.left : node.right;\n// \u5b50\u8282\u70b9\u6570\u91cf = 0 \uff0c\u76f4\u63a5\u5220\u9664 node \u5e76\u8fd4\u56de\nif (child == null)\nreturn null;\n// \u5b50\u8282\u70b9\u6570\u91cf = 1 \uff0c\u76f4\u63a5\u5220\u9664 node\nelse\nnode = child;\n} else {\n// \u5b50\u8282\u70b9\u6570\u91cf = 2 \uff0c\u5219\u5c06\u4e2d\u5e8f\u904d\u5386\u7684\u4e0b\u4e2a\u8282\u70b9\u5220\u9664\uff0c\u5e76\u7528\u8be5\u8282\u70b9\u66ff\u6362\u5f53\u524d\u8282\u70b9\nTreeNode? temp = node.right;\nwhile (temp.left != null) {\ntemp = temp.left;\n}\nnode.right = removeHelper(node.right, temp.val);\nnode.val = temp.val;\n}\n}\nupdateHeight(node);  // \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\n/* 2. \u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u8be5\u5b50\u6811\u91cd\u65b0\u6062\u590d\u5e73\u8861 */\nnode = rotate(node);\n// \u8fd4\u56de\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn node;\n}\n</code></pre> avl_tree.swift<pre><code>/* \u5220\u9664\u8282\u70b9 */\n@discardableResult\nfunc remove(val: Int) {\nroot = removeHelper(node: root, val: val)\n}\n/* \u9012\u5f52\u5220\u9664\u8282\u70b9\uff08\u8f85\u52a9\u65b9\u6cd5\uff09 */\nfunc removeHelper(node: TreeNode?, val: Int) -&gt; TreeNode? {\nvar node = node\nif node == nil {\nreturn nil\n}\n/* 1. \u67e5\u627e\u8282\u70b9\uff0c\u5e76\u5220\u9664\u4e4b */\nif val &lt; node!.val {\nnode?.left = removeHelper(node: node?.left, val: val)\n} else if val &gt; node!.val {\nnode?.right = removeHelper(node: node?.right, val: val)\n} else {\nif node?.left == nil || node?.right == nil {\nlet child = node?.left != nil ? node?.left : node?.right\n// \u5b50\u8282\u70b9\u6570\u91cf = 0 \uff0c\u76f4\u63a5\u5220\u9664 node \u5e76\u8fd4\u56de\nif child == nil {\nreturn nil\n}\n// \u5b50\u8282\u70b9\u6570\u91cf = 1 \uff0c\u76f4\u63a5\u5220\u9664 node\nelse {\nnode = child\n}\n} else {\n// \u5b50\u8282\u70b9\u6570\u91cf = 2 \uff0c\u5219\u5c06\u4e2d\u5e8f\u904d\u5386\u7684\u4e0b\u4e2a\u8282\u70b9\u5220\u9664\uff0c\u5e76\u7528\u8be5\u8282\u70b9\u66ff\u6362\u5f53\u524d\u8282\u70b9\nvar temp = node?.right\nwhile temp?.left != nil {\ntemp = temp?.left\n}\nnode?.right = removeHelper(node: node?.right, val: temp!.val)\nnode?.val = temp!.val\n}\n}\nupdateHeight(node: node) // \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\n/* 2. \u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u8be5\u5b50\u6811\u91cd\u65b0\u6062\u590d\u5e73\u8861 */\nnode = rotate(node: node)\n// \u8fd4\u56de\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn node\n}\n</code></pre> avl_tree.zig<pre><code>// \u5220\u9664\u8282\u70b9\nfn remove(self: *Self, val: T) void {\nself.root = self.removeHelper(self.root, val);\n}\n// \u9012\u5f52\u5220\u9664\u8282\u70b9\uff08\u8f85\u52a9\u65b9\u6cd5\uff09\nfn removeHelper(self: *Self, node_: ?*inc.TreeNode(T), val: T) ?*inc.TreeNode(T) {\nvar node = node_;\nif (node == null) return null;\n// 1. \u67e5\u627e\u8282\u70b9\uff0c\u5e76\u5220\u9664\u4e4b\nif (val &lt; node.?.val) {\nnode.?.left = self.removeHelper(node.?.left, val);\n} else if (val &gt; node.?.val) {\nnode.?.right = self.removeHelper(node.?.right, val);\n} else {\nif (node.?.left == null or node.?.right == null) {\nvar child = if (node.?.left != null) node.?.left else node.?.right;\n// \u5b50\u8282\u70b9\u6570\u91cf = 0 \uff0c\u76f4\u63a5\u5220\u9664 node \u5e76\u8fd4\u56de\nif (child == null) {\nreturn null;\n// \u5b50\u8282\u70b9\u6570\u91cf = 1 \uff0c\u76f4\u63a5\u5220\u9664 node\n} else {\nnode = child;\n}\n} else {\n// \u5b50\u8282\u70b9\u6570\u91cf = 2 \uff0c\u5219\u5c06\u4e2d\u5e8f\u904d\u5386\u7684\u4e0b\u4e2a\u8282\u70b9\u5220\u9664\uff0c\u5e76\u7528\u8be5\u8282\u70b9\u66ff\u6362\u5f53\u524d\u8282\u70b9\nvar temp = node.?.right;\nwhile (temp.?.left != null) {\ntemp = temp.?.left;\n}\nnode.?.right = self.removeHelper(node.?.right, temp.?.val);\nnode.?.val = temp.?.val;\n}\n}\nself.updateHeight(node); // \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\n// 2. \u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u8be5\u5b50\u6811\u91cd\u65b0\u6062\u590d\u5e73\u8861\nnode = self.rotate(node);\n// \u8fd4\u56de\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn node;\n}\n</code></pre> avl_tree.dart<pre><code>/* \u5220\u9664\u8282\u70b9 */\nvoid remove(int val) {\nroot = removeHelper(root, val);\n}\n/* \u9012\u5f52\u5220\u9664\u8282\u70b9\uff08\u8f85\u52a9\u65b9\u6cd5\uff09 */\nTreeNode? removeHelper(TreeNode? node, int val) {\nif (node == null) return null;\n/* 1. \u67e5\u627e\u8282\u70b9\uff0c\u5e76\u5220\u9664\u4e4b */\nif (val &lt; node.val)\nnode.left = removeHelper(node.left, val);\nelse if (val &gt; node.val)\nnode.right = removeHelper(node.right, val);\nelse {\nif (node.left == null || node.right == null) {\nTreeNode? child = node.left ?? node.right;\n// \u5b50\u8282\u70b9\u6570\u91cf = 0 \uff0c\u76f4\u63a5\u5220\u9664 node \u5e76\u8fd4\u56de\nif (child == null)\nreturn null;\n// \u5b50\u8282\u70b9\u6570\u91cf = 1 \uff0c\u76f4\u63a5\u5220\u9664 node\nelse\nnode = child;\n} else {\n// \u5b50\u8282\u70b9\u6570\u91cf = 2 \uff0c\u5219\u5c06\u4e2d\u5e8f\u904d\u5386\u7684\u4e0b\u4e2a\u8282\u70b9\u5220\u9664\uff0c\u5e76\u7528\u8be5\u8282\u70b9\u66ff\u6362\u5f53\u524d\u8282\u70b9\nTreeNode? temp = node.right;\nwhile (temp!.left != null) {\ntemp = temp.left;\n}\nnode.right = removeHelper(node.right, temp.val);\nnode.val = temp.val;\n}\n}\nupdateHeight(node); // \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\n/* 2. \u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u8be5\u5b50\u6811\u91cd\u65b0\u6062\u590d\u5e73\u8861 */\nnode = rotate(node);\n// \u8fd4\u56de\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn node;\n}\n</code></pre>"},{"location":"chapter_tree/avl_tree/#_10","title":"\u67e5\u627e\u8282\u70b9","text":"<p>AVL \u6811\u7684\u8282\u70b9\u67e5\u627e\u64cd\u4f5c\u4e0e\u4e8c\u53c9\u641c\u7d22\u6811\u4e00\u81f4\uff0c\u5728\u6b64\u4e0d\u518d\u8d58\u8ff0\u3002</p>"},{"location":"chapter_tree/avl_tree/#754-avl","title":"7.5.4. \u00a0 AVL \u6811\u5178\u578b\u5e94\u7528","text":"<ul> <li>\u7ec4\u7ec7\u548c\u5b58\u50a8\u5927\u578b\u6570\u636e\uff0c\u9002\u7528\u4e8e\u9ad8\u9891\u67e5\u627e\u3001\u4f4e\u9891\u589e\u5220\u7684\u573a\u666f\uff1b</li> <li>\u7528\u4e8e\u6784\u5efa\u6570\u636e\u5e93\u4e2d\u7684\u7d22\u5f15\u7cfb\u7edf\uff1b</li> </ul> <p>\u4e3a\u4ec0\u4e48\u7ea2\u9ed1\u6811\u6bd4 AVL \u6811\u66f4\u53d7\u6b22\u8fce\uff1f</p> <p>\u7ea2\u9ed1\u6811\u7684\u5e73\u8861\u6761\u4ef6\u76f8\u5bf9\u5bbd\u677e\uff0c\u56e0\u6b64\u5728\u7ea2\u9ed1\u6811\u4e2d\u63d2\u5165\u4e0e\u5220\u9664\u8282\u70b9\u6240\u9700\u7684\u65cb\u8f6c\u64cd\u4f5c\u76f8\u5bf9\u8f83\u5c11\uff0c\u5728\u8282\u70b9\u589e\u5220\u64cd\u4f5c\u4e0a\u7684\u5e73\u5747\u6548\u7387\u9ad8\u4e8e AVL \u6811\u3002</p>"},{"location":"chapter_tree/binary_search_tree/","title":"7.4. \u00a0 \u4e8c\u53c9\u641c\u7d22\u6811","text":"<p>\u300c\u4e8c\u53c9\u641c\u7d22\u6811 Binary Search Tree\u300d\u6ee1\u8db3\u4ee5\u4e0b\u6761\u4ef6\uff1a</p> <ol> <li>\u5bf9\u4e8e\u6839\u8282\u70b9\uff0c\u5de6\u5b50\u6811\u4e2d\u6240\u6709\u8282\u70b9\u7684\u503c \\(&lt;\\) \u6839\u8282\u70b9\u7684\u503c \\(&lt;\\) \u53f3\u5b50\u6811\u4e2d\u6240\u6709\u8282\u70b9\u7684\u503c\uff1b</li> <li>\u4efb\u610f\u8282\u70b9\u7684\u5de6\u3001\u53f3\u5b50\u6811\u4e5f\u662f\u4e8c\u53c9\u641c\u7d22\u6811\uff0c\u5373\u540c\u6837\u6ee1\u8db3\u6761\u4ef6 <code>1.</code> \uff1b</li> </ol> <p></p> <p> Fig. \u4e8c\u53c9\u641c\u7d22\u6811 </p>"},{"location":"chapter_tree/binary_search_tree/#741","title":"7.4.1. \u00a0 \u4e8c\u53c9\u641c\u7d22\u6811\u7684\u64cd\u4f5c","text":""},{"location":"chapter_tree/binary_search_tree/#_1","title":"\u67e5\u627e\u8282\u70b9","text":"<p>\u7ed9\u5b9a\u76ee\u6807\u8282\u70b9\u503c <code>num</code> \uff0c\u53ef\u4ee5\u6839\u636e\u4e8c\u53c9\u641c\u7d22\u6811\u7684\u6027\u8d28\u6765\u67e5\u627e\u3002\u6211\u4eec\u58f0\u660e\u4e00\u4e2a\u8282\u70b9 <code>cur</code> \uff0c\u4ece\u4e8c\u53c9\u6811\u7684\u6839\u8282\u70b9 <code>root</code> \u51fa\u53d1\uff0c\u5faa\u73af\u6bd4\u8f83\u8282\u70b9\u503c <code>cur.val</code> \u548c <code>num</code> \u4e4b\u95f4\u7684\u5927\u5c0f\u5173\u7cfb</p> <ul> <li>\u82e5 <code>cur.val &lt; num</code> \uff0c\u8bf4\u660e\u76ee\u6807\u8282\u70b9\u5728 <code>cur</code> \u7684\u53f3\u5b50\u6811\u4e2d\uff0c\u56e0\u6b64\u6267\u884c <code>cur = cur.right</code> \uff1b</li> <li>\u82e5 <code>cur.val &gt; num</code> \uff0c\u8bf4\u660e\u76ee\u6807\u8282\u70b9\u5728 <code>cur</code> \u7684\u5de6\u5b50\u6811\u4e2d\uff0c\u56e0\u6b64\u6267\u884c <code>cur = cur.left</code> \uff1b</li> <li>\u82e5 <code>cur.val = num</code> \uff0c\u8bf4\u660e\u627e\u5230\u76ee\u6807\u8282\u70b9\uff0c\u8df3\u51fa\u5faa\u73af\u5e76\u8fd4\u56de\u8be5\u8282\u70b9\uff1b</li> </ul> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt; <p></p> <p></p> <p></p> <p></p> <p>\u4e8c\u53c9\u641c\u7d22\u6811\u7684\u67e5\u627e\u64cd\u4f5c\u4e0e\u4e8c\u5206\u67e5\u627e\u7b97\u6cd5\u7684\u5de5\u4f5c\u539f\u7406\u4e00\u81f4\uff0c\u90fd\u662f\u6bcf\u8f6e\u6392\u9664\u4e00\u534a\u60c5\u51b5\u3002\u5faa\u73af\u6b21\u6570\u6700\u591a\u4e3a\u4e8c\u53c9\u6811\u7684\u9ad8\u5ea6\uff0c\u5f53\u4e8c\u53c9\u6811\u5e73\u8861\u65f6\uff0c\u4f7f\u7528 \\(O(\\log n)\\) \u65f6\u95f4\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart binary_search_tree.java<pre><code>/* \u67e5\u627e\u8282\u70b9 */\nTreeNode search(int num) {\nTreeNode cur = root;\n// \u5faa\u73af\u67e5\u627e\uff0c\u8d8a\u8fc7\u53f6\u8282\u70b9\u540e\u8df3\u51fa\nwhile (cur != null) {\n// \u76ee\u6807\u8282\u70b9\u5728 cur \u7684\u53f3\u5b50\u6811\u4e2d\nif (cur.val &lt; num)\ncur = cur.right;\n// \u76ee\u6807\u8282\u70b9\u5728 cur \u7684\u5de6\u5b50\u6811\u4e2d\nelse if (cur.val &gt; num)\ncur = cur.left;\n// \u627e\u5230\u76ee\u6807\u8282\u70b9\uff0c\u8df3\u51fa\u5faa\u73af\nelse\nbreak;\n}\n// \u8fd4\u56de\u76ee\u6807\u8282\u70b9\nreturn cur;\n}\n</code></pre> binary_search_tree.cpp<pre><code>/* \u67e5\u627e\u8282\u70b9 */\nTreeNode *search(int num) {\nTreeNode *cur = root;\n// \u5faa\u73af\u67e5\u627e\uff0c\u8d8a\u8fc7\u53f6\u8282\u70b9\u540e\u8df3\u51fa\nwhile (cur != nullptr) {\n// \u76ee\u6807\u8282\u70b9\u5728 cur \u7684\u53f3\u5b50\u6811\u4e2d\nif (cur-&gt;val &lt; num)\ncur = cur-&gt;right;\n// \u76ee\u6807\u8282\u70b9\u5728 cur \u7684\u5de6\u5b50\u6811\u4e2d\nelse if (cur-&gt;val &gt; num)\ncur = cur-&gt;left;\n// \u627e\u5230\u76ee\u6807\u8282\u70b9\uff0c\u8df3\u51fa\u5faa\u73af\nelse\nbreak;\n}\n// \u8fd4\u56de\u76ee\u6807\u8282\u70b9\nreturn cur;\n}\n</code></pre> binary_search_tree.py<pre><code>def search(self, num: int) -&gt; TreeNode | None:\n\"\"\"\u67e5\u627e\u8282\u70b9\"\"\"\ncur: TreeNode | None = self.root\n# \u5faa\u73af\u67e5\u627e\uff0c\u8d8a\u8fc7\u53f6\u8282\u70b9\u540e\u8df3\u51fa\nwhile cur is not None:\n# \u76ee\u6807\u8282\u70b9\u5728 cur \u7684\u53f3\u5b50\u6811\u4e2d\nif cur.val &lt; num:\ncur = cur.right\n# \u76ee\u6807\u8282\u70b9\u5728 cur \u7684\u5de6\u5b50\u6811\u4e2d\nelif cur.val &gt; num:\ncur = cur.left\n# \u627e\u5230\u76ee\u6807\u8282\u70b9\uff0c\u8df3\u51fa\u5faa\u73af\nelse:\nbreak\nreturn cur\n</code></pre> binary_search_tree.go<pre><code>/* \u67e5\u627e\u8282\u70b9 */\nfunc (bst *binarySearchTree) search(num int) *TreeNode {\nnode := bst.root\n// \u5faa\u73af\u67e5\u627e\uff0c\u8d8a\u8fc7\u53f6\u8282\u70b9\u540e\u8df3\u51fa\nfor node != nil {\nif node.Val &lt; num {\n// \u76ee\u6807\u8282\u70b9\u5728 cur \u7684\u53f3\u5b50\u6811\u4e2d\nnode = node.Right\n} else if node.Val &gt; num {\n// \u76ee\u6807\u8282\u70b9\u5728 cur \u7684\u5de6\u5b50\u6811\u4e2d\nnode = node.Left\n} else {\n// \u627e\u5230\u76ee\u6807\u8282\u70b9\uff0c\u8df3\u51fa\u5faa\u73af\nbreak\n}\n}\n// \u8fd4\u56de\u76ee\u6807\u8282\u70b9\nreturn node\n}\n</code></pre> binary_search_tree.js<pre><code>/* \u67e5\u627e\u8282\u70b9 */\nfunction search(num) {\nlet cur = root;\n// \u5faa\u73af\u67e5\u627e\uff0c\u8d8a\u8fc7\u53f6\u8282\u70b9\u540e\u8df3\u51fa\nwhile (cur !== null) {\n// \u76ee\u6807\u8282\u70b9\u5728 cur \u7684\u53f3\u5b50\u6811\u4e2d\nif (cur.val &lt; num) cur = cur.right;\n// \u76ee\u6807\u8282\u70b9\u5728 cur \u7684\u5de6\u5b50\u6811\u4e2d\nelse if (cur.val &gt; num) cur = cur.left;\n// \u627e\u5230\u76ee\u6807\u8282\u70b9\uff0c\u8df3\u51fa\u5faa\u73af\nelse break;\n}\n// \u8fd4\u56de\u76ee\u6807\u8282\u70b9\nreturn cur;\n}\n</code></pre> binary_search_tree.ts<pre><code>/* \u67e5\u627e\u8282\u70b9 */\nfunction search(num: number): TreeNode | null {\nlet cur = root;\n// \u5faa\u73af\u67e5\u627e\uff0c\u8d8a\u8fc7\u53f6\u8282\u70b9\u540e\u8df3\u51fa\nwhile (cur !== null) {\nif (cur.val &lt; num) {\ncur = cur.right; // \u76ee\u6807\u8282\u70b9\u5728 cur \u7684\u53f3\u5b50\u6811\u4e2d\n} else if (cur.val &gt; num) {\ncur = cur.left; // \u76ee\u6807\u8282\u70b9\u5728 cur \u7684\u5de6\u5b50\u6811\u4e2d\n} else {\nbreak; // \u627e\u5230\u76ee\u6807\u8282\u70b9\uff0c\u8df3\u51fa\u5faa\u73af\n}\n}\n// \u8fd4\u56de\u76ee\u6807\u8282\u70b9\nreturn cur;\n}\n</code></pre> binary_search_tree.c<pre><code>/* \u67e5\u627e\u8282\u70b9 */\nTreeNode *search(binarySearchTree *bst, int num) {\nTreeNode *cur = bst-&gt;root;\n// \u5faa\u73af\u67e5\u627e\uff0c\u8d8a\u8fc7\u53f6\u8282\u70b9\u540e\u8df3\u51fa\nwhile (cur != NULL) {\nif (cur-&gt;val &lt; num) {\n// \u76ee\u6807\u8282\u70b9\u5728 cur \u7684\u53f3\u5b50\u6811\u4e2d\ncur = cur-&gt;right;\n} else if (cur-&gt;val &gt; num) {\n// \u76ee\u6807\u8282\u70b9\u5728 cur \u7684\u5de6\u5b50\u6811\u4e2d\ncur = cur-&gt;left;\n} else {\n// \u627e\u5230\u76ee\u6807\u8282\u70b9\uff0c\u8df3\u51fa\u5faa\u73af\nbreak;\n}\n}\n// \u8fd4\u56de\u76ee\u6807\u8282\u70b9\nreturn cur;\n}\n</code></pre> binary_search_tree.cs<pre><code>/* \u67e5\u627e\u8282\u70b9 */\nTreeNode? search(int num) {\nTreeNode? cur = root;\n// \u5faa\u73af\u67e5\u627e\uff0c\u8d8a\u8fc7\u53f6\u8282\u70b9\u540e\u8df3\u51fa\nwhile (cur != null) {\n// \u76ee\u6807\u8282\u70b9\u5728 cur \u7684\u53f3\u5b50\u6811\u4e2d\nif (cur.val &lt; num) cur =\ncur.right;\n// \u76ee\u6807\u8282\u70b9\u5728 cur \u7684\u5de6\u5b50\u6811\u4e2d\nelse if (cur.val &gt; num)\ncur = cur.left;\n// \u627e\u5230\u76ee\u6807\u8282\u70b9\uff0c\u8df3\u51fa\u5faa\u73af\nelse\nbreak;\n}\n// \u8fd4\u56de\u76ee\u6807\u8282\u70b9\nreturn cur;\n}\n</code></pre> binary_search_tree.swift<pre><code>/* \u67e5\u627e\u8282\u70b9 */\nfunc search(num: Int) -&gt; TreeNode? {\nvar cur = root\n// \u5faa\u73af\u67e5\u627e\uff0c\u8d8a\u8fc7\u53f6\u8282\u70b9\u540e\u8df3\u51fa\nwhile cur != nil {\n// \u76ee\u6807\u8282\u70b9\u5728 cur \u7684\u53f3\u5b50\u6811\u4e2d\nif cur!.val &lt; num {\ncur = cur?.right\n}\n// \u76ee\u6807\u8282\u70b9\u5728 cur \u7684\u5de6\u5b50\u6811\u4e2d\nelse if cur!.val &gt; num {\ncur = cur?.left\n}\n// \u627e\u5230\u76ee\u6807\u8282\u70b9\uff0c\u8df3\u51fa\u5faa\u73af\nelse {\nbreak\n}\n}\n// \u8fd4\u56de\u76ee\u6807\u8282\u70b9\nreturn cur\n}\n</code></pre> binary_search_tree.zig<pre><code>// \u67e5\u627e\u8282\u70b9\nfn search(self: *Self, num: T) ?*inc.TreeNode(T) {\nvar cur = self.root;\n// \u5faa\u73af\u67e5\u627e\uff0c\u8d8a\u8fc7\u53f6\u8282\u70b9\u540e\u8df3\u51fa\nwhile (cur != null) {\n// \u76ee\u6807\u8282\u70b9\u5728 cur \u7684\u53f3\u5b50\u6811\u4e2d\nif (cur.?.val &lt; num) {\ncur = cur.?.right;\n// \u76ee\u6807\u8282\u70b9\u5728 cur \u7684\u5de6\u5b50\u6811\u4e2d\n} else if (cur.?.val &gt; num) {\ncur = cur.?.left;\n// \u627e\u5230\u76ee\u6807\u8282\u70b9\uff0c\u8df3\u51fa\u5faa\u73af\n} else {\nbreak;\n}\n}\n// \u8fd4\u56de\u76ee\u6807\u8282\u70b9\nreturn cur;\n}\n</code></pre> binary_search_tree.dart<pre><code>[class]{BinarySearchTree}-[func]{search}\n</code></pre>"},{"location":"chapter_tree/binary_search_tree/#_2","title":"\u63d2\u5165\u8282\u70b9","text":"<p>\u7ed9\u5b9a\u4e00\u4e2a\u5f85\u63d2\u5165\u5143\u7d20 <code>num</code> \uff0c\u4e3a\u4e86\u4fdd\u6301\u4e8c\u53c9\u641c\u7d22\u6811\u201c\u5de6\u5b50\u6811 &lt; \u6839\u8282\u70b9 &lt; \u53f3\u5b50\u6811\u201d\u7684\u6027\u8d28\uff0c\u63d2\u5165\u64cd\u4f5c\u5206\u4e3a\u4e24\u6b65\uff1a</p> <ol> <li>\u67e5\u627e\u63d2\u5165\u4f4d\u7f6e\uff1a\u4e0e\u67e5\u627e\u64cd\u4f5c\u76f8\u4f3c\uff0c\u4ece\u6839\u8282\u70b9\u51fa\u53d1\uff0c\u6839\u636e\u5f53\u524d\u8282\u70b9\u503c\u548c <code>num</code> \u7684\u5927\u5c0f\u5173\u7cfb\u5faa\u73af\u5411\u4e0b\u641c\u7d22\uff0c\u76f4\u5230\u8d8a\u8fc7\u53f6\u8282\u70b9\uff08\u904d\u5386\u81f3 \\(\\text{null}\\) \uff09\u65f6\u8df3\u51fa\u5faa\u73af\uff1b</li> <li>\u5728\u8be5\u4f4d\u7f6e\u63d2\u5165\u8282\u70b9\uff1a\u521d\u59cb\u5316\u8282\u70b9 <code>num</code> \uff0c\u5c06\u8be5\u8282\u70b9\u7f6e\u4e8e \\(\\text{null}\\) \u7684\u4f4d\u7f6e\uff1b</li> </ol> <p>\u4e8c\u53c9\u641c\u7d22\u6811\u4e0d\u5141\u8bb8\u5b58\u5728\u91cd\u590d\u8282\u70b9\uff0c\u5426\u5219\u5c06\u8fdd\u53cd\u5176\u5b9a\u4e49\u3002\u56e0\u6b64\uff0c\u82e5\u5f85\u63d2\u5165\u8282\u70b9\u5728\u6811\u4e2d\u5df2\u5b58\u5728\uff0c\u5219\u4e0d\u6267\u884c\u63d2\u5165\uff0c\u76f4\u63a5\u8fd4\u56de\u3002</p> <p></p> <p> Fig. \u5728\u4e8c\u53c9\u641c\u7d22\u6811\u4e2d\u63d2\u5165\u8282\u70b9 </p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart binary_search_tree.java<pre><code>/* \u63d2\u5165\u8282\u70b9 */\nvoid insert(int num) {\n// \u82e5\u6811\u4e3a\u7a7a\uff0c\u76f4\u63a5\u63d0\u524d\u8fd4\u56de\nif (root == null)\nreturn;\nTreeNode cur = root, pre = null;\n// \u5faa\u73af\u67e5\u627e\uff0c\u8d8a\u8fc7\u53f6\u8282\u70b9\u540e\u8df3\u51fa\nwhile (cur != null) {\n// \u627e\u5230\u91cd\u590d\u8282\u70b9\uff0c\u76f4\u63a5\u8fd4\u56de\nif (cur.val == num)\nreturn;\npre = cur;\n// \u63d2\u5165\u4f4d\u7f6e\u5728 cur \u7684\u53f3\u5b50\u6811\u4e2d\nif (cur.val &lt; num)\ncur = cur.right;\n// \u63d2\u5165\u4f4d\u7f6e\u5728 cur \u7684\u5de6\u5b50\u6811\u4e2d\nelse\ncur = cur.left;\n}\n// \u63d2\u5165\u8282\u70b9\nTreeNode node = new TreeNode(num);\nif (pre.val &lt; num)\npre.right = node;\nelse\npre.left = node;\n}\n</code></pre> binary_search_tree.cpp<pre><code>/* \u63d2\u5165\u8282\u70b9 */\nvoid insert(int num) {\n// \u82e5\u6811\u4e3a\u7a7a\uff0c\u76f4\u63a5\u63d0\u524d\u8fd4\u56de\nif (root == nullptr)\nreturn;\nTreeNode *cur = root, *pre = nullptr;\n// \u5faa\u73af\u67e5\u627e\uff0c\u8d8a\u8fc7\u53f6\u8282\u70b9\u540e\u8df3\u51fa\nwhile (cur != nullptr) {\n// \u627e\u5230\u91cd\u590d\u8282\u70b9\uff0c\u76f4\u63a5\u8fd4\u56de\nif (cur-&gt;val == num)\nreturn;\npre = cur;\n// \u63d2\u5165\u4f4d\u7f6e\u5728 cur \u7684\u53f3\u5b50\u6811\u4e2d\nif (cur-&gt;val &lt; num)\ncur = cur-&gt;right;\n// \u63d2\u5165\u4f4d\u7f6e\u5728 cur \u7684\u5de6\u5b50\u6811\u4e2d\nelse\ncur = cur-&gt;left;\n}\n// \u63d2\u5165\u8282\u70b9\nTreeNode *node = new TreeNode(num);\nif (pre-&gt;val &lt; num)\npre-&gt;right = node;\nelse\npre-&gt;left = node;\n}\n</code></pre> binary_search_tree.py<pre><code>def insert(self, num: int) -&gt; None:\n\"\"\"\u63d2\u5165\u8282\u70b9\"\"\"\n# \u82e5\u6811\u4e3a\u7a7a\uff0c\u76f4\u63a5\u63d0\u524d\u8fd4\u56de\nif self.root is None:\nreturn\n# \u5faa\u73af\u67e5\u627e\uff0c\u8d8a\u8fc7\u53f6\u8282\u70b9\u540e\u8df3\u51fa\ncur, pre = self.root, None\nwhile cur is not None:\n# \u627e\u5230\u91cd\u590d\u8282\u70b9\uff0c\u76f4\u63a5\u8fd4\u56de\nif cur.val == num:\nreturn\npre = cur\n# \u63d2\u5165\u4f4d\u7f6e\u5728 cur \u7684\u53f3\u5b50\u6811\u4e2d\nif cur.val &lt; num:\ncur = cur.right\n# \u63d2\u5165\u4f4d\u7f6e\u5728 cur \u7684\u5de6\u5b50\u6811\u4e2d\nelse:\ncur = cur.left\n# \u63d2\u5165\u8282\u70b9\nnode = TreeNode(num)\nif pre.val &lt; num:\npre.right = node\nelse:\npre.left = node\n</code></pre> binary_search_tree.go<pre><code>/* \u63d2\u5165\u8282\u70b9 */\nfunc (bst *binarySearchTree) insert(num int) {\ncur := bst.root\n// \u82e5\u6811\u4e3a\u7a7a\uff0c\u76f4\u63a5\u63d0\u524d\u8fd4\u56de\nif cur == nil {\nreturn\n}\n// \u5f85\u63d2\u5165\u8282\u70b9\u4e4b\u524d\u7684\u8282\u70b9\u4f4d\u7f6e\nvar pre *TreeNode = nil\n// \u5faa\u73af\u67e5\u627e\uff0c\u8d8a\u8fc7\u53f6\u8282\u70b9\u540e\u8df3\u51fa\nfor cur != nil {\nif cur.Val == num {\nreturn\n}\npre = cur\nif cur.Val &lt; num {\ncur = cur.Right\n} else {\ncur = cur.Left\n}\n}\n// \u63d2\u5165\u8282\u70b9\nnode := NewTreeNode(num)\nif pre.Val &lt; num {\npre.Right = node\n} else {\npre.Left = node\n}\n}\n</code></pre> binary_search_tree.js<pre><code>/* \u63d2\u5165\u8282\u70b9 */\nfunction insert(num) {\n// \u82e5\u6811\u4e3a\u7a7a\uff0c\u76f4\u63a5\u63d0\u524d\u8fd4\u56de\nif (root === null) return;\nlet cur = root,\npre = null;\n// \u5faa\u73af\u67e5\u627e\uff0c\u8d8a\u8fc7\u53f6\u8282\u70b9\u540e\u8df3\u51fa\nwhile (cur !== null) {\n// \u627e\u5230\u91cd\u590d\u8282\u70b9\uff0c\u76f4\u63a5\u8fd4\u56de\nif (cur.val === num) return;\npre = cur;\n// \u63d2\u5165\u4f4d\u7f6e\u5728 cur \u7684\u53f3\u5b50\u6811\u4e2d\nif (cur.val &lt; num) cur = cur.right;\n// \u63d2\u5165\u4f4d\u7f6e\u5728 cur \u7684\u5de6\u5b50\u6811\u4e2d\nelse cur = cur.left;\n}\n// \u63d2\u5165\u8282\u70b9\nlet node = new TreeNode(num);\nif (pre.val &lt; num) pre.right = node;\nelse pre.left = node;\n}\n</code></pre> binary_search_tree.ts<pre><code>/* \u63d2\u5165\u8282\u70b9 */\nfunction insert(num: number): void {\n// \u82e5\u6811\u4e3a\u7a7a\uff0c\u76f4\u63a5\u63d0\u524d\u8fd4\u56de\nif (root === null) {\nreturn;\n}\nlet cur = root,\npre: TreeNode | null = null;\n// \u5faa\u73af\u67e5\u627e\uff0c\u8d8a\u8fc7\u53f6\u8282\u70b9\u540e\u8df3\u51fa\nwhile (cur !== null) {\nif (cur.val === num) {\nreturn; // \u627e\u5230\u91cd\u590d\u8282\u70b9\uff0c\u76f4\u63a5\u8fd4\u56de\n}\npre = cur;\nif (cur.val &lt; num) {\ncur = cur.right as TreeNode; // \u63d2\u5165\u4f4d\u7f6e\u5728 cur \u7684\u53f3\u5b50\u6811\u4e2d\n} else {\ncur = cur.left as TreeNode; // \u63d2\u5165\u4f4d\u7f6e\u5728 cur \u7684\u5de6\u5b50\u6811\u4e2d\n}\n}\n// \u63d2\u5165\u8282\u70b9\nlet node = new TreeNode(num);\nif (pre!.val &lt; num) {\npre!.right = node;\n} else {\npre!.left = node;\n}\n}\n</code></pre> binary_search_tree.c<pre><code>/* \u63d2\u5165\u8282\u70b9 */\nvoid insert(binarySearchTree *bst, int num) {\n// \u82e5\u6811\u4e3a\u7a7a\uff0c\u76f4\u63a5\u63d0\u524d\u8fd4\u56de\nif (bst-&gt;root == NULL)\nreturn;\nTreeNode *cur = bst-&gt;root, *pre = NULL;\n// \u5faa\u73af\u67e5\u627e\uff0c\u8d8a\u8fc7\u53f6\u8282\u70b9\u540e\u8df3\u51fa\nwhile (cur != NULL) {\n// \u627e\u5230\u91cd\u590d\u8282\u70b9\uff0c\u76f4\u63a5\u8fd4\u56de\nif (cur-&gt;val == num) {\nreturn;\n}\npre = cur;\nif (cur-&gt;val &lt; num) {\n// \u63d2\u5165\u4f4d\u7f6e\u5728 cur \u7684\u53f3\u5b50\u6811\u4e2d\ncur = cur-&gt;right;\n} else {\n// \u63d2\u5165\u4f4d\u7f6e\u5728 cur \u7684\u5de6\u5b50\u6811\u4e2d\ncur = cur-&gt;left;\n}\n}\n// \u63d2\u5165\u8282\u70b9\nTreeNode *node = newTreeNode(num);\nif (pre-&gt;val &lt; num) {\npre-&gt;right = node;\n} else {\npre-&gt;left = node;\n}\n}\n</code></pre> binary_search_tree.cs<pre><code>/* \u63d2\u5165\u8282\u70b9 */\nvoid insert(int num) {\n// \u82e5\u6811\u4e3a\u7a7a\uff0c\u76f4\u63a5\u63d0\u524d\u8fd4\u56de\nif (root == null)\nreturn;\nTreeNode? cur = root, pre = null;\n// \u5faa\u73af\u67e5\u627e\uff0c\u8d8a\u8fc7\u53f6\u8282\u70b9\u540e\u8df3\u51fa\nwhile (cur != null) {\n// \u627e\u5230\u91cd\u590d\u8282\u70b9\uff0c\u76f4\u63a5\u8fd4\u56de\nif (cur.val == num)\nreturn;\npre = cur;\n// \u63d2\u5165\u4f4d\u7f6e\u5728 cur \u7684\u53f3\u5b50\u6811\u4e2d\nif (cur.val &lt; num)\ncur = cur.right;\n// \u63d2\u5165\u4f4d\u7f6e\u5728 cur \u7684\u5de6\u5b50\u6811\u4e2d\nelse\ncur = cur.left;\n}\n// \u63d2\u5165\u8282\u70b9\nTreeNode node = new TreeNode(num);\nif (pre != null) {\nif (pre.val &lt; num)\npre.right = node;\nelse\npre.left = node;\n}\n}\n</code></pre> binary_search_tree.swift<pre><code>/* \u63d2\u5165\u8282\u70b9 */\nfunc insert(num: Int) {\n// \u82e5\u6811\u4e3a\u7a7a\uff0c\u76f4\u63a5\u63d0\u524d\u8fd4\u56de\nif root == nil {\nreturn\n}\nvar cur = root\nvar pre: TreeNode?\n// \u5faa\u73af\u67e5\u627e\uff0c\u8d8a\u8fc7\u53f6\u8282\u70b9\u540e\u8df3\u51fa\nwhile cur != nil {\n// \u627e\u5230\u91cd\u590d\u8282\u70b9\uff0c\u76f4\u63a5\u8fd4\u56de\nif cur!.val == num {\nreturn\n}\npre = cur\n// \u63d2\u5165\u4f4d\u7f6e\u5728 cur \u7684\u53f3\u5b50\u6811\u4e2d\nif cur!.val &lt; num {\ncur = cur?.right\n}\n// \u63d2\u5165\u4f4d\u7f6e\u5728 cur \u7684\u5de6\u5b50\u6811\u4e2d\nelse {\ncur = cur?.left\n}\n}\n// \u63d2\u5165\u8282\u70b9\nlet node = TreeNode(x: num)\nif pre!.val &lt; num {\npre?.right = node\n} else {\npre?.left = node\n}\n}\n</code></pre> binary_search_tree.zig<pre><code>// \u63d2\u5165\u8282\u70b9\nfn insert(self: *Self, num: T) !void {\n// \u82e5\u6811\u4e3a\u7a7a\uff0c\u76f4\u63a5\u63d0\u524d\u8fd4\u56de\nif (self.root == null) return;\nvar cur = self.root;\nvar pre: ?*inc.TreeNode(T) = null;\n// \u5faa\u73af\u67e5\u627e\uff0c\u8d8a\u8fc7\u53f6\u8282\u70b9\u540e\u8df3\u51fa\nwhile (cur != null) {\n// \u627e\u5230\u91cd\u590d\u8282\u70b9\uff0c\u76f4\u63a5\u8fd4\u56de\nif (cur.?.val == num) return;\npre = cur;\n// \u63d2\u5165\u4f4d\u7f6e\u5728 cur \u7684\u53f3\u5b50\u6811\u4e2d\nif (cur.?.val &lt; num) {\ncur = cur.?.right;\n// \u63d2\u5165\u4f4d\u7f6e\u5728 cur \u7684\u5de6\u5b50\u6811\u4e2d\n} else {\ncur = cur.?.left;\n}\n}\n// \u63d2\u5165\u8282\u70b9\nvar node = try self.mem_allocator.create(inc.TreeNode(T));\nnode.init(num);\nif (pre.?.val &lt; num) {\npre.?.right = node;\n} else {\npre.?.left = node;\n}\n}\n</code></pre> binary_search_tree.dart<pre><code>[class]{BinarySearchTree}-[func]{insert}\n</code></pre> <p>\u4e3a\u4e86\u63d2\u5165\u8282\u70b9\uff0c\u6211\u4eec\u9700\u8981\u5229\u7528\u8f85\u52a9\u8282\u70b9 <code>pre</code> \u4fdd\u5b58\u4e0a\u4e00\u8f6e\u5faa\u73af\u7684\u8282\u70b9\uff0c\u8fd9\u6837\u5728\u904d\u5386\u81f3 \\(\\text{null}\\) \u65f6\uff0c\u6211\u4eec\u53ef\u4ee5\u83b7\u53d6\u5230\u5176\u7236\u8282\u70b9\uff0c\u4ece\u800c\u5b8c\u6210\u8282\u70b9\u63d2\u5165\u64cd\u4f5c\u3002</p> <p>\u4e0e\u67e5\u627e\u8282\u70b9\u76f8\u540c\uff0c\u63d2\u5165\u8282\u70b9\u4f7f\u7528 \\(O(\\log n)\\) \u65f6\u95f4\u3002</p>"},{"location":"chapter_tree/binary_search_tree/#_3","title":"\u5220\u9664\u8282\u70b9","text":"<p>\u4e0e\u63d2\u5165\u8282\u70b9\u7c7b\u4f3c\uff0c\u6211\u4eec\u9700\u8981\u5728\u5220\u9664\u64cd\u4f5c\u540e\u7ef4\u6301\u4e8c\u53c9\u641c\u7d22\u6811\u7684\u201c\u5de6\u5b50\u6811 &lt; \u6839\u8282\u70b9 &lt; \u53f3\u5b50\u6811\u201d\u7684\u6027\u8d28\u3002\u9996\u5148\uff0c\u6211\u4eec\u9700\u8981\u5728\u4e8c\u53c9\u6811\u4e2d\u6267\u884c\u67e5\u627e\u64cd\u4f5c\uff0c\u83b7\u53d6\u5f85\u5220\u9664\u8282\u70b9\u3002\u63a5\u4e0b\u6765\uff0c\u6839\u636e\u5f85\u5220\u9664\u8282\u70b9\u7684\u5b50\u8282\u70b9\u6570\u91cf\uff0c\u5220\u9664\u64cd\u4f5c\u9700\u5206\u4e3a\u4e09\u79cd\u60c5\u51b5\uff1a</p> <p>\u5f53\u5f85\u5220\u9664\u8282\u70b9\u7684\u5b50\u8282\u70b9\u6570\u91cf \\(= 0\\) \u65f6\uff0c\u8868\u793a\u5f85\u5220\u9664\u8282\u70b9\u662f\u53f6\u8282\u70b9\uff0c\u53ef\u4ee5\u76f4\u63a5\u5220\u9664\u3002</p> <p></p> <p> Fig. \u5728\u4e8c\u53c9\u641c\u7d22\u6811\u4e2d\u5220\u9664\u8282\u70b9\uff08\u5ea6\u4e3a 0\uff09 </p> <p>\u5f53\u5f85\u5220\u9664\u8282\u70b9\u7684\u5b50\u8282\u70b9\u6570\u91cf \\(= 1\\) \u65f6\uff0c\u5c06\u5f85\u5220\u9664\u8282\u70b9\u66ff\u6362\u4e3a\u5176\u5b50\u8282\u70b9\u5373\u53ef\u3002</p> <p></p> <p> Fig. \u5728\u4e8c\u53c9\u641c\u7d22\u6811\u4e2d\u5220\u9664\u8282\u70b9\uff08\u5ea6\u4e3a 1\uff09 </p> <p>\u5f53\u5f85\u5220\u9664\u8282\u70b9\u7684\u5b50\u8282\u70b9\u6570\u91cf \\(= 2\\) \u65f6\uff0c\u5220\u9664\u64cd\u4f5c\u5206\u4e3a\u4e09\u6b65\uff1a</p> <ol> <li>\u627e\u5230\u5f85\u5220\u9664\u8282\u70b9\u5728\u201c\u4e2d\u5e8f\u904d\u5386\u5e8f\u5217\u201d\u4e2d\u7684\u4e0b\u4e00\u4e2a\u8282\u70b9\uff0c\u8bb0\u4e3a <code>tmp</code> \uff1b</li> <li>\u5728\u6811\u4e2d\u9012\u5f52\u5220\u9664\u8282\u70b9 <code>tmp</code> \uff1b</li> <li>\u7528 <code>tmp</code> \u7684\u503c\u8986\u76d6\u5f85\u5220\u9664\u8282\u70b9\u7684\u503c\uff1b</li> </ol> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt; <p></p> <p></p> <p></p> <p></p> <p>\u5220\u9664\u8282\u70b9\u64cd\u4f5c\u540c\u6837\u4f7f\u7528 \\(O(\\log n)\\) \u65f6\u95f4\uff0c\u5176\u4e2d\u67e5\u627e\u5f85\u5220\u9664\u8282\u70b9\u9700\u8981 \\(O(\\log n)\\) \u65f6\u95f4\uff0c\u83b7\u53d6\u4e2d\u5e8f\u904d\u5386\u540e\u7ee7\u8282\u70b9\u9700\u8981 \\(O(\\log n)\\) \u65f6\u95f4\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart binary_search_tree.java<pre><code>/* \u5220\u9664\u8282\u70b9 */\nvoid remove(int num) {\n// \u82e5\u6811\u4e3a\u7a7a\uff0c\u76f4\u63a5\u63d0\u524d\u8fd4\u56de\nif (root == null)\nreturn;\nTreeNode cur = root, pre = null;\n// \u5faa\u73af\u67e5\u627e\uff0c\u8d8a\u8fc7\u53f6\u8282\u70b9\u540e\u8df3\u51fa\nwhile (cur != null) {\n// \u627e\u5230\u5f85\u5220\u9664\u8282\u70b9\uff0c\u8df3\u51fa\u5faa\u73af\nif (cur.val == num)\nbreak;\npre = cur;\n// \u5f85\u5220\u9664\u8282\u70b9\u5728 cur \u7684\u53f3\u5b50\u6811\u4e2d\nif (cur.val &lt; num)\ncur = cur.right;\n// \u5f85\u5220\u9664\u8282\u70b9\u5728 cur \u7684\u5de6\u5b50\u6811\u4e2d\nelse\ncur = cur.left;\n}\n// \u82e5\u65e0\u5f85\u5220\u9664\u8282\u70b9\uff0c\u5219\u76f4\u63a5\u8fd4\u56de\nif (cur == null)\nreturn;\n// \u5b50\u8282\u70b9\u6570\u91cf = 0 or 1\nif (cur.left == null || cur.right == null) {\n// \u5f53\u5b50\u8282\u70b9\u6570\u91cf = 0 / 1 \u65f6\uff0c child = null / \u8be5\u5b50\u8282\u70b9\nTreeNode child = cur.left != null ? cur.left : cur.right;\n// \u5220\u9664\u8282\u70b9 cur\nif (cur != root) {\nif (pre.left == cur)\npre.left = child;\nelse\npre.right = child;\n} else {\n// \u82e5\u5220\u9664\u8282\u70b9\u4e3a\u6839\u8282\u70b9\uff0c\u5219\u91cd\u65b0\u6307\u5b9a\u6839\u8282\u70b9\nroot = child;\n}\n}\n// \u5b50\u8282\u70b9\u6570\u91cf = 2\nelse {\n// \u83b7\u53d6\u4e2d\u5e8f\u904d\u5386\u4e2d cur \u7684\u4e0b\u4e00\u4e2a\u8282\u70b9\nTreeNode tmp = cur.right;\nwhile (tmp.left != null) {\ntmp = tmp.left;\n}\n// \u9012\u5f52\u5220\u9664\u8282\u70b9 tmp\nremove(tmp.val);\n// \u7528 tmp \u8986\u76d6 cur\ncur.val = tmp.val;\n}\n}\n</code></pre> binary_search_tree.cpp<pre><code>/* \u5220\u9664\u8282\u70b9 */\nvoid remove(int num) {\n// \u82e5\u6811\u4e3a\u7a7a\uff0c\u76f4\u63a5\u63d0\u524d\u8fd4\u56de\nif (root == nullptr)\nreturn;\nTreeNode *cur = root, *pre = nullptr;\n// \u5faa\u73af\u67e5\u627e\uff0c\u8d8a\u8fc7\u53f6\u8282\u70b9\u540e\u8df3\u51fa\nwhile (cur != nullptr) {\n// \u627e\u5230\u5f85\u5220\u9664\u8282\u70b9\uff0c\u8df3\u51fa\u5faa\u73af\nif (cur-&gt;val == num)\nbreak;\npre = cur;\n// \u5f85\u5220\u9664\u8282\u70b9\u5728 cur \u7684\u53f3\u5b50\u6811\u4e2d\nif (cur-&gt;val &lt; num)\ncur = cur-&gt;right;\n// \u5f85\u5220\u9664\u8282\u70b9\u5728 cur \u7684\u5de6\u5b50\u6811\u4e2d\nelse\ncur = cur-&gt;left;\n}\n// \u82e5\u65e0\u5f85\u5220\u9664\u8282\u70b9\uff0c\u5219\u76f4\u63a5\u8fd4\u56de\nif (cur == nullptr)\nreturn;\n// \u5b50\u8282\u70b9\u6570\u91cf = 0 or 1\nif (cur-&gt;left == nullptr || cur-&gt;right == nullptr) {\n// \u5f53\u5b50\u8282\u70b9\u6570\u91cf = 0 / 1 \u65f6\uff0c child = nullptr / \u8be5\u5b50\u8282\u70b9\nTreeNode *child = cur-&gt;left != nullptr ? cur-&gt;left : cur-&gt;right;\n// \u5220\u9664\u8282\u70b9 cur\nif (cur != root) {\nif (pre-&gt;left == cur)\npre-&gt;left = child;\nelse\npre-&gt;right = child;\n} else {\n// \u82e5\u5220\u9664\u8282\u70b9\u4e3a\u6839\u8282\u70b9\uff0c\u5219\u91cd\u65b0\u6307\u5b9a\u6839\u8282\u70b9\nroot = child;\n}\n// \u91ca\u653e\u5185\u5b58\ndelete cur;\n}\n// \u5b50\u8282\u70b9\u6570\u91cf = 2\nelse {\n// \u83b7\u53d6\u4e2d\u5e8f\u904d\u5386\u4e2d cur \u7684\u4e0b\u4e00\u4e2a\u8282\u70b9\nTreeNode *tmp = cur-&gt;right;\nwhile (tmp-&gt;left != nullptr) {\ntmp = tmp-&gt;left;\n}\nint tmpVal = tmp-&gt;val;\n// \u9012\u5f52\u5220\u9664\u8282\u70b9 tmp\nremove(tmp-&gt;val);\n// \u7528 tmp \u8986\u76d6 cur\ncur-&gt;val = tmpVal;\n}\n}\n</code></pre> binary_search_tree.py<pre><code>def remove(self, num: int) -&gt; None:\n\"\"\"\u5220\u9664\u8282\u70b9\"\"\"\n# \u82e5\u6811\u4e3a\u7a7a\uff0c\u76f4\u63a5\u63d0\u524d\u8fd4\u56de\nif self.root is None:\nreturn\n# \u5faa\u73af\u67e5\u627e\uff0c\u8d8a\u8fc7\u53f6\u8282\u70b9\u540e\u8df3\u51fa\ncur, pre = self.root, None\nwhile cur is not None:\n# \u627e\u5230\u5f85\u5220\u9664\u8282\u70b9\uff0c\u8df3\u51fa\u5faa\u73af\nif cur.val == num:\nbreak\npre = cur\n# \u5f85\u5220\u9664\u8282\u70b9\u5728 cur \u7684\u53f3\u5b50\u6811\u4e2d\nif cur.val &lt; num:\ncur = cur.right\n# \u5f85\u5220\u9664\u8282\u70b9\u5728 cur \u7684\u5de6\u5b50\u6811\u4e2d\nelse:\ncur = cur.left\n# \u82e5\u65e0\u5f85\u5220\u9664\u8282\u70b9\uff0c\u5219\u76f4\u63a5\u8fd4\u56de\nif cur is None:\nreturn\n# \u5b50\u8282\u70b9\u6570\u91cf = 0 or 1\nif cur.left is None or cur.right is None:\n# \u5f53\u5b50\u8282\u70b9\u6570\u91cf = 0 / 1 \u65f6\uff0c child = null / \u8be5\u5b50\u8282\u70b9\nchild = cur.left or cur.right\n# \u5220\u9664\u8282\u70b9 cur\nif cur != self.root:\nif pre.left == cur:\npre.left = child\nelse:\npre.right = child\nelse:\n# \u82e5\u5220\u9664\u8282\u70b9\u4e3a\u6839\u8282\u70b9\uff0c\u5219\u91cd\u65b0\u6307\u5b9a\u6839\u8282\u70b9\nself.__root = cur\n# \u5b50\u8282\u70b9\u6570\u91cf = 2\nelse:\n# \u83b7\u53d6\u4e2d\u5e8f\u904d\u5386\u4e2d cur \u7684\u4e0b\u4e00\u4e2a\u8282\u70b9\ntmp: TreeNode = cur.right\nwhile tmp.left is not None:\ntmp = tmp.left\n# \u9012\u5f52\u5220\u9664\u8282\u70b9 tmp\nself.remove(tmp.val)\n# \u7528 tmp \u8986\u76d6 cur\ncur.val = tmp.val\n</code></pre> binary_search_tree.go<pre><code>/* \u5220\u9664\u8282\u70b9 */\nfunc (bst *binarySearchTree) remove(num int) {\ncur := bst.root\n// \u82e5\u6811\u4e3a\u7a7a\uff0c\u76f4\u63a5\u63d0\u524d\u8fd4\u56de\nif cur == nil {\nreturn\n}\n// \u5f85\u5220\u9664\u8282\u70b9\u4e4b\u524d\u7684\u8282\u70b9\u4f4d\u7f6e\nvar pre *TreeNode = nil\n// \u5faa\u73af\u67e5\u627e\uff0c\u8d8a\u8fc7\u53f6\u8282\u70b9\u540e\u8df3\u51fa\nfor cur != nil {\nif cur.Val == num {\nbreak\n}\npre = cur\nif cur.Val &lt; num {\n// \u5f85\u5220\u9664\u8282\u70b9\u5728\u53f3\u5b50\u6811\u4e2d\ncur = cur.Right\n} else {\n// \u5f85\u5220\u9664\u8282\u70b9\u5728\u5de6\u5b50\u6811\u4e2d\ncur = cur.Left\n}\n}\n// \u82e5\u65e0\u5f85\u5220\u9664\u8282\u70b9\uff0c\u5219\u76f4\u63a5\u8fd4\u56de\nif cur == nil {\nreturn\n}\n// \u5b50\u8282\u70b9\u6570\u4e3a 0 \u6216 1\nif cur.Left == nil || cur.Right == nil {\nvar child *TreeNode = nil\n// \u53d6\u51fa\u5f85\u5220\u9664\u8282\u70b9\u7684\u5b50\u8282\u70b9\nif cur.Left != nil {\nchild = cur.Left\n} else {\nchild = cur.Right\n}\n// \u5220\u9664\u8282\u70b9 cur\nif cur != bst.root {\nif pre.Left == cur {\npre.Left = child\n} else {\npre.Right = child\n}\n} else {\n// \u82e5\u5220\u9664\u8282\u70b9\u4e3a\u6839\u8282\u70b9\uff0c\u5219\u91cd\u65b0\u6307\u5b9a\u6839\u8282\u70b9\nbst.root = child\n}\n// \u5b50\u8282\u70b9\u6570\u4e3a 2\n} else {\n// \u83b7\u53d6\u4e2d\u5e8f\u904d\u5386\u4e2d\u5f85\u5220\u9664\u8282\u70b9 cur \u7684\u4e0b\u4e00\u4e2a\u8282\u70b9\ntmp := cur.Right\nfor tmp.Left != nil {\ntmp = tmp.Left\n}\n// \u9012\u5f52\u5220\u9664\u8282\u70b9 tmp\nbst.remove(tmp.Val)\n// \u7528 tmp \u8986\u76d6 cur\ncur.Val = tmp.Val\n}\n}\n</code></pre> binary_search_tree.js<pre><code>/* \u5220\u9664\u8282\u70b9 */\nfunction remove(num) {\n// \u82e5\u6811\u4e3a\u7a7a\uff0c\u76f4\u63a5\u63d0\u524d\u8fd4\u56de\nif (root === null) return;\nlet cur = root,\npre = null;\n// \u5faa\u73af\u67e5\u627e\uff0c\u8d8a\u8fc7\u53f6\u8282\u70b9\u540e\u8df3\u51fa\nwhile (cur !== null) {\n// \u627e\u5230\u5f85\u5220\u9664\u8282\u70b9\uff0c\u8df3\u51fa\u5faa\u73af\nif (cur.val === num) break;\npre = cur;\n// \u5f85\u5220\u9664\u8282\u70b9\u5728 cur \u7684\u53f3\u5b50\u6811\u4e2d\nif (cur.val &lt; num) cur = cur.right;\n// \u5f85\u5220\u9664\u8282\u70b9\u5728 cur \u7684\u5de6\u5b50\u6811\u4e2d\nelse cur = cur.left;\n}\n// \u82e5\u65e0\u5f85\u5220\u9664\u8282\u70b9\uff0c\u5219\u76f4\u63a5\u8fd4\u56de\nif (cur === null) return;\n// \u5b50\u8282\u70b9\u6570\u91cf = 0 or 1\nif (cur.left === null || cur.right === null) {\n// \u5f53\u5b50\u8282\u70b9\u6570\u91cf = 0 / 1 \u65f6\uff0c child = null / \u8be5\u5b50\u8282\u70b9\nlet child = cur.left !== null ? cur.left : cur.right;\n// \u5220\u9664\u8282\u70b9 cur\nif (cur != root) {\nif (pre.left === cur) pre.left = child;\nelse pre.right = child;\n} else {\n// \u82e5\u5220\u9664\u8282\u70b9\u4e3a\u6839\u8282\u70b9\uff0c\u5219\u91cd\u65b0\u6307\u5b9a\u6839\u8282\u70b9\nroot = child;\n}\n}\n// \u5b50\u8282\u70b9\u6570\u91cf = 2\nelse {\n// \u83b7\u53d6\u4e2d\u5e8f\u904d\u5386\u4e2d cur \u7684\u4e0b\u4e00\u4e2a\u8282\u70b9\nlet tmp = cur.right;\nwhile (tmp.left !== null) {\ntmp = tmp.left;\n}\n// \u9012\u5f52\u5220\u9664\u8282\u70b9 tmp\nremove(tmp.val);\n// \u7528 tmp \u8986\u76d6 cur\ncur.val = tmp.val;\n}\n}\n</code></pre> binary_search_tree.ts<pre><code>/* \u5220\u9664\u8282\u70b9 */\nfunction remove(num: number): void {\n// \u82e5\u6811\u4e3a\u7a7a\uff0c\u76f4\u63a5\u63d0\u524d\u8fd4\u56de\nif (root === null) {\nreturn;\n}\nlet cur = root,\npre: TreeNode | null = null;\n// \u5faa\u73af\u67e5\u627e\uff0c\u8d8a\u8fc7\u53f6\u8282\u70b9\u540e\u8df3\u51fa\nwhile (cur !== null) {\n// \u627e\u5230\u5f85\u5220\u9664\u8282\u70b9\uff0c\u8df3\u51fa\u5faa\u73af\nif (cur.val === num) {\nbreak;\n}\npre = cur;\nif (cur.val &lt; num) {\ncur = cur.right as TreeNode; // \u5f85\u5220\u9664\u8282\u70b9\u5728 cur \u7684\u53f3\u5b50\u6811\u4e2d\n} else {\ncur = cur.left as TreeNode; // \u5f85\u5220\u9664\u8282\u70b9\u5728 cur \u7684\u5de6\u5b50\u6811\u4e2d\n}\n}\n// \u82e5\u65e0\u5f85\u5220\u9664\u8282\u70b9\uff0c\u5219\u76f4\u63a5\u8fd4\u56de\nif (cur === null) {\nreturn;\n}\n// \u5b50\u8282\u70b9\u6570\u91cf = 0 or 1\nif (cur.left === null || cur.right === null) {\n// \u5f53\u5b50\u8282\u70b9\u6570\u91cf = 0 / 1 \u65f6\uff0c child = null / \u8be5\u5b50\u8282\u70b9\nlet child = cur.left !== null ? cur.left : cur.right;\n// \u5220\u9664\u8282\u70b9 cur\nif (cur != root) {\nif (pre!.left === cur) {\npre!.left = child;\n} else {\npre!.right = child;\n}\n} else {\n// \u82e5\u5220\u9664\u8282\u70b9\u4e3a\u6839\u8282\u70b9\uff0c\u5219\u91cd\u65b0\u6307\u5b9a\u6839\u8282\u70b9\nroot = child;\n}\n}\n// \u5b50\u8282\u70b9\u6570\u91cf = 2\nelse {\n// \u83b7\u53d6\u4e2d\u5e8f\u904d\u5386\u4e2d cur \u7684\u4e0b\u4e00\u4e2a\u8282\u70b9\nlet tmp = cur.right;\nwhile (tmp.left !== null) {\ntmp = tmp.left;\n}\n// \u9012\u5f52\u5220\u9664\u8282\u70b9 tmp\nremove(tmp!.val);\n// \u7528 tmp \u8986\u76d6 cur\ncur.val = tmp.val;\n}\n}\n</code></pre> binary_search_tree.c<pre><code>/* \u5220\u9664\u8282\u70b9 */\n// \u7531\u4e8e\u5f15\u5165\u4e86 stdio.h \uff0c\u6b64\u5904\u65e0\u6cd5\u4f7f\u7528 remove \u5173\u952e\u8bcd\nvoid removeNode(binarySearchTree *bst, int num) {\n// \u82e5\u6811\u4e3a\u7a7a\uff0c\u76f4\u63a5\u63d0\u524d\u8fd4\u56de\nif (bst-&gt;root == NULL)\nreturn;\nTreeNode *cur = bst-&gt;root, *pre = NULL;\n// \u5faa\u73af\u67e5\u627e\uff0c\u8d8a\u8fc7\u53f6\u8282\u70b9\u540e\u8df3\u51fa\nwhile (cur != NULL) {\n// \u627e\u5230\u5f85\u5220\u9664\u8282\u70b9\uff0c\u8df3\u51fa\u5faa\u73af\nif (cur-&gt;val == num)\nbreak;\npre = cur;\nif (cur-&gt;val &lt; num) {\n// \u5f85\u5220\u9664\u8282\u70b9\u5728 root \u7684\u53f3\u5b50\u6811\u4e2d\ncur = cur-&gt;right;\n} else {\n// \u5f85\u5220\u9664\u8282\u70b9\u5728 root \u7684\u5de6\u5b50\u6811\u4e2d\ncur = cur-&gt;left;\n}\n}\n// \u82e5\u65e0\u5f85\u5220\u9664\u8282\u70b9\uff0c\u5219\u76f4\u63a5\u8fd4\u56de\nif (cur == NULL)\nreturn;\n// \u5224\u65ad\u5f85\u5220\u9664\u8282\u70b9\u662f\u5426\u5b58\u5728\u5b50\u8282\u70b9\nif (cur-&gt;left == NULL || cur-&gt;right == NULL) {\n/* \u5b50\u8282\u70b9\u6570\u91cf = 0 or 1 */\n// \u5f53\u5b50\u8282\u70b9\u6570\u91cf = 0 / 1 \u65f6\uff0c child = nullptr / \u8be5\u5b50\u8282\u70b9\nTreeNode *child = cur-&gt;left != NULL ? cur-&gt;left : cur-&gt;right;\n// \u5220\u9664\u8282\u70b9 cur\nif (pre-&gt;left == cur) {\npre-&gt;left = child;\n} else {\npre-&gt;right = child;\n}\n} else {\n/* \u5b50\u8282\u70b9\u6570\u91cf = 2 */\n// \u83b7\u53d6\u4e2d\u5e8f\u904d\u5386\u4e2d cur \u7684\u4e0b\u4e00\u4e2a\u8282\u70b9\nTreeNode *tmp = cur-&gt;right;\nwhile (tmp-&gt;left != NULL) {\ntmp = tmp-&gt;left;\n}\nint tmpVal = tmp-&gt;val;\n// \u9012\u5f52\u5220\u9664\u8282\u70b9 tmp\nremoveNode(bst, tmp-&gt;val);\n// \u7528 tmp \u8986\u76d6 cur\ncur-&gt;val = tmpVal;\n}\n}\n</code></pre> binary_search_tree.cs<pre><code>/* \u5220\u9664\u8282\u70b9 */\nvoid remove(int num) {\n// \u82e5\u6811\u4e3a\u7a7a\uff0c\u76f4\u63a5\u63d0\u524d\u8fd4\u56de\nif (root == null)\nreturn;\nTreeNode? cur = root, pre = null;\n// \u5faa\u73af\u67e5\u627e\uff0c\u8d8a\u8fc7\u53f6\u8282\u70b9\u540e\u8df3\u51fa\nwhile (cur != null) {\n// \u627e\u5230\u5f85\u5220\u9664\u8282\u70b9\uff0c\u8df3\u51fa\u5faa\u73af\nif (cur.val == num)\nbreak;\npre = cur;\n// \u5f85\u5220\u9664\u8282\u70b9\u5728 cur \u7684\u53f3\u5b50\u6811\u4e2d\nif (cur.val &lt; num)\ncur = cur.right;\n// \u5f85\u5220\u9664\u8282\u70b9\u5728 cur \u7684\u5de6\u5b50\u6811\u4e2d\nelse\ncur = cur.left;\n}\n// \u82e5\u65e0\u5f85\u5220\u9664\u8282\u70b9\uff0c\u5219\u76f4\u63a5\u8fd4\u56de\nif (cur == null || pre == null)\nreturn;\n// \u5b50\u8282\u70b9\u6570\u91cf = 0 or 1\nif (cur.left == null || cur.right == null) {\n// \u5f53\u5b50\u8282\u70b9\u6570\u91cf = 0 / 1 \u65f6\uff0c child = null / \u8be5\u5b50\u8282\u70b9\nTreeNode? child = cur.left != null ? cur.left : cur.right;\n// \u5220\u9664\u8282\u70b9 cur\nif (cur != root) {\nif (pre.left == cur)\npre.left = child;\nelse\npre.right = child;\n} else {\n// \u82e5\u5220\u9664\u8282\u70b9\u4e3a\u6839\u8282\u70b9\uff0c\u5219\u91cd\u65b0\u6307\u5b9a\u6839\u8282\u70b9\nroot = child;\n}\n}\n// \u5b50\u8282\u70b9\u6570\u91cf = 2\nelse {\n// \u83b7\u53d6\u4e2d\u5e8f\u904d\u5386\u4e2d cur \u7684\u4e0b\u4e00\u4e2a\u8282\u70b9\nTreeNode? tmp = cur.right;\nwhile (tmp.left != null) {\ntmp = tmp.left;\n}\n// \u9012\u5f52\u5220\u9664\u8282\u70b9 tmp\nremove(tmp.val);\n// \u7528 tmp \u8986\u76d6 cur\ncur.val = tmp.val;\n}\n}\n</code></pre> binary_search_tree.swift<pre><code>/* \u5220\u9664\u8282\u70b9 */\n@discardableResult\nfunc remove(num: Int) {\n// \u82e5\u6811\u4e3a\u7a7a\uff0c\u76f4\u63a5\u63d0\u524d\u8fd4\u56de\nif root == nil {\nreturn\n}\nvar cur = root\nvar pre: TreeNode?\n// \u5faa\u73af\u67e5\u627e\uff0c\u8d8a\u8fc7\u53f6\u8282\u70b9\u540e\u8df3\u51fa\nwhile cur != nil {\n// \u627e\u5230\u5f85\u5220\u9664\u8282\u70b9\uff0c\u8df3\u51fa\u5faa\u73af\nif cur!.val == num {\nbreak\n}\npre = cur\n// \u5f85\u5220\u9664\u8282\u70b9\u5728 cur \u7684\u53f3\u5b50\u6811\u4e2d\nif cur!.val &lt; num {\ncur = cur?.right\n}\n// \u5f85\u5220\u9664\u8282\u70b9\u5728 cur \u7684\u5de6\u5b50\u6811\u4e2d\nelse {\ncur = cur?.left\n}\n}\n// \u82e5\u65e0\u5f85\u5220\u9664\u8282\u70b9\uff0c\u5219\u76f4\u63a5\u8fd4\u56de\nif cur == nil {\nreturn\n}\n// \u5b50\u8282\u70b9\u6570\u91cf = 0 or 1\nif cur?.left == nil || cur?.right == nil {\n// \u5f53\u5b50\u8282\u70b9\u6570\u91cf = 0 / 1 \u65f6\uff0c child = null / \u8be5\u5b50\u8282\u70b9\nlet child = cur?.left != nil ? cur?.left : cur?.right\n// \u5220\u9664\u8282\u70b9 cur\nif cur != root {\nif pre?.left === cur {\npre?.left = child\n} else {\npre?.right = child\n}\n} else {\n// \u82e5\u5220\u9664\u8282\u70b9\u4e3a\u6839\u8282\u70b9\uff0c\u5219\u91cd\u65b0\u6307\u5b9a\u6839\u8282\u70b9\nroot = cur;\n}\n}\n// \u5b50\u8282\u70b9\u6570\u91cf = 2\nelse {\n// \u83b7\u53d6\u4e2d\u5e8f\u904d\u5386\u4e2d cur \u7684\u4e0b\u4e00\u4e2a\u8282\u70b9\nvar tmp = cur?.right\nwhile tmp?.left != nil {\ntmp = tmp?.left\n}\n// \u9012\u5f52\u5220\u9664\u8282\u70b9 tmp\nremove(num: tmp!.val)\n// \u7528 tmp \u8986\u76d6 cur\ncur?.val = tmp!.val\n}\n}\n</code></pre> binary_search_tree.zig<pre><code>// \u5220\u9664\u8282\u70b9\nfn remove(self: *Self, num: T) !void {\n// \u82e5\u6811\u4e3a\u7a7a\uff0c\u76f4\u63a5\u63d0\u524d\u8fd4\u56de\nif (self.root == null) return;\nvar cur = self.root;\nvar pre: ?*inc.TreeNode(T) = null;\n// \u5faa\u73af\u67e5\u627e\uff0c\u8d8a\u8fc7\u53f6\u8282\u70b9\u540e\u8df3\u51fa\nwhile (cur != null) {\n// \u627e\u5230\u5f85\u5220\u9664\u8282\u70b9\uff0c\u8df3\u51fa\u5faa\u73af\nif (cur.?.val == num) break;\npre = cur;\n// \u5f85\u5220\u9664\u8282\u70b9\u5728 cur \u7684\u53f3\u5b50\u6811\u4e2d\nif (cur.?.val &lt; num) {\ncur = cur.?.right;\n// \u5f85\u5220\u9664\u8282\u70b9\u5728 cur \u7684\u5de6\u5b50\u6811\u4e2d\n} else {\ncur = cur.?.left;\n}\n}\n// \u82e5\u65e0\u5f85\u5220\u9664\u8282\u70b9\uff0c\u5219\u76f4\u63a5\u8fd4\u56de\nif (cur == null) return;\n// \u5b50\u8282\u70b9\u6570\u91cf = 0 or 1\nif (cur.?.left == null or cur.?.right == null) {\n// \u5f53\u5b50\u8282\u70b9\u6570\u91cf = 0 / 1 \u65f6\uff0c child = null / \u8be5\u5b50\u8282\u70b9\nvar child = if (cur.?.left != null) cur.?.left else cur.?.right;\n// \u5220\u9664\u8282\u70b9 cur\nif (pre.?.left == cur) {\npre.?.left = child;\n} else {\npre.?.right = child;\n}\n// \u5b50\u8282\u70b9\u6570\u91cf = 2\n} else {\n// \u83b7\u53d6\u4e2d\u5e8f\u904d\u5386\u4e2d cur \u7684\u4e0b\u4e00\u4e2a\u8282\u70b9\nvar tmp = cur.?.right;\nwhile (tmp.?.left != null) {\ntmp = tmp.?.left;\n}\nvar tmpVal = tmp.?.val;\n// \u9012\u5f52\u5220\u9664\u8282\u70b9 tmp\n_ = self.remove(tmp.?.val);\n// \u7528 tmp \u8986\u76d6 cur\ncur.?.val = tmpVal;\n}\n}\n</code></pre> binary_search_tree.dart<pre><code>[class]{BinarySearchTree}-[func]{remove}\n</code></pre>"},{"location":"chapter_tree/binary_search_tree/#_4","title":"\u6392\u5e8f","text":"<p>\u6211\u4eec\u77e5\u9053\uff0c\u4e8c\u53c9\u6811\u7684\u4e2d\u5e8f\u904d\u5386\u9075\u5faa\u201c\u5de6 \\(\\rightarrow\\) \u6839 \\(\\rightarrow\\) \u53f3\u201d\u7684\u904d\u5386\u987a\u5e8f\uff0c\u800c\u4e8c\u53c9\u641c\u7d22\u6811\u6ee1\u8db3\u201c\u5de6\u5b50\u8282\u70b9 \\(&lt;\\) \u6839\u8282\u70b9 \\(&lt;\\) \u53f3\u5b50\u8282\u70b9\u201d\u7684\u5927\u5c0f\u5173\u7cfb\u3002\u56e0\u6b64\uff0c\u5728\u4e8c\u53c9\u641c\u7d22\u6811\u4e2d\u8fdb\u884c\u4e2d\u5e8f\u904d\u5386\u65f6\uff0c\u603b\u662f\u4f1a\u4f18\u5148\u904d\u5386\u4e0b\u4e00\u4e2a\u6700\u5c0f\u8282\u70b9\uff0c\u4ece\u800c\u5f97\u51fa\u4e00\u4e2a\u91cd\u8981\u6027\u8d28\uff1a\u4e8c\u53c9\u641c\u7d22\u6811\u7684\u4e2d\u5e8f\u904d\u5386\u5e8f\u5217\u662f\u5347\u5e8f\u7684\u3002</p> <p>\u5229\u7528\u4e2d\u5e8f\u904d\u5386\u5347\u5e8f\u7684\u6027\u8d28\uff0c\u6211\u4eec\u5728\u4e8c\u53c9\u641c\u7d22\u6811\u4e2d\u83b7\u53d6\u6709\u5e8f\u6570\u636e\u4ec5\u9700 \\(O(n)\\) \u65f6\u95f4\uff0c\u65e0\u9700\u989d\u5916\u6392\u5e8f\uff0c\u975e\u5e38\u9ad8\u6548\u3002</p> <p></p> <p> Fig. \u4e8c\u53c9\u641c\u7d22\u6811\u7684\u4e2d\u5e8f\u904d\u5386\u5e8f\u5217 </p>"},{"location":"chapter_tree/binary_search_tree/#742","title":"7.4.2. \u00a0 \u4e8c\u53c9\u641c\u7d22\u6811\u7684\u6548\u7387","text":"<p>\u7ed9\u5b9a\u4e00\u7ec4\u6570\u636e\uff0c\u6211\u4eec\u8003\u8651\u4f7f\u7528\u6570\u7ec4\u6216\u4e8c\u53c9\u641c\u7d22\u6811\u5b58\u50a8\u3002</p> <p>\u89c2\u5bdf\u53ef\u77e5\uff0c\u4e8c\u53c9\u641c\u7d22\u6811\u7684\u5404\u9879\u64cd\u4f5c\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u90fd\u662f\u5bf9\u6570\u9636\uff0c\u5177\u6709\u7a33\u5b9a\u4e14\u9ad8\u6548\u7684\u6027\u80fd\u8868\u73b0\u3002\u53ea\u6709\u5728\u9ad8\u9891\u6dfb\u52a0\u3001\u4f4e\u9891\u67e5\u627e\u5220\u9664\u7684\u6570\u636e\u9002\u7528\u573a\u666f\u4e0b\uff0c\u6570\u7ec4\u6bd4\u4e8c\u53c9\u641c\u7d22\u6811\u7684\u6548\u7387\u66f4\u9ad8\u3002</p> \u65e0\u5e8f\u6570\u7ec4 \u4e8c\u53c9\u641c\u7d22\u6811 \u67e5\u627e\u5143\u7d20 \\(O(n)\\) \\(O(\\log n)\\) \u63d2\u5165\u5143\u7d20 \\(O(1)\\) \\(O(\\log n)\\) \u5220\u9664\u5143\u7d20 \\(O(n)\\) \\(O(\\log n)\\) <p>\u5728\u7406\u60f3\u60c5\u51b5\u4e0b\uff0c\u4e8c\u53c9\u641c\u7d22\u6811\u662f\u201c\u5e73\u8861\u201d\u7684\uff0c\u8fd9\u6837\u5c31\u53ef\u4ee5\u5728 \\(\\log n\\) \u8f6e\u5faa\u73af\u5185\u67e5\u627e\u4efb\u610f\u8282\u70b9\u3002</p> <p>\u7136\u800c\uff0c\u5982\u679c\u6211\u4eec\u5728\u4e8c\u53c9\u641c\u7d22\u6811\u4e2d\u4e0d\u65ad\u5730\u63d2\u5165\u548c\u5220\u9664\u8282\u70b9\uff0c\u53ef\u80fd\u5bfc\u81f4\u4e8c\u53c9\u6811\u9000\u5316\u4e3a\u94fe\u8868\uff0c\u8fd9\u65f6\u5404\u79cd\u64cd\u4f5c\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e5f\u4f1a\u9000\u5316\u4e3a \\(O(n)\\) \u3002</p> <p></p> <p> Fig. \u4e8c\u53c9\u641c\u7d22\u6811\u7684\u5e73\u8861\u4e0e\u9000\u5316 </p>"},{"location":"chapter_tree/binary_search_tree/#743","title":"7.4.3. \u00a0 \u4e8c\u53c9\u641c\u7d22\u6811\u5e38\u89c1\u5e94\u7528","text":"<ul> <li>\u7528\u4f5c\u7cfb\u7edf\u4e2d\u7684\u591a\u7ea7\u7d22\u5f15\uff0c\u5b9e\u73b0\u9ad8\u6548\u7684\u67e5\u627e\u3001\u63d2\u5165\u3001\u5220\u9664\u64cd\u4f5c\u3002</li> <li>\u4f5c\u4e3a\u67d0\u4e9b\u641c\u7d22\u7b97\u6cd5\u7684\u5e95\u5c42\u6570\u636e\u7ed3\u6784\u3002</li> <li>\u7528\u4e8e\u5b58\u50a8\u6570\u636e\u6d41\uff0c\u4ee5\u4fdd\u6301\u5176\u6709\u5e8f\u72b6\u6001\u3002</li> </ul>"},{"location":"chapter_tree/binary_tree/","title":"7.1. \u00a0 \u4e8c\u53c9\u6811","text":"<p>\u300c\u4e8c\u53c9\u6811 Binary Tree\u300d\u662f\u4e00\u79cd\u975e\u7ebf\u6027\u6570\u636e\u7ed3\u6784\uff0c\u4ee3\u8868\u7740\u7956\u5148\u4e0e\u540e\u4ee3\u4e4b\u95f4\u7684\u6d3e\u751f\u5173\u7cfb\uff0c\u4f53\u73b0\u7740\u201c\u4e00\u5206\u4e3a\u4e8c\u201d\u7684\u5206\u6cbb\u903b\u8f91\u3002\u4e0e\u94fe\u8868\u7c7b\u4f3c\uff0c\u4e8c\u53c9\u6811\u7684\u57fa\u672c\u5355\u5143\u662f\u8282\u70b9\uff0c\u6bcf\u4e2a\u8282\u70b9\u5305\u542b\u4e00\u4e2a\u300c\u503c\u300d\u548c\u4e24\u4e2a\u300c\u6307\u9488\u300d\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart <pre><code>/* \u4e8c\u53c9\u6811\u8282\u70b9\u7c7b */\nclass TreeNode {\nint val;         // \u8282\u70b9\u503c\nTreeNode left;   // \u5de6\u5b50\u8282\u70b9\u6307\u9488\nTreeNode right;  // \u53f3\u5b50\u8282\u70b9\u6307\u9488\nTreeNode(int x) { val = x; }\n}\n</code></pre> <pre><code>/* \u4e8c\u53c9\u6811\u8282\u70b9\u7ed3\u6784\u4f53 */\nstruct TreeNode {\nint val;          // \u8282\u70b9\u503c\nTreeNode *left;   // \u5de6\u5b50\u8282\u70b9\u6307\u9488\nTreeNode *right;  // \u53f3\u5b50\u8282\u70b9\u6307\u9488\nTreeNode(int x) : val(x), left(nullptr), right(nullptr) {}\n};\n</code></pre> <pre><code>class TreeNode:\n\"\"\"\u4e8c\u53c9\u6811\u8282\u70b9\u7c7b\"\"\"\ndef __init__(self, val: int):\nself.val: int = val                   # \u8282\u70b9\u503c\nself.left: Optional[TreeNode] = None  # \u5de6\u5b50\u8282\u70b9\u6307\u9488\nself.right: Optional[TreeNode] = None # \u53f3\u5b50\u8282\u70b9\u6307\u9488\n</code></pre> <pre><code>/* \u4e8c\u53c9\u6811\u8282\u70b9\u7ed3\u6784\u4f53 */\ntype TreeNode struct {\nVal   int\nLeft  *TreeNode\nRight *TreeNode\n}\n/* \u8282\u70b9\u521d\u59cb\u5316\u65b9\u6cd5 */\nfunc NewTreeNode(v int) *TreeNode {\nreturn &amp;TreeNode{\nLeft:  nil,\nRight: nil,\nVal:   v,\n}\n}\n</code></pre> <pre><code>/* \u4e8c\u53c9\u6811\u8282\u70b9\u7c7b */\nfunction TreeNode(val, left, right) {\nthis.val = (val === undefined ? 0 : val); // \u8282\u70b9\u503c\nthis.left = (left === undefined ? null : left); // \u5de6\u5b50\u8282\u70b9\u6307\u9488\nthis.right = (right === undefined ? null : right); // \u53f3\u5b50\u8282\u70b9\u6307\u9488\n}\n</code></pre> <pre><code>/* \u4e8c\u53c9\u6811\u8282\u70b9\u7c7b */\nclass TreeNode {\nval: number;\nleft: TreeNode | null;\nright: TreeNode | null;\nconstructor(val?: number, left?: TreeNode | null, right?: TreeNode | null) {\nthis.val = val === undefined ? 0 : val; // \u8282\u70b9\u503c\nthis.left = left === undefined ? null : left; // \u5de6\u5b50\u8282\u70b9\u6307\u9488\nthis.right = right === undefined ? null : right; // \u53f3\u5b50\u8282\u70b9\u6307\u9488\n}\n}\n</code></pre> <pre><code>/* \u4e8c\u53c9\u6811\u8282\u70b9\u7ed3\u6784\u4f53 */\nstruct TreeNode {\nint val;                // \u8282\u70b9\u503c\nint height;             // \u8282\u70b9\u9ad8\u5ea6\nstruct TreeNode *left;  // \u5de6\u5b50\u8282\u70b9\u6307\u9488\nstruct TreeNode *right; // \u53f3\u5b50\u8282\u70b9\u6307\u9488\n};\ntypedef struct TreeNode TreeNode;\n/* \u6784\u9020\u51fd\u6570 */\nTreeNode *newTreeNode(int val) {\nTreeNode *node;\nnode = (TreeNode *)malloc(sizeof(TreeNode));\nnode-&gt;val = val;\nnode-&gt;height = 0;\nnode-&gt;left = NULL;\nnode-&gt;right = NULL;\nreturn node;\n}\n</code></pre> <pre><code>/* \u4e8c\u53c9\u6811\u8282\u70b9\u7c7b */\nclass TreeNode {\nint val;          // \u8282\u70b9\u503c\nTreeNode? left;   // \u5de6\u5b50\u8282\u70b9\u6307\u9488\nTreeNode? right;  // \u53f3\u5b50\u8282\u70b9\u6307\u9488\nTreeNode(int x) { val = x; }\n}\n</code></pre> <pre><code>/* \u4e8c\u53c9\u6811\u8282\u70b9\u7c7b */\nclass TreeNode {\nvar val: Int // \u8282\u70b9\u503c\nvar left: TreeNode? // \u5de6\u5b50\u8282\u70b9\u6307\u9488\nvar right: TreeNode? // \u53f3\u5b50\u8282\u70b9\u6307\u9488\ninit(x: Int) {\nval = x\n}\n}\n</code></pre> <pre><code>\n</code></pre> <pre><code>/* \u4e8c\u53c9\u6811\u8282\u70b9\u7c7b */\nclass TreeNode {\nint val;         // \u8282\u70b9\u503c\nTreeNode? left;  // \u5de6\u5b50\u8282\u70b9\u6307\u9488\nTreeNode? right; // \u53f3\u5b50\u8282\u70b9\u6307\u9488\nTreeNode(this.val, [this.left, this.right]);\n}\n</code></pre> <p>\u8282\u70b9\u7684\u4e24\u4e2a\u6307\u9488\u5206\u522b\u6307\u5411\u300c\u5de6\u5b50\u8282\u70b9\u300d\u548c\u300c\u53f3\u5b50\u8282\u70b9\u300d\uff0c\u540c\u65f6\u8be5\u8282\u70b9\u88ab\u79f0\u4e3a\u8fd9\u4e24\u4e2a\u5b50\u8282\u70b9\u7684\u300c\u7236\u8282\u70b9\u300d\u3002\u5f53\u7ed9\u5b9a\u4e00\u4e2a\u4e8c\u53c9\u6811\u7684\u8282\u70b9\u65f6\uff0c\u6211\u4eec\u5c06\u8be5\u8282\u70b9\u7684\u5de6\u5b50\u8282\u70b9\u53ca\u5176\u4ee5\u4e0b\u8282\u70b9\u5f62\u6210\u7684\u6811\u79f0\u4e3a\u8be5\u8282\u70b9\u7684\u300c\u5de6\u5b50\u6811\u300d\uff0c\u540c\u7406\u53ef\u5f97\u300c\u53f3\u5b50\u6811\u300d\u3002</p> <p>\u5728\u4e8c\u53c9\u6811\u4e2d\uff0c\u9664\u53f6\u8282\u70b9\u5916\uff0c\u5176\u4ed6\u6240\u6709\u8282\u70b9\u90fd\u5305\u542b\u5b50\u8282\u70b9\u548c\u975e\u7a7a\u5b50\u6811\u3002\u4f8b\u5982\uff0c\u5728\u4ee5\u4e0b\u793a\u4f8b\u4e2d\uff0c\u82e5\u5c06\u201c\u8282\u70b9 2\u201d\u89c6\u4e3a\u7236\u8282\u70b9\uff0c\u5219\u5176\u5de6\u5b50\u8282\u70b9\u548c\u53f3\u5b50\u8282\u70b9\u5206\u522b\u662f\u201c\u8282\u70b9 4\u201d\u548c\u201c\u8282\u70b9 5\u201d\uff0c\u5de6\u5b50\u6811\u662f\u201c\u8282\u70b9 4 \u53ca\u5176\u4ee5\u4e0b\u8282\u70b9\u5f62\u6210\u7684\u6811\u201d\uff0c\u53f3\u5b50\u6811\u662f\u201c\u8282\u70b9 5 \u53ca\u5176\u4ee5\u4e0b\u8282\u70b9\u5f62\u6210\u7684\u6811\u201d\u3002</p> <p></p> <p> Fig. \u7236\u8282\u70b9\u3001\u5b50\u8282\u70b9\u3001\u5b50\u6811 </p>"},{"location":"chapter_tree/binary_tree/#711","title":"7.1.1. \u00a0 \u4e8c\u53c9\u6811\u5e38\u89c1\u672f\u8bed","text":"<p>\u4e8c\u53c9\u6811\u6d89\u53ca\u7684\u672f\u8bed\u8f83\u591a\uff0c\u5efa\u8bae\u5c3d\u91cf\u7406\u89e3\u5e76\u8bb0\u4f4f\u3002</p> <ul> <li>\u300c\u6839\u8282\u70b9 Root Node\u300d\uff1a\u4f4d\u4e8e\u4e8c\u53c9\u6811\u9876\u5c42\u7684\u8282\u70b9\uff0c\u6ca1\u6709\u7236\u8282\u70b9\uff1b</li> <li>\u300c\u53f6\u8282\u70b9 Leaf Node\u300d\uff1a\u6ca1\u6709\u5b50\u8282\u70b9\u7684\u8282\u70b9\uff0c\u5176\u4e24\u4e2a\u6307\u9488\u5747\u6307\u5411 \\(\\text{null}\\) \uff1b</li> <li>\u8282\u70b9\u7684\u300c\u5c42 Level\u300d\uff1a\u4ece\u9876\u81f3\u5e95\u9012\u589e\uff0c\u6839\u8282\u70b9\u6240\u5728\u5c42\u4e3a 1 \uff1b</li> <li>\u8282\u70b9\u7684\u300c\u5ea6 Degree\u300d\uff1a\u8282\u70b9\u7684\u5b50\u8282\u70b9\u7684\u6570\u91cf\u3002\u5728\u4e8c\u53c9\u6811\u4e2d\uff0c\u5ea6\u7684\u8303\u56f4\u662f 0, 1, 2 \uff1b</li> <li>\u300c\u8fb9 Edge\u300d\uff1a\u8fde\u63a5\u4e24\u4e2a\u8282\u70b9\u7684\u7ebf\u6bb5\uff0c\u5373\u8282\u70b9\u6307\u9488\uff1b</li> <li>\u4e8c\u53c9\u6811\u7684\u300c\u9ad8\u5ea6\u300d\uff1a\u4ece\u6839\u8282\u70b9\u5230\u6700\u8fdc\u53f6\u8282\u70b9\u6240\u7ecf\u8fc7\u7684\u8fb9\u7684\u6570\u91cf\uff1b</li> <li>\u8282\u70b9\u7684\u300c\u6df1\u5ea6 Depth\u300d \uff1a\u4ece\u6839\u8282\u70b9\u5230\u8be5\u8282\u70b9\u6240\u7ecf\u8fc7\u7684\u8fb9\u7684\u6570\u91cf\uff1b</li> <li>\u8282\u70b9\u7684\u300c\u9ad8\u5ea6 Height\u300d\uff1a\u4ece\u6700\u8fdc\u53f6\u8282\u70b9\u5230\u8be5\u8282\u70b9\u6240\u7ecf\u8fc7\u7684\u8fb9\u7684\u6570\u91cf\uff1b</li> </ul> <p></p> <p> Fig. \u4e8c\u53c9\u6811\u7684\u5e38\u7528\u672f\u8bed </p> <p>\u9ad8\u5ea6\u4e0e\u6df1\u5ea6\u7684\u5b9a\u4e49</p> <p>\u8bf7\u6ce8\u610f\uff0c\u6211\u4eec\u901a\u5e38\u5c06\u300c\u9ad8\u5ea6\u300d\u548c\u300c\u6df1\u5ea6\u300d\u5b9a\u4e49\u4e3a\u201c\u8d70\u8fc7\u8fb9\u7684\u6570\u91cf\u201d\uff0c\u4f46\u6709\u4e9b\u9898\u76ee\u6216\u6559\u6750\u53ef\u80fd\u4f1a\u5c06\u5176\u5b9a\u4e49\u4e3a\u201c\u8d70\u8fc7\u8282\u70b9\u7684\u6570\u91cf\u201d\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u9ad8\u5ea6\u548c\u6df1\u5ea6\u90fd\u9700\u8981\u52a0 1 \u3002</p>"},{"location":"chapter_tree/binary_tree/#712","title":"7.1.2. \u00a0 \u4e8c\u53c9\u6811\u57fa\u672c\u64cd\u4f5c","text":"<p>\u521d\u59cb\u5316\u4e8c\u53c9\u6811\u3002\u4e0e\u94fe\u8868\u7c7b\u4f3c\uff0c\u9996\u5148\u521d\u59cb\u5316\u8282\u70b9\uff0c\u7136\u540e\u6784\u5efa\u5f15\u7528\u6307\u5411\uff08\u5373\u6307\u9488\uff09\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart binary_tree.java<pre><code>// \u521d\u59cb\u5316\u8282\u70b9\nTreeNode n1 = new TreeNode(1);\nTreeNode n2 = new TreeNode(2);\nTreeNode n3 = new TreeNode(3);\nTreeNode n4 = new TreeNode(4);\nTreeNode n5 = new TreeNode(5);\n// \u6784\u5efa\u5f15\u7528\u6307\u5411\uff08\u5373\u6307\u9488\uff09\nn1.left = n2;\nn1.right = n3;\nn2.left = n4;\nn2.right = n5;\n</code></pre> binary_tree.cpp<pre><code>/* \u521d\u59cb\u5316\u4e8c\u53c9\u6811 */\n// \u521d\u59cb\u5316\u8282\u70b9\nTreeNode* n1 = new TreeNode(1);\nTreeNode* n2 = new TreeNode(2);\nTreeNode* n3 = new TreeNode(3);\nTreeNode* n4 = new TreeNode(4);\nTreeNode* n5 = new TreeNode(5);\n// \u6784\u5efa\u5f15\u7528\u6307\u5411\uff08\u5373\u6307\u9488\uff09\nn1-&gt;left = n2;\nn1-&gt;right = n3;\nn2-&gt;left = n4;\nn2-&gt;right = n5;\n</code></pre> binary_tree.py<pre><code># \u521d\u59cb\u5316\u4e8c\u53c9\u6811\n# \u521d\u59cb\u5316\u8282\u70b9\nn1 = TreeNode(val=1)\nn2 = TreeNode(val=2)\nn3 = TreeNode(val=3)\nn4 = TreeNode(val=4)\nn5 = TreeNode(val=5)\n# \u6784\u5efa\u5f15\u7528\u6307\u5411\uff08\u5373\u6307\u9488\uff09\nn1.left = n2\nn1.right = n3\nn2.left = n4\nn2.right = n5\n</code></pre> binary_tree.go<pre><code>/* \u521d\u59cb\u5316\u4e8c\u53c9\u6811 */\n// \u521d\u59cb\u5316\u8282\u70b9\nn1 := NewTreeNode(1)\nn2 := NewTreeNode(2)\nn3 := NewTreeNode(3)\nn4 := NewTreeNode(4)\nn5 := NewTreeNode(5)\n// \u6784\u5efa\u5f15\u7528\u6307\u5411\uff08\u5373\u6307\u9488\uff09\nn1.Left = n2\nn1.Right = n3\nn2.Left = n4\nn2.Right = n5\n</code></pre> binary_tree.js<pre><code>/* \u521d\u59cb\u5316\u4e8c\u53c9\u6811 */\n// \u521d\u59cb\u5316\u8282\u70b9\nlet n1 = new TreeNode(1),\nn2 = new TreeNode(2),\nn3 = new TreeNode(3),\nn4 = new TreeNode(4),\nn5 = new TreeNode(5);\n// \u6784\u5efa\u5f15\u7528\u6307\u5411\uff08\u5373\u6307\u9488\uff09\nn1.left = n2;\nn1.right = n3;\nn2.left = n4;\nn2.right = n5;\n</code></pre> binary_tree.ts<pre><code>/* \u521d\u59cb\u5316\u4e8c\u53c9\u6811 */\n// \u521d\u59cb\u5316\u8282\u70b9\nlet n1 = new TreeNode(1),\nn2 = new TreeNode(2),\nn3 = new TreeNode(3),\nn4 = new TreeNode(4),\nn5 = new TreeNode(5);\n// \u6784\u5efa\u5f15\u7528\u6307\u5411\uff08\u5373\u6307\u9488\uff09\nn1.left = n2;\nn1.right = n3;\nn2.left = n4;\nn2.right = n5;\n</code></pre> binary_tree.c<pre><code>/* \u521d\u59cb\u5316\u4e8c\u53c9\u6811 */\n// \u521d\u59cb\u5316\u8282\u70b9\nTreeNode *n1 = newTreeNode(1);\nTreeNode *n2 = newTreeNode(2);\nTreeNode *n3 = newTreeNode(3);\nTreeNode *n4 = newTreeNode(4);\nTreeNode *n5 = newTreeNode(5);\n// \u6784\u5efa\u5f15\u7528\u6307\u5411\uff08\u5373\u6307\u9488\uff09\nn1-&gt;left = n2;\nn1-&gt;right = n3;\nn2-&gt;left = n4;\nn2-&gt;right = n5;\n</code></pre> binary_tree.cs<pre><code>/* \u521d\u59cb\u5316\u4e8c\u53c9\u6811 */\n// \u521d\u59cb\u5316\u8282\u70b9\nTreeNode n1 = new TreeNode(1);\nTreeNode n2 = new TreeNode(2);\nTreeNode n3 = new TreeNode(3);\nTreeNode n4 = new TreeNode(4);\nTreeNode n5 = new TreeNode(5);\n// \u6784\u5efa\u5f15\u7528\u6307\u5411\uff08\u5373\u6307\u9488\uff09\nn1.left = n2;\nn1.right = n3;\nn2.left = n4;\nn2.right = n5;\n</code></pre> binary_tree.swift<pre><code>// \u521d\u59cb\u5316\u8282\u70b9\nlet n1 = TreeNode(x: 1)\nlet n2 = TreeNode(x: 2)\nlet n3 = TreeNode(x: 3)\nlet n4 = TreeNode(x: 4)\nlet n5 = TreeNode(x: 5)\n// \u6784\u5efa\u5f15\u7528\u6307\u5411\uff08\u5373\u6307\u9488\uff09\nn1.left = n2\nn1.right = n3\nn2.left = n4\nn2.right = n5\n</code></pre> binary_tree.zig<pre><code>\n</code></pre> binary_tree.dart<pre><code>/* \u521d\u59cb\u5316\u4e8c\u53c9\u6811 */\n// \u521d\u59cb\u5316\u8282\u70b9\nTreeNode n1 = new TreeNode(1);\nTreeNode n2 = new TreeNode(2);\nTreeNode n3 = new TreeNode(3);\nTreeNode n4 = new TreeNode(4);\nTreeNode n5 = new TreeNode(5);\n// \u6784\u5efa\u5f15\u7528\u6307\u5411\uff08\u5373\u6307\u9488\uff09\nn1.left = n2;\nn1.right = n3;\nn2.left = n4;\nn2.right = n5;\n</code></pre> <p>\u63d2\u5165\u4e0e\u5220\u9664\u8282\u70b9\u3002\u4e0e\u94fe\u8868\u7c7b\u4f3c\uff0c\u901a\u8fc7\u4fee\u6539\u6307\u9488\u6765\u5b9e\u73b0\u63d2\u5165\u4e0e\u5220\u9664\u8282\u70b9\u3002</p> <p></p> <p> Fig. \u5728\u4e8c\u53c9\u6811\u4e2d\u63d2\u5165\u4e0e\u5220\u9664\u8282\u70b9 </p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart binary_tree.java<pre><code>TreeNode P = new TreeNode(0);\n// \u5728 n1 -&gt; n2 \u4e2d\u95f4\u63d2\u5165\u8282\u70b9 P\nn1.left = P;\nP.left = n2;\n// \u5220\u9664\u8282\u70b9 P\nn1.left = n2;\n</code></pre> binary_tree.cpp<pre><code>/* \u63d2\u5165\u4e0e\u5220\u9664\u8282\u70b9 */\nTreeNode* P = new TreeNode(0);\n// \u5728 n1 -&gt; n2 \u4e2d\u95f4\u63d2\u5165\u8282\u70b9 P\nn1-&gt;left = P;\nP-&gt;left = n2;\n// \u5220\u9664\u8282\u70b9 P\nn1-&gt;left = n2;\n</code></pre> binary_tree.py<pre><code># \u63d2\u5165\u4e0e\u5220\u9664\u8282\u70b9\np = TreeNode(0)\n# \u5728 n1 -&gt; n2 \u4e2d\u95f4\u63d2\u5165\u8282\u70b9 P\nn1.left = p\np.left = n2\n# \u5220\u9664\u8282\u70b9 P\nn1.left = n2\n</code></pre> binary_tree.go<pre><code>/* \u63d2\u5165\u4e0e\u5220\u9664\u8282\u70b9 */\n// \u5728 n1 -&gt; n2 \u4e2d\u95f4\u63d2\u5165\u8282\u70b9 P\np := NewTreeNode(0)\nn1.Left = p\np.Left = n2\n// \u5220\u9664\u8282\u70b9 P\nn1.Left = n2\n</code></pre> binary_tree.js<pre><code>/* \u63d2\u5165\u4e0e\u5220\u9664\u8282\u70b9 */\nlet P = new TreeNode(0);\n// \u5728 n1 -&gt; n2 \u4e2d\u95f4\u63d2\u5165\u8282\u70b9 P\nn1.left = P;\nP.left = n2;\n// \u5220\u9664\u8282\u70b9 P\nn1.left = n2;\n</code></pre> binary_tree.ts<pre><code>/* \u63d2\u5165\u4e0e\u5220\u9664\u8282\u70b9 */\nconst P = new TreeNode(0);\n// \u5728 n1 -&gt; n2 \u4e2d\u95f4\u63d2\u5165\u8282\u70b9 P\nn1.left = P;\nP.left = n2;\n// \u5220\u9664\u8282\u70b9 P\nn1.left = n2;\n</code></pre> binary_tree.c<pre><code>/* \u63d2\u5165\u4e0e\u5220\u9664\u8282\u70b9 */\nTreeNode *P = newTreeNode(0);\n// \u5728 n1 -&gt; n2 \u4e2d\u95f4\u63d2\u5165\u8282\u70b9 P\nn1-&gt;left = P;\nP-&gt;left = n2;\n// \u5220\u9664\u8282\u70b9 P\nn1-&gt;left = n2;\n</code></pre> binary_tree.cs<pre><code>/* \u63d2\u5165\u4e0e\u5220\u9664\u8282\u70b9 */\nTreeNode P = new TreeNode(0);\n// \u5728 n1 -&gt; n2 \u4e2d\u95f4\u63d2\u5165\u8282\u70b9 P\nn1.left = P;\nP.left = n2;\n// \u5220\u9664\u8282\u70b9 P\nn1.left = n2;\n</code></pre> binary_tree.swift<pre><code>let P = TreeNode(x: 0)\n// \u5728 n1 -&gt; n2 \u4e2d\u95f4\u63d2\u5165\u8282\u70b9 P\nn1.left = P\nP.left = n2\n// \u5220\u9664\u8282\u70b9 P\nn1.left = n2\n</code></pre> binary_tree.zig<pre><code>\n</code></pre> binary_tree.dart<pre><code>/* \u63d2\u5165\u4e0e\u5220\u9664\u8282\u70b9 */\nTreeNode P = new TreeNode(0);\n// \u5728 n1 -&gt; n2 \u4e2d\u95f4\u63d2\u5165\u8282\u70b9 P\nn1.left = P;\nP.left = n2;\n// \u5220\u9664\u8282\u70b9 P\nn1.left = n2;\n</code></pre> <p>Note</p> <p>\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u63d2\u5165\u8282\u70b9\u53ef\u80fd\u4f1a\u6539\u53d8\u4e8c\u53c9\u6811\u7684\u539f\u6709\u903b\u8f91\u7ed3\u6784\uff0c\u800c\u5220\u9664\u8282\u70b9\u901a\u5e38\u610f\u5473\u7740\u5220\u9664\u8be5\u8282\u70b9\u53ca\u5176\u6240\u6709\u5b50\u6811\u3002\u56e0\u6b64\uff0c\u5728\u4e8c\u53c9\u6811\u4e2d\uff0c\u63d2\u5165\u4e0e\u5220\u9664\u64cd\u4f5c\u901a\u5e38\u662f\u7531\u4e00\u5957\u64cd\u4f5c\u914d\u5408\u5b8c\u6210\u7684\uff0c\u4ee5\u5b9e\u73b0\u6709\u5b9e\u9645\u610f\u4e49\u7684\u64cd\u4f5c\u3002</p>"},{"location":"chapter_tree/binary_tree/#713","title":"7.1.3. \u00a0 \u5e38\u89c1\u4e8c\u53c9\u6811\u7c7b\u578b","text":""},{"location":"chapter_tree/binary_tree/#_1","title":"\u5b8c\u7f8e\u4e8c\u53c9\u6811","text":"<p>\u300c\u5b8c\u7f8e\u4e8c\u53c9\u6811 Perfect Binary Tree\u300d\u9664\u4e86\u6700\u5e95\u5c42\u5916\uff0c\u5176\u4f59\u6240\u6709\u5c42\u7684\u8282\u70b9\u90fd\u88ab\u5b8c\u5168\u586b\u6ee1\u3002\u5728\u5b8c\u7f8e\u4e8c\u53c9\u6811\u4e2d\uff0c\u53f6\u8282\u70b9\u7684\u5ea6\u4e3a \\(0\\) \uff0c\u5176\u4f59\u6240\u6709\u8282\u70b9\u7684\u5ea6\u90fd\u4e3a \\(2\\) \uff1b\u82e5\u6811\u9ad8\u5ea6\u4e3a \\(h\\) \uff0c\u5219\u8282\u70b9\u603b\u6570\u4e3a \\(2^{h+1} - 1\\) \uff0c\u5448\u73b0\u6807\u51c6\u7684\u6307\u6570\u7ea7\u5173\u7cfb\uff0c\u53cd\u6620\u4e86\u81ea\u7136\u754c\u4e2d\u5e38\u89c1\u7684\u7ec6\u80de\u5206\u88c2\u73b0\u8c61\u3002</p> <p>Tip</p> <p>\u5728\u4e2d\u6587\u793e\u533a\u4e2d\uff0c\u5b8c\u7f8e\u4e8c\u53c9\u6811\u5e38\u88ab\u79f0\u4e3a\u300c\u6ee1\u4e8c\u53c9\u6811\u300d\uff0c\u8bf7\u6ce8\u610f\u533a\u5206\u3002</p> <p></p> <p> Fig. \u5b8c\u7f8e\u4e8c\u53c9\u6811 </p>"},{"location":"chapter_tree/binary_tree/#_2","title":"\u5b8c\u5168\u4e8c\u53c9\u6811","text":"<p>\u300c\u5b8c\u5168\u4e8c\u53c9\u6811 Complete Binary Tree\u300d\u53ea\u6709\u6700\u5e95\u5c42\u7684\u8282\u70b9\u672a\u88ab\u586b\u6ee1\uff0c\u4e14\u6700\u5e95\u5c42\u8282\u70b9\u5c3d\u91cf\u9760\u5de6\u586b\u5145\u3002</p> <p></p> <p> Fig. \u5b8c\u5168\u4e8c\u53c9\u6811 </p>"},{"location":"chapter_tree/binary_tree/#_3","title":"\u5b8c\u6ee1\u4e8c\u53c9\u6811","text":"<p>\u300c\u5b8c\u6ee1\u4e8c\u53c9\u6811 Full Binary Tree\u300d\u9664\u4e86\u53f6\u8282\u70b9\u4e4b\u5916\uff0c\u5176\u4f59\u6240\u6709\u8282\u70b9\u90fd\u6709\u4e24\u4e2a\u5b50\u8282\u70b9\u3002</p> <p></p> <p> Fig. \u5b8c\u6ee1\u4e8c\u53c9\u6811 </p>"},{"location":"chapter_tree/binary_tree/#_4","title":"\u5e73\u8861\u4e8c\u53c9\u6811","text":"<p>\u300c\u5e73\u8861\u4e8c\u53c9\u6811 Balanced Binary Tree\u300d\u4e2d\u4efb\u610f\u8282\u70b9\u7684\u5de6\u5b50\u6811\u548c\u53f3\u5b50\u6811\u7684\u9ad8\u5ea6\u4e4b\u5dee\u7684\u7edd\u5bf9\u503c\u4e0d\u8d85\u8fc7 1 \u3002</p> <p></p> <p> Fig. \u5e73\u8861\u4e8c\u53c9\u6811 </p>"},{"location":"chapter_tree/binary_tree/#714","title":"7.1.4. \u00a0 \u4e8c\u53c9\u6811\u7684\u9000\u5316","text":"<p>\u5f53\u4e8c\u53c9\u6811\u7684\u6bcf\u5c42\u8282\u70b9\u90fd\u88ab\u586b\u6ee1\u65f6\uff0c\u8fbe\u5230\u300c\u5b8c\u7f8e\u4e8c\u53c9\u6811\u300d\uff1b\u800c\u5f53\u6240\u6709\u8282\u70b9\u90fd\u504f\u5411\u4e00\u4fa7\u65f6\uff0c\u4e8c\u53c9\u6811\u9000\u5316\u4e3a\u300c\u94fe\u8868\u300d\u3002</p> <ul> <li>\u5b8c\u7f8e\u4e8c\u53c9\u6811\u662f\u7406\u60f3\u60c5\u51b5\uff0c\u53ef\u4ee5\u5145\u5206\u53d1\u6325\u4e8c\u53c9\u6811\u201c\u5206\u6cbb\u201d\u7684\u4f18\u52bf\uff1b</li> <li>\u94fe\u8868\u5219\u662f\u53e6\u4e00\u4e2a\u6781\u7aef\uff0c\u5404\u9879\u64cd\u4f5c\u90fd\u53d8\u4e3a\u7ebf\u6027\u64cd\u4f5c\uff0c\u65f6\u95f4\u590d\u6742\u5ea6\u9000\u5316\u81f3 \\(O(n)\\) \uff1b</li> </ul> <p></p> <p> Fig. \u4e8c\u53c9\u6811\u7684\u6700\u4f73\u4e0e\u6700\u5dee\u7ed3\u6784 </p> <p>\u5982\u4e0b\u8868\u6240\u793a\uff0c\u5728\u6700\u4f73\u548c\u6700\u5dee\u7ed3\u6784\u4e0b\uff0c\u4e8c\u53c9\u6811\u7684\u53f6\u8282\u70b9\u6570\u91cf\u3001\u8282\u70b9\u603b\u6570\u3001\u9ad8\u5ea6\u7b49\u8fbe\u5230\u6781\u5927\u6216\u6781\u5c0f\u503c\u3002</p> \u5b8c\u7f8e\u4e8c\u53c9\u6811 \u94fe\u8868 \u7b2c \\(i\\) \u5c42\u7684\u8282\u70b9\u6570\u91cf \\(2^{i-1}\\) \\(1\\) \u6811\u7684\u9ad8\u5ea6\u4e3a \\(h\\) \u65f6\u7684\u53f6\u8282\u70b9\u6570\u91cf \\(2^h\\) \\(1\\) \u6811\u7684\u9ad8\u5ea6\u4e3a \\(h\\) \u65f6\u7684\u8282\u70b9\u603b\u6570 \\(2^{h+1} - 1\\) \\(h + 1\\) \u6811\u7684\u8282\u70b9\u603b\u6570\u4e3a \\(n\\) \u65f6\u7684\u9ad8\u5ea6 \\(\\log_2 (n+1) - 1\\) \\(n - 1\\)"},{"location":"chapter_tree/binary_tree_traversal/","title":"7.2. \u00a0 \u4e8c\u53c9\u6811\u904d\u5386","text":"<p>\u4ece\u7269\u7406\u7ed3\u6784\u7684\u89d2\u5ea6\u6765\u770b\uff0c\u6811\u662f\u4e00\u79cd\u57fa\u4e8e\u94fe\u8868\u7684\u6570\u636e\u7ed3\u6784\uff0c\u56e0\u6b64\u5176\u904d\u5386\u65b9\u5f0f\u662f\u901a\u8fc7\u6307\u9488\u9010\u4e2a\u8bbf\u95ee\u8282\u70b9\u3002\u7136\u800c\uff0c\u6811\u662f\u4e00\u79cd\u975e\u7ebf\u6027\u6570\u636e\u7ed3\u6784\uff0c\u8fd9\u4f7f\u5f97\u904d\u5386\u6811\u6bd4\u904d\u5386\u94fe\u8868\u66f4\u52a0\u590d\u6742\uff0c\u9700\u8981\u501f\u52a9\u641c\u7d22\u7b97\u6cd5\u6765\u5b9e\u73b0\u3002</p> <p>\u4e8c\u53c9\u6811\u5e38\u89c1\u7684\u904d\u5386\u65b9\u5f0f\u5305\u62ec\u5c42\u5e8f\u904d\u5386\u3001\u524d\u5e8f\u904d\u5386\u3001\u4e2d\u5e8f\u904d\u5386\u548c\u540e\u5e8f\u904d\u5386\u7b49\u3002</p>"},{"location":"chapter_tree/binary_tree_traversal/#721","title":"7.2.1. \u00a0 \u5c42\u5e8f\u904d\u5386","text":"<p>\u300c\u5c42\u5e8f\u904d\u5386 Level-Order Traversal\u300d\u4ece\u9876\u90e8\u5230\u5e95\u90e8\u9010\u5c42\u904d\u5386\u4e8c\u53c9\u6811\uff0c\u5e76\u5728\u6bcf\u4e00\u5c42\u6309\u7167\u4ece\u5de6\u5230\u53f3\u7684\u987a\u5e8f\u8bbf\u95ee\u8282\u70b9\u3002</p> <p>\u5c42\u5e8f\u904d\u5386\u672c\u8d28\u4e0a\u5c5e\u4e8e\u300c\u5e7f\u5ea6\u4f18\u5148\u641c\u7d22 Breadth-First Traversal\u300d\uff0c\u5b83\u4f53\u73b0\u4e86\u4e00\u79cd\u201c\u4e00\u5708\u4e00\u5708\u5411\u5916\u6269\u5c55\u201d\u7684\u9010\u5c42\u641c\u7d22\u65b9\u5f0f\u3002</p> <p></p> <p> Fig. \u4e8c\u53c9\u6811\u7684\u5c42\u5e8f\u904d\u5386 </p>"},{"location":"chapter_tree/binary_tree_traversal/#_1","title":"\u7b97\u6cd5\u5b9e\u73b0","text":"<p>\u5e7f\u5ea6\u4f18\u5148\u904d\u5386\u901a\u5e38\u501f\u52a9\u300c\u961f\u5217\u300d\u6765\u5b9e\u73b0\u3002\u961f\u5217\u9075\u5faa\u201c\u5148\u8fdb\u5148\u51fa\u201d\u7684\u89c4\u5219\uff0c\u800c\u5e7f\u5ea6\u4f18\u5148\u904d\u5386\u5219\u9075\u5faa\u201c\u9010\u5c42\u63a8\u8fdb\u201d\u7684\u89c4\u5219\uff0c\u4e24\u8005\u80cc\u540e\u7684\u601d\u60f3\u662f\u4e00\u81f4\u7684\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart binary_tree_bfs.java<pre><code>/* \u5c42\u5e8f\u904d\u5386 */\nList&lt;Integer&gt; levelOrder(TreeNode root) {\n// \u521d\u59cb\u5316\u961f\u5217\uff0c\u52a0\u5165\u6839\u8282\u70b9\nQueue&lt;TreeNode&gt; queue = new LinkedList&lt;&gt;() {{ add(root); }};\n// \u521d\u59cb\u5316\u4e00\u4e2a\u5217\u8868\uff0c\u7528\u4e8e\u4fdd\u5b58\u904d\u5386\u5e8f\u5217\nList&lt;Integer&gt; list = new ArrayList&lt;&gt;();\nwhile (!queue.isEmpty()) {\nTreeNode node = queue.poll(); // \u961f\u5217\u51fa\u961f\nlist.add(node.val);           // \u4fdd\u5b58\u8282\u70b9\u503c\nif (node.left != null)\nqueue.offer(node.left);   // \u5de6\u5b50\u8282\u70b9\u5165\u961f\nif (node.right != null)\nqueue.offer(node.right);  // \u53f3\u5b50\u8282\u70b9\u5165\u961f\n}\nreturn list;\n}\n</code></pre> binary_tree_bfs.cpp<pre><code>/* \u5c42\u5e8f\u904d\u5386 */\nvector&lt;int&gt; levelOrder(TreeNode *root) {\n// \u521d\u59cb\u5316\u961f\u5217\uff0c\u52a0\u5165\u6839\u8282\u70b9\nqueue&lt;TreeNode *&gt; queue;\nqueue.push(root);\n// \u521d\u59cb\u5316\u4e00\u4e2a\u5217\u8868\uff0c\u7528\u4e8e\u4fdd\u5b58\u904d\u5386\u5e8f\u5217\nvector&lt;int&gt; vec;\nwhile (!queue.empty()) {\nTreeNode *node = queue.front();\nqueue.pop();              // \u961f\u5217\u51fa\u961f\nvec.push_back(node-&gt;val); // \u4fdd\u5b58\u8282\u70b9\u503c\nif (node-&gt;left != nullptr)\nqueue.push(node-&gt;left); // \u5de6\u5b50\u8282\u70b9\u5165\u961f\nif (node-&gt;right != nullptr)\nqueue.push(node-&gt;right); // \u53f3\u5b50\u8282\u70b9\u5165\u961f\n}\nreturn vec;\n}\n</code></pre> binary_tree_bfs.py<pre><code>def level_order(root: TreeNode | None) -&gt; list[int]:\n\"\"\"\u5c42\u5e8f\u904d\u5386\"\"\"\n# \u521d\u59cb\u5316\u961f\u5217\uff0c\u52a0\u5165\u6839\u8282\u70b9\nqueue: deque[TreeNode] = deque()\nqueue.append(root)\n# \u521d\u59cb\u5316\u4e00\u4e2a\u5217\u8868\uff0c\u7528\u4e8e\u4fdd\u5b58\u904d\u5386\u5e8f\u5217\nres = []\nwhile queue:\nnode: TreeNode = queue.popleft()  # \u961f\u5217\u51fa\u961f\nres.append(node.val)  # \u4fdd\u5b58\u8282\u70b9\u503c\nif node.left is not None:\nqueue.append(node.left)  # \u5de6\u5b50\u8282\u70b9\u5165\u961f\nif node.right is not None:\nqueue.append(node.right)  # \u53f3\u5b50\u8282\u70b9\u5165\u961f\nreturn res\n</code></pre> binary_tree_bfs.go<pre><code>/* \u5c42\u5e8f\u904d\u5386 */\nfunc levelOrder(root *TreeNode) []int {\n// \u521d\u59cb\u5316\u961f\u5217\uff0c\u52a0\u5165\u6839\u8282\u70b9\nqueue := list.New()\nqueue.PushBack(root)\n// \u521d\u59cb\u5316\u4e00\u4e2a\u5207\u7247\uff0c\u7528\u4e8e\u4fdd\u5b58\u904d\u5386\u5e8f\u5217\nnums := make([]int, 0)\nfor queue.Len() &gt; 0 {\n// \u961f\u5217\u51fa\u961f\nnode := queue.Remove(queue.Front()).(*TreeNode)\n// \u4fdd\u5b58\u8282\u70b9\u503c\nnums = append(nums, node.Val)\nif node.Left != nil {\n// \u5de6\u5b50\u8282\u70b9\u5165\u961f\nqueue.PushBack(node.Left)\n}\nif node.Right != nil {\n// \u53f3\u5b50\u8282\u70b9\u5165\u961f\nqueue.PushBack(node.Right)\n}\n}\nreturn nums\n}\n</code></pre> binary_tree_bfs.js<pre><code>/* \u5c42\u5e8f\u904d\u5386 */\nfunction levelOrder(root) {\n// \u521d\u59cb\u5316\u961f\u5217\uff0c\u52a0\u5165\u6839\u8282\u70b9\nconst queue = [root];\n// \u521d\u59cb\u5316\u4e00\u4e2a\u5217\u8868\uff0c\u7528\u4e8e\u4fdd\u5b58\u904d\u5386\u5e8f\u5217\nconst list = [];\nwhile (queue.length) {\nlet node = queue.shift(); // \u961f\u5217\u51fa\u961f\nlist.push(node.val); // \u4fdd\u5b58\u8282\u70b9\u503c\nif (node.left) queue.push(node.left); // \u5de6\u5b50\u8282\u70b9\u5165\u961f\nif (node.right) queue.push(node.right); // \u53f3\u5b50\u8282\u70b9\u5165\u961f\n}\nreturn list;\n}\n</code></pre> binary_tree_bfs.ts<pre><code>/* \u5c42\u5e8f\u904d\u5386 */\nfunction levelOrder(root: TreeNode | null): number[] {\n// \u521d\u59cb\u5316\u961f\u5217\uff0c\u52a0\u5165\u6839\u8282\u70b9\nconst queue = [root];\n// \u521d\u59cb\u5316\u4e00\u4e2a\u5217\u8868\uff0c\u7528\u4e8e\u4fdd\u5b58\u904d\u5386\u5e8f\u5217\nconst list: number[] = [];\nwhile (queue.length) {\nlet node = queue.shift() as TreeNode; // \u961f\u5217\u51fa\u961f\nlist.push(node.val); // \u4fdd\u5b58\u8282\u70b9\u503c\nif (node.left) {\nqueue.push(node.left); // \u5de6\u5b50\u8282\u70b9\u5165\u961f\n}\nif (node.right) {\nqueue.push(node.right); // \u53f3\u5b50\u8282\u70b9\u5165\u961f\n}\n}\nreturn list;\n}\n</code></pre> binary_tree_bfs.c<pre><code>/* \u5c42\u5e8f\u904d\u5386 */\nint *levelOrder(TreeNode *root, int *size) {\n/* \u8f85\u52a9\u961f\u5217 */\nint front, rear;\nint index, *arr;\nTreeNode *node;\nTreeNode **queue;\n/* \u8f85\u52a9\u961f\u5217 */\nqueue = (TreeNode **)malloc(sizeof(TreeNode *) * MAX_NODE_SIZE);\n// \u961f\u5217\u6307\u9488\nfront = 0, rear = 0;\n// \u52a0\u5165\u6839\u8282\u70b9\nqueue[rear++] = root;\n// \u521d\u59cb\u5316\u4e00\u4e2a\u5217\u8868\uff0c\u7528\u4e8e\u4fdd\u5b58\u904d\u5386\u5e8f\u5217\n/* \u8f85\u52a9\u6570\u7ec4 */\narr = (int *)malloc(sizeof(int) * MAX_NODE_SIZE);\n// \u6570\u7ec4\u6307\u9488\nindex = 0;\nwhile (front &lt; rear) {\n// \u961f\u5217\u51fa\u961f\nnode = queue[front++];\n// \u4fdd\u5b58\u8282\u70b9\u503c\narr[index++] = node-&gt;val;\nif (node-&gt;left != NULL) {\n// \u5de6\u5b50\u8282\u70b9\u5165\u961f\nqueue[rear++] = node-&gt;left;\n}\nif (node-&gt;right != NULL) {\n// \u53f3\u5b50\u8282\u70b9\u5165\u961f\nqueue[rear++] = node-&gt;right;\n}\n}\n// \u66f4\u65b0\u6570\u7ec4\u957f\u5ea6\u7684\u503c\n*size = index;\narr = realloc(arr, sizeof(int) * (*size));\n// \u91ca\u653e\u8f85\u52a9\u6570\u7ec4\u7a7a\u95f4\nfree(queue);\nreturn arr;\n}\n</code></pre> binary_tree_bfs.cs<pre><code>/* \u5c42\u5e8f\u904d\u5386 */\nList&lt;int&gt; levelOrder(TreeNode root) {\n// \u521d\u59cb\u5316\u961f\u5217\uff0c\u52a0\u5165\u6839\u8282\u70b9\nQueue&lt;TreeNode&gt; queue = new();\nqueue.Enqueue(root);\n// \u521d\u59cb\u5316\u4e00\u4e2a\u5217\u8868\uff0c\u7528\u4e8e\u4fdd\u5b58\u904d\u5386\u5e8f\u5217\nList&lt;int&gt; list = new();\nwhile (queue.Count != 0) {\nTreeNode node = queue.Dequeue(); // \u961f\u5217\u51fa\u961f\nlist.Add(node.val);              // \u4fdd\u5b58\u8282\u70b9\u503c\nif (node.left != null)\nqueue.Enqueue(node.left);    // \u5de6\u5b50\u8282\u70b9\u5165\u961f\nif (node.right != null)\nqueue.Enqueue(node.right);   // \u53f3\u5b50\u8282\u70b9\u5165\u961f\n}\nreturn list;\n}\n</code></pre> binary_tree_bfs.swift<pre><code>/* \u5c42\u5e8f\u904d\u5386 */\nfunc levelOrder(root: TreeNode) -&gt; [Int] {\n// \u521d\u59cb\u5316\u961f\u5217\uff0c\u52a0\u5165\u6839\u8282\u70b9\nvar queue: [TreeNode] = [root]\n// \u521d\u59cb\u5316\u4e00\u4e2a\u5217\u8868\uff0c\u7528\u4e8e\u4fdd\u5b58\u904d\u5386\u5e8f\u5217\nvar list: [Int] = []\nwhile !queue.isEmpty {\nlet node = queue.removeFirst() // \u961f\u5217\u51fa\u961f\nlist.append(node.val) // \u4fdd\u5b58\u8282\u70b9\u503c\nif let left = node.left {\nqueue.append(left) // \u5de6\u5b50\u8282\u70b9\u5165\u961f\n}\nif let right = node.right {\nqueue.append(right) // \u53f3\u5b50\u8282\u70b9\u5165\u961f\n}\n}\nreturn list\n}\n</code></pre> binary_tree_bfs.zig<pre><code>// \u5c42\u5e8f\u904d\u5386\nfn levelOrder(comptime T: type, mem_allocator: std.mem.Allocator, root: *inc.TreeNode(T)) !std.ArrayList(T) {\n// \u521d\u59cb\u5316\u961f\u5217\uff0c\u52a0\u5165\u6839\u8282\u70b9\nconst L = std.TailQueue(*inc.TreeNode(T));\nvar queue = L{};\nvar root_node = try mem_allocator.create(L.Node);\nroot_node.data = root;\nqueue.append(root_node); // \u521d\u59cb\u5316\u4e00\u4e2a\u5217\u8868\uff0c\u7528\u4e8e\u4fdd\u5b58\u904d\u5386\u5e8f\u5217\nvar list = std.ArrayList(T).init(std.heap.page_allocator);\nwhile (queue.len &gt; 0) {\nvar queue_node = queue.popFirst().?;    // \u961f\u5217\u51fa\u961f\nvar node = queue_node.data;\ntry list.append(node.val);              // \u4fdd\u5b58\u8282\u70b9\u503c\nif (node.left != null) {\nvar tmp_node = try mem_allocator.create(L.Node);\ntmp_node.data = node.left.?;\nqueue.append(tmp_node);             // \u5de6\u5b50\u8282\u70b9\u5165\u961f\n}\nif (node.right != null) {\nvar tmp_node = try mem_allocator.create(L.Node);\ntmp_node.data = node.right.?;\nqueue.append(tmp_node);             // \u53f3\u5b50\u8282\u70b9\u5165\u961f\n}        }\nreturn list;\n}\n</code></pre> binary_tree_bfs.dart<pre><code>/* \u5c42\u5e8f\u904d\u5386 */\nList&lt;int&gt; levelOrder(TreeNode? root) {\n// \u521d\u59cb\u5316\u961f\u5217\uff0c\u52a0\u5165\u6839\u8282\u70b9\nQueue&lt;TreeNode?&gt; queue = Queue();\nqueue.add(root);\n// \u521d\u59cb\u5316\u4e00\u4e2a\u5217\u8868\uff0c\u7528\u4e8e\u4fdd\u5b58\u904d\u5386\u5e8f\u5217\nList&lt;int&gt; res = [];\nwhile (queue.isNotEmpty) {\nTreeNode? node = queue.removeFirst(); // \u961f\u5217\u51fa\u961f\nres.add(node!.val); // \u4fdd\u5b58\u8282\u70b9\u503c\nif (node.left != null) queue.add(node.left); // \u5de6\u5b50\u8282\u70b9\u5165\u961f\nif (node.right != null) queue.add(node.right); // \u53f3\u5b50\u8282\u70b9\u5165\u961f\n}\nreturn res;\n}\n</code></pre>"},{"location":"chapter_tree/binary_tree_traversal/#_2","title":"\u590d\u6742\u5ea6\u5206\u6790","text":"<p>\u65f6\u95f4\u590d\u6742\u5ea6\uff1a\u6240\u6709\u8282\u70b9\u88ab\u8bbf\u95ee\u4e00\u6b21\uff0c\u4f7f\u7528 \\(O(n)\\) \u65f6\u95f4\uff0c\u5176\u4e2d \\(n\\) \u4e3a\u8282\u70b9\u6570\u91cf\u3002</p> <p>\u7a7a\u95f4\u590d\u6742\u5ea6\uff1a\u5728\u6700\u5dee\u60c5\u51b5\u4e0b\uff0c\u5373\u6ee1\u4e8c\u53c9\u6811\u65f6\uff0c\u904d\u5386\u5230\u6700\u5e95\u5c42\u4e4b\u524d\uff0c\u961f\u5217\u4e2d\u6700\u591a\u540c\u65f6\u5b58\u5728 \\(\\frac{n + 1}{2}\\) \u4e2a\u8282\u70b9\uff0c\u5360\u7528 \\(O(n)\\) \u7a7a\u95f4\u3002</p>"},{"location":"chapter_tree/binary_tree_traversal/#722","title":"7.2.2. \u00a0 \u524d\u5e8f\u3001\u4e2d\u5e8f\u3001\u540e\u5e8f\u904d\u5386","text":"<p>\u76f8\u5e94\u5730\uff0c\u524d\u5e8f\u3001\u4e2d\u5e8f\u548c\u540e\u5e8f\u904d\u5386\u90fd\u5c5e\u4e8e\u300c\u6df1\u5ea6\u4f18\u5148\u904d\u5386 Depth-First Traversal\u300d\uff0c\u5b83\u4f53\u73b0\u4e86\u4e00\u79cd\u201c\u5148\u8d70\u5230\u5c3d\u5934\uff0c\u518d\u56de\u6eaf\u7ee7\u7eed\u201d\u7684\u904d\u5386\u65b9\u5f0f\u3002</p> <p>\u5982\u4e0b\u56fe\u6240\u793a\uff0c\u5de6\u4fa7\u662f\u6df1\u5ea6\u4f18\u5148\u904d\u5386\u7684\u793a\u610f\u56fe\uff0c\u53f3\u4e0a\u65b9\u662f\u5bf9\u5e94\u7684\u9012\u5f52\u5b9e\u73b0\u4ee3\u7801\u3002\u6df1\u5ea6\u4f18\u5148\u904d\u5386\u5c31\u50cf\u662f\u7ed5\u7740\u6574\u4e2a\u4e8c\u53c9\u6811\u7684\u5916\u56f4\u201c\u8d70\u201d\u4e00\u5708\uff0c\u5728\u8fd9\u4e2a\u8fc7\u7a0b\u4e2d\uff0c\u5728\u6bcf\u4e2a\u8282\u70b9\u90fd\u4f1a\u9047\u5230\u4e09\u4e2a\u4f4d\u7f6e\uff0c\u5206\u522b\u5bf9\u5e94\u524d\u5e8f\u904d\u5386\u3001\u4e2d\u5e8f\u904d\u5386\u548c\u540e\u5e8f\u904d\u5386\u3002</p> <p></p> <p> Fig. \u4e8c\u53c9\u641c\u7d22\u6811\u7684\u524d\u3001\u4e2d\u3001\u540e\u5e8f\u904d\u5386 </p> \u4f4d\u7f6e \u542b\u4e49 \u6b64\u5904\u8bbf\u95ee\u8282\u70b9\u65f6\u5bf9\u5e94 \u6a59\u8272\u5706\u5708\u5904 \u521a\u8fdb\u5165\u6b64\u8282\u70b9\uff0c\u5373\u5c06\u8bbf\u95ee\u8be5\u8282\u70b9\u7684\u5de6\u5b50\u6811 \u524d\u5e8f\u904d\u5386 Pre-Order Traversal \u84dd\u8272\u5706\u5708\u5904 \u5df2\u8bbf\u95ee\u5b8c\u5de6\u5b50\u6811\uff0c\u5373\u5c06\u8bbf\u95ee\u53f3\u5b50\u6811 \u4e2d\u5e8f\u904d\u5386 In-Order Traversal \u7d2b\u8272\u5706\u5708\u5904 \u5df2\u8bbf\u95ee\u5b8c\u5de6\u5b50\u6811\u548c\u53f3\u5b50\u6811\uff0c\u5373\u5c06\u8fd4\u56de \u540e\u5e8f\u904d\u5386 Post-Order Traversal"},{"location":"chapter_tree/binary_tree_traversal/#_3","title":"\u7b97\u6cd5\u5b9e\u73b0","text":"JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart binary_tree_dfs.java<pre><code>/* \u524d\u5e8f\u904d\u5386 */\nvoid preOrder(TreeNode root) {\nif (root == null)\nreturn;\n// \u8bbf\u95ee\u4f18\u5148\u7ea7\uff1a\u6839\u8282\u70b9 -&gt; \u5de6\u5b50\u6811 -&gt; \u53f3\u5b50\u6811\nlist.add(root.val);\npreOrder(root.left);\npreOrder(root.right);\n}\n/* \u4e2d\u5e8f\u904d\u5386 */\nvoid inOrder(TreeNode root) {\nif (root == null)\nreturn;\n// \u8bbf\u95ee\u4f18\u5148\u7ea7\uff1a\u5de6\u5b50\u6811 -&gt; \u6839\u8282\u70b9 -&gt; \u53f3\u5b50\u6811\ninOrder(root.left);\nlist.add(root.val);\ninOrder(root.right);\n}\n/* \u540e\u5e8f\u904d\u5386 */\nvoid postOrder(TreeNode root) {\nif (root == null)\nreturn;\n// \u8bbf\u95ee\u4f18\u5148\u7ea7\uff1a\u5de6\u5b50\u6811 -&gt; \u53f3\u5b50\u6811 -&gt; \u6839\u8282\u70b9\npostOrder(root.left);\npostOrder(root.right);\nlist.add(root.val);\n}\n</code></pre> binary_tree_dfs.cpp<pre><code>/* \u524d\u5e8f\u904d\u5386 */\nvoid preOrder(TreeNode *root) {\nif (root == nullptr)\nreturn;\n// \u8bbf\u95ee\u4f18\u5148\u7ea7\uff1a\u6839\u8282\u70b9 -&gt; \u5de6\u5b50\u6811 -&gt; \u53f3\u5b50\u6811\nvec.push_back(root-&gt;val);\npreOrder(root-&gt;left);\npreOrder(root-&gt;right);\n}\n/* \u4e2d\u5e8f\u904d\u5386 */\nvoid inOrder(TreeNode *root) {\nif (root == nullptr)\nreturn;\n// \u8bbf\u95ee\u4f18\u5148\u7ea7\uff1a\u5de6\u5b50\u6811 -&gt; \u6839\u8282\u70b9 -&gt; \u53f3\u5b50\u6811\ninOrder(root-&gt;left);\nvec.push_back(root-&gt;val);\ninOrder(root-&gt;right);\n}\n/* \u540e\u5e8f\u904d\u5386 */\nvoid postOrder(TreeNode *root) {\nif (root == nullptr)\nreturn;\n// \u8bbf\u95ee\u4f18\u5148\u7ea7\uff1a\u5de6\u5b50\u6811 -&gt; \u53f3\u5b50\u6811 -&gt; \u6839\u8282\u70b9\npostOrder(root-&gt;left);\npostOrder(root-&gt;right);\nvec.push_back(root-&gt;val);\n}\n</code></pre> binary_tree_dfs.py<pre><code>def pre_order(root: TreeNode | None) -&gt; None:\n\"\"\"\u524d\u5e8f\u904d\u5386\"\"\"\nif root is None:\nreturn\n# \u8bbf\u95ee\u4f18\u5148\u7ea7\uff1a\u6839\u8282\u70b9 -&gt; \u5de6\u5b50\u6811 -&gt; \u53f3\u5b50\u6811\nres.append(root.val)\npre_order(root=root.left)\npre_order(root=root.right)\ndef in_order(root: TreeNode | None) -&gt; None:\n\"\"\"\u4e2d\u5e8f\u904d\u5386\"\"\"\nif root is None:\nreturn\n# \u8bbf\u95ee\u4f18\u5148\u7ea7\uff1a\u5de6\u5b50\u6811 -&gt; \u6839\u8282\u70b9 -&gt; \u53f3\u5b50\u6811\nin_order(root=root.left)\nres.append(root.val)\nin_order(root=root.right)\ndef post_order(root: TreeNode | None) -&gt; None:\n\"\"\"\u540e\u5e8f\u904d\u5386\"\"\"\nif root is None:\nreturn\n# \u8bbf\u95ee\u4f18\u5148\u7ea7\uff1a\u5de6\u5b50\u6811 -&gt; \u53f3\u5b50\u6811 -&gt; \u6839\u8282\u70b9\npost_order(root=root.left)\npost_order(root=root.right)\nres.append(root.val)\n</code></pre> binary_tree_dfs.go<pre><code>/* \u524d\u5e8f\u904d\u5386 */\nfunc preOrder(node *TreeNode) {\nif node == nil {\nreturn\n}\n// \u8bbf\u95ee\u4f18\u5148\u7ea7\uff1a\u6839\u8282\u70b9 -&gt; \u5de6\u5b50\u6811 -&gt; \u53f3\u5b50\u6811\nnums = append(nums, node.Val)\npreOrder(node.Left)\npreOrder(node.Right)\n}\n/* \u4e2d\u5e8f\u904d\u5386 */\nfunc inOrder(node *TreeNode) {\nif node == nil {\nreturn\n}\n// \u8bbf\u95ee\u4f18\u5148\u7ea7\uff1a\u5de6\u5b50\u6811 -&gt; \u6839\u8282\u70b9 -&gt; \u53f3\u5b50\u6811\ninOrder(node.Left)\nnums = append(nums, node.Val)\ninOrder(node.Right)\n}\n/* \u540e\u5e8f\u904d\u5386 */\nfunc postOrder(node *TreeNode) {\nif node == nil {\nreturn\n}\n// \u8bbf\u95ee\u4f18\u5148\u7ea7\uff1a\u5de6\u5b50\u6811 -&gt; \u53f3\u5b50\u6811 -&gt; \u6839\u8282\u70b9\npostOrder(node.Left)\npostOrder(node.Right)\nnums = append(nums, node.Val)\n}\n</code></pre> binary_tree_dfs.js<pre><code>/* \u524d\u5e8f\u904d\u5386 */\nfunction preOrder(root) {\nif (root === null) return;\n// \u8bbf\u95ee\u4f18\u5148\u7ea7\uff1a\u6839\u8282\u70b9 -&gt; \u5de6\u5b50\u6811 -&gt; \u53f3\u5b50\u6811\nlist.push(root.val);\npreOrder(root.left);\npreOrder(root.right);\n}\n/* \u4e2d\u5e8f\u904d\u5386 */\nfunction inOrder(root) {\nif (root === null) return;\n// \u8bbf\u95ee\u4f18\u5148\u7ea7\uff1a\u5de6\u5b50\u6811 -&gt; \u6839\u8282\u70b9 -&gt; \u53f3\u5b50\u6811\ninOrder(root.left);\nlist.push(root.val);\ninOrder(root.right);\n}\n/* \u540e\u5e8f\u904d\u5386 */\nfunction postOrder(root) {\nif (root === null) return;\n// \u8bbf\u95ee\u4f18\u5148\u7ea7\uff1a\u5de6\u5b50\u6811 -&gt; \u53f3\u5b50\u6811 -&gt; \u6839\u8282\u70b9\npostOrder(root.left);\npostOrder(root.right);\nlist.push(root.val);\n}\n</code></pre> binary_tree_dfs.ts<pre><code>/* \u524d\u5e8f\u904d\u5386 */\nfunction preOrder(root: TreeNode | null): void {\nif (root === null) {\nreturn;\n}\n// \u8bbf\u95ee\u4f18\u5148\u7ea7\uff1a\u6839\u8282\u70b9 -&gt; \u5de6\u5b50\u6811 -&gt; \u53f3\u5b50\u6811\nlist.push(root.val);\npreOrder(root.left);\npreOrder(root.right);\n}\n/* \u4e2d\u5e8f\u904d\u5386 */\nfunction inOrder(root: TreeNode | null): void {\nif (root === null) {\nreturn;\n}\n// \u8bbf\u95ee\u4f18\u5148\u7ea7\uff1a\u5de6\u5b50\u6811 -&gt; \u6839\u8282\u70b9 -&gt; \u53f3\u5b50\u6811\ninOrder(root.left);\nlist.push(root.val);\ninOrder(root.right);\n}\n/* \u540e\u5e8f\u904d\u5386 */\nfunction postOrder(root: TreeNode | null): void {\nif (root === null) {\nreturn;\n}\n// \u8bbf\u95ee\u4f18\u5148\u7ea7\uff1a\u5de6\u5b50\u6811 -&gt; \u53f3\u5b50\u6811 -&gt; \u6839\u8282\u70b9\npostOrder(root.left);\npostOrder(root.right);\nlist.push(root.val);\n}\n</code></pre> binary_tree_dfs.c<pre><code>/* \u524d\u5e8f\u904d\u5386 */\nvoid preOrder(TreeNode *root, int *size) {\nif (root == NULL)\nreturn;\n// \u8bbf\u95ee\u4f18\u5148\u7ea7\uff1a\u6839\u8282\u70b9 -&gt; \u5de6\u5b50\u6811 -&gt; \u53f3\u5b50\u6811\narr[(*size)++] = root-&gt;val;\npreOrder(root-&gt;left, size);\npreOrder(root-&gt;right, size);\n}\n/* \u4e2d\u5e8f\u904d\u5386 */\nvoid inOrder(TreeNode *root, int *size) {\nif (root == NULL)\nreturn;\n// \u8bbf\u95ee\u4f18\u5148\u7ea7\uff1a\u5de6\u5b50\u6811 -&gt; \u6839\u8282\u70b9 -&gt; \u53f3\u5b50\u6811\ninOrder(root-&gt;left, size);\narr[(*size)++] = root-&gt;val;\ninOrder(root-&gt;right, size);\n}\n/* \u540e\u5e8f\u904d\u5386 */\nvoid postOrder(TreeNode *root, int *size) {\nif (root == NULL)\nreturn;\n// \u8bbf\u95ee\u4f18\u5148\u7ea7\uff1a\u5de6\u5b50\u6811 -&gt; \u53f3\u5b50\u6811 -&gt; \u6839\u8282\u70b9\npostOrder(root-&gt;left, size);\npostOrder(root-&gt;right, size);\narr[(*size)++] = root-&gt;val;\n}\n</code></pre> binary_tree_dfs.cs<pre><code>/* \u524d\u5e8f\u904d\u5386 */\nvoid preOrder(TreeNode? root) {\nif (root == null) return;\n// \u8bbf\u95ee\u4f18\u5148\u7ea7\uff1a\u6839\u8282\u70b9 -&gt; \u5de6\u5b50\u6811 -&gt; \u53f3\u5b50\u6811\nlist.Add(root.val);\npreOrder(root.left);\npreOrder(root.right);\n}\n/* \u4e2d\u5e8f\u904d\u5386 */\nvoid inOrder(TreeNode? root) {\nif (root == null) return;\n// \u8bbf\u95ee\u4f18\u5148\u7ea7\uff1a\u5de6\u5b50\u6811 -&gt; \u6839\u8282\u70b9 -&gt; \u53f3\u5b50\u6811\ninOrder(root.left);\nlist.Add(root.val);\ninOrder(root.right);\n}\n/* \u540e\u5e8f\u904d\u5386 */\nvoid postOrder(TreeNode? root) {\nif (root == null) return;\n// \u8bbf\u95ee\u4f18\u5148\u7ea7\uff1a\u5de6\u5b50\u6811 -&gt; \u53f3\u5b50\u6811 -&gt; \u6839\u8282\u70b9\npostOrder(root.left);\npostOrder(root.right);\nlist.Add(root.val);\n}\n</code></pre> binary_tree_dfs.swift<pre><code>/* \u524d\u5e8f\u904d\u5386 */\nfunc preOrder(root: TreeNode?) {\nguard let root = root else {\nreturn\n}\n// \u8bbf\u95ee\u4f18\u5148\u7ea7\uff1a\u6839\u8282\u70b9 -&gt; \u5de6\u5b50\u6811 -&gt; \u53f3\u5b50\u6811\nlist.append(root.val)\npreOrder(root: root.left)\npreOrder(root: root.right)\n}\n/* \u4e2d\u5e8f\u904d\u5386 */\nfunc inOrder(root: TreeNode?) {\nguard let root = root else {\nreturn\n}\n// \u8bbf\u95ee\u4f18\u5148\u7ea7\uff1a\u5de6\u5b50\u6811 -&gt; \u6839\u8282\u70b9 -&gt; \u53f3\u5b50\u6811\ninOrder(root: root.left)\nlist.append(root.val)\ninOrder(root: root.right)\n}\n/* \u540e\u5e8f\u904d\u5386 */\nfunc postOrder(root: TreeNode?) {\nguard let root = root else {\nreturn\n}\n// \u8bbf\u95ee\u4f18\u5148\u7ea7\uff1a\u5de6\u5b50\u6811 -&gt; \u53f3\u5b50\u6811 -&gt; \u6839\u8282\u70b9\npostOrder(root: root.left)\npostOrder(root: root.right)\nlist.append(root.val)\n}\n</code></pre> binary_tree_dfs.zig<pre><code>// \u524d\u5e8f\u904d\u5386\nfn preOrder(comptime T: type, root: ?*inc.TreeNode(T)) !void {\nif (root == null) return;\n// \u8bbf\u95ee\u4f18\u5148\u7ea7\uff1a\u6839\u8282\u70b9 -&gt; \u5de6\u5b50\u6811 -&gt; \u53f3\u5b50\u6811\ntry list.append(root.?.val);\ntry preOrder(T, root.?.left);\ntry preOrder(T, root.?.right);\n}\n// \u4e2d\u5e8f\u904d\u5386\nfn inOrder(comptime T: type, root: ?*inc.TreeNode(T)) !void {\nif (root == null) return;\n// \u8bbf\u95ee\u4f18\u5148\u7ea7\uff1a\u5de6\u5b50\u6811 -&gt; \u6839\u8282\u70b9 -&gt; \u53f3\u5b50\u6811\ntry inOrder(T, root.?.left);\ntry list.append(root.?.val);\ntry inOrder(T, root.?.right);\n}\n// \u540e\u5e8f\u904d\u5386\nfn postOrder(comptime T: type, root: ?*inc.TreeNode(T)) !void {\nif (root == null) return;\n// \u8bbf\u95ee\u4f18\u5148\u7ea7\uff1a\u5de6\u5b50\u6811 -&gt; \u53f3\u5b50\u6811 -&gt; \u6839\u8282\u70b9\ntry postOrder(T, root.?.left);\ntry postOrder(T, root.?.right);\ntry list.append(root.?.val);\n}\n</code></pre> binary_tree_dfs.dart<pre><code>/* \u524d\u5e8f\u904d\u5386 */\nvoid preOrder(TreeNode? node) {\nif (node == null) return;\n// \u8bbf\u95ee\u4f18\u5148\u7ea7\uff1a\u6839\u8282\u70b9 -&gt; \u5de6\u5b50\u6811 -&gt; \u53f3\u5b50\u6811\nlist.add(node.val);\npreOrder(node.left);\npreOrder(node.right);\n}\n/* \u4e2d\u5e8f\u904d\u5386 */\nvoid inOrder(TreeNode? node) {\nif (node == null) return;\n// \u8bbf\u95ee\u4f18\u5148\u7ea7\uff1a\u5de6\u5b50\u6811 -&gt; \u6839\u8282\u70b9 -&gt; \u53f3\u5b50\u6811\ninOrder(node.left);\nlist.add(node.val);\ninOrder(node.right);\n}\n/* \u540e\u5e8f\u904d\u5386 */\nvoid postOrder(TreeNode? node) {\nif (node == null) return;\n// \u8bbf\u95ee\u4f18\u5148\u7ea7\uff1a\u5de6\u5b50\u6811 -&gt; \u53f3\u5b50\u6811 -&gt; \u6839\u8282\u70b9\npostOrder(node.left);\npostOrder(node.right);\nlist.add(node.val);\n}\n</code></pre> <p>Note</p> <p>\u6211\u4eec\u4e5f\u53ef\u4ee5\u4ec5\u57fa\u4e8e\u5faa\u73af\u5b9e\u73b0\u524d\u3001\u4e2d\u3001\u540e\u5e8f\u904d\u5386\uff0c\u6709\u5174\u8da3\u7684\u540c\u5b66\u53ef\u4ee5\u81ea\u884c\u5b9e\u73b0\u3002</p> <p>\u9012\u5f52\u8fc7\u7a0b\u53ef\u5206\u4e3a\u201c\u9012\u201d\u548c\u201c\u5f52\u201d\u4e24\u4e2a\u76f8\u53cd\u7684\u90e8\u5206\u3002\u201c\u9012\u201d\u8868\u793a\u5f00\u542f\u65b0\u65b9\u6cd5\uff0c\u7a0b\u5e8f\u5728\u6b64\u8fc7\u7a0b\u4e2d\u8bbf\u95ee\u4e0b\u4e00\u4e2a\u8282\u70b9\uff1b\u201c\u5f52\u201d\u8868\u793a\u51fd\u6570\u8fd4\u56de\uff0c\u4ee3\u8868\u8be5\u8282\u70b9\u5df2\u7ecf\u8bbf\u95ee\u5b8c\u6bd5\u3002\u5982\u4e0b\u56fe\u6240\u793a\uff0c\u4e3a\u524d\u5e8f\u904d\u5386\u4e8c\u53c9\u6811\u7684\u9012\u5f52\u8fc7\u7a0b\u3002</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt;&lt;11&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p>"},{"location":"chapter_tree/binary_tree_traversal/#_4","title":"\u590d\u6742\u5ea6\u5206\u6790","text":"<p>\u65f6\u95f4\u590d\u6742\u5ea6\uff1a\u6240\u6709\u8282\u70b9\u88ab\u8bbf\u95ee\u4e00\u6b21\uff0c\u4f7f\u7528 \\(O(n)\\) \u65f6\u95f4\uff0c\u5176\u4e2d \\(n\\) \u4e3a\u8282\u70b9\u6570\u91cf\u3002</p> <p>\u7a7a\u95f4\u590d\u6742\u5ea6\uff1a\u5728\u6700\u5dee\u60c5\u51b5\u4e0b\uff0c\u5373\u6811\u9000\u5316\u4e3a\u94fe\u8868\u65f6\uff0c\u9012\u5f52\u6df1\u5ea6\u8fbe\u5230 \\(n\\) \uff0c\u7cfb\u7edf\u5360\u7528 \\(O(n)\\) \u6808\u5e27\u7a7a\u95f4\u3002</p>"},{"location":"chapter_tree/summary/","title":"7.6. \u00a0 \u5c0f\u7ed3","text":"<ul> <li>\u4e8c\u53c9\u6811\u662f\u4e00\u79cd\u975e\u7ebf\u6027\u6570\u636e\u7ed3\u6784\uff0c\u4f53\u73b0\u201c\u4e00\u5206\u4e3a\u4e8c\u201d\u7684\u5206\u6cbb\u903b\u8f91\u3002\u6bcf\u4e2a\u4e8c\u53c9\u6811\u8282\u70b9\u5305\u542b\u4e00\u4e2a\u503c\u4ee5\u53ca\u4e24\u4e2a\u6307\u9488\uff0c\u5206\u522b\u6307\u5411\u5176\u5de6\u5b50\u8282\u70b9\u548c\u53f3\u5b50\u8282\u70b9\u3002</li> <li>\u5bf9\u4e8e\u4e8c\u53c9\u6811\u4e2d\u7684\u67d0\u4e2a\u8282\u70b9\uff0c\u5176\u5de6\uff08\u53f3\uff09\u5b50\u8282\u70b9\u53ca\u5176\u4ee5\u4e0b\u5f62\u6210\u7684\u6811\u88ab\u79f0\u4e3a\u8be5\u8282\u70b9\u7684\u5de6\uff08\u53f3\uff09\u5b50\u6811\u3002</li> <li>\u4e8c\u53c9\u6811\u7684\u76f8\u5173\u672f\u8bed\u5305\u62ec\u6839\u8282\u70b9\u3001\u53f6\u8282\u70b9\u3001\u5c42\u3001\u5ea6\u3001\u8fb9\u3001\u9ad8\u5ea6\u548c\u6df1\u5ea6\u7b49\u3002</li> <li>\u4e8c\u53c9\u6811\u7684\u521d\u59cb\u5316\u3001\u8282\u70b9\u63d2\u5165\u548c\u8282\u70b9\u5220\u9664\u64cd\u4f5c\u4e0e\u94fe\u8868\u64cd\u4f5c\u65b9\u6cd5\u7c7b\u4f3c\u3002</li> <li>\u5e38\u89c1\u7684\u4e8c\u53c9\u6811\u7c7b\u578b\u6709\u5b8c\u7f8e\u4e8c\u53c9\u6811\u3001\u5b8c\u5168\u4e8c\u53c9\u6811\u3001\u6ee1\u4e8c\u53c9\u6811\u548c\u5e73\u8861\u4e8c\u53c9\u6811\u3002\u5b8c\u7f8e\u4e8c\u53c9\u6811\u662f\u6700\u7406\u60f3\u7684\u72b6\u6001\uff0c\u800c\u94fe\u8868\u662f\u9000\u5316\u540e\u7684\u6700\u5dee\u72b6\u6001\u3002</li> <li>\u4e8c\u53c9\u6811\u53ef\u4ee5\u7528\u6570\u7ec4\u8868\u793a\uff0c\u65b9\u6cd5\u662f\u5c06\u8282\u70b9\u503c\u548c\u7a7a\u4f4d\u6309\u5c42\u5e8f\u904d\u5386\u987a\u5e8f\u6392\u5217\uff0c\u5e76\u6839\u636e\u7236\u8282\u70b9\u4e0e\u5b50\u8282\u70b9\u4e4b\u95f4\u7684\u7d22\u5f15\u6620\u5c04\u5173\u7cfb\u6765\u5b9e\u73b0\u6307\u9488\u3002</li> <li>\u4e8c\u53c9\u6811\u7684\u5c42\u5e8f\u904d\u5386\u662f\u4e00\u79cd\u5e7f\u5ea6\u4f18\u5148\u641c\u7d22\u65b9\u6cd5\uff0c\u5b83\u4f53\u73b0\u4e86\u201c\u4e00\u5708\u4e00\u5708\u5411\u5916\u201d\u7684\u5206\u5c42\u904d\u5386\u65b9\u5f0f\uff0c\u901a\u5e38\u901a\u8fc7\u961f\u5217\u6765\u5b9e\u73b0\u3002</li> <li>\u524d\u5e8f\u3001\u4e2d\u5e8f\u3001\u540e\u5e8f\u904d\u5386\u7686\u5c5e\u4e8e\u6df1\u5ea6\u4f18\u5148\u641c\u7d22\uff0c\u5b83\u4eec\u4f53\u73b0\u4e86\u201c\u8d70\u5230\u5c3d\u5934\uff0c\u518d\u56de\u5934\u7ee7\u7eed\u201d\u7684\u56de\u6eaf\u904d\u5386\u65b9\u5f0f\uff0c\u901a\u5e38\u4f7f\u7528\u9012\u5f52\u6765\u5b9e\u73b0\u3002</li> <li>\u4e8c\u53c9\u641c\u7d22\u6811\u662f\u4e00\u79cd\u9ad8\u6548\u7684\u5143\u7d20\u67e5\u627e\u6570\u636e\u7ed3\u6784\uff0c\u5176\u67e5\u627e\u3001\u63d2\u5165\u548c\u5220\u9664\u64cd\u4f5c\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u5747\u4e3a \\(O(\\log n)\\) \u3002\u5f53\u4e8c\u53c9\u641c\u7d22\u6811\u9000\u5316\u4e3a\u94fe\u8868\u65f6\uff0c\u5404\u9879\u65f6\u95f4\u590d\u6742\u5ea6\u4f1a\u52a3\u5316\u81f3 \\(O(n)\\) \u3002</li> <li>AVL \u6811\uff0c\u4e5f\u79f0\u4e3a\u5e73\u8861\u4e8c\u53c9\u641c\u7d22\u6811\uff0c\u5b83\u901a\u8fc7\u65cb\u8f6c\u64cd\u4f5c\uff0c\u786e\u4fdd\u5728\u4e0d\u65ad\u63d2\u5165\u548c\u5220\u9664\u8282\u70b9\u540e\uff0c\u6811\u4ecd\u7136\u4fdd\u6301\u5e73\u8861\u3002</li> <li>AVL \u6811\u7684\u65cb\u8f6c\u64cd\u4f5c\u5305\u62ec\u53f3\u65cb\u3001\u5de6\u65cb\u3001\u5148\u53f3\u65cb\u518d\u5de6\u65cb\u3001\u5148\u5de6\u65cb\u518d\u53f3\u65cb\u3002\u5728\u63d2\u5165\u6216\u5220\u9664\u8282\u70b9\u540e\uff0cAVL \u6811\u4f1a\u4ece\u5e95\u5411\u9876\u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u6811\u91cd\u65b0\u6062\u590d\u5e73\u8861\u3002</li> </ul>"}]}
\ No newline at end of file
+{"config":{"lang":["ja"],"separator":"[\\s\\-\uff0c\u3002]+","pipeline":["stemmer"]},"docs":[{"location":"","title":"Home","text":"<p>  \u300a Hello \u7b97\u6cd5 \u300b  <p> \u52a8\u753b\u56fe\u89e3\u3001\u80fd\u8fd0\u884c\u3001\u53ef\u63d0\u95ee\u7684\u6570\u636e\u7ed3\u6784\u4e0e\u7b97\u6cd5\u5feb\u901f\u5165\u95e8\u6559\u7a0b </p> <p> </p> @Krahets </p>  \u63a8\u8350\u8bed  <p>Quote</p> <p>\u201c\u4e00\u672c\u901a\u4fd7\u6613\u61c2\u7684\u6570\u636e\u7ed3\u6784\u4e0e\u7b97\u6cd5\u5165\u95e8\u4e66\uff0c\u5f15\u5bfc\u8bfb\u8005\u624b\u8111\u5e76\u7528\u5730\u5b66\u4e60\uff0c\u5f3a\u70c8\u63a8\u8350\u7b97\u6cd5\u521d\u5b66\u8005\u9605\u8bfb\u3002\u201d</p> <p>\u2014\u2014 \u9093\u4fca\u8f89\uff0c\u6e05\u534e\u5927\u5b66\u8ba1\u7b97\u673a\u7cfb\u6559\u6388</p> <p>Quote</p> <p>\u201c\u5982\u679c\u6211\u5f53\u5e74\u5b66\u6570\u636e\u7ed3\u6784\u4e0e\u7b97\u6cd5\u7684\u65f6\u5019\u6709\u300aHello \u7b97\u6cd5\u300b\uff0c\u5b66\u8d77\u6765\u5e94\u8be5\u4f1a\u7b80\u5355 10 \u500d\uff01\u201d</p> <p>\u2014\u2014 \u674e\u6c90\uff0c\u4e9a\u9a6c\u900a\u8d44\u6df1\u9996\u5e2d\u79d1\u5b66\u5bb6</p>  \u300c\u5168\u4e66\u52a8\u753b\u56fe\u89e3\u300d  <p> \u5185\u5bb9\u6e05\u6670\u6613\u61c2\u3001\u5b66\u4e60\u66f2\u7ebf\u5e73\u6ed1\u7535\u8111\u3001\u5e73\u677f\u3001\u624b\u673a\u5168\u7ec8\u7aef\u9605\u8bfb </p> <p></p> <p><p> \"A picture is worth a thousand words.\" </p> <p> \u201c\u4e00\u56fe\u80dc\u5343\u8a00\u201d </p></p>  \u300c\u4ee3\u7801\u4e00\u952e\u8fd0\u884c\u300d  <p> \u63d0\u4f9b\u5404\u4e2a\u7b97\u6cd5\u4e0e\u6570\u636e\u7ed3\u6784\u7684\u7b80\u6d01\u5b9e\u73b0\u4e0e\u6d4b\u8bd5\u6837\u4f8b\uff0c\u7686\u53ef\u76f4\u63a5\u8fd0\u884c\u652f\u6301 Java, C++, Python, Go, JS, TS, C#, Swift, Zig \u7b49\u8bed\u8a00 </p> <p></p> <p><p> \"Talk is cheap. Show me the code.\" </p> <p> \u201c\u5c11\u5439\u725b\uff0c\u770b\u4ee3\u7801\u201d </p></p>  \u300c\u53ef\u8ba8\u8bba\u4e0e\u63d0\u95ee\u300d  <p> \u9f13\u52b1\u5c0f\u4f19\u4f34\u4eec\u4e92\u5e2e\u4e92\u52a9\u3001\u5171\u540c\u6210\u957f\u63d0\u95ee\u4e0e\u8bc4\u8bba\u4e00\u822c\u80fd\u5728\u4e24\u65e5\u5185\u5f97\u5230\u56de\u590d </p> <p></p> <p><p> \u201c\u8ffd\u98ce\u8d76\u6708\u83ab\u505c\u7559\uff0c\u5e73\u829c\u5c3d\u5904\u662f\u6625\u5c71\u201d </p> <p> \u4e00\u8d77\u52a0\u6cb9\uff01 </p></p>  \u5e8f  <p>\u4e24\u5e74\u524d\uff0c\u6211\u5728\u529b\u6263\u4e0a\u5206\u4eab\u4e86\u300a\u5251\u6307 Offer\u300b\u7cfb\u5217\u9898\u89e3\uff0c\u53d7\u5230\u4e86\u8bb8\u591a\u670b\u53cb\u7684\u559c\u7231\u4e0e\u652f\u6301\u3002\u5728\u6b64\u671f\u95f4\uff0c\u6211\u56de\u7b54\u4e86\u4f17\u591a\u8bfb\u8005\u7684\u8bc4\u8bba\u95ee\u9898\uff0c\u5176\u4e2d\u6700\u5e38\u89c1\u7684\u4e00\u4e2a\u95ee\u9898\u662f\u201c\u5982\u4f55\u5165\u95e8\u5b66\u4e60\u7b97\u6cd5\u201d\u3002\u6211\u9010\u6e10\u4e5f\u5bf9\u8fd9\u4e2a\u95ee\u9898\u4ea7\u751f\u4e86\u6d53\u539a\u7684\u5174\u8da3\u3002</p> <p>\u4e24\u773c\u4e00\u62b9\u9ed1\u5730\u5237\u9898\u4f3c\u4e4e\u662f\u6700\u53d7\u6b22\u8fce\u7684\u65b9\u6cd5\uff0c\u7b80\u5355\u76f4\u63a5\u4e14\u6709\u6548\u3002\u7136\u800c\uff0c\u5237\u9898\u5c31\u5982\u540c\u73a9\u201c\u626b\u96f7\u201d\u6e38\u620f\uff0c\u81ea\u5b66\u80fd\u529b\u5f3a\u7684\u540c\u5b66\u80fd\u591f\u987a\u5229\u5730\u5c06\u5730\u96f7\u9010\u4e2a\u6392\u6389\uff0c\u800c\u57fa\u7840\u4e0d\u8db3\u7684\u540c\u5b66\u5f88\u53ef\u80fd\u88ab\u70b8\u7684\u6ee1\u5934\u662f\u5305\uff0c\u5e76\u5728\u632b\u6298\u4e2d\u6b65\u6b65\u9000\u7f29\u3002\u901a\u8bfb\u6559\u6750\u4e66\u7c4d\u4e5f\u662f\u4e00\u79cd\u5e38\u89c1\u505a\u6cd5\uff0c\u4f46\u5bf9\u4e8e\u9762\u5411\u6c42\u804c\u7684\u540c\u5b66\u6765\u8bf4\uff0c\u6bd5\u4e1a\u5b63\u3001\u6295\u9012\u7b80\u5386\u3001\u51c6\u5907\u7b14\u8bd5\u9762\u8bd5\u5df2\u7ecf\u5360\u636e\u4e86\u5927\u90e8\u5206\u7cbe\u529b\uff0c\u539a\u91cd\u7684\u4e66\u7c4d\u5f80\u5f80\u53d8\u6210\u4e86\u4e00\u9879\u8270\u5de8\u7684\u6311\u6218\u3002</p> <p>\u5982\u679c\u4f60\u4e5f\u9762\u4e34\u7c7b\u4f3c\u7684\u56f0\u6270\uff0c\u90a3\u4e48\u5f88\u5e78\u8fd0\u8fd9\u672c\u4e66\u627e\u5230\u4e86\u4f60\u3002\u672c\u4e66\u662f\u6211\u5bf9\u6b64\u95ee\u9898\u7684\u7ed9\u51fa\u7684\u7b54\u6848\uff0c\u867d\u7136\u4e0d\u4e00\u5b9a\u6b63\u786e\uff0c\u4f46\u81f3\u5c11\u662f\u4e00\u6b21\u79ef\u6781\u7684\u5c1d\u8bd5\u3002\u8fd9\u672c\u4e66\u867d\u7136\u4e0d\u8db3\u4ee5\u8ba9\u4f60\u76f4\u63a5\u62ff\u5230 Offer \uff0c\u4f46\u4f1a\u5f15\u5bfc\u4f60\u63a2\u7d22\u6570\u636e\u7ed3\u6784\u4e0e\u7b97\u6cd5\u7684\u201c\u77e5\u8bc6\u5730\u56fe\u201d\uff0c\u5e26\u4f60\u4e86\u89e3\u4e0d\u540c\u201c\u5730\u96f7\u201d\u7684\u5f62\u72b6\u5927\u5c0f\u548c\u5206\u5e03\u4f4d\u7f6e\uff0c\u8ba9\u4f60\u638c\u63e1\u5404\u79cd\u201c\u6392\u96f7\u65b9\u6cd5\u201d\u3002\u6709\u4e86\u8fd9\u4e9b\u672c\u9886\uff0c\u76f8\u4fe1\u4f60\u53ef\u4ee5\u66f4\u52a0\u81ea\u5982\u5730\u5e94\u5bf9\u5237\u9898\u548c\u9605\u8bfb\u6587\u732e\uff0c\u9010\u6b65\u6784\u5efa\u8d77\u5b8c\u6574\u7684\u77e5\u8bc6\u4f53\u7cfb\u3002</p>  \u4f5c\u8005\u7b80\u4ecb  <p>\u9773\u5b87\u680b (Krahets)\uff0c\u5927\u5382\u9ad8\u7ea7\u7b97\u6cd5\u5de5\u7a0b\u5e08\uff0c\u4e0a\u6d77\u4ea4\u901a\u5927\u5b66\u7855\u58eb\u3002\u529b\u6263\uff08LeetCode\uff09\u5168\u7f51\u9605\u8bfb\u91cf\u6700\u9ad8\u535a\u4e3b\uff0c\u5176 LeetBook\u300a\u56fe\u89e3\u7b97\u6cd5\u6570\u636e\u7ed3\u6784\u300b\u5df2\u88ab\u8ba2\u9605 24 \u4e07\u672c\u3002</p>  \u81f4\u8c22  <p>\u672c\u4e66\u5728\u5f00\u6e90\u793e\u533a\u4f17\u591a\u8d21\u732e\u8005\u7684\u5171\u540c\u52aa\u529b\u4e0b\u4e0d\u65ad\u6210\u957f\u3002\u611f\u8c22\u6bcf\u4e00\u4f4d\u6295\u5165\u65f6\u95f4\u4e0e\u7cbe\u529b\u7684\u64b0\u7a3f\u4eba\uff0c\u662f\u4ed6\u4eec\u65e0\u79c1\u5949\u732e\u4f7f\u8fd9\u672c\u4e66\u8d8a\u53d8\u8d8a\u597d\uff0c\u4ed6\u4eec\u662f\uff08\u6309\u7167 GitHub \u81ea\u52a8\u751f\u6210\u7684\u987a\u5e8f\u6392\u5217\uff09\uff1a</p> <p> </p> <p>\u672c\u4e66\u7684\u4ee3\u7801\u5ba1\u9605\u5de5\u4f5c\u7531 Gonglja, gvenusleo, justin\u2010tse, krahets, nuomi1, Reanon, sjinzh \u5b8c\u6210\uff08\u6309\u7167\u9996\u5b57\u6bcd\u987a\u5e8f\u6392\u5217\uff09\u3002\u611f\u8c22\u4ed6\u4eec\u4ed8\u51fa\u7684\u65f6\u95f4\u4e0e\u7cbe\u529b\uff0c\u6b63\u662f\u4ed6\u4eec\u786e\u4fdd\u4e86\u5404\u8bed\u8a00\u4ee3\u7801\u7684\u89c4\u8303\u4e0e\u7edf\u4e00\u3002</p> GongljaC / C++ gvenusleoDart justin-tseJS / TS krahetsJava / Python nuomi1Swift ReanonGo / C sjinzhRust / Zig"},{"location":"chapter_appendix/contribution/","title":"13.2. \u00a0 \u4e00\u8d77\u53c2\u4e0e\u521b\u4f5c","text":"<p>\u5f00\u6e90\u7684\u9b45\u529b</p> <p>\u7eb8\u8d28\u4e66\u7c4d\u7684\u4e24\u6b21\u5370\u5237\u7684\u95f4\u9694\u65f6\u95f4\u5f80\u5f80\u9700\u8981\u6570\u5e74\uff0c\u5185\u5bb9\u66f4\u65b0\u975e\u5e38\u4e0d\u65b9\u4fbf\u3002\u4f46\u5728\u672c\u5f00\u6e90\u4e66\u4e2d\uff0c\u5185\u5bb9\u66f4\u8fed\u7684\u65f6\u95f4\u88ab\u7f29\u77ed\u81f3\u6570\u65e5\u751a\u81f3\u51e0\u4e2a\u5c0f\u65f6\u3002</p> <p>\u7531\u4e8e\u4f5c\u8005\u80fd\u529b\u6709\u9650\uff0c\u4e66\u4e2d\u96be\u514d\u5b58\u5728\u4e00\u4e9b\u9057\u6f0f\u548c\u9519\u8bef\uff0c\u8bf7\u60a8\u8c05\u89e3\u3002\u5982\u679c\u60a8\u53d1\u73b0\u4e86\u7b14\u8bef\u3001\u5931\u6548\u94fe\u63a5\u3001\u5185\u5bb9\u7f3a\u5931\u3001\u6587\u5b57\u6b67\u4e49\u3001\u89e3\u91ca\u4e0d\u6e05\u6670\u6216\u884c\u6587\u7ed3\u6784\u4e0d\u5408\u7406\u7b49\u95ee\u9898\uff0c\u8bf7\u534f\u52a9\u6211\u4eec\u8fdb\u884c\u4fee\u6b63\uff0c\u4ee5\u5e2e\u52a9\u5176\u4ed6\u8bfb\u8005\u83b7\u5f97\u66f4\u4f18\u8d28\u7684\u5b66\u4e60\u8d44\u6e90\u3002\u6240\u6709\u64b0\u7a3f\u4eba\u5c06\u5728\u4ed3\u5e93\u548c\u7f51\u7ad9\u4e3b\u9875\u4e0a\u5c55\u793a\uff0c\u4ee5\u611f\u8c22\u4ed6\u4eec\u5bf9\u5f00\u6e90\u793e\u533a\u7684\u65e0\u79c1\u5949\u732e\uff01</p>"},{"location":"chapter_appendix/contribution/#1321","title":"13.2.1. \u00a0 \u5185\u5bb9\u5fae\u8c03","text":"<p>\u5728\u6bcf\u4e2a\u9875\u9762\u7684\u53f3\u4e0a\u89d2\u6709\u4e00\u4e2a\u300c\u7f16\u8f91\u300d\u56fe\u6807\uff0c\u60a8\u53ef\u4ee5\u6309\u7167\u4ee5\u4e0b\u6b65\u9aa4\u4fee\u6539\u6587\u672c\u6216\u4ee3\u7801\uff1a</p> <ol> <li>\u70b9\u51fb\u7f16\u8f91\u6309\u94ae\uff0c\u5982\u679c\u9047\u5230\u201c\u9700\u8981 Fork \u6b64\u4ed3\u5e93\u201d\u7684\u63d0\u793a\uff0c\u8bf7\u540c\u610f\u8be5\u64cd\u4f5c\uff1b</li> <li>\u4fee\u6539 Markdown \u6e90\u6587\u4ef6\u5185\u5bb9\uff0c\u5e76\u786e\u4fdd\u5185\u5bb9\u6b63\u786e\uff0c\u540c\u65f6\u5c3d\u91cf\u4fdd\u6301\u6392\u7248\u683c\u5f0f\u7684\u7edf\u4e00\uff1b</li> <li>\u5728\u9875\u9762\u5e95\u90e8\u586b\u5199\u4fee\u6539\u8bf4\u660e\uff0c\u7136\u540e\u70b9\u51fb\u201cPropose file change\u201d\u6309\u94ae\uff1b\u9875\u9762\u8df3\u8f6c\u540e\uff0c\u70b9\u51fb\u201cCreate pull request\u201d\u6309\u94ae\u5373\u53ef\u53d1\u8d77\u62c9\u53d6\u8bf7\u6c42\u3002</li> </ol> <p></p> <p> Fig. \u9875\u9762\u7f16\u8f91\u6309\u952e </p> <p>\u7531\u4e8e\u56fe\u7247\u65e0\u6cd5\u76f4\u63a5\u4fee\u6539\uff0c\u56e0\u6b64\u9700\u8981\u901a\u8fc7\u65b0\u5efa Issue \u6216\u8bc4\u8bba\u7559\u8a00\u6765\u63cf\u8ff0\u56fe\u7247\u95ee\u9898\uff0c\u6211\u4eec\u4f1a\u5c3d\u5feb\u91cd\u65b0\u7ed8\u5236\u5e76\u66ff\u6362\u56fe\u7247\u3002</p>"},{"location":"chapter_appendix/contribution/#1322","title":"13.2.2. \u00a0 \u5185\u5bb9\u521b\u4f5c","text":"<p>\u5982\u679c\u60a8\u6709\u5174\u8da3\u53c2\u4e0e\u6b64\u5f00\u6e90\u9879\u76ee\uff0c\u5305\u62ec\u5c06\u4ee3\u7801\u7ffb\u8bd1\u6210\u5176\u4ed6\u7f16\u7a0b\u8bed\u8a00\u3001\u6269\u5c55\u6587\u7ae0\u5185\u5bb9\u7b49\uff0c\u90a3\u4e48\u9700\u8981\u5b9e\u65bd Pull Request \u5de5\u4f5c\u6d41\u7a0b\uff1a</p> <ol> <li>\u767b\u5f55 GitHub \uff0c\u5c06\u672c\u4ed3\u5e93 Fork \u5230\u4e2a\u4eba\u8d26\u53f7\u4e0b\uff1b</li> <li>\u8fdb\u5165\u60a8\u7684 Fork \u4ed3\u5e93\u7f51\u9875\uff0c\u4f7f\u7528 git clone \u547d\u4ee4\u5c06\u4ed3\u5e93\u514b\u9686\u81f3\u672c\u5730\uff1b</li> <li>\u5728\u672c\u5730\u8fdb\u884c\u5185\u5bb9\u521b\u4f5c\uff0c\u5e76\u901a\u8fc7\u8fd0\u884c\u6d4b\u8bd5\u4ee5\u9a8c\u8bc1\u4ee3\u7801\u7684\u6b63\u786e\u6027\uff1b</li> <li>\u5c06\u672c\u5730\u6240\u505a\u66f4\u6539 Commit \uff0c\u7136\u540e Push \u81f3\u8fdc\u7a0b\u4ed3\u5e93\uff1b</li> <li>\u5237\u65b0\u4ed3\u5e93\u7f51\u9875\uff0c\u70b9\u51fb\u201cCreate pull request\u201d\u6309\u94ae\u5373\u53ef\u53d1\u8d77\u62c9\u53d6\u8bf7\u6c42\uff1b</li> </ol>"},{"location":"chapter_appendix/contribution/#1323-docker","title":"13.2.3. \u00a0 Docker \u90e8\u7f72","text":"<p>\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7 Docker \u6765\u90e8\u7f72\u672c\u9879\u76ee\u3002\u6267\u884c\u4ee5\u4e0b\u811a\u672c\uff0c\u7a0d\u7b49\u7247\u523b\u540e\uff0c\u5373\u53ef\u4f7f\u7528\u6d4f\u89c8\u5668\u6253\u5f00 <code>http://localhost:8000</code> \u6765\u8bbf\u95ee\u672c\u9879\u76ee\u3002</p> <pre><code>git clone https://github.com/krahets/hello-algo.git\ncd hello-algo\ndocker-compose up -d\n</code></pre> <p>\u4f7f\u7528\u4ee5\u4e0b\u547d\u4ee4\u5373\u53ef\u5220\u9664\u90e8\u7f72\u3002</p> <pre><code>docker-compose down\n</code></pre>"},{"location":"chapter_appendix/installation/","title":"13.1. \u00a0 \u7f16\u7a0b\u73af\u5883\u5b89\u88c5","text":""},{"location":"chapter_appendix/installation/#1311-vscode","title":"13.1.1. \u00a0 VSCode","text":"<p>\u672c\u4e66\u63a8\u8350\u4f7f\u7528\u5f00\u6e90\u8f7b\u91cf\u7684 VSCode \u4f5c\u4e3a\u672c\u5730 IDE \uff0c\u4e0b\u8f7d\u5e76\u5b89\u88c5 VSCode \u3002</p>"},{"location":"chapter_appendix/installation/#1312-java","title":"13.1.2. \u00a0 Java \u73af\u5883","text":"<ol> <li>\u4e0b\u8f7d\u5e76\u5b89\u88c5 OpenJDK\uff08\u7248\u672c\u9700\u6ee1\u8db3 &gt; JDK 9\uff09\u3002</li> <li>\u5728 VSCode \u7684\u63d2\u4ef6\u5e02\u573a\u4e2d\u641c\u7d22 <code>java</code> \uff0c\u5b89\u88c5 Extension Pack for Java \u3002</li> </ol>"},{"location":"chapter_appendix/installation/#1313-cc","title":"13.1.3. \u00a0 C/C++ \u73af\u5883","text":"<ol> <li>Windows \u7cfb\u7edf\u9700\u8981\u5b89\u88c5 MinGW\uff08\u914d\u7f6e\u6559\u7a0b\uff09\uff0cMacOS \u81ea\u5e26 Clang \u65e0\u9700\u5b89\u88c5\u3002</li> <li>\u5728 VSCode \u7684\u63d2\u4ef6\u5e02\u573a\u4e2d\u641c\u7d22 <code>c++</code> \uff0c\u5b89\u88c5 C/C++ Extension Pack \u3002</li> <li>\uff08\u53ef\u9009\uff09\u6253\u5f00 Settings \u9875\u9762\uff0c\u641c\u7d22 <code>Clang_format_fallback Style</code> \u4ee3\u7801\u683c\u5f0f\u5316\u9009\u9879\uff0c\u8bbe\u7f6e\u4e3a <code>{ BasedOnStyle: Microsoft, BreakBeforeBraces: Attach }</code> \u3002</li> </ol>"},{"location":"chapter_appendix/installation/#1314-python","title":"13.1.4. \u00a0 Python \u73af\u5883","text":"<ol> <li>\u4e0b\u8f7d\u5e76\u5b89\u88c5 Miniconda3 \u3002</li> <li>\u5728 VSCode \u7684\u63d2\u4ef6\u5e02\u573a\u4e2d\u641c\u7d22 <code>python</code> \uff0c\u5b89\u88c5 Python Extension Pack \u3002</li> <li>\uff08\u53ef\u9009\uff09\u5728\u547d\u4ee4\u884c\u8f93\u5165 <code>pip install black</code> \uff0c\u5b89\u88c5\u4ee3\u7801\u683c\u5f0f\u5316\u5de5\u5177\u3002</li> </ol>"},{"location":"chapter_appendix/installation/#1315-go","title":"13.1.5. \u00a0 Go \u73af\u5883","text":"<ol> <li>\u4e0b\u8f7d\u5e76\u5b89\u88c5 go \u3002</li> <li>\u5728 VSCode \u7684\u63d2\u4ef6\u5e02\u573a\u4e2d\u641c\u7d22 <code>go</code> \uff0c\u5b89\u88c5 Go \u3002</li> <li>\u5feb\u6377\u952e <code>Ctrl + Shift + P</code> \u547c\u51fa\u547d\u4ee4\u680f\uff0c\u8f93\u5165 go \uff0c\u9009\u62e9 <code>Go: Install/Update Tools</code> \uff0c\u5168\u90e8\u52fe\u9009\u5e76\u5b89\u88c5\u5373\u53ef\u3002</li> </ol>"},{"location":"chapter_appendix/installation/#1316-javascript","title":"13.1.6. \u00a0 JavaScript \u73af\u5883","text":"<ol> <li>\u4e0b\u8f7d\u5e76\u5b89\u88c5 node.js \u3002</li> <li>\u5728 VSCode \u7684\u63d2\u4ef6\u5e02\u573a\u4e2d\u641c\u7d22 <code>javascript</code> \uff0c\u5b89\u88c5 JavaScript (ES6) code snippets \u3002</li> <li>\uff08\u53ef\u9009\uff09\u5728 VSCode \u7684\u63d2\u4ef6\u5e02\u573a\u4e2d\u641c\u7d22 <code>Prettier</code> \uff0c\u5b89\u88c5\u4ee3\u7801\u683c\u5f0f\u5316\u5de5\u5177\u3002</li> </ol>"},{"location":"chapter_appendix/installation/#1317-c","title":"13.1.7. \u00a0 C# \u73af\u5883","text":"<ol> <li>\u4e0b\u8f7d\u5e76\u5b89\u88c5 .Net 6.0 \uff1b</li> <li>\u5728 VSCode \u7684\u63d2\u4ef6\u5e02\u573a\u4e2d\u641c\u7d22 <code>c#</code> \uff0c\u5b89\u88c5 c# \u3002</li> </ol>"},{"location":"chapter_appendix/installation/#1318-swift","title":"13.1.8. \u00a0 Swift \u73af\u5883","text":"<ol> <li>\u4e0b\u8f7d\u5e76\u5b89\u88c5 Swift\uff1b</li> <li>\u5728 VSCode \u7684\u63d2\u4ef6\u5e02\u573a\u4e2d\u641c\u7d22 <code>swift</code> \uff0c\u5b89\u88c5 Swift for Visual Studio Code\u3002</li> </ol>"},{"location":"chapter_appendix/installation/#1319-rust","title":"13.1.9. \u00a0 Rust \u73af\u5883","text":"<ol> <li>\u4e0b\u8f7d\u5e76\u5b89\u88c5 Rust\uff1b</li> <li>\u5728 VSCode \u7684\u63d2\u4ef6\u5e02\u573a\u4e2d\u641c\u7d22 <code>rust</code> \uff0c\u5b89\u88c5 rust-analyzer\u3002</li> </ol>"},{"location":"chapter_array_and_linkedlist/","title":"4. \u00a0 \u6570\u7ec4\u4e0e\u94fe\u8868","text":""},{"location":"chapter_array_and_linkedlist/array/","title":"4.1. \u00a0 \u6570\u7ec4","text":"<p>\u300c\u6570\u7ec4 Array\u300d\u662f\u4e00\u79cd\u7ebf\u6027\u6570\u636e\u7ed3\u6784\uff0c\u5176\u5c06\u76f8\u540c\u7c7b\u578b\u5143\u7d20\u5b58\u50a8\u5728\u8fde\u7eed\u7684\u5185\u5b58\u7a7a\u95f4\u4e2d\u3002\u6211\u4eec\u5c06\u5143\u7d20\u5728\u6570\u7ec4\u4e2d\u7684\u4f4d\u7f6e\u79f0\u4e3a\u5143\u7d20\u7684\u300c\u7d22\u5f15 Index\u300d\u3002</p> <p></p> <p> Fig. \u6570\u7ec4\u5b9a\u4e49\u4e0e\u5b58\u50a8\u65b9\u5f0f </p> <p>\u6570\u7ec4\u521d\u59cb\u5316\u3002\u901a\u5e38\u6709\u65e0\u521d\u59cb\u503c\u548c\u7ed9\u5b9a\u521d\u59cb\u503c\u4e24\u79cd\u65b9\u5f0f\uff0c\u6211\u4eec\u53ef\u6839\u636e\u9700\u6c42\u9009\u62e9\u5408\u9002\u7684\u65b9\u6cd5\u3002\u5728\u672a\u7ed9\u5b9a\u521d\u59cb\u503c\u7684\u60c5\u51b5\u4e0b\uff0c\u6570\u7ec4\u7684\u6240\u6709\u5143\u7d20\u901a\u5e38\u4f1a\u88ab\u521d\u59cb\u5316\u4e3a\u9ed8\u8ba4\u503c \\(0\\) \u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart array.java<pre><code>/* \u521d\u59cb\u5316\u6570\u7ec4 */\nint[] arr = new int[5]; // { 0, 0, 0, 0, 0 }\nint[] nums = { 1, 3, 2, 5, 4 };\n</code></pre> array.cpp<pre><code>/* \u521d\u59cb\u5316\u6570\u7ec4 */\n// \u5b58\u50a8\u5728\u6808\u4e0a\nint arr[5];\nint nums[5] { 1, 3, 2, 5, 4 };\n// \u5b58\u50a8\u5728\u5806\u4e0a\nint* arr1 = new int[5];\nint* nums1 = new int[5] { 1, 3, 2, 5, 4 };\n</code></pre> array.py<pre><code># \u521d\u59cb\u5316\u6570\u7ec4\narr: List[int] = [0] * 5  # [ 0, 0, 0, 0, 0 ]\nnums: List[int] = [1, 3, 2, 5, 4]  \n</code></pre> array.go<pre><code>/* \u521d\u59cb\u5316\u6570\u7ec4 */\nvar arr [5]int\n// \u5728 Go \u4e2d\uff0c\u6307\u5b9a\u957f\u5ea6\u65f6\uff08[5]int\uff09\u4e3a\u6570\u7ec4\uff0c\u4e0d\u6307\u5b9a\u957f\u5ea6\u65f6\uff08[]int\uff09\u4e3a\u5207\u7247\n// \u7531\u4e8e Go \u7684\u6570\u7ec4\u88ab\u8bbe\u8ba1\u4e3a\u5728\u7f16\u8bd1\u671f\u786e\u5b9a\u957f\u5ea6\uff0c\u56e0\u6b64\u53ea\u80fd\u4f7f\u7528\u5e38\u91cf\u6765\u6307\u5b9a\u957f\u5ea6\n// \u4e3a\u4e86\u65b9\u4fbf\u5b9e\u73b0\u6269\u5bb9 extend() \u65b9\u6cd5\uff0c\u4ee5\u4e0b\u5c06\u5207\u7247\uff08Slice\uff09\u770b\u4f5c\u6570\u7ec4\uff08Array\uff09\nnums := []int{1, 3, 2, 5, 4}\n</code></pre> array.js<pre><code>/* \u521d\u59cb\u5316\u6570\u7ec4 */\nvar arr = new Array(5).fill(0);\nvar nums = [1, 3, 2, 5, 4];\n</code></pre> array.ts<pre><code>/* \u521d\u59cb\u5316\u6570\u7ec4 */\nlet arr: number[] = new Array(5).fill(0);\nlet nums: number[] = [1, 3, 2, 5, 4];\n</code></pre> array.c<pre><code>int arr[5] = { 0 }; // { 0, 0, 0, 0, 0 }\nint nums[5] = { 1, 3, 2, 5, 4 };\n</code></pre> array.cs<pre><code>/* \u521d\u59cb\u5316\u6570\u7ec4 */\nint[] arr = new int[5]; // { 0, 0, 0, 0, 0 }\nint[] nums = { 1, 3, 2, 5, 4 };\n</code></pre> array.swift<pre><code>/* \u521d\u59cb\u5316\u6570\u7ec4 */\nlet arr = Array(repeating: 0, count: 5) // [0, 0, 0, 0, 0]\nlet nums = [1, 3, 2, 5, 4]\n</code></pre> array.zig<pre><code>// \u521d\u59cb\u5316\u6570\u7ec4\nvar arr = [_]i32{0} ** 5; // { 0, 0, 0, 0, 0 }\nvar nums = [_]i32{ 1, 3, 2, 5, 4 };\n</code></pre> array.dart<pre><code>/* \u521d\u59cb\u5316\u6570\u7ec4 */\nList&lt;int&gt; arr = List.filled(5, 0); // [0, 0, 0, 0, 0]\nList&lt;int&gt; nums = [1, 3, 2, 5, 4];\n</code></pre>"},{"location":"chapter_array_and_linkedlist/array/#411","title":"4.1.1. \u00a0 \u6570\u7ec4\u4f18\u70b9","text":"<p>\u5728\u6570\u7ec4\u4e2d\u8bbf\u95ee\u5143\u7d20\u975e\u5e38\u9ad8\u6548\u3002\u7531\u4e8e\u6570\u7ec4\u5143\u7d20\u88ab\u5b58\u50a8\u5728\u8fde\u7eed\u7684\u5185\u5b58\u7a7a\u95f4\u4e2d\uff0c\u56e0\u6b64\u8ba1\u7b97\u6570\u7ec4\u5143\u7d20\u7684\u5185\u5b58\u5730\u5740\u975e\u5e38\u5bb9\u6613\u3002\u7ed9\u5b9a\u6570\u7ec4\u9996\u4e2a\u5143\u7d20\u7684\u5730\u5740\u548c\u67d0\u4e2a\u5143\u7d20\u7684\u7d22\u5f15\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u4ee5\u4e0b\u516c\u5f0f\u8ba1\u7b97\u5f97\u5230\u8be5\u5143\u7d20\u7684\u5185\u5b58\u5730\u5740\uff0c\u4ece\u800c\u76f4\u63a5\u8bbf\u95ee\u6b64\u5143\u7d20\u3002</p> <p></p> <p> Fig. \u6570\u7ec4\u5143\u7d20\u7684\u5185\u5b58\u5730\u5740\u8ba1\u7b97 </p> <pre><code># \u5143\u7d20\u5185\u5b58\u5730\u5740 = \u6570\u7ec4\u5185\u5b58\u5730\u5740 + \u5143\u7d20\u957f\u5ea6 * \u5143\u7d20\u7d22\u5f15\nelementAddr = firtstElementAddr + elementLength * elementIndex\n</code></pre> <p>\u4e3a\u4ec0\u4e48\u6570\u7ec4\u5143\u7d20\u7684\u7d22\u5f15\u8981\u4ece \\(0\\) \u5f00\u59cb\u7f16\u53f7\u5462\uff1f</p> <p>\u89c2\u5bdf\u4e0a\u56fe\uff0c\u6211\u4eec\u53d1\u73b0\u6570\u7ec4\u9996\u4e2a\u5143\u7d20\u7684\u7d22\u5f15\u4e3a \\(0\\) \uff0c\u8fd9\u4f3c\u4e4e\u6709\u4e9b\u53cd\u76f4\u89c9\uff0c\u56e0\u4e3a\u4ece \\(1\\) \u5f00\u59cb\u8ba1\u6570\u4f1a\u66f4\u81ea\u7136\u3002</p> <p>\u7136\u800c\uff0c\u4ece\u5730\u5740\u8ba1\u7b97\u516c\u5f0f\u7684\u89d2\u5ea6\u770b\uff0c\u7d22\u5f15\u672c\u8d28\u4e0a\u8868\u793a\u7684\u662f\u5185\u5b58\u5730\u5740\u7684\u504f\u79fb\u91cf\u3002\u9996\u4e2a\u5143\u7d20\u7684\u5730\u5740\u504f\u79fb\u91cf\u662f \\(0\\) \uff0c\u56e0\u6b64\u7d22\u5f15\u4e3a \\(0\\) \u4e5f\u662f\u5408\u7406\u7684\u3002</p> <p>\u8bbf\u95ee\u5143\u7d20\u7684\u9ad8\u6548\u6027\u5e26\u6765\u4e86\u8bf8\u591a\u4fbf\u5229\u3002\u4f8b\u5982\uff0c\u6211\u4eec\u53ef\u4ee5\u5728 \\(O(1)\\) \u65f6\u95f4\u5185\u968f\u673a\u83b7\u53d6\u6570\u7ec4\u4e2d\u7684\u4efb\u610f\u4e00\u4e2a\u5143\u7d20\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart array.java<pre><code>/* \u968f\u673a\u8fd4\u56de\u4e00\u4e2a\u6570\u7ec4\u5143\u7d20 */\nint randomAccess(int[] nums) {\n// \u5728\u533a\u95f4 [0, nums.length) \u4e2d\u968f\u673a\u62bd\u53d6\u4e00\u4e2a\u6570\u5b57\nint randomIndex = ThreadLocalRandom.current().nextInt(0, nums.length);\n// \u83b7\u53d6\u5e76\u8fd4\u56de\u968f\u673a\u5143\u7d20\nint randomNum = nums[randomIndex];\nreturn randomNum;\n}\n</code></pre> array.cpp<pre><code>/* \u968f\u673a\u8fd4\u56de\u4e00\u4e2a\u6570\u7ec4\u5143\u7d20 */\nint randomAccess(int *nums, int size) {\n// \u5728\u533a\u95f4 [0, size) \u4e2d\u968f\u673a\u62bd\u53d6\u4e00\u4e2a\u6570\u5b57\nint randomIndex = rand() % size;\n// \u83b7\u53d6\u5e76\u8fd4\u56de\u968f\u673a\u5143\u7d20\nint randomNum = nums[randomIndex];\nreturn randomNum;\n}\n</code></pre> array.py<pre><code>def random_access(nums: list[int]) -&gt; int:\n\"\"\"\u968f\u673a\u8bbf\u95ee\u5143\u7d20\"\"\"\n# \u5728\u533a\u95f4 [0, len(nums)-1] \u4e2d\u968f\u673a\u62bd\u53d6\u4e00\u4e2a\u6570\u5b57\nrandom_index = random.randint(0, len(nums) - 1)\n# \u83b7\u53d6\u5e76\u8fd4\u56de\u968f\u673a\u5143\u7d20\nrandom_num = nums[random_index]\nreturn random_num\n</code></pre> array.go<pre><code>/* \u968f\u673a\u8fd4\u56de\u4e00\u4e2a\u6570\u7ec4\u5143\u7d20 */\nfunc randomAccess(nums []int) (randomNum int) {\n// \u5728\u533a\u95f4 [0, nums.length) \u4e2d\u968f\u673a\u62bd\u53d6\u4e00\u4e2a\u6570\u5b57\nrandomIndex := rand.Intn(len(nums))\n// \u83b7\u53d6\u5e76\u8fd4\u56de\u968f\u673a\u5143\u7d20\nrandomNum = nums[randomIndex]\nreturn\n}\n</code></pre> array.js<pre><code>/* \u968f\u673a\u8fd4\u56de\u4e00\u4e2a\u6570\u7ec4\u5143\u7d20 */\nfunction randomAccess(nums) {\n// \u5728\u533a\u95f4 [0, nums.length) \u4e2d\u968f\u673a\u62bd\u53d6\u4e00\u4e2a\u6570\u5b57\nconst random_index = Math.floor(Math.random() * nums.length);\n// \u83b7\u53d6\u5e76\u8fd4\u56de\u968f\u673a\u5143\u7d20\nconst random_num = nums[random_index];\nreturn random_num;\n}\n</code></pre> array.ts<pre><code>/* \u968f\u673a\u8fd4\u56de\u4e00\u4e2a\u6570\u7ec4\u5143\u7d20 */\nfunction randomAccess(nums: number[]): number {\n// \u5728\u533a\u95f4 [0, nums.length) \u4e2d\u968f\u673a\u62bd\u53d6\u4e00\u4e2a\u6570\u5b57\nconst random_index = Math.floor(Math.random() * nums.length);\n// \u83b7\u53d6\u5e76\u8fd4\u56de\u968f\u673a\u5143\u7d20\nconst random_num = nums[random_index];\nreturn random_num;\n}\n</code></pre> array.c<pre><code>/* \u968f\u673a\u8fd4\u56de\u4e00\u4e2a\u6570\u7ec4\u5143\u7d20 */\nint randomAccess(int *nums, int size) {\n// \u5728\u533a\u95f4 [0, size) \u4e2d\u968f\u673a\u62bd\u53d6\u4e00\u4e2a\u6570\u5b57\nint randomIndex = rand() % size;\n// \u83b7\u53d6\u5e76\u8fd4\u56de\u968f\u673a\u5143\u7d20\nint randomNum = nums[randomIndex];\nreturn randomNum;\n}\n</code></pre> array.cs<pre><code>/* \u968f\u673a\u8fd4\u56de\u4e00\u4e2a\u6570\u7ec4\u5143\u7d20 */\nint randomAccess(int[] nums) {\nRandom random = new();\n// \u5728\u533a\u95f4 [0, nums.Length) \u4e2d\u968f\u673a\u62bd\u53d6\u4e00\u4e2a\u6570\u5b57\nint randomIndex = random.Next(nums.Length);\n// \u83b7\u53d6\u5e76\u8fd4\u56de\u968f\u673a\u5143\u7d20\nint randomNum = nums[randomIndex];\nreturn randomNum;\n}\n</code></pre> array.swift<pre><code>/* \u968f\u673a\u8fd4\u56de\u4e00\u4e2a\u6570\u7ec4\u5143\u7d20 */\nfunc randomAccess(nums: [Int]) -&gt; Int {\n// \u5728\u533a\u95f4 [0, nums.count) \u4e2d\u968f\u673a\u62bd\u53d6\u4e00\u4e2a\u6570\u5b57\nlet randomIndex = nums.indices.randomElement()!\n// \u83b7\u53d6\u5e76\u8fd4\u56de\u968f\u673a\u5143\u7d20\nlet randomNum = nums[randomIndex]\nreturn randomNum\n}\n</code></pre> array.zig<pre><code>// \u968f\u673a\u8fd4\u56de\u4e00\u4e2a\u6570\u7ec4\u5143\u7d20\nfn randomAccess(nums: []i32) i32 {\n// \u5728\u533a\u95f4 [0, nums.len) \u4e2d\u968f\u673a\u62bd\u53d6\u4e00\u4e2a\u6574\u6570\nvar randomIndex = std.crypto.random.intRangeLessThan(usize, 0, nums.len);\n// \u83b7\u53d6\u5e76\u8fd4\u56de\u968f\u673a\u5143\u7d20\nvar randomNum = nums[randomIndex];\nreturn randomNum;\n}\n</code></pre> array.dart<pre><code>/* \u968f\u673a\u8fd4\u56de\u4e00\u4e2a\u6570\u7ec4\u5143\u7d20 */\nint randomAccess(List nums) {\n// \u5728\u533a\u95f4 [0, nums.length) \u4e2d\u968f\u673a\u62bd\u53d6\u4e00\u4e2a\u6570\u5b57\nint randomIndex = Random().nextInt(nums.length);\n// \u83b7\u53d6\u5e76\u8fd4\u56de\u968f\u673a\u5143\u7d20\nint randomNum = nums[randomIndex];\nreturn randomNum;\n}\n</code></pre>"},{"location":"chapter_array_and_linkedlist/array/#412","title":"4.1.2. \u00a0 \u6570\u7ec4\u7f3a\u70b9","text":"<p>\u6570\u7ec4\u5728\u521d\u59cb\u5316\u540e\u957f\u5ea6\u4e0d\u53ef\u53d8\u3002\u7531\u4e8e\u7cfb\u7edf\u65e0\u6cd5\u4fdd\u8bc1\u6570\u7ec4\u4e4b\u540e\u7684\u5185\u5b58\u7a7a\u95f4\u662f\u53ef\u7528\u7684\uff0c\u56e0\u6b64\u6570\u7ec4\u957f\u5ea6\u65e0\u6cd5\u6269\u5c55\u3002\u800c\u82e5\u5e0c\u671b\u6269\u5bb9\u6570\u7ec4\uff0c\u5219\u9700\u65b0\u5efa\u4e00\u4e2a\u6570\u7ec4\uff0c\u7136\u540e\u628a\u539f\u6570\u7ec4\u5143\u7d20\u4f9d\u6b21\u62f7\u8d1d\u5230\u65b0\u6570\u7ec4\uff0c\u5728\u6570\u7ec4\u5f88\u5927\u7684\u60c5\u51b5\u4e0b\uff0c\u8fd9\u662f\u975e\u5e38\u8017\u65f6\u7684\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart array.java<pre><code>/* \u6269\u5c55\u6570\u7ec4\u957f\u5ea6 */\nint[] extend(int[] nums, int enlarge) {\n// \u521d\u59cb\u5316\u4e00\u4e2a\u6269\u5c55\u957f\u5ea6\u540e\u7684\u6570\u7ec4\nint[] res = new int[nums.length + enlarge];\n// \u5c06\u539f\u6570\u7ec4\u4e2d\u7684\u6240\u6709\u5143\u7d20\u590d\u5236\u5230\u65b0\u6570\u7ec4\nfor (int i = 0; i &lt; nums.length; i++) {\nres[i] = nums[i];\n}\n// \u8fd4\u56de\u6269\u5c55\u540e\u7684\u65b0\u6570\u7ec4\nreturn res;\n}\n</code></pre> array.cpp<pre><code>/* \u6269\u5c55\u6570\u7ec4\u957f\u5ea6 */\nint *extend(int *nums, int size, int enlarge) {\n// \u521d\u59cb\u5316\u4e00\u4e2a\u6269\u5c55\u957f\u5ea6\u540e\u7684\u6570\u7ec4\nint *res = new int[size + enlarge];\n// \u5c06\u539f\u6570\u7ec4\u4e2d\u7684\u6240\u6709\u5143\u7d20\u590d\u5236\u5230\u65b0\u6570\u7ec4\nfor (int i = 0; i &lt; size; i++) {\nres[i] = nums[i];\n}\n// \u91ca\u653e\u5185\u5b58\ndelete[] nums;\n// \u8fd4\u56de\u6269\u5c55\u540e\u7684\u65b0\u6570\u7ec4\nreturn res;\n}\n</code></pre> array.py<pre><code>def extend(nums: list[int], enlarge: int) -&gt; list[int]:\n\"\"\"\u6269\u5c55\u6570\u7ec4\u957f\u5ea6\"\"\"\n# \u521d\u59cb\u5316\u4e00\u4e2a\u6269\u5c55\u957f\u5ea6\u540e\u7684\u6570\u7ec4\nres = [0] * (len(nums) + enlarge)\n# \u5c06\u539f\u6570\u7ec4\u4e2d\u7684\u6240\u6709\u5143\u7d20\u590d\u5236\u5230\u65b0\u6570\u7ec4\nfor i in range(len(nums)):\nres[i] = nums[i]\n# \u8fd4\u56de\u6269\u5c55\u540e\u7684\u65b0\u6570\u7ec4\nreturn res\n</code></pre> array.go<pre><code>/* \u6269\u5c55\u6570\u7ec4\u957f\u5ea6 */\nfunc extend(nums []int, enlarge int) []int {\n// \u521d\u59cb\u5316\u4e00\u4e2a\u6269\u5c55\u957f\u5ea6\u540e\u7684\u6570\u7ec4\nres := make([]int, len(nums)+enlarge)\n// \u5c06\u539f\u6570\u7ec4\u4e2d\u7684\u6240\u6709\u5143\u7d20\u590d\u5236\u5230\u65b0\u6570\u7ec4\nfor i, num := range nums {\nres[i] = num\n}\n// \u8fd4\u56de\u6269\u5c55\u540e\u7684\u65b0\u6570\u7ec4\nreturn res\n}\n</code></pre> array.js<pre><code>/* \u6269\u5c55\u6570\u7ec4\u957f\u5ea6 */\n// \u8bf7\u6ce8\u610f\uff0cJavaScript \u7684 Array \u662f\u52a8\u6001\u6570\u7ec4\uff0c\u53ef\u4ee5\u76f4\u63a5\u6269\u5c55\n// \u4e3a\u4e86\u65b9\u4fbf\u5b66\u4e60\uff0c\u672c\u51fd\u6570\u5c06 Array \u770b\u4f5c\u662f\u957f\u5ea6\u4e0d\u53ef\u53d8\u7684\u6570\u7ec4\nfunction extend(nums, enlarge) {\n// \u521d\u59cb\u5316\u4e00\u4e2a\u6269\u5c55\u957f\u5ea6\u540e\u7684\u6570\u7ec4\nconst res = new Array(nums.length + enlarge).fill(0);\n// \u5c06\u539f\u6570\u7ec4\u4e2d\u7684\u6240\u6709\u5143\u7d20\u590d\u5236\u5230\u65b0\u6570\u7ec4\nfor (let i = 0; i &lt; nums.length; i++) {\nres[i] = nums[i];\n}\n// \u8fd4\u56de\u6269\u5c55\u540e\u7684\u65b0\u6570\u7ec4\nreturn res;\n}\n</code></pre> array.ts<pre><code>/* \u6269\u5c55\u6570\u7ec4\u957f\u5ea6 */\n// \u8bf7\u6ce8\u610f\uff0cTypeScript \u7684 Array \u662f\u52a8\u6001\u6570\u7ec4\uff0c\u53ef\u4ee5\u76f4\u63a5\u6269\u5c55\n// \u4e3a\u4e86\u65b9\u4fbf\u5b66\u4e60\uff0c\u672c\u51fd\u6570\u5c06 Array \u770b\u4f5c\u662f\u957f\u5ea6\u4e0d\u53ef\u53d8\u7684\u6570\u7ec4\nfunction extend(nums: number[], enlarge: number): number[] {\n// \u521d\u59cb\u5316\u4e00\u4e2a\u6269\u5c55\u957f\u5ea6\u540e\u7684\u6570\u7ec4\nconst res = new Array(nums.length + enlarge).fill(0);\n// \u5c06\u539f\u6570\u7ec4\u4e2d\u7684\u6240\u6709\u5143\u7d20\u590d\u5236\u5230\u65b0\u6570\u7ec4\nfor (let i = 0; i &lt; nums.length; i++) {\nres[i] = nums[i];\n}\n// \u8fd4\u56de\u6269\u5c55\u540e\u7684\u65b0\u6570\u7ec4\nreturn res;\n}\n</code></pre> array.c<pre><code>/* \u6269\u5c55\u6570\u7ec4\u957f\u5ea6 */\nint *extend(int *nums, int size, int enlarge) {\n// \u521d\u59cb\u5316\u4e00\u4e2a\u6269\u5c55\u957f\u5ea6\u540e\u7684\u6570\u7ec4\nint *res = (int *)malloc(sizeof(int) * (size + enlarge));\n// \u5c06\u539f\u6570\u7ec4\u4e2d\u7684\u6240\u6709\u5143\u7d20\u590d\u5236\u5230\u65b0\u6570\u7ec4\nfor (int i = 0; i &lt; size; i++) {\nres[i] = nums[i];\n}\n// \u521d\u59cb\u5316\u6269\u5c55\u540e\u7684\u7a7a\u95f4\nfor (int i = size; i &lt; size + enlarge; i++) {\nres[i] = 0;\n}\n// \u8fd4\u56de\u6269\u5c55\u540e\u7684\u65b0\u6570\u7ec4\nreturn res;\n}\n</code></pre> array.cs<pre><code>/* \u6269\u5c55\u6570\u7ec4\u957f\u5ea6 */\nint[] extend(int[] nums, int enlarge) {\n// \u521d\u59cb\u5316\u4e00\u4e2a\u6269\u5c55\u957f\u5ea6\u540e\u7684\u6570\u7ec4\nint[] res = new int[nums.Length + enlarge];\n// \u5c06\u539f\u6570\u7ec4\u4e2d\u7684\u6240\u6709\u5143\u7d20\u590d\u5236\u5230\u65b0\u6570\u7ec4\nfor (int i = 0; i &lt; nums.Length; i++) {\nres[i] = nums[i];\n}\n// \u8fd4\u56de\u6269\u5c55\u540e\u7684\u65b0\u6570\u7ec4\nreturn res;\n}\n</code></pre> array.swift<pre><code>/* \u6269\u5c55\u6570\u7ec4\u957f\u5ea6 */\nfunc extend(nums: [Int], enlarge: Int) -&gt; [Int] {\n// \u521d\u59cb\u5316\u4e00\u4e2a\u6269\u5c55\u957f\u5ea6\u540e\u7684\u6570\u7ec4\nvar res = Array(repeating: 0, count: nums.count + enlarge)\n// \u5c06\u539f\u6570\u7ec4\u4e2d\u7684\u6240\u6709\u5143\u7d20\u590d\u5236\u5230\u65b0\u6570\u7ec4\nfor i in nums.indices {\nres[i] = nums[i]\n}\n// \u8fd4\u56de\u6269\u5c55\u540e\u7684\u65b0\u6570\u7ec4\nreturn res\n}\n</code></pre> array.zig<pre><code>// \u6269\u5c55\u6570\u7ec4\u957f\u5ea6\nfn extend(mem_allocator: std.mem.Allocator, nums: []i32, enlarge: usize) ![]i32 {\n// \u521d\u59cb\u5316\u4e00\u4e2a\u6269\u5c55\u957f\u5ea6\u540e\u7684\u6570\u7ec4\nvar res = try mem_allocator.alloc(i32, nums.len + enlarge);\nstd.mem.set(i32, res, 0);\n// \u5c06\u539f\u6570\u7ec4\u4e2d\u7684\u6240\u6709\u5143\u7d20\u590d\u5236\u5230\u65b0\u6570\u7ec4\nstd.mem.copy(i32, res, nums);\n// \u8fd4\u56de\u6269\u5c55\u540e\u7684\u65b0\u6570\u7ec4\nreturn res;\n}\n</code></pre> array.dart<pre><code>/* \u6269\u5c55\u6570\u7ec4\u957f\u5ea6 */\nList extend(List nums, int enlarge) {\n// \u521d\u59cb\u5316\u4e00\u4e2a\u6269\u5c55\u957f\u5ea6\u540e\u7684\u6570\u7ec4\nList&lt;int&gt; res = List.filled(nums.length + enlarge, 0);\n// \u5c06\u539f\u6570\u7ec4\u4e2d\u7684\u6240\u6709\u5143\u7d20\u590d\u5236\u5230\u65b0\u6570\u7ec4\nfor (var i = 0; i &lt; nums.length; i++) {\nres[i] = nums[i];\n}\n// \u8fd4\u56de\u6269\u5c55\u540e\u7684\u65b0\u6570\u7ec4\nreturn res;\n}\n</code></pre> <p>\u6570\u7ec4\u4e2d\u63d2\u5165\u6216\u5220\u9664\u5143\u7d20\u6548\u7387\u4f4e\u4e0b\u3002\u5982\u679c\u6211\u4eec\u60f3\u8981\u5728\u6570\u7ec4\u4e2d\u95f4\u63d2\u5165\u4e00\u4e2a\u5143\u7d20\uff0c\u7531\u4e8e\u6570\u7ec4\u5143\u7d20\u5728\u5185\u5b58\u4e2d\u662f\u201c\u7d27\u6328\u7740\u7684\u201d\uff0c\u5b83\u4eec\u4e4b\u95f4\u6ca1\u6709\u7a7a\u95f4\u518d\u653e\u4efb\u4f55\u6570\u636e\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u4e0d\u5f97\u4e0d\u5c06\u6b64\u7d22\u5f15\u4e4b\u540e\u7684\u6240\u6709\u5143\u7d20\u90fd\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\uff0c\u7136\u540e\u518d\u628a\u5143\u7d20\u8d4b\u503c\u7ed9\u8be5\u7d22\u5f15\u3002</p> <p></p> <p> Fig. \u6570\u7ec4\u63d2\u5165\u5143\u7d20 </p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart array.java<pre><code>/* \u5728\u6570\u7ec4\u7684\u7d22\u5f15 index \u5904\u63d2\u5165\u5143\u7d20 num */\nvoid insert(int[] nums, int num, int index) {\n// \u628a\u7d22\u5f15 index \u4ee5\u53ca\u4e4b\u540e\u7684\u6240\u6709\u5143\u7d20\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\nfor (int i = nums.length - 1; i &gt; index; i--) {\nnums[i] = nums[i - 1];\n}\n// \u5c06 num \u8d4b\u7ed9 index \u5904\u5143\u7d20\nnums[index] = num;\n}\n</code></pre> array.cpp<pre><code>/* \u5728\u6570\u7ec4\u7684\u7d22\u5f15 index \u5904\u63d2\u5165\u5143\u7d20 num */\nvoid insert(int *nums, int size, int num, int index) {\n// \u628a\u7d22\u5f15 index \u4ee5\u53ca\u4e4b\u540e\u7684\u6240\u6709\u5143\u7d20\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\nfor (int i = size - 1; i &gt; index; i--) {\nnums[i] = nums[i - 1];\n}\n// \u5c06 num \u8d4b\u7ed9 index \u5904\u5143\u7d20\nnums[index] = num;\n}\n</code></pre> array.py<pre><code>def insert(nums: list[int], num: int, index: int) -&gt; None:\n\"\"\"\u5728\u6570\u7ec4\u7684\u7d22\u5f15 index \u5904\u63d2\u5165\u5143\u7d20 num\"\"\"\n# \u628a\u7d22\u5f15 index \u4ee5\u53ca\u4e4b\u540e\u7684\u6240\u6709\u5143\u7d20\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\nfor i in range(len(nums) - 1, index, -1):\nnums[i] = nums[i - 1]\n# \u5c06 num \u8d4b\u7ed9 index \u5904\u5143\u7d20\nnums[index] = num\n</code></pre> array.go<pre><code>/* \u5728\u6570\u7ec4\u7684\u7d22\u5f15 index \u5904\u63d2\u5165\u5143\u7d20 num */\nfunc insert(nums []int, num int, index int) {\n// \u628a\u7d22\u5f15 index \u4ee5\u53ca\u4e4b\u540e\u7684\u6240\u6709\u5143\u7d20\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\nfor i := len(nums) - 1; i &gt; index; i-- {\nnums[i] = nums[i-1]\n}\n// \u5c06 num \u8d4b\u7ed9 index \u5904\u5143\u7d20\nnums[index] = num\n}\n</code></pre> array.js<pre><code>/* \u5728\u6570\u7ec4\u7684\u7d22\u5f15 index \u5904\u63d2\u5165\u5143\u7d20 num */\nfunction insert(nums, num, index) {\n// \u628a\u7d22\u5f15 index \u4ee5\u53ca\u4e4b\u540e\u7684\u6240\u6709\u5143\u7d20\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\nfor (let i = nums.length - 1; i &gt; index; i--) {\nnums[i] = nums[i - 1];\n}\n// \u5c06 num \u8d4b\u7ed9 index \u5904\u5143\u7d20\nnums[index] = num;\n}\n</code></pre> array.ts<pre><code>/* \u5728\u6570\u7ec4\u7684\u7d22\u5f15 index \u5904\u63d2\u5165\u5143\u7d20 num */\nfunction insert(nums: number[], num: number, index: number): void {\n// \u628a\u7d22\u5f15 index \u4ee5\u53ca\u4e4b\u540e\u7684\u6240\u6709\u5143\u7d20\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\nfor (let i = nums.length - 1; i &gt; index; i--) {\nnums[i] = nums[i - 1];\n}\n// \u5c06 num \u8d4b\u7ed9 index \u5904\u5143\u7d20\nnums[index] = num;\n}\n</code></pre> array.c<pre><code>/* \u5728\u6570\u7ec4\u7684\u7d22\u5f15 index \u5904\u63d2\u5165\u5143\u7d20 num */\nvoid insert(int *nums, int size, int num, int index) {\n// \u628a\u7d22\u5f15 index \u4ee5\u53ca\u4e4b\u540e\u7684\u6240\u6709\u5143\u7d20\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\nfor (int i = size - 1; i &gt; index; i--) {\nnums[i] = nums[i - 1];\n}\n// \u5c06 num \u8d4b\u7ed9 index \u5904\u5143\u7d20\nnums[index] = num;\n}\n</code></pre> array.cs<pre><code>/* \u5728\u6570\u7ec4\u7684\u7d22\u5f15 index \u5904\u63d2\u5165\u5143\u7d20 num */\nvoid insert(int[] nums, int num, int index) {\n// \u628a\u7d22\u5f15 index \u4ee5\u53ca\u4e4b\u540e\u7684\u6240\u6709\u5143\u7d20\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\nfor (int i = nums.Length - 1; i &gt; index; i--) {\nnums[i] = nums[i - 1];\n}\n// \u5c06 num \u8d4b\u7ed9 index \u5904\u5143\u7d20\nnums[index] = num;\n}\n</code></pre> array.swift<pre><code>/* \u5728\u6570\u7ec4\u7684\u7d22\u5f15 index \u5904\u63d2\u5165\u5143\u7d20 num */\nfunc insert(nums: inout [Int], num: Int, index: Int) {\n// \u628a\u7d22\u5f15 index \u4ee5\u53ca\u4e4b\u540e\u7684\u6240\u6709\u5143\u7d20\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\nfor i in sequence(first: nums.count - 1, next: { $0 &gt; index + 1 ? $0 - 1 : nil }) {\nnums[i] = nums[i - 1]\n}\n// \u5c06 num \u8d4b\u7ed9 index \u5904\u5143\u7d20\nnums[index] = num\n}\n</code></pre> array.zig<pre><code>// \u5728\u6570\u7ec4\u7684\u7d22\u5f15 index \u5904\u63d2\u5165\u5143\u7d20 num\nfn insert(nums: []i32, num: i32, index: usize) void {\n// \u628a\u7d22\u5f15 index \u4ee5\u53ca\u4e4b\u540e\u7684\u6240\u6709\u5143\u7d20\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\nvar i = nums.len - 1;\nwhile (i &gt; index) : (i -= 1) {\nnums[i] = nums[i - 1];\n}\n// \u5c06 num \u8d4b\u7ed9 index \u5904\u5143\u7d20\nnums[index] = num;\n}\n</code></pre> array.dart<pre><code>/* \u5728\u6570\u7ec4\u7684\u7d22\u5f15 index \u5904\u63d2\u5165\u5143\u7d20 num */\nvoid insert(List nums, int num, int index) {\n// \u628a\u7d22\u5f15 index \u4ee5\u53ca\u4e4b\u540e\u7684\u6240\u6709\u5143\u7d20\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\nfor (var i = nums.length - 1; i &gt; index; i--) {\nnums[i] = nums[i - 1];\n}\n// \u5c06 num \u8d4b\u7ed9 index \u5904\u5143\u7d20\nnums[index] = num;\n}\n</code></pre> <p>\u5220\u9664\u5143\u7d20\u4e5f\u7c7b\u4f3c\uff0c\u5982\u679c\u6211\u4eec\u60f3\u8981\u5220\u9664\u7d22\u5f15 \\(i\\) \u5904\u7684\u5143\u7d20\uff0c\u5219\u9700\u8981\u628a\u7d22\u5f15 \\(i\\) \u4e4b\u540e\u7684\u5143\u7d20\u90fd\u5411\u524d\u79fb\u52a8\u4e00\u4f4d\u3002\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u5220\u9664\u5143\u7d20\u540e\uff0c\u539f\u5148\u672b\u5c3e\u7684\u5143\u7d20\u53d8\u5f97\u201c\u65e0\u610f\u4e49\u201d\u4e86\uff0c\u6211\u4eec\u65e0\u9700\u7279\u610f\u53bb\u4fee\u6539\u5b83\u3002</p> <p></p> <p> Fig. \u6570\u7ec4\u5220\u9664\u5143\u7d20 </p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart array.java<pre><code>/* \u5220\u9664\u7d22\u5f15 index \u5904\u5143\u7d20 */\nvoid remove(int[] nums, int index) {\n// \u628a\u7d22\u5f15 index \u4e4b\u540e\u7684\u6240\u6709\u5143\u7d20\u5411\u524d\u79fb\u52a8\u4e00\u4f4d\nfor (int i = index; i &lt; nums.length - 1; i++) {\nnums[i] = nums[i + 1];\n}\n}\n</code></pre> array.cpp<pre><code>/* \u5220\u9664\u7d22\u5f15 index \u5904\u5143\u7d20 */\nvoid remove(int *nums, int size, int index) {\n// \u628a\u7d22\u5f15 index \u4e4b\u540e\u7684\u6240\u6709\u5143\u7d20\u5411\u524d\u79fb\u52a8\u4e00\u4f4d\nfor (int i = index; i &lt; size - 1; i++) {\nnums[i] = nums[i + 1];\n}\n}\n</code></pre> array.py<pre><code>def remove(nums: list[int], index: int) -&gt; None:\n\"\"\"\u5220\u9664\u7d22\u5f15 index \u5904\u5143\u7d20\"\"\"\n# \u628a\u7d22\u5f15 index \u4e4b\u540e\u7684\u6240\u6709\u5143\u7d20\u5411\u524d\u79fb\u52a8\u4e00\u4f4d\nfor i in range(index, len(nums) - 1):\nnums[i] = nums[i + 1]\n</code></pre> array.go<pre><code>/* \u5220\u9664\u7d22\u5f15 index \u5904\u5143\u7d20 */\nfunc remove(nums []int, index int) {\n// \u628a\u7d22\u5f15 index \u4e4b\u540e\u7684\u6240\u6709\u5143\u7d20\u5411\u524d\u79fb\u52a8\u4e00\u4f4d\nfor i := index; i &lt; len(nums)-1; i++ {\nnums[i] = nums[i+1]\n}\n}\n</code></pre> array.js<pre><code>/* \u5220\u9664\u7d22\u5f15 index \u5904\u5143\u7d20 */\nfunction remove(nums, index) {\n// \u628a\u7d22\u5f15 index \u4e4b\u540e\u7684\u6240\u6709\u5143\u7d20\u5411\u524d\u79fb\u52a8\u4e00\u4f4d\nfor (let i = index; i &lt; nums.length - 1; i++) {\nnums[i] = nums[i + 1];\n}\n}\n</code></pre> array.ts<pre><code>/* \u5220\u9664\u7d22\u5f15 index \u5904\u5143\u7d20 */\nfunction remove(nums: number[], index: number): void {\n// \u628a\u7d22\u5f15 index \u4e4b\u540e\u7684\u6240\u6709\u5143\u7d20\u5411\u524d\u79fb\u52a8\u4e00\u4f4d\nfor (let i = index; i &lt; nums.length - 1; i++) {\nnums[i] = nums[i + 1];\n}\n}\n</code></pre> array.c<pre><code>/* \u5220\u9664\u7d22\u5f15 index \u5904\u5143\u7d20 */\n// \u6ce8\u610f\uff1astdio.h \u5360\u7528\u4e86 remove \u5173\u952e\u8bcd\nvoid removeItem(int *nums, int size, int index) {\n// \u628a\u7d22\u5f15 index \u4e4b\u540e\u7684\u6240\u6709\u5143\u7d20\u5411\u524d\u79fb\u52a8\u4e00\u4f4d\nfor (int i = index; i &lt; size - 1; i++) {\nnums[i] = nums[i + 1];\n}\n}\n</code></pre> array.cs<pre><code>/* \u5220\u9664\u7d22\u5f15 index \u5904\u5143\u7d20 */\nvoid remove(int[] nums, int index) {\n// \u628a\u7d22\u5f15 index \u4e4b\u540e\u7684\u6240\u6709\u5143\u7d20\u5411\u524d\u79fb\u52a8\u4e00\u4f4d\nfor (int i = index; i &lt; nums.Length - 1; i++) {\nnums[i] = nums[i + 1];\n}\n}\n</code></pre> array.swift<pre><code>/* \u5220\u9664\u7d22\u5f15 index \u5904\u5143\u7d20 */\nfunc remove(nums: inout [Int], index: Int) {\nlet count = nums.count\n// \u628a\u7d22\u5f15 index \u4e4b\u540e\u7684\u6240\u6709\u5143\u7d20\u5411\u524d\u79fb\u52a8\u4e00\u4f4d\nfor i in sequence(first: index, next: { $0 &lt; count - 1 - 1 ? $0 + 1 : nil }) {\nnums[i] = nums[i + 1]\n}\n}\n</code></pre> array.zig<pre><code>// \u5220\u9664\u7d22\u5f15 index \u5904\u5143\u7d20\nfn remove(nums: []i32, index: usize) void {\n// \u628a\u7d22\u5f15 index \u4e4b\u540e\u7684\u6240\u6709\u5143\u7d20\u5411\u524d\u79fb\u52a8\u4e00\u4f4d\nvar i = index;\nwhile (i &lt; nums.len - 1) : (i += 1) {\nnums[i] = nums[i + 1];\n}\n}\n</code></pre> array.dart<pre><code>/* \u5220\u9664\u7d22\u5f15 index \u5904\u5143\u7d20 */\nvoid remove(List nums, int index) {\n// \u628a\u7d22\u5f15 index \u4e4b\u540e\u7684\u6240\u6709\u5143\u7d20\u5411\u524d\u79fb\u52a8\u4e00\u4f4d\nfor (var i = index; i &lt; nums.length - 1; i++) {\nnums[i] = nums[i + 1];\n}\n}\n</code></pre> <p>\u603b\u7ed3\u6765\u770b\uff0c\u6570\u7ec4\u7684\u63d2\u5165\u4e0e\u5220\u9664\u64cd\u4f5c\u6709\u4ee5\u4e0b\u7f3a\u70b9\uff1a</p> <ul> <li>\u65f6\u95f4\u590d\u6742\u5ea6\u9ad8\uff1a\u6570\u7ec4\u7684\u63d2\u5165\u548c\u5220\u9664\u7684\u5e73\u5747\u65f6\u95f4\u590d\u6742\u5ea6\u5747\u4e3a \\(O(n)\\) \uff0c\u5176\u4e2d \\(n\\) \u4e3a\u6570\u7ec4\u957f\u5ea6\u3002</li> <li>\u4e22\u5931\u5143\u7d20\uff1a\u7531\u4e8e\u6570\u7ec4\u7684\u957f\u5ea6\u4e0d\u53ef\u53d8\uff0c\u56e0\u6b64\u5728\u63d2\u5165\u5143\u7d20\u540e\uff0c\u8d85\u51fa\u6570\u7ec4\u957f\u5ea6\u8303\u56f4\u7684\u5143\u7d20\u4f1a\u4e22\u5931\u3002</li> <li>\u5185\u5b58\u6d6a\u8d39\uff1a\u6211\u4eec\u53ef\u4ee5\u521d\u59cb\u5316\u4e00\u4e2a\u6bd4\u8f83\u957f\u7684\u6570\u7ec4\uff0c\u53ea\u7528\u524d\u9762\u4e00\u90e8\u5206\uff0c\u8fd9\u6837\u5728\u63d2\u5165\u6570\u636e\u65f6\uff0c\u4e22\u5931\u7684\u672b\u5c3e\u5143\u7d20\u90fd\u662f\u6211\u4eec\u4e0d\u5173\u5fc3\u7684\uff0c\u4f46\u8fd9\u6837\u505a\u540c\u65f6\u4e5f\u4f1a\u9020\u6210\u5185\u5b58\u7a7a\u95f4\u7684\u6d6a\u8d39\u3002</li> </ul>"},{"location":"chapter_array_and_linkedlist/array/#413","title":"4.1.3. \u00a0 \u6570\u7ec4\u5e38\u7528\u64cd\u4f5c","text":"<p>\u6570\u7ec4\u904d\u5386\u3002\u4ee5\u4e0b\u4ecb\u7ecd\u4e24\u79cd\u5e38\u7528\u7684\u904d\u5386\u65b9\u6cd5\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart array.java<pre><code>/* \u904d\u5386\u6570\u7ec4 */\nvoid traverse(int[] nums) {\nint count = 0;\n// \u901a\u8fc7\u7d22\u5f15\u904d\u5386\u6570\u7ec4\nfor (int i = 0; i &lt; nums.length; i++) {\ncount++;\n}\n// \u76f4\u63a5\u904d\u5386\u6570\u7ec4\nfor (int num : nums) {\ncount++;\n}\n}\n</code></pre> array.cpp<pre><code>/* \u904d\u5386\u6570\u7ec4 */\nvoid traverse(int *nums, int size) {\nint count = 0;\n// \u901a\u8fc7\u7d22\u5f15\u904d\u5386\u6570\u7ec4\nfor (int i = 0; i &lt; size; i++) {\ncount++;\n}\n}\n</code></pre> array.py<pre><code>def traverse(nums: list[int]) -&gt; None:\n\"\"\"\u904d\u5386\u6570\u7ec4\"\"\"\ncount = 0\n# \u901a\u8fc7\u7d22\u5f15\u904d\u5386\u6570\u7ec4\nfor i in range(len(nums)):\ncount += 1\n# \u76f4\u63a5\u904d\u5386\u6570\u7ec4\nfor num in nums:\ncount += 1\n# \u540c\u65f6\u904d\u5386\u6570\u636e\u7d22\u5f15\u548c\u5143\u7d20\nfor i, num in enumerate(nums):\ncount += 1\n</code></pre> array.go<pre><code>/* \u904d\u5386\u6570\u7ec4 */\nfunc traverse(nums []int) {\ncount := 0\n// \u901a\u8fc7\u7d22\u5f15\u904d\u5386\u6570\u7ec4\nfor i := 0; i &lt; len(nums); i++ {\ncount++\n}\ncount = 0\n// \u76f4\u63a5\u904d\u5386\u6570\u7ec4\nfor range nums {\ncount++\n}\n}\n</code></pre> array.js<pre><code>/* \u904d\u5386\u6570\u7ec4 */\nfunction traverse(nums) {\nlet count = 0;\n// \u901a\u8fc7\u7d22\u5f15\u904d\u5386\u6570\u7ec4\nfor (let i = 0; i &lt; nums.length; i++) {\ncount++;\n}\n// \u76f4\u63a5\u904d\u5386\u6570\u7ec4\nfor (let num of nums) {\ncount += 1;\n}\n}\n</code></pre> array.ts<pre><code>/* \u904d\u5386\u6570\u7ec4 */\nfunction traverse(nums: number[]): void {\nlet count = 0;\n// \u901a\u8fc7\u7d22\u5f15\u904d\u5386\u6570\u7ec4\nfor (let i = 0; i &lt; nums.length; i++) {\ncount++;\n}\n// \u76f4\u63a5\u904d\u5386\u6570\u7ec4\nfor (let num of nums) {\ncount += 1;\n}\n}\n</code></pre> array.c<pre><code>/* \u904d\u5386\u6570\u7ec4 */\nvoid traverse(int *nums, int size) {\nint count = 0;\n// \u901a\u8fc7\u7d22\u5f15\u904d\u5386\u6570\u7ec4\nfor (int i = 0; i &lt; size; i++) {\ncount++;\n}\n}\n</code></pre> array.cs<pre><code>/* \u904d\u5386\u6570\u7ec4 */\nvoid traverse(int[] nums) {\nint count = 0;\n// \u901a\u8fc7\u7d22\u5f15\u904d\u5386\u6570\u7ec4\nfor (int i = 0; i &lt; nums.Length; i++) {\ncount++;\n}\n// \u76f4\u63a5\u904d\u5386\u6570\u7ec4\nforeach (int num in nums) {\ncount++;\n}\n}\n</code></pre> array.swift<pre><code>/* \u904d\u5386\u6570\u7ec4 */\nfunc traverse(nums: [Int]) {\nvar count = 0\n// \u901a\u8fc7\u7d22\u5f15\u904d\u5386\u6570\u7ec4\nfor _ in nums.indices {\ncount += 1\n}\n// \u76f4\u63a5\u904d\u5386\u6570\u7ec4\nfor _ in nums {\ncount += 1\n}\n}\n</code></pre> array.zig<pre><code>// \u904d\u5386\u6570\u7ec4\nfn traverse(nums: []i32) void {\nvar count: i32 = 0;\n// \u901a\u8fc7\u7d22\u5f15\u904d\u5386\u6570\u7ec4\nvar i: i32 = 0;\nwhile (i &lt; nums.len) : (i += 1) {\ncount += 1;\n}\ncount = 0;\n// \u76f4\u63a5\u904d\u5386\u6570\u7ec4\nfor (nums) |_| {\ncount += 1;\n}\n}\n</code></pre> array.dart<pre><code>/* \u904d\u5386\u6570\u7ec4\u5143\u7d20 */\nvoid traverse(List nums) {\nvar count = 0;\n// \u901a\u8fc7\u7d22\u5f15\u904d\u5386\u6570\u7ec4\nfor (var i = 0; i &lt; nums.length; i++) {\ncount++;\n}\n// \u76f4\u63a5\u904d\u5386\u6570\u7ec4\nfor (var num in nums) {\ncount++;\n}\n// \u901a\u8fc7 forEach \u65b9\u6cd5\u904d\u5386\u6570\u7ec4\nnums.forEach((element) {\ncount++;\n});\n}\n</code></pre> <p>\u6570\u7ec4\u67e5\u627e\u3002\u901a\u8fc7\u904d\u5386\u6570\u7ec4\uff0c\u67e5\u627e\u6570\u7ec4\u5185\u7684\u6307\u5b9a\u5143\u7d20\uff0c\u5e76\u8f93\u51fa\u5bf9\u5e94\u7d22\u5f15\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart array.java<pre><code>/* \u5728\u6570\u7ec4\u4e2d\u67e5\u627e\u6307\u5b9a\u5143\u7d20 */\nint find(int[] nums, int target) {\nfor (int i = 0; i &lt; nums.length; i++) {\nif (nums[i] == target)\nreturn i;\n}\nreturn -1;\n}\n</code></pre> array.cpp<pre><code>/* \u5728\u6570\u7ec4\u4e2d\u67e5\u627e\u6307\u5b9a\u5143\u7d20 */\nint find(int *nums, int size, int target) {\nfor (int i = 0; i &lt; size; i++) {\nif (nums[i] == target)\nreturn i;\n}\nreturn -1;\n}\n</code></pre> array.py<pre><code>def find(nums: list[int], target: int) -&gt; int:\n\"\"\"\u5728\u6570\u7ec4\u4e2d\u67e5\u627e\u6307\u5b9a\u5143\u7d20\"\"\"\nfor i in range(len(nums)):\nif nums[i] == target:\nreturn i\nreturn -1\n</code></pre> array.go<pre><code>/* \u5728\u6570\u7ec4\u4e2d\u67e5\u627e\u6307\u5b9a\u5143\u7d20 */\nfunc find(nums []int, target int) (index int) {\nindex = -1\nfor i := 0; i &lt; len(nums); i++ {\nif nums[i] == target {\nindex = i\nbreak\n}\n}\nreturn\n}\n</code></pre> array.js<pre><code>/* \u5728\u6570\u7ec4\u4e2d\u67e5\u627e\u6307\u5b9a\u5143\u7d20 */\nfunction find(nums, target) {\nfor (let i = 0; i &lt; nums.length; i++) {\nif (nums[i] == target) return i;\n}\nreturn -1;\n}\n</code></pre> array.ts<pre><code>/* \u5728\u6570\u7ec4\u4e2d\u67e5\u627e\u6307\u5b9a\u5143\u7d20 */\nfunction find(nums: number[], target: number): number {\nfor (let i = 0; i &lt; nums.length; i++) {\nif (nums[i] === target) {\nreturn i;\n}\n}\nreturn -1;\n}\n</code></pre> array.c<pre><code>/* \u5728\u6570\u7ec4\u4e2d\u67e5\u627e\u6307\u5b9a\u5143\u7d20 */\nint find(int *nums, int size, int target) {\nfor (int i = 0; i &lt; size; i++) {\nif (nums[i] == target)\nreturn i;\n}\nreturn -1;\n}\n</code></pre> array.cs<pre><code>/* \u5728\u6570\u7ec4\u4e2d\u67e5\u627e\u6307\u5b9a\u5143\u7d20 */\nint find(int[] nums, int target) {\nfor (int i = 0; i &lt; nums.Length; i++) {\nif (nums[i] == target)\nreturn i;\n}\nreturn -1;\n}\n</code></pre> array.swift<pre><code>/* \u5728\u6570\u7ec4\u4e2d\u67e5\u627e\u6307\u5b9a\u5143\u7d20 */\nfunc find(nums: [Int], target: Int) -&gt; Int {\nfor i in nums.indices {\nif nums[i] == target {\nreturn i\n}\n}\nreturn -1\n}\n</code></pre> array.zig<pre><code>// \u5728\u6570\u7ec4\u4e2d\u67e5\u627e\u6307\u5b9a\u5143\u7d20\nfn find(nums: []i32, target: i32) i32 {\nfor (nums) |num, i| {\nif (num == target) return @intCast(i32, i);\n}\nreturn -1;\n}\n</code></pre> array.dart<pre><code>/* \u5728\u6570\u7ec4\u4e2d\u67e5\u627e\u6307\u5b9a\u5143\u7d20 */\nint find(List nums, int target) {\nfor (var i = 0; i &lt; nums.length; i++) {\nif (nums[i] == target) return i;\n}\nreturn -1;\n}\n</code></pre>"},{"location":"chapter_array_and_linkedlist/array/#414","title":"4.1.4. \u00a0 \u6570\u7ec4\u5178\u578b\u5e94\u7528","text":"<p>\u968f\u673a\u8bbf\u95ee\u3002\u5982\u679c\u6211\u4eec\u60f3\u8981\u968f\u673a\u62bd\u53d6\u4e00\u4e9b\u6837\u672c\uff0c\u90a3\u4e48\u53ef\u4ee5\u7528\u6570\u7ec4\u5b58\u50a8\uff0c\u5e76\u751f\u6210\u4e00\u4e2a\u968f\u673a\u5e8f\u5217\uff0c\u6839\u636e\u7d22\u5f15\u5b9e\u73b0\u6837\u672c\u7684\u968f\u673a\u62bd\u53d6\u3002</p> <p>\u4e8c\u5206\u67e5\u627e\u3002\u4f8b\u5982\u524d\u6587\u67e5\u5b57\u5178\u7684\u4f8b\u5b50\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u5b57\u5178\u4e2d\u7684\u6240\u6709\u5b57\u6309\u7167\u62fc\u97f3\u987a\u5e8f\u5b58\u50a8\u5728\u6570\u7ec4\u4e2d\uff0c\u7136\u540e\u4f7f\u7528\u4e0e\u65e5\u5e38\u67e5\u7eb8\u8d28\u5b57\u5178\u76f8\u540c\u7684\u201c\u7ffb\u5f00\u4e2d\u95f4\uff0c\u6392\u9664\u4e00\u534a\u201d\u7684\u65b9\u5f0f\uff0c\u6765\u5b9e\u73b0\u4e00\u4e2a\u67e5\u7535\u5b50\u5b57\u5178\u7684\u7b97\u6cd5\u3002</p> <p>\u6df1\u5ea6\u5b66\u4e60\u3002\u795e\u7ecf\u7f51\u7edc\u4e2d\u5927\u91cf\u4f7f\u7528\u4e86\u5411\u91cf\u3001\u77e9\u9635\u3001\u5f20\u91cf\u4e4b\u95f4\u7684\u7ebf\u6027\u4ee3\u6570\u8fd0\u7b97\uff0c\u8fd9\u4e9b\u6570\u636e\u90fd\u662f\u4ee5\u6570\u7ec4\u7684\u5f62\u5f0f\u6784\u5efa\u7684\u3002\u6570\u7ec4\u662f\u795e\u7ecf\u7f51\u7edc\u7f16\u7a0b\u4e2d\u6700\u5e38\u4f7f\u7528\u7684\u6570\u636e\u7ed3\u6784\u3002</p>"},{"location":"chapter_array_and_linkedlist/linked_list/","title":"4.2. \u00a0 \u94fe\u8868","text":"<p>\u5185\u5b58\u7a7a\u95f4\u662f\u6240\u6709\u7a0b\u5e8f\u7684\u516c\u5171\u8d44\u6e90\uff0c\u6392\u9664\u5df2\u88ab\u5360\u7528\u7684\u5185\u5b58\u7a7a\u95f4\uff0c\u7a7a\u95f2\u5185\u5b58\u7a7a\u95f4\u901a\u5e38\u6563\u843d\u5728\u5185\u5b58\u5404\u5904\u3002\u5728\u4e0a\u4e00\u8282\u4e2d\uff0c\u6211\u4eec\u63d0\u5230\u5b58\u50a8\u6570\u7ec4\u7684\u5185\u5b58\u7a7a\u95f4\u5fc5\u987b\u662f\u8fde\u7eed\u7684\uff0c\u800c\u5f53\u6211\u4eec\u9700\u8981\u7533\u8bf7\u4e00\u4e2a\u975e\u5e38\u5927\u7684\u6570\u7ec4\u65f6\uff0c\u7a7a\u95f2\u5185\u5b58\u4e2d\u53ef\u80fd\u6ca1\u6709\u8fd9\u4e48\u5927\u7684\u8fde\u7eed\u7a7a\u95f4\u3002\u4e0e\u6570\u7ec4\u76f8\u6bd4\uff0c\u94fe\u8868\u66f4\u5177\u7075\u6d3b\u6027\uff0c\u5b83\u53ef\u4ee5\u88ab\u5b58\u50a8\u5728\u975e\u8fde\u7eed\u7684\u5185\u5b58\u7a7a\u95f4\u4e2d\u3002</p> <p>\u300c\u94fe\u8868 Linked List\u300d\u662f\u4e00\u79cd\u7ebf\u6027\u6570\u636e\u7ed3\u6784\uff0c\u5176\u6bcf\u4e2a\u5143\u7d20\u90fd\u662f\u4e00\u4e2a\u8282\u70b9\u5bf9\u8c61\uff0c\u5404\u4e2a\u8282\u70b9\u4e4b\u95f4\u901a\u8fc7\u6307\u9488\u8fde\u63a5\uff0c\u4ece\u5f53\u524d\u8282\u70b9\u901a\u8fc7\u6307\u9488\u53ef\u4ee5\u8bbf\u95ee\u5230\u4e0b\u4e00\u4e2a\u8282\u70b9\u3002\u7531\u4e8e\u6307\u9488\u8bb0\u5f55\u4e86\u4e0b\u4e2a\u8282\u70b9\u7684\u5185\u5b58\u5730\u5740\uff0c\u56e0\u6b64\u65e0\u9700\u4fdd\u8bc1\u5185\u5b58\u5730\u5740\u7684\u8fde\u7eed\u6027\uff0c\u4ece\u800c\u53ef\u4ee5\u5c06\u5404\u4e2a\u8282\u70b9\u5206\u6563\u5b58\u50a8\u5728\u5185\u5b58\u5404\u5904\u3002</p> <p>\u94fe\u8868\u300c\u8282\u70b9 Node\u300d\u5305\u542b\u4e24\u9879\u6570\u636e\uff0c\u4e00\u662f\u8282\u70b9\u300c\u503c Value\u300d\uff0c\u4e8c\u662f\u6307\u5411\u4e0b\u4e00\u8282\u70b9\u7684\u300c\u6307\u9488 Pointer\u300d\uff0c\u6216\u79f0\u300c\u5f15\u7528 Reference\u300d\u3002</p> <p></p> <p> Fig. \u94fe\u8868\u5b9a\u4e49\u4e0e\u5b58\u50a8\u65b9\u5f0f </p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart <pre><code>/* \u94fe\u8868\u8282\u70b9\u7c7b */\nclass ListNode {\nint val;        // \u8282\u70b9\u503c\nListNode next;  // \u6307\u5411\u4e0b\u4e00\u8282\u70b9\u7684\u6307\u9488\uff08\u5f15\u7528\uff09\nListNode(int x) { val = x; }  // \u6784\u9020\u51fd\u6570\n}\n</code></pre> <pre><code>/* \u94fe\u8868\u8282\u70b9\u7ed3\u6784\u4f53 */\nstruct ListNode {\nint val;         // \u8282\u70b9\u503c\nListNode *next;  // \u6307\u5411\u4e0b\u4e00\u8282\u70b9\u7684\u6307\u9488\uff08\u5f15\u7528\uff09\nListNode(int x) : val(x), next(nullptr) {}  // \u6784\u9020\u51fd\u6570\n};\n</code></pre> <pre><code>class ListNode:\n\"\"\"\u94fe\u8868\u8282\u70b9\u7c7b\"\"\"\ndef __init__(self, val: int):\nself.val: int = val                  # \u8282\u70b9\u503c\nself.next: Optional[ListNode] = None # \u6307\u5411\u4e0b\u4e00\u8282\u70b9\u7684\u6307\u9488\uff08\u5f15\u7528\uff09\n</code></pre> <pre><code>/* \u94fe\u8868\u8282\u70b9\u7ed3\u6784\u4f53 */\ntype ListNode struct {\nVal  int       // \u8282\u70b9\u503c\nNext *ListNode // \u6307\u5411\u4e0b\u4e00\u8282\u70b9\u7684\u6307\u9488\uff08\u5f15\u7528\uff09\n}\n// NewListNode \u6784\u9020\u51fd\u6570\uff0c\u521b\u5efa\u4e00\u4e2a\u65b0\u7684\u94fe\u8868\nfunc NewListNode(val int) *ListNode {\nreturn &amp;ListNode{\nVal:  val,\nNext: nil,\n}\n}\n</code></pre> <pre><code>/* \u94fe\u8868\u8282\u70b9\u7c7b */\nclass ListNode {\nval;\nnext;\nconstructor(val, next) {\nthis.val = (val === undefined ? 0 : val);       // \u8282\u70b9\u503c\nthis.next = (next === undefined ? null : next); // \u6307\u5411\u4e0b\u4e00\u8282\u70b9\u7684\u5f15\u7528\n}\n}\n</code></pre> <pre><code>/* \u94fe\u8868\u8282\u70b9\u7c7b */\nclass ListNode {\nval: number;\nnext: ListNode | null;\nconstructor(val?: number, next?: ListNode | null) {\nthis.val = val === undefined ? 0 : val;        // \u8282\u70b9\u503c\nthis.next = next === undefined ? null : next;  // \u6307\u5411\u4e0b\u4e00\u8282\u70b9\u7684\u5f15\u7528\n}\n}\n</code></pre> <pre><code>/* \u94fe\u8868\u8282\u70b9\u7ed3\u6784\u4f53 */\nstruct ListNode {\nint val;               // \u8282\u70b9\u503c\nstruct ListNode *next; // \u6307\u5411\u4e0b\u4e00\u8282\u70b9\u7684\u6307\u9488\uff08\u5f15\u7528\uff09\n};\ntypedef struct ListNode ListNode;\n/* \u6784\u9020\u51fd\u6570 */\nListNode *newListNode(int val) {\nListNode *node, *next;\nnode = (ListNode *) malloc(sizeof(ListNode));\nnode-&gt;val = val;\nnode-&gt;next = NULL;\nreturn node;\n}\n</code></pre> <pre><code>/* \u94fe\u8868\u8282\u70b9\u7c7b */\nclass ListNode\n{\nint val;         // \u8282\u70b9\u503c\nListNode next;   // \u6307\u5411\u4e0b\u4e00\u8282\u70b9\u7684\u5f15\u7528\nListNode(int x) =&gt; val = x;  //\u6784\u9020\u51fd\u6570\n}\n</code></pre> <pre><code>/* \u94fe\u8868\u8282\u70b9\u7c7b */\nclass ListNode {\nvar val: Int // \u8282\u70b9\u503c\nvar next: ListNode? // \u6307\u5411\u4e0b\u4e00\u8282\u70b9\u7684\u6307\u9488\uff08\u5f15\u7528\uff09\ninit(x: Int) { // \u6784\u9020\u51fd\u6570\nval = x\n}\n}\n</code></pre> <pre><code>// \u94fe\u8868\u8282\u70b9\u7c7b\npub fn ListNode(comptime T: type) type {\nreturn struct {\nconst Self = @This();\nval: T = 0, // \u8282\u70b9\u503c\nnext: ?*Self = null, // \u6307\u5411\u4e0b\u4e00\u8282\u70b9\u7684\u6307\u9488\uff08\u5f15\u7528\uff09\n// \u6784\u9020\u51fd\u6570\npub fn init(self: *Self, x: i32) void {\nself.val = x;\nself.next = null;\n}\n};\n}\n</code></pre> <pre><code>/* \u94fe\u8868\u8282\u70b9\u7c7b */\nclass ListNode {\nint val; // \u8282\u70b9\u503c\nListNode? next; // \u6307\u5411\u4e0b\u4e00\u8282\u70b9\u7684\u6307\u9488\uff08\u5f15\u7528\uff09\nListNode(this.val, [this.next]); // \u6784\u9020\u51fd\u6570\n}\n</code></pre> <p>\u5c3e\u8282\u70b9\u6307\u5411\u4ec0\u4e48\uff1f</p> <p>\u6211\u4eec\u5c06\u94fe\u8868\u7684\u6700\u540e\u4e00\u4e2a\u8282\u70b9\u79f0\u4e3a\u300c\u5c3e\u8282\u70b9\u300d\uff0c\u5176\u6307\u5411\u7684\u662f\u201c\u7a7a\u201d\uff0c\u5728 Java, C++, Python \u4e2d\u5206\u522b\u8bb0\u4e3a \\(\\text{null}\\) , \\(\\text{nullptr}\\) , \\(\\text{None}\\) \u3002\u5728\u4e0d\u5f15\u8d77\u6b67\u4e49\u7684\u524d\u63d0\u4e0b\uff0c\u672c\u4e66\u90fd\u4f7f\u7528 \\(\\text{null}\\) \u6765\u8868\u793a\u7a7a\u3002</p> <p>\u5982\u4f55\u79f0\u547c\u94fe\u8868\uff1f</p> <p>\u5728\u7f16\u7a0b\u8bed\u8a00\u4e2d\uff0c\u6570\u7ec4\u6574\u4f53\u5c31\u662f\u4e00\u4e2a\u53d8\u91cf\uff0c\u4f8b\u5982\u6570\u7ec4 <code>nums</code> \uff0c\u5305\u542b\u5404\u4e2a\u5143\u7d20 <code>nums[0]</code> , <code>nums[1]</code> \u7b49\u7b49\u3002\u800c\u94fe\u8868\u662f\u7531\u591a\u4e2a\u8282\u70b9\u5bf9\u8c61\u7ec4\u6210\uff0c\u6211\u4eec\u901a\u5e38\u5c06\u5934\u8282\u70b9\u5f53\u4f5c\u94fe\u8868\u7684\u4ee3\u79f0\uff0c\u4f8b\u5982\u5934\u8282\u70b9 <code>head</code> \u548c\u94fe\u8868 <code>head</code> \u5b9e\u9645\u4e0a\u662f\u540c\u4e49\u7684\u3002</p> <p>\u94fe\u8868\u521d\u59cb\u5316\u65b9\u6cd5\u3002\u5efa\u7acb\u94fe\u8868\u5206\u4e3a\u4e24\u6b65\uff0c\u7b2c\u4e00\u6b65\u662f\u521d\u59cb\u5316\u5404\u4e2a\u8282\u70b9\u5bf9\u8c61\uff0c\u7b2c\u4e8c\u6b65\u662f\u6784\u5efa\u5f15\u7528\u6307\u5411\u5173\u7cfb\u3002\u5b8c\u6210\u540e\uff0c\u5373\u53ef\u4ee5\u4ece\u94fe\u8868\u7684\u5934\u8282\u70b9\uff08\u5373\u9996\u4e2a\u8282\u70b9\uff09\u51fa\u53d1\uff0c\u901a\u8fc7\u6307\u9488 <code>next</code> \u4f9d\u6b21\u8bbf\u95ee\u6240\u6709\u8282\u70b9\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart linked_list.java<pre><code>/* \u521d\u59cb\u5316\u94fe\u8868 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */\n// \u521d\u59cb\u5316\u5404\u4e2a\u8282\u70b9 \nListNode n0 = new ListNode(1);\nListNode n1 = new ListNode(3);\nListNode n2 = new ListNode(2);\nListNode n3 = new ListNode(5);\nListNode n4 = new ListNode(4);\n// \u6784\u5efa\u5f15\u7528\u6307\u5411\nn0.next = n1;\nn1.next = n2;\nn2.next = n3;\nn3.next = n4;\n</code></pre> linked_list.cpp<pre><code>/* \u521d\u59cb\u5316\u94fe\u8868 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */\n// \u521d\u59cb\u5316\u5404\u4e2a\u8282\u70b9 \nListNode* n0 = new ListNode(1);\nListNode* n1 = new ListNode(3);\nListNode* n2 = new ListNode(2);\nListNode* n3 = new ListNode(5);\nListNode* n4 = new ListNode(4);\n// \u6784\u5efa\u5f15\u7528\u6307\u5411\nn0-&gt;next = n1;\nn1-&gt;next = n2;\nn2-&gt;next = n3;\nn3-&gt;next = n4;\n</code></pre> linked_list.py<pre><code># \u521d\u59cb\u5316\u94fe\u8868 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4\n# \u521d\u59cb\u5316\u5404\u4e2a\u8282\u70b9 \nn0 = ListNode(1)\nn1 = ListNode(3)\nn2 = ListNode(2)\nn3 = ListNode(5)\nn4 = ListNode(4)\n# \u6784\u5efa\u5f15\u7528\u6307\u5411\nn0.next = n1\nn1.next = n2\nn2.next = n3\nn3.next = n4\n</code></pre> linked_list.go<pre><code>/* \u521d\u59cb\u5316\u94fe\u8868 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */\n// \u521d\u59cb\u5316\u5404\u4e2a\u8282\u70b9\nn0 := NewListNode(1)\nn1 := NewListNode(3)\nn2 := NewListNode(2)\nn3 := NewListNode(5)\nn4 := NewListNode(4)\n// \u6784\u5efa\u5f15\u7528\u6307\u5411\nn0.Next = n1\nn1.Next = n2\nn2.Next = n3\nn3.Next = n4\n</code></pre> linked_list.js<pre><code>/* \u521d\u59cb\u5316\u94fe\u8868 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */\n// \u521d\u59cb\u5316\u5404\u4e2a\u8282\u70b9\nconst n0 = new ListNode(1);\nconst n1 = new ListNode(3);\nconst n2 = new ListNode(2);\nconst n3 = new ListNode(5);\nconst n4 = new ListNode(4);\n// \u6784\u5efa\u5f15\u7528\u6307\u5411\nn0.next = n1;\nn1.next = n2;\nn2.next = n3;\nn3.next = n4;\n</code></pre> linked_list.ts<pre><code>/* \u521d\u59cb\u5316\u94fe\u8868 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */\n// \u521d\u59cb\u5316\u5404\u4e2a\u8282\u70b9\nconst n0 = new ListNode(1);\nconst n1 = new ListNode(3);\nconst n2 = new ListNode(2);\nconst n3 = new ListNode(5);\nconst n4 = new ListNode(4);\n// \u6784\u5efa\u5f15\u7528\u6307\u5411\nn0.next = n1;\nn1.next = n2;\nn2.next = n3;\nn3.next = n4;\n</code></pre> linked_list.c<pre><code>/* \u521d\u59cb\u5316\u94fe\u8868 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */\n// \u521d\u59cb\u5316\u5404\u4e2a\u8282\u70b9 \nListNode* n0 = newListNode(1);\nListNode* n1 = newListNode(3);\nListNode* n2 = newListNode(2);\nListNode* n3 = newListNode(5);\nListNode* n4 = newListNode(4);\n// \u6784\u5efa\u5f15\u7528\u6307\u5411\nn0-&gt;next = n1;\nn1-&gt;next = n2;\nn2-&gt;next = n3;\nn3-&gt;next = n4;\n</code></pre> linked_list.cs<pre><code>/* \u521d\u59cb\u5316\u94fe\u8868 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */\n// \u521d\u59cb\u5316\u5404\u4e2a\u8282\u70b9 \nListNode n0 = new ListNode(1);\nListNode n1 = new ListNode(3);\nListNode n2 = new ListNode(2);\nListNode n3 = new ListNode(5);\nListNode n4 = new ListNode(4);\n// \u6784\u5efa\u5f15\u7528\u6307\u5411\nn0.next = n1;\nn1.next = n2;\nn2.next = n3;\nn3.next = n4;\n</code></pre> linked_list.swift<pre><code>/* \u521d\u59cb\u5316\u94fe\u8868 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */\n// \u521d\u59cb\u5316\u5404\u4e2a\u8282\u70b9\nlet n0 = ListNode(x: 1)\nlet n1 = ListNode(x: 3)\nlet n2 = ListNode(x: 2)\nlet n3 = ListNode(x: 5)\nlet n4 = ListNode(x: 4)\n// \u6784\u5efa\u5f15\u7528\u6307\u5411\nn0.next = n1\nn1.next = n2\nn2.next = n3\nn3.next = n4\n</code></pre> linked_list.zig<pre><code>// \u521d\u59cb\u5316\u94fe\u8868\n// \u521d\u59cb\u5316\u5404\u4e2a\u8282\u70b9 \nvar n0 = inc.ListNode(i32){.val = 1};\nvar n1 = inc.ListNode(i32){.val = 3};\nvar n2 = inc.ListNode(i32){.val = 2};\nvar n3 = inc.ListNode(i32){.val = 5};\nvar n4 = inc.ListNode(i32){.val = 4};\n// \u6784\u5efa\u5f15\u7528\u6307\u5411\nn0.next = &amp;n1;\nn1.next = &amp;n2;\nn2.next = &amp;n3;\nn3.next = &amp;n4;\n</code></pre> linked_list.dart<pre><code>/* \u521d\u59cb\u5316\u94fe\u8868 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */\\\n// \u521d\u59cb\u5316\u5404\u4e2a\u8282\u70b9\nListNode n0 = ListNode(1);\nListNode n1 = ListNode(3);\nListNode n2 = ListNode(2);\nListNode n3 = ListNode(5);\nListNode n4 = ListNode(4);\n// \u6784\u5efa\u5f15\u7528\u6307\u5411\nn0.next = n1;\nn1.next = n2;\nn2.next = n3;\nn3.next = n4;\n</code></pre>"},{"location":"chapter_array_and_linkedlist/linked_list/#421","title":"4.2.1. \u00a0 \u94fe\u8868\u4f18\u70b9","text":"<p>\u94fe\u8868\u4e2d\u63d2\u5165\u4e0e\u5220\u9664\u8282\u70b9\u7684\u64cd\u4f5c\u6548\u7387\u9ad8\u3002\u4f8b\u5982\uff0c\u5982\u679c\u6211\u4eec\u60f3\u5728\u94fe\u8868\u4e2d\u95f4\u7684\u4e24\u4e2a\u8282\u70b9 <code>A</code> , <code>B</code> \u4e4b\u95f4\u63d2\u5165\u4e00\u4e2a\u65b0\u8282\u70b9 <code>P</code> \uff0c\u6211\u4eec\u53ea\u9700\u8981\u6539\u53d8\u4e24\u4e2a\u8282\u70b9\u6307\u9488\u5373\u53ef\uff0c\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(1)\\) \uff1b\u76f8\u6bd4\u4e4b\u4e0b\uff0c\u6570\u7ec4\u7684\u63d2\u5165\u64cd\u4f5c\u6548\u7387\u8981\u4f4e\u5f97\u591a\u3002</p> <p></p> <p> Fig. \u94fe\u8868\u63d2\u5165\u8282\u70b9 </p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart linked_list.java<pre><code>/* \u5728\u94fe\u8868\u7684\u8282\u70b9 n0 \u4e4b\u540e\u63d2\u5165\u8282\u70b9 P */\nvoid insert(ListNode n0, ListNode P) {\nListNode n1 = n0.next;\nP.next = n1;\nn0.next = P;\n}\n</code></pre> linked_list.cpp<pre><code>/* \u5728\u94fe\u8868\u7684\u8282\u70b9 n0 \u4e4b\u540e\u63d2\u5165\u8282\u70b9 P */\nvoid insert(ListNode *n0, ListNode *P) {\nListNode *n1 = n0-&gt;next;\nP-&gt;next = n1;\nn0-&gt;next = P;\n}\n</code></pre> linked_list.py<pre><code>def insert(n0: ListNode, P: ListNode) -&gt; None:\n\"\"\"\u5728\u94fe\u8868\u7684\u8282\u70b9 n0 \u4e4b\u540e\u63d2\u5165\u8282\u70b9 P\"\"\"\nn1 = n0.next\nP.next = n1\nn0.next = P\n</code></pre> linked_list.go<pre><code>/* \u5728\u94fe\u8868\u7684\u8282\u70b9 n0 \u4e4b\u540e\u63d2\u5165\u8282\u70b9 P */\nfunc insertNode(n0 *ListNode, P *ListNode) {\nn1 := n0.Next\nP.Next = n1\nn0.Next = P\n}\n</code></pre> linked_list.js<pre><code>/* \u5728\u94fe\u8868\u7684\u8282\u70b9 n0 \u4e4b\u540e\u63d2\u5165\u8282\u70b9 P */\nfunction insert(n0, P) {\nconst n1 = n0.next;\nP.next = n1;\nn0.next = P;\n}\n</code></pre> linked_list.ts<pre><code>/* \u5728\u94fe\u8868\u7684\u8282\u70b9 n0 \u4e4b\u540e\u63d2\u5165\u8282\u70b9 P */\nfunction insert(n0: ListNode, P: ListNode): void {\nconst n1 = n0.next;\nP.next = n1;\nn0.next = P;\n}\n</code></pre> linked_list.c<pre><code>/* \u5728\u94fe\u8868\u7684\u8282\u70b9 n0 \u4e4b\u540e\u63d2\u5165\u8282\u70b9 P */\nvoid insert(ListNode *n0, ListNode *P) {\nListNode *n1 = n0-&gt;next;\nP-&gt;next = n1;\nn0-&gt;next = P;\n}\n</code></pre> linked_list.cs<pre><code>/* \u5728\u94fe\u8868\u7684\u8282\u70b9 n0 \u4e4b\u540e\u63d2\u5165\u8282\u70b9 P */\nvoid insert(ListNode n0, ListNode P) {\nListNode? n1 = n0.next;\nP.next = n1;\nn0.next = P;\n}\n</code></pre> linked_list.swift<pre><code>/* \u5728\u94fe\u8868\u7684\u8282\u70b9 n0 \u4e4b\u540e\u63d2\u5165\u8282\u70b9 P */\nfunc insert(n0: ListNode, P: ListNode) {\nlet n1 = n0.next\nP.next = n1\nn0.next = P\n}\n</code></pre> linked_list.zig<pre><code>// \u5728\u94fe\u8868\u7684\u8282\u70b9 n0 \u4e4b\u540e\u63d2\u5165\u8282\u70b9 P\nfn insert(n0: ?*inc.ListNode(i32), P: ?*inc.ListNode(i32)) void {\nvar n1 = n0.?.next;\nP.?.next = n1;\nn0.?.next = P;\n}\n</code></pre> linked_list.dart<pre><code>/* \u5728\u94fe\u8868\u7684\u8282\u70b9 n0 \u4e4b\u540e\u63d2\u5165\u8282\u70b9 P */\nvoid insert(ListNode n0, ListNode P) {\nListNode? n1 = n0.next;\nP.next = n1;\nn0.next = P;\n}\n</code></pre> <p>\u5728\u94fe\u8868\u4e2d\u5220\u9664\u8282\u70b9\u4e5f\u975e\u5e38\u65b9\u4fbf\uff0c\u53ea\u9700\u6539\u53d8\u4e00\u4e2a\u8282\u70b9\u7684\u6307\u9488\u5373\u53ef\u3002\u5982\u4e0b\u56fe\u6240\u793a\uff0c\u5c3d\u7ba1\u5728\u5220\u9664\u64cd\u4f5c\u5b8c\u6210\u540e\uff0c\u8282\u70b9 <code>P</code> \u4ecd\u7136\u6307\u5411 <code>n1</code> \uff0c\u4f46\u5b9e\u9645\u4e0a <code>P</code> \u5df2\u7ecf\u4e0d\u518d\u5c5e\u4e8e\u6b64\u94fe\u8868\uff0c\u56e0\u4e3a\u904d\u5386\u6b64\u94fe\u8868\u65f6\u65e0\u6cd5\u8bbf\u95ee\u5230 <code>P</code> \u3002</p> <p></p> <p> Fig. \u94fe\u8868\u5220\u9664\u8282\u70b9 </p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart linked_list.java<pre><code>/* \u5220\u9664\u94fe\u8868\u7684\u8282\u70b9 n0 \u4e4b\u540e\u7684\u9996\u4e2a\u8282\u70b9 */\nvoid remove(ListNode n0) {\nif (n0.next == null)\nreturn;\n// n0 -&gt; P -&gt; n1\nListNode P = n0.next;\nListNode n1 = P.next;\nn0.next = n1;\n}\n</code></pre> linked_list.cpp<pre><code>/* \u5220\u9664\u94fe\u8868\u7684\u8282\u70b9 n0 \u4e4b\u540e\u7684\u9996\u4e2a\u8282\u70b9 */\nvoid remove(ListNode *n0) {\nif (n0-&gt;next == nullptr)\nreturn;\n// n0 -&gt; P -&gt; n1\nListNode *P = n0-&gt;next;\nListNode *n1 = P-&gt;next;\nn0-&gt;next = n1;\n// \u91ca\u653e\u5185\u5b58\ndelete P;\n}\n</code></pre> linked_list.py<pre><code>def remove(n0: ListNode) -&gt; None:\n\"\"\"\u5220\u9664\u94fe\u8868\u7684\u8282\u70b9 n0 \u4e4b\u540e\u7684\u9996\u4e2a\u8282\u70b9\"\"\"\nif not n0.next:\nreturn\n# n0 -&gt; P -&gt; n1\nP = n0.next\nn1 = P.next\nn0.next = n1\n</code></pre> linked_list.go<pre><code>/* \u5220\u9664\u94fe\u8868\u7684\u8282\u70b9 n0 \u4e4b\u540e\u7684\u9996\u4e2a\u8282\u70b9 */\nfunc removeNode(n0 *ListNode) {\nif n0.Next == nil {\nreturn\n}\n// n0 -&gt; P -&gt; n1\nP := n0.Next\nn1 := P.Next\nn0.Next = n1\n}\n</code></pre> linked_list.js<pre><code>/* \u5220\u9664\u94fe\u8868\u7684\u8282\u70b9 n0 \u4e4b\u540e\u7684\u9996\u4e2a\u8282\u70b9 */\nfunction remove(n0) {\nif (!n0.next) return;\n// n0 -&gt; P -&gt; n1\nconst P = n0.next;\nconst n1 = P.next;\nn0.next = n1;\n}\n</code></pre> linked_list.ts<pre><code>/* \u5220\u9664\u94fe\u8868\u7684\u8282\u70b9 n0 \u4e4b\u540e\u7684\u9996\u4e2a\u8282\u70b9 */\nfunction remove(n0: ListNode): void {\nif (!n0.next) {\nreturn;\n}\n// n0 -&gt; P -&gt; n1\nconst P = n0.next;\nconst n1 = P.next;\nn0.next = n1;\n}\n</code></pre> linked_list.c<pre><code>/* \u5220\u9664\u94fe\u8868\u7684\u8282\u70b9 n0 \u4e4b\u540e\u7684\u9996\u4e2a\u8282\u70b9 */\n// \u6ce8\u610f\uff1astdio.h \u5360\u7528\u4e86 remove \u5173\u952e\u8bcd\nvoid removeNode(ListNode *n0) {\nif (!n0-&gt;next)\nreturn;\n// n0 -&gt; P -&gt; n1\nListNode *P = n0-&gt;next;\nListNode *n1 = P-&gt;next;\nn0-&gt;next = n1;\n// \u91ca\u653e\u5185\u5b58\nfree(P);\n}\n</code></pre> linked_list.cs<pre><code>/* \u5220\u9664\u94fe\u8868\u7684\u8282\u70b9 n0 \u4e4b\u540e\u7684\u9996\u4e2a\u8282\u70b9 */\nvoid remove(ListNode n0) {\nif (n0.next == null)\nreturn;\n// n0 -&gt; P -&gt; n1\nListNode P = n0.next;\nListNode? n1 = P.next;\nn0.next = n1;\n}\n</code></pre> linked_list.swift<pre><code>/* \u5220\u9664\u94fe\u8868\u7684\u8282\u70b9 n0 \u4e4b\u540e\u7684\u9996\u4e2a\u8282\u70b9 */\nfunc remove(n0: ListNode) {\nif n0.next == nil {\nreturn\n}\n// n0 -&gt; P -&gt; n1\nlet P = n0.next\nlet n1 = P?.next\nn0.next = n1\nP?.next = nil\n}\n</code></pre> linked_list.zig<pre><code>// \u5220\u9664\u94fe\u8868\u7684\u8282\u70b9 n0 \u4e4b\u540e\u7684\u9996\u4e2a\u8282\u70b9\nfn remove(n0: ?*inc.ListNode(i32)) void {\nif (n0.?.next == null) return;\n// n0 -&gt; P -&gt; n1\nvar P = n0.?.next;\nvar n1 = P.?.next;\nn0.?.next = n1;\n}\n</code></pre> linked_list.dart<pre><code>/* \u5220\u9664\u94fe\u8868\u7684\u8282\u70b9 n0 \u4e4b\u540e\u7684\u9996\u4e2a\u8282\u70b9 */\nvoid remove(ListNode n0) {\nif (n0.next == null) return;\n// n0 -&gt; P -&gt; n1\nListNode P = n0.next!;\nListNode? n1 = P.next;\nn0.next = n1;\n}\n</code></pre>"},{"location":"chapter_array_and_linkedlist/linked_list/#422","title":"4.2.2. \u00a0 \u94fe\u8868\u7f3a\u70b9","text":"<p>\u94fe\u8868\u8bbf\u95ee\u8282\u70b9\u6548\u7387\u8f83\u4f4e\u3002\u5982\u4e0a\u8282\u6240\u8ff0\uff0c\u6570\u7ec4\u53ef\u4ee5\u5728 \\(O(1)\\) \u65f6\u95f4\u4e0b\u8bbf\u95ee\u4efb\u610f\u5143\u7d20\u3002\u7136\u800c\uff0c\u94fe\u8868\u65e0\u6cd5\u76f4\u63a5\u8bbf\u95ee\u4efb\u610f\u8282\u70b9\uff0c\u8fd9\u662f\u56e0\u4e3a\u7cfb\u7edf\u9700\u8981\u4ece\u5934\u8282\u70b9\u51fa\u53d1\uff0c\u9010\u4e2a\u5411\u540e\u904d\u5386\u76f4\u81f3\u627e\u5230\u76ee\u6807\u8282\u70b9\u3002\u4f8b\u5982\uff0c\u82e5\u8981\u8bbf\u95ee\u94fe\u8868\u7d22\u5f15\u4e3a <code>index</code>\uff08\u5373\u7b2c <code>index + 1</code> \u4e2a\uff09\u7684\u8282\u70b9\uff0c\u5219\u9700\u8981\u5411\u540e\u904d\u5386 <code>index</code> \u8f6e\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart linked_list.java<pre><code>/* \u8bbf\u95ee\u94fe\u8868\u4e2d\u7d22\u5f15\u4e3a index \u7684\u8282\u70b9 */\nListNode access(ListNode head, int index) {\nfor (int i = 0; i &lt; index; i++) {\nif (head == null)\nreturn null;\nhead = head.next;\n}\nreturn head;\n}\n</code></pre> linked_list.cpp<pre><code>/* \u8bbf\u95ee\u94fe\u8868\u4e2d\u7d22\u5f15\u4e3a index \u7684\u8282\u70b9 */\nListNode *access(ListNode *head, int index) {\nfor (int i = 0; i &lt; index; i++) {\nif (head == nullptr)\nreturn nullptr;\nhead = head-&gt;next;\n}\nreturn head;\n}\n</code></pre> linked_list.py<pre><code>def access(head: ListNode, index: int) -&gt; ListNode | None:\n\"\"\"\u8bbf\u95ee\u94fe\u8868\u4e2d\u7d22\u5f15\u4e3a index \u7684\u8282\u70b9\"\"\"\nfor _ in range(index):\nif not head:\nreturn None\nhead = head.next\nreturn head\n</code></pre> linked_list.go<pre><code>/* \u8bbf\u95ee\u94fe\u8868\u4e2d\u7d22\u5f15\u4e3a index \u7684\u8282\u70b9 */\nfunc access(head *ListNode, index int) *ListNode {\nfor i := 0; i &lt; index; i++ {\nif head == nil {\nreturn nil\n}\nhead = head.Next\n}\nreturn head\n}\n</code></pre> linked_list.js<pre><code>/* \u8bbf\u95ee\u94fe\u8868\u4e2d\u7d22\u5f15\u4e3a index \u7684\u8282\u70b9 */\nfunction access(head, index) {\nfor (let i = 0; i &lt; index; i++) {\nif (!head) {\nreturn null;\n}\nhead = head.next;\n}\nreturn head;\n}\n</code></pre> linked_list.ts<pre><code>/* \u8bbf\u95ee\u94fe\u8868\u4e2d\u7d22\u5f15\u4e3a index \u7684\u8282\u70b9 */\nfunction access(head: ListNode | null, index: number): ListNode | null {\nfor (let i = 0; i &lt; index; i++) {\nif (!head) {\nreturn null;\n}\nhead = head.next;\n}\nreturn head;\n}\n</code></pre> linked_list.c<pre><code>/* \u8bbf\u95ee\u94fe\u8868\u4e2d\u7d22\u5f15\u4e3a index \u7684\u8282\u70b9 */\nListNode *access(ListNode *head, int index) {\nwhile (head &amp;&amp; head-&gt;next &amp;&amp; index) {\nhead = head-&gt;next;\nindex--;\n}\nreturn head;\n}\n</code></pre> linked_list.cs<pre><code>/* \u8bbf\u95ee\u94fe\u8868\u4e2d\u7d22\u5f15\u4e3a index \u7684\u8282\u70b9 */\nListNode? access(ListNode head, int index) {\nfor (int i = 0; i &lt; index; i++) {\nif (head == null)\nreturn null;\nhead = head.next;\n}\nreturn head;\n}\n</code></pre> linked_list.swift<pre><code>/* \u8bbf\u95ee\u94fe\u8868\u4e2d\u7d22\u5f15\u4e3a index \u7684\u8282\u70b9 */\nfunc access(head: ListNode, index: Int) -&gt; ListNode? {\nvar head: ListNode? = head\nfor _ in 0 ..&lt; index {\nif head == nil {\nreturn nil\n}\nhead = head?.next\n}\nreturn head\n}\n</code></pre> linked_list.zig<pre><code>// \u8bbf\u95ee\u94fe\u8868\u4e2d\u7d22\u5f15\u4e3a index \u7684\u8282\u70b9\nfn access(node: ?*inc.ListNode(i32), index: i32) ?*inc.ListNode(i32) {\nvar head = node;\nvar i: i32 = 0;\nwhile (i &lt; index) : (i += 1) {\nhead = head.?.next;\nif (head == null) return null;\n}\nreturn head;\n}\n</code></pre> linked_list.dart<pre><code>/* \u8bbf\u95ee\u94fe\u8868\u4e2d\u7d22\u5f15\u4e3a index \u7684\u8282\u70b9 */\nListNode? access(ListNode? head, int index) {\nfor (var i = 0; i &lt; index; i++) {\nif (head == null) return null;\nhead = head.next;\n}\nreturn head;\n}\n</code></pre> <p>\u94fe\u8868\u7684\u5185\u5b58\u5360\u7528\u8f83\u5927\u3002\u94fe\u8868\u4ee5\u8282\u70b9\u4e3a\u5355\u4f4d\uff0c\u6bcf\u4e2a\u8282\u70b9\u9664\u4e86\u4fdd\u5b58\u503c\u4e4b\u5916\uff0c\u8fd8\u9700\u989d\u5916\u4fdd\u5b58\u6307\u9488\uff08\u5f15\u7528\uff09\u3002\u8fd9\u610f\u5473\u7740\u5728\u76f8\u540c\u6570\u636e\u91cf\u7684\u60c5\u51b5\u4e0b\uff0c\u94fe\u8868\u6bd4\u6570\u7ec4\u9700\u8981\u5360\u7528\u66f4\u591a\u7684\u5185\u5b58\u7a7a\u95f4\u3002</p>"},{"location":"chapter_array_and_linkedlist/linked_list/#423","title":"4.2.3. \u00a0 \u94fe\u8868\u5e38\u7528\u64cd\u4f5c","text":"<p>\u904d\u5386\u94fe\u8868\u67e5\u627e\u3002\u904d\u5386\u94fe\u8868\uff0c\u67e5\u627e\u94fe\u8868\u5185\u503c\u4e3a <code>target</code> \u7684\u8282\u70b9\uff0c\u8f93\u51fa\u8282\u70b9\u5728\u94fe\u8868\u4e2d\u7684\u7d22\u5f15\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart linked_list.java<pre><code>/* \u5728\u94fe\u8868\u4e2d\u67e5\u627e\u503c\u4e3a target \u7684\u9996\u4e2a\u8282\u70b9 */\nint find(ListNode head, int target) {\nint index = 0;\nwhile (head != null) {\nif (head.val == target)\nreturn index;\nhead = head.next;\nindex++;\n}\nreturn -1;\n}\n</code></pre> linked_list.cpp<pre><code>/* \u5728\u94fe\u8868\u4e2d\u67e5\u627e\u503c\u4e3a target \u7684\u9996\u4e2a\u8282\u70b9 */\nint find(ListNode *head, int target) {\nint index = 0;\nwhile (head != nullptr) {\nif (head-&gt;val == target)\nreturn index;\nhead = head-&gt;next;\nindex++;\n}\nreturn -1;\n}\n</code></pre> linked_list.py<pre><code>def find(head: ListNode, target: int) -&gt; int:\n\"\"\"\u5728\u94fe\u8868\u4e2d\u67e5\u627e\u503c\u4e3a target \u7684\u9996\u4e2a\u8282\u70b9\"\"\"\nindex = 0\nwhile head:\nif head.val == target:\nreturn index\nhead = head.next\nindex += 1\nreturn -1\n</code></pre> linked_list.go<pre><code>/* \u5728\u94fe\u8868\u4e2d\u67e5\u627e\u503c\u4e3a target \u7684\u9996\u4e2a\u8282\u70b9 */\nfunc findNode(head *ListNode, target int) int {\nindex := 0\nfor head != nil {\nif head.Val == target {\nreturn index\n}\nhead = head.Next\nindex++\n}\nreturn -1\n}\n</code></pre> linked_list.js<pre><code>/* \u5728\u94fe\u8868\u4e2d\u67e5\u627e\u503c\u4e3a target \u7684\u9996\u4e2a\u8282\u70b9 */\nfunction find(head, target) {\nlet index = 0;\nwhile (head !== null) {\nif (head.val === target) {\nreturn index;\n}\nhead = head.next;\nindex += 1;\n}\nreturn -1;\n}\n</code></pre> linked_list.ts<pre><code>/* \u5728\u94fe\u8868\u4e2d\u67e5\u627e\u503c\u4e3a target \u7684\u9996\u4e2a\u8282\u70b9 */\nfunction find(head: ListNode | null, target: number): number {\nlet index = 0;\nwhile (head !== null) {\nif (head.val === target) {\nreturn index;\n}\nhead = head.next;\nindex += 1;\n}\nreturn -1;\n}\n</code></pre> linked_list.c<pre><code>/* \u5728\u94fe\u8868\u4e2d\u67e5\u627e\u503c\u4e3a target \u7684\u9996\u4e2a\u8282\u70b9 */\nint find(ListNode *head, int target) {\nint index = 0;\nwhile (head) {\nif (head-&gt;val == target)\nreturn index;\nhead = head-&gt;next;\nindex++;\n}\nreturn -1;\n}\n</code></pre> linked_list.cs<pre><code>/* \u5728\u94fe\u8868\u4e2d\u67e5\u627e\u503c\u4e3a target \u7684\u9996\u4e2a\u8282\u70b9 */\nint find(ListNode head, int target) {\nint index = 0;\nwhile (head != null) {\nif (head.val == target)\nreturn index;\nhead = head.next;\nindex++;\n}\nreturn -1;\n}\n</code></pre> linked_list.swift<pre><code>/* \u5728\u94fe\u8868\u4e2d\u67e5\u627e\u503c\u4e3a target \u7684\u9996\u4e2a\u8282\u70b9 */\nfunc find(head: ListNode, target: Int) -&gt; Int {\nvar head: ListNode? = head\nvar index = 0\nwhile head != nil {\nif head?.val == target {\nreturn index\n}\nhead = head?.next\nindex += 1\n}\nreturn -1\n}\n</code></pre> linked_list.zig<pre><code>// \u5728\u94fe\u8868\u4e2d\u67e5\u627e\u503c\u4e3a target \u7684\u9996\u4e2a\u8282\u70b9\nfn find(node: ?*inc.ListNode(i32), target: i32) i32 {\nvar head = node;\nvar index: i32 = 0;\nwhile (head != null) {\nif (head.?.val == target) return index;\nhead = head.?.next;\nindex += 1;\n}\nreturn -1;\n}\n</code></pre> linked_list.dart<pre><code>/* \u5728\u94fe\u8868\u4e2d\u67e5\u627e\u503c\u4e3a target \u7684\u9996\u4e2a\u8282\u70b9 */\nint find(ListNode? head, int target) {\nint index = 0;\nwhile (head != null) {\nif (head.val == target) {\nreturn index;\n}\nhead = head.next;\nindex++;\n}\nreturn -1;\n}\n</code></pre>"},{"location":"chapter_array_and_linkedlist/linked_list/#424","title":"4.2.4. \u00a0 \u5e38\u89c1\u94fe\u8868\u7c7b\u578b","text":"<p>\u5355\u5411\u94fe\u8868\u3002\u5373\u4e0a\u8ff0\u4ecb\u7ecd\u7684\u666e\u901a\u94fe\u8868\u3002\u5355\u5411\u94fe\u8868\u7684\u8282\u70b9\u5305\u542b\u503c\u548c\u6307\u5411\u4e0b\u4e00\u8282\u70b9\u7684\u6307\u9488\uff08\u5f15\u7528\uff09\u4e24\u9879\u6570\u636e\u3002\u6211\u4eec\u5c06\u9996\u4e2a\u8282\u70b9\u79f0\u4e3a\u5934\u8282\u70b9\uff0c\u5c06\u6700\u540e\u4e00\u4e2a\u8282\u70b9\u6210\u4e3a\u5c3e\u8282\u70b9\uff0c\u5c3e\u8282\u70b9\u6307\u5411 \\(\\text{null}\\) \u3002</p> <p>\u73af\u5f62\u94fe\u8868\u3002\u5982\u679c\u6211\u4eec\u4ee4\u5355\u5411\u94fe\u8868\u7684\u5c3e\u8282\u70b9\u6307\u5411\u5934\u8282\u70b9\uff08\u5373\u9996\u5c3e\u76f8\u63a5\uff09\uff0c\u5219\u5f97\u5230\u4e00\u4e2a\u73af\u5f62\u94fe\u8868\u3002\u5728\u73af\u5f62\u94fe\u8868\u4e2d\uff0c\u4efb\u610f\u8282\u70b9\u90fd\u53ef\u4ee5\u89c6\u4f5c\u5934\u8282\u70b9\u3002</p> <p>\u53cc\u5411\u94fe\u8868\u3002\u4e0e\u5355\u5411\u94fe\u8868\u76f8\u6bd4\uff0c\u53cc\u5411\u94fe\u8868\u8bb0\u5f55\u4e86\u4e24\u4e2a\u65b9\u5411\u7684\u6307\u9488\uff08\u5f15\u7528\uff09\u3002\u53cc\u5411\u94fe\u8868\u7684\u8282\u70b9\u5b9a\u4e49\u540c\u65f6\u5305\u542b\u6307\u5411\u540e\u7ee7\u8282\u70b9\uff08\u4e0b\u4e00\u8282\u70b9\uff09\u548c\u524d\u9a71\u8282\u70b9\uff08\u4e0a\u4e00\u8282\u70b9\uff09\u7684\u6307\u9488\u3002\u76f8\u8f83\u4e8e\u5355\u5411\u94fe\u8868\uff0c\u53cc\u5411\u94fe\u8868\u66f4\u5177\u7075\u6d3b\u6027\uff0c\u53ef\u4ee5\u671d\u4e24\u4e2a\u65b9\u5411\u904d\u5386\u94fe\u8868\uff0c\u4f46\u76f8\u5e94\u5730\u4e5f\u9700\u8981\u5360\u7528\u66f4\u591a\u7684\u5185\u5b58\u7a7a\u95f4\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart <pre><code>/* \u53cc\u5411\u94fe\u8868\u8282\u70b9\u7c7b */\nclass ListNode {\nint val;        // \u8282\u70b9\u503c\nListNode next;  // \u6307\u5411\u540e\u7ee7\u8282\u70b9\u7684\u6307\u9488\uff08\u5f15\u7528\uff09\nListNode prev;  // \u6307\u5411\u524d\u9a71\u8282\u70b9\u7684\u6307\u9488\uff08\u5f15\u7528\uff09\nListNode(int x) { val = x; }  // \u6784\u9020\u51fd\u6570\n}\n</code></pre> <pre><code>/* \u53cc\u5411\u94fe\u8868\u8282\u70b9\u7ed3\u6784\u4f53 */\nstruct ListNode {\nint val;         // \u8282\u70b9\u503c\nListNode *next;  // \u6307\u5411\u540e\u7ee7\u8282\u70b9\u7684\u6307\u9488\uff08\u5f15\u7528\uff09\nListNode *prev;  // \u6307\u5411\u524d\u9a71\u8282\u70b9\u7684\u6307\u9488\uff08\u5f15\u7528\uff09\nListNode(int x) : val(x), next(nullptr), prev(nullptr) {}  // \u6784\u9020\u51fd\u6570\n};\n</code></pre> <pre><code>class ListNode:\n\"\"\"\u53cc\u5411\u94fe\u8868\u8282\u70b9\u7c7b\"\"\"\ndef __init__(self, val: int):\nself.val: int = val                   # \u8282\u70b9\u503c\nself.next: Optional[ListNode] = None  # \u6307\u5411\u540e\u7ee7\u8282\u70b9\u7684\u6307\u9488\uff08\u5f15\u7528\uff09\nself.prev: Optional[ListNode] = None  # \u6307\u5411\u524d\u9a71\u8282\u70b9\u7684\u6307\u9488\uff08\u5f15\u7528\uff09\n</code></pre> <pre><code>/* \u53cc\u5411\u94fe\u8868\u8282\u70b9\u7ed3\u6784\u4f53 */\ntype DoublyListNode struct {\nVal  int             // \u8282\u70b9\u503c\nNext *DoublyListNode // \u6307\u5411\u540e\u7ee7\u8282\u70b9\u7684\u6307\u9488\uff08\u5f15\u7528\uff09\nPrev *DoublyListNode // \u6307\u5411\u524d\u9a71\u8282\u70b9\u7684\u6307\u9488\uff08\u5f15\u7528\uff09\n}\n// NewDoublyListNode \u521d\u59cb\u5316\nfunc NewDoublyListNode(val int) *DoublyListNode {\nreturn &amp;DoublyListNode{\nVal:  val,\nNext: nil,\nPrev: nil,\n}\n}\n</code></pre> <pre><code>/* \u53cc\u5411\u94fe\u8868\u8282\u70b9\u7c7b */\nclass ListNode {\nval;\nnext;\nprev;\nconstructor(val, next, prev) {\nthis.val = val  ===  undefined ? 0 : val;        // \u8282\u70b9\u503c\nthis.next = next  ===  undefined ? null : next;  // \u6307\u5411\u540e\u7ee7\u8282\u70b9\u7684\u6307\u9488\uff08\u5f15\u7528\uff09\nthis.prev = prev  ===  undefined ? null : prev;  // \u6307\u5411\u524d\u9a71\u8282\u70b9\u7684\u6307\u9488\uff08\u5f15\u7528\uff09\n}\n}\n</code></pre> <pre><code>/* \u53cc\u5411\u94fe\u8868\u8282\u70b9\u7c7b */\nclass ListNode {\nval: number;\nnext: ListNode | null;\nprev: ListNode | null;\nconstructor(val?: number, next?: ListNode | null, prev?: ListNode | null) {\nthis.val = val  ===  undefined ? 0 : val;        // \u8282\u70b9\u503c\nthis.next = next  ===  undefined ? null : next;  // \u6307\u5411\u540e\u7ee7\u8282\u70b9\u7684\u6307\u9488\uff08\u5f15\u7528\uff09\nthis.prev = prev  ===  undefined ? null : prev;  // \u6307\u5411\u524d\u9a71\u8282\u70b9\u7684\u6307\u9488\uff08\u5f15\u7528\uff09\n}\n}\n</code></pre> <pre><code>/* \u53cc\u5411\u94fe\u8868\u8282\u70b9\u7ed3\u6784\u4f53 */\nstruct ListNode {\nint val;               // \u8282\u70b9\u503c\nstruct ListNode *next; // \u6307\u5411\u540e\u7ee7\u8282\u70b9\u7684\u6307\u9488\uff08\u5f15\u7528\uff09\nstruct ListNode *prev; // \u6307\u5411\u524d\u9a71\u8282\u70b9\u7684\u6307\u9488\uff08\u5f15\u7528\uff09\n};\ntypedef struct ListNode ListNode;\n/* \u6784\u9020\u51fd\u6570 */\nListNode *newListNode(int val) {\nListNode *node, *next;\nnode = (ListNode *) malloc(sizeof(ListNode));\nnode-&gt;val = val;\nnode-&gt;next = NULL;\nnode-&gt;prev = NULL;\nreturn node;\n}\n</code></pre> <pre><code>/* \u53cc\u5411\u94fe\u8868\u8282\u70b9\u7c7b */\nclass ListNode {\nint val;        // \u8282\u70b9\u503c\nListNode next;  // \u6307\u5411\u540e\u7ee7\u8282\u70b9\u7684\u6307\u9488\uff08\u5f15\u7528\uff09\nListNode prev;  // \u6307\u5411\u524d\u9a71\u8282\u70b9\u7684\u6307\u9488\uff08\u5f15\u7528\uff09\nListNode(int x) =&gt; val = x;  // \u6784\u9020\u51fd\u6570\n}\n</code></pre> <pre><code>/* \u53cc\u5411\u94fe\u8868\u8282\u70b9\u7c7b */\nclass ListNode {\nvar val: Int // \u8282\u70b9\u503c\nvar next: ListNode? // \u6307\u5411\u540e\u7ee7\u8282\u70b9\u7684\u6307\u9488\uff08\u5f15\u7528\uff09\nvar prev: ListNode? // \u6307\u5411\u524d\u9a71\u8282\u70b9\u7684\u6307\u9488\uff08\u5f15\u7528\uff09\ninit(x: Int) { // \u6784\u9020\u51fd\u6570\nval = x\n}\n}\n</code></pre> <pre><code>// \u53cc\u5411\u94fe\u8868\u8282\u70b9\u7c7b\npub fn ListNode(comptime T: type) type {\nreturn struct {\nconst Self = @This();\nval: T = 0, // \u8282\u70b9\u503c\nnext: ?*Self = null, // \u6307\u5411\u540e\u7ee7\u8282\u70b9\u7684\u6307\u9488\uff08\u5f15\u7528\uff09\nprev: ?*Self = null, // \u6307\u5411\u524d\u9a71\u8282\u70b9\u7684\u6307\u9488\uff08\u5f15\u7528\uff09\n// \u6784\u9020\u51fd\u6570\npub fn init(self: *Self, x: i32) void {\nself.val = x;\nself.next = null;\nself.prev = null;\n}\n};\n}\n</code></pre> <pre><code>/* \u53cc\u5411\u94fe\u8868\u8282\u70b9\u7c7b */\nclass ListNode {\nint val;        // \u8282\u70b9\u503c\nListNode next;  // \u6307\u5411\u540e\u7ee7\u8282\u70b9\u7684\u6307\u9488\uff08\u5f15\u7528\uff09\nListNode prev;  // \u6307\u5411\u524d\u9a71\u8282\u70b9\u7684\u6307\u9488\uff08\u5f15\u7528\uff09\nListNode(this.val, [this.next, this.prev]);  // \u6784\u9020\u51fd\u6570\n}\n</code></pre> <p></p> <p> Fig. \u5e38\u89c1\u94fe\u8868\u79cd\u7c7b </p>"},{"location":"chapter_array_and_linkedlist/list/","title":"4.3. \u00a0 \u5217\u8868","text":"<p>\u6570\u7ec4\u957f\u5ea6\u4e0d\u53ef\u53d8\u5bfc\u81f4\u5b9e\u7528\u6027\u964d\u4f4e\u3002\u5728\u8bb8\u591a\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u4e8b\u5148\u65e0\u6cd5\u786e\u5b9a\u9700\u8981\u5b58\u50a8\u591a\u5c11\u6570\u636e\uff0c\u8fd9\u4f7f\u6570\u7ec4\u957f\u5ea6\u7684\u9009\u62e9\u53d8\u5f97\u56f0\u96be\u3002\u82e5\u957f\u5ea6\u8fc7\u5c0f\uff0c\u9700\u8981\u5728\u6301\u7eed\u6dfb\u52a0\u6570\u636e\u65f6\u9891\u7e41\u6269\u5bb9\u6570\u7ec4\uff1b\u82e5\u957f\u5ea6\u8fc7\u5927\uff0c\u5219\u4f1a\u9020\u6210\u5185\u5b58\u7a7a\u95f4\u7684\u6d6a\u8d39\u3002</p> <p>\u4e3a\u89e3\u51b3\u6b64\u95ee\u9898\uff0c\u51fa\u73b0\u4e86\u4e00\u79cd\u88ab\u79f0\u4e3a\u300c\u52a8\u6001\u6570\u7ec4 Dynamic Array\u300d\u7684\u6570\u636e\u7ed3\u6784\uff0c\u5373\u957f\u5ea6\u53ef\u53d8\u7684\u6570\u7ec4\uff0c\u4e5f\u5e38\u88ab\u79f0\u4e3a\u300c\u5217\u8868 List\u300d\u3002\u5217\u8868\u57fa\u4e8e\u6570\u7ec4\u5b9e\u73b0\uff0c\u7ee7\u627f\u4e86\u6570\u7ec4\u7684\u4f18\u70b9\uff0c\u5e76\u4e14\u53ef\u4ee5\u5728\u7a0b\u5e8f\u8fd0\u884c\u8fc7\u7a0b\u4e2d\u52a8\u6001\u6269\u5bb9\u3002\u5728\u5217\u8868\u4e2d\uff0c\u6211\u4eec\u53ef\u4ee5\u81ea\u7531\u6dfb\u52a0\u5143\u7d20\uff0c\u800c\u65e0\u9700\u62c5\u5fc3\u8d85\u8fc7\u5bb9\u91cf\u9650\u5236\u3002</p>"},{"location":"chapter_array_and_linkedlist/list/#431","title":"4.3.1. \u00a0 \u5217\u8868\u5e38\u7528\u64cd\u4f5c","text":"<p>\u521d\u59cb\u5316\u5217\u8868\u3002\u901a\u5e38\u6211\u4eec\u4f1a\u4f7f\u7528\u201c\u65e0\u521d\u59cb\u503c\u201d\u548c\u201c\u6709\u521d\u59cb\u503c\u201d\u7684\u4e24\u79cd\u521d\u59cb\u5316\u65b9\u6cd5\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart list.java<pre><code>/* \u521d\u59cb\u5316\u5217\u8868 */\n// \u65e0\u521d\u59cb\u503c\nList&lt;Integer&gt; list1 = new ArrayList&lt;&gt;();\n// \u6709\u521d\u59cb\u503c\uff08\u6ce8\u610f\u6570\u7ec4\u7684\u5143\u7d20\u7c7b\u578b\u9700\u4e3a int[] \u7684\u5305\u88c5\u7c7b Integer[]\uff09\nInteger[] numbers = new Integer[] { 1, 3, 2, 5, 4 };\nList&lt;Integer&gt; list = new ArrayList&lt;&gt;(Arrays.asList(numbers));\n</code></pre> list.cpp<pre><code>/* \u521d\u59cb\u5316\u5217\u8868 */\n// \u9700\u6ce8\u610f\uff0cC++ \u4e2d vector \u5373\u662f\u672c\u6587\u63cf\u8ff0\u7684 list\n// \u65e0\u521d\u59cb\u503c\nvector&lt;int&gt; list1;\n// \u6709\u521d\u59cb\u503c\nvector&lt;int&gt; list = { 1, 3, 2, 5, 4 };\n</code></pre> list.py<pre><code># \u521d\u59cb\u5316\u5217\u8868\n# \u65e0\u521d\u59cb\u503c\nlist1: List[int] = []\n# \u6709\u521d\u59cb\u503c\nlist: List[int] = [1, 3, 2, 5, 4]\n</code></pre> list_test.go<pre><code>/* \u521d\u59cb\u5316\u5217\u8868 */\n// \u65e0\u521d\u59cb\u503c\nlist1 := []int\n// \u6709\u521d\u59cb\u503c\nlist := []int{1, 3, 2, 5, 4}\n</code></pre> list.js<pre><code>/* \u521d\u59cb\u5316\u5217\u8868 */\n// \u65e0\u521d\u59cb\u503c\nconst list1 = [];\n// \u6709\u521d\u59cb\u503c\nconst list = [1, 3, 2, 5, 4];\n</code></pre> list.ts<pre><code>/* \u521d\u59cb\u5316\u5217\u8868 */\n// \u65e0\u521d\u59cb\u503c\nconst list1: number[] = [];\n// \u6709\u521d\u59cb\u503c\nconst list: number[] = [1, 3, 2, 5, 4];\n</code></pre> list.c<pre><code>// C \u672a\u63d0\u4f9b\u5185\u7f6e\u52a8\u6001\u6570\u7ec4\n</code></pre> list.cs<pre><code>/* \u521d\u59cb\u5316\u5217\u8868 */\n// \u65e0\u521d\u59cb\u503c\nList&lt;int&gt; list1 = new ();\n// \u6709\u521d\u59cb\u503c\nint[] numbers = new int[] { 1, 3, 2, 5, 4 };\nList&lt;int&gt; list = numbers.ToList();\n</code></pre> list.swift<pre><code>/* \u521d\u59cb\u5316\u5217\u8868 */\n// \u65e0\u521d\u59cb\u503c\nlet list1: [Int] = []\n// \u6709\u521d\u59cb\u503c\nvar list = [1, 3, 2, 5, 4]\n</code></pre> list.zig<pre><code>// \u521d\u59cb\u5316\u5217\u8868\nvar list = std.ArrayList(i32).init(std.heap.page_allocator);\ndefer list.deinit();\ntry list.appendSlice(&amp;[_]i32{ 1, 3, 2, 5, 4 });\n</code></pre> list.dart<pre><code>/* \u521d\u59cb\u5316\u5217\u8868 */\n// \u65e0\u521d\u59cb\u503c\nList&lt;int&gt; list1 = [];\n// \u6709\u521d\u59cb\u503c\nList&lt;int&gt; list = [1, 3, 2, 5, 4];\n</code></pre> <p>\u8bbf\u95ee\u4e0e\u66f4\u65b0\u5143\u7d20\u3002\u7531\u4e8e\u5217\u8868\u7684\u5e95\u5c42\u6570\u636e\u7ed3\u6784\u662f\u6570\u7ec4\uff0c\u56e0\u6b64\u53ef\u4ee5\u5728 \\(O(1)\\) \u65f6\u95f4\u5185\u8bbf\u95ee\u548c\u66f4\u65b0\u5143\u7d20\uff0c\u6548\u7387\u5f88\u9ad8\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart list.java<pre><code>/* \u8bbf\u95ee\u5143\u7d20 */\nint num = list.get(1);  // \u8bbf\u95ee\u7d22\u5f15 1 \u5904\u7684\u5143\u7d20\n/* \u66f4\u65b0\u5143\u7d20 */\nlist.set(1, 0);  // \u5c06\u7d22\u5f15 1 \u5904\u7684\u5143\u7d20\u66f4\u65b0\u4e3a 0\n</code></pre> list.cpp<pre><code>/* \u8bbf\u95ee\u5143\u7d20 */\nint num = list[1];  // \u8bbf\u95ee\u7d22\u5f15 1 \u5904\u7684\u5143\u7d20\n/* \u66f4\u65b0\u5143\u7d20 */\nlist[1] = 0;  // \u5c06\u7d22\u5f15 1 \u5904\u7684\u5143\u7d20\u66f4\u65b0\u4e3a 0\n</code></pre> list.py<pre><code># \u8bbf\u95ee\u5143\u7d20\nnum: int = list[1]  # \u8bbf\u95ee\u7d22\u5f15 1 \u5904\u7684\u5143\u7d20\n# \u66f4\u65b0\u5143\u7d20\nlist[1] = 0    # \u5c06\u7d22\u5f15 1 \u5904\u7684\u5143\u7d20\u66f4\u65b0\u4e3a 0\n</code></pre> list_test.go<pre><code>/* \u8bbf\u95ee\u5143\u7d20 */\nnum := list[1]  // \u8bbf\u95ee\u7d22\u5f15 1 \u5904\u7684\u5143\u7d20\n/* \u66f4\u65b0\u5143\u7d20 */\nlist[1] = 0     // \u5c06\u7d22\u5f15 1 \u5904\u7684\u5143\u7d20\u66f4\u65b0\u4e3a 0\n</code></pre> list.js<pre><code>/* \u8bbf\u95ee\u5143\u7d20 */\nconst num = list[1];  // \u8bbf\u95ee\u7d22\u5f15 1 \u5904\u7684\u5143\u7d20\n/* \u66f4\u65b0\u5143\u7d20 */\nlist[1] = 0;  // \u5c06\u7d22\u5f15 1 \u5904\u7684\u5143\u7d20\u66f4\u65b0\u4e3a 0\n</code></pre> list.ts<pre><code>/* \u8bbf\u95ee\u5143\u7d20 */\nconst num: number = list[1];  // \u8bbf\u95ee\u7d22\u5f15 1 \u5904\u7684\u5143\u7d20\n/* \u66f4\u65b0\u5143\u7d20 */\nlist[1] = 0;  // \u5c06\u7d22\u5f15 1 \u5904\u7684\u5143\u7d20\u66f4\u65b0\u4e3a 0\n</code></pre> list.c<pre><code>// C \u672a\u63d0\u4f9b\u5185\u7f6e\u52a8\u6001\u6570\u7ec4\n</code></pre> list.cs<pre><code>/* \u8bbf\u95ee\u5143\u7d20 */\nint num = list[1];  // \u8bbf\u95ee\u7d22\u5f15 1 \u5904\u7684\u5143\u7d20\n/* \u66f4\u65b0\u5143\u7d20 */\nlist[1] = 0;  // \u5c06\u7d22\u5f15 1 \u5904\u7684\u5143\u7d20\u66f4\u65b0\u4e3a 0\n</code></pre> list.swift<pre><code>/* \u8bbf\u95ee\u5143\u7d20 */\nlet num = list[1] // \u8bbf\u95ee\u7d22\u5f15 1 \u5904\u7684\u5143\u7d20\n/* \u66f4\u65b0\u5143\u7d20 */\nlist[1] = 0 // \u5c06\u7d22\u5f15 1 \u5904\u7684\u5143\u7d20\u66f4\u65b0\u4e3a 0\n</code></pre> list.zig<pre><code>// \u8bbf\u95ee\u5143\u7d20\nvar num = list.items[1]; // \u8bbf\u95ee\u7d22\u5f15 1 \u5904\u7684\u5143\u7d20\n// \u66f4\u65b0\u5143\u7d20\nlist.items[1] = 0; // \u5c06\u7d22\u5f15 1 \u5904\u7684\u5143\u7d20\u66f4\u65b0\u4e3a 0  \n</code></pre> list.dart<pre><code>/* \u8bbf\u95ee\u5143\u7d20 */\nint num = list[1];  // \u8bbf\u95ee\u7d22\u5f15 1 \u5904\u7684\u5143\u7d20\n/* \u66f4\u65b0\u5143\u7d20 */\nlist[1] = 0;  // \u5c06\u7d22\u5f15 1 \u5904\u7684\u5143\u7d20\u66f4\u65b0\u4e3a 0\n</code></pre> <p>\u5728\u5217\u8868\u4e2d\u6dfb\u52a0\u3001\u63d2\u5165\u3001\u5220\u9664\u5143\u7d20\u3002\u76f8\u8f83\u4e8e\u6570\u7ec4\uff0c\u5217\u8868\u53ef\u4ee5\u81ea\u7531\u5730\u6dfb\u52a0\u4e0e\u5220\u9664\u5143\u7d20\u3002\u5728\u5217\u8868\u5c3e\u90e8\u6dfb\u52a0\u5143\u7d20\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(1)\\) \uff0c\u4f46\u63d2\u5165\u548c\u5220\u9664\u5143\u7d20\u7684\u6548\u7387\u4ecd\u4e0e\u6570\u7ec4\u76f8\u540c\uff0c\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(N)\\) \u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart list.java<pre><code>/* \u6e05\u7a7a\u5217\u8868 */\nlist.clear();\n/* \u5c3e\u90e8\u6dfb\u52a0\u5143\u7d20 */\nlist.add(1);\nlist.add(3);\nlist.add(2);\nlist.add(5);\nlist.add(4);\n/* \u4e2d\u95f4\u63d2\u5165\u5143\u7d20 */\nlist.add(3, 6);  // \u5728\u7d22\u5f15 3 \u5904\u63d2\u5165\u6570\u5b57 6\n/* \u5220\u9664\u5143\u7d20 */\nlist.remove(3);  // \u5220\u9664\u7d22\u5f15 3 \u5904\u7684\u5143\u7d20\n</code></pre> list.cpp<pre><code>/* \u6e05\u7a7a\u5217\u8868 */\nlist.clear();\n/* \u5c3e\u90e8\u6dfb\u52a0\u5143\u7d20 */\nlist.push_back(1);\nlist.push_back(3);\nlist.push_back(2);\nlist.push_back(5);\nlist.push_back(4);\n/* \u4e2d\u95f4\u63d2\u5165\u5143\u7d20 */\nlist.insert(list.begin() + 3, 6);  // \u5728\u7d22\u5f15 3 \u5904\u63d2\u5165\u6570\u5b57 6\n/* \u5220\u9664\u5143\u7d20 */\nlist.erase(list.begin() + 3);      // \u5220\u9664\u7d22\u5f15 3 \u5904\u7684\u5143\u7d20\n</code></pre> list.py<pre><code># \u6e05\u7a7a\u5217\u8868\nlist.clear()\n# \u5c3e\u90e8\u6dfb\u52a0\u5143\u7d20\nlist.append(1)\nlist.append(3)\nlist.append(2)\nlist.append(5)\nlist.append(4)\n# \u4e2d\u95f4\u63d2\u5165\u5143\u7d20\nlist.insert(3, 6)  # \u5728\u7d22\u5f15 3 \u5904\u63d2\u5165\u6570\u5b57 6\n# \u5220\u9664\u5143\u7d20\nlist.pop(3)        # \u5220\u9664\u7d22\u5f15 3 \u5904\u7684\u5143\u7d20\n</code></pre> list_test.go<pre><code>/* \u6e05\u7a7a\u5217\u8868 */\nlist = nil\n/* \u5c3e\u90e8\u6dfb\u52a0\u5143\u7d20 */\nlist = append(list, 1)\nlist = append(list, 3)\nlist = append(list, 2)\nlist = append(list, 5)\nlist = append(list, 4)\n/* \u4e2d\u95f4\u63d2\u5165\u5143\u7d20 */\nlist = append(list[:3], append([]int{6}, list[3:]...)...) // \u5728\u7d22\u5f15 3 \u5904\u63d2\u5165\u6570\u5b57 6\n/* \u5220\u9664\u5143\u7d20 */\nlist = append(list[:3], list[4:]...) // \u5220\u9664\u7d22\u5f15 3 \u5904\u7684\u5143\u7d20\n</code></pre> list.js<pre><code>/* \u6e05\u7a7a\u5217\u8868 */\nlist.length = 0;\n/* \u5c3e\u90e8\u6dfb\u52a0\u5143\u7d20 */\nlist.push(1);\nlist.push(3);\nlist.push(2);\nlist.push(5);\nlist.push(4);\n/* \u4e2d\u95f4\u63d2\u5165\u5143\u7d20 */\nlist.splice(3, 0, 6);\n/* \u5220\u9664\u5143\u7d20 */\nlist.splice(3, 1);\n</code></pre> list.ts<pre><code>/* \u6e05\u7a7a\u5217\u8868 */\nlist.length = 0;\n/* \u5c3e\u90e8\u6dfb\u52a0\u5143\u7d20 */\nlist.push(1);\nlist.push(3);\nlist.push(2);\nlist.push(5);\nlist.push(4);\n/* \u4e2d\u95f4\u63d2\u5165\u5143\u7d20 */\nlist.splice(3, 0, 6);\n/* \u5220\u9664\u5143\u7d20 */\nlist.splice(3, 1);\n</code></pre> list.c<pre><code>// C \u672a\u63d0\u4f9b\u5185\u7f6e\u52a8\u6001\u6570\u7ec4\n</code></pre> list.cs<pre><code>/* \u6e05\u7a7a\u5217\u8868 */\nlist.Clear();\n/* \u5c3e\u90e8\u6dfb\u52a0\u5143\u7d20 */\nlist.Add(1);\nlist.Add(3);\nlist.Add(2);\nlist.Add(5);\nlist.Add(4);\n/* \u4e2d\u95f4\u63d2\u5165\u5143\u7d20 */\nlist.Insert(3, 6);\n/* \u5220\u9664\u5143\u7d20 */\nlist.RemoveAt(3);\n</code></pre> list.swift<pre><code>/* \u6e05\u7a7a\u5217\u8868 */\nlist.removeAll()\n/* \u5c3e\u90e8\u6dfb\u52a0\u5143\u7d20 */\nlist.append(1)\nlist.append(3)\nlist.append(2)\nlist.append(5)\nlist.append(4)\n/* \u4e2d\u95f4\u63d2\u5165\u5143\u7d20 */\nlist.insert(6, at: 3) // \u5728\u7d22\u5f15 3 \u5904\u63d2\u5165\u6570\u5b57 6\n/* \u5220\u9664\u5143\u7d20 */\nlist.remove(at: 3) // \u5220\u9664\u7d22\u5f15 3 \u5904\u7684\u5143\u7d20\n</code></pre> list.zig<pre><code>// \u6e05\u7a7a\u5217\u8868\nlist.clearRetainingCapacity();\n// \u5c3e\u90e8\u6dfb\u52a0\u5143\u7d20\ntry list.append(1);\ntry list.append(3);\ntry list.append(2);\ntry list.append(5);\ntry list.append(4);\n// \u4e2d\u95f4\u63d2\u5165\u5143\u7d20\ntry list.insert(3, 6); // \u5728\u7d22\u5f15 3 \u5904\u63d2\u5165\u6570\u5b57 6\n// \u5220\u9664\u5143\u7d20\n_ = list.orderedRemove(3); // \u5220\u9664\u7d22\u5f15 3 \u5904\u7684\u5143\u7d20\n</code></pre> list.dart<pre><code>/* \u6e05\u7a7a\u5217\u8868 */\nlist.clear();\n/* \u5c3e\u90e8\u6dfb\u52a0\u5143\u7d20 */\nlist.add(1);\nlist.add(3);\nlist.add(2);\nlist.add(5);\nlist.add(4);\n/* \u4e2d\u95f4\u63d2\u5165\u5143\u7d20 */\nlist.insert(3, 6); // \u5728\u7d22\u5f15 3 \u5904\u63d2\u5165\u6570\u5b57 6\n/* \u5220\u9664\u5143\u7d20 */\nlist.removeAt(3); // \u5220\u9664\u7d22\u5f15 3 \u5904\u7684\u5143\u7d20\n</code></pre> <p>\u904d\u5386\u5217\u8868\u3002\u4e0e\u6570\u7ec4\u4e00\u6837\uff0c\u5217\u8868\u53ef\u4ee5\u6839\u636e\u7d22\u5f15\u904d\u5386\uff0c\u4e5f\u53ef\u4ee5\u76f4\u63a5\u904d\u5386\u5404\u5143\u7d20\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart list.java<pre><code>/* \u901a\u8fc7\u7d22\u5f15\u904d\u5386\u5217\u8868 */\nint count = 0;\nfor (int i = 0; i &lt; list.size(); i++) {\ncount++;\n}\n/* \u76f4\u63a5\u904d\u5386\u5217\u8868\u5143\u7d20 */\ncount = 0;\nfor (int n : list) {\ncount++;\n}\n</code></pre> list.cpp<pre><code>/* \u901a\u8fc7\u7d22\u5f15\u904d\u5386\u5217\u8868 */\nint count = 0;\nfor (int i = 0; i &lt; list.size(); i++) {\ncount++;\n}\n/* \u76f4\u63a5\u904d\u5386\u5217\u8868\u5143\u7d20 */\ncount = 0;\nfor (int n : list) {\ncount++;\n}\n</code></pre> list.py<pre><code># \u901a\u8fc7\u7d22\u5f15\u904d\u5386\u5217\u8868\ncount = 0\nfor i in range(len(list)):\ncount += 1\n# \u76f4\u63a5\u904d\u5386\u5217\u8868\u5143\u7d20\ncount = 0\nfor n in list:\ncount += 1\n</code></pre> list_test.go<pre><code>/* \u901a\u8fc7\u7d22\u5f15\u904d\u5386\u5217\u8868 */\ncount := 0\nfor i := 0; i &lt; len(list); i++ {\ncount++\n}\n/* \u76f4\u63a5\u904d\u5386\u5217\u8868\u5143\u7d20 */\ncount = 0\nfor range list {\ncount++\n}\n</code></pre> list.js<pre><code>/* \u901a\u8fc7\u7d22\u5f15\u904d\u5386\u5217\u8868 */\nlet count = 0;\nfor (let i = 0; i &lt; list.length; i++) {\ncount++;\n}\n/* \u76f4\u63a5\u904d\u5386\u5217\u8868\u5143\u7d20 */\ncount = 0;\nfor (const n of list) {\ncount++;\n}\n</code></pre> list.ts<pre><code>/* \u901a\u8fc7\u7d22\u5f15\u904d\u5386\u5217\u8868 */\nlet count = 0;\nfor (let i = 0; i &lt; list.length; i++) {\ncount++;\n}\n/* \u76f4\u63a5\u904d\u5386\u5217\u8868\u5143\u7d20 */\ncount = 0;\nfor (const n of list) {\ncount++;\n}\n</code></pre> list.c<pre><code>// C \u672a\u63d0\u4f9b\u5185\u7f6e\u52a8\u6001\u6570\u7ec4\n</code></pre> list.cs<pre><code>/* \u901a\u8fc7\u7d22\u5f15\u904d\u5386\u5217\u8868 */\nint count = 0;\nfor (int i = 0; i &lt; list.Count(); i++)\n{\ncount++;\n}\n/* \u76f4\u63a5\u904d\u5386\u5217\u8868\u5143\u7d20 */\ncount = 0;\nforeach (int n in list)\n{\ncount++;\n}\n</code></pre> list.swift<pre><code>/* \u901a\u8fc7\u7d22\u5f15\u904d\u5386\u5217\u8868 */\nvar count = 0\nfor _ in list.indices {\ncount += 1\n}\n/* \u76f4\u63a5\u904d\u5386\u5217\u8868\u5143\u7d20 */\ncount = 0\nfor _ in list {\ncount += 1\n}\n</code></pre> list.zig<pre><code>// \u901a\u8fc7\u7d22\u5f15\u904d\u5386\u5217\u8868\nvar count: i32 = 0;\nvar i: i32 = 0;\nwhile (i &lt; list.items.len) : (i += 1) {\ncount += 1;\n}\n// \u76f4\u63a5\u904d\u5386\u5217\u8868\u5143\u7d20\ncount = 0;\nfor (list.items) |_| {\ncount += 1;\n}\n</code></pre> list.dart<pre><code>/* \u901a\u8fc7\u7d22\u5f15\u904d\u5386\u5217\u8868 */\nint count = 0;\nfor (int i = 0; i &lt; list.length; i++) {\ncount++;\n}\n/* \u76f4\u63a5\u904d\u5386\u5217\u8868\u5143\u7d20 */\ncount = 0;\nfor (int n in list) {\ncount++;\n}\n</code></pre> <p>\u62fc\u63a5\u4e24\u4e2a\u5217\u8868\u3002\u7ed9\u5b9a\u4e00\u4e2a\u65b0\u5217\u8868 <code>list1</code> \uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u8be5\u5217\u8868\u62fc\u63a5\u5230\u539f\u5217\u8868\u7684\u5c3e\u90e8\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart list.java<pre><code>/* \u62fc\u63a5\u4e24\u4e2a\u5217\u8868 */\nList&lt;Integer&gt; list1 = new ArrayList&lt;&gt;(Arrays.asList(new Integer[] { 6, 8, 7, 10, 9 }));\nlist.addAll(list1);  // \u5c06\u5217\u8868 list1 \u62fc\u63a5\u5230 list \u4e4b\u540e\n</code></pre> list.cpp<pre><code>/* \u62fc\u63a5\u4e24\u4e2a\u5217\u8868 */\nvector&lt;int&gt; list1 = { 6, 8, 7, 10, 9 };\n// \u5c06\u5217\u8868 list1 \u62fc\u63a5\u5230 list \u4e4b\u540e\nlist.insert(list.end(), list1.begin(), list1.end());\n</code></pre> list.py<pre><code># \u62fc\u63a5\u4e24\u4e2a\u5217\u8868\nlist1: List[int] = [6, 8, 7, 10, 9]\nlist += list1  # \u5c06\u5217\u8868 list1 \u62fc\u63a5\u5230 list \u4e4b\u540e\n</code></pre> list_test.go<pre><code>/* \u62fc\u63a5\u4e24\u4e2a\u5217\u8868 */\nlist1 := []int{6, 8, 7, 10, 9}\nlist = append(list, list1...)  // \u5c06\u5217\u8868 list1 \u62fc\u63a5\u5230 list \u4e4b\u540e\n</code></pre> list.js<pre><code>/* \u62fc\u63a5\u4e24\u4e2a\u5217\u8868 */\nconst list1 = [6, 8, 7, 10, 9];\nlist.push(...list1);  // \u5c06\u5217\u8868 list1 \u62fc\u63a5\u5230 list \u4e4b\u540e\n</code></pre> list.ts<pre><code>/* \u62fc\u63a5\u4e24\u4e2a\u5217\u8868 */\nconst list1: number[] = [6, 8, 7, 10, 9];\nlist.push(...list1);  // \u5c06\u5217\u8868 list1 \u62fc\u63a5\u5230 list \u4e4b\u540e\n</code></pre> list.c<pre><code>// C \u672a\u63d0\u4f9b\u5185\u7f6e\u52a8\u6001\u6570\u7ec4\n</code></pre> list.cs<pre><code>/* \u62fc\u63a5\u4e24\u4e2a\u5217\u8868 */\nList&lt;int&gt; list1 = new() { 6, 8, 7, 10, 9 };\nlist.AddRange(list1);  // \u5c06\u5217\u8868 list1 \u62fc\u63a5\u5230 list \u4e4b\u540e\n</code></pre> list.swift<pre><code>/* \u62fc\u63a5\u4e24\u4e2a\u5217\u8868 */\nlet list1 = [6, 8, 7, 10, 9]\nlist.append(contentsOf: list1) // \u5c06\u5217\u8868 list1 \u62fc\u63a5\u5230 list \u4e4b\u540e\n</code></pre> list.zig<pre><code>// \u62fc\u63a5\u4e24\u4e2a\u5217\u8868\nvar list1 = std.ArrayList(i32).init(std.heap.page_allocator);\ndefer list1.deinit();\ntry list1.appendSlice(&amp;[_]i32{ 6, 8, 7, 10, 9 });\ntry list.insertSlice(list.items.len, list1.items); // \u5c06\u5217\u8868 list1 \u62fc\u63a5\u5230 list \u4e4b\u540e\n</code></pre> list.dart<pre><code>/* \u62fc\u63a5\u4e24\u4e2a\u5217\u8868 */\nList&lt;int&gt; list1 = [6, 8, 7, 10, 9];\nlist.addAll(list1);  // \u5c06\u5217\u8868 list1 \u62fc\u63a5\u5230 list \u4e4b\u540e\n</code></pre> <p>\u6392\u5e8f\u5217\u8868\u3002\u6392\u5e8f\u4e5f\u662f\u5e38\u7528\u7684\u65b9\u6cd5\u4e4b\u4e00\u3002\u5b8c\u6210\u5217\u8868\u6392\u5e8f\u540e\uff0c\u6211\u4eec\u4fbf\u53ef\u4ee5\u4f7f\u7528\u5728\u6570\u7ec4\u7c7b\u7b97\u6cd5\u9898\u4e2d\u7ecf\u5e38\u8003\u5bdf\u7684\u300c\u4e8c\u5206\u67e5\u627e\u300d\u548c\u300c\u53cc\u6307\u9488\u300d\u7b97\u6cd5\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart list.java<pre><code>/* \u6392\u5e8f\u5217\u8868 */\nCollections.sort(list);  // \u6392\u5e8f\u540e\uff0c\u5217\u8868\u5143\u7d20\u4ece\u5c0f\u5230\u5927\u6392\u5217\n</code></pre> list.cpp<pre><code>/* \u6392\u5e8f\u5217\u8868 */\nsort(list.begin(), list.end());  // \u6392\u5e8f\u540e\uff0c\u5217\u8868\u5143\u7d20\u4ece\u5c0f\u5230\u5927\u6392\u5217\n</code></pre> list.py<pre><code># \u6392\u5e8f\u5217\u8868\nlist.sort()  # \u6392\u5e8f\u540e\uff0c\u5217\u8868\u5143\u7d20\u4ece\u5c0f\u5230\u5927\u6392\u5217\n</code></pre> list_test.go<pre><code>/* \u6392\u5e8f\u5217\u8868 */\nsort.Ints(list)  // \u6392\u5e8f\u540e\uff0c\u5217\u8868\u5143\u7d20\u4ece\u5c0f\u5230\u5927\u6392\u5217\n</code></pre> list.js<pre><code>/* \u6392\u5e8f\u5217\u8868 */  list.sort((a, b) =&gt; a - b);  // \u6392\u5e8f\u540e\uff0c\u5217\u8868\u5143\u7d20\u4ece\u5c0f\u5230\u5927\u6392\u5217\n</code></pre> list.ts<pre><code>/* \u6392\u5e8f\u5217\u8868 */\nlist.sort((a, b) =&gt; a - b);  // \u6392\u5e8f\u540e\uff0c\u5217\u8868\u5143\u7d20\u4ece\u5c0f\u5230\u5927\u6392\u5217\n</code></pre> list.c<pre><code>// C \u672a\u63d0\u4f9b\u5185\u7f6e\u52a8\u6001\u6570\u7ec4\n</code></pre> list.cs<pre><code>/* \u6392\u5e8f\u5217\u8868 */\nlist.Sort(); // \u6392\u5e8f\u540e\uff0c\u5217\u8868\u5143\u7d20\u4ece\u5c0f\u5230\u5927\u6392\u5217\n</code></pre> list.swift<pre><code>/* \u6392\u5e8f\u5217\u8868 */\nlist.sort() // \u6392\u5e8f\u540e\uff0c\u5217\u8868\u5143\u7d20\u4ece\u5c0f\u5230\u5927\u6392\u5217\n</code></pre> list.zig<pre><code>// \u6392\u5e8f\u5217\u8868\nstd.sort.sort(i32, list.items, {}, comptime std.sort.asc(i32));\n</code></pre> list.dart<pre><code>/* \u6392\u5e8f\u5217\u8868 */\nlist.sort(); // \u6392\u5e8f\u540e\uff0c\u5217\u8868\u5143\u7d20\u4ece\u5c0f\u5230\u5927\u6392\u5217\n</code></pre>"},{"location":"chapter_array_and_linkedlist/list/#432","title":"4.3.2. \u00a0 \u5217\u8868\u5b9e\u73b0 *","text":"<p>\u4e3a\u4e86\u5e2e\u52a9\u52a0\u6df1\u5bf9\u5217\u8868\u7684\u7406\u89e3\uff0c\u6211\u4eec\u5728\u6b64\u63d0\u4f9b\u4e00\u4e2a\u7b80\u6613\u7248\u5217\u8868\u5b9e\u73b0\u3002\u9700\u8981\u5173\u6ce8\u4e09\u4e2a\u6838\u5fc3\u70b9\uff1a</p> <ul> <li>\u521d\u59cb\u5bb9\u91cf\uff1a\u9009\u53d6\u4e00\u4e2a\u5408\u7406\u7684\u6570\u7ec4\u521d\u59cb\u5bb9\u91cf\u3002\u5728\u672c\u793a\u4f8b\u4e2d\uff0c\u6211\u4eec\u9009\u62e9 10 \u4f5c\u4e3a\u521d\u59cb\u5bb9\u91cf\u3002</li> <li>\u6570\u91cf\u8bb0\u5f55\uff1a\u58f0\u660e\u4e00\u4e2a\u53d8\u91cf size\uff0c\u7528\u4e8e\u8bb0\u5f55\u5217\u8868\u5f53\u524d\u5143\u7d20\u6570\u91cf\uff0c\u5e76\u968f\u7740\u5143\u7d20\u63d2\u5165\u548c\u5220\u9664\u5b9e\u65f6\u66f4\u65b0\u3002\u6839\u636e\u6b64\u53d8\u91cf\uff0c\u6211\u4eec\u53ef\u4ee5\u5b9a\u4f4d\u5217\u8868\u5c3e\u90e8\uff0c\u4ee5\u53ca\u5224\u65ad\u662f\u5426\u9700\u8981\u6269\u5bb9\u3002</li> <li>\u6269\u5bb9\u673a\u5236\uff1a\u63d2\u5165\u5143\u7d20\u65f6\u53ef\u80fd\u8d85\u51fa\u5217\u8868\u5bb9\u91cf\uff0c\u6b64\u65f6\u9700\u8981\u6269\u5bb9\u5217\u8868\u3002\u6269\u5bb9\u65b9\u6cd5\u662f\u6839\u636e\u6269\u5bb9\u500d\u6570\u521b\u5efa\u4e00\u4e2a\u66f4\u5927\u7684\u6570\u7ec4\uff0c\u5e76\u5c06\u5f53\u524d\u6570\u7ec4\u7684\u6240\u6709\u5143\u7d20\u4f9d\u6b21\u79fb\u52a8\u81f3\u65b0\u6570\u7ec4\u3002\u5728\u672c\u793a\u4f8b\u4e2d\uff0c\u6211\u4eec\u89c4\u5b9a\u6bcf\u6b21\u5c06\u6570\u7ec4\u6269\u5bb9\u81f3\u4e4b\u524d\u7684 2 \u500d\u3002</li> </ul> <p>\u672c\u793a\u4f8b\u65e8\u5728\u5e2e\u52a9\u8bfb\u8005\u76f4\u89c2\u7406\u89e3\u5217\u8868\u7684\u5de5\u4f5c\u673a\u5236\u3002\u5b9e\u9645\u7f16\u7a0b\u8bed\u8a00\u4e2d\uff0c\u5217\u8868\u5b9e\u73b0\u66f4\u52a0\u6807\u51c6\u548c\u590d\u6742\uff0c\u5404\u4e2a\u53c2\u6570\u7684\u8bbe\u5b9a\u4e5f\u975e\u5e38\u6709\u8003\u7a76\uff0c\u4f8b\u5982\u521d\u59cb\u5bb9\u91cf\u3001\u6269\u5bb9\u500d\u6570\u7b49\u3002\u611f\u5174\u8da3\u7684\u8bfb\u8005\u53ef\u4ee5\u67e5\u9605\u6e90\u7801\u8fdb\u884c\u5b66\u4e60\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart my_list.java<pre><code>/* \u5217\u8868\u7c7b\u7b80\u6613\u5b9e\u73b0 */\nclass MyList {\nprivate int[] nums; // \u6570\u7ec4\uff08\u5b58\u50a8\u5217\u8868\u5143\u7d20\uff09\nprivate int capacity = 10; // \u5217\u8868\u5bb9\u91cf\nprivate int size = 0; // \u5217\u8868\u957f\u5ea6\uff08\u5373\u5f53\u524d\u5143\u7d20\u6570\u91cf\uff09\nprivate int extendRatio = 2; // \u6bcf\u6b21\u5217\u8868\u6269\u5bb9\u7684\u500d\u6570\n/* \u6784\u9020\u65b9\u6cd5 */\npublic MyList() {\nnums = new int[capacity];\n}\n/* \u83b7\u53d6\u5217\u8868\u957f\u5ea6\uff08\u5373\u5f53\u524d\u5143\u7d20\u6570\u91cf\uff09 */\npublic int size() {\nreturn size;\n}\n/* \u83b7\u53d6\u5217\u8868\u5bb9\u91cf */\npublic int capacity() {\nreturn capacity;\n}\n/* \u8bbf\u95ee\u5143\u7d20 */\npublic int get(int index) {\n// \u7d22\u5f15\u5982\u679c\u8d8a\u754c\u5219\u629b\u51fa\u5f02\u5e38\uff0c\u4e0b\u540c\nif (index &lt; 0 || index &gt;= size)\nthrow new IndexOutOfBoundsException(\"\u7d22\u5f15\u8d8a\u754c\");\nreturn nums[index];\n}\n/* \u66f4\u65b0\u5143\u7d20 */\npublic void set(int index, int num) {\nif (index &lt; 0 || index &gt;= size)\nthrow new IndexOutOfBoundsException(\"\u7d22\u5f15\u8d8a\u754c\");\nnums[index] = num;\n}\n/* \u5c3e\u90e8\u6dfb\u52a0\u5143\u7d20 */\npublic void add(int num) {\n// \u5143\u7d20\u6570\u91cf\u8d85\u51fa\u5bb9\u91cf\u65f6\uff0c\u89e6\u53d1\u6269\u5bb9\u673a\u5236\nif (size == capacity())\nextendCapacity();\nnums[size] = num;\n// \u66f4\u65b0\u5143\u7d20\u6570\u91cf\nsize++;\n}\n/* \u4e2d\u95f4\u63d2\u5165\u5143\u7d20 */\npublic void insert(int index, int num) {\nif (index &lt; 0 || index &gt;= size)\nthrow new IndexOutOfBoundsException(\"\u7d22\u5f15\u8d8a\u754c\");\n// \u5143\u7d20\u6570\u91cf\u8d85\u51fa\u5bb9\u91cf\u65f6\uff0c\u89e6\u53d1\u6269\u5bb9\u673a\u5236\nif (size == capacity())\nextendCapacity();\n// \u5c06\u7d22\u5f15 index \u4ee5\u53ca\u4e4b\u540e\u7684\u5143\u7d20\u90fd\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\nfor (int j = size - 1; j &gt;= index; j--) {\nnums[j + 1] = nums[j];\n}\nnums[index] = num;\n// \u66f4\u65b0\u5143\u7d20\u6570\u91cf\nsize++;\n}\n/* \u5220\u9664\u5143\u7d20 */\npublic int remove(int index) {\nif (index &lt; 0 || index &gt;= size)\nthrow new IndexOutOfBoundsException(\"\u7d22\u5f15\u8d8a\u754c\");\nint num = nums[index];\n// \u5c06\u7d22\u5f15 index \u4e4b\u540e\u7684\u5143\u7d20\u90fd\u5411\u524d\u79fb\u52a8\u4e00\u4f4d\nfor (int j = index; j &lt; size - 1; j++) {\nnums[j] = nums[j + 1];\n}\n// \u66f4\u65b0\u5143\u7d20\u6570\u91cf\nsize--;\n// \u8fd4\u56de\u88ab\u5220\u9664\u5143\u7d20\nreturn num;\n}\n/* \u5217\u8868\u6269\u5bb9 */\npublic void extendCapacity() {\n// \u65b0\u5efa\u4e00\u4e2a\u957f\u5ea6\u4e3a\u539f\u6570\u7ec4 extendRatio \u500d\u7684\u65b0\u6570\u7ec4\uff0c\u5e76\u5c06\u539f\u6570\u7ec4\u62f7\u8d1d\u5230\u65b0\u6570\u7ec4\nnums = Arrays.copyOf(nums, capacity() * extendRatio);\n// \u66f4\u65b0\u5217\u8868\u5bb9\u91cf\ncapacity = nums.length;\n}\n/* \u5c06\u5217\u8868\u8f6c\u6362\u4e3a\u6570\u7ec4 */\npublic int[] toArray() {\nint size = size();\n// \u4ec5\u8f6c\u6362\u6709\u6548\u957f\u5ea6\u8303\u56f4\u5185\u7684\u5217\u8868\u5143\u7d20\nint[] nums = new int[size];\nfor (int i = 0; i &lt; size; i++) {\nnums[i] = get(i);\n}\nreturn nums;\n}\n}\n</code></pre> my_list.cpp<pre><code>/* \u5217\u8868\u7c7b\u7b80\u6613\u5b9e\u73b0 */\nclass MyList {\nprivate:\nint *nums;             // \u6570\u7ec4\uff08\u5b58\u50a8\u5217\u8868\u5143\u7d20\uff09\nint numsCapacity = 10; // \u5217\u8868\u5bb9\u91cf\nint numsSize = 0;      // \u5217\u8868\u957f\u5ea6\uff08\u5373\u5f53\u524d\u5143\u7d20\u6570\u91cf\uff09\nint extendRatio = 2;   // \u6bcf\u6b21\u5217\u8868\u6269\u5bb9\u7684\u500d\u6570\npublic:\n/* \u6784\u9020\u65b9\u6cd5 */\nMyList() {\nnums = new int[numsCapacity];\n}\n/* \u6790\u6784\u65b9\u6cd5 */\n~MyList() {\ndelete[] nums;\n}\n/* \u83b7\u53d6\u5217\u8868\u957f\u5ea6\uff08\u5373\u5f53\u524d\u5143\u7d20\u6570\u91cf\uff09*/\nint size() {\nreturn numsSize;\n}\n/* \u83b7\u53d6\u5217\u8868\u5bb9\u91cf */\nint capacity() {\nreturn numsCapacity;\n}\n/* \u8bbf\u95ee\u5143\u7d20 */\nint get(int index) {\n// \u7d22\u5f15\u5982\u679c\u8d8a\u754c\u5219\u629b\u51fa\u5f02\u5e38\uff0c\u4e0b\u540c\nif (index &lt; 0 || index &gt;= size())\nthrow out_of_range(\"\u7d22\u5f15\u8d8a\u754c\");\nreturn nums[index];\n}\n/* \u66f4\u65b0\u5143\u7d20 */\nvoid set(int index, int num) {\nif (index &lt; 0 || index &gt;= size())\nthrow out_of_range(\"\u7d22\u5f15\u8d8a\u754c\");\nnums[index] = num;\n}\n/* \u5c3e\u90e8\u6dfb\u52a0\u5143\u7d20 */\nvoid add(int num) {\n// \u5143\u7d20\u6570\u91cf\u8d85\u51fa\u5bb9\u91cf\u65f6\uff0c\u89e6\u53d1\u6269\u5bb9\u673a\u5236\nif (size() == capacity())\nextendCapacity();\nnums[size()] = num;\n// \u66f4\u65b0\u5143\u7d20\u6570\u91cf\nnumsSize++;\n}\n/* \u4e2d\u95f4\u63d2\u5165\u5143\u7d20 */\nvoid insert(int index, int num) {\nif (index &lt; 0 || index &gt;= size())\nthrow out_of_range(\"\u7d22\u5f15\u8d8a\u754c\");\n// \u5143\u7d20\u6570\u91cf\u8d85\u51fa\u5bb9\u91cf\u65f6\uff0c\u89e6\u53d1\u6269\u5bb9\u673a\u5236\nif (size() == capacity())\nextendCapacity();\n// \u7d22\u5f15 i \u4ee5\u53ca\u4e4b\u540e\u7684\u5143\u7d20\u90fd\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\nfor (int j = size() - 1; j &gt;= index; j--) {\nnums[j + 1] = nums[j];\n}\nnums[index] = num;\n// \u66f4\u65b0\u5143\u7d20\u6570\u91cf\nnumsSize++;\n}\n/* \u5220\u9664\u5143\u7d20 */\nint remove(int index) {\nif (index &lt; 0 || index &gt;= size())\nthrow out_of_range(\"\u7d22\u5f15\u8d8a\u754c\");\nint num = nums[index];\n// \u7d22\u5f15 i \u4e4b\u540e\u7684\u5143\u7d20\u90fd\u5411\u524d\u79fb\u52a8\u4e00\u4f4d\nfor (int j = index; j &lt; size() - 1; j++) {\nnums[j] = nums[j + 1];\n}\n// \u66f4\u65b0\u5143\u7d20\u6570\u91cf\nnumsSize--;\n// \u8fd4\u56de\u88ab\u5220\u9664\u5143\u7d20\nreturn num;\n}\n/* \u5217\u8868\u6269\u5bb9 */\nvoid extendCapacity() {\n// \u65b0\u5efa\u4e00\u4e2a\u957f\u5ea6\u4e3a\u539f\u6570\u7ec4 extendRatio \u500d\u7684\u65b0\u6570\u7ec4\nint newCapacity = capacity() * extendRatio;\nint *tmp = nums;\nnums = new int[newCapacity];\n// \u5c06\u539f\u6570\u7ec4\u4e2d\u7684\u6240\u6709\u5143\u7d20\u590d\u5236\u5230\u65b0\u6570\u7ec4\nfor (int i = 0; i &lt; size(); i++) {\nnums[i] = tmp[i];\n}\n// \u91ca\u653e\u5185\u5b58\ndelete[] tmp;\nnumsCapacity = newCapacity;\n}\n/* \u5c06\u5217\u8868\u8f6c\u6362\u4e3a Vector \u7528\u4e8e\u6253\u5370 */\nvector&lt;int&gt; toVector() {\n// \u4ec5\u8f6c\u6362\u6709\u6548\u957f\u5ea6\u8303\u56f4\u5185\u7684\u5217\u8868\u5143\u7d20\nvector&lt;int&gt; vec(size());\nfor (int i = 0; i &lt; size(); i++) {\nvec[i] = nums[i];\n}\nreturn vec;\n}\n};\n</code></pre> my_list.py<pre><code>class MyList:\n\"\"\"\u5217\u8868\u7c7b\u7b80\u6613\u5b9e\u73b0\"\"\"\ndef __init__(self):\n\"\"\"\u6784\u9020\u65b9\u6cd5\"\"\"\nself.__capacity: int = 10  # \u5217\u8868\u5bb9\u91cf\nself.__nums: list[int] = [0] * self.__capacity  # \u6570\u7ec4\uff08\u5b58\u50a8\u5217\u8868\u5143\u7d20\uff09\nself.__size: int = 0  # \u5217\u8868\u957f\u5ea6\uff08\u5373\u5f53\u524d\u5143\u7d20\u6570\u91cf\uff09\nself.__extend_ratio: int = 2  # \u6bcf\u6b21\u5217\u8868\u6269\u5bb9\u7684\u500d\u6570\ndef size(self) -&gt; int:\n\"\"\"\u83b7\u53d6\u5217\u8868\u957f\u5ea6\uff08\u5373\u5f53\u524d\u5143\u7d20\u6570\u91cf\uff09\"\"\"\nreturn self.__size\ndef capacity(self) -&gt; int:\n\"\"\"\u83b7\u53d6\u5217\u8868\u5bb9\u91cf\"\"\"\nreturn self.__capacity\ndef get(self, index: int) -&gt; int:\n\"\"\"\u8bbf\u95ee\u5143\u7d20\"\"\"\n# \u7d22\u5f15\u5982\u679c\u8d8a\u754c\u5219\u629b\u51fa\u5f02\u5e38\uff0c\u4e0b\u540c\nif index &lt; 0 or index &gt;= self.__size:\nraise IndexError(\"\u7d22\u5f15\u8d8a\u754c\")\nreturn self.__nums[index]\ndef set(self, num: int, index: int) -&gt; None:\n\"\"\"\u66f4\u65b0\u5143\u7d20\"\"\"\nif index &lt; 0 or index &gt;= self.__size:\nraise IndexError(\"\u7d22\u5f15\u8d8a\u754c\")\nself.__nums[index] = num\ndef add(self, num: int) -&gt; None:\n\"\"\"\u5c3e\u90e8\u6dfb\u52a0\u5143\u7d20\"\"\"\n# \u5143\u7d20\u6570\u91cf\u8d85\u51fa\u5bb9\u91cf\u65f6\uff0c\u89e6\u53d1\u6269\u5bb9\u673a\u5236\nif self.size() == self.capacity():\nself.extend_capacity()\nself.__nums[self.__size] = num\nself.__size += 1\ndef insert(self, num: int, index: int) -&gt; None:\n\"\"\"\u4e2d\u95f4\u63d2\u5165\u5143\u7d20\"\"\"\nif index &lt; 0 or index &gt;= self.__size:\nraise IndexError(\"\u7d22\u5f15\u8d8a\u754c\")\n# \u5143\u7d20\u6570\u91cf\u8d85\u51fa\u5bb9\u91cf\u65f6\uff0c\u89e6\u53d1\u6269\u5bb9\u673a\u5236\nif self.__size == self.capacity():\nself.extend_capacity()\n# \u7d22\u5f15 i \u4ee5\u53ca\u4e4b\u540e\u7684\u5143\u7d20\u90fd\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\nfor j in range(self.__size - 1, index - 1, -1):\nself.__nums[j + 1] = self.__nums[j]\nself.__nums[index] = num\n# \u66f4\u65b0\u5143\u7d20\u6570\u91cf\nself.__size += 1\ndef remove(self, index: int) -&gt; int:\n\"\"\"\u5220\u9664\u5143\u7d20\"\"\"\nif index &lt; 0 or index &gt;= self.__size:\nraise IndexError(\"\u7d22\u5f15\u8d8a\u754c\")\nnum = self.__nums[index]\n# \u7d22\u5f15 i \u4e4b\u540e\u7684\u5143\u7d20\u90fd\u5411\u524d\u79fb\u52a8\u4e00\u4f4d\nfor j in range(index, self.__size - 1):\nself.__nums[j] = self.__nums[j + 1]\n# \u66f4\u65b0\u5143\u7d20\u6570\u91cf\nself.__size -= 1\n# \u8fd4\u56de\u88ab\u5220\u9664\u5143\u7d20\nreturn num\ndef extend_capacity(self) -&gt; None:\n\"\"\"\u5217\u8868\u6269\u5bb9\"\"\"\n# \u65b0\u5efa\u4e00\u4e2a\u957f\u5ea6\u4e3a\u539f\u6570\u7ec4 __extend_ratio \u500d\u7684\u65b0\u6570\u7ec4\uff0c\u5e76\u5c06\u539f\u6570\u7ec4\u62f7\u8d1d\u5230\u65b0\u6570\u7ec4\nself.__nums = self.__nums + [0] * self.capacity() * (self.__extend_ratio - 1)\n# \u66f4\u65b0\u5217\u8868\u5bb9\u91cf\nself.__capacity = len(self.__nums)\ndef to_array(self) -&gt; list[int]:\n\"\"\"\u8fd4\u56de\u6709\u6548\u957f\u5ea6\u7684\u5217\u8868\"\"\"\nreturn self.__nums[: self.__size]\n</code></pre> my_list.go<pre><code>/* \u5217\u8868\u7c7b\u7b80\u6613\u5b9e\u73b0 */\ntype myList struct {\nnumsCapacity int\nnums         []int\nnumsSize     int\nextendRatio  int\n}\n/* \u6784\u9020\u65b9\u6cd5 */\nfunc newMyList() *myList {\nreturn &amp;myList{\nnumsCapacity: 10,              // \u5217\u8868\u5bb9\u91cf\nnums:         make([]int, 10), // \u6570\u7ec4\uff08\u5b58\u50a8\u5217\u8868\u5143\u7d20\uff09\nnumsSize:     0,               // \u5217\u8868\u957f\u5ea6\uff08\u5373\u5f53\u524d\u5143\u7d20\u6570\u91cf\uff09\nextendRatio:  2,               // \u6bcf\u6b21\u5217\u8868\u6269\u5bb9\u7684\u500d\u6570\n}\n}\n/* \u83b7\u53d6\u5217\u8868\u957f\u5ea6\uff08\u5373\u5f53\u524d\u5143\u7d20\u6570\u91cf\uff09 */\nfunc (l *myList) size() int {\nreturn l.numsSize\n}\n/*  \u83b7\u53d6\u5217\u8868\u5bb9\u91cf */\nfunc (l *myList) capacity() int {\nreturn l.numsCapacity\n}\n/* \u8bbf\u95ee\u5143\u7d20 */\nfunc (l *myList) get(index int) int {\n// \u7d22\u5f15\u5982\u679c\u8d8a\u754c\u5219\u629b\u51fa\u5f02\u5e38\uff0c\u4e0b\u540c\nif index &lt; 0 || index &gt;= l.numsSize {\npanic(\"\u7d22\u5f15\u8d8a\u754c\")\n}\nreturn l.nums[index]\n}\n/* \u66f4\u65b0\u5143\u7d20 */\nfunc (l *myList) set(num, index int) {\nif index &lt; 0 || index &gt;= l.numsSize {\npanic(\"\u7d22\u5f15\u8d8a\u754c\")\n}\nl.nums[index] = num\n}\n/* \u5c3e\u90e8\u6dfb\u52a0\u5143\u7d20 */\nfunc (l *myList) add(num int) {\n// \u5143\u7d20\u6570\u91cf\u8d85\u51fa\u5bb9\u91cf\u65f6\uff0c\u89e6\u53d1\u6269\u5bb9\u673a\u5236\nif l.numsSize == l.numsCapacity {\nl.extendCapacity()\n}\nl.nums[l.numsSize] = num\n// \u66f4\u65b0\u5143\u7d20\u6570\u91cf\nl.numsSize++\n}\n/* \u4e2d\u95f4\u63d2\u5165\u5143\u7d20 */\nfunc (l *myList) insert(num, index int) {\nif index &lt; 0 || index &gt;= l.numsSize {\npanic(\"\u7d22\u5f15\u8d8a\u754c\")\n}\n// \u5143\u7d20\u6570\u91cf\u8d85\u51fa\u5bb9\u91cf\u65f6\uff0c\u89e6\u53d1\u6269\u5bb9\u673a\u5236\nif l.numsSize == l.numsCapacity {\nl.extendCapacity()\n}\n// \u7d22\u5f15 i \u4ee5\u53ca\u4e4b\u540e\u7684\u5143\u7d20\u90fd\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\nfor j := l.numsSize - 1; j &gt;= index; j-- {\nl.nums[j+1] = l.nums[j]\n}\nl.nums[index] = num\n// \u66f4\u65b0\u5143\u7d20\u6570\u91cf\nl.numsSize++\n}\n/* \u5220\u9664\u5143\u7d20 */\nfunc (l *myList) remove(index int) int {\nif index &lt; 0 || index &gt;= l.numsSize {\npanic(\"\u7d22\u5f15\u8d8a\u754c\")\n}\nnum := l.nums[index]\n// \u7d22\u5f15 i \u4e4b\u540e\u7684\u5143\u7d20\u90fd\u5411\u524d\u79fb\u52a8\u4e00\u4f4d\nfor j := index; j &lt; l.numsSize-1; j++ {\nl.nums[j] = l.nums[j+1]\n}\n// \u66f4\u65b0\u5143\u7d20\u6570\u91cf\nl.numsSize--\n// \u8fd4\u56de\u88ab\u5220\u9664\u5143\u7d20\nreturn num\n}\n/* \u5217\u8868\u6269\u5bb9 */\nfunc (l *myList) extendCapacity() {\n// \u65b0\u5efa\u4e00\u4e2a\u957f\u5ea6\u4e3a\u539f\u6570\u7ec4 extendRatio \u500d\u7684\u65b0\u6570\u7ec4\uff0c\u5e76\u5c06\u539f\u6570\u7ec4\u62f7\u8d1d\u5230\u65b0\u6570\u7ec4\nl.nums = append(l.nums, make([]int, l.numsCapacity*(l.extendRatio-1))...)\n// \u66f4\u65b0\u5217\u8868\u5bb9\u91cf\nl.numsCapacity = len(l.nums)\n}\n/* \u8fd4\u56de\u6709\u6548\u957f\u5ea6\u7684\u5217\u8868 */\nfunc (l *myList) toArray() []int {\n// \u4ec5\u8f6c\u6362\u6709\u6548\u957f\u5ea6\u8303\u56f4\u5185\u7684\u5217\u8868\u5143\u7d20\nreturn l.nums[:l.numsSize]\n}\n</code></pre> my_list.js<pre><code>/* \u5217\u8868\u7c7b\u7b80\u6613\u5b9e\u73b0 */\nclass MyList {\n#nums = new Array(); // \u6570\u7ec4\uff08\u5b58\u50a8\u5217\u8868\u5143\u7d20\uff09\n#capacity = 10; // \u5217\u8868\u5bb9\u91cf\n#size = 0; // \u5217\u8868\u957f\u5ea6\uff08\u5373\u5f53\u524d\u5143\u7d20\u6570\u91cf\uff09\n#extendRatio = 2; // \u6bcf\u6b21\u5217\u8868\u6269\u5bb9\u7684\u500d\u6570\n/* \u6784\u9020\u65b9\u6cd5 */\nconstructor() {\nthis.#nums = new Array(this.#capacity);\n}\n/* \u83b7\u53d6\u5217\u8868\u957f\u5ea6\uff08\u5373\u5f53\u524d\u5143\u7d20\u6570\u91cf\uff09*/\nsize() {\nreturn this.#size;\n}\n/* \u83b7\u53d6\u5217\u8868\u5bb9\u91cf */\ncapacity() {\nreturn this.#capacity;\n}\n/* \u8bbf\u95ee\u5143\u7d20 */\nget(index) {\n// \u7d22\u5f15\u5982\u679c\u8d8a\u754c\u5219\u629b\u51fa\u5f02\u5e38\uff0c\u4e0b\u540c\nif (index &lt; 0 || index &gt;= this.#size) throw new Error('\u7d22\u5f15\u8d8a\u754c');\nreturn this.#nums[index];\n}\n/* \u66f4\u65b0\u5143\u7d20 */\nset(index, num) {\nif (index &lt; 0 || index &gt;= this.#size) throw new Error('\u7d22\u5f15\u8d8a\u754c');\nthis.#nums[index] = num;\n}\n/* \u5c3e\u90e8\u6dfb\u52a0\u5143\u7d20 */\nadd(num) {\n// \u5982\u679c\u957f\u5ea6\u7b49\u4e8e\u5bb9\u91cf\uff0c\u5219\u9700\u8981\u6269\u5bb9\nif (this.#size === this.#capacity) {\nthis.extendCapacity();\n}\n// \u5c06\u65b0\u5143\u7d20\u6dfb\u52a0\u5230\u5217\u8868\u5c3e\u90e8\nthis.#nums[this.#size] = num;\nthis.#size++;\n}\n/* \u4e2d\u95f4\u63d2\u5165\u5143\u7d20 */\ninsert(index, num) {\nif (index &lt; 0 || index &gt;= this.#size) throw new Error('\u7d22\u5f15\u8d8a\u754c');\n// \u5143\u7d20\u6570\u91cf\u8d85\u51fa\u5bb9\u91cf\u65f6\uff0c\u89e6\u53d1\u6269\u5bb9\u673a\u5236\nif (this.#size === this.#capacity) {\nthis.extendCapacity();\n}\n// \u5c06\u7d22\u5f15 index \u4ee5\u53ca\u4e4b\u540e\u7684\u5143\u7d20\u90fd\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\nfor (let j = this.#size - 1; j &gt;= index; j--) {\nthis.#nums[j + 1] = this.#nums[j];\n}\n// \u66f4\u65b0\u5143\u7d20\u6570\u91cf\nthis.#nums[index] = num;\nthis.#size++;\n}\n/* \u5220\u9664\u5143\u7d20 */\nremove(index) {\nif (index &lt; 0 || index &gt;= this.#size) throw new Error('\u7d22\u5f15\u8d8a\u754c');\nlet num = this.#nums[index];\n// \u5c06\u7d22\u5f15 index \u4e4b\u540e\u7684\u5143\u7d20\u90fd\u5411\u524d\u79fb\u52a8\u4e00\u4f4d\nfor (let j = index; j &lt; this.#size - 1; j++) {\nthis.#nums[j] = this.#nums[j + 1];\n}\n// \u66f4\u65b0\u5143\u7d20\u6570\u91cf\nthis.#size--;\n// \u8fd4\u56de\u88ab\u5220\u9664\u5143\u7d20\nreturn num;\n}\n/* \u5217\u8868\u6269\u5bb9 */\nextendCapacity() {\n// \u65b0\u5efa\u4e00\u4e2a\u957f\u5ea6\u4e3a\u539f\u6570\u7ec4 extendRatio \u500d\u7684\u65b0\u6570\u7ec4\uff0c\u5e76\u5c06\u539f\u6570\u7ec4\u62f7\u8d1d\u5230\u65b0\u6570\u7ec4\nthis.#nums = this.#nums.concat(\nnew Array(this.capacity() * (this.#extendRatio - 1))\n);\n// \u66f4\u65b0\u5217\u8868\u5bb9\u91cf\nthis.#capacity = this.#nums.length;\n}\n/* \u5c06\u5217\u8868\u8f6c\u6362\u4e3a\u6570\u7ec4 */\ntoArray() {\nlet size = this.size();\n// \u4ec5\u8f6c\u6362\u6709\u6548\u957f\u5ea6\u8303\u56f4\u5185\u7684\u5217\u8868\u5143\u7d20\nconst nums = new Array(size);\nfor (let i = 0; i &lt; size; i++) {\nnums[i] = this.get(i);\n}\nreturn nums;\n}\n}\n</code></pre> my_list.ts<pre><code>/* \u5217\u8868\u7c7b\u7b80\u6613\u5b9e\u73b0 */\nclass MyList {\nprivate nums: Array&lt;number&gt;; // \u6570\u7ec4\uff08\u5b58\u50a8\u5217\u8868\u5143\u7d20\uff09\nprivate _capacity: number = 10; // \u5217\u8868\u5bb9\u91cf\nprivate _size: number = 0; // \u5217\u8868\u957f\u5ea6\uff08\u5373\u5f53\u524d\u5143\u7d20\u6570\u91cf\uff09\nprivate extendRatio: number = 2; // \u6bcf\u6b21\u5217\u8868\u6269\u5bb9\u7684\u500d\u6570\n/* \u6784\u9020\u65b9\u6cd5 */\nconstructor() {\nthis.nums = new Array(this._capacity);\n}\n/* \u83b7\u53d6\u5217\u8868\u957f\u5ea6\uff08\u5373\u5f53\u524d\u5143\u7d20\u6570\u91cf\uff09*/\npublic size(): number {\nreturn this._size;\n}\n/* \u83b7\u53d6\u5217\u8868\u5bb9\u91cf */\npublic capacity(): number {\nreturn this._capacity;\n}\n/* \u8bbf\u95ee\u5143\u7d20 */\npublic get(index: number): number {\n// \u7d22\u5f15\u5982\u679c\u8d8a\u754c\u5219\u629b\u51fa\u5f02\u5e38\uff0c\u4e0b\u540c\nif (index &lt; 0 || index &gt;= this._size) throw new Error('\u7d22\u5f15\u8d8a\u754c');\nreturn this.nums[index];\n}\n/* \u66f4\u65b0\u5143\u7d20 */\npublic set(index: number, num: number): void {\nif (index &lt; 0 || index &gt;= this._size) throw new Error('\u7d22\u5f15\u8d8a\u754c');\nthis.nums[index] = num;\n}\n/* \u5c3e\u90e8\u6dfb\u52a0\u5143\u7d20 */\npublic add(num: number): void {\n// \u5982\u679c\u957f\u5ea6\u7b49\u4e8e\u5bb9\u91cf\uff0c\u5219\u9700\u8981\u6269\u5bb9\nif (this._size === this._capacity) this.extendCapacity();\n// \u5c06\u65b0\u5143\u7d20\u6dfb\u52a0\u5230\u5217\u8868\u5c3e\u90e8\nthis.nums[this._size] = num;\nthis._size++;\n}\n/* \u4e2d\u95f4\u63d2\u5165\u5143\u7d20 */\npublic insert(index: number, num: number): void {\nif (index &lt; 0 || index &gt;= this._size) throw new Error('\u7d22\u5f15\u8d8a\u754c');\n// \u5143\u7d20\u6570\u91cf\u8d85\u51fa\u5bb9\u91cf\u65f6\uff0c\u89e6\u53d1\u6269\u5bb9\u673a\u5236\nif (this._size === this._capacity) {\nthis.extendCapacity();\n}\n// \u5c06\u7d22\u5f15 index \u4ee5\u53ca\u4e4b\u540e\u7684\u5143\u7d20\u90fd\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\nfor (let j = this._size - 1; j &gt;= index; j--) {\nthis.nums[j + 1] = this.nums[j];\n}\n// \u66f4\u65b0\u5143\u7d20\u6570\u91cf\nthis.nums[index] = num;\nthis._size++;\n}\n/* \u5220\u9664\u5143\u7d20 */\npublic remove(index: number): number {\nif (index &lt; 0 || index &gt;= this._size) throw new Error('\u7d22\u5f15\u8d8a\u754c');\nlet num = this.nums[index];\n// \u5c06\u7d22\u5f15 index \u4e4b\u540e\u7684\u5143\u7d20\u90fd\u5411\u524d\u79fb\u52a8\u4e00\u4f4d\nfor (let j = index; j &lt; this._size - 1; j++) {\nthis.nums[j] = this.nums[j + 1];\n}\n// \u66f4\u65b0\u5143\u7d20\u6570\u91cf\nthis._size--;\n// \u8fd4\u56de\u88ab\u5220\u9664\u5143\u7d20\nreturn num;\n}\n/* \u5217\u8868\u6269\u5bb9 */\npublic extendCapacity(): void {\n// \u65b0\u5efa\u4e00\u4e2a\u957f\u5ea6\u4e3a size \u7684\u6570\u7ec4\uff0c\u5e76\u5c06\u539f\u6570\u7ec4\u62f7\u8d1d\u5230\u65b0\u6570\u7ec4\nthis.nums = this.nums.concat(\nnew Array(this.capacity() * (this.extendRatio - 1))\n);\n// \u66f4\u65b0\u5217\u8868\u5bb9\u91cf\nthis._capacity = this.nums.length;\n}\n/* \u5c06\u5217\u8868\u8f6c\u6362\u4e3a\u6570\u7ec4 */\npublic toArray(): number[] {\nlet size = this.size();\n// \u4ec5\u8f6c\u6362\u6709\u6548\u957f\u5ea6\u8303\u56f4\u5185\u7684\u5217\u8868\u5143\u7d20\nconst nums = new Array(size);\nfor (let i = 0; i &lt; size; i++) {\nnums[i] = this.get(i);\n}\nreturn nums;\n}\n}\n</code></pre> my_list.c<pre><code>/* \u5217\u8868\u7c7b\u7b80\u6613\u5b9e\u73b0 */\nstruct myList {\nint *nums;       // \u6570\u7ec4\uff08\u5b58\u50a8\u5217\u8868\u5143\u7d20\uff09\nint capacity;    // \u5217\u8868\u5bb9\u91cf\nint size;        // \u5217\u8868\u5927\u5c0f\nint extendRatio; // \u5217\u8868\u6bcf\u6b21\u6269\u5bb9\u7684\u500d\u6570\n};\ntypedef struct myList myList;\n/* \u6784\u9020\u51fd\u6570 */\nmyList *newMyList() {\nmyList *list = malloc(sizeof(myList));\nlist-&gt;capacity = 10;\nlist-&gt;nums = malloc(sizeof(int) * list-&gt;capacity);\nlist-&gt;size = 0;\nlist-&gt;extendRatio = 2;\nreturn list;\n}\n/* \u6790\u6784\u51fd\u6570 */\nvoid delMyList(myList *list) {\nfree(list-&gt;nums);\nfree(list);\n}\n/* \u83b7\u53d6\u5217\u8868\u957f\u5ea6 */\nint size(myList *list) {\nreturn list-&gt;size;\n}\n/* \u83b7\u53d6\u5217\u8868\u5bb9\u91cf */\nint capacity(myList *list) {\nreturn list-&gt;capacity;\n}\n/* \u8bbf\u95ee\u5143\u7d20 */\nint get(myList *list, int index) {\nassert(index &gt;= 0 &amp;&amp; index &lt; list-&gt;size);\nreturn list-&gt;nums[index];\n}\n/* \u66f4\u65b0\u5143\u7d20 */\nvoid set(myList *list, int index, int num) {\nassert(index &gt;= 0 &amp;&amp; index &lt; list-&gt;size);\nlist-&gt;nums[index] = num;\n}\n/* \u5c3e\u90e8\u6dfb\u52a0\u5143\u7d20 */\nvoid add(myList *list, int num) {\nif (size(list) == capacity(list)) {\nextendCapacity(list); // \u6269\u5bb9\n}\nlist-&gt;nums[size(list)] = num;\nlist-&gt;size++;\n}\n/* \u4e2d\u95f4\u63d2\u5165\u5143\u7d20 */\nvoid insert(myList *list, int index, int num) {\nassert(index &gt;= 0 &amp;&amp; index &lt; size(list));\nfor (int i = size(list); i &gt; index; --i) {\nlist-&gt;nums[i] = list-&gt;nums[i - 1];\n}\nlist-&gt;nums[index] = num;\nlist-&gt;size++;\n}\n/* \u5220\u9664\u5143\u7d20 */\n// \u6ce8\u610f\uff1astdio.h \u5360\u7528\u4e86 remove \u5173\u952e\u8bcd\nint removeNum(myList *list, int index) {\nassert(index &gt;= 0 &amp;&amp; index &lt; size(list));\nint num = list-&gt;nums[index];\nfor (int i = index; i &lt; size(list) - 1; i++) {\nlist-&gt;nums[i] = list-&gt;nums[i + 1];\n}\nlist-&gt;size--;\nreturn num;\n}\n/* \u5217\u8868\u6269\u5bb9 */\nvoid extendCapacity(myList *list) {\n// \u5148\u5206\u914d\u7a7a\u95f4\nint newCapacity = capacity(list) * list-&gt;extendRatio;\nint *extend = (int *)malloc(sizeof(int) * newCapacity);\nint *temp = list-&gt;nums;\n// \u62f7\u8d1d\u65e7\u6570\u636e\u5230\u65b0\u6570\u636e\nfor (int i = 0; i &lt; size(list); i++)\nextend[i] = list-&gt;nums[i];\n// \u91ca\u653e\u65e7\u6570\u636e\nfree(temp);\n// \u66f4\u65b0\u65b0\u6570\u636e\nlist-&gt;nums = extend;\nlist-&gt;capacity = newCapacity;\n}\n/* \u5c06\u5217\u8868\u8f6c\u6362\u4e3a Array \u7528\u4e8e\u6253\u5370 */\nint *toArray(myList *list) {\nreturn list-&gt;nums;\n}\n</code></pre> my_list.cs<pre><code>/* \u5217\u8868\u7c7b\u7b80\u6613\u5b9e\u73b0 */\nclass MyList {\nprivate int[] nums;           // \u6570\u7ec4\uff08\u5b58\u50a8\u5217\u8868\u5143\u7d20\uff09\nprivate int numsCapacity = 10;    // \u5217\u8868\u5bb9\u91cf\nprivate int numsSize = 0;         // \u5217\u8868\u957f\u5ea6\uff08\u5373\u5f53\u524d\u5143\u7d20\u6570\u91cf\uff09\nprivate int extendRatio = 2;  // \u6bcf\u6b21\u5217\u8868\u6269\u5bb9\u7684\u500d\u6570\n/* \u6784\u9020\u65b9\u6cd5 */\npublic MyList() {\nnums = new int[numsCapacity];\n}\n/* \u83b7\u53d6\u5217\u8868\u957f\u5ea6\uff08\u5373\u5f53\u524d\u5143\u7d20\u6570\u91cf\uff09*/\npublic int size() {\nreturn numsSize;\n}\n/* \u83b7\u53d6\u5217\u8868\u5bb9\u91cf */\npublic int capacity() {\nreturn numsCapacity;\n}\n/* \u8bbf\u95ee\u5143\u7d20 */\npublic int get(int index) {\n// \u7d22\u5f15\u5982\u679c\u8d8a\u754c\u5219\u629b\u51fa\u5f02\u5e38\uff0c\u4e0b\u540c\nif (index &lt; 0 || index &gt;= numsSize)\nthrow new IndexOutOfRangeException(\"\u7d22\u5f15\u8d8a\u754c\");\nreturn nums[index];\n}\n/* \u66f4\u65b0\u5143\u7d20 */\npublic void set(int index, int num) {\nif (index &lt; 0 || index &gt;= numsSize)\nthrow new IndexOutOfRangeException(\"\u7d22\u5f15\u8d8a\u754c\");\nnums[index] = num;\n}\n/* \u5c3e\u90e8\u6dfb\u52a0\u5143\u7d20 */\npublic void add(int num) {\n// \u5143\u7d20\u6570\u91cf\u8d85\u51fa\u5bb9\u91cf\u65f6\uff0c\u89e6\u53d1\u6269\u5bb9\u673a\u5236\nif (numsSize == numsCapacity)\nextendCapacity();\nnums[numsSize] = num;\n// \u66f4\u65b0\u5143\u7d20\u6570\u91cf\nnumsSize++;\n}\n/* \u4e2d\u95f4\u63d2\u5165\u5143\u7d20 */\npublic void insert(int index, int num) {\nif (index &lt; 0 || index &gt;= numsSize)\nthrow new IndexOutOfRangeException(\"\u7d22\u5f15\u8d8a\u754c\");\n// \u5143\u7d20\u6570\u91cf\u8d85\u51fa\u5bb9\u91cf\u65f6\uff0c\u89e6\u53d1\u6269\u5bb9\u673a\u5236\nif (numsSize == numsCapacity)\nextendCapacity();\n// \u5c06\u7d22\u5f15 index \u4ee5\u53ca\u4e4b\u540e\u7684\u5143\u7d20\u90fd\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\nfor (int j = numsSize - 1; j &gt;= index; j--) {\nnums[j + 1] = nums[j];\n}\nnums[index] = num;\n// \u66f4\u65b0\u5143\u7d20\u6570\u91cf\nnumsSize++;\n}\n/* \u5220\u9664\u5143\u7d20 */\npublic int remove(int index) {\nif (index &lt; 0 || index &gt;= numsSize)\nthrow new IndexOutOfRangeException(\"\u7d22\u5f15\u8d8a\u754c\");\nint num = nums[index];\n// \u5c06\u7d22\u5f15 index \u4e4b\u540e\u7684\u5143\u7d20\u90fd\u5411\u524d\u79fb\u52a8\u4e00\u4f4d\nfor (int j = index; j &lt; numsSize - 1; j++) {\nnums[j] = nums[j + 1];\n}\n// \u66f4\u65b0\u5143\u7d20\u6570\u91cf\nnumsSize--;\n// \u8fd4\u56de\u88ab\u5220\u9664\u5143\u7d20\nreturn num;\n}\n/* \u5217\u8868\u6269\u5bb9 */\npublic void extendCapacity() {\n// \u65b0\u5efa\u4e00\u4e2a\u957f\u5ea6\u4e3a numsCapacity * extendRatio \u7684\u6570\u7ec4\uff0c\u5e76\u5c06\u539f\u6570\u7ec4\u62f7\u8d1d\u5230\u65b0\u6570\u7ec4\nSystem.Array.Resize(ref nums, numsCapacity * extendRatio);\n// \u66f4\u65b0\u5217\u8868\u5bb9\u91cf\nnumsCapacity = nums.Length;\n}\n/* \u5c06\u5217\u8868\u8f6c\u6362\u4e3a\u6570\u7ec4 */\npublic int[] toArray() {\n// \u4ec5\u8f6c\u6362\u6709\u6548\u957f\u5ea6\u8303\u56f4\u5185\u7684\u5217\u8868\u5143\u7d20\nint[] nums = new int[numsSize];\nfor (int i = 0; i &lt; numsSize; i++) {\nnums[i] = get(i);\n}\nreturn nums;\n}\n}\n</code></pre> my_list.swift<pre><code>/* \u5217\u8868\u7c7b\u7b80\u6613\u5b9e\u73b0 */\nclass MyList {\nprivate var nums: [Int] // \u6570\u7ec4\uff08\u5b58\u50a8\u5217\u8868\u5143\u7d20\uff09\nprivate var _capacity = 10 // \u5217\u8868\u5bb9\u91cf\nprivate var _size = 0 // \u5217\u8868\u957f\u5ea6\uff08\u5373\u5f53\u524d\u5143\u7d20\u6570\u91cf\uff09\nprivate let extendRatio = 2 // \u6bcf\u6b21\u5217\u8868\u6269\u5bb9\u7684\u500d\u6570\n/* \u6784\u9020\u65b9\u6cd5 */\ninit() {\nnums = Array(repeating: 0, count: _capacity)\n}\n/* \u83b7\u53d6\u5217\u8868\u957f\u5ea6\uff08\u5373\u5f53\u524d\u5143\u7d20\u6570\u91cf\uff09*/\nfunc size() -&gt; Int {\n_size\n}\n/* \u83b7\u53d6\u5217\u8868\u5bb9\u91cf */\nfunc capacity() -&gt; Int {\n_capacity\n}\n/* \u8bbf\u95ee\u5143\u7d20 */\nfunc get(index: Int) -&gt; Int {\n// \u7d22\u5f15\u5982\u679c\u8d8a\u754c\u5219\u629b\u51fa\u9519\u8bef\uff0c\u4e0b\u540c\nif index &lt; 0 || index &gt;= _size {\nfatalError(\"\u7d22\u5f15\u8d8a\u754c\")\n}\nreturn nums[index]\n}\n/* \u66f4\u65b0\u5143\u7d20 */\nfunc set(index: Int, num: Int) {\nif index &lt; 0 || index &gt;= _size {\nfatalError(\"\u7d22\u5f15\u8d8a\u754c\")\n}\nnums[index] = num\n}\n/* \u5c3e\u90e8\u6dfb\u52a0\u5143\u7d20 */\nfunc add(num: Int) {\n// \u5143\u7d20\u6570\u91cf\u8d85\u51fa\u5bb9\u91cf\u65f6\uff0c\u89e6\u53d1\u6269\u5bb9\u673a\u5236\nif _size == _capacity {\nextendCapacity()\n}\nnums[_size] = num\n// \u66f4\u65b0\u5143\u7d20\u6570\u91cf\n_size += 1\n}\n/* \u4e2d\u95f4\u63d2\u5165\u5143\u7d20 */\nfunc insert(index: Int, num: Int) {\nif index &lt; 0 || index &gt;= _size {\nfatalError(\"\u7d22\u5f15\u8d8a\u754c\")\n}\n// \u5143\u7d20\u6570\u91cf\u8d85\u51fa\u5bb9\u91cf\u65f6\uff0c\u89e6\u53d1\u6269\u5bb9\u673a\u5236\nif _size == _capacity {\nextendCapacity()\n}\n// \u5c06\u7d22\u5f15 index \u4ee5\u53ca\u4e4b\u540e\u7684\u5143\u7d20\u90fd\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\nfor j in sequence(first: _size - 1, next: { $0 &gt;= index + 1 ? $0 - 1 : nil }) {\nnums[j + 1] = nums[j]\n}\nnums[index] = num\n// \u66f4\u65b0\u5143\u7d20\u6570\u91cf\n_size += 1\n}\n/* \u5220\u9664\u5143\u7d20 */\n@discardableResult\nfunc remove(index: Int) -&gt; Int {\nif index &lt; 0 || index &gt;= _size {\nfatalError(\"\u7d22\u5f15\u8d8a\u754c\")\n}\nlet num = nums[index]\n// \u5c06\u7d22\u5f15 index \u4e4b\u540e\u7684\u5143\u7d20\u90fd\u5411\u524d\u79fb\u52a8\u4e00\u4f4d\nfor j in index ..&lt; (_size - 1) {\nnums[j] = nums[j + 1]\n}\n// \u66f4\u65b0\u5143\u7d20\u6570\u91cf\n_size -= 1\n// \u8fd4\u56de\u88ab\u5220\u9664\u5143\u7d20\nreturn num\n}\n/* \u5217\u8868\u6269\u5bb9 */\nfunc extendCapacity() {\n// \u65b0\u5efa\u4e00\u4e2a\u957f\u5ea6\u4e3a\u539f\u6570\u7ec4 extendRatio \u500d\u7684\u65b0\u6570\u7ec4\uff0c\u5e76\u5c06\u539f\u6570\u7ec4\u62f7\u8d1d\u5230\u65b0\u6570\u7ec4\nnums = nums + Array(repeating: 0, count: _capacity * (extendRatio - 1))\n// \u66f4\u65b0\u5217\u8868\u5bb9\u91cf\n_capacity = nums.count\n}\n/* \u5c06\u5217\u8868\u8f6c\u6362\u4e3a\u6570\u7ec4 */\nfunc toArray() -&gt; [Int] {\nvar nums = Array(repeating: 0, count: _size)\nfor i in 0 ..&lt; _size {\nnums[i] = get(index: i)\n}\nreturn nums\n}\n}\n</code></pre> my_list.zig<pre><code>// \u5217\u8868\u7c7b\u7b80\u6613\u5b9e\u73b0\nfn MyList(comptime T: type) type {\nreturn struct {\nconst Self = @This();\nnums: []T = undefined,                        // \u6570\u7ec4\uff08\u5b58\u50a8\u5217\u8868\u5143\u7d20\uff09\nnums_capacity: usize = 10,                     // \u5217\u8868\u5bb9\u91cf\nnum_size: usize = 0,                           // \u5217\u8868\u957f\u5ea6\uff08\u5373\u5f53\u524d\u5143\u7d20\u6570\u91cf\uff09\nextend_ratio: usize = 2,                       // \u6bcf\u6b21\u5217\u8868\u6269\u5bb9\u7684\u500d\u6570\nmem_arena: ?std.heap.ArenaAllocator = null,\nmem_allocator: std.mem.Allocator = undefined, // \u5185\u5b58\u5206\u914d\u5668\n// \u6784\u9020\u65b9\u6cd5\uff08\u5206\u914d\u5185\u5b58+\u521d\u59cb\u5316\u5217\u8868\uff09\npub fn init(self: *Self, allocator: std.mem.Allocator) !void {\nif (self.mem_arena == null) {\nself.mem_arena = std.heap.ArenaAllocator.init(allocator);\nself.mem_allocator = self.mem_arena.?.allocator();\n}\nself.nums = try self.mem_allocator.alloc(T, self.nums_capacity);\nstd.mem.set(T, self.nums, @as(T, 0));\n}\n// \u6790\u6784\u65b9\u6cd5\uff08\u91ca\u653e\u5185\u5b58\uff09\npub fn deinit(self: *Self) void {\nif (self.mem_arena == null) return;\nself.mem_arena.?.deinit();\n}\n// \u83b7\u53d6\u5217\u8868\u957f\u5ea6\uff08\u5373\u5f53\u524d\u5143\u7d20\u6570\u91cf\uff09\npub fn size(self: *Self) usize {\nreturn self.num_size;\n}\n// \u83b7\u53d6\u5217\u8868\u5bb9\u91cf\npub fn capacity(self: *Self) usize {\nreturn self.nums_capacity;\n}\n// \u8bbf\u95ee\u5143\u7d20\npub fn get(self: *Self, index: usize) T {\n// \u7d22\u5f15\u5982\u679c\u8d8a\u754c\u5219\u629b\u51fa\u5f02\u5e38\uff0c\u4e0b\u540c\nif (index &lt; 0 or index &gt;= self.size()) @panic(\"\u7d22\u5f15\u8d8a\u754c\");\nreturn self.nums[index];\n}  // \u66f4\u65b0\u5143\u7d20\npub fn set(self: *Self, index: usize, num: T) void {\n// \u7d22\u5f15\u5982\u679c\u8d8a\u754c\u5219\u629b\u51fa\u5f02\u5e38\uff0c\u4e0b\u540c\nif (index &lt; 0 or index &gt;= self.size()) @panic(\"\u7d22\u5f15\u8d8a\u754c\");\nself.nums[index] = num;\n}  // \u5c3e\u90e8\u6dfb\u52a0\u5143\u7d20\npub fn add(self: *Self, num: T) !void {\n// \u5143\u7d20\u6570\u91cf\u8d85\u51fa\u5bb9\u91cf\u65f6\uff0c\u89e6\u53d1\u6269\u5bb9\u673a\u5236\nif (self.size() == self.capacity()) try self.extendCapacity();\nself.nums[self.size()] = num;\n// \u66f4\u65b0\u5143\u7d20\u6570\u91cf\nself.num_size += 1;\n}  // \u4e2d\u95f4\u63d2\u5165\u5143\u7d20\npub fn insert(self: *Self, index: usize, num: T) !void {\nif (index &lt; 0 or index &gt;= self.size()) @panic(\"\u7d22\u5f15\u8d8a\u754c\");\n// \u5143\u7d20\u6570\u91cf\u8d85\u51fa\u5bb9\u91cf\u65f6\uff0c\u89e6\u53d1\u6269\u5bb9\u673a\u5236\nif (self.size() == self.capacity()) try self.extendCapacity();\n// \u7d22\u5f15 i \u4ee5\u53ca\u4e4b\u540e\u7684\u5143\u7d20\u90fd\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\nvar j = self.size() - 1;\nwhile (j &gt;= index) : (j -= 1) {\nself.nums[j + 1] = self.nums[j];\n}\nself.nums[index] = num;\n// \u66f4\u65b0\u5143\u7d20\u6570\u91cf\nself.num_size += 1;\n}\n// \u5220\u9664\u5143\u7d20\npub fn remove(self: *Self, index: usize) T {\nif (index &lt; 0 or index &gt;= self.size()) @panic(\"\u7d22\u5f15\u8d8a\u754c\");\nvar num = self.nums[index];\n// \u7d22\u5f15 i \u4e4b\u540e\u7684\u5143\u7d20\u90fd\u5411\u524d\u79fb\u52a8\u4e00\u4f4d\nvar j = index;\nwhile (j &lt; self.size() - 1) : (j += 1) {\nself.nums[j] = self.nums[j + 1];\n}\n// \u66f4\u65b0\u5143\u7d20\u6570\u91cf\nself.num_size -= 1;\n// \u8fd4\u56de\u88ab\u5220\u9664\u5143\u7d20\nreturn num;\n}\n// \u5217\u8868\u6269\u5bb9\npub fn extendCapacity(self: *Self) !void {\n// \u65b0\u5efa\u4e00\u4e2a\u957f\u5ea6\u4e3a\u539f\u6570\u7ec4 extendRatio \u500d\u7684\u65b0\u6570\u7ec4\uff0c\u5e76\u5c06\u539f\u6570\u7ec4\u62f7\u8d1d\u5230\u65b0\u6570\u7ec4\nvar newCapacity = self.capacity() * self.extend_ratio;\nvar extend = try self.mem_allocator.alloc(T, newCapacity);\nstd.mem.set(T, extend, @as(T, 0));\n// \u5c06\u539f\u6570\u7ec4\u4e2d\u7684\u6240\u6709\u5143\u7d20\u590d\u5236\u5230\u65b0\u6570\u7ec4\nstd.mem.copy(T, extend, self.nums);\nself.nums = extend;\n// \u66f4\u65b0\u5217\u8868\u5bb9\u91cf\nself.nums_capacity = newCapacity;\n}\n// \u5c06\u5217\u8868\u8f6c\u6362\u4e3a\u6570\u7ec4\npub fn toArray(self: *Self) ![]T {\n// \u4ec5\u8f6c\u6362\u6709\u6548\u957f\u5ea6\u8303\u56f4\u5185\u7684\u5217\u8868\u5143\u7d20\nvar nums = try self.mem_allocator.alloc(T, self.size());\nstd.mem.set(T, nums, @as(T, 0));\nfor (nums) |*num, i| {\nnum.* = self.get(i);\n}\nreturn nums;\n}\n};\n}\n</code></pre> my_list.dart<pre><code>/* \u5217\u8868\u7c7b\u7b80\u6613\u5b9e\u73b0 */\nclass MyList {\nlate List&lt;int&gt; _nums; // \u6570\u7ec4\uff08\u5b58\u50a8\u5217\u8868\u5143\u7d20\uff09\nint _capacity = 10; // \u5217\u8868\u5bb9\u91cf\nint _size = 0; // \u5217\u8868\u957f\u5ea6\uff08\u5373\u5f53\u524d\u5143\u7d20\u6570\u91cf\uff09\nint _extendRatio = 2; // \u6bcf\u6b21\u5217\u8868\u6269\u5bb9\u7684\u500d\u6570\n/* \u6784\u9020\u65b9\u6cd5 */\nMyList() {\n_nums = List.filled(_capacity, 0);\n}\n/* \u83b7\u53d6\u5217\u8868\u957f\u5ea6\uff08\u5373\u5f53\u524d\u5143\u7d20\u6570\u91cf\uff09*/\nint size() =&gt; _size;\n/* \u83b7\u53d6\u5217\u8868\u5bb9\u91cf */\nint capacity() =&gt; _capacity;\n/* \u8bbf\u95ee\u5143\u7d20 */\nint get(int index) {\nif (index &gt;= _size) throw RangeError('\u7d22\u5f15\u8d8a\u754c');\nreturn _nums[index];\n}\n/* \u66f4\u65b0\u5143\u7d20 */\nvoid set(int index, int num) {\nif (index &gt;= _size) throw RangeError('\u7d22\u5f15\u8d8a\u754c');\n_nums[index] = num;\n}\n/* \u5c3e\u90e8\u6dfb\u52a0\u5143\u7d20 */\nvoid add(int num) {\n// \u5143\u7d20\u6570\u91cf\u8d85\u51fa\u5bb9\u91cf\u65f6\uff0c\u89e6\u53d1\u6269\u5bb9\u673a\u5236\nif (_size == _capacity) extendCapacity();\n_nums[_size] = num;\n// \u66f4\u65b0\u5143\u7d20\u6570\u91cf\n_size++;\n}\n/* \u4e2d\u95f4\u63d2\u5165\u5143\u7d20 */\nvoid insert(int index, int num) {\nif (index &gt;= _size) throw RangeError('\u7d22\u5f15\u8d8a\u754c');\n// \u5143\u7d20\u6570\u91cf\u8d85\u51fa\u5bb9\u91cf\u65f6\uff0c\u89e6\u53d1\u6269\u5bb9\u673a\u5236\nif (_size == _capacity) extendCapacity();\n// \u5c06\u7d22\u5f15 index \u4ee5\u53ca\u4e4b\u540e\u7684\u5143\u7d20\u90fd\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\nfor (var j = _size - 1; j &gt;= index; j--) {\n_nums[j + 1] = _nums[j];\n}\n_nums[index] = num;\n// \u66f4\u65b0\u5143\u7d20\u6570\u91cf\n_size++;\n}\n/* \u5220\u9664\u5143\u7d20 */\nint remove(int index) {\nif (index &gt;= _size) throw RangeError('\u7d22\u5f15\u8d8a\u754c');\nint num = _nums[index];\n// \u5c06\u7d22\u5f15 index \u4e4b\u540e\u7684\u5143\u7d20\u90fd\u5411\u524d\u79fb\u52a8\u4e00\u4f4d\nfor (var j = index; j &lt; _size - 1; j++) {\n_nums[j] = _nums[j + 1];\n}\n// \u66f4\u65b0\u5143\u7d20\u6570\u91cf\n_size--;\n// \u8fd4\u56de\u88ab\u5220\u9664\u5143\u7d20\nreturn num;\n}\n/* \u5217\u8868\u6269\u5bb9 */\nvoid extendCapacity() {\n// \u65b0\u5efa\u4e00\u4e2a\u957f\u5ea6\u4e3a\u539f\u6570\u7ec4 _extendRatio \u500d\u7684\u65b0\u6570\u7ec4\nfinal _newNums = List.filled(_capacity * _extendRatio, 0);\n// \u5c06\u539f\u6570\u7ec4\u62f7\u8d1d\u5230\u65b0\u6570\u7ec4\nList.copyRange(_newNums, 0, _nums);\n// \u66f4\u65b0 _nums \u7684\u5f15\u7528\n_nums = _newNums;\n// \u66f4\u65b0\u5217\u8868\u5bb9\u91cf\n_capacity = _nums.length;\n}\n/* \u5c06\u5217\u8868\u8f6c\u6362\u4e3a\u6570\u7ec4 */\nList&lt;int&gt; toArray() {\nList&lt;int&gt; nums = [];\nfor (var i = 0; i &lt; _size; i++) {\nnums.add(get(i));\n}\nreturn nums;\n}\n}\n</code></pre>"},{"location":"chapter_array_and_linkedlist/summary/","title":"4.4. \u00a0 \u5c0f\u7ed3","text":"<ul> <li>\u6570\u7ec4\u548c\u94fe\u8868\u662f\u4e24\u79cd\u57fa\u672c\u6570\u636e\u7ed3\u6784\uff0c\u5206\u522b\u4ee3\u8868\u6570\u636e\u5728\u8ba1\u7b97\u673a\u5185\u5b58\u4e2d\u7684\u8fde\u7eed\u7a7a\u95f4\u5b58\u50a8\u548c\u79bb\u6563\u7a7a\u95f4\u5b58\u50a8\u65b9\u5f0f\u3002\u4e24\u8005\u7684\u4f18\u7f3a\u70b9\u5448\u73b0\u51fa\u4e92\u8865\u7684\u7279\u6027\u3002</li> <li>\u6570\u7ec4\u652f\u6301\u968f\u673a\u8bbf\u95ee\u3001\u5360\u7528\u5185\u5b58\u8f83\u5c11\uff1b\u4f46\u63d2\u5165\u548c\u5220\u9664\u5143\u7d20\u6548\u7387\u4f4e\uff0c\u4e14\u521d\u59cb\u5316\u540e\u957f\u5ea6\u4e0d\u53ef\u53d8\u3002</li> <li>\u94fe\u8868\u901a\u8fc7\u66f4\u6539\u6307\u9488\u5b9e\u73b0\u9ad8\u6548\u7684\u8282\u70b9\u63d2\u5165\u4e0e\u5220\u9664\uff0c\u4e14\u53ef\u4ee5\u7075\u6d3b\u8c03\u6574\u957f\u5ea6\uff1b\u4f46\u8282\u70b9\u8bbf\u95ee\u6548\u7387\u4f4e\u3001\u5360\u7528\u5185\u5b58\u8f83\u591a\u3002\u5e38\u89c1\u7684\u94fe\u8868\u7c7b\u578b\u5305\u62ec\u5355\u5411\u94fe\u8868\u3001\u5faa\u73af\u94fe\u8868\u3001\u53cc\u5411\u94fe\u8868\u3002</li> <li>\u52a8\u6001\u6570\u7ec4\uff0c\u53c8\u79f0\u5217\u8868\uff0c\u662f\u57fa\u4e8e\u6570\u7ec4\u5b9e\u73b0\u7684\u4e00\u79cd\u6570\u636e\u7ed3\u6784\u3002\u5b83\u4fdd\u7559\u4e86\u6570\u7ec4\u7684\u4f18\u52bf\uff0c\u540c\u65f6\u53ef\u4ee5\u7075\u6d3b\u8c03\u6574\u957f\u5ea6\u3002\u5217\u8868\u7684\u51fa\u73b0\u6781\u5927\u5730\u63d0\u9ad8\u4e86\u6570\u7ec4\u7684\u6613\u7528\u6027\uff0c\u4f46\u53ef\u80fd\u5bfc\u81f4\u90e8\u5206\u5185\u5b58\u7a7a\u95f4\u6d6a\u8d39\u3002</li> <li>\u4e0b\u8868\u603b\u7ed3\u5e76\u5bf9\u6bd4\u4e86\u6570\u7ec4\u4e0e\u94fe\u8868\u7684\u5404\u9879\u7279\u6027\u4e0e\u64cd\u4f5c\u6548\u7387\u3002</li> </ul> \u6570\u7ec4 \u94fe\u8868 \u5b58\u50a8\u65b9\u5f0f \u8fde\u7eed\u5185\u5b58\u7a7a\u95f4 \u79bb\u6563\u5185\u5b58\u7a7a\u95f4 \u6570\u636e\u7ed3\u6784\u957f\u5ea6 \u957f\u5ea6\u4e0d\u53ef\u53d8 \u957f\u5ea6\u53ef\u53d8 \u5185\u5b58\u4f7f\u7528\u7387 \u5360\u7528\u5185\u5b58\u5c11\u3001\u7f13\u5b58\u5c40\u90e8\u6027\u597d \u5360\u7528\u5185\u5b58\u591a \u4f18\u52bf\u64cd\u4f5c \u968f\u673a\u8bbf\u95ee \u63d2\u5165\u3001\u5220\u9664 \u8bbf\u95ee\u5143\u7d20 \\(O(1)\\) \\(O(N)\\) \u6dfb\u52a0\u5143\u7d20 \\(O(N)\\) \\(O(1)\\) \u5220\u9664\u5143\u7d20 \\(O(N)\\) \\(O(1)\\) <p>\u7f13\u5b58\u5c40\u90e8\u6027</p> <p>\u5728\u8ba1\u7b97\u673a\u4e2d\uff0c\u6570\u636e\u8bfb\u5199\u901f\u5ea6\u6392\u5e8f\u662f\u201c\u786c\u76d8 &lt; \u5185\u5b58 &lt; CPU \u7f13\u5b58\u201d\u3002\u5f53\u6211\u4eec\u8bbf\u95ee\u6570\u7ec4\u5143\u7d20\u65f6\uff0c\u8ba1\u7b97\u673a\u4e0d\u4ec5\u4f1a\u52a0\u8f7d\u5b83\uff0c\u8fd8\u4f1a\u7f13\u5b58\u5176\u5468\u56f4\u7684\u5176\u4ed6\u6570\u636e\uff0c\u4ece\u800c\u501f\u52a9\u9ad8\u901f\u7f13\u5b58\u6765\u63d0\u5347\u540e\u7eed\u64cd\u4f5c\u7684\u6267\u884c\u901f\u5ea6\u3002\u94fe\u8868\u5219\u4e0d\u7136\uff0c\u8ba1\u7b97\u673a\u53ea\u80fd\u6328\u4e2a\u5730\u7f13\u5b58\u5404\u4e2a\u8282\u70b9\uff0c\u8fd9\u6837\u7684\u591a\u6b21\u201c\u642c\u8fd0\u201d\u964d\u4f4e\u4e86\u6574\u4f53\u6548\u7387\u3002</p>"},{"location":"chapter_array_and_linkedlist/summary/#441-q-a","title":"4.4.1. \u00a0 Q &amp; A","text":"<p>\u6570\u7ec4\u5b58\u50a8\u5728\u6808\u4e0a\u548c\u5b58\u50a8\u5728\u5806\u4e0a\uff0c\u5bf9\u65f6\u95f4\u6548\u7387\u548c\u7a7a\u95f4\u6548\u7387\u662f\u5426\u6709\u5f71\u54cd\uff1f</p> <p>\u6808\u5185\u5b58\u5206\u914d\u7531\u7f16\u8bd1\u5668\u81ea\u52a8\u5b8c\u6210\uff0c\u800c\u5806\u5185\u5b58\u7531\u7a0b\u5e8f\u5458\u5728\u4ee3\u7801\u4e2d\u5206\u914d\uff08\u6ce8\u610f\uff0c\u8fd9\u91cc\u7684\u6808\u548c\u5806\u548c\u6570\u636e\u7ed3\u6784\u4e2d\u7684\u6808\u548c\u5806\u4e0d\u662f\u540c\u4e00\u6982\u5ff5\uff09\u3002</p> <ol> <li>\u6808\u4e0d\u7075\u6d3b\uff0c\u5206\u914d\u7684\u5185\u5b58\u5927\u5c0f\u4e0d\u53ef\u66f4\u6539\uff1b\u5806\u76f8\u5bf9\u7075\u6d3b\uff0c\u53ef\u4ee5\u52a8\u6001\u5206\u914d\u5185\u5b58\uff1b</li> <li>\u6808\u662f\u4e00\u5757\u6bd4\u8f83\u5c0f\u7684\u5185\u5b58\uff0c\u5bb9\u6613\u51fa\u73b0\u5185\u5b58\u4e0d\u8db3\uff1b\u5806\u5185\u5b58\u5f88\u5927\uff0c\u4f46\u662f\u7531\u4e8e\u662f\u52a8\u6001\u5206\u914d\uff0c\u5bb9\u6613\u788e\u7247\u5316\uff0c\u7ba1\u7406\u5806\u5185\u5b58\u7684\u96be\u5ea6\u66f4\u5927\u3001\u6210\u672c\u66f4\u9ad8\uff1b</li> <li>\u8bbf\u95ee\u6808\u6bd4\u8bbf\u95ee\u5806\u66f4\u5feb\uff0c\u56e0\u4e3a\u6808\u5185\u5b58\u8f83\u5c0f\u3001\u5bf9\u7f13\u5b58\u53cb\u597d\uff0c\u5806\u5e27\u5206\u6563\u5728\u5f88\u5927\u7684\u7a7a\u95f4\u5185\uff0c\u4f1a\u51fa\u73b0\u66f4\u591a\u7684\u7f13\u5b58\u672a\u547d\u4e2d\uff1b</li> </ol> <p>\u4e3a\u4ec0\u4e48\u6570\u7ec4\u4f1a\u5f3a\u8c03\u8981\u6c42\u76f8\u540c\u7c7b\u578b\u7684\u5143\u7d20\uff0c\u800c\u5728\u94fe\u8868\u4e2d\u5374\u6ca1\u6709\u5f3a\u8c03\u540c\u7c7b\u578b\u5462\uff1f</p> <p>\u94fe\u8868\u7531\u7ed3\u70b9\u7ec4\u6210\uff0c\u7ed3\u70b9\u4e4b\u95f4\u7531\u6307\u9488\u8fde\u63a5\uff0c\u5404\u4e2a\u7ed3\u70b9\u53ef\u4ee5\u5b58\u50a8\u4e0d\u540c\u7c7b\u578b\u7684\u6570\u636e\uff0c\u4f8b\u5982 int, double, string, object \u7b49\u3002</p> <p>\u76f8\u5bf9\u5730\uff0c\u6570\u7ec4\u5143\u7d20\u5219\u5fc5\u987b\u662f\u76f8\u540c\u7c7b\u578b\u7684\uff0c\u8fd9\u6837\u624d\u80fd\u901a\u8fc7\u8ba1\u7b97\u504f\u79fb\u91cf\u6765\u83b7\u53d6\u5bf9\u5e94\u5143\u7d20\u4f4d\u7f6e\u3002\u4f8b\u5982\uff0c\u5982\u679c\u6570\u7ec4\u540c\u65f6\u5305\u542b int \u548c long \u4e24\u79cd\u7c7b\u578b\uff0c\u5355\u4e2a\u5143\u7d20\u5206\u522b\u5360\u7528 4 bytes \u548c 8 bytes \uff0c\u90a3\u4e48\u6b64\u65f6\u5c31\u4e0d\u80fd\u7528\u4ee5\u4e0b\u516c\u5f0f\u8ba1\u7b97\u504f\u79fb\u91cf\u4e86\uff0c\u56e0\u4e3a\u6570\u7ec4\u4e2d\u5305\u542b\u4e86\u4e24\u79cd <code>elementLength</code> \u3002</p> <pre><code>// \u5143\u7d20\u5185\u5b58\u5730\u5740 = \u6570\u7ec4\u5185\u5b58\u5730\u5740 + \u5143\u7d20\u957f\u5ea6 * \u5143\u7d20\u7d22\u5f15\nelementAddr = firtstElementAddr + elementLength * elementIndex\n</code></pre> <p>\u5220\u9664\u8282\u70b9\u540e\uff0c\u662f\u5426\u9700\u8981\u628a <code>P.next</code> \u8bbe\u4e3a \\(\\text{None}\\) \u5462\uff1f</p> <p>\u4e0d\u4fee\u6539 <code>P.next</code> \u4e5f\u53ef\u4ee5\u3002\u4ece\u8be5\u94fe\u8868\u7684\u89d2\u5ea6\u770b\uff0c\u4ece\u5934\u7ed3\u70b9\u904d\u5386\u5230\u5c3e\u7ed3\u70b9\u5df2\u7ecf\u9047\u4e0d\u5230 <code>P</code> \u4e86\u3002\u8fd9\u610f\u5473\u7740\u7ed3\u70b9 <code>P</code> \u5df2\u7ecf\u4ece\u94fe\u8868\u4e2d\u5220\u9664\u4e86\uff0c\u6b64\u65f6\u7ed3\u70b9 <code>P</code> \u6307\u5411\u54ea\u91cc\u90fd\u4e0d\u4f1a\u5bf9\u8fd9\u6761\u94fe\u8868\u4ea7\u751f\u5f71\u54cd\u4e86\u3002</p> <p>\u4ece\u5783\u573e\u56de\u6536\u7684\u89d2\u5ea6\u770b\uff0c\u5bf9\u4e8e Java, Python, Go \u7b49\u62e5\u6709\u81ea\u52a8\u5783\u573e\u56de\u6536\u7684\u8bed\u8a00\u6765\u8bf4\uff0c\u8282\u70b9 <code>P</code> \u662f\u5426\u88ab\u56de\u6536\u53d6\u51b3\u4e8e\u662f\u5426\u6709\u4ecd\u5b58\u5728\u6307\u5411\u5b83\u7684\u5f15\u7528\uff0c\u800c\u4e0d\u662f <code>P.next</code> \u7684\u503c\u3002\u5728 C, C++ \u7b49\u8bed\u8a00\u4e2d\uff0c\u6211\u4eec\u9700\u8981\u624b\u52a8\u91ca\u653e\u8282\u70b9\u5185\u5b58\u3002</p> <p>\u5728\u94fe\u8868\u4e2d\u63d2\u5165\u548c\u5220\u9664\u64cd\u4f5c\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u662f \\(O(1)\\) \u3002\u4f46\u662f\u589e\u5220\u4e4b\u524d\u90fd\u9700\u8981 \\(O(n)\\) \u67e5\u627e\u5143\u7d20\uff0c\u90a3\u4e3a\u4ec0\u4e48\u65f6\u95f4\u590d\u6742\u5ea6\u4e0d\u662f \\(O(n)\\) \u5462\uff1f</p> <p>\u5982\u679c\u662f\u5148\u67e5\u627e\u5143\u7d20\u3001\u518d\u5220\u9664\u5143\u7d20\uff0c\u786e\u5b9e\u662f \\(O(n)\\) \u3002\u7136\u800c\uff0c\u94fe\u8868\u7684 \\(O(1)\\) \u589e\u5220\u7684\u4f18\u52bf\u53ef\u4ee5\u5728\u5176\u4ed6\u5e94\u7528\u4e0a\u5f97\u5230\u4f53\u73b0\u3002\u4f8b\u5982\uff0c\u53cc\u5411\u961f\u5217\u9002\u5408\u4f7f\u7528\u94fe\u8868\u5b9e\u73b0\uff0c\u6211\u4eec\u7ef4\u62a4\u4e00\u4e2a\u6307\u9488\u53d8\u91cf\u59cb\u7ec8\u6307\u5411\u5934\u7ed3\u70b9\u3001\u5c3e\u7ed3\u70b9\uff0c\u6bcf\u6b21\u63d2\u5165\u4e0e\u5220\u9664\u64cd\u4f5c\u90fd\u662f \\(O(1)\\) \u3002</p> <p>\u56fe\u7247\u201c\u94fe\u8868\u5b9a\u4e49\u4e0e\u5b58\u50a8\u65b9\u5f0f\u201d\u4e2d\uff0c\u6d45\u84dd\u8272\u7684\u5b58\u50a8\u7ed3\u70b9\u6307\u9488\u662f\u5360\u7528\u4e00\u5757\u5185\u5b58\u5730\u5740\u5417\uff1f\u8fd8\u662f\u548c\u7ed3\u70b9\u503c\u5404\u5360\u4e00\u534a\u5462\uff1f</p> <p>\u6587\u4e2d\u53ea\u662f\u4e00\u4e2a\u793a\u610f\u56fe\uff0c\u53ea\u662f\u5b9a\u6027\u8868\u793a\u3002\u5b9a\u91cf\u7684\u8bdd\u9700\u8981\u6839\u636e\u5177\u4f53\u60c5\u51b5\u5206\u6790\uff1a</p> <ul> <li>\u4e0d\u540c\u7c7b\u578b\u7684\u7ed3\u70b9\u503c\u5360\u7528\u7684\u7a7a\u95f4\u662f\u4e0d\u540c\u7684\uff0c\u6bd4\u5982 int, long, double, \u6216\u8005\u662f\u7c7b\u7684\u5b9e\u4f8b\u7b49\u7b49\u3002</li> <li>\u6307\u9488\u53d8\u91cf\u5360\u7528\u7684\u5185\u5b58\u7a7a\u95f4\u5927\u5c0f\u6839\u636e\u6240\u4f7f\u7528\u7684\u64cd\u4f5c\u7cfb\u7edf\u53ca\u7f16\u8bd1\u73af\u5883\u800c\u5b9a\uff0c\u5927\u591a\u4e3a 8 \u5b57\u8282\u6216 4 \u5b57\u8282\u3002</li> </ul> <p>\u5728\u5217\u8868\u672b\u5c3e\u6dfb\u52a0\u5143\u7d20\u662f\u5426\u65f6\u65f6\u523b\u523b\u90fd\u4e3a \\(O(1)\\) \uff1f</p> <p>\u5982\u679c\u6dfb\u52a0\u5143\u7d20\u65f6\u8d85\u51fa\u5217\u8868\u957f\u5ea6\uff0c\u5219\u9700\u8981\u5148\u6269\u5bb9\u5217\u8868\u518d\u6dfb\u52a0\u3002\u7cfb\u7edf\u4f1a\u7533\u8bf7\u4e00\u5757\u65b0\u7684\u5185\u5b58\uff0c\u5e76\u5c06\u539f\u5217\u8868\u7684\u6240\u6709\u5143\u7d20\u642c\u8fd0\u8fc7\u53bb\uff0c\u8fd9\u65f6\u5019\u65f6\u95f4\u590d\u6742\u5ea6\u5c31\u4f1a\u662f \\(O(n)\\) \u3002</p> <p>\u201c\u5217\u8868\u7684\u51fa\u73b0\u5927\u5927\u63d0\u5347\u4e86\u6570\u7ec4\u7684\u5b9e\u7528\u6027\uff0c\u4f46\u526f\u4f5c\u7528\u662f\u4f1a\u9020\u6210\u90e8\u5206\u5185\u5b58\u7a7a\u95f4\u6d6a\u8d39\u201d\uff0c\u8fd9\u91cc\u7684\u7a7a\u95f4\u6d6a\u8d39\u662f\u6307\u989d\u5916\u589e\u52a0\u7684\u53d8\u91cf\u5982\u5bb9\u91cf\u3001\u957f\u5ea6\u3001\u6269\u5bb9\u500d\u6570\u6240\u5360\u7684\u5185\u5b58\u5417\uff1f</p> <p>\u8fd9\u91cc\u7684\u7a7a\u95f4\u6d6a\u8d39\u4e3b\u8981\u6709\u4e24\u65b9\u9762\u542b\u4e49\uff1a\u4e00\u65b9\u9762\uff0c\u5217\u8868\u90fd\u4f1a\u8bbe\u5b9a\u4e00\u4e2a\u521d\u59cb\u957f\u5ea6\uff0c\u6211\u4eec\u4e0d\u4e00\u5b9a\u9700\u8981\u7528\u8fd9\u4e48\u591a\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u4e3a\u4e86\u9632\u6b62\u9891\u7e41\u6269\u5bb9\uff0c\u6269\u5bb9\u4e00\u822c\u90fd\u4f1a\u4e58\u4ee5\u4e00\u4e2a\u7cfb\u6570\uff0c\u6bd4\u5982 \\(\\times 1.5\\) \u3002\u8fd9\u6837\u4e00\u6765\uff0c\u4e5f\u4f1a\u51fa\u73b0\u5f88\u591a\u7a7a\u4f4d\uff0c\u6211\u4eec\u901a\u5e38\u4e0d\u80fd\u5b8c\u5168\u586b\u6ee1\u5b83\u4eec\u3002</p>"},{"location":"chapter_backtracking/","title":"12. \u00a0 \u56de\u6eaf","text":""},{"location":"chapter_backtracking/backtracking_algorithm/","title":"12.1. \u00a0 \u56de\u6eaf\u7b97\u6cd5","text":"<p>\u300c\u56de\u6eaf\u7b97\u6cd5 Backtracking Algorithm\u300d\u662f\u4e00\u79cd\u901a\u8fc7\u7a77\u4e3e\u6765\u89e3\u51b3\u95ee\u9898\u7684\u65b9\u6cd5\uff0c\u5b83\u7684\u6838\u5fc3\u601d\u60f3\u662f\u4ece\u4e00\u4e2a\u521d\u59cb\u72b6\u6001\u51fa\u53d1\uff0c\u66b4\u529b\u641c\u7d22\u6240\u6709\u53ef\u80fd\u7684\u89e3\u51b3\u65b9\u6848\uff0c\u5f53\u9047\u5230\u6b63\u786e\u7684\u89e3\u5219\u5c06\u5176\u8bb0\u5f55\uff0c\u76f4\u5230\u627e\u5230\u89e3\u6216\u8005\u5c1d\u8bd5\u4e86\u6240\u6709\u53ef\u80fd\u7684\u9009\u62e9\u90fd\u65e0\u6cd5\u627e\u5230\u89e3\u4e3a\u6b62\u3002</p> <p>\u56de\u6eaf\u7b97\u6cd5\u901a\u5e38\u91c7\u7528\u300c\u6df1\u5ea6\u4f18\u5148\u641c\u7d22\u300d\u6765\u904d\u5386\u89e3\u7a7a\u95f4\u3002\u5728\u4e8c\u53c9\u6811\u7ae0\u8282\u4e2d\uff0c\u6211\u4eec\u63d0\u5230\u524d\u5e8f\u3001\u4e2d\u5e8f\u548c\u540e\u5e8f\u904d\u5386\u90fd\u5c5e\u4e8e\u6df1\u5ea6\u4f18\u5148\u641c\u7d22\u3002\u4e0b\u9762\uff0c\u6211\u4eec\u4ece\u4e8c\u53c9\u6811\u7684\u524d\u5e8f\u904d\u5386\u5165\u624b\uff0c\u9010\u6b65\u4e86\u89e3\u56de\u6eaf\u7b97\u6cd5\u7684\u5de5\u4f5c\u539f\u7406\u3002</p> <p>\u4f8b\u9898\u4e00</p> <p>\u7ed9\u5b9a\u4e00\u4e2a\u4e8c\u53c9\u6811\uff0c\u641c\u7d22\u5e76\u8bb0\u5f55\u6240\u6709\u503c\u4e3a \\(7\\) \u7684\u8282\u70b9\uff0c\u8fd4\u56de\u8282\u70b9\u5217\u8868\u3002</p> <p>\u89e3\u9898\u601d\u8def\uff1a\u524d\u5e8f\u904d\u5386\u8fd9\u9897\u6811\uff0c\u5e76\u5224\u65ad\u5f53\u524d\u8282\u70b9\u7684\u503c\u662f\u5426\u4e3a \\(7\\) \uff0c\u82e5\u662f\u5219\u5c06\u8be5\u8282\u70b9\u7684\u503c\u52a0\u5165\u5230\u7ed3\u679c\u5217\u8868 <code>res</code> \u4e4b\u4e2d\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart preorder_traversal_i_compact.java<pre><code>/* \u524d\u5e8f\u904d\u5386\uff1a\u4f8b\u9898\u4e00 */\nvoid preOrder(TreeNode root) {\nif (root == null) {\nreturn;\n}\nif (root.val == 7) {\n// \u8bb0\u5f55\u89e3\nres.add(root);\n}\npreOrder(root.left);\npreOrder(root.right);\n}\n</code></pre> preorder_traversal_i_compact.cpp<pre><code>/* \u524d\u5e8f\u904d\u5386\uff1a\u4f8b\u9898\u4e00 */\nvoid preOrder(TreeNode *root) {\nif (root == nullptr) {\nreturn;\n}\nif (root-&gt;val == 7) {\n// \u8bb0\u5f55\u89e3\nres.push_back(root);\n}\npreOrder(root-&gt;left);\npreOrder(root-&gt;right);\n}\n</code></pre> preorder_traversal_i_compact.py<pre><code>def pre_order(root: TreeNode) -&gt; None:\n\"\"\"\u524d\u5e8f\u904d\u5386\uff1a\u4f8b\u9898\u4e00\"\"\"\nif root is None:\nreturn\nif root.val == 7:\n# \u8bb0\u5f55\u89e3\nres.append(root)\npre_order(root.left)\npre_order(root.right)\n</code></pre> preorder_traversal_i_compact.go<pre><code>/* \u524d\u5e8f\u904d\u5386\uff1a\u4f8b\u9898\u4e00 */\nfunc preOrderI(root *TreeNode, res *[]*TreeNode) {\nif root == nil {\nreturn\n}\nif int(root.Val) == 7 {\n// \u8bb0\u5f55\u89e3\n*res = append(*res, root)\n}\npreOrderI(root.Left, res)\npreOrderI(root.Right, res)\n}\n</code></pre> preorder_traversal_i_compact.js<pre><code>/* \u524d\u5e8f\u904d\u5386\uff1a\u4f8b\u9898\u4e00 */\nfunction preOrder(root, res) {\nif (root === null) {\nreturn;\n}\nif (root.val === 7) {\n// \u8bb0\u5f55\u89e3\nres.push(root);\n}\npreOrder(root.left, res);\npreOrder(root.right, res);\n}\n</code></pre> preorder_traversal_i_compact.ts<pre><code>/* \u524d\u5e8f\u904d\u5386\uff1a\u4f8b\u9898\u4e00 */\nfunction preOrder(root: TreeNode | null, res: TreeNode[]): void {\nif (root === null) {\nreturn;\n}\nif (root.val === 7) {\n// \u8bb0\u5f55\u89e3\nres.push(root);\n}\npreOrder(root.left, res);\npreOrder(root.right, res);\n}\n</code></pre> preorder_traversal_i_compact.c<pre><code>[class]{}-[func]{preOrder}\n</code></pre> preorder_traversal_i_compact.cs<pre><code>/* \u524d\u5e8f\u904d\u5386\uff1a\u4f8b\u9898\u4e00 */\nvoid preOrder(TreeNode root) {\nif (root == null) {\nreturn;\n}\nif (root.val == 7) {\n// \u8bb0\u5f55\u89e3\nres.Add(root);\n}\npreOrder(root.left);\npreOrder(root.right);\n}\n</code></pre> preorder_traversal_i_compact.swift<pre><code>/* \u524d\u5e8f\u904d\u5386\uff1a\u4f8b\u9898\u4e00 */\nfunc preOrder(root: TreeNode?) {\nguard let root = root else {\nreturn\n}\nif root.val == 7 {\n// \u8bb0\u5f55\u89e3\nres.append(root)\n}\npreOrder(root: root.left)\npreOrder(root: root.right)\n}\n</code></pre> preorder_traversal_i_compact.zig<pre><code>[class]{}-[func]{preOrder}\n</code></pre> preorder_traversal_i_compact.dart<pre><code>[class]{}-[func]{preOrder}\n</code></pre> <p></p> <p> Fig. \u5728\u524d\u5e8f\u904d\u5386\u4e2d\u641c\u7d22\u8282\u70b9 </p>"},{"location":"chapter_backtracking/backtracking_algorithm/#1211","title":"12.1.1. \u00a0 \u5c1d\u8bd5\u4e0e\u56de\u9000","text":"<p>\u4e4b\u6240\u4ee5\u79f0\u4e4b\u4e3a\u56de\u6eaf\u7b97\u6cd5\uff0c\u662f\u56e0\u4e3a\u8be5\u7b97\u6cd5\u5728\u641c\u7d22\u89e3\u7a7a\u95f4\u65f6\u4f1a\u91c7\u7528\u201c\u5c1d\u8bd5\u201d\u4e0e\u201c\u56de\u9000\u201d\u7684\u7b56\u7565\u3002\u5f53\u7b97\u6cd5\u5728\u641c\u7d22\u8fc7\u7a0b\u4e2d\u9047\u5230\u67d0\u4e2a\u72b6\u6001\u65e0\u6cd5\u7ee7\u7eed\u524d\u8fdb\u6216\u65e0\u6cd5\u5f97\u5230\u6ee1\u8db3\u6761\u4ef6\u7684\u89e3\u65f6\uff0c\u5b83\u4f1a\u64a4\u9500\u4e0a\u4e00\u6b65\u7684\u9009\u62e9\uff0c\u9000\u56de\u5230\u4e4b\u524d\u7684\u72b6\u6001\uff0c\u5e76\u5c1d\u8bd5\u5176\u4ed6\u53ef\u80fd\u7684\u9009\u62e9\u3002</p> <p>\u5bf9\u4e8e\u4f8b\u9898\u4e00\uff0c\u8bbf\u95ee\u6bcf\u4e2a\u8282\u70b9\u90fd\u4ee3\u8868\u4e00\u6b21\u201c\u5c1d\u8bd5\u201d\uff0c\u800c\u8d8a\u8fc7\u53f6\u7ed3\u70b9\u6216\u8fd4\u56de\u7236\u8282\u70b9\u7684 <code>return</code> \u5219\u8868\u793a\u201c\u56de\u9000\u201d\u3002</p> <p>\u503c\u5f97\u8bf4\u660e\u7684\u662f\uff0c\u56de\u9000\u5e76\u4e0d\u7b49\u4ef7\u4e8e\u51fd\u6570\u8fd4\u56de\u3002\u4e3a\u89e3\u91ca\u8fd9\u4e00\u70b9\uff0c\u6211\u4eec\u5bf9\u4f8b\u9898\u4e00\u7a0d\u4f5c\u62d3\u5c55\u3002</p> <p>\u4f8b\u9898\u4e8c</p> <p>\u5728\u4e8c\u53c9\u6811\u4e2d\u641c\u7d22\u6240\u6709\u503c\u4e3a \\(7\\) \u7684\u8282\u70b9\uff0c\u8fd4\u56de\u6839\u8282\u70b9\u5230\u8fd9\u4e9b\u8282\u70b9\u7684\u8def\u5f84\u3002</p> <p>\u89e3\u9898\u601d\u8def\uff1a\u5728\u4f8b\u9898\u4e00\u4ee3\u7801\u7684\u57fa\u7840\u4e0a\uff0c\u6211\u4eec\u9700\u8981\u501f\u52a9\u4e00\u4e2a\u5217\u8868 <code>path</code> \u8bb0\u5f55\u8bbf\u95ee\u8fc7\u7684\u8282\u70b9\u8def\u5f84\u3002\u5f53\u8bbf\u95ee\u5230\u503c\u4e3a \\(7\\) \u7684\u8282\u70b9\u65f6\uff0c\u5219\u590d\u5236 <code>path</code> \u5e76\u6dfb\u52a0\u8fdb\u7ed3\u679c\u5217\u8868 <code>res</code> \u3002\u904d\u5386\u5b8c\u6210\u540e\uff0c<code>res</code> \u4e2d\u4fdd\u5b58\u7684\u5c31\u662f\u6240\u6709\u7684\u89e3\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart preorder_traversal_ii_compact.java<pre><code>/* \u524d\u5e8f\u904d\u5386\uff1a\u4f8b\u9898\u4e8c */\nvoid preOrder(TreeNode root) {\nif (root == null) {\nreturn;\n}\n// \u5c1d\u8bd5\npath.add(root);\nif (root.val == 7) {\n// \u8bb0\u5f55\u89e3\nres.add(new ArrayList&lt;&gt;(path));\n}\npreOrder(root.left);\npreOrder(root.right);\n// \u56de\u9000\npath.remove(path.size() - 1);\n}\n</code></pre> preorder_traversal_ii_compact.cpp<pre><code>/* \u524d\u5e8f\u904d\u5386\uff1a\u4f8b\u9898\u4e8c */\nvoid preOrder(TreeNode *root) {\nif (root == nullptr) {\nreturn;\n}\n// \u5c1d\u8bd5\npath.push_back(root);\nif (root-&gt;val == 7) {\n// \u8bb0\u5f55\u89e3\nres.push_back(path);\n}\npreOrder(root-&gt;left);\npreOrder(root-&gt;right);\n// \u56de\u9000\npath.pop_back();\n}\n</code></pre> preorder_traversal_ii_compact.py<pre><code>def pre_order(root: TreeNode) -&gt; None:\n\"\"\"\u524d\u5e8f\u904d\u5386\uff1a\u4f8b\u9898\u4e8c\"\"\"\nif root is None:\nreturn\n# \u5c1d\u8bd5\npath.append(root)\nif root.val == 7:\n# \u8bb0\u5f55\u89e3\nres.append(list(path))\npre_order(root.left)\npre_order(root.right)\n# \u56de\u9000\npath.pop()\n</code></pre> preorder_traversal_ii_compact.go<pre><code>/* \u524d\u5e8f\u904d\u5386\uff1a\u4f8b\u9898\u4e8c */\nfunc preOrderII(root *TreeNode, res *[][]*TreeNode, path *[]*TreeNode) {\nif root == nil {\nreturn\n}\n// \u5c1d\u8bd5\n*path = append(*path, root)\nif int(root.Val) == 7 {\n// \u8bb0\u5f55\u89e3\n*res = append(*res, *path)\n}\npreOrderII(root.Left, res, path)\npreOrderII(root.Right, res, path)\n// \u56de\u9000\n*path = (*path)[:len(*path)-1]\n}\n</code></pre> preorder_traversal_ii_compact.js<pre><code>/* \u524d\u5e8f\u904d\u5386\uff1a\u4f8b\u9898\u4e8c */\nfunction preOrder(root, path, res) {\nif (root === null) {\nreturn;\n}\n// \u5c1d\u8bd5\npath.push(root);\nif (root.val === 7) {\n// \u8bb0\u5f55\u89e3\nres.push([...path]);\n}\npreOrder(root.left, path, res);\npreOrder(root.right, path, res);\n// \u56de\u9000\npath.pop();\n}\n</code></pre> preorder_traversal_ii_compact.ts<pre><code>/* \u524d\u5e8f\u904d\u5386\uff1a\u4f8b\u9898\u4e8c */\nfunction preOrder(\nroot: TreeNode | null,\npath: TreeNode[],\nres: TreeNode[][]\n): void {\nif (root === null) {\nreturn;\n}\n// \u5c1d\u8bd5\npath.push(root);\nif (root.val === 7) {\n// \u8bb0\u5f55\u89e3\nres.push([...path]);\n}\npreOrder(root.left, path, res);\npreOrder(root.right, path, res);\n// \u56de\u9000\npath.pop();\n}\n</code></pre> preorder_traversal_ii_compact.c<pre><code>[class]{}-[func]{preOrder}\n</code></pre> preorder_traversal_ii_compact.cs<pre><code>/* \u524d\u5e8f\u904d\u5386\uff1a\u4f8b\u9898\u4e8c */\nvoid preOrder(TreeNode root) {\nif (root == null) {\nreturn;\n}\n// \u5c1d\u8bd5\npath.Add(root);\nif (root.val == 7) {\n// \u8bb0\u5f55\u89e3\nres.Add(new List&lt;TreeNode&gt;(path));\n}\npreOrder(root.left);\npreOrder(root.right);\n// \u56de\u9000\npath.RemoveAt(path.Count - 1);\n}\n</code></pre> preorder_traversal_ii_compact.swift<pre><code>/* \u524d\u5e8f\u904d\u5386\uff1a\u4f8b\u9898\u4e8c */\nfunc preOrder(root: TreeNode?) {\nguard let root = root else {\nreturn\n}\n// \u5c1d\u8bd5\npath.append(root)\nif root.val == 7 {\n// \u8bb0\u5f55\u89e3\nres.append(path)\n}\npreOrder(root: root.left)\npreOrder(root: root.right)\n// \u56de\u9000\npath.removeLast()\n}\n</code></pre> preorder_traversal_ii_compact.zig<pre><code>[class]{}-[func]{preOrder}\n</code></pre> preorder_traversal_ii_compact.dart<pre><code>[class]{}-[func]{preOrder}\n</code></pre> <p>\u5728\u6bcf\u6b21\u201c\u5c1d\u8bd5\u201d\u4e2d\uff0c\u6211\u4eec\u901a\u8fc7\u5c06\u5f53\u524d\u8282\u70b9\u6dfb\u52a0\u8fdb <code>path</code> \u6765\u8bb0\u5f55\u8def\u5f84\uff1b\u800c\u5728\u201c\u56de\u9000\u201d\u524d\uff0c\u6211\u4eec\u9700\u8981\u5c06\u8be5\u8282\u70b9\u4ece <code>path</code> \u4e2d\u5f39\u51fa\uff0c\u4ee5\u6062\u590d\u672c\u6b21\u5c1d\u8bd5\u4e4b\u524d\u7684\u72b6\u6001\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u5c1d\u8bd5\u548c\u56de\u9000\u7406\u89e3\u4e3a\u201c\u524d\u8fdb\u201d\u4e0e\u201c\u64a4\u9500\u201d\uff0c\u4e24\u4e2a\u64cd\u4f5c\u662f\u4e92\u4e3a\u76f8\u53cd\u7684\u3002</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt;&lt;11&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p>"},{"location":"chapter_backtracking/backtracking_algorithm/#1212","title":"12.1.2. \u00a0 \u526a\u679d","text":"<p>\u590d\u6742\u7684\u56de\u6eaf\u95ee\u9898\u901a\u5e38\u5305\u542b\u4e00\u4e2a\u6216\u591a\u4e2a\u7ea6\u675f\u6761\u4ef6\uff0c\u7ea6\u675f\u6761\u4ef6\u901a\u5e38\u53ef\u7528\u4e8e\u201c\u526a\u679d\u201d\u3002</p> <p>\u4f8b\u9898\u4e09</p> <p>\u5728\u4e8c\u53c9\u6811\u4e2d\u641c\u7d22\u6240\u6709\u503c\u4e3a \\(7\\) \u7684\u8282\u70b9\uff0c\u8fd4\u56de\u6839\u8282\u70b9\u5230\u8fd9\u4e9b\u8282\u70b9\u7684\u8def\u5f84\uff0c\u8def\u5f84\u4e2d\u4e0d\u80fd\u5305\u542b\u503c\u4e3a \\(3\\) \u7684\u8282\u70b9\u3002</p> <p>\u89e3\u9898\u601d\u8def\uff1a\u5728\u4f8b\u9898\u4e8c\u7684\u57fa\u7840\u4e0a\u6dfb\u52a0\u526a\u679d\u64cd\u4f5c\uff0c\u5f53\u9047\u5230\u503c\u4e3a \\(3\\) \u7684\u8282\u70b9\u65f6\uff0c\u5219\u7ec8\u6b62\u7ee7\u7eed\u641c\u7d22\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart preorder_traversal_iii_compact.java<pre><code>/* \u524d\u5e8f\u904d\u5386\uff1a\u4f8b\u9898\u4e09 */\nvoid preOrder(TreeNode root) {\n// \u526a\u679d\nif (root == null || root.val == 3) {\nreturn;\n}\n// \u5c1d\u8bd5\npath.add(root);\nif (root.val == 7) {\n// \u8bb0\u5f55\u89e3\nres.add(new ArrayList&lt;&gt;(path));\n}\npreOrder(root.left);\npreOrder(root.right);\n// \u56de\u9000\npath.remove(path.size() - 1);\n}\n</code></pre> preorder_traversal_iii_compact.cpp<pre><code>/* \u524d\u5e8f\u904d\u5386\uff1a\u4f8b\u9898\u4e09 */\nvoid preOrder(TreeNode *root) {\n// \u526a\u679d\nif (root == nullptr || root-&gt;val == 3) {\nreturn;\n}\n// \u5c1d\u8bd5\npath.push_back(root);\nif (root-&gt;val == 7) {\n// \u8bb0\u5f55\u89e3\nres.push_back(path);\n}\npreOrder(root-&gt;left);\npreOrder(root-&gt;right);\n// \u56de\u9000\npath.pop_back();\n}\n</code></pre> preorder_traversal_iii_compact.py<pre><code>def pre_order(root: TreeNode) -&gt; None:\n\"\"\"\u524d\u5e8f\u904d\u5386\uff1a\u4f8b\u9898\u4e09\"\"\"\n# \u526a\u679d\nif root is None or root.val == 3:\nreturn\n# \u5c1d\u8bd5\npath.append(root)\nif root.val == 7:\n# \u8bb0\u5f55\u89e3\nres.append(list(path))\npre_order(root.left)\npre_order(root.right)\n# \u56de\u9000\npath.pop()\n</code></pre> preorder_traversal_iii_compact.go<pre><code>/* \u524d\u5e8f\u904d\u5386\uff1a\u4f8b\u9898\u4e09 */\nfunc preOrderIII(root *TreeNode, res *[][]*TreeNode, path *[]*TreeNode) {\n// \u526a\u679d\nif root == nil || root.Val == 3 {\nreturn\n}\n// \u5c1d\u8bd5\n*path = append(*path, root)\nif int(root.Val) == 7 {\n// \u8bb0\u5f55\u89e3\n*res = append(*res, *path)\n}\npreOrderIII(root.Left, res, path)\npreOrderIII(root.Right, res, path)\n// \u56de\u9000\n*path = (*path)[:len(*path)-1]\n}\n</code></pre> preorder_traversal_iii_compact.js<pre><code>/* \u524d\u5e8f\u904d\u5386\uff1a\u4f8b\u9898\u4e09 */\nfunction preOrder(root, path, res) {\n// \u526a\u679d\nif (root === null || root.val === 3) {\nreturn;\n}\n// \u5c1d\u8bd5\npath.push(root);\nif (root.val === 7) {\n// \u8bb0\u5f55\u89e3\nres.push([...path]);\n}\npreOrder(root.left, path, res);\npreOrder(root.right, path, res);\n// \u56de\u9000\npath.pop();\n}\n</code></pre> preorder_traversal_iii_compact.ts<pre><code>/* \u524d\u5e8f\u904d\u5386\uff1a\u4f8b\u9898\u4e09 */\nfunction preOrder(\nroot: TreeNode | null,\npath: TreeNode[],\nres: TreeNode[][]\n): void {\n// \u526a\u679d\nif (root === null || root.val === 3) {\nreturn;\n}\n// \u5c1d\u8bd5\npath.push(root);\nif (root.val === 7) {\n// \u8bb0\u5f55\u89e3\nres.push([...path]);\n}\npreOrder(root.left, path, res);\npreOrder(root.right, path, res);\n// \u56de\u9000\npath.pop();\n}\n</code></pre> preorder_traversal_iii_compact.c<pre><code>[class]{}-[func]{preOrder}\n</code></pre> preorder_traversal_iii_compact.cs<pre><code>/* \u524d\u5e8f\u904d\u5386\uff1a\u4f8b\u9898\u4e09 */\nvoid preOrder(TreeNode root) {\n// \u526a\u679d\nif (root == null || root.val == 3) {\nreturn;\n}\n// \u5c1d\u8bd5\npath.Add(root);\nif (root.val == 7) {\n// \u8bb0\u5f55\u89e3\nres.Add(new List&lt;TreeNode&gt;(path));\n}\npreOrder(root.left);\npreOrder(root.right);\n// \u56de\u9000\npath.RemoveAt(path.Count - 1);\n}\n</code></pre> preorder_traversal_iii_compact.swift<pre><code>/* \u524d\u5e8f\u904d\u5386\uff1a\u4f8b\u9898\u4e09 */\nfunc preOrder(root: TreeNode?) {\n// \u526a\u679d\nguard let root = root, root.val != 3 else {\nreturn\n}\n// \u5c1d\u8bd5\npath.append(root)\nif root.val == 7 {\n// \u8bb0\u5f55\u89e3\nres.append(path)\n}\npreOrder(root: root.left)\npreOrder(root: root.right)\n// \u56de\u9000\npath.removeLast()\n}\n</code></pre> preorder_traversal_iii_compact.zig<pre><code>[class]{}-[func]{preOrder}\n</code></pre> preorder_traversal_iii_compact.dart<pre><code>[class]{}-[func]{preOrder}\n</code></pre> <p>\u526a\u679d\u662f\u4e00\u4e2a\u975e\u5e38\u5f62\u8c61\u7684\u540d\u8bcd\u3002\u5728\u641c\u7d22\u8fc7\u7a0b\u4e2d\uff0c\u6211\u4eec\u5229\u7528\u7ea6\u675f\u6761\u4ef6\u201c\u526a\u6389\u201d\u4e86\u4e0d\u6ee1\u8db3\u7ea6\u675f\u6761\u4ef6\u7684\u641c\u7d22\u5206\u652f\uff0c\u907f\u514d\u8bb8\u591a\u65e0\u610f\u4e49\u7684\u5c1d\u8bd5\uff0c\u4ece\u800c\u63d0\u5347\u641c\u7d22\u6548\u7387\u3002</p> <p></p> <p> Fig. \u6839\u636e\u7ea6\u675f\u6761\u4ef6\u526a\u679d </p>"},{"location":"chapter_backtracking/backtracking_algorithm/#1213","title":"12.1.3. \u00a0 \u5e38\u7528\u672f\u8bed","text":"<p>\u4e3a\u4e86\u66f4\u6e05\u6670\u5730\u5206\u6790\u7b97\u6cd5\u95ee\u9898\uff0c\u6211\u4eec\u603b\u7ed3\u4e00\u4e0b\u56de\u6eaf\u7b97\u6cd5\u4e2d\u5e38\u7528\u672f\u8bed\u7684\u542b\u4e49\uff0c\u5e76\u5bf9\u7167\u4f8b\u9898\u4e09\u7ed9\u51fa\u5bf9\u5e94\u793a\u4f8b\u3002</p> \u540d\u8bcd \u5b9a\u4e49 \u4f8b\u9898\u4e09 \u89e3 Solution \u89e3\u662f\u6ee1\u8db3\u95ee\u9898\u7279\u5b9a\u6761\u4ef6\u7684\u7b54\u6848\u3002\u56de\u6eaf\u7b97\u6cd5\u7684\u76ee\u6807\u662f\u627e\u5230\u4e00\u4e2a\u6216\u591a\u4e2a\u6ee1\u8db3\u6761\u4ef6\u7684\u89e3 \u6839\u8282\u70b9\u5230\u8282\u70b9 \\(7\\) \u7684\u6240\u6709\u8def\u5f84\uff0c\u4e14\u8def\u5f84\u4e2d\u4e0d\u5305\u542b\u503c\u4e3a \\(3\\) \u7684\u8282\u70b9 \u72b6\u6001 State \u72b6\u6001\u8868\u793a\u95ee\u9898\u5728\u67d0\u4e00\u65f6\u523b\u7684\u60c5\u51b5\uff0c\u5305\u62ec\u5df2\u7ecf\u505a\u51fa\u7684\u9009\u62e9 \u5f53\u524d\u5df2\u8bbf\u95ee\u7684\u8282\u70b9\u8def\u5f84\uff0c\u5373 <code>path</code> \u8282\u70b9\u5217\u8868 \u7ea6\u675f\u6761\u4ef6 Constraint \u7ea6\u675f\u6761\u4ef6\u662f\u95ee\u9898\u4e2d\u9650\u5236\u89e3\u7684\u53ef\u884c\u6027\u7684\u6761\u4ef6\uff0c\u901a\u5e38\u7528\u4e8e\u526a\u679d \u8981\u6c42\u8def\u5f84\u4e2d\u4e0d\u80fd\u5305\u542b\u503c\u4e3a \\(3\\) \u7684\u8282\u70b9 \u5c1d\u8bd5 Attempt \u5c1d\u8bd5\u662f\u5728\u641c\u7d22\u8fc7\u7a0b\u4e2d\uff0c\u6839\u636e\u5f53\u524d\u72b6\u6001\u548c\u53ef\u7528\u9009\u62e9\u6765\u63a2\u7d22\u89e3\u7a7a\u95f4\u7684\u8fc7\u7a0b\u3002\u5c1d\u8bd5\u5305\u62ec\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\uff0c\u68c0\u67e5\u662f\u5426\u4e3a\u89e3 \u9012\u5f52\u8bbf\u95ee\u5de6\uff08\u53f3\uff09\u5b50\u8282\u70b9\uff0c\u5c06\u8282\u70b9\u6dfb\u52a0\u8fdb <code>path</code> \uff0c\u5224\u65ad\u8282\u70b9\u7684\u503c\u662f\u5426\u4e3a \\(7\\) \u56de\u9000 Backtracking \u56de\u9000\u6307\u5728\u641c\u7d22\u4e2d\u9047\u5230\u5230\u4e0d\u6ee1\u8db3\u7ea6\u675f\u6761\u4ef6\u6216\u65e0\u6cd5\u7ee7\u7eed\u641c\u7d22\u7684\u72b6\u6001\u65f6\uff0c\u64a4\u9500\u524d\u9762\u505a\u51fa\u7684\u9009\u62e9\uff0c\u56de\u5230\u4e0a\u4e00\u4e2a\u72b6\u6001 \u5f53\u8d8a\u8fc7\u53f6\u7ed3\u70b9\u3001\u7ed3\u675f\u7ed3\u70b9\u8bbf\u95ee\u3001\u9047\u5230\u503c\u4e3a \\(3\\) \u7684\u8282\u70b9\u65f6\u7ec8\u6b62\u641c\u7d22\uff0c\u51fd\u6570\u8fd4\u56de \u526a\u679d Pruning \u526a\u679d\u662f\u6839\u636e\u95ee\u9898\u7279\u6027\u548c\u7ea6\u675f\u6761\u4ef6\u907f\u514d\u65e0\u610f\u4e49\u7684\u641c\u7d22\u8def\u5f84\u7684\u65b9\u6cd5\uff0c\u53ef\u63d0\u9ad8\u641c\u7d22\u6548\u7387 \u5f53\u9047\u5230\u503c\u4e3a \\(3\\) \u7684\u8282\u70b9\u65f6\uff0c\u5219\u7ec8\u6b62\u7ee7\u7eed\u641c\u7d22 <p>Tip</p> <p>\u89e3\u3001\u72b6\u6001\u3001\u7ea6\u675f\u6761\u4ef6\u7b49\u672f\u8bed\u662f\u901a\u7528\u7684\uff0c\u9002\u7528\u4e8e\u56de\u6eaf\u7b97\u6cd5\u3001\u52a8\u6001\u89c4\u5212\u3001\u8d2a\u5fc3\u7b97\u6cd5\u7b49\u3002</p>"},{"location":"chapter_backtracking/backtracking_algorithm/#1214","title":"12.1.4. \u00a0 \u6846\u67b6\u4ee3\u7801","text":"<p>\u56de\u6eaf\u7b97\u6cd5\u53ef\u7528\u4e8e\u89e3\u51b3\u8bb8\u591a\u641c\u7d22\u95ee\u9898\u3001\u7ea6\u675f\u6ee1\u8db3\u95ee\u9898\u548c\u7ec4\u5408\u4f18\u5316\u95ee\u9898\u3002\u4e3a\u63d0\u5347\u4ee3\u7801\u901a\u7528\u6027\uff0c\u6211\u4eec\u5e0c\u671b\u5c06\u56de\u6eaf\u7b97\u6cd5\u7684\u201c\u5c1d\u8bd5\u3001\u56de\u9000\u3001\u526a\u679d\u201d\u7684\u4e3b\u4f53\u6846\u67b6\u63d0\u70bc\u51fa\u6765\u3002</p> <p>\u8bbe <code>state</code> \u4e3a\u95ee\u9898\u7684\u5f53\u524d\u72b6\u6001\uff0c<code>choices</code> \u8868\u793a\u5f53\u524d\u72b6\u6001\u4e0b\u53ef\u4ee5\u505a\u51fa\u7684\u9009\u62e9\uff0c\u5219\u53ef\u5f97\u5230\u4ee5\u4e0b\u56de\u6eaf\u7b97\u6cd5\u7684\u6846\u67b6\u4ee3\u7801\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart <pre><code>/* \u56de\u6eaf\u7b97\u6cd5\u6846\u67b6 */\nvoid backtrack(State state, List&lt;Choice&gt; choices, List&lt;State&gt; res) {\n// \u5224\u65ad\u662f\u5426\u4e3a\u89e3\nif (isSolution(state)) {\n// \u8bb0\u5f55\u89e3\nrecordSolution(state, res);\nreturn;\n}\n// \u904d\u5386\u6240\u6709\u9009\u62e9\nfor (Choice choice : choices) {\n// \u526a\u679d\uff1a\u5224\u65ad\u9009\u62e9\u662f\u5426\u5408\u6cd5\nif (isValid(state, choice)) {\n// \u5c1d\u8bd5\uff1a\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\nmakeChoice(state, choice);\nbacktrack(state, choices, res);\n// \u56de\u9000\uff1a\u64a4\u9500\u9009\u62e9\uff0c\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001\nundoChoice(state, choice);\n}\n}\n}\n</code></pre> <pre><code>/* \u56de\u6eaf\u7b97\u6cd5\u6846\u67b6 */\nvoid backtrack(State *state, vector&lt;Choice *&gt; &amp;choices, vector&lt;State *&gt; &amp;res) {\n// \u5224\u65ad\u662f\u5426\u4e3a\u89e3\nif (isSolution(state)) {\n// \u8bb0\u5f55\u89e3\nrecordSolution(state, res);\nreturn;\n}\n// \u904d\u5386\u6240\u6709\u9009\u62e9\nfor (Choice choice : choices) {\n// \u526a\u679d\uff1a\u5224\u65ad\u9009\u62e9\u662f\u5426\u5408\u6cd5\nif (isValid(state, choice)) {\n// \u5c1d\u8bd5\uff1a\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\nmakeChoice(state, choice);\nbacktrack(state, choices, res);\n// \u56de\u9000\uff1a\u64a4\u9500\u9009\u62e9\uff0c\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001\nundoChoice(state, choice);\n}\n}\n}\n</code></pre> <pre><code>def backtrack(state: State, choices: list[choice], res: list[state]) -&gt; None:\n\"\"\"\u56de\u6eaf\u7b97\u6cd5\u6846\u67b6\"\"\"\n# \u5224\u65ad\u662f\u5426\u4e3a\u89e3\nif is_solution(state):\n# \u8bb0\u5f55\u89e3\nrecord_solution(state, res)\nreturn\n# \u904d\u5386\u6240\u6709\u9009\u62e9\nfor choice in choices:\n# \u526a\u679d\uff1a\u5224\u65ad\u9009\u62e9\u662f\u5426\u5408\u6cd5\nif is_valid(state, choice):\n# \u5c1d\u8bd5\uff1a\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\nmake_choice(state, choice)\nbacktrack(state, choices, res)\n# \u56de\u9000\uff1a\u64a4\u9500\u9009\u62e9\uff0c\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001\nundo_choice(state, choice)\n</code></pre> <pre><code>/* \u56de\u6eaf\u7b97\u6cd5\u6846\u67b6 */\nfunc backtrack(state *State, choices []Choice, res *[]State) {\n// \u5224\u65ad\u662f\u5426\u4e3a\u89e3\nif isSolution(state) {\n// \u8bb0\u5f55\u89e3\nrecordSolution(state, res)\nreturn\n}\n// \u904d\u5386\u6240\u6709\u9009\u62e9\nfor _, choice := range choices {\n// \u526a\u679d\uff1a\u5224\u65ad\u9009\u62e9\u662f\u5426\u5408\u6cd5\nif isValid(state, choice) {\n// \u5c1d\u8bd5\uff1a\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\nmakeChoice(state, choice)\nbacktrack(state, choices, res)\n// \u56de\u9000\uff1a\u64a4\u9500\u9009\u62e9\uff0c\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001\nundoChoice(state, choice)\n}\n}\n}\n</code></pre> <pre><code>/* \u56de\u6eaf\u7b97\u6cd5\u6846\u67b6 */\nfunction backtrack(state, choices, res) {\n// \u5224\u65ad\u662f\u5426\u4e3a\u89e3\nif (isSolution(state)) {\n// \u8bb0\u5f55\u89e3\nrecordSolution(state, res);\nreturn;\n}\n// \u904d\u5386\u6240\u6709\u9009\u62e9\nfor (let choice of choices) {\n// \u526a\u679d\uff1a\u5224\u65ad\u9009\u62e9\u662f\u5426\u5408\u6cd5\nif (isValid(state, choice)) {\n// \u5c1d\u8bd5\uff1a\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\nmakeChoice(state, choice);\nbacktrack(state, choices, res);\n// \u56de\u9000\uff1a\u64a4\u9500\u9009\u62e9\uff0c\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001\nundoChoice(state, choice);\n}\n}\n}\n</code></pre> <pre><code>/* \u56de\u6eaf\u7b97\u6cd5\u6846\u67b6 */\nfunction backtrack(state: State, choices: Choice[], res: State[]): void {\n// \u5224\u65ad\u662f\u5426\u4e3a\u89e3\nif (isSolution(state)) {\n// \u8bb0\u5f55\u89e3\nrecordSolution(state, res);\nreturn;\n}\n// \u904d\u5386\u6240\u6709\u9009\u62e9\nfor (let choice of choices) {\n// \u526a\u679d\uff1a\u5224\u65ad\u9009\u62e9\u662f\u5426\u5408\u6cd5\nif (isValid(state, choice)) {\n// \u5c1d\u8bd5\uff1a\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\nmakeChoice(state, choice);\nbacktrack(state, choices, res);\n// \u56de\u9000\uff1a\u64a4\u9500\u9009\u62e9\uff0c\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001\nundoChoice(state, choice);\n}\n}\n}\n</code></pre> <pre><code>/* \u56de\u6eaf\u7b97\u6cd5\u6846\u67b6 */\nvoid backtrack(State *state, Choice *choices, int numChoices, State *res, int numRes) {\n// \u5224\u65ad\u662f\u5426\u4e3a\u89e3\nif (isSolution(state)) {\n// \u8bb0\u5f55\u89e3\nrecordSolution(state, res, numRes);\nreturn;\n}\n// \u904d\u5386\u6240\u6709\u9009\u62e9\nfor (int i = 0; i &lt; numChoices; i++) {\n// \u526a\u679d\uff1a\u5224\u65ad\u9009\u62e9\u662f\u5426\u5408\u6cd5\nif (isValid(state, &amp;choices[i])) {\n// \u5c1d\u8bd5\uff1a\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\nmakeChoice(state, &amp;choices[i]);\nbacktrack(state, choices, numChoices, res, numRes);\n// \u56de\u9000\uff1a\u64a4\u9500\u9009\u62e9\uff0c\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001\nundoChoice(state, &amp;choices[i]);\n}\n}\n}\n</code></pre> <pre><code>/* \u56de\u6eaf\u7b97\u6cd5\u6846\u67b6 */\nvoid backtrack(State state, List&lt;Choice&gt; choices, List&lt;State&gt; res) {\n// \u5224\u65ad\u662f\u5426\u4e3a\u89e3\nif (isSolution(state)) {\n// \u8bb0\u5f55\u89e3\nrecordSolution(state, res);\nreturn;\n}\n// \u904d\u5386\u6240\u6709\u9009\u62e9\nforeach (Choice choice in choices) {\n// \u526a\u679d\uff1a\u5224\u65ad\u9009\u62e9\u662f\u5426\u5408\u6cd5\nif (isValid(state, choice)) {\n// \u5c1d\u8bd5\uff1a\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\nmakeChoice(state, choice);\nbacktrack(state, choices, res);\n// \u56de\u9000\uff1a\u64a4\u9500\u9009\u62e9\uff0c\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001\nundoChoice(state, choice);\n}\n}\n}\n</code></pre> <pre><code>/* \u56de\u6eaf\u7b97\u6cd5\u6846\u67b6 */\nfunc backtrack(state: inout State, choices: [Choice], res: inout [State]) {\n// \u5224\u65ad\u662f\u5426\u4e3a\u89e3\nif isSolution(state: state) {\n// \u8bb0\u5f55\u89e3\nrecordSolution(state: state, res: &amp;res)\nreturn\n}\n// \u904d\u5386\u6240\u6709\u9009\u62e9\nfor choice in choices {\n// \u526a\u679d\uff1a\u5224\u65ad\u9009\u62e9\u662f\u5426\u5408\u6cd5\nif isValid(state: state, choice: choice) {\n// \u5c1d\u8bd5\uff1a\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\nmakeChoice(state: &amp;state, choice: choice)\nbacktrack(state: &amp;state, choices: choices, res: &amp;res)\n// \u56de\u9000\uff1a\u64a4\u9500\u9009\u62e9\uff0c\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001\nundoChoice(state: &amp;state, choice: choice)\n}\n}\n}\n</code></pre> <pre><code>\n</code></pre> <pre><code>/* \u56de\u6eaf\u7b97\u6cd5\u6846\u67b6 */\nvoid backtrack(State state, List&lt;Choice&gt;, List&lt;State&gt; res) {\n// \u5224\u65ad\u662f\u5426\u4e3a\u89e3\nif (isSolution(state)) {\n// \u8bb0\u5f55\u89e3\nrecordSolution(state, res);\nreturn;\n}\n// \u904d\u5386\u6240\u6709\u9009\u62e9\nfor (Choice choice in choices) {\n// \u526a\u679d\uff1a\u5224\u65ad\u9009\u62e9\u662f\u5426\u5408\u6cd5\nif (isValid(state, choice)) {\n// \u5c1d\u8bd5\uff1a\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\nmakeChoice(state, choice);\nbacktrack(state, choices, res);\n// \u56de\u9000\uff1a\u64a4\u9500\u9009\u62e9\uff0c\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001\nundoChoice(state, choice);\n}\n}\n}\n</code></pre> <p>\u4e0b\u9762\uff0c\u6211\u4eec\u5c1d\u8bd5\u57fa\u4e8e\u6b64\u6846\u67b6\u6765\u89e3\u51b3\u4f8b\u9898\u4e09\u3002\u5728\u4f8b\u9898\u4e09\u4e2d\uff0c\u72b6\u6001 <code>state</code> \u662f\u8282\u70b9\u904d\u5386\u8def\u5f84\uff0c\u9009\u62e9 <code>choices</code> \u662f\u5f53\u524d\u8282\u70b9\u7684\u5de6\u5b50\u8282\u70b9\u548c\u53f3\u5b50\u8282\u70b9\uff0c\u7ed3\u679c <code>res</code> \u662f\u8def\u5f84\u5217\u8868\uff0c\u5b9e\u73b0\u4ee3\u7801\u5982\u4e0b\u6240\u793a\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart preorder_traversal_iii_template.java<pre><code>/* \u5224\u65ad\u5f53\u524d\u72b6\u6001\u662f\u5426\u4e3a\u89e3 */\nboolean isSolution(List&lt;TreeNode&gt; state) {\nreturn !state.isEmpty() &amp;&amp; state.get(state.size() - 1).val == 7;\n}\n/* \u8bb0\u5f55\u89e3 */\nvoid recordSolution(List&lt;TreeNode&gt; state, List&lt;List&lt;TreeNode&gt;&gt; res) {\nres.add(new ArrayList&lt;&gt;(state));\n}\n/* \u5224\u65ad\u5728\u5f53\u524d\u72b6\u6001\u4e0b\uff0c\u8be5\u9009\u62e9\u662f\u5426\u5408\u6cd5 */\nboolean isValid(List&lt;TreeNode&gt; state, TreeNode choice) {\nreturn choice != null &amp;&amp; choice.val != 3;\n}\n/* \u66f4\u65b0\u72b6\u6001 */\nvoid makeChoice(List&lt;TreeNode&gt; state, TreeNode choice) {\nstate.add(choice);\n}\n/* \u6062\u590d\u72b6\u6001 */\nvoid undoChoice(List&lt;TreeNode&gt; state, TreeNode choice) {\nstate.remove(state.size() - 1);\n}\n/* \u56de\u6eaf\u7b97\u6cd5\uff1a\u4f8b\u9898\u4e09 */\nvoid backtrack(List&lt;TreeNode&gt; state, List&lt;TreeNode&gt; choices, List&lt;List&lt;TreeNode&gt;&gt; res) {\n// \u68c0\u67e5\u662f\u5426\u4e3a\u89e3\nif (isSolution(state)) {\n// \u8bb0\u5f55\u89e3\nrecordSolution(state, res);\nreturn;\n}\n// \u904d\u5386\u6240\u6709\u9009\u62e9\nfor (TreeNode choice : choices) {\n// \u526a\u679d\uff1a\u68c0\u67e5\u9009\u62e9\u662f\u5426\u5408\u6cd5\nif (isValid(state, choice)) {\n// \u5c1d\u8bd5\uff1a\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\nmakeChoice(state, choice);\n// \u8fdb\u884c\u4e0b\u4e00\u8f6e\u9009\u62e9\nbacktrack(state, Arrays.asList(choice.left, choice.right), res);\n// \u56de\u9000\uff1a\u64a4\u9500\u9009\u62e9\uff0c\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001\nundoChoice(state, choice);\n}\n}\n}\n</code></pre> preorder_traversal_iii_template.cpp<pre><code>/* \u5224\u65ad\u5f53\u524d\u72b6\u6001\u662f\u5426\u4e3a\u89e3 */\nbool isSolution(vector&lt;TreeNode *&gt; &amp;state) {\nreturn !state.empty() &amp;&amp; state.back()-&gt;val == 7;\n}\n/* \u8bb0\u5f55\u89e3 */\nvoid recordSolution(vector&lt;TreeNode *&gt; &amp;state, vector&lt;vector&lt;TreeNode *&gt;&gt; &amp;res) {\nres.push_back(state);\n}\n/* \u5224\u65ad\u5728\u5f53\u524d\u72b6\u6001\u4e0b\uff0c\u8be5\u9009\u62e9\u662f\u5426\u5408\u6cd5 */\nbool isValid(vector&lt;TreeNode *&gt; &amp;state, TreeNode *choice) {\nreturn choice != nullptr &amp;&amp; choice-&gt;val != 3;\n}\n/* \u66f4\u65b0\u72b6\u6001 */\nvoid makeChoice(vector&lt;TreeNode *&gt; &amp;state, TreeNode *choice) {\nstate.push_back(choice);\n}\n/* \u6062\u590d\u72b6\u6001 */\nvoid undoChoice(vector&lt;TreeNode *&gt; &amp;state, TreeNode *choice) {\nstate.pop_back();\n}\n/* \u56de\u6eaf\u7b97\u6cd5\uff1a\u4f8b\u9898\u4e09 */\nvoid backtrack(vector&lt;TreeNode *&gt; &amp;state, vector&lt;TreeNode *&gt; &amp;choices, vector&lt;vector&lt;TreeNode *&gt;&gt; &amp;res) {\n// \u68c0\u67e5\u662f\u5426\u4e3a\u89e3\nif (isSolution(state)) {\n// \u8bb0\u5f55\u89e3\nrecordSolution(state, res);\nreturn;\n}\n// \u904d\u5386\u6240\u6709\u9009\u62e9\nfor (TreeNode *choice : choices) {\n// \u526a\u679d\uff1a\u68c0\u67e5\u9009\u62e9\u662f\u5426\u5408\u6cd5\nif (isValid(state, choice)) {\n// \u5c1d\u8bd5\uff1a\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\nmakeChoice(state, choice);\n// \u8fdb\u884c\u4e0b\u4e00\u8f6e\u9009\u62e9\nvector&lt;TreeNode *&gt; nextChoices{choice-&gt;left, choice-&gt;right};\nbacktrack(state, nextChoices, res);\n// \u56de\u9000\uff1a\u64a4\u9500\u9009\u62e9\uff0c\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001\nundoChoice(state, choice);\n}\n}\n}\n</code></pre> preorder_traversal_iii_template.py<pre><code>def is_solution(state: list[TreeNode]) -&gt; bool:\n\"\"\"\u5224\u65ad\u5f53\u524d\u72b6\u6001\u662f\u5426\u4e3a\u89e3\"\"\"\nreturn state and state[-1].val == 7\ndef record_solution(state: list[TreeNode], res: list[list[TreeNode]]):\n\"\"\"\u8bb0\u5f55\u89e3\"\"\"\nres.append(list(state))\ndef is_valid(state: list[TreeNode], choice: TreeNode) -&gt; bool:\n\"\"\"\u5224\u65ad\u5728\u5f53\u524d\u72b6\u6001\u4e0b\uff0c\u8be5\u9009\u62e9\u662f\u5426\u5408\u6cd5\"\"\"\nreturn choice is not None and choice.val != 3\ndef make_choice(state: list[TreeNode], choice: TreeNode):\n\"\"\"\u66f4\u65b0\u72b6\u6001\"\"\"\nstate.append(choice)\ndef undo_choice(state: list[TreeNode], choice: TreeNode):\n\"\"\"\u6062\u590d\u72b6\u6001\"\"\"\nstate.pop()\ndef backtrack(\nstate: list[TreeNode], choices: list[TreeNode], res: list[list[TreeNode]]\n):\n\"\"\"\u56de\u6eaf\u7b97\u6cd5\uff1a\u4f8b\u9898\u4e09\"\"\"\n# \u68c0\u67e5\u662f\u5426\u4e3a\u89e3\nif is_solution(state):\n# \u8bb0\u5f55\u89e3\nrecord_solution(state, res)\nreturn\n# \u904d\u5386\u6240\u6709\u9009\u62e9\nfor choice in choices:\n# \u526a\u679d\uff1a\u68c0\u67e5\u9009\u62e9\u662f\u5426\u5408\u6cd5\nif is_valid(state, choice):\n# \u5c1d\u8bd5\uff1a\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\nmake_choice(state, choice)\n# \u8fdb\u884c\u4e0b\u4e00\u8f6e\u9009\u62e9\nbacktrack(state, [choice.left, choice.right], res)\n# \u56de\u9000\uff1a\u64a4\u9500\u9009\u62e9\uff0c\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001\nundo_choice(state, choice)\n</code></pre> preorder_traversal_iii_template.go<pre><code>/* \u5224\u65ad\u5f53\u524d\u72b6\u6001\u662f\u5426\u4e3a\u89e3 */\nfunc isSolution(state *[]*TreeNode) bool {\nreturn len(*state) != 0 &amp;&amp; (*state)[len(*state)-1].Val == 7\n}\n/* \u8bb0\u5f55\u89e3 */\nfunc recordSolution(state *[]*TreeNode, res *[][]*TreeNode) {\n*res = append(*res, *state)\n}\n/* \u5224\u65ad\u5728\u5f53\u524d\u72b6\u6001\u4e0b\uff0c\u8be5\u9009\u62e9\u662f\u5426\u5408\u6cd5 */\nfunc isValid(state *[]*TreeNode, choice *TreeNode) bool {\nreturn choice != nil &amp;&amp; choice.Val != 3\n}\n/* \u66f4\u65b0\u72b6\u6001 */\nfunc makeChoice(state *[]*TreeNode, choice *TreeNode) {\n*state = append(*state, choice)\n}\n/* \u6062\u590d\u72b6\u6001 */\nfunc undoChoice(state *[]*TreeNode, choice *TreeNode) {\n*state = (*state)[:len(*state)-1]\n}\n/* \u56de\u6eaf\u7b97\u6cd5\uff1a\u4f8b\u9898\u4e09 */\nfunc backtrackIII(state *[]*TreeNode, choices *[]*TreeNode, res *[][]*TreeNode) {\n// \u68c0\u67e5\u662f\u5426\u4e3a\u89e3\nif isSolution(state) {\n// \u8bb0\u5f55\u89e3\nrecordSolution(state, res)\nreturn\n}\n// \u904d\u5386\u6240\u6709\u9009\u62e9\nfor _, choice := range *choices {\n// \u526a\u679d\uff1a\u68c0\u67e5\u9009\u62e9\u662f\u5426\u5408\u6cd5\nif isValid(state, choice) {\n// \u5c1d\u8bd5\uff1a\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\nmakeChoice(state, choice)\n// \u8fdb\u884c\u4e0b\u4e00\u8f6e\u9009\u62e9\ntemp := make([]*TreeNode, 0)\ntemp = append(temp, choice.Left, choice.Right)\nbacktrackIII(state, &amp;temp, res)\n// \u56de\u9000\uff1a\u64a4\u9500\u9009\u62e9\uff0c\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001\nundoChoice(state, choice)\n}\n}\n}\n</code></pre> preorder_traversal_iii_template.js<pre><code>/* \u5224\u65ad\u5f53\u524d\u72b6\u6001\u662f\u5426\u4e3a\u89e3 */\nfunction isSolution(state) {\nreturn state &amp;&amp; state[state.length - 1]?.val === 7;\n}\n/* \u8bb0\u5f55\u89e3 */\nfunction recordSolution(state, res) {\nres.push([...state]);\n}\n/* \u5224\u65ad\u5728\u5f53\u524d\u72b6\u6001\u4e0b\uff0c\u8be5\u9009\u62e9\u662f\u5426\u5408\u6cd5 */\nfunction isValid(state, choice) {\nreturn choice !== null &amp;&amp; choice.val !== 3;\n}\n/* \u66f4\u65b0\u72b6\u6001 */\nfunction makeChoice(state, choice) {\nstate.push(choice);\n}\n/* \u6062\u590d\u72b6\u6001 */\nfunction undoChoice(state) {\nstate.pop();\n}\n/* \u56de\u6eaf\u7b97\u6cd5\uff1a\u4f8b\u9898\u4e09 */\nfunction backtrack(state, choices, res) {\n// \u68c0\u67e5\u662f\u5426\u4e3a\u89e3\nif (isSolution(state)) {\n// \u8bb0\u5f55\u89e3\nrecordSolution(state, res);\nreturn;\n}\n// \u904d\u5386\u6240\u6709\u9009\u62e9\nfor (const choice of choices) {\n// \u526a\u679d\uff1a\u68c0\u67e5\u9009\u62e9\u662f\u5426\u5408\u6cd5\nif (isValid(state, choice)) {\n// \u5c1d\u8bd5\uff1a\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\nmakeChoice(state, choice);\n// \u8fdb\u884c\u4e0b\u4e00\u8f6e\u9009\u62e9\nbacktrack(state, [choice.left, choice.right], res);\n// \u56de\u9000\uff1a\u64a4\u9500\u9009\u62e9\uff0c\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001\nundoChoice(state);\n}\n}\n}\n</code></pre> preorder_traversal_iii_template.ts<pre><code>/* \u5224\u65ad\u5f53\u524d\u72b6\u6001\u662f\u5426\u4e3a\u89e3 */\nfunction isSolution(state: TreeNode[]): boolean {\nreturn state &amp;&amp; state[state.length - 1]?.val === 7;\n}\n/* \u8bb0\u5f55\u89e3 */\nfunction recordSolution(state: TreeNode[], res: TreeNode[][]): void {\nres.push([...state]);\n}\n/* \u5224\u65ad\u5728\u5f53\u524d\u72b6\u6001\u4e0b\uff0c\u8be5\u9009\u62e9\u662f\u5426\u5408\u6cd5 */\nfunction isValid(state: TreeNode[], choice: TreeNode): boolean {\nreturn choice !== null &amp;&amp; choice.val !== 3;\n}\n/* \u66f4\u65b0\u72b6\u6001 */\nfunction makeChoice(state: TreeNode[], choice: TreeNode): void {\nstate.push(choice);\n}\n/* \u6062\u590d\u72b6\u6001 */\nfunction undoChoice(state: TreeNode[]): void {\nstate.pop();\n}\n/* \u56de\u6eaf\u7b97\u6cd5\uff1a\u4f8b\u9898\u4e09 */\nfunction backtrack(\nstate: TreeNode[],\nchoices: TreeNode[],\nres: TreeNode[][]\n): void {\n// \u68c0\u67e5\u662f\u5426\u4e3a\u89e3\nif (isSolution(state)) {\n// \u8bb0\u5f55\u89e3\nrecordSolution(state, res);\nreturn;\n}\n// \u904d\u5386\u6240\u6709\u9009\u62e9\nfor (const choice of choices) {\n// \u526a\u679d\uff1a\u68c0\u67e5\u9009\u62e9\u662f\u5426\u5408\u6cd5\nif (isValid(state, choice)) {\n// \u5c1d\u8bd5\uff1a\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\nmakeChoice(state, choice);\n// \u8fdb\u884c\u4e0b\u4e00\u8f6e\u9009\u62e9\nbacktrack(state, [choice.left, choice.right], res);\n// \u56de\u9000\uff1a\u64a4\u9500\u9009\u62e9\uff0c\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001\nundoChoice(state);\n}\n}\n}\n</code></pre> preorder_traversal_iii_template.c<pre><code>[class]{}-[func]{isSolution}\n[class]{}-[func]{recordSolution}\n[class]{}-[func]{isValid}\n[class]{}-[func]{makeChoice}\n[class]{}-[func]{undoChoice}\n[class]{}-[func]{backtrack}\n</code></pre> preorder_traversal_iii_template.cs<pre><code>/* \u5224\u65ad\u5f53\u524d\u72b6\u6001\u662f\u5426\u4e3a\u89e3 */\nbool isSolution(List&lt;TreeNode&gt; state) {\nreturn state.Count != 0 &amp;&amp; state[^1].val == 7;\n}\n/* \u8bb0\u5f55\u89e3 */\nvoid recordSolution(List&lt;TreeNode&gt; state, List&lt;List&lt;TreeNode&gt;&gt; res) {\nres.Add(new List&lt;TreeNode&gt;(state));\n}\n/* \u5224\u65ad\u5728\u5f53\u524d\u72b6\u6001\u4e0b\uff0c\u8be5\u9009\u62e9\u662f\u5426\u5408\u6cd5 */\nbool isValid(List&lt;TreeNode&gt; state, TreeNode choice) {\nreturn choice != null &amp;&amp; choice.val != 3;\n}\n/* \u66f4\u65b0\u72b6\u6001 */\nvoid makeChoice(List&lt;TreeNode&gt; state, TreeNode choice) {\nstate.Add(choice);\n}\n/* \u6062\u590d\u72b6\u6001 */\nvoid undoChoice(List&lt;TreeNode&gt; state, TreeNode choice) {\nstate.RemoveAt(state.Count - 1);\n}\n/* \u56de\u6eaf\u7b97\u6cd5\uff1a\u4f8b\u9898\u4e09 */\nvoid backtrack(List&lt;TreeNode&gt; state, List&lt;TreeNode&gt; choices, List&lt;List&lt;TreeNode&gt;&gt; res) {\n// \u68c0\u67e5\u662f\u5426\u4e3a\u89e3\nif (isSolution(state)) {\n// \u8bb0\u5f55\u89e3\nrecordSolution(state, res);\nreturn;\n}\n// \u904d\u5386\u6240\u6709\u9009\u62e9\nforeach (TreeNode choice in choices) {\n// \u526a\u679d\uff1a\u68c0\u67e5\u9009\u62e9\u662f\u5426\u5408\u6cd5\nif (isValid(state, choice)) {\n// \u5c1d\u8bd5\uff1a\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\nmakeChoice(state, choice);\n// \u8fdb\u884c\u4e0b\u4e00\u8f6e\u9009\u62e9\nbacktrack(state, new List&lt;TreeNode&gt; { choice.left, choice.right }, res);\n// \u56de\u9000\uff1a\u64a4\u9500\u9009\u62e9\uff0c\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001\nundoChoice(state, choice);\n}\n}\n}\n</code></pre> preorder_traversal_iii_template.swift<pre><code>/* \u5224\u65ad\u5f53\u524d\u72b6\u6001\u662f\u5426\u4e3a\u89e3 */\nfunc isSolution(state: [TreeNode]) -&gt; Bool {\n!state.isEmpty &amp;&amp; state.last!.val == 7\n}\n/* \u8bb0\u5f55\u89e3 */\nfunc recordSolution(state: [TreeNode], res: inout [[TreeNode]]) {\nres.append(state)\n}\n/* \u5224\u65ad\u5728\u5f53\u524d\u72b6\u6001\u4e0b\uff0c\u8be5\u9009\u62e9\u662f\u5426\u5408\u6cd5 */\nfunc isValid(state: [TreeNode], choice: TreeNode?) -&gt; Bool {\nchoice != nil &amp;&amp; choice!.val != 3\n}\n/* \u66f4\u65b0\u72b6\u6001 */\nfunc makeChoice(state: inout [TreeNode], choice: TreeNode) {\nstate.append(choice)\n}\n/* \u6062\u590d\u72b6\u6001 */\nfunc undoChoice(state: inout [TreeNode], choice: TreeNode) {\nstate.removeLast()\n}\n/* \u56de\u6eaf\u7b97\u6cd5\uff1a\u4f8b\u9898\u4e09 */\nfunc backtrack(state: inout [TreeNode], choices: [TreeNode], res: inout [[TreeNode]]) {\n// \u68c0\u67e5\u662f\u5426\u4e3a\u89e3\nif isSolution(state: state) {\nrecordSolution(state: state, res: &amp;res)\nreturn\n}\n// \u904d\u5386\u6240\u6709\u9009\u62e9\nfor choice in choices {\n// \u526a\u679d\uff1a\u68c0\u67e5\u9009\u62e9\u662f\u5426\u5408\u6cd5\nif isValid(state: state, choice: choice) {\n// \u5c1d\u8bd5\uff1a\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\nmakeChoice(state: &amp;state, choice: choice)\n// \u8fdb\u884c\u4e0b\u4e00\u8f6e\u9009\u62e9\nbacktrack(state: &amp;state, choices: [choice.left, choice.right].compactMap { $0 }, res: &amp;res)\n// \u56de\u9000\uff1a\u64a4\u9500\u9009\u62e9\uff0c\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001\nundoChoice(state: &amp;state, choice: choice)\n}\n}\n}\n</code></pre> preorder_traversal_iii_template.zig<pre><code>[class]{}-[func]{isSolution}\n[class]{}-[func]{recordSolution}\n[class]{}-[func]{isValid}\n[class]{}-[func]{makeChoice}\n[class]{}-[func]{undoChoice}\n[class]{}-[func]{backtrack}\n</code></pre> preorder_traversal_iii_template.dart<pre><code>[class]{}-[func]{isSolution}\n[class]{}-[func]{recordSolution}\n[class]{}-[func]{isValid}\n[class]{}-[func]{makeChoice}\n[class]{}-[func]{undoChoice}\n[class]{}-[func]{backtrack}\n</code></pre> <p>\u76f8\u8f83\u4e8e\u57fa\u4e8e\u524d\u5e8f\u904d\u5386\u7684\u5b9e\u73b0\u4ee3\u7801\uff0c\u57fa\u4e8e\u56de\u6eaf\u7b97\u6cd5\u6846\u67b6\u7684\u5b9e\u73b0\u4ee3\u7801\u867d\u7136\u663e\u5f97\u5570\u55e6\uff0c\u4f46\u901a\u7528\u6027\u66f4\u597d\u3002\u5b9e\u9645\u4e0a\uff0c\u6240\u6709\u56de\u6eaf\u95ee\u9898\u90fd\u53ef\u4ee5\u5728\u8be5\u6846\u67b6\u4e0b\u89e3\u51b3\u3002\u6211\u4eec\u9700\u8981\u6839\u636e\u5177\u4f53\u95ee\u9898\u6765\u5b9a\u4e49 <code>state</code> \u548c <code>choices</code> \uff0c\u5e76\u5b9e\u73b0\u6846\u67b6\u4e2d\u7684\u5404\u4e2a\u65b9\u6cd5\u3002</p>"},{"location":"chapter_backtracking/backtracking_algorithm/#1215","title":"12.1.5. \u00a0 \u5178\u578b\u4f8b\u9898","text":"<p>\u641c\u7d22\u95ee\u9898\uff1a\u8fd9\u7c7b\u95ee\u9898\u7684\u76ee\u6807\u662f\u627e\u5230\u6ee1\u8db3\u7279\u5b9a\u6761\u4ef6\u7684\u89e3\u51b3\u65b9\u6848\u3002</p> <ul> <li>\u5168\u6392\u5217\u95ee\u9898\uff1a\u7ed9\u5b9a\u4e00\u4e2a\u96c6\u5408\uff0c\u6c42\u51fa\u5176\u6240\u6709\u53ef\u80fd\u7684\u6392\u5217\u7ec4\u5408\u3002</li> <li>\u5b50\u96c6\u548c\u95ee\u9898\uff1a\u7ed9\u5b9a\u4e00\u4e2a\u96c6\u5408\u548c\u4e00\u4e2a\u76ee\u6807\u548c\uff0c\u627e\u5230\u96c6\u5408\u4e2d\u6240\u6709\u548c\u4e3a\u76ee\u6807\u548c\u7684\u5b50\u96c6\u3002</li> <li>\u6c49\u8bfa\u5854\u95ee\u9898\uff1a\u7ed9\u5b9a\u4e09\u4e2a\u67f1\u5b50\u548c\u4e00\u7cfb\u5217\u5927\u5c0f\u4e0d\u540c\u7684\u5706\u76d8\uff0c\u8981\u6c42\u5c06\u6240\u6709\u5706\u76d8\u4ece\u4e00\u4e2a\u67f1\u5b50\u79fb\u52a8\u5230\u53e6\u4e00\u4e2a\u67f1\u5b50\uff0c\u6bcf\u6b21\u53ea\u80fd\u79fb\u52a8\u4e00\u4e2a\u5706\u76d8\uff0c\u4e14\u4e0d\u80fd\u5c06\u5927\u5706\u76d8\u653e\u5728\u5c0f\u5706\u76d8\u4e0a\u3002</li> </ul> <p>\u7ea6\u675f\u6ee1\u8db3\u95ee\u9898\uff1a\u8fd9\u7c7b\u95ee\u9898\u7684\u76ee\u6807\u662f\u627e\u5230\u6ee1\u8db3\u6240\u6709\u7ea6\u675f\u6761\u4ef6\u7684\u89e3\u3002</p> <ul> <li>\\(n\\) \u7687\u540e\uff1a\u5728 \\(n \\times n\\) \u7684\u68cb\u76d8\u4e0a\u653e\u7f6e \\(n\\) \u4e2a\u7687\u540e\uff0c\u4f7f\u5f97\u5b83\u4eec\u4e92\u4e0d\u653b\u51fb\u3002</li> <li>\u6570\u72ec\uff1a\u5728 \\(9 \\times 9\\) \u7684\u7f51\u683c\u4e2d\u586b\u5165\u6570\u5b57 \\(1\\) ~ \\(9\\) \uff0c\u4f7f\u5f97\u6bcf\u884c\u3001\u6bcf\u5217\u548c\u6bcf\u4e2a \\(3 \\times 3\\) \u5b50\u7f51\u683c\u4e2d\u7684\u6570\u5b57\u4e0d\u91cd\u590d\u3002</li> <li>\u56fe\u7740\u8272\u95ee\u9898\uff1a\u7ed9\u5b9a\u4e00\u4e2a\u65e0\u5411\u56fe\uff0c\u7528\u6700\u5c11\u7684\u989c\u8272\u7ed9\u56fe\u7684\u6bcf\u4e2a\u9876\u70b9\u7740\u8272\uff0c\u4f7f\u5f97\u76f8\u90bb\u9876\u70b9\u989c\u8272\u4e0d\u540c\u3002</li> </ul> <p>\u7ec4\u5408\u4f18\u5316\u95ee\u9898\uff1a\u8fd9\u7c7b\u95ee\u9898\u7684\u76ee\u6807\u662f\u5728\u4e00\u4e2a\u7ec4\u5408\u7a7a\u95f4\u4e2d\u627e\u5230\u6ee1\u8db3\u67d0\u4e9b\u6761\u4ef6\u7684\u6700\u4f18\u89e3\u3002</p> <ul> <li>0-1 \u80cc\u5305\u95ee\u9898\uff1a\u7ed9\u5b9a\u4e00\u7ec4\u7269\u54c1\u548c\u4e00\u4e2a\u80cc\u5305\uff0c\u6bcf\u4e2a\u7269\u54c1\u6709\u4e00\u5b9a\u7684\u4ef7\u503c\u548c\u91cd\u91cf\uff0c\u8981\u6c42\u5728\u80cc\u5305\u5bb9\u91cf\u9650\u5236\u5185\uff0c\u9009\u62e9\u7269\u54c1\u4f7f\u5f97\u603b\u4ef7\u503c\u6700\u5927\u3002</li> <li>\u65c5\u884c\u5546\u95ee\u9898\uff1a\u5728\u4e00\u4e2a\u56fe\u4e2d\uff0c\u4ece\u4e00\u4e2a\u70b9\u51fa\u53d1\uff0c\u8bbf\u95ee\u6240\u6709\u5176\u4ed6\u70b9\u6070\u597d\u4e00\u6b21\u540e\u8fd4\u56de\u8d77\u70b9\uff0c\u6c42\u6700\u77ed\u8def\u5f84\u3002</li> <li>\u6700\u5927\u56e2\u95ee\u9898\uff1a\u7ed9\u5b9a\u4e00\u4e2a\u65e0\u5411\u56fe\uff0c\u627e\u5230\u6700\u5927\u7684\u5b8c\u5168\u5b50\u56fe\uff0c\u5373\u5b50\u56fe\u4e2d\u7684\u4efb\u610f\u4e24\u4e2a\u9876\u70b9\u4e4b\u95f4\u90fd\u6709\u8fb9\u76f8\u8fde\u3002</li> </ul> <p>\u5728\u63a5\u4e0b\u6765\u7684\u7ae0\u8282\u4e2d\uff0c\u6211\u4eec\u5c06\u4e00\u8d77\u653b\u514b\u51e0\u4e2a\u7ecf\u5178\u7684\u56de\u6eaf\u7b97\u6cd5\u95ee\u9898\u3002</p>"},{"location":"chapter_backtracking/n_queens_problem/","title":"12.3. \u00a0 N \u7687\u540e\u95ee\u9898","text":"<p>Question</p> <p>\u6839\u636e\u56fd\u9645\u8c61\u68cb\u7684\u89c4\u5219\uff0c\u7687\u540e\u53ef\u4ee5\u653b\u51fb\u4e0e\u4e4b\u5904\u5728\u540c\u4e00\u884c\u6216\u540c\u4e00\u5217\u6216\u540c\u4e00\u659c\u7ebf\u4e0a\u7684\u68cb\u5b50\u3002\u7ed9\u5b9a \\(n\\) \u4e2a\u7687\u540e\u548c\u4e00\u4e2a \\(n \\times n\\) \u5927\u5c0f\u7684\u68cb\u76d8\uff0c\u5bfb\u627e\u4f7f\u5f97\u6240\u6709\u7687\u540e\u4e4b\u95f4\u65e0\u6cd5\u76f8\u4e92\u653b\u51fb\u7684\u6446\u653e\u65b9\u6848\u3002</p> <p>\u5982\u4e0b\u56fe\u6240\u793a\uff0c\u5f53 \\(n = 4\\) \u65f6\uff0c\u5171\u53ef\u4ee5\u627e\u5230\u4e24\u4e2a\u89e3\u3002\u4ece\u56de\u6eaf\u7b97\u6cd5\u7684\u89d2\u5ea6\u770b\uff0c\\(n \\times n\\) \u5927\u5c0f\u7684\u68cb\u76d8\u5171\u6709 \\(n^2\\) \u4e2a\u683c\u5b50\uff0c\u7ed9\u51fa\u4e86\u6240\u6709\u7684\u9009\u62e9 <code>choices</code> \u3002\u5728\u9010\u4e2a\u653e\u7f6e\u7687\u540e\u7684\u8fc7\u7a0b\u4e2d\uff0c\u68cb\u76d8\u72b6\u6001\u5728\u4e0d\u65ad\u5730\u53d8\u5316\uff0c\u6bcf\u4e2a\u65f6\u523b\u7684\u68cb\u76d8\u5c31\u662f\u72b6\u6001 <code>state</code> \u3002</p> <p></p> <p> Fig. 4 \u7687\u540e\u95ee\u9898\u7684\u89e3 </p> <p>\u672c\u9898\u5171\u6709\u4e09\u4e2a\u7ea6\u675f\u6761\u4ef6\uff1a\u591a\u4e2a\u7687\u540e\u4e0d\u80fd\u5728\u540c\u4e00\u884c\u3001\u540c\u4e00\u5217\u548c\u540c\u4e00\u5bf9\u89d2\u7ebf\u3002\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u5bf9\u89d2\u7ebf\u5206\u4e3a\u4e3b\u5bf9\u89d2\u7ebf <code>\\</code> \u548c\u526f\u5bf9\u89d2\u7ebf <code>/</code> \u4e24\u79cd\u3002</p> <p></p> <p> Fig. n \u7687\u540e\u95ee\u9898\u7684\u7ea6\u675f\u6761\u4ef6 </p> <p>\u7687\u540e\u7684\u6570\u91cf\u548c\u68cb\u76d8\u7684\u884c\u6570\u90fd\u4e3a \\(n\\) \uff0c\u56e0\u6b64\u6211\u4eec\u5bb9\u6613\u5f97\u5230\u7b2c\u4e00\u4e2a\u63a8\u8bba\uff1a\u68cb\u76d8\u6bcf\u884c\u90fd\u5141\u8bb8\u4e14\u53ea\u5141\u8bb8\u653e\u7f6e\u4e00\u4e2a\u7687\u540e\u3002\u8fd9\u610f\u5473\u7740\uff0c\u6211\u4eec\u53ef\u4ee5\u91c7\u53d6\u9010\u884c\u653e\u7f6e\u7b56\u7565\uff1a\u4ece\u7b2c\u4e00\u884c\u5f00\u59cb\uff0c\u5728\u6bcf\u884c\u653e\u7f6e\u4e00\u4e2a\u7687\u540e\uff0c\u76f4\u81f3\u6700\u540e\u4e00\u884c\u7ed3\u675f\u3002\u6b64\u7b56\u7565\u8d77\u5230\u4e86\u526a\u679d\u7684\u4f5c\u7528\uff0c\u5b83\u907f\u514d\u4e86\u540c\u4e00\u884c\u51fa\u73b0\u591a\u4e2a\u7687\u540e\u7684\u6240\u6709\u641c\u7d22\u5206\u652f\u3002</p> <p>\u4e0b\u56fe\u5c55\u793a\u4e86 \\(4\\) \u7687\u540e\u95ee\u9898\u7684\u9010\u884c\u653e\u7f6e\u8fc7\u7a0b\u3002\u53d7\u7bc7\u5e45\u9650\u5236\uff0c\u4e0b\u56fe\u4ec5\u5c55\u5f00\u4e86\u7b2c\u4e00\u884c\u7684\u4e00\u4e2a\u641c\u7d22\u5206\u652f\u3002\u5728\u641c\u7d22\u8fc7\u7a0b\u4e2d\uff0c\u6211\u4eec\u5c06\u4e0d\u6ee1\u8db3\u5217\u7ea6\u675f\u548c\u5bf9\u89d2\u7ebf\u7ea6\u675f\u7684\u65b9\u6848\u90fd\u526a\u679d\u4e86\u3002</p> <p></p> <p> Fig. \u9010\u884c\u653e\u7f6e\u7b56\u7565 </p> <p>\u4e3a\u4e86\u5b9e\u73b0\u6839\u636e\u5217\u7ea6\u675f\u526a\u679d\uff0c\u6211\u4eec\u53ef\u4ee5\u5229\u7528\u4e00\u4e2a\u957f\u5ea6\u4e3a \\(n\\) \u7684\u5e03\u5c14\u578b\u6570\u7ec4 <code>cols</code> \u8bb0\u5f55\u6bcf\u4e00\u5217\u662f\u5426\u6709\u7687\u540e\u3002\u5728\u6bcf\u6b21\u51b3\u5b9a\u653e\u7f6e\u524d\uff0c\u6211\u4eec\u901a\u8fc7 <code>cols</code> \u5c06\u5df2\u6709\u7687\u540e\u7684\u5217\u526a\u679d\uff0c\u5e76\u5728\u56de\u6eaf\u4e2d\u52a8\u6001\u66f4\u65b0 <code>cols</code> \u7684\u72b6\u6001\u3002</p> <p>\u90a3\u4e48\uff0c\u5982\u4f55\u5904\u7406\u5bf9\u89d2\u7ebf\u7ea6\u675f\u5462\uff1f\u8bbe\u68cb\u76d8\u4e2d\u67d0\u4e2a\u683c\u5b50\u7684\u884c\u5217\u7d22\u5f15\u4e3a <code>(row, col)</code> \uff0c\u89c2\u5bdf\u77e9\u9635\u7684\u67d0\u6761\u4e3b\u5bf9\u89d2\u7ebf\uff0c\u6211\u4eec\u53d1\u73b0\u8be5\u5bf9\u89d2\u7ebf\u4e0a\u6240\u6709\u683c\u5b50\u7684\u884c\u7d22\u5f15\u51cf\u5217\u7d22\u5f15\u76f8\u7b49\uff0c\u5373 <code>row - col</code> \u4e3a\u6052\u5b9a\u503c\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u82e5\u4e24\u4e2a\u683c\u5b50\u6ee1\u8db3 <code>row1 - col1 == row2 - col2</code> \uff0c\u5219\u8fd9\u4e24\u4e2a\u683c\u5b50\u4e00\u5b9a\u5904\u5728\u4e00\u6761\u4e3b\u5bf9\u89d2\u7ebf\u4e0a\u3002</p> <p>\u5229\u7528\u8be5\u6027\u8d28\uff0c\u6211\u4eec\u53ef\u4ee5\u501f\u52a9\u4e00\u4e2a\u6570\u7ec4 <code>diag1</code> \u6765\u8bb0\u5f55\u6bcf\u6761\u4e3b\u5bf9\u89d2\u7ebf\u4e0a\u662f\u5426\u6709\u7687\u540e\u3002\u6ce8\u610f\uff0c\\(n\\) \u7ef4\u65b9\u9635 <code>row - col</code> \u7684\u8303\u56f4\u662f \\([-n + 1, n - 1]\\) \uff0c\u56e0\u6b64\u5171\u6709 \\(2n - 1\\) \u6761\u4e3b\u5bf9\u89d2\u7ebf\u3002</p> <p></p> <p> Fig. \u5904\u7406\u5217\u7ea6\u675f\u548c\u5bf9\u89d2\u7ebf\u7ea6\u675f </p> <p>\u540c\u7406\uff0c\u6b21\u5bf9\u89d2\u7ebf\u4e0a\u7684\u6240\u6709\u683c\u5b50\u7684 <code>row + col</code> \u662f\u6052\u5b9a\u503c\u3002\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u540c\u6837\u7684\u65b9\u6cd5\uff0c\u501f\u52a9\u6570\u7ec4 <code>diag2</code> \u6765\u5904\u7406\u6b21\u5bf9\u89d2\u7ebf\u7ea6\u675f\u3002</p> <p>\u6839\u636e\u4ee5\u4e0a\u5206\u6790\uff0c\u6211\u4eec\u4fbf\u53ef\u4ee5\u5199\u51fa \\(n\\) \u7687\u540e\u7684\u89e3\u9898\u4ee3\u7801\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart n_queens.java<pre><code>/* \u56de\u6eaf\u7b97\u6cd5\uff1aN \u7687\u540e */\nvoid backtrack(int row, int n, List&lt;List&lt;String&gt;&gt; state, List&lt;List&lt;List&lt;String&gt;&gt;&gt; res,\nboolean[] cols, boolean[] diags1, boolean[] diags2) {\n// \u5f53\u653e\u7f6e\u5b8c\u6240\u6709\u884c\u65f6\uff0c\u8bb0\u5f55\u89e3\nif (row == n) {\nList&lt;List&lt;String&gt;&gt; copyState = new ArrayList&lt;&gt;();\nfor (List&lt;String&gt; sRow : state) {\ncopyState.add(new ArrayList&lt;&gt;(sRow));\n}\nres.add(copyState);\nreturn;\n}\n// \u904d\u5386\u6240\u6709\u5217\nfor (int col = 0; col &lt; n; col++) {\n// \u8ba1\u7b97\u8be5\u683c\u5b50\u5bf9\u5e94\u7684\u4e3b\u5bf9\u89d2\u7ebf\u548c\u526f\u5bf9\u89d2\u7ebf\nint diag1 = row - col + n - 1;\nint diag2 = row + col;\n// \u526a\u679d\uff1a\u4e0d\u5141\u8bb8\u8be5\u683c\u5b50\u6240\u5728 (\u5217 \u6216 \u4e3b\u5bf9\u89d2\u7ebf \u6216 \u526f\u5bf9\u89d2\u7ebf) \u5305\u542b\u7687\u540e\nif (!(cols[col] || diags1[diag1] || diags2[diag2])) {\n// \u5c1d\u8bd5\uff1a\u5c06\u7687\u540e\u653e\u7f6e\u5728\u8be5\u683c\u5b50\nstate.get(row).set(col, \"Q\");\ncols[col] = diags1[diag1] = diags2[diag2] = true;\n// \u653e\u7f6e\u4e0b\u4e00\u884c\nbacktrack(row + 1, n, state, res, cols, diags1, diags2);\n// \u56de\u9000\uff1a\u5c06\u8be5\u683c\u5b50\u6062\u590d\u4e3a\u7a7a\u4f4d\nstate.get(row).set(col, \"#\");\ncols[col] = diags1[diag1] = diags2[diag2] = false;\n}\n}\n}\n/* \u6c42\u89e3 N \u7687\u540e */\nList&lt;List&lt;List&lt;String&gt;&gt;&gt; nQueens(int n) {\n// \u521d\u59cb\u5316 n*n \u5927\u5c0f\u7684\u68cb\u76d8\uff0c\u5176\u4e2d 'Q' \u4ee3\u8868\u7687\u540e\uff0c'#' \u4ee3\u8868\u7a7a\u4f4d\nList&lt;List&lt;String&gt;&gt; state = new ArrayList&lt;&gt;();\nfor (int i = 0; i &lt; n; i++) {\nList&lt;String&gt; row = new ArrayList&lt;&gt;();\nfor (int j = 0; j &lt; n; j++) {\nrow.add(\"#\");\n}\nstate.add(row);\n}\nboolean[] cols = new boolean[n]; // \u8bb0\u5f55\u5217\u662f\u5426\u6709\u7687\u540e\nboolean[] diags1 = new boolean[2 * n - 1]; // \u8bb0\u5f55\u4e3b\u5bf9\u89d2\u7ebf\u662f\u5426\u6709\u7687\u540e\nboolean[] diags2 = new boolean[2 * n - 1]; // \u8bb0\u5f55\u526f\u5bf9\u89d2\u7ebf\u662f\u5426\u6709\u7687\u540e\nList&lt;List&lt;List&lt;String&gt;&gt;&gt; res = new ArrayList&lt;&gt;();\nbacktrack(0, n, state, res, cols, diags1, diags2);\nreturn res;\n}\n</code></pre> n_queens.cpp<pre><code>/* \u56de\u6eaf\u7b97\u6cd5\uff1aN \u7687\u540e */\nvoid backtrack(int row, int n, vector&lt;vector&lt;string&gt;&gt; &amp;state, vector&lt;vector&lt;vector&lt;string&gt;&gt;&gt; &amp;res, vector&lt;bool&gt; &amp;cols,\nvector&lt;bool&gt; &amp;diags1, vector&lt;bool&gt; &amp;diags2) {\n// \u5f53\u653e\u7f6e\u5b8c\u6240\u6709\u884c\u65f6\uff0c\u8bb0\u5f55\u89e3\nif (row == n) {\nres.push_back(state);\nreturn;\n}\n// \u904d\u5386\u6240\u6709\u5217\nfor (int col = 0; col &lt; n; col++) {\n// \u8ba1\u7b97\u8be5\u683c\u5b50\u5bf9\u5e94\u7684\u4e3b\u5bf9\u89d2\u7ebf\u548c\u526f\u5bf9\u89d2\u7ebf\nint diag1 = row - col + n - 1;\nint diag2 = row + col;\n// \u526a\u679d\uff1a\u4e0d\u5141\u8bb8\u8be5\u683c\u5b50\u6240\u5728 (\u5217 \u6216 \u4e3b\u5bf9\u89d2\u7ebf \u6216 \u526f\u5bf9\u89d2\u7ebf) \u5305\u542b\u7687\u540e\nif (!(cols[col] || diags1[diag1] || diags2[diag2])) {\n// \u5c1d\u8bd5\uff1a\u5c06\u7687\u540e\u653e\u7f6e\u5728\u8be5\u683c\u5b50\nstate[row][col] = \"Q\";\ncols[col] = diags1[diag1] = diags2[diag2] = true;\n// \u653e\u7f6e\u4e0b\u4e00\u884c\nbacktrack(row + 1, n, state, res, cols, diags1, diags2);\n// \u56de\u9000\uff1a\u5c06\u8be5\u683c\u5b50\u6062\u590d\u4e3a\u7a7a\u4f4d\nstate[row][col] = \"#\";\ncols[col] = diags1[diag1] = diags2[diag2] = false;\n}\n}\n}\n/* \u6c42\u89e3 N \u7687\u540e */\nvector&lt;vector&lt;vector&lt;string&gt;&gt;&gt; nQueens(int n) {\n// \u521d\u59cb\u5316 n*n \u5927\u5c0f\u7684\u68cb\u76d8\uff0c\u5176\u4e2d 'Q' \u4ee3\u8868\u7687\u540e\uff0c'#' \u4ee3\u8868\u7a7a\u4f4d\nvector&lt;vector&lt;string&gt;&gt; state(n, vector&lt;string&gt;(n, \"#\"));\nvector&lt;bool&gt; cols(n, false);           // \u8bb0\u5f55\u5217\u662f\u5426\u6709\u7687\u540e\nvector&lt;bool&gt; diags1(2 * n - 1, false); // \u8bb0\u5f55\u4e3b\u5bf9\u89d2\u7ebf\u662f\u5426\u6709\u7687\u540e\nvector&lt;bool&gt; diags2(2 * n - 1, false); // \u8bb0\u5f55\u526f\u5bf9\u89d2\u7ebf\u662f\u5426\u6709\u7687\u540e\nvector&lt;vector&lt;vector&lt;string&gt;&gt;&gt; res;\nbacktrack(0, n, state, res, cols, diags1, diags2);\nreturn res;\n}\n</code></pre> n_queens.py<pre><code>def backtrack(\nrow: int,\nn: int,\nstate: list[list[str]],\nres: list[list[list[str]]],\ncols: list[bool],\ndiags1: list[bool],\ndiags2: list[bool],\n):\n\"\"\"\u56de\u6eaf\u7b97\u6cd5\uff1aN \u7687\u540e\"\"\"\n# \u5f53\u653e\u7f6e\u5b8c\u6240\u6709\u884c\u65f6\uff0c\u8bb0\u5f55\u89e3\nif row == n:\nres.append([list(row) for row in state])\nreturn\n# \u904d\u5386\u6240\u6709\u5217\nfor col in range(n):\n# \u8ba1\u7b97\u8be5\u683c\u5b50\u5bf9\u5e94\u7684\u4e3b\u5bf9\u89d2\u7ebf\u548c\u526f\u5bf9\u89d2\u7ebf\ndiag1 = row - col + n - 1\ndiag2 = row + col\n# \u526a\u679d\uff1a\u4e0d\u5141\u8bb8\u8be5\u683c\u5b50\u6240\u5728 (\u5217 \u6216 \u4e3b\u5bf9\u89d2\u7ebf \u6216 \u526f\u5bf9\u89d2\u7ebf) \u5305\u542b\u7687\u540e\nif not (cols[col] or diags1[diag1] or diags2[diag2]):\n# \u5c1d\u8bd5\uff1a\u5c06\u7687\u540e\u653e\u7f6e\u5728\u8be5\u683c\u5b50\nstate[row][col] = \"Q\"\ncols[col] = diags1[diag1] = diags2[diag2] = True\n# \u653e\u7f6e\u4e0b\u4e00\u884c\nbacktrack(row + 1, n, state, res, cols, diags1, diags2)\n# \u56de\u9000\uff1a\u5c06\u8be5\u683c\u5b50\u6062\u590d\u4e3a\u7a7a\u4f4d\nstate[row][col] = \"#\"\ncols[col] = diags1[diag1] = diags2[diag2] = False\ndef n_queens(n: int) -&gt; list[list[list[str]]]:\n\"\"\"\u6c42\u89e3 N \u7687\u540e\"\"\"\n# \u521d\u59cb\u5316 n*n \u5927\u5c0f\u7684\u68cb\u76d8\uff0c\u5176\u4e2d 'Q' \u4ee3\u8868\u7687\u540e\uff0c'#' \u4ee3\u8868\u7a7a\u4f4d\nstate = [[\"#\" for _ in range(n)] for _ in range(n)]\ncols = [False] * n  # \u8bb0\u5f55\u5217\u662f\u5426\u6709\u7687\u540e\ndiags1 = [False] * (2 * n - 1)  # \u8bb0\u5f55\u4e3b\u5bf9\u89d2\u7ebf\u662f\u5426\u6709\u7687\u540e\ndiags2 = [False] * (2 * n - 1)  # \u8bb0\u5f55\u526f\u5bf9\u89d2\u7ebf\u662f\u5426\u6709\u7687\u540e\nres = []\nbacktrack(0, n, state, res, cols, diags1, diags2)\nreturn res\n</code></pre> n_queens.go<pre><code>/* \u56de\u6eaf\u7b97\u6cd5\uff1aN \u7687\u540e */\nfunc backtrack(row, n int, state *[][]string, res *[][][]string, cols, diags1, diags2 *[]bool) {\n// \u5f53\u653e\u7f6e\u5b8c\u6240\u6709\u884c\u65f6\uff0c\u8bb0\u5f55\u89e3\nif row == n {\nnewState := make([][]string, len(*state))\nfor i, _ := range newState {\nnewState[i] = make([]string, len((*state)[0]))\ncopy(newState[i], (*state)[i])\n}\n*res = append(*res, newState)\n}\n// \u904d\u5386\u6240\u6709\u5217\nfor col := 0; col &lt; n; col++ {\n// \u8ba1\u7b97\u8be5\u683c\u5b50\u5bf9\u5e94\u7684\u4e3b\u5bf9\u89d2\u7ebf\u548c\u526f\u5bf9\u89d2\u7ebf\ndiag1 := row - col + n - 1\ndiag2 := row + col\n// \u526a\u679d\uff1a\u4e0d\u5141\u8bb8\u8be5\u683c\u5b50\u6240\u5728 (\u5217 \u6216 \u4e3b\u5bf9\u89d2\u7ebf \u6216 \u526f\u5bf9\u89d2\u7ebf) \u5305\u542b\u7687\u540e\nif !((*cols)[col] || (*diags1)[diag1] || (*diags2)[diag2]) {\n// \u5c1d\u8bd5\uff1a\u5c06\u7687\u540e\u653e\u7f6e\u5728\u8be5\u683c\u5b50\n(*state)[row][col] = \"Q\"\n(*cols)[col], (*diags1)[diag1], (*diags2)[diag2] = true, true, true\n// \u653e\u7f6e\u4e0b\u4e00\u884c\nbacktrack(row+1, n, state, res, cols, diags1, diags2)\n// \u56de\u9000\uff1a\u5c06\u8be5\u683c\u5b50\u6062\u590d\u4e3a\u7a7a\u4f4d\n(*state)[row][col] = \"#\"\n(*cols)[col], (*diags1)[diag1], (*diags2)[diag2] = false, false, false\n}\n}\n}\n/* \u56de\u6eaf\u7b97\u6cd5\uff1aN \u7687\u540e */\nfunc backtrack(row, n int, state *[][]string, res *[][][]string, cols, diags1, diags2 *[]bool) {\n// \u5f53\u653e\u7f6e\u5b8c\u6240\u6709\u884c\u65f6\uff0c\u8bb0\u5f55\u89e3\nif row == n {\nnewState := make([][]string, len(*state))\nfor i, _ := range newState {\nnewState[i] = make([]string, len((*state)[0]))\ncopy(newState[i], (*state)[i])\n}\n*res = append(*res, newState)\n}\n// \u904d\u5386\u6240\u6709\u5217\nfor col := 0; col &lt; n; col++ {\n// \u8ba1\u7b97\u8be5\u683c\u5b50\u5bf9\u5e94\u7684\u4e3b\u5bf9\u89d2\u7ebf\u548c\u526f\u5bf9\u89d2\u7ebf\ndiag1 := row - col + n - 1\ndiag2 := row + col\n// \u526a\u679d\uff1a\u4e0d\u5141\u8bb8\u8be5\u683c\u5b50\u6240\u5728 (\u5217 \u6216 \u4e3b\u5bf9\u89d2\u7ebf \u6216 \u526f\u5bf9\u89d2\u7ebf) \u5305\u542b\u7687\u540e\nif !((*cols)[col] || (*diags1)[diag1] || (*diags2)[diag2]) {\n// \u5c1d\u8bd5\uff1a\u5c06\u7687\u540e\u653e\u7f6e\u5728\u8be5\u683c\u5b50\n(*state)[row][col] = \"Q\"\n(*cols)[col], (*diags1)[diag1], (*diags2)[diag2] = true, true, true\n// \u653e\u7f6e\u4e0b\u4e00\u884c\nbacktrack(row+1, n, state, res, cols, diags1, diags2)\n// \u56de\u9000\uff1a\u5c06\u8be5\u683c\u5b50\u6062\u590d\u4e3a\u7a7a\u4f4d\n(*state)[row][col] = \"#\"\n(*cols)[col], (*diags1)[diag1], (*diags2)[diag2] = false, false, false\n}\n}\n}\nfunc nQueens(n int) [][][]string {\n// \u521d\u59cb\u5316 n*n \u5927\u5c0f\u7684\u68cb\u76d8\uff0c\u5176\u4e2d 'Q' \u4ee3\u8868\u7687\u540e\uff0c'#' \u4ee3\u8868\u7a7a\u4f4d\nstate := make([][]string, n)\nfor i := 0; i &lt; n; i++ {\nrow := make([]string, n)\nfor i := 0; i &lt; n; i++ {\nrow[i] = \"#\"\n}\nstate[i] = row\n}\n// \u8bb0\u5f55\u5217\u662f\u5426\u6709\u7687\u540e\ncols := make([]bool, n)\ndiags1 := make([]bool, 2*n-1)\ndiags2 := make([]bool, 2*n-1)\nres := make([][][]string, 0)\nbacktrack(0, n, &amp;state, &amp;res, &amp;cols, &amp;diags1, &amp;diags2)\nreturn res\n}\n</code></pre> n_queens.js<pre><code>/* \u56de\u6eaf\u7b97\u6cd5\uff1aN \u7687\u540e */\nfunction backtrack(row, n, state, res, cols, diags1, diags2) {\n// \u5f53\u653e\u7f6e\u5b8c\u6240\u6709\u884c\u65f6\uff0c\u8bb0\u5f55\u89e3\nif (row === n) {\nres.push(state.map((row) =&gt; row.slice()));\nreturn;\n}\n// \u904d\u5386\u6240\u6709\u5217\nfor (let col = 0; col &lt; n; col++) {\n// \u8ba1\u7b97\u8be5\u683c\u5b50\u5bf9\u5e94\u7684\u4e3b\u5bf9\u89d2\u7ebf\u548c\u526f\u5bf9\u89d2\u7ebf\nconst diag1 = row - col + n - 1;\nconst diag2 = row + col;\n// \u526a\u679d\uff1a\u4e0d\u5141\u8bb8\u8be5\u683c\u5b50\u6240\u5728 (\u5217 \u6216 \u4e3b\u5bf9\u89d2\u7ebf \u6216 \u526f\u5bf9\u89d2\u7ebf) \u5305\u542b\u7687\u540e\nif (!(cols[col] || diags1[diag1] || diags2[diag2])) {\n// \u5c1d\u8bd5\uff1a\u5c06\u7687\u540e\u653e\u7f6e\u5728\u8be5\u683c\u5b50\nstate[row][col] = 'Q';\ncols[col] = diags1[diag1] = diags2[diag2] = true;\n// \u653e\u7f6e\u4e0b\u4e00\u884c\nbacktrack(row + 1, n, state, res, cols, diags1, diags2);\n// \u56de\u9000\uff1a\u5c06\u8be5\u683c\u5b50\u6062\u590d\u4e3a\u7a7a\u4f4d\nstate[row][col] = '#';\ncols[col] = diags1[diag1] = diags2[diag2] = false;\n}\n}\n}\n/* \u6c42\u89e3 N \u7687\u540e */\nfunction nQueens(n) {\n// \u521d\u59cb\u5316 n*n \u5927\u5c0f\u7684\u68cb\u76d8\uff0c\u5176\u4e2d 'Q' \u4ee3\u8868\u7687\u540e\uff0c'#' \u4ee3\u8868\u7a7a\u4f4d\nconst state = Array.from({ length: n }, () =&gt; Array(n).fill('#'));\nconst cols = Array(n).fill(false); // \u8bb0\u5f55\u5217\u662f\u5426\u6709\u7687\u540e\nconst diags1 = Array(2 * n - 1).fill(false); // \u8bb0\u5f55\u4e3b\u5bf9\u89d2\u7ebf\u662f\u5426\u6709\u7687\u540e\nconst diags2 = Array(2 * n - 1).fill(false); // \u8bb0\u5f55\u526f\u5bf9\u89d2\u7ebf\u662f\u5426\u6709\u7687\u540e\nconst res = [];\nbacktrack(0, n, state, res, cols, diags1, diags2);\nreturn res;\n}\n</code></pre> n_queens.ts<pre><code>/* \u56de\u6eaf\u7b97\u6cd5\uff1aN \u7687\u540e */\nfunction backtrack(\nrow: number,\nn: number,\nstate: string[][],\nres: string[][][],\ncols: boolean[],\ndiags1: boolean[],\ndiags2: boolean[]\n): void {\n// \u5f53\u653e\u7f6e\u5b8c\u6240\u6709\u884c\u65f6\uff0c\u8bb0\u5f55\u89e3\nif (row === n) {\nres.push(state.map((row) =&gt; row.slice()));\nreturn;\n}\n// \u904d\u5386\u6240\u6709\u5217\nfor (let col = 0; col &lt; n; col++) {\n// \u8ba1\u7b97\u8be5\u683c\u5b50\u5bf9\u5e94\u7684\u4e3b\u5bf9\u89d2\u7ebf\u548c\u526f\u5bf9\u89d2\u7ebf\nconst diag1 = row - col + n - 1;\nconst diag2 = row + col;\n// \u526a\u679d\uff1a\u4e0d\u5141\u8bb8\u8be5\u683c\u5b50\u6240\u5728 (\u5217 \u6216 \u4e3b\u5bf9\u89d2\u7ebf \u6216 \u526f\u5bf9\u89d2\u7ebf) \u5305\u542b\u7687\u540e\nif (!(cols[col] || diags1[diag1] || diags2[diag2])) {\n// \u5c1d\u8bd5\uff1a\u5c06\u7687\u540e\u653e\u7f6e\u5728\u8be5\u683c\u5b50\nstate[row][col] = 'Q';\ncols[col] = diags1[diag1] = diags2[diag2] = true;\n// \u653e\u7f6e\u4e0b\u4e00\u884c\nbacktrack(row + 1, n, state, res, cols, diags1, diags2);\n// \u56de\u9000\uff1a\u5c06\u8be5\u683c\u5b50\u6062\u590d\u4e3a\u7a7a\u4f4d\nstate[row][col] = '#';\ncols[col] = diags1[diag1] = diags2[diag2] = false;\n}\n}\n}\n/* \u6c42\u89e3 N \u7687\u540e */\nfunction nQueens(n: number): string[][][] {\n// \u521d\u59cb\u5316 n*n \u5927\u5c0f\u7684\u68cb\u76d8\uff0c\u5176\u4e2d 'Q' \u4ee3\u8868\u7687\u540e\uff0c'#' \u4ee3\u8868\u7a7a\u4f4d\nconst state = Array.from({ length: n }, () =&gt; Array(n).fill('#'));\nconst cols = Array(n).fill(false); // \u8bb0\u5f55\u5217\u662f\u5426\u6709\u7687\u540e\nconst diags1 = Array(2 * n - 1).fill(false); // \u8bb0\u5f55\u4e3b\u5bf9\u89d2\u7ebf\u662f\u5426\u6709\u7687\u540e\nconst diags2 = Array(2 * n - 1).fill(false); // \u8bb0\u5f55\u526f\u5bf9\u89d2\u7ebf\u662f\u5426\u6709\u7687\u540e\nconst res: string[][][] = [];\nbacktrack(0, n, state, res, cols, diags1, diags2);\nreturn res;\n}\n</code></pre> n_queens.c<pre><code>[class]{}-[func]{backtrack}\n[class]{}-[func]{nQueens}\n</code></pre> n_queens.cs<pre><code>/* \u56de\u6eaf\u7b97\u6cd5\uff1aN \u7687\u540e */\nvoid backtrack(int row, int n, List&lt;List&lt;string&gt;&gt; state, List&lt;List&lt;List&lt;string&gt;&gt;&gt; res,\nbool[] cols, bool[] diags1, bool[] diags2) {\n// \u5f53\u653e\u7f6e\u5b8c\u6240\u6709\u884c\u65f6\uff0c\u8bb0\u5f55\u89e3\nif (row == n) {\nList&lt;List&lt;string&gt;&gt; copyState = new List&lt;List&lt;string&gt;&gt;();\nforeach (List&lt;string&gt; sRow in state) {\ncopyState.Add(new List&lt;string&gt;(sRow));\n}\nres.Add(copyState);\nreturn;\n}\n// \u904d\u5386\u6240\u6709\u5217\nfor (int col = 0; col &lt; n; col++) {\n// \u8ba1\u7b97\u8be5\u683c\u5b50\u5bf9\u5e94\u7684\u4e3b\u5bf9\u89d2\u7ebf\u548c\u526f\u5bf9\u89d2\u7ebf\nint diag1 = row - col + n - 1;\nint diag2 = row + col;\n// \u526a\u679d\uff1a\u4e0d\u5141\u8bb8\u8be5\u683c\u5b50\u6240\u5728 (\u5217 \u6216 \u4e3b\u5bf9\u89d2\u7ebf \u6216 \u526f\u5bf9\u89d2\u7ebf) \u5305\u542b\u7687\u540e\nif (!(cols[col] || diags1[diag1] || diags2[diag2])) {\n// \u5c1d\u8bd5\uff1a\u5c06\u7687\u540e\u653e\u7f6e\u5728\u8be5\u683c\u5b50\nstate[row][col] = \"Q\";\ncols[col] = diags1[diag1] = diags2[diag2] = true;\n// \u653e\u7f6e\u4e0b\u4e00\u884c\nbacktrack(row + 1, n, state, res, cols, diags1, diags2);\n// \u56de\u9000\uff1a\u5c06\u8be5\u683c\u5b50\u6062\u590d\u4e3a\u7a7a\u4f4d\nstate[row][col] = \"#\";\ncols[col] = diags1[diag1] = diags2[diag2] = false;\n}\n}\n}\n/* \u6c42\u89e3 N \u7687\u540e */\nList&lt;List&lt;List&lt;string&gt;&gt;&gt; nQueens(int n) {\n// \u521d\u59cb\u5316 n*n \u5927\u5c0f\u7684\u68cb\u76d8\uff0c\u5176\u4e2d 'Q' \u4ee3\u8868\u7687\u540e\uff0c'#' \u4ee3\u8868\u7a7a\u4f4d\nList&lt;List&lt;string&gt;&gt; state = new List&lt;List&lt;string&gt;&gt;();\nfor (int i = 0; i &lt; n; i++) {\nList&lt;string&gt; row = new List&lt;string&gt;();\nfor (int j = 0; j &lt; n; j++) {\nrow.Add(\"#\");\n}\nstate.Add(row);\n}\nbool[] cols = new bool[n]; // \u8bb0\u5f55\u5217\u662f\u5426\u6709\u7687\u540e\nbool[] diags1 = new bool[2 * n - 1]; // \u8bb0\u5f55\u4e3b\u5bf9\u89d2\u7ebf\u662f\u5426\u6709\u7687\u540e\nbool[] diags2 = new bool[2 * n - 1]; // \u8bb0\u5f55\u526f\u5bf9\u89d2\u7ebf\u662f\u5426\u6709\u7687\u540e\nList&lt;List&lt;List&lt;string&gt;&gt;&gt; res = new List&lt;List&lt;List&lt;string&gt;&gt;&gt;();\nbacktrack(0, n, state, res, cols, diags1, diags2);\nreturn res;\n}\n</code></pre> n_queens.swift<pre><code>/* \u56de\u6eaf\u7b97\u6cd5\uff1aN \u7687\u540e */\nfunc backtrack(row: Int, n: Int, state: inout [[String]], res: inout [[[String]]], cols: inout [Bool], diags1: inout [Bool], diags2: inout [Bool]) {\n// \u5f53\u653e\u7f6e\u5b8c\u6240\u6709\u884c\u65f6\uff0c\u8bb0\u5f55\u89e3\nif row == n {\nres.append(state)\nreturn\n}\n// \u904d\u5386\u6240\u6709\u5217\nfor col in 0 ..&lt; n {\n// \u8ba1\u7b97\u8be5\u683c\u5b50\u5bf9\u5e94\u7684\u4e3b\u5bf9\u89d2\u7ebf\u548c\u526f\u5bf9\u89d2\u7ebf\nlet diag1 = row - col + n - 1\nlet diag2 = row + col\n// \u526a\u679d\uff1a\u4e0d\u5141\u8bb8\u8be5\u683c\u5b50\u6240\u5728 (\u5217 \u6216 \u4e3b\u5bf9\u89d2\u7ebf \u6216 \u526f\u5bf9\u89d2\u7ebf) \u5305\u542b\u7687\u540e\nif !(cols[col] || diags1[diag1] || diags2[diag2]) {\n// \u5c1d\u8bd5\uff1a\u5c06\u7687\u540e\u653e\u7f6e\u5728\u8be5\u683c\u5b50\nstate[row][col] = \"Q\"\ncols[col] = true\ndiags1[diag1] = true\ndiags2[diag2] = true\n// \u653e\u7f6e\u4e0b\u4e00\u884c\nbacktrack(row: row + 1, n: n, state: &amp;state, res: &amp;res, cols: &amp;cols, diags1: &amp;diags1, diags2: &amp;diags2)\n// \u56de\u9000\uff1a\u5c06\u8be5\u683c\u5b50\u6062\u590d\u4e3a\u7a7a\u4f4d\nstate[row][col] = \"#\"\ncols[col] = false\ndiags1[diag1] = false\ndiags2[diag2] = false\n}\n}\n}\n/* \u6c42\u89e3 N \u7687\u540e */\nfunc nQueens(n: Int) -&gt; [[[String]]] {\n// \u521d\u59cb\u5316 n*n \u5927\u5c0f\u7684\u68cb\u76d8\uff0c\u5176\u4e2d 'Q' \u4ee3\u8868\u7687\u540e\uff0c'#' \u4ee3\u8868\u7a7a\u4f4d\nvar state = Array(repeating: Array(repeating: \"#\", count: n), count: n)\nvar cols = Array(repeating: false, count: n) // \u8bb0\u5f55\u5217\u662f\u5426\u6709\u7687\u540e\nvar diags1 = Array(repeating: false, count: 2 * n - 1) // \u8bb0\u5f55\u4e3b\u5bf9\u89d2\u7ebf\u662f\u5426\u6709\u7687\u540e\nvar diags2 = Array(repeating: false, count: 2 * n - 1) // \u8bb0\u5f55\u526f\u5bf9\u89d2\u7ebf\u662f\u5426\u6709\u7687\u540e\nvar res: [[[String]]] = []\nbacktrack(row: 0, n: n, state: &amp;state, res: &amp;res, cols: &amp;cols, diags1: &amp;diags1, diags2: &amp;diags2)\nreturn res\n}\n</code></pre> n_queens.zig<pre><code>[class]{}-[func]{backtrack}\n[class]{}-[func]{nQueens}\n</code></pre> n_queens.dart<pre><code>[class]{}-[func]{backtrack}\n[class]{}-[func]{nQueens}\n</code></pre>"},{"location":"chapter_backtracking/n_queens_problem/#1231","title":"12.3.1. \u00a0 \u590d\u6742\u5ea6\u5206\u6790","text":"<p>\u9010\u884c\u653e\u7f6e \\(n\\) \u6b21\uff0c\u8003\u8651\u5217\u7ea6\u675f\uff0c\u5219\u4ece\u7b2c\u4e00\u884c\u5230\u6700\u540e\u4e00\u884c\u5206\u522b\u6709 \\(n, n-1, \\cdots, 2, 1\\) \u4e2a\u9009\u62e9\uff0c\u56e0\u6b64\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(n!)\\) \u3002\u5b9e\u9645\u4e0a\uff0c\u6839\u636e\u5bf9\u89d2\u7ebf\u7ea6\u675f\u7684\u526a\u679d\u4e5f\u80fd\u591f\u5927\u5e45\u5730\u7f29\u5c0f\u641c\u7d22\u7a7a\u95f4\uff0c\u56e0\u800c\u641c\u7d22\u6548\u7387\u5f80\u5f80\u4f18\u4e8e\u4ee5\u4e0a\u65f6\u95f4\u590d\u6742\u5ea6\u3002</p> <p><code>state</code> \u4f7f\u7528 \\(O(n^2)\\) \u7a7a\u95f4\uff0c<code>cols</code> , <code>diags1</code> , <code>diags2</code> \u7686\u4f7f\u7528 \\(O(n)\\) \u7a7a\u95f4\u3002\u6700\u5927\u9012\u5f52\u6df1\u5ea6\u4e3a \\(n\\) \uff0c\u4f7f\u7528 \\(O(n)\\) \u6808\u5e27\u7a7a\u95f4\u3002\u56e0\u6b64\uff0c\u7a7a\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(n^2)\\) \u3002</p>"},{"location":"chapter_backtracking/permutations_problem/","title":"12.2. \u00a0 \u5168\u6392\u5217\u95ee\u9898","text":"<p>\u5168\u6392\u5217\u95ee\u9898\u662f\u56de\u6eaf\u7b97\u6cd5\u7684\u4e00\u4e2a\u5178\u578b\u5e94\u7528\u3002\u5b83\u7684\u5b9a\u4e49\u662f\u5728\u7ed9\u5b9a\u4e00\u4e2a\u96c6\u5408\uff08\u5982\u4e00\u4e2a\u6570\u7ec4\u6216\u5b57\u7b26\u4e32\uff09\u7684\u60c5\u51b5\u4e0b\uff0c\u627e\u51fa\u8fd9\u4e2a\u96c6\u5408\u4e2d\u5143\u7d20\u7684\u6240\u6709\u53ef\u80fd\u7684\u6392\u5217\u3002</p> <p>\u5982\u4e0b\u8868\u6240\u793a\uff0c\u5217\u4e3e\u4e86\u51e0\u4e2a\u793a\u4f8b\u6570\u7ec4\u548c\u5176\u5bf9\u5e94\u7684\u6240\u6709\u6392\u5217\u3002</p> \u8f93\u5165\u6570\u7ec4 \u6240\u6709\u6392\u5217 \\([1]\\) \\([1]\\) \\([1, 2]\\) \\([1, 2], [2, 1]\\) \\([1, 2, 3]\\) \\([1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2], [3, 2, 1]\\)"},{"location":"chapter_backtracking/permutations_problem/#1221","title":"12.2.1. \u00a0 \u65e0\u91cd\u590d\u7684\u60c5\u51b5","text":"<p>Question</p> <p>\u8f93\u5165\u4e00\u4e2a\u6574\u6570\u6570\u7ec4\uff0c\u6570\u7ec4\u4e2d\u4e0d\u5305\u542b\u91cd\u590d\u5143\u7d20\uff0c\u8fd4\u56de\u6240\u6709\u53ef\u80fd\u7684\u6392\u5217\u3002</p> <p>\u4ece\u56de\u6eaf\u7b97\u6cd5\u7684\u89d2\u5ea6\u770b\uff0c\u6211\u4eec\u53ef\u4ee5\u628a\u751f\u6210\u6392\u5217\u7684\u8fc7\u7a0b\u60f3\u8c61\u6210\u4e00\u7cfb\u5217\u9009\u62e9\u7684\u7ed3\u679c\u3002\u5047\u8bbe\u8f93\u5165\u6570\u7ec4\u4e3a \\([1, 2, 3]\\) \uff0c\u5982\u679c\u6211\u4eec\u5148\u9009\u62e9 \\(1\\) \u3001\u518d\u9009\u62e9 \\(3\\) \u3001\u6700\u540e\u9009\u62e9 \\(2\\) \uff0c\u5219\u83b7\u5f97\u6392\u5217 \\([1, 3, 2]\\) \u3002\u56de\u9000\u8868\u793a\u64a4\u9500\u4e00\u4e2a\u9009\u62e9\uff0c\u4e4b\u540e\u7ee7\u7eed\u5c1d\u8bd5\u5176\u4ed6\u9009\u62e9\u3002</p> <p>\u4ece\u56de\u6eaf\u7b97\u6cd5\u4ee3\u7801\u7684\u89d2\u5ea6\u770b\uff0c\u5019\u9009\u96c6\u5408 <code>choices</code> \u662f\u8f93\u5165\u6570\u7ec4\u4e2d\u7684\u6240\u6709\u5143\u7d20\uff0c\u72b6\u6001 <code>state</code> \u662f\u76f4\u81f3\u76ee\u524d\u5df2\u88ab\u9009\u62e9\u7684\u5143\u7d20\u3002\u6ce8\u610f\uff0c\u6bcf\u4e2a\u5143\u7d20\u53ea\u5141\u8bb8\u88ab\u9009\u62e9\u4e00\u6b21\uff0c\u56e0\u6b64\u5728\u904d\u5386\u9009\u62e9\u65f6\uff0c\u5e94\u5f53\u6392\u9664\u5df2\u7ecf\u9009\u62e9\u8fc7\u7684\u5143\u7d20\u3002</p> <p>\u5982\u4e0b\u56fe\u6240\u793a\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u641c\u7d22\u8fc7\u7a0b\u5c55\u5f00\u6210\u4e00\u4e2a\u9012\u5f52\u6811\uff0c\u6811\u4e2d\u7684\u6bcf\u4e2a\u8282\u70b9\u4ee3\u8868\u5f53\u524d\u72b6\u6001 <code>state</code> \u3002\u4ece\u6839\u8282\u70b9\u5f00\u59cb\uff0c\u7ecf\u8fc7\u4e09\u8f6e\u9009\u62e9\u540e\u5230\u8fbe\u53f6\u8282\u70b9\uff0c\u6bcf\u4e2a\u53f6\u8282\u70b9\u90fd\u5bf9\u5e94\u4e00\u4e2a\u6392\u5217\u3002</p> <p></p> <p> Fig. \u5168\u6392\u5217\u7684\u9012\u5f52\u6811 </p> <p>\u60f3\u6e05\u695a\u4ee5\u4e0a\u4fe1\u606f\u4e4b\u540e\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u5728\u6846\u67b6\u4ee3\u7801\u4e2d\u505a\u201c\u5b8c\u5f62\u586b\u7a7a\u201d\u4e86\u3002\u4e3a\u4e86\u7f29\u77ed\u4ee3\u7801\u884c\u6570\uff0c\u6211\u4eec\u4e0d\u5355\u72ec\u5b9e\u73b0\u6846\u67b6\u4ee3\u7801\u4e2d\u7684\u5404\u4e2a\u51fd\u6570\uff0c\u800c\u662f\u5c06\u4ed6\u4eec\u5c55\u5f00\u5728 <code>backtrack()</code> \u51fd\u6570\u4e2d\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart permutations_i.java<pre><code>/* \u56de\u6eaf\u7b97\u6cd5\uff1a\u5168\u6392\u5217 I */\nvoid backtrack(List&lt;Integer&gt; state, int[] choices, boolean[] selected, List&lt;List&lt;Integer&gt;&gt; res) {\n// \u5f53\u72b6\u6001\u957f\u5ea6\u7b49\u4e8e\u5143\u7d20\u6570\u91cf\u65f6\uff0c\u8bb0\u5f55\u89e3\nif (state.size() == choices.length) {\nres.add(new ArrayList&lt;Integer&gt;(state));\nreturn;\n}\n// \u904d\u5386\u6240\u6709\u9009\u62e9\nfor (int i = 0; i &lt; choices.length; i++) {\nint choice = choices[i];\n// \u526a\u679d\uff1a\u4e0d\u5141\u8bb8\u91cd\u590d\u9009\u62e9\u5143\u7d20 \u4e14 \u4e0d\u5141\u8bb8\u91cd\u590d\u9009\u62e9\u76f8\u7b49\u5143\u7d20\nif (!selected[i]) {\n// \u5c1d\u8bd5\uff1a\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\nselected[i] = true;\nstate.add(choice);\n// \u8fdb\u884c\u4e0b\u4e00\u8f6e\u9009\u62e9\nbacktrack(state, choices, selected, res);\n// \u56de\u9000\uff1a\u64a4\u9500\u9009\u62e9\uff0c\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001\nselected[i] = false;\nstate.remove(state.size() - 1);\n}\n}\n}\n/* \u5168\u6392\u5217 I */\nList&lt;List&lt;Integer&gt;&gt; permutationsI(int[] nums) {\nList&lt;List&lt;Integer&gt;&gt; res = new ArrayList&lt;List&lt;Integer&gt;&gt;();\nbacktrack(new ArrayList&lt;Integer&gt;(), nums, new boolean[nums.length], res);\nreturn res;\n}\n</code></pre> permutations_i.cpp<pre><code>/* \u56de\u6eaf\u7b97\u6cd5\uff1a\u5168\u6392\u5217 I */\nvoid backtrack(vector&lt;int&gt; &amp;state, const vector&lt;int&gt; &amp;choices, vector&lt;bool&gt; &amp;selected, vector&lt;vector&lt;int&gt;&gt; &amp;res) {\n// \u5f53\u72b6\u6001\u957f\u5ea6\u7b49\u4e8e\u5143\u7d20\u6570\u91cf\u65f6\uff0c\u8bb0\u5f55\u89e3\nif (state.size() == choices.size()) {\nres.push_back(state);\nreturn;\n}\n// \u904d\u5386\u6240\u6709\u9009\u62e9\nfor (int i = 0; i &lt; choices.size(); i++) {\nint choice = choices[i];\n// \u526a\u679d\uff1a\u4e0d\u5141\u8bb8\u91cd\u590d\u9009\u62e9\u5143\u7d20 \u4e14 \u4e0d\u5141\u8bb8\u91cd\u590d\u9009\u62e9\u76f8\u7b49\u5143\u7d20\nif (!selected[i]) {\n// \u5c1d\u8bd5\uff1a\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\nselected[i] = true;\nstate.push_back(choice);\n// \u8fdb\u884c\u4e0b\u4e00\u8f6e\u9009\u62e9\nbacktrack(state, choices, selected, res);\n// \u56de\u9000\uff1a\u64a4\u9500\u9009\u62e9\uff0c\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001\nselected[i] = false;\nstate.pop_back();\n}\n}\n}\n/* \u5168\u6392\u5217 I */\nvector&lt;vector&lt;int&gt;&gt; permutationsI(vector&lt;int&gt; nums) {\nvector&lt;int&gt; state;\nvector&lt;bool&gt; selected(nums.size(), false);\nvector&lt;vector&lt;int&gt;&gt; res;\nbacktrack(state, nums, selected, res);\nreturn res;\n}\n</code></pre> permutations_i.py<pre><code>def backtrack(\nstate: list[int], choices: list[int], selected: list[bool], res: list[list[int]]\n):\n\"\"\"\u56de\u6eaf\u7b97\u6cd5\uff1a\u5168\u6392\u5217 I\"\"\"\n# \u5f53\u72b6\u6001\u957f\u5ea6\u7b49\u4e8e\u5143\u7d20\u6570\u91cf\u65f6\uff0c\u8bb0\u5f55\u89e3\nif len(state) == len(choices):\nres.append(list(state))\nreturn\n# \u904d\u5386\u6240\u6709\u9009\u62e9\nfor i, choice in enumerate(choices):\n# \u526a\u679d\uff1a\u4e0d\u5141\u8bb8\u91cd\u590d\u9009\u62e9\u5143\u7d20\nif not selected[i]:\n# \u5c1d\u8bd5\uff1a\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\nselected[i] = True\nstate.append(choice)\n# \u8fdb\u884c\u4e0b\u4e00\u8f6e\u9009\u62e9\nbacktrack(state, choices, selected, res)\n# \u56de\u9000\uff1a\u64a4\u9500\u9009\u62e9\uff0c\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001\nselected[i] = False\nstate.pop()\ndef permutations_i(nums: list[int]) -&gt; list[list[int]]:\n\"\"\"\u5168\u6392\u5217 I\"\"\"\nres = []\nbacktrack(state=[], choices=nums, selected=[False] * len(nums), res=res)\nreturn res\n</code></pre> permutations_i.go<pre><code>/* \u56de\u6eaf\u7b97\u6cd5\uff1a\u5168\u6392\u5217 I */\nfunc backtrackI(state *[]int, choices *[]int, selected *[]bool, res *[][]int) {\n// \u5f53\u72b6\u6001\u957f\u5ea6\u7b49\u4e8e\u5143\u7d20\u6570\u91cf\u65f6\uff0c\u8bb0\u5f55\u89e3\nif len(*state) == len(*choices) {\nnewState := append([]int{}, *state...)\n*res = append(*res, newState)\n}\n// \u904d\u5386\u6240\u6709\u9009\u62e9\nfor i := 0; i &lt; len(*choices); i++ {\nchoice := (*choices)[i]\n// \u526a\u679d\uff1a\u4e0d\u5141\u8bb8\u91cd\u590d\u9009\u62e9\u5143\u7d20 \u4e14 \u4e0d\u5141\u8bb8\u91cd\u590d\u9009\u62e9\u76f8\u7b49\u5143\u7d20\nif !(*selected)[i] {\n// \u5c1d\u8bd5\uff1a\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\n(*selected)[i] = true\n*state = append(*state, choice)\n// \u8fdb\u884c\u4e0b\u4e00\u8f6e\u9009\u62e9\nbacktrackI(state, choices, selected, res)\n// \u56de\u9000\uff1a\u64a4\u9500\u9009\u62e9\uff0c\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001\n(*selected)[i] = false\n*state = (*state)[:len(*state)-1]\n}\n}\n}\n/* \u5168\u6392\u5217 I */\nfunc permutationsI(nums []int) [][]int {\nres := make([][]int, 0)\nstate := make([]int, 0)\nselected := make([]bool, len(nums))\nbacktrackI(&amp;state, &amp;nums, &amp;selected, &amp;res)\nreturn res\n}\n</code></pre> permutations_i.js<pre><code>/* \u56de\u6eaf\u7b97\u6cd5\uff1a\u5168\u6392\u5217 I */\nfunction backtrack(state, choices, selected, res) {\n// \u5f53\u72b6\u6001\u957f\u5ea6\u7b49\u4e8e\u5143\u7d20\u6570\u91cf\u65f6\uff0c\u8bb0\u5f55\u89e3\nif (state.length === choices.length) {\nres.push([...state]);\nreturn;\n}\n// \u904d\u5386\u6240\u6709\u9009\u62e9\nchoices.forEach((choice, i) =&gt; {\n// \u526a\u679d\uff1a\u4e0d\u5141\u8bb8\u91cd\u590d\u9009\u62e9\u5143\u7d20 \u4e14 \u4e0d\u5141\u8bb8\u91cd\u590d\u9009\u62e9\u76f8\u7b49\u5143\u7d20\nif (!selected[i]) {\n// \u5c1d\u8bd5\uff1a\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\nselected[i] = true;\nstate.push(choice);\n// \u8fdb\u884c\u4e0b\u4e00\u8f6e\u9009\u62e9\nbacktrack(state, choices, selected, res);\n// \u56de\u9000\uff1a\u64a4\u9500\u9009\u62e9\uff0c\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001\nselected[i] = false;\nstate.pop();\n}\n});\n}\n/* \u5168\u6392\u5217 I */\nfunction permutationsI(nums) {\nconst res = [];\nbacktrack([], nums, Array(nums.length).fill(false), res);\nreturn res;\n}\n</code></pre> permutations_i.ts<pre><code>/* \u56de\u6eaf\u7b97\u6cd5\uff1a\u5168\u6392\u5217 I */\nfunction backtrack(\nstate: number[],\nchoices: number[],\nselected: boolean[],\nres: number[][]\n): void {\n// \u5f53\u72b6\u6001\u957f\u5ea6\u7b49\u4e8e\u5143\u7d20\u6570\u91cf\u65f6\uff0c\u8bb0\u5f55\u89e3\nif (state.length === choices.length) {\nres.push([...state]);\nreturn;\n}\n// \u904d\u5386\u6240\u6709\u9009\u62e9\nchoices.forEach((choice, i) =&gt; {\n// \u526a\u679d\uff1a\u4e0d\u5141\u8bb8\u91cd\u590d\u9009\u62e9\u5143\u7d20 \u4e14 \u4e0d\u5141\u8bb8\u91cd\u590d\u9009\u62e9\u76f8\u7b49\u5143\u7d20\nif (!selected[i]) {\n// \u5c1d\u8bd5\uff1a\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\nselected[i] = true;\nstate.push(choice);\n// \u8fdb\u884c\u4e0b\u4e00\u8f6e\u9009\u62e9\nbacktrack(state, choices, selected, res);\n// \u56de\u9000\uff1a\u64a4\u9500\u9009\u62e9\uff0c\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001\nselected[i] = false;\nstate.pop();\n}\n});\n}\n/* \u5168\u6392\u5217 I */\nfunction permutationsI(nums: number[]): number[][] {\nconst res: number[][] = [];\nbacktrack([], nums, Array(nums.length).fill(false), res);\nreturn res;\n}\n</code></pre> permutations_i.c<pre><code>[class]{}-[func]{backtrack}\n[class]{}-[func]{permutationsI}\n</code></pre> permutations_i.cs<pre><code>/* \u56de\u6eaf\u7b97\u6cd5\uff1a\u5168\u6392\u5217 I */\nvoid backtrack(List&lt;int&gt; state, int[] choices, bool[] selected, List&lt;List&lt;int&gt;&gt; res) {\n// \u5f53\u72b6\u6001\u957f\u5ea6\u7b49\u4e8e\u5143\u7d20\u6570\u91cf\u65f6\uff0c\u8bb0\u5f55\u89e3\nif (state.Count == choices.Length) {\nres.Add(new List&lt;int&gt;(state));\nreturn;\n}\n// \u904d\u5386\u6240\u6709\u9009\u62e9\nfor (int i = 0; i &lt; choices.Length; i++) {\nint choice = choices[i];\n// \u526a\u679d\uff1a\u4e0d\u5141\u8bb8\u91cd\u590d\u9009\u62e9\u5143\u7d20 \u4e14 \u4e0d\u5141\u8bb8\u91cd\u590d\u9009\u62e9\u76f8\u7b49\u5143\u7d20\nif (!selected[i]) {\n// \u5c1d\u8bd5\uff1a\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\nselected[i] = true;\nstate.Add(choice);\n// \u8fdb\u884c\u4e0b\u4e00\u8f6e\u9009\u62e9\nbacktrack(state, choices, selected, res);\n// \u56de\u9000\uff1a\u64a4\u9500\u9009\u62e9\uff0c\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001\nselected[i] = false;\nstate.RemoveAt(state.Count - 1);\n}\n}\n}\n/* \u5168\u6392\u5217 I */\nList&lt;List&lt;int&gt;&gt; permutationsI(int[] nums) {\nList&lt;List&lt;int&gt;&gt; res = new List&lt;List&lt;int&gt;&gt;();\nbacktrack(new List&lt;int&gt;(), nums, new bool[nums.Length], res);\nreturn res;\n}\n</code></pre> permutations_i.swift<pre><code>/* \u56de\u6eaf\u7b97\u6cd5\uff1a\u5168\u6392\u5217 I */\nfunc backtrack(state: inout [Int], choices: [Int], selected: inout [Bool], res: inout [[Int]]) {\n// \u5f53\u72b6\u6001\u957f\u5ea6\u7b49\u4e8e\u5143\u7d20\u6570\u91cf\u65f6\uff0c\u8bb0\u5f55\u89e3\nif state.count == choices.count {\nres.append(state)\nreturn\n}\n// \u904d\u5386\u6240\u6709\u9009\u62e9\nfor (i, choice) in choices.enumerated() {\n// \u526a\u679d\uff1a\u4e0d\u5141\u8bb8\u91cd\u590d\u9009\u62e9\u5143\u7d20 \u4e14 \u4e0d\u5141\u8bb8\u91cd\u590d\u9009\u62e9\u76f8\u7b49\u5143\u7d20\nif !selected[i] {\n// \u5c1d\u8bd5\uff1a\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\nselected[i] = true\nstate.append(choice)\n// \u8fdb\u884c\u4e0b\u4e00\u8f6e\u9009\u62e9\nbacktrack(state: &amp;state, choices: choices, selected: &amp;selected, res: &amp;res)\n// \u56de\u9000\uff1a\u64a4\u9500\u9009\u62e9\uff0c\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001\nselected[i] = false\nstate.removeLast()\n}\n}\n}\n/* \u5168\u6392\u5217 I */\nfunc permutationsI(nums: [Int]) -&gt; [[Int]] {\nvar state: [Int] = []\nvar selected = Array(repeating: false, count: nums.count)\nvar res: [[Int]] = []\nbacktrack(state: &amp;state, choices: nums, selected: &amp;selected, res: &amp;res)\nreturn res\n}\n</code></pre> permutations_i.zig<pre><code>[class]{}-[func]{backtrack}\n[class]{}-[func]{permutationsI}\n</code></pre> permutations_i.dart<pre><code>[class]{}-[func]{backtrack}\n[class]{}-[func]{permutationsI}\n</code></pre> <p>\u9700\u8981\u91cd\u70b9\u5173\u6ce8\u7684\u662f\uff0c\u6211\u4eec\u5f15\u5165\u4e86\u4e00\u4e2a\u5e03\u5c14\u578b\u6570\u7ec4 <code>selected</code> \uff0c\u5b83\u7684\u957f\u5ea6\u4e0e\u8f93\u5165\u6570\u7ec4\u957f\u5ea6\u76f8\u7b49\uff0c\u5176\u4e2d <code>selected[i]</code> \u8868\u793a <code>choices[i]</code> \u662f\u5426\u5df2\u88ab\u9009\u62e9\u3002\u6211\u4eec\u5229\u7528 <code>selected</code> \u907f\u514d\u67d0\u4e2a\u5143\u7d20\u88ab\u91cd\u590d\u9009\u62e9\uff0c\u4ece\u800c\u5b9e\u73b0\u526a\u679d\u3002</p> <p>\u5982\u4e0b\u56fe\u6240\u793a\uff0c\u5047\u8bbe\u6211\u4eec\u7b2c\u4e00\u8f6e\u9009\u62e9 1 \uff0c\u7b2c\u4e8c\u8f6e\u9009\u62e9 3 \uff0c\u7b2c\u4e09\u8f6e\u9009\u62e9 2 \uff0c\u5219\u9700\u8981\u5728\u7b2c\u4e8c\u8f6e\u526a\u6389\u5143\u7d20 1 \u7684\u5206\u652f\uff0c\u5728\u7b2c\u4e09\u8f6e\u526a\u6389\u5143\u7d20 1, 3 \u7684\u5206\u652f\u3002\u4ece\u672c\u8d28\u4e0a\u7406\u89e3\uff0c\u6b64\u526a\u679d\u64cd\u4f5c\u53ef\u5c06\u641c\u7d22\u7a7a\u95f4\u5927\u5c0f\u4ece \\(O(n^n)\\) \u964d\u4f4e\u81f3 \\(O(n!)\\) \u3002</p> <p></p> <p> Fig. \u5168\u6392\u5217\u526a\u679d\u793a\u4f8b </p>"},{"location":"chapter_backtracking/permutations_problem/#1222","title":"12.2.2. \u00a0 \u8003\u8651\u91cd\u590d\u7684\u60c5\u51b5","text":"<p>Question</p> <p>\u8f93\u5165\u4e00\u4e2a\u6574\u6570\u6570\u7ec4\uff0c\u6570\u7ec4\u4e2d\u53ef\u80fd\u5305\u542b\u91cd\u590d\u5143\u7d20\uff0c\u8fd4\u56de\u6240\u6709\u4e0d\u91cd\u590d\u7684\u6392\u5217\u3002</p> <p>\u5047\u8bbe\u8f93\u5165\u6570\u7ec4\u4e3a \\([1, 1, 2]\\) \u3002\u4e3a\u4e86\u65b9\u4fbf\u533a\u5206\u4e24\u4e2a\u91cd\u590d\u7684\u5143\u7d20 \\(1\\) \uff0c\u63a5\u4e0b\u6765\u6211\u4eec\u5c06\u7b2c\u4e8c\u4e2a\u5143\u7d20\u8bb0\u4e3a \\(\\hat{1}\\) \u3002\u5982\u4e0b\u56fe\u6240\u793a\uff0c\u4e0a\u8ff0\u65b9\u6cd5\u751f\u6210\u7684\u6392\u5217\u6709\u4e00\u534a\u90fd\u662f\u91cd\u590d\u7684\u3002</p> <p></p> <p> Fig. \u91cd\u590d\u6392\u5217 </p> <p>\u90a3\u4e48\uff0c\u5982\u4f55\u53bb\u9664\u91cd\u590d\u7684\u6392\u5217\u5462\uff1f\u6700\u76f4\u63a5\u5730\uff0c\u6211\u4eec\u53ef\u4ee5\u501f\u52a9\u4e00\u4e2a\u54c8\u5e0c\u8868\uff0c\u76f4\u63a5\u5bf9\u6392\u5217\u7ed3\u679c\u8fdb\u884c\u53bb\u91cd\u3002\u7136\u800c\uff0c\u8fd9\u6837\u505a\u4e0d\u591f\u4f18\u96c5\uff0c\u56e0\u4e3a\u751f\u6210\u91cd\u590d\u6392\u5217\u7684\u641c\u7d22\u5206\u652f\u662f\u6ca1\u6709\u5fc5\u8981\u7684\uff0c\u5e94\u5f53\u88ab\u63d0\u524d\u8bc6\u522b\u5e76\u526a\u679d\uff0c\u8fd9\u6837\u53ef\u4ee5\u63d0\u5347\u7b97\u6cd5\u6548\u7387\u3002</p> <p>\u89c2\u5bdf\u53d1\u73b0\uff0c\u5728\u7b2c\u4e00\u8f6e\u4e2d\uff0c\u9009\u62e9 \\(1\\) \u6216\u9009\u62e9 \\(\\hat{1}\\) \u662f\u7b49\u4ef7\u7684\uff0c\u56e0\u4e3a\u5728\u8fd9\u4e24\u4e2a\u9009\u62e9\u4e4b\u4e0b\u751f\u6210\u7684\u6240\u6709\u6392\u5217\u90fd\u662f\u91cd\u590d\u7684\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u5e94\u8be5\u628a \\(\\hat{1}\\) \u526a\u679d\u6389\u3002\u540c\u7406\uff0c\u5728\u7b2c\u4e00\u8f6e\u9009\u62e9 \\(2\\) \u540e\uff0c\u7b2c\u4e8c\u8f6e\u9009\u62e9\u4e2d\u7684 \\(1\\) \u548c \\(\\hat{1}\\) \u4e5f\u4f1a\u4ea7\u751f\u91cd\u590d\u5206\u652f\uff0c\u56e0\u6b64\u4e5f\u9700\u8981\u5c06\u7b2c\u4e8c\u8f6e\u7684 \\(\\hat{1}\\) \u526a\u679d\u3002</p> <p></p> <p> Fig. \u91cd\u590d\u6392\u5217\u526a\u679d </p> <p>\u672c\u8d28\u4e0a\u770b\uff0c\u6211\u4eec\u7684\u76ee\u6807\u662f\u5b9e\u73b0\u5728\u67d0\u4e00\u8f6e\u9009\u62e9\u4e2d\uff0c\u591a\u4e2a\u76f8\u7b49\u7684\u5143\u7d20\u4ec5\u88ab\u9009\u62e9\u4e00\u6b21\u3002\u56e0\u6b64\uff0c\u5728\u4e0a\u4e00\u9898\u7684\u4ee3\u7801\u7684\u57fa\u7840\u4e0a\uff0c\u6211\u4eec\u8003\u8651\u5728\u6bcf\u4e00\u8f6e\u9009\u62e9\u4e2d\u5f00\u542f\u4e00\u4e2a\u54c8\u5e0c\u8868 <code>duplicated</code> \uff0c\u7528\u4e8e\u8bb0\u5f55\u8be5\u8f6e\u4e2d\u5df2\u7ecf\u5c1d\u8bd5\u8fc7\u7684\u5143\u7d20\uff0c\u5e76\u5c06\u91cd\u590d\u5143\u7d20\u526a\u679d\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart permutations_ii.java<pre><code>/* \u56de\u6eaf\u7b97\u6cd5\uff1a\u5168\u6392\u5217 II */\nvoid backtrack(List&lt;Integer&gt; state, int[] choices, boolean[] selected, List&lt;List&lt;Integer&gt;&gt; res) {\n// \u5f53\u72b6\u6001\u957f\u5ea6\u7b49\u4e8e\u5143\u7d20\u6570\u91cf\u65f6\uff0c\u8bb0\u5f55\u89e3\nif (state.size() == choices.length) {\nres.add(new ArrayList&lt;Integer&gt;(state));\nreturn;\n}\n// \u904d\u5386\u6240\u6709\u9009\u62e9\nSet&lt;Integer&gt; duplicated = new HashSet&lt;Integer&gt;();\nfor (int i = 0; i &lt; choices.length; i++) {\nint choice = choices[i];\n// \u526a\u679d\uff1a\u4e0d\u5141\u8bb8\u91cd\u590d\u9009\u62e9\u5143\u7d20 \u4e14 \u4e0d\u5141\u8bb8\u91cd\u590d\u9009\u62e9\u76f8\u7b49\u5143\u7d20\nif (!selected[i] &amp;&amp; !duplicated.contains(choice)) {\n// \u5c1d\u8bd5\uff1a\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\nduplicated.add(choice); // \u8bb0\u5f55\u9009\u62e9\u8fc7\u7684\u5143\u7d20\u503c\nselected[i] = true;\nstate.add(choice);\n// \u8fdb\u884c\u4e0b\u4e00\u8f6e\u9009\u62e9\nbacktrack(state, choices, selected, res);\n// \u56de\u9000\uff1a\u64a4\u9500\u9009\u62e9\uff0c\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001\nselected[i] = false;\nstate.remove(state.size() - 1);\n}\n}\n}\n/* \u5168\u6392\u5217 II */\nList&lt;List&lt;Integer&gt;&gt; permutationsII(int[] nums) {\nList&lt;List&lt;Integer&gt;&gt; res = new ArrayList&lt;List&lt;Integer&gt;&gt;();\nbacktrack(new ArrayList&lt;Integer&gt;(), nums, new boolean[nums.length], res);\nreturn res;\n}\n</code></pre> permutations_ii.cpp<pre><code>/* \u56de\u6eaf\u7b97\u6cd5\uff1a\u5168\u6392\u5217 II */\nvoid backtrack(vector&lt;int&gt; &amp;state, const vector&lt;int&gt; &amp;choices, vector&lt;bool&gt; &amp;selected, vector&lt;vector&lt;int&gt;&gt; &amp;res) {\n// \u5f53\u72b6\u6001\u957f\u5ea6\u7b49\u4e8e\u5143\u7d20\u6570\u91cf\u65f6\uff0c\u8bb0\u5f55\u89e3\nif (state.size() == choices.size()) {\nres.push_back(state);\nreturn;\n}\n// \u904d\u5386\u6240\u6709\u9009\u62e9\nunordered_set&lt;int&gt; duplicated;\nfor (int i = 0; i &lt; choices.size(); i++) {\nint choice = choices[i];\n// \u526a\u679d\uff1a\u4e0d\u5141\u8bb8\u91cd\u590d\u9009\u62e9\u5143\u7d20 \u4e14 \u4e0d\u5141\u8bb8\u91cd\u590d\u9009\u62e9\u76f8\u7b49\u5143\u7d20\nif (!selected[i] &amp;&amp; duplicated.find(choice) == duplicated.end()) {\n// \u5c1d\u8bd5\uff1a\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\nduplicated.emplace(choice); // \u8bb0\u5f55\u9009\u62e9\u8fc7\u7684\u5143\u7d20\u503c\nselected[i] = true;\nstate.push_back(choice);\n// \u8fdb\u884c\u4e0b\u4e00\u8f6e\u9009\u62e9\nbacktrack(state, choices, selected, res);\n// \u56de\u9000\uff1a\u64a4\u9500\u9009\u62e9\uff0c\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001\nselected[i] = false;\nstate.pop_back();\n}\n}\n}\n/* \u5168\u6392\u5217 II */\nvector&lt;vector&lt;int&gt;&gt; permutationsII(vector&lt;int&gt; nums) {\nvector&lt;int&gt; state;\nvector&lt;bool&gt; selected(nums.size(), false);\nvector&lt;vector&lt;int&gt;&gt; res;\nbacktrack(state, nums, selected, res);\nreturn res;\n}\n</code></pre> permutations_ii.py<pre><code>def backtrack(\nstate: list[int], choices: list[int], selected: list[bool], res: list[list[int]]\n):\n\"\"\"\u56de\u6eaf\u7b97\u6cd5\uff1a\u5168\u6392\u5217 II\"\"\"\n# \u5f53\u72b6\u6001\u957f\u5ea6\u7b49\u4e8e\u5143\u7d20\u6570\u91cf\u65f6\uff0c\u8bb0\u5f55\u89e3\nif len(state) == len(choices):\nres.append(list(state))\nreturn\n# \u904d\u5386\u6240\u6709\u9009\u62e9\nduplicated = set[int]()\nfor i, choice in enumerate(choices):\n# \u526a\u679d\uff1a\u4e0d\u5141\u8bb8\u91cd\u590d\u9009\u62e9\u5143\u7d20 \u4e14 \u4e0d\u5141\u8bb8\u91cd\u590d\u9009\u62e9\u76f8\u7b49\u5143\u7d20\nif not selected[i] and choice not in duplicated:\n# \u5c1d\u8bd5\uff1a\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\nduplicated.add(choice)  # \u8bb0\u5f55\u9009\u62e9\u8fc7\u7684\u5143\u7d20\u503c\nselected[i] = True\nstate.append(choice)\n# \u8fdb\u884c\u4e0b\u4e00\u8f6e\u9009\u62e9\nbacktrack(state, choices, selected, res)\n# \u56de\u9000\uff1a\u64a4\u9500\u9009\u62e9\uff0c\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001\nselected[i] = False\nstate.pop()\ndef permutations_ii(nums: list[int]) -&gt; list[list[int]]:\n\"\"\"\u5168\u6392\u5217 II\"\"\"\nres = []\nbacktrack(state=[], choices=nums, selected=[False] * len(nums), res=res)\nreturn res\n</code></pre> permutations_ii.go<pre><code>/* \u56de\u6eaf\u7b97\u6cd5\uff1a\u5168\u6392\u5217 II */\nfunc backtrackII(state *[]int, choices *[]int, selected *[]bool, res *[][]int) {\n// \u5f53\u72b6\u6001\u957f\u5ea6\u7b49\u4e8e\u5143\u7d20\u6570\u91cf\u65f6\uff0c\u8bb0\u5f55\u89e3\nif len(*state) == len(*choices) {\nnewState := append([]int{}, *state...)\n*res = append(*res, newState)\n}\n// \u904d\u5386\u6240\u6709\u9009\u62e9\nduplicated := make(map[int]struct{}, 0)\nfor i := 0; i &lt; len(*choices); i++ {\nchoice := (*choices)[i]\n// \u526a\u679d\uff1a\u4e0d\u5141\u8bb8\u91cd\u590d\u9009\u62e9\u5143\u7d20 \u4e14 \u4e0d\u5141\u8bb8\u91cd\u590d\u9009\u62e9\u76f8\u7b49\u5143\u7d20\nif _, ok := duplicated[choice]; !ok &amp;&amp; !(*selected)[i] {\n// \u5c1d\u8bd5\uff1a\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\n// \u8bb0\u5f55\u9009\u62e9\u8fc7\u7684\u5143\u7d20\u503c\nduplicated[choice] = struct{}{}\n(*selected)[i] = true\n*state = append(*state, choice)\n// \u8fdb\u884c\u4e0b\u4e00\u8f6e\u9009\u62e9\nbacktrackI(state, choices, selected, res)\n// \u56de\u9000\uff1a\u64a4\u9500\u9009\u62e9\uff0c\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001\n(*selected)[i] = false\n*state = (*state)[:len(*state)-1]\n}\n}\n}\n/* \u5168\u6392\u5217 II */\nfunc permutationsII(nums []int) [][]int {\nres := make([][]int, 0)\nstate := make([]int, 0)\nselected := make([]bool, len(nums))\nbacktrackII(&amp;state, &amp;nums, &amp;selected, &amp;res)\nreturn res\n}\n</code></pre> permutations_ii.js<pre><code>/* \u56de\u6eaf\u7b97\u6cd5\uff1a\u5168\u6392\u5217 II */\nfunction backtrack(state, choices, selected, res) {\n// \u5f53\u72b6\u6001\u957f\u5ea6\u7b49\u4e8e\u5143\u7d20\u6570\u91cf\u65f6\uff0c\u8bb0\u5f55\u89e3\nif (state.length === choices.length) {\nres.push([...state]);\nreturn;\n}\n// \u904d\u5386\u6240\u6709\u9009\u62e9\nconst duplicated = new Set();\nchoices.forEach((choice, i) =&gt; {\n// \u526a\u679d\uff1a\u4e0d\u5141\u8bb8\u91cd\u590d\u9009\u62e9\u5143\u7d20 \u4e14 \u4e0d\u5141\u8bb8\u91cd\u590d\u9009\u62e9\u76f8\u7b49\u5143\u7d20\nif (!selected[i] &amp;&amp; !duplicated.has(choice)) {\n// \u5c1d\u8bd5\uff1a\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\nduplicated.add(choice); // \u8bb0\u5f55\u9009\u62e9\u8fc7\u7684\u5143\u7d20\u503c\nselected[i] = true;\nstate.push(choice);\n// \u8fdb\u884c\u4e0b\u4e00\u8f6e\u9009\u62e9\nbacktrack(state, choices, selected, res);\n// \u56de\u9000\uff1a\u64a4\u9500\u9009\u62e9\uff0c\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001\nselected[i] = false;\nstate.pop();\n}\n});\n}\n/* \u5168\u6392\u5217 II */\nfunction permutationsII(nums) {\nconst res = [];\nbacktrack([], nums, Array(nums.length).fill(false), res);\nreturn res;\n}\n</code></pre> permutations_ii.ts<pre><code>/* \u56de\u6eaf\u7b97\u6cd5\uff1a\u5168\u6392\u5217 II */\nfunction backtrack(\nstate: number[],\nchoices: number[],\nselected: boolean[],\nres: number[][]\n): void {\n// \u5f53\u72b6\u6001\u957f\u5ea6\u7b49\u4e8e\u5143\u7d20\u6570\u91cf\u65f6\uff0c\u8bb0\u5f55\u89e3\nif (state.length === choices.length) {\nres.push([...state]);\nreturn;\n}\n// \u904d\u5386\u6240\u6709\u9009\u62e9\nconst duplicated = new Set();\nchoices.forEach((choice, i) =&gt; {\n// \u526a\u679d\uff1a\u4e0d\u5141\u8bb8\u91cd\u590d\u9009\u62e9\u5143\u7d20 \u4e14 \u4e0d\u5141\u8bb8\u91cd\u590d\u9009\u62e9\u76f8\u7b49\u5143\u7d20\nif (!selected[i] &amp;&amp; !duplicated.has(choice)) {\n// \u5c1d\u8bd5\uff1a\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\nduplicated.add(choice); // \u8bb0\u5f55\u9009\u62e9\u8fc7\u7684\u5143\u7d20\u503c\nselected[i] = true;\nstate.push(choice);\n// \u8fdb\u884c\u4e0b\u4e00\u8f6e\u9009\u62e9\nbacktrack(state, choices, selected, res);\n// \u56de\u9000\uff1a\u64a4\u9500\u9009\u62e9\uff0c\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001\nselected[i] = false;\nstate.pop();\n}\n});\n}\n/* \u5168\u6392\u5217 II */\nfunction permutationsII(nums: number[]): number[][] {\nconst res: number[][] = [];\nbacktrack([], nums, Array(nums.length).fill(false), res);\nreturn res;\n}\n</code></pre> permutations_ii.c<pre><code>[class]{}-[func]{backtrack}\n[class]{}-[func]{permutationsII}\n</code></pre> permutations_ii.cs<pre><code>/* \u56de\u6eaf\u7b97\u6cd5\uff1a\u5168\u6392\u5217 II */\nvoid backtrack(List&lt;int&gt; state, int[] choices, bool[] selected, List&lt;List&lt;int&gt;&gt; res) {\n// \u5f53\u72b6\u6001\u957f\u5ea6\u7b49\u4e8e\u5143\u7d20\u6570\u91cf\u65f6\uff0c\u8bb0\u5f55\u89e3\nif (state.Count == choices.Length) {\nres.Add(new List&lt;int&gt;(state));\nreturn;\n}\n// \u904d\u5386\u6240\u6709\u9009\u62e9\nISet&lt;int&gt; duplicated = new HashSet&lt;int&gt;();\nfor (int i = 0; i &lt; choices.Length; i++) {\nint choice = choices[i];\n// \u526a\u679d\uff1a\u4e0d\u5141\u8bb8\u91cd\u590d\u9009\u62e9\u5143\u7d20 \u4e14 \u4e0d\u5141\u8bb8\u91cd\u590d\u9009\u62e9\u76f8\u7b49\u5143\u7d20\nif (!selected[i] &amp;&amp; !duplicated.Contains(choice)) {\n// \u5c1d\u8bd5\uff1a\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\nduplicated.Add(choice); // \u8bb0\u5f55\u9009\u62e9\u8fc7\u7684\u5143\u7d20\u503c\nselected[i] = true;\nstate.Add(choice);\n// \u8fdb\u884c\u4e0b\u4e00\u8f6e\u9009\u62e9\nbacktrack(state, choices, selected, res);\n// \u56de\u9000\uff1a\u64a4\u9500\u9009\u62e9\uff0c\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001\nselected[i] = false;\nstate.RemoveAt(state.Count - 1);\n}\n}\n}\n/* \u5168\u6392\u5217 II */\nList&lt;List&lt;int&gt;&gt; permutationsII(int[] nums) {\nList&lt;List&lt;int&gt;&gt; res = new List&lt;List&lt;int&gt;&gt;();\nbacktrack(new List&lt;int&gt;(), nums, new bool[nums.Length], res);\nreturn res;\n}\n</code></pre> permutations_ii.swift<pre><code>/* \u56de\u6eaf\u7b97\u6cd5\uff1a\u5168\u6392\u5217 II */\nfunc backtrack(state: inout [Int], choices: [Int], selected: inout [Bool], res: inout [[Int]]) {\n// \u5f53\u72b6\u6001\u957f\u5ea6\u7b49\u4e8e\u5143\u7d20\u6570\u91cf\u65f6\uff0c\u8bb0\u5f55\u89e3\nif state.count == choices.count {\nres.append(state)\nreturn\n}\n// \u904d\u5386\u6240\u6709\u9009\u62e9\nvar duplicated: Set&lt;Int&gt; = []\nfor (i, choice) in choices.enumerated() {\n// \u526a\u679d\uff1a\u4e0d\u5141\u8bb8\u91cd\u590d\u9009\u62e9\u5143\u7d20 \u4e14 \u4e0d\u5141\u8bb8\u91cd\u590d\u9009\u62e9\u76f8\u7b49\u5143\u7d20\nif !selected[i], !duplicated.contains(choice) {\n// \u5c1d\u8bd5\uff1a\u505a\u51fa\u9009\u62e9\uff0c\u66f4\u65b0\u72b6\u6001\nduplicated.insert(choice) // \u8bb0\u5f55\u9009\u62e9\u8fc7\u7684\u5143\u7d20\u503c\nselected[i] = true\nstate.append(choice)\n// \u8fdb\u884c\u4e0b\u4e00\u8f6e\u9009\u62e9\nbacktrack(state: &amp;state, choices: choices, selected: &amp;selected, res: &amp;res)\n// \u56de\u9000\uff1a\u64a4\u9500\u9009\u62e9\uff0c\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001\nselected[i] = false\nstate.removeLast()\n}\n}\n}\n/* \u5168\u6392\u5217 II */\nfunc permutationsII(nums: [Int]) -&gt; [[Int]] {\nvar state: [Int] = []\nvar selected = Array(repeating: false, count: nums.count)\nvar res: [[Int]] = []\nbacktrack(state: &amp;state, choices: nums, selected: &amp;selected, res: &amp;res)\nreturn res\n}\n</code></pre> permutations_ii.zig<pre><code>[class]{}-[func]{backtrack}\n[class]{}-[func]{permutationsII}\n</code></pre> permutations_ii.dart<pre><code>[class]{}-[func]{backtrack}\n[class]{}-[func]{permutationsII}\n</code></pre> <p>\u6ce8\u610f\uff0c\u867d\u7136 <code>selected</code> \u548c <code>duplicated</code> \u90fd\u8d77\u5230\u526a\u679d\u7684\u4f5c\u7528\uff0c\u4f46\u4ed6\u4eec\u526a\u6389\u7684\u662f\u4e0d\u540c\u7684\u5206\u652f\uff1a</p> <ul> <li>\u526a\u679d\u6761\u4ef6\u4e00\uff1a\u6574\u4e2a\u641c\u7d22\u8fc7\u7a0b\u4e2d\u53ea\u6709\u4e00\u4e2a <code>selected</code> \u3002\u5b83\u8bb0\u5f55\u7684\u662f\u5f53\u524d\u72b6\u6001\u4e2d\u5305\u542b\u54ea\u4e9b\u5143\u7d20\uff0c\u4f5c\u7528\u662f\u907f\u514d\u67d0\u4e2a\u5143\u7d20\u5728 <code>state</code> \u4e2d\u91cd\u590d\u51fa\u73b0\u3002</li> <li>\u526a\u679d\u6761\u4ef6\u4e8c\uff1a\u6bcf\u8f6e\u9009\u62e9\uff08\u5373\u6bcf\u4e2a\u5f00\u542f\u7684 <code>backtrack</code> \u51fd\u6570\uff09\u90fd\u5305\u542b\u4e00\u4e2a <code>duplicated</code> \u3002\u5b83\u8bb0\u5f55\u7684\u662f\u5728\u904d\u5386\u4e2d\u54ea\u4e9b\u5143\u7d20\u5df2\u88ab\u9009\u62e9\u8fc7\uff0c\u4f5c\u7528\u662f\u4fdd\u8bc1\u76f8\u7b49\u5143\u7d20\u53ea\u88ab\u9009\u62e9\u4e00\u6b21\uff0c\u4ee5\u907f\u514d\u4ea7\u751f\u91cd\u590d\u7684\u641c\u7d22\u5206\u652f\u3002</li> </ul> <p>\u4e0b\u56fe\u5c55\u793a\u4e86\u4e24\u4e2a\u526a\u679d\u6761\u4ef6\u7684\u751f\u6548\u8303\u56f4\u3002\u6ce8\u610f\uff0c\u6811\u4e2d\u7684\u6bcf\u4e2a\u8282\u70b9\u4ee3\u8868\u4e00\u4e2a\u9009\u62e9\uff0c\u4ece\u6839\u8282\u70b9\u5230\u53f6\u8282\u70b9\u7684\u8def\u5f84\u4e0a\u7684\u5404\u4e2a\u8282\u70b9\u6784\u6210\u4e00\u4e2a\u6392\u5217\u3002</p> <p></p> <p> Fig. \u4e24\u79cd\u526a\u679d\u6761\u4ef6\u7684\u4f5c\u7528\u8303\u56f4 </p>"},{"location":"chapter_backtracking/permutations_problem/#1223","title":"12.2.3. \u00a0 \u590d\u6742\u5ea6\u5206\u6790","text":"<p>\u5047\u8bbe\u5143\u7d20\u4e24\u4e24\u4e4b\u95f4\u4e92\u4e0d\u76f8\u540c\uff0c\u5219 \\(n\\) \u4e2a\u5143\u7d20\u5171\u6709 \\(n!\\)  \u79cd\u6392\u5217\uff08\u9636\u4e58\uff09\uff1b\u5728\u8bb0\u5f55\u7ed3\u679c\u65f6\uff0c\u9700\u8981\u590d\u5236\u957f\u5ea6\u4e3a \\(n\\) \u7684\u5217\u8868\uff0c\u4f7f\u7528 \\(O(n)\\) \u65f6\u95f4\u3002\u56e0\u6b64\uff0c\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(n!n)\\) \u3002</p> <p>\u6700\u5927\u9012\u5f52\u6df1\u5ea6\u4e3a \\(n\\) \uff0c\u4f7f\u7528 \\(O(n)\\) \u6808\u5e27\u7a7a\u95f4\u3002<code>selected</code> \u4f7f\u7528 \\(O(n)\\) \u7a7a\u95f4\u3002\u540c\u4e00\u65f6\u523b\u6700\u591a\u5171\u6709 \\(n\\) \u4e2a <code>duplicated</code> \uff0c\u4f7f\u7528 \\(O(n^2)\\) \u7a7a\u95f4\u3002\u56e0\u6b64\uff0c\u5168\u6392\u5217 I \u7684\u7a7a\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(n)\\) \uff0c\u5168\u6392\u5217 II \u7684\u7a7a\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(n^2)\\) \u3002</p>"},{"location":"chapter_computational_complexity/","title":"2. \u00a0 \u590d\u6742\u5ea6\u5206\u6790","text":""},{"location":"chapter_computational_complexity/performance_evaluation/","title":"2.1. \u00a0 \u7b97\u6cd5\u6548\u7387\u8bc4\u4f30","text":""},{"location":"chapter_computational_complexity/performance_evaluation/#211","title":"2.1.1. \u00a0 \u7b97\u6cd5\u8bc4\u4ef7\u7ef4\u5ea6","text":"<p>\u4ece\u603b\u4f53\u4e0a\u770b\uff0c\u7b97\u6cd5\u8bbe\u8ba1\u8ffd\u6c42\u4ee5\u4e0b\u4e24\u4e2a\u5c42\u9762\u7684\u76ee\u6807\uff1a</p> <ol> <li>\u627e\u5230\u95ee\u9898\u89e3\u6cd5\u3002\u7b97\u6cd5\u9700\u8981\u5728\u89c4\u5b9a\u7684\u8f93\u5165\u8303\u56f4\u5185\uff0c\u53ef\u9760\u5730\u6c42\u5f97\u95ee\u9898\u7684\u6b63\u786e\u89e3\u3002</li> <li>\u5bfb\u6c42\u6700\u4f18\u89e3\u6cd5\u3002\u540c\u4e00\u4e2a\u95ee\u9898\u53ef\u80fd\u5b58\u5728\u591a\u79cd\u89e3\u6cd5\uff0c\u6211\u4eec\u5e0c\u671b\u627e\u5230\u5c3d\u53ef\u80fd\u9ad8\u6548\u7684\u7b97\u6cd5\u3002</li> </ol> <p>\u56e0\u6b64\uff0c\u5728\u80fd\u591f\u89e3\u51b3\u95ee\u9898\u7684\u524d\u63d0\u4e0b\uff0c\u7b97\u6cd5\u6548\u7387\u6210\u4e3a\u4e3b\u8981\u7684\u8bc4\u4ef7\u7ef4\u5ea6\uff0c\u4e3b\u8981\u5305\u62ec\uff1a</p> <ul> <li>\u65f6\u95f4\u6548\u7387\uff0c\u5373\u7b97\u6cd5\u8fd0\u884c\u901f\u5ea6\u7684\u5feb\u6162\u3002</li> <li>\u7a7a\u95f4\u6548\u7387\uff0c\u5373\u7b97\u6cd5\u5360\u7528\u5185\u5b58\u7a7a\u95f4\u7684\u5927\u5c0f\u3002</li> </ul> <p>\u7b80\u800c\u8a00\u4e4b\uff0c\u6211\u4eec\u7684\u76ee\u6807\u662f\u8bbe\u8ba1\u201c\u65e2\u5feb\u53c8\u7701\u201d\u7684\u6570\u636e\u7ed3\u6784\u4e0e\u7b97\u6cd5\u3002\u638c\u63e1\u8bc4\u4f30\u7b97\u6cd5\u6548\u7387\u7684\u65b9\u6cd5\u5219\u81f3\u5173\u91cd\u8981\uff0c\u56e0\u4e3a\u53ea\u6709\u4e86\u89e3\u8bc4\u4ef7\u6807\u51c6\uff0c\u6211\u4eec\u624d\u80fd\u8fdb\u884c\u7b97\u6cd5\u4e4b\u95f4\u7684\u5bf9\u6bd4\u5206\u6790\uff0c\u4ece\u800c\u6307\u5bfc\u7b97\u6cd5\u8bbe\u8ba1\u4e0e\u4f18\u5316\u8fc7\u7a0b\u3002</p>"},{"location":"chapter_computational_complexity/performance_evaluation/#212","title":"2.1.2. \u00a0 \u6548\u7387\u8bc4\u4f30\u65b9\u6cd5","text":""},{"location":"chapter_computational_complexity/performance_evaluation/#_1","title":"\u5b9e\u9645\u6d4b\u8bd5","text":"<p>\u5047\u8bbe\u6211\u4eec\u73b0\u5728\u6709\u7b97\u6cd5 A \u548c\u7b97\u6cd5 B\uff0c\u5b83\u4eec\u90fd\u80fd\u89e3\u51b3\u540c\u4e00\u95ee\u9898\uff0c\u73b0\u5728\u9700\u8981\u5bf9\u6bd4\u8fd9\u4e24\u4e2a\u7b97\u6cd5\u7684\u6548\u7387\u3002\u6211\u4eec\u6700\u76f4\u63a5\u7684\u65b9\u6cd5\u5c31\u662f\u627e\u4e00\u53f0\u8ba1\u7b97\u673a\uff0c\u8fd0\u884c\u8fd9\u4e24\u4e2a\u7b97\u6cd5\uff0c\u5e76\u76d1\u63a7\u8bb0\u5f55\u5b83\u4eec\u7684\u8fd0\u884c\u65f6\u95f4\u548c\u5185\u5b58\u5360\u7528\u60c5\u51b5\u3002\u8fd9\u79cd\u8bc4\u4f30\u65b9\u5f0f\u80fd\u591f\u53cd\u6620\u771f\u5b9e\u60c5\u51b5\uff0c\u4f46\u4e5f\u5b58\u5728\u8f83\u5927\u5c40\u9650\u6027\u3002</p> <p>\u96be\u4ee5\u6392\u9664\u6d4b\u8bd5\u73af\u5883\u7684\u5e72\u6270\u56e0\u7d20\u3002\u786c\u4ef6\u914d\u7f6e\u4f1a\u5f71\u54cd\u7b97\u6cd5\u7684\u6027\u80fd\u8868\u73b0\u3002\u4f8b\u5982\uff0c\u5728\u67d0\u53f0\u8ba1\u7b97\u673a\u4e2d\uff0c\u7b97\u6cd5 A \u7684\u8fd0\u884c\u65f6\u95f4\u6bd4\u7b97\u6cd5 B \u77ed\uff1b\u4f46\u5728\u53e6\u4e00\u53f0\u914d\u7f6e\u4e0d\u540c\u7684\u8ba1\u7b97\u673a\u4e2d\uff0c\u6211\u4eec\u53ef\u80fd\u5f97\u5230\u76f8\u53cd\u7684\u6d4b\u8bd5\u7ed3\u679c\u3002\u8fd9\u610f\u5473\u7740\u6211\u4eec\u9700\u8981\u5728\u5404\u79cd\u673a\u5668\u4e0a\u8fdb\u884c\u6d4b\u8bd5\uff0c\u800c\u8fd9\u662f\u4e0d\u73b0\u5b9e\u7684\u3002</p> <p>\u5c55\u5f00\u5b8c\u6574\u6d4b\u8bd5\u975e\u5e38\u8017\u8d39\u8d44\u6e90\u3002\u968f\u7740\u8f93\u5165\u6570\u636e\u91cf\u7684\u53d8\u5316\uff0c\u7b97\u6cd5\u4f1a\u8868\u73b0\u51fa\u4e0d\u540c\u7684\u6548\u7387\u3002\u4f8b\u5982\uff0c\u8f93\u5165\u6570\u636e\u91cf\u8f83\u5c0f\u65f6\uff0c\u7b97\u6cd5 A \u7684\u8fd0\u884c\u65f6\u95f4\u53ef\u80fd\u77ed\u4e8e\u7b97\u6cd5 B\uff1b\u800c\u8f93\u5165\u6570\u636e\u91cf\u8f83\u5927\u65f6\uff0c\u6d4b\u8bd5\u7ed3\u679c\u53ef\u80fd\u76f8\u53cd\u3002\u56e0\u6b64\uff0c\u4e3a\u4e86\u5f97\u5230\u6709\u8bf4\u670d\u529b\u7684\u7ed3\u8bba\uff0c\u6211\u4eec\u9700\u8981\u6d4b\u8bd5\u5404\u79cd\u89c4\u6a21\u7684\u8f93\u5165\u6570\u636e\uff0c\u8fd9\u6837\u9700\u8981\u5360\u7528\u5927\u91cf\u7684\u8ba1\u7b97\u8d44\u6e90\u3002</p>"},{"location":"chapter_computational_complexity/performance_evaluation/#_2","title":"\u7406\u8bba\u4f30\u7b97","text":"<p>\u7531\u4e8e\u5b9e\u9645\u6d4b\u8bd5\u5177\u6709\u8f83\u5927\u7684\u5c40\u9650\u6027\uff0c\u6211\u4eec\u53ef\u4ee5\u8003\u8651\u4ec5\u901a\u8fc7\u4e00\u4e9b\u8ba1\u7b97\u6765\u8bc4\u4f30\u7b97\u6cd5\u7684\u6548\u7387\u3002\u8fd9\u79cd\u4f30\u7b97\u65b9\u6cd5\u88ab\u79f0\u4e3a\u300c\u590d\u6742\u5ea6\u5206\u6790 Complexity Analysis\u300d\u6216\u300c\u6e10\u8fd1\u590d\u6742\u5ea6\u5206\u6790 Asymptotic Complexity Analysis\u300d\u3002</p> <p>\u590d\u6742\u5ea6\u5206\u6790\u8bc4\u4f30\u7684\u662f\u7b97\u6cd5\u8fd0\u884c\u6548\u7387\u968f\u7740\u8f93\u5165\u6570\u636e\u91cf\u589e\u591a\u65f6\u7684\u589e\u957f\u8d8b\u52bf\u3002\u8fd9\u4e2a\u5b9a\u4e49\u6709\u4e9b\u62d7\u53e3\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u5176\u5206\u4e3a\u4e09\u4e2a\u91cd\u70b9\u6765\u7406\u89e3\uff1a</p> <ul> <li>\u201c\u7b97\u6cd5\u8fd0\u884c\u6548\u7387\u201d\u53ef\u5206\u4e3a\u201c\u8fd0\u884c\u65f6\u95f4\u201d\u548c\u201c\u5360\u7528\u7a7a\u95f4\u201d\uff0c\u56e0\u6b64\u6211\u4eec\u53ef\u4ee5\u5c06\u590d\u6742\u5ea6\u5206\u4e3a\u300c\u65f6\u95f4\u590d\u6742\u5ea6 Time Complexity\u300d\u548c\u300c\u7a7a\u95f4\u590d\u6742\u5ea6 Space Complexity\u300d\uff1b</li> <li>\u201c\u968f\u7740\u8f93\u5165\u6570\u636e\u91cf\u589e\u591a\u65f6\u201d\u8868\u793a\u590d\u6742\u5ea6\u4e0e\u8f93\u5165\u6570\u636e\u91cf\u6709\u5173\uff0c\u53cd\u6620\u4e86\u7b97\u6cd5\u8fd0\u884c\u6548\u7387\u4e0e\u8f93\u5165\u6570\u636e\u91cf\u4e4b\u95f4\u7684\u5173\u7cfb\uff1b</li> <li>\u201c\u589e\u957f\u8d8b\u52bf\u201d\u8868\u793a\u590d\u6742\u5ea6\u5206\u6790\u5173\u6ce8\u7684\u662f\u7b97\u6cd5\u65f6\u95f4\u4e0e\u7a7a\u95f4\u7684\u589e\u957f\u8d8b\u52bf\uff0c\u800c\u975e\u5177\u4f53\u7684\u8fd0\u884c\u65f6\u95f4\u6216\u5360\u7528\u7a7a\u95f4\uff1b</li> </ul> <p>\u590d\u6742\u5ea6\u5206\u6790\u514b\u670d\u4e86\u5b9e\u9645\u6d4b\u8bd5\u65b9\u6cd5\u7684\u5f0a\u7aef\u3002\u9996\u5148\uff0c\u5b83\u72ec\u7acb\u4e8e\u6d4b\u8bd5\u73af\u5883\uff0c\u56e0\u6b64\u5206\u6790\u7ed3\u679c\u9002\u7528\u4e8e\u6240\u6709\u8fd0\u884c\u5e73\u53f0\u3002\u5176\u6b21\uff0c\u5b83\u53ef\u4ee5\u4f53\u73b0\u4e0d\u540c\u6570\u636e\u91cf\u4e0b\u7684\u7b97\u6cd5\u6548\u7387\uff0c\u5c24\u5176\u662f\u5728\u5927\u6570\u636e\u91cf\u4e0b\u7684\u7b97\u6cd5\u6027\u80fd\u3002</p> <p>\u5982\u679c\u4f60\u5bf9\u590d\u6742\u5ea6\u5206\u6790\u7684\u6982\u5ff5\u4ecd\u611f\u5230\u56f0\u60d1\uff0c\u65e0\u9700\u62c5\u5fc3\uff0c\u6211\u4eec\u4f1a\u5728\u540e\u7eed\u7ae0\u8282\u8be6\u7ec6\u4ecb\u7ecd\u3002</p>"},{"location":"chapter_computational_complexity/performance_evaluation/#213","title":"2.1.3. \u00a0 \u590d\u6742\u5ea6\u5206\u6790\u91cd\u8981\u6027","text":"<p>\u590d\u6742\u5ea6\u5206\u6790\u4e3a\u6211\u4eec\u63d0\u4f9b\u4e86\u4e00\u628a\u8bc4\u4f30\u7b97\u6cd5\u6548\u7387\u7684\u201c\u6807\u5c3a\u201d\uff0c\u544a\u8bc9\u6211\u4eec\u6267\u884c\u67d0\u4e2a\u7b97\u6cd5\u6240\u9700\u7684\u65f6\u95f4\u548c\u7a7a\u95f4\u8d44\u6e90\uff0c\u5e76\u4f7f\u6211\u4eec\u80fd\u591f\u5bf9\u6bd4\u4e0d\u540c\u7b97\u6cd5\u4e4b\u95f4\u7684\u6548\u7387\u3002</p> <p>\u590d\u6742\u5ea6\u662f\u4e2a\u6570\u5b66\u6982\u5ff5\uff0c\u5bf9\u4e8e\u521d\u5b66\u8005\u53ef\u80fd\u6bd4\u8f83\u62bd\u8c61\uff0c\u5b66\u4e60\u96be\u5ea6\u76f8\u5bf9\u8f83\u9ad8\u3002\u4ece\u8fd9\u4e2a\u89d2\u5ea6\u770b\uff0c\u590d\u6742\u5ea6\u5206\u6790\u53ef\u80fd\u4e0d\u592a\u9002\u5408\u4f5c\u4e3a\u7b2c\u4e00\u7ae0\u7684\u5185\u5bb9\u3002\u7136\u800c\uff0c\u5f53\u6211\u4eec\u8ba8\u8bba\u67d0\u4e2a\u6570\u636e\u7ed3\u6784\u6216\u7b97\u6cd5\u7684\u7279\u70b9\u65f6\uff0c\u6211\u4eec\u96be\u4ee5\u907f\u514d\u8981\u5206\u6790\u5176\u8fd0\u884c\u901f\u5ea6\u548c\u7a7a\u95f4\u4f7f\u7528\u60c5\u51b5\u3002\u56e0\u6b64\uff0c\u5728\u6df1\u5165\u5b66\u4e60\u6570\u636e\u7ed3\u6784\u4e0e\u7b97\u6cd5\u4e4b\u524d\uff0c\u5efa\u8bae\u8bfb\u8005\u5148\u5bf9\u590d\u6742\u5ea6\u5efa\u7acb\u521d\u6b65\u7684\u4e86\u89e3\uff0c\u5e76\u80fd\u591f\u5b8c\u6210\u7b80\u5355\u6848\u4f8b\u7684\u590d\u6742\u5ea6\u5206\u6790\u3002</p>"},{"location":"chapter_computational_complexity/space_complexity/","title":"2.3. \u00a0 \u7a7a\u95f4\u590d\u6742\u5ea6","text":"<p>\u300c\u7a7a\u95f4\u590d\u6742\u5ea6 Space Complexity\u300d\u7528\u4e8e\u8861\u91cf\u7b97\u6cd5\u4f7f\u7528\u5185\u5b58\u7a7a\u95f4\u968f\u7740\u6570\u636e\u91cf\u53d8\u5927\u65f6\u7684\u589e\u957f\u8d8b\u52bf\u3002\u8fd9\u4e2a\u6982\u5ff5\u4e0e\u65f6\u95f4\u590d\u6742\u5ea6\u975e\u5e38\u7c7b\u4f3c\u3002</p>"},{"location":"chapter_computational_complexity/space_complexity/#231","title":"2.3.1. \u00a0 \u7b97\u6cd5\u76f8\u5173\u7a7a\u95f4","text":"<p>\u7b97\u6cd5\u8fd0\u884c\u8fc7\u7a0b\u4e2d\u4f7f\u7528\u7684\u5185\u5b58\u7a7a\u95f4\u4e3b\u8981\u5305\u62ec\u4ee5\u4e0b\u51e0\u79cd\uff1a</p> <ul> <li>\u300c\u8f93\u5165\u7a7a\u95f4\u300d\u7528\u4e8e\u5b58\u50a8\u7b97\u6cd5\u7684\u8f93\u5165\u6570\u636e\uff1b</li> <li>\u300c\u6682\u5b58\u7a7a\u95f4\u300d\u7528\u4e8e\u5b58\u50a8\u7b97\u6cd5\u8fd0\u884c\u8fc7\u7a0b\u4e2d\u7684\u53d8\u91cf\u3001\u5bf9\u8c61\u3001\u51fd\u6570\u4e0a\u4e0b\u6587\u7b49\u6570\u636e\uff1b</li> <li>\u300c\u8f93\u51fa\u7a7a\u95f4\u300d\u7528\u4e8e\u5b58\u50a8\u7b97\u6cd5\u7684\u8f93\u51fa\u6570\u636e\uff1b</li> </ul> <p>\u901a\u5e38\u60c5\u51b5\u4e0b\uff0c\u7a7a\u95f4\u590d\u6742\u5ea6\u7edf\u8ba1\u8303\u56f4\u662f\u300c\u6682\u5b58\u7a7a\u95f4\u300d+\u300c\u8f93\u51fa\u7a7a\u95f4\u300d\u3002</p> <p>\u6682\u5b58\u7a7a\u95f4\u53ef\u4ee5\u8fdb\u4e00\u6b65\u5212\u5206\u4e3a\u4e09\u4e2a\u90e8\u5206\uff1a</p> <ul> <li>\u300c\u6682\u5b58\u6570\u636e\u300d\u7528\u4e8e\u4fdd\u5b58\u7b97\u6cd5\u8fd0\u884c\u8fc7\u7a0b\u4e2d\u7684\u5404\u79cd\u5e38\u91cf\u3001\u53d8\u91cf\u3001\u5bf9\u8c61\u7b49\u3002</li> <li>\u300c\u6808\u5e27\u7a7a\u95f4\u300d\u7528\u4e8e\u4fdd\u5b58\u8c03\u7528\u51fd\u6570\u7684\u4e0a\u4e0b\u6587\u6570\u636e\u3002\u7cfb\u7edf\u5728\u6bcf\u6b21\u8c03\u7528\u51fd\u6570\u65f6\u90fd\u4f1a\u5728\u6808\u9876\u90e8\u521b\u5efa\u4e00\u4e2a\u6808\u5e27\uff0c\u51fd\u6570\u8fd4\u56de\u540e\uff0c\u6808\u5e27\u7a7a\u95f4\u4f1a\u88ab\u91ca\u653e\u3002</li> <li>\u300c\u6307\u4ee4\u7a7a\u95f4\u300d\u7528\u4e8e\u4fdd\u5b58\u7f16\u8bd1\u540e\u7684\u7a0b\u5e8f\u6307\u4ee4\uff0c\u5728\u5b9e\u9645\u7edf\u8ba1\u4e2d\u901a\u5e38\u5ffd\u7565\u4e0d\u8ba1\u3002</li> </ul> <p>\u56e0\u6b64\uff0c\u5728\u5206\u6790\u4e00\u6bb5\u7a0b\u5e8f\u7684\u7a7a\u95f4\u590d\u6742\u5ea6\u65f6\uff0c\u6211\u4eec\u4e00\u822c\u7edf\u8ba1 \u6682\u5b58\u6570\u636e\u3001\u8f93\u51fa\u6570\u636e\u3001\u6808\u5e27\u7a7a\u95f4 \u4e09\u90e8\u5206\u3002</p> <p></p> <p> Fig. \u7b97\u6cd5\u4f7f\u7528\u7684\u76f8\u5173\u7a7a\u95f4 </p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart <pre><code>/* \u7c7b */\nclass Node {\nint val;\nNode next;\nNode(int x) { val = x; }\n}\n/* \u51fd\u6570 */\nint function() {\n// do something...\nreturn 0;\n}\nint algorithm(int n) {        // \u8f93\u5165\u6570\u636e\nfinal int a = 0;          // \u6682\u5b58\u6570\u636e\uff08\u5e38\u91cf\uff09\nint b = 0;                // \u6682\u5b58\u6570\u636e\uff08\u53d8\u91cf\uff09\nNode node = new Node(0);  // \u6682\u5b58\u6570\u636e\uff08\u5bf9\u8c61\uff09\nint c = function();       // \u6808\u5e27\u7a7a\u95f4\uff08\u8c03\u7528\u51fd\u6570\uff09\nreturn a + b + c;         // \u8f93\u51fa\u6570\u636e\n}\n</code></pre> <pre><code>/* \u7ed3\u6784\u4f53 */\nstruct Node {\nint val;\nNode *next;\nNode(int x) : val(x), next(nullptr) {}\n};\n/* \u51fd\u6570 */\nint func() {\n// do something...\nreturn 0;\n}\nint algorithm(int n) {        // \u8f93\u5165\u6570\u636e\nconst int a = 0;          // \u6682\u5b58\u6570\u636e\uff08\u5e38\u91cf\uff09\nint b = 0;                // \u6682\u5b58\u6570\u636e\uff08\u53d8\u91cf\uff09\nNode* node = new Node(0); // \u6682\u5b58\u6570\u636e\uff08\u5bf9\u8c61\uff09\nint c = func();           // \u6808\u5e27\u7a7a\u95f4\uff08\u8c03\u7528\u51fd\u6570\uff09\nreturn a + b + c;         // \u8f93\u51fa\u6570\u636e\n}\n</code></pre> <pre><code>class Node:\n\"\"\"\u7c7b\"\"\"\ndef __init__(self, x: int):\nself.val: int = x                 # \u8282\u70b9\u503c\nself.next: Optional[Node] = None  # \u6307\u5411\u4e0b\u4e00\u8282\u70b9\u7684\u6307\u9488\uff08\u5f15\u7528\uff09\ndef function() -&gt; int:\n\"\"\"\u51fd\u6570\"\"\"\n# do something...\nreturn 0\ndef algorithm(n) -&gt; int:  # \u8f93\u5165\u6570\u636e\nA = 0                 # \u6682\u5b58\u6570\u636e\uff08\u5e38\u91cf\uff0c\u4e00\u822c\u7528\u5927\u5199\u5b57\u6bcd\u8868\u793a\uff09\nb = 0                 # \u6682\u5b58\u6570\u636e\uff08\u53d8\u91cf\uff09\nnode = Node(0)        # \u6682\u5b58\u6570\u636e\uff08\u5bf9\u8c61\uff09\nc = function()        # \u6808\u5e27\u7a7a\u95f4\uff08\u8c03\u7528\u51fd\u6570\uff09\nreturn A + b + c      # \u8f93\u51fa\u6570\u636e\n</code></pre> <pre><code>/* \u7ed3\u6784\u4f53 */\ntype node struct {\nval  int\nnext *node\n}\n/* \u521b\u5efa node \u7ed3\u6784\u4f53  */\nfunc newNode(val int) *node {\nreturn &amp;node{val: val}\n}\n/* \u51fd\u6570 */\nfunc function() int {\n// do something...\nreturn 0\n}\nfunc algorithm(n int) int { // \u8f93\u5165\u6570\u636e\nconst a = 0             // \u6682\u5b58\u6570\u636e\uff08\u5e38\u91cf\uff09\nb := 0                  // \u6682\u5b58\u6570\u636e\uff08\u53d8\u91cf\uff09\nnewNode(0)              // \u6682\u5b58\u6570\u636e\uff08\u5bf9\u8c61\uff09\nc := function()         // \u6808\u5e27\u7a7a\u95f4\uff08\u8c03\u7528\u51fd\u6570\uff09\nreturn a + b + c        // \u8f93\u51fa\u6570\u636e\n}\n</code></pre> <pre><code>/* \u7c7b */\nclass Node {\nval;\nnext;\nconstructor(val) {\nthis.val = val === undefined ? 0 : val; // \u8282\u70b9\u503c\nthis.next = null;                       // \u6307\u5411\u4e0b\u4e00\u8282\u70b9\u7684\u5f15\u7528\n}\n}\n/* \u51fd\u6570 */\nfunction constFunc() {\n// do something\nreturn 0;\n}\nfunction algorithm(n) {       // \u8f93\u5165\u6570\u636e\nconst a = 0;              // \u6682\u5b58\u6570\u636e\uff08\u5e38\u91cf\uff09\nlet b = 0;                // \u6682\u5b58\u6570\u636e\uff08\u53d8\u91cf\uff09\nconst node = new Node(0); // \u6682\u5b58\u6570\u636e\uff08\u5bf9\u8c61\uff09\nconst c = constFunc();    // \u6808\u5e27\u7a7a\u95f4\uff08\u8c03\u7528\u51fd\u6570\uff09\nreturn a + b + c;         // \u8f93\u51fa\u6570\u636e\n}\n</code></pre> <pre><code>/* \u7c7b */\nclass Node {\nval: number;\nnext: Node | null;\nconstructor(val?: number) {\nthis.val = val === undefined ? 0 : val; // \u8282\u70b9\u503c\nthis.next = null;                       // \u6307\u5411\u4e0b\u4e00\u8282\u70b9\u7684\u5f15\u7528\n}\n}\n/* \u51fd\u6570 */\nfunction constFunc(): number {\n// do something\nreturn 0;\n}\nfunction algorithm(n: number): number { // \u8f93\u5165\u6570\u636e\nconst a = 0;                        // \u6682\u5b58\u6570\u636e\uff08\u5e38\u91cf\uff09\nlet b = 0;                          // \u6682\u5b58\u6570\u636e\uff08\u53d8\u91cf\uff09\nconst node = new Node(0);           // \u6682\u5b58\u6570\u636e\uff08\u5bf9\u8c61\uff09\nconst c = constFunc();              // \u6808\u5e27\u7a7a\u95f4\uff08\u8c03\u7528\u51fd\u6570\uff09\nreturn a + b + c;                   // \u8f93\u51fa\u6570\u636e\n}\n</code></pre> <pre><code>/* \u51fd\u6570 */\nint func() {\n// do something...\nreturn 0;\n}\nint algorithm(int n) { // \u8f93\u5165\u6570\u636e\nconst int a = 0;   // \u6682\u5b58\u6570\u636e\uff08\u5e38\u91cf\uff09\nint b = 0;         // \u6682\u5b58\u6570\u636e\uff08\u53d8\u91cf\uff09\nint c = func();    // \u6808\u5e27\u7a7a\u95f4\uff08\u8c03\u7528\u51fd\u6570\uff09\nreturn a + b + c;  // \u8f93\u51fa\u6570\u636e\n}\n</code></pre> <pre><code>/* \u7c7b */\nclass Node\n{\nint val;\nNode next;\nNode(int x) { val = x; }\n}\n/* \u51fd\u6570 */\nint function()\n{\n// do something...\nreturn 0;\n}\nint algorithm(int n)          // \u8f93\u5165\u6570\u636e\n{\nconst int a = 0;          // \u6682\u5b58\u6570\u636e\uff08\u5e38\u91cf\uff09\nint b = 0;                // \u6682\u5b58\u6570\u636e\uff08\u53d8\u91cf\uff09\nNode node = new Node(0);  // \u6682\u5b58\u6570\u636e\uff08\u5bf9\u8c61\uff09\nint c = function();       // \u6808\u5e27\u7a7a\u95f4\uff08\u8c03\u7528\u51fd\u6570\uff09\nreturn a + b + c;         // \u8f93\u51fa\u6570\u636e\n}\n</code></pre> <pre><code>/* \u7c7b */\nclass Node {\nvar val: Int\nvar next: Node?\ninit(x: Int) {\nval = x\n}\n}\n/* \u51fd\u6570 */\nfunc function() -&gt; Int {\n// do something...\nreturn 0\n}\nfunc algorithm(n: Int) -&gt; Int { // \u8f93\u5165\u6570\u636e\nlet a = 0             // \u6682\u5b58\u6570\u636e\uff08\u5e38\u91cf\uff09\nvar b = 0             // \u6682\u5b58\u6570\u636e\uff08\u53d8\u91cf\uff09\nlet node = Node(x: 0) // \u6682\u5b58\u6570\u636e\uff08\u5bf9\u8c61\uff09\nlet c = function()    // \u6808\u5e27\u7a7a\u95f4\uff08\u8c03\u7528\u51fd\u6570\uff09\nreturn a + b + c      // \u8f93\u51fa\u6570\u636e\n}\n</code></pre> <pre><code>\n</code></pre> <pre><code>/* \u7c7b */\nclass Node {\nint val;\nNode next;\nNode(this.val, [this.next]);\n}\n/* \u51fd\u6570 */\nint function() {\n// do something...\nreturn 0;\n}\nint algorithm(int n) {  // \u8f93\u5165\u6570\u636e\nconst int a = 0;      // \u6682\u5b58\u6570\u636e\uff08\u5e38\u91cf\uff09\nint b = 0;            // \u6682\u5b58\u6570\u636e\uff08\u53d8\u91cf\uff09\nNode node = Node(0);  // \u6682\u5b58\u6570\u636e\uff08\u5bf9\u8c61\uff09\nint c = function();   // \u6808\u5e27\u7a7a\u95f4\uff08\u8c03\u7528\u51fd\u6570\uff09\nreturn a + b + c;     // \u8f93\u51fa\u6570\u636e\n}\n</code></pre>"},{"location":"chapter_computational_complexity/space_complexity/#232","title":"2.3.2. \u00a0 \u63a8\u7b97\u65b9\u6cd5","text":"<p>\u7a7a\u95f4\u590d\u6742\u5ea6\u7684\u63a8\u7b97\u65b9\u6cd5\u4e0e\u65f6\u95f4\u590d\u6742\u5ea6\u5927\u81f4\u76f8\u540c\uff0c\u53ea\u662f\u5c06\u7edf\u8ba1\u5bf9\u8c61\u4ece\u201c\u8ba1\u7b97\u64cd\u4f5c\u6570\u91cf\u201d\u8f6c\u4e3a\u201c\u4f7f\u7528\u7a7a\u95f4\u5927\u5c0f\u201d\u3002\u4e0e\u65f6\u95f4\u590d\u6742\u5ea6\u4e0d\u540c\u7684\u662f\uff0c\u6211\u4eec\u901a\u5e38\u53ea\u5173\u6ce8\u300c\u6700\u5dee\u7a7a\u95f4\u590d\u6742\u5ea6\u300d\uff0c\u8fd9\u662f\u56e0\u4e3a\u5185\u5b58\u7a7a\u95f4\u662f\u4e00\u9879\u786c\u6027\u8981\u6c42\uff0c\u6211\u4eec\u5fc5\u987b\u786e\u4fdd\u5728\u6240\u6709\u8f93\u5165\u6570\u636e\u4e0b\u90fd\u6709\u8db3\u591f\u7684\u5185\u5b58\u7a7a\u95f4\u9884\u7559\u3002</p> <p>\u6700\u5dee\u7a7a\u95f4\u590d\u6742\u5ea6\u4e2d\u7684\u201c\u6700\u5dee\u201d\u6709\u4e24\u5c42\u542b\u4e49\uff0c\u5206\u522b\u662f\u8f93\u5165\u6570\u636e\u7684\u6700\u5dee\u5206\u5e03\u548c\u7b97\u6cd5\u8fd0\u884c\u8fc7\u7a0b\u4e2d\u7684\u6700\u5dee\u65f6\u95f4\u70b9\u3002</p> <ul> <li>\u4ee5\u6700\u5dee\u8f93\u5165\u6570\u636e\u4e3a\u51c6\u3002\u5f53 \\(n &lt; 10\\) \u65f6\uff0c\u7a7a\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(1)\\) \uff1b\u4f46\u5f53 \\(n &gt; 10\\) \u65f6\uff0c\u521d\u59cb\u5316\u7684\u6570\u7ec4 <code>nums</code> \u5360\u7528 \\(O(n)\\) \u7a7a\u95f4\uff1b\u56e0\u6b64\u6700\u5dee\u7a7a\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(n)\\) \uff1b</li> <li>\u4ee5\u7b97\u6cd5\u8fd0\u884c\u8fc7\u7a0b\u4e2d\u7684\u5cf0\u503c\u5185\u5b58\u4e3a\u51c6\u3002\u4f8b\u5982\uff0c\u7a0b\u5e8f\u5728\u6267\u884c\u6700\u540e\u4e00\u884c\u4e4b\u524d\uff0c\u5360\u7528 \\(O(1)\\) \u7a7a\u95f4\uff1b\u5f53\u521d\u59cb\u5316\u6570\u7ec4 <code>nums</code> \u65f6\uff0c\u7a0b\u5e8f\u5360\u7528 \\(O(n)\\) \u7a7a\u95f4\uff1b\u56e0\u6b64\u6700\u5dee\u7a7a\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(n)\\) \uff1b</li> </ul> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart <pre><code>void algorithm(int n) {\nint a = 0;                   // O(1)\nint[] b = new int[10000];    // O(1)\nif (n &gt; 10)\nint[] nums = new int[n]; // O(n)\n}\n</code></pre> <pre><code>void algorithm(int n) {\nint a = 0;               // O(1)\nvector&lt;int&gt; b(10000);    // O(1)\nif (n &gt; 10)\nvector&lt;int&gt; nums(n); // O(n)\n}\n</code></pre> <pre><code>def algorithm(n: int) -&gt; None:\na = 0                     # O(1)\nb = [0] * 10000     # O(1)\nif n &gt; 10:\nnums = [0] * n  # O(n)\n</code></pre> <pre><code>func algorithm(n int) {\na := 0                      // O(1)\nb := make([]int, 10000)     // O(1)\nvar nums []int\nif n &gt; 10 {\nnums := make([]int, n)  // O(n)\n}\nfmt.Println(a, b, nums)\n}\n</code></pre> <pre><code>function algorithm(n) {\nconst a = 0;                   // O(1)\nconst b = new Array(10000);    // O(1)\nif (n &gt; 10) {\nconst nums = new Array(n); // O(n)\n}\n}\n</code></pre> <pre><code>function algorithm(n: number): void {\nconst a = 0;                   // O(1)\nconst b = new Array(10000);    // O(1)\nif (n &gt; 10) {\nconst nums = new Array(n); // O(n)\n}\n}\n</code></pre> <pre><code>void algorithm(int n) {\nint a = 0;               // O(1)\nint b[10000];            // O(1)\nif (n &gt; 10)\nvector&lt;int&gt; nums(n); // O(n)\n}\n</code></pre> <pre><code>void algorithm(int n)\n{\nint a = 0;                   // O(1)\nint[] b = new int[10000];    // O(1)\nif (n &gt; 10)\n{\nint[] nums = new int[n]; // O(n)\n}\n}\n</code></pre> <pre><code>func algorithm(n: Int) {\nlet a = 0 // O(1)\nlet b = Array(repeating: 0, count: 10000) // O(1)\nif n &gt; 10 {\nlet nums = Array(repeating: 0, count: n) // O(n)\n}\n}\n</code></pre> <pre><code>\n</code></pre> <pre><code>void algorithm(int n) {\nint a = 0;                            // O(1)\nList&lt;int&gt; b = List.filled(10000, 0);  // O(1)\nif (n &gt; 10) {\nList&lt;int&gt; nums = List.filled(n, 0); // O(n)\n}\n}\n</code></pre> <p>\u5728\u9012\u5f52\u51fd\u6570\u4e2d\uff0c\u9700\u8981\u6ce8\u610f\u7edf\u8ba1\u6808\u5e27\u7a7a\u95f4\u3002\u4f8b\u5982\uff0c\u51fd\u6570 <code>loop()</code> \u5728\u5faa\u73af\u4e2d\u8c03\u7528\u4e86 \\(n\\) \u6b21 <code>function()</code> \uff0c\u6bcf\u8f6e\u4e2d\u7684 <code>function()</code> \u90fd\u8fd4\u56de\u5e76\u91ca\u653e\u4e86\u6808\u5e27\u7a7a\u95f4\uff0c\u56e0\u6b64\u7a7a\u95f4\u590d\u6742\u5ea6\u4ecd\u4e3a \\(O(1)\\) \u3002\u800c\u9012\u5f52\u51fd\u6570 <code>recur()</code> \u5728\u8fd0\u884c\u8fc7\u7a0b\u4e2d\u4f1a\u540c\u65f6\u5b58\u5728 \\(n\\) \u4e2a\u672a\u8fd4\u56de\u7684 <code>recur()</code> \uff0c\u4ece\u800c\u5360\u7528 \\(O(n)\\) \u7684\u6808\u5e27\u7a7a\u95f4\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart <pre><code>int function() {\n// do something\nreturn 0;\n}\n/* \u5faa\u73af O(1) */\nvoid loop(int n) {\nfor (int i = 0; i &lt; n; i++) {\nfunction();\n}\n}\n/* \u9012\u5f52 O(n) */\nvoid recur(int n) {\nif (n == 1) return;\nreturn recur(n - 1);\n}\n</code></pre> <pre><code>int func() {\n// do something\nreturn 0;\n}\n/* \u5faa\u73af O(1) */\nvoid loop(int n) {\nfor (int i = 0; i &lt; n; i++) {\nfunc();\n}\n}\n/* \u9012\u5f52 O(n) */\nvoid recur(int n) {\nif (n == 1) return;\nreturn recur(n - 1);\n}\n</code></pre> <pre><code>def function() -&gt; int:\n# do something\nreturn 0\ndef loop(n: int) -&gt; None:\n\"\"\"\u5faa\u73af O(1)\"\"\"\nfor _ in range(n):\nfunction()\ndef recur(n: int) -&gt; int:\n\"\"\"\u9012\u5f52 O(n)\"\"\"\nif n == 1: return\nreturn recur(n - 1)\n</code></pre> <pre><code>func function() int {\n// do something\nreturn 0\n}\n/* \u5faa\u73af O(1) */\nfunc loop(n int) {\nfor i := 0; i &lt; n; i++ {\nfunction()\n}\n}\n/* \u9012\u5f52 O(n) */\nfunc recur(n int) {\nif n == 1 {\nreturn\n}\nrecur(n - 1)\n}\n</code></pre> <pre><code>function constFunc() {\n// do something\nreturn 0;\n}\n/* \u5faa\u73af O(1) */\nfunction loop(n) {\nfor (let i = 0; i &lt; n; i++) {\nconstFunc();\n}\n}\n/* \u9012\u5f52 O(n) */\nfunction recur(n) {\nif (n === 1) return;\nreturn recur(n - 1);\n}\n</code></pre> <pre><code>function constFunc(): number {\n// do something\nreturn 0;\n}\n/* \u5faa\u73af O(1) */\nfunction loop(n: number): void {\nfor (let i = 0; i &lt; n; i++) {\nconstFunc();\n}\n}\n/* \u9012\u5f52 O(n) */\nfunction recur(n: number): void {\nif (n === 1) return;\nreturn recur(n - 1);\n}\n</code></pre> <pre><code>int func() {\n// do something\nreturn 0;\n}\n/* \u5faa\u73af O(1) */\nvoid loop(int n) {\nfor (int i = 0; i &lt; n; i++) {\nfunc();\n}\n}\n/* \u9012\u5f52 O(n) */\nvoid recur(int n) {\nif (n == 1) return;\nreturn recur(n - 1);\n}\n</code></pre> <pre><code>int function()\n{\n// do something\nreturn 0;\n}\n/* \u5faa\u73af O(1) */\nvoid loop(int n)\n{\nfor (int i = 0; i &lt; n; i++)\n{\nfunction();\n}\n}\n/* \u9012\u5f52 O(n) */\nint recur(int n)\n{\nif (n == 1) return 1;\nreturn recur(n - 1);\n}\n</code></pre> <pre><code>@discardableResult\nfunc function() -&gt; Int {\n// do something\nreturn 0\n}\n/* \u5faa\u73af O(1) */\nfunc loop(n: Int) {\nfor _ in 0 ..&lt; n {\nfunction()\n}\n}\n/* \u9012\u5f52 O(n) */\nfunc recur(n: Int) {\nif n == 1 {\nreturn\n}\nrecur(n: n - 1)\n}\n</code></pre> <pre><code>\n</code></pre> <pre><code>int function() {\n// do something\nreturn 0;\n}\n/* \u5faa\u73af O(1) */\nvoid loop(int n) {\nfor (int i = 0; i &lt; n; i++) {\nfunction();\n}\n}\n/* \u9012\u5f52 O(n) */\nvoid recur(int n) {\nif (n == 1) return;\nreturn recur(n - 1);\n}\n</code></pre>"},{"location":"chapter_computational_complexity/space_complexity/#233","title":"2.3.3. \u00a0 \u5e38\u89c1\u7c7b\u578b","text":"<p>\u8bbe\u8f93\u5165\u6570\u636e\u5927\u5c0f\u4e3a \\(n\\) \uff0c\u5e38\u89c1\u7684\u7a7a\u95f4\u590d\u6742\u5ea6\u7c7b\u578b\u6709\uff08\u4ece\u4f4e\u5230\u9ad8\u6392\u5217\uff09</p> \\[ \\begin{aligned} O(1) &lt; O(\\log n) &lt; O(n) &lt; O(n^2) &lt; O(2^n) \\newline \\text{\u5e38\u6570\u9636} &lt; \\text{\u5bf9\u6570\u9636} &lt; \\text{\u7ebf\u6027\u9636} &lt; \\text{\u5e73\u65b9\u9636} &lt; \\text{\u6307\u6570\u9636} \\end{aligned} \\] <p></p> <p> Fig. \u7a7a\u95f4\u590d\u6742\u5ea6\u7684\u5e38\u89c1\u7c7b\u578b </p> <p>Tip</p> <p>\u90e8\u5206\u793a\u4f8b\u4ee3\u7801\u9700\u8981\u4e00\u4e9b\u524d\u7f6e\u77e5\u8bc6\uff0c\u5305\u62ec\u6570\u7ec4\u3001\u94fe\u8868\u3001\u4e8c\u53c9\u6811\u3001\u9012\u5f52\u7b97\u6cd5\u7b49\u3002\u5982\u679c\u9047\u5230\u770b\u4e0d\u61c2\u7684\u5730\u65b9\u65e0\u9700\u62c5\u5fc3\uff0c\u53ef\u4ee5\u5728\u5b66\u4e60\u5b8c\u540e\u9762\u7ae0\u8282\u540e\u518d\u6765\u590d\u4e60\uff0c\u73b0\u9636\u6bb5\u6211\u4eec\u5148\u4e13\u6ce8\u4e8e\u7406\u89e3\u7a7a\u95f4\u590d\u6742\u5ea6\u7684\u542b\u4e49\u548c\u63a8\u7b97\u65b9\u6cd5\u3002</p>"},{"location":"chapter_computational_complexity/space_complexity/#o1","title":"\u5e38\u6570\u9636 \\(O(1)\\)","text":"<p>\u5e38\u6570\u9636\u5e38\u89c1\u4e8e\u6570\u91cf\u4e0e\u8f93\u5165\u6570\u636e\u5927\u5c0f \\(n\\) \u65e0\u5173\u7684\u5e38\u91cf\u3001\u53d8\u91cf\u3001\u5bf9\u8c61\u3002</p> <p>\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u5728\u5faa\u73af\u4e2d\u521d\u59cb\u5316\u53d8\u91cf\u6216\u8c03\u7528\u51fd\u6570\u800c\u5360\u7528\u7684\u5185\u5b58\uff0c\u5728\u8fdb\u5165\u4e0b\u4e00\u5faa\u73af\u540e\u5c31\u4f1a\u88ab\u91ca\u653e\uff0c\u5373\u4e0d\u4f1a\u7d2f\u79ef\u5360\u7528\u7a7a\u95f4\uff0c\u7a7a\u95f4\u590d\u6742\u5ea6\u4ecd\u4e3a \\(O(1)\\) \u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart space_complexity.java<pre><code>/* \u5e38\u6570\u9636 */\nvoid constant(int n) {\n// \u5e38\u91cf\u3001\u53d8\u91cf\u3001\u5bf9\u8c61\u5360\u7528 O(1) \u7a7a\u95f4\nfinal int a = 0;\nint b = 0;\nint[] nums = new int[10000];\nListNode node = new ListNode(0);\n// \u5faa\u73af\u4e2d\u7684\u53d8\u91cf\u5360\u7528 O(1) \u7a7a\u95f4\nfor (int i = 0; i &lt; n; i++) {\nint c = 0;\n}\n// \u5faa\u73af\u4e2d\u7684\u51fd\u6570\u5360\u7528 O(1) \u7a7a\u95f4\nfor (int i = 0; i &lt; n; i++) {\nfunction();\n}\n}\n</code></pre> space_complexity.cpp<pre><code>/* \u5e38\u6570\u9636 */\nvoid constant(int n) {\n// \u5e38\u91cf\u3001\u53d8\u91cf\u3001\u5bf9\u8c61\u5360\u7528 O(1) \u7a7a\u95f4\nconst int a = 0;\nint b = 0;\nvector&lt;int&gt; nums(10000);\nListNode node(0);\n// \u5faa\u73af\u4e2d\u7684\u53d8\u91cf\u5360\u7528 O(1) \u7a7a\u95f4\nfor (int i = 0; i &lt; n; i++) {\nint c = 0;\n}\n// \u5faa\u73af\u4e2d\u7684\u51fd\u6570\u5360\u7528 O(1) \u7a7a\u95f4\nfor (int i = 0; i &lt; n; i++) {\nfunc();\n}\n}\n</code></pre> space_complexity.py<pre><code>def constant(n: int) -&gt; None:\n\"\"\"\u5e38\u6570\u9636\"\"\"\n# \u5e38\u91cf\u3001\u53d8\u91cf\u3001\u5bf9\u8c61\u5360\u7528 O(1) \u7a7a\u95f4\na = 0\nnums = [0] * 10000\nnode = ListNode(0)\n# \u5faa\u73af\u4e2d\u7684\u53d8\u91cf\u5360\u7528 O(1) \u7a7a\u95f4\nfor _ in range(n):\nc = 0\n# \u5faa\u73af\u4e2d\u7684\u51fd\u6570\u5360\u7528 O(1) \u7a7a\u95f4\nfor _ in range(n):\nfunction()\n</code></pre> space_complexity.go<pre><code>/* \u5e38\u6570\u9636 */\nfunc spaceConstant(n int) {\n// \u5e38\u91cf\u3001\u53d8\u91cf\u3001\u5bf9\u8c61\u5360\u7528 O(1) \u7a7a\u95f4\nconst a = 0\nb := 0\nnums := make([]int, 10000)\nListNode := newNode(0)\n// \u5faa\u73af\u4e2d\u7684\u53d8\u91cf\u5360\u7528 O(1) \u7a7a\u95f4\nvar c int\nfor i := 0; i &lt; n; i++ {\nc = 0\n}\n// \u5faa\u73af\u4e2d\u7684\u51fd\u6570\u5360\u7528 O(1) \u7a7a\u95f4\nfor i := 0; i &lt; n; i++ {\nfunction()\n}\nfmt.Println(a, b, nums, c, ListNode)\n}\n</code></pre> space_complexity.js<pre><code>/* \u5e38\u6570\u9636 */\nfunction constant(n) {\n// \u5e38\u91cf\u3001\u53d8\u91cf\u3001\u5bf9\u8c61\u5360\u7528 O(1) \u7a7a\u95f4\nconst a = 0;\nconst b = 0;\nconst nums = new Array(10000);\nconst node = new ListNode(0);\n// \u5faa\u73af\u4e2d\u7684\u53d8\u91cf\u5360\u7528 O(1) \u7a7a\u95f4\nfor (let i = 0; i &lt; n; i++) {\nconst c = 0;\n}\n// \u5faa\u73af\u4e2d\u7684\u51fd\u6570\u5360\u7528 O(1) \u7a7a\u95f4\nfor (let i = 0; i &lt; n; i++) {\nconstFunc();\n}\n}\n</code></pre> space_complexity.ts<pre><code>/* \u5e38\u6570\u9636 */\nfunction constant(n: number): void {\n// \u5e38\u91cf\u3001\u53d8\u91cf\u3001\u5bf9\u8c61\u5360\u7528 O(1) \u7a7a\u95f4\nconst a = 0;\nconst b = 0;\nconst nums = new Array(10000);\nconst node = new ListNode(0);\n// \u5faa\u73af\u4e2d\u7684\u53d8\u91cf\u5360\u7528 O(1) \u7a7a\u95f4\nfor (let i = 0; i &lt; n; i++) {\nconst c = 0;\n}\n// \u5faa\u73af\u4e2d\u7684\u51fd\u6570\u5360\u7528 O(1) \u7a7a\u95f4\nfor (let i = 0; i &lt; n; i++) {\nconstFunc();\n}\n}\n</code></pre> space_complexity.c<pre><code>/* \u5e38\u6570\u9636 */\nvoid constant(int n) {\n// \u5e38\u91cf\u3001\u53d8\u91cf\u3001\u5bf9\u8c61\u5360\u7528 O(1) \u7a7a\u95f4\nconst int a = 0;\nint b = 0;\nint nums[1000];\nListNode *node = newListNode(0);\nfree(node);\n// \u5faa\u73af\u4e2d\u7684\u53d8\u91cf\u5360\u7528 O(1) \u7a7a\u95f4\nfor (int i = 0; i &lt; n; i++) {\nint c = 0;\n}\n// \u5faa\u73af\u4e2d\u7684\u51fd\u6570\u5360\u7528 O(1) \u7a7a\u95f4\nfor (int i = 0; i &lt; n; i++) {\nfunc();\n}\n}\n</code></pre> space_complexity.cs<pre><code>/* \u5e38\u6570\u9636 */\nvoid constant(int n) {\n// \u5e38\u91cf\u3001\u53d8\u91cf\u3001\u5bf9\u8c61\u5360\u7528 O(1) \u7a7a\u95f4\nint a = 0;\nint b = 0;\nint[] nums = new int[10000];\nListNode node = new ListNode(0);\n// \u5faa\u73af\u4e2d\u7684\u53d8\u91cf\u5360\u7528 O(1) \u7a7a\u95f4\nfor (int i = 0; i &lt; n; i++) {\nint c = 0;\n}\n// \u5faa\u73af\u4e2d\u7684\u51fd\u6570\u5360\u7528 O(1) \u7a7a\u95f4\nfor (int i = 0; i &lt; n; i++) {\nfunction();\n}\n}\n</code></pre> space_complexity.swift<pre><code>/* \u5e38\u6570\u9636 */\nfunc constant(n: Int) {\n// \u5e38\u91cf\u3001\u53d8\u91cf\u3001\u5bf9\u8c61\u5360\u7528 O(1) \u7a7a\u95f4\nlet a = 0\nvar b = 0\nlet nums = Array(repeating: 0, count: 10000)\nlet node = ListNode(x: 0)\n// \u5faa\u73af\u4e2d\u7684\u53d8\u91cf\u5360\u7528 O(1) \u7a7a\u95f4\nfor _ in 0 ..&lt; n {\nlet c = 0\n}\n// \u5faa\u73af\u4e2d\u7684\u51fd\u6570\u5360\u7528 O(1) \u7a7a\u95f4\nfor _ in 0 ..&lt; n {\nfunction()\n}\n}\n</code></pre> space_complexity.zig<pre><code>// \u5e38\u6570\u9636\nfn constant(n: i32) void {\n// \u5e38\u91cf\u3001\u53d8\u91cf\u3001\u5bf9\u8c61\u5360\u7528 O(1) \u7a7a\u95f4\nconst a: i32 = 0;\nvar b: i32 = 0;\nvar nums = [_]i32{0}**10000;\nvar node = inc.ListNode(i32){.val = 0};\nvar i: i32 = 0;\n// \u5faa\u73af\u4e2d\u7684\u53d8\u91cf\u5360\u7528 O(1) \u7a7a\u95f4\nwhile (i &lt; n) : (i += 1) {\nvar c: i32 = 0;\n_ = c;\n}\n// \u5faa\u73af\u4e2d\u7684\u51fd\u6570\u5360\u7528 O(1) \u7a7a\u95f4\ni = 0;\nwhile (i &lt; n) : (i += 1) {\n_ = function();\n}\n_ = a;\n_ = b;\n_ = nums;\n_ = node;\n}\n</code></pre> space_complexity.dart<pre><code>/* \u5e38\u6570\u9636 */\nvoid constant(int n) {\n// \u5e38\u91cf\u3001\u53d8\u91cf\u3001\u5bf9\u8c61\u5360\u7528 O(1) \u7a7a\u95f4\nfinal int a = 0;\nint b = 0;\nList&lt;int&gt; nums = List.filled(10000, 0);\n// \u5faa\u73af\u4e2d\u7684\u53d8\u91cf\u5360\u7528 O(1) \u7a7a\u95f4\nfor (var i = 0; i &lt; n; i++) {\nint c = 0;\n}\n// \u5faa\u73af\u4e2d\u7684\u51fd\u6570\u5360\u7528 O(1) \u7a7a\u95f4\nfor (var i = 0; i &lt; n; i++) {\nfunction();\n}\n}\n</code></pre>"},{"location":"chapter_computational_complexity/space_complexity/#on","title":"\u7ebf\u6027\u9636 \\(O(n)\\)","text":"<p>\u7ebf\u6027\u9636\u5e38\u89c1\u4e8e\u5143\u7d20\u6570\u91cf\u4e0e \\(n\\) \u6210\u6b63\u6bd4\u7684\u6570\u7ec4\u3001\u94fe\u8868\u3001\u6808\u3001\u961f\u5217\u7b49\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart space_complexity.java<pre><code>/* \u7ebf\u6027\u9636 */\nvoid linear(int n) {\n// \u957f\u5ea6\u4e3a n \u7684\u6570\u7ec4\u5360\u7528 O(n) \u7a7a\u95f4\nint[] nums = new int[n];\n// \u957f\u5ea6\u4e3a n \u7684\u5217\u8868\u5360\u7528 O(n) \u7a7a\u95f4\nList&lt;ListNode&gt; nodes = new ArrayList&lt;&gt;();\nfor (int i = 0; i &lt; n; i++) {\nnodes.add(new ListNode(i));\n}\n// \u957f\u5ea6\u4e3a n \u7684\u54c8\u5e0c\u8868\u5360\u7528 O(n) \u7a7a\u95f4\nMap&lt;Integer, String&gt; map = new HashMap&lt;&gt;();\nfor (int i = 0; i &lt; n; i++) {\nmap.put(i, String.valueOf(i));\n}\n}\n</code></pre> space_complexity.cpp<pre><code>/* \u7ebf\u6027\u9636 */\nvoid linear(int n) {\n// \u957f\u5ea6\u4e3a n \u7684\u6570\u7ec4\u5360\u7528 O(n) \u7a7a\u95f4\nvector&lt;int&gt; nums(n);\n// \u957f\u5ea6\u4e3a n \u7684\u5217\u8868\u5360\u7528 O(n) \u7a7a\u95f4\nvector&lt;ListNode&gt; nodes;\nfor (int i = 0; i &lt; n; i++) {\nnodes.push_back(ListNode(i));\n}\n// \u957f\u5ea6\u4e3a n \u7684\u54c8\u5e0c\u8868\u5360\u7528 O(n) \u7a7a\u95f4\nunordered_map&lt;int, string&gt; map;\nfor (int i = 0; i &lt; n; i++) {\nmap[i] = to_string(i);\n}\n}\n</code></pre> space_complexity.py<pre><code>def linear(n: int) -&gt; None:\n\"\"\"\u7ebf\u6027\u9636\"\"\"\n# \u957f\u5ea6\u4e3a n \u7684\u5217\u8868\u5360\u7528 O(n) \u7a7a\u95f4\nnums = [0] * n\n# \u957f\u5ea6\u4e3a n \u7684\u54c8\u5e0c\u8868\u5360\u7528 O(n) \u7a7a\u95f4\nmapp = dict[int, str]()\nfor i in range(n):\nmapp[i] = str(i)\n</code></pre> space_complexity.go<pre><code>/* \u7ebf\u6027\u9636 */\nfunc spaceLinear(n int) {\n// \u957f\u5ea6\u4e3a n \u7684\u6570\u7ec4\u5360\u7528 O(n) \u7a7a\u95f4\n_ = make([]int, n)\n// \u957f\u5ea6\u4e3a n \u7684\u5217\u8868\u5360\u7528 O(n) \u7a7a\u95f4\nvar nodes []*node\nfor i := 0; i &lt; n; i++ {\nnodes = append(nodes, newNode(i))\n}\n// \u957f\u5ea6\u4e3a n \u7684\u54c8\u5e0c\u8868\u5360\u7528 O(n) \u7a7a\u95f4\nm := make(map[int]string, n)\nfor i := 0; i &lt; n; i++ {\nm[i] = strconv.Itoa(i)\n}\n}\n</code></pre> space_complexity.js<pre><code>/* \u7ebf\u6027\u9636 */\nfunction linear(n) {\n// \u957f\u5ea6\u4e3a n \u7684\u6570\u7ec4\u5360\u7528 O(n) \u7a7a\u95f4\nconst nums = new Array(n);\n// \u957f\u5ea6\u4e3a n \u7684\u5217\u8868\u5360\u7528 O(n) \u7a7a\u95f4\nconst nodes = [];\nfor (let i = 0; i &lt; n; i++) {\nnodes.push(new ListNode(i));\n}\n// \u957f\u5ea6\u4e3a n \u7684\u54c8\u5e0c\u8868\u5360\u7528 O(n) \u7a7a\u95f4\nconst map = new Map();\nfor (let i = 0; i &lt; n; i++) {\nmap.set(i, i.toString());\n}\n}\n</code></pre> space_complexity.ts<pre><code>/* \u7ebf\u6027\u9636 */\nfunction linear(n: number): void {\n// \u957f\u5ea6\u4e3a n \u7684\u6570\u7ec4\u5360\u7528 O(n) \u7a7a\u95f4\nconst nums = new Array(n);\n// \u957f\u5ea6\u4e3a n \u7684\u5217\u8868\u5360\u7528 O(n) \u7a7a\u95f4\nconst nodes: ListNode[] = [];\nfor (let i = 0; i &lt; n; i++) {\nnodes.push(new ListNode(i));\n}\n// \u957f\u5ea6\u4e3a n \u7684\u54c8\u5e0c\u8868\u5360\u7528 O(n) \u7a7a\u95f4\nconst map = new Map();\nfor (let i = 0; i &lt; n; i++) {\nmap.set(i, i.toString());\n}\n}\n</code></pre> space_complexity.c<pre><code>/* \u54c8\u5e0c\u8868 */\nstruct hashTable {\nint key;\nint val;\nUT_hash_handle hh; // \u57fa\u4e8e uthash.h \u5b9e\u73b0\n};\ntypedef struct hashTable hashTable;\n/* \u7ebf\u6027\u9636 */\nvoid linear(int n) {\n// \u957f\u5ea6\u4e3a n \u7684\u6570\u7ec4\u5360\u7528 O(n) \u7a7a\u95f4\nint *nums = malloc(sizeof(int) * n);\nfree(nums);\n// \u957f\u5ea6\u4e3a n \u7684\u5217\u8868\u5360\u7528 O(n) \u7a7a\u95f4\nListNode **nodes = malloc(sizeof(ListNode *) * n);\nfor (int i = 0; i &lt; n; i++) {\nnodes[i] = newListNode(i);\n}\n// \u5185\u5b58\u91ca\u653e\nfor (int i = 0; i &lt; n; i++) {\nfree(nodes[i]);\n}\nfree(nodes);\n// \u957f\u5ea6\u4e3a n \u7684\u54c8\u5e0c\u8868\u5360\u7528 O(n) \u7a7a\u95f4\nhashTable *h = NULL;\nfor (int i = 0; i &lt; n; i++) {\nhashTable *tmp = malloc(sizeof(hashTable));\ntmp-&gt;key = i;\ntmp-&gt;val = i;\nHASH_ADD_INT(h, key, tmp);\n}\n// \u5185\u5b58\u91ca\u653e\nhashTable *curr, *tmp;\nHASH_ITER(hh, h, curr, tmp) {\nHASH_DEL(h, curr);\nfree(curr);\n}\n}\n</code></pre> space_complexity.cs<pre><code>/* \u7ebf\u6027\u9636 */\nvoid linear(int n) {\n// \u957f\u5ea6\u4e3a n \u7684\u6570\u7ec4\u5360\u7528 O(n) \u7a7a\u95f4\nint[] nums = new int[n];\n// \u957f\u5ea6\u4e3a n \u7684\u5217\u8868\u5360\u7528 O(n) \u7a7a\u95f4\nList&lt;ListNode&gt; nodes = new();\nfor (int i = 0; i &lt; n; i++) {\nnodes.Add(new ListNode(i));\n}\n// \u957f\u5ea6\u4e3a n \u7684\u54c8\u5e0c\u8868\u5360\u7528 O(n) \u7a7a\u95f4\nDictionary&lt;int, string&gt; map = new();\nfor (int i = 0; i &lt; n; i++) {\nmap.Add(i, i.ToString());\n}\n}\n</code></pre> space_complexity.swift<pre><code>/* \u7ebf\u6027\u9636 */\nfunc linear(n: Int) {\n// \u957f\u5ea6\u4e3a n \u7684\u6570\u7ec4\u5360\u7528 O(n) \u7a7a\u95f4\nlet nums = Array(repeating: 0, count: n)\n// \u957f\u5ea6\u4e3a n \u7684\u5217\u8868\u5360\u7528 O(n) \u7a7a\u95f4\nlet nodes = (0 ..&lt; n).map { ListNode(x: $0) }\n// \u957f\u5ea6\u4e3a n \u7684\u54c8\u5e0c\u8868\u5360\u7528 O(n) \u7a7a\u95f4\nlet map = Dictionary(uniqueKeysWithValues: (0 ..&lt; n).map { ($0, \"\\($0)\") })\n}\n</code></pre> space_complexity.zig<pre><code>// \u7ebf\u6027\u9636\nfn linear(comptime n: i32) !void {\n// \u957f\u5ea6\u4e3a n \u7684\u6570\u7ec4\u5360\u7528 O(n) \u7a7a\u95f4\nvar nums = [_]i32{0}**n;\n// \u957f\u5ea6\u4e3a n \u7684\u5217\u8868\u5360\u7528 O(n) \u7a7a\u95f4\nvar nodes = std.ArrayList(i32).init(std.heap.page_allocator);\ndefer nodes.deinit();\nvar i: i32 = 0;\nwhile (i &lt; n) : (i += 1) {\ntry nodes.append(i);\n}\n// \u957f\u5ea6\u4e3a n \u7684\u54c8\u5e0c\u8868\u5360\u7528 O(n) \u7a7a\u95f4\nvar map = std.AutoArrayHashMap(i32, []const u8).init(std.heap.page_allocator);\ndefer map.deinit();\nvar j: i32 = 0;\nwhile (j &lt; n) : (j += 1) {\nconst string = try std.fmt.allocPrint(std.heap.page_allocator, \"{d}\", .{j});\ndefer std.heap.page_allocator.free(string);\ntry map.put(i, string);\n}\n_ = nums;\n}\n</code></pre> space_complexity.dart<pre><code>/* \u7ebf\u6027\u9636 */\nvoid linear(int n) {\n// \u957f\u5ea6\u4e3a n \u7684\u6570\u7ec4\u5360\u7528 O(n) \u7a7a\u95f4\nList&lt;int&gt; nums = List.filled(n, 0);\n// \u957f\u5ea6\u4e3a n \u7684\u5217\u8868\u5360\u7528 O(n) \u7a7a\u95f4\nList&lt;ListNode&gt; nodes = [];\nfor (var i = 0; i &lt; n; i++) {\nnodes.add(ListNode(i));\n}\n// \u957f\u5ea6\u4e3a n \u7684\u54c8\u5e0c\u8868\u5360\u7528 O(n) \u7a7a\u95f4\nMap&lt;int, String&gt; map = HashMap();\nfor (var i = 0; i &lt; n; i++) {\nmap.putIfAbsent(i, () =&gt; i.toString());\n}\n}\n</code></pre> <p>\u4ee5\u4e0b\u9012\u5f52\u51fd\u6570\u4f1a\u540c\u65f6\u5b58\u5728 \\(n\\) \u4e2a\u672a\u8fd4\u56de\u7684 <code>algorithm()</code> \u51fd\u6570\uff0c\u4f7f\u7528 \\(O(n)\\) \u5927\u5c0f\u7684\u6808\u5e27\u7a7a\u95f4\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart space_complexity.java<pre><code>/* \u7ebf\u6027\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nvoid linearRecur(int n) {\nSystem.out.println(\"\u9012\u5f52 n = \" + n);\nif (n == 1)\nreturn;\nlinearRecur(n - 1);\n}\n</code></pre> space_complexity.cpp<pre><code>/* \u7ebf\u6027\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nvoid linearRecur(int n) {\ncout &lt;&lt; \"\u9012\u5f52 n = \" &lt;&lt; n &lt;&lt; endl;\nif (n == 1)\nreturn;\nlinearRecur(n - 1);\n}\n</code></pre> space_complexity.py<pre><code>def linear_recur(n: int) -&gt; None:\n\"\"\"\u7ebf\u6027\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09\"\"\"\nprint(\"\u9012\u5f52 n =\", n)\nif n == 1:\nreturn\nlinear_recur(n - 1)\n</code></pre> space_complexity.go<pre><code>/* \u7ebf\u6027\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nfunc spaceLinearRecur(n int) {\nfmt.Println(\"\u9012\u5f52 n =\", n)\nif n == 1 {\nreturn\n}\nspaceLinearRecur(n - 1)\n}\n</code></pre> space_complexity.js<pre><code>/* \u7ebf\u6027\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nfunction linearRecur(n) {\nconsole.log(`\u9012\u5f52 n = ${n}`);\nif (n === 1) return;\nlinearRecur(n - 1);\n}\n</code></pre> space_complexity.ts<pre><code>/* \u7ebf\u6027\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nfunction linearRecur(n: number): void {\nconsole.log(`\u9012\u5f52 n = ${n}`);\nif (n === 1) return;\nlinearRecur(n - 1);\n}\n</code></pre> space_complexity.c<pre><code>/* \u7ebf\u6027\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nvoid linearRecur(int n) {\nprintf(\"\u9012\u5f52 n = %d\\r\\n\", n);\nif (n == 1)\nreturn;\nlinearRecur(n - 1);\n}\n</code></pre> space_complexity.cs<pre><code>/* \u7ebf\u6027\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nvoid linearRecur(int n) {\nConsole.WriteLine(\"\u9012\u5f52 n = \" + n);\nif (n == 1) return;\nlinearRecur(n - 1);\n}\n</code></pre> space_complexity.swift<pre><code>/* \u7ebf\u6027\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nfunc linearRecur(n: Int) {\nprint(\"\u9012\u5f52 n = \\(n)\")\nif n == 1 {\nreturn\n}\nlinearRecur(n: n - 1)\n}\n</code></pre> space_complexity.zig<pre><code>// \u7ebf\u6027\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09\nfn linearRecur(comptime n: i32) void {\nstd.debug.print(\"\u9012\u5f52 n = {}\\n\", .{n});\nif (n == 1) return;\nlinearRecur(n - 1);\n}\n</code></pre> space_complexity.dart<pre><code>/* \u7ebf\u6027\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nvoid linearRecur(int n) {\nprint('\u9012\u5f52 n = $n');\nif (n == 1) return;\nlinearRecur(n - 1);\n}\n</code></pre> <p></p> <p> Fig. \u9012\u5f52\u51fd\u6570\u4ea7\u751f\u7684\u7ebf\u6027\u9636\u7a7a\u95f4\u590d\u6742\u5ea6 </p>"},{"location":"chapter_computational_complexity/space_complexity/#on2","title":"\u5e73\u65b9\u9636 \\(O(n^2)\\)","text":"<p>\u5e73\u65b9\u9636\u5e38\u89c1\u4e8e\u77e9\u9635\u548c\u56fe\uff0c\u5143\u7d20\u6570\u91cf\u4e0e \\(n\\) \u6210\u5e73\u65b9\u5173\u7cfb\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart space_complexity.java<pre><code>/* \u5e73\u65b9\u9636 */\nvoid quadratic(int n) {\n// \u77e9\u9635\u5360\u7528 O(n^2) \u7a7a\u95f4\nint[][] numMatrix = new int[n][n];\n// \u4e8c\u7ef4\u5217\u8868\u5360\u7528 O(n^2) \u7a7a\u95f4\nList&lt;List&lt;Integer&gt;&gt; numList = new ArrayList&lt;&gt;();\nfor (int i = 0; i &lt; n; i++) {\nList&lt;Integer&gt; tmp = new ArrayList&lt;&gt;();\nfor (int j = 0; j &lt; n; j++) {\ntmp.add(0);\n}\nnumList.add(tmp);\n}\n}\n</code></pre> space_complexity.cpp<pre><code>/* \u5e73\u65b9\u9636 */\nvoid quadratic(int n) {\n// \u4e8c\u7ef4\u5217\u8868\u5360\u7528 O(n^2) \u7a7a\u95f4\nvector&lt;vector&lt;int&gt;&gt; numMatrix;\nfor (int i = 0; i &lt; n; i++) {\nvector&lt;int&gt; tmp;\nfor (int j = 0; j &lt; n; j++) {\ntmp.push_back(0);\n}\nnumMatrix.push_back(tmp);\n}\n}\n</code></pre> space_complexity.py<pre><code>def quadratic(n: int) -&gt; None:\n\"\"\"\u5e73\u65b9\u9636\"\"\"\n# \u4e8c\u7ef4\u5217\u8868\u5360\u7528 O(n^2) \u7a7a\u95f4\nnum_matrix = [[0] * n for _ in range(n)]\n</code></pre> space_complexity.go<pre><code>/* \u5e73\u65b9\u9636 */\nfunc spaceQuadratic(n int) {\n// \u77e9\u9635\u5360\u7528 O(n^2) \u7a7a\u95f4\nnumMatrix := make([][]int, n)\nfor i := 0; i &lt; n; i++ {\nnumMatrix[i] = make([]int, n)\n}\n}\n</code></pre> space_complexity.js<pre><code>/* \u5e73\u65b9\u9636 */\nfunction quadratic(n) {\n// \u77e9\u9635\u5360\u7528 O(n^2) \u7a7a\u95f4\nconst numMatrix = Array(n)\n.fill(null)\n.map(() =&gt; Array(n).fill(null));\n// \u4e8c\u7ef4\u5217\u8868\u5360\u7528 O(n^2) \u7a7a\u95f4\nconst numList = [];\nfor (let i = 0; i &lt; n; i++) {\nconst tmp = [];\nfor (let j = 0; j &lt; n; j++) {\ntmp.push(0);\n}\nnumList.push(tmp);\n}\n}\n</code></pre> space_complexity.ts<pre><code>/* \u5e73\u65b9\u9636 */\nfunction quadratic(n: number): void {\n// \u77e9\u9635\u5360\u7528 O(n^2) \u7a7a\u95f4\nconst numMatrix = Array(n)\n.fill(null)\n.map(() =&gt; Array(n).fill(null));\n// \u4e8c\u7ef4\u5217\u8868\u5360\u7528 O(n^2) \u7a7a\u95f4\nconst numList = [];\nfor (let i = 0; i &lt; n; i++) {\nconst tmp = [];\nfor (let j = 0; j &lt; n; j++) {\ntmp.push(0);\n}\nnumList.push(tmp);\n}\n}\n</code></pre> space_complexity.c<pre><code>/* \u5e73\u65b9\u9636 */\nvoid quadratic(int n) {\n// \u4e8c\u7ef4\u5217\u8868\u5360\u7528 O(n^2) \u7a7a\u95f4\nint **numMatrix = malloc(sizeof(int *) * n);\nfor (int i = 0; i &lt; n; i++) {\nint *tmp = malloc(sizeof(int) * n);\nfor (int j = 0; j &lt; n; j++) {\ntmp[j] = 0;\n}\nnumMatrix[i] = tmp;\n}\n// \u5185\u5b58\u91ca\u653e\nfor (int i = 0; i &lt; n; i++) {\nfree(numMatrix[i]);\n}\nfree(numMatrix);\n}\n</code></pre> space_complexity.cs<pre><code>/* \u5e73\u65b9\u9636 */\nvoid quadratic(int n) {\n// \u77e9\u9635\u5360\u7528 O(n^2) \u7a7a\u95f4\nint[,] numMatrix = new int[n, n];\n// \u4e8c\u7ef4\u5217\u8868\u5360\u7528 O(n^2) \u7a7a\u95f4\nList&lt;List&lt;int&gt;&gt; numList = new();\nfor (int i = 0; i &lt; n; i++) {\nList&lt;int&gt; tmp = new();\nfor (int j = 0; j &lt; n; j++) {\ntmp.Add(0);\n}\nnumList.Add(tmp);\n}\n}\n</code></pre> space_complexity.swift<pre><code>/* \u5e73\u65b9\u9636 */\nfunc quadratic(n: Int) {\n// \u4e8c\u7ef4\u5217\u8868\u5360\u7528 O(n^2) \u7a7a\u95f4\nlet numList = Array(repeating: Array(repeating: 0, count: n), count: n)\n}\n</code></pre> space_complexity.zig<pre><code>// \u5e73\u65b9\u9636\nfn quadratic(n: i32) !void {\n// \u4e8c\u7ef4\u5217\u8868\u5360\u7528 O(n^2) \u7a7a\u95f4\nvar nodes = std.ArrayList(std.ArrayList(i32)).init(std.heap.page_allocator);\ndefer nodes.deinit();\nvar i: i32 = 0;\nwhile (i &lt; n) : (i += 1) {\nvar tmp = std.ArrayList(i32).init(std.heap.page_allocator);\ndefer tmp.deinit();\nvar j: i32 = 0;\nwhile (j &lt; n) : (j += 1) {\ntry tmp.append(0);\n}\ntry nodes.append(tmp);\n}\n}\n</code></pre> space_complexity.dart<pre><code>/* \u5e73\u65b9\u9636 */\nvoid quadratic(int n) {\n// \u77e9\u9635\u5360\u7528 O(n^2) \u7a7a\u95f4\nList&lt;List&lt;int&gt;&gt; numMatrix = List.generate(n, (_) =&gt; List.filled(n, 0));\n// \u4e8c\u7ef4\u5217\u8868\u5360\u7528 O(n^2) \u7a7a\u95f4\nList&lt;List&lt;int&gt;&gt; numList = [];\nfor (var i = 0; i &lt; n; i++) {\nList&lt;int&gt; tmp = [];\nfor (int j = 0; j &lt; n; j++) {\ntmp.add(0);\n}\nnumList.add(tmp);\n}\n}\n</code></pre> <p>\u5728\u4ee5\u4e0b\u9012\u5f52\u51fd\u6570\u4e2d\uff0c\u540c\u65f6\u5b58\u5728 \\(n\\) \u4e2a\u672a\u8fd4\u56de\u7684 <code>algorithm()</code> \uff0c\u5e76\u4e14\u6bcf\u4e2a\u51fd\u6570\u4e2d\u90fd\u521d\u59cb\u5316\u4e86\u4e00\u4e2a\u6570\u7ec4\uff0c\u957f\u5ea6\u5206\u522b\u4e3a \\(n, n-1, n-2, ..., 2, 1\\) \uff0c\u5e73\u5747\u957f\u5ea6\u4e3a \\(\\frac{n}{2}\\) \uff0c\u56e0\u6b64\u603b\u4f53\u5360\u7528 \\(O(n^2)\\) \u7a7a\u95f4\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart space_complexity.java<pre><code>/* \u5e73\u65b9\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nint quadraticRecur(int n) {\nif (n &lt;= 0)\nreturn 0;\n// \u6570\u7ec4 nums \u957f\u5ea6\u4e3a n, n-1, ..., 2, 1\nint[] nums = new int[n];\nSystem.out.println(\"\u9012\u5f52 n = \" + n + \" \u4e2d\u7684 nums \u957f\u5ea6 = \" + nums.length);\nreturn quadraticRecur(n - 1);\n}\n</code></pre> space_complexity.cpp<pre><code>/* \u5e73\u65b9\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nint quadraticRecur(int n) {\nif (n &lt;= 0)\nreturn 0;\nvector&lt;int&gt; nums(n);\ncout &lt;&lt; \"\u9012\u5f52 n = \" &lt;&lt; n &lt;&lt; \" \u4e2d\u7684 nums \u957f\u5ea6 = \" &lt;&lt; nums.size() &lt;&lt; endl;\nreturn quadraticRecur(n - 1);\n}\n</code></pre> space_complexity.py<pre><code>def quadratic_recur(n: int) -&gt; int:\n\"\"\"\u5e73\u65b9\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09\"\"\"\nif n &lt;= 0:\nreturn 0\n# \u6570\u7ec4 nums \u957f\u5ea6\u4e3a n, n-1, ..., 2, 1\nnums = [0] * n\nreturn quadratic_recur(n - 1)\n</code></pre> space_complexity.go<pre><code>/* \u5e73\u65b9\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nfunc spaceQuadraticRecur(n int) int {\nif n &lt;= 0 {\nreturn 0\n}\nnums := make([]int, n)\nfmt.Printf(\"\u9012\u5f52 n = %d \u4e2d\u7684 nums \u957f\u5ea6 = %d \\n\", n, len(nums))\nreturn spaceQuadraticRecur(n - 1)\n}\n</code></pre> space_complexity.js<pre><code>/* \u5e73\u65b9\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nfunction quadraticRecur(n) {\nif (n &lt;= 0) return 0;\nconst nums = new Array(n);\nconsole.log(`\u9012\u5f52 n = ${n} \u4e2d\u7684 nums \u957f\u5ea6 = ${nums.length}`);\nreturn quadraticRecur(n - 1);\n}\n</code></pre> space_complexity.ts<pre><code>/* \u5e73\u65b9\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nfunction quadraticRecur(n: number): number {\nif (n &lt;= 0) return 0;\nconst nums = new Array(n);\nconsole.log(`\u9012\u5f52 n = ${n} \u4e2d\u7684 nums \u957f\u5ea6 = ${nums.length}`);\nreturn quadraticRecur(n - 1);\n}\n</code></pre> space_complexity.c<pre><code>/* \u5e73\u65b9\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nint quadraticRecur(int n) {\nif (n &lt;= 0)\nreturn 0;\nint *nums = malloc(sizeof(int) * n);\nprintf(\"\u9012\u5f52 n = %d \u4e2d\u7684 nums \u957f\u5ea6 = %d\\r\\n\", n, n);\nfree(nums);\nreturn quadraticRecur(n - 1);\n}\n</code></pre> space_complexity.cs<pre><code>/* \u5e73\u65b9\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nint quadraticRecur(int n) {\nif (n &lt;= 0) return 0;\nint[] nums = new int[n];\nConsole.WriteLine(\"\u9012\u5f52 n = \" + n + \" \u4e2d\u7684 nums \u957f\u5ea6 = \" + nums.Length);\nreturn quadraticRecur(n - 1);\n}\n</code></pre> space_complexity.swift<pre><code>/* \u5e73\u65b9\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\n@discardableResult\nfunc quadraticRecur(n: Int) -&gt; Int {\nif n &lt;= 0 {\nreturn 0\n}\n// \u6570\u7ec4 nums \u957f\u5ea6\u4e3a n, n-1, ..., 2, 1\nlet nums = Array(repeating: 0, count: n)\nprint(\"\u9012\u5f52 n = \\(n) \u4e2d\u7684 nums \u957f\u5ea6 = \\(nums.count)\")\nreturn quadraticRecur(n: n - 1)\n}\n</code></pre> space_complexity.zig<pre><code>// \u5e73\u65b9\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09\nfn quadraticRecur(comptime n: i32) i32 {\nif (n &lt;= 0) return 0;\nvar nums = [_]i32{0}**n;\nstd.debug.print(\"\u9012\u5f52 n = {} \u4e2d\u7684 nums \u957f\u5ea6 = {}\\n\", .{n, nums.len});\nreturn quadraticRecur(n - 1);\n}\n</code></pre> space_complexity.dart<pre><code>/* \u5e73\u65b9\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nint quadraticRecur(int n) {\nif (n &lt;= 0) return 0;\nList&lt;int&gt; nums = List.filled(n, 0);\nprint('\u9012\u5f52 n = $n \u4e2d\u7684 nums \u957f\u5ea6 = ${nums.length}');\nreturn quadraticRecur(n - 1);\n}\n</code></pre> <p></p> <p> Fig. \u9012\u5f52\u51fd\u6570\u4ea7\u751f\u7684\u5e73\u65b9\u9636\u7a7a\u95f4\u590d\u6742\u5ea6 </p>"},{"location":"chapter_computational_complexity/space_complexity/#o2n","title":"\u6307\u6570\u9636 \\(O(2^n)\\)","text":"<p>\u6307\u6570\u9636\u5e38\u89c1\u4e8e\u4e8c\u53c9\u6811\u3002\u9ad8\u5ea6\u4e3a \\(n\\) \u7684\u300c\u6ee1\u4e8c\u53c9\u6811\u300d\u7684\u8282\u70b9\u6570\u91cf\u4e3a \\(2^n - 1\\) \uff0c\u5360\u7528 \\(O(2^n)\\) \u7a7a\u95f4\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart space_complexity.java<pre><code>/* \u6307\u6570\u9636\uff08\u5efa\u7acb\u6ee1\u4e8c\u53c9\u6811\uff09 */\nTreeNode buildTree(int n) {\nif (n == 0)\nreturn null;\nTreeNode root = new TreeNode(0);\nroot.left = buildTree(n - 1);\nroot.right = buildTree(n - 1);\nreturn root;\n}\n</code></pre> space_complexity.cpp<pre><code>/* \u6307\u6570\u9636\uff08\u5efa\u7acb\u6ee1\u4e8c\u53c9\u6811\uff09 */\nTreeNode *buildTree(int n) {\nif (n == 0)\nreturn nullptr;\nTreeNode *root = new TreeNode(0);\nroot-&gt;left = buildTree(n - 1);\nroot-&gt;right = buildTree(n - 1);\nreturn root;\n}\n</code></pre> space_complexity.py<pre><code>def build_tree(n: int) -&gt; TreeNode | None:\n\"\"\"\u6307\u6570\u9636\uff08\u5efa\u7acb\u6ee1\u4e8c\u53c9\u6811\uff09\"\"\"\nif n == 0:\nreturn None\nroot = TreeNode(0)\nroot.left = build_tree(n - 1)\nroot.right = build_tree(n - 1)\nreturn root\n</code></pre> space_complexity.go<pre><code>/* \u6307\u6570\u9636\uff08\u5efa\u7acb\u6ee1\u4e8c\u53c9\u6811\uff09 */\nfunc buildTree(n int) *treeNode {\nif n == 0 {\nreturn nil\n}\nroot := newTreeNode(0)\nroot.left = buildTree(n - 1)\nroot.right = buildTree(n - 1)\nreturn root\n}\n</code></pre> space_complexity.js<pre><code>/* \u6307\u6570\u9636\uff08\u5efa\u7acb\u6ee1\u4e8c\u53c9\u6811\uff09 */\nfunction buildTree(n) {\nif (n === 0) return null;\nconst root = new TreeNode(0);\nroot.left = buildTree(n - 1);\nroot.right = buildTree(n - 1);\nreturn root;\n}\n</code></pre> space_complexity.ts<pre><code>/* \u6307\u6570\u9636\uff08\u5efa\u7acb\u6ee1\u4e8c\u53c9\u6811\uff09 */\nfunction buildTree(n: number): TreeNode | null {\nif (n === 0) return null;\nconst root = new TreeNode(0);\nroot.left = buildTree(n - 1);\nroot.right = buildTree(n - 1);\nreturn root;\n}\n</code></pre> space_complexity.c<pre><code>/* \u6307\u6570\u9636\uff08\u5efa\u7acb\u6ee1\u4e8c\u53c9\u6811\uff09 */\nTreeNode *buildTree(int n) {\nif (n == 0)\nreturn NULL;\nTreeNode *root = newTreeNode(0);\nroot-&gt;left = buildTree(n - 1);\nroot-&gt;right = buildTree(n - 1);\nreturn root;\n}\n</code></pre> space_complexity.cs<pre><code>/* \u6307\u6570\u9636\uff08\u5efa\u7acb\u6ee1\u4e8c\u53c9\u6811\uff09 */\nTreeNode? buildTree(int n) {\nif (n == 0) return null;\nTreeNode root = new TreeNode(0);\nroot.left = buildTree(n - 1);\nroot.right = buildTree(n - 1);\nreturn root;\n}\n</code></pre> space_complexity.swift<pre><code>/* \u6307\u6570\u9636\uff08\u5efa\u7acb\u6ee1\u4e8c\u53c9\u6811\uff09 */\nfunc buildTree(n: Int) -&gt; TreeNode? {\nif n == 0 {\nreturn nil\n}\nlet root = TreeNode(x: 0)\nroot.left = buildTree(n: n - 1)\nroot.right = buildTree(n: n - 1)\nreturn root\n}\n</code></pre> space_complexity.zig<pre><code>// \u6307\u6570\u9636\uff08\u5efa\u7acb\u6ee1\u4e8c\u53c9\u6811\uff09\nfn buildTree(mem_allocator: std.mem.Allocator, n: i32) !?*inc.TreeNode(i32) {\nif (n == 0) return null;\nconst root = try mem_allocator.create(inc.TreeNode(i32));\nroot.init(0);\nroot.left = try buildTree(mem_allocator, n - 1);\nroot.right = try buildTree(mem_allocator, n - 1);\nreturn root;\n}\n</code></pre> space_complexity.dart<pre><code>/* \u6307\u6570\u9636\uff08\u5efa\u7acb\u6ee1\u4e8c\u53c9\u6811\uff09 */\nTreeNode? buildTree(int n) {\nif (n == 0) return null;\nTreeNode root = TreeNode(0);\nroot.left = buildTree(n - 1);\nroot.right = buildTree(n - 1);\nreturn root;\n}\n</code></pre> <p></p> <p> Fig. \u6ee1\u4e8c\u53c9\u6811\u4ea7\u751f\u7684\u6307\u6570\u9636\u7a7a\u95f4\u590d\u6742\u5ea6 </p>"},{"location":"chapter_computational_complexity/space_complexity/#olog-n","title":"\u5bf9\u6570\u9636 \\(O(\\log n)\\)","text":"<p>\u5bf9\u6570\u9636\u5e38\u89c1\u4e8e\u5206\u6cbb\u7b97\u6cd5\u548c\u6570\u636e\u7c7b\u578b\u8f6c\u6362\u7b49\u3002</p> <p>\u4f8b\u5982\u201c\u5f52\u5e76\u6392\u5e8f\u201d\u7b97\u6cd5\uff0c\u8f93\u5165\u957f\u5ea6\u4e3a \\(n\\) \u7684\u6570\u7ec4\uff0c\u6bcf\u8f6e\u9012\u5f52\u5c06\u6570\u7ec4\u4ece\u4e2d\u70b9\u5212\u5206\u4e3a\u4e24\u534a\uff0c\u5f62\u6210\u9ad8\u5ea6\u4e3a \\(\\log n\\) \u7684\u9012\u5f52\u6811\uff0c\u4f7f\u7528 \\(O(\\log n)\\) \u6808\u5e27\u7a7a\u95f4\u3002</p> <p>\u518d\u4f8b\u5982\u201c\u6570\u5b57\u8f6c\u5316\u4e3a\u5b57\u7b26\u4e32\u201d\uff0c\u8f93\u5165\u4efb\u610f\u6b63\u6574\u6570 \\(n\\) \uff0c\u5b83\u7684\u4f4d\u6570\u4e3a \\(\\log_{10} n\\) \uff0c\u5373\u5bf9\u5e94\u5b57\u7b26\u4e32\u957f\u5ea6\u4e3a \\(\\log_{10} n\\) \uff0c\u56e0\u6b64\u7a7a\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(\\log_{10} n) = O(\\log n)\\) \u3002</p>"},{"location":"chapter_computational_complexity/space_complexity/#234","title":"2.3.4. \u00a0 \u6743\u8861\u65f6\u95f4\u4e0e\u7a7a\u95f4","text":"<p>\u7406\u60f3\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u5e0c\u671b\u7b97\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u548c\u7a7a\u95f4\u590d\u6742\u5ea6\u90fd\u80fd\u8fbe\u5230\u6700\u4f18\u3002\u7136\u800c\u5728\u5b9e\u9645\u60c5\u51b5\u4e2d\uff0c\u540c\u65f6\u4f18\u5316\u65f6\u95f4\u590d\u6742\u5ea6\u548c\u7a7a\u95f4\u590d\u6742\u5ea6\u901a\u5e38\u662f\u975e\u5e38\u56f0\u96be\u7684\u3002</p> <p>\u964d\u4f4e\u65f6\u95f4\u590d\u6742\u5ea6\u901a\u5e38\u9700\u8981\u4ee5\u63d0\u5347\u7a7a\u95f4\u590d\u6742\u5ea6\u4e3a\u4ee3\u4ef7\uff0c\u53cd\u4e4b\u4ea6\u7136\u3002\u6211\u4eec\u5c06\u727a\u7272\u5185\u5b58\u7a7a\u95f4\u6765\u63d0\u5347\u7b97\u6cd5\u8fd0\u884c\u901f\u5ea6\u7684\u601d\u8def\u79f0\u4e3a\u201c\u4ee5\u7a7a\u95f4\u6362\u65f6\u95f4\u201d\uff1b\u53cd\u4e4b\uff0c\u5219\u79f0\u4e3a\u201c\u4ee5\u65f6\u95f4\u6362\u7a7a\u95f4\u201d\u3002</p> <p>\u9009\u62e9\u54ea\u79cd\u601d\u8def\u53d6\u51b3\u4e8e\u6211\u4eec\u66f4\u770b\u91cd\u54ea\u4e2a\u65b9\u9762\u3002\u5728\u5927\u591a\u6570\u60c5\u51b5\u4e0b\uff0c\u65f6\u95f4\u6bd4\u7a7a\u95f4\u66f4\u5b9d\u8d35\uff0c\u56e0\u6b64\u4ee5\u7a7a\u95f4\u6362\u65f6\u95f4\u901a\u5e38\u662f\u66f4\u5e38\u7528\u7684\u7b56\u7565\u3002\u5f53\u7136\uff0c\u5728\u6570\u636e\u91cf\u5f88\u5927\u7684\u60c5\u51b5\u4e0b\uff0c\u63a7\u5236\u7a7a\u95f4\u590d\u6742\u5ea6\u4e5f\u662f\u975e\u5e38\u91cd\u8981\u7684\u3002</p>"},{"location":"chapter_computational_complexity/summary/","title":"2.4. \u00a0 \u5c0f\u7ed3","text":"<p>\u7b97\u6cd5\u6548\u7387\u8bc4\u4f30</p> <ul> <li>\u65f6\u95f4\u6548\u7387\u548c\u7a7a\u95f4\u6548\u7387\u662f\u8bc4\u4ef7\u7b97\u6cd5\u6027\u80fd\u7684\u4e24\u4e2a\u5173\u952e\u7ef4\u5ea6\u3002</li> <li>\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u5b9e\u9645\u6d4b\u8bd5\u6765\u8bc4\u4f30\u7b97\u6cd5\u6548\u7387\uff0c\u4f46\u96be\u4ee5\u6d88\u9664\u6d4b\u8bd5\u73af\u5883\u7684\u5f71\u54cd\uff0c\u4e14\u4f1a\u8017\u8d39\u5927\u91cf\u8ba1\u7b97\u8d44\u6e90\u3002</li> <li>\u590d\u6742\u5ea6\u5206\u6790\u53ef\u4ee5\u514b\u670d\u5b9e\u9645\u6d4b\u8bd5\u7684\u5f0a\u7aef\uff0c\u5206\u6790\u7ed3\u679c\u9002\u7528\u4e8e\u6240\u6709\u8fd0\u884c\u5e73\u53f0\uff0c\u5e76\u4e14\u80fd\u591f\u63ed\u793a\u7b97\u6cd5\u5728\u4e0d\u540c\u6570\u636e\u89c4\u6a21\u4e0b\u7684\u6548\u7387\u3002</li> </ul> <p>\u65f6\u95f4\u590d\u6742\u5ea6</p> <ul> <li>\u65f6\u95f4\u590d\u6742\u5ea6\u7528\u4e8e\u8861\u91cf\u7b97\u6cd5\u8fd0\u884c\u65f6\u95f4\u968f\u6570\u636e\u91cf\u589e\u957f\u7684\u8d8b\u52bf\uff0c\u53ef\u4ee5\u6709\u6548\u8bc4\u4f30\u7b97\u6cd5\u6548\u7387\uff0c\u4f46\u5728\u67d0\u4e9b\u60c5\u51b5\u4e0b\u53ef\u80fd\u5931\u6548\uff0c\u5982\u5728\u8f93\u5165\u6570\u636e\u91cf\u8f83\u5c0f\u6216\u65f6\u95f4\u590d\u6742\u5ea6\u76f8\u540c\u65f6\uff0c\u65e0\u6cd5\u7cbe\u786e\u5bf9\u6bd4\u7b97\u6cd5\u6548\u7387\u7684\u4f18\u52a3\u3002</li> <li>\u6700\u5dee\u65f6\u95f4\u590d\u6742\u5ea6\u4f7f\u7528\u5927 \\(O\\) \u7b26\u53f7\u8868\u793a\uff0c\u5373\u51fd\u6570\u6e10\u8fd1\u4e0a\u754c\uff0c\u53cd\u6620\u5f53 \\(n\\) \u8d8b\u5411\u6b63\u65e0\u7a77\u65f6\uff0c\\(T(n)\\) \u7684\u589e\u957f\u7ea7\u522b\u3002</li> <li>\u63a8\u7b97\u65f6\u95f4\u590d\u6742\u5ea6\u5206\u4e3a\u4e24\u6b65\uff0c\u9996\u5148\u7edf\u8ba1\u8ba1\u7b97\u64cd\u4f5c\u6570\u91cf\uff0c\u7136\u540e\u5224\u65ad\u6e10\u8fd1\u4e0a\u754c\u3002</li> <li>\u5e38\u89c1\u65f6\u95f4\u590d\u6742\u5ea6\u4ece\u5c0f\u5230\u5927\u6392\u5217\u6709 \\(O(1)\\) , \\(O(\\log n)\\) , \\(O(n)\\) , \\(O(n \\log n)\\) , \\(O(n^2)\\) , \\(O(2^n)\\) , \\(O(n!)\\) \u7b49\u3002</li> <li>\u67d0\u4e9b\u7b97\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u975e\u56fa\u5b9a\uff0c\u800c\u662f\u4e0e\u8f93\u5165\u6570\u636e\u7684\u5206\u5e03\u6709\u5173\u3002\u65f6\u95f4\u590d\u6742\u5ea6\u5206\u4e3a\u6700\u5dee\u3001\u6700\u4f73\u3001\u5e73\u5747\u65f6\u95f4\u590d\u6742\u5ea6\uff0c\u6700\u4f73\u65f6\u95f4\u590d\u6742\u5ea6\u51e0\u4e4e\u4e0d\u7528\uff0c\u56e0\u4e3a\u8f93\u5165\u6570\u636e\u4e00\u822c\u9700\u8981\u6ee1\u8db3\u4e25\u683c\u6761\u4ef6\u624d\u80fd\u8fbe\u5230\u6700\u4f73\u60c5\u51b5\u3002</li> <li>\u5e73\u5747\u65f6\u95f4\u590d\u6742\u5ea6\u53cd\u6620\u7b97\u6cd5\u5728\u968f\u673a\u6570\u636e\u8f93\u5165\u4e0b\u7684\u8fd0\u884c\u6548\u7387\uff0c\u6700\u63a5\u8fd1\u5b9e\u9645\u5e94\u7528\u4e2d\u7684\u7b97\u6cd5\u6027\u80fd\u3002\u8ba1\u7b97\u5e73\u5747\u65f6\u95f4\u590d\u6742\u5ea6\u9700\u8981\u7edf\u8ba1\u8f93\u5165\u6570\u636e\u5206\u5e03\u4ee5\u53ca\u7efc\u5408\u540e\u7684\u6570\u5b66\u671f\u671b\u3002</li> </ul> <p>\u7a7a\u95f4\u590d\u6742\u5ea6</p> <ul> <li>\u7c7b\u4f3c\u4e8e\u65f6\u95f4\u590d\u6742\u5ea6\uff0c\u7a7a\u95f4\u590d\u6742\u5ea6\u7528\u4e8e\u8861\u91cf\u7b97\u6cd5\u5360\u7528\u7a7a\u95f4\u968f\u6570\u636e\u91cf\u589e\u957f\u7684\u8d8b\u52bf\u3002</li> <li>\u7b97\u6cd5\u8fd0\u884c\u8fc7\u7a0b\u4e2d\u7684\u76f8\u5173\u5185\u5b58\u7a7a\u95f4\u53ef\u5206\u4e3a\u8f93\u5165\u7a7a\u95f4\u3001\u6682\u5b58\u7a7a\u95f4\u3001\u8f93\u51fa\u7a7a\u95f4\u3002\u901a\u5e38\u60c5\u51b5\u4e0b\uff0c\u8f93\u5165\u7a7a\u95f4\u4e0d\u8ba1\u5165\u7a7a\u95f4\u590d\u6742\u5ea6\u8ba1\u7b97\u3002\u6682\u5b58\u7a7a\u95f4\u53ef\u5206\u4e3a\u6307\u4ee4\u7a7a\u95f4\u3001\u6570\u636e\u7a7a\u95f4\u3001\u6808\u5e27\u7a7a\u95f4\uff0c\u5176\u4e2d\u6808\u5e27\u7a7a\u95f4\u901a\u5e38\u4ec5\u5728\u9012\u5f52\u51fd\u6570\u4e2d\u5f71\u54cd\u7a7a\u95f4\u590d\u6742\u5ea6\u3002</li> <li>\u6211\u4eec\u901a\u5e38\u53ea\u5173\u6ce8\u6700\u5dee\u7a7a\u95f4\u590d\u6742\u5ea6\uff0c\u5373\u7edf\u8ba1\u7b97\u6cd5\u5728\u6700\u5dee\u8f93\u5165\u6570\u636e\u548c\u6700\u5dee\u8fd0\u884c\u65f6\u95f4\u70b9\u4e0b\u7684\u7a7a\u95f4\u590d\u6742\u5ea6\u3002</li> <li>\u5e38\u89c1\u7a7a\u95f4\u590d\u6742\u5ea6\u4ece\u5c0f\u5230\u5927\u6392\u5217\u6709 \\(O(1)\\) , \\(O(\\log n)\\) , \\(O(n)\\) , \\(O(n^2)\\) , \\(O(2^n)\\) \u7b49\u3002</li> </ul>"},{"location":"chapter_computational_complexity/summary/#241-q-a","title":"2.4.1. \u00a0 Q &amp; A","text":"<p>\u5c3e\u9012\u5f52\u7684\u7a7a\u95f4\u590d\u6742\u5ea6\u662f \\(O(1)\\) \u5417\uff1f</p> <p>\u7406\u8bba\u4e0a\uff0c\u5c3e\u9012\u5f52\u51fd\u6570\u7684\u7a7a\u95f4\u590d\u6742\u5ea6\u53ef\u4ee5\u88ab\u4f18\u5316\u81f3 \\(O(1)\\) \u3002\u4e0d\u8fc7\u7edd\u5927\u591a\u6570\u7f16\u7a0b\u8bed\u8a00\uff08\u4f8b\u5982 Java, Python, C++, Go, C# \u7b49\uff09 \u90fd\u4e0d\u652f\u6301\u81ea\u52a8\u4f18\u5316\u5c3e\u9012\u5f52\uff0c\u56e0\u6b64\u4e00\u822c\u6765\u8bf4\u7a7a\u95f4\u590d\u6742\u5ea6\u662f \\(O(n)\\) \u3002</p> <p>\u51fd\u6570\u548c\u65b9\u6cd5\u8fd9\u4e24\u4e2a\u672f\u8bed\u7684\u533a\u522b\u662f\u4ec0\u4e48\uff1f</p> <p>\u51fd\u6570\uff08function\uff09\u53ef\u4ee5\u72ec\u7acb\u88ab\u6267\u884c\uff0c\u6240\u6709\u53c2\u6570\u90fd\u4ee5\u663e\u5f0f\u4f20\u9012\u3002 \u65b9\u6cd5\uff08method\uff09\u4e0e\u4e00\u4e2a\u5bf9\u8c61\u5173\u8054\uff0c\u65b9\u6cd5\u88ab\u9690\u5f0f\u4f20\u9012\u7ed9\u8c03\u7528\u5b83\u7684\u5bf9\u8c61\uff0c\u65b9\u6cd5\u80fd\u591f\u5bf9\u7c7b\u7684\u5b9e\u4f8b\u4e2d\u5305\u542b\u7684\u6570\u636e\u8fdb\u884c\u64cd\u4f5c\u3002</p> <p>\u56fe\u7247\u201c\u7a7a\u95f4\u590d\u6742\u5ea6\u7684\u5e38\u89c1\u7c7b\u578b\u201d\u53cd\u6620\u7684\u662f\u5426\u662f\u5360\u7528\u7a7a\u95f4\u7684\u7edd\u5bf9\u5927\u5c0f\uff1f</p> <p>\u4e0d\u662f\uff0c\u8be5\u56fe\u7247\u5c55\u793a\u7684\u662f\u7a7a\u95f4\u590d\u6742\u5ea6\uff08\u5373\u589e\u957f\u8d8b\u52bf\uff09\uff0c\u800c\u4e0d\u662f\u5360\u7528\u7a7a\u95f4\u7684\u7edd\u5bf9\u5927\u5c0f\u3002\u6bcf\u4e2a\u66f2\u7ebf\u90fd\u5305\u542b\u4e00\u4e2a\u5e38\u6570\u9879\uff0c\u7528\u6765\u628a\u6240\u6709\u66f2\u7ebf\u7684\u53d6\u503c\u8303\u56f4\u538b\u7f29\u5230\u4e00\u4e2a\u89c6\u89c9\u8212\u9002\u7684\u8303\u56f4\u5185\u3002 \u5b9e\u9645\u4e2d\uff0c\u56e0\u4e3a\u6211\u4eec\u901a\u5e38\u4e0d\u77e5\u9053\u6bcf\u4e2a\u65b9\u6cd5\u7684\u201c\u5e38\u6570\u9879\u201d\u590d\u6742\u5ea6\u662f\u591a\u5c11\uff0c\u6240\u4ee5\u4e00\u822c\u65e0\u6cd5\u4ec5\u51ed\u590d\u6742\u5ea6\u6765\u9009\u62e9 \\(n = 8\\) \u4e4b\u4e0b\u7684\u6700\u4f18\u89e3\u6cd5\uff1b\u4f46\u76f8\u5bf9\u5730 \\(n = 8^5\\) \u5c31\u5f88\u597d\u9009\u4e86\uff0c\u8fd9\u662f\u590d\u6742\u5ea6\u5360\u4e3b\u5bfc\u7684\u60c5\u51b5\u3002</p>"},{"location":"chapter_computational_complexity/time_complexity/","title":"2.2. \u00a0 \u65f6\u95f4\u590d\u6742\u5ea6","text":""},{"location":"chapter_computational_complexity/time_complexity/#221","title":"2.2.1. \u00a0 \u7edf\u8ba1\u7b97\u6cd5\u8fd0\u884c\u65f6\u95f4","text":"<p>\u8fd0\u884c\u65f6\u95f4\u53ef\u4ee5\u76f4\u89c2\u4e14\u51c6\u786e\u5730\u53cd\u6620\u7b97\u6cd5\u7684\u6548\u7387\u3002\u7136\u800c\uff0c\u5982\u679c\u6211\u4eec\u60f3\u8981\u51c6\u786e\u9884\u4f30\u4e00\u6bb5\u4ee3\u7801\u7684\u8fd0\u884c\u65f6\u95f4\uff0c\u5e94\u8be5\u5982\u4f55\u64cd\u4f5c\u5462\uff1f</p> <ol> <li>\u786e\u5b9a\u8fd0\u884c\u5e73\u53f0\uff0c\u5305\u62ec\u786c\u4ef6\u914d\u7f6e\u3001\u7f16\u7a0b\u8bed\u8a00\u3001\u7cfb\u7edf\u73af\u5883\u7b49\uff0c\u8fd9\u4e9b\u56e0\u7d20\u90fd\u4f1a\u5f71\u54cd\u4ee3\u7801\u7684\u8fd0\u884c\u6548\u7387\u3002</li> <li>\u8bc4\u4f30\u5404\u79cd\u8ba1\u7b97\u64cd\u4f5c\u6240\u9700\u7684\u8fd0\u884c\u65f6\u95f4\uff0c\u4f8b\u5982\u52a0\u6cd5\u64cd\u4f5c <code>+</code> \u9700\u8981 1 ns\uff0c\u4e58\u6cd5\u64cd\u4f5c <code>*</code> \u9700\u8981 10 ns\uff0c\u6253\u5370\u64cd\u4f5c\u9700\u8981 5 ns \u7b49\u3002</li> <li>\u7edf\u8ba1\u4ee3\u7801\u4e2d\u6240\u6709\u7684\u8ba1\u7b97\u64cd\u4f5c\uff0c\u5e76\u5c06\u6240\u6709\u64cd\u4f5c\u7684\u6267\u884c\u65f6\u95f4\u6c42\u548c\uff0c\u4ece\u800c\u5f97\u5230\u8fd0\u884c\u65f6\u95f4\u3002</li> </ol> <p>\u4f8b\u5982\u4ee5\u4e0b\u4ee3\u7801\uff0c\u8f93\u5165\u6570\u636e\u5927\u5c0f\u4e3a \\(n\\) \uff0c\u6839\u636e\u4ee5\u4e0a\u65b9\u6cd5\uff0c\u53ef\u4ee5\u5f97\u5230\u7b97\u6cd5\u8fd0\u884c\u65f6\u95f4\u4e3a \\(6n + 12\\) ns \u3002</p> \\[ 1 + 1 + 10 + (1 + 5) \\times n = 6n + 12 \\] JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart <pre><code>// \u5728\u67d0\u8fd0\u884c\u5e73\u53f0\u4e0b\nvoid algorithm(int n) {\nint a = 2;  // 1 ns\na = a + 1;  // 1 ns\na = a * 2;  // 10 ns\n// \u5faa\u73af n \u6b21\nfor (int i = 0; i &lt; n; i++) {  // 1 ns \uff0c\u6bcf\u8f6e\u90fd\u8981\u6267\u884c i++\nSystem.out.println(0);     // 5 ns\n}\n}\n</code></pre> <pre><code>// \u5728\u67d0\u8fd0\u884c\u5e73\u53f0\u4e0b\nvoid algorithm(int n) {\nint a = 2;  // 1 ns\na = a + 1;  // 1 ns\na = a * 2;  // 10 ns\n// \u5faa\u73af n \u6b21\nfor (int i = 0; i &lt; n; i++) {  // 1 ns \uff0c\u6bcf\u8f6e\u90fd\u8981\u6267\u884c i++\ncout &lt;&lt; 0 &lt;&lt; endl;         // 5 ns\n}\n}\n</code></pre> <pre><code># \u5728\u67d0\u8fd0\u884c\u5e73\u53f0\u4e0b\ndef algorithm(n: int) -&gt; None:\na = 2      # 1 ns\na = a + 1  # 1 ns\na = a * 2  # 10 ns\n# \u5faa\u73af n \u6b21\nfor _ in range(n):  # 1 ns\nprint(0)        # 5 ns\n</code></pre> <pre><code>// \u5728\u67d0\u8fd0\u884c\u5e73\u53f0\u4e0b\nfunc algorithm(n int) {\na := 2      // 1 ns\na = a + 1   // 1 ns\na = a * 2   // 10 ns\n// \u5faa\u73af n \u6b21\nfor i := 0; i &lt; n; i++ {    // 1 ns\nfmt.Println(a)          // 5 ns\n}\n}\n</code></pre> <pre><code>// \u5728\u67d0\u8fd0\u884c\u5e73\u53f0\u4e0b\nfunction algorithm(n) {\nvar a = 2; // 1 ns\na = a + 1; // 1 ns\na = a * 2; // 10 ns\n// \u5faa\u73af n \u6b21\nfor(let i = 0; i &lt; n; i++) { // 1 ns \uff0c\u6bcf\u8f6e\u90fd\u8981\u6267\u884c i++\nconsole.log(0); // 5 ns\n}\n}\n</code></pre> <pre><code>// \u5728\u67d0\u8fd0\u884c\u5e73\u53f0\u4e0b\nfunction algorithm(n: number): void {\nvar a: number = 2; // 1 ns\na = a + 1; // 1 ns\na = a * 2; // 10 ns\n// \u5faa\u73af n \u6b21\nfor(let i = 0; i &lt; n; i++) { // 1 ns \uff0c\u6bcf\u8f6e\u90fd\u8981\u6267\u884c i++\nconsole.log(0); // 5 ns\n}\n}\n</code></pre> <pre><code>// \u5728\u67d0\u8fd0\u884c\u5e73\u53f0\u4e0b\nvoid algorithm(int n) {\nint a = 2;  // 1 ns\na = a + 1;  // 1 ns\na = a * 2;  // 10 ns\n// \u5faa\u73af n \u6b21\nfor (int i = 0; i &lt; n; i++) {   // 1 ns \uff0c\u6bcf\u8f6e\u90fd\u8981\u6267\u884c i++\nprintf(\"%d\", 0);            // 5 ns\n}\n}\n</code></pre> <pre><code>// \u5728\u67d0\u8fd0\u884c\u5e73\u53f0\u4e0b\nvoid algorithm(int n)\n{\nint a = 2;  // 1 ns\na = a + 1;  // 1 ns\na = a * 2;  // 10 ns\n// \u5faa\u73af n \u6b21\nfor (int i = 0; i &lt; n; i++)\n{  // 1 ns \uff0c\u6bcf\u8f6e\u90fd\u8981\u6267\u884c i++\nConsole.WriteLine(0);     // 5 ns\n}\n}\n</code></pre> <pre><code>// \u5728\u67d0\u8fd0\u884c\u5e73\u53f0\u4e0b\nfunc algorithm(n: Int) {\nvar a = 2 // 1 ns\na = a + 1 // 1 ns\na = a * 2 // 10 ns\n// \u5faa\u73af n \u6b21\nfor _ in 0 ..&lt; n { // 1 ns\nprint(0) // 5 ns\n}\n}\n</code></pre> <pre><code>\n</code></pre> <pre><code>// \u5728\u67d0\u8fd0\u884c\u5e73\u53f0\u4e0b\nvoid algorithm(int n) {\nint a = 2; // 1 ns\na = a + 1; // 1 ns\na = a * 2; // 10 ns\n// \u5faa\u73af n \u6b21\nfor (int i = 0; i &lt; n; i++) { // 1 ns \uff0c\u6bcf\u8f6e\u90fd\u8981\u6267\u884c i++\nprint(0); // 5 ns\n}\n}\n</code></pre> <p>\u7136\u800c\u5b9e\u9645\u4e0a\uff0c\u7edf\u8ba1\u7b97\u6cd5\u7684\u8fd0\u884c\u65f6\u95f4\u65e2\u4e0d\u5408\u7406\u4e5f\u4e0d\u73b0\u5b9e\u3002\u9996\u5148\uff0c\u6211\u4eec\u4e0d\u5e0c\u671b\u9884\u4f30\u65f6\u95f4\u548c\u8fd0\u884c\u5e73\u53f0\u7ed1\u5b9a\uff0c\u56e0\u4e3a\u7b97\u6cd5\u9700\u8981\u5728\u5404\u79cd\u4e0d\u540c\u7684\u5e73\u53f0\u4e0a\u8fd0\u884c\u3002\u5176\u6b21\uff0c\u6211\u4eec\u5f88\u96be\u83b7\u77e5\u6bcf\u79cd\u64cd\u4f5c\u7684\u8fd0\u884c\u65f6\u95f4\uff0c\u8fd9\u7ed9\u9884\u4f30\u8fc7\u7a0b\u5e26\u6765\u4e86\u6781\u5927\u7684\u96be\u5ea6\u3002</p>"},{"location":"chapter_computational_complexity/time_complexity/#222","title":"2.2.2. \u00a0 \u7edf\u8ba1\u65f6\u95f4\u589e\u957f\u8d8b\u52bf","text":"<p>\u300c\u65f6\u95f4\u590d\u6742\u5ea6\u5206\u6790\u300d\u91c7\u53d6\u4e86\u4e00\u79cd\u4e0d\u540c\u7684\u65b9\u6cd5\uff0c\u5176\u7edf\u8ba1\u7684\u4e0d\u662f\u7b97\u6cd5\u8fd0\u884c\u65f6\u95f4\uff0c\u800c\u662f\u7b97\u6cd5\u8fd0\u884c\u65f6\u95f4\u968f\u7740\u6570\u636e\u91cf\u53d8\u5927\u65f6\u7684\u589e\u957f\u8d8b\u52bf\u3002</p> <p>\u201c\u65f6\u95f4\u589e\u957f\u8d8b\u52bf\u201d\u8fd9\u4e2a\u6982\u5ff5\u8f83\u4e3a\u62bd\u8c61\uff0c\u6211\u4eec\u901a\u8fc7\u4e00\u4e2a\u4f8b\u5b50\u6765\u52a0\u4ee5\u7406\u89e3\u3002\u5047\u8bbe\u8f93\u5165\u6570\u636e\u5927\u5c0f\u4e3a \\(n\\) \uff0c\u7ed9\u5b9a\u4e09\u4e2a\u7b97\u6cd5 <code>A</code> , <code>B</code> , <code>C</code> \u3002</p> <ul> <li>\u7b97\u6cd5 <code>A</code> \u53ea\u6709 \\(1\\) \u4e2a\u6253\u5370\u64cd\u4f5c\uff0c\u7b97\u6cd5\u8fd0\u884c\u65f6\u95f4\u4e0d\u968f\u7740 \\(n\\) \u589e\u5927\u800c\u589e\u957f\u3002\u6211\u4eec\u79f0\u6b64\u7b97\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a\u300c\u5e38\u6570\u9636\u300d\u3002</li> <li>\u7b97\u6cd5 <code>B</code> \u4e2d\u7684\u6253\u5370\u64cd\u4f5c\u9700\u8981\u5faa\u73af \\(n\\) \u6b21\uff0c\u7b97\u6cd5\u8fd0\u884c\u65f6\u95f4\u968f\u7740 \\(n\\) \u589e\u5927\u5448\u7ebf\u6027\u589e\u957f\u3002\u6b64\u7b97\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u88ab\u79f0\u4e3a\u300c\u7ebf\u6027\u9636\u300d\u3002</li> <li>\u7b97\u6cd5 <code>C</code> \u4e2d\u7684\u6253\u5370\u64cd\u4f5c\u9700\u8981\u5faa\u73af \\(1000000\\) \u6b21\uff0c\u4f46\u8fd0\u884c\u65f6\u95f4\u4ecd\u4e0e\u8f93\u5165\u6570\u636e\u5927\u5c0f \\(n\\) \u65e0\u5173\u3002\u56e0\u6b64 <code>C</code> \u7684\u65f6\u95f4\u590d\u6742\u5ea6\u548c <code>A</code> \u76f8\u540c\uff0c\u4ecd\u4e3a\u300c\u5e38\u6570\u9636\u300d\u3002</li> </ul> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart <pre><code>// \u7b97\u6cd5 A \u65f6\u95f4\u590d\u6742\u5ea6\uff1a\u5e38\u6570\u9636\nvoid algorithm_A(int n) {\nSystem.out.println(0);\n}\n// \u7b97\u6cd5 B \u65f6\u95f4\u590d\u6742\u5ea6\uff1a\u7ebf\u6027\u9636\nvoid algorithm_B(int n) {\nfor (int i = 0; i &lt; n; i++) {\nSystem.out.println(0);\n}\n}\n// \u7b97\u6cd5 C \u65f6\u95f4\u590d\u6742\u5ea6\uff1a\u5e38\u6570\u9636\nvoid algorithm_C(int n) {\nfor (int i = 0; i &lt; 1000000; i++) {\nSystem.out.println(0);\n}\n}\n</code></pre> <pre><code>// \u7b97\u6cd5 A \u65f6\u95f4\u590d\u6742\u5ea6\uff1a\u5e38\u6570\u9636\nvoid algorithm_A(int n) {\ncout &lt;&lt; 0 &lt;&lt; endl;\n}\n// \u7b97\u6cd5 B \u65f6\u95f4\u590d\u6742\u5ea6\uff1a\u7ebf\u6027\u9636\nvoid algorithm_B(int n) {\nfor (int i = 0; i &lt; n; i++) {\ncout &lt;&lt; 0 &lt;&lt; endl;\n}\n}\n// \u7b97\u6cd5 C \u65f6\u95f4\u590d\u6742\u5ea6\uff1a\u5e38\u6570\u9636\nvoid algorithm_C(int n) {\nfor (int i = 0; i &lt; 1000000; i++) {\ncout &lt;&lt; 0 &lt;&lt; endl;\n}\n}\n</code></pre> <pre><code># \u7b97\u6cd5 A \u65f6\u95f4\u590d\u6742\u5ea6\uff1a\u5e38\u6570\u9636\ndef algorithm_A(n: int) -&gt; None:\nprint(0)\n# \u7b97\u6cd5 B \u65f6\u95f4\u590d\u6742\u5ea6\uff1a\u7ebf\u6027\u9636\ndef algorithm_B(n: int) -&gt; None:\nfor _ in range(n):\nprint(0)\n# \u7b97\u6cd5 C \u65f6\u95f4\u590d\u6742\u5ea6\uff1a\u5e38\u6570\u9636\ndef algorithm_C(n: int) -&gt; None:\nfor _ in range(1000000):\nprint(0)\n</code></pre> <pre><code>// \u7b97\u6cd5 A \u65f6\u95f4\u590d\u6742\u5ea6\uff1a\u5e38\u6570\u9636\nfunc algorithm_A(n int) {\nfmt.Println(0)\n}\n// \u7b97\u6cd5 B \u65f6\u95f4\u590d\u6742\u5ea6\uff1a\u7ebf\u6027\u9636\nfunc algorithm_B(n int) {\nfor i := 0; i &lt; n; i++ {\nfmt.Println(0)\n}\n}\n// \u7b97\u6cd5 C \u65f6\u95f4\u590d\u6742\u5ea6\uff1a\u5e38\u6570\u9636\nfunc algorithm_C(n int) {\nfor i := 0; i &lt; 1000000; i++ {\nfmt.Println(0)\n}\n}\n</code></pre> <pre><code>// \u7b97\u6cd5 A \u65f6\u95f4\u590d\u6742\u5ea6\uff1a\u5e38\u6570\u9636\nfunction algorithm_A(n) {\nconsole.log(0);\n}\n// \u7b97\u6cd5 B \u65f6\u95f4\u590d\u6742\u5ea6\uff1a\u7ebf\u6027\u9636\nfunction algorithm_B(n) {\nfor (let i = 0; i &lt; n; i++) {\nconsole.log(0);\n}\n}\n// \u7b97\u6cd5 C \u65f6\u95f4\u590d\u6742\u5ea6\uff1a\u5e38\u6570\u9636\nfunction algorithm_C(n) {\nfor (let i = 0; i &lt; 1000000; i++) {\nconsole.log(0);\n}\n}\n</code></pre> <pre><code>// \u7b97\u6cd5 A \u65f6\u95f4\u590d\u6742\u5ea6\uff1a\u5e38\u6570\u9636\nfunction algorithm_A(n: number): void {\nconsole.log(0);\n}\n// \u7b97\u6cd5 B \u65f6\u95f4\u590d\u6742\u5ea6\uff1a\u7ebf\u6027\u9636\nfunction algorithm_B(n: number): void {\nfor (let i = 0; i &lt; n; i++) {\nconsole.log(0);\n}\n}\n// \u7b97\u6cd5 C \u65f6\u95f4\u590d\u6742\u5ea6\uff1a\u5e38\u6570\u9636\nfunction algorithm_C(n: number): void {\nfor (let i = 0; i &lt; 1000000; i++) {\nconsole.log(0);\n}\n}\n</code></pre> <pre><code>// \u7b97\u6cd5 A \u65f6\u95f4\u590d\u6742\u5ea6\uff1a\u5e38\u6570\u9636\nvoid algorithm_A(int n) {\nprintf(\"%d\", 0);\n}\n// \u7b97\u6cd5 B \u65f6\u95f4\u590d\u6742\u5ea6\uff1a\u7ebf\u6027\u9636\nvoid algorithm_B(int n) {\nfor (int i = 0; i &lt; n; i++) {\nprintf(\"%d\", 0);\n}\n}\n// \u7b97\u6cd5 C \u65f6\u95f4\u590d\u6742\u5ea6\uff1a\u5e38\u6570\u9636\nvoid algorithm_C(int n) {\nfor (int i = 0; i &lt; 1000000; i++) {\nprintf(\"%d\", 0);\n}\n}\n</code></pre> <pre><code>// \u7b97\u6cd5 A \u65f6\u95f4\u590d\u6742\u5ea6\uff1a\u5e38\u6570\u9636\nvoid algorithm_A(int n)\n{\nConsole.WriteLine(0);\n}\n// \u7b97\u6cd5 B \u65f6\u95f4\u590d\u6742\u5ea6\uff1a\u7ebf\u6027\u9636\nvoid algorithm_B(int n)\n{\nfor (int i = 0; i &lt; n; i++)\n{\nConsole.WriteLine(0);\n}\n}\n// \u7b97\u6cd5 C \u65f6\u95f4\u590d\u6742\u5ea6\uff1a\u5e38\u6570\u9636\nvoid algorithm_C(int n)\n{\nfor (int i = 0; i &lt; 1000000; i++)\n{\nConsole.WriteLine(0);\n}\n}\n</code></pre> <pre><code>// \u7b97\u6cd5 A \u65f6\u95f4\u590d\u6742\u5ea6\uff1a\u5e38\u6570\u9636\nfunc algorithmA(n: Int) {\nprint(0)\n}\n// \u7b97\u6cd5 B \u65f6\u95f4\u590d\u6742\u5ea6\uff1a\u7ebf\u6027\u9636\nfunc algorithmB(n: Int) {\nfor _ in 0 ..&lt; n {\nprint(0)\n}\n}\n// \u7b97\u6cd5 C \u65f6\u95f4\u590d\u6742\u5ea6\uff1a\u5e38\u6570\u9636\nfunc algorithmC(n: Int) {\nfor _ in 0 ..&lt; 1000000 {\nprint(0)\n}\n}\n</code></pre> <pre><code>\n</code></pre> <pre><code>// \u7b97\u6cd5 A \u65f6\u95f4\u590d\u6742\u5ea6\uff1a\u5e38\u6570\u9636\nvoid algorithmA(int n) {\nprint(0);\n}\n// \u7b97\u6cd5 B \u65f6\u95f4\u590d\u6742\u5ea6\uff1a\u7ebf\u6027\u9636\nvoid algorithmB(int n) {\nfor (int i = 0; i &lt; n; i++) {\nprint(0);\n}\n}\n// \u7b97\u6cd5 C \u65f6\u95f4\u590d\u6742\u5ea6\uff1a\u5e38\u6570\u9636\nvoid algorithmC(int n) {\nfor (int i = 0; i &lt; 1000000; i++) {\nprint(0);\n}\n}\n</code></pre> <p></p> <p> Fig. \u7b97\u6cd5 A, B, C \u7684\u65f6\u95f4\u589e\u957f\u8d8b\u52bf </p> <p>\u76f8\u8f83\u4e8e\u76f4\u63a5\u7edf\u8ba1\u7b97\u6cd5\u8fd0\u884c\u65f6\u95f4\uff0c\u65f6\u95f4\u590d\u6742\u5ea6\u5206\u6790\u6709\u54ea\u4e9b\u4f18\u52bf\u548c\u5c40\u9650\u6027\u5462\uff1f</p> <p>\u65f6\u95f4\u590d\u6742\u5ea6\u80fd\u591f\u6709\u6548\u8bc4\u4f30\u7b97\u6cd5\u6548\u7387\u3002\u4f8b\u5982\uff0c\u7b97\u6cd5 <code>B</code> \u7684\u8fd0\u884c\u65f6\u95f4\u5448\u7ebf\u6027\u589e\u957f\uff0c\u5728 \\(n &gt; 1\\) \u65f6\u6bd4\u7b97\u6cd5 <code>A</code> \u6162\uff0c\u5728 \\(n &gt; 1000000\\) \u65f6\u6bd4\u7b97\u6cd5 <code>C</code> \u6162\u3002\u4e8b\u5b9e\u4e0a\uff0c\u53ea\u8981\u8f93\u5165\u6570\u636e\u5927\u5c0f \\(n\\) \u8db3\u591f\u5927\uff0c\u590d\u6742\u5ea6\u4e3a\u300c\u5e38\u6570\u9636\u300d\u7684\u7b97\u6cd5\u4e00\u5b9a\u4f18\u4e8e\u300c\u7ebf\u6027\u9636\u300d\u7684\u7b97\u6cd5\uff0c\u8fd9\u6b63\u662f\u65f6\u95f4\u589e\u957f\u8d8b\u52bf\u6240\u8868\u8fbe\u7684\u542b\u4e49\u3002</p> <p>\u65f6\u95f4\u590d\u6742\u5ea6\u7684\u63a8\u7b97\u65b9\u6cd5\u66f4\u7b80\u4fbf\u3002\u663e\u7136\uff0c\u8fd0\u884c\u5e73\u53f0\u548c\u8ba1\u7b97\u64cd\u4f5c\u7c7b\u578b\u90fd\u4e0e\u7b97\u6cd5\u8fd0\u884c\u65f6\u95f4\u7684\u589e\u957f\u8d8b\u52bf\u65e0\u5173\u3002\u56e0\u6b64\u5728\u65f6\u95f4\u590d\u6742\u5ea6\u5206\u6790\u4e2d\uff0c\u6211\u4eec\u53ef\u4ee5\u7b80\u5355\u5730\u5c06\u6240\u6709\u8ba1\u7b97\u64cd\u4f5c\u7684\u6267\u884c\u65f6\u95f4\u89c6\u4e3a\u76f8\u540c\u7684\u201c\u5355\u4f4d\u65f6\u95f4\u201d\uff0c\u4ece\u800c\u5c06\u201c\u8ba1\u7b97\u64cd\u4f5c\u7684\u8fd0\u884c\u65f6\u95f4\u7684\u7edf\u8ba1\u201d\u7b80\u5316\u4e3a\u201c\u8ba1\u7b97\u64cd\u4f5c\u7684\u6570\u91cf\u7684\u7edf\u8ba1\u201d\uff0c\u8fd9\u6837\u7684\u7b80\u5316\u65b9\u6cd5\u5927\u5927\u964d\u4f4e\u4e86\u4f30\u7b97\u96be\u5ea6\u3002</p> <p>\u65f6\u95f4\u590d\u6742\u5ea6\u4e5f\u5b58\u5728\u4e00\u5b9a\u7684\u5c40\u9650\u6027\u3002\u4f8b\u5982\uff0c\u5c3d\u7ba1\u7b97\u6cd5 <code>A</code> \u548c <code>C</code> \u7684\u65f6\u95f4\u590d\u6742\u5ea6\u76f8\u540c\uff0c\u4f46\u5b9e\u9645\u8fd0\u884c\u65f6\u95f4\u5dee\u522b\u5f88\u5927\u3002\u540c\u6837\uff0c\u5c3d\u7ba1\u7b97\u6cd5 <code>B</code> \u7684\u65f6\u95f4\u590d\u6742\u5ea6\u6bd4 <code>C</code> \u9ad8\uff0c\u4f46\u5728\u8f93\u5165\u6570\u636e\u5927\u5c0f \\(n\\) \u8f83\u5c0f\u65f6\uff0c\u7b97\u6cd5 <code>B</code> \u660e\u663e\u4f18\u4e8e\u7b97\u6cd5 <code>C</code> \u3002\u5728\u8fd9\u4e9b\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u5f88\u96be\u4ec5\u51ed\u65f6\u95f4\u590d\u6742\u5ea6\u5224\u65ad\u7b97\u6cd5\u6548\u7387\u9ad8\u4f4e\u3002\u5f53\u7136\uff0c\u5c3d\u7ba1\u5b58\u5728\u4e0a\u8ff0\u95ee\u9898\uff0c\u590d\u6742\u5ea6\u5206\u6790\u4ecd\u7136\u662f\u8bc4\u5224\u7b97\u6cd5\u6548\u7387\u6700\u6709\u6548\u4e14\u5e38\u7528\u7684\u65b9\u6cd5\u3002</p>"},{"location":"chapter_computational_complexity/time_complexity/#223","title":"2.2.3. \u00a0 \u51fd\u6570\u6e10\u8fd1\u4e0a\u754c","text":"<p>\u8bbe\u7b97\u6cd5\u7684\u8ba1\u7b97\u64cd\u4f5c\u6570\u91cf\u662f\u4e00\u4e2a\u5173\u4e8e\u8f93\u5165\u6570\u636e\u5927\u5c0f \\(n\\) \u7684\u51fd\u6570\uff0c\u8bb0\u4e3a \\(T(n)\\) \uff0c\u5219\u4ee5\u4e0b\u7b97\u6cd5\u7684\u64cd\u4f5c\u6570\u91cf\u4e3a</p> \\[ T(n) = 3 + 2n \\] JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart <pre><code>void algorithm(int n) {\nint a = 1;  // +1\na = a + 1;  // +1\na = a * 2;  // +1\n// \u5faa\u73af n \u6b21\nfor (int i = 0; i &lt; n; i++) { // +1\uff08\u6bcf\u8f6e\u90fd\u6267\u884c i ++\uff09\nSystem.out.println(0);    // +1\n}\n}\n</code></pre> <pre><code>void algorithm(int n) {\nint a = 1;  // +1\na = a + 1;  // +1\na = a * 2;  // +1\n// \u5faa\u73af n \u6b21\nfor (int i = 0; i &lt; n; i++) { // +1\uff08\u6bcf\u8f6e\u90fd\u6267\u884c i ++\uff09\ncout &lt;&lt; 0 &lt;&lt; endl;    // +1\n}\n}\n</code></pre> <pre><code>def algorithm(n: int) -&gt; None:\na = 1      # +1\na = a + 1  # +1\na = a * 2  # +1\n# \u5faa\u73af n \u6b21\nfor i in range(n):  # +1\nprint(0)        # +1\n</code></pre> <pre><code>func algorithm(n int) {\na := 1      // +1\na = a + 1   // +1\na = a * 2   // +1\n// \u5faa\u73af n \u6b21\nfor i := 0; i &lt; n; i++ {   // +1\nfmt.Println(a)         // +1\n}\n}\n</code></pre> <pre><code>function algorithm(n) {\nvar a = 1; // +1\na += 1; // +1\na *= 2; // +1\n// \u5faa\u73af n \u6b21\nfor(let i = 0; i &lt; n; i++){ // +1\uff08\u6bcf\u8f6e\u90fd\u6267\u884c i ++\uff09\nconsole.log(0); // +1\n}\n}\n</code></pre> <pre><code>function algorithm(n: number): void{\nvar a: number = 1; // +1\na += 1; // +1\na *= 2; // +1\n// \u5faa\u73af n \u6b21\nfor(let i = 0; i &lt; n; i++){ // +1\uff08\u6bcf\u8f6e\u90fd\u6267\u884c i ++\uff09\nconsole.log(0); // +1\n}\n}\n</code></pre> <pre><code>void algorithm(int n) {\nint a = 1;  // +1\na = a + 1;  // +1\na = a * 2;  // +1\n// \u5faa\u73af n \u6b21\nfor (int i = 0; i &lt; n; i++) {   // +1\uff08\u6bcf\u8f6e\u90fd\u6267\u884c i ++\uff09\nprintf(\"%d\", 0);            // +1\n}\n}  </code></pre> <pre><code>void algorithm(int n)\n{\nint a = 1;  // +1\na = a + 1;  // +1\na = a * 2;  // +1\n// \u5faa\u73af n \u6b21\nfor (int i = 0; i &lt; n; i++) // +1\uff08\u6bcf\u8f6e\u90fd\u6267\u884c i ++\uff09\n{\nConsole.WriteLine(0);   // +1\n}\n}\n</code></pre> <pre><code>func algorithm(n: Int) {\nvar a = 1 // +1\na = a + 1 // +1\na = a * 2 // +1\n// \u5faa\u73af n \u6b21\nfor _ in 0 ..&lt; n { // +1\nprint(0) // +1\n}\n}\n</code></pre> <pre><code>\n</code></pre> <pre><code>void algorithm(int n) {\nint a = 1; // +1\na = a + 1; // +1\na = a * 2; // +1\n// \u5faa\u73af n \u6b21\nfor (int i = 0; i &lt; n; i++) { // +1\uff08\u6bcf\u8f6e\u90fd\u6267\u884c i ++\uff09\nprint(0); // +1\n}\n}\n</code></pre> <p>\\(T(n)\\) \u662f\u4e00\u6b21\u51fd\u6570\uff0c\u8bf4\u660e\u65f6\u95f4\u589e\u957f\u8d8b\u52bf\u662f\u7ebf\u6027\u7684\uff0c\u56e0\u6b64\u53ef\u4ee5\u5f97\u51fa\u65f6\u95f4\u590d\u6742\u5ea6\u662f\u7ebf\u6027\u9636\u3002</p> <p>\u6211\u4eec\u5c06\u7ebf\u6027\u9636\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u8bb0\u4e3a \\(O(n)\\) \uff0c\u8fd9\u4e2a\u6570\u5b66\u7b26\u53f7\u79f0\u4e3a\u300c\u5927 \\(O\\) \u8bb0\u53f7 Big-\\(O\\) Notation\u300d\uff0c\u8868\u793a\u51fd\u6570 \\(T(n)\\) \u7684\u300c\u6e10\u8fd1\u4e0a\u754c Asymptotic Upper Bound\u300d\u3002</p> <p>\u63a8\u7b97\u65f6\u95f4\u590d\u6742\u5ea6\u672c\u8d28\u4e0a\u662f\u8ba1\u7b97\u201c\u64cd\u4f5c\u6570\u91cf\u51fd\u6570 \\(T(n)\\)\u201d\u7684\u6e10\u8fd1\u4e0a\u754c\u3002\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u6765\u770b\u51fd\u6570\u6e10\u8fd1\u4e0a\u754c\u7684\u6570\u5b66\u5b9a\u4e49\u3002</p> <p>\u51fd\u6570\u6e10\u8fd1\u4e0a\u754c</p> <p>\u82e5\u5b58\u5728\u6b63\u5b9e\u6570 \\(c\\) \u548c\u5b9e\u6570 \\(n_0\\) \uff0c\u4f7f\u5f97\u5bf9\u4e8e\u6240\u6709\u7684 \\(n &gt; n_0\\) \uff0c\u5747\u6709 $$ T(n) \\leq c \\cdot f(n) $$ \u5219\u53ef\u8ba4\u4e3a \\(f(n)\\) \u7ed9\u51fa\u4e86 \\(T(n)\\) \u7684\u4e00\u4e2a\u6e10\u8fd1\u4e0a\u754c\uff0c\u8bb0\u4e3a $$ T(n) = O(f(n)) $$</p> <p></p> <p> Fig. \u51fd\u6570\u7684\u6e10\u8fd1\u4e0a\u754c </p> <p>\u4ece\u672c\u8d28\u4e0a\u8bb2\uff0c\u8ba1\u7b97\u6e10\u8fd1\u4e0a\u754c\u5c31\u662f\u5bfb\u627e\u4e00\u4e2a\u51fd\u6570 \\(f(n)\\) \uff0c\u4f7f\u5f97\u5f53 \\(n\\) \u8d8b\u5411\u4e8e\u65e0\u7a77\u5927\u65f6\uff0c\\(T(n)\\) \u548c \\(f(n)\\) \u5904\u4e8e\u76f8\u540c\u7684\u589e\u957f\u7ea7\u522b\uff0c\u4ec5\u76f8\u5dee\u4e00\u4e2a\u5e38\u6570\u9879 \\(c\\) \u7684\u500d\u6570\u3002</p>"},{"location":"chapter_computational_complexity/time_complexity/#224","title":"2.2.4. \u00a0 \u63a8\u7b97\u65b9\u6cd5","text":"<p>\u6e10\u8fd1\u4e0a\u754c\u7684\u6570\u5b66\u5473\u513f\u6709\u70b9\u91cd\uff0c\u5982\u679c\u4f60\u611f\u89c9\u6ca1\u6709\u5b8c\u5168\u7406\u89e3\uff0c\u4e5f\u65e0\u9700\u62c5\u5fc3\u3002\u56e0\u4e3a\u5728\u5b9e\u9645\u4f7f\u7528\u4e2d\uff0c\u6211\u4eec\u53ea\u9700\u8981\u638c\u63e1\u63a8\u7b97\u65b9\u6cd5\uff0c\u6570\u5b66\u610f\u4e49\u53ef\u4ee5\u9010\u6e10\u9886\u609f\u3002</p> <p>\u6839\u636e\u5b9a\u4e49\uff0c\u786e\u5b9a \\(f(n)\\) \u4e4b\u540e\uff0c\u6211\u4eec\u4fbf\u53ef\u5f97\u5230\u65f6\u95f4\u590d\u6742\u5ea6 \\(O(f(n))\\) \u3002\u90a3\u4e48\u5982\u4f55\u786e\u5b9a\u6e10\u8fd1\u4e0a\u754c \\(f(n)\\) \u5462\uff1f\u603b\u4f53\u5206\u4e3a\u4e24\u6b65\uff1a\u9996\u5148\u7edf\u8ba1\u64cd\u4f5c\u6570\u91cf\uff0c\u7136\u540e\u5224\u65ad\u6e10\u8fd1\u4e0a\u754c\u3002</p>"},{"location":"chapter_computational_complexity/time_complexity/#_1","title":"\u7b2c\u4e00\u6b65\uff1a\u7edf\u8ba1\u64cd\u4f5c\u6570\u91cf","text":"<p>\u9488\u5bf9\u4ee3\u7801\uff0c\u9010\u884c\u4ece\u4e0a\u5230\u4e0b\u8ba1\u7b97\u5373\u53ef\u3002\u7136\u800c\uff0c\u7531\u4e8e\u4e0a\u8ff0 \\(c \\cdot f(n)\\) \u4e2d\u7684\u5e38\u6570\u9879 \\(c\\) \u53ef\u4ee5\u53d6\u4efb\u610f\u5927\u5c0f\uff0c\u56e0\u6b64\u64cd\u4f5c\u6570\u91cf \\(T(n)\\) \u4e2d\u7684\u5404\u79cd\u7cfb\u6570\u3001\u5e38\u6570\u9879\u90fd\u53ef\u4ee5\u88ab\u5ffd\u7565\u3002\u6839\u636e\u6b64\u539f\u5219\uff0c\u53ef\u4ee5\u603b\u7ed3\u51fa\u4ee5\u4e0b\u8ba1\u6570\u7b80\u5316\u6280\u5de7\uff1a</p> <ol> <li>\u5ffd\u7565\u4e0e \\(n\\) \u65e0\u5173\u7684\u64cd\u4f5c\u3002\u56e0\u4e3a\u5b83\u4eec\u90fd\u662f \\(T(n)\\) \u4e2d\u7684\u5e38\u6570\u9879\uff0c\u5bf9\u65f6\u95f4\u590d\u6742\u5ea6\u4e0d\u4ea7\u751f\u5f71\u54cd\u3002</li> <li>\u7701\u7565\u6240\u6709\u7cfb\u6570\u3002\u4f8b\u5982\uff0c\u5faa\u73af \\(2n\\) \u6b21\u3001\\(5n + 1\\) \u6b21\u7b49\uff0c\u90fd\u53ef\u4ee5\u7b80\u5316\u8bb0\u4e3a \\(n\\) \u6b21\uff0c\u56e0\u4e3a \\(n\\) \u524d\u9762\u7684\u7cfb\u6570\u5bf9\u65f6\u95f4\u590d\u6742\u5ea6\u6ca1\u6709\u5f71\u54cd\u3002</li> <li>\u5faa\u73af\u5d4c\u5957\u65f6\u4f7f\u7528\u4e58\u6cd5\u3002\u603b\u64cd\u4f5c\u6570\u91cf\u7b49\u4e8e\u5916\u5c42\u5faa\u73af\u548c\u5185\u5c42\u5faa\u73af\u64cd\u4f5c\u6570\u91cf\u4e4b\u79ef\uff0c\u6bcf\u4e00\u5c42\u5faa\u73af\u4f9d\u7136\u53ef\u4ee5\u5206\u522b\u5957\u7528\u4e0a\u8ff0 <code>1.</code> \u548c <code>2.</code> \u6280\u5de7\u3002</li> </ol> <p>\u4ee5\u4e0b\u793a\u4f8b\u5c55\u793a\u4e86\u4f7f\u7528\u4e0a\u8ff0\u6280\u5de7\u524d\u3001\u540e\u7684\u7edf\u8ba1\u7ed3\u679c\u3002</p> \\[ \\begin{aligned} T(n) &amp; = 2n(n + 1) + (5n + 1) + 2 &amp; \\text{\u5b8c\u6574\u7edf\u8ba1 (-.-|||)} \\newline &amp; = 2n^2 + 7n + 3 \\newline T(n) &amp; = n^2 + n &amp; \\text{\u5077\u61d2\u7edf\u8ba1 (o.O)} \\end{aligned} \\] <p>\u6700\u7ec8\uff0c\u4e24\u8005\u90fd\u80fd\u63a8\u51fa\u76f8\u540c\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u7ed3\u679c\uff0c\u5373 \\(O(n^2)\\) \u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart <pre><code>void algorithm(int n) {\nint a = 1;  // +0\uff08\u6280\u5de7 1\uff09\na = a + n;  // +0\uff08\u6280\u5de7 1\uff09\n// +n\uff08\u6280\u5de7 2\uff09\nfor (int i = 0; i &lt; 5 * n + 1; i++) {\nSystem.out.println(0);\n}\n// +n*n\uff08\u6280\u5de7 3\uff09\nfor (int i = 0; i &lt; 2 * n; i++) {\nfor (int j = 0; j &lt; n + 1; j++) {\nSystem.out.println(0);\n}\n}\n}\n</code></pre> <pre><code>void algorithm(int n) {\nint a = 1;  // +0\uff08\u6280\u5de7 1\uff09\na = a + n;  // +0\uff08\u6280\u5de7 1\uff09\n// +n\uff08\u6280\u5de7 2\uff09\nfor (int i = 0; i &lt; 5 * n + 1; i++) {\ncout &lt;&lt; 0 &lt;&lt; endl;\n}\n// +n*n\uff08\u6280\u5de7 3\uff09\nfor (int i = 0; i &lt; 2 * n; i++) {\nfor (int j = 0; j &lt; n + 1; j++) {\ncout &lt;&lt; 0 &lt;&lt; endl;\n}\n}\n}\n</code></pre> <pre><code>def algorithm(n: int) -&gt; None:\na = 1      # +0\uff08\u6280\u5de7 1\uff09\na = a + n  # +0\uff08\u6280\u5de7 1\uff09\n# +n\uff08\u6280\u5de7 2\uff09\nfor i in range(5 * n + 1):\nprint(0)\n# +n*n\uff08\u6280\u5de7 3\uff09\nfor i in range(2 * n):\nfor j in range(n + 1):\nprint(0)\n</code></pre> <pre><code>func algorithm(n int) {\na := 1     // +0\uff08\u6280\u5de7 1\uff09\na = a + n  // +0\uff08\u6280\u5de7 1\uff09\n// +n\uff08\u6280\u5de7 2\uff09\nfor i := 0; i &lt; 5 * n + 1; i++ {\nfmt.Println(0)\n}\n// +n*n\uff08\u6280\u5de7 3\uff09\nfor i := 0; i &lt; 2 * n; i++ {\nfor j := 0; j &lt; n + 1; j++ {\nfmt.Println(0)\n}\n}\n}\n</code></pre> <pre><code>function algorithm(n) {\nlet a = 1;  // +0\uff08\u6280\u5de7 1\uff09\na = a + n;  // +0\uff08\u6280\u5de7 1\uff09\n// +n\uff08\u6280\u5de7 2\uff09\nfor (let i = 0; i &lt; 5 * n + 1; i++) {\nconsole.log(0);\n}\n// +n*n\uff08\u6280\u5de7 3\uff09\nfor (let i = 0; i &lt; 2 * n; i++) {\nfor (let j = 0; j &lt; n + 1; j++) {\nconsole.log(0);\n}\n}\n}\n</code></pre> <pre><code>function algorithm(n: number): void {\nlet a = 1;  // +0\uff08\u6280\u5de7 1\uff09\na = a + n;  // +0\uff08\u6280\u5de7 1\uff09\n// +n\uff08\u6280\u5de7 2\uff09\nfor (let i = 0; i &lt; 5 * n + 1; i++) {\nconsole.log(0);\n}\n// +n*n\uff08\u6280\u5de7 3\uff09\nfor (let i = 0; i &lt; 2 * n; i++) {\nfor (let j = 0; j &lt; n + 1; j++) {\nconsole.log(0);\n}\n}\n}\n</code></pre> <pre><code>void algorithm(int n) {\nint a = 1;  // +0\uff08\u6280\u5de7 1\uff09\na = a + n;  // +0\uff08\u6280\u5de7 1\uff09\n// +n\uff08\u6280\u5de7 2\uff09\nfor (int i = 0; i &lt; 5 * n + 1; i++) {\nprintf(\"%d\", 0);\n}\n// +n*n\uff08\u6280\u5de7 3\uff09\nfor (int i = 0; i &lt; 2 * n; i++) {\nfor (int j = 0; j &lt; n + 1; j++) {\nprintf(\"%d\", 0);\n}\n}\n}\n</code></pre> <pre><code>void algorithm(int n)\n{\nint a = 1;  // +0\uff08\u6280\u5de7 1\uff09\na = a + n;  // +0\uff08\u6280\u5de7 1\uff09\n// +n\uff08\u6280\u5de7 2\uff09\nfor (int i = 0; i &lt; 5 * n + 1; i++)\n{\nConsole.WriteLine(0);\n}\n// +n*n\uff08\u6280\u5de7 3\uff09\nfor (int i = 0; i &lt; 2 * n; i++)\n{\nfor (int j = 0; j &lt; n + 1; j++)\n{\nConsole.WriteLine(0);\n}\n}\n}\n</code></pre> <pre><code>func algorithm(n: Int) {\nvar a = 1 // +0\uff08\u6280\u5de7 1\uff09\na = a + n // +0\uff08\u6280\u5de7 1\uff09\n// +n\uff08\u6280\u5de7 2\uff09\nfor _ in 0 ..&lt; (5 * n + 1) {\nprint(0)\n}\n// +n*n\uff08\u6280\u5de7 3\uff09\nfor _ in 0 ..&lt; (2 * n) {\nfor _ in 0 ..&lt; (n + 1) {\nprint(0)\n}\n}\n}\n</code></pre> <pre><code>\n</code></pre> <pre><code>void algorithm(int n) {\nint a = 1; // +0\uff08\u6280\u5de7 1\uff09\na = a + n; // +0\uff08\u6280\u5de7 1\uff09\n// +n\uff08\u6280\u5de7 2\uff09\nfor (int i = 0; i &lt; 5 * n + 1; i++) {\nprint(0);\n}\n// +n*n\uff08\u6280\u5de7 3\uff09\nfor (int i = 0; i &lt; 2 * n; i++) {\nfor (int j = 0; j &lt; n + 1; j++) {\nprint(0);\n}\n}\n}\n</code></pre>"},{"location":"chapter_computational_complexity/time_complexity/#_2","title":"\u7b2c\u4e8c\u6b65\uff1a\u5224\u65ad\u6e10\u8fd1\u4e0a\u754c","text":"<p>\u65f6\u95f4\u590d\u6742\u5ea6\u7531\u591a\u9879\u5f0f \\(T(n)\\) \u4e2d\u6700\u9ad8\u9636\u7684\u9879\u6765\u51b3\u5b9a\u3002\u8fd9\u662f\u56e0\u4e3a\u5728 \\(n\\) \u8d8b\u4e8e\u65e0\u7a77\u5927\u65f6\uff0c\u6700\u9ad8\u9636\u7684\u9879\u5c06\u53d1\u6325\u4e3b\u5bfc\u4f5c\u7528\uff0c\u5176\u4ed6\u9879\u7684\u5f71\u54cd\u90fd\u53ef\u4ee5\u88ab\u5ffd\u7565\u3002</p> <p>\u4ee5\u4e0b\u8868\u683c\u5c55\u793a\u4e86\u4e00\u4e9b\u4f8b\u5b50\uff0c\u5176\u4e2d\u4e00\u4e9b\u5938\u5f20\u7684\u503c\u662f\u4e3a\u4e86\u5f3a\u8c03\u201c\u7cfb\u6570\u65e0\u6cd5\u64bc\u52a8\u9636\u6570\u201d\u8fd9\u4e00\u7ed3\u8bba\u3002\u5f53 \\(n\\) \u8d8b\u4e8e\u65e0\u7a77\u5927\u65f6\uff0c\u8fd9\u4e9b\u5e38\u6570\u53d8\u5f97\u65e0\u8db3\u8f7b\u91cd\u3002</p> \u64cd\u4f5c\u6570\u91cf \\(T(n)\\) \u65f6\u95f4\u590d\u6742\u5ea6 \\(O(f(n))\\) \\(100000\\) \\(O(1)\\) \\(3n + 2\\) \\(O(n)\\) \\(2n^2 + 3n + 2\\) \\(O(n^2)\\) \\(n^3 + 10000n^2\\) \\(O(n^3)\\) \\(2^n + 10000n^{10000}\\) \\(O(2^n)\\)"},{"location":"chapter_computational_complexity/time_complexity/#225","title":"2.2.5. \u00a0 \u5e38\u89c1\u7c7b\u578b","text":"<p>\u8bbe\u8f93\u5165\u6570\u636e\u5927\u5c0f\u4e3a \\(n\\) \uff0c\u5e38\u89c1\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u7c7b\u578b\u5305\u62ec\uff08\u6309\u7167\u4ece\u4f4e\u5230\u9ad8\u7684\u987a\u5e8f\u6392\u5217\uff09\uff1a</p> \\[ \\begin{aligned} O(1) &lt; O(\\log n) &lt; O(n) &lt; O(n \\log n) &lt; O(n^2) &lt; O(2^n) &lt; O(n!) \\newline \\text{\u5e38\u6570\u9636} &lt; \\text{\u5bf9\u6570\u9636} &lt; \\text{\u7ebf\u6027\u9636} &lt; \\text{\u7ebf\u6027\u5bf9\u6570\u9636} &lt; \\text{\u5e73\u65b9\u9636} &lt; \\text{\u6307\u6570\u9636} &lt; \\text{\u9636\u4e58\u9636} \\end{aligned} \\] <p></p> <p> Fig. \u65f6\u95f4\u590d\u6742\u5ea6\u7684\u5e38\u89c1\u7c7b\u578b </p> <p>Tip</p> <p>\u90e8\u5206\u793a\u4f8b\u4ee3\u7801\u9700\u8981\u4e00\u4e9b\u9884\u5907\u77e5\u8bc6\uff0c\u5305\u62ec\u6570\u7ec4\u3001\u9012\u5f52\u7b97\u6cd5\u7b49\u3002\u5982\u679c\u9047\u5230\u4e0d\u7406\u89e3\u7684\u90e8\u5206\uff0c\u8bf7\u4e0d\u8981\u62c5\u5fc3\uff0c\u53ef\u4ee5\u5728\u5b66\u4e60\u5b8c\u540e\u9762\u7ae0\u8282\u540e\u518d\u56de\u987e\u3002\u73b0\u9636\u6bb5\uff0c\u8bf7\u5148\u4e13\u6ce8\u4e8e\u7406\u89e3\u65f6\u95f4\u590d\u6742\u5ea6\u7684\u542b\u4e49\u548c\u63a8\u7b97\u65b9\u6cd5\u3002</p>"},{"location":"chapter_computational_complexity/time_complexity/#o1","title":"\u5e38\u6570\u9636 \\(O(1)\\)","text":"<p>\u5e38\u6570\u9636\u7684\u64cd\u4f5c\u6570\u91cf\u4e0e\u8f93\u5165\u6570\u636e\u5927\u5c0f \\(n\\) \u65e0\u5173\uff0c\u5373\u4e0d\u968f\u7740 \\(n\\) \u7684\u53d8\u5316\u800c\u53d8\u5316\u3002</p> <p>\u5bf9\u4e8e\u4ee5\u4e0b\u7b97\u6cd5\uff0c\u5c3d\u7ba1\u64cd\u4f5c\u6570\u91cf <code>size</code> \u53ef\u80fd\u5f88\u5927\uff0c\u4f46\u7531\u4e8e\u5176\u4e0e\u6570\u636e\u5927\u5c0f \\(n\\) \u65e0\u5173\uff0c\u56e0\u6b64\u65f6\u95f4\u590d\u6742\u5ea6\u4ecd\u4e3a \\(O(1)\\) \u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart time_complexity.java<pre><code>/* \u5e38\u6570\u9636 */\nint constant(int n) {\nint count = 0;\nint size = 100000;\nfor (int i = 0; i &lt; size; i++)\ncount++;\nreturn count;\n}\n</code></pre> time_complexity.cpp<pre><code>/* \u5e38\u6570\u9636 */\nint constant(int n) {\nint count = 0;\nint size = 100000;\nfor (int i = 0; i &lt; size; i++)\ncount++;\nreturn count;\n}\n</code></pre> time_complexity.py<pre><code>def constant(n: int) -&gt; int:\n\"\"\"\u5e38\u6570\u9636\"\"\"\ncount = 0\nsize = 100000\nfor _ in range(size):\ncount += 1\nreturn count\n</code></pre> time_complexity.go<pre><code>/* \u5e38\u6570\u9636 */\nfunc constant(n int) int {\ncount := 0\nsize := 100000\nfor i := 0; i &lt; size; i++ {\ncount++\n}\nreturn count\n}\n</code></pre> time_complexity.js<pre><code>/* \u5e38\u6570\u9636 */\nfunction constant(n) {\nlet count = 0;\nconst size = 100000;\nfor (let i = 0; i &lt; size; i++) count++;\nreturn count;\n}\n</code></pre> time_complexity.ts<pre><code>/* \u5e38\u6570\u9636 */\nfunction constant(n: number): number {\nlet count = 0;\nconst size = 100000;\nfor (let i = 0; i &lt; size; i++) count++;\nreturn count;\n}\n</code></pre> time_complexity.c<pre><code>/* \u5e38\u6570\u9636 */\nint constant(int n) {\nint count = 0;\nint size = 100000;\nint i = 0;\nfor (int i = 0; i &lt; size; i++) {\ncount++;\n}\nreturn count;\n}\n</code></pre> time_complexity.cs<pre><code>/* \u5e38\u6570\u9636 */\nint constant(int n) {\nint count = 0;\nint size = 100000;\nfor (int i = 0; i &lt; size; i++)\ncount++;\nreturn count;\n}\n</code></pre> time_complexity.swift<pre><code>/* \u5e38\u6570\u9636 */\nfunc constant(n: Int) -&gt; Int {\nvar count = 0\nlet size = 100_000\nfor _ in 0 ..&lt; size {\ncount += 1\n}\nreturn count\n}\n</code></pre> time_complexity.zig<pre><code>// \u5e38\u6570\u9636\nfn constant(n: i32) i32 {\n_ = n;\nvar count: i32 = 0;\nconst size: i32 = 100_000;\nvar i: i32 = 0;\nwhile(i&lt;size) : (i += 1) {\ncount += 1;\n}\nreturn count;\n}\n</code></pre> time_complexity.dart<pre><code>/* \u5e38\u6570\u9636 */\nint constant(int n) {\nint count = 0;\nint size = 100000;\nfor (var i = 0; i &lt; size; i++) {\ncount++;\n}\nreturn count;\n}\n</code></pre>"},{"location":"chapter_computational_complexity/time_complexity/#on","title":"\u7ebf\u6027\u9636 \\(O(n)\\)","text":"<p>\u7ebf\u6027\u9636\u7684\u64cd\u4f5c\u6570\u91cf\u76f8\u5bf9\u4e8e\u8f93\u5165\u6570\u636e\u5927\u5c0f\u4ee5\u7ebf\u6027\u7ea7\u522b\u589e\u957f\u3002\u7ebf\u6027\u9636\u901a\u5e38\u51fa\u73b0\u5728\u5355\u5c42\u5faa\u73af\u4e2d\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart time_complexity.java<pre><code>/* \u7ebf\u6027\u9636 */\nint linear(int n) {\nint count = 0;\nfor (int i = 0; i &lt; n; i++)\ncount++;\nreturn count;\n}\n</code></pre> time_complexity.cpp<pre><code>/* \u7ebf\u6027\u9636 */\nint linear(int n) {\nint count = 0;\nfor (int i = 0; i &lt; n; i++)\ncount++;\nreturn count;\n}\n</code></pre> time_complexity.py<pre><code>def linear(n: int) -&gt; int:\n\"\"\"\u7ebf\u6027\u9636\"\"\"\ncount = 0\nfor _ in range(n):\ncount += 1\nreturn count\n</code></pre> time_complexity.go<pre><code>/* \u7ebf\u6027\u9636 */\nfunc linear(n int) int {\ncount := 0\nfor i := 0; i &lt; n; i++ {\ncount++\n}\nreturn count\n}\n</code></pre> time_complexity.js<pre><code>/* \u7ebf\u6027\u9636 */\nfunction linear(n) {\nlet count = 0;\nfor (let i = 0; i &lt; n; i++) count++;\nreturn count;\n}\n</code></pre> time_complexity.ts<pre><code>/* \u7ebf\u6027\u9636 */\nfunction linear(n: number): number {\nlet count = 0;\nfor (let i = 0; i &lt; n; i++) count++;\nreturn count;\n}\n</code></pre> time_complexity.c<pre><code>/* \u7ebf\u6027\u9636 */\nint linear(int n) {\nint count = 0;\nfor (int i = 0; i &lt; n; i++) {\ncount++;\n}\nreturn count;\n}\n</code></pre> time_complexity.cs<pre><code>/* \u7ebf\u6027\u9636 */\nint linear(int n) {\nint count = 0;\nfor (int i = 0; i &lt; n; i++)\ncount++;\nreturn count;\n}\n</code></pre> time_complexity.swift<pre><code>/* \u7ebf\u6027\u9636 */\nfunc linear(n: Int) -&gt; Int {\nvar count = 0\nfor _ in 0 ..&lt; n {\ncount += 1\n}\nreturn count\n}\n</code></pre> time_complexity.zig<pre><code>// \u7ebf\u6027\u9636\nfn linear(n: i32) i32 {\nvar count: i32 = 0;\nvar i: i32 = 0;\nwhile (i &lt; n) : (i += 1) {\ncount += 1;\n}\nreturn count;\n}\n</code></pre> time_complexity.dart<pre><code>/* \u7ebf\u6027\u9636 */\nint linear(int n) {\nint count = 0;\nfor (var i = 0; i &lt; n; i++) {\ncount++;\n}\nreturn count;\n}\n</code></pre> <p>\u904d\u5386\u6570\u7ec4\u548c\u904d\u5386\u94fe\u8868\u7b49\u64cd\u4f5c\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u5747\u4e3a \\(O(n)\\) \uff0c\u5176\u4e2d \\(n\\) \u4e3a\u6570\u7ec4\u6216\u94fe\u8868\u7684\u957f\u5ea6\u3002</p> <p>\u5982\u4f55\u786e\u5b9a\u8f93\u5165\u6570\u636e\u5927\u5c0f \\(n\\) \uff1f</p> <p>\u6570\u636e\u5927\u5c0f \\(n\\) \u9700\u6839\u636e\u8f93\u5165\u6570\u636e\u7684\u7c7b\u578b\u6765\u5177\u4f53\u786e\u5b9a\u3002\u4f8b\u5982\uff0c\u5728\u4e0a\u8ff0\u793a\u4f8b\u4e2d\uff0c\u6211\u4eec\u76f4\u63a5\u5c06 \\(n\\) \u89c6\u4e3a\u8f93\u5165\u6570\u636e\u5927\u5c0f\uff1b\u5728\u4e0b\u9762\u904d\u5386\u6570\u7ec4\u7684\u793a\u4f8b\u4e2d\uff0c\u6570\u636e\u5927\u5c0f \\(n\\) \u4e3a\u6570\u7ec4\u7684\u957f\u5ea6\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart time_complexity.java<pre><code>/* \u7ebf\u6027\u9636\uff08\u904d\u5386\u6570\u7ec4\uff09 */\nint arrayTraversal(int[] nums) {\nint count = 0;\n// \u5faa\u73af\u6b21\u6570\u4e0e\u6570\u7ec4\u957f\u5ea6\u6210\u6b63\u6bd4\nfor (int num : nums) {\ncount++;\n}\nreturn count;\n}\n</code></pre> time_complexity.cpp<pre><code>/* \u7ebf\u6027\u9636\uff08\u904d\u5386\u6570\u7ec4\uff09 */\nint arrayTraversal(vector&lt;int&gt; &amp;nums) {\nint count = 0;\n// \u5faa\u73af\u6b21\u6570\u4e0e\u6570\u7ec4\u957f\u5ea6\u6210\u6b63\u6bd4\nfor (int num : nums) {\ncount++;\n}\nreturn count;\n}\n</code></pre> time_complexity.py<pre><code>def array_traversal(nums: list[int]) -&gt; int:\n\"\"\"\u7ebf\u6027\u9636\uff08\u904d\u5386\u6570\u7ec4\uff09\"\"\"\ncount = 0\n# \u5faa\u73af\u6b21\u6570\u4e0e\u6570\u7ec4\u957f\u5ea6\u6210\u6b63\u6bd4\nfor num in nums:\ncount += 1\nreturn count\n</code></pre> time_complexity.go<pre><code>/* \u7ebf\u6027\u9636\uff08\u904d\u5386\u6570\u7ec4\uff09 */\nfunc arrayTraversal(nums []int) int {\ncount := 0\n// \u5faa\u73af\u6b21\u6570\u4e0e\u6570\u7ec4\u957f\u5ea6\u6210\u6b63\u6bd4\nfor range nums {\ncount++\n}\nreturn count\n}\n</code></pre> time_complexity.js<pre><code>/* \u7ebf\u6027\u9636\uff08\u904d\u5386\u6570\u7ec4\uff09 */\nfunction arrayTraversal(nums) {\nlet count = 0;\n// \u5faa\u73af\u6b21\u6570\u4e0e\u6570\u7ec4\u957f\u5ea6\u6210\u6b63\u6bd4\nfor (let i = 0; i &lt; nums.length; i++) {\ncount++;\n}\nreturn count;\n}\n</code></pre> time_complexity.ts<pre><code>/* \u7ebf\u6027\u9636\uff08\u904d\u5386\u6570\u7ec4\uff09 */\nfunction arrayTraversal(nums: number[]): number {\nlet count = 0;\n// \u5faa\u73af\u6b21\u6570\u4e0e\u6570\u7ec4\u957f\u5ea6\u6210\u6b63\u6bd4\nfor (let i = 0; i &lt; nums.length; i++) {\ncount++;\n}\nreturn count;\n}\n</code></pre> time_complexity.c<pre><code>/* \u7ebf\u6027\u9636\uff08\u904d\u5386\u6570\u7ec4\uff09 */\nint arrayTraversal(int *nums, int n) {\nint count = 0;\n// \u5faa\u73af\u6b21\u6570\u4e0e\u6570\u7ec4\u957f\u5ea6\u6210\u6b63\u6bd4\nfor (int i = 0; i &lt; n; i++) {\ncount++;\n}\nreturn count;\n}\n</code></pre> time_complexity.cs<pre><code>/* \u7ebf\u6027\u9636\uff08\u904d\u5386\u6570\u7ec4\uff09 */\nint arrayTraversal(int[] nums) {\nint count = 0;\n// \u5faa\u73af\u6b21\u6570\u4e0e\u6570\u7ec4\u957f\u5ea6\u6210\u6b63\u6bd4\nforeach (int num in nums) {\ncount++;\n}\nreturn count;\n}\n</code></pre> time_complexity.swift<pre><code>/* \u7ebf\u6027\u9636\uff08\u904d\u5386\u6570\u7ec4\uff09 */\nfunc arrayTraversal(nums: [Int]) -&gt; Int {\nvar count = 0\n// \u5faa\u73af\u6b21\u6570\u4e0e\u6570\u7ec4\u957f\u5ea6\u6210\u6b63\u6bd4\nfor _ in nums {\ncount += 1\n}\nreturn count\n}\n</code></pre> time_complexity.zig<pre><code>// \u7ebf\u6027\u9636\uff08\u904d\u5386\u6570\u7ec4\uff09\nfn arrayTraversal(nums: []i32) i32 {\nvar count: i32 = 0;\n// \u5faa\u73af\u6b21\u6570\u4e0e\u6570\u7ec4\u957f\u5ea6\u6210\u6b63\u6bd4\nfor (nums) |_| {\ncount += 1;\n}\nreturn count;\n}\n</code></pre> time_complexity.dart<pre><code>/* \u7ebf\u6027\u9636\uff08\u904d\u5386\u6570\u7ec4\uff09 */\nint arrayTraversal(List&lt;int&gt; nums) {\nint count = 0;\n// \u5faa\u73af\u6b21\u6570\u4e0e\u6570\u7ec4\u957f\u5ea6\u6210\u6b63\u6bd4\nfor (var num in nums) {\ncount++;\n}\nreturn count;\n}\n</code></pre>"},{"location":"chapter_computational_complexity/time_complexity/#on2","title":"\u5e73\u65b9\u9636 \\(O(n^2)\\)","text":"<p>\u5e73\u65b9\u9636\u7684\u64cd\u4f5c\u6570\u91cf\u76f8\u5bf9\u4e8e\u8f93\u5165\u6570\u636e\u5927\u5c0f\u4ee5\u5e73\u65b9\u7ea7\u522b\u589e\u957f\u3002\u5e73\u65b9\u9636\u901a\u5e38\u51fa\u73b0\u5728\u5d4c\u5957\u5faa\u73af\u4e2d\uff0c\u5916\u5c42\u5faa\u73af\u548c\u5185\u5c42\u5faa\u73af\u90fd\u4e3a \\(O(n)\\) \uff0c\u56e0\u6b64\u603b\u4f53\u4e3a \\(O(n^2)\\) \u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart time_complexity.java<pre><code>/* \u5e73\u65b9\u9636 */\nint quadratic(int n) {\nint count = 0;\n// \u5faa\u73af\u6b21\u6570\u4e0e\u6570\u7ec4\u957f\u5ea6\u6210\u5e73\u65b9\u5173\u7cfb\nfor (int i = 0; i &lt; n; i++) {\nfor (int j = 0; j &lt; n; j++) {\ncount++;\n}\n}\nreturn count;\n}\n</code></pre> time_complexity.cpp<pre><code>/* \u5e73\u65b9\u9636 */\nint quadratic(int n) {\nint count = 0;\n// \u5faa\u73af\u6b21\u6570\u4e0e\u6570\u7ec4\u957f\u5ea6\u6210\u5e73\u65b9\u5173\u7cfb\nfor (int i = 0; i &lt; n; i++) {\nfor (int j = 0; j &lt; n; j++) {\ncount++;\n}\n}\nreturn count;\n}\n</code></pre> time_complexity.py<pre><code>def quadratic(n: int) -&gt; int:\n\"\"\"\u5e73\u65b9\u9636\"\"\"\ncount = 0\n# \u5faa\u73af\u6b21\u6570\u4e0e\u6570\u7ec4\u957f\u5ea6\u6210\u5e73\u65b9\u5173\u7cfb\nfor i in range(n):\nfor j in range(n):\ncount += 1\nreturn count\n</code></pre> time_complexity.go<pre><code>/* \u5e73\u65b9\u9636 */\nfunc quadratic(n int) int {\ncount := 0\n// \u5faa\u73af\u6b21\u6570\u4e0e\u6570\u7ec4\u957f\u5ea6\u6210\u5e73\u65b9\u5173\u7cfb\nfor i := 0; i &lt; n; i++ {\nfor j := 0; j &lt; n; j++ {\ncount++\n}\n}\nreturn count\n}\n</code></pre> time_complexity.js<pre><code>/* \u5e73\u65b9\u9636 */\nfunction quadratic(n) {\nlet count = 0;\n// \u5faa\u73af\u6b21\u6570\u4e0e\u6570\u7ec4\u957f\u5ea6\u6210\u5e73\u65b9\u5173\u7cfb\nfor (let i = 0; i &lt; n; i++) {\nfor (let j = 0; j &lt; n; j++) {\ncount++;\n}\n}\nreturn count;\n}\n</code></pre> time_complexity.ts<pre><code>/* \u5e73\u65b9\u9636 */\nfunction quadratic(n: number): number {\nlet count = 0;\n// \u5faa\u73af\u6b21\u6570\u4e0e\u6570\u7ec4\u957f\u5ea6\u6210\u5e73\u65b9\u5173\u7cfb\nfor (let i = 0; i &lt; n; i++) {\nfor (let j = 0; j &lt; n; j++) {\ncount++;\n}\n}\nreturn count;\n}\n</code></pre> time_complexity.c<pre><code>/* \u5e73\u65b9\u9636 */\nint quadratic(int n) {\nint count = 0;\n// \u5faa\u73af\u6b21\u6570\u4e0e\u6570\u7ec4\u957f\u5ea6\u6210\u5e73\u65b9\u5173\u7cfb\nfor (int i = 0; i &lt; n; i++) {\nfor (int j = 0; j &lt; n; j++) {\ncount++;\n}\n}\nreturn count;\n}\n</code></pre> time_complexity.cs<pre><code>/* \u5e73\u65b9\u9636 */\nint quadratic(int n) {\nint count = 0;\n// \u5faa\u73af\u6b21\u6570\u4e0e\u6570\u7ec4\u957f\u5ea6\u6210\u5e73\u65b9\u5173\u7cfb\nfor (int i = 0; i &lt; n; i++) {\nfor (int j = 0; j &lt; n; j++) {\ncount++;\n}\n}\nreturn count;\n}\n</code></pre> time_complexity.swift<pre><code>/* \u5e73\u65b9\u9636 */\nfunc quadratic(n: Int) -&gt; Int {\nvar count = 0\n// \u5faa\u73af\u6b21\u6570\u4e0e\u6570\u7ec4\u957f\u5ea6\u6210\u5e73\u65b9\u5173\u7cfb\nfor _ in 0 ..&lt; n {\nfor _ in 0 ..&lt; n {\ncount += 1\n}\n}\nreturn count\n}\n</code></pre> time_complexity.zig<pre><code>// \u5e73\u65b9\u9636\nfn quadratic(n: i32) i32 {\nvar count: i32 = 0;\nvar i: i32 = 0;\n// \u5faa\u73af\u6b21\u6570\u4e0e\u6570\u7ec4\u957f\u5ea6\u6210\u5e73\u65b9\u5173\u7cfb\nwhile (i &lt; n) : (i += 1) {\nvar j: i32 = 0;\nwhile (j &lt; n) : (j += 1) {\ncount += 1;\n}\n}\nreturn count;\n}\n</code></pre> time_complexity.dart<pre><code>/* \u5e73\u65b9\u9636 */\nint quadratic(int n) {\nint count = 0;\n// \u5faa\u73af\u6b21\u6570\u4e0e\u6570\u7ec4\u957f\u5ea6\u6210\u5e73\u65b9\u5173\u7cfb\nfor (int i = 0; i &lt; n; i++) {\nfor (int j = 0; j &lt; n; j++) {\ncount++;\n}\n}\nreturn count;\n}\n</code></pre> <p></p> <p> Fig. \u5e38\u6570\u9636\u3001\u7ebf\u6027\u9636\u3001\u5e73\u65b9\u9636\u7684\u65f6\u95f4\u590d\u6742\u5ea6 </p> <p>\u4ee5\u300c\u5192\u6ce1\u6392\u5e8f\u300d\u4e3a\u4f8b\uff0c\u5916\u5c42\u5faa\u73af\u6267\u884c \\(n - 1\\) \u6b21\uff0c\u5185\u5c42\u5faa\u73af\u6267\u884c \\(n-1, n-2, \\cdots, 2, 1\\) \u6b21\uff0c\u5e73\u5747\u4e3a \\(\\frac{n}{2}\\) \u6b21\uff0c\u56e0\u6b64\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(n^2)\\) \u3002</p> \\[ O((n - 1) \\frac{n}{2}) = O(n^2) \\] JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart time_complexity.java<pre><code>/* \u5e73\u65b9\u9636\uff08\u5192\u6ce1\u6392\u5e8f\uff09 */\nint bubbleSort(int[] nums) {\nint count = 0; // \u8ba1\u6570\u5668\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [0, i]\nfor (int i = nums.length - 1; i &gt; 0; i--) {\n// \u5185\u5faa\u73af\uff1a\u5c06\u672a\u6392\u5e8f\u533a\u95f4 [0, i] \u4e2d\u7684\u6700\u5927\u5143\u7d20\u4ea4\u6362\u81f3\u8be5\u533a\u95f4\u7684\u6700\u53f3\u7aef \nfor (int j = 0; j &lt; i; j++) {\nif (nums[j] &gt; nums[j + 1]) {\n// \u4ea4\u6362 nums[j] \u4e0e nums[j + 1]\nint tmp = nums[j];\nnums[j] = nums[j + 1];\nnums[j + 1] = tmp;\ncount += 3; // \u5143\u7d20\u4ea4\u6362\u5305\u542b 3 \u4e2a\u5355\u5143\u64cd\u4f5c\n}\n}\n}\nreturn count;\n}\n</code></pre> time_complexity.cpp<pre><code>/* \u5e73\u65b9\u9636\uff08\u5192\u6ce1\u6392\u5e8f\uff09 */\nint bubbleSort(vector&lt;int&gt; &amp;nums) {\nint count = 0; // \u8ba1\u6570\u5668\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [0, i]\nfor (int i = nums.size() - 1; i &gt; 0; i--) {\n// \u5185\u5faa\u73af\uff1a\u5c06\u672a\u6392\u5e8f\u533a\u95f4 [0, i] \u4e2d\u7684\u6700\u5927\u5143\u7d20\u4ea4\u6362\u81f3\u8be5\u533a\u95f4\u7684\u6700\u53f3\u7aef \nfor (int j = 0; j &lt; i; j++) {\nif (nums[j] &gt; nums[j + 1]) {\n// \u4ea4\u6362 nums[j] \u4e0e nums[j + 1]\nint tmp = nums[j];\nnums[j] = nums[j + 1];\nnums[j + 1] = tmp;\ncount += 3; // \u5143\u7d20\u4ea4\u6362\u5305\u542b 3 \u4e2a\u5355\u5143\u64cd\u4f5c\n}\n}\n}\nreturn count;\n}\n</code></pre> time_complexity.py<pre><code>def bubble_sort(nums: list[int]) -&gt; int:\n\"\"\"\u5e73\u65b9\u9636\uff08\u5192\u6ce1\u6392\u5e8f\uff09\"\"\"\ncount = 0  # \u8ba1\u6570\u5668\n# \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [0, i]\nfor i in range(len(nums) - 1, 0, -1):\n# \u5185\u5faa\u73af\uff1a\u5c06\u672a\u6392\u5e8f\u533a\u95f4 [0, i] \u4e2d\u7684\u6700\u5927\u5143\u7d20\u4ea4\u6362\u81f3\u8be5\u533a\u95f4\u7684\u6700\u53f3\u7aef \nfor j in range(i):\nif nums[j] &gt; nums[j + 1]:\n# \u4ea4\u6362 nums[j] \u4e0e nums[j + 1]\ntmp: int = nums[j]\nnums[j] = nums[j + 1]\nnums[j + 1] = tmp\ncount += 3  # \u5143\u7d20\u4ea4\u6362\u5305\u542b 3 \u4e2a\u5355\u5143\u64cd\u4f5c\nreturn count\n</code></pre> time_complexity.go<pre><code>/* \u5e73\u65b9\u9636\uff08\u5192\u6ce1\u6392\u5e8f\uff09 */\nfunc bubbleSort(nums []int) int {\ncount := 0 // \u8ba1\u6570\u5668\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [0, i]\nfor i := len(nums) - 1; i &gt; 0; i-- {\n// \u5185\u5faa\u73af\uff1a\u5c06\u672a\u6392\u5e8f\u533a\u95f4 [0, i] \u4e2d\u7684\u6700\u5927\u5143\u7d20\u4ea4\u6362\u81f3\u8be5\u533a\u95f4\u7684\u6700\u53f3\u7aef\nfor j := 0; j &lt; i; j++ {\nif nums[j] &gt; nums[j+1] {\n// \u4ea4\u6362 nums[j] \u4e0e nums[j + 1]\ntmp := nums[j]\nnums[j] = nums[j+1]\nnums[j+1] = tmp\ncount += 3 // \u5143\u7d20\u4ea4\u6362\u5305\u542b 3 \u4e2a\u5355\u5143\u64cd\u4f5c\n}\n}\n}\nreturn count\n}\n</code></pre> time_complexity.js<pre><code>/* \u5e73\u65b9\u9636\uff08\u5192\u6ce1\u6392\u5e8f\uff09 */\nfunction bubbleSort(nums) {\nlet count = 0; // \u8ba1\u6570\u5668\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [0, i]\nfor (let i = nums.length - 1; i &gt; 0; i--) {\n// \u5185\u5faa\u73af\uff1a\u5c06\u672a\u6392\u5e8f\u533a\u95f4 [0, i] \u4e2d\u7684\u6700\u5927\u5143\u7d20\u4ea4\u6362\u81f3\u8be5\u533a\u95f4\u7684\u6700\u53f3\u7aef \nfor (let j = 0; j &lt; i; j++) {\nif (nums[j] &gt; nums[j + 1]) {\n// \u4ea4\u6362 nums[j] \u4e0e nums[j + 1]\nlet tmp = nums[j];\nnums[j] = nums[j + 1];\nnums[j + 1] = tmp;\ncount += 3; // \u5143\u7d20\u4ea4\u6362\u5305\u542b 3 \u4e2a\u5355\u5143\u64cd\u4f5c\n}\n}\n}\nreturn count;\n}\n</code></pre> time_complexity.ts<pre><code>/* \u5e73\u65b9\u9636\uff08\u5192\u6ce1\u6392\u5e8f\uff09 */\nfunction bubbleSort(nums: number[]): number {\nlet count = 0; // \u8ba1\u6570\u5668\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [0, i]\nfor (let i = nums.length - 1; i &gt; 0; i--) {\n// \u5185\u5faa\u73af\uff1a\u5c06\u672a\u6392\u5e8f\u533a\u95f4 [0, i] \u4e2d\u7684\u6700\u5927\u5143\u7d20\u4ea4\u6362\u81f3\u8be5\u533a\u95f4\u7684\u6700\u53f3\u7aef \nfor (let j = 0; j &lt; i; j++) {\nif (nums[j] &gt; nums[j + 1]) {\n// \u4ea4\u6362 nums[j] \u4e0e nums[j + 1]\nlet tmp = nums[j];\nnums[j] = nums[j + 1];\nnums[j + 1] = tmp;\ncount += 3; // \u5143\u7d20\u4ea4\u6362\u5305\u542b 3 \u4e2a\u5355\u5143\u64cd\u4f5c\n}\n}\n}\nreturn count;\n}\n</code></pre> time_complexity.c<pre><code>/* \u5e73\u65b9\u9636\uff08\u5192\u6ce1\u6392\u5e8f\uff09 */\nint bubbleSort(int *nums, int n) {\nint count = 0; // \u8ba1\u6570\u5668\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [0, i]\nfor (int i = n - 1; i &gt; 0; i--) {\n// \u5185\u5faa\u73af\uff1a\u5c06\u672a\u6392\u5e8f\u533a\u95f4 [0, i] \u4e2d\u7684\u6700\u5927\u5143\u7d20\u4ea4\u6362\u81f3\u8be5\u533a\u95f4\u7684\u6700\u53f3\u7aef \nfor (int j = 0; j &lt; i; j++) {\nif (nums[j] &gt; nums[j + 1]) {\n// \u4ea4\u6362 nums[j] \u4e0e nums[j + 1]\nint tmp = nums[j];\nnums[j] = nums[j + 1];\nnums[j + 1] = tmp;\ncount += 3; // \u5143\u7d20\u4ea4\u6362\u5305\u542b 3 \u4e2a\u5355\u5143\u64cd\u4f5c\n}\n}\n}\nreturn count;\n}\n</code></pre> time_complexity.cs<pre><code>/* \u5e73\u65b9\u9636\uff08\u5192\u6ce1\u6392\u5e8f\uff09 */\nint bubbleSort(int[] nums) {\nint count = 0;  // \u8ba1\u6570\u5668\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [0, i]\nfor (int i = nums.Length - 1; i &gt; 0; i--) {\n// \u5185\u5faa\u73af\uff1a\u5c06\u672a\u6392\u5e8f\u533a\u95f4 [0, i] \u4e2d\u7684\u6700\u5927\u5143\u7d20\u4ea4\u6362\u81f3\u8be5\u533a\u95f4\u7684\u6700\u53f3\u7aef \nfor (int j = 0; j &lt; i; j++) {\nif (nums[j] &gt; nums[j + 1]) {\n// \u4ea4\u6362 nums[j] \u4e0e nums[j + 1]\nint tmp = nums[j];\nnums[j] = nums[j + 1];\nnums[j + 1] = tmp;\ncount += 3;  // \u5143\u7d20\u4ea4\u6362\u5305\u542b 3 \u4e2a\u5355\u5143\u64cd\u4f5c\n}\n}\n}\nreturn count;\n}\n</code></pre> time_complexity.swift<pre><code>/* \u5e73\u65b9\u9636\uff08\u5192\u6ce1\u6392\u5e8f\uff09 */\nfunc bubbleSort(nums: inout [Int]) -&gt; Int {\nvar count = 0 // \u8ba1\u6570\u5668\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [0, i]\nfor i in stride(from: nums.count - 1, to: 0, by: -1) {\n// \u5185\u5faa\u73af\uff1a\u5c06\u672a\u6392\u5e8f\u533a\u95f4 [0, i] \u4e2d\u7684\u6700\u5927\u5143\u7d20\u4ea4\u6362\u81f3\u8be5\u533a\u95f4\u7684\u6700\u53f3\u7aef \nfor j in 0 ..&lt; i {\nif nums[j] &gt; nums[j + 1] {\n// \u4ea4\u6362 nums[j] \u4e0e nums[j + 1]\nlet tmp = nums[j]\nnums[j] = nums[j + 1]\nnums[j + 1] = tmp\ncount += 3 // \u5143\u7d20\u4ea4\u6362\u5305\u542b 3 \u4e2a\u5355\u5143\u64cd\u4f5c\n}\n}\n}\nreturn count\n}\n</code></pre> time_complexity.zig<pre><code>// \u5e73\u65b9\u9636\uff08\u5192\u6ce1\u6392\u5e8f\uff09\nfn bubbleSort(nums: []i32) i32 {\nvar count: i32 = 0;  // \u8ba1\u6570\u5668 \n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [0, i]\nvar i: i32 = @intCast(i32, nums.len ) - 1;\nwhile (i &gt; 0) : (i -= 1) {\nvar j: usize = 0;\n// \u5185\u5faa\u73af\uff1a\u5c06\u672a\u6392\u5e8f\u533a\u95f4 [0, i] \u4e2d\u7684\u6700\u5927\u5143\u7d20\u4ea4\u6362\u81f3\u8be5\u533a\u95f4\u7684\u6700\u53f3\u7aef \nwhile (j &lt; i) : (j += 1) {\nif (nums[j] &gt; nums[j + 1]) {\n// \u4ea4\u6362 nums[j] \u4e0e nums[j + 1]\nvar tmp = nums[j];\nnums[j] = nums[j + 1];\nnums[j + 1] = tmp;\ncount += 3;  // \u5143\u7d20\u4ea4\u6362\u5305\u542b 3 \u4e2a\u5355\u5143\u64cd\u4f5c\n}\n}\n}\nreturn count;\n}\n</code></pre> time_complexity.dart<pre><code>/* \u5e73\u65b9\u9636\uff08\u5192\u6ce1\u6392\u5e8f\uff09 */\nint bubbleSort(List&lt;int&gt; nums) {\nint count = 0; // \u8ba1\u6570\u5668\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [0, i]\nfor (var i = nums.length - 1; i &gt; 0; i--) {\n// \u5185\u5faa\u73af\uff1a\u5c06\u672a\u6392\u5e8f\u533a\u95f4 [0, i] \u4e2d\u7684\u6700\u5927\u5143\u7d20\u4ea4\u6362\u81f3\u8be5\u533a\u95f4\u7684\u6700\u53f3\u7aef\nfor (var j = 0; j &lt; i; j++) {\nif (nums[j] &gt; nums[j + 1]) {\n// \u4ea4\u6362 nums[j] \u4e0e nums[j + 1]\nint tmp = nums[j];\nnums[j] = nums[j + 1];\nnums[j + 1] = tmp;\ncount += 3; // \u5143\u7d20\u4ea4\u6362\u5305\u542b 3 \u4e2a\u5355\u5143\u64cd\u4f5c\n}\n}\n}\nreturn count;\n}\n</code></pre>"},{"location":"chapter_computational_complexity/time_complexity/#o2n","title":"\u6307\u6570\u9636 \\(O(2^n)\\)","text":"<p>Note</p> <p>\u751f\u7269\u5b66\u7684\u201c\u7ec6\u80de\u5206\u88c2\u201d\u662f\u6307\u6570\u9636\u589e\u957f\u7684\u5178\u578b\u4f8b\u5b50\uff1a\u521d\u59cb\u72b6\u6001\u4e3a \\(1\\) \u4e2a\u7ec6\u80de\uff0c\u5206\u88c2\u4e00\u8f6e\u540e\u53d8\u4e3a \\(2\\) \u4e2a\uff0c\u5206\u88c2\u4e24\u8f6e\u540e\u53d8\u4e3a \\(4\\) \u4e2a\uff0c\u4ee5\u6b64\u7c7b\u63a8\uff0c\u5206\u88c2 \\(n\\) \u8f6e\u540e\u6709 \\(2^n\\) \u4e2a\u7ec6\u80de\u3002</p> <p>\u6307\u6570\u9636\u589e\u957f\u975e\u5e38\u8fc5\u901f\uff0c\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\u901a\u5e38\u662f\u4e0d\u53ef\u63a5\u53d7\u7684\u3002\u82e5\u4e00\u4e2a\u95ee\u9898\u4f7f\u7528\u300c\u66b4\u529b\u679a\u4e3e\u300d\u6c42\u89e3\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(2^n)\\) \uff0c\u90a3\u4e48\u901a\u5e38\u9700\u8981\u4f7f\u7528\u300c\u52a8\u6001\u89c4\u5212\u300d\u6216\u300c\u8d2a\u5fc3\u7b97\u6cd5\u300d\u7b49\u65b9\u6cd5\u6765\u89e3\u51b3\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart time_complexity.java<pre><code>/* \u6307\u6570\u9636\uff08\u5faa\u73af\u5b9e\u73b0\uff09 */\nint exponential(int n) {\nint count = 0, base = 1;\n// cell \u6bcf\u8f6e\u4e00\u5206\u4e3a\u4e8c\uff0c\u5f62\u6210\u6570\u5217 1, 2, 4, 8, ..., 2^(n-1)\nfor (int i = 0; i &lt; n; i++) {\nfor (int j = 0; j &lt; base; j++) {\ncount++;\n}\nbase *= 2;\n}\n// count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\nreturn count;\n}\n</code></pre> time_complexity.cpp<pre><code>/* \u6307\u6570\u9636\uff08\u5faa\u73af\u5b9e\u73b0\uff09 */\nint exponential(int n) {\nint count = 0, base = 1;\n// cell \u6bcf\u8f6e\u4e00\u5206\u4e3a\u4e8c\uff0c\u5f62\u6210\u6570\u5217 1, 2, 4, 8, ..., 2^(n-1)\nfor (int i = 0; i &lt; n; i++) {\nfor (int j = 0; j &lt; base; j++) {\ncount++;\n}\nbase *= 2;\n}\n// count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\nreturn count;\n}\n</code></pre> time_complexity.py<pre><code>def exponential(n: int) -&gt; int:\n\"\"\"\u6307\u6570\u9636\uff08\u5faa\u73af\u5b9e\u73b0\uff09\"\"\"\ncount = 0\nbase = 1\n# cell \u6bcf\u8f6e\u4e00\u5206\u4e3a\u4e8c\uff0c\u5f62\u6210\u6570\u5217 1, 2, 4, 8, ..., 2^(n-1)\nfor _ in range(n):\nfor _ in range(base):\ncount += 1\nbase *= 2\n# count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\nreturn count\n</code></pre> time_complexity.go<pre><code>/* \u6307\u6570\u9636\uff08\u5faa\u73af\u5b9e\u73b0\uff09*/\nfunc exponential(n int) int {\ncount, base := 0, 1\n// cell \u6bcf\u8f6e\u4e00\u5206\u4e3a\u4e8c\uff0c\u5f62\u6210\u6570\u5217 1, 2, 4, 8, ..., 2^(n-1)\nfor i := 0; i &lt; n; i++ {\nfor j := 0; j &lt; base; j++ {\ncount++\n}\nbase *= 2\n}\n// count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\nreturn count\n}\n</code></pre> time_complexity.js<pre><code>/* \u6307\u6570\u9636\uff08\u5faa\u73af\u5b9e\u73b0\uff09 */\nfunction exponential(n) {\nlet count = 0,\nbase = 1;\n// cell \u6bcf\u8f6e\u4e00\u5206\u4e3a\u4e8c\uff0c\u5f62\u6210\u6570\u5217 1, 2, 4, 8, ..., 2^(n-1)\nfor (let i = 0; i &lt; n; i++) {\nfor (let j = 0; j &lt; base; j++) {\ncount++;\n}\nbase *= 2;\n}\n// count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\nreturn count;\n}\n</code></pre> time_complexity.ts<pre><code>/* \u6307\u6570\u9636\uff08\u5faa\u73af\u5b9e\u73b0\uff09 */\nfunction exponential(n: number): number {\nlet count = 0,\nbase = 1;\n// cell \u6bcf\u8f6e\u4e00\u5206\u4e3a\u4e8c\uff0c\u5f62\u6210\u6570\u5217 1, 2, 4, 8, ..., 2^(n-1)\nfor (let i = 0; i &lt; n; i++) {\nfor (let j = 0; j &lt; base; j++) {\ncount++;\n}\nbase *= 2;\n}\n// count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\nreturn count;\n}\n</code></pre> time_complexity.c<pre><code>/* \u6307\u6570\u9636\uff08\u5faa\u73af\u5b9e\u73b0\uff09 */\nint exponential(int n) {\nint count = 0;\nint bas = 1;\n// cell \u6bcf\u8f6e\u4e00\u5206\u4e3a\u4e8c\uff0c\u5f62\u6210\u6570\u5217 1, 2, 4, 8, ..., 2^(n-1)\nfor (int i = 0; i &lt; n; i++) {\nfor (int j = 0; j &lt; bas; j++) {\ncount++;\n}\nbas *= 2;\n}\n// count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\nreturn count;\n}\n</code></pre> time_complexity.cs<pre><code>/* \u6307\u6570\u9636\uff08\u5faa\u73af\u5b9e\u73b0\uff09 */\nint exponential(int n) {\nint count = 0, bas = 1;\n// cell \u6bcf\u8f6e\u4e00\u5206\u4e3a\u4e8c\uff0c\u5f62\u6210\u6570\u5217 1, 2, 4, 8, ..., 2^(n-1)\nfor (int i = 0; i &lt; n; i++) {\nfor (int j = 0; j &lt; bas; j++) {\ncount++;\n}\nbas *= 2;\n}\n// count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\nreturn count;\n}\n</code></pre> time_complexity.swift<pre><code>/* \u6307\u6570\u9636\uff08\u5faa\u73af\u5b9e\u73b0\uff09 */\nfunc exponential(n: Int) -&gt; Int {\nvar count = 0\nvar base = 1\n// cell \u6bcf\u8f6e\u4e00\u5206\u4e3a\u4e8c\uff0c\u5f62\u6210\u6570\u5217 1, 2, 4, 8, ..., 2^(n-1)\nfor _ in 0 ..&lt; n {\nfor _ in 0 ..&lt; base {\ncount += 1\n}\nbase *= 2\n}\n// count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\nreturn count\n}\n</code></pre> time_complexity.zig<pre><code>// \u6307\u6570\u9636\uff08\u5faa\u73af\u5b9e\u73b0\uff09\nfn exponential(n: i32) i32 {\nvar count: i32 = 0;\nvar bas: i32 = 1;\nvar i: i32 = 0;\n// cell \u6bcf\u8f6e\u4e00\u5206\u4e3a\u4e8c\uff0c\u5f62\u6210\u6570\u5217 1, 2, 4, 8, ..., 2^(n-1)\nwhile (i &lt; n) : (i += 1) {\nvar j: i32 = 0;\nwhile (j &lt; bas) : (j += 1) {\ncount += 1;\n}\nbas *= 2;\n}\n// count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\nreturn count;\n}\n</code></pre> time_complexity.dart<pre><code>/* \u6307\u6570\u9636\uff08\u5faa\u73af\u5b9e\u73b0\uff09 */\nint exponential(int n) {\nint count = 0, base = 1;\n// cell \u6bcf\u8f6e\u4e00\u5206\u4e3a\u4e8c\uff0c\u5f62\u6210\u6570\u5217 1, 2, 4, 8, ..., 2^(n-1)\nfor (var i = 0; i &lt; n; i++) {\nfor (var j = 0; j &lt; base; j++) {\ncount++;\n}\nbase *= 2;\n}\n// count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\nreturn count;\n}\n</code></pre> <p></p> <p> Fig. \u6307\u6570\u9636\u7684\u65f6\u95f4\u590d\u6742\u5ea6 </p> <p>\u5728\u5b9e\u9645\u7b97\u6cd5\u4e2d\uff0c\u6307\u6570\u9636\u5e38\u51fa\u73b0\u4e8e\u9012\u5f52\u51fd\u6570\u3002\u4f8b\u5982\u4ee5\u4e0b\u4ee3\u7801\uff0c\u4e0d\u65ad\u5730\u4e00\u5206\u4e3a\u4e8c\uff0c\u7ecf\u8fc7 \\(n\\) \u6b21\u5206\u88c2\u540e\u505c\u6b62\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart time_complexity.java<pre><code>/* \u6307\u6570\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nint expRecur(int n) {\nif (n == 1)\nreturn 1;\nreturn expRecur(n - 1) + expRecur(n - 1) + 1;\n}\n</code></pre> time_complexity.cpp<pre><code>/* \u6307\u6570\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nint expRecur(int n) {\nif (n == 1)\nreturn 1;\nreturn expRecur(n - 1) + expRecur(n - 1) + 1;\n}\n</code></pre> time_complexity.py<pre><code>def exp_recur(n: int) -&gt; int:\n\"\"\"\u6307\u6570\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09\"\"\"\nif n == 1:\nreturn 1\nreturn exp_recur(n - 1) + exp_recur(n - 1) + 1\n</code></pre> time_complexity.go<pre><code>/* \u6307\u6570\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09*/\nfunc expRecur(n int) int {\nif n == 1 {\nreturn 1\n}\nreturn expRecur(n-1) + expRecur(n-1) + 1\n}\n</code></pre> time_complexity.js<pre><code>/* \u6307\u6570\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nfunction expRecur(n) {\nif (n == 1) return 1;\nreturn expRecur(n - 1) + expRecur(n - 1) + 1;\n}\n</code></pre> time_complexity.ts<pre><code>/* \u6307\u6570\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nfunction expRecur(n: number): number {\nif (n == 1) return 1;\nreturn expRecur(n - 1) + expRecur(n - 1) + 1;\n}\n</code></pre> time_complexity.c<pre><code>/* \u6307\u6570\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nint expRecur(int n) {\nif (n == 1)\nreturn 1;\nreturn expRecur(n - 1) + expRecur(n - 1) + 1;\n}\n</code></pre> time_complexity.cs<pre><code>/* \u6307\u6570\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nint expRecur(int n) {\nif (n == 1) return 1;\nreturn expRecur(n - 1) + expRecur(n - 1) + 1;\n}\n</code></pre> time_complexity.swift<pre><code>/* \u6307\u6570\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nfunc expRecur(n: Int) -&gt; Int {\nif n == 1 {\nreturn 1\n}\nreturn expRecur(n: n - 1) + expRecur(n: n - 1) + 1\n}\n</code></pre> time_complexity.zig<pre><code>// \u6307\u6570\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09\nfn expRecur(n: i32) i32 {\nif (n == 1) return 1;\nreturn expRecur(n - 1) + expRecur(n - 1) + 1;\n}\n</code></pre> time_complexity.dart<pre><code>/* \u6307\u6570\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nint expRecur(int n) {\nif (n == 1) return 1;\nreturn expRecur(n - 1) + expRecur(n - 1) + 1;\n}\n</code></pre>"},{"location":"chapter_computational_complexity/time_complexity/#olog-n","title":"\u5bf9\u6570\u9636 \\(O(\\log n)\\)","text":"<p>\u4e0e\u6307\u6570\u9636\u76f8\u53cd\uff0c\u5bf9\u6570\u9636\u53cd\u6620\u4e86\u201c\u6bcf\u8f6e\u7f29\u51cf\u5230\u4e00\u534a\u7684\u60c5\u51b5\u201d\u3002\u5bf9\u6570\u9636\u4ec5\u6b21\u4e8e\u5e38\u6570\u9636\uff0c\u65f6\u95f4\u589e\u957f\u7f13\u6162\uff0c\u662f\u7406\u60f3\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u3002</p> <p>\u5bf9\u6570\u9636\u5e38\u51fa\u73b0\u4e8e\u300c\u4e8c\u5206\u67e5\u627e\u300d\u548c\u300c\u5206\u6cbb\u7b97\u6cd5\u300d\u4e2d\uff0c\u4f53\u73b0\u4e86\u201c\u4e00\u5206\u4e3a\u591a\u201d\u548c\u201c\u5316\u7e41\u4e3a\u7b80\u201d\u7684\u7b97\u6cd5\u601d\u60f3\u3002</p> <p>\u8bbe\u8f93\u5165\u6570\u636e\u5927\u5c0f\u4e3a \\(n\\) \uff0c\u7531\u4e8e\u6bcf\u8f6e\u7f29\u51cf\u5230\u4e00\u534a\uff0c\u56e0\u6b64\u5faa\u73af\u6b21\u6570\u662f \\(\\log_2 n\\) \uff0c\u5373 \\(2^n\\) \u7684\u53cd\u51fd\u6570\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart time_complexity.java<pre><code>/* \u5bf9\u6570\u9636\uff08\u5faa\u73af\u5b9e\u73b0\uff09 */\nint logarithmic(float n) {\nint count = 0;\nwhile (n &gt; 1) {\nn = n / 2;\ncount++;\n}\nreturn count;\n}\n</code></pre> time_complexity.cpp<pre><code>/* \u5bf9\u6570\u9636\uff08\u5faa\u73af\u5b9e\u73b0\uff09 */\nint logarithmic(float n) {\nint count = 0;\nwhile (n &gt; 1) {\nn = n / 2;\ncount++;\n}\nreturn count;\n}\n</code></pre> time_complexity.py<pre><code>def logarithmic(n: float) -&gt; int:\n\"\"\"\u5bf9\u6570\u9636\uff08\u5faa\u73af\u5b9e\u73b0\uff09\"\"\"\ncount = 0\nwhile n &gt; 1:\nn = n / 2\ncount += 1\nreturn count\n</code></pre> time_complexity.go<pre><code>/* \u5bf9\u6570\u9636\uff08\u5faa\u73af\u5b9e\u73b0\uff09*/\nfunc logarithmic(n float64) int {\ncount := 0\nfor n &gt; 1 {\nn = n / 2\ncount++\n}\nreturn count\n}\n</code></pre> time_complexity.js<pre><code>/* \u5bf9\u6570\u9636\uff08\u5faa\u73af\u5b9e\u73b0\uff09 */\nfunction logarithmic(n) {\nlet count = 0;\nwhile (n &gt; 1) {\nn = n / 2;\ncount++;\n}\nreturn count;\n}\n</code></pre> time_complexity.ts<pre><code>/* \u5bf9\u6570\u9636\uff08\u5faa\u73af\u5b9e\u73b0\uff09 */\nfunction logarithmic(n: number): number {\nlet count = 0;\nwhile (n &gt; 1) {\nn = n / 2;\ncount++;\n}\nreturn count;\n}\n</code></pre> time_complexity.c<pre><code>/* \u5bf9\u6570\u9636\uff08\u5faa\u73af\u5b9e\u73b0\uff09 */\nint logarithmic(float n) {\nint count = 0;\nwhile (n &gt; 1) {\nn = n / 2;\ncount++;\n}\nreturn count;\n}\n</code></pre> time_complexity.cs<pre><code>/* \u5bf9\u6570\u9636\uff08\u5faa\u73af\u5b9e\u73b0\uff09 */\nint logarithmic(float n) {\nint count = 0;\nwhile (n &gt; 1) {\nn = n / 2;\ncount++;\n}\nreturn count;\n}\n</code></pre> time_complexity.swift<pre><code>/* \u5bf9\u6570\u9636\uff08\u5faa\u73af\u5b9e\u73b0\uff09 */\nfunc logarithmic(n: Double) -&gt; Int {\nvar count = 0\nvar n = n\nwhile n &gt; 1 {\nn = n / 2\ncount += 1\n}\nreturn count\n}\n</code></pre> time_complexity.zig<pre><code>// \u5bf9\u6570\u9636\uff08\u5faa\u73af\u5b9e\u73b0\uff09\nfn logarithmic(n: f32) i32 {\nvar count: i32 = 0;\nvar n_var = n;\nwhile (n_var &gt; 1)\n{\nn_var = n_var / 2;\ncount +=1;\n}\nreturn count;\n}\n</code></pre> time_complexity.dart<pre><code>/* \u5bf9\u6570\u9636\uff08\u5faa\u73af\u5b9e\u73b0\uff09 */\nint logarithmic(num n) {\nint count = 0;\nwhile (n &gt; 1) {\nn = n / 2;\ncount++;\n}\nreturn count;\n}\n</code></pre> <p></p> <p> Fig. \u5bf9\u6570\u9636\u7684\u65f6\u95f4\u590d\u6742\u5ea6 </p> <p>\u4e0e\u6307\u6570\u9636\u7c7b\u4f3c\uff0c\u5bf9\u6570\u9636\u4e5f\u5e38\u51fa\u73b0\u4e8e\u9012\u5f52\u51fd\u6570\u3002\u4ee5\u4e0b\u4ee3\u7801\u5f62\u6210\u4e86\u4e00\u4e2a\u9ad8\u5ea6\u4e3a \\(\\log_2 n\\) \u7684\u9012\u5f52\u6811\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart time_complexity.java<pre><code>/* \u5bf9\u6570\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nint logRecur(float n) {\nif (n &lt;= 1)\nreturn 0;\nreturn logRecur(n / 2) + 1;\n}\n</code></pre> time_complexity.cpp<pre><code>/* \u5bf9\u6570\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nint logRecur(float n) {\nif (n &lt;= 1)\nreturn 0;\nreturn logRecur(n / 2) + 1;\n}\n</code></pre> time_complexity.py<pre><code>def log_recur(n: float) -&gt; int:\n\"\"\"\u5bf9\u6570\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09\"\"\"\nif n &lt;= 1:\nreturn 0\nreturn log_recur(n / 2) + 1\n</code></pre> time_complexity.go<pre><code>/* \u5bf9\u6570\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09*/\nfunc logRecur(n float64) int {\nif n &lt;= 1 {\nreturn 0\n}\nreturn logRecur(n/2) + 1\n}\n</code></pre> time_complexity.js<pre><code>/* \u5bf9\u6570\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nfunction logRecur(n) {\nif (n &lt;= 1) return 0;\nreturn logRecur(n / 2) + 1;\n}\n</code></pre> time_complexity.ts<pre><code>/* \u5bf9\u6570\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nfunction logRecur(n: number): number {\nif (n &lt;= 1) return 0;\nreturn logRecur(n / 2) + 1;\n}\n</code></pre> time_complexity.c<pre><code>/* \u5bf9\u6570\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nint logRecur(float n) {\nif (n &lt;= 1)\nreturn 0;\nreturn logRecur(n / 2) + 1;\n}\n</code></pre> time_complexity.cs<pre><code>/* \u5bf9\u6570\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nint logRecur(float n) {\nif (n &lt;= 1) return 0;\nreturn logRecur(n / 2) + 1;\n}\n</code></pre> time_complexity.swift<pre><code>/* \u5bf9\u6570\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nfunc logRecur(n: Double) -&gt; Int {\nif n &lt;= 1 {\nreturn 0\n}\nreturn logRecur(n: n / 2) + 1\n}\n</code></pre> time_complexity.zig<pre><code>// \u5bf9\u6570\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09\nfn logRecur(n: f32) i32 {\nif (n &lt;= 1) return 0;\nreturn logRecur(n / 2) + 1;\n}\n</code></pre> time_complexity.dart<pre><code>/* \u5bf9\u6570\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nint logRecur(num n) {\nif (n &lt;= 1) return 0;\nreturn logRecur(n / 2) + 1;\n}\n</code></pre>"},{"location":"chapter_computational_complexity/time_complexity/#on-log-n","title":"\u7ebf\u6027\u5bf9\u6570\u9636 \\(O(n \\log n)\\)","text":"<p>\u7ebf\u6027\u5bf9\u6570\u9636\u5e38\u51fa\u73b0\u4e8e\u5d4c\u5957\u5faa\u73af\u4e2d\uff0c\u4e24\u5c42\u5faa\u73af\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u5206\u522b\u4e3a \\(O(\\log n)\\) \u548c \\(O(n)\\) \u3002</p> <p>\u4e3b\u6d41\u6392\u5e8f\u7b97\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u901a\u5e38\u4e3a \\(O(n \\log n)\\) \uff0c\u4f8b\u5982\u5feb\u901f\u6392\u5e8f\u3001\u5f52\u5e76\u6392\u5e8f\u3001\u5806\u6392\u5e8f\u7b49\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart time_complexity.java<pre><code>/* \u7ebf\u6027\u5bf9\u6570\u9636 */\nint linearLogRecur(float n) {\nif (n &lt;= 1)\nreturn 1;\nint count = linearLogRecur(n / 2) +\nlinearLogRecur(n / 2);\nfor (int i = 0; i &lt; n; i++) {\ncount++;\n}\nreturn count;\n}\n</code></pre> time_complexity.cpp<pre><code>/* \u7ebf\u6027\u5bf9\u6570\u9636 */\nint linearLogRecur(float n) {\nif (n &lt;= 1)\nreturn 1;\nint count = linearLogRecur(n / 2) + linearLogRecur(n / 2);\nfor (int i = 0; i &lt; n; i++) {\ncount++;\n}\nreturn count;\n}\n</code></pre> time_complexity.py<pre><code>def linear_log_recur(n: float) -&gt; int:\n\"\"\"\u7ebf\u6027\u5bf9\u6570\u9636\"\"\"\nif n &lt;= 1:\nreturn 1\ncount: int = linear_log_recur(n // 2) + linear_log_recur(n // 2)\nfor _ in range(n):\ncount += 1\nreturn count\n</code></pre> time_complexity.go<pre><code>/* \u7ebf\u6027\u5bf9\u6570\u9636 */\nfunc linearLogRecur(n float64) int {\nif n &lt;= 1 {\nreturn 1\n}\ncount := linearLogRecur(n/2) +\nlinearLogRecur(n/2)\nfor i := 0.0; i &lt; n; i++ {\ncount++\n}\nreturn count\n}\n</code></pre> time_complexity.js<pre><code>/* \u7ebf\u6027\u5bf9\u6570\u9636 */\nfunction linearLogRecur(n) {\nif (n &lt;= 1) return 1;\nlet count = linearLogRecur(n / 2) + linearLogRecur(n / 2);\nfor (let i = 0; i &lt; n; i++) {\ncount++;\n}\nreturn count;\n}\n</code></pre> time_complexity.ts<pre><code>/* \u7ebf\u6027\u5bf9\u6570\u9636 */\nfunction linearLogRecur(n: number): number {\nif (n &lt;= 1) return 1;\nlet count = linearLogRecur(n / 2) + linearLogRecur(n / 2);\nfor (let i = 0; i &lt; n; i++) {\ncount++;\n}\nreturn count;\n}\n</code></pre> time_complexity.c<pre><code>/* \u7ebf\u6027\u5bf9\u6570\u9636 */\nint linearLogRecur(float n) {\nif (n &lt;= 1)\nreturn 1;\nint count = linearLogRecur(n / 2) + linearLogRecur(n / 2);\nfor (int i = 0; i &lt; n; i++) {\ncount++;\n}\nreturn count;\n}\n</code></pre> time_complexity.cs<pre><code>/* \u7ebf\u6027\u5bf9\u6570\u9636 */\nint linearLogRecur(float n) {\nif (n &lt;= 1) return 1;\nint count = linearLogRecur(n / 2) +\nlinearLogRecur(n / 2);\nfor (int i = 0; i &lt; n; i++) {\ncount++;\n}\nreturn count;\n}\n</code></pre> time_complexity.swift<pre><code>/* \u7ebf\u6027\u5bf9\u6570\u9636 */\nfunc linearLogRecur(n: Double) -&gt; Int {\nif n &lt;= 1 {\nreturn 1\n}\nvar count = linearLogRecur(n: n / 2) + linearLogRecur(n: n / 2)\nfor _ in stride(from: 0, to: n, by: 1) {\ncount += 1\n}\nreturn count\n}\n</code></pre> time_complexity.zig<pre><code>// \u7ebf\u6027\u5bf9\u6570\u9636\nfn linearLogRecur(n: f32) i32 {\nif (n &lt;= 1) return 1;\nvar count: i32 = linearLogRecur(n / 2) +\nlinearLogRecur(n / 2);\nvar i: f32 = 0;\nwhile (i &lt; n) : (i += 1) {\ncount += 1;\n}\nreturn count;\n}\n</code></pre> time_complexity.dart<pre><code>/* \u7ebf\u6027\u5bf9\u6570\u9636 */\nint linearLogRecur(num n) {\nif (n &lt;= 1) return 1;\nint count = linearLogRecur(n / 2) + linearLogRecur(n / 2);\nfor (var i = 0; i &lt; n; i++) {\ncount++;\n}\nreturn count;\n}\n</code></pre> <p></p> <p> Fig. \u7ebf\u6027\u5bf9\u6570\u9636\u7684\u65f6\u95f4\u590d\u6742\u5ea6 </p>"},{"location":"chapter_computational_complexity/time_complexity/#on_1","title":"\u9636\u4e58\u9636 \\(O(n!)\\)","text":"<p>\u9636\u4e58\u9636\u5bf9\u5e94\u6570\u5b66\u4e0a\u7684\u300c\u5168\u6392\u5217\u300d\u95ee\u9898\u3002\u7ed9\u5b9a \\(n\\) \u4e2a\u4e92\u4e0d\u91cd\u590d\u7684\u5143\u7d20\uff0c\u6c42\u5176\u6240\u6709\u53ef\u80fd\u7684\u6392\u5217\u65b9\u6848\uff0c\u65b9\u6848\u6570\u91cf\u4e3a\uff1a</p> \\[ n! = n \\times (n - 1) \\times (n - 2) \\times \\cdots \\times 2 \\times 1 \\] <p>\u9636\u4e58\u901a\u5e38\u4f7f\u7528\u9012\u5f52\u5b9e\u73b0\u3002\u4f8b\u5982\u4ee5\u4e0b\u4ee3\u7801\uff0c\u7b2c\u4e00\u5c42\u5206\u88c2\u51fa \\(n\\) \u4e2a\uff0c\u7b2c\u4e8c\u5c42\u5206\u88c2\u51fa \\(n - 1\\) \u4e2a\uff0c\u4ee5\u6b64\u7c7b\u63a8\uff0c\u76f4\u81f3\u7b2c \\(n\\) \u5c42\u65f6\u7ec8\u6b62\u5206\u88c2\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart time_complexity.java<pre><code>/* \u9636\u4e58\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nint factorialRecur(int n) {\nif (n == 0)\nreturn 1;\nint count = 0;\n// \u4ece 1 \u4e2a\u5206\u88c2\u51fa n \u4e2a\nfor (int i = 0; i &lt; n; i++) {\ncount += factorialRecur(n - 1);\n}\nreturn count;\n}\n</code></pre> time_complexity.cpp<pre><code>/* \u9636\u4e58\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nint factorialRecur(int n) {\nif (n == 0)\nreturn 1;\nint count = 0;\n// \u4ece 1 \u4e2a\u5206\u88c2\u51fa n \u4e2a\nfor (int i = 0; i &lt; n; i++) {\ncount += factorialRecur(n - 1);\n}\nreturn count;\n}\n</code></pre> time_complexity.py<pre><code>def factorial_recur(n: int) -&gt; int:\n\"\"\"\u9636\u4e58\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09\"\"\"\nif n == 0:\nreturn 1\ncount = 0\n# \u4ece 1 \u4e2a\u5206\u88c2\u51fa n \u4e2a\nfor _ in range(n):\ncount += factorial_recur(n - 1)\nreturn count\n</code></pre> time_complexity.go<pre><code>/* \u9636\u4e58\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nfunc factorialRecur(n int) int {\nif n == 0 {\nreturn 1\n}\ncount := 0\n// \u4ece 1 \u4e2a\u5206\u88c2\u51fa n \u4e2a\nfor i := 0; i &lt; n; i++ {\ncount += factorialRecur(n - 1)\n}\nreturn count\n}\n</code></pre> time_complexity.js<pre><code>/* \u9636\u4e58\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nfunction factorialRecur(n) {\nif (n == 0) return 1;\nlet count = 0;\n// \u4ece 1 \u4e2a\u5206\u88c2\u51fa n \u4e2a\nfor (let i = 0; i &lt; n; i++) {\ncount += factorialRecur(n - 1);\n}\nreturn count;\n}\n</code></pre> time_complexity.ts<pre><code>/* \u9636\u4e58\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nfunction factorialRecur(n: number): number {\nif (n == 0) return 1;\nlet count = 0;\n// \u4ece 1 \u4e2a\u5206\u88c2\u51fa n \u4e2a\nfor (let i = 0; i &lt; n; i++) {\ncount += factorialRecur(n - 1);\n}\nreturn count;\n}\n</code></pre> time_complexity.c<pre><code>/* \u9636\u4e58\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nint factorialRecur(int n) {\nif (n == 0)\nreturn 1;\nint count = 0;\nfor (int i = 0; i &lt; n; i++) {\ncount += factorialRecur(n - 1);\n}\nreturn count;\n}\n</code></pre> time_complexity.cs<pre><code>/* \u9636\u4e58\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nint factorialRecur(int n) {\nif (n == 0) return 1;\nint count = 0;\n// \u4ece 1 \u4e2a\u5206\u88c2\u51fa n \u4e2a\nfor (int i = 0; i &lt; n; i++) {\ncount += factorialRecur(n - 1);\n}\nreturn count;\n}\n</code></pre> time_complexity.swift<pre><code>/* \u9636\u4e58\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nfunc factorialRecur(n: Int) -&gt; Int {\nif n == 0 {\nreturn 1\n}\nvar count = 0\n// \u4ece 1 \u4e2a\u5206\u88c2\u51fa n \u4e2a\nfor _ in 0 ..&lt; n {\ncount += factorialRecur(n: n - 1)\n}\nreturn count\n}\n</code></pre> time_complexity.zig<pre><code>// \u9636\u4e58\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09\nfn factorialRecur(n: i32) i32 {\nif (n == 0) return 1;\nvar count: i32 = 0;\nvar i: i32 = 0;\n// \u4ece 1 \u4e2a\u5206\u88c2\u51fa n \u4e2a\nwhile (i &lt; n) : (i += 1) {\ncount += factorialRecur(n - 1);\n}\nreturn count;\n}\n</code></pre> time_complexity.dart<pre><code>/* \u9636\u4e58\u9636\uff08\u9012\u5f52\u5b9e\u73b0\uff09 */\nint factorialRecur(int n) {\nif (n == 0) return 1;\nint count = 0;\n// \u4ece 1 \u4e2a\u5206\u88c2\u51fa n \u4e2a\nfor (var i = 0; i &lt; n; i++) {\ncount += factorialRecur(n - 1);\n}\nreturn count;\n}\n</code></pre> <p></p> <p> Fig. \u9636\u4e58\u9636\u7684\u65f6\u95f4\u590d\u6742\u5ea6 </p>"},{"location":"chapter_computational_complexity/time_complexity/#226","title":"2.2.6. \u00a0 \u6700\u5dee\u3001\u6700\u4f73\u3001\u5e73\u5747\u65f6\u95f4\u590d\u6742\u5ea6","text":"<p>\u67d0\u4e9b\u7b97\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e0d\u662f\u56fa\u5b9a\u7684\uff0c\u800c\u662f\u4e0e\u8f93\u5165\u6570\u636e\u7684\u5206\u5e03\u6709\u5173\u3002\u4f8b\u5982\uff0c\u5047\u8bbe\u8f93\u5165\u4e00\u4e2a\u957f\u5ea6\u4e3a \\(n\\) \u7684\u6570\u7ec4 <code>nums</code> \uff0c\u5176\u4e2d <code>nums</code> \u7531\u4ece \\(1\\) \u81f3 \\(n\\) \u7684\u6570\u5b57\u7ec4\u6210\uff0c\u4f46\u5143\u7d20\u987a\u5e8f\u662f\u968f\u673a\u6253\u4e71\u7684\uff1b\u7b97\u6cd5\u7684\u4efb\u52a1\u662f\u8fd4\u56de\u5143\u7d20 \\(1\\) \u7684\u7d22\u5f15\u3002\u6211\u4eec\u53ef\u4ee5\u5f97\u51fa\u4ee5\u4e0b\u7ed3\u8bba\uff1a</p> <ul> <li>\u5f53 <code>nums = [?, ?, ..., 1]</code> \uff0c\u5373\u5f53\u672b\u5c3e\u5143\u7d20\u662f \\(1\\) \u65f6\uff0c\u9700\u8981\u5b8c\u6574\u904d\u5386\u6570\u7ec4\uff0c\u6b64\u65f6\u8fbe\u5230 \u6700\u5dee\u65f6\u95f4\u590d\u6742\u5ea6 \\(O(n)\\)\uff1b</li> <li>\u5f53 <code>nums = [1, ?, ?, ...]</code> \uff0c\u5373\u5f53\u9996\u4e2a\u6570\u5b57\u4e3a \\(1\\) \u65f6\uff0c\u65e0\u8bba\u6570\u7ec4\u591a\u957f\u90fd\u4e0d\u9700\u8981\u7ee7\u7eed\u904d\u5386\uff0c\u6b64\u65f6\u8fbe\u5230 \u6700\u4f73\u65f6\u95f4\u590d\u6742\u5ea6 \\(\\Omega(1)\\)\uff1b</li> </ul> <p>\u201c\u51fd\u6570\u6e10\u8fd1\u4e0a\u754c\u201d\u4f7f\u7528\u5927 \\(O\\) \u8bb0\u53f7\u8868\u793a\uff0c\u4ee3\u8868\u300c\u6700\u5dee\u65f6\u95f4\u590d\u6742\u5ea6\u300d\u3002\u76f8\u5e94\u5730\uff0c\u201c\u51fd\u6570\u6e10\u8fd1\u4e0b\u754c\u201d\u7528 \\(\\Omega\\) \u8bb0\u53f7\u6765\u8868\u793a\uff0c\u4ee3\u8868\u300c\u6700\u4f73\u65f6\u95f4\u590d\u6742\u5ea6\u300d\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart worst_best_time_complexity.java<pre><code>/* \u751f\u6210\u4e00\u4e2a\u6570\u7ec4\uff0c\u5143\u7d20\u4e3a { 1, 2, ..., n }\uff0c\u987a\u5e8f\u88ab\u6253\u4e71 */\nint[] randomNumbers(int n) {\nInteger[] nums = new Integer[n];\n// \u751f\u6210\u6570\u7ec4 nums = { 1, 2, 3, ..., n }\nfor (int i = 0; i &lt; n; i++) {\nnums[i] = i + 1;\n}\n// \u968f\u673a\u6253\u4e71\u6570\u7ec4\u5143\u7d20\nCollections.shuffle(Arrays.asList(nums));\n// Integer[] -&gt; int[]\nint[] res = new int[n];\nfor (int i = 0; i &lt; n; i++) {\nres[i] = nums[i];\n}\nreturn res;\n}\n/* \u67e5\u627e\u6570\u7ec4 nums \u4e2d\u6570\u5b57 1 \u6240\u5728\u7d22\u5f15 */\nint findOne(int[] nums) {\nfor (int i = 0; i &lt; nums.length; i++) {\n// \u5f53\u5143\u7d20 1 \u5728\u6570\u7ec4\u5934\u90e8\u65f6\uff0c\u8fbe\u5230\u6700\u4f73\u65f6\u95f4\u590d\u6742\u5ea6 O(1)\n// \u5f53\u5143\u7d20 1 \u5728\u6570\u7ec4\u5c3e\u90e8\u65f6\uff0c\u8fbe\u5230\u6700\u5dee\u65f6\u95f4\u590d\u6742\u5ea6 O(n)\nif (nums[i] == 1)\nreturn i;\n}\nreturn -1;\n}\n</code></pre> worst_best_time_complexity.cpp<pre><code>/* \u751f\u6210\u4e00\u4e2a\u6570\u7ec4\uff0c\u5143\u7d20\u4e3a { 1, 2, ..., n }\uff0c\u987a\u5e8f\u88ab\u6253\u4e71 */\nvector&lt;int&gt; randomNumbers(int n) {\nvector&lt;int&gt; nums(n);\n// \u751f\u6210\u6570\u7ec4 nums = { 1, 2, 3, ..., n }\nfor (int i = 0; i &lt; n; i++) {\nnums[i] = i + 1;\n}\n// \u4f7f\u7528\u7cfb\u7edf\u65f6\u95f4\u751f\u6210\u968f\u673a\u79cd\u5b50\nunsigned seed = chrono::system_clock::now().time_since_epoch().count();\n// \u968f\u673a\u6253\u4e71\u6570\u7ec4\u5143\u7d20\nshuffle(nums.begin(), nums.end(), default_random_engine(seed));\nreturn nums;\n}\n/* \u67e5\u627e\u6570\u7ec4 nums \u4e2d\u6570\u5b57 1 \u6240\u5728\u7d22\u5f15 */\nint findOne(vector&lt;int&gt; &amp;nums) {\nfor (int i = 0; i &lt; nums.size(); i++) {\n// \u5f53\u5143\u7d20 1 \u5728\u6570\u7ec4\u5934\u90e8\u65f6\uff0c\u8fbe\u5230\u6700\u4f73\u65f6\u95f4\u590d\u6742\u5ea6 O(1)\n// \u5f53\u5143\u7d20 1 \u5728\u6570\u7ec4\u5c3e\u90e8\u65f6\uff0c\u8fbe\u5230\u6700\u5dee\u65f6\u95f4\u590d\u6742\u5ea6 O(n)\nif (nums[i] == 1)\nreturn i;\n}\nreturn -1;\n}\n</code></pre> worst_best_time_complexity.py<pre><code>def random_numbers(n: int) -&gt; list[int]:\n\"\"\"\u751f\u6210\u4e00\u4e2a\u6570\u7ec4\uff0c\u5143\u7d20\u4e3a: 1, 2, ..., n \uff0c\u987a\u5e8f\u88ab\u6253\u4e71\"\"\"\n# \u751f\u6210\u6570\u7ec4 nums =: 1, 2, 3, ..., n\nnums = [i for i in range(1, n + 1)]\n# \u968f\u673a\u6253\u4e71\u6570\u7ec4\u5143\u7d20\nrandom.shuffle(nums)\nreturn nums\ndef find_one(nums: list[int]) -&gt; int:\n\"\"\"\u67e5\u627e\u6570\u7ec4 nums \u4e2d\u6570\u5b57 1 \u6240\u5728\u7d22\u5f15\"\"\"\nfor i in range(len(nums)):\n# \u5f53\u5143\u7d20 1 \u5728\u6570\u7ec4\u5934\u90e8\u65f6\uff0c\u8fbe\u5230\u6700\u4f73\u65f6\u95f4\u590d\u6742\u5ea6 O(1)\n# \u5f53\u5143\u7d20 1 \u5728\u6570\u7ec4\u5c3e\u90e8\u65f6\uff0c\u8fbe\u5230\u6700\u5dee\u65f6\u95f4\u590d\u6742\u5ea6 O(n)\nif nums[i] == 1:\nreturn i\nreturn -1\n</code></pre> worst_best_time_complexity.go<pre><code>/* \u751f\u6210\u4e00\u4e2a\u6570\u7ec4\uff0c\u5143\u7d20\u4e3a { 1, 2, ..., n }\uff0c\u987a\u5e8f\u88ab\u6253\u4e71 */\nfunc randomNumbers(n int) []int {\nnums := make([]int, n)\n// \u751f\u6210\u6570\u7ec4 nums = { 1, 2, 3, ..., n }\nfor i := 0; i &lt; n; i++ {\nnums[i] = i + 1\n}\n// \u968f\u673a\u6253\u4e71\u6570\u7ec4\u5143\u7d20\nrand.Shuffle(len(nums), func(i, j int) {\nnums[i], nums[j] = nums[j], nums[i]\n})\nreturn nums\n}\n/* \u67e5\u627e\u6570\u7ec4 nums \u4e2d\u6570\u5b57 1 \u6240\u5728\u7d22\u5f15 */\nfunc findOne(nums []int) int {\nfor i := 0; i &lt; len(nums); i++ {\n// \u5f53\u5143\u7d20 1 \u5728\u6570\u7ec4\u5934\u90e8\u65f6\uff0c\u8fbe\u5230\u6700\u4f73\u65f6\u95f4\u590d\u6742\u5ea6 O(1)\n// \u5f53\u5143\u7d20 1 \u5728\u6570\u7ec4\u5c3e\u90e8\u65f6\uff0c\u8fbe\u5230\u6700\u5dee\u65f6\u95f4\u590d\u6742\u5ea6 O(n)\nif nums[i] == 1 {\nreturn i\n}\n}\nreturn -1\n}\n</code></pre> worst_best_time_complexity.js<pre><code>/* \u751f\u6210\u4e00\u4e2a\u6570\u7ec4\uff0c\u5143\u7d20\u4e3a { 1, 2, ..., n }\uff0c\u987a\u5e8f\u88ab\u6253\u4e71 */\nfunction randomNumbers(n) {\nconst nums = Array(n);\n// \u751f\u6210\u6570\u7ec4 nums = { 1, 2, 3, ..., n }\nfor (let i = 0; i &lt; n; i++) {\nnums[i] = i + 1;\n}\n// \u968f\u673a\u6253\u4e71\u6570\u7ec4\u5143\u7d20\nfor (let i = 0; i &lt; n; i++) {\nconst r = Math.floor(Math.random() * (i + 1));\nconst temp = nums[i];\nnums[i] = nums[r];\nnums[r] = temp;\n}\nreturn nums;\n}\n/* \u67e5\u627e\u6570\u7ec4 nums \u4e2d\u6570\u5b57 1 \u6240\u5728\u7d22\u5f15 */\nfunction findOne(nums) {\nfor (let i = 0; i &lt; nums.length; i++) {\n// \u5f53\u5143\u7d20 1 \u5728\u6570\u7ec4\u5934\u90e8\u65f6\uff0c\u8fbe\u5230\u6700\u4f73\u65f6\u95f4\u590d\u6742\u5ea6 O(1)\n// \u5f53\u5143\u7d20 1 \u5728\u6570\u7ec4\u5c3e\u90e8\u65f6\uff0c\u8fbe\u5230\u6700\u5dee\u65f6\u95f4\u590d\u6742\u5ea6 O(n)\nif (nums[i] === 1) {\nreturn i;\n}\n}\nreturn -1;\n}\n</code></pre> worst_best_time_complexity.ts<pre><code>/* \u751f\u6210\u4e00\u4e2a\u6570\u7ec4\uff0c\u5143\u7d20\u4e3a { 1, 2, ..., n }\uff0c\u987a\u5e8f\u88ab\u6253\u4e71 */\nfunction randomNumbers(n: number): number[] {\nconst nums = Array(n);\n// \u751f\u6210\u6570\u7ec4 nums = { 1, 2, 3, ..., n }\nfor (let i = 0; i &lt; n; i++) {\nnums[i] = i + 1;\n}\n// \u968f\u673a\u6253\u4e71\u6570\u7ec4\u5143\u7d20\nfor (let i = 0; i &lt; n; i++) {\nconst r = Math.floor(Math.random() * (i + 1));\nconst temp = nums[i];\nnums[i] = nums[r];\nnums[r] = temp;\n}\nreturn nums;\n}\n/* \u67e5\u627e\u6570\u7ec4 nums \u4e2d\u6570\u5b57 1 \u6240\u5728\u7d22\u5f15 */\nfunction findOne(nums: number[]): number {\nfor (let i = 0; i &lt; nums.length; i++) {\n// \u5f53\u5143\u7d20 1 \u5728\u6570\u7ec4\u5934\u90e8\u65f6\uff0c\u8fbe\u5230\u6700\u4f73\u65f6\u95f4\u590d\u6742\u5ea6 O(1)\n// \u5f53\u5143\u7d20 1 \u5728\u6570\u7ec4\u5c3e\u90e8\u65f6\uff0c\u8fbe\u5230\u6700\u5dee\u65f6\u95f4\u590d\u6742\u5ea6 O(n)\nif (nums[i] === 1) {\nreturn i;\n}\n}\nreturn -1;\n}\n</code></pre> worst_best_time_complexity.c<pre><code>/* \u751f\u6210\u4e00\u4e2a\u6570\u7ec4\uff0c\u5143\u7d20\u4e3a { 1, 2, ..., n }\uff0c\u987a\u5e8f\u88ab\u6253\u4e71 */\nint *randomNumbers(int n) {\n// \u5206\u914d\u5806\u533a\u5185\u5b58\uff08\u521b\u5efa\u4e00\u7ef4\u53ef\u53d8\u957f\u6570\u7ec4\uff1a\u6570\u7ec4\u4e2d\u5143\u7d20\u6570\u91cf\u4e3an\uff0c\u5143\u7d20\u7c7b\u578b\u4e3aint\uff09\nint *nums = (int *)malloc(n * sizeof(int));\n// \u751f\u6210\u6570\u7ec4 nums = { 1, 2, 3, ..., n }\nfor (int i = 0; i &lt; n; i++) {\nnums[i] = i + 1;\n}\n// \u968f\u673a\u6253\u4e71\u6570\u7ec4\u5143\u7d20\nfor (int i = n - 1; i &gt; 0; i--) {\nint j = rand() % (i + 1);\nint temp = nums[i];\nnums[i] = nums[j];\nnums[j] = temp;\n}\nreturn nums;\n}\n/* \u67e5\u627e\u6570\u7ec4 nums \u4e2d\u6570\u5b57 1 \u6240\u5728\u7d22\u5f15 */\nint findOne(int *nums, int n) {\nfor (int i = 0; i &lt; n; i++) {\n// \u5f53\u5143\u7d20 1 \u5728\u6570\u7ec4\u5934\u90e8\u65f6\uff0c\u8fbe\u5230\u6700\u4f73\u65f6\u95f4\u590d\u6742\u5ea6 O(1)\n// \u5f53\u5143\u7d20 1 \u5728\u6570\u7ec4\u5c3e\u90e8\u65f6\uff0c\u8fbe\u5230\u6700\u5dee\u65f6\u95f4\u590d\u6742\u5ea6 O(n)\nif (nums[i] == 1)\nreturn i;\n}\nreturn -1;\n}\n</code></pre> worst_best_time_complexity.cs<pre><code>/* \u751f\u6210\u4e00\u4e2a\u6570\u7ec4\uff0c\u5143\u7d20\u4e3a { 1, 2, ..., n }\uff0c\u987a\u5e8f\u88ab\u6253\u4e71 */\nint[] randomNumbers(int n) {\nint[] nums = new int[n];\n// \u751f\u6210\u6570\u7ec4 nums = { 1, 2, 3, ..., n }\nfor (int i = 0; i &lt; n; i++) {\nnums[i] = i + 1;\n}\n// \u968f\u673a\u6253\u4e71\u6570\u7ec4\u5143\u7d20\nfor (int i = 0; i &lt; nums.Length; i++) {\nvar index = new Random().Next(i, nums.Length);\nvar tmp = nums[i];\nvar ran = nums[index];\nnums[i] = ran;\nnums[index] = tmp;\n}\nreturn nums;\n}\n/* \u67e5\u627e\u6570\u7ec4 nums \u4e2d\u6570\u5b57 1 \u6240\u5728\u7d22\u5f15 */\nint findOne(int[] nums) {\nfor (int i = 0; i &lt; nums.Length; i++) {\n// \u5f53\u5143\u7d20 1 \u5728\u6570\u7ec4\u5934\u90e8\u65f6\uff0c\u8fbe\u5230\u6700\u4f73\u65f6\u95f4\u590d\u6742\u5ea6 O(1)\n// \u5f53\u5143\u7d20 1 \u5728\u6570\u7ec4\u5c3e\u90e8\u65f6\uff0c\u8fbe\u5230\u6700\u5dee\u65f6\u95f4\u590d\u6742\u5ea6 O(n)\nif (nums[i] == 1)\nreturn i;\n}\nreturn -1;\n}\n</code></pre> worst_best_time_complexity.swift<pre><code>/* \u751f\u6210\u4e00\u4e2a\u6570\u7ec4\uff0c\u5143\u7d20\u4e3a { 1, 2, ..., n }\uff0c\u987a\u5e8f\u88ab\u6253\u4e71 */\nfunc randomNumbers(n: Int) -&gt; [Int] {\n// \u751f\u6210\u6570\u7ec4 nums = { 1, 2, 3, ..., n }\nvar nums = Array(1 ... n)\n// \u968f\u673a\u6253\u4e71\u6570\u7ec4\u5143\u7d20\nnums.shuffle()\nreturn nums\n}\n/* \u67e5\u627e\u6570\u7ec4 nums \u4e2d\u6570\u5b57 1 \u6240\u5728\u7d22\u5f15 */\nfunc findOne(nums: [Int]) -&gt; Int {\nfor i in nums.indices {\n// \u5f53\u5143\u7d20 1 \u5728\u6570\u7ec4\u5934\u90e8\u65f6\uff0c\u8fbe\u5230\u6700\u4f73\u65f6\u95f4\u590d\u6742\u5ea6 O(1)\n// \u5f53\u5143\u7d20 1 \u5728\u6570\u7ec4\u5c3e\u90e8\u65f6\uff0c\u8fbe\u5230\u6700\u5dee\u65f6\u95f4\u590d\u6742\u5ea6 O(n)\nif nums[i] == 1 {\nreturn i\n}\n}\nreturn -1\n}\n</code></pre> worst_best_time_complexity.zig<pre><code>// \u751f\u6210\u4e00\u4e2a\u6570\u7ec4\uff0c\u5143\u7d20\u4e3a { 1, 2, ..., n }\uff0c\u987a\u5e8f\u88ab\u6253\u4e71\npub fn randomNumbers(comptime n: usize) [n]i32 {\nvar nums: [n]i32 = undefined;\n// \u751f\u6210\u6570\u7ec4 nums = { 1, 2, 3, ..., n }\nfor (nums) |*num, i| {\nnum.* = @intCast(i32, i) + 1;\n}\n// \u968f\u673a\u6253\u4e71\u6570\u7ec4\u5143\u7d20\nconst rand = std.crypto.random;\nrand.shuffle(i32, &amp;nums);\nreturn nums;\n}\n// \u67e5\u627e\u6570\u7ec4 nums \u4e2d\u6570\u5b57 1 \u6240\u5728\u7d22\u5f15\npub fn findOne(nums: []i32) i32 {\nfor (nums) |num, i| {\n// \u5f53\u5143\u7d20 1 \u5728\u6570\u7ec4\u5934\u90e8\u65f6\uff0c\u8fbe\u5230\u6700\u4f73\u65f6\u95f4\u590d\u6742\u5ea6 O(1)\n// \u5f53\u5143\u7d20 1 \u5728\u6570\u7ec4\u5c3e\u90e8\u65f6\uff0c\u8fbe\u5230\u6700\u5dee\u65f6\u95f4\u590d\u6742\u5ea6 O(n)\nif (num == 1) return @intCast(i32, i);\n}\nreturn -1;\n}\n</code></pre> worst_best_time_complexity.dart<pre><code>/* \u751f\u6210\u4e00\u4e2a\u6570\u7ec4\uff0c\u5143\u7d20\u4e3a { 1, 2, ..., n }\uff0c\u987a\u5e8f\u88ab\u6253\u4e71 */\nList&lt;int&gt; randomNumbers(int n) {\nfinal nums = List.filled(n, 0);\n// \u751f\u6210\u6570\u7ec4 nums = { 1, 2, 3, ..., n }\nfor (var i = 0; i &lt; n; i++) {\nnums[i] = i + 1;\n}\n// \u968f\u673a\u6253\u4e71\u6570\u7ec4\u5143\u7d20\nnums.shuffle();\nreturn nums;\n}\n/* \u67e5\u627e\u6570\u7ec4 nums \u4e2d\u6570\u5b57 1 \u6240\u5728\u7d22\u5f15 */\nint findOne(List&lt;int&gt; nums) {\nfor (var i = 0; i &lt; nums.length; i++) {\n// \u5f53\u5143\u7d20 1 \u5728\u6570\u7ec4\u5934\u90e8\u65f6\uff0c\u8fbe\u5230\u6700\u4f73\u65f6\u95f4\u590d\u6742\u5ea6 O(1)\n// \u5f53\u5143\u7d20 1 \u5728\u6570\u7ec4\u5c3e\u90e8\u65f6\uff0c\u8fbe\u5230\u6700\u5dee\u65f6\u95f4\u590d\u6742\u5ea6 O(n)\nif (nums[i] == 1) return i;\n}\nreturn -1;\n}\n</code></pre> <p>Tip</p> <p>\u5b9e\u9645\u5e94\u7528\u4e2d\u6211\u4eec\u5f88\u5c11\u4f7f\u7528\u300c\u6700\u4f73\u65f6\u95f4\u590d\u6742\u5ea6\u300d\uff0c\u56e0\u4e3a\u901a\u5e38\u53ea\u6709\u5728\u5f88\u5c0f\u6982\u7387\u4e0b\u624d\u80fd\u8fbe\u5230\uff0c\u53ef\u80fd\u4f1a\u5e26\u6765\u4e00\u5b9a\u7684\u8bef\u5bfc\u6027\u3002\u76f8\u53cd\uff0c\u300c\u6700\u5dee\u65f6\u95f4\u590d\u6742\u5ea6\u300d\u66f4\u4e3a\u5b9e\u7528\uff0c\u56e0\u4e3a\u5b83\u7ed9\u51fa\u4e86\u4e00\u4e2a\u201c\u6548\u7387\u5b89\u5168\u503c\u201d\uff0c\u8ba9\u6211\u4eec\u53ef\u4ee5\u653e\u5fc3\u5730\u4f7f\u7528\u7b97\u6cd5\u3002</p> <p>\u4ece\u4e0a\u8ff0\u793a\u4f8b\u53ef\u4ee5\u770b\u51fa\uff0c\u6700\u5dee\u6216\u6700\u4f73\u65f6\u95f4\u590d\u6742\u5ea6\u53ea\u51fa\u73b0\u5728\u201c\u7279\u6b8a\u5206\u5e03\u7684\u6570\u636e\u201d\u4e2d\uff0c\u8fd9\u4e9b\u60c5\u51b5\u7684\u51fa\u73b0\u6982\u7387\u53ef\u80fd\u5f88\u5c0f\uff0c\u56e0\u6b64\u5e76\u4e0d\u80fd\u6700\u771f\u5b9e\u5730\u53cd\u6620\u7b97\u6cd5\u8fd0\u884c\u6548\u7387\u3002\u76f8\u8f83\u4e4b\u4e0b\uff0c\u300c\u5e73\u5747\u65f6\u95f4\u590d\u6742\u5ea6\u300d\u53ef\u4ee5\u4f53\u73b0\u7b97\u6cd5\u5728\u968f\u673a\u8f93\u5165\u6570\u636e\u4e0b\u7684\u8fd0\u884c\u6548\u7387\uff0c\u7528 \\(\\Theta\\) \u8bb0\u53f7\u6765\u8868\u793a\u3002</p> <p>\u5bf9\u4e8e\u90e8\u5206\u7b97\u6cd5\uff0c\u6211\u4eec\u53ef\u4ee5\u7b80\u5355\u5730\u63a8\u7b97\u51fa\u968f\u673a\u6570\u636e\u5206\u5e03\u4e0b\u7684\u5e73\u5747\u60c5\u51b5\u3002\u6bd4\u5982\u4e0a\u8ff0\u793a\u4f8b\uff0c\u7531\u4e8e\u8f93\u5165\u6570\u7ec4\u662f\u88ab\u6253\u4e71\u7684\uff0c\u56e0\u6b64\u5143\u7d20 \\(1\\) \u51fa\u73b0\u5728\u4efb\u610f\u7d22\u5f15\u7684\u6982\u7387\u90fd\u662f\u76f8\u7b49\u7684\uff0c\u90a3\u4e48\u7b97\u6cd5\u7684\u5e73\u5747\u5faa\u73af\u6b21\u6570\u5219\u662f\u6570\u7ec4\u957f\u5ea6\u7684\u4e00\u534a \\(\\frac{n}{2}\\) \uff0c\u5e73\u5747\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(\\Theta(\\frac{n}{2}) = \\Theta(n)\\) \u3002</p> <p>\u4f46\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u5c24\u5176\u662f\u8f83\u4e3a\u590d\u6742\u7684\u7b97\u6cd5\uff0c\u8ba1\u7b97\u5e73\u5747\u65f6\u95f4\u590d\u6742\u5ea6\u6bd4\u8f83\u56f0\u96be\uff0c\u56e0\u4e3a\u5f88\u96be\u7b80\u4fbf\u5730\u5206\u6790\u51fa\u5728\u6570\u636e\u5206\u5e03\u4e0b\u7684\u6574\u4f53\u6570\u5b66\u671f\u671b\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u901a\u5e38\u4f7f\u7528\u6700\u5dee\u65f6\u95f4\u590d\u6742\u5ea6\u4f5c\u4e3a\u7b97\u6cd5\u6548\u7387\u7684\u8bc4\u5224\u6807\u51c6\u3002</p> <p>\u4e3a\u4ec0\u4e48\u5f88\u5c11\u770b\u5230 \\(\\Theta\\) \u7b26\u53f7\uff1f</p> <p>\u53ef\u80fd\u7531\u4e8e \\(O\\) \u7b26\u53f7\u8fc7\u4e8e\u6717\u6717\u4e0a\u53e3\uff0c\u6211\u4eec\u5e38\u5e38\u4f7f\u7528\u5b83\u6765\u8868\u793a\u300c\u5e73\u5747\u590d\u6742\u5ea6\u300d\uff0c\u4f46\u4ece\u4e25\u683c\u610f\u4e49\u4e0a\u770b\uff0c\u8fd9\u79cd\u505a\u6cd5\u5e76\u4e0d\u89c4\u8303\u3002\u5728\u672c\u4e66\u548c\u5176\u4ed6\u8d44\u6599\u4e2d\uff0c\u82e5\u9047\u5230\u7c7b\u4f3c\u201c\u5e73\u5747\u65f6\u95f4\u590d\u6742\u5ea6 \\(O(n)\\)\u201d\u7684\u8868\u8ff0\uff0c\u8bf7\u5c06\u5176\u76f4\u63a5\u7406\u89e3\u4e3a \\(\\Theta(n)\\) \u3002</p>"},{"location":"chapter_data_structure/","title":"3. \u00a0 \u6570\u636e\u7ed3\u6784\u7b80\u4ecb","text":""},{"location":"chapter_data_structure/basic_data_types/","title":"3.2. \u00a0 \u57fa\u672c\u6570\u636e\u7c7b\u578b","text":"<p>\u8c08\u53ca\u8ba1\u7b97\u673a\u4e2d\u7684\u6570\u636e\uff0c\u6211\u4eec\u4f1a\u60f3\u5230\u6587\u672c\u3001\u56fe\u7247\u3001\u89c6\u9891\u3001\u8bed\u97f3\u30013D \u6a21\u578b\u7b49\u5404\u79cd\u5f62\u5f0f\u3002\u5c3d\u7ba1\u8fd9\u4e9b\u6570\u636e\u7684\u7ec4\u7ec7\u5f62\u5f0f\u5404\u5f02\uff0c\u4f46\u5b83\u4eec\u90fd\u7531\u5404\u79cd\u57fa\u672c\u6570\u636e\u7c7b\u578b\u6784\u6210\u3002</p> <p>\u57fa\u672c\u6570\u636e\u7c7b\u578b\u662f CPU \u53ef\u4ee5\u76f4\u63a5\u8fdb\u884c\u8fd0\u7b97\u7684\u7c7b\u578b\uff0c\u5728\u7b97\u6cd5\u4e2d\u76f4\u63a5\u88ab\u4f7f\u7528\u3002\u5b83\u5305\u62ec\uff1a</p> <ul> <li>\u6574\u6570\u7c7b\u578b <code>byte</code> , <code>short</code> , <code>int</code> , <code>long</code> \uff1b</li> <li>\u6d6e\u70b9\u6570\u7c7b\u578b <code>float</code> , <code>double</code> \uff0c\u7528\u4e8e\u8868\u793a\u5c0f\u6570\uff1b</li> <li>\u5b57\u7b26\u7c7b\u578b <code>char</code> \uff0c\u7528\u4e8e\u8868\u793a\u5404\u79cd\u8bed\u8a00\u7684\u5b57\u6bcd\u3001\u6807\u70b9\u7b26\u53f7\u3001\u751a\u81f3\u8868\u60c5\u7b26\u53f7\u7b49\uff1b</li> <li>\u5e03\u5c14\u7c7b\u578b <code>bool</code> \uff0c\u7528\u4e8e\u8868\u793a\u201c\u662f\u201d\u4e0e\u201c\u5426\u201d\u5224\u65ad\uff1b</li> </ul> <p>\u6240\u6709\u57fa\u672c\u6570\u636e\u7c7b\u578b\u90fd\u4ee5\u4e8c\u8fdb\u5236\u7684\u5f62\u5f0f\u5b58\u50a8\u5728\u8ba1\u7b97\u673a\u4e2d\u3002\u5728\u8ba1\u7b97\u673a\u4e2d\uff0c\u6211\u4eec\u5c06 \\(1\\) \u4e2a\u4e8c\u8fdb\u5236\u4f4d\u79f0\u4e3a \\(1\\) \u6bd4\u7279\uff0c\u5e76\u89c4\u5b9a \\(1\\) \u5b57\u8282\uff08byte\uff09\u7531 \\(8\\) \u6bd4\u7279\uff08bits\uff09\u7ec4\u6210\u3002\u57fa\u672c\u6570\u636e\u7c7b\u578b\u7684\u53d6\u503c\u8303\u56f4\u53d6\u51b3\u4e8e\u5176\u5360\u7528\u7684\u7a7a\u95f4\u5927\u5c0f\uff0c\u4f8b\u5982\uff1a</p> <ul> <li>\u6574\u6570\u7c7b\u578b <code>byte</code> \u5360\u7528 \\(1\\) byte = \\(8\\) bits \uff0c\u53ef\u4ee5\u8868\u793a \\(2^{8}\\) \u4e2a\u4e0d\u540c\u7684\u6570\u5b57\uff1b</li> <li>\u6574\u6570\u7c7b\u578b <code>int</code> \u5360\u7528 \\(4\\) bytes = \\(32\\) bits \uff0c\u53ef\u4ee5\u8868\u793a \\(2^{32}\\) \u4e2a\u6570\u5b57\uff1b</li> </ul> <p>\u4e0b\u8868\u5217\u4e3e\u4e86\u5404\u79cd\u57fa\u672c\u6570\u636e\u7c7b\u578b\u7684\u5360\u7528\u7a7a\u95f4\u3001\u53d6\u503c\u8303\u56f4\u548c\u9ed8\u8ba4\u503c\u3002\u6b64\u8868\u683c\u65e0\u9700\u786c\u80cc\uff0c\u5927\u81f4\u7406\u89e3\u5373\u53ef\uff0c\u9700\u8981\u65f6\u53ef\u4ee5\u901a\u8fc7\u67e5\u8868\u6765\u56de\u5fc6\u3002</p> \u7c7b\u578b \u7b26\u53f7 \u5360\u7528\u7a7a\u95f4 \u6700\u5c0f\u503c \u6700\u5927\u503c \u9ed8\u8ba4\u503c \u6574\u6570 <code>byte</code> 1 byte \\(-2^7\\) (\\(-128\\)) \\(2^7 - 1\\) (\\(127\\)) \\(0\\) <code>short</code> 2 bytes \\(-2^{15}\\) \\(2^{15} - 1\\) \\(0\\) <code>int</code> 4 bytes \\(-2^{31}\\) \\(2^{31} - 1\\) \\(0\\) <code>long</code> 8 bytes \\(-2^{63}\\) \\(2^{63} - 1\\) \\(0\\) \u6d6e\u70b9\u6570 <code>float</code> 4 bytes \\(1.175 \\times 10^{-38}\\) \\(3.403 \\times 10^{38}\\) \\(0.0 f\\) <code>double</code> 8 bytes \\(2.225 \\times 10^{-308}\\) \\(1.798 \\times 10^{308}\\) \\(0.0\\) \u5b57\u7b26 <code>char</code> 2 bytes / 1 byte \\(0\\) \\(2^{16} - 1\\) \\(0\\) \u5e03\u5c14 <code>bool</code> 1 byte \\(\\text{false}\\) \\(\\text{true}\\) \\(\\text{false}\\) <p>Tip</p> <p>\u5b57\u7b26\u7684\u5360\u7528\u7a7a\u95f4\u5927\u5c0f\u53d6\u51b3\u4e8e\u7f16\u7a0b\u8bed\u8a00\u91c7\u7528\u7684\u5b57\u7b26\u7f16\u7801\u65b9\u6cd5\uff0c\u8be6\u89c1\u300c\u5b57\u7b26\u7f16\u7801\u300d\u7ae0\u8282\u3002</p> <p>\u73b0\u4ee3\u8ba1\u7b97\u673a CPU \u901a\u5e38\u5c06 1 \u5b57\u8282\u4f5c\u4e3a\u6700\u5c0f\u5bfb\u5740\u5185\u5b58\u5355\u5143\u3002\u56e0\u6b64\uff0c\u5373\u4f7f\u8868\u793a\u5e03\u5c14\u91cf\u4ec5\u9700 1 \u4f4d\uff08\\(0\\) \u6216 \\(1\\)\uff09\uff0c\u5b83\u5728\u5185\u5b58\u4e2d\u901a\u5e38\u88ab\u5b58\u50a8\u4e3a 1 \u5b57\u8282\u3002</p> <p>\u90a3\u4e48\uff0c\u57fa\u672c\u6570\u636e\u7c7b\u578b\u4e0e\u6570\u636e\u7ed3\u6784\u4e4b\u95f4\u6709\u4ec0\u4e48\u8054\u7cfb\u4e0e\u533a\u522b\u5462\uff1f\u6211\u4eec\u77e5\u9053\uff0c\u6570\u636e\u7ed3\u6784\u662f\u5728\u8ba1\u7b97\u673a\u4e2d\u7ec4\u7ec7\u4e0e\u5b58\u50a8\u6570\u636e\u7684\u65b9\u5f0f\u3002\u5b83\u7684\u4e3b\u8bed\u662f\u201c\u7ed3\u6784\u201d\uff0c\u800c\u975e\u201c\u6570\u636e\u201d\u3002\u5982\u679c\u60f3\u8981\u8868\u793a\u201c\u4e00\u6392\u6570\u5b57\u201d\uff0c\u6211\u4eec\u81ea\u7136\u4f1a\u60f3\u5230\u4f7f\u7528\u6570\u7ec4\u3002\u8fd9\u662f\u56e0\u4e3a\u6570\u7ec4\u7684\u7ebf\u6027\u7ed3\u6784\u53ef\u4ee5\u8868\u793a\u6570\u5b57\u7684\u76f8\u90bb\u5173\u7cfb\u548c\u987a\u5e8f\u5173\u7cfb\uff0c\u4f46\u81f3\u4e8e\u5b58\u50a8\u7684\u5185\u5bb9\u662f\u6574\u6570 <code>int</code> \u3001\u5c0f\u6570 <code>float</code> \u3001\u8fd8\u662f\u5b57\u7b26 <code>char</code> \uff0c\u5219\u4e0e\u201c\u6570\u636e\u7ed3\u6784\u201d\u65e0\u5173\u3002</p> <p>\u6362\u53e5\u8bdd\u8bf4\uff0c\u57fa\u672c\u6570\u636e\u7c7b\u578b\u63d0\u4f9b\u4e86\u6570\u636e\u7684\u201c\u5185\u5bb9\u7c7b\u578b\u201d\uff0c\u800c\u6570\u636e\u7ed3\u6784\u63d0\u4f9b\u4e86\u6570\u636e\u7684\u201c\u7ec4\u7ec7\u65b9\u5f0f\u201d\u3002\u5982\u4ee5\u4e0b\u4ee3\u7801\u6240\u793a\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u4e0d\u540c\u57fa\u672c\u6570\u636e\u7c7b\u578b\u6765\u521d\u59cb\u5316\u6570\u7ec4\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart <pre><code>/* \u4f7f\u7528\u591a\u79cd\u300c\u57fa\u672c\u6570\u636e\u7c7b\u578b\u300d\u6765\u521d\u59cb\u5316\u300c\u6570\u7ec4\u300d */\nint[] numbers = new int[5];\nfloat[] decimals = new float[5];\nchar[] characters = new char[5];\nboolean[] booleans = new boolean[5];\n</code></pre> <pre><code>/* \u4f7f\u7528\u591a\u79cd\u300c\u57fa\u672c\u6570\u636e\u7c7b\u578b\u300d\u6765\u521d\u59cb\u5316\u300c\u6570\u7ec4\u300d */\nint numbers[5];\nfloat decimals[5];\nchar characters[5];\nbool booleans[5];\n</code></pre> <pre><code># Python \u7684 list \u53ef\u4ee5\u81ea\u7531\u5b58\u50a8\u5404\u79cd\u57fa\u672c\u6570\u636e\u7c7b\u578b\u548c\u5bf9\u8c61\nlist = [0, 0.0, 'a', False]\n</code></pre> <pre><code>// \u4f7f\u7528\u591a\u79cd\u300c\u57fa\u672c\u6570\u636e\u7c7b\u578b\u300d\u6765\u521d\u59cb\u5316\u300c\u6570\u7ec4\u300d\nvar numbers = [5]int{}\nvar decimals = [5]float64{}\nvar characters = [5]byte{}\nvar booleans = [5]bool{}\n</code></pre> <pre><code>/* JavaScript \u7684\u6570\u7ec4\u53ef\u4ee5\u81ea\u7531\u5b58\u50a8\u5404\u79cd\u57fa\u672c\u6570\u636e\u7c7b\u578b\u548c\u5bf9\u8c61 */\nconst array = [0, 0.0, 'a', false];\n</code></pre> <pre><code>/* \u4f7f\u7528\u591a\u79cd\u300c\u57fa\u672c\u6570\u636e\u7c7b\u578b\u300d\u6765\u521d\u59cb\u5316\u300c\u6570\u7ec4\u300d */\nconst numbers: number[] = [];\nconst characters: string[] = [];\nconst booleans: boolean[] = [];\n</code></pre> <pre><code>/* \u4f7f\u7528\u591a\u79cd\u300c\u57fa\u672c\u6570\u636e\u7c7b\u578b\u300d\u6765\u521d\u59cb\u5316\u300c\u6570\u7ec4\u300d */\nint numbers[10];\nfloat decimals[10];\nchar characters[10];\nbool booleans[10];\n</code></pre> <pre><code>/* \u4f7f\u7528\u591a\u79cd\u300c\u57fa\u672c\u6570\u636e\u7c7b\u578b\u300d\u6765\u521d\u59cb\u5316\u300c\u6570\u7ec4\u300d */\nint[] numbers = new int[5];\nfloat[] decimals = new float[5];\nchar[] characters = new char[5];\nbool[] booleans = new bool[5];\n</code></pre> <pre><code>/* \u4f7f\u7528\u591a\u79cd\u300c\u57fa\u672c\u6570\u636e\u7c7b\u578b\u300d\u6765\u521d\u59cb\u5316\u300c\u6570\u7ec4\u300d */\nlet numbers = Array(repeating: Int(), count: 5)\nlet decimals = Array(repeating: Double(), count: 5)\nlet characters = Array(repeating: Character(\"a\"), count: 5)\nlet booleans = Array(repeating: Bool(), count: 5)\n</code></pre> <pre><code>\n</code></pre> <pre><code>/* \u4f7f\u7528\u591a\u79cd\u300c\u57fa\u672c\u6570\u636e\u7c7b\u578b\u300d\u6765\u521d\u59cb\u5316\u300c\u6570\u7ec4\u300d */\nList&lt;int&gt; numbers = List.filled(5, 0);\nList&lt;double&gt; decimals = List.filled(5, 0.0);\nList&lt;String&gt; characters = List.filled(5, 'a');\nList&lt;bool&gt; booleans = List.filled(5, false);\n</code></pre>"},{"location":"chapter_data_structure/character_encoding/","title":"3.4. \u00a0 \u5b57\u7b26\u7f16\u7801 *","text":"<p>\u5728\u8ba1\u7b97\u673a\u4e2d\uff0c\u6240\u6709\u6570\u636e\u90fd\u662f\u4ee5\u4e8c\u8fdb\u5236\u6570\u7684\u5f62\u5f0f\u5b58\u50a8\u7684\uff0c\u5b57\u7b26 <code>char</code> \u4e5f\u4e0d\u4f8b\u5916\u3002\u4e3a\u4e86\u8868\u793a\u5b57\u7b26\uff0c\u6211\u4eec\u9700\u8981\u5efa\u7acb\u4e00\u5957\u300c\u5b57\u7b26\u96c6\u300d\uff0c\u89c4\u5b9a\u6bcf\u4e2a\u5b57\u7b26\u548c\u4e8c\u8fdb\u5236\u6570\u4e4b\u95f4\u7684\u4e00\u4e00\u5bf9\u5e94\u5173\u7cfb\u3002\u6709\u4e86\u5b57\u7b26\u96c6\u4e4b\u540e\uff0c\u8ba1\u7b97\u673a\u5c31\u53ef\u4ee5\u901a\u8fc7\u67e5\u8868\u5b8c\u6210\u4e8c\u8fdb\u5236\u6570\u5230\u5b57\u7b26\u7684\u8f6c\u6362\u3002</p>"},{"location":"chapter_data_structure/character_encoding/#341-ascii","title":"3.4.1. \u00a0 ASCII \u5b57\u7b26\u96c6","text":"<p>\u300cASCII \u7801\u300d\u662f\u6700\u65e9\u51fa\u73b0\u7684\u5b57\u7b26\u96c6\uff0c\u5168\u79f0\u4e3a\u201c\u7f8e\u56fd\u6807\u51c6\u4fe1\u606f\u4ea4\u6362\u4ee3\u7801\u201d\u3002\u5b83\u4f7f\u7528 7 \u4f4d\u4e8c\u8fdb\u5236\u6570\uff08\u5373\u4e00\u4e2a\u5b57\u8282\u7684\u4f4e 7 \u4f4d\uff09\u8868\u793a\u4e00\u4e2a\u5b57\u7b26\uff0c\u6700\u591a\u80fd\u591f\u8868\u793a 128 \u4e2a\u4e0d\u540c\u7684\u5b57\u7b26\u3002\u8fd9\u5305\u62ec\u82f1\u6587\u5b57\u6bcd\u7684\u5927\u5c0f\u5199\u3001\u6570\u5b57 0-9 \u3001\u4e00\u4e9b\u6807\u70b9\u7b26\u53f7\uff0c\u4ee5\u53ca\u4e00\u4e9b\u63a7\u5236\u5b57\u7b26\uff08\u5982\u6362\u884c\u7b26\u548c\u5236\u8868\u7b26\uff09\u3002</p> <p></p> <p> Fig. ASCII \u7801 </p> <p>\u7136\u800c\uff0cASCII \u7801\u4ec5\u80fd\u591f\u8868\u793a\u82f1\u6587\u3002\u968f\u7740\u8ba1\u7b97\u673a\u7684\u5168\u7403\u5316\uff0c\u8bde\u751f\u4e86\u4e00\u79cd\u80fd\u591f\u8868\u793a\u66f4\u591a\u8bed\u8a00\u7684\u5b57\u7b26\u96c6\u300cEASCII\u300d\u3002\u5b83\u5728 ASCII \u7684 7 \u4f4d\u57fa\u7840\u4e0a\u6269\u5c55\u5230 8 \u4f4d\uff0c\u80fd\u591f\u8868\u793a 256 \u4e2a\u4e0d\u540c\u7684\u5b57\u7b26\u3002\u5728\u4e16\u754c\u8303\u56f4\u5185\uff0c\u9646\u7eed\u51fa\u73b0\u4e86\u4e00\u6279\u9002\u7528\u4e8e\u4e0d\u540c\u5730\u533a\u7684 EASCII \u5b57\u7b26\u96c6\u3002\u8fd9\u4e9b\u5b57\u7b26\u96c6\u7684\u524d 128 \u4e2a\u5b57\u7b26\u7edf\u4e00\u4e3a ASCII \u7801\uff0c\u540e 128 \u4e2a\u5b57\u7b26\u5b9a\u4e49\u4e0d\u540c\uff0c\u4ee5\u9002\u5e94\u4e0d\u540c\u8bed\u8a00\u7684\u9700\u6c42\u3002</p>"},{"location":"chapter_data_structure/character_encoding/#342-gbk","title":"3.4.2. \u00a0 GBK \u5b57\u7b26\u96c6","text":"<p>\u540e\u6765\u4eba\u4eec\u53d1\u73b0\uff0cEASCII \u7801\u4ecd\u7136\u65e0\u6cd5\u6ee1\u8db3\u8bb8\u591a\u8bed\u8a00\u7684\u5b57\u7b26\u6570\u91cf\u8981\u6c42\u3002\u4f8b\u5982\uff0c\u6c49\u5b57\u5927\u7ea6\u6709\u8fd1\u5341\u4e07\u4e2a\uff0c\u5149\u65e5\u5e38\u4f7f\u7528\u7684\u5c31\u6709\u51e0\u5343\u4e2a\u3002\u4e2d\u56fd\u56fd\u5bb6\u6807\u51c6\u603b\u5c40\u4e8e 1980 \u5e74\u53d1\u5e03\u4e86\u300cGB2312\u300d\u5b57\u7b26\u96c6\uff0c\u5176\u6536\u5f55\u4e86 6763 \u4e2a\u6c49\u5b57\uff0c\u57fa\u672c\u6ee1\u8db3\u4e86\u6c49\u5b57\u7684\u8ba1\u7b97\u673a\u5904\u7406\u9700\u8981\u3002</p> <p>\u7136\u800c\uff0cGB2312 \u65e0\u6cd5\u5904\u7406\u90e8\u5206\u7684\u7f55\u89c1\u5b57\u548c\u7e41\u4f53\u5b57\u3002\u4e4b\u540e\u5728 GB2312 \u7684\u57fa\u7840\u4e0a\uff0c\u6269\u5c55\u5f97\u5230\u4e86\u300cGBK\u300d\u5b57\u7b26\u96c6\uff0c\u5b83\u5171\u6536\u5f55\u4e86 21886 \u4e2a\u6c49\u5b57\u3002\u5728 GBK \u7f16\u7801\u65b9\u6848\u4e2d\uff0cASCII \u5b57\u7b26\u4f7f\u7528\u4e00\u4e2a\u5b57\u8282\u8868\u793a\uff0c\u6c49\u5b57\u4f7f\u7528\u4e24\u4e2a\u5b57\u8282\u8868\u793a\u3002</p>"},{"location":"chapter_data_structure/character_encoding/#343-unicode","title":"3.4.3. \u00a0 Unicode \u5b57\u7b26\u96c6","text":"<p>\u968f\u7740\u8ba1\u7b97\u673a\u7684\u84ec\u52c3\u53d1\u5c55\uff0c\u5b57\u7b26\u96c6\u4e0e\u7f16\u7801\u6807\u51c6\u767e\u82b1\u9f50\u653e\uff0c\u800c\u8fd9\u5e26\u6765\u4e86\u8bb8\u591a\u95ee\u9898\u3002\u4e00\u65b9\u9762\uff0c\u8fd9\u4e9b\u5b57\u7b26\u96c6\u4e00\u822c\u53ea\u5b9a\u4e49\u4e86\u7279\u5b9a\u8bed\u8a00\u7684\u5b57\u7b26\uff0c\u65e0\u6cd5\u5728\u591a\u8bed\u8a00\u73af\u5883\u4e0b\u6b63\u5e38\u5de5\u4f5c\uff1b\u53e6\u4e00\u65b9\u9762\uff0c\u540c\u4e00\u79cd\u8bed\u8a00\u4e5f\u5b58\u5728\u591a\u79cd\u5b57\u7b26\u96c6\u6807\u51c6\uff0c\u5982\u679c\u4e24\u53f0\u7535\u8111\u5b89\u88c5\u7684\u662f\u4e0d\u540c\u7684\u7f16\u7801\u6807\u51c6\uff0c\u5219\u5728\u4fe1\u606f\u4f20\u9012\u65f6\u5c31\u4f1a\u51fa\u73b0\u4e71\u7801\u3002</p> <p>\u90a3\u4e2a\u65f6\u4ee3\u7684\u4eba\u4eec\u5c31\u5728\u60f3\uff1a\u5982\u679c\u63a8\u51fa\u4e00\u4e2a\u8db3\u591f\u5b8c\u6574\u7684\u5b57\u7b26\u96c6\uff0c\u5c06\u4e16\u754c\u8303\u56f4\u5185\u7684\u6240\u6709\u8bed\u8a00\u548c\u7b26\u53f7\u90fd\u6536\u5f55\u5176\u4e2d\uff0c\u4e0d\u5c31\u53ef\u4ee5\u89e3\u51b3\u8de8\u8bed\u8a00\u73af\u5883\u548c\u4e71\u7801\u95ee\u9898\u4e86\u5417\uff1f\u5728\u8fd9\u79cd\u60f3\u6cd5\u7684\u9a71\u52a8\u4e0b\uff0c\u4e00\u4e2a\u5927\u800c\u5168\u7684\u5b57\u7b26\u96c6 Unicode \u5e94\u8fd0\u800c\u751f\u3002</p> <p>\u300cUnicode\u300d\u7684\u5168\u79f0\u4e3a\u201c\u7edf\u4e00\u5b57\u7b26\u7f16\u7801\u201d\uff0c\u7406\u8bba\u4e0a\u80fd\u5bb9\u7eb3\u4e00\u767e\u591a\u4e07\u4e2a\u5b57\u7b26\u3002\u5b83\u81f4\u529b\u4e8e\u5c06\u5168\u7403\u8303\u56f4\u5185\u7684\u5b57\u7b26\u7eb3\u5165\u5230\u7edf\u4e00\u7684\u5b57\u7b26\u96c6\u4e4b\u4e2d\uff0c\u63d0\u4f9b\u4e00\u79cd\u901a\u7528\u7684\u5b57\u7b26\u96c6\u6765\u5904\u7406\u548c\u663e\u793a\u5404\u79cd\u8bed\u8a00\u6587\u5b57\uff0c\u51cf\u5c11\u56e0\u4e3a\u7f16\u7801\u6807\u51c6\u4e0d\u540c\u800c\u4ea7\u751f\u7684\u4e71\u7801\u95ee\u9898\u3002</p> <p>\u81ea 1991 \u5e74\u53d1\u5e03\u4ee5\u6765\uff0cUnicode \u4e0d\u65ad\u6269\u5145\u65b0\u7684\u8bed\u8a00\u4e0e\u5b57\u7b26\u3002\u622a\u6b62 2022 \u5e74 9 \u6708\uff0cUnicode \u5df2\u7ecf\u5305\u542b 149186 \u4e2a\u5b57\u7b26\uff0c\u5305\u62ec\u5404\u79cd\u8bed\u8a00\u7684\u5b57\u7b26\u3001\u7b26\u53f7\u3001\u751a\u81f3\u662f\u8868\u60c5\u7b26\u53f7\u7b49\u3002\u5728\u5e9e\u5927\u7684 Unicode \u5b57\u7b26\u96c6\u4e2d\uff0c\u5e38\u7528\u7684\u5b57\u7b26\u5360\u7528 2 \u5b57\u8282\uff0c\u6709\u4e9b\u751f\u50fb\u7684\u5b57\u7b26\u5360 3 \u5b57\u8282\u751a\u81f3 4 \u5b57\u8282\u3002</p> <p>Unicode \u662f\u4e00\u79cd\u5b57\u7b26\u96c6\u6807\u51c6\uff0c\u672c\u8d28\u4e0a\u662f\u7ed9\u6bcf\u4e2a\u5b57\u7b26\u5206\u914d\u4e00\u4e2a\u7f16\u53f7\uff08\u79f0\u4e3a\u201c\u7801\u70b9\u201d\uff09\uff0c\u4f46\u5b83\u5e76\u6ca1\u6709\u89c4\u5b9a\u5728\u8ba1\u7b97\u673a\u4e2d\u5982\u4f55\u5b58\u50a8\u8fd9\u4e9b\u5b57\u7b26\u7801\u70b9\u3002\u6211\u4eec\u4e0d\u7981\u4f1a\u95ee\uff1a\u5f53\u591a\u79cd\u957f\u5ea6\u7684 Unicode \u7801\u70b9\u540c\u65f6\u51fa\u73b0\u5728\u540c\u4e00\u4e2a\u6587\u672c\u4e2d\u65f6\uff0c\u7cfb\u7edf\u5982\u4f55\u89e3\u6790\u5b57\u7b26\uff1f\u4f8b\u5982\uff0c\u7ed9\u5b9a\u4e00\u4e2a\u957f\u5ea6\u4e3a 2 \u5b57\u8282\u7684\u7f16\u7801\uff0c\u7cfb\u7edf\u5982\u4f55\u786e\u8ba4\u5b83\u662f\u4e00\u4e2a 2 \u5b57\u8282\u7684\u5b57\u7b26\u8fd8\u662f\u4e24\u4e2a 1 \u5b57\u8282\u7684\u5b57\u7b26\uff1f</p> <p>\u5bf9\u4e8e\u4ee5\u4e0a\u95ee\u9898\uff0c\u4e00\u79cd\u76f4\u63a5\u7684\u89e3\u51b3\u65b9\u6848\u662f\u5c06\u6240\u6709\u5b57\u7b26\u5b58\u50a8\u4e3a\u7b49\u957f\u7684\u7f16\u7801\u3002\u5982\u4e0b\u56fe\u6240\u793a\uff0c\u201cHello\u201d\u4e2d\u7684\u6bcf\u4e2a\u5b57\u7b26\u5360\u7528 1 \u5b57\u8282\uff0c\u201c\u7b97\u6cd5\u201d\u4e2d\u7684\u6bcf\u4e2a\u5b57\u7b26\u5360\u7528 2 \u5b57\u8282\u3002\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u9ad8\u4f4d\u586b 0 \uff0c\u5c06\u201cHello \u7b97\u6cd5\u201d\u4e2d\u7684\u6240\u6709\u5b57\u7b26\u90fd\u7f16\u7801\u4e3a 2 \u5b57\u8282\u957f\u5ea6\u3002\u8fd9\u6837\u7cfb\u7edf\u5c31\u53ef\u4ee5\u6bcf\u9694 2 \u5b57\u8282\u89e3\u6790\u4e00\u4e2a\u5b57\u7b26\uff0c\u6062\u590d\u51fa\u8fd9\u4e2a\u77ed\u8bed\u7684\u5185\u5bb9\u4e86\u3002</p> <p></p> <p> Fig. Unicode \u7f16\u7801\u793a\u4f8b </p> <p>\u7136\u800c\uff0cASCII \u7801\u5df2\u7ecf\u5411\u6211\u4eec\u8bc1\u660e\uff0c\u7f16\u7801\u82f1\u6587\u53ea\u9700\u8981 1 \u5b57\u8282\u3002\u82e5\u91c7\u7528\u4e0a\u8ff0\u65b9\u6848\uff0c\u82f1\u6587\u6587\u672c\u5360\u7528\u7a7a\u95f4\u7684\u5927\u5c0f\u5c06\u4f1a\u662f ASCII \u7f16\u7801\u4e0b\u5927\u5c0f\u7684 2 \u500d\uff0c\u975e\u5e38\u6d6a\u8d39\u5185\u5b58\u7a7a\u95f4\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u9700\u8981\u4e00\u79cd\u66f4\u52a0\u9ad8\u6548\u7684 Unicode \u7f16\u7801\u65b9\u6cd5\u3002</p>"},{"location":"chapter_data_structure/character_encoding/#344-utf-8","title":"3.4.4. \u00a0 UTF-8 \u7f16\u7801","text":"<p>\u76ee\u524d\uff0cUTF-8 \u5df2\u6210\u4e3a\u56fd\u9645\u4e0a\u4f7f\u7528\u6700\u5e7f\u6cdb\u7684 Unicode \u7f16\u7801\u65b9\u6cd5\u3002\u5b83\u662f\u4e00\u79cd\u53ef\u53d8\u957f\u7684\u7f16\u7801\uff0c\u4f7f\u7528 1 \u5230 4 \u4e2a\u5b57\u8282\u6765\u8868\u793a\u4e00\u4e2a\u5b57\u7b26\uff0c\u6839\u636e\u5b57\u7b26\u7684\u590d\u6742\u6027\u800c\u53d8\u3002ASCII \u5b57\u7b26\u53ea\u9700\u8981 1 \u4e2a\u5b57\u8282\uff0c\u62c9\u4e01\u5b57\u6bcd\u548c\u5e0c\u814a\u5b57\u6bcd\u9700\u8981 2 \u4e2a\u5b57\u8282\uff0c\u5e38\u7528\u7684\u4e2d\u6587\u5b57\u7b26\u9700\u8981 3 \u4e2a\u5b57\u8282\uff0c\u5176\u4ed6\u7684\u4e00\u4e9b\u751f\u50fb\u5b57\u7b26\u9700\u8981 4 \u4e2a\u5b57\u8282\u3002</p> <p>UTF-8 \u7684\u7f16\u7801\u89c4\u5219\u5e76\u4e0d\u590d\u6742\uff0c\u5206\u4e3a\u4e24\u79cd\u60c5\u51b5\uff1a</p> <ul> <li>\u5bf9\u4e8e\u957f\u5ea6\u4e3a 1 \u5b57\u8282\u7684\u5b57\u7b26\uff0c\u5c06\u6700\u9ad8\u4f4d\u8bbe\u7f6e\u4e3a \\(0\\) \u3001\u5176\u4f59 7 \u4f4d\u8bbe\u7f6e\u4e3a Unicode \u7801\u70b9\u3002\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0cASCII \u5b57\u7b26\u5728 Unicode \u5b57\u7b26\u96c6\u4e2d\u5360\u636e\u4e86\u524d 128 \u4e2a\u7801\u70b9\u3002\u4e5f\u5c31\u662f\u8bf4\uff0cUTF-8 \u7f16\u7801\u53ef\u4ee5\u5411\u4e0b\u517c\u5bb9 ASCII \u7801\u3002\u8fd9\u610f\u5473\u7740\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528 UTF-8 \u6765\u89e3\u6790\u5e74\u4ee3\u4e45\u8fdc\u7684 ASCII \u7801\u6587\u672c\u3002</li> <li>\u5bf9\u4e8e\u957f\u5ea6\u4e3a \\(n\\) \u5b57\u8282\u7684\u5b57\u7b26\uff08\u5176\u4e2d \\(n &gt; 1\\)\uff09\uff0c\u5c06\u9996\u4e2a\u5b57\u8282\u7684\u9ad8 \\(n\\) \u4f4d\u90fd\u8bbe\u7f6e\u4e3a \\(1\\) \u3001\u7b2c \\(n + 1\\) \u4f4d\u8bbe\u7f6e\u4e3a \\(0\\) \uff1b\u4ece\u7b2c\u4e8c\u4e2a\u5b57\u8282\u5f00\u59cb\uff0c\u5c06\u6bcf\u4e2a\u5b57\u8282\u7684\u9ad8 2 \u4f4d\u90fd\u8bbe\u7f6e\u4e3a \\(10\\) \uff1b\u5176\u4f59\u6240\u6709\u4f4d\u7528\u4e8e\u586b\u5145\u5b57\u7b26\u7684 Unicode \u7801\u70b9\u3002</li> </ul> <p>\u4e0b\u56fe\u5c55\u793a\u4e86\u201cHello\u7b97\u6cd5\u201d\u5bf9\u5e94\u7684 UTF-8 \u7f16\u7801\u3002\u5c06\u6700\u9ad8 \\(n\\) \u4f4d\u8bbe\u7f6e\u4e3a \\(1\\) \u6bd4\u8f83\u5bb9\u6613\u7406\u89e3\uff0c\u53ef\u4ee5\u5411\u7cfb\u7edf\u6307\u51fa\u5b57\u7b26\u7684\u957f\u5ea6\u4e3a \\(n\\) \u3002\u90a3\u4e48\uff0c\u4e3a\u4ec0\u4e48\u8981\u5c06\u5176\u4f59\u6240\u6709\u5b57\u8282\u7684\u9ad8 2 \u4f4d\u90fd\u8bbe\u7f6e\u4e3a \\(10\\) \u5462\uff1f\u5b9e\u9645\u4e0a\uff0c\u8fd9\u4e2a \\(10\\) \u80fd\u591f\u8d77\u5230\u6821\u9a8c\u7b26\u7684\u4f5c\u7528\uff0c\u56e0\u4e3a\u5728 UTF-8 \u7f16\u7801\u89c4\u5219\u4e0b\uff0c\u4e0d\u53ef\u80fd\u6709\u5b57\u7b26\u7684\u6700\u9ad8\u4e24\u4f4d\u662f \\(10\\) \u3002\u8fd9\u662f\u56e0\u4e3a\u957f\u5ea6\u4e3a 1 \u5b57\u8282\u7684\u5b57\u7b26\u7684\u6700\u9ad8\u4e00\u4f4d\u662f \\(0\\) \u3002\u5047\u8bbe\u7cfb\u7edf\u4ece\u4e00\u4e2a\u9519\u8bef\u7684\u5b57\u8282\u5f00\u59cb\u89e3\u6790\u6587\u672c\uff0c\u5b57\u8282\u5934\u90e8\u7684 \\(10\\) \u80fd\u591f\u5e2e\u52a9\u7cfb\u7edf\u5feb\u901f\u7684\u5224\u65ad\u51fa\u5f02\u5e38\u3002</p> <p></p> <p> Fig. UTF-8 \u7f16\u7801\u793a\u4f8b </p> <p>\u9664\u4e86 UTF-8 \u4e4b\u5916\uff0c\u5e38\u89c1\u7684\u7f16\u7801\u65b9\u5f0f\u8fd8\u5305\u62ec UTF-16 \u548c UTF-32 \u3002\u5b83\u4eec\u4e3a Unicode \u5b57\u7b26\u96c6\u63d0\u4f9b\u4e86\u4e0d\u540c\u7684\u7f16\u7801\u65b9\u6cd5\u3002</p> <ul> <li>UTF-16 \u7f16\u7801\uff1a\u4f7f\u7528 2 \u6216 4 \u4e2a\u5b57\u8282\u6765\u8868\u793a\u4e00\u4e2a\u5b57\u7b26\u3002\u6240\u6709\u7684 ASCII \u5b57\u7b26\u548c\u5f88\u591a\u5e38\u7528\u7684\u975e\u82f1\u6587\u5b57\u7b26\uff0c\u90fd\u7528 2 \u4e2a\u5b57\u8282\u8868\u793a\uff1b\u5c11\u6570\u5b57\u7b26\u9700\u8981\u7528\u5230 4 \u4e2a\u5b57\u8282\u8868\u793a\u3002\u5bf9\u4e8e 2 \u5b57\u8282\u7684\u5b57\u7b26\uff0cUTF-16 \u7f16\u7801\u4e0e Unicode \u7801\u70b9\u76f8\u7b49\u3002</li> <li>UTF-32 \u7f16\u7801\uff1a\u6bcf\u4e2a\u5b57\u7b26\u90fd\u4f7f\u7528 4 \u4e2a\u5b57\u8282\u3002\u8fd9\u610f\u5473\u7740 UTF-32 \u4f1a\u6bd4 UTF-8 \u548c UTF-16 \u66f4\u5360\u7528\u7a7a\u95f4\uff0c\u7279\u522b\u662f\u5bf9\u4e8e\u4e3b\u8981\u4f7f\u7528 ASCII \u5b57\u7b26\u7684\u6587\u672c\u3002</li> </ul> <p>\u4ece\u5b58\u50a8\u7a7a\u95f4\u7684\u89d2\u5ea6\u770b\uff0c\u4f7f\u7528 UTF-8 \u8868\u793a\u82f1\u6587\u5b57\u7b26\u975e\u5e38\u9ad8\u6548\uff0c\u56e0\u4e3a\u5b83\u4ec5\u9700 1 \u4e2a\u5b57\u8282\uff1b\u4f7f\u7528 UTF-16 \u7f16\u7801\u67d0\u4e9b\u975e\u82f1\u6587\u5b57\u7b26\uff08\u4f8b\u5982\u4e2d\u6587\uff09\u4f1a\u66f4\u52a0\u9ad8\u6548\uff0c\u56e0\u4e3a\u5b83\u53ea\u9700\u8981 2 \u4e2a\u5b57\u8282\uff0c\u800c UTF-8 \u53ef\u80fd\u9700\u8981 3 \u4e2a\u5b57\u8282\u3002\u4ece\u517c\u5bb9\u6027\u7684\u89d2\u5ea6\u770b\uff0cUTF-8 \u7684\u901a\u7528\u6027\u6700\u4f73\uff0c\u8bb8\u591a\u5de5\u5177\u548c\u5e93\u90fd\u4f18\u5148\u652f\u6301 UTF-8 \u3002</p>"},{"location":"chapter_data_structure/character_encoding/#345","title":"3.4.5. \u00a0 \u7f16\u7a0b\u8bed\u8a00\u7684\u5b57\u7b26\u7f16\u7801","text":"<p>\u5bf9\u4e8e\u4ee5\u5f80\u7684\u5927\u591a\u6570\u7f16\u7a0b\u8bed\u8a00\uff0c\u7a0b\u5e8f\u8fd0\u884c\u4e2d\u7684\u5b57\u7b26\u4e32\u90fd\u91c7\u7528 UTF-16 \u6216 UTF-32 \u8fd9\u7c7b\u7b49\u957f\u7684\u7f16\u7801\u3002\u8fd9\u662f\u56e0\u4e3a\u5728\u7b49\u957f\u7f16\u7801\u4e0b\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u5b57\u7b26\u4e32\u770b\u4f5c\u6570\u7ec4\u6765\u5904\u7406\uff0c\u5177\u4f53\u6765\u8bf4\uff1a</p> <ul> <li>\u968f\u673a\u8bbf\u95ee: UTF-16 \u7f16\u7801\u7684\u5b57\u7b26\u4e32\u53ef\u4ee5\u5f88\u5bb9\u6613\u5730\u8fdb\u884c\u968f\u673a\u8bbf\u95ee\u3002UTF-8 \u662f\u4e00\u79cd\u53d8\u957f\u7f16\u7801\uff0c\u8981\u627e\u5230\u7b2c \\(i\\) \u4e2a\u5b57\u7b26\uff0c\u6211\u4eec\u9700\u8981\u4ece\u5b57\u7b26\u4e32\u7684\u5f00\u59cb\u5904\u904d\u5386\u5230\u7b2c \\(i\\) \u4e2a\u5b57\u7b26\uff0c\u8fd9\u9700\u8981 \\(O(n)\\) \u7684\u65f6\u95f4\u3002</li> <li>\u5b57\u7b26\u8ba1\u6570: \u4e0e\u968f\u673a\u8bbf\u95ee\u7c7b\u4f3c\uff0c\u8ba1\u7b97 UTF-16 \u5b57\u7b26\u4e32\u7684\u957f\u5ea6\u4e5f\u662f \\(O(1)\\) \u7684\u64cd\u4f5c\u3002\u4f46\u662f\uff0c\u8ba1\u7b97 UTF-8 \u7f16\u7801\u7684\u5b57\u7b26\u4e32\u7684\u957f\u5ea6\u9700\u8981\u904d\u5386\u6574\u4e2a\u5b57\u7b26\u4e32\u3002</li> <li>\u5b57\u7b26\u4e32\u64cd\u4f5c: \u5728 UTF-16 \u7f16\u7801\u7684\u5b57\u7b26\u4e32\u4e2d\uff0c\u5f88\u591a\u5b57\u7b26\u4e32\u64cd\u4f5c\uff08\u5982\u5206\u5272\u3001\u8fde\u63a5\u3001\u63d2\u5165\u3001\u5220\u9664\u7b49\uff09\u90fd\u66f4\u5bb9\u6613\u8fdb\u884c\u3002\u5728 UTF-8 \u7f16\u7801\u7684\u5b57\u7b26\u4e32\u4e0a\u8fdb\u884c\u8fd9\u4e9b\u64cd\u4f5c\u901a\u5e38\u9700\u8981\u989d\u5916\u7684\u8ba1\u7b97\uff0c\u4ee5\u786e\u4fdd\u4e0d\u4f1a\u4ea7\u751f\u65e0\u6548\u7684 UTF-8 \u7f16\u7801\u3002</li> </ul> <p>\u7f16\u7a0b\u8bed\u8a00\u7684\u5b57\u7b26\u7f16\u7801\u65b9\u6848\u8bbe\u8ba1\u662f\u4e00\u4e2a\u5f88\u6709\u8da3\u7684\u8bdd\u9898\uff0c\u6d89\u53ca\u5230\u8bb8\u591a\u56e0\u7d20\uff1a</p> <ul> <li>Java \u7684 <code>String</code> \u7c7b\u578b\u4f7f\u7528 UTF-16 \u7f16\u7801\uff0c\u6bcf\u4e2a\u5b57\u7b26\u5360\u7528 2 \u5b57\u8282\u3002\u8fd9\u662f\u56e0\u4e3a Java \u8bed\u8a00\u8bbe\u8ba1\u4e4b\u521d\uff0c\u4eba\u4eec\u8ba4\u4e3a 16 \u4f4d\u8db3\u4ee5\u8868\u793a\u6240\u6709\u53ef\u80fd\u7684\u5b57\u7b26\u3002\u7136\u800c\uff0c\u8fd9\u662f\u4e00\u4e2a\u4e0d\u6b63\u786e\u7684\u5224\u65ad\u3002\u540e\u6765 Unicode \u89c4\u8303\u6269\u5c55\u5230\u4e86\u8d85\u8fc7 16 \u4f4d\uff0c\u6240\u4ee5 Java \u4e2d\u7684\u5b57\u7b26\u73b0\u5728\u53ef\u80fd\u7531\u4e00\u5bf9 16 \u4f4d\u7684\u503c\uff08\u79f0\u4e3a\u201c\u4ee3\u7406\u5bf9\u201d\uff09\u8868\u793a\u3002</li> <li>JavaScript \u548c TypeScript \u7684\u5b57\u7b26\u4e32\u4f7f\u7528 UTF-16 \u7f16\u7801\u7684\u539f\u56e0\u4e0e Java \u7c7b\u4f3c\u3002\u5f53 JavaScript \u8bed\u8a00\u5728 1995 \u5e74\u88ab Netscape \u516c\u53f8\u9996\u6b21\u5f15\u5165\u65f6\uff0cUnicode \u8fd8\u5904\u4e8e\u76f8\u5bf9\u65e9\u671f\u7684\u9636\u6bb5\uff0c\u90a3\u65f6\u5019\u4f7f\u7528 16 \u4f4d\u7684\u7f16\u7801\u5c31\u8db3\u591f\u8868\u793a\u6240\u6709\u7684 Unicode \u5b57\u7b26\u4e86\u3002</li> <li>C# \u4f7f\u7528 UTF-16 \u7f16\u7801\uff0c\u4e3b\u8981\u56e0\u4e3a .NET \u5e73\u53f0\u662f\u7531 Microsoft \u8bbe\u8ba1\u7684\uff0c\u800c Microsoft \u7684\u5f88\u591a\u6280\u672f\uff0c\u5305\u62ec Windows \u64cd\u4f5c\u7cfb\u7edf\uff0c\u90fd\u5e7f\u6cdb\u5730\u4f7f\u7528 UTF-16 \u7f16\u7801\u3002</li> </ul> <p>\u7531\u4e8e\u4ee5\u4e0a\u7f16\u7a0b\u8bed\u8a00\u5bf9\u5b57\u7b26\u6570\u91cf\u7684\u4f4e\u4f30\uff0c\u5b83\u4eec\u4e0d\u5f97\u4e0d\u91c7\u53d6\u201c\u4ee3\u7406\u5bf9\u201d\u7684\u65b9\u5f0f\u6765\u8868\u793a\u8d85\u8fc7 16 \u4f4d\u957f\u5ea6\u7684 Unicode \u5b57\u7b26\u3002\u8fd9\u662f\u4e00\u4e2a\u4e0d\u5f97\u5df2\u4e3a\u4e4b\u7684\u65e0\u5948\u4e4b\u4e3e\u3002\u4e00\u65b9\u9762\uff0c\u5305\u542b\u4ee3\u7406\u5bf9\u7684\u5b57\u7b26\u4e32\u4e2d\uff0c\u4e00\u4e2a\u5b57\u7b26\u53ef\u80fd\u5360\u7528 2 \u5b57\u8282\u6216 4 \u5b57\u8282\uff0c\u56e0\u6b64\u4e27\u5931\u4e86\u7b49\u957f\u7f16\u7801\u7684\u4f18\u52bf\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u5904\u7406\u4ee3\u7406\u5bf9\u9700\u8981\u589e\u52a0\u989d\u5916\u4ee3\u7801\uff0c\u8fd9\u589e\u52a0\u4e86\u7f16\u7a0b\u7684\u590d\u6742\u6027\u548c Debug \u96be\u5ea6\u3002</p> <p>\u51fa\u4e8e\u4ee5\u4e0a\u539f\u56e0\uff0c\u90e8\u5206\u7f16\u7a0b\u8bed\u8a00\u63d0\u51fa\u4e86\u4e0d\u540c\u7684\u7f16\u7801\u65b9\u6848\uff1a</p> <ul> <li>Python 3 \u4f7f\u7528\u4e00\u79cd\u7075\u6d3b\u7684\u5b57\u7b26\u4e32\u8868\u793a\uff0c\u5b58\u50a8\u7684\u5b57\u7b26\u957f\u5ea6\u53d6\u51b3\u4e8e\u5b57\u7b26\u4e32\u4e2d\u6700\u5927\u7684 Unicode \u7801\u70b9\u3002\u5bf9\u4e8e\u5168\u90e8\u662f ASCII \u5b57\u7b26\u7684\u5b57\u7b26\u4e32\uff0c\u6bcf\u4e2a\u5b57\u7b26\u5360\u7528 1 \u4e2a\u5b57\u8282\uff1b\u5982\u679c\u5b57\u7b26\u4e32\u4e2d\u5305\u542b\u7684\u5b57\u7b26\u8d85\u51fa\u4e86 ASCII \u8303\u56f4\uff0c\u4f46\u5168\u90e8\u5728\u57fa\u672c\u591a\u8bed\u8a00\u5e73\u9762\uff08BMP\uff09\u5185\uff0c\u6bcf\u4e2a\u5b57\u7b26\u5360\u7528 2 \u4e2a\u5b57\u8282\uff1b\u5982\u679c\u5b57\u7b26\u4e32\u4e2d\u6709\u8d85\u51fa BMP \u7684\u5b57\u7b26\uff0c\u90a3\u4e48\u6bcf\u4e2a\u5b57\u7b26\u5360\u7528 4 \u4e2a\u5b57\u8282\u3002</li> <li>Go \u8bed\u8a00\u7684 <code>string</code> \u7c7b\u578b\u5728\u5185\u90e8\u4f7f\u7528 UTF-8 \u7f16\u7801\u3002Go \u8bed\u8a00\u8fd8\u63d0\u4f9b\u4e86 <code>rune</code> \u7c7b\u578b\uff0c\u5b83\u7528\u4e8e\u8868\u793a\u5355\u4e2a Unicode \u7801\u70b9\u3002</li> <li>Rust \u8bed\u8a00\u7684 str \u548c String \u7c7b\u578b\u5728\u5185\u90e8\u4f7f\u7528 UTF-8 \u7f16\u7801\u3002Rust \u4e5f\u63d0\u4f9b\u4e86 char \u7c7b\u578b\uff0c\u7528\u4e8e\u8868\u793a\u5355\u4e2a Unicode \u7801\u70b9\u3002</li> </ul> <p>\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u4ee5\u4e0a\u8ba8\u8bba\u7684\u90fd\u662f\u5b57\u7b26\u4e32\u5728\u7f16\u7a0b\u8bed\u8a00\u4e2d\u7684\u5b58\u50a8\u65b9\u5f0f\uff0c\u8fd9\u548c\u5b57\u7b26\u4e32\u5982\u4f55\u5728\u6587\u4ef6\u4e2d\u5b58\u50a8\u6216\u5728\u7f51\u7edc\u4e2d\u4f20\u8f93\u662f\u4e24\u4e2a\u4e0d\u540c\u7684\u95ee\u9898\u3002\u5728\u6587\u4ef6\u5b58\u50a8\u6216\u7f51\u7edc\u4f20\u8f93\u4e2d\uff0c\u6211\u4eec\u4e00\u822c\u4f1a\u5c06\u5b57\u7b26\u4e32\u7f16\u7801\u4e3a UTF-8 \u683c\u5f0f\uff0c\u4ee5\u8fbe\u5230\u6700\u4f18\u7684\u517c\u5bb9\u6027\u548c\u7a7a\u95f4\u6548\u7387\u3002</p>"},{"location":"chapter_data_structure/classification_of_data_structure/","title":"3.1. \u00a0 \u6570\u636e\u7ed3\u6784\u5206\u7c7b","text":"<p>\u6570\u636e\u7ed3\u6784\u53ef\u4ee5\u4ece\u903b\u8f91\u7ed3\u6784\u548c\u7269\u7406\u7ed3\u6784\u4e24\u4e2a\u7ef4\u5ea6\u8fdb\u884c\u5206\u7c7b\u3002</p>"},{"location":"chapter_data_structure/classification_of_data_structure/#311","title":"3.1.1. \u00a0 \u903b\u8f91\u7ed3\u6784\uff1a\u7ebf\u6027\u4e0e\u975e\u7ebf\u6027","text":"<p>\u300c\u903b\u8f91\u7ed3\u6784\u300d\u63ed\u793a\u4e86\u6570\u636e\u5143\u7d20\u4e4b\u95f4\u7684\u903b\u8f91\u5173\u7cfb\u3002\u5728\u6570\u7ec4\u548c\u94fe\u8868\u4e2d\uff0c\u6570\u636e\u6309\u7167\u987a\u5e8f\u4f9d\u6b21\u6392\u5217\uff0c\u4f53\u73b0\u4e86\u6570\u636e\u4e4b\u95f4\u7684\u7ebf\u6027\u5173\u7cfb\uff1b\u800c\u5728\u6811\u4e2d\uff0c\u6570\u636e\u4ece\u9876\u90e8\u5411\u4e0b\u6309\u5c42\u6b21\u6392\u5217\uff0c\u8868\u73b0\u51fa\u7956\u5148\u4e0e\u540e\u4ee3\u4e4b\u95f4\u7684\u6d3e\u751f\u5173\u7cfb\uff1b\u56fe\u5219\u7531\u8282\u70b9\u548c\u8fb9\u6784\u6210\uff0c\u53cd\u6620\u4e86\u590d\u6742\u7684\u7f51\u7edc\u5173\u7cfb\u3002</p> <p>\u903b\u8f91\u7ed3\u6784\u901a\u5e38\u5206\u4e3a\u300c\u7ebf\u6027\u300d\u548c\u300c\u975e\u7ebf\u6027\u300d\u4e24\u7c7b\u3002\u7ebf\u6027\u7ed3\u6784\u6bd4\u8f83\u76f4\u89c2\uff0c\u6307\u6570\u636e\u5728\u903b\u8f91\u5173\u7cfb\u4e0a\u5448\u7ebf\u6027\u6392\u5217\uff1b\u975e\u7ebf\u6027\u7ed3\u6784\u5219\u76f8\u53cd\uff0c\u5448\u975e\u7ebf\u6027\u6392\u5217\uff0c\u4f8b\u5982\u7f51\u72b6\u6216\u6811\u72b6\u7ed3\u6784\u3002</p> <ul> <li>\u7ebf\u6027\u6570\u636e\u7ed3\u6784\uff1a\u6570\u7ec4\u3001\u94fe\u8868\u3001\u6808\u3001\u961f\u5217\u3001\u54c8\u5e0c\u8868\uff1b</li> <li>\u975e\u7ebf\u6027\u6570\u636e\u7ed3\u6784\uff1a\u6811\u3001\u56fe\u3001\u5806\u3001\u54c8\u5e0c\u8868\uff1b</li> </ul> <p></p> <p> Fig. \u7ebf\u6027\u4e0e\u975e\u7ebf\u6027\u6570\u636e\u7ed3\u6784 </p>"},{"location":"chapter_data_structure/classification_of_data_structure/#312","title":"3.1.2. \u00a0 \u7269\u7406\u7ed3\u6784\uff1a\u8fde\u7eed\u4e0e\u79bb\u6563","text":"<p>\u5728\u8ba1\u7b97\u673a\u4e2d\uff0c\u5185\u5b58\u548c\u786c\u76d8\u662f\u4e24\u79cd\u4e3b\u8981\u7684\u5b58\u50a8\u786c\u4ef6\u8bbe\u5907\u3002\u300c\u786c\u76d8\u300d\u4e3b\u8981\u7528\u4e8e\u957f\u671f\u5b58\u50a8\u6570\u636e\uff0c\u5bb9\u91cf\u8f83\u5927\uff08\u901a\u5e38\u53ef\u8fbe\u5230 TB \u7ea7\u522b\uff09\u3001\u901f\u5ea6\u8f83\u6162\u3002\u300c\u5185\u5b58\u300d\u7528\u4e8e\u8fd0\u884c\u7a0b\u5e8f\u65f6\u6682\u5b58\u6570\u636e\uff0c\u901f\u5ea6\u8f83\u5feb\uff0c\u4f46\u5bb9\u91cf\u8f83\u5c0f\uff08\u901a\u5e38\u4e3a GB \u7ea7\u522b\uff09\u3002</p> <p>\u5728\u7b97\u6cd5\u8fd0\u884c\u8fc7\u7a0b\u4e2d\uff0c\u76f8\u5173\u6570\u636e\u90fd\u5b58\u50a8\u5728\u5185\u5b58\u4e2d\u3002\u4e0b\u56fe\u5c55\u793a\u4e86\u4e00\u4e2a\u8ba1\u7b97\u673a\u5185\u5b58\u6761\uff0c\u5176\u4e2d\u6bcf\u4e2a\u9ed1\u8272\u65b9\u5757\u90fd\u5305\u542b\u4e00\u5757\u5185\u5b58\u7a7a\u95f4\u3002\u6211\u4eec\u53ef\u4ee5\u5c06\u5185\u5b58\u60f3\u8c61\u6210\u4e00\u4e2a\u5de8\u5927\u7684 Excel \u8868\u683c\uff0c\u5176\u4e2d\u6bcf\u4e2a\u5355\u5143\u683c\u90fd\u53ef\u4ee5\u5b58\u50a8 1 byte \u7684\u6570\u636e\uff0c\u5728\u7b97\u6cd5\u8fd0\u884c\u65f6\uff0c\u6240\u6709\u6570\u636e\u90fd\u88ab\u5b58\u50a8\u5728\u8fd9\u4e9b\u5355\u5143\u683c\u4e2d\u3002</p> <p>\u7cfb\u7edf\u901a\u8fc7\u300c\u5185\u5b58\u5730\u5740 Memory Location\u300d\u6765\u8bbf\u95ee\u76ee\u6807\u5185\u5b58\u4f4d\u7f6e\u7684\u6570\u636e\u3002\u8ba1\u7b97\u673a\u6839\u636e\u7279\u5b9a\u89c4\u5219\u4e3a\u8868\u683c\u4e2d\u7684\u6bcf\u4e2a\u5355\u5143\u683c\u5206\u914d\u7f16\u53f7\uff0c\u786e\u4fdd\u6bcf\u4e2a\u5185\u5b58\u7a7a\u95f4\u90fd\u6709\u552f\u4e00\u7684\u5185\u5b58\u5730\u5740\u3002\u6709\u4e86\u8fd9\u4e9b\u5730\u5740\uff0c\u7a0b\u5e8f\u4fbf\u53ef\u4ee5\u8bbf\u95ee\u5185\u5b58\u4e2d\u7684\u6570\u636e\u3002</p> <p></p> <p> Fig. \u5185\u5b58\u6761\u3001\u5185\u5b58\u7a7a\u95f4\u3001\u5185\u5b58\u5730\u5740 </p> <p>\u5185\u5b58\u662f\u6240\u6709\u7a0b\u5e8f\u7684\u5171\u4eab\u8d44\u6e90\uff0c\u5f53\u5185\u5b58\u88ab\u67d0\u4e2a\u7a0b\u5e8f\u5360\u7528\u65f6\uff0c\u5176\u4ed6\u7a0b\u5e8f\u65e0\u6cd5\u540c\u65f6\u4f7f\u7528\u3002\u56e0\u6b64\uff0c\u5728\u6570\u636e\u7ed3\u6784\u4e0e\u7b97\u6cd5\u7684\u8bbe\u8ba1\u4e2d\uff0c\u5185\u5b58\u8d44\u6e90\u662f\u4e00\u4e2a\u91cd\u8981\u7684\u8003\u8651\u56e0\u7d20\u3002\u4f8b\u5982\uff0c\u7b97\u6cd5\u6240\u5360\u7528\u7684\u5185\u5b58\u5cf0\u503c\u4e0d\u5e94\u8d85\u8fc7\u7cfb\u7edf\u5269\u4f59\u7a7a\u95f2\u5185\u5b58\uff1b\u5982\u679c\u8fd0\u884c\u7684\u7a0b\u5e8f\u5f88\u591a\u5e76\u4e14\u7f3a\u5c11\u5927\u91cf\u8fde\u7eed\u7684\u5185\u5b58\u7a7a\u95f4\uff0c\u90a3\u4e48\u6240\u9009\u7528\u7684\u6570\u636e\u7ed3\u6784\u5fc5\u987b\u80fd\u591f\u5b58\u50a8\u5728\u79bb\u6563\u7684\u5185\u5b58\u7a7a\u95f4\u5185\u3002</p> <p>\u300c\u7269\u7406\u7ed3\u6784\u300d\u53cd\u6620\u4e86\u6570\u636e\u5728\u8ba1\u7b97\u673a\u5185\u5b58\u4e2d\u7684\u5b58\u50a8\u65b9\u5f0f\uff0c\u53ef\u5206\u4e3a\u6570\u7ec4\u7684\u8fde\u7eed\u7a7a\u95f4\u5b58\u50a8\u548c\u94fe\u8868\u7684\u79bb\u6563\u7a7a\u95f4\u5b58\u50a8\u3002\u7269\u7406\u7ed3\u6784\u4ece\u5e95\u5c42\u51b3\u5b9a\u4e86\u6570\u636e\u7684\u8bbf\u95ee\u3001\u66f4\u65b0\u3001\u589e\u5220\u7b49\u64cd\u4f5c\u65b9\u6cd5\uff0c\u540c\u65f6\u5728\u65f6\u95f4\u6548\u7387\u548c\u7a7a\u95f4\u6548\u7387\u65b9\u9762\u5448\u73b0\u51fa\u4e92\u8865\u7684\u7279\u70b9\u3002</p> <p></p> <p> Fig. \u8fde\u7eed\u7a7a\u95f4\u5b58\u50a8\u4e0e\u79bb\u6563\u7a7a\u95f4\u5b58\u50a8 </p> <p>\u6240\u6709\u6570\u636e\u7ed3\u6784\u90fd\u662f\u57fa\u4e8e\u6570\u7ec4\u3001\u94fe\u8868\u6216\u4e8c\u8005\u7684\u7ec4\u5408\u5b9e\u73b0\u7684\u3002\u4f8b\u5982\uff0c\u6808\u548c\u961f\u5217\u65e2\u53ef\u4ee5\u4f7f\u7528\u6570\u7ec4\u5b9e\u73b0\uff0c\u4e5f\u53ef\u4ee5\u4f7f\u7528\u94fe\u8868\u5b9e\u73b0\uff1b\u800c\u54c8\u5e0c\u8868\u7684\u5b9e\u73b0\u53ef\u80fd\u540c\u65f6\u5305\u542b\u6570\u7ec4\u548c\u94fe\u8868\u3002</p> <ul> <li>\u57fa\u4e8e\u6570\u7ec4\u53ef\u5b9e\u73b0\uff1a\u6808\u3001\u961f\u5217\u3001\u54c8\u5e0c\u8868\u3001\u6811\u3001\u5806\u3001\u56fe\u3001\u77e9\u9635\u3001\u5f20\u91cf\uff08\u7ef4\u5ea6 \\(\\geq 3\\) \u7684\u6570\u7ec4\uff09\u7b49\uff1b</li> <li>\u57fa\u4e8e\u94fe\u8868\u53ef\u5b9e\u73b0\uff1a\u6808\u3001\u961f\u5217\u3001\u54c8\u5e0c\u8868\u3001\u6811\u3001\u5806\u3001\u56fe\u7b49\uff1b</li> </ul> <p>\u57fa\u4e8e\u6570\u7ec4\u5b9e\u73b0\u7684\u6570\u636e\u7ed3\u6784\u4e5f\u88ab\u79f0\u4e3a\u300c\u9759\u6001\u6570\u636e\u7ed3\u6784\u300d\uff0c\u8fd9\u610f\u5473\u7740\u6b64\u7c7b\u6570\u636e\u7ed3\u6784\u5728\u521d\u59cb\u5316\u540e\u957f\u5ea6\u4e0d\u53ef\u53d8\u3002\u76f8\u5bf9\u5e94\u5730\uff0c\u57fa\u4e8e\u94fe\u8868\u5b9e\u73b0\u7684\u6570\u636e\u7ed3\u6784\u88ab\u79f0\u4e3a\u300c\u52a8\u6001\u6570\u636e\u7ed3\u6784\u300d\uff0c\u8fd9\u7c7b\u6570\u636e\u7ed3\u6784\u5728\u521d\u59cb\u5316\u540e\uff0c\u4ecd\u53ef\u4ee5\u5728\u7a0b\u5e8f\u8fd0\u884c\u8fc7\u7a0b\u4e2d\u5bf9\u5176\u957f\u5ea6\u8fdb\u884c\u8c03\u6574\u3002</p> <p>Tip</p> <p>\u5982\u82e5\u611f\u89c9\u7406\u89e3\u7269\u7406\u7ed3\u6784\u6709\u56f0\u96be\uff0c\u5efa\u8bae\u5148\u9605\u8bfb\u4e0b\u4e00\u7ae0\u201c\u6570\u7ec4\u4e0e\u94fe\u8868\u201d\uff0c\u7136\u540e\u518d\u56de\u5934\u7406\u89e3\u7269\u7406\u7ed3\u6784\u7684\u542b\u4e49\u3002\u6570\u7ec4\u4e0e\u94fe\u8868\u662f\u5176\u4ed6\u6240\u6709\u6570\u636e\u7ed3\u6784\u7684\u57fa\u77f3\uff0c\u5efa\u8bae\u4f60\u6295\u5165\u66f4\u591a\u65f6\u95f4\u6df1\u5165\u4e86\u89e3\u8fd9\u4e24\u79cd\u57fa\u672c\u6570\u636e\u7ed3\u6784\u3002</p>"},{"location":"chapter_data_structure/number_encoding/","title":"3.3. \u00a0 \u6570\u5b57\u7f16\u7801 *","text":"<p>Note</p> <p>\u5728\u672c\u4e66\u4e2d\uff0c\u6807\u9898\u5e26\u6709\u7684 * \u7b26\u53f7\u7684\u662f\u9009\u8bfb\u7ae0\u8282\u3002\u5982\u679c\u4f60\u65f6\u95f4\u6709\u9650\u6216\u611f\u5230\u7406\u89e3\u56f0\u96be\uff0c\u5efa\u8bae\u5148\u8df3\u8fc7\uff0c\u7b49\u5b66\u5b8c\u5fc5\u8bfb\u7ae0\u8282\u540e\u518d\u5355\u72ec\u653b\u514b\u3002</p>"},{"location":"chapter_data_structure/number_encoding/#331","title":"3.3.1. \u00a0 \u539f\u7801\u3001\u53cd\u7801\u548c\u8865\u7801","text":"<p>\u4ece\u4e0a\u4e00\u8282\u7684\u8868\u683c\u4e2d\u6211\u4eec\u53d1\u73b0\uff0c\u6240\u6709\u6574\u6570\u7c7b\u578b\u80fd\u591f\u8868\u793a\u7684\u8d1f\u6570\u90fd\u6bd4\u6b63\u6570\u591a\u4e00\u4e2a\u3002\u4f8b\u5982\uff0c<code>byte</code> \u7684\u53d6\u503c\u8303\u56f4\u662f \\([-128, 127]\\) \u3002\u8fd9\u4e2a\u73b0\u8c61\u6bd4\u8f83\u53cd\u76f4\u89c9\uff0c\u5b83\u7684\u5185\u5728\u539f\u56e0\u6d89\u53ca\u5230\u539f\u7801\u3001\u53cd\u7801\u3001\u8865\u7801\u7684\u76f8\u5173\u77e5\u8bc6\u3002\u5728\u5c55\u5f00\u5206\u6790\u4e4b\u524d\uff0c\u6211\u4eec\u9996\u5148\u7ed9\u51fa\u4e09\u8005\u7684\u5b9a\u4e49\uff1a</p> <ul> <li>\u539f\u7801\uff1a\u6211\u4eec\u5c06\u6570\u5b57\u7684\u4e8c\u8fdb\u5236\u8868\u793a\u7684\u6700\u9ad8\u4f4d\u89c6\u4e3a\u7b26\u53f7\u4f4d\uff0c\u5176\u4e2d \\(0\\) \u8868\u793a\u6b63\u6570\uff0c\\(1\\) \u8868\u793a\u8d1f\u6570\uff0c\u5176\u4f59\u4f4d\u8868\u793a\u6570\u5b57\u7684\u503c\u3002</li> <li>\u53cd\u7801\uff1a\u6b63\u6570\u7684\u53cd\u7801\u4e0e\u5176\u539f\u7801\u76f8\u540c\uff0c\u8d1f\u6570\u7684\u53cd\u7801\u662f\u5bf9\u5176\u539f\u7801\u9664\u7b26\u53f7\u4f4d\u5916\u7684\u6240\u6709\u4f4d\u53d6\u53cd\u3002</li> <li>\u8865\u7801\uff1a\u6b63\u6570\u7684\u8865\u7801\u4e0e\u5176\u539f\u7801\u76f8\u540c\uff0c\u8d1f\u6570\u7684\u8865\u7801\u662f\u5728\u5176\u53cd\u7801\u7684\u57fa\u7840\u4e0a\u52a0 \\(1\\) \u3002</li> </ul> <p></p> <p> Fig. \u539f\u7801\u3001\u53cd\u7801\u4e0e\u8865\u7801\u4e4b\u95f4\u7684\u76f8\u4e92\u8f6c\u6362 </p> <p>\u663e\u7136\uff0c\u300c\u539f\u7801\u300d\u6700\u4e3a\u76f4\u89c2\uff0c\u7136\u800c\u6570\u5b57\u5374\u662f\u4ee5\u300c\u8865\u7801\u300d\u7684\u5f62\u5f0f\u5b58\u50a8\u5728\u8ba1\u7b97\u673a\u4e2d\u7684\u3002\u8fd9\u662f\u56e0\u4e3a\u539f\u7801\u5b58\u5728\u4e00\u4e9b\u5c40\u9650\u6027\u3002</p> <p>\u4e00\u65b9\u9762\uff0c\u8d1f\u6570\u7684\u539f\u7801\u4e0d\u80fd\u76f4\u63a5\u7528\u4e8e\u8fd0\u7b97\u3002\u4f8b\u5982\uff0c\u6211\u4eec\u5728\u539f\u7801\u4e0b\u8ba1\u7b97 \\(1 + (-2)\\) \uff0c\u5f97\u5230\u7684\u7ed3\u679c\u662f \\(-3\\) \uff0c\u8fd9\u663e\u7136\u662f\u4e0d\u5bf9\u7684\u3002</p> \\[ \\begin{aligned} &amp; 1 + (-2) \\newline &amp; = 0000 \\space 0001 + 1000 \\space 0010 \\newline &amp; = 1000 \\space 0011 \\newline &amp; = -3 \\end{aligned} \\] <p>\u4e3a\u4e86\u89e3\u51b3\u6b64\u95ee\u9898\uff0c\u8ba1\u7b97\u673a\u5f15\u5165\u4e86\u300c\u53cd\u7801\u300d\u3002\u4f8b\u5982\uff0c\u6211\u4eec\u5148\u5c06\u539f\u7801\u8f6c\u6362\u4e3a\u53cd\u7801\uff0c\u5e76\u5728\u53cd\u7801\u4e0b\u8ba1\u7b97 \\(1 + (-2)\\) \uff0c\u5e76\u5c06\u7ed3\u679c\u4ece\u53cd\u7801\u8f6c\u5316\u56de\u539f\u7801\uff0c\u5219\u53ef\u5f97\u5230\u6b63\u786e\u7ed3\u679c \\(-1\\) \u3002</p> \\[ \\begin{aligned} &amp; 1 + (-2) \\newline &amp; = 0000 \\space 0001 \\space \\text{(\u539f\u7801)} + 1000 \\space 0010 \\space \\text{(\u539f\u7801)} \\newline &amp; = 0000 \\space 0001 \\space \\text{(\u53cd\u7801)} + 1111  \\space 1101 \\space \\text{(\u53cd\u7801)} \\newline &amp; = 1111 \\space 1110 \\space \\text{(\u53cd\u7801)} \\newline &amp; = 1000 \\space 0001 \\space \\text{(\u539f\u7801)} \\newline &amp; = -1 \\end{aligned} \\] <p>\u53e6\u4e00\u65b9\u9762\uff0c\u6570\u5b57\u96f6\u7684\u539f\u7801\u6709 \\(+0\\) \u548c \\(-0\\) \u4e24\u79cd\u8868\u793a\u65b9\u5f0f\u3002\u8fd9\u610f\u5473\u7740\u6570\u5b57\u96f6\u5bf9\u5e94\u7740\u4e24\u4e2a\u4e0d\u540c\u7684\u4e8c\u8fdb\u5236\u7f16\u7801\uff0c\u800c\u8fd9\u53ef\u80fd\u4f1a\u5e26\u6765\u6b67\u4e49\u95ee\u9898\u3002\u4f8b\u5982\uff0c\u5728\u6761\u4ef6\u5224\u65ad\u4e2d\uff0c\u5982\u679c\u6ca1\u6709\u533a\u5206\u6b63\u96f6\u548c\u8d1f\u96f6\uff0c\u53ef\u80fd\u4f1a\u5bfc\u81f4\u9519\u8bef\u7684\u5224\u65ad\u7ed3\u679c\u3002\u5982\u679c\u6211\u4eec\u60f3\u8981\u5904\u7406\u6b63\u96f6\u548c\u8d1f\u96f6\u6b67\u4e49\uff0c\u5219\u9700\u8981\u5f15\u5165\u989d\u5916\u7684\u5224\u65ad\u64cd\u4f5c\uff0c\u5176\u53ef\u80fd\u4f1a\u964d\u4f4e\u8ba1\u7b97\u673a\u7684\u8fd0\u7b97\u6548\u7387\u3002</p> \\[ \\begin{aligned} +0 &amp; = 0000 \\space 0000 \\newline -0 &amp; = 1000 \\space 0000 \\end{aligned} \\] <p>\u4e0e\u539f\u7801\u4e00\u6837\uff0c\u53cd\u7801\u4e5f\u5b58\u5728\u6b63\u8d1f\u96f6\u6b67\u4e49\u95ee\u9898\u3002\u4e3a\u6b64\uff0c\u8ba1\u7b97\u673a\u8fdb\u4e00\u6b65\u5f15\u5165\u4e86\u300c\u8865\u7801\u300d\u3002\u90a3\u4e48\uff0c\u8865\u7801\u6709\u4ec0\u4e48\u4f5c\u7528\u5462\uff1f\u6211\u4eec\u5148\u6765\u5206\u6790\u4e00\u4e0b\u8d1f\u96f6\u7684\u8865\u7801\u7684\u8ba1\u7b97\u8fc7\u7a0b\uff1a</p> \\[ \\begin{aligned} -0 = \\space &amp; 1000 \\space 0000 \\space \\text{(\u539f\u7801)} \\newline = \\space &amp; 1111 \\space 1111 \\space \\text{(\u53cd\u7801)} \\newline = 1 \\space &amp; 0000 \\space 0000 \\space \\text{(\u8865\u7801)} \\newline \\end{aligned} \\] <p>\u5728\u8d1f\u96f6\u7684\u53cd\u7801\u57fa\u7840\u4e0a\u52a0 \\(1\\) \u4f1a\u4ea7\u751f\u8fdb\u4f4d\uff0c\u800c\u7531\u4e8e byte \u7684\u957f\u5ea6\u53ea\u6709 8 \u4f4d\uff0c\u56e0\u6b64\u6ea2\u51fa\u5230\u7b2c 9 \u4f4d\u7684 \\(1\\) \u4f1a\u88ab\u820d\u5f03\u3002\u4ece\u800c\u5f97\u5230\u8d1f\u96f6\u7684\u8865\u7801\u4e3a \\(0000 \\space 0000\\) \uff0c\u4e0e\u6b63\u96f6\u7684\u8865\u7801\u76f8\u540c\u3002\u8fd9\u610f\u5473\u7740\u5728\u8865\u7801\u8868\u793a\u4e2d\u53ea\u5b58\u5728\u4e00\u4e2a\u96f6\uff0c\u4ece\u800c\u89e3\u51b3\u4e86\u6b63\u8d1f\u96f6\u6b67\u4e49\u95ee\u9898\u3002</p> <p>\u8fd8\u5269\u4f59\u6700\u540e\u4e00\u4e2a\u7591\u60d1\uff1abyte \u7684\u53d6\u503c\u8303\u56f4\u662f \\([-128, 127]\\) \uff0c\u591a\u51fa\u6765\u7684\u4e00\u4e2a\u8d1f\u6570 \\(-128\\) \u662f\u5982\u4f55\u5f97\u5230\u7684\u5462\uff1f\u6211\u4eec\u6ce8\u610f\u5230\uff0c\u533a\u95f4 \\([-127, +127]\\) \u5185\u7684\u6240\u6709\u6574\u6570\u90fd\u6709\u5bf9\u5e94\u7684\u539f\u7801\u3001\u53cd\u7801\u548c\u8865\u7801\uff0c\u5e76\u4e14\u539f\u7801\u548c\u8865\u7801\u4e4b\u95f4\u662f\u53ef\u4ee5\u4e92\u76f8\u8f6c\u6362\u7684\u3002</p> <p>\u7136\u800c\uff0c\u8865\u7801 \\(1000 \\space 0000\\) \u662f\u4e00\u4e2a\u4f8b\u5916\uff0c\u5b83\u5e76\u6ca1\u6709\u5bf9\u5e94\u7684\u539f\u7801\u3002\u6839\u636e\u8f6c\u6362\u65b9\u6cd5\uff0c\u6211\u4eec\u5f97\u5230\u8be5\u8865\u7801\u7684\u539f\u7801\u4e3a \\(0000 \\space 0000\\) \u3002\u8fd9\u663e\u7136\u662f\u77db\u76fe\u7684\uff0c\u56e0\u4e3a\u8be5\u539f\u7801\u8868\u793a\u6570\u5b57 \\(0\\) \uff0c\u5b83\u7684\u8865\u7801\u5e94\u8be5\u662f\u81ea\u8eab\u3002\u8ba1\u7b97\u673a\u89c4\u5b9a\u8fd9\u4e2a\u7279\u6b8a\u7684\u8865\u7801 \\(1000 \\space 0000\\) \u4ee3\u8868 \\(-128\\) \u3002\u5b9e\u9645\u4e0a\uff0c\\((-1) + (-127)\\) \u5728\u8865\u7801\u4e0b\u7684\u8ba1\u7b97\u7ed3\u679c\u5c31\u662f \\(-128\\) \u3002</p> \\[ \\begin{aligned} &amp; (-127) + (-1) \\newline &amp; = 1111 \\space 1111 \\space \\text{(\u539f\u7801)} + 1000 \\space 0001 \\space \\text{(\u539f\u7801)} \\newline &amp; = 1000 \\space 0000 \\space \\text{(\u53cd\u7801)} + 1111  \\space 1110 \\space \\text{(\u53cd\u7801)} \\newline &amp; = 1000 \\space 0001 \\space \\text{(\u8865\u7801)} + 1111  \\space 1111 \\space \\text{(\u8865\u7801)} \\newline &amp; = 1000 \\space 0000 \\space \\text{(\u8865\u7801)} \\newline &amp; = -128 \\end{aligned} \\] <p>\u4f60\u53ef\u80fd\u5df2\u7ecf\u53d1\u73b0\uff0c\u4e0a\u8ff0\u7684\u6240\u6709\u8ba1\u7b97\u90fd\u662f\u52a0\u6cd5\u8fd0\u7b97\u3002\u8fd9\u6697\u793a\u7740\u4e00\u4e2a\u91cd\u8981\u4e8b\u5b9e\uff1a\u8ba1\u7b97\u673a\u5185\u90e8\u7684\u786c\u4ef6\u7535\u8def\u4e3b\u8981\u662f\u57fa\u4e8e\u52a0\u6cd5\u8fd0\u7b97\u8bbe\u8ba1\u7684\u3002\u8fd9\u662f\u56e0\u4e3a\u52a0\u6cd5\u8fd0\u7b97\u76f8\u5bf9\u4e8e\u5176\u4ed6\u8fd0\u7b97\uff08\u6bd4\u5982\u4e58\u6cd5\u3001\u9664\u6cd5\u548c\u51cf\u6cd5\uff09\u6765\u8bf4\uff0c\u786c\u4ef6\u5b9e\u73b0\u8d77\u6765\u66f4\u7b80\u5355\uff0c\u66f4\u5bb9\u6613\u8fdb\u884c\u5e76\u884c\u5316\u5904\u7406\uff0c\u4ece\u800c\u63d0\u9ad8\u8fd0\u7b97\u901f\u5ea6\u3002</p> <p>\u7136\u800c\uff0c\u8fd9\u5e76\u4e0d\u610f\u5473\u7740\u8ba1\u7b97\u673a\u53ea\u80fd\u505a\u52a0\u6cd5\u3002\u901a\u8fc7\u5c06\u52a0\u6cd5\u4e0e\u4e00\u4e9b\u57fa\u672c\u903b\u8f91\u8fd0\u7b97\u7ed3\u5408\uff0c\u8ba1\u7b97\u673a\u80fd\u591f\u5b9e\u73b0\u5404\u79cd\u5176\u4ed6\u7684\u6570\u5b66\u8fd0\u7b97\u3002\u4f8b\u5982\uff0c\u8ba1\u7b97\u51cf\u6cd5 \\(a - b\\) \u53ef\u4ee5\u8f6c\u6362\u4e3a\u8ba1\u7b97\u52a0\u6cd5 \\(a + (-b)\\) \uff1b\u8ba1\u7b97\u4e58\u6cd5\u548c\u9664\u6cd5\u53ef\u4ee5\u8f6c\u6362\u4e3a\u8ba1\u7b97\u591a\u6b21\u52a0\u6cd5\u6216\u51cf\u6cd5\u3002</p> <p>\u73b0\u5728\uff0c\u6211\u4eec\u53ef\u4ee5\u603b\u7ed3\u51fa\u8ba1\u7b97\u673a\u4f7f\u7528\u8865\u7801\u7684\u539f\u56e0\uff1a\u57fa\u4e8e\u8865\u7801\u8868\u793a\uff0c\u8ba1\u7b97\u673a\u53ef\u4ee5\u7528\u540c\u6837\u7684\u7535\u8def\u548c\u64cd\u4f5c\u6765\u5904\u7406\u6b63\u6570\u548c\u8d1f\u6570\u7684\u52a0\u6cd5\uff0c\u4e0d\u9700\u8981\u8bbe\u8ba1\u7279\u6b8a\u7684\u786c\u4ef6\u7535\u8def\u6765\u5904\u7406\u51cf\u6cd5\uff0c\u5e76\u4e14\u65e0\u9700\u7279\u522b\u5904\u7406\u6b63\u8d1f\u96f6\u7684\u6b67\u4e49\u95ee\u9898\u3002\u8fd9\u5927\u5927\u7b80\u5316\u4e86\u786c\u4ef6\u8bbe\u8ba1\uff0c\u5e76\u63d0\u9ad8\u4e86\u8fd0\u7b97\u6548\u7387\u3002</p> <p>\u8865\u7801\u7684\u8bbe\u8ba1\u975e\u5e38\u7cbe\u5999\uff0c\u7531\u4e8e\u7bc7\u5e45\u5173\u7cfb\u6211\u4eec\u5148\u4ecb\u7ecd\u5230\u8fd9\u91cc\u3002\u5efa\u8bae\u6709\u5174\u8da3\u7684\u8bfb\u8005\u8fdb\u4e00\u6b65\u6df1\u5ea6\u4e86\u89e3\u3002</p>"},{"location":"chapter_data_structure/number_encoding/#332","title":"3.3.2. \u00a0 \u6d6e\u70b9\u6570\u7f16\u7801","text":"<p>\u7ec6\u5fc3\u7684\u4f60\u53ef\u80fd\u4f1a\u53d1\u73b0\uff1a<code>int</code> \u548c <code>float</code> \u957f\u5ea6\u76f8\u540c\uff0c\u90fd\u662f 4 bytes\uff0c\u4f46\u4e3a\u4ec0\u4e48 <code>float</code> \u7684\u53d6\u503c\u8303\u56f4\u8fdc\u5927\u4e8e <code>int</code> \uff1f\u8fd9\u975e\u5e38\u53cd\u76f4\u89c9\uff0c\u56e0\u4e3a\u6309\u7406\u8bf4 <code>float</code> \u9700\u8981\u8868\u793a\u5c0f\u6570\uff0c\u53d6\u503c\u8303\u56f4\u5e94\u8be5\u53d8\u5c0f\u624d\u5bf9\u3002</p> <p>\u5b9e\u9645\u4e0a\uff0c\u8fd9\u662f\u56e0\u4e3a\u6d6e\u70b9\u6570 <code>float</code> \u91c7\u7528\u4e86\u4e0d\u540c\u7684\u8868\u793a\u65b9\u5f0f\u3002\u6839\u636e IEEE 754 \u6807\u51c6\uff0c32-bit \u957f\u5ea6\u7684 <code>float</code> \u7531\u4ee5\u4e0b\u90e8\u5206\u6784\u6210\uff1a</p> <ul> <li>\u7b26\u53f7\u4f4d \\(\\mathrm{S}\\) \uff1a\u5360 1 bit \uff1b</li> <li>\u6307\u6570\u4f4d \\(\\mathrm{E}\\) \uff1a\u5360 8 bits \uff1b</li> <li>\u5206\u6570\u4f4d \\(\\mathrm{N}\\) \uff1a\u5360 24 bits \uff0c\u5176\u4e2d 23 \u4f4d\u663e\u5f0f\u5b58\u50a8\uff1b</li> </ul> <p>\u8bbe 32-bit \u4e8c\u8fdb\u5236\u6570\u7684\u7b2c \\(i\\) \u4f4d\u4e3a \\(b_i\\) \uff0c\u5219 <code>float</code> \u503c\u7684\u8ba1\u7b97\u65b9\u6cd5\u5b9a\u4e49\u4e3a\uff1a</p> \\[ \\text { val } = (-1)^{b_{31}} \\times 2^{\\left(b_{30} b_{29} \\ldots b_{23}\\right)_2-127} \\times\\left(1 . b_{22} b_{21} \\ldots b_0\\right)_2 \\] <p>\u8f6c\u5316\u5230\u5341\u8fdb\u5236\u4e0b\u7684\u8ba1\u7b97\u516c\u5f0f\u4e3a</p> \\[ \\text { val }=(-1)^{\\mathrm{S}} \\times 2^{\\mathrm{E} -127} \\times (1 + \\mathrm{N}) \\] <p>\u5176\u4e2d\u5404\u9879\u7684\u53d6\u503c\u8303\u56f4\u4e3a</p> \\[ \\begin{aligned} \\mathrm{S} \\in &amp; \\{ 0, 1\\} , \\quad \\mathrm{E} \\in \\{ 1, 2, \\dots, 254 \\} \\newline (1 + \\mathrm{N}) = &amp; (1 + \\sum_{i=1}^{23} b_{23-i} 2^{-i}) \\subset [1, 2 - 2^{-23}] \\end{aligned} \\] <p></p> <p> Fig. IEEE 754 \u6807\u51c6\u4e0b\u7684 float \u8868\u793a\u65b9\u5f0f </p> <p>\u4ee5\u4e0a\u56fe\u4e3a\u4f8b\uff0c\\(\\mathrm{S} = 0\\) \uff0c \\(\\mathrm{E} = 124\\) \uff0c\\(\\mathrm{N} = 2^{-2} + 2^{-3} = 0.375\\) \uff0c\u6613\u5f97</p> \\[ \\text { val } = (-1)^0 \\times 2^{124 - 127} \\times (1 + 0.375) = 0.171875 \\] <p>\u73b0\u5728\u6211\u4eec\u53ef\u4ee5\u56de\u7b54\u6700\u521d\u7684\u95ee\u9898\uff1a<code>float</code> \u7684\u8868\u793a\u65b9\u5f0f\u5305\u542b\u6307\u6570\u4f4d\uff0c\u5bfc\u81f4\u5176\u53d6\u503c\u8303\u56f4\u8fdc\u5927\u4e8e <code>int</code> \u3002\u6839\u636e\u4ee5\u4e0a\u8ba1\u7b97\uff0c<code>float</code> \u53ef\u8868\u793a\u7684\u6700\u5927\u6b63\u6570\u4e3a \\(2^{254 - 127} \\times (2 - 2^{-23}) \\approx 3.4 \\times 10^{38}\\) \uff0c\u5207\u6362\u7b26\u53f7\u4f4d\u4fbf\u53ef\u5f97\u5230\u6700\u5c0f\u8d1f\u6570\u3002</p> <p>\u5c3d\u7ba1\u6d6e\u70b9\u6570 <code>float</code> \u6269\u5c55\u4e86\u53d6\u503c\u8303\u56f4\uff0c\u4f46\u5176\u526f\u4f5c\u7528\u662f\u727a\u7272\u4e86\u7cbe\u5ea6\u3002\u6574\u6570\u7c7b\u578b <code>int</code> \u5c06\u5168\u90e8 32 \u4f4d\u7528\u4e8e\u8868\u793a\u6570\u5b57\uff0c\u6570\u5b57\u662f\u5747\u5300\u5206\u5e03\u7684\uff1b\u800c\u7531\u4e8e\u6307\u6570\u4f4d\u7684\u5b58\u5728\uff0c\u6d6e\u70b9\u6570 <code>float</code> \u7684\u6570\u503c\u8d8a\u5927\uff0c\u76f8\u90bb\u4e24\u4e2a\u6570\u5b57\u4e4b\u95f4\u7684\u5dee\u503c\u5c31\u4f1a\u8d8b\u5411\u8d8a\u5927\u3002</p> <p>\u8fdb\u4e00\u6b65\u5730\uff0c\u6307\u6570\u4f4d \\(E = 0\\) \u548c \\(E = 255\\) \u5177\u6709\u7279\u6b8a\u542b\u4e49\uff0c\u7528\u4e8e\u8868\u793a\u96f6\u3001\u65e0\u7a77\u5927\u3001\\(\\mathrm{NaN}\\) \u7b49\u3002</p> \u6307\u6570\u4f4d E \u5206\u6570\u4f4d \\(\\mathrm{N} = 0\\) \u5206\u6570\u4f4d \\(\\mathrm{N} \\ne 0\\) \u8ba1\u7b97\u516c\u5f0f \\(0\\) \\(\\pm 0\\) \u6b21\u6b63\u89c4\u6570 \\((-1)^{\\mathrm{S}} \\times 2^{-126} \\times (0.\\mathrm{N})\\) \\(1, 2, \\dots, 254\\) \u6b63\u89c4\u6570 \u6b63\u89c4\u6570 \\((-1)^{\\mathrm{S}} \\times 2^{(\\mathrm{E} -127)} \\times (1.\\mathrm{N})\\) \\(255\\) \\(\\pm \\infty\\) \\(\\mathrm{NaN}\\) <p>\u7279\u522b\u5730\uff0c\u6b21\u6b63\u89c4\u6570\u663e\u8457\u63d0\u5347\u4e86\u6d6e\u70b9\u6570\u7684\u7cbe\u5ea6\uff0c\u8fd9\u662f\u56e0\u4e3a\uff1a</p> <ul> <li>\u6700\u5c0f\u6b63\u6b63\u89c4\u6570\u4e3a \\(2^{-126} \\approx 1.18 \\times 10^{-38}\\) \uff1b</li> <li>\u6700\u5c0f\u6b63\u6b21\u6b63\u89c4\u6570\u4e3a \\(2^{-126} \\times 2^{-23} \\approx 1.4 \\times 10^{-45}\\) \uff1b</li> </ul> <p>\u53cc\u7cbe\u5ea6 <code>double</code> \u4e5f\u91c7\u7528\u7c7b\u4f3c <code>float</code> \u7684\u8868\u793a\u65b9\u6cd5\uff0c\u6b64\u5904\u4e0d\u518d\u8be6\u8ff0\u3002</p>"},{"location":"chapter_data_structure/summary/","title":"3.5. \u00a0 \u5c0f\u7ed3","text":"<p>\u6570\u636e\u7ed3\u6784\u5206\u7c7b</p> <ul> <li>\u6570\u636e\u7ed3\u6784\u53ef\u4ee5\u4ece\u903b\u8f91\u7ed3\u6784\u548c\u7269\u7406\u7ed3\u6784\u4e24\u4e2a\u89d2\u5ea6\u8fdb\u884c\u5206\u7c7b\u3002\u903b\u8f91\u7ed3\u6784\u63cf\u8ff0\u4e86\u6570\u636e\u5143\u7d20\u4e4b\u95f4\u7684\u903b\u8f91\u5173\u7cfb\uff0c\u800c\u7269\u7406\u7ed3\u6784\u63cf\u8ff0\u4e86\u6570\u636e\u5728\u8ba1\u7b97\u673a\u5185\u5b58\u4e2d\u7684\u5b58\u50a8\u65b9\u5f0f\u3002</li> <li>\u5e38\u89c1\u7684\u903b\u8f91\u7ed3\u6784\u5305\u62ec\u7ebf\u6027\u3001\u6811\u72b6\u548c\u7f51\u72b6\u7b49\u3002\u901a\u5e38\u6211\u4eec\u6839\u636e\u903b\u8f91\u7ed3\u6784\u5c06\u6570\u636e\u7ed3\u6784\u5206\u4e3a\u7ebf\u6027\uff08\u6570\u7ec4\u3001\u94fe\u8868\u3001\u6808\u3001\u961f\u5217\uff09\u548c\u975e\u7ebf\u6027\uff08\u6811\u3001\u56fe\u3001\u5806\uff09\u4e24\u79cd\u3002\u54c8\u5e0c\u8868\u7684\u5b9e\u73b0\u53ef\u80fd\u540c\u65f6\u5305\u542b\u7ebf\u6027\u548c\u975e\u7ebf\u6027\u7ed3\u6784\u3002</li> <li>\u5f53\u7a0b\u5e8f\u8fd0\u884c\u65f6\uff0c\u6570\u636e\u88ab\u5b58\u50a8\u5728\u8ba1\u7b97\u673a\u5185\u5b58\u4e2d\u3002\u6bcf\u4e2a\u5185\u5b58\u7a7a\u95f4\u90fd\u62e5\u6709\u5bf9\u5e94\u7684\u5185\u5b58\u5730\u5740\uff0c\u7a0b\u5e8f\u901a\u8fc7\u8fd9\u4e9b\u5185\u5b58\u5730\u5740\u8bbf\u95ee\u6570\u636e\u3002</li> <li>\u7269\u7406\u7ed3\u6784\u4e3b\u8981\u5206\u4e3a\u8fde\u7eed\u7a7a\u95f4\u5b58\u50a8\uff08\u6570\u7ec4\uff09\u548c\u79bb\u6563\u7a7a\u95f4\u5b58\u50a8\uff08\u94fe\u8868\uff09\u3002\u6240\u6709\u6570\u636e\u7ed3\u6784\u90fd\u662f\u7531\u6570\u7ec4\u3001\u94fe\u8868\u6216\u4e24\u8005\u7684\u7ec4\u5408\u5b9e\u73b0\u7684\u3002</li> </ul> <p>\u6570\u636e\u7c7b\u578b\u4e0e\u7f16\u7801</p> <ul> <li>\u8ba1\u7b97\u673a\u4e2d\u7684\u57fa\u672c\u6570\u636e\u7c7b\u578b\u5305\u62ec\u6574\u6570 byte, short, int, long \u3001\u6d6e\u70b9\u6570 float, double \u3001\u5b57\u7b26 char \u548c\u5e03\u5c14 boolean \u3002\u5b83\u4eec\u7684\u53d6\u503c\u8303\u56f4\u53d6\u51b3\u4e8e\u5360\u7528\u7a7a\u95f4\u5927\u5c0f\u548c\u8868\u793a\u65b9\u5f0f\u3002</li> <li>\u539f\u7801\u3001\u53cd\u7801\u548c\u8865\u7801\u662f\u5728\u8ba1\u7b97\u673a\u4e2d\u7f16\u7801\u6570\u5b57\u7684\u4e09\u79cd\u65b9\u6cd5\uff0c\u5b83\u4eec\u4e4b\u95f4\u662f\u53ef\u4ee5\u76f8\u4e92\u8f6c\u6362\u7684\u3002\u6574\u6570\u7684\u539f\u7801\u7684\u6700\u9ad8\u4f4d\u662f\u7b26\u53f7\u4f4d\uff0c\u5176\u4f59\u4f4d\u662f\u6570\u5b57\u7684\u503c\u3002</li> <li>\u6574\u6570\u5728\u8ba1\u7b97\u673a\u4e2d\u662f\u4ee5\u8865\u7801\u7684\u5f62\u5f0f\u5b58\u50a8\u7684\u3002\u5728\u8865\u7801\u8868\u793a\u4e0b\uff0c\u8ba1\u7b97\u673a\u53ef\u4ee5\u5bf9\u6b63\u6570\u548c\u8d1f\u6570\u7684\u52a0\u6cd5\u4e00\u89c6\u540c\u4ec1\uff0c\u4e0d\u9700\u8981\u4e3a\u51cf\u6cd5\u64cd\u4f5c\u5355\u72ec\u8bbe\u8ba1\u7279\u6b8a\u7684\u786c\u4ef6\u7535\u8def\uff0c\u5e76\u4e14\u4e0d\u5b58\u5728\u6b63\u8d1f\u96f6\u6b67\u4e49\u7684\u95ee\u9898\u3002</li> <li>\u6d6e\u70b9\u6570\u7684\u7f16\u7801\u7531 1 \u4f4d\u7b26\u53f7\u4f4d\u30018 \u4f4d\u6307\u6570\u4f4d\u548c 23 \u4f4d\u5206\u6570\u4f4d\u6784\u6210\u3002\u7531\u4e8e\u5b58\u5728\u6307\u6570\u4f4d\uff0c\u6d6e\u70b9\u6570\u7684\u53d6\u503c\u8303\u56f4\u8fdc\u5927\u4e8e\u6574\u6570\uff0c\u4ee3\u4ef7\u662f\u727a\u7272\u4e86\u7cbe\u5ea6\u3002</li> <li>ASCII \u7801\u662f\u6700\u65e9\u51fa\u73b0\u7684\u82f1\u6587\u5b57\u7b26\u96c6\uff0c\u957f\u5ea6\u4e3a 1 \u5b57\u8282\uff0c\u5171\u6536\u5f55 127 \u4e2a\u5b57\u7b26\u3002GBK \u5b57\u7b26\u96c6\u662f\u5e38\u7528\u7684\u4e2d\u6587\u5b57\u7b26\u96c6\uff0c\u5171\u6536\u5f55\u4e24\u4e07\u591a\u4e2a\u6c49\u5b57\u3002Unicode \u81f4\u529b\u4e8e\u63d0\u4f9b\u4e00\u4e2a\u5b8c\u6574\u7684\u5b57\u7b26\u96c6\u6807\u51c6\uff0c\u6536\u5f55\u4e16\u754c\u5185\u5404\u79cd\u8bed\u8a00\u7684\u5b57\u7b26\uff0c\u4ece\u800c\u89e3\u51b3\u7531\u4e8e\u5b57\u7b26\u7f16\u7801\u65b9\u6cd5\u4e0d\u4e00\u81f4\u800c\u5bfc\u81f4\u7684\u4e71\u7801\u95ee\u9898\u3002</li> <li>UTF-8 \u662f\u6700\u53d7\u6b22\u8fce\u7684 Unicode \u7f16\u7801\u65b9\u6cd5\uff0c\u901a\u7528\u6027\u975e\u5e38\u597d\u3002\u5b83\u662f\u4e00\u79cd\u53d8\u957f\u7684\u7f16\u7801\u65b9\u6cd5\uff0c\u5177\u6709\u5f88\u597d\u7684\u6269\u5c55\u6027\uff0c\u6709\u6548\u63d0\u5347\u4e86\u5b58\u50a8\u7a7a\u95f4\u7684\u4f7f\u7528\u6548\u7387\u3002UTF-16 \u548c UTF-32 \u662f\u7b49\u957f\u7684\u7f16\u7801\u65b9\u6cd5\u3002\u5728\u7f16\u7801\u4e2d\u6587\u65f6\uff0cUTF-16 \u6bd4 UTF-8 \u7684\u5360\u7528\u7a7a\u95f4\u66f4\u5c0f\u3002Java, C# \u7b49\u7f16\u7a0b\u8bed\u8a00\u9ed8\u8ba4\u4f7f\u7528 UTF-16 \u7f16\u7801\u3002</li> </ul>"},{"location":"chapter_data_structure/summary/#351-q-a","title":"3.5.1. \u00a0 Q &amp; A","text":"<p>\u4e3a\u4ec0\u4e48\u54c8\u5e0c\u8868\u540c\u65f6\u5305\u542b\u7ebf\u6027\u6570\u636e\u7ed3\u6784\u548c\u975e\u7ebf\u6027\u6570\u636e\u7ed3\u6784\uff1f</p> <p>\u54c8\u5e0c\u8868\u5e95\u5c42\u662f\u6570\u7ec4\uff0c\u800c\u4e3a\u4e86\u89e3\u51b3\u54c8\u5e0c\u51b2\u7a81\uff0c\u6211\u4eec\u53ef\u80fd\u4f1a\u4f7f\u7528\u201c\u62c9\u94fe\u6cd5\u201d\uff08\u540e\u7eed\u6563\u5217\u8868\u7ae0\u8282\u4f1a\u8bb2\uff09\u3002\u5728\u62c9\u94fe\u6cd5\u4e2d\uff0c\u6570\u7ec4\u4e2d\u6bcf\u4e2a\u5730\u5740\uff08\u6876\uff09\u6307\u5411\u4e00\u4e2a\u94fe\u8868\uff1b\u5f53\u8fd9\u4e2a\u94fe\u8868\u957f\u5ea6\u8d85\u8fc7\u4e00\u5b9a\u9608\u503c\u65f6\uff0c\u53c8\u53ef\u80fd\u88ab\u8f6c\u5316\u4e3a\u6811\uff08\u901a\u5e38\u4e3a\u7ea2\u9ed1\u6811\uff09\u3002\u56e0\u6b64\uff0c\u54c8\u5e0c\u8868\u53ef\u80fd\u540c\u65f6\u5305\u542b\u7ebf\u6027\uff08\u6570\u7ec4\u3001\u94fe\u8868\uff09\u548c\u975e\u7ebf\u6027\uff08\u6811\uff09\u6570\u636e\u7ed3\u6784\u3002</p> <p>char \u7c7b\u578b\u7684\u957f\u5ea6\u662f 1 bytes \u5417\uff1f</p> <p>\u8fd9\u4e2a\u4e0e\u7f16\u7a0b\u8bed\u8a00\u91c7\u7528\u7684\u7f16\u7801\u65b9\u6cd5\u6709\u5173\u3002\u4f8b\u5982\uff0cJava, JS, TS, C# \u90fd\u91c7\u7528 UTF-16 \u7f16\u7801\uff08\u4fdd\u5b58 Unicode \u7801\u70b9\uff09\uff0c\u56e0\u6b64 char \u7c7b\u578b\u7684\u957f\u5ea6\u4e3a 2 bytes \u3002</p>"},{"location":"chapter_graph/","title":"9. \u00a0 \u56fe","text":""},{"location":"chapter_graph/graph/","title":"9.1. \u00a0 \u56fe","text":"<p>\u300c\u56fe Graph\u300d\u662f\u4e00\u79cd\u975e\u7ebf\u6027\u6570\u636e\u7ed3\u6784\uff0c\u7531\u300c\u9876\u70b9 Vertex\u300d\u548c\u300c\u8fb9 Edge\u300d\u7ec4\u6210\u3002\u6211\u4eec\u53ef\u4ee5\u5c06\u56fe \\(G\\) \u62bd\u8c61\u5730\u8868\u793a\u4e3a\u4e00\u7ec4\u9876\u70b9 \\(V\\) \u548c\u4e00\u7ec4\u8fb9 \\(E\\) \u7684\u96c6\u5408\u3002\u4ee5\u4e0b\u793a\u4f8b\u5c55\u793a\u4e86\u4e00\u4e2a\u5305\u542b 5 \u4e2a\u9876\u70b9\u548c 7 \u6761\u8fb9\u7684\u56fe\u3002</p> \\[ \\begin{aligned} V &amp; = \\{ 1, 2, 3, 4, 5 \\} \\newline E &amp; = \\{ (1,2), (1,3), (1,5), (2,3), (2,4), (2,5), (4,5) \\} \\newline G &amp; = \\{ V, E \\} \\newline \\end{aligned} \\] <p></p> <p> Fig. \u94fe\u8868\u3001\u6811\u3001\u56fe\u4e4b\u95f4\u7684\u5173\u7cfb </p> <p>\u90a3\u4e48\uff0c\u56fe\u4e0e\u5176\u4ed6\u6570\u636e\u7ed3\u6784\u7684\u5173\u7cfb\u662f\u4ec0\u4e48\uff1f\u5982\u679c\u6211\u4eec\u628a\u300c\u9876\u70b9\u300d\u770b\u4f5c\u8282\u70b9\uff0c\u628a\u300c\u8fb9\u300d\u770b\u4f5c\u8fde\u63a5\u5404\u4e2a\u8282\u70b9\u7684\u6307\u9488\uff0c\u5219\u53ef\u5c06\u300c\u56fe\u300d\u770b\u4f5c\u662f\u4e00\u79cd\u4ece\u300c\u94fe\u8868\u300d\u62d3\u5c55\u800c\u6765\u7684\u6570\u636e\u7ed3\u6784\u3002\u76f8\u8f83\u4e8e\u7ebf\u6027\u5173\u7cfb\uff08\u94fe\u8868\uff09\u548c\u5206\u6cbb\u5173\u7cfb\uff08\u6811\uff09\uff0c\u7f51\u7edc\u5173\u7cfb\uff08\u56fe\uff09\u7684\u81ea\u7531\u5ea6\u66f4\u9ad8\uff0c\u4ece\u800c\u66f4\u4e3a\u590d\u6742\u3002</p>"},{"location":"chapter_graph/graph/#911","title":"9.1.1. \u00a0 \u56fe\u5e38\u89c1\u7c7b\u578b","text":"<p>\u6839\u636e\u8fb9\u662f\u5426\u5177\u6709\u65b9\u5411\uff0c\u53ef\u5206\u4e3a\u300c\u65e0\u5411\u56fe Undirected Graph\u300d\u548c\u300c\u6709\u5411\u56fe Directed Graph\u300d\u3002</p> <ul> <li>\u5728\u65e0\u5411\u56fe\u4e2d\uff0c\u8fb9\u8868\u793a\u4e24\u9876\u70b9\u4e4b\u95f4\u7684\u201c\u53cc\u5411\u201d\u8fde\u63a5\u5173\u7cfb\uff0c\u4f8b\u5982\u5fae\u4fe1\u6216 QQ \u4e2d\u7684\u201c\u597d\u53cb\u5173\u7cfb\u201d\uff1b</li> <li>\u5728\u6709\u5411\u56fe\u4e2d\uff0c\u8fb9\u5177\u6709\u65b9\u5411\u6027\uff0c\u5373 \\(A \\rightarrow B\\) \u548c \\(A \\leftarrow B\\) \u4e24\u4e2a\u65b9\u5411\u7684\u8fb9\u662f\u76f8\u4e92\u72ec\u7acb\u7684\uff0c\u4f8b\u5982\u5fae\u535a\u6216\u6296\u97f3\u4e0a\u7684\u201c\u5173\u6ce8\u201d\u4e0e\u201c\u88ab\u5173\u6ce8\u201d\u5173\u7cfb\uff1b</li> </ul> <p></p> <p> Fig. \u6709\u5411\u56fe\u4e0e\u65e0\u5411\u56fe </p> <p>\u6839\u636e\u6240\u6709\u9876\u70b9\u662f\u5426\u8fde\u901a\uff0c\u53ef\u5206\u4e3a\u300c\u8fde\u901a\u56fe Connected Graph\u300d\u548c\u300c\u975e\u8fde\u901a\u56fe Disconnected Graph\u300d\u3002</p> <ul> <li>\u5bf9\u4e8e\u8fde\u901a\u56fe\uff0c\u4ece\u67d0\u4e2a\u9876\u70b9\u51fa\u53d1\uff0c\u53ef\u4ee5\u5230\u8fbe\u5176\u4f59\u4efb\u610f\u9876\u70b9\uff1b</li> <li>\u5bf9\u4e8e\u975e\u8fde\u901a\u56fe\uff0c\u4ece\u67d0\u4e2a\u9876\u70b9\u51fa\u53d1\uff0c\u81f3\u5c11\u6709\u4e00\u4e2a\u9876\u70b9\u65e0\u6cd5\u5230\u8fbe\uff1b</li> </ul> <p></p> <p> Fig. \u8fde\u901a\u56fe\u4e0e\u975e\u8fde\u901a\u56fe </p> <p>\u6211\u4eec\u8fd8\u53ef\u4ee5\u4e3a\u8fb9\u6dfb\u52a0\u201c\u6743\u91cd\u201d\u53d8\u91cf\uff0c\u4ece\u800c\u5f97\u5230\u300c\u6709\u6743\u56fe Weighted Graph\u300d\u3002\u4f8b\u5982\uff0c\u5728\u738b\u8005\u8363\u8000\u7b49\u624b\u6e38\u4e2d\uff0c\u7cfb\u7edf\u4f1a\u6839\u636e\u5171\u540c\u6e38\u620f\u65f6\u95f4\u6765\u8ba1\u7b97\u73a9\u5bb6\u4e4b\u95f4\u7684\u201c\u4eb2\u5bc6\u5ea6\u201d\uff0c\u8fd9\u79cd\u4eb2\u5bc6\u5ea6\u7f51\u7edc\u5c31\u53ef\u4ee5\u7528\u6709\u6743\u56fe\u6765\u8868\u793a\u3002</p> <p></p> <p> Fig. \u6709\u6743\u56fe\u4e0e\u65e0\u6743\u56fe </p>"},{"location":"chapter_graph/graph/#912","title":"9.1.2. \u00a0 \u56fe\u5e38\u7528\u672f\u8bed","text":"<ul> <li>\u300c\u90bb\u63a5 Adjacency\u300d\uff1a\u5f53\u4e24\u9876\u70b9\u4e4b\u95f4\u5b58\u5728\u8fb9\u76f8\u8fde\u65f6\uff0c\u79f0\u8fd9\u4e24\u9876\u70b9\u201c\u90bb\u63a5\u201d\u3002\u5728\u4e0a\u56fe\u4e2d\uff0c\u9876\u70b9 1 \u7684\u90bb\u63a5\u9876\u70b9\u4e3a\u9876\u70b9 2\u30013\u30015\u3002</li> <li>\u300c\u8def\u5f84 Path\u300d\uff1a\u4ece\u9876\u70b9 A \u5230\u9876\u70b9 B \u7ecf\u8fc7\u7684\u8fb9\u6784\u6210\u7684\u5e8f\u5217\u88ab\u79f0\u4e3a\u4ece A \u5230 B \u7684\u201c\u8def\u5f84\u201d\u3002\u5728\u4e0a\u56fe\u4e2d\uff0c\u8fb9\u5e8f\u5217 1-5-2-4 \u662f\u9876\u70b9 1 \u5230\u9876\u70b9 4 \u7684\u4e00\u6761\u8def\u5f84\u3002</li> <li>\u300c\u5ea6 Degree\u300d\u8868\u793a\u4e00\u4e2a\u9876\u70b9\u62e5\u6709\u7684\u8fb9\u6570\u3002\u5bf9\u4e8e\u6709\u5411\u56fe\uff0c\u300c\u5165\u5ea6 In-Degree\u300d\u8868\u793a\u6709\u591a\u5c11\u6761\u8fb9\u6307\u5411\u8be5\u9876\u70b9\uff0c\u300c\u51fa\u5ea6 Out-Degree\u300d\u8868\u793a\u6709\u591a\u5c11\u6761\u8fb9\u4ece\u8be5\u9876\u70b9\u6307\u51fa\u3002</li> </ul>"},{"location":"chapter_graph/graph/#913","title":"9.1.3. \u00a0 \u56fe\u7684\u8868\u793a","text":"<p>\u56fe\u7684\u5e38\u7528\u8868\u793a\u65b9\u6cd5\u5305\u62ec\u300c\u90bb\u63a5\u77e9\u9635\u300d\u548c\u300c\u90bb\u63a5\u8868\u300d\u3002\u4ee5\u4e0b\u4f7f\u7528\u65e0\u5411\u56fe\u8fdb\u884c\u4e3e\u4f8b\u3002</p>"},{"location":"chapter_graph/graph/#_1","title":"\u90bb\u63a5\u77e9\u9635","text":"<p>\u8bbe\u56fe\u7684\u9876\u70b9\u6570\u91cf\u4e3a \\(n\\) \uff0c\u300c\u90bb\u63a5\u77e9\u9635 Adjacency Matrix\u300d\u4f7f\u7528\u4e00\u4e2a \\(n \\times n\\) \u5927\u5c0f\u7684\u77e9\u9635\u6765\u8868\u793a\u56fe\uff0c\u6bcf\u4e00\u884c\uff08\u5217\uff09\u4ee3\u8868\u4e00\u4e2a\u9876\u70b9\uff0c\u77e9\u9635\u5143\u7d20\u4ee3\u8868\u8fb9\uff0c\u7528 \\(1\\) \u6216 \\(0\\) \u8868\u793a\u4e24\u4e2a\u9876\u70b9\u4e4b\u95f4\u662f\u5426\u5b58\u5728\u8fb9\u3002</p> <p>\u5982\u4e0b\u56fe\u6240\u793a\uff0c\u8bbe\u90bb\u63a5\u77e9\u9635\u4e3a \\(M\\) \u3001\u9876\u70b9\u5217\u8868\u4e3a \\(V\\) \uff0c\u90a3\u4e48\u77e9\u9635\u5143\u7d20 \\(M[i][j] = 1\\) \u8868\u793a\u9876\u70b9 \\(V[i]\\) \u5230\u9876\u70b9 \\(V[j]\\) \u4e4b\u95f4\u5b58\u5728\u8fb9\uff0c\u53cd\u4e4b \\(M[i][j] = 0\\) \u8868\u793a\u4e24\u9876\u70b9\u4e4b\u95f4\u65e0\u8fb9\u3002</p> <p></p> <p> Fig. \u56fe\u7684\u90bb\u63a5\u77e9\u9635\u8868\u793a </p> <p>\u90bb\u63a5\u77e9\u9635\u5177\u6709\u4ee5\u4e0b\u7279\u6027\uff1a</p> <ul> <li>\u9876\u70b9\u4e0d\u80fd\u4e0e\u81ea\u8eab\u76f8\u8fde\uff0c\u56e0\u6b64\u90bb\u63a5\u77e9\u9635\u4e3b\u5bf9\u89d2\u7ebf\u5143\u7d20\u6ca1\u6709\u610f\u4e49\u3002</li> <li>\u5bf9\u4e8e\u65e0\u5411\u56fe\uff0c\u4e24\u4e2a\u65b9\u5411\u7684\u8fb9\u7b49\u4ef7\uff0c\u6b64\u65f6\u90bb\u63a5\u77e9\u9635\u5173\u4e8e\u4e3b\u5bf9\u89d2\u7ebf\u5bf9\u79f0\u3002</li> <li>\u5c06\u90bb\u63a5\u77e9\u9635\u7684\u5143\u7d20\u4ece \\(1\\) , \\(0\\) \u66ff\u6362\u4e3a\u6743\u91cd\uff0c\u5219\u53ef\u8868\u793a\u6709\u6743\u56fe\u3002</li> </ul> <p>\u4f7f\u7528\u90bb\u63a5\u77e9\u9635\u8868\u793a\u56fe\u65f6\uff0c\u6211\u4eec\u53ef\u4ee5\u76f4\u63a5\u8bbf\u95ee\u77e9\u9635\u5143\u7d20\u4ee5\u83b7\u53d6\u8fb9\uff0c\u56e0\u6b64\u589e\u5220\u67e5\u64cd\u4f5c\u7684\u6548\u7387\u5f88\u9ad8\uff0c\u65f6\u95f4\u590d\u6742\u5ea6\u5747\u4e3a \\(O(1)\\) \u3002\u7136\u800c\uff0c\u77e9\u9635\u7684\u7a7a\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(n^2)\\) \uff0c\u5185\u5b58\u5360\u7528\u8f83\u591a\u3002</p>"},{"location":"chapter_graph/graph/#_2","title":"\u90bb\u63a5\u8868","text":"<p>\u300c\u90bb\u63a5\u8868 Adjacency List\u300d\u4f7f\u7528 \\(n\\) \u4e2a\u94fe\u8868\u6765\u8868\u793a\u56fe\uff0c\u94fe\u8868\u8282\u70b9\u8868\u793a\u9876\u70b9\u3002\u7b2c \\(i\\) \u6761\u94fe\u8868\u5bf9\u5e94\u9876\u70b9 \\(i\\) \uff0c\u5176\u4e2d\u5b58\u50a8\u4e86\u8be5\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\uff08\u5373\u4e0e\u8be5\u9876\u70b9\u76f8\u8fde\u7684\u9876\u70b9\uff09\u3002</p> <p></p> <p> Fig. \u56fe\u7684\u90bb\u63a5\u8868\u8868\u793a </p> <p>\u90bb\u63a5\u8868\u4ec5\u5b58\u50a8\u5b9e\u9645\u5b58\u5728\u7684\u8fb9\uff0c\u800c\u8fb9\u7684\u603b\u6570\u901a\u5e38\u8fdc\u5c0f\u4e8e \\(n^2\\) \uff0c\u56e0\u6b64\u5b83\u66f4\u52a0\u8282\u7701\u7a7a\u95f4\u3002\u7136\u800c\uff0c\u5728\u90bb\u63a5\u8868\u4e2d\u9700\u8981\u901a\u8fc7\u904d\u5386\u94fe\u8868\u6765\u67e5\u627e\u8fb9\uff0c\u56e0\u6b64\u5176\u65f6\u95f4\u6548\u7387\u4e0d\u5982\u90bb\u63a5\u77e9\u9635\u3002</p> <p>\u89c2\u5bdf\u4e0a\u56fe\u53ef\u53d1\u73b0\uff0c\u90bb\u63a5\u8868\u7ed3\u6784\u4e0e\u54c8\u5e0c\u8868\u4e2d\u7684\u300c\u94fe\u5730\u5740\u6cd5\u300d\u975e\u5e38\u76f8\u4f3c\uff0c\u56e0\u6b64\u6211\u4eec\u4e5f\u53ef\u4ee5\u91c7\u7528\u7c7b\u4f3c\u65b9\u6cd5\u6765\u4f18\u5316\u6548\u7387\u3002\u4f8b\u5982\uff0c\u5f53\u94fe\u8868\u8f83\u957f\u65f6\uff0c\u53ef\u4ee5\u5c06\u94fe\u8868\u8f6c\u5316\u4e3a AVL \u6811\u6216\u7ea2\u9ed1\u6811\uff0c\u4ece\u800c\u5c06\u65f6\u95f4\u6548\u7387\u4ece \\(O(n)\\) \u4f18\u5316\u81f3 \\(O(\\log n)\\) \uff0c\u8fd8\u53ef\u4ee5\u901a\u8fc7\u4e2d\u5e8f\u904d\u5386\u83b7\u53d6\u6709\u5e8f\u5e8f\u5217\uff1b\u6b64\u5916\uff0c\u8fd8\u53ef\u4ee5\u5c06\u94fe\u8868\u8f6c\u6362\u4e3a\u54c8\u5e0c\u8868\uff0c\u5c06\u65f6\u95f4\u590d\u6742\u5ea6\u964d\u4f4e\u81f3 \\(O(1)\\) \u3002</p>"},{"location":"chapter_graph/graph/#914","title":"9.1.4. \u00a0 \u56fe\u5e38\u89c1\u5e94\u7528","text":"<p>\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u8bb8\u591a\u7cfb\u7edf\u90fd\u53ef\u4ee5\u7528\u56fe\u6765\u5efa\u6a21\uff0c\u76f8\u5e94\u7684\u5f85\u6c42\u89e3\u95ee\u9898\u4e5f\u53ef\u4ee5\u7ea6\u5316\u4e3a\u56fe\u8ba1\u7b97\u95ee\u9898\u3002</p> \u9876\u70b9 \u8fb9 \u56fe\u8ba1\u7b97\u95ee\u9898 \u793e\u4ea4\u7f51\u7edc \u7528\u6237 \u597d\u53cb\u5173\u7cfb \u6f5c\u5728\u597d\u53cb\u63a8\u8350 \u5730\u94c1\u7ebf\u8def \u7ad9\u70b9 \u7ad9\u70b9\u95f4\u7684\u8fde\u901a\u6027 \u6700\u77ed\u8def\u7ebf\u63a8\u8350 \u592a\u9633\u7cfb \u661f\u4f53 \u661f\u4f53\u95f4\u7684\u4e07\u6709\u5f15\u529b\u4f5c\u7528 \u884c\u661f\u8f68\u9053\u8ba1\u7b97"},{"location":"chapter_graph/graph_operations/","title":"9.2. \u00a0 \u56fe\u57fa\u7840\u64cd\u4f5c","text":"<p>\u56fe\u7684\u57fa\u7840\u64cd\u4f5c\u53ef\u5206\u4e3a\u5bf9\u300c\u8fb9\u300d\u7684\u64cd\u4f5c\u548c\u5bf9\u300c\u9876\u70b9\u300d\u7684\u64cd\u4f5c\u3002\u5728\u300c\u90bb\u63a5\u77e9\u9635\u300d\u548c\u300c\u90bb\u63a5\u8868\u300d\u4e24\u79cd\u8868\u793a\u65b9\u6cd5\u4e0b\uff0c\u5b9e\u73b0\u65b9\u5f0f\u6709\u6240\u4e0d\u540c\u3002</p>"},{"location":"chapter_graph/graph_operations/#921","title":"9.2.1. \u00a0 \u57fa\u4e8e\u90bb\u63a5\u77e9\u9635\u7684\u5b9e\u73b0","text":"<p>\u7ed9\u5b9a\u4e00\u4e2a\u9876\u70b9\u6570\u91cf\u4e3a \\(n\\) \u7684\u65e0\u5411\u56fe\uff0c\u5219\u6709\uff1a</p> <ul> <li>\u6dfb\u52a0\u6216\u5220\u9664\u8fb9\uff1a\u76f4\u63a5\u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u4fee\u6539\u6307\u5b9a\u7684\u8fb9\u5373\u53ef\uff0c\u4f7f\u7528 \\(O(1)\\) \u65f6\u95f4\u3002\u800c\u7531\u4e8e\u662f\u65e0\u5411\u56fe\uff0c\u56e0\u6b64\u9700\u8981\u540c\u65f6\u66f4\u65b0\u4e24\u4e2a\u65b9\u5411\u7684\u8fb9\u3002</li> <li>\u6dfb\u52a0\u9876\u70b9\uff1a\u5728\u90bb\u63a5\u77e9\u9635\u7684\u5c3e\u90e8\u6dfb\u52a0\u4e00\u884c\u4e00\u5217\uff0c\u5e76\u5168\u90e8\u586b \\(0\\) \u5373\u53ef\uff0c\u4f7f\u7528 \\(O(n)\\) \u65f6\u95f4\u3002</li> <li>\u5220\u9664\u9876\u70b9\uff1a\u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u5220\u9664\u4e00\u884c\u4e00\u5217\u3002\u5f53\u5220\u9664\u9996\u884c\u9996\u5217\u65f6\u8fbe\u5230\u6700\u5dee\u60c5\u51b5\uff0c\u9700\u8981\u5c06 \\((n-1)^2\\) \u4e2a\u5143\u7d20\u201c\u5411\u5de6\u4e0a\u79fb\u52a8\u201d\uff0c\u4ece\u800c\u4f7f\u7528 \\(O(n^2)\\) \u65f6\u95f4\u3002</li> <li>\u521d\u59cb\u5316\uff1a\u4f20\u5165 \\(n\\) \u4e2a\u9876\u70b9\uff0c\u521d\u59cb\u5316\u957f\u5ea6\u4e3a \\(n\\) \u7684\u9876\u70b9\u5217\u8868 <code>vertices</code> \uff0c\u4f7f\u7528 \\(O(n)\\) \u65f6\u95f4\uff1b\u521d\u59cb\u5316 \\(n \\times n\\) \u5927\u5c0f\u7684\u90bb\u63a5\u77e9\u9635 <code>adjMat</code> \uff0c\u4f7f\u7528 \\(O(n^2)\\) \u65f6\u95f4\u3002</li> </ul> \u521d\u59cb\u5316\u90bb\u63a5\u77e9\u9635\u6dfb\u52a0\u8fb9\u5220\u9664\u8fb9\u6dfb\u52a0\u9876\u70b9\u5220\u9664\u9876\u70b9 <p></p> <p></p> <p></p> <p></p> <p></p> <p>\u4ee5\u4e0b\u662f\u57fa\u4e8e\u90bb\u63a5\u77e9\u9635\u8868\u793a\u56fe\u7684\u5b9e\u73b0\u4ee3\u7801\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart graph_adjacency_matrix.java<pre><code>/* \u57fa\u4e8e\u90bb\u63a5\u77e9\u9635\u5b9e\u73b0\u7684\u65e0\u5411\u56fe\u7c7b */\nclass GraphAdjMat {\nList&lt;Integer&gt; vertices; // \u9876\u70b9\u5217\u8868\uff0c\u5143\u7d20\u4ee3\u8868\u201c\u9876\u70b9\u503c\u201d\uff0c\u7d22\u5f15\u4ee3\u8868\u201c\u9876\u70b9\u7d22\u5f15\u201d\nList&lt;List&lt;Integer&gt;&gt; adjMat; // \u90bb\u63a5\u77e9\u9635\uff0c\u884c\u5217\u7d22\u5f15\u5bf9\u5e94\u201c\u9876\u70b9\u7d22\u5f15\u201d\n/* \u6784\u9020\u65b9\u6cd5 */\npublic GraphAdjMat(int[] vertices, int[][] edges) {\nthis.vertices = new ArrayList&lt;&gt;();\nthis.adjMat = new ArrayList&lt;&gt;();\n// \u6dfb\u52a0\u9876\u70b9\nfor (int val : vertices) {\naddVertex(val);\n}\n// \u6dfb\u52a0\u8fb9\n// \u8bf7\u6ce8\u610f\uff0cedges \u5143\u7d20\u4ee3\u8868\u9876\u70b9\u7d22\u5f15\uff0c\u5373\u5bf9\u5e94 vertices \u5143\u7d20\u7d22\u5f15\nfor (int[] e : edges) {\naddEdge(e[0], e[1]);\n}\n}\n/* \u83b7\u53d6\u9876\u70b9\u6570\u91cf */\npublic int size() {\nreturn vertices.size();\n}\n/* \u6dfb\u52a0\u9876\u70b9 */\npublic void addVertex(int val) {\nint n = size();\n// \u5411\u9876\u70b9\u5217\u8868\u4e2d\u6dfb\u52a0\u65b0\u9876\u70b9\u7684\u503c\nvertices.add(val);\n// \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u6dfb\u52a0\u4e00\u884c\nList&lt;Integer&gt; newRow = new ArrayList&lt;&gt;(n);\nfor (int j = 0; j &lt; n; j++) {\nnewRow.add(0);\n}\nadjMat.add(newRow);\n// \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u6dfb\u52a0\u4e00\u5217\nfor (List&lt;Integer&gt; row : adjMat) {\nrow.add(0);\n}\n}\n/* \u5220\u9664\u9876\u70b9 */\npublic void removeVertex(int index) {\nif (index &gt;= size())\nthrow new IndexOutOfBoundsException();\n// \u5728\u9876\u70b9\u5217\u8868\u4e2d\u79fb\u9664\u7d22\u5f15 index \u7684\u9876\u70b9\nvertices.remove(index);\n// \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u5220\u9664\u7d22\u5f15 index \u7684\u884c\nadjMat.remove(index);\n// \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u5220\u9664\u7d22\u5f15 index \u7684\u5217\nfor (List&lt;Integer&gt; row : adjMat) {\nrow.remove(index);\n}\n}\n/* \u6dfb\u52a0\u8fb9 */\n// \u53c2\u6570 i, j \u5bf9\u5e94 vertices \u5143\u7d20\u7d22\u5f15\npublic void addEdge(int i, int j) {\n// \u7d22\u5f15\u8d8a\u754c\u4e0e\u76f8\u7b49\u5904\u7406\nif (i &lt; 0 || j &lt; 0 || i &gt;= size() || j &gt;= size() || i == j)\nthrow new IndexOutOfBoundsException();\n// \u5728\u65e0\u5411\u56fe\u4e2d\uff0c\u90bb\u63a5\u77e9\u9635\u6cbf\u4e3b\u5bf9\u89d2\u7ebf\u5bf9\u79f0\uff0c\u5373\u6ee1\u8db3 (i, j) == (j, i)\nadjMat.get(i).set(j, 1);\nadjMat.get(j).set(i, 1);\n}\n/* \u5220\u9664\u8fb9 */\n// \u53c2\u6570 i, j \u5bf9\u5e94 vertices \u5143\u7d20\u7d22\u5f15\npublic void removeEdge(int i, int j) {\n// \u7d22\u5f15\u8d8a\u754c\u4e0e\u76f8\u7b49\u5904\u7406\nif (i &lt; 0 || j &lt; 0 || i &gt;= size() || j &gt;= size() || i == j)\nthrow new IndexOutOfBoundsException();\nadjMat.get(i).set(j, 0);\nadjMat.get(j).set(i, 0);\n}\n/* \u6253\u5370\u90bb\u63a5\u77e9\u9635 */\npublic void print() {\nSystem.out.print(\"\u9876\u70b9\u5217\u8868 = \");\nSystem.out.println(vertices);\nSystem.out.println(\"\u90bb\u63a5\u77e9\u9635 =\");\nPrintUtil.printMatrix(adjMat);\n}\n}\n</code></pre> graph_adjacency_matrix.cpp<pre><code>/* \u57fa\u4e8e\u90bb\u63a5\u77e9\u9635\u5b9e\u73b0\u7684\u65e0\u5411\u56fe\u7c7b */\nclass GraphAdjMat {\nvector&lt;int&gt; vertices;       // \u9876\u70b9\u5217\u8868\uff0c\u5143\u7d20\u4ee3\u8868\u201c\u9876\u70b9\u503c\u201d\uff0c\u7d22\u5f15\u4ee3\u8868\u201c\u9876\u70b9\u7d22\u5f15\u201d\nvector&lt;vector&lt;int&gt;&gt; adjMat; // \u90bb\u63a5\u77e9\u9635\uff0c\u884c\u5217\u7d22\u5f15\u5bf9\u5e94\u201c\u9876\u70b9\u7d22\u5f15\u201d\npublic:\n/* \u6784\u9020\u65b9\u6cd5 */\nGraphAdjMat(const vector&lt;int&gt; &amp;vertices, const vector&lt;vector&lt;int&gt;&gt; &amp;edges) {\n// \u6dfb\u52a0\u9876\u70b9\nfor (int val : vertices) {\naddVertex(val);\n}\n// \u6dfb\u52a0\u8fb9\n// \u8bf7\u6ce8\u610f\uff0cedges \u5143\u7d20\u4ee3\u8868\u9876\u70b9\u7d22\u5f15\uff0c\u5373\u5bf9\u5e94 vertices \u5143\u7d20\u7d22\u5f15\nfor (const vector&lt;int&gt; &amp;edge : edges) {\naddEdge(edge[0], edge[1]);\n}\n}\n/* \u83b7\u53d6\u9876\u70b9\u6570\u91cf */\nint size() const {\nreturn vertices.size();\n}\n/* \u6dfb\u52a0\u9876\u70b9 */\nvoid addVertex(int val) {\nint n = size();\n// \u5411\u9876\u70b9\u5217\u8868\u4e2d\u6dfb\u52a0\u65b0\u9876\u70b9\u7684\u503c\nvertices.push_back(val);\n// \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u6dfb\u52a0\u4e00\u884c\nadjMat.emplace_back(n, 0);\n// \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u6dfb\u52a0\u4e00\u5217\nfor (vector&lt;int&gt; &amp;row : adjMat) {\nrow.push_back(0);\n}\n}\n/* \u5220\u9664\u9876\u70b9 */\nvoid removeVertex(int index) {\nif (index &gt;= size()) {\nthrow out_of_range(\"\u9876\u70b9\u4e0d\u5b58\u5728\");\n}\n// \u5728\u9876\u70b9\u5217\u8868\u4e2d\u79fb\u9664\u7d22\u5f15 index \u7684\u9876\u70b9\nvertices.erase(vertices.begin() + index);\n// \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u5220\u9664\u7d22\u5f15 index \u7684\u884c\nadjMat.erase(adjMat.begin() + index);\n// \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u5220\u9664\u7d22\u5f15 index \u7684\u5217\nfor (vector&lt;int&gt; &amp;row : adjMat) {\nrow.erase(row.begin() + index);\n}\n}\n/* \u6dfb\u52a0\u8fb9 */\n// \u53c2\u6570 i, j \u5bf9\u5e94 vertices \u5143\u7d20\u7d22\u5f15\nvoid addEdge(int i, int j) {\n// \u7d22\u5f15\u8d8a\u754c\u4e0e\u76f8\u7b49\u5904\u7406\nif (i &lt; 0 || j &lt; 0 || i &gt;= size() || j &gt;= size() || i == j) {\nthrow out_of_range(\"\u9876\u70b9\u4e0d\u5b58\u5728\");\n}\n// \u5728\u65e0\u5411\u56fe\u4e2d\uff0c\u90bb\u63a5\u77e9\u9635\u6cbf\u4e3b\u5bf9\u89d2\u7ebf\u5bf9\u79f0\uff0c\u5373\u6ee1\u8db3 (i, j) == (j, i)\nadjMat[i][j] = 1;\nadjMat[j][i] = 1;\n}\n/* \u5220\u9664\u8fb9 */\n// \u53c2\u6570 i, j \u5bf9\u5e94 vertices \u5143\u7d20\u7d22\u5f15\nvoid removeEdge(int i, int j) {\n// \u7d22\u5f15\u8d8a\u754c\u4e0e\u76f8\u7b49\u5904\u7406\nif (i &lt; 0 || j &lt; 0 || i &gt;= size() || j &gt;= size() || i == j) {\nthrow out_of_range(\"\u9876\u70b9\u4e0d\u5b58\u5728\");\n}\nadjMat[i][j] = 0;\nadjMat[j][i] = 0;\n}\n/* \u6253\u5370\u90bb\u63a5\u77e9\u9635 */\nvoid print() {\ncout &lt;&lt; \"\u9876\u70b9\u5217\u8868 = \";\nprintVector(vertices);\ncout &lt;&lt; \"\u90bb\u63a5\u77e9\u9635 =\" &lt;&lt; endl;\nprintVectorMatrix(adjMat);\n}\n};\n</code></pre> graph_adjacency_matrix.py<pre><code>class GraphAdjMat:\n\"\"\"\u57fa\u4e8e\u90bb\u63a5\u77e9\u9635\u5b9e\u73b0\u7684\u65e0\u5411\u56fe\u7c7b\"\"\"\n# \u9876\u70b9\u5217\u8868\uff0c\u5143\u7d20\u4ee3\u8868\u201c\u9876\u70b9\u503c\u201d\uff0c\u7d22\u5f15\u4ee3\u8868\u201c\u9876\u70b9\u7d22\u5f15\u201d\nvertices: list[int] = []\n# \u90bb\u63a5\u77e9\u9635\uff0c\u884c\u5217\u7d22\u5f15\u5bf9\u5e94\u201c\u9876\u70b9\u7d22\u5f15\u201d\nadj_mat: list[list[int]] = []\ndef __init__(self, vertices: list[int], edges: list[list[int]]) -&gt; None:\n\"\"\"\u6784\u9020\u65b9\u6cd5\"\"\"\nself.vertices: list[int] = []\nself.adj_mat: list[list[int]] = []\n# \u6dfb\u52a0\u9876\u70b9\nfor val in vertices:\nself.add_vertex(val)\n# \u6dfb\u52a0\u8fb9\n# \u8bf7\u6ce8\u610f\uff0cedges \u5143\u7d20\u4ee3\u8868\u9876\u70b9\u7d22\u5f15\uff0c\u5373\u5bf9\u5e94 vertices \u5143\u7d20\u7d22\u5f15\nfor e in edges:\nself.add_edge(e[0], e[1])\ndef size(self) -&gt; int:\n\"\"\"\u83b7\u53d6\u9876\u70b9\u6570\u91cf\"\"\"\nreturn len(self.vertices)\ndef add_vertex(self, val: int) -&gt; None:\n\"\"\"\u6dfb\u52a0\u9876\u70b9\"\"\"\nn = self.size()\n# \u5411\u9876\u70b9\u5217\u8868\u4e2d\u6dfb\u52a0\u65b0\u9876\u70b9\u7684\u503c\nself.vertices.append(val)\n# \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u6dfb\u52a0\u4e00\u884c\nnew_row = [0] * n\nself.adj_mat.append(new_row)\n# \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u6dfb\u52a0\u4e00\u5217\nfor row in self.adj_mat:\nrow.append(0)\ndef remove_vertex(self, index: int) -&gt; None:\n\"\"\"\u5220\u9664\u9876\u70b9\"\"\"\nif index &gt;= self.size():\nraise IndexError()\n# \u5728\u9876\u70b9\u5217\u8868\u4e2d\u79fb\u9664\u7d22\u5f15 index \u7684\u9876\u70b9\nself.vertices.pop(index)\n# \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u5220\u9664\u7d22\u5f15 index \u7684\u884c\nself.adj_mat.pop(index)\n# \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u5220\u9664\u7d22\u5f15 index \u7684\u5217\nfor row in self.adj_mat:\nrow.pop(index)\ndef add_edge(self, i: int, j: int) -&gt; None:\n\"\"\"\u6dfb\u52a0\u8fb9\"\"\"\n# \u53c2\u6570 i, j \u5bf9\u5e94 vertices \u5143\u7d20\u7d22\u5f15\n# \u7d22\u5f15\u8d8a\u754c\u4e0e\u76f8\u7b49\u5904\u7406\nif i &lt; 0 or j &lt; 0 or i &gt;= self.size() or j &gt;= self.size() or i == j:\nraise IndexError()\n# \u5728\u65e0\u5411\u56fe\u4e2d\uff0c\u90bb\u63a5\u77e9\u9635\u6cbf\u4e3b\u5bf9\u89d2\u7ebf\u5bf9\u79f0\uff0c\u5373\u6ee1\u8db3 (i, j) == (j, i)\nself.adj_mat[i][j] = 1\nself.adj_mat[j][i] = 1\ndef remove_edge(self, i: int, j: int) -&gt; None:\n\"\"\"\u5220\u9664\u8fb9\"\"\"\n# \u53c2\u6570 i, j \u5bf9\u5e94 vertices \u5143\u7d20\u7d22\u5f15\n# \u7d22\u5f15\u8d8a\u754c\u4e0e\u76f8\u7b49\u5904\u7406\nif i &lt; 0 or j &lt; 0 or i &gt;= self.size() or j &gt;= self.size() or i == j:\nraise IndexError()\nself.adj_mat[i][j] = 0\nself.adj_mat[j][i] = 0\ndef print(self) -&gt; None:\n\"\"\"\u6253\u5370\u90bb\u63a5\u77e9\u9635\"\"\"\nprint(\"\u9876\u70b9\u5217\u8868 =\", self.vertices)\nprint(\"\u90bb\u63a5\u77e9\u9635 =\")\nprint_matrix(self.adj_mat)\n</code></pre> graph_adjacency_matrix.go<pre><code>/* \u57fa\u4e8e\u90bb\u63a5\u77e9\u9635\u5b9e\u73b0\u7684\u65e0\u5411\u56fe\u7c7b */\ntype graphAdjMat struct {\n// \u9876\u70b9\u5217\u8868\uff0c\u5143\u7d20\u4ee3\u8868\u201c\u9876\u70b9\u503c\u201d\uff0c\u7d22\u5f15\u4ee3\u8868\u201c\u9876\u70b9\u7d22\u5f15\u201d\nvertices []int\n// \u90bb\u63a5\u77e9\u9635\uff0c\u884c\u5217\u7d22\u5f15\u5bf9\u5e94\u201c\u9876\u70b9\u7d22\u5f15\u201d\nadjMat [][]int\n}\n/* \u6784\u9020\u65b9\u6cd5 */\nfunc newGraphAdjMat(vertices []int, edges [][]int) *graphAdjMat {\n// \u6dfb\u52a0\u9876\u70b9\nn := len(vertices)\nadjMat := make([][]int, n)\nfor i := range adjMat {\nadjMat[i] = make([]int, n)\n}\n// \u521d\u59cb\u5316\u56fe\ng := &amp;graphAdjMat{\nvertices: vertices,\nadjMat:   adjMat,\n}\n// \u6dfb\u52a0\u8fb9\n// \u8bf7\u6ce8\u610f\uff0cedges \u5143\u7d20\u4ee3\u8868\u9876\u70b9\u7d22\u5f15\uff0c\u5373\u5bf9\u5e94 vertices \u5143\u7d20\u7d22\u5f15\nfor i := range edges {\ng.addEdge(edges[i][0], edges[i][1])\n}\nreturn g\n}\n/* \u83b7\u53d6\u9876\u70b9\u6570\u91cf */\nfunc (g *graphAdjMat) size() int {\nreturn len(g.vertices)\n}\n/* \u6dfb\u52a0\u9876\u70b9 */\nfunc (g *graphAdjMat) addVertex(val int) {\nn := g.size()\n// \u5411\u9876\u70b9\u5217\u8868\u4e2d\u6dfb\u52a0\u65b0\u9876\u70b9\u7684\u503c\ng.vertices = append(g.vertices, val)\n// \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u6dfb\u52a0\u4e00\u884c\nnewRow := make([]int, n)\ng.adjMat = append(g.adjMat, newRow)\n// \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u6dfb\u52a0\u4e00\u5217\nfor i := range g.adjMat {\ng.adjMat[i] = append(g.adjMat[i], 0)\n}\n}\n/* \u5220\u9664\u9876\u70b9 */\nfunc (g *graphAdjMat) removeVertex(index int) {\nif index &gt;= g.size() {\nreturn\n}\n// \u5728\u9876\u70b9\u5217\u8868\u4e2d\u79fb\u9664\u7d22\u5f15 index \u7684\u9876\u70b9\ng.vertices = append(g.vertices[:index], g.vertices[index+1:]...)\n// \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u5220\u9664\u7d22\u5f15 index \u7684\u884c\ng.adjMat = append(g.adjMat[:index], g.adjMat[index+1:]...)\n// \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u5220\u9664\u7d22\u5f15 index \u7684\u5217\nfor i := range g.adjMat {\ng.adjMat[i] = append(g.adjMat[i][:index], g.adjMat[i][index+1:]...)\n}\n}\n/* \u6dfb\u52a0\u8fb9 */\n// \u53c2\u6570 i, j \u5bf9\u5e94 vertices \u5143\u7d20\u7d22\u5f15\nfunc (g *graphAdjMat) addEdge(i, j int) {\n// \u7d22\u5f15\u8d8a\u754c\u4e0e\u76f8\u7b49\u5904\u7406\nif i &lt; 0 || j &lt; 0 || i &gt;= g.size() || j &gt;= g.size() || i == j {\nfmt.Errorf(\"%s\", \"Index Out Of Bounds Exception\")\n}\n// \u5728\u65e0\u5411\u56fe\u4e2d\uff0c\u90bb\u63a5\u77e9\u9635\u6cbf\u4e3b\u5bf9\u89d2\u7ebf\u5bf9\u79f0\uff0c\u5373\u6ee1\u8db3 (i, j) == (j, i)\ng.adjMat[i][j] = 1\ng.adjMat[j][i] = 1\n}\n/* \u5220\u9664\u8fb9 */\n// \u53c2\u6570 i, j \u5bf9\u5e94 vertices \u5143\u7d20\u7d22\u5f15\nfunc (g *graphAdjMat) removeEdge(i, j int) {\n// \u7d22\u5f15\u8d8a\u754c\u4e0e\u76f8\u7b49\u5904\u7406\nif i &lt; 0 || j &lt; 0 || i &gt;= g.size() || j &gt;= g.size() || i == j {\nfmt.Errorf(\"%s\", \"Index Out Of Bounds Exception\")\n}\ng.adjMat[i][j] = 0\ng.adjMat[j][i] = 0\n}\n/* \u6253\u5370\u90bb\u63a5\u77e9\u9635 */\nfunc (g *graphAdjMat) print() {\nfmt.Printf(\"\\t\u9876\u70b9\u5217\u8868 = %v\\n\", g.vertices)\nfmt.Printf(\"\\t\u90bb\u63a5\u77e9\u9635 = \\n\")\nfor i := range g.adjMat {\nfmt.Printf(\"\\t\\t\\t%v\\n\", g.adjMat[i])\n}\n}\n</code></pre> graph_adjacency_matrix.js<pre><code>/* \u57fa\u4e8e\u90bb\u63a5\u77e9\u9635\u5b9e\u73b0\u7684\u65e0\u5411\u56fe\u7c7b */\nclass GraphAdjMat {\nvertices; // \u9876\u70b9\u5217\u8868\uff0c\u5143\u7d20\u4ee3\u8868\u201c\u9876\u70b9\u503c\u201d\uff0c\u7d22\u5f15\u4ee3\u8868\u201c\u9876\u70b9\u7d22\u5f15\u201d\nadjMat; // \u90bb\u63a5\u77e9\u9635\uff0c\u884c\u5217\u7d22\u5f15\u5bf9\u5e94\u201c\u9876\u70b9\u7d22\u5f15\u201d\n/* \u6784\u9020\u51fd\u6570 */\nconstructor(vertices, edges) {\nthis.vertices = [];\nthis.adjMat = [];\n// \u6dfb\u52a0\u9876\u70b9\nfor (const val of vertices) {\nthis.addVertex(val);\n}\n// \u6dfb\u52a0\u8fb9\n// \u8bf7\u6ce8\u610f\uff0cedges \u5143\u7d20\u4ee3\u8868\u9876\u70b9\u7d22\u5f15\uff0c\u5373\u5bf9\u5e94 vertices \u5143\u7d20\u7d22\u5f15\nfor (const e of edges) {\nthis.addEdge(e[0], e[1]);\n}\n}\n/* \u83b7\u53d6\u9876\u70b9\u6570\u91cf */\nsize() {\nreturn this.vertices.length;\n}\n/* \u6dfb\u52a0\u9876\u70b9 */\naddVertex(val) {\nconst n = this.size();\n// \u5411\u9876\u70b9\u5217\u8868\u4e2d\u6dfb\u52a0\u65b0\u9876\u70b9\u7684\u503c\nthis.vertices.push(val);\n// \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u6dfb\u52a0\u4e00\u884c\nconst newRow = [];\nfor (let j = 0; j &lt; n; j++) {\nnewRow.push(0);\n}\nthis.adjMat.push(newRow);\n// \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u6dfb\u52a0\u4e00\u5217\nfor (const row of this.adjMat) {\nrow.push(0);\n}\n}\n/* \u5220\u9664\u9876\u70b9 */\nremoveVertex(index) {\nif (index &gt;= this.size()) {\nthrow new RangeError('Index Out Of Bounds Exception');\n}\n// \u5728\u9876\u70b9\u5217\u8868\u4e2d\u79fb\u9664\u7d22\u5f15 index \u7684\u9876\u70b9\nthis.vertices.splice(index, 1);\n// \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u5220\u9664\u7d22\u5f15 index \u7684\u884c\nthis.adjMat.splice(index, 1);\n// \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u5220\u9664\u7d22\u5f15 index \u7684\u5217\nfor (const row of this.adjMat) {\nrow.splice(index, 1);\n}\n}\n/* \u6dfb\u52a0\u8fb9 */\n// \u53c2\u6570 i, j \u5bf9\u5e94 vertices \u5143\u7d20\u7d22\u5f15\naddEdge(i, j) {\n// \u7d22\u5f15\u8d8a\u754c\u4e0e\u76f8\u7b49\u5904\u7406\nif (i &lt; 0 || j &lt; 0 || i &gt;= this.size() || j &gt;= this.size() || i === j) {\nthrow new RangeError('Index Out Of Bounds Exception');\n}\n// \u5728\u65e0\u5411\u56fe\u4e2d\uff0c\u90bb\u63a5\u77e9\u9635\u6cbf\u4e3b\u5bf9\u89d2\u7ebf\u5bf9\u79f0\uff0c\u5373\u6ee1\u8db3 (i, j) == (j, i)\nthis.adjMat[i][j] = 1;\nthis.adjMat[j][i] = 1;\n}\n/* \u5220\u9664\u8fb9 */\n// \u53c2\u6570 i, j \u5bf9\u5e94 vertices \u5143\u7d20\u7d22\u5f15\nremoveEdge(i, j) {\n// \u7d22\u5f15\u8d8a\u754c\u4e0e\u76f8\u7b49\u5904\u7406\nif (i &lt; 0 || j &lt; 0 || i &gt;= this.size() || j &gt;= this.size() || i === j) {\nthrow new RangeError('Index Out Of Bounds Exception');\n}\nthis.adjMat[i][j] = 0;\nthis.adjMat[j][i] = 0;\n}\n/* \u6253\u5370\u90bb\u63a5\u77e9\u9635 */\nprint() {\nconsole.log('\u9876\u70b9\u5217\u8868 = ', this.vertices);\nconsole.log('\u90bb\u63a5\u77e9\u9635 =', this.adjMat);\n}\n}\n</code></pre> graph_adjacency_matrix.ts<pre><code>/* \u57fa\u4e8e\u90bb\u63a5\u77e9\u9635\u5b9e\u73b0\u7684\u65e0\u5411\u56fe\u7c7b */\nclass GraphAdjMat {\nvertices: number[]; // \u9876\u70b9\u5217\u8868\uff0c\u5143\u7d20\u4ee3\u8868\u201c\u9876\u70b9\u503c\u201d\uff0c\u7d22\u5f15\u4ee3\u8868\u201c\u9876\u70b9\u7d22\u5f15\u201d\nadjMat: number[][]; // \u90bb\u63a5\u77e9\u9635\uff0c\u884c\u5217\u7d22\u5f15\u5bf9\u5e94\u201c\u9876\u70b9\u7d22\u5f15\u201d\n/* \u6784\u9020\u51fd\u6570 */\nconstructor(vertices: number[], edges: number[][]) {\nthis.vertices = [];\nthis.adjMat = [];\n// \u6dfb\u52a0\u9876\u70b9\nfor (const val of vertices) {\nthis.addVertex(val);\n}\n// \u6dfb\u52a0\u8fb9\n// \u8bf7\u6ce8\u610f\uff0cedges \u5143\u7d20\u4ee3\u8868\u9876\u70b9\u7d22\u5f15\uff0c\u5373\u5bf9\u5e94 vertices \u5143\u7d20\u7d22\u5f15\nfor (const e of edges) {\nthis.addEdge(e[0], e[1]);\n}\n}\n/* \u83b7\u53d6\u9876\u70b9\u6570\u91cf */\nsize(): number {\nreturn this.vertices.length;\n}\n/* \u6dfb\u52a0\u9876\u70b9 */\naddVertex(val: number): void {\nconst n: number = this.size();\n// \u5411\u9876\u70b9\u5217\u8868\u4e2d\u6dfb\u52a0\u65b0\u9876\u70b9\u7684\u503c\nthis.vertices.push(val);\n// \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u6dfb\u52a0\u4e00\u884c\nconst newRow: number[] = [];\nfor (let j: number = 0; j &lt; n; j++) {\nnewRow.push(0);\n}\nthis.adjMat.push(newRow);\n// \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u6dfb\u52a0\u4e00\u5217\nfor (const row of this.adjMat) {\nrow.push(0);\n}\n}\n/* \u5220\u9664\u9876\u70b9 */\nremoveVertex(index: number): void {\nif (index &gt;= this.size()) {\nthrow new RangeError('Index Out Of Bounds Exception');\n}\n// \u5728\u9876\u70b9\u5217\u8868\u4e2d\u79fb\u9664\u7d22\u5f15 index \u7684\u9876\u70b9\nthis.vertices.splice(index, 1);\n// \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u5220\u9664\u7d22\u5f15 index \u7684\u884c\nthis.adjMat.splice(index, 1);\n// \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u5220\u9664\u7d22\u5f15 index \u7684\u5217\nfor (const row of this.adjMat) {\nrow.splice(index, 1);\n}\n}\n/* \u6dfb\u52a0\u8fb9 */\n// \u53c2\u6570 i, j \u5bf9\u5e94 vertices \u5143\u7d20\u7d22\u5f15\naddEdge(i: number, j: number): void {\n// \u7d22\u5f15\u8d8a\u754c\u4e0e\u76f8\u7b49\u5904\u7406\nif (i &lt; 0 || j &lt; 0 || i &gt;= this.size() || j &gt;= this.size() || i === j) {\nthrow new RangeError('Index Out Of Bounds Exception');\n}\n// \u5728\u65e0\u5411\u56fe\u4e2d\uff0c\u90bb\u63a5\u77e9\u9635\u6cbf\u4e3b\u5bf9\u89d2\u7ebf\u5bf9\u79f0\uff0c\u5373\u6ee1\u8db3 (i, j) == (j, i)\nthis.adjMat[i][j] = 1;\nthis.adjMat[j][i] = 1;\n}\n/* \u5220\u9664\u8fb9 */\n// \u53c2\u6570 i, j \u5bf9\u5e94 vertices \u5143\u7d20\u7d22\u5f15\nremoveEdge(i: number, j: number): void {\n// \u7d22\u5f15\u8d8a\u754c\u4e0e\u76f8\u7b49\u5904\u7406\nif (i &lt; 0 || j &lt; 0 || i &gt;= this.size() || j &gt;= this.size() || i === j) {\nthrow new RangeError('Index Out Of Bounds Exception');\n}\nthis.adjMat[i][j] = 0;\nthis.adjMat[j][i] = 0;\n}\n/* \u6253\u5370\u90bb\u63a5\u77e9\u9635 */\nprint(): void {\nconsole.log('\u9876\u70b9\u5217\u8868 = ', this.vertices);\nconsole.log('\u90bb\u63a5\u77e9\u9635 =', this.adjMat);\n}\n}\n</code></pre> graph_adjacency_matrix.c<pre><code>[class]{graphAdjMat}-[func]{}\n</code></pre> graph_adjacency_matrix.cs<pre><code>/* \u57fa\u4e8e\u90bb\u63a5\u77e9\u9635\u5b9e\u73b0\u7684\u65e0\u5411\u56fe\u7c7b */\nclass GraphAdjMat {\nList&lt;int&gt; vertices;     // \u9876\u70b9\u5217\u8868\uff0c\u5143\u7d20\u4ee3\u8868\u201c\u9876\u70b9\u503c\u201d\uff0c\u7d22\u5f15\u4ee3\u8868\u201c\u9876\u70b9\u7d22\u5f15\u201d\nList&lt;List&lt;int&gt;&gt; adjMat; // \u90bb\u63a5\u77e9\u9635\uff0c\u884c\u5217\u7d22\u5f15\u5bf9\u5e94\u201c\u9876\u70b9\u7d22\u5f15\u201d\n/* \u6784\u9020\u51fd\u6570 */\npublic GraphAdjMat(int[] vertices, int[][] edges) {\nthis.vertices = new List&lt;int&gt;();\nthis.adjMat = new List&lt;List&lt;int&gt;&gt;();\n// \u6dfb\u52a0\u9876\u70b9\nforeach (int val in vertices) {\naddVertex(val);\n}\n// \u6dfb\u52a0\u8fb9\n// \u8bf7\u6ce8\u610f\uff0cedges \u5143\u7d20\u4ee3\u8868\u9876\u70b9\u7d22\u5f15\uff0c\u5373\u5bf9\u5e94 vertices \u5143\u7d20\u7d22\u5f15\nforeach (int[] e in edges) {\naddEdge(e[0], e[1]);\n}\n}\n/* \u83b7\u53d6\u9876\u70b9\u6570\u91cf */\npublic int size() {\nreturn vertices.Count;\n}\n/* \u6dfb\u52a0\u9876\u70b9 */\npublic void addVertex(int val) {\nint n = size();\n// \u5411\u9876\u70b9\u5217\u8868\u4e2d\u6dfb\u52a0\u65b0\u9876\u70b9\u7684\u503c\nvertices.Add(val);\n// \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u6dfb\u52a0\u4e00\u884c\nList&lt;int&gt; newRow = new List&lt;int&gt;(n);\nfor (int j = 0; j &lt; n; j++) {\nnewRow.Add(0);\n}\nadjMat.Add(newRow);\n// \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u6dfb\u52a0\u4e00\u5217\nforeach (List&lt;int&gt; row in adjMat) {\nrow.Add(0);\n}\n}\n/* \u5220\u9664\u9876\u70b9 */\npublic void removeVertex(int index) {\nif (index &gt;= size())\nthrow new IndexOutOfRangeException();\n// \u5728\u9876\u70b9\u5217\u8868\u4e2d\u79fb\u9664\u7d22\u5f15 index \u7684\u9876\u70b9\nvertices.RemoveAt(index);\n// \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u5220\u9664\u7d22\u5f15 index \u7684\u884c\nadjMat.RemoveAt(index);\n// \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u5220\u9664\u7d22\u5f15 index \u7684\u5217\nforeach (List&lt;int&gt; row in adjMat) {\nrow.RemoveAt(index);\n}\n}\n/* \u6dfb\u52a0\u8fb9 */\n// \u53c2\u6570 i, j \u5bf9\u5e94 vertices \u5143\u7d20\u7d22\u5f15\npublic void addEdge(int i, int j) {\n// \u7d22\u5f15\u8d8a\u754c\u4e0e\u76f8\u7b49\u5904\u7406\nif (i &lt; 0 || j &lt; 0 || i &gt;= size() || j &gt;= size() || i == j)\nthrow new IndexOutOfRangeException();\n// \u5728\u65e0\u5411\u56fe\u4e2d\uff0c\u90bb\u63a5\u77e9\u9635\u6cbf\u4e3b\u5bf9\u89d2\u7ebf\u5bf9\u79f0\uff0c\u5373\u6ee1\u8db3 (i, j) == (j, i)\nadjMat[i][j] = 1;\nadjMat[j][i] = 1;\n}\n/* \u5220\u9664\u8fb9 */\n// \u53c2\u6570 i, j \u5bf9\u5e94 vertices \u5143\u7d20\u7d22\u5f15\npublic void removeEdge(int i, int j) {\n// \u7d22\u5f15\u8d8a\u754c\u4e0e\u76f8\u7b49\u5904\u7406\nif (i &lt; 0 || j &lt; 0 || i &gt;= size() || j &gt;= size() || i == j)\nthrow new IndexOutOfRangeException();\nadjMat[i][j] = 0;\nadjMat[j][i] = 0;\n}\n/* \u6253\u5370\u90bb\u63a5\u77e9\u9635 */\npublic void print() {\nConsole.Write(\"\u9876\u70b9\u5217\u8868 = \");\nPrintUtil.PrintList(vertices);\nConsole.WriteLine(\"\u90bb\u63a5\u77e9\u9635 =\");\nPrintUtil.PrintMatrix(adjMat);\n}\n}\n</code></pre> graph_adjacency_matrix.swift<pre><code>/* \u57fa\u4e8e\u90bb\u63a5\u77e9\u9635\u5b9e\u73b0\u7684\u65e0\u5411\u56fe\u7c7b */\nclass GraphAdjMat {\nprivate var vertices: [Int] // \u9876\u70b9\u5217\u8868\uff0c\u5143\u7d20\u4ee3\u8868\u201c\u9876\u70b9\u503c\u201d\uff0c\u7d22\u5f15\u4ee3\u8868\u201c\u9876\u70b9\u7d22\u5f15\u201d\nprivate var adjMat: [[Int]] // \u90bb\u63a5\u77e9\u9635\uff0c\u884c\u5217\u7d22\u5f15\u5bf9\u5e94\u201c\u9876\u70b9\u7d22\u5f15\u201d\n/* \u6784\u9020\u65b9\u6cd5 */\ninit(vertices: [Int], edges: [[Int]]) {\nself.vertices = []\nadjMat = []\n// \u6dfb\u52a0\u9876\u70b9\nfor val in vertices {\naddVertex(val: val)\n}\n// \u6dfb\u52a0\u8fb9\n// \u8bf7\u6ce8\u610f\uff0cedges \u5143\u7d20\u4ee3\u8868\u9876\u70b9\u7d22\u5f15\uff0c\u5373\u5bf9\u5e94 vertices \u5143\u7d20\u7d22\u5f15\nfor e in edges {\naddEdge(i: e[0], j: e[1])\n}\n}\n/* \u83b7\u53d6\u9876\u70b9\u6570\u91cf */\nfunc size() -&gt; Int {\nvertices.count\n}\n/* \u6dfb\u52a0\u9876\u70b9 */\nfunc addVertex(val: Int) {\nlet n = size()\n// \u5411\u9876\u70b9\u5217\u8868\u4e2d\u6dfb\u52a0\u65b0\u9876\u70b9\u7684\u503c\nvertices.append(val)\n// \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u6dfb\u52a0\u4e00\u884c\nlet newRow = Array(repeating: 0, count: n)\nadjMat.append(newRow)\n// \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u6dfb\u52a0\u4e00\u5217\nfor i in adjMat.indices {\nadjMat[i].append(0)\n}\n}\n/* \u5220\u9664\u9876\u70b9 */\nfunc removeVertex(index: Int) {\nif index &gt;= size() {\nfatalError(\"\u8d8a\u754c\")\n}\n// \u5728\u9876\u70b9\u5217\u8868\u4e2d\u79fb\u9664\u7d22\u5f15 index \u7684\u9876\u70b9\nvertices.remove(at: index)\n// \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u5220\u9664\u7d22\u5f15 index \u7684\u884c\nadjMat.remove(at: index)\n// \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u5220\u9664\u7d22\u5f15 index \u7684\u5217\nfor i in adjMat.indices {\nadjMat[i].remove(at: index)\n}\n}\n/* \u6dfb\u52a0\u8fb9 */\n// \u53c2\u6570 i, j \u5bf9\u5e94 vertices \u5143\u7d20\u7d22\u5f15\nfunc addEdge(i: Int, j: Int) {\n// \u7d22\u5f15\u8d8a\u754c\u4e0e\u76f8\u7b49\u5904\u7406\nif i &lt; 0 || j &lt; 0 || i &gt;= size() || j &gt;= size() || i == j {\nfatalError(\"\u8d8a\u754c\")\n}\n// \u5728\u65e0\u5411\u56fe\u4e2d\uff0c\u90bb\u63a5\u77e9\u9635\u6cbf\u4e3b\u5bf9\u89d2\u7ebf\u5bf9\u79f0\uff0c\u5373\u6ee1\u8db3 (i, j) == (j, i)\nadjMat[i][j] = 1\nadjMat[j][i] = 1\n}\n/* \u5220\u9664\u8fb9 */\n// \u53c2\u6570 i, j \u5bf9\u5e94 vertices \u5143\u7d20\u7d22\u5f15\nfunc removeEdge(i: Int, j: Int) {\n// \u7d22\u5f15\u8d8a\u754c\u4e0e\u76f8\u7b49\u5904\u7406\nif i &lt; 0 || j &lt; 0 || i &gt;= size() || j &gt;= size() || i == j {\nfatalError(\"\u8d8a\u754c\")\n}\nadjMat[i][j] = 0\nadjMat[j][i] = 0\n}\n/* \u6253\u5370\u90bb\u63a5\u77e9\u9635 */\nfunc print() {\nSwift.print(\"\u9876\u70b9\u5217\u8868 = \", terminator: \"\")\nSwift.print(vertices)\nSwift.print(\"\u90bb\u63a5\u77e9\u9635 =\")\nPrintUtil.printMatrix(matrix: adjMat)\n}\n}\n</code></pre> graph_adjacency_matrix.zig<pre><code>\n</code></pre> graph_adjacency_matrix.dart<pre><code>/* \u57fa\u4e8e\u90bb\u63a5\u77e9\u9635\u5b9e\u73b0\u7684\u65e0\u5411\u56fe\u7c7b */\nclass GraphAdjMat {\nList&lt;int&gt; vertices = []; // \u9876\u70b9\u5143\u7d20\uff0c\u5143\u7d20\u4ee3\u8868\u201c\u9876\u70b9\u503c\u201d\uff0c\u7d22\u5f15\u4ee3\u8868\u201c\u9876\u70b9\u7d22\u5f15\u201d\nList&lt;List&lt;int&gt;&gt; adjMat = []; //\u90bb\u63a5\u77e9\u9635\uff0c\u884c\u5217\u7d22\u5f15\u5bf9\u5e94\u201c\u9876\u70b9\u7d22\u5f15\u201d\n/* \u6784\u9020\u65b9\u6cd5 */\nGraphAdjMat(List&lt;int&gt; vertices, List&lt;List&lt;int&gt;&gt; edges) {\nthis.vertices = [];\nthis.adjMat = [];\n// \u6dfb\u52a0\u9876\u70b9\nfor (int val in vertices) {\naddVertex(val);\n}\n// \u6dfb\u52a0\u8fb9\n// \u8bf7\u6ce8\u610f\uff0cedges \u5143\u7d20\u4ee3\u8868\u9876\u70b9\u7d22\u5f15\uff0c\u5373\u5bf9\u5e94 vertices \u5143\u7d20\u7d22\u5f15\nfor (List&lt;int&gt; e in edges) {\naddEdge(e[0], e[1]);\n}\n}\n/* \u83b7\u53d6\u9876\u70b9\u6570\u91cf */\nint size() {\nreturn vertices.length;\n}\n/* \u6dfb\u52a0\u9876\u70b9 */\nvoid addVertex(int val) {\nint n = size();\n// \u5411\u9876\u70b9\u5217\u8868\u4e2d\u6dfb\u52a0\u65b0\u9876\u70b9\u7684\u503c\nvertices.add(val);\n// \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u6dfb\u52a0\u4e00\u884c\nList&lt;int&gt; newRow = List.filled(n, 0, growable: true);\nadjMat.add(newRow);\n// \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u6dfb\u52a0\u4e00\u5217\nfor (List&lt;int&gt; row in adjMat) {\nrow.add(0);\n}\n}\n/* \u5220\u9664\u9876\u70b9 */\nvoid removeVertex(int index) {\nif (index &gt;= size()) {\nthrow IndexError;\n}\n// \u5728\u9876\u70b9\u5217\u8868\u4e2d\u79fb\u9664\u7d22\u5f15 index \u7684\u9876\u70b9\nvertices.removeAt(index);\n// \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u5220\u9664\u7d22\u5f15 index \u7684\u884c\nadjMat.removeAt(index);\n// \u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u5220\u9664\u7d22\u5f15 index \u7684\u5217\nfor (List&lt;int&gt; row in adjMat) {\nrow.removeAt(index);\n}\n}\n/* \u6dfb\u52a0\u8fb9 */\n// \u53c2\u6570 i, j \u5bf9\u5e94 vertices \u5143\u7d20\u7d22\u5f15\nvoid addEdge(int i, int j) {\n// \u7d22\u5f15\u8d8a\u754c\u4e0e\u76f8\u7b49\u5904\u7406\nif (i &lt; 0 || j &lt; 0 || i &gt;= size() || j &gt;= size() || i == j) {\nthrow IndexError;\n}\n// \u5728\u65e0\u5411\u56fe\u4e2d\uff0c\u90bb\u63a5\u77e9\u9635\u6cbf\u4e3b\u5bf9\u89d2\u7ebf\u5bf9\u79f0\uff0c\u5373\u6ee1\u8db3 (i, j) == (j, i)\nadjMat[i][j] = 1;\nadjMat[j][i] = 1;\n}\n/* \u5220\u9664\u8fb9 */\n// \u53c2\u6570 i, j \u5bf9\u5e94 vertices \u5143\u7d20\u7d22\u5f15\nvoid removeEdge(int i, int j) {\n// \u7d22\u5f15\u8d8a\u754c\u4e0e\u76f8\u7b49\u5904\u7406\nif (i &lt; 0 || j &lt; 0 || i &gt;= size() || j &gt;= size() || i == j) {\nthrow IndexError;\n}\nadjMat[i][j] = 0;\nadjMat[j][i] = 0;\n}\n/* \u6253\u5370\u90bb\u63a5\u77e9\u9635 */\nvoid printAdjMat() {\nprint(\"\u9876\u70b9\u5217\u8868 = $vertices\");\nprint(\"\u90bb\u63a5\u77e9\u9635 = \");\nprintMatrix(adjMat);\n}\n}\n</code></pre>"},{"location":"chapter_graph/graph_operations/#922","title":"9.2.2. \u00a0 \u57fa\u4e8e\u90bb\u63a5\u8868\u7684\u5b9e\u73b0","text":"<p>\u8bbe\u65e0\u5411\u56fe\u7684\u9876\u70b9\u603b\u6570\u4e3a \\(n\\) \u3001\u8fb9\u603b\u6570\u4e3a \\(m\\) \uff0c\u5219\u6709\uff1a</p> <ul> <li>\u6dfb\u52a0\u8fb9\uff1a\u5728\u9876\u70b9\u5bf9\u5e94\u94fe\u8868\u7684\u672b\u5c3e\u6dfb\u52a0\u8fb9\u5373\u53ef\uff0c\u4f7f\u7528 \\(O(1)\\) \u65f6\u95f4\u3002\u56e0\u4e3a\u662f\u65e0\u5411\u56fe\uff0c\u6240\u4ee5\u9700\u8981\u540c\u65f6\u6dfb\u52a0\u4e24\u4e2a\u65b9\u5411\u7684\u8fb9\u3002</li> <li>\u5220\u9664\u8fb9\uff1a\u5728\u9876\u70b9\u5bf9\u5e94\u94fe\u8868\u4e2d\u67e5\u627e\u5e76\u5220\u9664\u6307\u5b9a\u8fb9\uff0c\u4f7f\u7528 \\(O(m)\\) \u65f6\u95f4\u3002\u5728\u65e0\u5411\u56fe\u4e2d\uff0c\u9700\u8981\u540c\u65f6\u5220\u9664\u4e24\u4e2a\u65b9\u5411\u7684\u8fb9\u3002</li> <li>\u6dfb\u52a0\u9876\u70b9\uff1a\u5728\u90bb\u63a5\u8868\u4e2d\u6dfb\u52a0\u4e00\u4e2a\u94fe\u8868\uff0c\u5e76\u5c06\u65b0\u589e\u9876\u70b9\u4f5c\u4e3a\u94fe\u8868\u5934\u8282\u70b9\uff0c\u4f7f\u7528 \\(O(1)\\) \u65f6\u95f4\u3002</li> <li>\u5220\u9664\u9876\u70b9\uff1a\u9700\u904d\u5386\u6574\u4e2a\u90bb\u63a5\u8868\uff0c\u5220\u9664\u5305\u542b\u6307\u5b9a\u9876\u70b9\u7684\u6240\u6709\u8fb9\uff0c\u4f7f\u7528 \\(O(n + m)\\) \u65f6\u95f4\u3002</li> <li>\u521d\u59cb\u5316\uff1a\u5728\u90bb\u63a5\u8868\u4e2d\u521b\u5efa \\(n\\) \u4e2a\u9876\u70b9\u548c \\(2m\\) \u6761\u8fb9\uff0c\u4f7f\u7528 \\(O(n + m)\\) \u65f6\u95f4\u3002</li> </ul> \u521d\u59cb\u5316\u90bb\u63a5\u8868\u6dfb\u52a0\u8fb9\u5220\u9664\u8fb9\u6dfb\u52a0\u9876\u70b9\u5220\u9664\u9876\u70b9 <p></p> <p></p> <p></p> <p></p> <p></p> <p>\u4ee5\u4e0b\u662f\u57fa\u4e8e\u90bb\u63a5\u8868\u5b9e\u73b0\u56fe\u7684\u4ee3\u7801\u793a\u4f8b\u3002\u7ec6\u5fc3\u7684\u540c\u5b66\u53ef\u80fd\u6ce8\u610f\u5230\uff0c\u6211\u4eec\u5728\u90bb\u63a5\u8868\u4e2d\u4f7f\u7528 <code>Vertex</code> \u8282\u70b9\u7c7b\u6765\u8868\u793a\u9876\u70b9\uff0c\u8fd9\u6837\u505a\u7684\u539f\u56e0\u6709\uff1a</p> <ul> <li>\u5982\u679c\u6211\u4eec\u9009\u62e9\u901a\u8fc7\u9876\u70b9\u503c\u6765\u533a\u5206\u4e0d\u540c\u9876\u70b9\uff0c\u90a3\u4e48\u503c\u91cd\u590d\u7684\u9876\u70b9\u5c06\u65e0\u6cd5\u88ab\u533a\u5206\u3002</li> <li>\u5982\u679c\u7c7b\u4f3c\u90bb\u63a5\u77e9\u9635\u90a3\u6837\uff0c\u4f7f\u7528\u9876\u70b9\u5217\u8868\u7d22\u5f15\u6765\u533a\u5206\u4e0d\u540c\u9876\u70b9\u3002\u90a3\u4e48\uff0c\u5047\u8bbe\u6211\u4eec\u60f3\u8981\u5220\u9664\u7d22\u5f15\u4e3a \\(i\\) \u7684\u9876\u70b9\uff0c\u5219\u9700\u8981\u904d\u5386\u6574\u4e2a\u90bb\u63a5\u8868\uff0c\u5c06\u5176\u4e2d \\(&gt; i\\) \u7684\u7d22\u5f15\u5168\u90e8\u51cf \\(1\\) \uff0c\u8fd9\u6837\u64cd\u4f5c\u6548\u7387\u8f83\u4f4e\u3002</li> <li>\u56e0\u6b64\u6211\u4eec\u8003\u8651\u5f15\u5165\u9876\u70b9\u7c7b <code>Vertex</code> \uff0c\u4f7f\u5f97\u6bcf\u4e2a\u9876\u70b9\u90fd\u662f\u552f\u4e00\u7684\u5bf9\u8c61\uff0c\u6b64\u65f6\u5220\u9664\u9876\u70b9\u65f6\u5c31\u65e0\u9700\u6539\u52a8\u5176\u4f59\u9876\u70b9\u4e86\u3002</li> </ul> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart graph_adjacency_list.java<pre><code>/* \u57fa\u4e8e\u90bb\u63a5\u8868\u5b9e\u73b0\u7684\u65e0\u5411\u56fe\u7c7b */\nclass GraphAdjList {\n// \u90bb\u63a5\u8868\uff0ckey: \u9876\u70b9\uff0cvalue\uff1a\u8be5\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nMap&lt;Vertex, List&lt;Vertex&gt;&gt; adjList;\n/* \u6784\u9020\u65b9\u6cd5 */\npublic GraphAdjList(Vertex[][] edges) {\nthis.adjList = new HashMap&lt;&gt;();\n// \u6dfb\u52a0\u6240\u6709\u9876\u70b9\u548c\u8fb9\nfor (Vertex[] edge : edges) {\naddVertex(edge[0]);\naddVertex(edge[1]);\naddEdge(edge[0], edge[1]);\n}\n}\n/* \u83b7\u53d6\u9876\u70b9\u6570\u91cf */\npublic int size() {\nreturn adjList.size();\n}\n/* \u6dfb\u52a0\u8fb9 */\npublic void addEdge(Vertex vet1, Vertex vet2) {\nif (!adjList.containsKey(vet1) || !adjList.containsKey(vet2) || vet1 == vet2)\nthrow new IllegalArgumentException();\n// \u6dfb\u52a0\u8fb9 vet1 - vet2\nadjList.get(vet1).add(vet2);\nadjList.get(vet2).add(vet1);\n}\n/* \u5220\u9664\u8fb9 */\npublic void removeEdge(Vertex vet1, Vertex vet2) {\nif (!adjList.containsKey(vet1) || !adjList.containsKey(vet2) || vet1 == vet2)\nthrow new IllegalArgumentException();\n// \u5220\u9664\u8fb9 vet1 - vet2\nadjList.get(vet1).remove(vet2);\nadjList.get(vet2).remove(vet1);\n}\n/* \u6dfb\u52a0\u9876\u70b9 */\npublic void addVertex(Vertex vet) {\nif (adjList.containsKey(vet))\nreturn;\n// \u5728\u90bb\u63a5\u8868\u4e2d\u6dfb\u52a0\u4e00\u4e2a\u65b0\u94fe\u8868\nadjList.put(vet, new ArrayList&lt;&gt;());\n}\n/* \u5220\u9664\u9876\u70b9 */\npublic void removeVertex(Vertex vet) {\nif (!adjList.containsKey(vet))\nthrow new IllegalArgumentException();\n// \u5728\u90bb\u63a5\u8868\u4e2d\u5220\u9664\u9876\u70b9 vet \u5bf9\u5e94\u7684\u94fe\u8868\nadjList.remove(vet);\n// \u904d\u5386\u5176\u4ed6\u9876\u70b9\u7684\u94fe\u8868\uff0c\u5220\u9664\u6240\u6709\u5305\u542b vet \u7684\u8fb9\nfor (List&lt;Vertex&gt; list : adjList.values()) {\nlist.remove(vet);\n}\n}\n/* \u6253\u5370\u90bb\u63a5\u8868 */\npublic void print() {\nSystem.out.println(\"\u90bb\u63a5\u8868 =\");\nfor (Map.Entry&lt;Vertex, List&lt;Vertex&gt;&gt; pair : adjList.entrySet()) {\nList&lt;Integer&gt; tmp = new ArrayList&lt;&gt;();\nfor (Vertex vertex : pair.getValue())\ntmp.add(vertex.val);\nSystem.out.println(pair.getKey().val + \": \" + tmp + \",\");\n}\n}\n}\n</code></pre> graph_adjacency_list.cpp<pre><code>/* \u57fa\u4e8e\u90bb\u63a5\u8868\u5b9e\u73b0\u7684\u65e0\u5411\u56fe\u7c7b */\nclass GraphAdjList {\npublic:\n// \u90bb\u63a5\u8868\uff0ckey: \u9876\u70b9\uff0cvalue\uff1a\u8be5\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nunordered_map&lt;Vertex *, vector&lt;Vertex *&gt;&gt; adjList;\n/* \u5728 vector \u4e2d\u5220\u9664\u6307\u5b9a\u8282\u70b9 */\nvoid remove(vector&lt;Vertex *&gt; &amp;vec, Vertex *vet) {\nfor (int i = 0; i &lt; vec.size(); i++) {\nif (vec[i] == vet) {\nvec.erase(vec.begin() + i);\nbreak;\n}\n}\n}\n/* \u6784\u9020\u65b9\u6cd5 */\nGraphAdjList(const vector&lt;vector&lt;Vertex *&gt;&gt; &amp;edges) {\n// \u6dfb\u52a0\u6240\u6709\u9876\u70b9\u548c\u8fb9\nfor (const vector&lt;Vertex *&gt; &amp;edge : edges) {\naddVertex(edge[0]);\naddVertex(edge[1]);\naddEdge(edge[0], edge[1]);\n}\n}\n/* \u83b7\u53d6\u9876\u70b9\u6570\u91cf */\nint size() {\nreturn adjList.size();\n}\n/* \u6dfb\u52a0\u8fb9 */\nvoid addEdge(Vertex *vet1, Vertex *vet2) {\nif (!adjList.count(vet1) || !adjList.count(vet2) || vet1 == vet2)\nthrow invalid_argument(\"\u4e0d\u5b58\u5728\u9876\u70b9\");\n// \u6dfb\u52a0\u8fb9 vet1 - vet2\nadjList[vet1].push_back(vet2);\nadjList[vet2].push_back(vet1);\n}\n/* \u5220\u9664\u8fb9 */\nvoid removeEdge(Vertex *vet1, Vertex *vet2) {\nif (!adjList.count(vet1) || !adjList.count(vet2) || vet1 == vet2)\nthrow invalid_argument(\"\u4e0d\u5b58\u5728\u9876\u70b9\");\n// \u5220\u9664\u8fb9 vet1 - vet2\nremove(adjList[vet1], vet2);\nremove(adjList[vet2], vet1);\n}\n/* \u6dfb\u52a0\u9876\u70b9 */\nvoid addVertex(Vertex *vet) {\nif (adjList.count(vet))\nreturn;\n// \u5728\u90bb\u63a5\u8868\u4e2d\u6dfb\u52a0\u4e00\u4e2a\u65b0\u94fe\u8868\nadjList[vet] = vector&lt;Vertex *&gt;();\n}\n/* \u5220\u9664\u9876\u70b9 */\nvoid removeVertex(Vertex *vet) {\nif (!adjList.count(vet))\nthrow invalid_argument(\"\u4e0d\u5b58\u5728\u9876\u70b9\");\n// \u5728\u90bb\u63a5\u8868\u4e2d\u5220\u9664\u9876\u70b9 vet \u5bf9\u5e94\u7684\u94fe\u8868\nadjList.erase(vet);\n// \u904d\u5386\u5176\u4ed6\u9876\u70b9\u7684\u94fe\u8868\uff0c\u5220\u9664\u6240\u6709\u5305\u542b vet \u7684\u8fb9\nfor (auto &amp;adj : adjList) {\nremove(adj.second, vet);\n}\n}\n/* \u6253\u5370\u90bb\u63a5\u8868 */\nvoid print() {\ncout &lt;&lt; \"\u90bb\u63a5\u8868 =\" &lt;&lt; endl;\nfor (auto &amp;adj : adjList) {\nconst auto &amp;key = adj.first;\nconst auto &amp;vec = adj.second;\ncout &lt;&lt; key-&gt;val &lt;&lt; \": \";\nprintVector(vetsToVals(vec));\n}\n}\n};\n</code></pre> graph_adjacency_list.py<pre><code>class GraphAdjList:\n\"\"\"\u57fa\u4e8e\u90bb\u63a5\u8868\u5b9e\u73b0\u7684\u65e0\u5411\u56fe\u7c7b\"\"\"\ndef __init__(self, edges: list[list[Vertex]]) -&gt; None:\n\"\"\"\u6784\u9020\u65b9\u6cd5\"\"\"\n# \u90bb\u63a5\u8868\uff0ckey: \u9876\u70b9\uff0cvalue\uff1a\u8be5\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nself.adj_list = dict[Vertex, Vertex]()\n# \u6dfb\u52a0\u6240\u6709\u9876\u70b9\u548c\u8fb9\nfor edge in edges:\nself.add_vertex(edge[0])\nself.add_vertex(edge[1])\nself.add_edge(edge[0], edge[1])\ndef size(self) -&gt; int:\n\"\"\"\u83b7\u53d6\u9876\u70b9\u6570\u91cf\"\"\"\nreturn len(self.adj_list)\ndef add_edge(self, vet1: Vertex, vet2: Vertex) -&gt; None:\n\"\"\"\u6dfb\u52a0\u8fb9\"\"\"\nif vet1 not in self.adj_list or vet2 not in self.adj_list or vet1 == vet2:\nraise ValueError()\n# \u6dfb\u52a0\u8fb9 vet1 - vet2\nself.adj_list[vet1].append(vet2)\nself.adj_list[vet2].append(vet1)\ndef remove_edge(self, vet1: Vertex, vet2: Vertex) -&gt; None:\n\"\"\"\u5220\u9664\u8fb9\"\"\"\nif vet1 not in self.adj_list or vet2 not in self.adj_list or vet1 == vet2:\nraise ValueError()\n# \u5220\u9664\u8fb9 vet1 - vet2\nself.adj_list[vet1].remove(vet2)\nself.adj_list[vet2].remove(vet1)\ndef add_vertex(self, vet: Vertex) -&gt; None:\n\"\"\"\u6dfb\u52a0\u9876\u70b9\"\"\"\nif vet in self.adj_list:\nreturn\n# \u5728\u90bb\u63a5\u8868\u4e2d\u6dfb\u52a0\u4e00\u4e2a\u65b0\u94fe\u8868\nself.adj_list[vet] = []\ndef remove_vertex(self, vet: Vertex) -&gt; None:\n\"\"\"\u5220\u9664\u9876\u70b9\"\"\"\nif vet not in self.adj_list:\nraise ValueError()\n# \u5728\u90bb\u63a5\u8868\u4e2d\u5220\u9664\u9876\u70b9 vet \u5bf9\u5e94\u7684\u94fe\u8868\nself.adj_list.pop(vet)\n# \u904d\u5386\u5176\u4ed6\u9876\u70b9\u7684\u94fe\u8868\uff0c\u5220\u9664\u6240\u6709\u5305\u542b vet \u7684\u8fb9\nfor vertex in self.adj_list:\nif vet in self.adj_list[vertex]:\nself.adj_list[vertex].remove(vet)\ndef print(self) -&gt; None:\n\"\"\"\u6253\u5370\u90bb\u63a5\u8868\"\"\"\nprint(\"\u90bb\u63a5\u8868 =\")\nfor vertex in self.adj_list:\ntmp = [v.val for v in self.adj_list[vertex]]\nprint(f\"{vertex.val}: {tmp},\")\n</code></pre> graph_adjacency_list.go<pre><code>/* \u57fa\u4e8e\u90bb\u63a5\u8868\u5b9e\u73b0\u7684\u65e0\u5411\u56fe\u7c7b */\ntype graphAdjList struct {\n// \u90bb\u63a5\u8868\uff0ckey: \u9876\u70b9\uff0cvalue\uff1a\u8be5\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nadjList map[Vertex][]Vertex\n}\n/* \u6784\u9020\u65b9\u6cd5 */\nfunc newGraphAdjList(edges [][]Vertex) *graphAdjList {\ng := &amp;graphAdjList{\nadjList: make(map[Vertex][]Vertex),\n}\n// \u6dfb\u52a0\u6240\u6709\u9876\u70b9\u548c\u8fb9\nfor _, edge := range edges {\ng.addVertex(edge[0])\ng.addVertex(edge[1])\ng.addEdge(edge[0], edge[1])\n}\nreturn g\n}\n/* \u83b7\u53d6\u9876\u70b9\u6570\u91cf */\nfunc (g *graphAdjList) size() int {\nreturn len(g.adjList)\n}\n/* \u6dfb\u52a0\u8fb9 */\nfunc (g *graphAdjList) addEdge(vet1 Vertex, vet2 Vertex) {\n_, ok1 := g.adjList[vet1]\n_, ok2 := g.adjList[vet2]\nif !ok1 || !ok2 || vet1 == vet2 {\npanic(\"error\")\n}\n// \u6dfb\u52a0\u8fb9 vet1 - vet2, \u6dfb\u52a0\u533f\u540d struct{},\ng.adjList[vet1] = append(g.adjList[vet1], vet2)\ng.adjList[vet2] = append(g.adjList[vet2], vet1)\n}\n/* \u5220\u9664\u8fb9 */\nfunc (g *graphAdjList) removeEdge(vet1 Vertex, vet2 Vertex) {\n_, ok1 := g.adjList[vet1]\n_, ok2 := g.adjList[vet2]\nif !ok1 || !ok2 || vet1 == vet2 {\npanic(\"error\")\n}\n// \u5220\u9664\u8fb9 vet1 - vet2\nDeleteSliceElms(g.adjList[vet1], vet2)\nDeleteSliceElms(g.adjList[vet2], vet1)\n}\n/* \u6dfb\u52a0\u9876\u70b9 */\nfunc (g *graphAdjList) addVertex(vet Vertex) {\n_, ok := g.adjList[vet]\nif ok {\nreturn\n}\n// \u5728\u90bb\u63a5\u8868\u4e2d\u6dfb\u52a0\u4e00\u4e2a\u65b0\u94fe\u8868\ng.adjList[vet] = make([]Vertex, 0)\n}\n/* \u5220\u9664\u9876\u70b9 */\nfunc (g *graphAdjList) removeVertex(vet Vertex) {\n_, ok := g.adjList[vet]\nif !ok {\npanic(\"error\")\n}\n// \u5728\u90bb\u63a5\u8868\u4e2d\u5220\u9664\u9876\u70b9 vet \u5bf9\u5e94\u7684\u94fe\u8868\ndelete(g.adjList, vet)\n// \u904d\u5386\u5176\u4ed6\u9876\u70b9\u7684\u94fe\u8868\uff0c\u5220\u9664\u6240\u6709\u5305\u542b vet \u7684\u8fb9\nfor _, list := range g.adjList {\nDeleteSliceElms(list, vet)\n}\n}\n/* \u6253\u5370\u90bb\u63a5\u8868 */\nfunc (g *graphAdjList) print() {\nvar builder strings.Builder\nfmt.Printf(\"\u90bb\u63a5\u8868 = \\n\")\nfor k, v := range g.adjList {\nbuilder.WriteString(\"\\t\\t\" + strconv.Itoa(k.Val) + \": \")\nfor _, vet := range v {\nbuilder.WriteString(strconv.Itoa(vet.Val) + \" \")\n}\nfmt.Println(builder.String())\nbuilder.Reset()\n}\n}\n</code></pre> graph_adjacency_list.js<pre><code>/* \u57fa\u4e8e\u90bb\u63a5\u8868\u5b9e\u73b0\u7684\u65e0\u5411\u56fe\u7c7b */\nclass GraphAdjList {\n// \u90bb\u63a5\u8868\uff0ckey: \u9876\u70b9\uff0cvalue\uff1a\u8be5\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nadjList;\n/* \u6784\u9020\u65b9\u6cd5 */\nconstructor(edges) {\nthis.adjList = new Map();\n// \u6dfb\u52a0\u6240\u6709\u9876\u70b9\u548c\u8fb9\nfor (const edge of edges) {\nthis.addVertex(edge[0]);\nthis.addVertex(edge[1]);\nthis.addEdge(edge[0], edge[1]);\n}\n}\n/* \u83b7\u53d6\u9876\u70b9\u6570\u91cf */\nsize() {\nreturn this.adjList.size;\n}\n/* \u6dfb\u52a0\u8fb9 */\naddEdge(vet1, vet2) {\nif (\n!this.adjList.has(vet1) ||\n!this.adjList.has(vet2) ||\nvet1 === vet2\n) {\nthrow new Error('Illegal Argument Exception');\n}\n// \u6dfb\u52a0\u8fb9 vet1 - vet2\nthis.adjList.get(vet1).push(vet2);\nthis.adjList.get(vet2).push(vet1);\n}\n/* \u5220\u9664\u8fb9 */\nremoveEdge(vet1, vet2) {\nif (\n!this.adjList.has(vet1) ||\n!this.adjList.has(vet2) ||\nvet1 === vet2\n) {\nthrow new Error('Illegal Argument Exception');\n}\n// \u5220\u9664\u8fb9 vet1 - vet2\nthis.adjList.get(vet1).splice(this.adjList.get(vet1).indexOf(vet2), 1);\nthis.adjList.get(vet2).splice(this.adjList.get(vet2).indexOf(vet1), 1);\n}\n/* \u6dfb\u52a0\u9876\u70b9 */\naddVertex(vet) {\nif (this.adjList.has(vet)) return;\n// \u5728\u90bb\u63a5\u8868\u4e2d\u6dfb\u52a0\u4e00\u4e2a\u65b0\u94fe\u8868\nthis.adjList.set(vet, []);\n}\n/* \u5220\u9664\u9876\u70b9 */\nremoveVertex(vet) {\nif (!this.adjList.has(vet)) {\nthrow new Error('Illegal Argument Exception');\n}\n// \u5728\u90bb\u63a5\u8868\u4e2d\u5220\u9664\u9876\u70b9 vet \u5bf9\u5e94\u7684\u94fe\u8868\nthis.adjList.delete(vet);\n// \u904d\u5386\u5176\u4ed6\u9876\u70b9\u7684\u94fe\u8868\uff0c\u5220\u9664\u6240\u6709\u5305\u542b vet \u7684\u8fb9\nfor (let set of this.adjList.values()) {\nconst index = set.indexOf(vet);\nif (index &gt; -1) {\nset.splice(index, 1);\n}\n}\n}\n/* \u6253\u5370\u90bb\u63a5\u8868 */\nprint() {\nconsole.log('\u90bb\u63a5\u8868 =');\nfor (const [key, value] of this.adjList) {\nconst tmp = [];\nfor (const vertex of value) {\ntmp.push(vertex.val);\n}\nconsole.log(key.val + ': ' + tmp.join());\n}\n}\n}\n</code></pre> graph_adjacency_list.ts<pre><code>/* \u57fa\u4e8e\u90bb\u63a5\u8868\u5b9e\u73b0\u7684\u65e0\u5411\u56fe\u7c7b */\nclass GraphAdjList {\n// \u90bb\u63a5\u8868\uff0ckey: \u9876\u70b9\uff0cvalue\uff1a\u8be5\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nadjList: Map&lt;Vertex, Vertex[]&gt;;\n/* \u6784\u9020\u65b9\u6cd5 */\nconstructor(edges: Vertex[][]) {\nthis.adjList = new Map();\n// \u6dfb\u52a0\u6240\u6709\u9876\u70b9\u548c\u8fb9\nfor (const edge of edges) {\nthis.addVertex(edge[0]);\nthis.addVertex(edge[1]);\nthis.addEdge(edge[0], edge[1]);\n}\n}\n/* \u83b7\u53d6\u9876\u70b9\u6570\u91cf */\nsize(): number {\nreturn this.adjList.size;\n}\n/* \u6dfb\u52a0\u8fb9 */\naddEdge(vet1: Vertex, vet2: Vertex): void {\nif (\n!this.adjList.has(vet1) ||\n!this.adjList.has(vet2) ||\nvet1 === vet2\n) {\nthrow new Error('Illegal Argument Exception');\n}\n// \u6dfb\u52a0\u8fb9 vet1 - vet2\nthis.adjList.get(vet1).push(vet2);\nthis.adjList.get(vet2).push(vet1);\n}\n/* \u5220\u9664\u8fb9 */\nremoveEdge(vet1: Vertex, vet2: Vertex): void {\nif (\n!this.adjList.has(vet1) ||\n!this.adjList.has(vet2) ||\nvet1 === vet2\n) {\nthrow new Error('Illegal Argument Exception');\n}\n// \u5220\u9664\u8fb9 vet1 - vet2\nthis.adjList.get(vet1).splice(this.adjList.get(vet1).indexOf(vet2), 1);\nthis.adjList.get(vet2).splice(this.adjList.get(vet2).indexOf(vet1), 1);\n}\n/* \u6dfb\u52a0\u9876\u70b9 */\naddVertex(vet: Vertex): void {\nif (this.adjList.has(vet)) return;\n// \u5728\u90bb\u63a5\u8868\u4e2d\u6dfb\u52a0\u4e00\u4e2a\u65b0\u94fe\u8868\nthis.adjList.set(vet, []);\n}\n/* \u5220\u9664\u9876\u70b9 */\nremoveVertex(vet: Vertex): void {\nif (!this.adjList.has(vet)) {\nthrow new Error('Illegal Argument Exception');\n}\n// \u5728\u90bb\u63a5\u8868\u4e2d\u5220\u9664\u9876\u70b9 vet \u5bf9\u5e94\u7684\u94fe\u8868\nthis.adjList.delete(vet);\n// \u904d\u5386\u5176\u4ed6\u9876\u70b9\u7684\u94fe\u8868\uff0c\u5220\u9664\u6240\u6709\u5305\u542b vet \u7684\u8fb9\nfor (let set of this.adjList.values()) {\nconst index: number = set.indexOf(vet);\nif (index &gt; -1) {\nset.splice(index, 1);\n}\n}\n}\n/* \u6253\u5370\u90bb\u63a5\u8868 */\nprint(): void {\nconsole.log('\u90bb\u63a5\u8868 =');\nfor (const [key, value] of this.adjList.entries()) {\nconst tmp = [];\nfor (const vertex of value) {\ntmp.push(vertex.val);\n}\nconsole.log(key.val + ': ' + tmp.join());\n}\n}\n}\n</code></pre> graph_adjacency_list.c<pre><code>[class]{graphAdjList}-[func]{}\n</code></pre> graph_adjacency_list.cs<pre><code>/* \u57fa\u4e8e\u90bb\u63a5\u8868\u5b9e\u73b0\u7684\u65e0\u5411\u56fe\u7c7b */\nclass GraphAdjList {\n// \u90bb\u63a5\u8868\uff0ckey: \u9876\u70b9\uff0cvalue\uff1a\u8be5\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\npublic Dictionary&lt;Vertex, List&lt;Vertex&gt;&gt; adjList;\n/* \u6784\u9020\u51fd\u6570 */\npublic GraphAdjList(Vertex[][] edges) {\nthis.adjList = new Dictionary&lt;Vertex, List&lt;Vertex&gt;&gt;();\n// \u6dfb\u52a0\u6240\u6709\u9876\u70b9\u548c\u8fb9\nforeach (Vertex[] edge in edges) {\naddVertex(edge[0]);\naddVertex(edge[1]);\naddEdge(edge[0], edge[1]);\n}\n}\n/* \u83b7\u53d6\u9876\u70b9\u6570\u91cf */\npublic int size() {\nreturn adjList.Count;\n}\n/* \u6dfb\u52a0\u8fb9 */\npublic void addEdge(Vertex vet1, Vertex vet2) {\nif (!adjList.ContainsKey(vet1) || !adjList.ContainsKey(vet2) || vet1 == vet2)\nthrow new InvalidOperationException();\n// \u6dfb\u52a0\u8fb9 vet1 - vet2\nadjList[vet1].Add(vet2);\nadjList[vet2].Add(vet1);\n}\n/* \u5220\u9664\u8fb9 */\npublic void removeEdge(Vertex vet1, Vertex vet2) {\nif (!adjList.ContainsKey(vet1) || !adjList.ContainsKey(vet2) || vet1 == vet2)\nthrow new InvalidOperationException();\n// \u5220\u9664\u8fb9 vet1 - vet2\nadjList[vet1].Remove(vet2);\nadjList[vet2].Remove(vet1);\n}\n/* \u6dfb\u52a0\u9876\u70b9 */\npublic void addVertex(Vertex vet) {\nif (adjList.ContainsKey(vet))\nreturn;\n// \u5728\u90bb\u63a5\u8868\u4e2d\u6dfb\u52a0\u4e00\u4e2a\u65b0\u94fe\u8868\nadjList.Add(vet, new List&lt;Vertex&gt;());\n}\n/* \u5220\u9664\u9876\u70b9 */\npublic void removeVertex(Vertex vet) {\nif (!adjList.ContainsKey(vet))\nthrow new InvalidOperationException();\n// \u5728\u90bb\u63a5\u8868\u4e2d\u5220\u9664\u9876\u70b9 vet \u5bf9\u5e94\u7684\u94fe\u8868\nadjList.Remove(vet);\n// \u904d\u5386\u5176\u4ed6\u9876\u70b9\u7684\u94fe\u8868\uff0c\u5220\u9664\u6240\u6709\u5305\u542b vet \u7684\u8fb9\nforeach (List&lt;Vertex&gt; list in adjList.Values) {\nlist.Remove(vet);\n}\n}\n/* \u6253\u5370\u90bb\u63a5\u8868 */\npublic void print() {\nConsole.WriteLine(\"\u90bb\u63a5\u8868 =\");\nforeach (KeyValuePair&lt;Vertex, List&lt;Vertex&gt;&gt; pair in adjList) {\nList&lt;int&gt; tmp = new List&lt;int&gt;();\nforeach (Vertex vertex in pair.Value)\ntmp.Add(vertex.val);\nConsole.WriteLine(pair.Key.val + \": [\" + string.Join(\", \", tmp) + \"],\");\n}\n}\n}\n</code></pre> graph_adjacency_list.swift<pre><code>/* \u57fa\u4e8e\u90bb\u63a5\u8868\u5b9e\u73b0\u7684\u65e0\u5411\u56fe\u7c7b */\nclass GraphAdjList {\n// \u90bb\u63a5\u8868\uff0ckey: \u9876\u70b9\uff0cvalue\uff1a\u8be5\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\npublic private(set) var adjList: [Vertex: [Vertex]]\n/* \u6784\u9020\u65b9\u6cd5 */\npublic init(edges: [[Vertex]]) {\nadjList = [:]\n// \u6dfb\u52a0\u6240\u6709\u9876\u70b9\u548c\u8fb9\nfor edge in edges {\naddVertex(vet: edge[0])\naddVertex(vet: edge[1])\naddEdge(vet1: edge[0], vet2: edge[1])\n}\n}\n/* \u83b7\u53d6\u9876\u70b9\u6570\u91cf */\npublic func size() -&gt; Int {\nadjList.count\n}\n/* \u6dfb\u52a0\u8fb9 */\npublic func addEdge(vet1: Vertex, vet2: Vertex) {\nif adjList[vet1] == nil || adjList[vet2] == nil || vet1 == vet2 {\nfatalError(\"\u53c2\u6570\u9519\u8bef\")\n}\n// \u6dfb\u52a0\u8fb9 vet1 - vet2\nadjList[vet1]?.append(vet2)\nadjList[vet2]?.append(vet1)\n}\n/* \u5220\u9664\u8fb9 */\npublic func removeEdge(vet1: Vertex, vet2: Vertex) {\nif adjList[vet1] == nil || adjList[vet2] == nil || vet1 == vet2 {\nfatalError(\"\u53c2\u6570\u9519\u8bef\")\n}\n// \u5220\u9664\u8fb9 vet1 - vet2\nadjList[vet1]?.removeAll(where: { $0 == vet2 })\nadjList[vet2]?.removeAll(where: { $0 == vet1 })\n}\n/* \u6dfb\u52a0\u9876\u70b9 */\npublic func addVertex(vet: Vertex) {\nif adjList[vet] != nil {\nreturn\n}\n// \u5728\u90bb\u63a5\u8868\u4e2d\u6dfb\u52a0\u4e00\u4e2a\u65b0\u94fe\u8868\nadjList[vet] = []\n}\n/* \u5220\u9664\u9876\u70b9 */\npublic func removeVertex(vet: Vertex) {\nif adjList[vet] == nil {\nfatalError(\"\u53c2\u6570\u9519\u8bef\")\n}\n// \u5728\u90bb\u63a5\u8868\u4e2d\u5220\u9664\u9876\u70b9 vet \u5bf9\u5e94\u7684\u94fe\u8868\nadjList.removeValue(forKey: vet)\n// \u904d\u5386\u5176\u4ed6\u9876\u70b9\u7684\u94fe\u8868\uff0c\u5220\u9664\u6240\u6709\u5305\u542b vet \u7684\u8fb9\nfor key in adjList.keys {\nadjList[key]?.removeAll(where: { $0 == vet })\n}\n}\n/* \u6253\u5370\u90bb\u63a5\u8868 */\npublic func print() {\nSwift.print(\"\u90bb\u63a5\u8868 =\")\nfor pair in adjList {\nvar tmp: [Int] = []\nfor vertex in pair.value {\ntmp.append(vertex.val)\n}\nSwift.print(\"\\(pair.key.val): \\(tmp),\")\n}\n}\n}\n</code></pre> graph_adjacency_list.zig<pre><code>[class]{GraphAdjList}-[func]{}\n</code></pre> graph_adjacency_list.dart<pre><code>/* \u57fa\u4e8e\u90bb\u63a5\u8868\u5b9e\u73b0\u7684\u65e0\u5411\u56fe\u7c7b */\nclass GraphAdjList {\n// \u90bb\u63a5\u8868\uff0ckey: \u9876\u70b9\uff0cvalue\uff1a\u8be5\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nMap&lt;Vertex, List&lt;Vertex&gt;&gt; adjList = {};\n/* \u6784\u9020\u65b9\u6cd5 */\nGraphAdjList(List&lt;List&lt;Vertex&gt;&gt; edges) {\nfor (List&lt;Vertex&gt; edge in edges) {\naddVertex(edge[0]);\naddVertex(edge[1]);\naddEdge(edge[0], edge[1]);\n}\n}\n/* \u83b7\u53d6\u9876\u70b9\u6570\u91cf */\nint size() {\nreturn adjList.length;\n}\n/* \u6dfb\u52a0\u8fb9 */\nvoid addEdge(Vertex vet1, Vertex vet2) {\nif (!adjList.containsKey(vet1) ||\n!adjList.containsKey(vet2) ||\nvet1 == vet2) {\nthrow ArgumentError;\n}\n// \u6dfb\u52a0\u8fb9 vet1 - vet2\nadjList[vet1]!.add(vet2);\nadjList[vet2]!.add(vet1);\n}\n/* \u5220\u9664\u8fb9 */\nvoid removeEdge(Vertex vet1, Vertex vet2) {\nif (!adjList.containsKey(vet1) ||\n!adjList.containsKey(vet2) ||\nvet1 == vet2) {\nthrow ArgumentError;\n}\n// \u5220\u9664\u8fb9 vet1 - vet2\nadjList[vet1]!.remove(vet2);\nadjList[vet2]!.remove(vet1);\n}\n/* \u6dfb\u52a0\u9876\u70b9 */\nvoid addVertex(Vertex vet) {\nif (adjList.containsKey(vet)) return;\n// \u5728\u90bb\u63a5\u8868\u4e2d\u6dfb\u52a0\u4e00\u4e2a\u65b0\u94fe\u8868\nadjList[vet] = [];\n}\n/* \u5220\u9664\u9876\u70b9 */\nvoid removeVertex(Vertex vet) {\nif (!adjList.containsKey(vet)) {\nthrow ArgumentError;\n}\n// \u5728\u90bb\u63a5\u8868\u4e2d\u5220\u9664\u9876\u70b9 vet \u5bf9\u5e94\u7684\u94fe\u8868\nadjList.remove(vet);\n// \u904d\u5386\u5176\u4ed6\u9876\u70b9\u7684\u94fe\u8868\uff0c\u5220\u9664\u6240\u6709\u5305\u542b vet \u7684\u8fb9\nadjList.forEach((key, value) {\nvalue.remove(vet);\n});\n}\n/* \u6253\u5370\u90bb\u63a5\u8868 */\nvoid printAdjList() {\nprint(\"\u90bb\u63a5\u8868 =\");\nadjList.forEach((key, value) {\nList&lt;int&gt; tmp = [];\nfor (Vertex vertex in value) {\ntmp.add(vertex.val);\n}\nprint(\"${key.val}: $tmp,\");\n});\n}\n}\n</code></pre>"},{"location":"chapter_graph/graph_operations/#923","title":"9.2.3. \u00a0 \u6548\u7387\u5bf9\u6bd4","text":"<p>\u8bbe\u56fe\u4e2d\u5171\u6709 \\(n\\) \u4e2a\u9876\u70b9\u548c \\(m\\) \u6761\u8fb9\uff0c\u4e0b\u8868\u4e3a\u90bb\u63a5\u77e9\u9635\u548c\u90bb\u63a5\u8868\u7684\u65f6\u95f4\u548c\u7a7a\u95f4\u6548\u7387\u5bf9\u6bd4\u3002</p> \u90bb\u63a5\u77e9\u9635 \u90bb\u63a5\u8868\uff08\u94fe\u8868\uff09 \u90bb\u63a5\u8868\uff08\u54c8\u5e0c\u8868\uff09 \u5224\u65ad\u662f\u5426\u90bb\u63a5 \\(O(1)\\) \\(O(m)\\) \\(O(1)\\) \u6dfb\u52a0\u8fb9 \\(O(1)\\) \\(O(1)\\) \\(O(1)\\) \u5220\u9664\u8fb9 \\(O(1)\\) \\(O(m)\\) \\(O(1)\\) \u6dfb\u52a0\u9876\u70b9 \\(O(n)\\) \\(O(1)\\) \\(O(1)\\) \u5220\u9664\u9876\u70b9 \\(O(n^2)\\) \\(O(n + m)\\) \\(O(n)\\) \u5185\u5b58\u7a7a\u95f4\u5360\u7528 \\(O(n^2)\\) \\(O(n + m)\\) \\(O(n + m)\\) <p>\u89c2\u5bdf\u4e0a\u8868\uff0c\u4f3c\u4e4e\u90bb\u63a5\u8868\uff08\u54c8\u5e0c\u8868\uff09\u7684\u65f6\u95f4\u4e0e\u7a7a\u95f4\u6548\u7387\u6700\u4f18\u3002\u4f46\u5b9e\u9645\u4e0a\uff0c\u5728\u90bb\u63a5\u77e9\u9635\u4e2d\u64cd\u4f5c\u8fb9\u7684\u6548\u7387\u66f4\u9ad8\uff0c\u53ea\u9700\u8981\u4e00\u6b21\u6570\u7ec4\u8bbf\u95ee\u6216\u8d4b\u503c\u64cd\u4f5c\u5373\u53ef\u3002\u7efc\u5408\u6765\u770b\uff0c\u90bb\u63a5\u77e9\u9635\u4f53\u73b0\u4e86\u201c\u4ee5\u7a7a\u95f4\u6362\u65f6\u95f4\u201d\u7684\u539f\u5219\uff0c\u800c\u90bb\u63a5\u8868\u4f53\u73b0\u4e86\u201c\u4ee5\u65f6\u95f4\u6362\u7a7a\u95f4\u201d\u7684\u539f\u5219\u3002</p>"},{"location":"chapter_graph/graph_traversal/","title":"9.3. \u00a0 \u56fe\u7684\u904d\u5386","text":"<p>\u56fe\u4e0e\u6811\u7684\u5173\u7cfb</p> <p>\u6811\u4ee3\u8868\u7684\u662f\u201c\u4e00\u5bf9\u591a\u201d\u7684\u5173\u7cfb\uff0c\u800c\u56fe\u5219\u5177\u6709\u66f4\u9ad8\u7684\u81ea\u7531\u5ea6\uff0c\u53ef\u4ee5\u8868\u793a\u4efb\u610f\u7684\u201c\u591a\u5bf9\u591a\u201d\u5173\u7cfb\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u53ef\u4ee5\u628a\u6811\u770b\u4f5c\u662f\u56fe\u7684\u4e00\u79cd\u7279\u4f8b\u3002\u663e\u7136\uff0c\u6811\u7684\u904d\u5386\u64cd\u4f5c\u4e5f\u662f\u56fe\u7684\u904d\u5386\u64cd\u4f5c\u7684\u4e00\u79cd\u7279\u4f8b\uff0c\u5efa\u8bae\u4f60\u5728\u5b66\u4e60\u672c\u7ae0\u8282\u65f6\u878d\u4f1a\u8d2f\u901a\u4e24\u8005\u7684\u6982\u5ff5\u4e0e\u5b9e\u73b0\u65b9\u6cd5\u3002</p> <p>\u300c\u56fe\u300d\u548c\u300c\u6811\u300d\u90fd\u662f\u975e\u7ebf\u6027\u6570\u636e\u7ed3\u6784\uff0c\u90fd\u9700\u8981\u4f7f\u7528\u300c\u641c\u7d22\u7b97\u6cd5\u300d\u6765\u5b9e\u73b0\u904d\u5386\u64cd\u4f5c\u3002</p> <p>\u4e0e\u6811\u7c7b\u4f3c\uff0c\u56fe\u7684\u904d\u5386\u65b9\u5f0f\u4e5f\u53ef\u5206\u4e3a\u4e24\u79cd\uff0c\u5373\u300c\u5e7f\u5ea6\u4f18\u5148\u904d\u5386 Breadth-First Traversal\u300d\u548c\u300c\u6df1\u5ea6\u4f18\u5148\u904d\u5386 Depth-First Traversal\u300d\uff0c\u4e5f\u79f0\u4e3a\u300c\u5e7f\u5ea6\u4f18\u5148\u641c\u7d22 Breadth-First Search\u300d\u548c\u300c\u6df1\u5ea6\u4f18\u5148\u641c\u7d22 Depth-First Search\u300d\uff0c\u7b80\u79f0 BFS \u548c DFS\u3002</p>"},{"location":"chapter_graph/graph_traversal/#931","title":"9.3.1. \u00a0 \u5e7f\u5ea6\u4f18\u5148\u904d\u5386","text":"<p>\u5e7f\u5ea6\u4f18\u5148\u904d\u5386\u662f\u4e00\u79cd\u7531\u8fd1\u53ca\u8fdc\u7684\u904d\u5386\u65b9\u5f0f\uff0c\u4ece\u8ddd\u79bb\u6700\u8fd1\u7684\u9876\u70b9\u5f00\u59cb\u8bbf\u95ee\uff0c\u5e76\u4e00\u5c42\u5c42\u5411\u5916\u6269\u5f20\u3002\u5177\u4f53\u6765\u8bf4\uff0c\u4ece\u67d0\u4e2a\u9876\u70b9\u51fa\u53d1\uff0c\u5148\u904d\u5386\u8be5\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\uff0c\u7136\u540e\u904d\u5386\u4e0b\u4e00\u4e2a\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\uff0c\u4ee5\u6b64\u7c7b\u63a8\uff0c\u76f4\u81f3\u6240\u6709\u9876\u70b9\u8bbf\u95ee\u5b8c\u6bd5\u3002</p> <p></p> <p> Fig. \u56fe\u7684\u5e7f\u5ea6\u4f18\u5148\u904d\u5386 </p>"},{"location":"chapter_graph/graph_traversal/#_1","title":"\u7b97\u6cd5\u5b9e\u73b0","text":"<p>BFS \u901a\u5e38\u501f\u52a9\u300c\u961f\u5217\u300d\u6765\u5b9e\u73b0\u3002\u961f\u5217\u5177\u6709\u201c\u5148\u5165\u5148\u51fa\u201d\u7684\u6027\u8d28\uff0c\u8fd9\u4e0e BFS \u7684\u201c\u7531\u8fd1\u53ca\u8fdc\u201d\u7684\u601d\u60f3\u5f02\u66f2\u540c\u5de5\u3002</p> <ol> <li>\u5c06\u904d\u5386\u8d77\u59cb\u9876\u70b9 <code>startVet</code> \u52a0\u5165\u961f\u5217\uff0c\u5e76\u5f00\u542f\u5faa\u73af\uff1b</li> <li>\u5728\u5faa\u73af\u7684\u6bcf\u8f6e\u8fed\u4ee3\u4e2d\uff0c\u5f39\u51fa\u961f\u9996\u9876\u70b9\u5e76\u8bb0\u5f55\u8bbf\u95ee\uff0c\u7136\u540e\u5c06\u8be5\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\u52a0\u5165\u5230\u961f\u5217\u5c3e\u90e8\uff1b</li> <li>\u5faa\u73af\u6b65\u9aa4 <code>2.</code> \uff0c\u76f4\u5230\u6240\u6709\u9876\u70b9\u88ab\u8bbf\u95ee\u5b8c\u6210\u540e\u7ed3\u675f\uff1b</li> </ol> <p>\u4e3a\u4e86\u9632\u6b62\u91cd\u590d\u904d\u5386\u9876\u70b9\uff0c\u6211\u4eec\u9700\u8981\u501f\u52a9\u4e00\u4e2a\u54c8\u5e0c\u8868 <code>visited</code> \u6765\u8bb0\u5f55\u54ea\u4e9b\u8282\u70b9\u5df2\u88ab\u8bbf\u95ee\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart graph_bfs.java<pre><code>/* \u5e7f\u5ea6\u4f18\u5148\u904d\u5386 BFS */\n// \u4f7f\u7528\u90bb\u63a5\u8868\u6765\u8868\u793a\u56fe\uff0c\u4ee5\u4fbf\u83b7\u53d6\u6307\u5b9a\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nList&lt;Vertex&gt; graphBFS(GraphAdjList graph, Vertex startVet) {\n// \u9876\u70b9\u904d\u5386\u5e8f\u5217\nList&lt;Vertex&gt; res = new ArrayList&lt;&gt;();\n// \u54c8\u5e0c\u8868\uff0c\u7528\u4e8e\u8bb0\u5f55\u5df2\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9\nSet&lt;Vertex&gt; visited = new HashSet&lt;&gt;() {{ add(startVet); }};\n// \u961f\u5217\u7528\u4e8e\u5b9e\u73b0 BFS\nQueue&lt;Vertex&gt; que = new LinkedList&lt;&gt;() {{ offer(startVet); }};\n// \u4ee5\u9876\u70b9 vet \u4e3a\u8d77\u70b9\uff0c\u5faa\u73af\u76f4\u81f3\u8bbf\u95ee\u5b8c\u6240\u6709\u9876\u70b9\nwhile (!que.isEmpty()) {\nVertex vet = que.poll(); // \u961f\u9996\u9876\u70b9\u51fa\u961f\nres.add(vet);            // \u8bb0\u5f55\u8bbf\u95ee\u9876\u70b9\n// \u904d\u5386\u8be5\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nfor (Vertex adjVet : graph.adjList.get(vet)) {\nif (visited.contains(adjVet))\ncontinue;        // \u8df3\u8fc7\u5df2\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9\nque.offer(adjVet);   // \u53ea\u5165\u961f\u672a\u8bbf\u95ee\u7684\u9876\u70b9\nvisited.add(adjVet); // \u6807\u8bb0\u8be5\u9876\u70b9\u5df2\u88ab\u8bbf\u95ee\n}\n}\n// \u8fd4\u56de\u9876\u70b9\u904d\u5386\u5e8f\u5217\nreturn res;\n}\n</code></pre> graph_bfs.cpp<pre><code>/* \u5e7f\u5ea6\u4f18\u5148\u904d\u5386 BFS */\n// \u4f7f\u7528\u90bb\u63a5\u8868\u6765\u8868\u793a\u56fe\uff0c\u4ee5\u4fbf\u83b7\u53d6\u6307\u5b9a\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nvector&lt;Vertex *&gt; graphBFS(GraphAdjList &amp;graph, Vertex *startVet) {\n// \u9876\u70b9\u904d\u5386\u5e8f\u5217\nvector&lt;Vertex *&gt; res;\n// \u54c8\u5e0c\u8868\uff0c\u7528\u4e8e\u8bb0\u5f55\u5df2\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9\nunordered_set&lt;Vertex *&gt; visited = {startVet};\n// \u961f\u5217\u7528\u4e8e\u5b9e\u73b0 BFS\nqueue&lt;Vertex *&gt; que;\nque.push(startVet);\n// \u4ee5\u9876\u70b9 vet \u4e3a\u8d77\u70b9\uff0c\u5faa\u73af\u76f4\u81f3\u8bbf\u95ee\u5b8c\u6240\u6709\u9876\u70b9\nwhile (!que.empty()) {\nVertex *vet = que.front();\nque.pop();          // \u961f\u9996\u9876\u70b9\u51fa\u961f\nres.push_back(vet); // \u8bb0\u5f55\u8bbf\u95ee\u9876\u70b9\n// \u904d\u5386\u8be5\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nfor (auto adjVet : graph.adjList[vet]) {\nif (visited.count(adjVet))\ncontinue;            // \u8df3\u8fc7\u5df2\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9\nque.push(adjVet);        // \u53ea\u5165\u961f\u672a\u8bbf\u95ee\u7684\u9876\u70b9\nvisited.emplace(adjVet); // \u6807\u8bb0\u8be5\u9876\u70b9\u5df2\u88ab\u8bbf\u95ee\n}\n}\n// \u8fd4\u56de\u9876\u70b9\u904d\u5386\u5e8f\u5217\nreturn res;\n}\n</code></pre> graph_bfs.py<pre><code>def graph_bfs(graph: GraphAdjList, start_vet: Vertex) -&gt; list[Vertex]:\n\"\"\"\u5e7f\u5ea6\u4f18\u5148\u904d\u5386 BFS\"\"\"\n# \u4f7f\u7528\u90bb\u63a5\u8868\u6765\u8868\u793a\u56fe\uff0c\u4ee5\u4fbf\u83b7\u53d6\u6307\u5b9a\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\n# \u9876\u70b9\u904d\u5386\u5e8f\u5217\nres = []\n# \u54c8\u5e0c\u8868\uff0c\u7528\u4e8e\u8bb0\u5f55\u5df2\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9\nvisited = set[Vertex]([start_vet])\n# \u961f\u5217\u7528\u4e8e\u5b9e\u73b0 BFS\nque = deque[Vertex]([start_vet])\n# \u4ee5\u9876\u70b9 vet \u4e3a\u8d77\u70b9\uff0c\u5faa\u73af\u76f4\u81f3\u8bbf\u95ee\u5b8c\u6240\u6709\u9876\u70b9\nwhile len(que) &gt; 0:\nvet = que.popleft()  # \u961f\u9996\u9876\u70b9\u51fa\u961f\nres.append(vet)  # \u8bb0\u5f55\u8bbf\u95ee\u9876\u70b9\n# \u904d\u5386\u8be5\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nfor adj_vet in graph.adj_list[vet]:\nif adj_vet in visited:\ncontinue  # \u8df3\u8fc7\u5df2\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9\nque.append(adj_vet)  # \u53ea\u5165\u961f\u672a\u8bbf\u95ee\u7684\u9876\u70b9\nvisited.add(adj_vet)  # \u6807\u8bb0\u8be5\u9876\u70b9\u5df2\u88ab\u8bbf\u95ee\n# \u8fd4\u56de\u9876\u70b9\u904d\u5386\u5e8f\u5217\nreturn res\n</code></pre> graph_bfs.go<pre><code>/* \u5e7f\u5ea6\u4f18\u5148\u904d\u5386 BFS */\n// \u4f7f\u7528\u90bb\u63a5\u8868\u6765\u8868\u793a\u56fe\uff0c\u4ee5\u4fbf\u83b7\u53d6\u6307\u5b9a\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nfunc graphBFS(g *graphAdjList, startVet Vertex) []Vertex {\n// \u9876\u70b9\u904d\u5386\u5e8f\u5217\nres := make([]Vertex, 0)\n// \u54c8\u5e0c\u8868\uff0c\u7528\u4e8e\u8bb0\u5f55\u5df2\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9\nvisited := make(map[Vertex]struct{})\nvisited[startVet] = struct{}{}\n// \u961f\u5217\u7528\u4e8e\u5b9e\u73b0 BFS, \u4f7f\u7528\u5207\u7247\u6a21\u62df\u961f\u5217\nqueue := make([]Vertex, 0)\nqueue = append(queue, startVet)\n// \u4ee5\u9876\u70b9 vet \u4e3a\u8d77\u70b9\uff0c\u5faa\u73af\u76f4\u81f3\u8bbf\u95ee\u5b8c\u6240\u6709\u9876\u70b9\nfor len(queue) &gt; 0 {\n// \u961f\u9996\u9876\u70b9\u51fa\u961f\nvet := queue[0]\nqueue = queue[1:]\n// \u8bb0\u5f55\u8bbf\u95ee\u9876\u70b9\nres = append(res, vet)\n// \u904d\u5386\u8be5\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nfor _, adjVet := range g.adjList[vet] {\n_, isExist := visited[adjVet]\n// \u53ea\u5165\u961f\u672a\u8bbf\u95ee\u7684\u9876\u70b9\nif !isExist {\nqueue = append(queue, adjVet)\nvisited[adjVet] = struct{}{}\n}\n}\n}\n// \u8fd4\u56de\u9876\u70b9\u904d\u5386\u5e8f\u5217\nreturn res\n}\n</code></pre> graph_bfs.js<pre><code>/* \u5e7f\u5ea6\u4f18\u5148\u904d\u5386 BFS */\n// \u4f7f\u7528\u90bb\u63a5\u8868\u6765\u8868\u793a\u56fe\uff0c\u4ee5\u4fbf\u83b7\u53d6\u6307\u5b9a\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nfunction graphBFS(graph, startVet) {\n// \u9876\u70b9\u904d\u5386\u5e8f\u5217\nconst res = [];\n// \u54c8\u5e0c\u8868\uff0c\u7528\u4e8e\u8bb0\u5f55\u5df2\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9\nconst visited = new Set();\nvisited.add(startVet);\n// \u961f\u5217\u7528\u4e8e\u5b9e\u73b0 BFS\nconst que = [startVet];\n// \u4ee5\u9876\u70b9 vet \u4e3a\u8d77\u70b9\uff0c\u5faa\u73af\u76f4\u81f3\u8bbf\u95ee\u5b8c\u6240\u6709\u9876\u70b9\nwhile (que.length) {\nconst vet = que.shift(); // \u961f\u9996\u9876\u70b9\u51fa\u961f\nres.push(vet); // \u8bb0\u5f55\u8bbf\u95ee\u9876\u70b9\n// \u904d\u5386\u8be5\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nfor (const adjVet of graph.adjList.get(vet) ?? []) {\nif (visited.has(adjVet)) {\ncontinue; // \u8df3\u8fc7\u5df2\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9\n}\nque.push(adjVet); // \u53ea\u5165\u961f\u672a\u8bbf\u95ee\u7684\u9876\u70b9\nvisited.add(adjVet); // \u6807\u8bb0\u8be5\u9876\u70b9\u5df2\u88ab\u8bbf\u95ee\n}\n}\n// \u8fd4\u56de\u9876\u70b9\u904d\u5386\u5e8f\u5217\nreturn res;\n}\n</code></pre> graph_bfs.ts<pre><code>/* \u5e7f\u5ea6\u4f18\u5148\u904d\u5386 BFS */\n// \u4f7f\u7528\u90bb\u63a5\u8868\u6765\u8868\u793a\u56fe\uff0c\u4ee5\u4fbf\u83b7\u53d6\u6307\u5b9a\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nfunction graphBFS(graph: GraphAdjList, startVet: Vertex): Vertex[] {\n// \u9876\u70b9\u904d\u5386\u5e8f\u5217\nconst res: Vertex[] = [];\n// \u54c8\u5e0c\u8868\uff0c\u7528\u4e8e\u8bb0\u5f55\u5df2\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9\nconst visited: Set&lt;Vertex&gt; = new Set();\nvisited.add(startVet);\n// \u961f\u5217\u7528\u4e8e\u5b9e\u73b0 BFS\nconst que = [startVet];\n// \u4ee5\u9876\u70b9 vet \u4e3a\u8d77\u70b9\uff0c\u5faa\u73af\u76f4\u81f3\u8bbf\u95ee\u5b8c\u6240\u6709\u9876\u70b9\nwhile (que.length) {\nconst vet = que.shift(); // \u961f\u9996\u9876\u70b9\u51fa\u961f\nres.push(vet); // \u8bb0\u5f55\u8bbf\u95ee\u9876\u70b9\n// \u904d\u5386\u8be5\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nfor (const adjVet of graph.adjList.get(vet) ?? []) {\nif (visited.has(adjVet)) {\ncontinue; // \u8df3\u8fc7\u5df2\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9\n}\nque.push(adjVet); // \u53ea\u5165\u961f\u672a\u8bbf\u95ee\nvisited.add(adjVet); // \u6807\u8bb0\u8be5\u9876\u70b9\u5df2\u88ab\u8bbf\u95ee\n}\n}\n// \u8fd4\u56de\u9876\u70b9\u904d\u5386\u5e8f\u5217\nreturn res;\n}\n</code></pre> graph_bfs.c<pre><code>[class]{}-[func]{graphBFS}\n</code></pre> graph_bfs.cs<pre><code>/* \u5e7f\u5ea6\u4f18\u5148\u904d\u5386 BFS */\n// \u4f7f\u7528\u90bb\u63a5\u8868\u6765\u8868\u793a\u56fe\uff0c\u4ee5\u4fbf\u83b7\u53d6\u6307\u5b9a\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nList&lt;Vertex&gt; graphBFS(GraphAdjList graph, Vertex startVet) {\n// \u9876\u70b9\u904d\u5386\u5e8f\u5217\nList&lt;Vertex&gt; res = new List&lt;Vertex&gt;();\n// \u54c8\u5e0c\u8868\uff0c\u7528\u4e8e\u8bb0\u5f55\u5df2\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9\nHashSet&lt;Vertex&gt; visited = new HashSet&lt;Vertex&gt;() { startVet };\n// \u961f\u5217\u7528\u4e8e\u5b9e\u73b0 BFS\nQueue&lt;Vertex&gt; que = new Queue&lt;Vertex&gt;();\nque.Enqueue(startVet);\n// \u4ee5\u9876\u70b9 vet \u4e3a\u8d77\u70b9\uff0c\u5faa\u73af\u76f4\u81f3\u8bbf\u95ee\u5b8c\u6240\u6709\u9876\u70b9\nwhile (que.Count &gt; 0) {\nVertex vet = que.Dequeue(); // \u961f\u9996\u9876\u70b9\u51fa\u961f\nres.Add(vet);               // \u8bb0\u5f55\u8bbf\u95ee\u9876\u70b9\nforeach (Vertex adjVet in graph.adjList[vet]) {\nif (visited.Contains(adjVet)) {\ncontinue;          // \u8df3\u8fc7\u5df2\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9\n}\nque.Enqueue(adjVet);   // \u53ea\u5165\u961f\u672a\u8bbf\u95ee\u7684\u9876\u70b9\nvisited.Add(adjVet);   // \u6807\u8bb0\u8be5\u9876\u70b9\u5df2\u88ab\u8bbf\u95ee\n}\n}\n// \u8fd4\u56de\u9876\u70b9\u904d\u5386\u5e8f\u5217\nreturn res;\n}\n</code></pre> graph_bfs.swift<pre><code>/* \u5e7f\u5ea6\u4f18\u5148\u904d\u5386 BFS */\n// \u4f7f\u7528\u90bb\u63a5\u8868\u6765\u8868\u793a\u56fe\uff0c\u4ee5\u4fbf\u83b7\u53d6\u6307\u5b9a\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nfunc graphBFS(graph: GraphAdjList, startVet: Vertex) -&gt; [Vertex] {\n// \u9876\u70b9\u904d\u5386\u5e8f\u5217\nvar res: [Vertex] = []\n// \u54c8\u5e0c\u8868\uff0c\u7528\u4e8e\u8bb0\u5f55\u5df2\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9\nvar visited: Set&lt;Vertex&gt; = [startVet]\n// \u961f\u5217\u7528\u4e8e\u5b9e\u73b0 BFS\nvar que: [Vertex] = [startVet]\n// \u4ee5\u9876\u70b9 vet \u4e3a\u8d77\u70b9\uff0c\u5faa\u73af\u76f4\u81f3\u8bbf\u95ee\u5b8c\u6240\u6709\u9876\u70b9\nwhile !que.isEmpty {\nlet vet = que.removeFirst() // \u961f\u9996\u9876\u70b9\u51fa\u961f\nres.append(vet) // \u8bb0\u5f55\u8bbf\u95ee\u9876\u70b9\n// \u904d\u5386\u8be5\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nfor adjVet in graph.adjList[vet] ?? [] {\nif visited.contains(adjVet) {\ncontinue // \u8df3\u8fc7\u5df2\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9\n}\nque.append(adjVet) // \u53ea\u5165\u961f\u672a\u8bbf\u95ee\u7684\u9876\u70b9\nvisited.insert(adjVet) // \u6807\u8bb0\u8be5\u9876\u70b9\u5df2\u88ab\u8bbf\u95ee\n}\n}\n// \u8fd4\u56de\u9876\u70b9\u904d\u5386\u5e8f\u5217\nreturn res\n}\n</code></pre> graph_bfs.zig<pre><code>[class]{}-[func]{graphBFS}\n</code></pre> graph_bfs.dart<pre><code>/* \u5e7f\u5ea6\u4f18\u5148\u904d\u5386 BFS */\nList&lt;Vertex&gt; graphBFS(GraphAdjList graph, Vertex startVet) {\n// \u4f7f\u7528\u90bb\u63a5\u8868\u6765\u8868\u793a\u56fe\uff0c\u4ee5\u4fbf\u83b7\u53d6\u6307\u5b9a\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\n// \u9876\u70b9\u904d\u5386\u5e8f\u5217\nList&lt;Vertex&gt; res = [];\n// \u54c8\u5e0c\u8868\uff0c\u7528\u4e8e\u8bb0\u5f55\u5df2\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9\nSet&lt;Vertex&gt; visited = {};\nvisited.add(startVet);\n// \u961f\u5217\u7528\u4e8e\u5b9e\u73b0 BFS\nQueue&lt;Vertex&gt; que = Queue();\nque.add(startVet);\n// \u4ee5\u9876\u70b9 vet \u4e3a\u8d77\u70b9\uff0c\u5faa\u73af\u76f4\u81f3\u8bbf\u95ee\u5b8c\u6240\u6709\u9876\u70b9\nwhile (que.isNotEmpty) {\nVertex vet = que.removeFirst(); // \u961f\u9996\u9876\u70b9\u51fa\u961f\nres.add(vet); // \u8bb0\u5f55\u8bbf\u95ee\u9876\u70b9\n// \u904d\u5386\u8be5\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nfor (Vertex adjVet in graph.adjList[vet]!) {\nif (visited.contains(adjVet)) {\ncontinue; // \u8df3\u8fc7\u5df2\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9\n}\nque.add(adjVet); // \u53ea\u5165\u961f\u672a\u8bbf\u95ee\u7684\u9876\u70b9\nvisited.add(adjVet); // \u6807\u8bb0\u8be5\u9876\u70b9\u5df2\u88ab\u8bbf\u95ee\n}\n}\n// \u8fd4\u56de\u9876\u70b9\u904d\u5386\u5e8f\u5217\nreturn res;\n}\n</code></pre> <p>\u4ee3\u7801\u76f8\u5bf9\u62bd\u8c61\uff0c\u5efa\u8bae\u5bf9\u7167\u4ee5\u4e0b\u52a8\u753b\u56fe\u793a\u6765\u52a0\u6df1\u7406\u89e3\u3002</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt;&lt;11&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p>\u5e7f\u5ea6\u4f18\u5148\u904d\u5386\u7684\u5e8f\u5217\u662f\u5426\u552f\u4e00\uff1f</p> <p>\u4e0d\u552f\u4e00\u3002\u5e7f\u5ea6\u4f18\u5148\u904d\u5386\u53ea\u8981\u6c42\u6309\u201c\u7531\u8fd1\u53ca\u8fdc\u201d\u7684\u987a\u5e8f\u904d\u5386\uff0c\u800c\u591a\u4e2a\u76f8\u540c\u8ddd\u79bb\u7684\u9876\u70b9\u7684\u904d\u5386\u987a\u5e8f\u662f\u5141\u8bb8\u88ab\u4efb\u610f\u6253\u4e71\u7684\u3002\u4ee5\u4e0a\u56fe\u4e3a\u4f8b\uff0c\u9876\u70b9 \\(1\\) , \\(3\\) \u7684\u8bbf\u95ee\u987a\u5e8f\u53ef\u4ee5\u4ea4\u6362\u3001\u9876\u70b9 \\(2\\) , \\(4\\) , \\(6\\) \u7684\u8bbf\u95ee\u987a\u5e8f\u4e5f\u53ef\u4ee5\u4efb\u610f\u4ea4\u6362\u3002</p>"},{"location":"chapter_graph/graph_traversal/#_2","title":"\u590d\u6742\u5ea6\u5206\u6790","text":"<p>\u65f6\u95f4\u590d\u6742\u5ea6\uff1a \u6240\u6709\u9876\u70b9\u90fd\u4f1a\u5165\u961f\u5e76\u51fa\u961f\u4e00\u6b21\uff0c\u4f7f\u7528 \\(O(|V|)\\) \u65f6\u95f4\uff1b\u5728\u904d\u5386\u90bb\u63a5\u9876\u70b9\u7684\u8fc7\u7a0b\u4e2d\uff0c\u7531\u4e8e\u662f\u65e0\u5411\u56fe\uff0c\u56e0\u6b64\u6240\u6709\u8fb9\u90fd\u4f1a\u88ab\u8bbf\u95ee \\(2\\) \u6b21\uff0c\u4f7f\u7528 \\(O(2|E|)\\) \u65f6\u95f4\uff1b\u603b\u4f53\u4f7f\u7528 \\(O(|V| + |E|)\\) \u65f6\u95f4\u3002</p> <p>\u7a7a\u95f4\u590d\u6742\u5ea6\uff1a \u5217\u8868 <code>res</code> \uff0c\u54c8\u5e0c\u8868 <code>visited</code> \uff0c\u961f\u5217 <code>que</code> \u4e2d\u7684\u9876\u70b9\u6570\u91cf\u6700\u591a\u4e3a \\(|V|\\) \uff0c\u4f7f\u7528 \\(O(|V|)\\) \u7a7a\u95f4\u3002</p>"},{"location":"chapter_graph/graph_traversal/#932","title":"9.3.2. \u00a0 \u6df1\u5ea6\u4f18\u5148\u904d\u5386","text":"<p>\u6df1\u5ea6\u4f18\u5148\u904d\u5386\u662f\u4e00\u79cd\u4f18\u5148\u8d70\u5230\u5e95\u3001\u65e0\u8def\u53ef\u8d70\u518d\u56de\u5934\u7684\u904d\u5386\u65b9\u5f0f\u3002\u5177\u4f53\u5730\uff0c\u4ece\u67d0\u4e2a\u9876\u70b9\u51fa\u53d1\uff0c\u8bbf\u95ee\u5f53\u524d\u9876\u70b9\u7684\u67d0\u4e2a\u90bb\u63a5\u9876\u70b9\uff0c\u76f4\u5230\u8d70\u5230\u5c3d\u5934\u65f6\u8fd4\u56de\uff0c\u518d\u7ee7\u7eed\u8d70\u5230\u5c3d\u5934\u5e76\u8fd4\u56de\uff0c\u4ee5\u6b64\u7c7b\u63a8\uff0c\u76f4\u81f3\u6240\u6709\u9876\u70b9\u904d\u5386\u5b8c\u6210\u3002</p> <p></p> <p> Fig. \u56fe\u7684\u6df1\u5ea6\u4f18\u5148\u904d\u5386 </p>"},{"location":"chapter_graph/graph_traversal/#_3","title":"\u7b97\u6cd5\u5b9e\u73b0","text":"<p>\u8fd9\u79cd\u201c\u8d70\u5230\u5c3d\u5934 + \u56de\u6eaf\u201d\u7684\u7b97\u6cd5\u5f62\u5f0f\u901a\u5e38\u57fa\u4e8e\u9012\u5f52\u6765\u5b9e\u73b0\u3002\u4e0e BFS \u7c7b\u4f3c\uff0c\u5728 DFS \u4e2d\u6211\u4eec\u4e5f\u9700\u8981\u501f\u52a9\u4e00\u4e2a\u54c8\u5e0c\u8868 <code>visited</code> \u6765\u8bb0\u5f55\u5df2\u88ab\u8bbf\u95ee\u7684\u9876\u70b9\uff0c\u4ee5\u907f\u514d\u91cd\u590d\u8bbf\u95ee\u9876\u70b9\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart graph_dfs.java<pre><code>/* \u6df1\u5ea6\u4f18\u5148\u904d\u5386 DFS \u8f85\u52a9\u51fd\u6570 */\nvoid dfs(GraphAdjList graph, Set&lt;Vertex&gt; visited, List&lt;Vertex&gt; res, Vertex vet) {\nres.add(vet);     // \u8bb0\u5f55\u8bbf\u95ee\u9876\u70b9\nvisited.add(vet); // \u6807\u8bb0\u8be5\u9876\u70b9\u5df2\u88ab\u8bbf\u95ee\n// \u904d\u5386\u8be5\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nfor (Vertex adjVet : graph.adjList.get(vet)) {\nif (visited.contains(adjVet))\ncontinue; // \u8df3\u8fc7\u5df2\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9\n// \u9012\u5f52\u8bbf\u95ee\u90bb\u63a5\u9876\u70b9\ndfs(graph, visited, res, adjVet);\n}\n}\n/* \u6df1\u5ea6\u4f18\u5148\u904d\u5386 DFS */\n// \u4f7f\u7528\u90bb\u63a5\u8868\u6765\u8868\u793a\u56fe\uff0c\u4ee5\u4fbf\u83b7\u53d6\u6307\u5b9a\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nList&lt;Vertex&gt; graphDFS(GraphAdjList graph, Vertex startVet) {\n// \u9876\u70b9\u904d\u5386\u5e8f\u5217\nList&lt;Vertex&gt; res = new ArrayList&lt;&gt;();\n// \u54c8\u5e0c\u8868\uff0c\u7528\u4e8e\u8bb0\u5f55\u5df2\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9\nSet&lt;Vertex&gt; visited = new HashSet&lt;&gt;();\ndfs(graph, visited, res, startVet);\nreturn res;\n}\n</code></pre> graph_dfs.cpp<pre><code>/* \u6df1\u5ea6\u4f18\u5148\u904d\u5386 DFS \u8f85\u52a9\u51fd\u6570 */\nvoid dfs(GraphAdjList &amp;graph, unordered_set&lt;Vertex *&gt; &amp;visited, vector&lt;Vertex *&gt; &amp;res, Vertex *vet) {\nres.push_back(vet);   // \u8bb0\u5f55\u8bbf\u95ee\u9876\u70b9\nvisited.emplace(vet); // \u6807\u8bb0\u8be5\u9876\u70b9\u5df2\u88ab\u8bbf\u95ee\n// \u904d\u5386\u8be5\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nfor (Vertex *adjVet : graph.adjList[vet]) {\nif (visited.count(adjVet))\ncontinue; // \u8df3\u8fc7\u5df2\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9\n// \u9012\u5f52\u8bbf\u95ee\u90bb\u63a5\u9876\u70b9\ndfs(graph, visited, res, adjVet);\n}\n}\n/* \u6df1\u5ea6\u4f18\u5148\u904d\u5386 DFS */\n// \u4f7f\u7528\u90bb\u63a5\u8868\u6765\u8868\u793a\u56fe\uff0c\u4ee5\u4fbf\u83b7\u53d6\u6307\u5b9a\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nvector&lt;Vertex *&gt; graphDFS(GraphAdjList &amp;graph, Vertex *startVet) {\n// \u9876\u70b9\u904d\u5386\u5e8f\u5217\nvector&lt;Vertex *&gt; res;\n// \u54c8\u5e0c\u8868\uff0c\u7528\u4e8e\u8bb0\u5f55\u5df2\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9\nunordered_set&lt;Vertex *&gt; visited;\ndfs(graph, visited, res, startVet);\nreturn res;\n}\n</code></pre> graph_dfs.py<pre><code>def dfs(graph: GraphAdjList, visited: set[Vertex], res: list[Vertex], vet: Vertex):\n\"\"\"\u6df1\u5ea6\u4f18\u5148\u904d\u5386 DFS \u8f85\u52a9\u51fd\u6570\"\"\"\nres.append(vet)  # \u8bb0\u5f55\u8bbf\u95ee\u9876\u70b9\nvisited.add(vet)  # \u6807\u8bb0\u8be5\u9876\u70b9\u5df2\u88ab\u8bbf\u95ee\n# \u904d\u5386\u8be5\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nfor adjVet in graph.adj_list[vet]:\nif adjVet in visited:\ncontinue  # \u8df3\u8fc7\u5df2\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9\n# \u9012\u5f52\u8bbf\u95ee\u90bb\u63a5\u9876\u70b9\ndfs(graph, visited, res, adjVet)\ndef graph_dfs(graph: GraphAdjList, start_vet: Vertex) -&gt; list[Vertex]:\n\"\"\"\u6df1\u5ea6\u4f18\u5148\u904d\u5386 DFS\"\"\"\n# \u9876\u70b9\u904d\u5386\u5e8f\u5217\nres = []\n# \u54c8\u5e0c\u8868\uff0c\u7528\u4e8e\u8bb0\u5f55\u5df2\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9\nvisited = set[Vertex]()\ndfs(graph, visited, res, start_vet)\nreturn res\n</code></pre> graph_dfs.go<pre><code>/* \u6df1\u5ea6\u4f18\u5148\u904d\u5386 DFS \u8f85\u52a9\u51fd\u6570 */\nfunc dfs(g *graphAdjList, visited map[Vertex]struct{}, res *[]Vertex, vet Vertex) {\n// append \u64cd\u4f5c\u4f1a\u8fd4\u56de\u65b0\u7684\u7684\u5f15\u7528\uff0c\u5fc5\u987b\u8ba9\u539f\u5f15\u7528\u91cd\u65b0\u8d4b\u503c\u4e3a\u65b0slice\u7684\u5f15\u7528\n*res = append(*res, vet)\nvisited[vet] = struct{}{}\n// \u904d\u5386\u8be5\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nfor _, adjVet := range g.adjList[vet] {\n_, isExist := visited[adjVet]\n// \u9012\u5f52\u8bbf\u95ee\u90bb\u63a5\u9876\u70b9\nif !isExist {\ndfs(g, visited, res, adjVet)\n}\n}\n}\n/* \u6df1\u5ea6\u4f18\u5148\u904d\u5386 DFS */\n// \u4f7f\u7528\u90bb\u63a5\u8868\u6765\u8868\u793a\u56fe\uff0c\u4ee5\u4fbf\u83b7\u53d6\u6307\u5b9a\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nfunc graphDFS(g *graphAdjList, startVet Vertex) []Vertex {\n// \u9876\u70b9\u904d\u5386\u5e8f\u5217\nres := make([]Vertex, 0)\n// \u54c8\u5e0c\u8868\uff0c\u7528\u4e8e\u8bb0\u5f55\u5df2\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9\nvisited := make(map[Vertex]struct{})\ndfs(g, visited, &amp;res, startVet)\n// \u8fd4\u56de\u9876\u70b9\u904d\u5386\u5e8f\u5217\nreturn res\n}\n</code></pre> graph_dfs.js<pre><code>/* \u6df1\u5ea6\u4f18\u5148\u904d\u5386 DFS */\n// \u4f7f\u7528\u90bb\u63a5\u8868\u6765\u8868\u793a\u56fe\uff0c\u4ee5\u4fbf\u83b7\u53d6\u6307\u5b9a\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nfunction dfs(graph, visited, res, vet) {\nres.push(vet); // \u8bb0\u5f55\u8bbf\u95ee\u9876\u70b9\nvisited.add(vet); // \u6807\u8bb0\u8be5\u9876\u70b9\u5df2\u88ab\u8bbf\u95ee\n// \u904d\u5386\u8be5\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nfor (const adjVet of graph.adjList.get(vet)) {\nif (visited.has(adjVet)) {\ncontinue; // \u8df3\u8fc7\u5df2\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9\n}\n// \u9012\u5f52\u8bbf\u95ee\u90bb\u63a5\u9876\u70b9\ndfs(graph, visited, res, adjVet);\n}\n}\n/* \u6df1\u5ea6\u4f18\u5148\u904d\u5386 DFS */\n// \u4f7f\u7528\u90bb\u63a5\u8868\u6765\u8868\u793a\u56fe\uff0c\u4ee5\u4fbf\u83b7\u53d6\u6307\u5b9a\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nfunction graphDFS(graph, startVet) {\n// \u9876\u70b9\u904d\u5386\u5e8f\u5217\nconst res = [];\n// \u54c8\u5e0c\u8868\uff0c\u7528\u4e8e\u8bb0\u5f55\u5df2\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9\nconst visited = new Set();\ndfs(graph, visited, res, startVet);\nreturn res;\n}\n</code></pre> graph_dfs.ts<pre><code>/* \u6df1\u5ea6\u4f18\u5148\u904d\u5386 DFS \u8f85\u52a9\u51fd\u6570 */\nfunction dfs(\ngraph: GraphAdjList,\nvisited: Set&lt;Vertex&gt;,\nres: Vertex[],\nvet: Vertex\n): void {\nres.push(vet); // \u8bb0\u5f55\u8bbf\u95ee\u9876\u70b9\nvisited.add(vet); // \u6807\u8bb0\u8be5\u9876\u70b9\u5df2\u88ab\u8bbf\u95ee\n// \u904d\u5386\u8be5\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nfor (const adjVet of graph.adjList.get(vet)) {\nif (visited.has(adjVet)) {\ncontinue; // \u8df3\u8fc7\u5df2\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9\n}\n// \u9012\u5f52\u8bbf\u95ee\u90bb\u63a5\u9876\u70b9\ndfs(graph, visited, res, adjVet);\n}\n}\n/* \u6df1\u5ea6\u4f18\u5148\u904d\u5386 DFS */\n// \u4f7f\u7528\u90bb\u63a5\u8868\u6765\u8868\u793a\u56fe\uff0c\u4ee5\u4fbf\u83b7\u53d6\u6307\u5b9a\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nfunction graphDFS(graph: GraphAdjList, startVet: Vertex): Vertex[] {\n// \u9876\u70b9\u904d\u5386\u5e8f\u5217\nconst res: Vertex[] = [];\n// \u54c8\u5e0c\u8868\uff0c\u7528\u4e8e\u8bb0\u5f55\u5df2\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9\nconst visited: Set&lt;Vertex&gt; = new Set();\ndfs(graph, visited, res, startVet);\nreturn res;\n}\n</code></pre> graph_dfs.c<pre><code>[class]{}-[func]{dfs}\n[class]{}-[func]{graphDFS}\n</code></pre> graph_dfs.cs<pre><code>/* \u6df1\u5ea6\u4f18\u5148\u904d\u5386 DFS \u8f85\u52a9\u51fd\u6570 */\nvoid dfs(GraphAdjList graph, HashSet&lt;Vertex&gt; visited, List&lt;Vertex&gt; res, Vertex vet) {\nres.Add(vet);     // \u8bb0\u5f55\u8bbf\u95ee\u9876\u70b9\nvisited.Add(vet); // \u6807\u8bb0\u8be5\u9876\u70b9\u5df2\u88ab\u8bbf\u95ee\n// \u904d\u5386\u8be5\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nforeach (Vertex adjVet in graph.adjList[vet]) {\nif (visited.Contains(adjVet)) {\ncontinue; // \u8df3\u8fc7\u5df2\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9                             \n}\n// \u9012\u5f52\u8bbf\u95ee\u90bb\u63a5\u9876\u70b9\ndfs(graph, visited, res, adjVet);\n}\n}\n/* \u6df1\u5ea6\u4f18\u5148\u904d\u5386 DFS */\n// \u4f7f\u7528\u90bb\u63a5\u8868\u6765\u8868\u793a\u56fe\uff0c\u4ee5\u4fbf\u83b7\u53d6\u6307\u5b9a\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nList&lt;Vertex&gt; graphDFS(GraphAdjList graph, Vertex startVet) {\n// \u9876\u70b9\u904d\u5386\u5e8f\u5217\nList&lt;Vertex&gt; res = new List&lt;Vertex&gt;();\n// \u54c8\u5e0c\u8868\uff0c\u7528\u4e8e\u8bb0\u5f55\u5df2\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9\nHashSet&lt;Vertex&gt; visited = new HashSet&lt;Vertex&gt;();\ndfs(graph, visited, res, startVet);\nreturn res;\n}\n</code></pre> graph_dfs.swift<pre><code>/* \u6df1\u5ea6\u4f18\u5148\u904d\u5386 DFS \u8f85\u52a9\u51fd\u6570 */\nfunc dfs(graph: GraphAdjList, visited: inout Set&lt;Vertex&gt;, res: inout [Vertex], vet: Vertex) {\nres.append(vet) // \u8bb0\u5f55\u8bbf\u95ee\u9876\u70b9\nvisited.insert(vet) // \u6807\u8bb0\u8be5\u9876\u70b9\u5df2\u88ab\u8bbf\u95ee\n// \u904d\u5386\u8be5\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nfor adjVet in graph.adjList[vet] ?? [] {\nif visited.contains(adjVet) {\ncontinue // \u8df3\u8fc7\u5df2\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9\n}\n// \u9012\u5f52\u8bbf\u95ee\u90bb\u63a5\u9876\u70b9\ndfs(graph: graph, visited: &amp;visited, res: &amp;res, vet: adjVet)\n}\n}\n/* \u6df1\u5ea6\u4f18\u5148\u904d\u5386 DFS */\n// \u4f7f\u7528\u90bb\u63a5\u8868\u6765\u8868\u793a\u56fe\uff0c\u4ee5\u4fbf\u83b7\u53d6\u6307\u5b9a\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nfunc graphDFS(graph: GraphAdjList, startVet: Vertex) -&gt; [Vertex] {\n// \u9876\u70b9\u904d\u5386\u5e8f\u5217\nvar res: [Vertex] = []\n// \u54c8\u5e0c\u8868\uff0c\u7528\u4e8e\u8bb0\u5f55\u5df2\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9\nvar visited: Set&lt;Vertex&gt; = []\ndfs(graph: graph, visited: &amp;visited, res: &amp;res, vet: startVet)\nreturn res\n}\n</code></pre> graph_dfs.zig<pre><code>[class]{}-[func]{dfs}\n[class]{}-[func]{graphDFS}\n</code></pre> graph_dfs.dart<pre><code>/* \u6df1\u5ea6\u4f18\u5148\u904d\u5386 DFS \u8f85\u52a9\u51fd\u6570 */\nvoid dfs(\nGraphAdjList graph,\nSet&lt;Vertex&gt; visited,\nList&lt;Vertex&gt; res,\nVertex vet,\n) {\nres.add(vet); // \u8bb0\u5f55\u8bbf\u95ee\u9876\u70b9\nvisited.add(vet); // \u6807\u8bb0\u8be5\u9876\u70b9\u5df2\u88ab\u8bbf\u95ee\n// \u904d\u5386\u8be5\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\nfor (Vertex adjVet in graph.adjList[vet]!) {\nif (visited.contains(adjVet)) {\ncontinue; // \u8df3\u8fc7\u5df2\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9\n}\n// \u9012\u5f52\u8bbf\u95ee\u90bb\u63a5\u9876\u70b9\ndfs(graph, visited, res, adjVet);\n}\n}\n/* \u6df1\u5ea6\u4f18\u5148\u904d\u5386 DFS */\nList&lt;Vertex&gt; graphDFS(GraphAdjList graph, Vertex startVet) {\n// \u9876\u70b9\u904d\u5386\u5e8f\u5217\nList&lt;Vertex&gt; res = [];\n// \u54c8\u5e0c\u8868\uff0c\u7528\u4e8e\u8bb0\u5f55\u5df2\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9\nSet&lt;Vertex&gt; visited = {};\ndfs(graph, visited, res, startVet);\nreturn res;\n}\n</code></pre> <p>\u6df1\u5ea6\u4f18\u5148\u904d\u5386\u7684\u7b97\u6cd5\u6d41\u7a0b\u5982\u4e0b\u56fe\u6240\u793a\uff0c\u5176\u4e2d\uff1a</p> <ul> <li>\u76f4\u865a\u7ebf\u4ee3\u8868\u5411\u4e0b\u9012\u63a8\uff0c\u8868\u793a\u5f00\u542f\u4e86\u4e00\u4e2a\u65b0\u7684\u9012\u5f52\u65b9\u6cd5\u6765\u8bbf\u95ee\u65b0\u9876\u70b9\uff1b</li> <li>\u66f2\u865a\u7ebf\u4ee3\u8868\u5411\u4e0a\u56de\u6eaf\uff0c\u8868\u793a\u6b64\u9012\u5f52\u65b9\u6cd5\u5df2\u7ecf\u8fd4\u56de\uff0c\u56de\u6eaf\u5230\u4e86\u5f00\u542f\u6b64\u9012\u5f52\u65b9\u6cd5\u7684\u4f4d\u7f6e\uff1b</li> </ul> <p>\u4e3a\u4e86\u52a0\u6df1\u7406\u89e3\uff0c\u5efa\u8bae\u5c06\u56fe\u793a\u4e0e\u4ee3\u7801\u7ed3\u5408\u8d77\u6765\uff0c\u5728\u8111\u4e2d\uff08\u6216\u8005\u7528\u7b14\u753b\u4e0b\u6765\uff09\u6a21\u62df\u6574\u4e2a DFS \u8fc7\u7a0b\uff0c\u5305\u62ec\u6bcf\u4e2a\u9012\u5f52\u65b9\u6cd5\u4f55\u65f6\u5f00\u542f\u3001\u4f55\u65f6\u8fd4\u56de\u3002</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt;&lt;11&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p>\u6df1\u5ea6\u4f18\u5148\u904d\u5386\u7684\u5e8f\u5217\u662f\u5426\u552f\u4e00\uff1f</p> <p>\u4e0e\u5e7f\u5ea6\u4f18\u5148\u904d\u5386\u7c7b\u4f3c\uff0c\u6df1\u5ea6\u4f18\u5148\u904d\u5386\u5e8f\u5217\u7684\u987a\u5e8f\u4e5f\u4e0d\u662f\u552f\u4e00\u7684\u3002\u7ed9\u5b9a\u67d0\u9876\u70b9\uff0c\u5148\u5f80\u54ea\u4e2a\u65b9\u5411\u63a2\u7d22\u90fd\u53ef\u4ee5\uff0c\u5373\u90bb\u63a5\u9876\u70b9\u7684\u987a\u5e8f\u53ef\u4ee5\u4efb\u610f\u6253\u4e71\uff0c\u90fd\u662f\u6df1\u5ea6\u4f18\u5148\u904d\u5386\u3002</p> <p>\u4ee5\u6811\u7684\u904d\u5386\u4e3a\u4f8b\uff0c\u201c\u6839 \\(\\rightarrow\\) \u5de6 \\(\\rightarrow\\) \u53f3\u201d\u3001\u201c\u5de6 \\(\\rightarrow\\) \u6839 \\(\\rightarrow\\) \u53f3\u201d\u3001\u201c\u5de6 \\(\\rightarrow\\) \u53f3 \\(\\rightarrow\\) \u6839\u201d\u5206\u522b\u5bf9\u5e94\u524d\u5e8f\u3001\u4e2d\u5e8f\u3001\u540e\u5e8f\u904d\u5386\uff0c\u5b83\u4eec\u5c55\u793a\u4e86\u4e09\u79cd\u4e0d\u540c\u7684\u904d\u5386\u4f18\u5148\u7ea7\uff0c\u7136\u800c\u8fd9\u4e09\u8005\u90fd\u5c5e\u4e8e\u6df1\u5ea6\u4f18\u5148\u904d\u5386\u3002</p>"},{"location":"chapter_graph/graph_traversal/#_4","title":"\u590d\u6742\u5ea6\u5206\u6790","text":"<p>\u65f6\u95f4\u590d\u6742\u5ea6\uff1a \u6240\u6709\u9876\u70b9\u90fd\u4f1a\u88ab\u8bbf\u95ee \\(1\\) \u6b21\uff0c\u4f7f\u7528 \\(O(|V|)\\) \u65f6\u95f4\uff1b\u6240\u6709\u8fb9\u90fd\u4f1a\u88ab\u8bbf\u95ee \\(2\\) \u6b21\uff0c\u4f7f\u7528 \\(O(2|E|)\\) \u65f6\u95f4\uff1b\u603b\u4f53\u4f7f\u7528 \\(O(|V| + |E|)\\) \u65f6\u95f4\u3002</p> <p>\u7a7a\u95f4\u590d\u6742\u5ea6\uff1a \u5217\u8868 <code>res</code> \uff0c\u54c8\u5e0c\u8868 <code>visited</code> \u9876\u70b9\u6570\u91cf\u6700\u591a\u4e3a \\(|V|\\) \uff0c\u9012\u5f52\u6df1\u5ea6\u6700\u5927\u4e3a \\(|V|\\) \uff0c\u56e0\u6b64\u4f7f\u7528 \\(O(|V|)\\) \u7a7a\u95f4\u3002</p>"},{"location":"chapter_graph/summary/","title":"9.4. \u00a0 \u5c0f\u7ed3","text":"<ul> <li>\u56fe\u7531\u9876\u70b9\u548c\u8fb9\u7ec4\u6210\uff0c\u53ef\u4ee5\u88ab\u8868\u793a\u4e3a\u4e00\u7ec4\u9876\u70b9\u548c\u4e00\u7ec4\u8fb9\u6784\u6210\u7684\u96c6\u5408\u3002</li> <li>\u76f8\u8f83\u4e8e\u7ebf\u6027\u5173\u7cfb\uff08\u94fe\u8868\uff09\u548c\u5206\u6cbb\u5173\u7cfb\uff08\u6811\uff09\uff0c\u7f51\u7edc\u5173\u7cfb\uff08\u56fe\uff09\u5177\u6709\u66f4\u9ad8\u7684\u81ea\u7531\u5ea6\uff0c\u56e0\u800c\u66f4\u4e3a\u590d\u6742\u3002</li> <li>\u6709\u5411\u56fe\u7684\u8fb9\u5177\u6709\u65b9\u5411\u6027\uff0c\u8fde\u901a\u56fe\u4e2d\u7684\u4efb\u610f\u9876\u70b9\u5747\u53ef\u8fbe\uff0c\u6709\u6743\u56fe\u7684\u6bcf\u6761\u8fb9\u90fd\u5305\u542b\u6743\u91cd\u53d8\u91cf\u3002</li> <li>\u90bb\u63a5\u77e9\u9635\u5229\u7528\u77e9\u9635\u6765\u8868\u793a\u56fe\uff0c\u6bcf\u4e00\u884c\uff08\u5217\uff09\u4ee3\u8868\u4e00\u4e2a\u9876\u70b9\uff0c\u77e9\u9635\u5143\u7d20\u4ee3\u8868\u8fb9\uff0c\u7528 \\(1\\) \u6216 \\(0\\) \u8868\u793a\u4e24\u4e2a\u9876\u70b9\u4e4b\u95f4\u6709\u8fb9\u6216\u65e0\u8fb9\u3002\u90bb\u63a5\u77e9\u9635\u5728\u589e\u5220\u67e5\u64cd\u4f5c\u4e0a\u6548\u7387\u5f88\u9ad8\uff0c\u4f46\u7a7a\u95f4\u5360\u7528\u8f83\u591a\u3002</li> <li>\u90bb\u63a5\u8868\u4f7f\u7528\u591a\u4e2a\u94fe\u8868\u6765\u8868\u793a\u56fe\uff0c\u7b2c \\(i\\) \u6761\u94fe\u8868\u5bf9\u5e94\u9876\u70b9 \\(i\\) \uff0c\u5176\u4e2d\u5b58\u50a8\u4e86\u8be5\u9876\u70b9\u7684\u6240\u6709\u90bb\u63a5\u9876\u70b9\u3002\u90bb\u63a5\u8868\u76f8\u5bf9\u4e8e\u90bb\u63a5\u77e9\u9635\u66f4\u52a0\u8282\u7701\u7a7a\u95f4\uff0c\u4f46\u7531\u4e8e\u9700\u8981\u904d\u5386\u94fe\u8868\u6765\u67e5\u627e\u8fb9\uff0c\u65f6\u95f4\u6548\u7387\u8f83\u4f4e\u3002</li> <li>\u5f53\u90bb\u63a5\u8868\u4e2d\u7684\u94fe\u8868\u8fc7\u957f\u65f6\uff0c\u53ef\u4ee5\u5c06\u5176\u8f6c\u6362\u4e3a\u7ea2\u9ed1\u6811\u6216\u54c8\u5e0c\u8868\uff0c\u4ece\u800c\u63d0\u5347\u67e5\u8be2\u6548\u7387\u3002</li> <li>\u4ece\u7b97\u6cd5\u601d\u60f3\u89d2\u5ea6\u5206\u6790\uff0c\u90bb\u63a5\u77e9\u9635\u4f53\u73b0\u201c\u4ee5\u7a7a\u95f4\u6362\u65f6\u95f4\u201d\uff0c\u90bb\u63a5\u8868\u4f53\u73b0\u201c\u4ee5\u65f6\u95f4\u6362\u7a7a\u95f4\u201d\u3002</li> <li>\u56fe\u53ef\u7528\u4e8e\u5efa\u6a21\u5404\u7c7b\u73b0\u5b9e\u7cfb\u7edf\uff0c\u5982\u793e\u4ea4\u7f51\u7edc\u3001\u5730\u94c1\u7ebf\u8def\u7b49\u3002</li> <li>\u6811\u662f\u56fe\u7684\u4e00\u79cd\u7279\u4f8b\uff0c\u6811\u7684\u904d\u5386\u4e5f\u662f\u56fe\u7684\u904d\u5386\u7684\u4e00\u79cd\u7279\u4f8b\u3002</li> <li>\u56fe\u7684\u5e7f\u5ea6\u4f18\u5148\u904d\u5386\u662f\u4e00\u79cd\u7531\u8fd1\u53ca\u8fdc\u3001\u5c42\u5c42\u6269\u5f20\u7684\u641c\u7d22\u65b9\u5f0f\uff0c\u901a\u5e38\u501f\u52a9\u961f\u5217\u5b9e\u73b0\u3002</li> <li>\u56fe\u7684\u6df1\u5ea6\u4f18\u5148\u904d\u5386\u662f\u4e00\u79cd\u4f18\u5148\u8d70\u5230\u5e95\u3001\u65e0\u8def\u53ef\u8d70\u65f6\u518d\u56de\u6eaf\u7684\u641c\u7d22\u65b9\u5f0f\uff0c\u5e38\u57fa\u4e8e\u9012\u5f52\u6765\u5b9e\u73b0\u3002</li> </ul>"},{"location":"chapter_graph/summary/#941-q-a","title":"9.4.1. \u00a0 Q &amp; A","text":"<p>\u8def\u5f84\u7684\u5b9a\u4e49\u662f\u9876\u70b9\u5e8f\u5217\u8fd8\u662f\u8fb9\u5e8f\u5217\uff1f</p> <p>\u7ef4\u57fa\u767e\u79d1\u4e0a\u4e0d\u540c\u8bed\u8a00\u7248\u672c\u7684\u5b9a\u4e49\u4e0d\u4e00\u81f4\uff1a\u82f1\u6587\u7248\u662f\u201c\u8def\u5f84\u662f\u4e00\u4e2a\u8fb9\u5e8f\u5217\u201d\uff0c\u800c\u4e2d\u6587\u7248\u662f\u201c\u8def\u5f84\u662f\u4e00\u4e2a\u9876\u70b9\u5e8f\u5217\u201d\u3002\u4ee5\u4e0b\u662f\u82f1\u6587\u7248\u539f\u6587\uff1aIn graph theory, a path in a graph is a finite or infinite sequence of edges which joins a sequence of vertices. \u5728\u672c\u6587\u4e2d\uff0c\u8def\u5f84\u88ab\u8ba4\u4e3a\u662f\u4e00\u4e2a\u8fb9\u5e8f\u5217\uff0c\u800c\u4e0d\u662f\u4e00\u4e2a\u9876\u70b9\u5e8f\u5217\u3002\u8fd9\u662f\u56e0\u4e3a\u4e24\u4e2a\u9876\u70b9\u4e4b\u95f4\u53ef\u80fd\u5b58\u5728\u591a\u6761\u8fb9\u8fde\u63a5\uff0c\u6b64\u65f6\u6bcf\u6761\u8fb9\u90fd\u5bf9\u5e94\u4e00\u6761\u8def\u5f84\u3002</p> <p>\u975e\u8fde\u901a\u56fe\u4e2d\uff0c\u662f\u5426\u4f1a\u6709\u65e0\u6cd5\u904d\u5386\u5230\u7684\u70b9\uff1f</p> <p>\u5728\u975e\u8fde\u901a\u56fe\u4e2d\uff0c\u4ece\u67d0\u4e2a\u9876\u70b9\u51fa\u53d1\uff0c\u81f3\u5c11\u6709\u4e00\u4e2a\u9876\u70b9\u65e0\u6cd5\u5230\u8fbe\u3002\u904d\u5386\u975e\u8fde\u901a\u56fe\u9700\u8981\u8bbe\u7f6e\u591a\u4e2a\u8d77\u70b9\uff0c\u4ee5\u904d\u5386\u5230\u56fe\u7684\u6240\u6709\u8fde\u901a\u5206\u91cf\u3002</p> <p>\u5728\u90bb\u63a5\u8868\u4e2d\uff0c\u201c\u4e0e\u8be5\u9876\u70b9\u76f8\u8fde\u7684\u6240\u6709\u9876\u70b9\u201d\u7684\u9876\u70b9\u987a\u5e8f\u662f\u5426\u6709\u8981\u6c42\uff1f</p> <p>\u53ef\u4ee5\u662f\u4efb\u610f\u987a\u5e8f\u3002\u4f46\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u53ef\u80fd\u4f1a\u9700\u8981\u6309\u7167\u6307\u5b9a\u89c4\u5219\u6765\u6392\u5e8f\uff0c\u6bd4\u5982\u6309\u7167\u9876\u70b9\u6dfb\u52a0\u7684\u6b21\u5e8f\u3001\u6216\u8005\u6309\u7167\u9876\u70b9\u503c\u5927\u5c0f\u7684\u987a\u5e8f\u7b49\u7b49\uff0c\u8fd9\u6837\u53ef\u4ee5\u6709\u52a9\u4e8e\u5feb\u901f\u67e5\u627e\u201c\u5e26\u6709\u67d0\u79cd\u6781\u503c\u201d\u7684\u9876\u70b9\u3002</p>"},{"location":"chapter_hashing/","title":"6. \u00a0 \u6563\u5217\u8868","text":""},{"location":"chapter_hashing/hash_collision/","title":"6.2. \u00a0 \u54c8\u5e0c\u51b2\u7a81","text":"<p>\u5728\u7406\u60f3\u60c5\u51b5\u4e0b\uff0c\u54c8\u5e0c\u51fd\u6570\u4e3a\u6bcf\u4e2a\u8f93\u5165\u751f\u6210\u552f\u4e00\u7684\u8f93\u51fa\uff0c\u5b9e\u73b0 key \u548c\u6570\u7ec4\u7d22\u5f15\u7684\u4e00\u4e00\u5bf9\u5e94\u3002\u4f46\u5b9e\u9645\u4e0a\uff0c\u54c8\u5e0c\u51fd\u6570\u7684\u8f93\u5165\u7a7a\u95f4\u901a\u5e38\u8fdc\u5927\u4e8e\u8f93\u51fa\u7a7a\u95f4\uff0c\u56e0\u6b64\u591a\u4e2a\u8f93\u5165\u4ea7\u751f\u76f8\u540c\u8f93\u51fa\u7684\u60c5\u51b5\u662f\u4e0d\u53ef\u907f\u514d\u7684\u3002\u4f8b\u5982\uff0c\u8f93\u5165\u7a7a\u95f4\u4e3a\u5168\u4f53\u6574\u6570\uff0c\u8f93\u51fa\u7a7a\u95f4\u4e3a\u6570\u7ec4\u5bb9\u91cf\u5927\u5c0f\uff0c\u5219\u5fc5\u7136\u6709\u591a\u4e2a\u6574\u6570\u6620\u5c04\u81f3\u540c\u4e00\u6570\u7ec4\u7d22\u5f15\u3002</p> <p>\u8fd9\u79cd\u591a\u4e2a\u8f93\u5165\u5bf9\u5e94\u540c\u4e00\u8f93\u51fa\u7d22\u5f15\u7684\u73b0\u8c61\u88ab\u79f0\u4e3a\u300c\u54c8\u5e0c\u51b2\u7a81 Hash Collision\u300d\u3002\u54c8\u5e0c\u51b2\u7a81\u4f1a\u5bfc\u81f4\u67e5\u8be2\u7ed3\u679c\u9519\u8bef\uff0c\u4e25\u91cd\u5f71\u54cd\u54c8\u5e0c\u8868\u7684\u53ef\u7528\u6027\u3002\u54c8\u5e0c\u51b2\u7a81\u7684\u5904\u7406\u65b9\u6cd5\u4e3b\u8981\u6709\u4e24\u79cd\uff1a</p> <ul> <li>\u6269\u5927\u54c8\u5e0c\u8868\u5bb9\u91cf\uff1a\u54c8\u5e0c\u8868\u5bb9\u91cf\u8d8a\u5927\uff0c\u952e\u503c\u5bf9\u805a\u96c6\u7684\u6982\u7387\u5c31\u8d8a\u4f4e\u3002\u6781\u7aef\u60c5\u51b5\u4e0b\uff0c\u5f53\u8f93\u5165\u7a7a\u95f4\u548c\u8f93\u51fa\u7a7a\u95f4\u5927\u5c0f\u76f8\u7b49\u65f6\uff0c\u54c8\u5e0c\u8868\u7b49\u540c\u4e8e\u6570\u7ec4\uff0c\u6bcf\u4e2a key \u90fd\u5bf9\u5e94\u552f\u4e00\u7684\u6570\u7ec4\u7d22\u5f15\u3002</li> <li>\u4f18\u5316\u54c8\u5e0c\u8868\u7ed3\u6784\uff1a\u5e38\u7528\u65b9\u6cd5\u5305\u62ec\u94fe\u5f0f\u5730\u5740\u548c\u5f00\u653e\u5bfb\u5740\u3002\u8fd9\u7c7b\u65b9\u6cd5\u7684\u601d\u8def\u662f\u901a\u8fc7\u6539\u826f\u6570\u636e\u7ed3\u6784\uff0c\u4f7f\u5f97\u54c8\u5e0c\u8868\u53ef\u4ee5\u5728\u53d1\u751f\u54c8\u5e0c\u51b2\u7a81\u65f6\u4ecd\u7136\u53ef\u4ee5\u6b63\u5e38\u5de5\u4f5c\u3002\u5f53\u7136\uff0c\u8fd9\u4e9b\u4f18\u5316\u5f80\u5f80\u662f\u4ee5\u727a\u7272\u65f6\u95f4\u6548\u7387\u4e3a\u4ee3\u4ef7\u7684\u3002</li> </ul>"},{"location":"chapter_hashing/hash_collision/#621","title":"6.2.1. \u00a0 \u54c8\u5e0c\u8868\u6269\u5bb9","text":"<p>\u54c8\u5e0c\u51fd\u6570\u7684\u6700\u540e\u4e00\u6b65\u901a\u5e38\u662f\u5bf9\u6876\u6570\u91cf \\(n\\) \u53d6\u4f59\uff0c\u4f5c\u7528\u662f\u5c06\u54c8\u5e0c\u503c\u6620\u5c04\u5230\u6876\u7d22\u5f15\u8303\u56f4\uff0c\u4ece\u800c\u5c06 key \u653e\u5165\u5bf9\u5e94\u7684\u6876\u4e2d\u3002\u5f53\u54c8\u5e0c\u8868\u5bb9\u91cf\u8d8a\u5927\uff08\u5373 \\(n\\) \u8d8a\u5927\uff09\u65f6\uff0c\u591a\u4e2a key \u88ab\u5206\u914d\u5230\u540c\u4e00\u4e2a\u6876\u4e2d\u7684\u6982\u7387\u5c31\u8d8a\u4f4e\uff0c\u51b2\u7a81\u5c31\u8d8a\u5c11\u3002\u56e0\u6b64\uff0c\u5f53\u54c8\u5e0c\u8868\u5185\u7684\u51b2\u7a81\u603b\u4f53\u8f83\u4e3a\u4e25\u91cd\u65f6\uff0c\u7f16\u7a0b\u8bed\u8a00\u901a\u5e38\u901a\u8fc7\u6269\u5bb9\u54c8\u5e0c\u8868\u6765\u7f13\u89e3\u51b2\u7a81\u3002\u7c7b\u4f3c\u4e8e\u6570\u7ec4\u6269\u5bb9\uff0c\u54c8\u5e0c\u8868\u6269\u5bb9\u9700\u5c06\u6240\u6709\u952e\u503c\u5bf9\u4ece\u539f\u54c8\u5e0c\u8868\u8fc1\u79fb\u81f3\u65b0\u54c8\u5e0c\u8868\uff0c\u5f00\u9500\u8f83\u5927\u3002</p> <p>\u7f16\u7a0b\u8bed\u8a00\u901a\u5e38\u4f7f\u7528\u300c\u8d1f\u8f7d\u56e0\u5b50 Load Factor\u300d\u6765\u8861\u91cf\u54c8\u5e0c\u51b2\u7a81\u7684\u4e25\u91cd\u7a0b\u5ea6\uff0c\u5b9a\u4e49\u4e3a\u54c8\u5e0c\u8868\u4e2d\u5143\u7d20\u6570\u91cf\u9664\u4ee5\u6876\u6570\u91cf\uff0c\u5e38\u4f5c\u4e3a\u54c8\u5e0c\u8868\u6269\u5bb9\u7684\u89e6\u53d1\u6761\u4ef6\u3002\u5728 Java \u4e2d\uff0c\u5f53\u8d1f\u8f7d\u56e0\u5b50\u8d85\u8fc7 \\(0.75\\) \u65f6\uff0c\u7cfb\u7edf\u4f1a\u5c06 HashMap \u5bb9\u91cf\u6269\u5c55\u4e3a\u539f\u5148\u7684 \\(2\\) \u500d\u3002</p>"},{"location":"chapter_hashing/hash_collision/#622","title":"6.2.2. \u00a0 \u94fe\u5f0f\u5730\u5740","text":"<p>\u5728\u539f\u59cb\u54c8\u5e0c\u8868\u4e2d\uff0c\u6bcf\u4e2a\u6876\u4ec5\u80fd\u5b58\u50a8\u4e00\u4e2a\u952e\u503c\u5bf9\u3002\u300c\u94fe\u5f0f\u5730\u5740 Separate Chaining\u300d\u5c06\u5355\u4e2a\u5143\u7d20\u8f6c\u6362\u4e3a\u94fe\u8868\uff0c\u5c06\u952e\u503c\u5bf9\u4f5c\u4e3a\u94fe\u8868\u8282\u70b9\uff0c\u5c06\u6240\u6709\u53d1\u751f\u51b2\u7a81\u7684\u952e\u503c\u5bf9\u90fd\u5b58\u50a8\u5728\u540c\u4e00\u94fe\u8868\u4e2d\u3002</p> <p></p> <p> Fig. \u94fe\u5f0f\u5730\u5740\u54c8\u5e0c\u8868 </p> <p>\u94fe\u5f0f\u5730\u5740\u4e0b\uff0c\u54c8\u5e0c\u8868\u7684\u64cd\u4f5c\u65b9\u6cd5\u5305\u62ec\uff1a</p> <ul> <li>\u67e5\u8be2\u5143\u7d20\uff1a\u8f93\u5165 key \uff0c\u7ecf\u8fc7\u54c8\u5e0c\u51fd\u6570\u5f97\u5230\u6570\u7ec4\u7d22\u5f15\uff0c\u5373\u53ef\u8bbf\u95ee\u94fe\u8868\u5934\u8282\u70b9\uff0c\u7136\u540e\u904d\u5386\u94fe\u8868\u5e76\u5bf9\u6bd4 key \u4ee5\u67e5\u627e\u76ee\u6807\u952e\u503c\u5bf9\u3002</li> <li>\u6dfb\u52a0\u5143\u7d20\uff1a\u5148\u901a\u8fc7\u54c8\u5e0c\u51fd\u6570\u8bbf\u95ee\u94fe\u8868\u5934\u8282\u70b9\uff0c\u7136\u540e\u5c06\u8282\u70b9\uff08\u5373\u952e\u503c\u5bf9\uff09\u6dfb\u52a0\u5230\u94fe\u8868\u4e2d\u3002</li> <li>\u5220\u9664\u5143\u7d20\uff1a\u6839\u636e\u54c8\u5e0c\u51fd\u6570\u7684\u7ed3\u679c\u8bbf\u95ee\u94fe\u8868\u5934\u90e8\uff0c\u63a5\u7740\u904d\u5386\u94fe\u8868\u4ee5\u67e5\u627e\u76ee\u6807\u8282\u70b9\uff0c\u5e76\u5c06\u5176\u5220\u9664\u3002</li> </ul> <p>\u8be5\u65b9\u6cd5\u5b58\u5728\u4e00\u4e9b\u5c40\u9650\u6027\uff0c\u5305\u62ec\uff1a</p> <ul> <li>\u5360\u7528\u7a7a\u95f4\u589e\u5927\uff0c\u7531\u4e8e\u94fe\u8868\u6216\u4e8c\u53c9\u6811\u5305\u542b\u8282\u70b9\u6307\u9488\uff0c\u76f8\u6bd4\u6570\u7ec4\u66f4\u52a0\u8017\u8d39\u5185\u5b58\u7a7a\u95f4\uff1b</li> <li>\u67e5\u8be2\u6548\u7387\u964d\u4f4e\uff0c\u56e0\u4e3a\u9700\u8981\u7ebf\u6027\u904d\u5386\u94fe\u8868\u6765\u67e5\u627e\u5bf9\u5e94\u5143\u7d20\uff1b</li> </ul> <p>\u4ee5\u4e0b\u7ed9\u51fa\u4e86\u94fe\u5f0f\u5730\u5740\u54c8\u5e0c\u8868\u7684\u7b80\u5355\u5b9e\u73b0\uff0c\u9700\u8981\u6ce8\u610f\uff1a</p> <ul> <li>\u4e3a\u4e86\u4f7f\u5f97\u4ee3\u7801\u5c3d\u91cf\u7b80\u77ed\uff0c\u6211\u4eec\u4f7f\u7528\u5217\u8868\uff08\u52a8\u6001\u6570\u7ec4\uff09\u4ee3\u66ff\u94fe\u8868\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u54c8\u5e0c\u8868\uff08\u6570\u7ec4\uff09\u5305\u542b\u591a\u4e2a\u6876\uff0c\u6bcf\u4e2a\u6876\u90fd\u662f\u4e00\u4e2a\u5217\u8868\u3002</li> <li>\u4ee5\u4e0b\u4ee3\u7801\u5b9e\u73b0\u4e86\u54c8\u5e0c\u8868\u6269\u5bb9\u65b9\u6cd5\u3002\u5177\u4f53\u6765\u770b\uff0c\u5f53\u8d1f\u8f7d\u56e0\u5b50\u8d85\u8fc7 \\(0.75\\) \u65f6\uff0c\u6211\u4eec\u5c06\u54c8\u5e0c\u8868\u6269\u5bb9\u81f3 \\(2\\) \u500d\u3002</li> </ul> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart hash_map_chaining.java<pre><code>/* \u952e\u503c\u5bf9 */\nclass Pair {\npublic int key;\npublic String val;\npublic Pair(int key, String val) {\nthis.key = key;\nthis.val = val;\n}\n}\n/* \u94fe\u5f0f\u5730\u5740\u54c8\u5e0c\u8868 */\nclass HashMapChaining {\nint size; // \u952e\u503c\u5bf9\u6570\u91cf\nint capacity; // \u54c8\u5e0c\u8868\u5bb9\u91cf\ndouble loadThres; // \u89e6\u53d1\u6269\u5bb9\u7684\u8d1f\u8f7d\u56e0\u5b50\u9608\u503c\nint extendRatio; // \u6269\u5bb9\u500d\u6570\nList&lt;List&lt;Pair&gt;&gt; buckets; // \u6876\u6570\u7ec4\n/* \u6784\u9020\u65b9\u6cd5 */\npublic HashMapChaining() {\nsize = 0;\ncapacity = 4;\nloadThres = 2 / 3.0;\nextendRatio = 2;\nbuckets = new ArrayList&lt;&gt;(capacity);\nfor (int i = 0; i &lt; capacity; i++) {\nbuckets.add(new ArrayList&lt;&gt;());\n}\n}\n/* \u54c8\u5e0c\u51fd\u6570 */\nint hashFunc(int key) {\nreturn key % capacity;\n}\n/* \u8d1f\u8f7d\u56e0\u5b50 */\ndouble loadFactor() {\nreturn (double) size / capacity;\n}\n/* \u67e5\u8be2\u64cd\u4f5c */\nString get(int key) {\nint index = hashFunc(key);\nList&lt;Pair&gt; bucket = buckets.get(index);\n// \u904d\u5386\u6876\uff0c\u82e5\u627e\u5230 key \u5219\u8fd4\u56de\u5bf9\u5e94 val\nfor (Pair pair : bucket) {\nif (pair.key == key) {\nreturn pair.val;\n}\n}\n// \u82e5\u672a\u627e\u5230 key \u5219\u8fd4\u56de null\nreturn null;\n}\n/* \u6dfb\u52a0\u64cd\u4f5c */\nvoid put(int key, String val) {\n// \u5f53\u8d1f\u8f7d\u56e0\u5b50\u8d85\u8fc7\u9608\u503c\u65f6\uff0c\u6267\u884c\u6269\u5bb9\nif (loadFactor() &gt; loadThres) {\nextend();\n}\nint index = hashFunc(key);\nList&lt;Pair&gt; bucket = buckets.get(index);\n// \u904d\u5386\u6876\uff0c\u82e5\u9047\u5230\u6307\u5b9a key \uff0c\u5219\u66f4\u65b0\u5bf9\u5e94 val \u5e76\u8fd4\u56de\nfor (Pair pair : bucket) {\nif (pair.key == key) {\npair.val = val;\nreturn;\n}\n}\n// \u82e5\u65e0\u8be5 key \uff0c\u5219\u5c06\u952e\u503c\u5bf9\u6dfb\u52a0\u81f3\u5c3e\u90e8\nPair pair = new Pair(key, val);\nbucket.add(pair);\nsize++;\n}\n/* \u5220\u9664\u64cd\u4f5c */\nvoid remove(int key) {\nint index = hashFunc(key);\nList&lt;Pair&gt; bucket = buckets.get(index);\n// \u904d\u5386\u6876\uff0c\u4ece\u4e2d\u5220\u9664\u952e\u503c\u5bf9\nfor (Pair pair : bucket) {\nif (pair.key == key)\nbucket.remove(pair);\n}\nsize--;\n}\n/* \u6269\u5bb9\u54c8\u5e0c\u8868 */\nvoid extend() {\n// \u6682\u5b58\u539f\u54c8\u5e0c\u8868\nList&lt;List&lt;Pair&gt;&gt; bucketsTmp = buckets;\n// \u521d\u59cb\u5316\u6269\u5bb9\u540e\u7684\u65b0\u54c8\u5e0c\u8868\ncapacity *= extendRatio;\nbuckets = new ArrayList&lt;&gt;(capacity);\nfor (int i = 0; i &lt; capacity; i++) {\nbuckets.add(new ArrayList&lt;&gt;());\n}\nsize = 0;\n// \u5c06\u952e\u503c\u5bf9\u4ece\u539f\u54c8\u5e0c\u8868\u642c\u8fd0\u81f3\u65b0\u54c8\u5e0c\u8868\nfor (List&lt;Pair&gt; bucket : bucketsTmp) {\nfor (Pair pair : bucket) {\nput(pair.key, pair.val);\n}\n}\n}\n/* \u6253\u5370\u54c8\u5e0c\u8868 */\nvoid print() {\nfor (List&lt;Pair&gt; bucket : buckets) {\nList&lt;String&gt; res = new ArrayList&lt;&gt;();\nfor (Pair pair : bucket) {\nres.add(pair.key + \" -&gt; \" + pair.val);\n}\nSystem.out.println(res);\n}\n}\n}\n</code></pre> hash_map_chaining.cpp<pre><code>/* \u952e\u503c\u5bf9 */\nstruct Pair {\npublic:\nint key;\nstring val;\nPair(int key, string val) {\nthis-&gt;key = key;\nthis-&gt;val = val;\n}\n};\n/* \u94fe\u5f0f\u5730\u5740\u54c8\u5e0c\u8868 */\nclass HashMapChaining {\nprivate:\nint size;                       // \u952e\u503c\u5bf9\u6570\u91cf\nint capacity;                   // \u54c8\u5e0c\u8868\u5bb9\u91cf\ndouble loadThres;               // \u89e6\u53d1\u6269\u5bb9\u7684\u8d1f\u8f7d\u56e0\u5b50\u9608\u503c\nint extendRatio;                // \u6269\u5bb9\u500d\u6570\nvector&lt;vector&lt;Pair *&gt;&gt; buckets; // \u6876\u6570\u7ec4\npublic:\n/* \u6784\u9020\u65b9\u6cd5 */\nHashMapChaining() : size(0), capacity(4), loadThres(2.0 / 3), extendRatio(2) {\nbuckets.resize(capacity);\n}\n/* \u54c8\u5e0c\u51fd\u6570 */\nint hashFunc(int key) {\nreturn key % capacity;\n}\n/* \u8d1f\u8f7d\u56e0\u5b50 */\ndouble loadFactor() {\nreturn (double)size / (double)capacity;\n}\n/* \u67e5\u8be2\u64cd\u4f5c */\nstring get(int key) {\nint index = hashFunc(key);\n// \u904d\u5386\u6876\uff0c\u82e5\u627e\u5230 key \u5219\u8fd4\u56de\u5bf9\u5e94 val\nfor (Pair *pair : buckets[index]) {\nif (pair-&gt;key == key) {\nreturn pair-&gt;val;\n}\n}\n// \u82e5\u672a\u627e\u5230 key \u5219\u8fd4\u56de nullptr\nreturn nullptr;\n}\n/* \u6dfb\u52a0\u64cd\u4f5c */\nvoid put(int key, string val) {\n// \u5f53\u8d1f\u8f7d\u56e0\u5b50\u8d85\u8fc7\u9608\u503c\u65f6\uff0c\u6267\u884c\u6269\u5bb9\nif (loadFactor() &gt; loadThres) {\nextend();\n}\nint index = hashFunc(key);\n// \u904d\u5386\u6876\uff0c\u82e5\u9047\u5230\u6307\u5b9a key \uff0c\u5219\u66f4\u65b0\u5bf9\u5e94 val \u5e76\u8fd4\u56de\nfor (Pair *pair : buckets[index]) {\nif (pair-&gt;key == key) {\npair-&gt;val = val;\nreturn;\n}\n}\n// \u82e5\u65e0\u8be5 key \uff0c\u5219\u5c06\u952e\u503c\u5bf9\u6dfb\u52a0\u81f3\u5c3e\u90e8\nbuckets[index].push_back(new Pair(key, val));\nsize++;\n}\n/* \u5220\u9664\u64cd\u4f5c */\nvoid remove(int key) {\nint index = hashFunc(key);\nauto &amp;bucket = buckets[index];\n// \u904d\u5386\u6876\uff0c\u4ece\u4e2d\u5220\u9664\u952e\u503c\u5bf9\nfor (int i = 0; i &lt; bucket.size(); i++) {\nif (bucket[i]-&gt;key == key) {\nPair *tmp = bucket[i];\nbucket.erase(bucket.begin() + i); // \u4ece\u4e2d\u5220\u9664\u952e\u503c\u5bf9\ndelete tmp;                       // \u91ca\u653e\u5185\u5b58\nsize--;\nreturn;\n}\n}\n}\n/* \u6269\u5bb9\u54c8\u5e0c\u8868 */\nvoid extend() {\n// \u6682\u5b58\u539f\u54c8\u5e0c\u8868\nvector&lt;vector&lt;Pair *&gt;&gt; bucketsTmp = buckets;\n// \u521d\u59cb\u5316\u6269\u5bb9\u540e\u7684\u65b0\u54c8\u5e0c\u8868\ncapacity *= extendRatio;\nbuckets.clear();\nbuckets.resize(capacity);\nsize = 0;\n// \u5c06\u952e\u503c\u5bf9\u4ece\u539f\u54c8\u5e0c\u8868\u642c\u8fd0\u81f3\u65b0\u54c8\u5e0c\u8868\nfor (auto &amp;bucket : bucketsTmp) {\nfor (Pair *pair : bucket) {\nput(pair-&gt;key, pair-&gt;val);\n}\n}\n}\n/* \u6253\u5370\u54c8\u5e0c\u8868 */\nvoid print() {\nfor (auto &amp;bucket : buckets) {\ncout &lt;&lt; \"[\";\nfor (Pair *pair : bucket) {\ncout &lt;&lt; pair-&gt;key &lt;&lt; \" -&gt; \" &lt;&lt; pair-&gt;val &lt;&lt; \", \";\n}\ncout &lt;&lt; \"]\\n\";\n}\n}\n};\n</code></pre> hash_map_chaining.py<pre><code>class Pair:\n\"\"\"\u952e\u503c\u5bf9\"\"\"\ndef __init__(self, key: int, val: str):\nself.key = key\nself.val = val\nclass HashMapChaining:\n\"\"\"\u94fe\u5f0f\u5730\u5740\u54c8\u5e0c\u8868\"\"\"\ndef __init__(self):\n\"\"\"\u6784\u9020\u65b9\u6cd5\"\"\"\nself.size = 0  # \u952e\u503c\u5bf9\u6570\u91cf\nself.capacity = 4  # \u54c8\u5e0c\u8868\u5bb9\u91cf\nself.load_thres = 2 / 3  # \u89e6\u53d1\u6269\u5bb9\u7684\u8d1f\u8f7d\u56e0\u5b50\u9608\u503c\nself.extend_ratio = 2  # \u6269\u5bb9\u500d\u6570\nself.buckets = [[] for _ in range(self.capacity)]  # \u6876\u6570\u7ec4\ndef hash_func(self, key: int) -&gt; int:\n\"\"\"\u54c8\u5e0c\u51fd\u6570\"\"\"\nreturn key % self.capacity\ndef load_factor(self) -&gt; float:\n\"\"\"\u8d1f\u8f7d\u56e0\u5b50\"\"\"\nreturn self.size / self.capacity\ndef get(self, key: int) -&gt; str:\n\"\"\"\u67e5\u8be2\u64cd\u4f5c\"\"\"\nindex = self.hash_func(key)\nbucket = self.buckets[index]\n# \u904d\u5386\u6876\uff0c\u82e5\u627e\u5230 key \u5219\u8fd4\u56de\u5bf9\u5e94 val\nfor pair in bucket:\nif pair.key == key:\nreturn pair.val\n# \u82e5\u672a\u627e\u5230 key \u5219\u8fd4\u56de None\nreturn None\ndef put(self, key: int, val: str):\n\"\"\"\u6dfb\u52a0\u64cd\u4f5c\"\"\"\n# \u5f53\u8d1f\u8f7d\u56e0\u5b50\u8d85\u8fc7\u9608\u503c\u65f6\uff0c\u6267\u884c\u6269\u5bb9\nif self.load_factor() &gt; self.load_thres:\nself.extend()\nindex = self.hash_func(key)\nbucket = self.buckets[index]\n# \u904d\u5386\u6876\uff0c\u82e5\u9047\u5230\u6307\u5b9a key \uff0c\u5219\u66f4\u65b0\u5bf9\u5e94 val \u5e76\u8fd4\u56de\nfor pair in bucket:\nif pair.key == key:\npair.val = val\nreturn\n# \u82e5\u65e0\u8be5 key \uff0c\u5219\u5c06\u952e\u503c\u5bf9\u6dfb\u52a0\u81f3\u5c3e\u90e8\npair = Pair(key, val)\nbucket.append(pair)\nself.size += 1\ndef remove(self, key: int):\n\"\"\"\u5220\u9664\u64cd\u4f5c\"\"\"\nindex = self.hash_func(key)\nbucket = self.buckets[index]\n# \u904d\u5386\u6876\uff0c\u4ece\u4e2d\u5220\u9664\u952e\u503c\u5bf9\nfor pair in bucket:\nif pair.key == key:\nbucket.remove(pair)\nself.size -= 1\nreturn\ndef extend(self):\n\"\"\"\u6269\u5bb9\u54c8\u5e0c\u8868\"\"\"\n# \u6682\u5b58\u539f\u54c8\u5e0c\u8868\nbuckets = self.buckets\n# \u521d\u59cb\u5316\u6269\u5bb9\u540e\u7684\u65b0\u54c8\u5e0c\u8868\nself.capacity *= self.extend_ratio\nself.buckets = [[] for _ in range(self.capacity)]\nself.size = 0\n# \u5c06\u952e\u503c\u5bf9\u4ece\u539f\u54c8\u5e0c\u8868\u642c\u8fd0\u81f3\u65b0\u54c8\u5e0c\u8868\nfor bucket in buckets:\nfor pair in bucket:\nself.put(pair.key, pair.val)\ndef print(self):\n\"\"\"\u6253\u5370\u54c8\u5e0c\u8868\"\"\"\nfor bucket in self.buckets:\nres = []\nfor pair in bucket:\nres.append(str(pair.key) + \" -&gt; \" + pair.val)\nprint(res)\n</code></pre> hash_map_chaining.go<pre><code>[class]{pair}-[func]{}\n[class]{hashMapChaining}-[func]{}\n</code></pre> hash_map_chaining.js<pre><code>[class]{Pair}-[func]{}\n[class]{HashMapChaining}-[func]{}\n</code></pre> hash_map_chaining.ts<pre><code>[class]{Pair}-[func]{}\n[class]{HashMapChaining}-[func]{}\n</code></pre> hash_map_chaining.c<pre><code>[class]{pair}-[func]{}\n[class]{hashMapChaining}-[func]{}\n</code></pre> hash_map_chaining.cs<pre><code>[class]{Pair}-[func]{}\n[class]{HashMapChaining}-[func]{}\n</code></pre> hash_map_chaining.swift<pre><code>[class]{Pair}-[func]{}\n[class]{HashMapChaining}-[func]{}\n</code></pre> hash_map_chaining.zig<pre><code>[class]{Pair}-[func]{}\n[class]{HashMapChaining}-[func]{}\n</code></pre> hash_map_chaining.dart<pre><code>[class]{Pair}-[func]{}\n[class]{HashMapChaining}-[func]{}\n</code></pre> <p>Tip</p> <p>\u4e3a\u4e86\u63d0\u9ad8\u6548\u7387\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u94fe\u8868\u8f6c\u6362\u4e3a\u300cAVL \u6811\u300d\u6216\u300c\u7ea2\u9ed1\u6811\u300d\uff0c\u4ece\u800c\u5c06\u67e5\u8be2\u64cd\u4f5c\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4f18\u5316\u81f3 \\(O(\\log n)\\) \u3002</p>"},{"location":"chapter_hashing/hash_collision/#623","title":"6.2.3. \u00a0 \u5f00\u653e\u5bfb\u5740","text":"<p>\u300c\u5f00\u653e\u5bfb\u5740 Open Addressing\u300d\u4e0d\u5f15\u5165\u989d\u5916\u7684\u6570\u636e\u7ed3\u6784\uff0c\u800c\u662f\u901a\u8fc7\u201c\u591a\u6b21\u63a2\u6d4b\u201d\u6765\u5904\u7406\u54c8\u5e0c\u51b2\u7a81\uff0c\u63a2\u6d4b\u65b9\u5f0f\u4e3b\u8981\u5305\u62ec\u7ebf\u6027\u63a2\u6d4b\u3001\u5e73\u65b9\u63a2\u6d4b\u3001\u591a\u6b21\u54c8\u5e0c\u3002</p>"},{"location":"chapter_hashing/hash_collision/#_1","title":"\u7ebf\u6027\u63a2\u6d4b","text":"<p>\u7ebf\u6027\u63a2\u6d4b\u91c7\u7528\u56fa\u5b9a\u6b65\u957f\u7684\u7ebf\u6027\u67e5\u627e\u6765\u8fdb\u884c\u63a2\u6d4b\uff0c\u5bf9\u5e94\u7684\u54c8\u5e0c\u8868\u64cd\u4f5c\u65b9\u6cd5\u4e3a\uff1a</p> <ul> <li>\u63d2\u5165\u5143\u7d20\uff1a\u901a\u8fc7\u54c8\u5e0c\u51fd\u6570\u8ba1\u7b97\u6570\u7ec4\u7d22\u5f15\uff0c\u82e5\u53d1\u73b0\u6876\u5185\u5df2\u6709\u5143\u7d20\uff0c\u5219\u4ece\u51b2\u7a81\u4f4d\u7f6e\u5411\u540e\u7ebf\u6027\u904d\u5386\uff08\u6b65\u957f\u901a\u5e38\u4e3a \\(1\\) \uff09\uff0c\u76f4\u81f3\u627e\u5230\u7a7a\u4f4d\uff0c\u5c06\u5143\u7d20\u63d2\u5165\u5176\u4e2d\u3002</li> <li>\u67e5\u627e\u5143\u7d20\uff1a\u82e5\u53d1\u73b0\u54c8\u5e0c\u51b2\u7a81\uff0c\u5219\u4f7f\u7528\u76f8\u540c\u6b65\u957f\u5411\u540e\u7ebf\u6027\u904d\u5386\uff0c\u76f4\u5230\u627e\u5230\u5bf9\u5e94\u5143\u7d20\uff0c\u8fd4\u56de value \u5373\u53ef\uff1b\u6216\u8005\u82e5\u9047\u5230\u7a7a\u4f4d\uff0c\u8bf4\u660e\u76ee\u6807\u952e\u503c\u5bf9\u4e0d\u5728\u54c8\u5e0c\u8868\u4e2d\uff0c\u8fd4\u56de \\(\\text{None}\\) \u3002</li> </ul> <p></p> <p> Fig. \u7ebf\u6027\u63a2\u6d4b </p> <p>\u7136\u800c\uff0c\u7ebf\u6027\u63a2\u6d4b\u5b58\u5728\u4ee5\u4e0b\u7f3a\u9677\uff1a</p> <ul> <li>\u4e0d\u80fd\u76f4\u63a5\u5220\u9664\u5143\u7d20\u3002\u5220\u9664\u5143\u7d20\u4f1a\u5728\u6570\u7ec4\u5185\u4ea7\u751f\u4e00\u4e2a\u7a7a\u4f4d\uff0c\u67e5\u627e\u5176\u4ed6\u5143\u7d20\u65f6\uff0c\u8be5\u7a7a\u4f4d\u53ef\u80fd\u5bfc\u81f4\u7a0b\u5e8f\u8bef\u5224\u5143\u7d20\u4e0d\u5b58\u5728\u3002\u56e0\u6b64\uff0c\u9700\u8981\u501f\u52a9\u4e00\u4e2a\u6807\u5fd7\u4f4d\u6765\u6807\u8bb0\u5df2\u5220\u9664\u5143\u7d20\u3002</li> <li>\u5bb9\u6613\u4ea7\u751f\u805a\u96c6\u3002\u6570\u7ec4\u5185\u8fde\u7eed\u88ab\u5360\u7528\u4f4d\u7f6e\u8d8a\u957f\uff0c\u8fd9\u4e9b\u8fde\u7eed\u4f4d\u7f6e\u53d1\u751f\u54c8\u5e0c\u51b2\u7a81\u7684\u53ef\u80fd\u6027\u8d8a\u5927\uff0c\u8fdb\u4e00\u6b65\u4fc3\u4f7f\u8fd9\u4e00\u4f4d\u7f6e\u7684\u201c\u805a\u5806\u751f\u957f\u201d\uff0c\u6700\u7ec8\u5bfc\u81f4\u589e\u5220\u67e5\u6539\u64cd\u4f5c\u6548\u7387\u964d\u4f4e\u3002</li> </ul> <p>\u5982\u4ee5\u4e0b\u4ee3\u7801\u6240\u793a\uff0c\u4e3a\u5f00\u653e\u5bfb\u5740\uff08\u7ebf\u6027\u63a2\u6d4b\uff09\u54c8\u5e0c\u8868\u7684\u7b80\u5355\u5b9e\u73b0\uff0c\u91cd\u70b9\u5305\u62ec\uff1a</p> <ul> <li>\u6211\u4eec\u4f7f\u7528\u4e00\u4e2a\u56fa\u5b9a\u7684\u952e\u503c\u5bf9\u5b9e\u4f8b <code>removed</code> \u6765\u6807\u8bb0\u5df2\u5220\u9664\u5143\u7d20\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u5f53\u4e00\u4e2a\u6876\u4e3a \\(\\text{None}\\) \u6216 <code>removed</code> \u65f6\uff0c\u8fd9\u4e2a\u6876\u90fd\u662f\u7a7a\u7684\uff0c\u53ef\u7528\u4e8e\u653e\u7f6e\u952e\u503c\u5bf9\u3002</li> <li>\u88ab\u6807\u8bb0\u4e3a\u5df2\u5220\u9664\u7684\u7a7a\u95f4\u662f\u53ef\u4ee5\u518d\u6b21\u88ab\u4f7f\u7528\u7684\u3002\u5f53\u63d2\u5165\u5143\u7d20\u65f6\uff0c\u82e5\u901a\u8fc7\u54c8\u5e0c\u51fd\u6570\u627e\u5230\u4e86\u88ab\u6807\u8bb0\u4e3a\u5df2\u5220\u9664\u7684\u7d22\u5f15\uff0c\u5219\u53ef\u5c06\u8be5\u5143\u7d20\u653e\u7f6e\u5230\u8be5\u7d22\u5f15\u3002</li> <li>\u5728\u7ebf\u6027\u63a2\u6d4b\u65f6\uff0c\u6211\u4eec\u4ece\u5f53\u524d\u7d22\u5f15 <code>index</code> \u5411\u540e\u904d\u5386\uff1b\u800c\u5f53\u8d8a\u8fc7\u6570\u7ec4\u5c3e\u90e8\u65f6\uff0c\u9700\u8981\u56de\u5230\u5934\u90e8\u7ee7\u7eed\u904d\u5386\u3002</li> </ul> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart hash_map_open_addressing.java<pre><code>/* \u952e\u503c\u5bf9 */\nclass Pair {\npublic int key;\npublic String val;\npublic Pair(int key, String val) {\nthis.key = key;\nthis.val = val;\n}\n}\n/* \u5f00\u653e\u5bfb\u5740\u54c8\u5e0c\u8868 */\nclass HashMapOpenAddressing {\nprivate int size; // \u952e\u503c\u5bf9\u6570\u91cf\nprivate int capacity; // \u54c8\u5e0c\u8868\u5bb9\u91cf\nprivate double loadThres; // \u89e6\u53d1\u6269\u5bb9\u7684\u8d1f\u8f7d\u56e0\u5b50\u9608\u503c\nprivate int extendRatio; // \u6269\u5bb9\u500d\u6570\nprivate Pair[] buckets; // \u6876\u6570\u7ec4\nprivate Pair removed; // \u5220\u9664\u6807\u8bb0\n/* \u6784\u9020\u65b9\u6cd5 */\npublic HashMapOpenAddressing() {\nsize = 0;\ncapacity = 4;\nloadThres = 2.0 / 3.0;\nextendRatio = 2;\nbuckets = new Pair[capacity];\nremoved = new Pair(-1, \"-1\");\n}\n/* \u54c8\u5e0c\u51fd\u6570 */\npublic int hashFunc(int key) {\nreturn key % capacity;\n}\n/* \u8d1f\u8f7d\u56e0\u5b50 */\npublic double loadFactor() {\nreturn (double) size / capacity;\n}\n/* \u67e5\u8be2\u64cd\u4f5c */\npublic String get(int key) {\nint index = hashFunc(key);\n// \u7ebf\u6027\u63a2\u6d4b\uff0c\u4ece index \u5f00\u59cb\u5411\u540e\u904d\u5386\nfor (int i = 0; i &lt; capacity; i++) {\n// \u8ba1\u7b97\u6876\u7d22\u5f15\uff0c\u8d8a\u8fc7\u5c3e\u90e8\u8fd4\u56de\u5934\u90e8\nint j = (index + i) % capacity;\n// \u82e5\u9047\u5230\u7a7a\u6876\uff0c\u8bf4\u660e\u65e0\u6b64 key \uff0c\u5219\u8fd4\u56de null\nif (buckets[j] == null)\nreturn null;\n// \u82e5\u9047\u5230\u6307\u5b9a key \uff0c\u5219\u8fd4\u56de\u5bf9\u5e94 val\nif (buckets[j].key == key &amp;&amp; buckets[j] != removed)\nreturn buckets[j].val;\n}\nreturn null;\n}\n/* \u6dfb\u52a0\u64cd\u4f5c */\npublic void put(int key, String val) {\n// \u5f53\u8d1f\u8f7d\u56e0\u5b50\u8d85\u8fc7\u9608\u503c\u65f6\uff0c\u6267\u884c\u6269\u5bb9\nif (loadFactor() &gt; loadThres) {\nextend();\n}\nint index = hashFunc(key);\n// \u7ebf\u6027\u63a2\u6d4b\uff0c\u4ece index \u5f00\u59cb\u5411\u540e\u904d\u5386\nfor (int i = 0; i &lt; capacity; i++) {\n// \u8ba1\u7b97\u6876\u7d22\u5f15\uff0c\u8d8a\u8fc7\u5c3e\u90e8\u8fd4\u56de\u5934\u90e8\nint j = (index + i) % capacity;\n// \u82e5\u9047\u5230\u7a7a\u6876\u3001\u6216\u5e26\u6709\u5220\u9664\u6807\u8bb0\u7684\u6876\uff0c\u5219\u5c06\u952e\u503c\u5bf9\u653e\u5165\u8be5\u6876\nif (buckets[j] == null || buckets[j] == removed) {\nbuckets[j] = new Pair(key, val);\nsize += 1;\nreturn;\n}\n// \u82e5\u9047\u5230\u6307\u5b9a key \uff0c\u5219\u66f4\u65b0\u5bf9\u5e94 val\nif (buckets[j].key == key) {\nbuckets[j].val = val;\nreturn;\n}\n}\n}\n/* \u5220\u9664\u64cd\u4f5c */\npublic void remove(int key) {\nint index = hashFunc(key);\n// \u7ebf\u6027\u63a2\u6d4b\uff0c\u4ece index \u5f00\u59cb\u5411\u540e\u904d\u5386\nfor (int i = 0; i &lt; capacity; i++) {\n// \u8ba1\u7b97\u6876\u7d22\u5f15\uff0c\u8d8a\u8fc7\u5c3e\u90e8\u8fd4\u56de\u5934\u90e8\nint j = (index + i) % capacity;\n// \u82e5\u9047\u5230\u7a7a\u6876\uff0c\u8bf4\u660e\u65e0\u6b64 key \uff0c\u5219\u76f4\u63a5\u8fd4\u56de\nif (buckets[j] == null) {\nreturn;\n}\n// \u82e5\u9047\u5230\u6307\u5b9a key \uff0c\u5219\u6807\u8bb0\u5220\u9664\u5e76\u8fd4\u56de\nif (buckets[j].key == key) {\nbuckets[j] = removed;\nsize -= 1;\nreturn;\n}\n}\n}\n/* \u6269\u5bb9\u54c8\u5e0c\u8868 */\npublic void extend() {\n// \u6682\u5b58\u539f\u54c8\u5e0c\u8868\nPair[] bucketsTmp = buckets;\n// \u521d\u59cb\u5316\u6269\u5bb9\u540e\u7684\u65b0\u54c8\u5e0c\u8868\ncapacity *= extendRatio;\nbuckets = new Pair[capacity];\nsize = 0;\n// \u5c06\u952e\u503c\u5bf9\u4ece\u539f\u54c8\u5e0c\u8868\u642c\u8fd0\u81f3\u65b0\u54c8\u5e0c\u8868\nfor (Pair pair : bucketsTmp) {\nif (pair != null &amp;&amp; pair != removed) {\nput(pair.key, pair.val);\n}\n}\n}\n/* \u6253\u5370\u54c8\u5e0c\u8868 */\npublic void print() {\nfor (Pair pair : buckets) {\nif (pair != null) {\nSystem.out.println(pair.key + \" -&gt; \" + pair.val);\n} else {\nSystem.out.println(\"null\");\n}\n}\n}\n}\n</code></pre> hash_map_open_addressing.cpp<pre><code>/* \u952e\u503c\u5bf9 */\nstruct Pair {\nint key;\nstring val;\nPair(int k, string v) : key(k), val(v) {\n}\n};\n/* \u5f00\u653e\u5bfb\u5740\u54c8\u5e0c\u8868 */\nclass HashMapOpenAddressing {\nprivate:\nint size;               // \u952e\u503c\u5bf9\u6570\u91cf\nint capacity;           // \u54c8\u5e0c\u8868\u5bb9\u91cf\ndouble loadThres;       // \u89e6\u53d1\u6269\u5bb9\u7684\u8d1f\u8f7d\u56e0\u5b50\u9608\u503c\nint extendRatio;        // \u6269\u5bb9\u500d\u6570\nvector&lt;Pair *&gt; buckets; // \u6876\u6570\u7ec4\nPair *removed;          // \u5220\u9664\u6807\u8bb0\npublic:\n/* \u6784\u9020\u65b9\u6cd5 */\nHashMapOpenAddressing() {\n// \u6784\u9020\u65b9\u6cd5\nsize = 0;\ncapacity = 4;\nloadThres = 2.0 / 3.0;\nextendRatio = 2;\nbuckets = vector&lt;Pair *&gt;(capacity, nullptr);\nremoved = new Pair(-1, \"-1\");\n}\n/* \u54c8\u5e0c\u51fd\u6570 */\nint hashFunc(int key) {\nreturn key % capacity;\n}\n/* \u8d1f\u8f7d\u56e0\u5b50 */\ndouble loadFactor() {\nreturn static_cast&lt;double&gt;(size) / capacity;\n}\n/* \u67e5\u8be2\u64cd\u4f5c */\nstring get(int key) {\nint index = hashFunc(key);\n// \u7ebf\u6027\u63a2\u6d4b\uff0c\u4ece index \u5f00\u59cb\u5411\u540e\u904d\u5386\nfor (int i = 0; i &lt; capacity; i++) {\n// \u8ba1\u7b97\u6876\u7d22\u5f15\uff0c\u8d8a\u8fc7\u5c3e\u90e8\u8fd4\u56de\u5934\u90e8\nint j = (index + i) % capacity;\n// \u82e5\u9047\u5230\u7a7a\u6876\uff0c\u8bf4\u660e\u65e0\u6b64 key \uff0c\u5219\u8fd4\u56de nullptr\nif (buckets[j] == nullptr)\nreturn nullptr;\n// \u82e5\u9047\u5230\u6307\u5b9a key \uff0c\u5219\u8fd4\u56de\u5bf9\u5e94 val\nif (buckets[j]-&gt;key == key &amp;&amp; buckets[j] != removed)\nreturn buckets[j]-&gt;val;\n}\nreturn nullptr;\n}\n/* \u6dfb\u52a0\u64cd\u4f5c */\nvoid put(int key, string val) {\n// \u5f53\u8d1f\u8f7d\u56e0\u5b50\u8d85\u8fc7\u9608\u503c\u65f6\uff0c\u6267\u884c\u6269\u5bb9\nif (loadFactor() &gt; loadThres)\nextend();\nint index = hashFunc(key);\n// \u7ebf\u6027\u63a2\u6d4b\uff0c\u4ece index \u5f00\u59cb\u5411\u540e\u904d\u5386\nfor (int i = 0; i &lt; capacity; i++) {\n// \u8ba1\u7b97\u6876\u7d22\u5f15\uff0c\u8d8a\u8fc7\u5c3e\u90e8\u8fd4\u56de\u5934\u90e8\nint j = (index + i) % capacity;\n// \u82e5\u9047\u5230\u7a7a\u6876\u3001\u6216\u5e26\u6709\u5220\u9664\u6807\u8bb0\u7684\u6876\uff0c\u5219\u5c06\u952e\u503c\u5bf9\u653e\u5165\u8be5\u6876\nif (buckets[j] == nullptr || buckets[j] == removed) {\nbuckets[j] = new Pair(key, val);\nsize += 1;\nreturn;\n}\n// \u82e5\u9047\u5230\u6307\u5b9a key \uff0c\u5219\u66f4\u65b0\u5bf9\u5e94 val\nif (buckets[j]-&gt;key == key) {\nbuckets[j]-&gt;val = val;\nreturn;\n}\n}\n}\n/* \u5220\u9664\u64cd\u4f5c */\nvoid remove(int key) {\nint index = hashFunc(key);\n// \u7ebf\u6027\u63a2\u6d4b\uff0c\u4ece index \u5f00\u59cb\u5411\u540e\u904d\u5386\nfor (int i = 0; i &lt; capacity; i++) {\n// \u8ba1\u7b97\u6876\u7d22\u5f15\uff0c\u8d8a\u8fc7\u5c3e\u90e8\u8fd4\u56de\u5934\u90e8\nint j = (index + i) % capacity;\n// \u82e5\u9047\u5230\u7a7a\u6876\uff0c\u8bf4\u660e\u65e0\u6b64 key \uff0c\u5219\u76f4\u63a5\u8fd4\u56de\nif (buckets[j] == nullptr)\nreturn;\n// \u82e5\u9047\u5230\u6307\u5b9a key \uff0c\u5219\u6807\u8bb0\u5220\u9664\u5e76\u8fd4\u56de\nif (buckets[j]-&gt;key == key) {\ndelete buckets[j]; // \u91ca\u653e\u5185\u5b58\nbuckets[j] = removed;\nsize -= 1;\nreturn;\n}\n}\n}\n/* \u6269\u5bb9\u54c8\u5e0c\u8868 */\nvoid extend() {\n// \u6682\u5b58\u539f\u54c8\u5e0c\u8868\nvector&lt;Pair *&gt; bucketsTmp = buckets;\n// \u521d\u59cb\u5316\u6269\u5bb9\u540e\u7684\u65b0\u54c8\u5e0c\u8868\ncapacity *= extendRatio;\nbuckets = vector&lt;Pair *&gt;(capacity, nullptr);\nsize = 0;\n// \u5c06\u952e\u503c\u5bf9\u4ece\u539f\u54c8\u5e0c\u8868\u642c\u8fd0\u81f3\u65b0\u54c8\u5e0c\u8868\nfor (Pair *pair : bucketsTmp) {\nif (pair != nullptr &amp;&amp; pair != removed) {\nput(pair-&gt;key, pair-&gt;val);\n}\n}\n}\n/* \u6253\u5370\u54c8\u5e0c\u8868 */\nvoid print() {\nfor (auto &amp;pair : buckets) {\nif (pair != nullptr) {\ncout &lt;&lt; pair-&gt;key &lt;&lt; \" -&gt; \" &lt;&lt; pair-&gt;val &lt;&lt; endl;\n} else {\ncout &lt;&lt; \"nullptr\" &lt;&lt; endl;\n}\n}\n}\n};\n</code></pre> hash_map_open_addressing.py<pre><code>class Pair:\n\"\"\"\u952e\u503c\u5bf9\"\"\"\ndef __init__(self, key: int, val: str):\nself.key = key\nself.val = val\nclass HashMapOpenAddressing:\n\"\"\"\u5f00\u653e\u5bfb\u5740\u54c8\u5e0c\u8868\"\"\"\ndef __init__(self):\n\"\"\"\u6784\u9020\u65b9\u6cd5\"\"\"\nself.size = 0  # \u952e\u503c\u5bf9\u6570\u91cf\nself.capacity = 4  # \u54c8\u5e0c\u8868\u5bb9\u91cf\nself.load_thres = 2 / 3  # \u89e6\u53d1\u6269\u5bb9\u7684\u8d1f\u8f7d\u56e0\u5b50\u9608\u503c\nself.extend_ratio = 2  # \u6269\u5bb9\u500d\u6570\nself.buckets: list[Pair | None] = [None] * self.capacity  # \u6876\u6570\u7ec4\nself.removed = Pair(-1, \"-1\")  # \u5220\u9664\u6807\u8bb0\ndef hash_func(self, key: int) -&gt; int:\n\"\"\"\u54c8\u5e0c\u51fd\u6570\"\"\"\nreturn key % self.capacity\ndef load_factor(self) -&gt; float:\n\"\"\"\u8d1f\u8f7d\u56e0\u5b50\"\"\"\nreturn self.size / self.capacity\ndef get(self, key: int) -&gt; str:\n\"\"\"\u67e5\u8be2\u64cd\u4f5c\"\"\"\nindex = self.hash_func(key)\n# \u7ebf\u6027\u63a2\u6d4b\uff0c\u4ece index \u5f00\u59cb\u5411\u540e\u904d\u5386\nfor i in range(self.capacity):\n# \u8ba1\u7b97\u6876\u7d22\u5f15\uff0c\u8d8a\u8fc7\u5c3e\u90e8\u8fd4\u56de\u5934\u90e8\nj = (index + i) % self.capacity\n# \u82e5\u9047\u5230\u7a7a\u6876\uff0c\u8bf4\u660e\u65e0\u6b64 key \uff0c\u5219\u8fd4\u56de None\nif self.buckets[j] is None:\nreturn None\n# \u82e5\u9047\u5230\u6307\u5b9a key \uff0c\u5219\u8fd4\u56de\u5bf9\u5e94 val\nif self.buckets[j].key == key and self.buckets[j] != self.removed:\nreturn self.buckets[j].val\ndef put(self, key: int, val: str):\n\"\"\"\u6dfb\u52a0\u64cd\u4f5c\"\"\"\n# \u5f53\u8d1f\u8f7d\u56e0\u5b50\u8d85\u8fc7\u9608\u503c\u65f6\uff0c\u6267\u884c\u6269\u5bb9\nif self.load_factor() &gt; self.load_thres:\nself.extend()\nindex = self.hash_func(key)\n# \u7ebf\u6027\u63a2\u6d4b\uff0c\u4ece index \u5f00\u59cb\u5411\u540e\u904d\u5386\nfor i in range(self.capacity):\n# \u8ba1\u7b97\u6876\u7d22\u5f15\uff0c\u8d8a\u8fc7\u5c3e\u90e8\u8fd4\u56de\u5934\u90e8\nj = (index + i) % self.capacity\n# \u82e5\u9047\u5230\u7a7a\u6876\u3001\u6216\u5e26\u6709\u5220\u9664\u6807\u8bb0\u7684\u6876\uff0c\u5219\u5c06\u952e\u503c\u5bf9\u653e\u5165\u8be5\u6876\nif self.buckets[j] in [None, self.removed]:\nself.buckets[j] = Pair(key, val)\nself.size += 1\nreturn\n# \u82e5\u9047\u5230\u6307\u5b9a key \uff0c\u5219\u66f4\u65b0\u5bf9\u5e94 val\nif self.buckets[j].key == key:\nself.buckets[j].val = val\nreturn\ndef remove(self, key: int):\n\"\"\"\u5220\u9664\u64cd\u4f5c\"\"\"\nindex = self.hash_func(key)\n# \u7ebf\u6027\u63a2\u6d4b\uff0c\u4ece index \u5f00\u59cb\u5411\u540e\u904d\u5386\nfor i in range(self.capacity):\n# \u8ba1\u7b97\u6876\u7d22\u5f15\uff0c\u8d8a\u8fc7\u5c3e\u90e8\u8fd4\u56de\u5934\u90e8\nj = (index + i) % self.capacity\n# \u82e5\u9047\u5230\u7a7a\u6876\uff0c\u8bf4\u660e\u65e0\u6b64 key \uff0c\u5219\u76f4\u63a5\u8fd4\u56de\nif self.buckets[j] is None:\nreturn\n# \u82e5\u9047\u5230\u6307\u5b9a key \uff0c\u5219\u6807\u8bb0\u5220\u9664\u5e76\u8fd4\u56de\nif self.buckets[j].key == key:\nself.buckets[j] = self.removed\nself.size -= 1\nreturn\ndef extend(self):\n\"\"\"\u6269\u5bb9\u54c8\u5e0c\u8868\"\"\"\n# \u6682\u5b58\u539f\u54c8\u5e0c\u8868\nbuckets_tmp = self.buckets\n# \u521d\u59cb\u5316\u6269\u5bb9\u540e\u7684\u65b0\u54c8\u5e0c\u8868\nself.capacity *= self.extend_ratio\nself.buckets = [None] * self.capacity\nself.size = 0\n# \u5c06\u952e\u503c\u5bf9\u4ece\u539f\u54c8\u5e0c\u8868\u642c\u8fd0\u81f3\u65b0\u54c8\u5e0c\u8868\nfor pair in buckets_tmp:\nif pair not in [None, self.removed]:\nself.put(pair.key, pair.val)\ndef print(self) -&gt; None:\n\"\"\"\u6253\u5370\u54c8\u5e0c\u8868\"\"\"\nfor pair in self.buckets:\nif pair is not None:\nprint(pair.key, \"-&gt;\", pair.val)\nelse:\nprint(\"None\")\n</code></pre> hash_map_open_addressing.go<pre><code>[class]{pair}-[func]{}\n[class]{hashMapOpenAddressing}-[func]{}\n</code></pre> hash_map_open_addressing.js<pre><code>[class]{Pair}-[func]{}\n[class]{HashMapOpenAddressing}-[func]{}\n</code></pre> hash_map_open_addressing.ts<pre><code>[class]{Pair}-[func]{}\n[class]{HashMapOpenAddressing}-[func]{}\n</code></pre> hash_map_open_addressing.c<pre><code>[class]{pair}-[func]{}\n[class]{hashMapOpenAddressing}-[func]{}\n</code></pre> hash_map_open_addressing.cs<pre><code>[class]{Pair}-[func]{}\n[class]{HashMapOpenAddressing}-[func]{}\n</code></pre> hash_map_open_addressing.swift<pre><code>[class]{Pair}-[func]{}\n[class]{HashMapOpenAddressing}-[func]{}\n</code></pre> hash_map_open_addressing.zig<pre><code>[class]{Pair}-[func]{}\n[class]{HashMapOpenAddressing}-[func]{}\n</code></pre> hash_map_open_addressing.dart<pre><code>[class]{Pair}-[func]{}\n[class]{HashMapOpenAddressing}-[func]{}\n</code></pre>"},{"location":"chapter_hashing/hash_collision/#_2","title":"\u591a\u6b21\u54c8\u5e0c","text":"<p>\u987e\u540d\u601d\u4e49\uff0c\u591a\u6b21\u54c8\u5e0c\u65b9\u6cd5\u662f\u4f7f\u7528\u591a\u4e2a\u54c8\u5e0c\u51fd\u6570 \\(f_1(x)\\) , \\(f_2(x)\\) , \\(f_3(x)\\) , \\(\\cdots\\) \u8fdb\u884c\u63a2\u6d4b\u3002</p> <ul> <li>\u63d2\u5165\u5143\u7d20\uff1a\u82e5\u54c8\u5e0c\u51fd\u6570 \\(f_1(x)\\) \u51fa\u73b0\u51b2\u7a81\uff0c\u5219\u5c1d\u8bd5 \\(f_2(x)\\) \uff0c\u4ee5\u6b64\u7c7b\u63a8\uff0c\u76f4\u5230\u627e\u5230\u7a7a\u4f4d\u540e\u63d2\u5165\u5143\u7d20\u3002</li> <li>\u67e5\u627e\u5143\u7d20\uff1a\u5728\u76f8\u540c\u7684\u54c8\u5e0c\u51fd\u6570\u987a\u5e8f\u4e0b\u8fdb\u884c\u67e5\u627e\uff0c\u76f4\u5230\u627e\u5230\u76ee\u6807\u5143\u7d20\u65f6\u8fd4\u56de\uff1b\u6216\u9047\u5230\u7a7a\u4f4d\u6216\u5df2\u5c1d\u8bd5\u6240\u6709\u54c8\u5e0c\u51fd\u6570\uff0c\u8bf4\u660e\u54c8\u5e0c\u8868\u4e2d\u4e0d\u5b58\u5728\u8be5\u5143\u7d20\uff0c\u5219\u8fd4\u56de \\(\\text{None}\\) \u3002</li> </ul> <p>\u4e0e\u7ebf\u6027\u63a2\u6d4b\u76f8\u6bd4\uff0c\u591a\u6b21\u54c8\u5e0c\u65b9\u6cd5\u4e0d\u6613\u4ea7\u751f\u805a\u96c6\uff0c\u4f46\u591a\u4e2a\u54c8\u5e0c\u51fd\u6570\u4f1a\u589e\u52a0\u989d\u5916\u7684\u8ba1\u7b97\u91cf\u3002</p> <p>\u7f16\u7a0b\u8bed\u8a00\u7684\u9009\u62e9</p> <p>Java \u91c7\u7528\u94fe\u5f0f\u5730\u5740\u3002\u81ea JDK 1.8 \u4ee5\u6765\uff0c\u5f53 HashMap \u5185\u6570\u7ec4\u957f\u5ea6\u8fbe\u5230 64 \u4e14\u94fe\u8868\u957f\u5ea6\u8fbe\u5230 8 \u65f6\uff0c\u94fe\u8868\u4f1a\u88ab\u8f6c\u6362\u4e3a\u7ea2\u9ed1\u6811\u4ee5\u63d0\u5347\u67e5\u627e\u6027\u80fd\u3002</p> <p>Python \u91c7\u7528\u5f00\u653e\u5bfb\u5740\u3002\u5b57\u5178 dict \u4f7f\u7528\u4f2a\u968f\u673a\u6570\u8fdb\u884c\u63a2\u6d4b\u3002</p> <p>Golang \u91c7\u7528\u94fe\u5f0f\u5730\u5740\u3002Go \u89c4\u5b9a\u6bcf\u4e2a\u6876\u6700\u591a\u5b58\u50a8 8 \u4e2a\u952e\u503c\u5bf9\uff0c\u8d85\u51fa\u5bb9\u91cf\u5219\u8fde\u63a5\u4e00\u4e2a\u6ea2\u51fa\u6876\uff1b\u5f53\u6ea2\u51fa\u6876\u8fc7\u591a\u65f6\uff0c\u4f1a\u6267\u884c\u4e00\u6b21\u7279\u6b8a\u7684\u7b49\u91cf\u6269\u5bb9\u64cd\u4f5c\uff0c\u4ee5\u786e\u4fdd\u6027\u80fd\u3002</p>"},{"location":"chapter_hashing/hash_map/","title":"6.1. \u00a0 \u54c8\u5e0c\u8868","text":"<p>\u300c\u54c8\u5e0c\u8868 Hash Table\u300d\u901a\u8fc7\u5efa\u7acb\u952e <code>key</code> \u4e0e\u503c <code>value</code> \u4e4b\u95f4\u7684\u6620\u5c04\uff0c\u5b9e\u73b0\u9ad8\u6548\u7684\u5143\u7d20\u67e5\u8be2\u3002\u5177\u4f53\u800c\u8a00\uff0c\u6211\u4eec\u5411\u54c8\u5e0c\u8868\u8f93\u5165\u4e00\u4e2a <code>key</code> \uff0c\u5219\u53ef\u4ee5\u5728 \\(O(1)\\) \u65f6\u95f4\u5185\u83b7\u53d6\u5bf9\u5e94\u7684 <code>value</code> \u3002</p> <p>\u4ee5\u4e00\u4e2a\u5305\u542b \\(n\\) \u4e2a\u5b66\u751f\u7684\u6570\u636e\u5e93\u4e3a\u4f8b\uff0c\u6bcf\u4e2a\u5b66\u751f\u90fd\u6709\u201c\u59d3\u540d <code>name</code>\u201d\u548c\u201c\u5b66\u53f7 <code>id</code>\u201d\u4e24\u9879\u6570\u636e\u3002\u5047\u5982\u6211\u4eec\u5e0c\u671b\u5b9e\u73b0\u67e5\u8be2\u529f\u80fd\uff0c\u4f8b\u5982\u201c\u8f93\u5165\u4e00\u4e2a\u5b66\u53f7\uff0c\u8fd4\u56de\u5bf9\u5e94\u7684\u59d3\u540d\u201d\uff0c\u5219\u53ef\u4ee5\u91c7\u7528\u54c8\u5e0c\u8868\u6765\u5b9e\u73b0\u3002</p> <p></p> <p> Fig. \u54c8\u5e0c\u8868\u7684\u62bd\u8c61\u8868\u793a </p> <p>\u9664\u54c8\u5e0c\u8868\u5916\uff0c\u6211\u4eec\u8fd8\u53ef\u4ee5\u4f7f\u7528\u6570\u7ec4\u6216\u94fe\u8868\u5b9e\u73b0\u5143\u7d20\u67e5\u8be2\uff0c\u5176\u4e2d\uff1a</p> <ul> <li>\u67e5\u8be2\u5143\u7d20\u9700\u8981\u904d\u5386\u6240\u6709\u5143\u7d20\uff0c\u4f7f\u7528 \\(O(n)\\) \u65f6\u95f4\uff1b</li> <li>\u6dfb\u52a0\u5143\u7d20\u4ec5\u9700\u6dfb\u52a0\u81f3\u5c3e\u90e8\u5373\u53ef\uff0c\u4f7f\u7528 \\(O(1)\\) \u65f6\u95f4\uff1b</li> <li>\u5220\u9664\u5143\u7d20\u9700\u8981\u5148\u67e5\u8be2\u518d\u5220\u9664\uff0c\u4f7f\u7528 \\(O(n)\\) \u65f6\u95f4\uff1b</li> </ul> \u6570\u7ec4 \u94fe\u8868 \u54c8\u5e0c\u8868 \u67e5\u627e\u5143\u7d20 \\(O(n)\\) \\(O(n)\\) \\(O(1)\\) \u6dfb\u52a0\u5143\u7d20 \\(O(1)\\) \\(O(1)\\) \\(O(1)\\) \u5220\u9664\u5143\u7d20 \\(O(n)\\) \\(O(n)\\) \\(O(1)\\) <p>\u89c2\u5bdf\u53d1\u73b0\uff0c\u5728\u54c8\u5e0c\u8868\u4e2d\u8fdb\u884c\u589e\u5220\u67e5\u6539\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u90fd\u662f \\(O(1)\\) \uff0c\u975e\u5e38\u9ad8\u6548\u3002\u56e0\u6b64\uff0c\u54c8\u5e0c\u8868\u5e38\u7528\u4e8e\u5bf9\u67e5\u627e\u6548\u7387\u8981\u6c42\u8f83\u9ad8\u7684\u573a\u666f\u3002</p>"},{"location":"chapter_hashing/hash_map/#611","title":"6.1.1. \u00a0 \u54c8\u5e0c\u8868\u5e38\u7528\u64cd\u4f5c","text":"<p>\u54c8\u5e0c\u8868\u7684\u57fa\u672c\u64cd\u4f5c\u5305\u62ec \u521d\u59cb\u5316\u3001\u67e5\u8be2\u64cd\u4f5c\u3001\u6dfb\u52a0\u4e0e\u5220\u9664\u952e\u503c\u5bf9\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart hash_map.java<pre><code>/* \u521d\u59cb\u5316\u54c8\u5e0c\u8868 */\nMap&lt;Integer, String&gt; map = new HashMap&lt;&gt;();\n/* \u6dfb\u52a0\u64cd\u4f5c */\n// \u5728\u54c8\u5e0c\u8868\u4e2d\u6dfb\u52a0\u952e\u503c\u5bf9 (key, value)\nmap.put(12836, \"\u5c0f\u54c8\");   map.put(15937, \"\u5c0f\u5570\");   map.put(16750, \"\u5c0f\u7b97\");   map.put(13276, \"\u5c0f\u6cd5\");\nmap.put(10583, \"\u5c0f\u9e2d\");\n/* \u67e5\u8be2\u64cd\u4f5c */\n// \u5411\u54c8\u5e0c\u8868\u8f93\u5165\u952e key \uff0c\u5f97\u5230\u503c value\nString name = map.get(15937);\n/* \u5220\u9664\u64cd\u4f5c */\n// \u5728\u54c8\u5e0c\u8868\u4e2d\u5220\u9664\u952e\u503c\u5bf9 (key, value)\nmap.remove(10583);\n</code></pre> hash_map.cpp<pre><code>/* \u521d\u59cb\u5316\u54c8\u5e0c\u8868 */\nunordered_map&lt;int, string&gt; map;\n/* \u6dfb\u52a0\u64cd\u4f5c */\n// \u5728\u54c8\u5e0c\u8868\u4e2d\u6dfb\u52a0\u952e\u503c\u5bf9 (key, value)\nmap[12836] = \"\u5c0f\u54c8\";\nmap[15937] = \"\u5c0f\u5570\";\nmap[16750] = \"\u5c0f\u7b97\";\nmap[13276] = \"\u5c0f\u6cd5\";\nmap[10583] = \"\u5c0f\u9e2d\";\n/* \u67e5\u8be2\u64cd\u4f5c */\n// \u5411\u54c8\u5e0c\u8868\u8f93\u5165\u952e key \uff0c\u5f97\u5230\u503c value\nstring name = map[15937];\n/* \u5220\u9664\u64cd\u4f5c */\n// \u5728\u54c8\u5e0c\u8868\u4e2d\u5220\u9664\u952e\u503c\u5bf9 (key, value)\nmap.erase(10583);\n</code></pre> hash_map.py<pre><code># \u521d\u59cb\u5316\u54c8\u5e0c\u8868\nmapp: Dict = {}\n# \u6dfb\u52a0\u64cd\u4f5c\n# \u5728\u54c8\u5e0c\u8868\u4e2d\u6dfb\u52a0\u952e\u503c\u5bf9 (key, value)\nmapp[12836] = \"\u5c0f\u54c8\"\nmapp[15937] = \"\u5c0f\u5570\"\nmapp[16750] = \"\u5c0f\u7b97\"\nmapp[13276] = \"\u5c0f\u6cd5\"\nmapp[10583] = \"\u5c0f\u9e2d\"\n# \u67e5\u8be2\u64cd\u4f5c\n# \u5411\u54c8\u5e0c\u8868\u8f93\u5165\u952e key \uff0c\u5f97\u5230\u503c value\nname: str = mapp[15937]\n# \u5220\u9664\u64cd\u4f5c\n# \u5728\u54c8\u5e0c\u8868\u4e2d\u5220\u9664\u952e\u503c\u5bf9 (key, value)\nmapp.pop(10583)\n</code></pre> hash_map.go<pre><code>/* \u521d\u59cb\u5316\u54c8\u5e0c\u8868 */\nmapp := make(map[int]string)\n/* \u6dfb\u52a0\u64cd\u4f5c */\n// \u5728\u54c8\u5e0c\u8868\u4e2d\u6dfb\u52a0\u952e\u503c\u5bf9 (key, value)\nmapp[12836] = \"\u5c0f\u54c8\"\nmapp[15937] = \"\u5c0f\u5570\"\nmapp[16750] = \"\u5c0f\u7b97\"\nmapp[13276] = \"\u5c0f\u6cd5\"\nmapp[10583] = \"\u5c0f\u9e2d\"\n/* \u67e5\u8be2\u64cd\u4f5c */\n// \u5411\u54c8\u5e0c\u8868\u8f93\u5165\u952e key \uff0c\u5f97\u5230\u503c value\nname := mapp[15937]\n/* \u5220\u9664\u64cd\u4f5c */\n// \u5728\u54c8\u5e0c\u8868\u4e2d\u5220\u9664\u952e\u503c\u5bf9 (key, value)\ndelete(mapp, 10583)\n</code></pre> hash_map.js<pre><code>/* \u521d\u59cb\u5316\u54c8\u5e0c\u8868 */\nconst map = new ArrayHashMap();\n/* \u6dfb\u52a0\u64cd\u4f5c */\n// \u5728\u54c8\u5e0c\u8868\u4e2d\u6dfb\u52a0\u952e\u503c\u5bf9 (key, value)\nmap.set(12836, '\u5c0f\u54c8');\nmap.set(15937, '\u5c0f\u5570');\nmap.set(16750, '\u5c0f\u7b97');\nmap.set(13276, '\u5c0f\u6cd5');\nmap.set(10583, '\u5c0f\u9e2d');\n/* \u67e5\u8be2\u64cd\u4f5c */\n// \u5411\u54c8\u5e0c\u8868\u8f93\u5165\u952e key \uff0c\u5f97\u5230\u503c value\nlet name = map.get(15937);\n/* \u5220\u9664\u64cd\u4f5c */\n// \u5728\u54c8\u5e0c\u8868\u4e2d\u5220\u9664\u952e\u503c\u5bf9 (key, value)\nmap.delete(10583);\n</code></pre> hash_map.ts<pre><code>/* \u521d\u59cb\u5316\u54c8\u5e0c\u8868 */\nconst map = new Map&lt;number, string&gt;();\n/* \u6dfb\u52a0\u64cd\u4f5c */\n// \u5728\u54c8\u5e0c\u8868\u4e2d\u6dfb\u52a0\u952e\u503c\u5bf9 (key, value)\nmap.set(12836, '\u5c0f\u54c8');\nmap.set(15937, '\u5c0f\u5570');\nmap.set(16750, '\u5c0f\u7b97');\nmap.set(13276, '\u5c0f\u6cd5');\nmap.set(10583, '\u5c0f\u9e2d');\nconsole.info('\\n\u6dfb\u52a0\u5b8c\u6210\u540e\uff0c\u54c8\u5e0c\u8868\u4e3a\\nKey -&gt; Value');\nconsole.info(map);\n/* \u67e5\u8be2\u64cd\u4f5c */\n// \u5411\u54c8\u5e0c\u8868\u8f93\u5165\u952e key \uff0c\u5f97\u5230\u503c value\nlet name = map.get(15937);\nconsole.info('\\n\u8f93\u5165\u5b66\u53f7 15937 \uff0c\u67e5\u8be2\u5230\u59d3\u540d ' + name);\n/* \u5220\u9664\u64cd\u4f5c */\n// \u5728\u54c8\u5e0c\u8868\u4e2d\u5220\u9664\u952e\u503c\u5bf9 (key, value)\nmap.delete(10583);\nconsole.info('\\n\u5220\u9664 10583 \u540e\uff0c\u54c8\u5e0c\u8868\u4e3a\\nKey -&gt; Value');\nconsole.info(map);\n</code></pre> hash_map.c<pre><code>// C \u672a\u63d0\u4f9b\u5185\u7f6e\u54c8\u5e0c\u8868\n</code></pre> hash_map.cs<pre><code>/* \u521d\u59cb\u5316\u54c8\u5e0c\u8868 */\nDictionary&lt;int, String&gt; map = new ();\n/* \u6dfb\u52a0\u64cd\u4f5c */\n// \u5728\u54c8\u5e0c\u8868\u4e2d\u6dfb\u52a0\u952e\u503c\u5bf9 (key, value)\nmap.Add(12836, \"\u5c0f\u54c8\");\nmap.Add(15937, \"\u5c0f\u5570\");\nmap.Add(16750, \"\u5c0f\u7b97\");\nmap.Add(13276, \"\u5c0f\u6cd5\");\nmap.Add(10583, \"\u5c0f\u9e2d\");\n/* \u67e5\u8be2\u64cd\u4f5c */\n// \u5411\u54c8\u5e0c\u8868\u8f93\u5165\u952e key \uff0c\u5f97\u5230\u503c value\nString name = map[15937];\n/* \u5220\u9664\u64cd\u4f5c */\n// \u5728\u54c8\u5e0c\u8868\u4e2d\u5220\u9664\u952e\u503c\u5bf9 (key, value)\nmap.Remove(10583);\n</code></pre> hash_map.swift<pre><code>/* \u521d\u59cb\u5316\u54c8\u5e0c\u8868 */\nvar map: [Int: String] = [:]\n/* \u6dfb\u52a0\u64cd\u4f5c */\n// \u5728\u54c8\u5e0c\u8868\u4e2d\u6dfb\u52a0\u952e\u503c\u5bf9 (key, value)\nmap[12836] = \"\u5c0f\u54c8\"\nmap[15937] = \"\u5c0f\u5570\"\nmap[16750] = \"\u5c0f\u7b97\"\nmap[13276] = \"\u5c0f\u6cd5\"\nmap[10583] = \"\u5c0f\u9e2d\"\n/* \u67e5\u8be2\u64cd\u4f5c */\n// \u5411\u54c8\u5e0c\u8868\u8f93\u5165\u952e key \uff0c\u5f97\u5230\u503c value\nlet name = map[15937]!\n/* \u5220\u9664\u64cd\u4f5c */\n// \u5728\u54c8\u5e0c\u8868\u4e2d\u5220\u9664\u952e\u503c\u5bf9 (key, value)\nmap.removeValue(forKey: 10583)\n</code></pre> hash_map.zig<pre><code>\n</code></pre> hash_map.dart<pre><code>/* \u521d\u59cb\u5316\u54c8\u5e0c\u8868 */\nMap&lt;int, String&gt; map = {};\n/* \u6dfb\u52a0\u64cd\u4f5c */\n// \u5728\u54c8\u5e0c\u8868\u4e2d\u6dfb\u52a0\u952e\u503c\u5bf9 (key, value)\nmap[12836] = \"\u5c0f\u54c8\";\nmap[15937] = \"\u5c0f\u5570\";\nmap[16750] = \"\u5c0f\u7b97\";\nmap[13276] = \"\u5c0f\u6cd5\";\nmap[10583] = \"\u5c0f\u9e2d\";\n/* \u67e5\u8be2\u64cd\u4f5c */\n// \u5411\u54c8\u5e0c\u8868\u8f93\u5165\u952e key \uff0c\u5f97\u5230\u503c value\nString name = map[15937];\n/* \u5220\u9664\u64cd\u4f5c */\n// \u5728\u54c8\u5e0c\u8868\u4e2d\u5220\u9664\u952e\u503c\u5bf9 (key, value)\nmap.remove(10583);\n</code></pre> <p>\u904d\u5386\u54c8\u5e0c\u8868\u6709\u4e09\u79cd\u65b9\u5f0f\uff0c\u5373 \u904d\u5386\u952e\u503c\u5bf9\u3001\u904d\u5386\u952e\u3001\u904d\u5386\u503c\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart hash_map.java<pre><code>/* \u904d\u5386\u54c8\u5e0c\u8868 */\n// \u904d\u5386\u952e\u503c\u5bf9 key-&gt;value\nfor (Map.Entry &lt;Integer, String&gt; kv: map.entrySet()) {\nSystem.out.println(kv.getKey() + \" -&gt; \" + kv.getValue());\n}\n// \u5355\u72ec\u904d\u5386\u952e key\nfor (int key: map.keySet()) {\nSystem.out.println(key);\n}\n// \u5355\u72ec\u904d\u5386\u503c value\nfor (String val: map.values()) {\nSystem.out.println(val);\n}\n</code></pre> hash_map.cpp<pre><code>/* \u904d\u5386\u54c8\u5e0c\u8868 */\n// \u904d\u5386\u952e\u503c\u5bf9 key-&gt;value\nfor (auto kv: map) {\ncout &lt;&lt; kv.first &lt;&lt; \" -&gt; \" &lt;&lt; kv.second &lt;&lt; endl;\n}\n// \u5355\u72ec\u904d\u5386\u952e key\nfor (auto key: map) {\ncout &lt;&lt; key.first &lt;&lt; endl;\n}\n// \u5355\u72ec\u904d\u5386\u503c value\nfor (auto val: map) {\ncout &lt;&lt; val.second &lt;&lt; endl;\n}\n</code></pre> hash_map.py<pre><code># \u904d\u5386\u54c8\u5e0c\u8868\n# \u904d\u5386\u952e\u503c\u5bf9 key-&gt;value\nfor key, value in mapp.items():\nprint(key, \"-&gt;\", value)\n# \u5355\u72ec\u904d\u5386\u952e key\nfor key in mapp.keys():\nprint(key)\n# \u5355\u72ec\u904d\u5386\u503c value\nfor value in mapp.values():\nprint(value)\n</code></pre> hash_map_test.go<pre><code>/* \u904d\u5386\u54c8\u5e0c\u8868 */\n// \u904d\u5386\u952e\u503c\u5bf9 key-&gt;value\nfor key, value := range mapp {\nfmt.Println(key, \"-&gt;\", value)\n}\n// \u5355\u72ec\u904d\u5386\u952e key\nfor key := range mapp {\nfmt.Println(key)\n}\n// \u5355\u72ec\u904d\u5386\u503c value\nfor _, value := range mapp {\nfmt.Println(value)\n}\n</code></pre> hash_map.js<pre><code>/* \u904d\u5386\u54c8\u5e0c\u8868 */\nconsole.info('\\n\u904d\u5386\u952e\u503c\u5bf9 Key-&gt;Value');\nfor (const [k, v] of map.entries()) {\nconsole.info(k + ' -&gt; ' + v);\n}\nconsole.info('\\n\u5355\u72ec\u904d\u5386\u952e Key');\nfor (const k of map.keys()) {\nconsole.info(k);\n}\nconsole.info('\\n\u5355\u72ec\u904d\u5386\u503c Value');\nfor (const v of map.values()) {\nconsole.info(v);\n}\n</code></pre> hash_map.ts<pre><code>/* \u904d\u5386\u54c8\u5e0c\u8868 */\nconsole.info('\\n\u904d\u5386\u952e\u503c\u5bf9 Key-&gt;Value');\nfor (const [k, v] of map.entries()) {\nconsole.info(k + ' -&gt; ' + v);\n}\nconsole.info('\\n\u5355\u72ec\u904d\u5386\u952e Key');\nfor (const k of map.keys()) {\nconsole.info(k);\n}\nconsole.info('\\n\u5355\u72ec\u904d\u5386\u503c Value');\nfor (const v of map.values()) {\nconsole.info(v);\n}\n</code></pre> hash_map.c<pre><code>// C \u672a\u63d0\u4f9b\u5185\u7f6e\u54c8\u5e0c\u8868\n</code></pre> hash_map.cs<pre><code>/* \u904d\u5386\u54c8\u5e0c\u8868 */\n// \u904d\u5386\u952e\u503c\u5bf9 Key-&gt;Value\nforeach (var kv in map)\n{\nConsole.WriteLine(kv.Key + \" -&gt; \" + kv.Value);\n}\n// \u5355\u72ec\u904d\u5386\u952e key\nforeach (int key in map.Keys)\n{\nConsole.WriteLine(key);\n}\n// \u5355\u72ec\u904d\u5386\u503c value\nforeach (String val in map.Values)\n{\nConsole.WriteLine(val);\n}\n</code></pre> hash_map.swift<pre><code>/* \u904d\u5386\u54c8\u5e0c\u8868 */\n// \u904d\u5386\u952e\u503c\u5bf9 Key-&gt;Value\nfor (key, value) in map {\nprint(\"\\(key) -&gt; \\(value)\")\n}\n// \u5355\u72ec\u904d\u5386\u952e Key\nfor key in map.keys {\nprint(key)\n}\n// \u5355\u72ec\u904d\u5386\u503c Value\nfor value in map.values {\nprint(value)\n}\n</code></pre> hash_map.zig<pre><code>\n</code></pre> hash_map.dart<pre><code>/* \u904d\u5386\u54c8\u5e0c\u8868 */\n// \u904d\u5386\u952e\u503c\u5bf9 Key-&gt;Value\nmap.forEach((key, value) {\nprint('$key -&gt; $value');\n});\n// \u5355\u72ec\u904d\u5386\u952e Key\nmap.keys.forEach((key) {\nprint(key);\n});\n// \u5355\u72ec\u904d\u5386\u503c Value\nmap.values.forEach((value) {\nprint(value);\n});\n</code></pre>"},{"location":"chapter_hashing/hash_map/#612","title":"6.1.2. \u00a0 \u54c8\u5e0c\u8868\u7b80\u5355\u5b9e\u73b0","text":"<p>\u6211\u4eec\u5148\u8003\u8651\u6700\u7b80\u5355\u7684\u60c5\u51b5\uff0c\u4ec5\u7528\u4e00\u4e2a\u6570\u7ec4\u6765\u5b9e\u73b0\u54c8\u5e0c\u8868\u3002\u5728\u54c8\u5e0c\u8868\u4e2d\uff0c\u6211\u4eec\u901a\u5e38\u5c06\u6570\u7ec4\u4e2d\u7684\u6bcf\u4e2a\u7a7a\u4f4d\u79f0\u4e3a\u300c\u6876 Bucket\u300d\uff0c\u6bcf\u4e2a\u6876\u53ef\u5b58\u50a8\u4e00\u4e2a\u952e\u503c\u5bf9\u3002\u56e0\u6b64\uff0c\u67e5\u8be2\u64cd\u4f5c\u5c31\u662f\u5b9a\u4f4d\u8f93\u5165\u7684 <code>key</code> \u5bf9\u5e94\u7684\u6876\uff0c\u4ece\u800c\u5f97\u5230 <code>value</code> \u3002</p> <p>\u90a3\u4e48\uff0c\u5982\u4f55\u57fa\u4e8e <code>key</code> \u6765\u5b9a\u4f4d\u5bf9\u5e94\u7684\u6876\u5462\uff1f\u8fd9\u662f\u901a\u8fc7\u300c\u54c8\u5e0c\u51fd\u6570 Hash Function\u300d\u5b9e\u73b0\u7684\u3002\u54c8\u5e0c\u51fd\u6570\u7684\u4f5c\u7528\u662f\u5c06\u4e00\u4e2a\u8f83\u5927\u7684\u8f93\u5165\u7a7a\u95f4\u6620\u5c04\u5230\u4e00\u4e2a\u8f83\u5c0f\u7684\u8f93\u51fa\u7a7a\u95f4\u3002\u5728\u54c8\u5e0c\u8868\u4e2d\uff0c\u8f93\u5165\u7a7a\u95f4\u662f\u6240\u6709 <code>key</code> \uff0c\u8f93\u51fa\u7a7a\u95f4\u662f\u6240\u6709\u6876\uff08\u6570\u7ec4\u7d22\u5f15\uff09\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u8f93\u5165\u4e00\u4e2a <code>key</code> \uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u54c8\u5e0c\u51fd\u6570\u5f97\u5230\u8be5 <code>key</code> \u5bf9\u5e94\u7684\u952e\u503c\u5bf9\u5b58\u50a8\u5728\u6570\u7ec4\u4e2d\u7684\u4f4d\u7f6e\u3002</p> <p>\u54c8\u5e0c\u51fd\u6570\u7684\u8ba1\u7b97\u8fc7\u7a0b\u5206\u4e3a\u4e24\u6b65\uff1a\u8f93\u5165\u4e00\u4e2a <code>key</code> \uff0c\u9996\u5148\u901a\u8fc7\u51fd\u6570 <code>hash(key)</code> \u8ba1\u7b97\u5f97\u5230\u54c8\u5e0c\u503c\uff0c\u63a5\u4e0b\u6765\u5c06\u54c8\u5e0c\u503c\u5bf9\u6876\u6570\u91cf\uff08\u6570\u7ec4\u957f\u5ea6\uff09\u53d6\u6a21\uff0c\u4ece\u800c\u83b7\u53d6\u8be5 <code>key</code> \u5bf9\u5e94\u7684\u6570\u7ec4\u7d22\u5f15 <code>index</code> \u3002\u8ba1\u7b97\u516c\u5f0f\u5982\u4e0b</p> \\[ index = \\text{hash}(key) \\bmod {c} \\] <p>\u5176\u4e2d\uff0c \\(\\bmod\\) \u8868\u793a\u53d6\u4f59\u8fd0\u7b97\uff0c \\(c\\) \u4e3a\u6876\u6570\u91cf\uff08\u6570\u7ec4\u957f\u5ea6\uff09\u3002\u968f\u540e\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u5229\u7528 <code>index</code> \u5728\u54c8\u5e0c\u8868\u4e2d\u8bbf\u95ee\u5bf9\u5e94\u7684\u6876\uff0c\u4ece\u800c\u83b7\u53d6 <code>value</code> \u3002</p> <p>\u8bbe\u6570\u7ec4\u957f\u5ea6 \\(c = 100\\) , \\(\\text{hash}(key) = key\\) \uff0c\u6613\u5f97\u54c8\u5e0c\u51fd\u6570\u4e3a \\(key \\bmod 100\\) \u3002\u4e0b\u56fe\u4ee5 <code>key</code> \u5b66\u53f7\u548c <code>value</code> \u59d3\u540d\u4e3a\u4f8b\uff0c\u5c55\u793a\u4e86\u54c8\u5e0c\u51fd\u6570\u7684\u5de5\u4f5c\u539f\u7406\u3002</p> <p></p> <p> Fig. \u54c8\u5e0c\u51fd\u6570\u5de5\u4f5c\u539f\u7406 </p> <p>\u4ee5\u4e0b\u4ee3\u7801\u7ed9\u51fa\u4e86\u4e00\u4e2a\u7b80\u5355\u54c8\u5e0c\u8868\u5b9e\u73b0\u3002\u5176\u4e2d\uff0c\u6211\u4eec\u5c06 <code>key</code> \u548c <code>value</code> \u5c01\u88c5\u6210\u4e00\u4e2a\u7c7b <code>Pair</code> \uff0c\u4ee5\u8868\u793a\u952e\u503c\u5bf9\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart array_hash_map.java<pre><code>/* \u952e\u503c\u5bf9 */\nclass Pair {\npublic int key;\npublic String val;\npublic Pair(int key, String val) {\nthis.key = key;\nthis.val = val;\n}\n}\n/* \u57fa\u4e8e\u6570\u7ec4\u7b80\u6613\u5b9e\u73b0\u7684\u54c8\u5e0c\u8868 */\nclass ArrayHashMap {\nprivate List&lt;Pair&gt; buckets;\npublic ArrayHashMap() {\n// \u521d\u59cb\u5316\u6570\u7ec4\uff0c\u5305\u542b 100 \u4e2a\u6876\nbuckets = new ArrayList&lt;&gt;();\nfor (int i = 0; i &lt; 100; i++) {\nbuckets.add(null);\n}\n}\n/* \u54c8\u5e0c\u51fd\u6570 */\nprivate int hashFunc(int key) {\nint index = key % 100;\nreturn index;\n}\n/* \u67e5\u8be2\u64cd\u4f5c */\npublic String get(int key) {\nint index = hashFunc(key);\nPair pair = buckets.get(index);\nif (pair == null)\nreturn null;\nreturn pair.val;\n}\n/* \u6dfb\u52a0\u64cd\u4f5c */\npublic void put(int key, String val) {\nPair pair = new Pair(key, val);\nint index = hashFunc(key);\nbuckets.set(index, pair);\n}\n/* \u5220\u9664\u64cd\u4f5c */\npublic void remove(int key) {\nint index = hashFunc(key);\n// \u7f6e\u4e3a null \uff0c\u4ee3\u8868\u5220\u9664\nbuckets.set(index, null);\n}\n/* \u83b7\u53d6\u6240\u6709\u952e\u503c\u5bf9 */\npublic List&lt;Pair&gt; pairSet() {\nList&lt;Pair&gt; pairSet = new ArrayList&lt;&gt;();\nfor (Pair pair : buckets) {\nif (pair != null)\npairSet.add(pair);\n}\nreturn pairSet;\n}\n/* \u83b7\u53d6\u6240\u6709\u952e */\npublic List&lt;Integer&gt; keySet() {\nList&lt;Integer&gt; keySet = new ArrayList&lt;&gt;();\nfor (Pair pair : buckets) {\nif (pair != null)\nkeySet.add(pair.key);\n}\nreturn keySet;\n}\n/* \u83b7\u53d6\u6240\u6709\u503c */\npublic List&lt;String&gt; valueSet() {\nList&lt;String&gt; valueSet = new ArrayList&lt;&gt;();\nfor (Pair pair : buckets) {\nif (pair != null)\nvalueSet.add(pair.val);\n}\nreturn valueSet;\n}\n/* \u6253\u5370\u54c8\u5e0c\u8868 */\npublic void print() {\nfor (Pair kv : pairSet()) {\nSystem.out.println(kv.key + \" -&gt; \" + kv.val);\n}\n}\n}\n</code></pre> array_hash_map.cpp<pre><code>/* \u952e\u503c\u5bf9 */\nstruct Pair {\npublic:\nint key;\nstring val;\nPair(int key, string val) {\nthis-&gt;key = key;\nthis-&gt;val = val;\n}\n};\n/* \u57fa\u4e8e\u6570\u7ec4\u7b80\u6613\u5b9e\u73b0\u7684\u54c8\u5e0c\u8868 */\nclass ArrayHashMap {\nprivate:\nvector&lt;Pair *&gt; buckets;\npublic:\nArrayHashMap() {\n// \u521d\u59cb\u5316\u6570\u7ec4\uff0c\u5305\u542b 100 \u4e2a\u6876\nbuckets = vector&lt;Pair *&gt;(100);\n}\n~ArrayHashMap() {\n// \u91ca\u653e\u5185\u5b58\nfor (const auto &amp;bucket : buckets) {\ndelete bucket;\n}\nbuckets.clear();\n}\n/* \u54c8\u5e0c\u51fd\u6570 */\nint hashFunc(int key) {\nint index = key % 100;\nreturn index;\n}\n/* \u67e5\u8be2\u64cd\u4f5c */\nstring get(int key) {\nint index = hashFunc(key);\nPair *pair = buckets[index];\nif (pair == nullptr)\nreturn nullptr;\nreturn pair-&gt;val;\n}\n/* \u6dfb\u52a0\u64cd\u4f5c */\nvoid put(int key, string val) {\nPair *pair = new Pair(key, val);\nint index = hashFunc(key);\nbuckets[index] = pair;\n}\n/* \u5220\u9664\u64cd\u4f5c */\nvoid remove(int key) {\nint index = hashFunc(key);\n// \u91ca\u653e\u5185\u5b58\u5e76\u7f6e\u4e3a nullptr\ndelete buckets[index];\nbuckets[index] = nullptr;\n}\n/* \u83b7\u53d6\u6240\u6709\u952e\u503c\u5bf9 */\nvector&lt;Pair *&gt; pairSet() {\nvector&lt;Pair *&gt; pairSet;\nfor (Pair *pair : buckets) {\nif (pair != nullptr) {\npairSet.push_back(pair);\n}\n}\nreturn pairSet;\n}\n/* \u83b7\u53d6\u6240\u6709\u952e */\nvector&lt;int&gt; keySet() {\nvector&lt;int&gt; keySet;\nfor (Pair *pair : buckets) {\nif (pair != nullptr) {\nkeySet.push_back(pair-&gt;key);\n}\n}\nreturn keySet;\n}\n/* \u83b7\u53d6\u6240\u6709\u503c */\nvector&lt;string&gt; valueSet() {\nvector&lt;string&gt; valueSet;\nfor (Pair *pair : buckets) {\nif (pair != nullptr) {\nvalueSet.push_back(pair-&gt;val);\n}\n}\nreturn valueSet;\n}\n/* \u6253\u5370\u54c8\u5e0c\u8868 */\nvoid print() {\nfor (Pair *kv : pairSet()) {\ncout &lt;&lt; kv-&gt;key &lt;&lt; \" -&gt; \" &lt;&lt; kv-&gt;val &lt;&lt; endl;\n}\n}\n};\n</code></pre> array_hash_map.py<pre><code>class Pair:\n\"\"\"\u952e\u503c\u5bf9\"\"\"\ndef __init__(self, key: int, val: str):\nself.key = key\nself.val = val\nclass ArrayHashMap:\n\"\"\"\u57fa\u4e8e\u6570\u7ec4\u7b80\u6613\u5b9e\u73b0\u7684\u54c8\u5e0c\u8868\"\"\"\ndef __init__(self):\n\"\"\"\u6784\u9020\u65b9\u6cd5\"\"\"\n# \u521d\u59cb\u5316\u6570\u7ec4\uff0c\u5305\u542b 100 \u4e2a\u6876\nself.buckets: list[Pair | None] = [None] * 100\ndef hash_func(self, key: int) -&gt; int:\n\"\"\"\u54c8\u5e0c\u51fd\u6570\"\"\"\nindex = key % 100\nreturn index\ndef get(self, key: int) -&gt; str:\n\"\"\"\u67e5\u8be2\u64cd\u4f5c\"\"\"\nindex: int = self.hash_func(key)\npair: Pair = self.buckets[index]\nif pair is None:\nreturn None\nreturn pair.val\ndef put(self, key: int, val: str):\n\"\"\"\u6dfb\u52a0\u64cd\u4f5c\"\"\"\npair = Pair(key, val)\nindex: int = self.hash_func(key)\nself.buckets[index] = pair\ndef remove(self, key: int):\n\"\"\"\u5220\u9664\u64cd\u4f5c\"\"\"\nindex: int = self.hash_func(key)\n# \u7f6e\u4e3a None \uff0c\u4ee3\u8868\u5220\u9664\nself.buckets[index] = None\ndef entry_set(self) -&gt; list[Pair]:\n\"\"\"\u83b7\u53d6\u6240\u6709\u952e\u503c\u5bf9\"\"\"\nresult: list[Pair] = []\nfor pair in self.buckets:\nif pair is not None:\nresult.append(pair)\nreturn result\ndef key_set(self) -&gt; list[int]:\n\"\"\"\u83b7\u53d6\u6240\u6709\u952e\"\"\"\nresult = []\nfor pair in self.buckets:\nif pair is not None:\nresult.append(pair.key)\nreturn result\ndef value_set(self) -&gt; list[str]:\n\"\"\"\u83b7\u53d6\u6240\u6709\u503c\"\"\"\nresult = []\nfor pair in self.buckets:\nif pair is not None:\nresult.append(pair.val)\nreturn result\ndef print(self):\n\"\"\"\u6253\u5370\u54c8\u5e0c\u8868\"\"\"\nfor pair in self.buckets:\nif pair is not None:\nprint(pair.key, \"-&gt;\", pair.val)\n</code></pre> array_hash_map.go<pre><code>/* \u952e\u503c\u5bf9 */\ntype pair struct {\nkey int\nval string\n}\n/* \u57fa\u4e8e\u6570\u7ec4\u7b80\u6613\u5b9e\u73b0\u7684\u54c8\u5e0c\u8868 */\ntype arrayHashMap struct {\nbuckets []*pair\n}\n/* \u521d\u59cb\u5316\u54c8\u5e0c\u8868 */\nfunc newArrayHashMap() *arrayHashMap {\n// \u521d\u59cb\u5316\u6570\u7ec4\uff0c\u5305\u542b 100 \u4e2a\u6876\nbuckets := make([]*pair, 100)\nreturn &amp;arrayHashMap{buckets: buckets}\n}\n/* \u54c8\u5e0c\u51fd\u6570 */\nfunc (a *arrayHashMap) hashFunc(key int) int {\nindex := key % 100\nreturn index\n}\n/* \u67e5\u8be2\u64cd\u4f5c */\nfunc (a *arrayHashMap) get(key int) string {\nindex := a.hashFunc(key)\npair := a.buckets[index]\nif pair == nil {\nreturn \"Not Found\"\n}\nreturn pair.val\n}\n/* \u6dfb\u52a0\u64cd\u4f5c */\nfunc (a *arrayHashMap) put(key int, val string) {\npair := &amp;pair{key: key, val: val}\nindex := a.hashFunc(key)\na.buckets[index] = pair\n}\n/* \u5220\u9664\u64cd\u4f5c */\nfunc (a *arrayHashMap) remove(key int) {\nindex := a.hashFunc(key)\n// \u7f6e\u4e3a nil \uff0c\u4ee3\u8868\u5220\u9664\na.buckets[index] = nil\n}\n/* \u83b7\u53d6\u6240\u6709\u952e\u5bf9 */\nfunc (a *arrayHashMap) pairSet() []*pair {\nvar pairs []*pair\nfor _, pair := range a.buckets {\nif pair != nil {\npairs = append(pairs, pair)\n}\n}\nreturn pairs\n}\n/* \u83b7\u53d6\u6240\u6709\u952e */\nfunc (a *arrayHashMap) keySet() []int {\nvar keys []int\nfor _, pair := range a.buckets {\nif pair != nil {\nkeys = append(keys, pair.key)\n}\n}\nreturn keys\n}\n/* \u83b7\u53d6\u6240\u6709\u503c */\nfunc (a *arrayHashMap) valueSet() []string {\nvar values []string\nfor _, pair := range a.buckets {\nif pair != nil {\nvalues = append(values, pair.val)\n}\n}\nreturn values\n}\n/* \u6253\u5370\u54c8\u5e0c\u8868 */\nfunc (a *arrayHashMap) print() {\nfor _, pair := range a.buckets {\nif pair != nil {\nfmt.Println(pair.key, \"-&gt;\", pair.val)\n}\n}\n}\n</code></pre> array_hash_map.js<pre><code>/* \u952e\u503c\u5bf9 Number -&gt; String */\nclass Pair {\nconstructor(key, val) {\nthis.key = key;\nthis.val = val;\n}\n}\n/* \u57fa\u4e8e\u6570\u7ec4\u7b80\u6613\u5b9e\u73b0\u7684\u54c8\u5e0c\u8868 */\nclass ArrayHashMap {\n#buckets;\nconstructor() {\n// \u521d\u59cb\u5316\u6570\u7ec4\uff0c\u5305\u542b 100 \u4e2a\u6876\nthis.#buckets = new Array(100).fill(null);\n}\n/* \u54c8\u5e0c\u51fd\u6570 */\n#hashFunc(key) {\nreturn key % 100;\n}\n/* \u67e5\u8be2\u64cd\u4f5c */\nget(key) {\nlet index = this.#hashFunc(key);\nlet pair = this.#buckets[index];\nif (pair === null) return null;\nreturn pair.val;\n}\n/* \u6dfb\u52a0\u64cd\u4f5c */\nset(key, val) {\nlet index = this.#hashFunc(key);\nthis.#buckets[index] = new Pair(key, val);\n}\n/* \u5220\u9664\u64cd\u4f5c */\ndelete(key) {\nlet index = this.#hashFunc(key);\n// \u7f6e\u4e3a null \uff0c\u4ee3\u8868\u5220\u9664\nthis.#buckets[index] = null;\n}\n/* \u83b7\u53d6\u6240\u6709\u952e\u503c\u5bf9 */\nentries() {\nlet arr = [];\nfor (let i = 0; i &lt; this.#buckets.length; i++) {\nif (this.#buckets[i]) {\narr.push(this.#buckets[i]);\n}\n}\nreturn arr;\n}\n/* \u83b7\u53d6\u6240\u6709\u952e */\nkeys() {\nlet arr = [];\nfor (let i = 0; i &lt; this.#buckets.length; i++) {\nif (this.#buckets[i]) {\narr.push(this.#buckets[i]?.key);\n}\n}\nreturn arr;\n}\n/* \u83b7\u53d6\u6240\u6709\u503c */\nvalues() {\nlet arr = [];\nfor (let i = 0; i &lt; this.#buckets.length; i++) {\nif (this.#buckets[i]) {\narr.push(this.#buckets[i]?.val);\n}\n}\nreturn arr;\n}\n/* \u6253\u5370\u54c8\u5e0c\u8868 */\nprint() {\nlet pairSet = this.entries();\nfor (const pair of pairSet) {\nif (!pair) continue;\nconsole.info(`${pair.key} -&gt; ${pair.val}`);\n}\n}\n}\n</code></pre> array_hash_map.ts<pre><code>/* \u952e\u503c\u5bf9 Number -&gt; String */\nclass Pair {\npublic key: number;\npublic val: string;\nconstructor(key: number, val: string) {\nthis.key = key;\nthis.val = val;\n}\n}\n/* \u57fa\u4e8e\u6570\u7ec4\u7b80\u6613\u5b9e\u73b0\u7684\u54c8\u5e0c\u8868 */\nclass ArrayHashMap {\nprivate readonly buckets: (Pair | null)[];\nconstructor() {\n// \u521d\u59cb\u5316\u6570\u7ec4\uff0c\u5305\u542b 100 \u4e2a\u6876\nthis.buckets = new Array(100).fill(null);\n}\n/* \u54c8\u5e0c\u51fd\u6570 */\nprivate hashFunc(key: number): number {\nreturn key % 100;\n}\n/* \u67e5\u8be2\u64cd\u4f5c */\npublic get(key: number): string | null {\nlet index = this.hashFunc(key);\nlet pair = this.buckets[index];\nif (pair === null) return null;\nreturn pair.val;\n}\n/* \u6dfb\u52a0\u64cd\u4f5c */\npublic set(key: number, val: string) {\nlet index = this.hashFunc(key);\nthis.buckets[index] = new Pair(key, val);\n}\n/* \u5220\u9664\u64cd\u4f5c */\npublic delete(key: number) {\nlet index = this.hashFunc(key);\n// \u7f6e\u4e3a null \uff0c\u4ee3\u8868\u5220\u9664\nthis.buckets[index] = null;\n}\n/* \u83b7\u53d6\u6240\u6709\u952e\u503c\u5bf9 */\npublic entries(): (Pair | null)[] {\nlet arr: (Pair | null)[] = [];\nfor (let i = 0; i &lt; this.buckets.length; i++) {\nif (this.buckets[i]) {\narr.push(this.buckets[i]);\n}\n}\nreturn arr;\n}\n/* \u83b7\u53d6\u6240\u6709\u952e */\npublic keys(): (number | undefined)[] {\nlet arr: (number | undefined)[] = [];\nfor (let i = 0; i &lt; this.buckets.length; i++) {\nif (this.buckets[i]) {\narr.push(this.buckets[i]?.key);\n}\n}\nreturn arr;\n}\n/* \u83b7\u53d6\u6240\u6709\u503c */\npublic values(): (string | undefined)[] {\nlet arr: (string | undefined)[] = [];\nfor (let i = 0; i &lt; this.buckets.length; i++) {\nif (this.buckets[i]) {\narr.push(this.buckets[i]?.val);\n}\n}\nreturn arr;\n}\n/* \u6253\u5370\u54c8\u5e0c\u8868 */\npublic print() {\nlet pairSet = this.entries();\nfor (const pair of pairSet) {\nif (!pair) continue;\nconsole.info(`${pair.key} -&gt; ${pair.val}`);\n}\n}\n}\n</code></pre> array_hash_map.c<pre><code>/* \u952e\u503c\u5bf9 int-&gt;string */\nstruct pair {\nint key;\nchar *val;\n};\ntypedef struct pair pair;\n[class]{arrayHashMap}-[func]{}\n</code></pre> array_hash_map.cs<pre><code>/* \u952e\u503c\u5bf9 int-&gt;string */\nclass Pair {\npublic int key;\npublic string val;\npublic Pair(int key, string val) {\nthis.key = key;\nthis.val = val;\n}\n}\n/* \u57fa\u4e8e\u6570\u7ec4\u7b80\u6613\u5b9e\u73b0\u7684\u54c8\u5e0c\u8868 */\nclass ArrayHashMap {\nprivate List&lt;Pair?&gt; buckets;\npublic ArrayHashMap() {\n// \u521d\u59cb\u5316\u6570\u7ec4\uff0c\u5305\u542b 100 \u4e2a\u6876\nbuckets = new();\nfor (int i = 0; i &lt; 100; i++) {\nbuckets.Add(null);\n}\n}\n/* \u54c8\u5e0c\u51fd\u6570 */\nprivate int hashFunc(int key) {\nint index = key % 100;\nreturn index;\n}\n/* \u67e5\u8be2\u64cd\u4f5c */\npublic string? get(int key) {\nint index = hashFunc(key);\nPair? pair = buckets[index];\nif (pair == null) return null;\nreturn pair.val;\n}\n/* \u6dfb\u52a0\u64cd\u4f5c */\npublic void put(int key, string val) {\nPair pair = new Pair(key, val);\nint index = hashFunc(key);\nbuckets[index] = pair;\n}\n/* \u5220\u9664\u64cd\u4f5c */\npublic void remove(int key) {\nint index = hashFunc(key);\n// \u7f6e\u4e3a null \uff0c\u4ee3\u8868\u5220\u9664\nbuckets[index] = null;\n}\n/* \u83b7\u53d6\u6240\u6709\u952e\u503c\u5bf9 */\npublic List&lt;Pair&gt; pairSet() {\nList&lt;Pair&gt; pairSet = new();\nforeach (Pair? pair in buckets) {\nif (pair != null)\npairSet.Add(pair);\n}\nreturn pairSet;\n}\n/* \u83b7\u53d6\u6240\u6709\u952e */\npublic List&lt;int&gt; keySet() {\nList&lt;int&gt; keySet = new();\nforeach (Pair? pair in buckets) {\nif (pair != null)\nkeySet.Add(pair.key);\n}\nreturn keySet;\n}\n/* \u83b7\u53d6\u6240\u6709\u503c */\npublic List&lt;string&gt; valueSet() {\nList&lt;string&gt; valueSet = new();\nforeach (Pair? pair in buckets) {\nif (pair != null)\nvalueSet.Add(pair.val);\n}\nreturn valueSet;\n}\n/* \u6253\u5370\u54c8\u5e0c\u8868 */\npublic void print() {\nforeach (Pair kv in pairSet()) {\nConsole.WriteLine(kv.key + \" -&gt; \" + kv.val);\n}\n}\n}\n</code></pre> array_hash_map.swift<pre><code>/* \u952e\u503c\u5bf9 */\nclass Pair {\nvar key: Int\nvar val: String\ninit(key: Int, val: String) {\nself.key = key\nself.val = val\n}\n}\n/* \u57fa\u4e8e\u6570\u7ec4\u7b80\u6613\u5b9e\u73b0\u7684\u54c8\u5e0c\u8868 */\nclass ArrayHashMap {\nprivate var buckets: [Pair?] = []\ninit() {\n// \u521d\u59cb\u5316\u6570\u7ec4\uff0c\u5305\u542b 100 \u4e2a\u6876\nfor _ in 0 ..&lt; 100 {\nbuckets.append(nil)\n}\n}\n/* \u54c8\u5e0c\u51fd\u6570 */\nprivate func hashFunc(key: Int) -&gt; Int {\nlet index = key % 100\nreturn index\n}\n/* \u67e5\u8be2\u64cd\u4f5c */\nfunc get(key: Int) -&gt; String? {\nlet index = hashFunc(key: key)\nlet pair = buckets[index]\nreturn pair?.val\n}\n/* \u6dfb\u52a0\u64cd\u4f5c */\nfunc put(key: Int, val: String) {\nlet pair = Pair(key: key, val: val)\nlet index = hashFunc(key: key)\nbuckets[index] = pair\n}\n/* \u5220\u9664\u64cd\u4f5c */\nfunc remove(key: Int) {\nlet index = hashFunc(key: key)\n// \u7f6e\u4e3a nil \uff0c\u4ee3\u8868\u5220\u9664\nbuckets[index] = nil\n}\n/* \u83b7\u53d6\u6240\u6709\u952e\u503c\u5bf9 */\nfunc pairSet() -&gt; [Pair] {\nvar pairSet: [Pair] = []\nfor pair in buckets {\nif let pair = pair {\npairSet.append(pair)\n}\n}\nreturn pairSet\n}\n/* \u83b7\u53d6\u6240\u6709\u952e */\nfunc keySet() -&gt; [Int] {\nvar keySet: [Int] = []\nfor pair in buckets {\nif let pair = pair {\nkeySet.append(pair.key)\n}\n}\nreturn keySet\n}\n/* \u83b7\u53d6\u6240\u6709\u503c */\nfunc valueSet() -&gt; [String] {\nvar valueSet: [String] = []\nfor pair in buckets {\nif let pair = pair {\nvalueSet.append(pair.val)\n}\n}\nreturn valueSet\n}\n/* \u6253\u5370\u54c8\u5e0c\u8868 */\nfunc print() {\nfor pair in pairSet() {\nSwift.print(\"\\(pair.key) -&gt; \\(pair.val)\")\n}\n}\n}\n</code></pre> array_hash_map.zig<pre><code>// \u952e\u503c\u5bf9\nconst Pair = struct {\nkey: usize = undefined,\nval: []const u8 = undefined,\npub fn init(key: usize, val: []const u8) Pair {\nreturn Pair {\n.key = key,\n.val = val,\n};\n}\n};\n// \u57fa\u4e8e\u6570\u7ec4\u7b80\u6613\u5b9e\u73b0\u7684\u54c8\u5e0c\u8868\nfn ArrayHashMap(comptime T: type) type {\nreturn struct {\nbuckets: ?std.ArrayList(?T) = null,\nmem_allocator: std.mem.Allocator = undefined,\nconst Self = @This();\n// \u6784\u9020\u65b9\u6cd5\npub fn init(self: *Self, allocator: std.mem.Allocator) !void {\nself.mem_allocator = allocator;\n// \u521d\u59cb\u5316\u6570\u7ec4\uff0c\u5305\u542b 100 \u4e2a\u6876\nself.buckets = std.ArrayList(?T).init(self.mem_allocator);\nvar i: i32 = 0;\nwhile (i &lt; 100) : (i += 1) {\ntry self.buckets.?.append(null);\n}\n}\n// \u6790\u6784\u65b9\u6cd5\npub fn deinit(self: *Self) void {\nif (self.buckets != null) self.buckets.?.deinit();\n}\n// \u54c8\u5e0c\u51fd\u6570\nfn hashFunc(key: usize) usize {\nvar index = key % 100;\nreturn index;\n}\n// \u67e5\u8be2\u64cd\u4f5c\npub fn get(self: *Self, key: usize) []const u8 {\nvar index = hashFunc(key);\nvar pair = self.buckets.?.items[index];\nreturn pair.?.val;\n}\n// \u6dfb\u52a0\u64cd\u4f5c\npub fn put(self: *Self, key: usize, val: []const u8) !void {\nvar pair = Pair.init(key, val);\nvar index = hashFunc(key);\nself.buckets.?.items[index] = pair;\n}\n// \u5220\u9664\u64cd\u4f5c\npub fn remove(self: *Self, key: usize) !void {\nvar index = hashFunc(key);\n// \u7f6e\u4e3a null \uff0c\u4ee3\u8868\u5220\u9664\nself.buckets.?.items[index] = null;\n}       // \u83b7\u53d6\u6240\u6709\u952e\u503c\u5bf9\npub fn pairSet(self: *Self) !*std.ArrayList(T) {\nvar entry_set = std.ArrayList(T).init(self.mem_allocator);\nfor (self.buckets.?.items) |item| {\nif (item == null) continue;\ntry entry_set.append(item.?);\n}\nreturn &amp;entry_set;\n}  // \u83b7\u53d6\u6240\u6709\u952e\npub fn keySet(self: *Self) !*std.ArrayList(usize) {\nvar key_set = std.ArrayList(usize).init(self.mem_allocator);\nfor (self.buckets.?.items) |item| {\nif (item == null) continue;\ntry key_set.append(item.?.key);\n}\nreturn &amp;key_set;\n}  // \u83b7\u53d6\u6240\u6709\u503c\npub fn valueSet(self: *Self) !*std.ArrayList([]const u8) {\nvar value_set = std.ArrayList([]const u8).init(self.mem_allocator);\nfor (self.buckets.?.items) |item| {\nif (item == null) continue;\ntry value_set.append(item.?.val);\n}\nreturn &amp;value_set;\n}\n// \u6253\u5370\u54c8\u5e0c\u8868\npub fn print(self: *Self) !void {\nvar entry_set = try self.pairSet();\ndefer entry_set.deinit();\nfor (entry_set.items) |item| {\nstd.debug.print(\"{} -&gt; {s}\\n\", .{item.key, item.val});\n}\n}\n};\n}\n</code></pre> array_hash_map.dart<pre><code>/* \u952e\u503c\u5bf9 */\nclass Pair {\nint key;\nString val;\nPair(this.key, this.val);\n}\n/* \u57fa\u4e8e\u6570\u7ec4\u7b80\u6613\u5b9e\u73b0\u7684\u54c8\u5e0c\u8868 */\nclass ArrayHashMap {\nlate List&lt;Pair?&gt; _buckets;\nArrayHashMap() {\n// \u521d\u59cb\u5316\u6570\u7ec4\uff0c\u5305\u542b 100 \u4e2a\u6876\n_buckets = List.filled(100, null);\n}\n/* \u54c8\u5e0c\u51fd\u6570 */\nint _hashFunc(int key) {\nfinal int index = key % 100;\nreturn index;\n}\n/* \u67e5\u8be2\u64cd\u4f5c */\nString? get(int key) {\nfinal int index = _hashFunc(key);\nfinal Pair? pair = _buckets[index];\nif (pair == null) {\nreturn null;\n}\nreturn pair.val;\n}\n/* \u6dfb\u52a0\u64cd\u4f5c */\nvoid put(int key, String val) {\nfinal Pair pair = Pair(key, val);\nfinal int index = _hashFunc(key);\n_buckets[index] = pair;\n}\n/* \u5220\u9664\u64cd\u4f5c */\nvoid remove(int key) {\nfinal int index = _hashFunc(key);\n_buckets[index] = null;\n}\n/* \u83b7\u53d6\u6240\u6709\u952e\u503c\u5bf9 */\nList&lt;Pair&gt; pairSet() {\nList&lt;Pair&gt; pairSet = [];\nfor (final Pair? pair in _buckets) {\nif (pair != null) {\npairSet.add(pair);\n}\n}\nreturn pairSet;\n}\n/* \u83b7\u53d6\u6240\u6709\u952e */\nList&lt;int&gt; keySet() {\nList&lt;int&gt; keySet = [];\nfor (final Pair? pair in _buckets) {\nif (pair != null) {\nkeySet.add(pair.key);\n}\n}\nreturn keySet;\n}\n/* \u83b7\u53d6\u6240\u6709\u503c */\nList&lt;String&gt; values() {\nList&lt;String&gt; valueSet = [];\nfor (final Pair? pair in _buckets) {\nif (pair != null) {\nvalueSet.add(pair.val);\n}\n}\nreturn valueSet;\n}\n/* \u6253\u5370\u54c8\u5e0c\u8868 */\nvoid printHashMap() {\nfor (final Pair kv in pairSet()) {\nprint(\"${kv.key} -&gt; ${kv.val}\");\n}\n}\n}\n</code></pre>"},{"location":"chapter_hashing/hash_map/#613","title":"6.1.3. \u00a0 \u54c8\u5e0c\u51b2\u7a81","text":"<p>\u672c\u8d28\u4e0a\u770b\uff0c\u54c8\u5e0c\u51fd\u6570\u7684\u662f\u5c06\u4e00\u4e2a\u5e9e\u5927\u7684\u8f93\u5165\u7a7a\u95f4\uff08<code>key</code> \u8303\u56f4\uff09\u6620\u5c04\u5230\u4e00\u4e2a\u8f83\u5c0f\u7684\u8f93\u51fa\u7a7a\u95f4\uff08\u6570\u7ec4\u7d22\u5f15\u8303\u56f4\uff09\u3002\u56e0\u6b64\uff0c\u7406\u8bba\u4e0a\u4e00\u5b9a\u5b58\u5728\u201d\u591a\u4e2a\u8f93\u5165\u5bf9\u5e94\u76f8\u540c\u8f93\u51fa\u201d\u7684\u60c5\u51b5\u3002</p> <p>\u5bf9\u4e8e\u4e0a\u8ff0\u793a\u4f8b\u4e2d\u7684\u54c8\u5e0c\u51fd\u6570\uff0c\u5f53\u8f93\u5165\u7684 <code>key</code> \u540e\u4e24\u4f4d\u76f8\u540c\u65f6\uff0c\u54c8\u5e0c\u51fd\u6570\u7684\u8f93\u51fa\u7ed3\u679c\u4e5f\u76f8\u540c\u3002\u4f8b\u5982\uff0c\u67e5\u8be2\u5b66\u53f7\u4e3a \\(12836\\) \u548c \\(20336\\) \u7684\u4e24\u4e2a\u5b66\u751f\u65f6\uff0c\u6211\u4eec\u5f97\u5230\uff1a</p> \\[ 12836 \\bmod 100 = 20336 \\bmod 100 = 36 \\] <p>\u4e24\u4e2a\u5b66\u53f7\u6307\u5411\u4e86\u540c\u4e00\u4e2a\u59d3\u540d\uff0c\u8fd9\u663e\u7136\u662f\u4e0d\u5bf9\u7684\u3002\u6211\u4eec\u628a\u8fd9\u79cd\u60c5\u51b5\u79f0\u4e3a\u201c\u54c8\u5e0c\u51b2\u7a81\u201d\u3002\u5728\u4e0b\u8282\u4e2d\uff0c\u6211\u4eec\u5c06\u91cd\u70b9\u8ba8\u8bba\u5982\u4f55\u89e3\u51b3\u51b2\u7a81\u95ee\u9898\u3002</p> <p></p> <p> Fig. \u54c8\u5e0c\u51b2\u7a81\u793a\u4f8b </p>"},{"location":"chapter_hashing/summary/","title":"6.3. \u00a0 \u5c0f\u7ed3","text":"<ul> <li>\u54c8\u5e0c\u8868\u80fd\u591f\u5728 \\(O(1)\\) \u65f6\u95f4\u5185\u5c06\u952e key \u6620\u5c04\u5230\u503c value\uff0c\u6548\u7387\u975e\u5e38\u9ad8\u3002</li> <li>\u5e38\u89c1\u7684\u54c8\u5e0c\u8868\u64cd\u4f5c\u5305\u62ec\u67e5\u8be2\u3001\u6dfb\u52a0\u4e0e\u5220\u9664\u952e\u503c\u5bf9\u3001\u904d\u5386\u952e\u503c\u5bf9\u7b49\u3002</li> <li>\u54c8\u5e0c\u51fd\u6570\u5c06 key \u6620\u5c04\u4e3a\u6570\u7ec4\u7d22\u5f15\uff08\u6876\u7d22\u5f15\uff09\uff0c\u4ece\u800c\u8bbf\u95ee\u5bf9\u5e94\u7684\u503c value \u3002</li> <li>\u4e24\u4e2a\u4e0d\u540c\u7684 key \u53ef\u80fd\u5728\u7ecf\u8fc7\u54c8\u5e0c\u51fd\u6570\u540e\u5f97\u5230\u76f8\u540c\u7684\u7d22\u5f15\uff0c\u5bfc\u81f4\u67e5\u8be2\u7ed3\u679c\u51fa\u9519\uff0c\u8fd9\u79cd\u73b0\u8c61\u88ab\u79f0\u4e3a\u54c8\u5e0c\u51b2\u7a81\u3002</li> <li>\u7f13\u89e3\u54c8\u5e0c\u51b2\u7a81\u7684\u65b9\u6cd5\u4e3b\u8981\u6709\u6269\u5bb9\u54c8\u5e0c\u8868\u548c\u4f18\u5316\u54c8\u5e0c\u8868\u7684\u8868\u793a\u65b9\u6cd5\u3002</li> <li>\u8d1f\u8f7d\u56e0\u5b50\u5b9a\u4e49\u4e3a\u54c8\u5e0c\u8868\u4e2d\u5143\u7d20\u6570\u91cf\u9664\u4ee5\u6876\u6570\u91cf\uff0c\u53cd\u6620\u4e86\u54c8\u5e0c\u51b2\u7a81\u7684\u4e25\u91cd\u7a0b\u5ea6\uff0c\u5e38\u7528\u4f5c\u89e6\u53d1\u54c8\u5e0c\u8868\u6269\u5bb9\u7684\u6761\u4ef6\u3002\u4e0e\u6570\u7ec4\u6269\u5bb9\u7c7b\u4f3c\uff0c\u54c8\u5e0c\u8868\u6269\u5bb9\u64cd\u4f5c\u4e5f\u4f1a\u4ea7\u751f\u8f83\u5927\u7684\u5f00\u9500\u3002</li> <li>\u94fe\u5f0f\u5730\u5740\u901a\u8fc7\u5c06\u5355\u4e2a\u5143\u7d20\u8f6c\u5316\u4e3a\u94fe\u8868\uff0c\u5c06\u6240\u6709\u51b2\u7a81\u5143\u7d20\u5b58\u50a8\u5728\u540c\u4e00\u4e2a\u94fe\u8868\u4e2d\uff0c\u4ece\u800c\u89e3\u51b3\u54c8\u5e0c\u51b2\u7a81\u3002\u7136\u800c\uff0c\u8fc7\u957f\u7684\u94fe\u8868\u4f1a\u964d\u4f4e\u67e5\u8be2\u6548\u7387\uff0c\u53ef\u4ee5\u901a\u8fc7\u5c06\u94fe\u8868\u8f6c\u6362\u4e3a AVL \u6811\u6216\u7ea2\u9ed1\u6811\u6765\u6539\u5584\u3002</li> <li>\u5f00\u653e\u5bfb\u5740\u901a\u8fc7\u591a\u6b21\u63a2\u6d4b\u6765\u89e3\u51b3\u54c8\u5e0c\u51b2\u7a81\u3002\u7ebf\u6027\u63a2\u6d4b\u4f7f\u7528\u56fa\u5b9a\u6b65\u957f\uff0c\u7f3a\u70b9\u662f\u4e0d\u80fd\u5220\u9664\u5143\u7d20\u4e14\u5bb9\u6613\u4ea7\u751f\u805a\u96c6\u3002\u591a\u6b21\u54c8\u5e0c\u4f7f\u7528\u591a\u4e2a\u54c8\u5e0c\u51fd\u6570\u8fdb\u884c\u63a2\u6d4b\uff0c\u76f8\u5bf9\u7ebf\u6027\u63a2\u6d4b\u4e0d\u6613\u4ea7\u751f\u805a\u96c6\uff0c\u4f46\u591a\u4e2a\u54c8\u5e0c\u51fd\u6570\u589e\u52a0\u4e86\u8ba1\u7b97\u91cf\u3002</li> <li>\u4e0d\u540c\u7f16\u7a0b\u8bed\u8a00\u91c7\u53d6\u4e86\u4e0d\u540c\u7684\u54c8\u5e0c\u8868\u5b9e\u73b0\u7b56\u7565\u3002\u4f8b\u5982\uff0cJava \u7684 HashMap \u4f7f\u7528\u94fe\u5f0f\u5730\u5740\uff0c\u800c Python \u7684 Dict \u91c7\u7528\u5f00\u653e\u5bfb\u5740\u3002</li> </ul>"},{"location":"chapter_heap/","title":"8. \u00a0 \u5806","text":""},{"location":"chapter_heap/build_heap/","title":"8.2. \u00a0 \u5efa\u5806\u64cd\u4f5c","text":"<p>\u5982\u679c\u6211\u4eec\u60f3\u8981\u6839\u636e\u8f93\u5165\u5217\u8868\u751f\u6210\u4e00\u4e2a\u5806\uff0c\u8fd9\u4e2a\u8fc7\u7a0b\u88ab\u79f0\u4e3a\u300c\u5efa\u5806\u300d\u3002</p>"},{"location":"chapter_heap/build_heap/#821","title":"8.2.1. \u00a0 \u501f\u52a9\u5165\u5806\u65b9\u6cd5\u5b9e\u73b0","text":"<p>\u6700\u76f4\u63a5\u7684\u65b9\u6cd5\u662f\u501f\u52a9\u201c\u5143\u7d20\u5165\u5806\u64cd\u4f5c\u201d\u5b9e\u73b0\uff0c\u9996\u5148\u521b\u5efa\u4e00\u4e2a\u7a7a\u5806\uff0c\u7136\u540e\u5c06\u5217\u8868\u5143\u7d20\u4f9d\u6b21\u6dfb\u52a0\u5230\u5806\u4e2d\u3002</p> <p>\u8bbe\u5143\u7d20\u6570\u91cf\u4e3a \\(n\\) \uff0c\u5219\u6700\u540e\u4e00\u4e2a\u5143\u7d20\u5165\u5806\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(\\log n)\\) \u3002\u5728\u4f9d\u6b21\u6dfb\u52a0\u5143\u7d20\u65f6\uff0c\u5806\u7684\u5e73\u5747\u957f\u5ea6\u4e3a \\(\\frac{n}{2}\\) \uff0c\u56e0\u6b64\u8be5\u65b9\u6cd5\u7684\u603b\u4f53\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(n \\log n)\\) \u3002</p>"},{"location":"chapter_heap/build_heap/#822","title":"8.2.2. \u00a0 \u57fa\u4e8e\u5806\u5316\u64cd\u4f5c\u5b9e\u73b0","text":"<p>\u6709\u8da3\u7684\u662f\uff0c\u5b58\u5728\u4e00\u79cd\u66f4\u9ad8\u6548\u7684\u5efa\u5806\u65b9\u6cd5\uff0c\u5176\u65f6\u95f4\u590d\u6742\u5ea6\u4ec5\u4e3a \\(O(n)\\) \u3002\u6211\u4eec\u5148\u5c06\u5217\u8868\u6240\u6709\u5143\u7d20\u539f\u5c01\u4e0d\u52a8\u6dfb\u52a0\u5230\u5806\u4e2d\uff0c\u7136\u540e\u8fed\u4ee3\u5730\u5bf9\u5404\u4e2a\u8282\u70b9\u6267\u884c\u201c\u4ece\u9876\u81f3\u5e95\u5806\u5316\u201d\u3002\u5f53\u7136\uff0c\u6211\u4eec\u4e0d\u9700\u8981\u5bf9\u53f6\u8282\u70b9\u6267\u884c\u5806\u5316\u64cd\u4f5c\uff0c\u56e0\u4e3a\u5b83\u4eec\u6ca1\u6709\u5b50\u8282\u70b9\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart my_heap.java<pre><code>/* \u6784\u9020\u65b9\u6cd5\uff0c\u6839\u636e\u8f93\u5165\u5217\u8868\u5efa\u5806 */\nMaxHeap(List&lt;Integer&gt; nums) {\n// \u5c06\u5217\u8868\u5143\u7d20\u539f\u5c01\u4e0d\u52a8\u6dfb\u52a0\u8fdb\u5806\nmaxHeap = new ArrayList&lt;&gt;(nums);\n// \u5806\u5316\u9664\u53f6\u8282\u70b9\u4ee5\u5916\u7684\u5176\u4ed6\u6240\u6709\u8282\u70b9\nfor (int i = parent(size() - 1); i &gt;= 0; i--) {\nsiftDown(i);\n}\n}\n</code></pre> my_heap.cpp<pre><code>/* \u6784\u9020\u65b9\u6cd5\uff0c\u6839\u636e\u8f93\u5165\u5217\u8868\u5efa\u5806 */\nMaxHeap(vector&lt;int&gt; nums) {\n// \u5c06\u5217\u8868\u5143\u7d20\u539f\u5c01\u4e0d\u52a8\u6dfb\u52a0\u8fdb\u5806\nmaxHeap = nums;\n// \u5806\u5316\u9664\u53f6\u8282\u70b9\u4ee5\u5916\u7684\u5176\u4ed6\u6240\u6709\u8282\u70b9\nfor (int i = parent(size() - 1); i &gt;= 0; i--) {\nsiftDown(i);\n}\n}\n</code></pre> my_heap.py<pre><code>def __init__(self, nums: list[int]):\n\"\"\"\u6784\u9020\u65b9\u6cd5\uff0c\u6839\u636e\u8f93\u5165\u5217\u8868\u5efa\u5806\"\"\"\n# \u5c06\u5217\u8868\u5143\u7d20\u539f\u5c01\u4e0d\u52a8\u6dfb\u52a0\u8fdb\u5806\nself.max_heap = nums\n# \u5806\u5316\u9664\u53f6\u8282\u70b9\u4ee5\u5916\u7684\u5176\u4ed6\u6240\u6709\u8282\u70b9\nfor i in range(self.parent(self.size() - 1), -1, -1):\nself.sift_down(i)\n</code></pre> my_heap.go<pre><code>/* \u6784\u9020\u65b9\u6cd5\uff0c\u6839\u636e\u5207\u7247\u5efa\u5806 */\nfunc newMaxHeap(nums []any) *maxHeap {\n// \u5c06\u5217\u8868\u5143\u7d20\u539f\u5c01\u4e0d\u52a8\u6dfb\u52a0\u8fdb\u5806\nh := &amp;maxHeap{data: nums}\nfor i := len(h.data) - 1; i &gt;= 0; i-- {\n// \u5806\u5316\u9664\u53f6\u8282\u70b9\u4ee5\u5916\u7684\u5176\u4ed6\u6240\u6709\u8282\u70b9\nh.siftDown(i)\n}\nreturn h\n}\n</code></pre> my_heap.js<pre><code>/* \u6784\u9020\u65b9\u6cd5\uff0c\u5efa\u7acb\u7a7a\u5806\u6216\u6839\u636e\u8f93\u5165\u5217\u8868\u5efa\u5806 */\nconstructor(nums) {\n// \u5c06\u5217\u8868\u5143\u7d20\u539f\u5c01\u4e0d\u52a8\u6dfb\u52a0\u8fdb\u5806\nthis.#maxHeap = nums === undefined ? [] : [...nums];\n// \u5806\u5316\u9664\u53f6\u8282\u70b9\u4ee5\u5916\u7684\u5176\u4ed6\u6240\u6709\u8282\u70b9\nfor (let i = this.#parent(this.size() - 1); i &gt;= 0; i--) {\nthis.#siftDown(i);\n}\n}\n</code></pre> my_heap.ts<pre><code>/* \u6784\u9020\u65b9\u6cd5\uff0c\u5efa\u7acb\u7a7a\u5806\u6216\u6839\u636e\u8f93\u5165\u5217\u8868\u5efa\u5806 */\nconstructor(nums?: number[]) {\n// \u5c06\u5217\u8868\u5143\u7d20\u539f\u5c01\u4e0d\u52a8\u6dfb\u52a0\u8fdb\u5806\nthis.maxHeap = nums === undefined ? [] : [...nums];\n// \u5806\u5316\u9664\u53f6\u8282\u70b9\u4ee5\u5916\u7684\u5176\u4ed6\u6240\u6709\u8282\u70b9\nfor (let i = this.parent(this.size() - 1); i &gt;= 0; i--) {\nthis.siftDown(i);\n}\n}\n</code></pre> my_heap.c<pre><code>/* \u6784\u9020\u51fd\u6570\uff0c\u6839\u636e\u5207\u7247\u5efa\u5806 */\nmaxHeap *newMaxHeap(int nums[], int size) {\n// \u6240\u6709\u5143\u7d20\u5165\u5806\nmaxHeap *h = (maxHeap *)malloc(sizeof(maxHeap));\nh-&gt;size = size;\nmemcpy(h-&gt;data, nums, size * sizeof(int));\nfor (int i = size - 1; i &gt;= 0; i--) {\n// \u5806\u5316\u9664\u53f6\u8282\u70b9\u4ee5\u5916\u7684\u5176\u4ed6\u6240\u6709\u8282\u70b9\nsiftDown(h, i);\n}\nreturn h;\n}\n</code></pre> my_heap.cs<pre><code>/* \u6784\u9020\u51fd\u6570\uff0c\u6839\u636e\u8f93\u5165\u5217\u8868\u5efa\u5806 */\nMaxHeap(IEnumerable&lt;int&gt; nums) {\n// \u5c06\u5217\u8868\u5143\u7d20\u539f\u5c01\u4e0d\u52a8\u6dfb\u52a0\u8fdb\u5806\nmaxHeap = new List&lt;int&gt;(nums);\n// \u5806\u5316\u9664\u53f6\u8282\u70b9\u4ee5\u5916\u7684\u5176\u4ed6\u6240\u6709\u8282\u70b9\nvar size = parent(this.size() - 1);\nfor (int i = size; i &gt;= 0; i--) {\nsiftDown(i);\n}\n}\n</code></pre> my_heap.swift<pre><code>/* \u6784\u9020\u65b9\u6cd5\uff0c\u6839\u636e\u8f93\u5165\u5217\u8868\u5efa\u5806 */\ninit(nums: [Int]) {\n// \u5c06\u5217\u8868\u5143\u7d20\u539f\u5c01\u4e0d\u52a8\u6dfb\u52a0\u8fdb\u5806\nmaxHeap = nums\n// \u5806\u5316\u9664\u53f6\u8282\u70b9\u4ee5\u5916\u7684\u5176\u4ed6\u6240\u6709\u8282\u70b9\nfor i in stride(from: parent(i: size() - 1), through: 0, by: -1) {\nsiftDown(i: i)\n}\n}\n</code></pre> my_heap.zig<pre><code>// \u6784\u9020\u65b9\u6cd5\uff0c\u6839\u636e\u8f93\u5165\u5217\u8868\u5efa\u5806\nfn init(self: *Self, allocator: std.mem.Allocator, nums: []const T) !void {\nif (self.max_heap != null) return;\nself.max_heap = std.ArrayList(T).init(allocator);\n// \u5c06\u5217\u8868\u5143\u7d20\u539f\u5c01\u4e0d\u52a8\u6dfb\u52a0\u8fdb\u5806\ntry self.max_heap.?.appendSlice(nums);\n// \u5806\u5316\u9664\u53f6\u8282\u70b9\u4ee5\u5916\u7684\u5176\u4ed6\u6240\u6709\u8282\u70b9\nvar i: usize = parent(self.size() - 1) + 1;\nwhile (i &gt; 0) : (i -= 1) {\ntry self.siftDown(i - 1);\n}\n}\n</code></pre> my_heap.dart<pre><code>/* \u6784\u9020\u65b9\u6cd5\uff0c\u6839\u636e\u8f93\u5165\u5217\u8868\u5efa\u5806 */\nMaxHeap(List&lt;int&gt; nums) {\n// \u5c06\u5217\u8868\u5143\u7d20\u539f\u5c01\u4e0d\u52a8\u6dfb\u52a0\u8fdb\u5806\n_maxHeap = nums;\n// \u5806\u5316\u9664\u53f6\u8282\u70b9\u4ee5\u5916\u7684\u5176\u4ed6\u6240\u6709\u8282\u70b9\nfor (int i = _parent(size() - 1); i &gt;= 0; i--) {\n_siftDown(i);\n}\n}\n</code></pre>"},{"location":"chapter_heap/build_heap/#823","title":"8.2.3. \u00a0 \u590d\u6742\u5ea6\u5206\u6790","text":"<p>\u4e3a\u4ec0\u4e48\u7b2c\u4e8c\u79cd\u5efa\u5806\u65b9\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u662f \\(O(n)\\) \uff1f\u6211\u4eec\u6765\u5c55\u5f00\u63a8\u7b97\u4e00\u4e0b\u3002</p> <ul> <li>\u5b8c\u5168\u4e8c\u53c9\u6811\u4e2d\uff0c\u8bbe\u8282\u70b9\u603b\u6570\u4e3a \\(n\\) \uff0c\u5219\u53f6\u8282\u70b9\u6570\u91cf\u4e3a \\((n + 1) / 2\\) \uff0c\u5176\u4e2d \\(/\\) \u4e3a\u5411\u4e0b\u6574\u9664\u3002\u56e0\u6b64\uff0c\u5728\u6392\u9664\u53f6\u8282\u70b9\u540e\uff0c\u9700\u8981\u5806\u5316\u7684\u8282\u70b9\u6570\u91cf\u4e3a \\((n - 1)/2\\) \uff0c\u590d\u6742\u5ea6\u4e3a \\(O(n)\\) \uff1b</li> <li>\u5728\u4ece\u9876\u81f3\u5e95\u5806\u5316\u7684\u8fc7\u7a0b\u4e2d\uff0c\u6bcf\u4e2a\u8282\u70b9\u6700\u591a\u5806\u5316\u5230\u53f6\u8282\u70b9\uff0c\u56e0\u6b64\u6700\u5927\u8fed\u4ee3\u6b21\u6570\u4e3a\u4e8c\u53c9\u6811\u9ad8\u5ea6 \\(O(\\log n)\\) \uff1b</li> </ul> <p>\u5c06\u4e0a\u8ff0\u4e24\u8005\u76f8\u4e58\uff0c\u53ef\u5f97\u5230\u5efa\u5806\u8fc7\u7a0b\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(n \\log n)\\) \u3002\u7136\u800c\uff0c\u8fd9\u4e2a\u4f30\u7b97\u7ed3\u679c\u5e76\u4e0d\u51c6\u786e\uff0c\u56e0\u4e3a\u6211\u4eec\u6ca1\u6709\u8003\u8651\u5230\u4e8c\u53c9\u6811\u5e95\u5c42\u8282\u70b9\u6570\u91cf\u8fdc\u591a\u4e8e\u9876\u5c42\u8282\u70b9\u7684\u7279\u6027\u3002</p> <p>\u63a5\u4e0b\u6765\u6211\u4eec\u6765\u8fdb\u884c\u66f4\u4e3a\u8be6\u7ec6\u7684\u8ba1\u7b97\u3002\u4e3a\u4e86\u51cf\u5c0f\u8ba1\u7b97\u96be\u5ea6\uff0c\u6211\u4eec\u5047\u8bbe\u6811\u662f\u4e00\u4e2a\u201c\u5b8c\u7f8e\u4e8c\u53c9\u6811\u201d\uff0c\u8be5\u5047\u8bbe\u4e0d\u4f1a\u5f71\u54cd\u8ba1\u7b97\u7ed3\u679c\u7684\u6b63\u786e\u6027\u3002\u8bbe\u4e8c\u53c9\u6811\uff08\u5373\u5806\uff09\u8282\u70b9\u6570\u91cf\u4e3a \\(n\\) \uff0c\u6811\u9ad8\u5ea6\u4e3a \\(h\\) \u3002\u4e0a\u6587\u63d0\u5230\uff0c\u8282\u70b9\u5806\u5316\u6700\u5927\u8fed\u4ee3\u6b21\u6570\u7b49\u4e8e\u8be5\u8282\u70b9\u5230\u53f6\u8282\u70b9\u7684\u8ddd\u79bb\uff0c\u800c\u8be5\u8ddd\u79bb\u6b63\u662f\u201c\u8282\u70b9\u9ad8\u5ea6\u201d\u3002</p> <p></p> <p> Fig. \u5b8c\u7f8e\u4e8c\u53c9\u6811\u7684\u5404\u5c42\u8282\u70b9\u6570\u91cf </p> <p>\u56e0\u6b64\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u5404\u5c42\u7684\u201c\u8282\u70b9\u6570\u91cf \\(\\times\\) \u8282\u70b9\u9ad8\u5ea6\u201d\u6c42\u548c\uff0c\u4ece\u800c\u5f97\u5230\u6240\u6709\u8282\u70b9\u7684\u5806\u5316\u8fed\u4ee3\u6b21\u6570\u7684\u603b\u548c\u3002</p> \\[ T(h) = 2^0h + 2^1(h-1) + 2^2(h-2) + \\cdots + 2^{(h-1)}\\times1 \\] <p>\u5316\u7b80\u4e0a\u5f0f\u9700\u8981\u501f\u52a9\u4e2d\u5b66\u7684\u6570\u5217\u77e5\u8bc6\uff0c\u5148\u5bf9 \\(T(h)\\) \u4e58\u4ee5 \\(2\\) \uff0c\u5f97\u5230</p> \\[ \\begin{aligned} T(h) &amp; = 2^0h + 2^1(h-1) + 2^2(h-2) + \\cdots + 2^{h-1}\\times1 \\newline 2 T(h) &amp; = 2^1h + 2^2(h-1) + 2^3(h-2) + \\cdots + 2^{h}\\times1 \\newline \\end{aligned} \\] <p>\u4f7f\u7528\u9519\u4f4d\u76f8\u51cf\u6cd5\uff0c\u4ee4\u4e0b\u5f0f \\(2 T(h)\\) \u51cf\u53bb\u4e0a\u5f0f \\(T(h)\\) \uff0c\u53ef\u5f97</p> \\[ 2T(h) - T(h) = T(h) = -2^0h + 2^1 + 2^2 + \\cdots + 2^{h-1} + 2^h \\] <p>\u89c2\u5bdf\u4e0a\u5f0f\uff0c\u53d1\u73b0 \\(T(h)\\) \u662f\u4e00\u4e2a\u7b49\u6bd4\u6570\u5217\uff0c\u53ef\u76f4\u63a5\u4f7f\u7528\u6c42\u548c\u516c\u5f0f\uff0c\u5f97\u5230\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a</p> \\[ \\begin{aligned} T(h) &amp; = 2 \\frac{1 - 2^h}{1 - 2} - h \\newline &amp; = 2^{h+1} - h \\newline &amp; = O(2^h) \\end{aligned} \\] <p>\u8fdb\u4e00\u6b65\u5730\uff0c\u9ad8\u5ea6\u4e3a \\(h\\) \u7684\u5b8c\u7f8e\u4e8c\u53c9\u6811\u7684\u8282\u70b9\u6570\u91cf\u4e3a \\(n = 2^{h+1} - 1\\) \uff0c\u6613\u5f97\u590d\u6742\u5ea6\u4e3a \\(O(2^h) = O(n)\\) \u3002\u4ee5\u4e0a\u63a8\u7b97\u8868\u660e\uff0c\u8f93\u5165\u5217\u8868\u5e76\u5efa\u5806\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(n)\\) \uff0c\u975e\u5e38\u9ad8\u6548\u3002</p>"},{"location":"chapter_heap/heap/","title":"8.1. \u00a0 \u5806","text":"<p>\u300c\u5806 Heap\u300d\u662f\u4e00\u79cd\u6ee1\u8db3\u7279\u5b9a\u6761\u4ef6\u7684\u5b8c\u5168\u4e8c\u53c9\u6811\uff0c\u53ef\u5206\u4e3a\u4e24\u79cd\u7c7b\u578b\uff1a</p> <ul> <li>\u300c\u5927\u9876\u5806 Max Heap\u300d\uff0c\u4efb\u610f\u8282\u70b9\u7684\u503c \\(\\geq\\) \u5176\u5b50\u8282\u70b9\u7684\u503c\uff1b</li> <li>\u300c\u5c0f\u9876\u5806 Min Heap\u300d\uff0c\u4efb\u610f\u8282\u70b9\u7684\u503c \\(\\leq\\) \u5176\u5b50\u8282\u70b9\u7684\u503c\uff1b</li> </ul> <p></p> <p> Fig. \u5c0f\u9876\u5806\u4e0e\u5927\u9876\u5806 </p> <p>\u5806\u4f5c\u4e3a\u5b8c\u5168\u4e8c\u53c9\u6811\u7684\u4e00\u4e2a\u7279\u4f8b\uff0c\u5177\u6709\u4ee5\u4e0b\u7279\u6027\uff1a</p> <ul> <li>\u6700\u5e95\u5c42\u8282\u70b9\u9760\u5de6\u586b\u5145\uff0c\u5176\u4ed6\u5c42\u7684\u8282\u70b9\u90fd\u88ab\u586b\u6ee1\u3002</li> <li>\u6211\u4eec\u5c06\u4e8c\u53c9\u6811\u7684\u6839\u8282\u70b9\u79f0\u4e3a\u300c\u5806\u9876\u300d\uff0c\u5c06\u5e95\u5c42\u6700\u9760\u53f3\u7684\u8282\u70b9\u79f0\u4e3a\u300c\u5806\u5e95\u300d\u3002</li> <li>\u5bf9\u4e8e\u5927\u9876\u5806\uff08\u5c0f\u9876\u5806\uff09\uff0c\u5806\u9876\u5143\u7d20\uff08\u5373\u6839\u8282\u70b9\uff09\u7684\u503c\u5206\u522b\u662f\u6700\u5927\uff08\u6700\u5c0f\uff09\u7684\u3002</li> </ul>"},{"location":"chapter_heap/heap/#811","title":"8.1.1. \u00a0 \u5806\u5e38\u7528\u64cd\u4f5c","text":"<p>\u9700\u8981\u6307\u51fa\u7684\u662f\uff0c\u8bb8\u591a\u7f16\u7a0b\u8bed\u8a00\u63d0\u4f9b\u7684\u662f\u300c\u4f18\u5148\u961f\u5217 Priority Queue\u300d\uff0c\u8fd9\u662f\u4e00\u79cd\u62bd\u8c61\u6570\u636e\u7ed3\u6784\uff0c\u5b9a\u4e49\u4e3a\u5177\u6709\u4f18\u5148\u7ea7\u6392\u5e8f\u7684\u961f\u5217\u3002</p> <p>\u5b9e\u9645\u4e0a\uff0c\u5806\u901a\u5e38\u7528\u4f5c\u5b9e\u73b0\u4f18\u5148\u961f\u5217\uff0c\u5927\u9876\u5806\u76f8\u5f53\u4e8e\u5143\u7d20\u6309\u4ece\u5927\u5230\u5c0f\u987a\u5e8f\u51fa\u961f\u7684\u4f18\u5148\u961f\u5217\u3002\u4ece\u4f7f\u7528\u89d2\u5ea6\u6765\u770b\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u300c\u4f18\u5148\u961f\u5217\u300d\u548c\u300c\u5806\u300d\u770b\u4f5c\u7b49\u4ef7\u7684\u6570\u636e\u7ed3\u6784\u3002\u56e0\u6b64\uff0c\u672c\u4e66\u5bf9\u4e24\u8005\u4e0d\u505a\u7279\u522b\u533a\u5206\uff0c\u7edf\u4e00\u4f7f\u7528\u300c\u5806\u300d\u6765\u547d\u540d\u3002</p> <p>\u5806\u7684\u5e38\u7528\u64cd\u4f5c\u89c1\u4e0b\u8868\uff0c\u65b9\u6cd5\u540d\u9700\u8981\u6839\u636e\u7f16\u7a0b\u8bed\u8a00\u6765\u786e\u5b9a\u3002</p> \u65b9\u6cd5\u540d \u63cf\u8ff0 \u65f6\u95f4\u590d\u6742\u5ea6 push() \u5143\u7d20\u5165\u5806 \\(O(\\log n)\\) pop() \u5806\u9876\u5143\u7d20\u51fa\u5806 \\(O(\\log n)\\) peek() \u8bbf\u95ee\u5806\u9876\u5143\u7d20\uff08\u5927 / \u5c0f\u9876\u5806\u5206\u522b\u4e3a\u6700\u5927 / \u5c0f\u503c\uff09 \\(O(1)\\) size() \u83b7\u53d6\u5806\u7684\u5143\u7d20\u6570\u91cf \\(O(1)\\) isEmpty() \u5224\u65ad\u5806\u662f\u5426\u4e3a\u7a7a \\(O(1)\\) <p>\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u6211\u4eec\u53ef\u4ee5\u76f4\u63a5\u4f7f\u7528\u7f16\u7a0b\u8bed\u8a00\u63d0\u4f9b\u7684\u5806\u7c7b\uff08\u6216\u4f18\u5148\u961f\u5217\u7c7b\uff09\u3002</p> <p>Tip</p> <p>\u7c7b\u4f3c\u4e8e\u6392\u5e8f\u7b97\u6cd5\u4e2d\u7684\u201c\u4ece\u5c0f\u5230\u5927\u6392\u5217\u201d\u548c\u201c\u4ece\u5927\u5230\u5c0f\u6392\u5217\u201d\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u4fee\u6539 Comparator \u6765\u5b9e\u73b0\u201c\u5c0f\u9876\u5806\u201d\u4e0e\u201c\u5927\u9876\u5806\u201d\u4e4b\u95f4\u7684\u8f6c\u6362\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart heap.java<pre><code>/* \u521d\u59cb\u5316\u5806 */\n// \u521d\u59cb\u5316\u5c0f\u9876\u5806\nQueue&lt;Integer&gt; minHeap = new PriorityQueue&lt;&gt;();\n// \u521d\u59cb\u5316\u5927\u9876\u5806\uff08\u4f7f\u7528 lambda \u8868\u8fbe\u5f0f\u4fee\u6539 Comparator \u5373\u53ef\uff09\nQueue&lt;Integer&gt; maxHeap = new PriorityQueue&lt;&gt;((a, b) -&gt; b - a);\n/* \u5143\u7d20\u5165\u5806 */\nmaxHeap.offer(1);\nmaxHeap.offer(3);\nmaxHeap.offer(2);\nmaxHeap.offer(5);\nmaxHeap.offer(4);\n/* \u83b7\u53d6\u5806\u9876\u5143\u7d20 */\nint peek = maxHeap.peek(); // 5\n/* \u5806\u9876\u5143\u7d20\u51fa\u5806 */\n// \u51fa\u5806\u5143\u7d20\u4f1a\u5f62\u6210\u4e00\u4e2a\u4ece\u5927\u5230\u5c0f\u7684\u5e8f\u5217\npeek = heap.poll();  // 5\npeek = heap.poll();  // 4\npeek = heap.poll();  // 3\npeek = heap.poll();  // 2\npeek = heap.poll();  // 1\n/* \u83b7\u53d6\u5806\u5927\u5c0f */\nint size = maxHeap.size();\n/* \u5224\u65ad\u5806\u662f\u5426\u4e3a\u7a7a */\nboolean isEmpty = maxHeap.isEmpty();\n/* \u8f93\u5165\u5217\u8868\u5e76\u5efa\u5806 */\nminHeap = new PriorityQueue&lt;&gt;(Arrays.asList(1, 3, 2, 5, 4));\n</code></pre> heap.cpp<pre><code>/* \u521d\u59cb\u5316\u5806 */\n// \u521d\u59cb\u5316\u5c0f\u9876\u5806\npriority_queue&lt;int, vector&lt;int&gt;, greater&lt;int&gt;&gt; minHeap;\n// \u521d\u59cb\u5316\u5927\u9876\u5806\npriority_queue&lt;int, vector&lt;int&gt;, less&lt;int&gt;&gt; maxHeap;\n/* \u5143\u7d20\u5165\u5806 */\nmaxHeap.push(1);\nmaxHeap.push(3);\nmaxHeap.push(2);\nmaxHeap.push(5);\nmaxHeap.push(4);\n/* \u83b7\u53d6\u5806\u9876\u5143\u7d20 */\nint peek = maxHeap.top(); // 5\n/* \u5806\u9876\u5143\u7d20\u51fa\u5806 */\n// \u51fa\u5806\u5143\u7d20\u4f1a\u5f62\u6210\u4e00\u4e2a\u4ece\u5927\u5230\u5c0f\u7684\u5e8f\u5217\nmaxHeap.pop(); // 5\nmaxHeap.pop(); // 4\nmaxHeap.pop(); // 3\nmaxHeap.pop(); // 2\nmaxHeap.pop(); // 1\n/* \u83b7\u53d6\u5806\u5927\u5c0f */\nint size = maxHeap.size();\n/* \u5224\u65ad\u5806\u662f\u5426\u4e3a\u7a7a */\nbool isEmpty = maxHeap.empty();\n/* \u8f93\u5165\u5217\u8868\u5e76\u5efa\u5806 */\nvector&lt;int&gt; input{1, 3, 2, 5, 4};\npriority_queue&lt;int, vector&lt;int&gt;, greater&lt;int&gt;&gt; minHeap(input.begin(), input.end());\n</code></pre> heap.py<pre><code># \u521d\u59cb\u5316\u5c0f\u9876\u5806\nmin_heap, flag = [], 1\n# \u521d\u59cb\u5316\u5927\u9876\u5806\nmax_heap, flag = [], -1\n# Python \u7684 heapq \u6a21\u5757\u9ed8\u8ba4\u5b9e\u73b0\u5c0f\u9876\u5806\n# \u8003\u8651\u5c06\u201c\u5143\u7d20\u53d6\u8d1f\u201d\u540e\u518d\u5165\u5806\uff0c\u8fd9\u6837\u5c31\u53ef\u4ee5\u5c06\u5927\u5c0f\u5173\u7cfb\u98a0\u5012\uff0c\u4ece\u800c\u5b9e\u73b0\u5927\u9876\u5806\n# \u5728\u672c\u793a\u4f8b\u4e2d\uff0cflag = 1 \u65f6\u5bf9\u5e94\u5c0f\u9876\u5806\uff0cflag = -1 \u65f6\u5bf9\u5e94\u5927\u9876\u5806\n# \u5143\u7d20\u5165\u5806\nheapq.heappush(max_heap, flag * 1)\nheapq.heappush(max_heap, flag * 3)\nheapq.heappush(max_heap, flag * 2)\nheapq.heappush(max_heap, flag * 5)\nheapq.heappush(max_heap, flag * 4)\n# \u83b7\u53d6\u5806\u9876\u5143\u7d20\npeek: int = flag * max_heap[0] # 5\n# \u5806\u9876\u5143\u7d20\u51fa\u5806\n# \u51fa\u5806\u5143\u7d20\u4f1a\u5f62\u6210\u4e00\u4e2a\u4ece\u5927\u5230\u5c0f\u7684\u5e8f\u5217\nval = flag * heapq.heappop(max_heap) # 5\nval = flag * heapq.heappop(max_heap) # 4\nval = flag * heapq.heappop(max_heap) # 3\nval = flag * heapq.heappop(max_heap) # 2\nval = flag * heapq.heappop(max_heap) # 1\n# \u83b7\u53d6\u5806\u5927\u5c0f\nsize: int = len(max_heap)\n# \u5224\u65ad\u5806\u662f\u5426\u4e3a\u7a7a\nis_empty: bool = not max_heap\n# \u8f93\u5165\u5217\u8868\u5e76\u5efa\u5806\nmin_heap: List[int] = [1, 3, 2, 5, 4]\nheapq.heapify(min_heap)\n</code></pre> heap.go<pre><code>// Go \u8bed\u8a00\u4e2d\u53ef\u4ee5\u901a\u8fc7\u5b9e\u73b0 heap.Interface \u6765\u6784\u5efa\u6574\u6570\u5927\u9876\u5806\n// \u5b9e\u73b0 heap.Interface \u9700\u8981\u540c\u65f6\u5b9e\u73b0 sort.Interface\ntype intHeap []any\n// Push heap.Interface \u7684\u65b9\u6cd5\uff0c\u5b9e\u73b0\u63a8\u5165\u5143\u7d20\u5230\u5806\nfunc (h *intHeap) Push(x any) {\n// Push \u548c Pop \u4f7f\u7528 pointer receiver \u4f5c\u4e3a\u53c2\u6570\n// \u56e0\u4e3a\u5b83\u4eec\u4e0d\u4ec5\u4f1a\u5bf9\u5207\u7247\u7684\u5185\u5bb9\u8fdb\u884c\u8c03\u6574\uff0c\u8fd8\u4f1a\u4fee\u6539\u5207\u7247\u7684\u957f\u5ea6\u3002\n*h = append(*h, x.(int))\n}\n// Pop heap.Interface \u7684\u65b9\u6cd5\uff0c\u5b9e\u73b0\u5f39\u51fa\u5806\u9876\u5143\u7d20\nfunc (h *intHeap) Pop() any {\n// \u5f85\u51fa\u5806\u5143\u7d20\u5b58\u653e\u5728\u6700\u540e\nlast := (*h)[len(*h)-1]\n*h = (*h)[:len(*h)-1]\nreturn last\n}\n// Len sort.Interface \u7684\u65b9\u6cd5\nfunc (h *intHeap) Len() int {\nreturn len(*h)\n}\n// Less sort.Interface \u7684\u65b9\u6cd5\nfunc (h *intHeap) Less(i, j int) bool {\n// \u5982\u679c\u5b9e\u73b0\u5c0f\u9876\u5806\uff0c\u5219\u9700\u8981\u8c03\u6574\u4e3a\u5c0f\u4e8e\u53f7\nreturn (*h)[i].(int) &gt; (*h)[j].(int)\n}\n// Swap sort.Interface \u7684\u65b9\u6cd5\nfunc (h *intHeap) Swap(i, j int) {\n(*h)[i], (*h)[j] = (*h)[j], (*h)[i]\n}\n// Top \u83b7\u53d6\u5806\u9876\u5143\u7d20\nfunc (h *intHeap) Top() any {\nreturn (*h)[0]\n}\n/* Driver Code */\nfunc TestHeap(t *testing.T) {\n/* \u521d\u59cb\u5316\u5806 */\n// \u521d\u59cb\u5316\u5927\u9876\u5806\nmaxHeap := &amp;intHeap{}\nheap.Init(maxHeap)\n/* \u5143\u7d20\u5165\u5806 */\n// \u8c03\u7528 heap.Interface \u7684\u65b9\u6cd5\uff0c\u6765\u6dfb\u52a0\u5143\u7d20\nheap.Push(maxHeap, 1)\nheap.Push(maxHeap, 3)\nheap.Push(maxHeap, 2)\nheap.Push(maxHeap, 4)\nheap.Push(maxHeap, 5)\n/* \u83b7\u53d6\u5806\u9876\u5143\u7d20 */\ntop := maxHeap.Top()\nfmt.Printf(\"\u5806\u9876\u5143\u7d20\u4e3a %d\\n\", top)\n/* \u5806\u9876\u5143\u7d20\u51fa\u5806 */\n// \u8c03\u7528 heap.Interface \u7684\u65b9\u6cd5\uff0c\u6765\u79fb\u9664\u5143\u7d20\nheap.Pop(maxHeap) // 5\nheap.Pop(maxHeap) // 4\nheap.Pop(maxHeap) // 3\nheap.Pop(maxHeap) // 2\nheap.Pop(maxHeap) // 1\n/* \u83b7\u53d6\u5806\u5927\u5c0f */\nsize := len(*maxHeap)\nfmt.Printf(\"\u5806\u5143\u7d20\u6570\u91cf\u4e3a %d\\n\", size)\n/* \u5224\u65ad\u5806\u662f\u5426\u4e3a\u7a7a */\nisEmpty := len(*maxHeap) == 0\nfmt.Printf(\"\u5806\u662f\u5426\u4e3a\u7a7a %t\\n\", isEmpty)\n}\n</code></pre> heap.js<pre><code>// JavaScript \u672a\u63d0\u4f9b\u5185\u7f6e Heap \u7c7b\n</code></pre> heap.ts<pre><code>// TypeScript \u672a\u63d0\u4f9b\u5185\u7f6e Heap \u7c7b\n</code></pre> heap.c<pre><code>// C \u672a\u63d0\u4f9b\u5185\u7f6e Heap \u7c7b\n</code></pre> heap.cs<pre><code>/* \u521d\u59cb\u5316\u5806 */\n// \u521d\u59cb\u5316\u5c0f\u9876\u5806\nPriorityQueue&lt;int, int&gt; minHeap = new PriorityQueue&lt;int, int&gt;();\n// \u521d\u59cb\u5316\u5927\u9876\u5806\uff08\u4f7f\u7528 lambda \u8868\u8fbe\u5f0f\u4fee\u6539 Comparator \u5373\u53ef\uff09\nPriorityQueue&lt;int, int&gt; maxHeap = new PriorityQueue&lt;int, int&gt;(Comparer&lt;int&gt;.Create((x, y) =&gt; y - x));\n/* \u5143\u7d20\u5165\u5806 */\nmaxHeap.Enqueue(1, 1);\nmaxHeap.Enqueue(3, 3);\nmaxHeap.Enqueue(2, 2);\nmaxHeap.Enqueue(5, 5);\nmaxHeap.Enqueue(4, 4);\n/* \u83b7\u53d6\u5806\u9876\u5143\u7d20 */\nint peek = maxHeap.Peek();//5\n/* \u5806\u9876\u5143\u7d20\u51fa\u5806 */\n// \u51fa\u5806\u5143\u7d20\u4f1a\u5f62\u6210\u4e00\u4e2a\u4ece\u5927\u5230\u5c0f\u7684\u5e8f\u5217\npeek = maxHeap.Dequeue();  // 5\npeek = maxHeap.Dequeue();  // 4\npeek = maxHeap.Dequeue();  // 3\npeek = maxHeap.Dequeue();  // 2\npeek = maxHeap.Dequeue();  // 1\n/* \u83b7\u53d6\u5806\u5927\u5c0f */\nint size = maxHeap.Count;\n/* \u5224\u65ad\u5806\u662f\u5426\u4e3a\u7a7a */\nbool isEmpty = maxHeap.Count == 0;\n/* \u8f93\u5165\u5217\u8868\u5e76\u5efa\u5806 */\nminHeap = new PriorityQueue&lt;int, int&gt;(new List&lt;(int, int)&gt; { (1, 1), (3, 3), (2, 2), (5, 5), (4, 4), });\n</code></pre> heap.swift<pre><code>// Swift \u672a\u63d0\u4f9b\u5185\u7f6e Heap \u7c7b\n</code></pre> heap.zig<pre><code>\n</code></pre> heap.dart<pre><code>// Dart \u672a\u63d0\u4f9b\u5185\u7f6e Heap \u7c7b\n</code></pre>"},{"location":"chapter_heap/heap/#812","title":"8.1.2. \u00a0 \u5806\u7684\u5b9e\u73b0","text":"<p>\u4e0b\u6587\u5b9e\u73b0\u7684\u662f\u5927\u9876\u5806\u3002\u82e5\u8981\u5c06\u5176\u8f6c\u6362\u4e3a\u5c0f\u9876\u5806\uff0c\u53ea\u9700\u5c06\u6240\u6709\u5927\u5c0f\u903b\u8f91\u5224\u65ad\u53d6\u9006\uff08\u4f8b\u5982\uff0c\u5c06 \\(\\geq\\) \u66ff\u6362\u4e3a \\(\\leq\\) \uff09\u3002\u611f\u5174\u8da3\u7684\u8bfb\u8005\u53ef\u4ee5\u81ea\u884c\u5b9e\u73b0\u3002</p>"},{"location":"chapter_heap/heap/#_1","title":"\u5806\u7684\u5b58\u50a8\u4e0e\u8868\u793a","text":"<p>\u6211\u4eec\u5728\u4e8c\u53c9\u6811\u7ae0\u8282\u4e2d\u5b66\u4e60\u5230\uff0c\u5b8c\u5168\u4e8c\u53c9\u6811\u975e\u5e38\u9002\u5408\u7528\u6570\u7ec4\u6765\u8868\u793a\u3002\u7531\u4e8e\u5806\u6b63\u662f\u4e00\u79cd\u5b8c\u5168\u4e8c\u53c9\u6811\uff0c\u6211\u4eec\u5c06\u91c7\u7528\u6570\u7ec4\u6765\u5b58\u50a8\u5806\u3002</p> <p>\u5f53\u4f7f\u7528\u6570\u7ec4\u8868\u793a\u4e8c\u53c9\u6811\u65f6\uff0c\u5143\u7d20\u4ee3\u8868\u8282\u70b9\u503c\uff0c\u7d22\u5f15\u4ee3\u8868\u8282\u70b9\u5728\u4e8c\u53c9\u6811\u4e2d\u7684\u4f4d\u7f6e\u3002\u8282\u70b9\u6307\u9488\u901a\u8fc7\u7d22\u5f15\u6620\u5c04\u516c\u5f0f\u6765\u5b9e\u73b0\u3002</p> <p>\u5177\u4f53\u800c\u8a00\uff0c\u7ed9\u5b9a\u7d22\u5f15 \\(i\\) \uff0c\u5176\u5de6\u5b50\u8282\u70b9\u7d22\u5f15\u4e3a \\(2i + 1\\) \uff0c\u53f3\u5b50\u8282\u70b9\u7d22\u5f15\u4e3a \\(2i + 2\\) \uff0c\u7236\u8282\u70b9\u7d22\u5f15\u4e3a \\((i - 1) / 2\\)\uff08\u5411\u4e0b\u53d6\u6574\uff09\u3002\u5f53\u7d22\u5f15\u8d8a\u754c\u65f6\uff0c\u8868\u793a\u7a7a\u8282\u70b9\u6216\u8282\u70b9\u4e0d\u5b58\u5728\u3002</p> <p></p> <p> Fig. \u5806\u7684\u8868\u793a\u4e0e\u5b58\u50a8 </p> <p>\u6211\u4eec\u53ef\u4ee5\u5c06\u7d22\u5f15\u6620\u5c04\u516c\u5f0f\u5c01\u88c5\u6210\u51fd\u6570\uff0c\u65b9\u4fbf\u540e\u7eed\u4f7f\u7528\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart my_heap.java<pre><code>/* \u83b7\u53d6\u5de6\u5b50\u8282\u70b9\u7d22\u5f15 */\nint left(int i) {\nreturn 2 * i + 1;\n}\n/* \u83b7\u53d6\u53f3\u5b50\u8282\u70b9\u7d22\u5f15 */\nint right(int i) {\nreturn 2 * i + 2;\n}\n/* \u83b7\u53d6\u7236\u8282\u70b9\u7d22\u5f15 */\nint parent(int i) {\nreturn (i - 1) / 2; // \u5411\u4e0b\u6574\u9664\n}\n</code></pre> my_heap.cpp<pre><code>/* \u83b7\u53d6\u5de6\u5b50\u8282\u70b9\u7d22\u5f15 */\nint left(int i) {\nreturn 2 * i + 1;\n}\n/* \u83b7\u53d6\u53f3\u5b50\u8282\u70b9\u7d22\u5f15 */\nint right(int i) {\nreturn 2 * i + 2;\n}\n/* \u83b7\u53d6\u7236\u8282\u70b9\u7d22\u5f15 */\nint parent(int i) {\nreturn (i - 1) / 2; // \u5411\u4e0b\u53d6\u6574\n}\n</code></pre> my_heap.py<pre><code>def left(self, i: int) -&gt; int:\n\"\"\"\u83b7\u53d6\u5de6\u5b50\u8282\u70b9\u7d22\u5f15\"\"\"\nreturn 2 * i + 1\ndef right(self, i: int) -&gt; int:\n\"\"\"\u83b7\u53d6\u53f3\u5b50\u8282\u70b9\u7d22\u5f15\"\"\"\nreturn 2 * i + 2\ndef parent(self, i: int) -&gt; int:\n\"\"\"\u83b7\u53d6\u7236\u8282\u70b9\u7d22\u5f15\"\"\"\nreturn (i - 1) // 2  # \u5411\u4e0b\u6574\u9664\n</code></pre> my_heap.go<pre><code>/* \u83b7\u53d6\u5de6\u5b50\u8282\u70b9\u7d22\u5f15 */\nfunc (h *maxHeap) left(i int) int {\nreturn 2*i + 1\n}\n/* \u83b7\u53d6\u53f3\u5b50\u8282\u70b9\u7d22\u5f15 */\nfunc (h *maxHeap) right(i int) int {\nreturn 2*i + 2\n}\n/* \u83b7\u53d6\u7236\u8282\u70b9\u7d22\u5f15 */\nfunc (h *maxHeap) parent(i int) int {\n// \u5411\u4e0b\u6574\u9664\nreturn (i - 1) / 2\n}\n</code></pre> my_heap.js<pre><code>/* \u83b7\u53d6\u5de6\u5b50\u8282\u70b9\u7d22\u5f15 */\n#left(i) {\nreturn 2 * i + 1;\n}\n/* \u83b7\u53d6\u53f3\u5b50\u8282\u70b9\u7d22\u5f15 */\n#right(i) {\nreturn 2 * i + 2;\n}\n/* \u83b7\u53d6\u7236\u8282\u70b9\u7d22\u5f15 */\n#parent(i) {\nreturn Math.floor((i - 1) / 2); // \u5411\u4e0b\u6574\u9664\n}\n</code></pre> my_heap.ts<pre><code>/* \u83b7\u53d6\u5de6\u5b50\u8282\u70b9\u7d22\u5f15 */\nleft(i: number): number {\nreturn 2 * i + 1;\n}\n/* \u83b7\u53d6\u53f3\u5b50\u8282\u70b9\u7d22\u5f15 */\nright(i: number): number {\nreturn 2 * i + 2;\n}\n/* \u83b7\u53d6\u7236\u8282\u70b9\u7d22\u5f15 */\nparent(i: number): number {\nreturn Math.floor((i - 1) / 2); // \u5411\u4e0b\u6574\u9664\n}\n</code></pre> my_heap.c<pre><code>/* \u83b7\u53d6\u5de6\u5b50\u8282\u70b9\u7d22\u5f15 */\nint left(maxHeap *h, int i) {\nreturn 2 * i + 1;\n}\n/* \u83b7\u53d6\u53f3\u5b50\u8282\u70b9\u7d22\u5f15 */\nint right(maxHeap *h, int i) {\nreturn 2 * i + 2;\n}\n/* \u83b7\u53d6\u7236\u8282\u70b9\u7d22\u5f15 */\nint parent(maxHeap *h, int i) {\nreturn (i - 1) / 2;\n}\n</code></pre> my_heap.cs<pre><code>/* \u83b7\u53d6\u5de6\u5b50\u8282\u70b9\u7d22\u5f15 */\nint left(int i) {\nreturn 2 * i + 1;\n}\n/* \u83b7\u53d6\u53f3\u5b50\u8282\u70b9\u7d22\u5f15 */\nint right(int i) {\nreturn 2 * i + 2;\n}\n/* \u83b7\u53d6\u7236\u8282\u70b9\u7d22\u5f15 */\nint parent(int i) {\nreturn (i - 1) / 2; // \u5411\u4e0b\u6574\u9664\n}\n</code></pre> my_heap.swift<pre><code>/* \u83b7\u53d6\u5de6\u5b50\u8282\u70b9\u7d22\u5f15 */\nfunc left(i: Int) -&gt; Int {\n2 * i + 1\n}\n/* \u83b7\u53d6\u53f3\u5b50\u8282\u70b9\u7d22\u5f15 */\nfunc right(i: Int) -&gt; Int {\n2 * i + 2\n}\n/* \u83b7\u53d6\u7236\u8282\u70b9\u7d22\u5f15 */\nfunc parent(i: Int) -&gt; Int {\n(i - 1) / 2 // \u5411\u4e0b\u6574\u9664\n}\n</code></pre> my_heap.zig<pre><code>// \u83b7\u53d6\u5de6\u5b50\u8282\u70b9\u7d22\u5f15\nfn left(i: usize) usize {\nreturn 2 * i + 1;\n}\n// \u83b7\u53d6\u53f3\u5b50\u8282\u70b9\u7d22\u5f15\nfn right(i: usize) usize {\nreturn 2 * i + 2;\n}\n// \u83b7\u53d6\u7236\u8282\u70b9\u7d22\u5f15\nfn parent(i: usize) usize {\n// return (i - 1) / 2; // \u5411\u4e0b\u6574\u9664\nreturn @divFloor(i - 1, 2);\n}\n</code></pre> my_heap.dart<pre><code>/* \u83b7\u53d6\u5de6\u5b50\u8282\u70b9\u7d22\u5f15 */\nint _left(int i) {\nreturn 2 * i + 1;\n}\n/* \u83b7\u53d6\u53f3\u5b50\u8282\u70b9\u7d22\u5f15 */\nint _right(int i) {\nreturn 2 * i + 2;\n}\n/* \u83b7\u53d6\u7236\u8282\u70b9\u7d22\u5f15 */\nint _parent(int i) {\nreturn (i - 1) ~/ 2; // \u5411\u4e0b\u6574\u9664\n}\n</code></pre>"},{"location":"chapter_heap/heap/#_2","title":"\u8bbf\u95ee\u5806\u9876\u5143\u7d20","text":"<p>\u5806\u9876\u5143\u7d20\u5373\u4e3a\u4e8c\u53c9\u6811\u7684\u6839\u8282\u70b9\uff0c\u4e5f\u5c31\u662f\u5217\u8868\u7684\u9996\u4e2a\u5143\u7d20\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart my_heap.java<pre><code>/* \u8bbf\u95ee\u5806\u9876\u5143\u7d20 */\nint peek() {\nreturn maxHeap.get(0);\n}\n</code></pre> my_heap.cpp<pre><code>/* \u8bbf\u95ee\u5806\u9876\u5143\u7d20 */\nint peek() {\nreturn maxHeap[0];\n}\n</code></pre> my_heap.py<pre><code>def peek(self) -&gt; int:\n\"\"\"\u8bbf\u95ee\u5806\u9876\u5143\u7d20\"\"\"\nreturn self.max_heap[0]\n</code></pre> my_heap.go<pre><code>/* \u8bbf\u95ee\u5806\u9876\u5143\u7d20 */\nfunc (h *maxHeap) peek() any {\nreturn h.data[0]\n}\n</code></pre> my_heap.js<pre><code>/* \u8bbf\u95ee\u5806\u9876\u5143\u7d20 */\npeek() {\nreturn this.#maxHeap[0];\n}\n</code></pre> my_heap.ts<pre><code>/* \u8bbf\u95ee\u5806\u9876\u5143\u7d20 */\npeek(): number {\nreturn this.maxHeap[0];\n}\n</code></pre> my_heap.c<pre><code>/* \u8bbf\u95ee\u5806\u9876\u5143\u7d20 */\nint peek(maxHeap *h) {\nreturn h-&gt;data[0];\n}\n</code></pre> my_heap.cs<pre><code>/* \u8bbf\u95ee\u5806\u9876\u5143\u7d20 */\nint peek() {\nreturn maxHeap[0];\n}\n</code></pre> my_heap.swift<pre><code>/* \u8bbf\u95ee\u5806\u9876\u5143\u7d20 */\nfunc peek() -&gt; Int {\nmaxHeap[0]\n}\n</code></pre> my_heap.zig<pre><code>// \u8bbf\u95ee\u5806\u9876\u5143\u7d20\nfn peek(self: *Self) T {\nreturn self.max_heap.?.items[0];\n}  </code></pre> my_heap.dart<pre><code>/* \u8bbf\u95ee\u5806\u9876\u5143\u7d20 */\nint peek() {\nreturn _maxHeap[0];\n}\n</code></pre>"},{"location":"chapter_heap/heap/#_3","title":"\u5143\u7d20\u5165\u5806","text":"<p>\u7ed9\u5b9a\u5143\u7d20 <code>val</code> \uff0c\u6211\u4eec\u9996\u5148\u5c06\u5176\u6dfb\u52a0\u5230\u5806\u5e95\u3002\u6dfb\u52a0\u4e4b\u540e\uff0c\u7531\u4e8e val \u53ef\u80fd\u5927\u4e8e\u5806\u4e2d\u5176\u4ed6\u5143\u7d20\uff0c\u5806\u7684\u6210\u7acb\u6761\u4ef6\u53ef\u80fd\u5df2\u88ab\u7834\u574f\u3002\u56e0\u6b64\uff0c\u9700\u8981\u4fee\u590d\u4ece\u63d2\u5165\u8282\u70b9\u5230\u6839\u8282\u70b9\u7684\u8def\u5f84\u4e0a\u7684\u5404\u4e2a\u8282\u70b9\uff0c\u8fd9\u4e2a\u64cd\u4f5c\u88ab\u79f0\u4e3a\u300c\u5806\u5316 Heapify\u300d\u3002</p> <p>\u8003\u8651\u4ece\u5165\u5806\u8282\u70b9\u5f00\u59cb\uff0c\u4ece\u5e95\u81f3\u9876\u6267\u884c\u5806\u5316\u3002\u5177\u4f53\u6765\u8bf4\uff0c\u6211\u4eec\u6bd4\u8f83\u63d2\u5165\u8282\u70b9\u4e0e\u5176\u7236\u8282\u70b9\u7684\u503c\uff0c\u5982\u679c\u63d2\u5165\u8282\u70b9\u66f4\u5927\uff0c\u5219\u5c06\u5b83\u4eec\u4ea4\u6362\u3002\u7136\u540e\u7ee7\u7eed\u6267\u884c\u6b64\u64cd\u4f5c\uff0c\u4ece\u5e95\u81f3\u9876\u4fee\u590d\u5806\u4e2d\u7684\u5404\u4e2a\u8282\u70b9\uff0c\u76f4\u81f3\u8d8a\u8fc7\u6839\u8282\u70b9\u6216\u9047\u5230\u65e0\u9700\u4ea4\u6362\u7684\u8282\u70b9\u65f6\u7ed3\u675f\u3002</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p>\u8bbe\u8282\u70b9\u603b\u6570\u4e3a \\(n\\) \uff0c\u5219\u6811\u7684\u9ad8\u5ea6\u4e3a \\(O(\\log n)\\) \u3002\u7531\u6b64\u53ef\u77e5\uff0c\u5806\u5316\u64cd\u4f5c\u7684\u5faa\u73af\u8f6e\u6570\u6700\u591a\u4e3a \\(O(\\log n)\\) \uff0c\u5143\u7d20\u5165\u5806\u64cd\u4f5c\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(\\log n)\\) \u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart my_heap.java<pre><code>/* \u5143\u7d20\u5165\u5806 */\nvoid push(int val) {\n// \u6dfb\u52a0\u8282\u70b9\nmaxHeap.add(val);\n// \u4ece\u5e95\u81f3\u9876\u5806\u5316\nsiftUp(size() - 1);\n}\n/* \u4ece\u8282\u70b9 i \u5f00\u59cb\uff0c\u4ece\u5e95\u81f3\u9876\u5806\u5316 */\nvoid siftUp(int i) {\nwhile (true) {\n// \u83b7\u53d6\u8282\u70b9 i \u7684\u7236\u8282\u70b9\nint p = parent(i);\n// \u5f53\u201c\u8d8a\u8fc7\u6839\u8282\u70b9\u201d\u6216\u201c\u8282\u70b9\u65e0\u9700\u4fee\u590d\u201d\u65f6\uff0c\u7ed3\u675f\u5806\u5316\nif (p &lt; 0 || maxHeap.get(i) &lt;= maxHeap.get(p))\nbreak;\n// \u4ea4\u6362\u4e24\u8282\u70b9\nswap(i, p);\n// \u5faa\u73af\u5411\u4e0a\u5806\u5316\ni = p;\n}\n}\n</code></pre> my_heap.cpp<pre><code>/* \u5143\u7d20\u5165\u5806 */\nvoid push(int val) {\n// \u6dfb\u52a0\u8282\u70b9\nmaxHeap.push_back(val);\n// \u4ece\u5e95\u81f3\u9876\u5806\u5316\nsiftUp(size() - 1);\n}\n/* \u4ece\u8282\u70b9 i \u5f00\u59cb\uff0c\u4ece\u5e95\u81f3\u9876\u5806\u5316 */\nvoid siftUp(int i) {\nwhile (true) {\n// \u83b7\u53d6\u8282\u70b9 i \u7684\u7236\u8282\u70b9\nint p = parent(i);\n// \u5f53\u201c\u8d8a\u8fc7\u6839\u8282\u70b9\u201d\u6216\u201c\u8282\u70b9\u65e0\u9700\u4fee\u590d\u201d\u65f6\uff0c\u7ed3\u675f\u5806\u5316\nif (p &lt; 0 || maxHeap[i] &lt;= maxHeap[p])\nbreak;\n// \u4ea4\u6362\u4e24\u8282\u70b9\nswap(maxHeap[i], maxHeap[p]);\n// \u5faa\u73af\u5411\u4e0a\u5806\u5316\ni = p;\n}\n}\n</code></pre> my_heap.py<pre><code>def push(self, val: int):\n\"\"\"\u5143\u7d20\u5165\u5806\"\"\"\n# \u6dfb\u52a0\u8282\u70b9\nself.max_heap.append(val)\n# \u4ece\u5e95\u81f3\u9876\u5806\u5316\nself.sift_up(self.size() - 1)\ndef sift_up(self, i: int):\n\"\"\"\u4ece\u8282\u70b9 i \u5f00\u59cb\uff0c\u4ece\u5e95\u81f3\u9876\u5806\u5316\"\"\"\nwhile True:\n# \u83b7\u53d6\u8282\u70b9 i \u7684\u7236\u8282\u70b9\np = self.parent(i)\n# \u5f53\u201c\u8d8a\u8fc7\u6839\u8282\u70b9\u201d\u6216\u201c\u8282\u70b9\u65e0\u9700\u4fee\u590d\u201d\u65f6\uff0c\u7ed3\u675f\u5806\u5316\nif p &lt; 0 or self.max_heap[i] &lt;= self.max_heap[p]:\nbreak\n# \u4ea4\u6362\u4e24\u8282\u70b9\nself.swap(i, p)\n# \u5faa\u73af\u5411\u4e0a\u5806\u5316\ni = p\n</code></pre> my_heap.go<pre><code>/* \u5143\u7d20\u5165\u5806 */\nfunc (h *maxHeap) push(val any) {\n// \u6dfb\u52a0\u8282\u70b9\nh.data = append(h.data, val)\n// \u4ece\u5e95\u81f3\u9876\u5806\u5316\nh.siftUp(len(h.data) - 1)\n}\n/* \u4ece\u8282\u70b9 i \u5f00\u59cb\uff0c\u4ece\u5e95\u81f3\u9876\u5806\u5316 */\nfunc (h *maxHeap) siftUp(i int) {\nfor true {\n// \u83b7\u53d6\u8282\u70b9 i \u7684\u7236\u8282\u70b9\np := h.parent(i)\n// \u5f53\u201c\u8d8a\u8fc7\u6839\u8282\u70b9\u201d\u6216\u201c\u8282\u70b9\u65e0\u9700\u4fee\u590d\u201d\u65f6\uff0c\u7ed3\u675f\u5806\u5316\nif p &lt; 0 || h.data[i].(int) &lt;= h.data[p].(int) {\nbreak\n}\n// \u4ea4\u6362\u4e24\u8282\u70b9\nh.swap(i, p)\n// \u5faa\u73af\u5411\u4e0a\u5806\u5316\ni = p\n}\n}\n</code></pre> my_heap.js<pre><code>/* \u5143\u7d20\u5165\u5806 */\npush(val) {\n// \u6dfb\u52a0\u8282\u70b9\nthis.#maxHeap.push(val);\n// \u4ece\u5e95\u81f3\u9876\u5806\u5316\nthis.#siftUp(this.size() - 1);\n}\n/* \u4ece\u8282\u70b9 i \u5f00\u59cb\uff0c\u4ece\u5e95\u81f3\u9876\u5806\u5316 */\n#siftUp(i) {\nwhile (true) {\n// \u83b7\u53d6\u8282\u70b9 i \u7684\u7236\u8282\u70b9\nconst p = this.#parent(i);\n// \u5f53\u201c\u8d8a\u8fc7\u6839\u8282\u70b9\u201d\u6216\u201c\u8282\u70b9\u65e0\u9700\u4fee\u590d\u201d\u65f6\uff0c\u7ed3\u675f\u5806\u5316\nif (p &lt; 0 || this.#maxHeap[i] &lt;= this.#maxHeap[p]) break;\n// \u4ea4\u6362\u4e24\u8282\u70b9\nthis.#swap(i, p);\n// \u5faa\u73af\u5411\u4e0a\u5806\u5316\ni = p;\n}\n}\n</code></pre> my_heap.ts<pre><code>/* \u5143\u7d20\u5165\u5806 */\npush(val: number): void {\n// \u6dfb\u52a0\u8282\u70b9\nthis.maxHeap.push(val);\n// \u4ece\u5e95\u81f3\u9876\u5806\u5316\nthis.siftUp(this.size() - 1);\n}\n/* \u4ece\u8282\u70b9 i \u5f00\u59cb\uff0c\u4ece\u5e95\u81f3\u9876\u5806\u5316 */\nsiftUp(i: number): void {\nwhile (true) {\n// \u83b7\u53d6\u8282\u70b9 i \u7684\u7236\u8282\u70b9\nconst p = this.parent(i);\n// \u5f53\u201c\u8d8a\u8fc7\u6839\u8282\u70b9\u201d\u6216\u201c\u8282\u70b9\u65e0\u9700\u4fee\u590d\u201d\u65f6\uff0c\u7ed3\u675f\u5806\u5316\nif (p &lt; 0 || this.maxHeap[i] &lt;= this.maxHeap[p]) break;\n// \u4ea4\u6362\u4e24\u8282\u70b9\nthis.swap(i, p);\n// \u5faa\u73af\u5411\u4e0a\u5806\u5316\ni = p;\n}\n}\n</code></pre> my_heap.c<pre><code>/* \u5143\u7d20\u5165\u5806 */\nvoid push(maxHeap *h, int val) {\n// \u9ed8\u8ba4\u60c5\u51b5\u4e0b\uff0c\u4e0d\u5e94\u8be5\u6dfb\u52a0\u8fd9\u4e48\u591a\u8282\u70b9\nif (h-&gt;size == MAX_SIZE) {\nprintf(\"heap is full!\");\nreturn;\n}\n// \u6dfb\u52a0\u8282\u70b9\nh-&gt;data[h-&gt;size] = val;\nh-&gt;size++;\n// \u4ece\u5e95\u81f3\u9876\u5806\u5316\nsiftUp(h, h-&gt;size - 1);\n}\n/* \u4ece\u8282\u70b9 i \u5f00\u59cb\uff0c\u4ece\u5e95\u81f3\u9876\u5806\u5316 */\nvoid siftUp(maxHeap *h, int i) {\nwhile (true) {\n// \u83b7\u53d6\u8282\u70b9 i \u7684\u7236\u8282\u70b9\nint p = parent(h, i);\n// \u5f53\u201c\u8d8a\u8fc7\u6839\u8282\u70b9\u201d\u6216\u201c\u8282\u70b9\u65e0\u9700\u4fee\u590d\u201d\u65f6\uff0c\u7ed3\u675f\u5806\u5316\nif (p &lt; 0 || h-&gt;data[i] &lt;= h-&gt;data[p]) {\nbreak;\n}\n// \u4ea4\u6362\u4e24\u8282\u70b9\nswap(h, i, p);\n// \u5faa\u73af\u5411\u4e0a\u5806\u5316\ni = p;\n}\n}\n</code></pre> my_heap.cs<pre><code>/* \u5143\u7d20\u5165\u5806 */\nvoid push(int val) {\n// \u6dfb\u52a0\u8282\u70b9\nmaxHeap.Add(val);\n// \u4ece\u5e95\u81f3\u9876\u5806\u5316\nsiftUp(size() - 1);\n}\n/* \u4ece\u8282\u70b9 i \u5f00\u59cb\uff0c\u4ece\u5e95\u81f3\u9876\u5806\u5316 */\nvoid siftUp(int i) {\nwhile (true) {\n// \u83b7\u53d6\u8282\u70b9 i \u7684\u7236\u8282\u70b9\nint p = parent(i);\n// \u82e5\u201c\u8d8a\u8fc7\u6839\u8282\u70b9\u201d\u6216\u201c\u8282\u70b9\u65e0\u9700\u4fee\u590d\u201d\uff0c\u5219\u7ed3\u675f\u5806\u5316\nif (p &lt; 0 || maxHeap[i] &lt;= maxHeap[p])\nbreak;\n// \u4ea4\u6362\u4e24\u8282\u70b9\nswap(i, p);\n// \u5faa\u73af\u5411\u4e0a\u5806\u5316\ni = p;\n}\n}\n</code></pre> my_heap.swift<pre><code>/* \u5143\u7d20\u5165\u5806 */\nfunc push(val: Int) {\n// \u6dfb\u52a0\u8282\u70b9\nmaxHeap.append(val)\n// \u4ece\u5e95\u81f3\u9876\u5806\u5316\nsiftUp(i: size() - 1)\n}\n/* \u4ece\u8282\u70b9 i \u5f00\u59cb\uff0c\u4ece\u5e95\u81f3\u9876\u5806\u5316 */\nfunc siftUp(i: Int) {\nvar i = i\nwhile true {\n// \u83b7\u53d6\u8282\u70b9 i \u7684\u7236\u8282\u70b9\nlet p = parent(i: i)\n// \u5f53\u201c\u8d8a\u8fc7\u6839\u8282\u70b9\u201d\u6216\u201c\u8282\u70b9\u65e0\u9700\u4fee\u590d\u201d\u65f6\uff0c\u7ed3\u675f\u5806\u5316\nif p &lt; 0 || maxHeap[i] &lt;= maxHeap[p] {\nbreak\n}\n// \u4ea4\u6362\u4e24\u8282\u70b9\nswap(i: i, j: p)\n// \u5faa\u73af\u5411\u4e0a\u5806\u5316\ni = p\n}\n}\n</code></pre> my_heap.zig<pre><code>// \u5143\u7d20\u5165\u5806\nfn push(self: *Self, val: T) !void {\n// \u6dfb\u52a0\u8282\u70b9\ntry self.max_heap.?.append(val);\n// \u4ece\u5e95\u81f3\u9876\u5806\u5316\ntry self.siftUp(self.size() - 1);\n}  // \u4ece\u8282\u70b9 i \u5f00\u59cb\uff0c\u4ece\u5e95\u81f3\u9876\u5806\u5316\nfn siftUp(self: *Self, i_: usize) !void {\nvar i = i_;\nwhile (true) {\n// \u83b7\u53d6\u8282\u70b9 i \u7684\u7236\u8282\u70b9\nvar p = parent(i);\n// \u5f53\u201c\u8d8a\u8fc7\u6839\u8282\u70b9\u201d\u6216\u201c\u8282\u70b9\u65e0\u9700\u4fee\u590d\u201d\u65f6\uff0c\u7ed3\u675f\u5806\u5316\nif (p &lt; 0 or self.max_heap.?.items[i] &lt;= self.max_heap.?.items[p]) break;\n// \u4ea4\u6362\u4e24\u8282\u70b9\ntry self.swap(i, p);\n// \u5faa\u73af\u5411\u4e0a\u5806\u5316\ni = p;\n}\n}\n</code></pre> my_heap.dart<pre><code>/* \u5143\u7d20\u5165\u5806 */\nvoid push(int val) {\n// \u6dfb\u52a0\u8282\u70b9\n_maxHeap.add(val);\n// \u4ece\u5e95\u81f3\u9876\u5806\u5316\n_siftUp(size() - 1);\n}\n[class]{MaxHeap}-[func]{siftUp}\n</code></pre>"},{"location":"chapter_heap/heap/#_4","title":"\u5806\u9876\u5143\u7d20\u51fa\u5806","text":"<p>\u5806\u9876\u5143\u7d20\u662f\u4e8c\u53c9\u6811\u7684\u6839\u8282\u70b9\uff0c\u5373\u5217\u8868\u9996\u5143\u7d20\u3002\u5982\u679c\u6211\u4eec\u76f4\u63a5\u4ece\u5217\u8868\u4e2d\u5220\u9664\u9996\u5143\u7d20\uff0c\u90a3\u4e48\u4e8c\u53c9\u6811\u4e2d\u6240\u6709\u8282\u70b9\u7684\u7d22\u5f15\u90fd\u4f1a\u53d1\u751f\u53d8\u5316\uff0c\u8fd9\u5c06\u4f7f\u5f97\u540e\u7eed\u4f7f\u7528\u5806\u5316\u4fee\u590d\u53d8\u5f97\u56f0\u96be\u3002\u4e3a\u4e86\u5c3d\u91cf\u51cf\u5c11\u5143\u7d20\u7d22\u5f15\u7684\u53d8\u52a8\uff0c\u6211\u4eec\u91c7\u53d6\u4ee5\u4e0b\u64cd\u4f5c\u6b65\u9aa4\uff1a</p> <ol> <li>\u4ea4\u6362\u5806\u9876\u5143\u7d20\u4e0e\u5806\u5e95\u5143\u7d20\uff08\u5373\u4ea4\u6362\u6839\u8282\u70b9\u4e0e\u6700\u53f3\u53f6\u8282\u70b9\uff09\uff1b</li> <li>\u4ea4\u6362\u5b8c\u6210\u540e\uff0c\u5c06\u5806\u5e95\u4ece\u5217\u8868\u4e2d\u5220\u9664\uff08\u6ce8\u610f\uff0c\u7531\u4e8e\u5df2\u7ecf\u4ea4\u6362\uff0c\u5b9e\u9645\u4e0a\u5220\u9664\u7684\u662f\u539f\u6765\u7684\u5806\u9876\u5143\u7d20\uff09\uff1b</li> <li>\u4ece\u6839\u8282\u70b9\u5f00\u59cb\uff0c\u4ece\u9876\u81f3\u5e95\u6267\u884c\u5806\u5316\uff1b</li> </ol> <p>\u987e\u540d\u601d\u4e49\uff0c\u4ece\u9876\u81f3\u5e95\u5806\u5316\u7684\u64cd\u4f5c\u65b9\u5411\u4e0e\u4ece\u5e95\u81f3\u9876\u5806\u5316\u76f8\u53cd\uff0c\u6211\u4eec\u5c06\u6839\u8282\u70b9\u7684\u503c\u4e0e\u5176\u4e24\u4e2a\u5b50\u8282\u70b9\u7684\u503c\u8fdb\u884c\u6bd4\u8f83\uff0c\u5c06\u6700\u5927\u7684\u5b50\u8282\u70b9\u4e0e\u6839\u8282\u70b9\u4ea4\u6362\uff1b\u7136\u540e\u5faa\u73af\u6267\u884c\u6b64\u64cd\u4f5c\uff0c\u76f4\u5230\u8d8a\u8fc7\u53f6\u8282\u70b9\u6216\u9047\u5230\u65e0\u9700\u4ea4\u6362\u7684\u8282\u70b9\u65f6\u7ed3\u675f\u3002</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p>\u4e0e\u5143\u7d20\u5165\u5806\u64cd\u4f5c\u76f8\u4f3c\uff0c\u5806\u9876\u5143\u7d20\u51fa\u5806\u64cd\u4f5c\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e5f\u4e3a \\(O(\\log n)\\) \u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart my_heap.java<pre><code>/* \u5143\u7d20\u51fa\u5806 */\nint pop() {\n// \u5224\u7a7a\u5904\u7406\nif (isEmpty())\nthrow new IndexOutOfBoundsException();\n// \u4ea4\u6362\u6839\u8282\u70b9\u4e0e\u6700\u53f3\u53f6\u8282\u70b9\uff08\u5373\u4ea4\u6362\u9996\u5143\u7d20\u4e0e\u5c3e\u5143\u7d20\uff09\nswap(0, size() - 1);\n// \u5220\u9664\u8282\u70b9\nint val = maxHeap.remove(size() - 1);\n// \u4ece\u9876\u81f3\u5e95\u5806\u5316\nsiftDown(0);\n// \u8fd4\u56de\u5806\u9876\u5143\u7d20\nreturn val;\n}\n/* \u4ece\u8282\u70b9 i \u5f00\u59cb\uff0c\u4ece\u9876\u81f3\u5e95\u5806\u5316 */\nvoid siftDown(int i) {\nwhile (true) {\n// \u5224\u65ad\u8282\u70b9 i, l, r \u4e2d\u503c\u6700\u5927\u7684\u8282\u70b9\uff0c\u8bb0\u4e3a ma\nint l = left(i), r = right(i), ma = i;\nif (l &lt; size() &amp;&amp; maxHeap.get(l) &gt; maxHeap.get(ma))\nma = l;\nif (r &lt; size() &amp;&amp; maxHeap.get(r) &gt; maxHeap.get(ma))\nma = r;\n// \u82e5\u8282\u70b9 i \u6700\u5927\u6216\u7d22\u5f15 l, r \u8d8a\u754c\uff0c\u5219\u65e0\u9700\u7ee7\u7eed\u5806\u5316\uff0c\u8df3\u51fa\nif (ma == i)\nbreak;\n// \u4ea4\u6362\u4e24\u8282\u70b9\nswap(i, ma);\n// \u5faa\u73af\u5411\u4e0b\u5806\u5316\ni = ma;\n}\n}\n</code></pre> my_heap.cpp<pre><code>/* \u5143\u7d20\u51fa\u5806 */\nvoid pop() {\n// \u5224\u7a7a\u5904\u7406\nif (empty()) {\nthrow out_of_range(\"\u5806\u4e3a\u7a7a\");\n}\n// \u4ea4\u6362\u6839\u8282\u70b9\u4e0e\u6700\u53f3\u53f6\u8282\u70b9\uff08\u5373\u4ea4\u6362\u9996\u5143\u7d20\u4e0e\u5c3e\u5143\u7d20\uff09\nswap(maxHeap[0], maxHeap[size() - 1]);\n// \u5220\u9664\u8282\u70b9\nmaxHeap.pop_back();\n// \u4ece\u9876\u81f3\u5e95\u5806\u5316\nsiftDown(0);\n}\n/* \u4ece\u8282\u70b9 i \u5f00\u59cb\uff0c\u4ece\u9876\u81f3\u5e95\u5806\u5316 */\nvoid siftDown(int i) {\nwhile (true) {\n// \u5224\u65ad\u8282\u70b9 i, l, r \u4e2d\u503c\u6700\u5927\u7684\u8282\u70b9\uff0c\u8bb0\u4e3a ma\nint l = left(i), r = right(i), ma = i;\n// \u82e5\u8282\u70b9 i \u6700\u5927\u6216\u7d22\u5f15 l, r \u8d8a\u754c\uff0c\u5219\u65e0\u9700\u7ee7\u7eed\u5806\u5316\uff0c\u8df3\u51fa\nif (l &lt; size() &amp;&amp; maxHeap[l] &gt; maxHeap[ma])\nma = l;\nif (r &lt; size() &amp;&amp; maxHeap[r] &gt; maxHeap[ma])\nma = r;\n// \u82e5\u8282\u70b9 i \u6700\u5927\u6216\u7d22\u5f15 l, r \u8d8a\u754c\uff0c\u5219\u65e0\u9700\u7ee7\u7eed\u5806\u5316\uff0c\u8df3\u51fa\nif (ma == i)\nbreak;\nswap(maxHeap[i], maxHeap[ma]);\n// \u5faa\u73af\u5411\u4e0b\u5806\u5316\ni = ma;\n}\n}\n</code></pre> my_heap.py<pre><code>def pop(self) -&gt; int:\n\"\"\"\u5143\u7d20\u51fa\u5806\"\"\"\n# \u5224\u7a7a\u5904\u7406\nif self.is_empty():\nraise IndexError(\"\u5806\u4e3a\u7a7a\")\n# \u4ea4\u6362\u6839\u8282\u70b9\u4e0e\u6700\u53f3\u53f6\u8282\u70b9\uff08\u5373\u4ea4\u6362\u9996\u5143\u7d20\u4e0e\u5c3e\u5143\u7d20\uff09\nself.swap(0, self.size() - 1)\n# \u5220\u9664\u8282\u70b9\nval = self.max_heap.pop()\n# \u4ece\u9876\u81f3\u5e95\u5806\u5316\nself.sift_down(0)\n# \u8fd4\u56de\u5806\u9876\u5143\u7d20\nreturn val\ndef sift_down(self, i: int):\n\"\"\"\u4ece\u8282\u70b9 i \u5f00\u59cb\uff0c\u4ece\u9876\u81f3\u5e95\u5806\u5316\"\"\"\nwhile True:\n# \u5224\u65ad\u8282\u70b9 i, l, r \u4e2d\u503c\u6700\u5927\u7684\u8282\u70b9\uff0c\u8bb0\u4e3a ma\nl, r, ma = self.left(i), self.right(i), i\nif l &lt; self.size() and self.max_heap[l] &gt; self.max_heap[ma]:\nma = l\nif r &lt; self.size() and self.max_heap[r] &gt; self.max_heap[ma]:\nma = r\n# \u82e5\u8282\u70b9 i \u6700\u5927\u6216\u7d22\u5f15 l, r \u8d8a\u754c\uff0c\u5219\u65e0\u9700\u7ee7\u7eed\u5806\u5316\uff0c\u8df3\u51fa\nif ma == i:\nbreak\n# \u4ea4\u6362\u4e24\u8282\u70b9\nself.swap(i, ma)\n# \u5faa\u73af\u5411\u4e0b\u5806\u5316\ni = ma\n</code></pre> my_heap.go<pre><code>/* \u5143\u7d20\u51fa\u5806 */\nfunc (h *maxHeap) pop() any {\n// \u5224\u7a7a\u5904\u7406\nif h.isEmpty() {\nfmt.Println(\"error\")\nreturn nil\n}\n// \u4ea4\u6362\u6839\u8282\u70b9\u4e0e\u6700\u53f3\u53f6\u8282\u70b9\uff08\u5373\u4ea4\u6362\u9996\u5143\u7d20\u4e0e\u5c3e\u5143\u7d20\uff09\nh.swap(0, h.size()-1)\n// \u5220\u9664\u8282\u70b9\nval := h.data[len(h.data)-1]\nh.data = h.data[:len(h.data)-1]\n// \u4ece\u9876\u81f3\u5e95\u5806\u5316\nh.siftDown(0)\n// \u8fd4\u56de\u5806\u9876\u5143\u7d20\nreturn val\n}\n/* \u4ece\u8282\u70b9 i \u5f00\u59cb\uff0c\u4ece\u9876\u81f3\u5e95\u5806\u5316 */\nfunc (h *maxHeap) siftDown(i int) {\nfor true {\n// \u5224\u65ad\u8282\u70b9 i, l, r \u4e2d\u503c\u6700\u5927\u7684\u8282\u70b9\uff0c\u8bb0\u4e3a max\nl, r, max := h.left(i), h.right(i), i\nif l &lt; h.size() &amp;&amp; h.data[l].(int) &gt; h.data[max].(int) {\nmax = l\n}\nif r &lt; h.size() &amp;&amp; h.data[r].(int) &gt; h.data[max].(int) {\nmax = r\n}\n// \u82e5\u8282\u70b9 i \u6700\u5927\u6216\u7d22\u5f15 l, r \u8d8a\u754c\uff0c\u5219\u65e0\u9700\u7ee7\u7eed\u5806\u5316\uff0c\u8df3\u51fa\nif max == i {\nbreak\n}\n// \u4ea4\u6362\u4e24\u8282\u70b9\nh.swap(i, max)\n// \u5faa\u73af\u5411\u4e0b\u5806\u5316\ni = max\n}\n}\n</code></pre> my_heap.js<pre><code>/* \u5143\u7d20\u51fa\u5806 */\npop() {\n// \u5224\u7a7a\u5904\u7406\nif (this.isEmpty()) throw new Error('\u5806\u4e3a\u7a7a');\n// \u4ea4\u6362\u6839\u8282\u70b9\u4e0e\u6700\u53f3\u53f6\u8282\u70b9\uff08\u5373\u4ea4\u6362\u9996\u5143\u7d20\u4e0e\u5c3e\u5143\u7d20\uff09\nthis.#swap(0, this.size() - 1);\n// \u5220\u9664\u8282\u70b9\nconst val = this.#maxHeap.pop();\n// \u4ece\u9876\u81f3\u5e95\u5806\u5316\nthis.#siftDown(0);\n// \u8fd4\u56de\u5806\u9876\u5143\u7d20\nreturn val;\n}\n/* \u4ece\u8282\u70b9 i \u5f00\u59cb\uff0c\u4ece\u9876\u81f3\u5e95\u5806\u5316 */\n#siftDown(i) {\nwhile (true) {\n// \u5224\u65ad\u8282\u70b9 i, l, r \u4e2d\u503c\u6700\u5927\u7684\u8282\u70b9\uff0c\u8bb0\u4e3a ma\nconst l = this.#left(i),\nr = this.#right(i);\nlet ma = i;\nif (l &lt; this.size() &amp;&amp; this.#maxHeap[l] &gt; this.#maxHeap[ma]) ma = l;\nif (r &lt; this.size() &amp;&amp; this.#maxHeap[r] &gt; this.#maxHeap[ma]) ma = r;\n// \u82e5\u8282\u70b9 i \u6700\u5927\u6216\u7d22\u5f15 l, r \u8d8a\u754c\uff0c\u5219\u65e0\u9700\u7ee7\u7eed\u5806\u5316\uff0c\u8df3\u51fa\nif (ma == i) break;\n// \u4ea4\u6362\u4e24\u8282\u70b9\nthis.#swap(i, ma);\n// \u5faa\u73af\u5411\u4e0b\u5806\u5316\ni = ma;\n}\n}\n</code></pre> my_heap.ts<pre><code>/* \u5143\u7d20\u51fa\u5806 */\npop(): number {\n// \u5224\u7a7a\u5904\u7406\nif (this.isEmpty()) throw new RangeError('Heap is empty.');\n// \u4ea4\u6362\u6839\u8282\u70b9\u4e0e\u6700\u53f3\u53f6\u8282\u70b9\uff08\u5373\u4ea4\u6362\u9996\u5143\u7d20\u4e0e\u5c3e\u5143\u7d20\uff09\nthis.swap(0, this.size() - 1);\n// \u5220\u9664\u8282\u70b9\nconst val = this.maxHeap.pop();\n// \u4ece\u9876\u81f3\u5e95\u5806\u5316\nthis.siftDown(0);\n// \u8fd4\u56de\u5806\u9876\u5143\u7d20\nreturn val;\n}\n/* \u4ece\u8282\u70b9 i \u5f00\u59cb\uff0c\u4ece\u9876\u81f3\u5e95\u5806\u5316 */\nsiftDown(i: number): void {\nwhile (true) {\n// \u5224\u65ad\u8282\u70b9 i, l, r \u4e2d\u503c\u6700\u5927\u7684\u8282\u70b9\uff0c\u8bb0\u4e3a ma\nconst l = this.left(i),\nr = this.right(i);\nlet ma = i;\nif (l &lt; this.size() &amp;&amp; this.maxHeap[l] &gt; this.maxHeap[ma]) ma = l;\nif (r &lt; this.size() &amp;&amp; this.maxHeap[r] &gt; this.maxHeap[ma]) ma = r;\n// \u82e5\u8282\u70b9 i \u6700\u5927\u6216\u7d22\u5f15 l, r \u8d8a\u754c\uff0c\u5219\u65e0\u9700\u7ee7\u7eed\u5806\u5316\uff0c\u8df3\u51fa\nif (ma == i) break;\n// \u4ea4\u6362\u4e24\u8282\u70b9\nthis.swap(i, ma);\n// \u5faa\u73af\u5411\u4e0b\u5806\u5316\ni = ma;\n}\n}\n</code></pre> my_heap.c<pre><code>/* \u5143\u7d20\u51fa\u5806 */\nint pop(maxHeap *h) {\n// \u5224\u7a7a\u5904\u7406\nif (isEmpty(h)) {\nprintf(\"heap is empty!\");\nreturn INT_MAX;\n}\n// \u4ea4\u6362\u6839\u8282\u70b9\u4e0e\u6700\u53f3\u53f6\u8282\u70b9\uff08\u5373\u4ea4\u6362\u9996\u5143\u7d20\u4e0e\u5c3e\u5143\u7d20\uff09\nswap(h, 0, size(h) - 1);\n// \u5220\u9664\u8282\u70b9\nint val = h-&gt;data[h-&gt;size - 1];\nh-&gt;size--;\n// \u4ece\u9876\u81f3\u5e95\u5806\u5316\nsiftDown(h, 0);\n// \u8fd4\u56de\u5806\u9876\u5143\u7d20\nreturn val;\n}\n/* \u4ece\u8282\u70b9 i \u5f00\u59cb\uff0c\u4ece\u9876\u81f3\u5e95\u5806\u5316 */\nvoid siftDown(maxHeap *h, int i) {\nwhile (true) {\n// \u5224\u65ad\u8282\u70b9 i, l, r \u4e2d\u503c\u6700\u5927\u7684\u8282\u70b9\uff0c\u8bb0\u4e3a max\nint l = left(h, i);\nint r = right(h, i);\nint max = i;\nif (l &lt; size(h) &amp;&amp; h-&gt;data[l] &gt; h-&gt;data[max]) {\nmax = l;\n}\nif (r &lt; size(h) &amp;&amp; h-&gt;data[r] &gt; h-&gt;data[max]) {\nmax = r;\n}\n// \u82e5\u8282\u70b9 i \u6700\u5927\u6216\u7d22\u5f15 l, r \u8d8a\u754c\uff0c\u5219\u65e0\u9700\u7ee7\u7eed\u5806\u5316\uff0c\u8df3\u51fa\nif (max == i) {\nbreak;\n}\n// \u4ea4\u6362\u4e24\u8282\u70b9\nswap(h, i, max);\n// \u5faa\u73af\u5411\u4e0b\u5806\u5316\ni = max;\n}\n}\n</code></pre> my_heap.cs<pre><code>/* \u5143\u7d20\u51fa\u5806 */\nint pop() {\n// \u5224\u7a7a\u5904\u7406\nif (isEmpty())\nthrow new IndexOutOfRangeException();\n// \u4ea4\u6362\u6839\u8282\u70b9\u4e0e\u6700\u53f3\u53f6\u8282\u70b9\uff08\u5373\u4ea4\u6362\u9996\u5143\u7d20\u4e0e\u5c3e\u5143\u7d20\uff09\nswap(0, size() - 1);\n// \u5220\u9664\u8282\u70b9\nint val = maxHeap.Last();\nmaxHeap.RemoveAt(size() - 1);\n// \u4ece\u9876\u81f3\u5e95\u5806\u5316\nsiftDown(0);\n// \u8fd4\u56de\u5806\u9876\u5143\u7d20\nreturn val;\n}\n/* \u4ece\u8282\u70b9 i \u5f00\u59cb\uff0c\u4ece\u9876\u81f3\u5e95\u5806\u5316 */\nvoid siftDown(int i) {\nwhile (true) {\n// \u5224\u65ad\u8282\u70b9 i, l, r \u4e2d\u503c\u6700\u5927\u7684\u8282\u70b9\uff0c\u8bb0\u4e3a ma\nint l = left(i), r = right(i), ma = i;\nif (l &lt; size() &amp;&amp; maxHeap[l] &gt; maxHeap[ma])\nma = l;\nif (r &lt; size() &amp;&amp; maxHeap[r] &gt; maxHeap[ma])\nma = r;\n// \u82e5\u201c\u8282\u70b9 i \u6700\u5927\u201d\u6216\u201c\u8d8a\u8fc7\u53f6\u8282\u70b9\u201d\uff0c\u5219\u7ed3\u675f\u5806\u5316\nif (ma == i) break;\n// \u4ea4\u6362\u4e24\u8282\u70b9\nswap(i, ma);\n// \u5faa\u73af\u5411\u4e0b\u5806\u5316\ni = ma;\n}\n}\n</code></pre> my_heap.swift<pre><code>/* \u5143\u7d20\u51fa\u5806 */\nfunc pop() -&gt; Int {\n// \u5224\u7a7a\u5904\u7406\nif isEmpty() {\nfatalError(\"\u5806\u4e3a\u7a7a\")\n}\n// \u4ea4\u6362\u6839\u8282\u70b9\u4e0e\u6700\u53f3\u53f6\u8282\u70b9\uff08\u5373\u4ea4\u6362\u9996\u5143\u7d20\u4e0e\u5c3e\u5143\u7d20\uff09\nswap(i: 0, j: size() - 1)\n// \u5220\u9664\u8282\u70b9\nlet val = maxHeap.remove(at: size() - 1)\n// \u4ece\u9876\u81f3\u5e95\u5806\u5316\nsiftDown(i: 0)\n// \u8fd4\u56de\u5806\u9876\u5143\u7d20\nreturn val\n}\n/* \u4ece\u8282\u70b9 i \u5f00\u59cb\uff0c\u4ece\u9876\u81f3\u5e95\u5806\u5316 */\nfunc siftDown(i: Int) {\nvar i = i\nwhile true {\n// \u5224\u65ad\u8282\u70b9 i, l, r \u4e2d\u503c\u6700\u5927\u7684\u8282\u70b9\uff0c\u8bb0\u4e3a ma\nlet l = left(i: i)\nlet r = right(i: i)\nvar ma = i\nif l &lt; size(), maxHeap[l] &gt; maxHeap[ma] {\nma = l\n}\nif r &lt; size(), maxHeap[r] &gt; maxHeap[ma] {\nma = r\n}\n// \u82e5\u8282\u70b9 i \u6700\u5927\u6216\u7d22\u5f15 l, r \u8d8a\u754c\uff0c\u5219\u65e0\u9700\u7ee7\u7eed\u5806\u5316\uff0c\u8df3\u51fa\nif ma == i {\nbreak\n}\n// \u4ea4\u6362\u4e24\u8282\u70b9\nswap(i: i, j: ma)\n// \u5faa\u73af\u5411\u4e0b\u5806\u5316\ni = ma\n}\n}\n</code></pre> my_heap.zig<pre><code>// \u5143\u7d20\u51fa\u5806\nfn pop(self: *Self) !T {\n// \u5224\u65ad\u5904\u7406\nif (self.isEmpty()) unreachable;\n// \u4ea4\u6362\u6839\u8282\u70b9\u4e0e\u6700\u53f3\u53f6\u8282\u70b9\uff08\u5373\u4ea4\u6362\u9996\u5143\u7d20\u4e0e\u5c3e\u5143\u7d20\uff09\ntry self.swap(0, self.size() - 1);\n// \u5220\u9664\u8282\u70b9\nvar val = self.max_heap.?.pop();\n// \u4ece\u9876\u81f3\u5e95\u5806\u5316\ntry self.siftDown(0);\n// \u8fd4\u56de\u5806\u9876\u5143\u7d20\nreturn val;\n} // \u4ece\u8282\u70b9 i \u5f00\u59cb\uff0c\u4ece\u9876\u81f3\u5e95\u5806\u5316\nfn siftDown(self: *Self, i_: usize) !void {\nvar i = i_;\nwhile (true) {\n// \u5224\u65ad\u8282\u70b9 i, l, r \u4e2d\u503c\u6700\u5927\u7684\u8282\u70b9\uff0c\u8bb0\u4e3a ma\nvar l = left(i);\nvar r = right(i);\nvar ma = i;\nif (l &lt; self.size() and self.max_heap.?.items[l] &gt; self.max_heap.?.items[ma]) ma = l;\nif (r &lt; self.size() and self.max_heap.?.items[r] &gt; self.max_heap.?.items[ma]) ma = r;\n// \u82e5\u8282\u70b9 i \u6700\u5927\u6216\u7d22\u5f15 l, r \u8d8a\u754c\uff0c\u5219\u65e0\u9700\u7ee7\u7eed\u5806\u5316\uff0c\u8df3\u51fa\nif (ma == i) break;\n// \u4ea4\u6362\u4e24\u8282\u70b9\ntry self.swap(i, ma);\n// \u5faa\u73af\u5411\u4e0b\u5806\u5316\ni = ma;\n}\n}\n</code></pre> my_heap.dart<pre><code>/* \u5143\u7d20\u51fa\u5806 */\nint pop() {\n// \u5224\u7a7a\u5904\u7406\nif (isEmpty()) throw Exception('\u5806\u4e3a\u7a7a');\n// \u4ea4\u6362\u6839\u8282\u70b9\u4e0e\u6700\u53f3\u53f6\u8282\u70b9\uff08\u5373\u4ea4\u6362\u9996\u5143\u7d20\u4e0e\u5c3e\u5143\u7d20\uff09\n_swap(0, size() - 1);\n// \u5220\u9664\u8282\u70b9\nint val = _maxHeap.removeLast();\n// \u4ece\u9876\u81f3\u5e95\u5806\u5316\n_siftDown(0);\n// \u8fd4\u56de\u5806\u9876\u5143\u7d20\nreturn val;\n}\n[class]{MaxHeap}-[func]{siftDown}\n</code></pre>"},{"location":"chapter_heap/heap/#813","title":"8.1.3. \u00a0 \u5806\u5e38\u89c1\u5e94\u7528","text":"<ul> <li>\u4f18\u5148\u961f\u5217\uff1a\u5806\u901a\u5e38\u4f5c\u4e3a\u5b9e\u73b0\u4f18\u5148\u961f\u5217\u7684\u9996\u9009\u6570\u636e\u7ed3\u6784\uff0c\u5176\u5165\u961f\u548c\u51fa\u961f\u64cd\u4f5c\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u5747\u4e3a \\(O(\\log n)\\) \uff0c\u800c\u5efa\u961f\u64cd\u4f5c\u4e3a \\(O(n)\\) \uff0c\u8fd9\u4e9b\u64cd\u4f5c\u90fd\u975e\u5e38\u9ad8\u6548\u3002</li> <li>\u5806\u6392\u5e8f\uff1a\u7ed9\u5b9a\u4e00\u7ec4\u6570\u636e\uff0c\u6211\u4eec\u53ef\u4ee5\u7528\u5b83\u4eec\u5efa\u7acb\u4e00\u4e2a\u5806\uff0c\u7136\u540e\u4e0d\u65ad\u5730\u6267\u884c\u5143\u7d20\u51fa\u5806\u64cd\u4f5c\uff0c\u4ece\u800c\u5f97\u5230\u6709\u5e8f\u6570\u636e\u3002\u7136\u800c\uff0c\u6211\u4eec\u901a\u5e38\u4f1a\u4f7f\u7528\u4e00\u79cd\u66f4\u4f18\u96c5\u7684\u65b9\u5f0f\u5b9e\u73b0\u5806\u6392\u5e8f\uff0c\u8be6\u89c1\u540e\u7eed\u7684\u5806\u6392\u5e8f\u7ae0\u8282\u3002</li> <li>\u83b7\u53d6\u6700\u5927\u7684 \\(k\\) \u4e2a\u5143\u7d20\uff1a\u8fd9\u662f\u4e00\u4e2a\u7ecf\u5178\u7684\u7b97\u6cd5\u95ee\u9898\uff0c\u540c\u65f6\u4e5f\u662f\u4e00\u79cd\u5178\u578b\u5e94\u7528\uff0c\u4f8b\u5982\u9009\u62e9\u70ed\u5ea6\u524d 10 \u7684\u65b0\u95fb\u4f5c\u4e3a\u5fae\u535a\u70ed\u641c\uff0c\u9009\u53d6\u9500\u91cf\u524d 10 \u7684\u5546\u54c1\u7b49\u3002</li> </ul>"},{"location":"chapter_heap/summary/","title":"8.4. \u00a0 \u5c0f\u7ed3","text":"<ul> <li>\u5806\u662f\u4e00\u68f5\u5b8c\u5168\u4e8c\u53c9\u6811\uff0c\u6839\u636e\u6210\u7acb\u6761\u4ef6\u53ef\u5206\u4e3a\u5927\u9876\u5806\u548c\u5c0f\u9876\u5806\u3002\u5927\uff08\u5c0f\uff09\u9876\u5806\u7684\u5806\u9876\u5143\u7d20\u662f\u6700\u5927\uff08\u5c0f\uff09\u7684\u3002</li> <li>\u4f18\u5148\u961f\u5217\u7684\u5b9a\u4e49\u662f\u5177\u6709\u51fa\u961f\u4f18\u5148\u7ea7\u7684\u961f\u5217\uff0c\u901a\u5e38\u4f7f\u7528\u5806\u6765\u5b9e\u73b0\u3002</li> <li>\u5806\u7684\u5e38\u7528\u64cd\u4f5c\u53ca\u5176\u5bf9\u5e94\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u5305\u62ec\uff1a\u5143\u7d20\u5165\u5806 \\(O(\\log n)\\) \u3001\u5806\u9876\u5143\u7d20\u51fa\u5806 \\(O(\\log n)\\) \u548c\u8bbf\u95ee\u5806\u9876\u5143\u7d20 \\(O(1)\\) \u7b49\u3002</li> <li>\u5b8c\u5168\u4e8c\u53c9\u6811\u975e\u5e38\u9002\u5408\u7528\u6570\u7ec4\u8868\u793a\uff0c\u56e0\u6b64\u6211\u4eec\u901a\u5e38\u4f7f\u7528\u6570\u7ec4\u6765\u5b58\u50a8\u5806\u3002</li> <li>\u5806\u5316\u64cd\u4f5c\u7528\u4e8e\u7ef4\u62a4\u5806\u7684\u6027\u8d28\uff0c\u5728\u5165\u5806\u548c\u51fa\u5806\u64cd\u4f5c\u4e2d\u90fd\u4f1a\u7528\u5230\u3002</li> <li>\u8f93\u5165 \\(n\\) \u4e2a\u5143\u7d20\u5e76\u5efa\u5806\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u53ef\u4ee5\u4f18\u5316\u81f3 \\(O(n)\\) \uff0c\u975e\u5e38\u9ad8\u6548\u3002</li> </ul>"},{"location":"chapter_heap/top_k/","title":"8.3. \u00a0 Top-K \u95ee\u9898","text":"<p>Question</p> <p>\u7ed9\u5b9a\u4e00\u4e2a\u957f\u5ea6\u4e3a \\(n\\) \u65e0\u5e8f\u6570\u7ec4 <code>nums</code> \uff0c\u8bf7\u8fd4\u56de\u6570\u7ec4\u4e2d\u524d \\(k\\) \u5927\u7684\u5143\u7d20\u3002</p> <p>\u5bf9\u4e8e\u8be5\u95ee\u9898\uff0c\u6211\u4eec\u5148\u4ecb\u7ecd\u4e24\u79cd\u601d\u8def\u6bd4\u8f83\u76f4\u63a5\u7684\u89e3\u6cd5\uff0c\u518d\u4ecb\u7ecd\u6548\u7387\u66f4\u9ad8\u7684\u5806\u89e3\u6cd5\u3002</p>"},{"location":"chapter_heap/top_k/#831","title":"8.3.1. \u00a0 \u65b9\u6cd5\u4e00\uff1a\u904d\u5386\u9009\u62e9","text":"<p>\u6211\u4eec\u53ef\u4ee5\u8fdb\u884c \\(k\\) \u8f6e\u904d\u5386\uff0c\u5206\u522b\u5728\u6bcf\u8f6e\u4e2d\u63d0\u53d6\u7b2c \\(1\\) , \\(2\\) , \\(\\cdots\\) , \\(k\\) \u5927\u7684\u5143\u7d20\uff0c\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(nk)\\) \u3002</p> <p>\u8be5\u65b9\u6cd5\u53ea\u9002\u7528\u4e8e \\(k \\ll n\\) \u7684\u60c5\u51b5\uff0c\u56e0\u4e3a\u5f53 \\(k\\) \u4e0e \\(n\\) \u6bd4\u8f83\u63a5\u8fd1\u65f6\uff0c\u5176\u65f6\u95f4\u590d\u6742\u5ea6\u8d8b\u5411\u4e8e \\(O(n^2)\\) \uff0c\u975e\u5e38\u8017\u65f6\u3002</p> <p></p> <p> Fig. \u904d\u5386\u5bfb\u627e\u6700\u5927\u7684 k \u4e2a\u5143\u7d20 </p> <p>Tip</p> <p>\u5f53 \\(k = n\\) \u65f6\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\u4ece\u5927\u5230\u5c0f\u7684\u5e8f\u5217\uff0c\u7b49\u4ef7\u4e8e\u300c\u9009\u62e9\u6392\u5e8f\u300d\u7b97\u6cd5\u3002 </p>"},{"location":"chapter_heap/top_k/#832","title":"8.3.2. \u00a0 \u65b9\u6cd5\u4e8c\uff1a\u6392\u5e8f","text":"<p>\u6211\u4eec\u53ef\u4ee5\u5bf9\u6570\u7ec4 <code>nums</code> \u8fdb\u884c\u6392\u5e8f\uff0c\u5e76\u8fd4\u56de\u6700\u53f3\u8fb9\u7684 \\(k\\) \u4e2a\u5143\u7d20\uff0c\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(n \\log n)\\) \u3002</p> <p>\u663e\u7136\uff0c\u8be5\u65b9\u6cd5\u201c\u8d85\u989d\u201d\u5b8c\u6210\u4efb\u52a1\u4e86\uff0c\u56e0\u4e3a\u6211\u4eec\u53ea\u9700\u8981\u627e\u51fa\u6700\u5927\u7684 \\(k\\) \u4e2a\u5143\u7d20\u5373\u53ef\uff0c\u800c\u4e0d\u9700\u8981\u6392\u5e8f\u5176\u4ed6\u5143\u7d20\u3002</p> <p></p> <p> Fig. \u6392\u5e8f\u5bfb\u627e\u6700\u5927\u7684 k \u4e2a\u5143\u7d20 </p>"},{"location":"chapter_heap/top_k/#833","title":"8.3.3. \u00a0 \u65b9\u6cd5\u4e09\uff1a\u5806","text":"<p>\u6211\u4eec\u53ef\u4ee5\u57fa\u4e8e\u5806\u66f4\u52a0\u9ad8\u6548\u5730\u89e3\u51b3 Top-K \u95ee\u9898\uff0c\u6d41\u7a0b\u5982\u4e0b\uff1a</p> <ol> <li>\u521d\u59cb\u5316\u4e00\u4e2a\u5c0f\u9876\u5806\uff0c\u5176\u5806\u9876\u5143\u7d20\u6700\u5c0f\uff1b</li> <li>\u5148\u5c06\u6570\u7ec4\u7684\u524d \\(k\\) \u4e2a\u5143\u7d20\u4f9d\u6b21\u5165\u5806\uff1b</li> <li>\u4ece\u7b2c \\(k + 1\\) \u4e2a\u5143\u7d20\u5f00\u59cb\uff0c\u82e5\u5f53\u524d\u5143\u7d20\u5927\u4e8e\u5806\u9876\u5143\u7d20\uff0c\u5219\u5c06\u5806\u9876\u5143\u7d20\u51fa\u5806\uff0c\u5e76\u5c06\u5f53\u524d\u5143\u7d20\u5165\u5806\uff1b</li> <li>\u904d\u5386\u5b8c\u6210\u540e\uff0c\u5806\u4e2d\u4fdd\u5b58\u7684\u5c31\u662f\u6700\u5927\u7684 \\(k\\) \u4e2a\u5143\u7d20\uff1b</li> </ol> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p>\u603b\u5171\u6267\u884c\u4e86 \\(n\\) \u8f6e\u5165\u5806\u548c\u51fa\u5806\uff0c\u5806\u7684\u6700\u5927\u957f\u5ea6\u4e3a \\(k\\) \uff0c\u56e0\u6b64\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(n \\log k)\\) \u3002\u8be5\u65b9\u6cd5\u7684\u6548\u7387\u5f88\u9ad8\uff0c\u5f53 \\(k\\) \u8f83\u5c0f\u65f6\uff0c\u65f6\u95f4\u590d\u6742\u5ea6\u8d8b\u5411 \\(O(n)\\) \uff1b\u5f53 \\(k\\) \u8f83\u5927\u65f6\uff0c\u65f6\u95f4\u590d\u6742\u5ea6\u4e0d\u4f1a\u8d85\u8fc7 \\(O(n \\log n)\\) \u3002</p> <p>\u53e6\u5916\uff0c\u8be5\u65b9\u6cd5\u9002\u7528\u4e8e\u52a8\u6001\u6570\u636e\u6d41\u7684\u4f7f\u7528\u573a\u666f\u3002\u5728\u4e0d\u65ad\u52a0\u5165\u6570\u636e\u65f6\uff0c\u6211\u4eec\u53ef\u4ee5\u6301\u7eed\u7ef4\u62a4\u5806\u5185\u7684\u5143\u7d20\uff0c\u4ece\u800c\u5b9e\u73b0\u6700\u5927 \\(k\\) \u4e2a\u5143\u7d20\u7684\u52a8\u6001\u66f4\u65b0\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart top_k.java<pre><code>/* \u57fa\u4e8e\u5806\u67e5\u627e\u6570\u7ec4\u4e2d\u6700\u5927\u7684 k \u4e2a\u5143\u7d20 */\nQueue&lt;Integer&gt; topKHeap(int[] nums, int k) {\nQueue&lt;Integer&gt; heap = new PriorityQueue&lt;Integer&gt;();\n// \u5c06\u6570\u7ec4\u7684\u524d k \u4e2a\u5143\u7d20\u5165\u5806\nfor (int i = 0; i &lt; k; i++) {\nheap.add(nums[i]);\n}\n// \u4ece\u7b2c k+1 \u4e2a\u5143\u7d20\u5f00\u59cb\uff0c\u4fdd\u6301\u5806\u7684\u957f\u5ea6\u4e3a k\nfor (int i = k; i &lt; nums.length; i++) {\n// \u82e5\u5f53\u524d\u5143\u7d20\u5927\u4e8e\u5806\u9876\u5143\u7d20\uff0c\u5219\u5c06\u5806\u9876\u5143\u7d20\u51fa\u5806\u3001\u5f53\u524d\u5143\u7d20\u5165\u5806\nif (nums[i] &gt; heap.peek()) {\nheap.poll();\nheap.add(nums[i]);\n}\n}\nreturn heap;\n}\n</code></pre> top_k.cpp<pre><code>/* \u57fa\u4e8e\u5806\u67e5\u627e\u6570\u7ec4\u4e2d\u6700\u5927\u7684 k \u4e2a\u5143\u7d20 */\npriority_queue&lt;int, vector&lt;int&gt;, greater&lt;int&gt;&gt; topKHeap(vector&lt;int&gt; &amp;nums, int k) {\npriority_queue&lt;int, vector&lt;int&gt;, greater&lt;int&gt;&gt; heap;\n// \u5c06\u6570\u7ec4\u7684\u524d k \u4e2a\u5143\u7d20\u5165\u5806\nfor (int i = 0; i &lt; k; i++) {\nheap.push(nums[i]);\n}\n// \u4ece\u7b2c k+1 \u4e2a\u5143\u7d20\u5f00\u59cb\uff0c\u4fdd\u6301\u5806\u7684\u957f\u5ea6\u4e3a k\nfor (int i = k; i &lt; nums.size(); i++) {\n// \u82e5\u5f53\u524d\u5143\u7d20\u5927\u4e8e\u5806\u9876\u5143\u7d20\uff0c\u5219\u5c06\u5806\u9876\u5143\u7d20\u51fa\u5806\u3001\u5f53\u524d\u5143\u7d20\u5165\u5806\nif (nums[i] &gt; heap.top()) {\nheap.pop();\nheap.push(nums[i]);\n}\n}\nreturn heap;\n}\n</code></pre> top_k.py<pre><code>def top_k_heap(nums: list[int], k: int) -&gt; list[int]:\n\"\"\"\u57fa\u4e8e\u5806\u67e5\u627e\u6570\u7ec4\u4e2d\u6700\u5927\u7684 k \u4e2a\u5143\u7d20\"\"\"\nheap = []\n# \u5c06\u6570\u7ec4\u7684\u524d k \u4e2a\u5143\u7d20\u5165\u5806\nfor i in range(k):\nheapq.heappush(heap, nums[i])\n# \u4ece\u7b2c k+1 \u4e2a\u5143\u7d20\u5f00\u59cb\uff0c\u4fdd\u6301\u5806\u7684\u957f\u5ea6\u4e3a k\nfor i in range(k, len(nums)):\n# \u82e5\u5f53\u524d\u5143\u7d20\u5927\u4e8e\u5806\u9876\u5143\u7d20\uff0c\u5219\u5c06\u5806\u9876\u5143\u7d20\u51fa\u5806\u3001\u5f53\u524d\u5143\u7d20\u5165\u5806\nif nums[i] &gt; heap[0]:\nheapq.heappop(heap)\nheapq.heappush(heap, nums[i])\nreturn heap\n</code></pre> top_k.go<pre><code>[class]{maxHeap}-[func]{topKHeap}\n</code></pre> top_k.js<pre><code>[class]{}-[func]{topKHeap}\n</code></pre> top_k.ts<pre><code>[class]{}-[func]{topKHeap}\n</code></pre> top_k.c<pre><code>[class]{maxHeap}-[func]{topKHeap}\n</code></pre> top_k.cs<pre><code>[class]{top_k}-[func]{topKHeap}\n</code></pre> top_k.swift<pre><code>[class]{}-[func]{topKHeap}\n</code></pre> top_k.zig<pre><code>[class]{}-[func]{topKHeap}\n</code></pre> top_k.dart<pre><code>[class]{}-[func]{top_k_heap}\n</code></pre>"},{"location":"chapter_introduction/","title":"1. \u00a0 \u5f15\u8a00","text":""},{"location":"chapter_introduction/algorithms_are_everywhere/","title":"1.1. \u00a0 \u7b97\u6cd5\u65e0\u5904\u4e0d\u5728","text":"<p>\u5f53\u6211\u4eec\u542c\u5230\u201c\u7b97\u6cd5\u201d\u8fd9\u4e2a\u8bcd\u65f6\uff0c\u5f88\u81ea\u7136\u5730\u4f1a\u60f3\u5230\u6570\u5b66\u3002\u7136\u800c\u5b9e\u9645\u4e0a\uff0c\u8bb8\u591a\u7b97\u6cd5\u5e76\u4e0d\u6d89\u53ca\u590d\u6742\u6570\u5b66\uff0c\u800c\u662f\u66f4\u591a\u5730\u4f9d\u8d56\u4e8e\u57fa\u672c\u903b\u8f91\uff0c\u8fd9\u4e9b\u903b\u8f91\u5728\u6211\u4eec\u7684\u65e5\u5e38\u751f\u6d3b\u4e2d\u5904\u5904\u53ef\u89c1\u3002</p> <p>\u5728\u6b63\u5f0f\u63a2\u8ba8\u7b97\u6cd5\u4e4b\u524d\uff0c\u6709\u4e00\u4e2a\u6709\u8da3\u7684\u4e8b\u5b9e\u503c\u5f97\u5206\u4eab\uff1a\u5b9e\u9645\u4e0a\uff0c\u4f60\u5df2\u7ecf\u5b66\u4f1a\u4e86\u8bb8\u591a\u7b97\u6cd5\uff0c\u5e76\u4e60\u60ef\u5c06\u4ed6\u4eec\u5e94\u7528\u5230\u65e5\u5e38\u751f\u6d3b\u4e2d\u4e86\u3002\u4e0b\u9762\uff0c\u6211\u5c06\u4e3e\u4e24\u4e2a\u5177\u4f53\u4f8b\u5b50\u6765\u8bc1\u5b9e\u8fd9\u4e00\u70b9\u3002</p> <p>\u4f8b\u4e00\uff1a\u7ec4\u88c5\u79ef\u6728\u3002\u4e00\u5957\u79ef\u6728\uff0c\u9664\u4e86\u5305\u542b\u8bb8\u591a\u96f6\u4ef6\u4e4b\u5916\uff0c\u8fd8\u9644\u6709\u8be6\u7ec6\u7684\u7ec4\u88c5\u8bf4\u660e\u4e66\u3002\u6211\u4eec\u6309\u7167\u8bf4\u660e\u4e66\u4e00\u6b65\u6b65\u64cd\u4f5c\uff0c\u5c31\u80fd\u7ec4\u88c5\u51fa\u7cbe\u7f8e\u7684\u79ef\u6728\u6a21\u578b\u3002</p> <p>\u4ece\u6570\u636e\u7ed3\u6784\u4e0e\u7b97\u6cd5\u7684\u89d2\u5ea6\u6765\u770b\uff0c\u79ef\u6728\u7684\u5404\u79cd\u5f62\u72b6\u548c\u8fde\u63a5\u65b9\u5f0f\u4ee3\u8868\u6570\u636e\u7ed3\u6784\uff0c\u800c\u7ec4\u88c5\u8bf4\u660e\u4e66\u4e0a\u7684\u4e00\u7cfb\u5217\u6b65\u9aa4\u5219\u662f\u7b97\u6cd5\u3002</p> <p></p> <p> Fig. \u62fc\u88c5\u79ef\u6728 </p> <p>\u4f8b\u4e8c\uff1a\u67e5\u9605\u5b57\u5178\u3002\u5728\u5b57\u5178\u91cc\uff0c\u6bcf\u4e2a\u6c49\u5b57\u90fd\u5bf9\u5e94\u4e00\u4e2a\u62fc\u97f3\uff0c\u800c\u5b57\u5178\u662f\u6309\u7167\u62fc\u97f3\u7684\u82f1\u6587\u5b57\u6bcd\u987a\u5e8f\u6392\u5217\u7684\u3002\u5047\u8bbe\u6211\u4eec\u9700\u8981\u67e5\u627e\u4e00\u4e2a\u62fc\u97f3\u9996\u5b57\u6bcd\u4e3a \\(r\\) \u7684\u5b57\uff0c\u901a\u5e38\u4f1a\u8fd9\u6837\u64cd\u4f5c\uff1a</p> <ol> <li>\u7ffb\u5f00\u5b57\u5178\u7ea6\u4e00\u534a\u7684\u9875\u6570\uff0c\u67e5\u770b\u8be5\u9875\u9996\u5b57\u6bcd\u662f\u4ec0\u4e48\uff08\u5047\u8bbe\u4e3a \\(m\\) \uff09\uff1b</li> <li>\u7531\u4e8e\u5728\u82f1\u6587\u5b57\u6bcd\u8868\u4e2d \\(r\\) \u4f4d\u4e8e \\(m\\) \u4e4b\u540e\uff0c\u6240\u4ee5\u6392\u9664\u5b57\u5178\u524d\u534a\u90e8\u5206\uff0c\u67e5\u627e\u8303\u56f4\u7f29\u5c0f\u5230\u540e\u534a\u90e8\u5206\uff1b</li> <li>\u4e0d\u65ad\u91cd\u590d\u6b65\u9aa4 1-2 \uff0c\u76f4\u81f3\u627e\u5230\u62fc\u97f3\u9996\u5b57\u6bcd\u4e3a \\(r\\) \u7684\u9875\u7801\u4e3a\u6b62\u3002</li> </ol> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p>\u67e5\u9605\u5b57\u5178\u8fd9\u4e2a\u5c0f\u5b66\u751f\u5fc5\u5907\u6280\u80fd\uff0c\u5b9e\u9645\u4e0a\u5c31\u662f\u8457\u540d\u7684\u300c\u4e8c\u5206\u67e5\u627e\u300d\u3002\u4ece\u6570\u636e\u7ed3\u6784\u7684\u89d2\u5ea6\uff0c\u6211\u4eec\u53ef\u4ee5\u628a\u5b57\u5178\u89c6\u4e3a\u4e00\u4e2a\u5df2\u6392\u5e8f\u7684\u300c\u6570\u7ec4\u300d\uff1b\u4ece\u7b97\u6cd5\u7684\u89d2\u5ea6\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u4e0a\u8ff0\u67e5\u5b57\u5178\u7684\u4e00\u7cfb\u5217\u64cd\u4f5c\u770b\u4f5c\u662f\u300c\u4e8c\u5206\u67e5\u627e\u300d\u7b97\u6cd5\u3002</p> <p>\u5c0f\u5230\u70f9\u996a\u4e00\u9053\u83dc\uff0c\u5927\u5230\u661f\u9645\u822a\u884c\uff0c\u51e0\u4e4e\u6240\u6709\u95ee\u9898\u7684\u89e3\u51b3\u90fd\u79bb\u4e0d\u5f00\u7b97\u6cd5\u3002\u8ba1\u7b97\u673a\u7684\u51fa\u73b0\u4f7f\u6211\u4eec\u80fd\u591f\u901a\u8fc7\u7f16\u7a0b\u5c06\u6570\u636e\u7ed3\u6784\u5b58\u50a8\u5728\u5185\u5b58\u4e2d\uff0c\u540c\u65f6\u7f16\u5199\u4ee3\u7801\u8c03\u7528 CPU \u548c GPU \u6267\u884c\u7b97\u6cd5\u3002\u8fd9\u6837\u4e00\u6765\uff0c\u6211\u4eec\u5c31\u80fd\u628a\u751f\u6d3b\u4e2d\u7684\u95ee\u9898\u8f6c\u79fb\u5230\u8ba1\u7b97\u673a\u4e0a\uff0c\u4ee5\u66f4\u9ad8\u6548\u7684\u65b9\u5f0f\u89e3\u51b3\u5404\u79cd\u590d\u6742\u95ee\u9898\u3002</p> <p>Tip</p> <p>\u9605\u8bfb\u81f3\u6b64\uff0c\u5982\u679c\u4f60\u5bf9\u6570\u636e\u7ed3\u6784\u3001\u7b97\u6cd5\u3001\u6570\u7ec4\u548c\u4e8c\u5206\u67e5\u627e\u7b49\u6982\u5ff5\u4ecd\u611f\u5230\u4e00\u77e5\u534a\u89e3\uff0c\u90a3\u4e48\u592a\u597d\u4e86\uff01\u56e0\u4e3a\u8fd9\u6b63\u662f\u672c\u4e66\u5b58\u5728\u7684\u610f\u4e49\u3002\u63a5\u4e0b\u6765\uff0c\u8fd9\u672c\u4e66\u5c06\u4e00\u6b65\u6b65\u5f15\u5bfc\u4f60\u6df1\u5165\u6570\u636e\u7ed3\u6784\u4e0e\u7b97\u6cd5\u7684\u77e5\u8bc6\u6bbf\u5802\u3002</p>"},{"location":"chapter_introduction/summary/","title":"1.3. \u00a0 \u5c0f\u7ed3","text":"<ul> <li>\u7b97\u6cd5\u5728\u65e5\u5e38\u751f\u6d3b\u4e2d\u65e0\u5904\u4e0d\u5728\uff0c\u5e76\u4e0d\u662f\u9065\u4e0d\u53ef\u53ca\u7684\u9ad8\u6df1\u77e5\u8bc6\u3002\u5b9e\u9645\u4e0a\uff0c\u6211\u4eec\u5df2\u7ecf\u5728\u4e0d\u77e5\u4e0d\u89c9\u4e2d\u5b66\u4e60\u4e86\u8bb8\u591a\u201c\u7b97\u6cd5\u201d\uff0c\u7528\u4ee5\u89e3\u51b3\u751f\u6d3b\u4e2d\u7684\u5927\u5c0f\u95ee\u9898\u3002</li> <li>\u67e5\u9605\u5b57\u5178\u7684\u539f\u7406\u4e0e\u4e8c\u5206\u67e5\u627e\u7b97\u6cd5\u76f8\u4e00\u81f4\u3002\u4e8c\u5206\u67e5\u627e\u4f53\u73b0\u4e86\u5206\u800c\u6cbb\u4e4b\u7684\u91cd\u8981\u7b97\u6cd5\u601d\u60f3\u3002</li> <li>\u7b97\u6cd5\u662f\u5728\u6709\u9650\u65f6\u95f4\u5185\u89e3\u51b3\u7279\u5b9a\u95ee\u9898\u7684\u4e00\u7ec4\u6307\u4ee4\u6216\u64cd\u4f5c\u6b65\u9aa4\uff0c\u800c\u6570\u636e\u7ed3\u6784\u662f\u8ba1\u7b97\u673a\u4e2d\u7ec4\u7ec7\u548c\u5b58\u50a8\u6570\u636e\u7684\u65b9\u5f0f\u3002</li> <li>\u6570\u636e\u7ed3\u6784\u4e0e\u7b97\u6cd5\u7d27\u5bc6\u76f8\u8fde\u3002\u6570\u636e\u7ed3\u6784\u662f\u7b97\u6cd5\u7684\u57fa\u77f3\uff0c\u800c\u7b97\u6cd5\u5219\u662f\u53d1\u6325\u6570\u636e\u7ed3\u6784\u4f5c\u7528\u7684\u821e\u53f0\u3002</li> <li>\u4e50\u9ad8\u79ef\u6728\u5bf9\u5e94\u4e8e\u6570\u636e\uff0c\u79ef\u6728\u5f62\u72b6\u548c\u8fde\u63a5\u65b9\u5f0f\u4ee3\u8868\u6570\u636e\u7ed3\u6784\uff0c\u62fc\u88c5\u79ef\u6728\u7684\u6b65\u9aa4\u5219\u5bf9\u5e94\u7b97\u6cd5\u3002</li> </ul>"},{"location":"chapter_introduction/what_is_dsa/","title":"1.2. \u00a0 \u7b97\u6cd5\u662f\u4ec0\u4e48","text":""},{"location":"chapter_introduction/what_is_dsa/#121","title":"1.2.1. \u00a0 \u7b97\u6cd5\u5b9a\u4e49","text":"<p>\u300c\u7b97\u6cd5 Algorithm\u300d\u662f\u5728\u6709\u9650\u65f6\u95f4\u5185\u89e3\u51b3\u7279\u5b9a\u95ee\u9898\u7684\u4e00\u7ec4\u6307\u4ee4\u6216\u64cd\u4f5c\u6b65\u9aa4\u3002\u7b97\u6cd5\u5177\u6709\u4ee5\u4e0b\u7279\u6027\uff1a</p> <ul> <li>\u95ee\u9898\u662f\u660e\u786e\u7684\uff0c\u5177\u6709\u6e05\u6670\u7684\u8f93\u5165\u548c\u8f93\u51fa\u5b9a\u4e49\u3002</li> <li>\u89e3\u5177\u6709\u786e\u5b9a\u6027\uff0c\u5373\u7ed9\u5b9a\u76f8\u540c\u7684\u8f93\u5165\u65f6\uff0c\u8f93\u51fa\u59cb\u7ec8\u76f8\u540c\u3002</li> <li>\u5177\u6709\u53ef\u884c\u6027\uff0c\u5728\u6709\u9650\u6b65\u9aa4\u3001\u65f6\u95f4\u548c\u5185\u5b58\u7a7a\u95f4\u4e0b\u53ef\u5b8c\u6210\u3002</li> </ul>"},{"location":"chapter_introduction/what_is_dsa/#122","title":"1.2.2. \u00a0 \u6570\u636e\u7ed3\u6784\u5b9a\u4e49","text":"<p>\u300c\u6570\u636e\u7ed3\u6784 Data Structure\u300d\u662f\u8ba1\u7b97\u673a\u4e2d\u7ec4\u7ec7\u548c\u5b58\u50a8\u6570\u636e\u7684\u65b9\u5f0f\u3002\u4e3a\u4e86\u63d0\u9ad8\u6570\u636e\u5b58\u50a8\u548c\u64cd\u4f5c\u6027\u80fd\uff0c\u6570\u636e\u7ed3\u6784\u7684\u8bbe\u8ba1\u76ee\u6807\u5305\u62ec\uff1a</p> <ul> <li>\u7a7a\u95f4\u5360\u7528\u5c3d\u91cf\u51cf\u5c11\uff0c\u8282\u7701\u8ba1\u7b97\u673a\u5185\u5b58\u3002</li> <li>\u6570\u636e\u64cd\u4f5c\u5c3d\u53ef\u80fd\u5feb\u901f\uff0c\u6db5\u76d6\u6570\u636e\u8bbf\u95ee\u3001\u6dfb\u52a0\u3001\u5220\u9664\u3001\u66f4\u65b0\u7b49\u3002</li> <li>\u63d0\u4f9b\u7b80\u6d01\u7684\u6570\u636e\u8868\u793a\u548c\u903b\u8f91\u4fe1\u606f\uff0c\u4ee5\u5229\u4e8e\u7b97\u6cd5\u9ad8\u6548\u8fd0\u884c\u3002</li> </ul> <p>\u6570\u636e\u7ed3\u6784\u8bbe\u8ba1\u662f\u4e00\u4e2a\u5145\u6ee1\u6743\u8861\u7684\u8fc7\u7a0b\uff0c\u8fd9\u610f\u5473\u7740\u8981\u5728\u67d0\u65b9\u9762\u53d6\u5f97\u4f18\u52bf\uff0c\u5f80\u5f80\u9700\u8981\u5728\u53e6\u4e00\u65b9\u9762\u4f5c\u51fa\u59a5\u534f\u3002\u4f8b\u5982\uff0c\u94fe\u8868\u76f8\u8f83\u4e8e\u6570\u7ec4\uff0c\u5728\u6570\u636e\u6dfb\u52a0\u548c\u5220\u9664\u64cd\u4f5c\u4e0a\u66f4\u52a0\u4fbf\u6377\uff0c\u4f46\u727a\u7272\u4e86\u6570\u636e\u8bbf\u95ee\u901f\u5ea6\uff1b\u56fe\u76f8\u8f83\u4e8e\u94fe\u8868\uff0c\u63d0\u4f9b\u4e86\u66f4\u4e30\u5bcc\u7684\u903b\u8f91\u4fe1\u606f\uff0c\u4f46\u9700\u8981\u5360\u7528\u66f4\u5927\u7684\u5185\u5b58\u7a7a\u95f4\u3002</p>"},{"location":"chapter_introduction/what_is_dsa/#123","title":"1.2.3. \u00a0 \u6570\u636e\u7ed3\u6784\u4e0e\u7b97\u6cd5\u7684\u5173\u7cfb","text":"<p>\u300c\u6570\u636e\u7ed3\u6784\u300d\u4e0e\u300c\u7b97\u6cd5\u300d\u9ad8\u5ea6\u76f8\u5173\u4e14\u7d27\u5bc6\u7ed3\u5408\uff0c\u5177\u4f53\u8868\u73b0\u5728\uff1a</p> <ul> <li>\u6570\u636e\u7ed3\u6784\u662f\u7b97\u6cd5\u7684\u57fa\u77f3\u3002\u6570\u636e\u7ed3\u6784\u4e3a\u7b97\u6cd5\u63d0\u4f9b\u4e86\u7ed3\u6784\u5316\u5b58\u50a8\u7684\u6570\u636e\uff0c\u4ee5\u53ca\u7528\u4e8e\u64cd\u4f5c\u6570\u636e\u7684\u65b9\u6cd5\u3002</li> <li>\u7b97\u6cd5\u662f\u6570\u636e\u7ed3\u6784\u53d1\u6325\u7684\u821e\u53f0\u3002\u6570\u636e\u7ed3\u6784\u672c\u8eab\u4ec5\u5b58\u50a8\u6570\u636e\u4fe1\u606f\uff0c\u901a\u8fc7\u7ed3\u5408\u7b97\u6cd5\u624d\u80fd\u89e3\u51b3\u7279\u5b9a\u95ee\u9898\u3002</li> <li>\u7279\u5b9a\u7b97\u6cd5\u901a\u5e38\u6709\u5bf9\u5e94\u6700\u4f18\u7684\u6570\u636e\u7ed3\u6784\u3002\u7b97\u6cd5\u901a\u5e38\u53ef\u4ee5\u57fa\u4e8e\u4e0d\u540c\u7684\u6570\u636e\u7ed3\u6784\u8fdb\u884c\u5b9e\u73b0\uff0c\u4f46\u6700\u7ec8\u6267\u884c\u6548\u7387\u53ef\u80fd\u76f8\u5dee\u5f88\u5927\u3002</li> </ul> <p></p> <p> Fig. \u6570\u636e\u7ed3\u6784\u4e0e\u7b97\u6cd5\u7684\u5173\u7cfb </p> <p>\u7c7b\u6bd4\u300cLEGO \u4e50\u9ad8\u300d\u548c\u300c\u6570\u636e\u7ed3\u6784\u4e0e\u7b97\u6cd5\u300d\uff0c\u5219\u5bf9\u5e94\u5173\u7cfb\u5982\u4e0b\u8868\u6240\u793a\u3002</p> \u6570\u636e\u7ed3\u6784\u4e0e\u7b97\u6cd5 LEGO \u4e50\u9ad8 \u8f93\u5165\u6570\u636e \u672a\u62fc\u88c5\u7684\u79ef\u6728 \u6570\u636e\u7ed3\u6784 \u79ef\u6728\u7ec4\u7ec7\u5f62\u5f0f\uff0c\u5305\u62ec\u5f62\u72b6\u3001\u5927\u5c0f\u3001\u8fde\u63a5\u65b9\u5f0f\u7b49 \u7b97\u6cd5 \u628a\u79ef\u6728\u62fc\u6210\u76ee\u6807\u5f62\u6001\u7684\u4e00\u7cfb\u5217\u64cd\u4f5c\u6b65\u9aa4 \u8f93\u51fa\u6570\u636e \u79ef\u6728\u6a21\u578b <p>\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u6570\u636e\u7ed3\u6784\u4e0e\u7b97\u6cd5\u72ec\u7acb\u4e8e\u7f16\u7a0b\u8bed\u8a00\u3002\u6b63\u56e0\u5982\u6b64\uff0c\u672c\u4e66\u5f97\u4ee5\u63d0\u4f9b\u591a\u79cd\u7f16\u7a0b\u8bed\u8a00\u7684\u5b9e\u73b0\u3002</p> <p>\u7ea6\u5b9a\u4fd7\u6210\u7684\u7b80\u79f0</p> <p>\u5728\u5b9e\u9645\u8ba8\u8bba\u65f6\uff0c\u6211\u4eec\u901a\u5e38\u4f1a\u5c06\u300c\u6570\u636e\u7ed3\u6784\u4e0e\u7b97\u6cd5\u300d\u7b80\u79f0\u4e3a\u300c\u7b97\u6cd5\u300d\u3002\u4f8b\u5982\uff0c\u4f17\u6240\u5468\u77e5\u7684 LeetCode \u7b97\u6cd5\u9898\u76ee\uff0c\u5b9e\u9645\u4e0a\u540c\u65f6\u8003\u5bdf\u4e86\u6570\u636e\u7ed3\u6784\u548c\u7b97\u6cd5\u4e24\u65b9\u9762\u7684\u77e5\u8bc6\u3002</p>"},{"location":"chapter_preface/","title":"0. \u00a0 \u5199\u5728\u524d\u9762","text":""},{"location":"chapter_preface/about_the_book/","title":"0.1. \u00a0 \u5173\u4e8e\u672c\u4e66","text":"<p>\u672c\u9879\u76ee\u65e8\u5728\u521b\u5efa\u4e00\u672c\u5f00\u6e90\u514d\u8d39\u3001\u65b0\u624b\u53cb\u597d\u7684\u6570\u636e\u7ed3\u6784\u4e0e\u7b97\u6cd5\u5165\u95e8\u6559\u7a0b\u3002</p> <ul> <li>\u5168\u4e66\u91c7\u7528\u52a8\u753b\u56fe\u89e3\uff0c\u7ed3\u6784\u5316\u5730\u8bb2\u89e3\u6570\u636e\u7ed3\u6784\u4e0e\u7b97\u6cd5\u77e5\u8bc6\uff0c\u5185\u5bb9\u6e05\u6670\u6613\u61c2\u3001\u5b66\u4e60\u66f2\u7ebf\u5e73\u6ed1\uff1b</li> <li>\u7b97\u6cd5\u6e90\u4ee3\u7801\u7686\u53ef\u4e00\u952e\u8fd0\u884c\uff0c\u652f\u6301 Java, C++, Python, Go, JS, TS, C#, Swift, Zig \u7b49\u8bed\u8a00\uff1b</li> <li>\u9f13\u52b1\u8bfb\u8005\u5728\u7ae0\u8282\u8ba8\u8bba\u533a\u4e92\u5e2e\u4e92\u52a9\u3001\u5171\u540c\u8fdb\u6b65\uff0c\u63d0\u95ee\u4e0e\u8bc4\u8bba\u901a\u5e38\u53ef\u5728\u4e24\u65e5\u5185\u5f97\u5230\u56de\u590d\uff1b</li> </ul>"},{"location":"chapter_preface/about_the_book/#011","title":"0.1.1. \u00a0 \u8bfb\u8005\u5bf9\u8c61","text":"<p>\u82e5\u60a8\u662f\u300c\u7b97\u6cd5\u521d\u5b66\u8005\u300d\uff0c\u4ece\u672a\u63a5\u89e6\u8fc7\u7b97\u6cd5\uff0c\u6216\u8005\u5df2\u7ecf\u6709\u4e00\u4e9b\u5237\u9898\u7ecf\u9a8c\uff0c\u5bf9\u6570\u636e\u7ed3\u6784\u4e0e\u7b97\u6cd5\u6709\u6a21\u7cca\u7684\u8ba4\u8bc6\uff0c\u5728\u4f1a\u4e0e\u4e0d\u4f1a\u4e4b\u95f4\u53cd\u590d\u6a2a\u8df3\uff0c\u90a3\u4e48\u8fd9\u672c\u4e66\u6b63\u662f\u4e3a\u60a8\u91cf\u8eab\u5b9a\u5236\uff01</p> <p>\u5982\u679c\u60a8\u662f\u300c\u7b97\u6cd5\u8001\u624b\u300d\uff0c\u5df2\u7ecf\u79ef\u7d2f\u4e00\u5b9a\u5237\u9898\u91cf\uff0c\u719f\u6089\u5927\u90e8\u5206\u9898\u578b\uff0c\u90a3\u4e48\u672c\u4e66\u53ef\u52a9\u60a8\u56de\u987e\u4e0e\u68b3\u7406\u7b97\u6cd5\u77e5\u8bc6\u4f53\u7cfb\uff0c\u4ed3\u5e93\u6e90\u4ee3\u7801\u53ef\u4ee5\u88ab\u5f53\u4f5c\u201c\u5237\u9898\u5de5\u5177\u5e93\u201d\u6216\u201c\u7b97\u6cd5\u5b57\u5178\u201d\u6765\u4f7f\u7528\u3002</p> <p>\u82e5\u60a8\u662f\u300c\u7b97\u6cd5\u4e13\u5bb6\u300d\uff0c\u6211\u4eec\u671f\u5f85\u6536\u5230\u60a8\u7684\u5b9d\u8d35\u5efa\u8bae\uff0c\u6216\u8005\u4e00\u8d77\u53c2\u4e0e\u521b\u4f5c\u3002</p> <p>\u524d\u7f6e\u6761\u4ef6</p> <p>\u60a8\u9700\u8981\u81f3\u5c11\u5177\u5907\u4efb\u4e00\u8bed\u8a00\u7684\u7f16\u7a0b\u57fa\u7840\uff0c\u80fd\u591f\u9605\u8bfb\u548c\u7f16\u5199\u7b80\u5355\u4ee3\u7801\u3002</p>"},{"location":"chapter_preface/about_the_book/#012","title":"0.1.2. \u00a0 \u5185\u5bb9\u7ed3\u6784","text":"<p>\u672c\u4e66\u4e3b\u8981\u5185\u5bb9\u5305\u62ec\uff1a</p> <ul> <li>\u590d\u6742\u5ea6\u5206\u6790\uff1a\u6570\u636e\u7ed3\u6784\u4e0e\u7b97\u6cd5\u7684\u8bc4\u4ef7\u7ef4\u5ea6\u3001\u7b97\u6cd5\u6548\u7387\u7684\u8bc4\u4f30\u65b9\u6cd5\u3002\u65f6\u95f4\u590d\u6742\u5ea6\u3001\u7a7a\u95f4\u590d\u6742\u5ea6\uff0c\u5305\u62ec\u63a8\u7b97\u65b9\u6cd5\u3001\u5e38\u89c1\u7c7b\u578b\u3001\u793a\u4f8b\u7b49\u3002</li> <li>\u6570\u636e\u7ed3\u6784\uff1a\u5e38\u89c1\u57fa\u672c\u6570\u636e\u7c7b\u578b\uff0c\u6570\u636e\u5728\u5185\u5b58\u4e2d\u7684\u5b58\u50a8\u5f62\u5f0f\u3001\u6570\u636e\u7ed3\u6784\u7684\u5206\u7c7b\u65b9\u6cd5\u3002\u6d89\u53ca\u6570\u7ec4\u3001\u94fe\u8868\u3001\u6808\u3001\u961f\u5217\u3001\u6563\u5217\u8868\u3001\u6811\u3001\u5806\u3001\u56fe\u7b49\u6570\u636e\u7ed3\u6784\uff0c\u5185\u5bb9\u5305\u62ec\u5b9a\u4e49\u3001\u4f18\u7f3a\u70b9\u3001\u5e38\u7528\u64cd\u4f5c\u3001\u5e38\u89c1\u7c7b\u578b\u3001\u5178\u578b\u5e94\u7528\u3001\u5b9e\u73b0\u65b9\u6cd5\u7b49\u3002</li> <li>\u7b97\u6cd5\uff1a\u67e5\u627e\u7b97\u6cd5\u3001\u6392\u5e8f\u7b97\u6cd5\u3001\u641c\u7d22\u4e0e\u56de\u6eaf\u3001\u52a8\u6001\u89c4\u5212\u3001\u5206\u6cbb\u7b97\u6cd5\u7b49\uff0c\u5185\u5bb9\u6db5\u76d6\u5b9a\u4e49\u3001\u5e94\u7528\u573a\u666f\u3001\u4f18\u7f3a\u70b9\u3001\u65f6\u7a7a\u6548\u7387\u3001\u5b9e\u73b0\u65b9\u6cd5\u3001\u793a\u4f8b\u9898\u76ee\u7b49\u3002</li> </ul> <p></p> <p> Fig. Hello \u7b97\u6cd5\u5185\u5bb9\u7ed3\u6784 </p>"},{"location":"chapter_preface/about_the_book/#013","title":"0.1.3. \u00a0 \u81f4\u8c22","text":"<p>\u5728\u672c\u4e66\u7684\u521b\u4f5c\u8fc7\u7a0b\u4e2d\uff0c\u6211\u5f97\u5230\u4e86\u8bb8\u591a\u4eba\u7684\u5e2e\u52a9\uff0c\u5305\u62ec\u4f46\u4e0d\u9650\u4e8e\uff1a</p> <ul> <li>\u611f\u8c22\u6211\u5728\u516c\u53f8\u7684\u5bfc\u5e08\u674e\u6c50\u535a\u58eb\uff0c\u5728\u6df1\u5165\u4ea4\u8c08\u4e2d\u60a8\u9f13\u52b1\u6211\u201c\u884c\u52a8\u8d77\u6765\u201d\uff0c\u575a\u5b9a\u4e86\u6211\u5199\u8fd9\u672c\u4e66\u7684\u51b3\u5fc3\u3002</li> <li>\u611f\u8c22\u6211\u7684\u5973\u670b\u53cb\u6ce1\u6ce1\u4f5c\u4e3a\u672c\u4e66\u7684\u9996\u4f4d\u8bfb\u8005\uff0c\u4ece\u7b97\u6cd5\u5c0f\u767d\u7684\u89d2\u5ea6\u63d0\u51fa\u8bb8\u591a\u5b9d\u8d35\u5efa\u8bae\uff0c\u4f7f\u5f97\u672c\u4e66\u66f4\u9002\u5408\u65b0\u624b\u9605\u8bfb\u3002</li> <li>\u611f\u8c22\u817e\u5b9d\u3001\u7426\u5b9d\u3001\u98de\u5b9d\u4e3a\u672c\u4e66\u8d77\u4e86\u4e00\u4e2a\u5bcc\u6709\u521b\u610f\u7684\u540d\u5b57\uff0c\u5524\u8d77\u5927\u5bb6\u5199\u4e0b\u7b2c\u4e00\u884c\u4ee3\u7801 \"Hello World!\" \u7684\u7f8e\u597d\u56de\u5fc6\u3002</li> <li>\u611f\u8c22\u82cf\u6f7c\u4e3a\u672c\u4e66\u8bbe\u8ba1\u4e86\u7cbe\u7f8e\u7684\u5c01\u9762\u548c LOGO\uff0c\u5e76\u5728\u6211\u7684\u5f3a\u8feb\u75c7\u4e0b\u591a\u6b21\u8010\u5fc3\u4fee\u6539\u3002</li> <li>\u611f\u8c22 @squidfunk \u63d0\u4f9b\u7684\u5199\u4f5c\u6392\u7248\u5efa\u8bae\uff0c\u4ee5\u53ca\u6770\u51fa\u7684\u5f00\u6e90\u9879\u76ee Material-for-MkDocs \u3002</li> </ul> <p>\u5728\u5199\u4f5c\u8fc7\u7a0b\u4e2d\uff0c\u6211\u9605\u8bfb\u4e86\u8bb8\u591a\u5173\u4e8e\u6570\u636e\u7ed3\u6784\u4e0e\u7b97\u6cd5\u7684\u6559\u6750\u548c\u6587\u7ae0\u3002\u8fd9\u4e9b\u4f5c\u54c1\u4e3a\u672c\u4e66\u63d0\u4f9b\u4e86\u4f18\u79c0\u7684\u8303\u672c\uff0c\u786e\u4fdd\u4e86\u672c\u4e66\u5185\u5bb9\u7684\u51c6\u786e\u6027\u4e0e\u54c1\u8d28\u3002\u5728\u6b64\u611f\u8c22\u6240\u6709\u8001\u5e08\u548c\u524d\u8f88\u4eec\u7684\u6770\u51fa\u8d21\u732e\uff01</p> <p>\u672c\u4e66\u5021\u5bfc\u624b\u8111\u5e76\u7528\u7684\u5b66\u4e60\u65b9\u5f0f\uff0c\u5728\u8fd9\u4e00\u70b9\u4e0a\u6df1\u53d7\u300a\u52a8\u624b\u5b66\u6df1\u5ea6\u5b66\u4e60\u300b\u7684\u542f\u53d1\u3002\u5728\u6b64\u5411\u5404\u4f4d\u8bfb\u8005\u5f3a\u70c8\u63a8\u8350\u8fd9\u672c\u4f18\u79c0\u8457\u4f5c\u3002</p> <p>\u8877\u5fc3\u611f\u8c22\u6211\u7684\u7236\u6bcd\uff0c\u6b63\u662f\u4f60\u4eec\u4e00\u76f4\u4ee5\u6765\u7684\u652f\u6301\u4e0e\u9f13\u52b1\uff0c\u8ba9\u6211\u6709\u673a\u4f1a\u505a\u8fd9\u4e9b\u5bcc\u6709\u8da3\u5473\u7684\u4e8b\u3002</p>"},{"location":"chapter_preface/suggestions/","title":"0.2. \u00a0 \u5982\u4f55\u4f7f\u7528\u672c\u4e66","text":"<p>Tip</p> <p>\u4e3a\u4e86\u83b7\u5f97\u6700\u4f73\u7684\u9605\u8bfb\u4f53\u9a8c\uff0c\u5efa\u8bae\u60a8\u901a\u8bfb\u672c\u8282\u5185\u5bb9\u3002</p>"},{"location":"chapter_preface/suggestions/#021","title":"0.2.1. \u00a0 \u884c\u6587\u98ce\u683c\u7ea6\u5b9a","text":"<p>\u6807\u9898\u540e\u6807\u6ce8 <code>*</code> \u7684\u662f\u9009\u8bfb\u7ae0\u8282\uff0c\u5185\u5bb9\u76f8\u5bf9\u56f0\u96be\u3002\u5982\u679c\u4f60\u7684\u65f6\u95f4\u6709\u9650\uff0c\u5efa\u8bae\u53ef\u4ee5\u5148\u8df3\u8fc7\u3002</p> <p>\u6587\u7ae0\u4e2d\u7684\u91cd\u8981\u540d\u8bcd\u4f1a\u7528 <code>\u300c \u300d</code> \u62ec\u53f7\u6807\u6ce8\uff0c\u4f8b\u5982 <code>\u300c\u6570\u7ec4 Array\u300d</code> \u3002\u8bf7\u52a1\u5fc5\u8bb0\u4f4f\u8fd9\u4e9b\u540d\u8bcd\uff0c\u5305\u62ec\u82f1\u6587\u7ffb\u8bd1\uff0c\u4ee5\u4fbf\u540e\u7eed\u9605\u8bfb\u6587\u732e\u65f6\u4f7f\u7528\u3002</p> <p>\u52a0\u7c97\u7684\u6587\u5b57 \u8868\u793a\u91cd\u70b9\u5185\u5bb9\u6216\u603b\u7ed3\u6027\u8bed\u53e5\uff0c\u8fd9\u7c7b\u6587\u5b57\u503c\u5f97\u7279\u522b\u5173\u6ce8\u3002</p> <p>\u4e13\u6709\u540d\u8bcd\u548c\u6709\u7279\u6307\u542b\u4e49\u7684\u8bcd\u53e5\u4f1a\u4f7f\u7528 <code>\u201c\u53cc\u5f15\u53f7\u201d</code> \u6807\u6ce8\uff0c\u4ee5\u907f\u514d\u6b67\u4e49\u3002</p> <p>\u672c\u4e66\u90e8\u5206\u653e\u5f03\u4e86\u7f16\u7a0b\u8bed\u8a00\u7684\u6ce8\u91ca\u89c4\u8303\uff0c\u4ee5\u6362\u53d6\u66f4\u52a0\u7d27\u51d1\u7684\u5185\u5bb9\u6392\u7248\u3002\u6ce8\u91ca\u4e3b\u8981\u5206\u4e3a\u4e09\u79cd\u7c7b\u578b\uff1a\u6807\u9898\u6ce8\u91ca\u3001\u5185\u5bb9\u6ce8\u91ca\u3001\u591a\u884c\u6ce8\u91ca\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart <pre><code>/* \u6807\u9898\u6ce8\u91ca\uff0c\u7528\u4e8e\u6807\u6ce8\u51fd\u6570\u3001\u7c7b\u3001\u6d4b\u8bd5\u6837\u4f8b\u7b49 */\n// \u5185\u5bb9\u6ce8\u91ca\uff0c\u7528\u4e8e\u8be6\u89e3\u4ee3\u7801\n/**\n * \u591a\u884c\n * \u6ce8\u91ca\n */\n</code></pre> <pre><code>/* \u6807\u9898\u6ce8\u91ca\uff0c\u7528\u4e8e\u6807\u6ce8\u51fd\u6570\u3001\u7c7b\u3001\u6d4b\u8bd5\u6837\u4f8b\u7b49 */\n// \u5185\u5bb9\u6ce8\u91ca\uff0c\u7528\u4e8e\u8be6\u89e3\u4ee3\u7801\n/**\n * \u591a\u884c\n * \u6ce8\u91ca\n */\n</code></pre> <pre><code>\"\"\"\u6807\u9898\u6ce8\u91ca\uff0c\u7528\u4e8e\u6807\u6ce8\u51fd\u6570\u3001\u7c7b\u3001\u6d4b\u8bd5\u6837\u4f8b\u7b49\"\"\"\n# \u5185\u5bb9\u6ce8\u91ca\uff0c\u7528\u4e8e\u8be6\u89e3\u4ee3\u7801\n\"\"\"\n\u591a\u884c\n\u6ce8\u91ca\n\"\"\"\n</code></pre> <pre><code>/* \u6807\u9898\u6ce8\u91ca\uff0c\u7528\u4e8e\u6807\u6ce8\u51fd\u6570\u3001\u7c7b\u3001\u6d4b\u8bd5\u6837\u4f8b\u7b49 */\n// \u5185\u5bb9\u6ce8\u91ca\uff0c\u7528\u4e8e\u8be6\u89e3\u4ee3\u7801\n/**\n * \u591a\u884c\n * \u6ce8\u91ca\n */\n</code></pre> <pre><code>/* \u6807\u9898\u6ce8\u91ca\uff0c\u7528\u4e8e\u6807\u6ce8\u51fd\u6570\u3001\u7c7b\u3001\u6d4b\u8bd5\u6837\u4f8b\u7b49 */\n// \u5185\u5bb9\u6ce8\u91ca\uff0c\u7528\u4e8e\u8be6\u89e3\u4ee3\u7801\n/**\n * \u591a\u884c\n * \u6ce8\u91ca\n */\n</code></pre> <pre><code>/* \u6807\u9898\u6ce8\u91ca\uff0c\u7528\u4e8e\u6807\u6ce8\u51fd\u6570\u3001\u7c7b\u3001\u6d4b\u8bd5\u6837\u4f8b\u7b49 */\n// \u5185\u5bb9\u6ce8\u91ca\uff0c\u7528\u4e8e\u8be6\u89e3\u4ee3\u7801\n/**\n * \u591a\u884c\n * \u6ce8\u91ca\n */\n</code></pre> <pre><code>/* \u6807\u9898\u6ce8\u91ca\uff0c\u7528\u4e8e\u6807\u6ce8\u51fd\u6570\u3001\u7c7b\u3001\u6d4b\u8bd5\u6837\u4f8b\u7b49 */\n// \u5185\u5bb9\u6ce8\u91ca\uff0c\u7528\u4e8e\u8be6\u89e3\u4ee3\u7801\n/**\n * \u591a\u884c\n * \u6ce8\u91ca\n */\n</code></pre> <pre><code>/* \u6807\u9898\u6ce8\u91ca\uff0c\u7528\u4e8e\u6807\u6ce8\u51fd\u6570\u3001\u7c7b\u3001\u6d4b\u8bd5\u6837\u4f8b\u7b49 */\n// \u5185\u5bb9\u6ce8\u91ca\uff0c\u7528\u4e8e\u8be6\u89e3\u4ee3\u7801\n/**\n * \u591a\u884c\n * \u6ce8\u91ca\n */\n</code></pre> <pre><code>/* \u6807\u9898\u6ce8\u91ca\uff0c\u7528\u4e8e\u6807\u6ce8\u51fd\u6570\u3001\u7c7b\u3001\u6d4b\u8bd5\u6837\u4f8b\u7b49 */\n// \u5185\u5bb9\u6ce8\u91ca\uff0c\u7528\u4e8e\u8be6\u89e3\u4ee3\u7801\n/**\n * \u591a\u884c\n * \u6ce8\u91ca\n */\n</code></pre> <pre><code>// \u6807\u9898\u6ce8\u91ca\uff0c\u7528\u4e8e\u6807\u6ce8\u51fd\u6570\u3001\u7c7b\u3001\u6d4b\u8bd5\u6837\u4f8b\u7b49\n// \u5185\u5bb9\u6ce8\u91ca\uff0c\u7528\u4e8e\u8be6\u89e3\u4ee3\u7801\n// \u591a\u884c\n// \u6ce8\u91ca\n</code></pre> <pre><code>/* \u6807\u9898\u6ce8\u91ca\uff0c\u7528\u4e8e\u6807\u6ce8\u51fd\u6570\u3001\u7c7b\u3001\u6d4b\u8bd5\u6837\u4f8b\u7b49 */\n// \u5185\u5bb9\u6ce8\u91ca\uff0c\u7528\u4e8e\u8be6\u89e3\u4ee3\u7801\n/**\n * \u591a\u884c\n * \u6ce8\u91ca\n */\n</code></pre>"},{"location":"chapter_preface/suggestions/#022","title":"0.2.2. \u00a0 \u5728\u52a8\u753b\u56fe\u89e3\u4e2d\u9ad8\u6548\u5b66\u4e60","text":"<p>\u76f8\u8f83\u4e8e\u6587\u5b57\uff0c\u89c6\u9891\u548c\u56fe\u7247\u5177\u6709\u66f4\u9ad8\u7684\u4fe1\u606f\u5bc6\u5ea6\u548c\u7ed3\u6784\u5316\u7a0b\u5ea6\uff0c\u56e0\u6b64\u66f4\u6613\u4e8e\u7406\u89e3\u3002\u5728\u672c\u4e66\u4e2d\uff0c\u91cd\u70b9\u548c\u96be\u70b9\u77e5\u8bc6\u5c06\u4e3b\u8981\u901a\u8fc7\u52a8\u753b\u548c\u56fe\u89e3\u5f62\u5f0f\u5c55\u793a\uff0c\u800c\u6587\u5b57\u5219\u4f5c\u4e3a\u52a8\u753b\u548c\u56fe\u7247\u7684\u89e3\u91ca\u4e0e\u8865\u5145\u3002</p> <p>\u5728\u9605\u8bfb\u672c\u4e66\u65f6\uff0c\u5982\u679c\u53d1\u73b0\u67d0\u6bb5\u5185\u5bb9\u63d0\u4f9b\u4e86\u52a8\u753b\u6216\u56fe\u89e3\uff0c\u5efa\u8bae\u4ee5\u56fe\u4e3a\u4e3b\u7ebf\uff0c\u4ee5\u6587\u5b57\uff08\u901a\u5e38\u4f4d\u4e8e\u56fe\u50cf\u4e0a\u65b9\uff09\u4e3a\u8f85\uff0c\u7efc\u5408\u4e24\u8005\u6765\u7406\u89e3\u5185\u5bb9\u3002</p> <p></p> <p> Fig. \u52a8\u753b\u56fe\u89e3\u793a\u4f8b </p>"},{"location":"chapter_preface/suggestions/#023","title":"0.2.3. \u00a0 \u5728\u4ee3\u7801\u5b9e\u8df5\u4e2d\u52a0\u6df1\u7406\u89e3","text":"<p>\u672c\u4e66\u7684\u914d\u5957\u4ee3\u7801\u6258\u7ba1\u5728GitHub \u4ed3\u5e93\uff0c\u6e90\u4ee3\u7801\u5305\u542b\u8be6\u7ec6\u6ce8\u91ca\uff0c\u5e76\u9644\u6709\u6d4b\u8bd5\u6837\u4f8b\uff0c\u53ef\u76f4\u63a5\u8fd0\u884c\u3002</p> <p>\u5982\u679c\u5b66\u4e60\u65f6\u95f4\u6709\u9650\uff0c\u5efa\u8bae\u4f60\u81f3\u5c11\u901a\u8bfb\u5e76\u8fd0\u884c\u6240\u6709\u4ee3\u7801\u3002\u5982\u679c\u65f6\u95f4\u5145\u88d5\uff0c\u5efa\u8bae\u53c2\u7167\u4ee3\u7801\u81ea\u884c\u6572\u4e00\u904d\u3002\u4e0e\u4ec5\u9605\u8bfb\u4ee3\u7801\u76f8\u6bd4\uff0c\u7f16\u5199\u4ee3\u7801\u7684\u8fc7\u7a0b\u5f80\u5f80\u80fd\u5e26\u6765\u66f4\u591a\u6536\u83b7\u3002</p> <p></p> <p> Fig. \u8fd0\u884c\u4ee3\u7801\u793a\u4f8b </p> <p>\u7b2c\u4e00\u6b65\uff1a\u5b89\u88c5\u672c\u5730\u7f16\u7a0b\u73af\u5883\u3002\u8bf7\u53c2\u7167\u9644\u5f55\u6559\u7a0b\u8fdb\u884c\u5b89\u88c5\uff0c\u5982\u679c\u5df2\u5b89\u88c5\u5219\u53ef\u8df3\u8fc7\u6b64\u6b65\u9aa4\u3002</p> <p>\u7b2c\u4e8c\u6b65\uff1a\u4e0b\u8f7d\u4ee3\u7801\u4ed3\u3002\u5982\u679c\u5df2\u7ecf\u5b89\u88c5 Git \uff0c\u53ef\u4ee5\u901a\u8fc7\u4ee5\u4e0b\u547d\u4ee4\u514b\u9686\u672c\u4ed3\u5e93\u3002</p> <pre><code>git clone https://github.com/krahets/hello-algo.git\n</code></pre> <p>\u5f53\u7136\uff0c\u4f60\u4e5f\u53ef\u4ee5\u70b9\u51fb\u201cDownload ZIP\u201d\u76f4\u63a5\u4e0b\u8f7d\u4ee3\u7801\u538b\u7f29\u5305\uff0c\u7136\u540e\u5728\u672c\u5730\u89e3\u538b\u5373\u53ef\u3002</p> <p></p> <p> Fig. \u514b\u9686\u4ed3\u5e93\u4e0e\u4e0b\u8f7d\u4ee3\u7801 </p> <p>\u7b2c\u4e09\u6b65\uff1a\u8fd0\u884c\u6e90\u4ee3\u7801\u3002\u5982\u679c\u4ee3\u7801\u5757\u9876\u90e8\u6807\u6709\u6587\u4ef6\u540d\u79f0\uff0c\u5219\u53ef\u4ee5\u5728\u4ed3\u5e93\u7684 <code>codes</code> \u6587\u4ef6\u5939\u4e2d\u627e\u5230\u76f8\u5e94\u7684\u6e90\u4ee3\u7801\u6587\u4ef6\u3002\u6e90\u4ee3\u7801\u6587\u4ef6\u5c06\u5e2e\u52a9\u4f60\u8282\u7701\u4e0d\u5fc5\u8981\u7684\u8c03\u8bd5\u65f6\u95f4\uff0c\u8ba9\u4f60\u80fd\u591f\u4e13\u6ce8\u4e8e\u5b66\u4e60\u5185\u5bb9\u3002</p> <p></p> <p> Fig. \u4ee3\u7801\u5757\u4e0e\u5bf9\u5e94\u7684\u6e90\u4ee3\u7801\u6587\u4ef6 </p>"},{"location":"chapter_preface/suggestions/#024","title":"0.2.4. \u00a0 \u5728\u63d0\u95ee\u8ba8\u8bba\u4e2d\u5171\u540c\u6210\u957f","text":"<p>\u9605\u8bfb\u672c\u4e66\u65f6\uff0c\u8bf7\u4e0d\u8981\u201c\u60ef\u7740\u201d\u90a3\u4e9b\u6ca1\u5b66\u660e\u767d\u7684\u77e5\u8bc6\u70b9\u3002\u6b22\u8fce\u5728\u8bc4\u8bba\u533a\u63d0\u51fa\u4f60\u7684\u95ee\u9898\uff0c\u6211\u548c\u5176\u4ed6\u5c0f\u4f19\u4f34\u4eec\u5c06\u7aed\u8bda\u4e3a\u4f60\u89e3\u7b54\uff0c\u4e00\u822c\u60c5\u51b5\u4e0b\u53ef\u5728\u4e24\u5929\u5185\u5f97\u5230\u56de\u590d\u3002</p> <p>\u540c\u65f6\uff0c\u4e5f\u5e0c\u671b\u60a8\u80fd\u5728\u8bc4\u8bba\u533a\u591a\u82b1\u4e9b\u65f6\u95f4\u3002\u4e00\u65b9\u9762\uff0c\u60a8\u53ef\u4ee5\u4e86\u89e3\u5927\u5bb6\u9047\u5230\u7684\u95ee\u9898\uff0c\u4ece\u800c\u67e5\u6f0f\u8865\u7f3a\uff0c\u8fd9\u5c06\u6709\u52a9\u4e8e\u6fc0\u53d1\u66f4\u6df1\u5165\u7684\u601d\u8003\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u5e0c\u671b\u60a8\u80fd\u6177\u6168\u5730\u56de\u7b54\u5176\u4ed6\u5c0f\u4f19\u4f34\u7684\u95ee\u9898\u3001\u5206\u4eab\u60a8\u7684\u89c1\u89e3\uff0c\u8ba9\u5927\u5bb6\u5171\u540c\u5b66\u4e60\u548c\u8fdb\u6b65\u3002</p> <p></p> <p> Fig. \u8bc4\u8bba\u533a\u793a\u4f8b </p>"},{"location":"chapter_preface/suggestions/#025","title":"0.2.5. \u00a0 \u7b97\u6cd5\u5b66\u4e60\u8def\u7ebf","text":"<p>\u4ece\u603b\u4f53\u4e0a\u770b\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u5b66\u4e60\u6570\u636e\u7ed3\u6784\u4e0e\u7b97\u6cd5\u7684\u8fc7\u7a0b\u5212\u5206\u4e3a\u4e09\u4e2a\u9636\u6bb5\uff1a</p> <ol> <li>\u7b97\u6cd5\u5165\u95e8\u3002\u6211\u4eec\u9700\u8981\u719f\u6089\u5404\u79cd\u6570\u636e\u7ed3\u6784\u7684\u7279\u70b9\u548c\u7528\u6cd5\uff0c\u5b66\u4e60\u4e0d\u540c\u7b97\u6cd5\u7684\u539f\u7406\u3001\u6d41\u7a0b\u3001\u7528\u9014\u548c\u6548\u7387\u7b49\u65b9\u9762\u5185\u5bb9\u3002</li> <li>\u5237\u7b97\u6cd5\u9898\u3002\u5efa\u8bae\u4ece\u70ed\u95e8\u9898\u76ee\u5f00\u5237\uff0c\u5982\u5251\u6307 Offer\u548cLeetCode Hot 100\uff0c\u5148\u79ef\u7d2f\u81f3\u5c11 100 \u9053\u9898\u76ee\uff0c\u719f\u6089\u4e3b\u6d41\u7684\u7b97\u6cd5\u95ee\u9898\u3002\u521d\u6b21\u5237\u9898\u65f6\uff0c\u201c\u77e5\u8bc6\u9057\u5fd8\u201d\u53ef\u80fd\u662f\u4e00\u4e2a\u6311\u6218\uff0c\u4f46\u8bf7\u653e\u5fc3\uff0c\u8fd9\u662f\u5f88\u6b63\u5e38\u7684\u3002\u6211\u4eec\u53ef\u4ee5\u6309\u7167\u201c\u827e\u5bbe\u6d69\u65af\u9057\u5fd8\u66f2\u7ebf\u201d\u6765\u590d\u4e60\u9898\u76ee\uff0c\u901a\u5e38\u5728\u8fdb\u884c 3-5 \u8f6e\u7684\u91cd\u590d\u540e\uff0c\u5c31\u80fd\u5c06\u5176\u7262\u8bb0\u5728\u5fc3\u3002</li> <li>\u642d\u5efa\u77e5\u8bc6\u4f53\u7cfb\u3002\u5728\u5b66\u4e60\u65b9\u9762\uff0c\u6211\u4eec\u53ef\u4ee5\u9605\u8bfb\u7b97\u6cd5\u4e13\u680f\u6587\u7ae0\u3001\u89e3\u9898\u6846\u67b6\u548c\u7b97\u6cd5\u6559\u6750\uff0c\u4ee5\u4e0d\u65ad\u4e30\u5bcc\u77e5\u8bc6\u4f53\u7cfb\u3002\u5728\u5237\u9898\u65b9\u9762\uff0c\u53ef\u4ee5\u5c1d\u8bd5\u91c7\u7528\u8fdb\u9636\u5237\u9898\u7b56\u7565\uff0c\u5982\u6309\u4e13\u9898\u5206\u7c7b\u3001\u4e00\u9898\u591a\u89e3\u3001\u4e00\u89e3\u591a\u9898\u7b49\uff0c\u76f8\u5173\u7684\u5237\u9898\u5fc3\u5f97\u53ef\u4ee5\u5728\u5404\u4e2a\u793e\u533a\u627e\u5230\u3002</li> </ol> <p>\u4f5c\u4e3a\u4e00\u672c\u5165\u95e8\u6559\u7a0b\uff0c\u672c\u4e66\u5185\u5bb9\u4e3b\u8981\u6db5\u76d6\u201c\u7b2c\u4e00\u9636\u6bb5\u201d\uff0c\u65e8\u5728\u5e2e\u52a9\u4f60\u66f4\u9ad8\u6548\u5730\u5c55\u5f00\u7b2c\u4e8c\u548c\u7b2c\u4e09\u9636\u6bb5\u7684\u5b66\u4e60\u3002</p> <p></p> <p> Fig. \u7b97\u6cd5\u5b66\u4e60\u8def\u7ebf </p>"},{"location":"chapter_preface/summary/","title":"0.3. \u00a0 \u5c0f\u7ed3","text":"<ul> <li>\u672c\u4e66\u7684\u4e3b\u8981\u53d7\u4f17\u662f\u7b97\u6cd5\u521d\u5b66\u8005\u3002\u5982\u679c\u5df2\u6709\u4e00\u5b9a\u57fa\u7840\uff0c\u672c\u4e66\u80fd\u5e2e\u52a9\u60a8\u7cfb\u7edf\u56de\u987e\u7b97\u6cd5\u77e5\u8bc6\uff0c\u4e66\u5185\u6e90\u4ee3\u7801\u4e5f\u53ef\u4f5c\u4e3a\u201c\u5237\u9898\u5de5\u5177\u5e93\u201d\u4f7f\u7528\u3002</li> <li>\u4e66\u4e2d\u5185\u5bb9\u4e3b\u8981\u5305\u62ec\u590d\u6742\u5ea6\u5206\u6790\u3001\u6570\u636e\u7ed3\u6784\u3001\u7b97\u6cd5\u4e09\u90e8\u5206\uff0c\u6db5\u76d6\u4e86\u8be5\u9886\u57df\u7684\u5927\u90e8\u5206\u4e3b\u9898\u3002</li> <li>\u5bf9\u4e8e\u7b97\u6cd5\u65b0\u624b\uff0c\u5728\u521d\u5b66\u9636\u6bb5\u9605\u8bfb\u4e00\u672c\u5165\u95e8\u4e66\u7c4d\u81f3\u5173\u91cd\u8981\uff0c\u53ef\u4ee5\u5c11\u8d70\u8bb8\u591a\u5f2f\u8def\u3002</li> <li>\u4e66\u5185\u7684\u52a8\u753b\u548c\u56fe\u89e3\u901a\u5e38\u7528\u4e8e\u4ecb\u7ecd\u91cd\u70b9\u548c\u96be\u70b9\u77e5\u8bc6\u3002\u9605\u8bfb\u672c\u4e66\u65f6\uff0c\u5e94\u7ed9\u4e88\u8fd9\u4e9b\u5185\u5bb9\u66f4\u591a\u5173\u6ce8\u3002</li> <li>\u5b9e\u8df5\u4e43\u5b66\u4e60\u7f16\u7a0b\u4e4b\u6700\u4f73\u9014\u5f84\u3002\u5f3a\u70c8\u5efa\u8bae\u8fd0\u884c\u6e90\u4ee3\u7801\u5e76\u4eb2\u81ea\u6572\u6253\u4ee3\u7801\u3002</li> <li>\u672c\u4e66\u7f51\u9875\u7248\u7684\u6bcf\u4e2a\u7ae0\u8282\u90fd\u8bbe\u6709\u8ba8\u8bba\u533a\uff0c\u6b22\u8fce\u968f\u65f6\u5206\u4eab\u4f60\u7684\u7591\u60d1\u4e0e\u89c1\u89e3\u3002</li> </ul>"},{"location":"chapter_reference/","title":"\u53c2\u8003\u6587\u732e","text":"<p>[1] Thomas H. Cormen, et al. Introduction to Algorithms (3rd Edition).</p> <p>[2] Aditya Bhargava. Grokking Algorithms: An Illustrated Guide for Programmers and Other Curious People (1st Edition).</p> <p>[3] \u4e25\u851a\u654f. \u6570\u636e\u7ed3\u6784\uff08C \u8bed\u8a00\u7248\uff09.</p> <p>[4] \u9093\u4fca\u8f89. \u6570\u636e\u7ed3\u6784\uff08C++ \u8bed\u8a00\u7248\uff0c\u7b2c\u4e09\u7248\uff09.</p> <p>[5] \u9a6c\u514b \u827e\u4f26 \u7ef4\u65af\u8457\uff0c\u9648\u8d8a\u8bd1. \u6570\u636e\u7ed3\u6784\u4e0e\u7b97\u6cd5\u5206\u6790\uff1aJava\u8bed\u8a00\u63cf\u8ff0\uff08\u7b2c\u4e09\u7248\uff09.</p> <p>[6] \u7a0b\u6770. \u5927\u8bdd\u6570\u636e\u7ed3\u6784.</p> <p>[7] \u738b\u4e89. \u6570\u636e\u7ed3\u6784\u4e0e\u7b97\u6cd5\u4e4b\u7f8e.</p> <p>[8] Gayle Laakmann McDowell. Cracking the Coding Interview: 189 Programming Questions and Solutions (6th Edition). </p> <p>[9] Aston Zhang, et al. Dive into Deep Learning.</p>"},{"location":"chapter_searching/","title":"10. \u00a0 \u641c\u7d22","text":""},{"location":"chapter_searching/binary_search/","title":"10.1. \u00a0 \u4e8c\u5206\u67e5\u627e","text":"<p>\u300c\u4e8c\u5206\u67e5\u627e Binary Search\u300d\u662f\u4e00\u79cd\u57fa\u4e8e\u5206\u6cbb\u601d\u60f3\u7684\u9ad8\u6548\u641c\u7d22\u7b97\u6cd5\u3002\u5b83\u5229\u7528\u6570\u636e\u7684\u6709\u5e8f\u6027\uff0c\u6bcf\u8f6e\u51cf\u5c11\u4e00\u534a\u641c\u7d22\u8303\u56f4\uff0c\u76f4\u81f3\u627e\u5230\u76ee\u6807\u5143\u7d20\u6216\u641c\u7d22\u533a\u95f4\u4e3a\u7a7a\u4e3a\u6b62\u3002</p> <p>Question</p> <p>\u7ed9\u5b9a\u4e00\u4e2a\u957f\u5ea6\u4e3a \\(n\\) \u7684\u6570\u7ec4 <code>nums</code> \uff0c\u5143\u7d20\u6309\u4ece\u5c0f\u5230\u5927\u7684\u987a\u5e8f\u6392\u5217\uff0c\u6570\u7ec4\u4e0d\u5305\u542b\u91cd\u590d\u5143\u7d20\u3002\u8bf7\u67e5\u627e\u5e76\u8fd4\u56de\u5143\u7d20 <code>target</code> \u5728\u8be5\u6570\u7ec4\u4e2d\u7684\u7d22\u5f15\u3002\u82e5\u6570\u7ec4\u4e0d\u5305\u542b\u8be5\u5143\u7d20\uff0c\u5219\u8fd4\u56de \\(-1\\) \u3002</p> <p>\u5bf9\u4e8e\u4e0a\u8ff0\u95ee\u9898\uff0c\u6211\u4eec\u5148\u521d\u59cb\u5316\u6307\u9488 \\(i = 0\\) \u548c \\(j = n - 1\\) \uff0c\u5206\u522b\u6307\u5411\u6570\u7ec4\u9996\u5143\u7d20\u548c\u5c3e\u5143\u7d20\uff0c\u4ee3\u8868\u641c\u7d22\u533a\u95f4 \\([0, n - 1]\\) \u3002\u5176\u4e2d\uff0c\u4e2d\u62ec\u53f7\u8868\u793a\u201c\u95ed\u533a\u95f4\u201d\uff0c\u5373\u5305\u542b\u8fb9\u754c\u503c\u672c\u8eab\u3002</p> <p>\u63a5\u4e0b\u6765\uff0c\u5faa\u73af\u6267\u884c\u4ee5\u4e0b\u4e24\u4e2a\u6b65\u9aa4\uff1a</p> <ol> <li>\u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 \\(m = \\lfloor {(i + j) / 2} \\rfloor\\) \uff0c\u5176\u4e2d \\(\\lfloor \\space \\rfloor\\) \u8868\u793a\u5411\u4e0b\u53d6\u6574\u64cd\u4f5c\u3002</li> <li>\u5224\u65ad <code>nums[m]</code> \u548c <code>target</code> \u7684\u5927\u5c0f\u5173\u7cfb\uff0c\u5206\u4e3a\u4e09\u79cd\u60c5\u51b5\uff1a<ol> <li>\u5f53 <code>nums[m] &lt; target</code> \u65f6\uff0c\u8bf4\u660e <code>target</code> \u5728\u533a\u95f4 \\([m + 1, j]\\) \u4e2d\uff0c\u56e0\u6b64\u6267\u884c \\(i = m + 1\\) \uff1b</li> <li>\u5f53 <code>nums[m] &gt; target</code> \u65f6\uff0c\u8bf4\u660e <code>target</code> \u5728\u533a\u95f4 \\([i, m - 1]\\) \u4e2d\uff0c\u56e0\u6b64\u6267\u884c \\(j = m - 1\\) \uff1b</li> <li>\u5f53 <code>nums[m] = target</code> \u65f6\uff0c\u8bf4\u660e\u627e\u5230 <code>target</code> \uff0c\u56e0\u6b64\u8fd4\u56de\u7d22\u5f15 \\(m\\) \uff1b</li> </ol> </li> </ol> <p>\u82e5\u6570\u7ec4\u4e0d\u5305\u542b\u76ee\u6807\u5143\u7d20\uff0c\u641c\u7d22\u533a\u95f4\u6700\u7ec8\u4f1a\u7f29\u5c0f\u4e3a\u7a7a\u3002\u6b64\u65f6\u8fd4\u56de \\(-1\\) \u3002</p> &lt;0&gt;&lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p>\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u7531\u4e8e \\(i\\) \u548c \\(j\\) \u90fd\u662f <code>int</code> \u7c7b\u578b\uff0c\u56e0\u6b64 \\(i + j\\) \u53ef\u80fd\u4f1a\u8d85\u51fa <code>int</code> \u7c7b\u578b\u7684\u53d6\u503c\u8303\u56f4\u3002\u4e3a\u4e86\u907f\u514d\u5927\u6570\u8d8a\u754c\uff0c\u6211\u4eec\u901a\u5e38\u91c7\u7528\u516c\u5f0f \\(m = \\lfloor {i + (j - i) / 2} \\rfloor\\) \u6765\u8ba1\u7b97\u4e2d\u70b9\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart binary_search.java<pre><code>/* \u4e8c\u5206\u67e5\u627e\uff08\u53cc\u95ed\u533a\u95f4\uff09 */\nint binarySearch(int[] nums, int target) {\n// \u521d\u59cb\u5316\u53cc\u95ed\u533a\u95f4 [0, n-1] \uff0c\u5373 i, j \u5206\u522b\u6307\u5411\u6570\u7ec4\u9996\u5143\u7d20\u3001\u5c3e\u5143\u7d20\nint i = 0, j = nums.length - 1;\n// \u5faa\u73af\uff0c\u5f53\u641c\u7d22\u533a\u95f4\u4e3a\u7a7a\u65f6\u8df3\u51fa\uff08\u5f53 i &gt; j \u65f6\u4e3a\u7a7a\uff09\nwhile (i &lt;= j) {\nint m = i + (j - i) / 2; // \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nif (nums[m] &lt; target) // \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [m+1, j] \u4e2d\ni = m + 1;\nelse if (nums[m] &gt; target) // \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [i, m-1] \u4e2d\nj = m - 1;\nelse // \u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de\u5176\u7d22\u5f15\nreturn m;\n}\n// \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\nreturn -1;\n}\n</code></pre> binary_search.cpp<pre><code>/* \u4e8c\u5206\u67e5\u627e\uff08\u53cc\u95ed\u533a\u95f4\uff09 */\nint binarySearch(vector&lt;int&gt; &amp;nums, int target) {\n// \u521d\u59cb\u5316\u53cc\u95ed\u533a\u95f4 [0, n-1] \uff0c\u5373 i, j \u5206\u522b\u6307\u5411\u6570\u7ec4\u9996\u5143\u7d20\u3001\u5c3e\u5143\u7d20\nint i = 0, j = nums.size() - 1;\n// \u5faa\u73af\uff0c\u5f53\u641c\u7d22\u533a\u95f4\u4e3a\u7a7a\u65f6\u8df3\u51fa\uff08\u5f53 i &gt; j \u65f6\u4e3a\u7a7a\uff09\nwhile (i &lt;= j) {\nint m = i + (j - i) / 2; // \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nif (nums[m] &lt; target)    // \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [m+1, j] \u4e2d\ni = m + 1;\nelse if (nums[m] &gt; target) // \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [i, m-1] \u4e2d\nj = m - 1;\nelse // \u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de\u5176\u7d22\u5f15\nreturn m;\n}\n// \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\nreturn -1;\n}\n</code></pre> binary_search.py<pre><code>def binary_search(nums: list[int], target: int) -&gt; int:\n\"\"\"\u4e8c\u5206\u67e5\u627e\uff08\u53cc\u95ed\u533a\u95f4\uff09\"\"\"\n# \u521d\u59cb\u5316\u53cc\u95ed\u533a\u95f4 [0, n-1] \uff0c\u5373 i, j \u5206\u522b\u6307\u5411\u6570\u7ec4\u9996\u5143\u7d20\u3001\u5c3e\u5143\u7d20\ni, j = 0, len(nums) - 1\n# \u5faa\u73af\uff0c\u5f53\u641c\u7d22\u533a\u95f4\u4e3a\u7a7a\u65f6\u8df3\u51fa\uff08\u5f53 i &gt; j \u65f6\u4e3a\u7a7a\uff09\nwhile i &lt;= j:\n# \u7406\u8bba\u4e0a Python \u7684\u6570\u5b57\u53ef\u4ee5\u65e0\u9650\u5927\uff08\u53d6\u51b3\u4e8e\u5185\u5b58\u5927\u5c0f\uff09\uff0c\u65e0\u9700\u8003\u8651\u5927\u6570\u8d8a\u754c\u95ee\u9898\nm = (i + j) // 2  # \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nif nums[m] &lt; target:\ni = m + 1  # \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [m+1, j] \u4e2d\nelif nums[m] &gt; target:\nj = m - 1  # \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [i, m-1] \u4e2d\nelse:\nreturn m  # \u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de\u5176\u7d22\u5f15\nreturn -1  # \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\n</code></pre> binary_search.go<pre><code>/* \u4e8c\u5206\u67e5\u627e\uff08\u53cc\u95ed\u533a\u95f4\uff09 */\nfunc binarySearch(nums []int, target int) int {\n// \u521d\u59cb\u5316\u53cc\u95ed\u533a\u95f4 [0, n-1] \uff0c\u5373 i, j \u5206\u522b\u6307\u5411\u6570\u7ec4\u9996\u5143\u7d20\u3001\u5c3e\u5143\u7d20\ni, j := 0, len(nums)-1\n// \u5faa\u73af\uff0c\u5f53\u641c\u7d22\u533a\u95f4\u4e3a\u7a7a\u65f6\u8df3\u51fa\uff08\u5f53 i &gt; j \u65f6\u4e3a\u7a7a\uff09\nfor i &lt;= j {\nm := i + (j-i)/2      // \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nif nums[m] &lt; target { // \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [m+1, j] \u4e2d\ni = m + 1\n} else if nums[m] &gt; target { // \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [i, m-1] \u4e2d\nj = m - 1\n} else { // \u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de\u5176\u7d22\u5f15\nreturn m\n}\n}\n// \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\nreturn -1\n}\n</code></pre> binary_search.js<pre><code>/* \u4e8c\u5206\u67e5\u627e\uff08\u53cc\u95ed\u533a\u95f4\uff09 */\nfunction binarySearch(nums, target) {\n// \u521d\u59cb\u5316\u53cc\u95ed\u533a\u95f4 [0, n-1] \uff0c\u5373 i, j \u5206\u522b\u6307\u5411\u6570\u7ec4\u9996\u5143\u7d20\u3001\u5c3e\u5143\u7d20\nlet i = 0,\nj = nums.length - 1;\n// \u5faa\u73af\uff0c\u5f53\u641c\u7d22\u533a\u95f4\u4e3a\u7a7a\u65f6\u8df3\u51fa\uff08\u5f53 i &gt; j \u65f6\u4e3a\u7a7a\uff09\nwhile (i &lt;= j) {\n// \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m \uff0c\u4f7f\u7528 parseInt() \u5411\u4e0b\u53d6\u6574\nconst m = parseInt(i + (j - i) / 2);\nif (nums[m] &lt; target)\n// \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [m+1, j] \u4e2d\ni = m + 1;\nelse if (nums[m] &gt; target)\n// \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [i, m-1] \u4e2d\nj = m - 1;\nelse return m; // \u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de\u5176\u7d22\u5f15\n}\n// \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\nreturn -1;\n}\n</code></pre> binary_search.ts<pre><code>/* \u4e8c\u5206\u67e5\u627e\uff08\u53cc\u95ed\u533a\u95f4\uff09 */\nfunction binarySearch(nums: number[], target: number): number {\n// \u521d\u59cb\u5316\u53cc\u95ed\u533a\u95f4 [0, n-1] \uff0c\u5373 i, j \u5206\u522b\u6307\u5411\u6570\u7ec4\u9996\u5143\u7d20\u3001\u5c3e\u5143\u7d20\nlet i = 0,\nj = nums.length - 1;\n// \u5faa\u73af\uff0c\u5f53\u641c\u7d22\u533a\u95f4\u4e3a\u7a7a\u65f6\u8df3\u51fa\uff08\u5f53 i &gt; j \u65f6\u4e3a\u7a7a\uff09\nwhile (i &lt;= j) {\n// \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nconst m = Math.floor(i + (j - i) / 2);\nif (nums[m] &lt; target) {\n// \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [m+1, j] \u4e2d\ni = m + 1;\n} else if (nums[m] &gt; target) {\n// \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [i, m-1] \u4e2d\nj = m - 1;\n} else {\n// \u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de\u5176\u7d22\u5f15\nreturn m;\n}\n}\nreturn -1; // \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\n}\n</code></pre> binary_search.c<pre><code>/* \u4e8c\u5206\u67e5\u627e\uff08\u53cc\u95ed\u533a\u95f4\uff09 */\nint binarySearch(int *nums, int len, int target) {\n// \u521d\u59cb\u5316\u53cc\u95ed\u533a\u95f4 [0, n-1] \uff0c\u5373 i, j \u5206\u522b\u6307\u5411\u6570\u7ec4\u9996\u5143\u7d20\u3001\u5c3e\u5143\u7d20\nint i = 0, j = len - 1;\n// \u5faa\u73af\uff0c\u5f53\u641c\u7d22\u533a\u95f4\u4e3a\u7a7a\u65f6\u8df3\u51fa\uff08\u5f53 i &gt; j \u65f6\u4e3a\u7a7a\uff09\nwhile (i &lt;= j) {\nint m = i + (j - i) / 2; // \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nif (nums[m] &lt; target)    // \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [m+1, j] \u4e2d\ni = m + 1;\nelse if (nums[m] &gt; target) // \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [i, m-1] \u4e2d\nj = m - 1;\nelse // \u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de\u5176\u7d22\u5f15\nreturn m;\n}\n// \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\nreturn -1;\n}\n</code></pre> binary_search.cs<pre><code>/* \u4e8c\u5206\u67e5\u627e\uff08\u53cc\u95ed\u533a\u95f4\uff09 */\nint binarySearch(int[] nums, int target) {\n// \u521d\u59cb\u5316\u53cc\u95ed\u533a\u95f4 [0, n-1] \uff0c\u5373 i, j \u5206\u522b\u6307\u5411\u6570\u7ec4\u9996\u5143\u7d20\u3001\u5c3e\u5143\u7d20\nint i = 0, j = nums.Length - 1;\n// \u5faa\u73af\uff0c\u5f53\u641c\u7d22\u533a\u95f4\u4e3a\u7a7a\u65f6\u8df3\u51fa\uff08\u5f53 i &gt; j \u65f6\u4e3a\u7a7a\uff09\nwhile (i &lt;= j) {\nint m = i + (j - i) / 2;   // \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nif (nums[m] &lt; target)      // \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [m+1, j] \u4e2d\ni = m + 1;\nelse if (nums[m] &gt; target) // \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [i, m-1] \u4e2d\nj = m - 1;\nelse                       // \u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de\u5176\u7d22\u5f15\nreturn m;\n}\n// \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\nreturn -1;\n}\n</code></pre> binary_search.swift<pre><code>/* \u4e8c\u5206\u67e5\u627e\uff08\u53cc\u95ed\u533a\u95f4\uff09 */\nfunc binarySearch(nums: [Int], target: Int) -&gt; Int {\n// \u521d\u59cb\u5316\u53cc\u95ed\u533a\u95f4 [0, n-1] \uff0c\u5373 i, j \u5206\u522b\u6307\u5411\u6570\u7ec4\u9996\u5143\u7d20\u3001\u5c3e\u5143\u7d20\nvar i = 0\nvar j = nums.count - 1\n// \u5faa\u73af\uff0c\u5f53\u641c\u7d22\u533a\u95f4\u4e3a\u7a7a\u65f6\u8df3\u51fa\uff08\u5f53 i &gt; j \u65f6\u4e3a\u7a7a\uff09\nwhile i &lt;= j {\nlet m = i + (j - i) / 2 // \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nif nums[m] &lt; target { // \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [m+1, j] \u4e2d\ni = m + 1\n} else if nums[m] &gt; target { // \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [i, m-1] \u4e2d\nj = m - 1\n} else { // \u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de\u5176\u7d22\u5f15\nreturn m\n}\n}\n// \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\nreturn -1\n}\n</code></pre> binary_search.zig<pre><code>// \u4e8c\u5206\u67e5\u627e\uff08\u53cc\u95ed\u533a\u95f4\uff09\nfn binarySearch(comptime T: type, nums: std.ArrayList(T), target: T) T {\n// \u521d\u59cb\u5316\u53cc\u95ed\u533a\u95f4 [0, n-1] \uff0c\u5373 i, j \u5206\u522b\u6307\u5411\u6570\u7ec4\u9996\u5143\u7d20\u3001\u5c3e\u5143\u7d20\nvar i: usize = 0;\nvar j: usize = nums.items.len - 1;\n// \u5faa\u73af\uff0c\u5f53\u641c\u7d22\u533a\u95f4\u4e3a\u7a7a\u65f6\u8df3\u51fa\uff08\u5f53 i &gt; j \u65f6\u4e3a\u7a7a\uff09\nwhile (i &lt;= j) {\nvar m = i + (j - i) / 2;                // \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nif (nums.items[m] &lt; target) {           // \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [m+1, j] \u4e2d\ni = m + 1;\n} else if (nums.items[m] &gt; target) {    // \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [i, m-1] \u4e2d\nj = m - 1;\n} else {                                // \u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de\u5176\u7d22\u5f15\nreturn @intCast(T, m);\n}\n}\n// \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\nreturn -1;\n}\n</code></pre> binary_search.dart<pre><code>/* \u4e8c\u5206\u67e5\u627e\uff08\u53cc\u95ed\u533a\u95f4\uff09 */\nint binarySearch(List&lt;int&gt; nums, int target) {\n// \u521d\u59cb\u5316\u53cc\u95ed\u533a\u95f4 [0, n-1] \uff0c\u5373 i, j \u5206\u522b\u6307\u5411\u6570\u7ec4\u9996\u5143\u7d20\u3001\u5c3e\u5143\u7d20\nint i = 0, j = nums.length - 1;\n// \u5faa\u73af\uff0c\u5f53\u641c\u7d22\u533a\u95f4\u4e3a\u7a7a\u65f6\u8df3\u51fa\uff08\u5f53 i &gt; j \u65f6\u4e3a\u7a7a\uff09\nwhile (i &lt;= j) {\nint m = i + (j - i) ~/ 2; // \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nif (nums[m] &lt; target) {\n// \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [m+1, j] \u4e2d\ni = m + 1;\n} else if (nums[m] &gt; target) {\n// \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [i, m-1] \u4e2d\nj = m - 1;\n} else {\n// \u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de\u5176\u7d22\u5f15\nreturn m;\n}\n}\n// \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\nreturn -1;\n}\n</code></pre> <p>\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(\\log n)\\) \u3002\u6bcf\u8f6e\u7f29\u5c0f\u4e00\u534a\u533a\u95f4\uff0c\u56e0\u6b64\u4e8c\u5206\u5faa\u73af\u6b21\u6570\u4e3a \\(\\log_2 n\\) \u3002</p> <p>\u7a7a\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(1)\\)  \u3002\u6307\u9488 <code>i</code> , <code>j</code> \u4f7f\u7528\u5e38\u6570\u5927\u5c0f\u7a7a\u95f4\u3002</p>"},{"location":"chapter_searching/binary_search/#1011","title":"10.1.1. \u00a0 \u533a\u95f4\u8868\u793a\u65b9\u6cd5","text":"<p>\u9664\u4e86\u4e0a\u8ff0\u7684\u53cc\u95ed\u533a\u95f4\u5916\uff0c\u5e38\u89c1\u7684\u533a\u95f4\u8868\u793a\u8fd8\u6709\u201c\u5de6\u95ed\u53f3\u5f00\u201d\u533a\u95f4\uff0c\u5b9a\u4e49\u4e3a \\([0, n)\\) \uff0c\u5373\u5de6\u8fb9\u754c\u5305\u542b\u81ea\u8eab\uff0c\u53f3\u8fb9\u754c\u4e0d\u5305\u542b\u81ea\u8eab\u3002\u5728\u8be5\u8868\u793a\u4e0b\uff0c\u533a\u95f4 \\([i, j]\\) \u5728 \\(i = j\\) \u65f6\u4e3a\u7a7a\u3002</p> <p>\u6211\u4eec\u53ef\u4ee5\u57fa\u4e8e\u8be5\u8868\u793a\u5b9e\u73b0\u5177\u6709\u76f8\u540c\u529f\u80fd\u7684\u4e8c\u5206\u67e5\u627e\u7b97\u6cd5\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart binary_search.java<pre><code>/* \u4e8c\u5206\u67e5\u627e\uff08\u5de6\u95ed\u53f3\u5f00\uff09 */\nint binarySearchLCRO(int[] nums, int target) {\n// \u521d\u59cb\u5316\u5de6\u95ed\u53f3\u5f00 [0, n) \uff0c\u5373 i, j \u5206\u522b\u6307\u5411\u6570\u7ec4\u9996\u5143\u7d20\u3001\u5c3e\u5143\u7d20+1\nint i = 0, j = nums.length;\n// \u5faa\u73af\uff0c\u5f53\u641c\u7d22\u533a\u95f4\u4e3a\u7a7a\u65f6\u8df3\u51fa\uff08\u5f53 i = j \u65f6\u4e3a\u7a7a\uff09\nwhile (i &lt; j) {\nint m = i + (j - i) / 2; // \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nif (nums[m] &lt; target) // \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [m+1, j) \u4e2d\ni = m + 1;\nelse if (nums[m] &gt; target) // \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [i, m) \u4e2d\nj = m;\nelse // \u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de\u5176\u7d22\u5f15\nreturn m;\n}\n// \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\nreturn -1;\n}\n</code></pre> binary_search.cpp<pre><code>/* \u4e8c\u5206\u67e5\u627e\uff08\u5de6\u95ed\u53f3\u5f00\uff09 */\nint binarySearchLCRO(vector&lt;int&gt; &amp;nums, int target) {\n// \u521d\u59cb\u5316\u5de6\u95ed\u53f3\u5f00 [0, n) \uff0c\u5373 i, j \u5206\u522b\u6307\u5411\u6570\u7ec4\u9996\u5143\u7d20\u3001\u5c3e\u5143\u7d20+1\nint i = 0, j = nums.size();\n// \u5faa\u73af\uff0c\u5f53\u641c\u7d22\u533a\u95f4\u4e3a\u7a7a\u65f6\u8df3\u51fa\uff08\u5f53 i = j \u65f6\u4e3a\u7a7a\uff09\nwhile (i &lt; j) {\nint m = i + (j - i) / 2; // \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nif (nums[m] &lt; target)    // \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [m+1, j) \u4e2d\ni = m + 1;\nelse if (nums[m] &gt; target) // \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [i, m) \u4e2d\nj = m;\nelse // \u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de\u5176\u7d22\u5f15\nreturn m;\n}\n// \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\nreturn -1;\n}\n</code></pre> binary_search.py<pre><code>def binary_search_lcro(nums: list[int], target: int) -&gt; int:\n\"\"\"\u4e8c\u5206\u67e5\u627e\uff08\u5de6\u95ed\u53f3\u5f00\uff09\"\"\"\n# \u521d\u59cb\u5316\u5de6\u95ed\u53f3\u5f00 [0, n) \uff0c\u5373 i, j \u5206\u522b\u6307\u5411\u6570\u7ec4\u9996\u5143\u7d20\u3001\u5c3e\u5143\u7d20+1\ni, j = 0, len(nums)\n# \u5faa\u73af\uff0c\u5f53\u641c\u7d22\u533a\u95f4\u4e3a\u7a7a\u65f6\u8df3\u51fa\uff08\u5f53 i = j \u65f6\u4e3a\u7a7a\uff09\nwhile i &lt; j:\nm = (i + j) // 2  # \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nif nums[m] &lt; target:\ni = m + 1  # \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [m+1, j) \u4e2d\nelif nums[m] &gt; target:\nj = m  # \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [i, m) \u4e2d\nelse:\nreturn m  # \u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de\u5176\u7d22\u5f15\nreturn -1  # \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\n</code></pre> binary_search.go<pre><code>/* \u4e8c\u5206\u67e5\u627e\uff08\u5de6\u95ed\u53f3\u5f00\uff09 */\nfunc binarySearchLCRO(nums []int, target int) int {\n// \u521d\u59cb\u5316\u5de6\u95ed\u53f3\u5f00 [0, n) \uff0c\u5373 i, j \u5206\u522b\u6307\u5411\u6570\u7ec4\u9996\u5143\u7d20\u3001\u5c3e\u5143\u7d20+1\ni, j := 0, len(nums)\n// \u5faa\u73af\uff0c\u5f53\u641c\u7d22\u533a\u95f4\u4e3a\u7a7a\u65f6\u8df3\u51fa\uff08\u5f53 i = j \u65f6\u4e3a\u7a7a\uff09\nfor i &lt; j {\nm := i + (j-i)/2      // \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nif nums[m] &lt; target { // \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [m+1, j) \u4e2d\ni = m + 1\n} else if nums[m] &gt; target { // \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [i, m) \u4e2d\nj = m\n} else { // \u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de\u5176\u7d22\u5f15\nreturn m\n}\n}\n// \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\nreturn -1\n}\n</code></pre> binary_search.js<pre><code>/* \u4e8c\u5206\u67e5\u627e\uff08\u5de6\u95ed\u53f3\u5f00\uff09 */\nfunction binarySearchLCRO(nums, target) {\n// \u521d\u59cb\u5316\u5de6\u95ed\u53f3\u5f00 [0, n) \uff0c\u5373 i, j \u5206\u522b\u6307\u5411\u6570\u7ec4\u9996\u5143\u7d20\u3001\u5c3e\u5143\u7d20+1\nlet i = 0,\nj = nums.length;\n// \u5faa\u73af\uff0c\u5f53\u641c\u7d22\u533a\u95f4\u4e3a\u7a7a\u65f6\u8df3\u51fa\uff08\u5f53 i = j \u65f6\u4e3a\u7a7a\uff09\nwhile (i &lt; j) {\n// \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m \uff0c\u4f7f\u7528 parseInt() \u5411\u4e0b\u53d6\u6574\nconst m = parseInt(i + (j - i) / 2);\nif (nums[m] &lt; target)\n// \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [m+1, j) \u4e2d\ni = m + 1;\nelse if (nums[m] &gt; target)\n// \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [i, m) \u4e2d\nj = m;\n// \u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de\u5176\u7d22\u5f15\nelse return m;\n}\n// \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\nreturn -1;\n}\n</code></pre> binary_search.ts<pre><code>/* \u4e8c\u5206\u67e5\u627e\uff08\u5de6\u95ed\u53f3\u5f00\uff09 */\nfunction binarySearchLCRO(nums: number[], target: number): number {\n// \u521d\u59cb\u5316\u5de6\u95ed\u53f3\u5f00 [0, n) \uff0c\u5373 i, j \u5206\u522b\u6307\u5411\u6570\u7ec4\u9996\u5143\u7d20\u3001\u5c3e\u5143\u7d20+1\nlet i = 0,\nj = nums.length;\n// \u5faa\u73af\uff0c\u5f53\u641c\u7d22\u533a\u95f4\u4e3a\u7a7a\u65f6\u8df3\u51fa\uff08\u5f53 i = j \u65f6\u4e3a\u7a7a\uff09\nwhile (i &lt; j) {\n// \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nconst m = Math.floor(i + (j - i) / 2);\nif (nums[m] &lt; target) {\n// \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [m+1, j) \u4e2d\ni = m + 1;\n} else if (nums[m] &gt; target) {\n// \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [i, m) \u4e2d\nj = m;\n} else {\n// \u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de\u5176\u7d22\u5f15\nreturn m;\n}\n}\nreturn -1; // \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\n}\n</code></pre> binary_search.c<pre><code>/* \u4e8c\u5206\u67e5\u627e\uff08\u5de6\u95ed\u53f3\u5f00\uff09 */\nint binarySearchLCRO(int *nums, int len, int target) {\n// \u521d\u59cb\u5316\u5de6\u95ed\u53f3\u5f00 [0, n) \uff0c\u5373 i, j \u5206\u522b\u6307\u5411\u6570\u7ec4\u9996\u5143\u7d20\u3001\u5c3e\u5143\u7d20+1\nint i = 0, j = len;\n// \u5faa\u73af\uff0c\u5f53\u641c\u7d22\u533a\u95f4\u4e3a\u7a7a\u65f6\u8df3\u51fa\uff08\u5f53 i = j \u65f6\u4e3a\u7a7a\uff09\nwhile (i &lt; j) {\nint m = i + (j - i) / 2; // \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nif (nums[m] &lt; target)    // \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [m+1, j) \u4e2d\ni = m + 1;\nelse if (nums[m] &gt; target) // \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [i, m) \u4e2d\nj = m;\nelse // \u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de\u5176\u7d22\u5f15\nreturn m;\n}\n// \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\nreturn -1;\n}\n</code></pre> binary_search.cs<pre><code>/* \u4e8c\u5206\u67e5\u627e\uff08\u5de6\u95ed\u53f3\u5f00\uff09 */\nint binarySearchLCRO(int[] nums, int target) {\n// \u521d\u59cb\u5316\u5de6\u95ed\u53f3\u5f00 [0, n) \uff0c\u5373 i, j \u5206\u522b\u6307\u5411\u6570\u7ec4\u9996\u5143\u7d20\u3001\u5c3e\u5143\u7d20+1\nint i = 0, j = nums.Length;\n// \u5faa\u73af\uff0c\u5f53\u641c\u7d22\u533a\u95f4\u4e3a\u7a7a\u65f6\u8df3\u51fa\uff08\u5f53 i = j \u65f6\u4e3a\u7a7a\uff09\nwhile (i &lt; j) {\nint m = i + (j - i) / 2;   // \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nif (nums[m] &lt; target)      // \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [m+1, j) \u4e2d\ni = m + 1;\nelse if (nums[m] &gt; target) // \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [i, m) \u4e2d\nj = m;\nelse                       // \u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de\u5176\u7d22\u5f15\nreturn m;\n}\n// \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\nreturn -1;\n}\n</code></pre> binary_search.swift<pre><code>/* \u4e8c\u5206\u67e5\u627e\uff08\u5de6\u95ed\u53f3\u5f00\uff09 */\nfunc binarySearchLCRO(nums: [Int], target: Int) -&gt; Int {\n// \u521d\u59cb\u5316\u5de6\u95ed\u53f3\u5f00 [0, n) \uff0c\u5373 i, j \u5206\u522b\u6307\u5411\u6570\u7ec4\u9996\u5143\u7d20\u3001\u5c3e\u5143\u7d20+1\nvar i = 0\nvar j = nums.count\n// \u5faa\u73af\uff0c\u5f53\u641c\u7d22\u533a\u95f4\u4e3a\u7a7a\u65f6\u8df3\u51fa\uff08\u5f53 i = j \u65f6\u4e3a\u7a7a\uff09\nwhile i &lt; j {\nlet m = i + (j - i) / 2 // \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nif nums[m] &lt; target { // \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [m+1, j) \u4e2d\ni = m + 1\n} else if nums[m] &gt; target { // \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [i, m) \u4e2d\nj = m\n} else { // \u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de\u5176\u7d22\u5f15\nreturn m\n}\n}\n// \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\nreturn -1\n}\n</code></pre> binary_search.zig<pre><code>// \u4e8c\u5206\u67e5\u627e\uff08\u5de6\u95ed\u53f3\u5f00\uff09\nfn binarySearchLCRO(comptime T: type, nums: std.ArrayList(T), target: T) T {\n// \u521d\u59cb\u5316\u5de6\u95ed\u53f3\u5f00 [0, n) \uff0c\u5373 i, j \u5206\u522b\u6307\u5411\u6570\u7ec4\u9996\u5143\u7d20\u3001\u5c3e\u5143\u7d20+1\nvar i: usize = 0;\nvar j: usize = nums.items.len;\n// \u5faa\u73af\uff0c\u5f53\u641c\u7d22\u533a\u95f4\u4e3a\u7a7a\u65f6\u8df3\u51fa\uff08\u5f53 i = j \u65f6\u4e3a\u7a7a\uff09\nwhile (i &lt;= j) {\nvar m = i + (j - i) / 2;                // \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nif (nums.items[m] &lt; target) {           // \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [m+1, j) \u4e2d\ni = m + 1;\n} else if (nums.items[m] &gt; target) {    // \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [i, m) \u4e2d\nj = m;\n} else {                                // \u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de\u5176\u7d22\u5f15\nreturn @intCast(T, m);\n}\n}\n// \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\nreturn -1;\n}\n</code></pre> binary_search.dart<pre><code>/* \u4e8c\u5206\u67e5\u627e\uff08\u5de6\u95ed\u53f3\u5f00\u533a\u95f4\uff09 */\nint binarySearchLCRO(List&lt;int&gt; nums, int target) {\n// \u521d\u59cb\u5316\u5de6\u95ed\u53f3\u5f00 [0, n) \uff0c\u5373 i, j \u5206\u522b\u6307\u5411\u6570\u7ec4\u9996\u5143\u7d20\u3001\u5c3e\u5143\u7d20+1\nint i = 0, j = nums.length;\n// \u5faa\u73af\uff0c\u5f53\u641c\u7d22\u533a\u95f4\u4e3a\u7a7a\u65f6\u8df3\u51fa\uff08\u5f53 i = j \u65f6\u4e3a\u7a7a\uff09\nwhile (i &lt; j) {\nint m = i + (j - i) ~/ 2; // \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nif (nums[m] &lt; target) {\n// \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [m+1, j) \u4e2d\ni = m + 1;\n} else if (nums[m] &gt; target) {\n// \u6b64\u60c5\u51b5\u8bf4\u660e target \u5728\u533a\u95f4 [i, m) \u4e2d\nj = m;\n} else {\n// \u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de\u5176\u7d22\u5f15\nreturn m;\n}\n}\n// \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\nreturn -1;\n}\n</code></pre> <p>\u5982\u4e0b\u56fe\u6240\u793a\uff0c\u5728\u4e24\u79cd\u533a\u95f4\u8868\u793a\u4e0b\uff0c\u4e8c\u5206\u67e5\u627e\u7b97\u6cd5\u7684\u521d\u59cb\u5316\u3001\u5faa\u73af\u6761\u4ef6\u548c\u7f29\u5c0f\u533a\u95f4\u64cd\u4f5c\u7686\u6709\u6240\u4e0d\u540c\u3002</p> <p>\u5728\u201c\u53cc\u95ed\u533a\u95f4\u201d\u8868\u793a\u6cd5\u4e2d\uff0c\u7531\u4e8e\u5de6\u53f3\u8fb9\u754c\u90fd\u88ab\u5b9a\u4e49\u4e3a\u95ed\u533a\u95f4\uff0c\u56e0\u6b64\u6307\u9488 \\(i\\) \u548c \\(j\\) \u7f29\u5c0f\u533a\u95f4\u64cd\u4f5c\u4e5f\u662f\u5bf9\u79f0\u7684\u3002\u8fd9\u6837\u66f4\u4e0d\u5bb9\u6613\u51fa\u9519\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u901a\u5e38\u91c7\u7528\u201c\u53cc\u95ed\u533a\u95f4\u201d\u7684\u5199\u6cd5\u3002</p> <p></p> <p> Fig. \u4e24\u79cd\u533a\u95f4\u5b9a\u4e49 </p>"},{"location":"chapter_searching/binary_search/#1012","title":"10.1.2. \u00a0 \u4f18\u70b9\u4e0e\u5c40\u9650\u6027","text":"<p>\u4e8c\u5206\u67e5\u627e\u5728\u65f6\u95f4\u548c\u7a7a\u95f4\u65b9\u9762\u90fd\u6709\u8f83\u597d\u7684\u6027\u80fd\uff1a</p> <ul> <li>\u4e8c\u5206\u67e5\u627e\u7684\u65f6\u95f4\u6548\u7387\u9ad8\u3002\u5728\u5927\u6570\u636e\u91cf\u4e0b\uff0c\u5bf9\u6570\u9636\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u5177\u6709\u663e\u8457\u4f18\u52bf\u3002\u4f8b\u5982\uff0c\u5f53\u6570\u636e\u5927\u5c0f \\(n = 2^{20}\\) \u65f6\uff0c\u7ebf\u6027\u67e5\u627e\u9700\u8981 \\(2^{20} = 1048576\\) \u8f6e\u5faa\u73af\uff0c\u800c\u4e8c\u5206\u67e5\u627e\u4ec5\u9700 \\(\\log_2 2^{20} = 20\\) \u8f6e\u5faa\u73af\u3002</li> <li>\u4e8c\u5206\u67e5\u627e\u65e0\u9700\u989d\u5916\u7a7a\u95f4\u3002\u76f8\u8f83\u4e8e\u9700\u8981\u501f\u52a9\u989d\u5916\u7a7a\u95f4\u7684\u641c\u7d22\u7b97\u6cd5\uff08\u4f8b\u5982\u54c8\u5e0c\u67e5\u627e\uff09\uff0c\u4e8c\u5206\u67e5\u627e\u66f4\u52a0\u8282\u7701\u7a7a\u95f4\u3002</li> </ul> <p>\u7136\u800c\uff0c\u4e8c\u5206\u67e5\u627e\u5e76\u975e\u9002\u7528\u4e8e\u6240\u6709\u60c5\u51b5\uff0c\u539f\u56e0\u5982\u4e0b\uff1a</p> <ul> <li>\u4e8c\u5206\u67e5\u627e\u4ec5\u9002\u7528\u4e8e\u6709\u5e8f\u6570\u636e\u3002\u82e5\u8f93\u5165\u6570\u636e\u65e0\u5e8f\uff0c\u4e3a\u4e86\u4f7f\u7528\u4e8c\u5206\u67e5\u627e\u800c\u4e13\u95e8\u8fdb\u884c\u6392\u5e8f\uff0c\u5f97\u4e0d\u507f\u5931\u3002\u56e0\u4e3a\u6392\u5e8f\u7b97\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u901a\u5e38\u4e3a \\(O(n \\log n)\\) \uff0c\u6bd4\u7ebf\u6027\u67e5\u627e\u548c\u4e8c\u5206\u67e5\u627e\u90fd\u66f4\u9ad8\u3002\u5bf9\u4e8e\u9891\u7e41\u63d2\u5165\u5143\u7d20\u7684\u573a\u666f\uff0c\u4e3a\u4fdd\u6301\u6570\u7ec4\u6709\u5e8f\u6027\uff0c\u9700\u8981\u5c06\u5143\u7d20\u63d2\u5165\u5230\u7279\u5b9a\u4f4d\u7f6e\uff0c\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(n)\\) \uff0c\u4e5f\u662f\u975e\u5e38\u6602\u8d35\u7684\u3002</li> <li>\u4e8c\u5206\u67e5\u627e\u4ec5\u9002\u7528\u4e8e\u6570\u7ec4\u3002\u4e8c\u5206\u67e5\u627e\u9700\u8981\u8df3\u8dc3\u5f0f\uff08\u975e\u8fde\u7eed\u5730\uff09\u8bbf\u95ee\u5143\u7d20\uff0c\u800c\u5728\u94fe\u8868\u4e2d\u6267\u884c\u8df3\u8dc3\u5f0f\u8bbf\u95ee\u7684\u6548\u7387\u8f83\u4f4e\uff0c\u56e0\u6b64\u4e0d\u9002\u5408\u5e94\u7528\u5728\u94fe\u8868\u6216\u57fa\u4e8e\u94fe\u8868\u5b9e\u73b0\u7684\u6570\u636e\u7ed3\u6784\u3002</li> <li>\u5c0f\u6570\u636e\u91cf\u4e0b\uff0c\u7ebf\u6027\u67e5\u627e\u6027\u80fd\u66f4\u4f73\u3002\u5728\u7ebf\u6027\u67e5\u627e\u4e2d\uff0c\u6bcf\u8f6e\u53ea\u9700\u8981 1 \u6b21\u5224\u65ad\u64cd\u4f5c\uff1b\u800c\u5728\u4e8c\u5206\u67e5\u627e\u4e2d\uff0c\u9700\u8981 1 \u6b21\u52a0\u6cd5\u30011 \u6b21\u9664\u6cd5\u30011 ~ 3 \u6b21\u5224\u65ad\u64cd\u4f5c\u30011 \u6b21\u52a0\u6cd5\uff08\u51cf\u6cd5\uff09\uff0c\u5171 4 ~ 6 \u4e2a\u5355\u5143\u64cd\u4f5c\uff1b\u56e0\u6b64\uff0c\u5f53\u6570\u636e\u91cf \\(n\\) \u8f83\u5c0f\u65f6\uff0c\u7ebf\u6027\u67e5\u627e\u53cd\u800c\u6bd4\u4e8c\u5206\u67e5\u627e\u66f4\u5feb\u3002</li> </ul>"},{"location":"chapter_searching/binary_search_edge/","title":"10.2. \u00a0 \u4e8c\u5206\u67e5\u627e\u8fb9\u754c","text":"<p>\u5728\u4e0a\u4e00\u8282\u4e2d\uff0c\u9898\u76ee\u89c4\u5b9a\u6570\u7ec4\u4e2d\u6240\u6709\u5143\u7d20\u90fd\u662f\u552f\u4e00\u7684\u3002\u5982\u679c\u76ee\u6807\u5143\u7d20\u5728\u6570\u7ec4\u4e2d\u591a\u6b21\u51fa\u73b0\uff0c\u4e0a\u8282\u4ecb\u7ecd\u7684\u65b9\u6cd5\u53ea\u80fd\u4fdd\u8bc1\u8fd4\u56de\u5176\u4e2d\u4e00\u4e2a\u76ee\u6807\u5143\u7d20\u7684\u7d22\u5f15\uff0c\u800c\u65e0\u6cd5\u786e\u5b9a\u8be5\u7d22\u5f15\u7684\u5de6\u8fb9\u548c\u53f3\u8fb9\u8fd8\u6709\u591a\u5c11\u76ee\u6807\u5143\u7d20\u3002</p> <p>Question</p> <p>\u7ed9\u5b9a\u4e00\u4e2a\u957f\u5ea6\u4e3a \\(n\\) \u7684\u6709\u5e8f\u6570\u7ec4 <code>nums</code> \uff0c\u6570\u7ec4\u53ef\u80fd\u5305\u542b\u91cd\u590d\u5143\u7d20\u3002\u8bf7\u67e5\u627e\u5e76\u8fd4\u56de\u5143\u7d20 <code>target</code> \u5728\u6570\u7ec4\u4e2d\u9996\u6b21\u51fa\u73b0\u7684\u7d22\u5f15\u3002\u82e5\u6570\u7ec4\u4e2d\u4e0d\u5305\u542b\u8be5\u5143\u7d20\uff0c\u5219\u8fd4\u56de \\(-1\\) \u3002</p>"},{"location":"chapter_searching/binary_search_edge/#1021","title":"10.2.1. \u00a0 \u7b80\u5355\u65b9\u6cd5","text":"<p>\u4e3a\u4e86\u67e5\u627e\u6570\u7ec4\u4e2d\u6700\u5de6\u8fb9\u7684 <code>target</code> \uff0c\u6211\u4eec\u53ef\u4ee5\u5206\u4e3a\u4e24\u6b65\uff1a</p> <ol> <li>\u8fdb\u884c\u4e8c\u5206\u67e5\u627e\uff0c\u5b9a\u4f4d\u5230\u4efb\u610f\u4e00\u4e2a <code>target</code> \u7684\u7d22\u5f15\uff0c\u8bb0\u4e3a \\(k\\) \uff1b</li> <li>\u4ee5\u7d22\u5f15 \\(k\\) \u4e3a\u8d77\u59cb\u70b9\uff0c\u5411\u5de6\u8fdb\u884c\u7ebf\u6027\u904d\u5386\uff0c\u627e\u5230\u6700\u5de6\u8fb9\u7684 <code>target</code> \u8fd4\u56de\u5373\u53ef\u3002</li> </ol> <p></p> <p> Fig. \u7ebf\u6027\u67e5\u627e\u6700\u5de6\u8fb9\u7684\u5143\u7d20 </p> <p>\u8fd9\u4e2a\u65b9\u6cd5\u867d\u7136\u6709\u6548\uff0c\u4f46\u7531\u4e8e\u5305\u542b\u7ebf\u6027\u67e5\u627e\uff0c\u5176\u65f6\u95f4\u590d\u6742\u5ea6\u53ef\u80fd\u4f1a\u52a3\u5316\u81f3 \\(O(n)\\) \u3002</p>"},{"location":"chapter_searching/binary_search_edge/#1022","title":"10.2.2. \u00a0 \u4e8c\u5206\u65b9\u6cd5","text":"<p>\u5b9e\u9645\u4e0a\uff0c\u6211\u4eec\u53ef\u4ee5\u4ec5\u901a\u8fc7\u4e8c\u5206\u67e5\u627e\u89e3\u51b3\u4ee5\u4e0a\u95ee\u9898\u3002\u6574\u4f53\u7b97\u6cd5\u6d41\u7a0b\u4e0d\u53d8\uff0c\u5148\u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 \\(m\\) \uff0c\u518d\u5224\u65ad <code>target</code> \u548c <code>nums[m]</code> \u5927\u5c0f\u5173\u7cfb\uff1a</p> <ul> <li>\u5f53 <code>nums[m] &lt; target</code> \u6216 <code>nums[m] &gt; target</code> \u65f6\uff0c\u8bf4\u660e\u8fd8\u6ca1\u6709\u627e\u5230 <code>target</code> \uff0c\u56e0\u6b64\u91c7\u53d6\u4e0e\u4e0a\u8282\u4ee3\u7801\u76f8\u540c\u7684\u7f29\u5c0f\u533a\u95f4\u64cd\u4f5c\uff0c\u4ece\u800c\u4f7f\u6307\u9488 \\(i\\) \u548c \\(j\\) \u5411 <code>target</code> \u9760\u8fd1\u3002</li> <li>\u5f53 <code>nums[m] == target</code> \u65f6\uff0c\u8bf4\u660e\u201c\u5c0f\u4e8e <code>target</code> \u7684\u5143\u7d20\u201d\u5728\u533a\u95f4 \\([i, m - 1]\\) \u4e2d\uff0c\u56e0\u6b64\u91c7\u7528 \\(j = m - 1\\) \u6765\u7f29\u5c0f\u533a\u95f4\uff0c\u4ece\u800c\u4f7f\u6307\u9488 \\(j\\) \u5411\u5c0f\u4e8e <code>target</code> \u7684\u5143\u7d20\u9760\u8fd1\u3002</li> </ul> <p>\u4e8c\u5206\u67e5\u627e\u5b8c\u6210\u540e\uff0c\\(i\\) \u6307\u5411\u6700\u5de6\u8fb9\u7684 <code>target</code> \uff0c\\(j\\) \u6307\u5411\u9996\u4e2a\u5c0f\u4e8e <code>target</code> \u7684\u5143\u7d20\uff0c\u56e0\u6b64\u8fd4\u56de\u7d22\u5f15 \\(i\\) \u5373\u53ef\u3002</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p>\u6ce8\u610f\uff0c\u6570\u7ec4\u53ef\u80fd\u4e0d\u5305\u542b\u76ee\u6807\u5143\u7d20 <code>target</code> \u3002\u56e0\u6b64\u5728\u51fd\u6570\u8fd4\u56de\u524d\uff0c\u6211\u4eec\u9700\u8981\u5148\u5224\u65ad <code>nums[i]</code> \u4e0e <code>target</code> \u662f\u5426\u76f8\u7b49\uff0c\u4ee5\u53ca\u7d22\u5f15 \\(i\\) \u662f\u5426\u8d8a\u754c\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart binary_search_edge.java<pre><code>/* \u4e8c\u5206\u67e5\u627e\u6700\u5de6\u4e00\u4e2a\u5143\u7d20 */\nint binarySearchLeftEdge(int[] nums, int target) {\nint i = 0, j = nums.length - 1; // \u521d\u59cb\u5316\u53cc\u95ed\u533a\u95f4 [0, n-1]\nwhile (i &lt;= j) {\nint m = i + (j - i) / 2; // \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nif (nums[m] &lt; target)\ni = m + 1; // target \u5728\u533a\u95f4 [m+1, j] \u4e2d\nelse if (nums[m] &gt; target)\nj = m - 1; // target \u5728\u533a\u95f4 [i, m-1] \u4e2d\nelse\nj = m - 1; // \u9996\u4e2a\u5c0f\u4e8e target \u7684\u5143\u7d20\u5728\u533a\u95f4 [i, m-1] \u4e2d\n}\nif (i == nums.length || nums[i] != target)\nreturn -1; // \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\nreturn i;\n}\n</code></pre> binary_search_edge.cpp<pre><code>/* \u4e8c\u5206\u67e5\u627e\u6700\u5de6\u4e00\u4e2a\u5143\u7d20 */\nint binarySearchLeftEdge(vector&lt;int&gt; &amp;nums, int target) {\nint i = 0, j = nums.size() - 1; // \u521d\u59cb\u5316\u53cc\u95ed\u533a\u95f4 [0, n-1]\nwhile (i &lt;= j) {\nint m = i + (j - i) / 2; // \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nif (nums[m] &lt; target)\ni = m + 1; // target \u5728\u533a\u95f4 [m+1, j] \u4e2d\nelse if (nums[m] &gt; target)\nj = m - 1; // target \u5728\u533a\u95f4 [i, m-1] \u4e2d\nelse\nj = m - 1; // \u9996\u4e2a\u5c0f\u4e8e target \u7684\u5143\u7d20\u5728\u533a\u95f4 [i, m-1] \u4e2d\n}\nif (i == nums.size() || nums[i] != target)\nreturn -1; // \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\nreturn i;\n}\n</code></pre> binary_search_edge.py<pre><code>def binary_search_left_edge(nums: list[int], target: int) -&gt; int:\n\"\"\"\u4e8c\u5206\u67e5\u627e\u6700\u5de6\u4e00\u4e2a\u5143\u7d20\"\"\"\ni, j = 0, len(nums) - 1  # \u521d\u59cb\u5316\u53cc\u95ed\u533a\u95f4 [0, n-1]\nwhile i &lt;= j:\nm = (i + j) // 2  # \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nif nums[m] &lt; target:\ni = m + 1  # target \u5728\u533a\u95f4 [m+1, j] \u4e2d\nelif nums[m] &gt; target:\nj = m - 1  # target \u5728\u533a\u95f4 [i, m-1] \u4e2d\nelse:\nj = m - 1  # \u9996\u4e2a\u5c0f\u4e8e target \u7684\u5143\u7d20\u5728\u533a\u95f4 [i, m-1] \u4e2d\nif i == len(nums) or nums[i] != target:\nreturn -1  # \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\nreturn i\n</code></pre> binary_search_edge.go<pre><code>/* \u4e8c\u5206\u67e5\u627e\u6700\u5de6\u4e00\u4e2a\u5143\u7d20 */\nfunc binarySearchLeftEdge(nums []int, target int) int {\n// \u521d\u59cb\u5316\u53cc\u95ed\u533a\u95f4 [0, n-1]\ni, j := 0, len(nums)-1\nfor i &lt;= j {\n// \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nm := i + (j-i)/2\nif nums[m] &lt; target {\n// target \u5728\u533a\u95f4 [m+1, j] \u4e2d\ni = m + 1\n} else if nums[m] &gt; target {\n// target \u5728\u533a\u95f4 [i, m-1] \u4e2d\nj = m - 1\n} else {\n// \u9996\u4e2a\u5c0f\u4e8e target \u7684\u5143\u7d20\u5728\u533a\u95f4 [i, m-1] \u4e2d\nj = m - 1\n}\n}\nif i == len(nums) || nums[i] != target {\n// \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\nreturn -1\n}\nreturn i\n}\n</code></pre> binary_search_edge.js<pre><code>/* \u4e8c\u5206\u67e5\u627e\u6700\u5de6\u4e00\u4e2a\u5143\u7d20 */\nfunction binarySearchLeftEdge(nums, target) {\nlet i = 0,\nj = nums.length - 1; // \u521d\u59cb\u5316\u53cc\u95ed\u533a\u95f4 [0, n-1]\nwhile (i &lt;= j) {\nlet m = Math.floor((i + j) / 2); // \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nif (nums[m] &lt; target) {\ni = m + 1; // target \u5728\u533a\u95f4 [m+1, j] \u4e2d\n} else if (nums[m] &gt; target) {\nj = m - 1; // target \u5728\u533a\u95f4 [i, m-1] \u4e2d\n} else {\nj = m - 1; // \u9996\u4e2a\u5c0f\u4e8e target \u7684\u5143\u7d20\u5728\u533a\u95f4 [i, m-1] \u4e2d\n}\n}\nif (i == nums.length || nums[i] != target) {\nreturn -1; // \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\n}\nreturn i;\n}\n</code></pre> binary_search_edge.ts<pre><code>/* \u4e8c\u5206\u67e5\u627e\u6700\u5de6\u4e00\u4e2a\u5143\u7d20 */\nfunction binarySearchLeftEdge(nums: number[], target: number): number {\nlet i = 0, j = nums.length - 1;  // \u521d\u59cb\u5316\u53cc\u95ed\u533a\u95f4 [0, n-1]\nwhile (i &lt;= j) {\nlet m = Math.floor((i + j) / 2);  // \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nif (nums[m] &lt; target) {\ni = m + 1;  // target \u5728\u533a\u95f4 [m+1, j] \u4e2d\n} else if (nums[m] &gt; target) {\nj = m - 1;  // target \u5728\u533a\u95f4 [i, m-1] \u4e2d\n} else {\nj = m - 1;  // \u9996\u4e2a\u5c0f\u4e8e target \u7684\u5143\u7d20\u5728\u533a\u95f4 [i, m-1] \u4e2d\n}\n}\nif (i == nums.length || nums[i] != target) {\nreturn -1;  // \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\n}\nreturn i;\n}\n</code></pre> binary_search_edge.c<pre><code>/* \u4e8c\u5206\u67e5\u627e\u6700\u5de6\u4e00\u4e2a\u5143\u7d20 */\nint binarySearchLeftEdge(int *nums, int size, int target) {\nint i = 0, j = size - 1; // \u521d\u59cb\u5316\u53cc\u95ed\u533a\u95f4 [0, n-1]\nwhile (i &lt;= j) {\nint m = i + (j - i) / 2; // \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nif (nums[m] &lt; target)\ni = m + 1; // target \u5728\u533a\u95f4 [m+1, j] \u4e2d\nelse if (nums[m] &gt; target)\nj = m - 1; // target \u5728\u533a\u95f4 [i, m-1] \u4e2d\nelse\nj = m - 1; // \u9996\u4e2a\u5c0f\u4e8e target \u7684\u5143\u7d20\u5728\u533a\u95f4 [i, m-1] \u4e2d\n}\nif (i == size || nums[i] != target)\nreturn -1; // \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\nreturn i;\n}\n</code></pre> binary_search_edge.cs<pre><code>/* \u4e8c\u5206\u67e5\u627e\u6700\u5de6\u4e00\u4e2a\u5143\u7d20 */\nint binarySearchLeftEdge(int[] nums, int target) {\nint i = 0, j = nums.Length - 1; // \u521d\u59cb\u5316\u53cc\u95ed\u533a\u95f4 [0, n-1]\nwhile (i &lt;= j) {\nint m = i + (j - i) / 2; // \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nif (nums[m] &lt; target)\ni = m + 1; // target \u5728\u533a\u95f4 [m+1, j] \u4e2d\nelse if (nums[m] &gt; target)\nj = m - 1; // target \u5728\u533a\u95f4 [i, m-1] \u4e2d\nelse\nj = m - 1; // \u9996\u4e2a\u5c0f\u4e8e target \u7684\u5143\u7d20\u5728\u533a\u95f4 [i, m-1] \u4e2d\n}\nif (i == nums.Length || nums[i] != target)\nreturn -1; // \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\nreturn i;\n}\n</code></pre> binary_search_edge.swift<pre><code>/* \u4e8c\u5206\u67e5\u627e\u6700\u5de6\u4e00\u4e2a\u5143\u7d20 */\nfunc binarySearchLeftEdge(nums: [Int], target: Int) -&gt; Int {\n// \u521d\u59cb\u5316\u53cc\u95ed\u533a\u95f4 [0, n-1]\nvar i = 0\nvar j = nums.count - 1\nwhile i &lt;= j {\nlet m = i + (j - 1) / 2 // \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nif nums[m] &lt; target {\ni = m + 1 // target \u5728\u533a\u95f4 [m+1, j] \u4e2d\n} else if nums[m] &gt; target {\nj = m - 1 // target \u5728\u533a\u95f4 [i, m-1] \u4e2d\n} else {\nj = m - 1 // \u9996\u4e2a\u5c0f\u4e8e target \u7684\u5143\u7d20\u5728\u533a\u95f4 [i, m-1] \u4e2d\n}\n}\nif i == nums.count || nums[i] != target {\nreturn -1 // \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\n}\nreturn i\n}\n</code></pre> binary_search_edge.zig<pre><code>[class]{}-[func]{binarySearchLeftEdge}\n</code></pre> binary_search_edge.dart<pre><code>/* \u4e8c\u5206\u67e5\u627e\u6700\u5de6\u4e00\u4e2a\u5143\u7d20 */\nint binarySearchLeftEdge(List&lt;int&gt; nums, int target) {\nint i = 0, j = nums.length - 1; // \u521d\u59cb\u5316\u53cc\u95ed\u533a\u95f4 [0, n-1]\nwhile (i &lt;= j) {\nint m = i + (j - i) ~/ 2; // \u8ba1\u7b97\u4e2d\u95f4\u7d22\u5f15 m\nif (nums[m] &lt; target)\ni = m + 1; // target \u5728\u533a\u95f4 [m+1, j] \u4e2d\nelse if (nums[m] &gt; target)\nj = m - 1; // target \u5728\u533a\u95f4 [i, m-1] \u4e2d\nelse\nj = m - 1; // \u9996\u4e2a\u5c0f\u4e8e target \u7684\u5143\u7d20\u5728\u533a\u95f4 [i, m-1] \u4e2d\n}\nif (i == nums.length || nums[i] != target) return -1; // \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\nreturn i;\n}\n</code></pre>"},{"location":"chapter_searching/binary_search_edge/#1023","title":"10.2.3. \u00a0 \u67e5\u627e\u53f3\u8fb9\u754c","text":"<p>\u7c7b\u4f3c\u5730\uff0c\u6211\u4eec\u4e5f\u53ef\u4ee5\u4e8c\u5206\u67e5\u627e\u6700\u53f3\u8fb9\u7684 <code>target</code> \u3002\u5f53 <code>nums[m] == target</code> \u65f6\uff0c\u8bf4\u660e\u5927\u4e8e <code>target</code> \u7684\u5143\u7d20\u5728\u533a\u95f4 \\([m + 1, j]\\) \u4e2d\uff0c\u56e0\u6b64\u6267\u884c <code>i = m + 1</code> \uff0c\u4f7f\u5f97\u6307\u9488 \\(i\\) \u5411\u5927\u4e8e <code>target</code> \u7684\u5143\u7d20\u9760\u8fd1\u3002</p> <p>\u5b8c\u6210\u4e8c\u5206\u540e\uff0c\\(i\\) \u6307\u5411\u9996\u4e2a\u5927\u4e8e <code>target</code> \u7684\u5143\u7d20\uff0c\\(j\\) \u6307\u5411\u6700\u53f3\u8fb9\u7684 <code>target</code> \uff0c\u56e0\u6b64\u8fd4\u56de\u7d22\u5f15 \\(j\\) \u5373\u53ef\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart binary_search_edge.java<pre><code>/* \u4e8c\u5206\u67e5\u627e\u6700\u53f3\u4e00\u4e2a\u5143\u7d20 */\nint binarySearchRightEdge(int[] nums, int target) {\nint i = 0, j = nums.length - 1; // \u521d\u59cb\u5316\u53cc\u95ed\u533a\u95f4 [0, n-1]\nwhile (i &lt;= j) {\nint m = i + (j - i) / 2; // \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nif (nums[m] &lt; target)\ni = m + 1; // target \u5728\u533a\u95f4 [m+1, j] \u4e2d\nelse if (nums[m] &gt; target)\nj = m - 1; // target \u5728\u533a\u95f4 [i, m-1] \u4e2d\nelse\ni = m + 1; // \u9996\u4e2a\u5927\u4e8e target \u7684\u5143\u7d20\u5728\u533a\u95f4 [m+1, j] \u4e2d\n}\nif (j &lt; 0 || nums[j] != target)\nreturn -1; // \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\nreturn j;\n}\n</code></pre> binary_search_edge.cpp<pre><code>/* \u4e8c\u5206\u67e5\u627e\u6700\u53f3\u4e00\u4e2a\u5143\u7d20 */\nint binarySearchRightEdge(vector&lt;int&gt; &amp;nums, int target) {\nint i = 0, j = nums.size() - 1; // \u521d\u59cb\u5316\u53cc\u95ed\u533a\u95f4 [0, n-1]\nwhile (i &lt;= j) {\nint m = i + (j - i) / 2; // \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nif (nums[m] &lt; target)\ni = m + 1; // target \u5728\u533a\u95f4 [m+1, j] \u4e2d\nelse if (nums[m] &gt; target)\nj = m - 1; // target \u5728\u533a\u95f4 [i, m-1] \u4e2d\nelse\ni = m + 1; // \u9996\u4e2a\u5927\u4e8e target \u7684\u5143\u7d20\u5728\u533a\u95f4 [m+1, j] \u4e2d\n}\nif (j &lt; 0 || nums[j] != target)\nreturn -1; // \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\nreturn j;\n}\n</code></pre> binary_search_edge.py<pre><code>def binary_search_right_edge(nums: list[int], target: int) -&gt; int:\n\"\"\"\u4e8c\u5206\u67e5\u627e\u6700\u53f3\u4e00\u4e2a\u5143\u7d20\"\"\"\ni, j = 0, len(nums) - 1  # \u521d\u59cb\u5316\u53cc\u95ed\u533a\u95f4 [0, n-1]\nwhile i &lt;= j:\nm = (i + j) // 2  # \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nif nums[m] &lt; target:\ni = m + 1  # target \u5728\u533a\u95f4 [m+1, j] \u4e2d\nelif nums[m] &gt; target:\nj = m - 1  # target \u5728\u533a\u95f4 [i, m-1] \u4e2d\nelse:\ni = m + 1  # \u9996\u4e2a\u5927\u4e8e target \u7684\u5143\u7d20\u5728\u533a\u95f4 [m+1, j] \u4e2d\nif j == len(nums) or nums[j] != target:\nreturn -1  # \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\nreturn j\n</code></pre> binary_search_edge.go<pre><code>/* \u4e8c\u5206\u67e5\u627e\u6700\u53f3\u4e00\u4e2a\u5143\u7d20 */\nfunc binarySearchRightEdge(nums []int, target int) int {\n// \u521d\u59cb\u5316\u53cc\u95ed\u533a\u95f4 [0, n-1]\ni, j := 0, len(nums)-1\nfor i &lt;= j {\n// \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nm := i + (j-i)/2\nif nums[m] &lt; target {\n// target \u5728\u533a\u95f4 [m+1, j] \u4e2d\ni = m + 1\n} else if nums[m] &gt; target {\n// target \u5728\u533a\u95f4 [i, m-1] \u4e2d\nj = m - 1\n} else {\n// \u9996\u4e2a\u5927\u4e8e target \u7684\u5143\u7d20\u5728\u533a\u95f4 [m+1, j] \u4e2d\ni = m + 1\n}\n}\nif j &lt; 0 || nums[j] != target {\n// \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\nreturn -1\n}\nreturn j\n}\n</code></pre> binary_search_edge.js<pre><code>/* \u4e8c\u5206\u67e5\u627e\u6700\u53f3\u4e00\u4e2a\u5143\u7d20 */\nfunction binarySearchRightEdge(nums, target) {\nlet i = 0,\nj = nums.length - 1; // \u521d\u59cb\u5316\u53cc\u95ed\u533a\u95f4 [0, n-1]\nwhile (i &lt;= j) {\nlet m = Math.floor((i + j) / 2); // \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nif (nums[m] &lt; target) {\ni = m + 1; // target \u5728\u533a\u95f4 [m+1, j] \u4e2d\n} else if (nums[m] &gt; target) {\nj = m - 1; // target \u5728\u533a\u95f4 [i, m-1] \u4e2d\n} else {\ni = m + 1; // \u9996\u4e2a\u5927\u4e8e target \u7684\u5143\u7d20\u5728\u533a\u95f4 [m+1, j] \u4e2d\n}\n}\nif (j == nums.length || nums[j] != target) {\nreturn -1; // \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\n}\nreturn j;\n}\n</code></pre> binary_search_edge.ts<pre><code>/* \u4e8c\u5206\u67e5\u627e\u6700\u53f3\u4e00\u4e2a\u5143\u7d20 */\nfunction binarySearchRightEdge(nums: number[], target: number): number {\nlet i = 0, j = nums.length - 1;  // \u521d\u59cb\u5316\u53cc\u95ed\u533a\u95f4 [0, n-1]\nwhile (i &lt;= j) {\nlet m = Math.floor((i + j) / 2);  // \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nif (nums[m] &lt; target) {\ni = m + 1;  // target \u5728\u533a\u95f4 [m+1, j] \u4e2d\n} else if (nums[m] &gt; target) {\nj = m - 1;  // target \u5728\u533a\u95f4 [i, m-1] \u4e2d\n} else {\ni = m + 1;  // \u9996\u4e2a\u5927\u4e8e target \u7684\u5143\u7d20\u5728\u533a\u95f4 [m+1, j] \u4e2d\n}\n}\nif (j == nums.length || nums[j] != target) {\nreturn -1;  // \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\n}\nreturn j;\n}\n</code></pre> binary_search_edge.c<pre><code>/* \u4e8c\u5206\u67e5\u627e\u6700\u53f3\u4e00\u4e2a\u5143\u7d20 */\nint binarySearchRightEdge(int *nums, int size, int target) {\nint i = 0, j = size - 1; // \u521d\u59cb\u5316\u53cc\u95ed\u533a\u95f4 [0, n-1]\nwhile (i &lt;= j) {\nint m = i + (j - i) / 2; // \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nif (nums[m] &lt; target)\ni = m + 1; // target \u5728\u533a\u95f4 [m+1, j] \u4e2d\nelse if (nums[m] &gt; target)\nj = m - 1; // target \u5728\u533a\u95f4 [i, m-1] \u4e2d\nelse\ni = m + 1; // \u9996\u4e2a\u5927\u4e8e target \u7684\u5143\u7d20\u5728\u533a\u95f4 [m+1, j] \u4e2d\n}\nif (j &lt; 0 || nums[j] != target)\nreturn -1; // \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\nreturn j;\n}\n</code></pre> binary_search_edge.cs<pre><code>/* \u4e8c\u5206\u67e5\u627e\u6700\u53f3\u4e00\u4e2a\u5143\u7d20 */\nint binarySearchRightEdge(int[] nums, int target) {\nint i = 0, j = nums.Length - 1; // \u521d\u59cb\u5316\u53cc\u95ed\u533a\u95f4 [0, n-1]\nwhile (i &lt;= j) {\nint m = i + (j - i) / 2; // \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nif (nums[m] &lt; target)\ni = m + 1; // target \u5728\u533a\u95f4 [m+1, j] \u4e2d\nelse if (nums[m] &gt; target)\nj = m - 1; // target \u5728\u533a\u95f4 [i, m-1] \u4e2d\nelse\ni = m + 1; // \u9996\u4e2a\u5927\u4e8e target \u7684\u5143\u7d20\u5728\u533a\u95f4 [m+1, j] \u4e2d\n}\nif (j &lt; 0 || nums[j] != target)\nreturn -1; // \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\nreturn j;\n}\n</code></pre> binary_search_edge.swift<pre><code>/* \u4e8c\u5206\u67e5\u627e\u6700\u53f3\u4e00\u4e2a\u5143\u7d20 */\nfunc binarySearchRightEdge(nums: [Int], target: Int) -&gt; Int {\n// \u521d\u59cb\u5316\u53cc\u95ed\u533a\u95f4 [0, n-1]\nvar i = 0\nvar j = nums.count - 1\nwhile i &lt;= j {\nlet m = i + (j - i) / 2 // \u8ba1\u7b97\u4e2d\u70b9\u7d22\u5f15 m\nif nums[m] &lt; target {\ni = m + 1 // target \u5728\u533a\u95f4 [m+1, j] \u4e2d\n} else if nums[m] &gt; target {\nj = m - 1 // target \u5728\u533a\u95f4 [i, m-1] \u4e2d\n} else {\ni = m + 1 // \u9996\u4e2a\u5927\u4e8e target \u7684\u5143\u7d20\u5728\u533a\u95f4 [m+1, j] \u4e2d\n}\n}\nif j &lt; 0 || nums[j] != target {\nreturn -1 // \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\n}\nreturn j\n}\n</code></pre> binary_search_edge.zig<pre><code>[class]{}-[func]{binarySearchRightEdge}\n</code></pre> binary_search_edge.dart<pre><code>/* \u4e8c\u5206\u67e5\u627e\u6700\u53f3\u4e00\u4e2a\u5143\u7d20 */\nint binarySearchRightEdge(List&lt;int&gt; nums, int target) {\nint i = 0, j = nums.length - 1; // \u521d\u59cb\u5316\u53cc\u95ed\u533a\u95f4 [0, n-1]\nwhile (i &lt;= j) {\nint m = i + (j - i) ~/ 2; // \u8ba1\u7b97\u4e2d\u95f4\u7d22\u5f15 m\nif (nums[m] &lt; target)\ni = m + 1; // target \u5728\u533a\u95f4 [m+1, j] \u4e2d\nelse if (nums[m] &gt; target)\nj = m - 1; // target \u5728\u533a\u95f4 [i, m-1] \u4e2d\nelse\ni = m + 1; // \u9996\u4e2a\u5927\u4e8e target \u7684\u5143\u7d20\u5728\u533a\u95f4 [m+1, j] \u4e2d\n}\nif (j &lt; 0 || nums[j] != target) return -1; // \u672a\u627e\u5230\u76ee\u6807\u5143\u7d20\uff0c\u8fd4\u56de -1\nreturn j;\n}\n</code></pre> <p>\u89c2\u5bdf\u4e0b\u56fe\uff0c\u641c\u7d22\u6700\u53f3\u8fb9\u5143\u7d20\u65f6\u6307\u9488 \\(j\\) \u7684\u4f5c\u7528\u4e0e\u641c\u7d22\u6700\u5de6\u8fb9\u5143\u7d20\u65f6\u6307\u9488 \\(i\\) \u7684\u4f5c\u7528\u4e00\u81f4\uff0c\u53cd\u4e4b\u4ea6\u7136\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u641c\u7d22\u6700\u5de6\u8fb9\u5143\u7d20\u548c\u6700\u53f3\u8fb9\u5143\u7d20\u7684\u5b9e\u73b0\u662f\u955c\u50cf\u5bf9\u79f0\u7684\u3002</p> <p></p> <p> Fig. \u67e5\u627e\u6700\u5de6\u8fb9\u548c\u6700\u53f3\u8fb9\u5143\u7d20\u7684\u5bf9\u79f0\u6027 </p> <p>Tip</p> <p>\u4ee5\u4e0a\u4ee3\u7801\u91c7\u53d6\u7684\u90fd\u662f\u201c\u53cc\u95ed\u533a\u95f4\u201d\u5199\u6cd5\u3002\u6709\u5174\u8da3\u7684\u8bfb\u8005\u53ef\u4ee5\u81ea\u884c\u5b9e\u73b0\u201c\u5de6\u95ed\u53f3\u5f00\u201d\u5199\u6cd5\u3002</p>"},{"location":"chapter_searching/replace_linear_by_hashing/","title":"10.3. \u00a0 \u54c8\u5e0c\u4f18\u5316\u7b56\u7565","text":"<p>\u5728\u7b97\u6cd5\u9898\u4e2d\uff0c\u6211\u4eec\u5e38\u901a\u8fc7\u5c06\u7ebf\u6027\u67e5\u627e\u66ff\u6362\u4e3a\u54c8\u5e0c\u67e5\u627e\u6765\u964d\u4f4e\u7b97\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u3002\u6211\u4eec\u501f\u52a9\u4e00\u4e2a\u7b97\u6cd5\u9898\u6765\u52a0\u6df1\u7406\u89e3\u3002</p> <p>Question</p> <p>\u7ed9\u5b9a\u4e00\u4e2a\u6574\u6570\u6570\u7ec4 <code>nums</code> \u548c\u4e00\u4e2a\u76ee\u6807\u5143\u7d20 <code>target</code> \uff0c\u8bf7\u5728\u6570\u7ec4\u4e2d\u641c\u7d22\u201c\u548c\u201d\u4e3a <code>target</code> \u7684\u4e24\u4e2a\u5143\u7d20\uff0c\u5e76\u8fd4\u56de\u5b83\u4eec\u7684\u6570\u7ec4\u7d22\u5f15\u3002\u8fd4\u56de\u4efb\u610f\u4e00\u4e2a\u89e3\u5373\u53ef\u3002</p>"},{"location":"chapter_searching/replace_linear_by_hashing/#1031","title":"10.3.1. \u00a0 \u7ebf\u6027\u67e5\u627e\uff1a\u4ee5\u65f6\u95f4\u6362\u7a7a\u95f4","text":"<p>\u8003\u8651\u76f4\u63a5\u904d\u5386\u6240\u6709\u53ef\u80fd\u7684\u7ec4\u5408\u3002\u5f00\u542f\u4e00\u4e2a\u4e24\u5c42\u5faa\u73af\uff0c\u5728\u6bcf\u8f6e\u4e2d\u5224\u65ad\u4e24\u4e2a\u6574\u6570\u7684\u548c\u662f\u5426\u4e3a <code>target</code> \uff0c\u82e5\u662f\uff0c\u5219\u8fd4\u56de\u5b83\u4eec\u7684\u7d22\u5f15\u3002</p> <p></p> <p> Fig. \u7ebf\u6027\u67e5\u627e\u6c42\u89e3\u4e24\u6570\u4e4b\u548c </p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart two_sum.java<pre><code>/* \u65b9\u6cd5\u4e00\uff1a\u66b4\u529b\u679a\u4e3e */\nint[] twoSumBruteForce(int[] nums, int target) {\nint size = nums.length;\n// \u4e24\u5c42\u5faa\u73af\uff0c\u65f6\u95f4\u590d\u6742\u5ea6 O(n^2)\nfor (int i = 0; i &lt; size - 1; i++) {\nfor (int j = i + 1; j &lt; size; j++) {\nif (nums[i] + nums[j] == target)\nreturn new int[] { i, j };\n}\n}\nreturn new int[0];\n}\n</code></pre> two_sum.cpp<pre><code>/* \u65b9\u6cd5\u4e00\uff1a\u66b4\u529b\u679a\u4e3e */\nvector&lt;int&gt; twoSumBruteForce(vector&lt;int&gt; &amp;nums, int target) {\nint size = nums.size();\n// \u4e24\u5c42\u5faa\u73af\uff0c\u65f6\u95f4\u590d\u6742\u5ea6 O(n^2)\nfor (int i = 0; i &lt; size - 1; i++) {\nfor (int j = i + 1; j &lt; size; j++) {\nif (nums[i] + nums[j] == target)\nreturn {i, j};\n}\n}\nreturn {};\n}\n</code></pre> two_sum.py<pre><code>def two_sum_brute_force(nums: list[int], target: int) -&gt; list[int]:\n\"\"\"\u65b9\u6cd5\u4e00\uff1a\u66b4\u529b\u679a\u4e3e\"\"\"\n# \u4e24\u5c42\u5faa\u73af\uff0c\u65f6\u95f4\u590d\u6742\u5ea6 O(n^2)\nfor i in range(len(nums) - 1):\nfor j in range(i + 1, len(nums)):\nif nums[i] + nums[j] == target:\nreturn [i, j]\nreturn []\n</code></pre> two_sum.go<pre><code>/* \u65b9\u6cd5\u4e00\uff1a\u66b4\u529b\u679a\u4e3e */\nfunc twoSumBruteForce(nums []int, target int) []int {\nsize := len(nums)\n// \u4e24\u5c42\u5faa\u73af\uff0c\u65f6\u95f4\u590d\u6742\u5ea6 O(n^2)\nfor i := 0; i &lt; size-1; i++ {\nfor j := i + 1; i &lt; size; j++ {\nif nums[i]+nums[j] == target {\nreturn []int{i, j}\n}\n}\n}\nreturn nil\n}\n</code></pre> two_sum.js<pre><code>/* \u65b9\u6cd5\u4e00\uff1a\u66b4\u529b\u679a\u4e3e */\nfunction twoSumBruteForce(nums, target) {\nconst n = nums.length;\n// \u4e24\u5c42\u5faa\u73af\uff0c\u65f6\u95f4\u590d\u6742\u5ea6 O(n^2)\nfor (let i = 0; i &lt; n; i++) {\nfor (let j = i + 1; j &lt; n; j++) {\nif (nums[i] + nums[j] === target) {\nreturn [i, j];\n}\n}\n}\nreturn [];\n}\n</code></pre> two_sum.ts<pre><code>/* \u65b9\u6cd5\u4e00\uff1a\u66b4\u529b\u679a\u4e3e */\nfunction twoSumBruteForce(nums: number[], target: number): number[] {\nconst n = nums.length;\n// \u4e24\u5c42\u5faa\u73af\uff0c\u65f6\u95f4\u590d\u6742\u5ea6 O(n^2)\nfor (let i = 0; i &lt; n; i++) {\nfor (let j = i + 1; j &lt; n; j++) {\nif (nums[i] + nums[j] === target) {\nreturn [i, j];\n}\n}\n}\nreturn [];\n}\n</code></pre> two_sum.c<pre><code>/* \u65b9\u6cd5\u4e00\uff1a\u66b4\u529b\u679a\u4e3e */\nint *twoSumBruteForce(int *nums, int numsSize, int target, int *returnSize) {\nfor (int i = 0; i &lt; numsSize; ++i) {\nfor (int j = i + 1; j &lt; numsSize; ++j) {\nif (nums[i] + nums[j] == target) {\nint *res = malloc(sizeof(int) * 2);\nres[0] = i, res[1] = j;\n*returnSize = 2;\nreturn res;\n}\n}\n}\n*returnSize = 0;\nreturn NULL;\n}\n</code></pre> two_sum.cs<pre><code>/* \u65b9\u6cd5\u4e00\uff1a\u66b4\u529b\u679a\u4e3e */\nint[] twoSumBruteForce(int[] nums, int target) {\nint size = nums.Length;\n// \u4e24\u5c42\u5faa\u73af\uff0c\u65f6\u95f4\u590d\u6742\u5ea6 O(n^2)\nfor (int i = 0; i &lt; size - 1; i++) {\nfor (int j = i + 1; j &lt; size; j++) {\nif (nums[i] + nums[j] == target)\nreturn new int[] { i, j };\n}\n}\nreturn new int[0];\n}\n</code></pre> two_sum.swift<pre><code>/* \u65b9\u6cd5\u4e00\uff1a\u66b4\u529b\u679a\u4e3e */\nfunc twoSumBruteForce(nums: [Int], target: Int) -&gt; [Int] {\n// \u4e24\u5c42\u5faa\u73af\uff0c\u65f6\u95f4\u590d\u6742\u5ea6 O(n^2)\nfor i in nums.indices.dropLast() {\nfor j in nums.indices.dropFirst(i + 1) {\nif nums[i] + nums[j] == target {\nreturn [i, j]\n}\n}\n}\nreturn [0]\n}\n</code></pre> two_sum.zig<pre><code>// \u65b9\u6cd5\u4e00\uff1a\u66b4\u529b\u679a\u4e3e\nfn twoSumBruteForce(nums: []i32, target: i32) ?[2]i32 {\nvar size: usize = nums.len;\nvar i: usize = 0;\n// \u4e24\u5c42\u5faa\u73af\uff0c\u65f6\u95f4\u590d\u6742\u5ea6 O(n^2)\nwhile (i &lt; size - 1) : (i += 1) {\nvar j = i + 1;\nwhile (j &lt; size) : (j += 1) {\nif (nums[i] + nums[j] == target) {\nreturn [_]i32{@intCast(i32, i), @intCast(i32, j)};\n}\n}\n}\nreturn null;\n}\n</code></pre> two_sum.dart<pre><code>/* \u65b9\u6cd5\u4e00\uff1a \u66b4\u529b\u679a\u4e3e */\nList&lt;int&gt; twoSumBruteForce(List&lt;int&gt; nums, int target) {\nint size = nums.length;\nfor (var i = 0; i &lt; size - 1; i++) {\nfor (var j = i + 1; j &lt; size; j++) {\nif (nums[i] + nums[j] == target) return [i, j];\n}\n}\nreturn [0];\n}\n</code></pre> <p>\u6b64\u65b9\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(n^2)\\) \uff0c\u7a7a\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(1)\\) \uff0c\u5728\u5927\u6570\u636e\u91cf\u4e0b\u975e\u5e38\u8017\u65f6\u3002</p>"},{"location":"chapter_searching/replace_linear_by_hashing/#1032","title":"10.3.2. \u00a0 \u54c8\u5e0c\u67e5\u627e\uff1a\u4ee5\u7a7a\u95f4\u6362\u65f6\u95f4","text":"<p>\u8003\u8651\u501f\u52a9\u4e00\u4e2a\u54c8\u5e0c\u8868\uff0c\u952e\u503c\u5bf9\u5206\u522b\u4e3a\u6570\u7ec4\u5143\u7d20\u548c\u5143\u7d20\u7d22\u5f15\u3002\u5faa\u73af\u904d\u5386\u6570\u7ec4\uff0c\u6bcf\u8f6e\u6267\u884c\uff1a</p> <ol> <li>\u5224\u65ad\u6570\u5b57 <code>target - nums[i]</code> \u662f\u5426\u5728\u54c8\u5e0c\u8868\u4e2d\uff0c\u82e5\u662f\u5219\u76f4\u63a5\u8fd4\u56de\u8fd9\u4e24\u4e2a\u5143\u7d20\u7684\u7d22\u5f15\uff1b</li> <li>\u5c06\u952e\u503c\u5bf9 <code>nums[i]</code> \u548c\u7d22\u5f15 <code>i</code> \u6dfb\u52a0\u8fdb\u54c8\u5e0c\u8868\uff1b</li> </ol> &lt;1&gt;&lt;2&gt;&lt;3&gt; <p></p> <p></p> <p></p> <p>\u5b9e\u73b0\u4ee3\u7801\u5982\u4e0b\u6240\u793a\uff0c\u4ec5\u9700\u5355\u5c42\u5faa\u73af\u5373\u53ef\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart two_sum.java<pre><code>/* \u65b9\u6cd5\u4e8c\uff1a\u8f85\u52a9\u54c8\u5e0c\u8868 */\nint[] twoSumHashTable(int[] nums, int target) {\nint size = nums.length;\n// \u8f85\u52a9\u54c8\u5e0c\u8868\uff0c\u7a7a\u95f4\u590d\u6742\u5ea6 O(n)\nMap&lt;Integer, Integer&gt; dic = new HashMap&lt;&gt;();\n// \u5355\u5c42\u5faa\u73af\uff0c\u65f6\u95f4\u590d\u6742\u5ea6 O(n)\nfor (int i = 0; i &lt; size; i++) {\nif (dic.containsKey(target - nums[i])) {\nreturn new int[] { dic.get(target - nums[i]), i };\n}\ndic.put(nums[i], i);\n}\nreturn new int[0];\n}\n</code></pre> two_sum.cpp<pre><code>/* \u65b9\u6cd5\u4e8c\uff1a\u8f85\u52a9\u54c8\u5e0c\u8868 */\nvector&lt;int&gt; twoSumHashTable(vector&lt;int&gt; &amp;nums, int target) {\nint size = nums.size();\n// \u8f85\u52a9\u54c8\u5e0c\u8868\uff0c\u7a7a\u95f4\u590d\u6742\u5ea6 O(n)\nunordered_map&lt;int, int&gt; dic;\n// \u5355\u5c42\u5faa\u73af\uff0c\u65f6\u95f4\u590d\u6742\u5ea6 O(n)\nfor (int i = 0; i &lt; size; i++) {\nif (dic.find(target - nums[i]) != dic.end()) {\nreturn {dic[target - nums[i]], i};\n}\ndic.emplace(nums[i], i);\n}\nreturn {};\n}\n</code></pre> two_sum.py<pre><code>def two_sum_hash_table(nums: list[int], target: int) -&gt; list[int]:\n\"\"\"\u65b9\u6cd5\u4e8c\uff1a\u8f85\u52a9\u54c8\u5e0c\u8868\"\"\"\n# \u8f85\u52a9\u54c8\u5e0c\u8868\uff0c\u7a7a\u95f4\u590d\u6742\u5ea6 O(n)\ndic = {}\n# \u5355\u5c42\u5faa\u73af\uff0c\u65f6\u95f4\u590d\u6742\u5ea6 O(n)\nfor i in range(len(nums)):\nif target - nums[i] in dic:\nreturn [dic[target - nums[i]], i]\ndic[nums[i]] = i\nreturn []\n</code></pre> two_sum.go<pre><code>/* \u65b9\u6cd5\u4e8c\uff1a\u8f85\u52a9\u54c8\u5e0c\u8868 */\nfunc twoSumHashTable(nums []int, target int) []int {\n// \u8f85\u52a9\u54c8\u5e0c\u8868\uff0c\u7a7a\u95f4\u590d\u6742\u5ea6 O(n)\nhashTable := map[int]int{}\n// \u5355\u5c42\u5faa\u73af\uff0c\u65f6\u95f4\u590d\u6742\u5ea6 O(n)\nfor idx, val := range nums {\nif preIdx, ok := hashTable[target-val]; ok {\nreturn []int{preIdx, idx}\n}\nhashTable[val] = idx\n}\nreturn nil\n}\n</code></pre> two_sum.js<pre><code>/* \u65b9\u6cd5\u4e8c\uff1a\u8f85\u52a9\u54c8\u5e0c\u8868 */\nfunction twoSumHashTable(nums, target) {\n// \u8f85\u52a9\u54c8\u5e0c\u8868\uff0c\u7a7a\u95f4\u590d\u6742\u5ea6 O(n)\nlet m = {};\n// \u5355\u5c42\u5faa\u73af\uff0c\u65f6\u95f4\u590d\u6742\u5ea6 O(n)\nfor (let i = 0; i &lt; nums.length; i++) {\nif (m[nums[i]] !== undefined) {\nreturn [m[nums[i]], i];\n} else {\nm[target - nums[i]] = i;\n}\n}\nreturn [];\n}\n</code></pre> two_sum.ts<pre><code>/* \u65b9\u6cd5\u4e8c\uff1a\u8f85\u52a9\u54c8\u5e0c\u8868 */\nfunction twoSumHashTable(nums: number[], target: number): number[] {\n// \u8f85\u52a9\u54c8\u5e0c\u8868\uff0c\u7a7a\u95f4\u590d\u6742\u5ea6 O(n)\nlet m: Map&lt;number, number&gt; = new Map();\n// \u5355\u5c42\u5faa\u73af\uff0c\u65f6\u95f4\u590d\u6742\u5ea6 O(n)\nfor (let i = 0; i &lt; nums.length; i++) {\nlet index = m.get(nums[i]);\nif (index !== undefined) {\nreturn [index, i];\n} else {\nm.set(target - nums[i], i);\n}\n}\nreturn [];\n}\n</code></pre> two_sum.c<pre><code>/* \u54c8\u5e0c\u8868 */\nstruct hashTable {\nint key;\nint val;\nUT_hash_handle hh; // \u57fa\u4e8e uthash.h \u5b9e\u73b0\n};\ntypedef struct hashTable hashTable;\n/* \u54c8\u5e0c\u8868\u67e5\u8be2 */\nhashTable *find(hashTable *h, int key) {\nhashTable *tmp;\nHASH_FIND_INT(h, &amp;key, tmp);\nreturn tmp;\n}\n/* \u54c8\u5e0c\u8868\u5143\u7d20\u63d2\u5165 */\nvoid insert(hashTable *h, int key, int val) {\nhashTable *t = find(h, key);\nif (t == NULL) {\nhashTable *tmp = malloc(sizeof(hashTable));\ntmp-&gt;key = key, tmp-&gt;val = val;\nHASH_ADD_INT(h, key, tmp);\n} else {\nt-&gt;val = val;\n}\n}\n/* \u65b9\u6cd5\u4e8c\uff1a\u8f85\u52a9\u54c8\u5e0c\u8868 */\nint *twoSumHashTable(int *nums, int numsSize, int target, int *returnSize) {\nhashTable *hashtable = NULL;\nfor (int i = 0; i &lt; numsSize; i++) {\nhashTable *t = find(hashtable, target - nums[i]);\nif (t != NULL) {\nint *res = malloc(sizeof(int) * 2);\nres[0] = t-&gt;val, res[1] = i;\n*returnSize = 2;\nreturn res;\n}\ninsert(hashtable, nums[i], i);\n}\n*returnSize = 0;\nreturn NULL;\n}\n</code></pre> two_sum.cs<pre><code>/* \u65b9\u6cd5\u4e8c\uff1a\u8f85\u52a9\u54c8\u5e0c\u8868 */\nint[] twoSumHashTable(int[] nums, int target) {\nint size = nums.Length;\n// \u8f85\u52a9\u54c8\u5e0c\u8868\uff0c\u7a7a\u95f4\u590d\u6742\u5ea6 O(n)\nDictionary&lt;int, int&gt; dic = new();\n// \u5355\u5c42\u5faa\u73af\uff0c\u65f6\u95f4\u590d\u6742\u5ea6 O(n)\nfor (int i = 0; i &lt; size; i++) {\nif (dic.ContainsKey(target - nums[i])) {\nreturn new int[] { dic[target - nums[i]], i };\n}\ndic.Add(nums[i], i);\n}\nreturn new int[0];\n}\n</code></pre> two_sum.swift<pre><code>/* \u65b9\u6cd5\u4e8c\uff1a\u8f85\u52a9\u54c8\u5e0c\u8868 */\nfunc twoSumHashTable(nums: [Int], target: Int) -&gt; [Int] {\n// \u8f85\u52a9\u54c8\u5e0c\u8868\uff0c\u7a7a\u95f4\u590d\u6742\u5ea6 O(n)\nvar dic: [Int: Int] = [:]\n// \u5355\u5c42\u5faa\u73af\uff0c\u65f6\u95f4\u590d\u6742\u5ea6 O(n)\nfor i in nums.indices {\nif let j = dic[target - nums[i]] {\nreturn [j, i]\n}\ndic[nums[i]] = i\n}\nreturn [0]\n}\n</code></pre> two_sum.zig<pre><code>// \u65b9\u6cd5\u4e8c\uff1a\u8f85\u52a9\u54c8\u5e0c\u8868\nfn twoSumHashTable(nums: []i32, target: i32) !?[2]i32 {\nvar size: usize = nums.len;\n// \u8f85\u52a9\u54c8\u5e0c\u8868\uff0c\u7a7a\u95f4\u590d\u6742\u5ea6 O(n)\nvar dic = std.AutoHashMap(i32, i32).init(std.heap.page_allocator);\ndefer dic.deinit();\nvar i: usize = 0;\n// \u5355\u5c42\u5faa\u73af\uff0c\u65f6\u95f4\u590d\u6742\u5ea6 O(n)\nwhile (i &lt; size) : (i += 1) {\nif (dic.contains(target - nums[i])) {\nreturn [_]i32{dic.get(target - nums[i]).?, @intCast(i32, i)};\n}\ntry dic.put(nums[i], @intCast(i32, i));\n}\nreturn null;\n}\n</code></pre> two_sum.dart<pre><code>/* \u65b9\u6cd5\u4e8c\uff1a \u8f85\u52a9\u54c8\u5e0c\u8868 */\nList&lt;int&gt; twoSumHashTable(List&lt;int&gt; nums, int target) {\nint size = nums.length;\nMap&lt;int, int&gt; dic = HashMap();\nfor (var i = 0; i &lt; size; i++) {\nif (dic.containsKey(target - nums[i])) {\nreturn [dic[target - nums[i]]!, i];\n}\ndic.putIfAbsent(nums[i], () =&gt; i);\n}\nreturn [0];\n}\n</code></pre> <p>\u6b64\u65b9\u6cd5\u901a\u8fc7\u54c8\u5e0c\u67e5\u627e\u5c06\u65f6\u95f4\u590d\u6742\u5ea6\u4ece \\(O(n^2)\\) \u964d\u4f4e\u81f3 \\(O(n)\\) \uff0c\u5927\u5e45\u63d0\u5347\u8fd0\u884c\u6548\u7387\u3002</p> <p>\u7531\u4e8e\u9700\u8981\u7ef4\u62a4\u4e00\u4e2a\u989d\u5916\u7684\u54c8\u5e0c\u8868\uff0c\u56e0\u6b64\u7a7a\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(n)\\) \u3002\u5c3d\u7ba1\u5982\u6b64\uff0c\u8be5\u65b9\u6cd5\u7684\u6574\u4f53\u65f6\u7a7a\u6548\u7387\u66f4\u4e3a\u5747\u8861\uff0c\u56e0\u6b64\u5b83\u662f\u672c\u9898\u7684\u6700\u4f18\u89e3\u6cd5\u3002</p>"},{"location":"chapter_searching/searching_algorithm_revisited/","title":"10.4. \u00a0 \u91cd\u8bc6\u641c\u7d22\u7b97\u6cd5","text":"<p>\u300c\u641c\u7d22\u7b97\u6cd5 Searching Algorithm\u300d\u7528\u4e8e\u5728\u6570\u636e\u7ed3\u6784\uff08\u4f8b\u5982\u6570\u7ec4\u3001\u94fe\u8868\u3001\u6811\u6216\u56fe\uff09\u4e2d\u641c\u7d22\u4e00\u4e2a\u6216\u4e00\u7ec4\u6ee1\u8db3\u7279\u5b9a\u6761\u4ef6\u7684\u5143\u7d20\u3002</p> <p>\u6839\u636e\u5b9e\u73b0\u601d\u8def\uff0c\u641c\u7d22\u7b97\u6cd5\u603b\u4f53\u53ef\u5206\u4e3a\u4e24\u79cd\uff1a</p> <ul> <li>\u901a\u8fc7\u904d\u5386\u6570\u636e\u7ed3\u6784\u6765\u5b9a\u4f4d\u76ee\u6807\u5143\u7d20\uff0c\u4f8b\u5982\u6570\u7ec4\u3001\u94fe\u8868\u3001\u6811\u548c\u56fe\u7684\u904d\u5386\u7b49\u3002</li> <li>\u5229\u7528\u6570\u636e\u7ec4\u7ec7\u7ed3\u6784\u6216\u6570\u636e\u5305\u542b\u7684\u5148\u9a8c\u4fe1\u606f\uff0c\u5b9e\u73b0\u9ad8\u6548\u5143\u7d20\u67e5\u627e\uff0c\u4f8b\u5982\u4e8c\u5206\u67e5\u627e\u3001\u54c8\u5e0c\u67e5\u627e\u548c\u4e8c\u53c9\u641c\u7d22\u6811\u67e5\u627e\u7b49\u3002</li> </ul> <p>\u4e0d\u96be\u53d1\u73b0\uff0c\u8fd9\u4e9b\u77e5\u8bc6\u70b9\u90fd\u5df2\u5728\u524d\u9762\u7684\u7ae0\u8282\u4e2d\u4ecb\u7ecd\u8fc7\uff0c\u56e0\u6b64\u641c\u7d22\u7b97\u6cd5\u5bf9\u4e8e\u6211\u4eec\u6765\u8bf4\u5e76\u4e0d\u964c\u751f\u3002\u5728\u672c\u8282\u4e2d\uff0c\u6211\u4eec\u5c06\u4ece\u66f4\u52a0\u7cfb\u7edf\u7684\u89c6\u89d2\u5207\u5165\uff0c\u91cd\u65b0\u5ba1\u89c6\u641c\u7d22\u7b97\u6cd5\u3002</p>"},{"location":"chapter_searching/searching_algorithm_revisited/#1041","title":"10.4.1. \u00a0 \u66b4\u529b\u641c\u7d22","text":"<p>\u66b4\u529b\u641c\u7d22\u901a\u8fc7\u904d\u5386\u6570\u636e\u7ed3\u6784\u7684\u6bcf\u4e2a\u5143\u7d20\u6765\u5b9a\u4f4d\u76ee\u6807\u5143\u7d20\u3002</p> <ul> <li>\u300c\u7ebf\u6027\u641c\u7d22\u300d\u9002\u7528\u4e8e\u6570\u7ec4\u548c\u94fe\u8868\u7b49\u7ebf\u6027\u6570\u636e\u7ed3\u6784\u3002\u5b83\u4ece\u6570\u636e\u7ed3\u6784\u7684\u4e00\u7aef\u5f00\u59cb\uff0c\u9010\u4e2a\u8bbf\u95ee\u5143\u7d20\uff0c\u76f4\u5230\u627e\u5230\u76ee\u6807\u5143\u7d20\u6216\u5230\u8fbe\u53e6\u4e00\u7aef\u4ecd\u6ca1\u6709\u627e\u5230\u76ee\u6807\u5143\u7d20\u4e3a\u6b62\u3002</li> <li>\u300c\u5e7f\u5ea6\u4f18\u5148\u641c\u7d22\u300d\u548c\u300c\u6df1\u5ea6\u4f18\u5148\u641c\u7d22\u300d\u662f\u56fe\u548c\u6811\u7684\u4e24\u79cd\u904d\u5386\u7b56\u7565\u3002\u5e7f\u5ea6\u4f18\u5148\u641c\u7d22\u4ece\u521d\u59cb\u8282\u70b9\u5f00\u59cb\u9010\u5c42\u641c\u7d22\uff0c\u7531\u8fd1\u53ca\u8fdc\u5730\u8bbf\u95ee\u5404\u4e2a\u8282\u70b9\u3002\u6df1\u5ea6\u4f18\u5148\u641c\u7d22\u662f\u4ece\u521d\u59cb\u8282\u70b9\u5f00\u59cb\uff0c\u6cbf\u7740\u4e00\u6761\u8def\u5f84\u8d70\u5230\u5934\u4e3a\u6b62\uff0c\u518d\u56de\u6eaf\u5e76\u5c1d\u8bd5\u5176\u4ed6\u8def\u5f84\uff0c\u76f4\u5230\u904d\u5386\u5b8c\u6574\u4e2a\u6570\u636e\u7ed3\u6784\u3002</li> </ul> <p>\u66b4\u529b\u641c\u7d22\u7684\u4f18\u70b9\u662f\u7b80\u5355\u4e14\u901a\u7528\u6027\u597d\uff0c\u65e0\u9700\u5bf9\u6570\u636e\u505a\u9884\u5904\u7406\u548c\u501f\u52a9\u989d\u5916\u7684\u6570\u636e\u7ed3\u6784\u3002</p> <p>\u7136\u800c\uff0c\u6b64\u7c7b\u7b97\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(n)\\) \uff0c\u5176\u4e2d \\(n\\) \u4e3a\u5143\u7d20\u6570\u91cf\uff0c\u56e0\u6b64\u5728\u6570\u636e\u91cf\u8f83\u5927\u7684\u60c5\u51b5\u4e0b\u6027\u80fd\u8f83\u5dee\u3002</p>"},{"location":"chapter_searching/searching_algorithm_revisited/#1042","title":"10.4.2. \u00a0 \u81ea\u9002\u5e94\u641c\u7d22","text":"<p>\u81ea\u9002\u5e94\u641c\u7d22\u5229\u7528\u6570\u636e\u7684\u7279\u6709\u5c5e\u6027\uff08\u4f8b\u5982\u6709\u5e8f\u6027\uff09\u6765\u4f18\u5316\u641c\u7d22\u8fc7\u7a0b\uff0c\u4ece\u800c\u66f4\u9ad8\u6548\u5730\u5b9a\u4f4d\u76ee\u6807\u5143\u7d20\u3002</p> <ul> <li>\u300c\u4e8c\u5206\u67e5\u627e\u300d\u5229\u7528\u6570\u636e\u7684\u6709\u5e8f\u6027\u5b9e\u73b0\u9ad8\u6548\u67e5\u627e\uff0c\u4ec5\u9002\u7528\u4e8e\u6570\u7ec4\u3002</li> <li>\u300c\u54c8\u5e0c\u67e5\u627e\u300d\u5229\u7528\u54c8\u5e0c\u8868\u5c06\u641c\u7d22\u6570\u636e\u548c\u76ee\u6807\u6570\u636e\u5efa\u7acb\u4e3a\u952e\u503c\u5bf9\u6620\u5c04\uff0c\u4ece\u800c\u5b9e\u73b0\u67e5\u8be2\u64cd\u4f5c\u3002</li> <li>\u300c\u6811\u67e5\u627e\u300d\u5728\u7279\u5b9a\u7684\u6811\u7ed3\u6784\uff08\u4f8b\u5982\u4e8c\u53c9\u641c\u7d22\u6811\uff09\u4e2d\uff0c\u57fa\u4e8e\u6bd4\u8f83\u8282\u70b9\u503c\u6765\u5feb\u901f\u6392\u9664\u8282\u70b9\uff0c\u4ece\u800c\u5b9a\u4f4d\u76ee\u6807\u5143\u7d20\u3002</li> </ul> <p>\u6b64\u7c7b\u7b97\u6cd5\u7684\u4f18\u70b9\u662f\u6548\u7387\u9ad8\uff0c\u65f6\u95f4\u590d\u6742\u5ea6\u53ef\u8fbe\u5230 \\(O(\\log n)\\) \u751a\u81f3 \\(O(1)\\) \u3002</p> <p>\u7136\u800c\uff0c\u4f7f\u7528\u8fd9\u4e9b\u7b97\u6cd5\u5f80\u5f80\u9700\u8981\u5bf9\u6570\u636e\u8fdb\u884c\u9884\u5904\u7406\u3002\u4f8b\u5982\uff0c\u4e8c\u5206\u67e5\u627e\u9700\u8981\u9884\u5148\u5bf9\u6570\u7ec4\u8fdb\u884c\u6392\u5e8f\uff0c\u54c8\u5e0c\u67e5\u627e\u548c\u6811\u67e5\u627e\u90fd\u9700\u8981\u501f\u52a9\u989d\u5916\u7684\u6570\u636e\u7ed3\u6784\uff0c\u7ef4\u62a4\u8fd9\u4e9b\u6570\u636e\u7ed3\u6784\u4e5f\u9700\u8981\u989d\u5916\u7684\u65f6\u95f4\u548c\u7a7a\u95f4\u5f00\u652f\u3002</p> <p>Note</p> <p>\u81ea\u9002\u5e94\u641c\u7d22\u7b97\u6cd5\u5e38\u88ab\u79f0\u4e3a\u67e5\u627e\u7b97\u6cd5\uff0c\u4e3b\u8981\u5173\u6ce8\u5728\u7279\u5b9a\u6570\u636e\u7ed3\u6784\u4e2d\u5feb\u901f\u68c0\u7d22\u76ee\u6807\u5143\u7d20\u3002</p>"},{"location":"chapter_searching/searching_algorithm_revisited/#1043","title":"10.4.3. \u00a0 \u641c\u7d22\u65b9\u6cd5\u9009\u53d6","text":"<p>\u7ed9\u5b9a\u5927\u5c0f\u4e3a \\(n\\) \u7684\u4e00\u7ec4\u6570\u636e\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u7ebf\u6027\u641c\u7d22\u3001\u4e8c\u5206\u67e5\u627e\u3001\u6811\u67e5\u627e\u3001\u54c8\u5e0c\u67e5\u627e\u7b49\u591a\u79cd\u65b9\u6cd5\u5728\u8be5\u6570\u636e\u4e2d\u641c\u7d22\u76ee\u6807\u5143\u7d20\u3002\u5404\u4e2a\u65b9\u6cd5\u7684\u5de5\u4f5c\u539f\u7406\u5982\u4e0b\u56fe\u6240\u793a\u3002</p> <p></p> <p> Fig. \u591a\u79cd\u641c\u7d22\u7b56\u7565 </p> <p>\u4e0a\u8ff0\u51e0\u79cd\u65b9\u6cd5\u7684\u64cd\u4f5c\u6548\u7387\u4e0e\u7279\u6027\u5982\u4e0b\u8868\u6240\u793a\u3002</p> \u7ebf\u6027\u641c\u7d22 \u4e8c\u5206\u67e5\u627e \u6811\u67e5\u627e \u54c8\u5e0c\u67e5\u627e \u67e5\u627e\u5143\u7d20 \\(O(n)\\) \\(O(\\log n)\\) \\(O(\\log n)\\) \\(O(1)\\) \u63d2\u5165\u5143\u7d20 \\(O(1)\\) \\(O(n)\\) \\(O(\\log n)\\) \\(O(1)\\) \u5220\u9664\u5143\u7d20 \\(O(n)\\) \\(O(n)\\) \\(O(\\log n)\\) \\(O(1)\\) \u989d\u5916\u7a7a\u95f4 \\(O(1)\\) \\(O(1)\\) \\(O(n)\\) \\(O(n)\\) \u6570\u636e\u9884\u5904\u7406 / \u6392\u5e8f \\(O(n \\log n)\\) \u5efa\u6811 \\(O(n \\log n)\\) \u5efa\u54c8\u5e0c\u8868 \\(O(n)\\) \u6570\u636e\u662f\u5426\u6709\u5e8f \u65e0\u5e8f \u6709\u5e8f \u6709\u5e8f \u65e0\u5e8f <p>\u9664\u4e86\u4ee5\u4e0a\u8868\u683c\u5185\u5bb9\uff0c\u641c\u7d22\u7b97\u6cd5\u7684\u9009\u62e9\u8fd8\u53d6\u51b3\u4e8e\u6570\u636e\u4f53\u91cf\u3001\u641c\u7d22\u6027\u80fd\u8981\u6c42\u3001\u6570\u636e\u67e5\u8be2\u4e0e\u66f4\u65b0\u9891\u7387\u7b49\u3002</p> <p>\u7ebf\u6027\u641c\u7d22</p> <ul> <li>\u901a\u7528\u6027\u8f83\u597d\uff0c\u65e0\u9700\u4efb\u4f55\u6570\u636e\u9884\u5904\u7406\u64cd\u4f5c\u3002\u5047\u5982\u6211\u4eec\u4ec5\u9700\u67e5\u8be2\u4e00\u6b21\u6570\u636e\uff0c\u90a3\u4e48\u5176\u4ed6\u4e09\u79cd\u65b9\u6cd5\u7684\u6570\u636e\u9884\u5904\u7406\u7684\u65f6\u95f4\u6bd4\u7ebf\u6027\u641c\u7d22\u7684\u65f6\u95f4\u8fd8\u8981\u66f4\u957f\u3002</li> <li>\u9002\u7528\u4e8e\u4f53\u91cf\u8f83\u5c0f\u7684\u6570\u636e\uff0c\u6b64\u60c5\u51b5\u4e0b\u65f6\u95f4\u590d\u6742\u5ea6\u5bf9\u6548\u7387\u5f71\u54cd\u8f83\u5c0f\u3002</li> <li>\u9002\u7528\u4e8e\u6570\u636e\u66f4\u65b0\u9891\u7387\u8f83\u9ad8\u7684\u573a\u666f\uff0c\u56e0\u4e3a\u8be5\u65b9\u6cd5\u4e0d\u9700\u8981\u5bf9\u6570\u636e\u8fdb\u884c\u4efb\u4f55\u989d\u5916\u7ef4\u62a4\u3002</li> </ul> <p>\u4e8c\u5206\u67e5\u627e</p> <ul> <li>\u9002\u7528\u4e8e\u5927\u6570\u636e\u91cf\u7684\u60c5\u51b5\uff0c\u6548\u7387\u8868\u73b0\u7a33\u5b9a\uff0c\u6700\u5dee\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(\\log n)\\) \u3002</li> <li>\u6570\u636e\u91cf\u4e0d\u80fd\u8fc7\u5927\uff0c\u56e0\u4e3a\u5b58\u50a8\u6570\u7ec4\u9700\u8981\u8fde\u7eed\u7684\u5185\u5b58\u7a7a\u95f4\u3002</li> <li>\u4e0d\u9002\u7528\u4e8e\u9ad8\u9891\u589e\u5220\u6570\u636e\u7684\u573a\u666f\uff0c\u56e0\u4e3a\u7ef4\u62a4\u6709\u5e8f\u6570\u7ec4\u7684\u5f00\u9500\u8f83\u5927\u3002</li> </ul> <p>\u54c8\u5e0c\u67e5\u627e</p> <ul> <li>\u9002\u5408\u5bf9\u67e5\u8be2\u6027\u80fd\u8981\u6c42\u5f88\u9ad8\u7684\u573a\u666f\uff0c\u5e73\u5747\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(1)\\) \u3002</li> <li>\u4e0d\u9002\u5408\u9700\u8981\u6709\u5e8f\u6570\u636e\u6216\u8303\u56f4\u67e5\u627e\u7684\u573a\u666f\uff0c\u56e0\u4e3a\u54c8\u5e0c\u8868\u65e0\u6cd5\u7ef4\u62a4\u6570\u636e\u7684\u6709\u5e8f\u6027\u3002</li> <li>\u5bf9\u54c8\u5e0c\u51fd\u6570\u548c\u54c8\u5e0c\u51b2\u7a81\u5904\u7406\u7b56\u7565\u7684\u4f9d\u8d56\u6027\u8f83\u9ad8\uff0c\u5177\u6709\u8f83\u5927\u7684\u6027\u80fd\u52a3\u5316\u98ce\u9669\u3002</li> <li>\u4e0d\u9002\u5408\u6570\u636e\u91cf\u8fc7\u5927\u7684\u60c5\u51b5\uff0c\u56e0\u4e3a\u54c8\u5e0c\u8868\u9700\u8981\u989d\u5916\u7a7a\u95f4\u6765\u6700\u5927\u7a0b\u5ea6\u5730\u51cf\u5c11\u51b2\u7a81\uff0c\u4ece\u800c\u63d0\u4f9b\u826f\u597d\u7684\u67e5\u8be2\u6027\u80fd\u3002</li> </ul> <p>\u6811\u67e5\u627e</p> <ul> <li>\u9002\u7528\u4e8e\u6d77\u91cf\u6570\u636e\uff0c\u56e0\u4e3a\u6811\u8282\u70b9\u5728\u5185\u5b58\u4e2d\u662f\u79bb\u6563\u5b58\u50a8\u7684\u3002</li> <li>\u9002\u5408\u9700\u8981\u7ef4\u62a4\u6709\u5e8f\u6570\u636e\u6216\u8303\u56f4\u67e5\u627e\u7684\u573a\u666f\u3002</li> <li>\u5728\u6301\u7eed\u589e\u5220\u8282\u70b9\u7684\u8fc7\u7a0b\u4e2d\uff0c\u4e8c\u53c9\u641c\u7d22\u6811\u53ef\u80fd\u4ea7\u751f\u503e\u659c\uff0c\u65f6\u95f4\u590d\u6742\u5ea6\u52a3\u5316\u81f3 \\(O(n)\\) \u3002</li> <li>\u82e5\u4f7f\u7528 AVL \u6811\u6216\u7ea2\u9ed1\u6811\uff0c\u5219\u5404\u9879\u64cd\u4f5c\u53ef\u5728 \\(O(\\log n)\\) \u6548\u7387\u4e0b\u7a33\u5b9a\u8fd0\u884c\uff0c\u4f46\u7ef4\u62a4\u6811\u5e73\u8861\u7684\u64cd\u4f5c\u4f1a\u589e\u52a0\u989d\u5916\u5f00\u9500\u3002</li> </ul>"},{"location":"chapter_searching/summary/","title":"10.5. \u00a0 \u5c0f\u7ed3","text":"<ul> <li>\u4e8c\u5206\u67e5\u627e\u4f9d\u8d56\u4e8e\u6570\u636e\u7684\u6709\u5e8f\u6027\uff0c\u901a\u8fc7\u5faa\u73af\u9010\u6b65\u7f29\u51cf\u4e00\u534a\u641c\u7d22\u533a\u95f4\u6765\u5b9e\u73b0\u67e5\u627e\u3002\u5b83\u8981\u6c42\u8f93\u5165\u6570\u636e\u6709\u5e8f\uff0c\u4e14\u4ec5\u9002\u7528\u4e8e\u6570\u7ec4\u6216\u57fa\u4e8e\u6570\u7ec4\u5b9e\u73b0\u7684\u6570\u636e\u7ed3\u6784\u3002</li> <li>\u66b4\u529b\u641c\u7d22\u901a\u8fc7\u904d\u5386\u6570\u636e\u7ed3\u6784\u6765\u5b9a\u4f4d\u6570\u636e\u3002\u7ebf\u6027\u641c\u7d22\u9002\u7528\u4e8e\u6570\u7ec4\u548c\u94fe\u8868\uff0c\u5e7f\u5ea6\u4f18\u5148\u641c\u7d22\u548c\u6df1\u5ea6\u4f18\u5148\u641c\u7d22\u9002\u7528\u4e8e\u56fe\u548c\u6811\u3002\u6b64\u7c7b\u7b97\u6cd5\u901a\u7528\u6027\u597d\uff0c\u65e0\u9700\u5bf9\u6570\u636e\u9884\u5904\u7406\uff0c\u4f46\u65f6\u95f4\u590d\u6742\u5ea6 \\(O(n)\\) \u8f83\u9ad8\u3002</li> <li>\u54c8\u5e0c\u67e5\u627e\u3001\u6811\u67e5\u627e\u548c\u4e8c\u5206\u67e5\u627e\u5c5e\u4e8e\u9ad8\u6548\u641c\u7d22\u65b9\u6cd5\uff0c\u53ef\u5728\u7279\u5b9a\u6570\u636e\u7ed3\u6784\u4e2d\u5feb\u901f\u5b9a\u4f4d\u76ee\u6807\u5143\u7d20\u3002\u6b64\u7c7b\u7b97\u6cd5\u6548\u7387\u9ad8\uff0c\u65f6\u95f4\u590d\u6742\u5ea6\u53ef\u8fbe \\(O(\\log n)\\) \u751a\u81f3 \\(O(1)\\) \uff0c\u4f46\u901a\u5e38\u9700\u8981\u501f\u52a9\u989d\u5916\u6570\u636e\u7ed3\u6784\u3002</li> <li>\u5b9e\u9645\u4e2d\uff0c\u6211\u4eec\u9700\u8981\u5bf9\u6570\u636e\u4f53\u91cf\u3001\u641c\u7d22\u6027\u80fd\u8981\u6c42\u3001\u6570\u636e\u67e5\u8be2\u548c\u66f4\u65b0\u9891\u7387\u7b49\u56e0\u7d20\u8fdb\u884c\u5177\u4f53\u5206\u6790\uff0c\u4ece\u800c\u9009\u62e9\u5408\u9002\u7684\u641c\u7d22\u65b9\u6cd5\u3002</li> <li>\u7ebf\u6027\u641c\u7d22\u9002\u7528\u4e8e\u5c0f\u578b\u6216\u9891\u7e41\u66f4\u65b0\u7684\u6570\u636e\uff1b\u4e8c\u5206\u67e5\u627e\u9002\u7528\u4e8e\u5927\u578b\u3001\u6392\u5e8f\u7684\u6570\u636e\uff1b\u54c8\u5e0c\u67e5\u627e\u9002\u5408\u5bf9\u67e5\u8be2\u6548\u7387\u8981\u6c42\u8f83\u9ad8\u4e14\u65e0\u9700\u8303\u56f4\u67e5\u8be2\u7684\u6570\u636e\uff1b\u6811\u67e5\u627e\u9002\u7528\u4e8e\u9700\u8981\u7ef4\u62a4\u987a\u5e8f\u548c\u652f\u6301\u8303\u56f4\u67e5\u8be2\u7684\u5927\u578b\u52a8\u6001\u6570\u636e\u3002</li> <li>\u7528\u54c8\u5e0c\u67e5\u627e\u66ff\u6362\u7ebf\u6027\u67e5\u627e\u662f\u4e00\u79cd\u5e38\u7528\u7684\u4f18\u5316\u8fd0\u884c\u65f6\u95f4\u7684\u7b56\u7565\uff0c\u53ef\u5c06\u65f6\u95f4\u590d\u6742\u5ea6\u4ece \\(O(n)\\) \u964d\u4f4e\u81f3 \\(O(1)\\) \u3002 </li> </ul>"},{"location":"chapter_sorting/","title":"11. \u00a0 \u6392\u5e8f","text":""},{"location":"chapter_sorting/bubble_sort/","title":"11.3. \u00a0 \u5192\u6ce1\u6392\u5e8f","text":"<p>\u300c\u5192\u6ce1\u6392\u5e8f Bubble Sort\u300d\u901a\u8fc7\u8fde\u7eed\u5730\u6bd4\u8f83\u4e0e\u4ea4\u6362\u76f8\u90bb\u5143\u7d20\u5b9e\u73b0\u6392\u5e8f\u3002\u8fd9\u4e2a\u8fc7\u7a0b\u5c31\u50cf\u6c14\u6ce1\u4ece\u5e95\u90e8\u5347\u5230\u9876\u90e8\u4e00\u6837\uff0c\u56e0\u6b64\u5f97\u540d\u5192\u6ce1\u6392\u5e8f\u3002</p> <p>\u6211\u4eec\u53ef\u4ee5\u5229\u7528\u5143\u7d20\u4ea4\u6362\u64cd\u4f5c\u6a21\u62df\u4e0a\u8ff0\u8fc7\u7a0b\uff1a\u4ece\u6570\u7ec4\u6700\u5de6\u7aef\u5f00\u59cb\u5411\u53f3\u904d\u5386\uff0c\u4f9d\u6b21\u6bd4\u8f83\u76f8\u90bb\u5143\u7d20\u5927\u5c0f\uff0c\u5982\u679c\u201c\u5de6\u5143\u7d20 &gt; \u53f3\u5143\u7d20\u201d\u5c31\u4ea4\u6362\u5b83\u4fe9\u3002\u904d\u5386\u5b8c\u6210\u540e\uff0c\u6700\u5927\u7684\u5143\u7d20\u4f1a\u88ab\u79fb\u52a8\u5230\u6570\u7ec4\u7684\u6700\u53f3\u7aef\u3002</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p>"},{"location":"chapter_sorting/bubble_sort/#1131","title":"11.3.1. \u00a0 \u7b97\u6cd5\u6d41\u7a0b","text":"<p>\u8bbe\u6570\u7ec4\u7684\u957f\u5ea6\u4e3a \\(n\\) \uff0c\u5192\u6ce1\u6392\u5e8f\u7684\u6b65\u9aa4\u4e3a\uff1a</p> <ol> <li>\u9996\u5148\uff0c\u5bf9 \\(n\\) \u4e2a\u5143\u7d20\u6267\u884c\u201c\u5192\u6ce1\u201d\uff0c\u5c06\u6570\u7ec4\u7684\u6700\u5927\u5143\u7d20\u4ea4\u6362\u81f3\u6b63\u786e\u4f4d\u7f6e\uff0c</li> <li>\u63a5\u4e0b\u6765\uff0c\u5bf9\u5269\u4f59 \\(n - 1\\) \u4e2a\u5143\u7d20\u6267\u884c\u201c\u5192\u6ce1\u201d\uff0c\u5c06\u7b2c\u4e8c\u5927\u5143\u7d20\u4ea4\u6362\u81f3\u6b63\u786e\u4f4d\u7f6e\u3002</li> <li>\u4ee5\u6b64\u7c7b\u63a8\uff0c\u7ecf\u8fc7 \\(n - 1\\) \u8f6e\u201c\u5192\u6ce1\u201d\u540e\uff0c\u524d \\(n - 1\\) \u5927\u7684\u5143\u7d20\u90fd\u88ab\u4ea4\u6362\u81f3\u6b63\u786e\u4f4d\u7f6e\u3002</li> <li>\u4ec5\u5269\u7684\u4e00\u4e2a\u5143\u7d20\u5fc5\u5b9a\u662f\u6700\u5c0f\u5143\u7d20\uff0c\u65e0\u9700\u6392\u5e8f\uff0c\u56e0\u6b64\u6570\u7ec4\u6392\u5e8f\u5b8c\u6210\u3002</li> </ol> <p></p> <p> Fig. \u5192\u6ce1\u6392\u5e8f\u6d41\u7a0b </p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart bubble_sort.java<pre><code>/* \u5192\u6ce1\u6392\u5e8f */\nvoid bubbleSort(int[] nums) {\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [0, i]\nfor (int i = nums.length - 1; i &gt; 0; i--) {\n// \u5185\u5faa\u73af\uff1a\u5c06\u672a\u6392\u5e8f\u533a\u95f4 [0, i] \u4e2d\u7684\u6700\u5927\u5143\u7d20\u4ea4\u6362\u81f3\u8be5\u533a\u95f4\u7684\u6700\u53f3\u7aef \nfor (int j = 0; j &lt; i; j++) {\nif (nums[j] &gt; nums[j + 1]) {\n// \u4ea4\u6362 nums[j] \u4e0e nums[j + 1]\nint tmp = nums[j];\nnums[j] = nums[j + 1];\nnums[j + 1] = tmp;\n}\n}\n}\n}\n</code></pre> bubble_sort.cpp<pre><code>/* \u5192\u6ce1\u6392\u5e8f */\nvoid bubbleSort(vector&lt;int&gt; &amp;nums) {\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [0, i]\nfor (int i = nums.size() - 1; i &gt; 0; i--) {\n// \u5185\u5faa\u73af\uff1a\u5c06\u672a\u6392\u5e8f\u533a\u95f4 [0, i] \u4e2d\u7684\u6700\u5927\u5143\u7d20\u4ea4\u6362\u81f3\u8be5\u533a\u95f4\u7684\u6700\u53f3\u7aef \nfor (int j = 0; j &lt; i; j++) {\nif (nums[j] &gt; nums[j + 1]) {\n// \u4ea4\u6362 nums[j] \u4e0e nums[j + 1]\n// \u8fd9\u91cc\u4f7f\u7528\u4e86 std::swap() \u51fd\u6570\nswap(nums[j], nums[j + 1]);\n}\n}\n}\n}\n</code></pre> bubble_sort.py<pre><code>def bubble_sort(nums: list[int]) -&gt; None:\n\"\"\"\u5192\u6ce1\u6392\u5e8f\"\"\"\nn = len(nums)\n# \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [0, i]\nfor i in range(n - 1, 0, -1):\n# \u5185\u5faa\u73af\uff1a\u5c06\u672a\u6392\u5e8f\u533a\u95f4 [0, i] \u4e2d\u7684\u6700\u5927\u5143\u7d20\u4ea4\u6362\u81f3\u8be5\u533a\u95f4\u7684\u6700\u53f3\u7aef \nfor j in range(i):\nif nums[j] &gt; nums[j + 1]:\n# \u4ea4\u6362 nums[j] \u4e0e nums[j + 1]\nnums[j], nums[j + 1] = nums[j + 1], nums[j]\n</code></pre> bubble_sort.go<pre><code>/* \u5192\u6ce1\u6392\u5e8f */\nfunc bubbleSort(nums []int) {\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [0, i]\nfor i := len(nums) - 1; i &gt; 0; i-- {\n// \u5185\u5faa\u73af\uff1a\u5c06\u672a\u6392\u5e8f\u533a\u95f4 [0, i] \u4e2d\u7684\u6700\u5927\u5143\u7d20\u4ea4\u6362\u81f3\u8be5\u533a\u95f4\u7684\u6700\u53f3\u7aef\nfor j := 0; j &lt; i; j++ {\nif nums[j] &gt; nums[j+1] {\n// \u4ea4\u6362 nums[j] \u4e0e nums[j + 1]\nnums[j], nums[j+1] = nums[j+1], nums[j]\n}\n}\n}\n}\n</code></pre> bubble_sort.js<pre><code>/* \u5192\u6ce1\u6392\u5e8f */\nfunction bubbleSort(nums) {\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [0, i]\nfor (let i = nums.length - 1; i &gt; 0; i--) {\n// \u5185\u5faa\u73af\uff1a\u5c06\u672a\u6392\u5e8f\u533a\u95f4 [0, i] \u4e2d\u7684\u6700\u5927\u5143\u7d20\u4ea4\u6362\u81f3\u8be5\u533a\u95f4\u7684\u6700\u53f3\u7aef \nfor (let j = 0; j &lt; i; j++) {\nif (nums[j] &gt; nums[j + 1]) {\n// \u4ea4\u6362 nums[j] \u4e0e nums[j + 1]\nlet tmp = nums[j];\nnums[j] = nums[j + 1];\nnums[j + 1] = tmp;\n}\n}\n}\n}\n</code></pre> bubble_sort.ts<pre><code>/* \u5192\u6ce1\u6392\u5e8f */\nfunction bubbleSort(nums: number[]): void {\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [0, i]\nfor (let i = nums.length - 1; i &gt; 0; i--) {\n// \u5185\u5faa\u73af\uff1a\u5c06\u672a\u6392\u5e8f\u533a\u95f4 [0, i] \u4e2d\u7684\u6700\u5927\u5143\u7d20\u4ea4\u6362\u81f3\u8be5\u533a\u95f4\u7684\u6700\u53f3\u7aef \nfor (let j = 0; j &lt; i; j++) {\nif (nums[j] &gt; nums[j + 1]) {\n// \u4ea4\u6362 nums[j] \u4e0e nums[j + 1]\nlet tmp = nums[j];\nnums[j] = nums[j + 1];\nnums[j + 1] = tmp;\n}\n}\n}\n}\n</code></pre> bubble_sort.c<pre><code>/* \u5192\u6ce1\u6392\u5e8f */\nvoid bubbleSort(int nums[], int size) {\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [0, i]\nfor (int i = 0; i &lt; size - 1; i++) {\n// \u5185\u5faa\u73af\uff1a\u5c06\u672a\u6392\u5e8f\u533a\u95f4 [0, i] \u4e2d\u7684\u6700\u5927\u5143\u7d20\u4ea4\u6362\u81f3\u8be5\u533a\u95f4\u7684\u6700\u53f3\u7aef \nfor (int j = 0; j &lt; size - 1 - i; j++) {\nif (nums[j] &gt; nums[j + 1]) {\nint temp = nums[j];\nnums[j] = nums[j + 1];\nnums[j + 1] = temp;\n}\n}\n}\n}\n</code></pre> bubble_sort.cs<pre><code>/* \u5192\u6ce1\u6392\u5e8f */\nvoid bubbleSort(int[] nums) {\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [0, i]\nfor (int i = nums.Length - 1; i &gt; 0; i--) {\n// \u5185\u5faa\u73af\uff1a\u5c06\u672a\u6392\u5e8f\u533a\u95f4 [0, i] \u4e2d\u7684\u6700\u5927\u5143\u7d20\u4ea4\u6362\u81f3\u8be5\u533a\u95f4\u7684\u6700\u53f3\u7aef \nfor (int j = 0; j &lt; i; j++) {\nif (nums[j] &gt; nums[j + 1]) {\n// \u4ea4\u6362 nums[j] \u4e0e nums[j + 1]\nint tmp = nums[j];\nnums[j] = nums[j + 1];\nnums[j + 1] = tmp;\n}\n}\n}\n}\n</code></pre> bubble_sort.swift<pre><code>/* \u5192\u6ce1\u6392\u5e8f */\nfunc bubbleSort(nums: inout [Int]) {\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [0, i]\nfor i in stride(from: nums.count - 1, to: 0, by: -1) {\n// \u5185\u5faa\u73af\uff1a\u5c06\u672a\u6392\u5e8f\u533a\u95f4 [0, i] \u4e2d\u7684\u6700\u5927\u5143\u7d20\u4ea4\u6362\u81f3\u8be5\u533a\u95f4\u7684\u6700\u53f3\u7aef \nfor j in stride(from: 0, to: i, by: 1) {\nif nums[j] &gt; nums[j + 1] {\n// \u4ea4\u6362 nums[j] \u4e0e nums[j + 1]\nlet tmp = nums[j]\nnums[j] = nums[j + 1]\nnums[j + 1] = tmp\n}\n}\n}\n}\n</code></pre> bubble_sort.zig<pre><code>// \u5192\u6ce1\u6392\u5e8f\nfn bubbleSort(nums: []i32) void {\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [0, i]\nvar i: usize = nums.len - 1;\nwhile (i &gt; 0) : (i -= 1) {\nvar j: usize = 0;\n// \u5185\u5faa\u73af\uff1a\u5c06\u672a\u6392\u5e8f\u533a\u95f4 [0, i] \u4e2d\u7684\u6700\u5927\u5143\u7d20\u4ea4\u6362\u81f3\u8be5\u533a\u95f4\u7684\u6700\u53f3\u7aef \nwhile (j &lt; i) : (j += 1) {\nif (nums[j] &gt; nums[j + 1]) {\n// \u4ea4\u6362 nums[j] \u4e0e nums[j + 1]\nvar tmp = nums[j];\nnums[j] = nums[j + 1];\nnums[j + 1] = tmp;\n}\n}\n}\n}\n</code></pre> bubble_sort.dart<pre><code>/* \u5192\u6ce1\u6392\u5e8f */\nvoid bubbleSort(List&lt;int&gt; nums) {\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [0, i]\nfor (int i = nums.length - 1; i &gt; 0; i--) {\n// \u5185\u5faa\u73af\uff1a\u5c06\u672a\u6392\u5e8f\u533a\u95f4 [0, i] \u4e2d\u7684\u6700\u5927\u5143\u7d20\u4ea4\u6362\u81f3\u8be5\u533a\u95f4\u7684\u6700\u53f3\u7aef \nfor (int j = 0; j &lt; i; j++) {\nif (nums[j] &gt; nums[j + 1]) {\n// \u4ea4\u6362 nums[j] \u4e0e nums[j + 1]\nint tmp = nums[j];\nnums[j] = nums[j + 1];\nnums[j + 1] = tmp;\n}\n}\n}\n}\n</code></pre>"},{"location":"chapter_sorting/bubble_sort/#1132","title":"11.3.2. \u00a0 \u6548\u7387\u4f18\u5316","text":"<p>\u6211\u4eec\u53d1\u73b0\uff0c\u5982\u679c\u67d0\u8f6e\u201c\u5192\u6ce1\u201d\u4e2d\u6ca1\u6709\u6267\u884c\u4efb\u4f55\u4ea4\u6362\u64cd\u4f5c\uff0c\u8bf4\u660e\u6570\u7ec4\u5df2\u7ecf\u5b8c\u6210\u6392\u5e8f\uff0c\u53ef\u76f4\u63a5\u8fd4\u56de\u7ed3\u679c\u3002\u56e0\u6b64\uff0c\u53ef\u4ee5\u589e\u52a0\u4e00\u4e2a\u6807\u5fd7\u4f4d <code>flag</code> \u6765\u76d1\u6d4b\u8fd9\u79cd\u60c5\u51b5\uff0c\u4e00\u65e6\u51fa\u73b0\u5c31\u7acb\u5373\u8fd4\u56de\u3002</p> <p>\u7ecf\u8fc7\u4f18\u5316\uff0c\u5192\u6ce1\u6392\u5e8f\u7684\u6700\u5dee\u548c\u5e73\u5747\u65f6\u95f4\u590d\u6742\u5ea6\u4ecd\u4e3a \\(O(n^2)\\) \uff1b\u4f46\u5f53\u8f93\u5165\u6570\u7ec4\u5b8c\u5168\u6709\u5e8f\u65f6\uff0c\u53ef\u8fbe\u5230\u6700\u4f73\u65f6\u95f4\u590d\u6742\u5ea6 \\(O(n)\\) \u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart bubble_sort.java<pre><code>/* \u5192\u6ce1\u6392\u5e8f\uff08\u6807\u5fd7\u4f18\u5316\uff09 */\nvoid bubbleSortWithFlag(int[] nums) {\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [0, i]\nfor (int i = nums.length - 1; i &gt; 0; i--) {\nboolean flag = false; // \u521d\u59cb\u5316\u6807\u5fd7\u4f4d\n// \u5185\u5faa\u73af\uff1a\u5c06\u672a\u6392\u5e8f\u533a\u95f4 [0, i] \u4e2d\u7684\u6700\u5927\u5143\u7d20\u4ea4\u6362\u81f3\u8be5\u533a\u95f4\u7684\u6700\u53f3\u7aef \nfor (int j = 0; j &lt; i; j++) {\nif (nums[j] &gt; nums[j + 1]) {\n// \u4ea4\u6362 nums[j] \u4e0e nums[j + 1]\nint tmp = nums[j];\nnums[j] = nums[j + 1];\nnums[j + 1] = tmp;\nflag = true; // \u8bb0\u5f55\u4ea4\u6362\u5143\u7d20\n}\n}\nif (!flag)\nbreak; // \u6b64\u8f6e\u5192\u6ce1\u672a\u4ea4\u6362\u4efb\u4f55\u5143\u7d20\uff0c\u76f4\u63a5\u8df3\u51fa\n}\n}\n</code></pre> bubble_sort.cpp<pre><code>/* \u5192\u6ce1\u6392\u5e8f\uff08\u6807\u5fd7\u4f18\u5316\uff09*/\nvoid bubbleSortWithFlag(vector&lt;int&gt; &amp;nums) {\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [0, i]\nfor (int i = nums.size() - 1; i &gt; 0; i--) {\nbool flag = false; // \u521d\u59cb\u5316\u6807\u5fd7\u4f4d\n// \u5185\u5faa\u73af\uff1a\u5c06\u672a\u6392\u5e8f\u533a\u95f4 [0, i] \u4e2d\u7684\u6700\u5927\u5143\u7d20\u4ea4\u6362\u81f3\u8be5\u533a\u95f4\u7684\u6700\u53f3\u7aef \nfor (int j = 0; j &lt; i; j++) {\nif (nums[j] &gt; nums[j + 1]) {\n// \u4ea4\u6362 nums[j] \u4e0e nums[j + 1]\n// \u8fd9\u91cc\u4f7f\u7528\u4e86 std::swap() \u51fd\u6570\nswap(nums[j], nums[j + 1]);\nflag = true; // \u8bb0\u5f55\u4ea4\u6362\u5143\u7d20\n}\n}\nif (!flag)\nbreak; // \u6b64\u8f6e\u5192\u6ce1\u672a\u4ea4\u6362\u4efb\u4f55\u5143\u7d20\uff0c\u76f4\u63a5\u8df3\u51fa\n}\n}\n</code></pre> bubble_sort.py<pre><code>def bubble_sort_with_flag(nums: list[int]) -&gt; None:\n\"\"\"\u5192\u6ce1\u6392\u5e8f\uff08\u6807\u5fd7\u4f18\u5316\uff09\"\"\"\nn = len(nums)\n# \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [0, i]\nfor i in range(n - 1, 0, -1):\nflag = False  # \u521d\u59cb\u5316\u6807\u5fd7\u4f4d\n# \u5185\u5faa\u73af\uff1a\u5c06\u672a\u6392\u5e8f\u533a\u95f4 [0, i] \u4e2d\u7684\u6700\u5927\u5143\u7d20\u4ea4\u6362\u81f3\u8be5\u533a\u95f4\u7684\u6700\u53f3\u7aef \nfor j in range(i):\nif nums[j] &gt; nums[j + 1]:\n# \u4ea4\u6362 nums[j] \u4e0e nums[j + 1]\nnums[j], nums[j + 1] = nums[j + 1], nums[j]\nflag = True  # \u8bb0\u5f55\u4ea4\u6362\u5143\u7d20\nif not flag:\nbreak  # \u6b64\u8f6e\u5192\u6ce1\u672a\u4ea4\u6362\u4efb\u4f55\u5143\u7d20\uff0c\u76f4\u63a5\u8df3\u51fa\n</code></pre> bubble_sort.go<pre><code>/* \u5192\u6ce1\u6392\u5e8f\uff08\u6807\u5fd7\u4f18\u5316\uff09*/\nfunc bubbleSortWithFlag(nums []int) {\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [0, i]\nfor i := len(nums) - 1; i &gt; 0; i-- {\nflag := false // \u521d\u59cb\u5316\u6807\u5fd7\u4f4d\n// \u5185\u5faa\u73af\uff1a\u5c06\u672a\u6392\u5e8f\u533a\u95f4 [0, i] \u4e2d\u7684\u6700\u5927\u5143\u7d20\u4ea4\u6362\u81f3\u8be5\u533a\u95f4\u7684\u6700\u53f3\u7aef\nfor j := 0; j &lt; i; j++ {\nif nums[j] &gt; nums[j+1] {\n// \u4ea4\u6362 nums[j] \u4e0e nums[j + 1]\nnums[j], nums[j+1] = nums[j+1], nums[j]\nflag = true // \u8bb0\u5f55\u4ea4\u6362\u5143\u7d20\n}\n}\nif flag == false { // \u6b64\u8f6e\u5192\u6ce1\u672a\u4ea4\u6362\u4efb\u4f55\u5143\u7d20\uff0c\u76f4\u63a5\u8df3\u51fa\nbreak\n}\n}\n}\n</code></pre> bubble_sort.js<pre><code>/* \u5192\u6ce1\u6392\u5e8f\uff08\u6807\u5fd7\u4f18\u5316\uff09*/\nfunction bubbleSortWithFlag(nums) {\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [0, i]\nfor (let i = nums.length - 1; i &gt; 0; i--) {\nlet flag = false; // \u521d\u59cb\u5316\u6807\u5fd7\u4f4d\n// \u5185\u5faa\u73af\uff1a\u5c06\u672a\u6392\u5e8f\u533a\u95f4 [0, i] \u4e2d\u7684\u6700\u5927\u5143\u7d20\u4ea4\u6362\u81f3\u8be5\u533a\u95f4\u7684\u6700\u53f3\u7aef \nfor (let j = 0; j &lt; i; j++) {\nif (nums[j] &gt; nums[j + 1]) {\n// \u4ea4\u6362 nums[j] \u4e0e nums[j + 1]\nlet tmp = nums[j];\nnums[j] = nums[j + 1];\nnums[j + 1] = tmp;\nflag = true; // \u8bb0\u5f55\u4ea4\u6362\u5143\u7d20\n}\n}\nif (!flag) break; // \u6b64\u8f6e\u5192\u6ce1\u672a\u4ea4\u6362\u4efb\u4f55\u5143\u7d20\uff0c\u76f4\u63a5\u8df3\u51fa\n}\n}\n</code></pre> bubble_sort.ts<pre><code>/* \u5192\u6ce1\u6392\u5e8f\uff08\u6807\u5fd7\u4f18\u5316\uff09*/\nfunction bubbleSortWithFlag(nums: number[]): void {\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [0, i]\nfor (let i = nums.length - 1; i &gt; 0; i--) {\nlet flag = false; // \u521d\u59cb\u5316\u6807\u5fd7\u4f4d\n// \u5185\u5faa\u73af\uff1a\u5c06\u672a\u6392\u5e8f\u533a\u95f4 [0, i] \u4e2d\u7684\u6700\u5927\u5143\u7d20\u4ea4\u6362\u81f3\u8be5\u533a\u95f4\u7684\u6700\u53f3\u7aef \nfor (let j = 0; j &lt; i; j++) {\nif (nums[j] &gt; nums[j + 1]) {\n// \u4ea4\u6362 nums[j] \u4e0e nums[j + 1]\nlet tmp = nums[j];\nnums[j] = nums[j + 1];\nnums[j + 1] = tmp;\nflag = true; // \u8bb0\u5f55\u4ea4\u6362\u5143\u7d20\n}\n}\nif (!flag) break; // \u6b64\u8f6e\u5192\u6ce1\u672a\u4ea4\u6362\u4efb\u4f55\u5143\u7d20\uff0c\u76f4\u63a5\u8df3\u51fa\n}\n}\n</code></pre> bubble_sort.c<pre><code>/* \u5192\u6ce1\u6392\u5e8f\uff08\u6807\u5fd7\u4f18\u5316\uff09*/\nvoid bubbleSortWithFlag(int nums[], int size) {\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [0, i]\nfor (int i = 0; i &lt; size - 1; i++) {\nbool flag = false;\n// \u5185\u5faa\u73af\uff1a\u5c06\u672a\u6392\u5e8f\u533a\u95f4 [0, i] \u4e2d\u7684\u6700\u5927\u5143\u7d20\u4ea4\u6362\u81f3\u8be5\u533a\u95f4\u7684\u6700\u53f3\u7aef \nfor (int j = 0; j &lt; size - 1 - i; j++) {\nif (nums[j] &gt; nums[j + 1]) {\nint temp = nums[j];\nnums[j] = nums[j + 1];\nnums[j + 1] = temp;\nflag = true;\n}\n}\nif (!flag)\nbreak;\n}\n}\n</code></pre> bubble_sort.cs<pre><code>/* \u5192\u6ce1\u6392\u5e8f\uff08\u6807\u5fd7\u4f18\u5316\uff09*/\nvoid bubbleSortWithFlag(int[] nums) {\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [0, i]\nfor (int i = nums.Length - 1; i &gt; 0; i--) {\nbool flag = false; // \u521d\u59cb\u5316\u6807\u5fd7\u4f4d\n// \u5185\u5faa\u73af\uff1a\u5c06\u672a\u6392\u5e8f\u533a\u95f4 [0, i] \u4e2d\u7684\u6700\u5927\u5143\u7d20\u4ea4\u6362\u81f3\u8be5\u533a\u95f4\u7684\u6700\u53f3\u7aef \nfor (int j = 0; j &lt; i; j++) {\nif (nums[j] &gt; nums[j + 1]) {\n// \u4ea4\u6362 nums[j] \u4e0e nums[j + 1]\nint tmp = nums[j];\nnums[j] = nums[j + 1];\nnums[j + 1] = tmp;\nflag = true;  // \u8bb0\u5f55\u4ea4\u6362\u5143\u7d20\n}\n}\nif (!flag) break;     // \u6b64\u8f6e\u5192\u6ce1\u672a\u4ea4\u6362\u4efb\u4f55\u5143\u7d20\uff0c\u76f4\u63a5\u8df3\u51fa\n}\n}\n</code></pre> bubble_sort.swift<pre><code>/* \u5192\u6ce1\u6392\u5e8f\uff08\u6807\u5fd7\u4f18\u5316\uff09*/\nfunc bubbleSortWithFlag(nums: inout [Int]) {\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [0, i]\nfor i in stride(from: nums.count - 1, to: 0, by: -1) {\nvar flag = false // \u521d\u59cb\u5316\u6807\u5fd7\u4f4d\nfor j in stride(from: 0, to: i, by: 1) {\nif nums[j] &gt; nums[j + 1] {\n// \u4ea4\u6362 nums[j] \u4e0e nums[j + 1]\nlet tmp = nums[j]\nnums[j] = nums[j + 1]\nnums[j + 1] = tmp\nflag = true // \u8bb0\u5f55\u4ea4\u6362\u5143\u7d20\n}\n}\nif !flag { // \u6b64\u8f6e\u5192\u6ce1\u672a\u4ea4\u6362\u4efb\u4f55\u5143\u7d20\uff0c\u76f4\u63a5\u8df3\u51fa\nbreak\n}\n}\n}\n</code></pre> bubble_sort.zig<pre><code>// \u5192\u6ce1\u6392\u5e8f\uff08\u6807\u5fd7\u4f18\u5316\uff09\nfn bubbleSortWithFlag(nums: []i32) void {\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [0, i]\nvar i: usize = nums.len - 1;\nwhile (i &gt; 0) : (i -= 1) {\nvar flag = false;   // \u521d\u59cb\u5316\u6807\u5fd7\u4f4d\nvar j: usize = 0;\n// \u5185\u5faa\u73af\uff1a\u5c06\u672a\u6392\u5e8f\u533a\u95f4 [0, i] \u4e2d\u7684\u6700\u5927\u5143\u7d20\u4ea4\u6362\u81f3\u8be5\u533a\u95f4\u7684\u6700\u53f3\u7aef \nwhile (j &lt; i) : (j += 1) {\nif (nums[j] &gt; nums[j + 1]) {\n// \u4ea4\u6362 nums[j] \u4e0e nums[j + 1]\nvar tmp = nums[j];\nnums[j] = nums[j + 1];\nnums[j + 1] = tmp;\nflag = true;\n}\n}\nif (!flag) break;   // \u6b64\u8f6e\u5192\u6ce1\u672a\u4ea4\u6362\u4efb\u4f55\u5143\u7d20\uff0c\u76f4\u63a5\u8df3\u51fa\n}\n}\n</code></pre> bubble_sort.dart<pre><code>/* \u5192\u6ce1\u6392\u5e8f\uff08\u6807\u5fd7\u4f18\u5316\uff09*/\nvoid bubbleSortWithFlag(List&lt;int&gt; nums) {\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [0, i]\nfor (int i = nums.length - 1; i &gt; 0; i--) {\nbool flag = false; // \u521d\u59cb\u5316\u6807\u5fd7\u4f4d\n// \u5185\u5faa\u73af\uff1a\u5c06\u672a\u6392\u5e8f\u533a\u95f4 [0, i] \u4e2d\u7684\u6700\u5927\u5143\u7d20\u4ea4\u6362\u81f3\u8be5\u533a\u95f4\u7684\u6700\u53f3\u7aef \nfor (int j = 0; j &lt; i; j++) {\nif (nums[j] &gt; nums[j + 1]) {\n// \u4ea4\u6362 nums[j] \u4e0e nums[j + 1]\nint tmp = nums[j];\nnums[j] = nums[j + 1];\nnums[j + 1] = tmp;\nflag = true; // \u8bb0\u5f55\u4ea4\u6362\u5143\u7d20\n}\n}\nif (!flag) break; // \u6b64\u8f6e\u5192\u6ce1\u672a\u4ea4\u6362\u4efb\u4f55\u5143\u7d20\uff0c\u76f4\u63a5\u8df3\u51fa\n}\n}\n</code></pre>"},{"location":"chapter_sorting/bubble_sort/#1133","title":"11.3.3. \u00a0 \u7b97\u6cd5\u7279\u6027","text":"<ul> <li>\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(n^2)\\) \u3001\u81ea\u9002\u5e94\u6392\u5e8f \uff1a\u5404\u8f6e\u201c\u5192\u6ce1\u201d\u904d\u5386\u7684\u6570\u7ec4\u957f\u5ea6\u4f9d\u6b21\u4e3a \\(n - 1\\) , \\(n - 2\\) , \\(\\cdots\\) , \\(2\\) , \\(1\\) \uff0c\u603b\u548c\u4e3a \\(\\frac{(n - 1) n}{2}\\) \u3002\u5728\u5f15\u5165 <code>flag</code> \u4f18\u5316\u540e\uff0c\u6700\u4f73\u65f6\u95f4\u590d\u6742\u5ea6\u53ef\u8fbe\u5230 \\(O(n)\\) \u3002</li> <li>\u7a7a\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(1)\\) \u3001\u539f\u5730\u6392\u5e8f\uff1a\u6307\u9488 \\(i\\) , \\(j\\) \u4f7f\u7528\u5e38\u6570\u5927\u5c0f\u7684\u989d\u5916\u7a7a\u95f4\u3002</li> <li>\u7a33\u5b9a\u6392\u5e8f\uff1a\u7531\u4e8e\u5728\u201c\u5192\u6ce1\u201d\u4e2d\u9047\u5230\u76f8\u7b49\u5143\u7d20\u4e0d\u4ea4\u6362\u3002</li> </ul>"},{"location":"chapter_sorting/bucket_sort/","title":"11.8. \u00a0 \u6876\u6392\u5e8f","text":"<p>\u524d\u8ff0\u7684\u51e0\u79cd\u6392\u5e8f\u7b97\u6cd5\u90fd\u5c5e\u4e8e\u201c\u57fa\u4e8e\u6bd4\u8f83\u7684\u6392\u5e8f\u7b97\u6cd5\u201d\uff0c\u5b83\u4eec\u901a\u8fc7\u6bd4\u8f83\u5143\u7d20\u95f4\u7684\u5927\u5c0f\u6765\u5b9e\u73b0\u6392\u5e8f\u3002\u6b64\u7c7b\u6392\u5e8f\u7b97\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u65e0\u6cd5\u8d85\u8d8a \\(O(n \\log n)\\) \u3002\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u5c06\u63a2\u8ba8\u51e0\u79cd\u201c\u975e\u6bd4\u8f83\u6392\u5e8f\u7b97\u6cd5\u201d\uff0c\u5b83\u4eec\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u53ef\u4ee5\u8fbe\u5230\u7ebf\u6027\u6c34\u5e73\u3002</p> <p>\u300c\u6876\u6392\u5e8f Bucket Sort\u300d\u662f\u5206\u6cbb\u601d\u60f3\u7684\u4e00\u4e2a\u5178\u578b\u5e94\u7528\u3002\u5b83\u901a\u8fc7\u8bbe\u7f6e\u4e00\u4e9b\u5177\u6709\u5927\u5c0f\u987a\u5e8f\u7684\u6876\uff0c\u6bcf\u4e2a\u6876\u5bf9\u5e94\u4e00\u4e2a\u6570\u636e\u8303\u56f4\uff0c\u5c06\u6570\u636e\u5e73\u5747\u5206\u914d\u5230\u5404\u4e2a\u6876\u4e2d\uff1b\u7136\u540e\uff0c\u5728\u6bcf\u4e2a\u6876\u5185\u90e8\u5206\u522b\u6267\u884c\u6392\u5e8f\uff1b\u6700\u7ec8\u6309\u7167\u6876\u7684\u987a\u5e8f\u5c06\u6240\u6709\u6570\u636e\u5408\u5e76\u3002</p>"},{"location":"chapter_sorting/bucket_sort/#1181","title":"11.8.1. \u00a0 \u7b97\u6cd5\u6d41\u7a0b","text":"<p>\u8003\u8651\u4e00\u4e2a\u957f\u5ea6\u4e3a \\(n\\) \u7684\u6570\u7ec4\uff0c\u5143\u7d20\u662f\u8303\u56f4 \\([0, 1)\\) \u7684\u6d6e\u70b9\u6570\u3002\u6876\u6392\u5e8f\u7684\u6d41\u7a0b\u5982\u4e0b\uff1a</p> <ol> <li>\u521d\u59cb\u5316 \\(k\\) \u4e2a\u6876\uff0c\u5c06 \\(n\\) \u4e2a\u5143\u7d20\u5206\u914d\u5230 \\(k\\) \u4e2a\u6876\u4e2d\uff1b</li> <li>\u5bf9\u6bcf\u4e2a\u6876\u5206\u522b\u6267\u884c\u6392\u5e8f\uff08\u672c\u6587\u91c7\u7528\u7f16\u7a0b\u8bed\u8a00\u7684\u5185\u7f6e\u6392\u5e8f\u51fd\u6570\uff09\uff1b</li> <li>\u6309\u7167\u6876\u7684\u4ece\u5c0f\u5230\u5927\u7684\u987a\u5e8f\uff0c\u5408\u5e76\u7ed3\u679c\uff1b</li> </ol> <p></p> <p> Fig. \u6876\u6392\u5e8f\u7b97\u6cd5\u6d41\u7a0b </p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart bucket_sort.java<pre><code>/* \u6876\u6392\u5e8f */\nvoid bucketSort(float[] nums) {\n// \u521d\u59cb\u5316 k = n/2 \u4e2a\u6876\uff0c\u9884\u671f\u5411\u6bcf\u4e2a\u6876\u5206\u914d 2 \u4e2a\u5143\u7d20\nint k = nums.length / 2;\nList&lt;List&lt;Float&gt;&gt; buckets = new ArrayList&lt;&gt;();\nfor (int i = 0; i &lt; k; i++) {\nbuckets.add(new ArrayList&lt;&gt;());\n}\n// 1. \u5c06\u6570\u7ec4\u5143\u7d20\u5206\u914d\u5230\u5404\u4e2a\u6876\u4e2d\nfor (float num : nums) {\n// \u8f93\u5165\u6570\u636e\u8303\u56f4 [0, 1)\uff0c\u4f7f\u7528 num * k \u6620\u5c04\u5230\u7d22\u5f15\u8303\u56f4 [0, k-1]\nint i = (int) (num * k);\n// \u5c06 num \u6dfb\u52a0\u8fdb\u6876 i\nbuckets.get(i).add(num);\n}\n// 2. \u5bf9\u5404\u4e2a\u6876\u6267\u884c\u6392\u5e8f\nfor (List&lt;Float&gt; bucket : buckets) {\n// \u4f7f\u7528\u5185\u7f6e\u6392\u5e8f\u51fd\u6570\uff0c\u4e5f\u53ef\u4ee5\u66ff\u6362\u6210\u5176\u4ed6\u6392\u5e8f\u7b97\u6cd5\nCollections.sort(bucket);\n}\n// 3. \u904d\u5386\u6876\u5408\u5e76\u7ed3\u679c\nint i = 0;\nfor (List&lt;Float&gt; bucket : buckets) {\nfor (float num : bucket) {\nnums[i++] = num;\n}\n}\n}\n</code></pre> bucket_sort.cpp<pre><code>/* \u6876\u6392\u5e8f */\nvoid bucketSort(vector&lt;float&gt; &amp;nums) {\n// \u521d\u59cb\u5316 k = n/2 \u4e2a\u6876\uff0c\u9884\u671f\u5411\u6bcf\u4e2a\u6876\u5206\u914d 2 \u4e2a\u5143\u7d20\nint k = nums.size() / 2;\nvector&lt;vector&lt;float&gt;&gt; buckets(k);\n// 1. \u5c06\u6570\u7ec4\u5143\u7d20\u5206\u914d\u5230\u5404\u4e2a\u6876\u4e2d\nfor (float num : nums) {\n// \u8f93\u5165\u6570\u636e\u8303\u56f4 [0, 1)\uff0c\u4f7f\u7528 num * k \u6620\u5c04\u5230\u7d22\u5f15\u8303\u56f4 [0, k-1]\nint i = num * k;\n// \u5c06 num \u6dfb\u52a0\u8fdb\u6876 bucket_idx\nbuckets[i].push_back(num);\n}\n// 2. \u5bf9\u5404\u4e2a\u6876\u6267\u884c\u6392\u5e8f\nfor (vector&lt;float&gt; &amp;bucket : buckets) {\n// \u4f7f\u7528\u5185\u7f6e\u6392\u5e8f\u51fd\u6570\uff0c\u4e5f\u53ef\u4ee5\u66ff\u6362\u6210\u5176\u4ed6\u6392\u5e8f\u7b97\u6cd5\nsort(bucket.begin(), bucket.end());\n}\n// 3. \u904d\u5386\u6876\u5408\u5e76\u7ed3\u679c\nint i = 0;\nfor (vector&lt;float&gt; &amp;bucket : buckets) {\nfor (float num : bucket) {\nnums[i++] = num;\n}\n}\n}\n</code></pre> bucket_sort.py<pre><code>def bucket_sort(nums: list[float]) -&gt; None:\n\"\"\"\u6876\u6392\u5e8f\"\"\"\n# \u521d\u59cb\u5316 k = n/2 \u4e2a\u6876\uff0c\u9884\u671f\u5411\u6bcf\u4e2a\u6876\u5206\u914d 2 \u4e2a\u5143\u7d20\nk = len(nums) // 2\nbuckets = [[] for _ in range(k)]\n# 1. \u5c06\u6570\u7ec4\u5143\u7d20\u5206\u914d\u5230\u5404\u4e2a\u6876\u4e2d\nfor num in nums:\n# \u8f93\u5165\u6570\u636e\u8303\u56f4 [0, 1)\uff0c\u4f7f\u7528 num * k \u6620\u5c04\u5230\u7d22\u5f15\u8303\u56f4 [0, k-1]\ni = int(num * k)\n# \u5c06 num \u6dfb\u52a0\u8fdb\u6876 i\nbuckets[i].append(num)\n# 2. \u5bf9\u5404\u4e2a\u6876\u6267\u884c\u6392\u5e8f5\nfor bucket in buckets:\n# \u4f7f\u7528\u5185\u7f6e\u6392\u5e8f\u51fd\u6570\uff0c\u4e5f\u53ef\u4ee5\u66ff\u6362\u6210\u5176\u4ed6\u6392\u5e8f\u7b97\u6cd5\nbucket.sort()\n# 3. \u904d\u5386\u6876\u5408\u5e76\u7ed3\u679c\ni = 0\nfor bucket in buckets:\nfor num in bucket:\nnums[i] = num\ni += 1\n</code></pre> bucket_sort.go<pre><code>/* \u6876\u6392\u5e8f */\nfunc bucketSort(nums []float64) {\n// \u521d\u59cb\u5316 k = n/2 \u4e2a\u6876\uff0c\u9884\u671f\u5411\u6bcf\u4e2a\u6876\u5206\u914d 2 \u4e2a\u5143\u7d20\nk := len(nums) / 2\nbuckets := make([][]float64, k)\nfor i := 0; i &lt; k; i++ {\nbuckets[i] = make([]float64, 0)\n}\n// 1. \u5c06\u6570\u7ec4\u5143\u7d20\u5206\u914d\u5230\u5404\u4e2a\u6876\u4e2d\nfor _, num := range nums {\n// \u8f93\u5165\u6570\u636e\u8303\u56f4 [0, 1)\uff0c\u4f7f\u7528 num * k \u6620\u5c04\u5230\u7d22\u5f15\u8303\u56f4 [0, k-1]\ni := int(num * float64(k))\n// \u5c06 num \u6dfb\u52a0\u8fdb\u6876 i\nbuckets[i] = append(buckets[i], num)\n}\n// 2. \u5bf9\u5404\u4e2a\u6876\u6267\u884c\u6392\u5e8f\nfor i := 0; i &lt; k; i++ {\n// \u4f7f\u7528\u5185\u7f6e\u5207\u7247\u6392\u5e8f\u51fd\u6570\uff0c\u4e5f\u53ef\u4ee5\u66ff\u6362\u6210\u5176\u4ed6\u6392\u5e8f\u7b97\u6cd5\nsort.Float64s(buckets[i])\n}\n// 3. \u904d\u5386\u6876\u5408\u5e76\u7ed3\u679c\ni := 0\nfor _, bucket := range buckets {\nfor _, num := range bucket {\nnums[i] = num\ni++\n}\n}\n}\n</code></pre> bucket_sort.js<pre><code>/* \u6876\u6392\u5e8f */\nfunction bucketSort(nums) {\n// \u521d\u59cb\u5316 k = n/2 \u4e2a\u6876\uff0c\u9884\u671f\u5411\u6bcf\u4e2a\u6876\u5206\u914d 2 \u4e2a\u5143\u7d20\nconst k = nums.length / 2;\nconst buckets = [];\nfor (let i = 0; i &lt; k; i++) {\nbuckets.push([]);\n}\n// 1. \u5c06\u6570\u7ec4\u5143\u7d20\u5206\u914d\u5230\u5404\u4e2a\u6876\u4e2d\nfor (const num of nums) {\n// \u8f93\u5165\u6570\u636e\u8303\u56f4 [0, 1)\uff0c\u4f7f\u7528 num * k \u6620\u5c04\u5230\u7d22\u5f15\u8303\u56f4 [0, k-1]\nconst i = Math.floor(num * k);\n// \u5c06 num \u6dfb\u52a0\u8fdb\u6876 i\nbuckets[i].push(num);\n}\n// 2. \u5bf9\u5404\u4e2a\u6876\u6267\u884c\u6392\u5e8f\nfor (const bucket of buckets) {\n// \u4f7f\u7528\u5185\u7f6e\u6392\u5e8f\u51fd\u6570\uff0c\u4e5f\u53ef\u4ee5\u66ff\u6362\u6210\u5176\u4ed6\u6392\u5e8f\u7b97\u6cd5\nbucket.sort((a, b) =&gt; a - b);\n}\n// 3. \u904d\u5386\u6876\u5408\u5e76\u7ed3\u679c\nlet i = 0;\nfor (const bucket of buckets) {\nfor (const num of bucket) {\nnums[i++] = num;\n}\n}\n}\n</code></pre> bucket_sort.ts<pre><code>/* \u6876\u6392\u5e8f */\nfunction bucketSort(nums: number[]): void {\n// \u521d\u59cb\u5316 k = n/2 \u4e2a\u6876\uff0c\u9884\u671f\u5411\u6bcf\u4e2a\u6876\u5206\u914d 2 \u4e2a\u5143\u7d20\nconst k = nums.length / 2;\nconst buckets: number[][] = [];\nfor (let i = 0; i &lt; k; i++) {\nbuckets.push([]);\n}\n// 1. \u5c06\u6570\u7ec4\u5143\u7d20\u5206\u914d\u5230\u5404\u4e2a\u6876\u4e2d\nfor (const num of nums) {\n// \u8f93\u5165\u6570\u636e\u8303\u56f4 [0, 1)\uff0c\u4f7f\u7528 num * k \u6620\u5c04\u5230\u7d22\u5f15\u8303\u56f4 [0, k-1]\nconst i = Math.floor(num * k);\n// \u5c06 num \u6dfb\u52a0\u8fdb\u6876 i\nbuckets[i].push(num);\n}\n// 2. \u5bf9\u5404\u4e2a\u6876\u6267\u884c\u6392\u5e8f\nfor (const bucket of buckets) {\n// \u4f7f\u7528\u5185\u7f6e\u6392\u5e8f\u51fd\u6570\uff0c\u4e5f\u53ef\u4ee5\u66ff\u6362\u6210\u5176\u4ed6\u6392\u5e8f\u7b97\u6cd5\nbucket.sort((a, b) =&gt; a - b);\n}\n// 3. \u904d\u5386\u6876\u5408\u5e76\u7ed3\u679c\nlet i = 0;\nfor (const bucket of buckets) {\nfor (const num of bucket) {\nnums[i++] = num;\n}\n}\n}\n</code></pre> bucket_sort.c<pre><code>/* \u6876\u6392\u5e8f */\nvoid bucketSort(float nums[], int size) {\n// \u521d\u59cb\u5316 k = n/2 \u4e2a\u6876\uff0c\u9884\u671f\u5411\u6bcf\u4e2a\u6876\u5206\u914d 2 \u4e2a\u5143\u7d20\nint k = size / 2;\nfloat **buckets = calloc(k, sizeof(float *));\nfor (int i = 0; i &lt; k; i++) {\n// \u6bcf\u4e2a\u6876\u6700\u591a\u53ef\u4ee5\u5206\u914d k \u4e2a\u5143\u7d20\nbuckets[i] = calloc(ARRAY_SIZE, sizeof(float));\n}\n// 1. \u5c06\u6570\u7ec4\u5143\u7d20\u5206\u914d\u5230\u5404\u4e2a\u6876\u4e2d\nfor (int i = 0; i &lt; size; i++) {\n// \u8f93\u5165\u6570\u636e\u8303\u56f4 [0, 1)\uff0c\u4f7f\u7528 num * k \u6620\u5c04\u5230\u7d22\u5f15\u8303\u56f4 [0, k-1]\nint bucket_idx = nums[i] * k;\nint j = 0;\n// \u5982\u679c\u6876\u4e2d\u6709\u6570\u636e\u4e14\u6570\u636e\u5c0f\u4e8e\u5f53\u524d\u503c nums[i], \u8981\u5c06\u5176\u653e\u5230\u5f53\u524d\u6876\u7684\u540e\u9762\uff0c\u76f8\u5f53\u4e8e cpp \u4e2d\u7684 push_back\nwhile (buckets[bucket_idx][j] &gt; 0 &amp;&amp; buckets[bucket_idx][j] &lt; nums[i]) {\nj++;\n}\nfloat temp = nums[i];\nwhile (j &lt; ARRAY_SIZE &amp;&amp; buckets[bucket_idx][j] &gt; 0) {\nswap(&amp;temp, &amp;buckets[bucket_idx][j]);\nj++;\n}\nbuckets[bucket_idx][j] = temp;\n}\n// 2. \u5bf9\u5404\u4e2a\u6876\u6267\u884c\u6392\u5e8f\nfor (int i = 0; i &lt; k; i++) {\nqsort(buckets[i], ARRAY_SIZE, sizeof(float), compare_float);\n}\n// 3. \u904d\u5386\u6876\u5408\u5e76\u7ed3\u679c\nfor (int i = 0, j = 0; j &lt; k; j++) {\nfor (int l = 0; l &lt; ARRAY_SIZE; l++) {\nif (buckets[j][l] &gt; 0) {\nnums[i++] = buckets[j][l];\n}\n}\n}\n// \u91ca\u653e\u4e0a\u8ff0\u5206\u914d\u7684\u5185\u5b58\nfor (int i = 0; i &lt; k; i++) {\nfree(buckets[i]);\n}\nfree(buckets);\n}\n</code></pre> bucket_sort.cs<pre><code>/* \u6876\u6392\u5e8f */\nvoid bucketSort(float[] nums) {\n// \u521d\u59cb\u5316 k = n/2 \u4e2a\u6876\uff0c\u9884\u671f\u5411\u6bcf\u4e2a\u6876\u5206\u914d 2 \u4e2a\u5143\u7d20\nint k = nums.Length / 2;\nList&lt;List&lt;float&gt;&gt; buckets = new List&lt;List&lt;float&gt;&gt;();\nfor (int i = 0; i &lt; k; i++) {\nbuckets.Add(new List&lt;float&gt;());\n}\n// 1. \u5c06\u6570\u7ec4\u5143\u7d20\u5206\u914d\u5230\u5404\u4e2a\u6876\u4e2d\nforeach (float num in nums) {\n// \u8f93\u5165\u6570\u636e\u8303\u56f4 [0, 1)\uff0c\u4f7f\u7528 num * k \u6620\u5c04\u5230\u7d22\u5f15\u8303\u56f4 [0, k-1]\nint i = (int) (num * k);\n// \u5c06 num \u6dfb\u52a0\u8fdb\u6876 i\nbuckets[i].Add(num);\n}\n// 2. \u5bf9\u5404\u4e2a\u6876\u6267\u884c\u6392\u5e8f\nforeach (List&lt;float&gt; bucket in buckets) {\n// \u4f7f\u7528\u5185\u7f6e\u6392\u5e8f\u51fd\u6570\uff0c\u4e5f\u53ef\u4ee5\u66ff\u6362\u6210\u5176\u4ed6\u6392\u5e8f\u7b97\u6cd5\nbucket.Sort();\n}\n// 3. \u904d\u5386\u6876\u5408\u5e76\u7ed3\u679c\nint j = 0;\nforeach (List&lt;float&gt; bucket in buckets) {\nforeach (float num in bucket) {\nnums[j++] = num;\n}\n}\n}\n</code></pre> bucket_sort.swift<pre><code>/* \u6876\u6392\u5e8f */\nfunc bucketSort(nums: inout [Double]) {\n// \u521d\u59cb\u5316 k = n/2 \u4e2a\u6876\uff0c\u9884\u671f\u5411\u6bcf\u4e2a\u6876\u5206\u914d 2 \u4e2a\u5143\u7d20\nlet k = nums.count / 2\nvar buckets = (0 ..&lt; k).map { _ in [Double]() }\n// 1. \u5c06\u6570\u7ec4\u5143\u7d20\u5206\u914d\u5230\u5404\u4e2a\u6876\u4e2d\nfor num in nums {\n// \u8f93\u5165\u6570\u636e\u8303\u56f4 [0, 1)\uff0c\u4f7f\u7528 num * k \u6620\u5c04\u5230\u7d22\u5f15\u8303\u56f4 [0, k-1]\nlet i = Int(num * k)\n// \u5c06 num \u6dfb\u52a0\u8fdb\u6876 i\nbuckets[i].append(num)\n}\n// 2. \u5bf9\u5404\u4e2a\u6876\u6267\u884c\u6392\u5e8f\nfor i in buckets.indices {\n// \u4f7f\u7528\u5185\u7f6e\u6392\u5e8f\u51fd\u6570\uff0c\u4e5f\u53ef\u4ee5\u66ff\u6362\u6210\u5176\u4ed6\u6392\u5e8f\u7b97\u6cd5\nbuckets[i].sort()\n}\n// 3. \u904d\u5386\u6876\u5408\u5e76\u7ed3\u679c\nvar i = nums.startIndex\nfor bucket in buckets {\nfor num in bucket {\nnums[i] = num\nnums.formIndex(after: &amp;i)\n}\n}\n}\n</code></pre> bucket_sort.zig<pre><code>[class]{}-[func]{bucketSort}\n</code></pre> bucket_sort.dart<pre><code>/* \u6876\u6392\u5e8f */\nvoid bucketSort(List&lt;double&gt; nums) {\n// \u521d\u59cb\u5316 k = n/2 \u4e2a\u6876\uff0c\u9884\u671f\u5411\u6bcf\u4e2a\u6876\u5206\u914d 2 \u4e2a\u5143\u7d20\nint k = nums.length ~/ 2;\nList&lt;List&lt;double&gt;&gt; buckets = List.generate(k, (index) =&gt; []);\n// 1. \u5c06\u6570\u7ec4\u5143\u7d20\u5206\u914d\u5230\u5404\u4e2a\u6876\u4e2d\nfor (double num in nums) {\n// \u8f93\u5165\u6570\u636e\u8303\u56f4 [0, 1)\uff0c\u4f7f\u7528 num * k \u6620\u5c04\u5230\u7d22\u5f15\u8303\u56f4 [0, k-1]\nint i = (num * k).toInt();\n// \u5c06 num \u6dfb\u52a0\u8fdb\u6876 bucket_idx\nbuckets[i].add(num);\n}\n// 2. \u5bf9\u5404\u4e2a\u6876\u6267\u884c\u6392\u5e8f\nfor (List&lt;double&gt; bucket in buckets) {\nbucket.sort();\n}\n// 3. \u904d\u5386\u6876\u5408\u5e76\u7ed3\u679c\nint i = 0;\nfor (List&lt;double&gt; bucket in buckets) {\nfor (double num in bucket) {\nnums[i++] = num;\n}\n}\n}\n</code></pre> <p>\u6876\u6392\u5e8f\u7684\u9002\u7528\u573a\u666f\u662f\u4ec0\u4e48\uff1f</p> <p>\u6876\u6392\u5e8f\u9002\u7528\u4e8e\u5904\u7406\u4f53\u91cf\u5f88\u5927\u7684\u6570\u636e\u3002\u4f8b\u5982\uff0c\u8f93\u5165\u6570\u636e\u5305\u542b 100 \u4e07\u4e2a\u5143\u7d20\uff0c\u7531\u4e8e\u7a7a\u95f4\u9650\u5236\uff0c\u7cfb\u7edf\u5185\u5b58\u65e0\u6cd5\u4e00\u6b21\u6027\u52a0\u8f7d\u6240\u6709\u6570\u636e\u3002\u6b64\u65f6\uff0c\u53ef\u4ee5\u5c06\u6570\u636e\u5206\u6210 1000 \u4e2a\u6876\uff0c\u7136\u540e\u5206\u522b\u5bf9\u6bcf\u4e2a\u6876\u8fdb\u884c\u6392\u5e8f\uff0c\u6700\u540e\u5c06\u7ed3\u679c\u5408\u5e76\u3002</p>"},{"location":"chapter_sorting/bucket_sort/#1182","title":"11.8.2. \u00a0 \u7b97\u6cd5\u7279\u6027","text":"<ul> <li>\u65f6\u95f4\u590d\u6742\u5ea6 \\(O(n + k)\\) \uff1a\u5047\u8bbe\u5143\u7d20\u5728\u5404\u4e2a\u6876\u5185\u5e73\u5747\u5206\u5e03\uff0c\u90a3\u4e48\u6bcf\u4e2a\u6876\u5185\u7684\u5143\u7d20\u6570\u91cf\u4e3a \\(\\frac{n}{k}\\) \u3002\u5047\u8bbe\u6392\u5e8f\u5355\u4e2a\u6876\u4f7f\u7528 \\(O(\\frac{n}{k} \\log\\frac{n}{k})\\) \u65f6\u95f4\uff0c\u5219\u6392\u5e8f\u6240\u6709\u6876\u4f7f\u7528 \\(O(n \\log\\frac{n}{k})\\) \u65f6\u95f4\u3002\u5f53\u6876\u6570\u91cf \\(k\\) \u6bd4\u8f83\u5927\u65f6\uff0c\u65f6\u95f4\u590d\u6742\u5ea6\u5219\u8d8b\u5411\u4e8e \\(O(n)\\) \u3002\u5408\u5e76\u7ed3\u679c\u65f6\u9700\u8981\u904d\u5386 \\(n\\) \u4e2a\u6876\uff0c\u82b1\u8d39 \\(O(k)\\) \u65f6\u95f4\u3002</li> <li>\u81ea\u9002\u5e94\u6392\u5e8f\uff1a\u5728\u6700\u574f\u60c5\u51b5\u4e0b\uff0c\u6240\u6709\u6570\u636e\u88ab\u5206\u914d\u5230\u4e00\u4e2a\u6876\u4e2d\uff0c\u4e14\u6392\u5e8f\u8be5\u6876\u4f7f\u7528 \\(O(n^2)\\) \u65f6\u95f4\u3002</li> <li>\u7a7a\u95f4\u590d\u6742\u5ea6 \\(O(n + k)\\) \u3001\u975e\u539f\u5730\u6392\u5e8f \uff1a\u9700\u8981\u501f\u52a9 \\(k\\) \u4e2a\u6876\u548c\u603b\u5171 \\(n\\) \u4e2a\u5143\u7d20\u7684\u989d\u5916\u7a7a\u95f4\u3002</li> <li>\u6876\u6392\u5e8f\u662f\u5426\u7a33\u5b9a\u53d6\u51b3\u4e8e\u6392\u5e8f\u6876\u5185\u5143\u7d20\u7684\u7b97\u6cd5\u662f\u5426\u7a33\u5b9a\u3002</li> </ul>"},{"location":"chapter_sorting/bucket_sort/#1183","title":"11.8.3. \u00a0 \u5982\u4f55\u5b9e\u73b0\u5e73\u5747\u5206\u914d","text":"<p>\u6876\u6392\u5e8f\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u7406\u8bba\u4e0a\u53ef\u4ee5\u8fbe\u5230 \\(O(n)\\) \uff0c\u5173\u952e\u5728\u4e8e\u5c06\u5143\u7d20\u5747\u5300\u5206\u914d\u5230\u5404\u4e2a\u6876\u4e2d\uff0c\u56e0\u4e3a\u5b9e\u9645\u6570\u636e\u5f80\u5f80\u4e0d\u662f\u5747\u5300\u5206\u5e03\u7684\u3002\u4f8b\u5982\uff0c\u6211\u4eec\u60f3\u8981\u5c06\u6dd8\u5b9d\u4e0a\u7684\u6240\u6709\u5546\u54c1\u6309\u4ef7\u683c\u8303\u56f4\u5e73\u5747\u5206\u914d\u5230 10 \u4e2a\u6876\u4e2d\uff0c\u4f46\u5546\u54c1\u4ef7\u683c\u5206\u5e03\u4e0d\u5747\uff0c\u4f4e\u4e8e 100 \u5143\u7684\u975e\u5e38\u591a\uff0c\u9ad8\u4e8e 1000 \u5143\u7684\u975e\u5e38\u5c11\u3002\u82e5\u5c06\u4ef7\u683c\u533a\u95f4\u5e73\u5747\u5212\u5206\u4e3a 10 \u4efd\uff0c\u5404\u4e2a\u6876\u4e2d\u7684\u5546\u54c1\u6570\u91cf\u5dee\u8ddd\u4f1a\u975e\u5e38\u5927\u3002</p> <p>\u4e3a\u5b9e\u73b0\u5e73\u5747\u5206\u914d\uff0c\u6211\u4eec\u53ef\u4ee5\u5148\u8bbe\u5b9a\u4e00\u4e2a\u5927\u81f4\u7684\u5206\u754c\u7ebf\uff0c\u5c06\u6570\u636e\u7c97\u7565\u5730\u5206\u5230 3 \u4e2a\u6876\u4e2d\u3002\u5206\u914d\u5b8c\u6bd5\u540e\uff0c\u518d\u5c06\u5546\u54c1\u8f83\u591a\u7684\u6876\u7ee7\u7eed\u5212\u5206\u4e3a 3 \u4e2a\u6876\uff0c\u76f4\u81f3\u6240\u6709\u6876\u4e2d\u7684\u5143\u7d20\u6570\u91cf\u5927\u81f4\u76f8\u7b49\u3002\u8fd9\u79cd\u65b9\u6cd5\u672c\u8d28\u4e0a\u662f\u521b\u5efa\u4e00\u4e2a\u9012\u5f52\u6811\uff0c\u4f7f\u53f6\u8282\u70b9\u7684\u503c\u5c3d\u53ef\u80fd\u5e73\u5747\u3002\u5f53\u7136\uff0c\u4e0d\u4e00\u5b9a\u8981\u6bcf\u8f6e\u5c06\u6570\u636e\u5212\u5206\u4e3a 3 \u4e2a\u6876\uff0c\u5177\u4f53\u5212\u5206\u65b9\u5f0f\u53ef\u6839\u636e\u6570\u636e\u7279\u70b9\u7075\u6d3b\u9009\u62e9\u3002</p> <p></p> <p> Fig. \u9012\u5f52\u5212\u5206\u6876 </p> <p>\u5982\u679c\u6211\u4eec\u63d0\u524d\u77e5\u9053\u5546\u54c1\u4ef7\u683c\u7684\u6982\u7387\u5206\u5e03\uff0c\u5219\u53ef\u4ee5\u6839\u636e\u6570\u636e\u6982\u7387\u5206\u5e03\u8bbe\u7f6e\u6bcf\u4e2a\u6876\u7684\u4ef7\u683c\u5206\u754c\u7ebf\u3002\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u6570\u636e\u5206\u5e03\u5e76\u4e0d\u4e00\u5b9a\u9700\u8981\u7279\u610f\u7edf\u8ba1\uff0c\u4e5f\u53ef\u4ee5\u6839\u636e\u6570\u636e\u7279\u70b9\u91c7\u7528\u67d0\u79cd\u6982\u7387\u6a21\u578b\u8fdb\u884c\u8fd1\u4f3c\u3002\u5982\u4e0b\u56fe\u6240\u793a\uff0c\u6211\u4eec\u5047\u8bbe\u5546\u54c1\u4ef7\u683c\u670d\u4ece\u6b63\u6001\u5206\u5e03\uff0c\u8fd9\u6837\u5c31\u53ef\u4ee5\u5408\u7406\u5730\u8bbe\u5b9a\u4ef7\u683c\u533a\u95f4\uff0c\u4ece\u800c\u5c06\u5546\u54c1\u5e73\u5747\u5206\u914d\u5230\u5404\u4e2a\u6876\u4e2d\u3002</p> <p></p> <p> Fig. \u6839\u636e\u6982\u7387\u5206\u5e03\u5212\u5206\u6876 </p>"},{"location":"chapter_sorting/counting_sort/","title":"11.9. \u00a0 \u8ba1\u6570\u6392\u5e8f","text":"<p>\u300c\u8ba1\u6570\u6392\u5e8f Counting Sort\u300d\u901a\u8fc7\u7edf\u8ba1\u5143\u7d20\u6570\u91cf\u6765\u5b9e\u73b0\u6392\u5e8f\uff0c\u901a\u5e38\u5e94\u7528\u4e8e\u6574\u6570\u6570\u7ec4\u3002</p>"},{"location":"chapter_sorting/counting_sort/#1191","title":"11.9.1. \u00a0 \u7b80\u5355\u5b9e\u73b0","text":"<p>\u5148\u6765\u770b\u4e00\u4e2a\u7b80\u5355\u7684\u4f8b\u5b50\u3002\u7ed9\u5b9a\u4e00\u4e2a\u957f\u5ea6\u4e3a \\(n\\) \u7684\u6570\u7ec4 <code>nums</code> \uff0c\u5176\u4e2d\u7684\u5143\u7d20\u90fd\u662f\u201c\u975e\u8d1f\u6574\u6570\u201d\u3002\u8ba1\u6570\u6392\u5e8f\u7684\u6574\u4f53\u6d41\u7a0b\u5982\u4e0b\uff1a</p> <ol> <li>\u904d\u5386\u6570\u7ec4\uff0c\u627e\u51fa\u6570\u7ec4\u4e2d\u7684\u6700\u5927\u6570\u5b57\uff0c\u8bb0\u4e3a \\(m\\) \uff0c\u7136\u540e\u521b\u5efa\u4e00\u4e2a\u957f\u5ea6\u4e3a \\(m + 1\\) \u7684\u8f85\u52a9\u6570\u7ec4 <code>counter</code> \uff1b</li> <li>\u501f\u52a9 <code>counter</code> \u7edf\u8ba1 <code>nums</code> \u4e2d\u5404\u6570\u5b57\u7684\u51fa\u73b0\u6b21\u6570\uff0c\u5176\u4e2d <code>counter[num]</code> \u5bf9\u5e94\u6570\u5b57 <code>num</code> \u7684\u51fa\u73b0\u6b21\u6570\u3002\u7edf\u8ba1\u65b9\u6cd5\u5f88\u7b80\u5355\uff0c\u53ea\u9700\u904d\u5386 <code>nums</code>\uff08\u8bbe\u5f53\u524d\u6570\u5b57\u4e3a <code>num</code>\uff09\uff0c\u6bcf\u8f6e\u5c06 <code>counter[num]</code> \u589e\u52a0 \\(1\\) \u5373\u53ef\u3002</li> <li>\u7531\u4e8e <code>counter</code> \u7684\u5404\u4e2a\u7d22\u5f15\u5929\u7136\u6709\u5e8f\uff0c\u56e0\u6b64\u76f8\u5f53\u4e8e\u6240\u6709\u6570\u5b57\u5df2\u7ecf\u88ab\u6392\u5e8f\u597d\u4e86\u3002\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u904d\u5386 <code>counter</code> \uff0c\u6839\u636e\u5404\u6570\u5b57\u7684\u51fa\u73b0\u6b21\u6570\uff0c\u5c06\u5b83\u4eec\u6309\u4ece\u5c0f\u5230\u5927\u7684\u987a\u5e8f\u586b\u5165 <code>nums</code> \u5373\u53ef\u3002</li> </ol> <p></p> <p> Fig. \u8ba1\u6570\u6392\u5e8f\u6d41\u7a0b </p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart counting_sort.java<pre><code>/* \u8ba1\u6570\u6392\u5e8f */\n// \u7b80\u5355\u5b9e\u73b0\uff0c\u65e0\u6cd5\u7528\u4e8e\u6392\u5e8f\u5bf9\u8c61\nvoid countingSortNaive(int[] nums) {\n// 1. \u7edf\u8ba1\u6570\u7ec4\u6700\u5927\u5143\u7d20 m\nint m = 0;\nfor (int num : nums) {\nm = Math.max(m, num);\n}\n// 2. \u7edf\u8ba1\u5404\u6570\u5b57\u7684\u51fa\u73b0\u6b21\u6570\n// counter[num] \u4ee3\u8868 num \u7684\u51fa\u73b0\u6b21\u6570\nint[] counter = new int[m + 1];\nfor (int num : nums) {\ncounter[num]++;\n}\n// 3. \u904d\u5386 counter \uff0c\u5c06\u5404\u5143\u7d20\u586b\u5165\u539f\u6570\u7ec4 nums\nint i = 0;\nfor (int num = 0; num &lt; m + 1; num++) {\nfor (int j = 0; j &lt; counter[num]; j++, i++) {\nnums[i] = num;\n}\n}\n}\n</code></pre> counting_sort.cpp<pre><code>/* \u8ba1\u6570\u6392\u5e8f */\n// \u7b80\u5355\u5b9e\u73b0\uff0c\u65e0\u6cd5\u7528\u4e8e\u6392\u5e8f\u5bf9\u8c61\nvoid countingSortNaive(vector&lt;int&gt; &amp;nums) {\n// 1. \u7edf\u8ba1\u6570\u7ec4\u6700\u5927\u5143\u7d20 m\nint m = 0;\nfor (int num : nums) {\nm = max(m, num);\n}\n// 2. \u7edf\u8ba1\u5404\u6570\u5b57\u7684\u51fa\u73b0\u6b21\u6570\n// counter[num] \u4ee3\u8868 num \u7684\u51fa\u73b0\u6b21\u6570\nvector&lt;int&gt; counter(m + 1, 0);\nfor (int num : nums) {\ncounter[num]++;\n}\n// 3. \u904d\u5386 counter \uff0c\u5c06\u5404\u5143\u7d20\u586b\u5165\u539f\u6570\u7ec4 nums\nint i = 0;\nfor (int num = 0; num &lt; m + 1; num++) {\nfor (int j = 0; j &lt; counter[num]; j++, i++) {\nnums[i] = num;\n}\n}\n}\n</code></pre> counting_sort.py<pre><code>def counting_sort_naive(nums: list[int]) -&gt; None:\n\"\"\"\u8ba1\u6570\u6392\u5e8f\"\"\"\n# \u7b80\u5355\u5b9e\u73b0\uff0c\u65e0\u6cd5\u7528\u4e8e\u6392\u5e8f\u5bf9\u8c61\n# 1. \u7edf\u8ba1\u6570\u7ec4\u6700\u5927\u5143\u7d20 m\nm = 0\nfor num in nums:\nm = max(m, num)\n# 2. \u7edf\u8ba1\u5404\u6570\u5b57\u7684\u51fa\u73b0\u6b21\u6570\n# counter[num] \u4ee3\u8868 num \u7684\u51fa\u73b0\u6b21\u6570\ncounter = [0] * (m + 1)\nfor num in nums:\ncounter[num] += 1\n# 3. \u904d\u5386 counter \uff0c\u5c06\u5404\u5143\u7d20\u586b\u5165\u539f\u6570\u7ec4 nums\ni = 0\nfor num in range(m + 1):\nfor _ in range(counter[num]):\nnums[i] = num\ni += 1\n</code></pre> counting_sort.go<pre><code>/* \u8ba1\u6570\u6392\u5e8f */\n// \u7b80\u5355\u5b9e\u73b0\uff0c\u65e0\u6cd5\u7528\u4e8e\u6392\u5e8f\u5bf9\u8c61\nfunc countingSortNaive(nums []int) {\n// 1. \u7edf\u8ba1\u6570\u7ec4\u6700\u5927\u5143\u7d20 m\nm := 0\nfor _, num := range nums {\nif num &gt; m {\nm = num\n}\n}\n// 2. \u7edf\u8ba1\u5404\u6570\u5b57\u7684\u51fa\u73b0\u6b21\u6570\n// counter[num] \u4ee3\u8868 num \u7684\u51fa\u73b0\u6b21\u6570\ncounter := make([]int, m+1)\nfor _, num := range nums {\ncounter[num]++\n}\n// 3. \u904d\u5386 counter \uff0c\u5c06\u5404\u5143\u7d20\u586b\u5165\u539f\u6570\u7ec4 nums\nfor i, num := 0, 0; num &lt; m+1; num++ {\nfor j := 0; j &lt; counter[num]; j++ {\nnums[i] = num\ni++\n}\n}\n}\n</code></pre> counting_sort.js<pre><code>/* \u8ba1\u6570\u6392\u5e8f */\n// \u7b80\u5355\u5b9e\u73b0\uff0c\u65e0\u6cd5\u7528\u4e8e\u6392\u5e8f\u5bf9\u8c61\nfunction countingSortNaive(nums) {\n// 1. \u7edf\u8ba1\u6570\u7ec4\u6700\u5927\u5143\u7d20 m\nlet m = 0;\nfor (const num of nums) {\nm = Math.max(m, num);\n}\n// 2. \u7edf\u8ba1\u5404\u6570\u5b57\u7684\u51fa\u73b0\u6b21\u6570\n// counter[num] \u4ee3\u8868 num \u7684\u51fa\u73b0\u6b21\u6570\nconst counter = new Array(m + 1).fill(0);\nfor (const num of nums) {\ncounter[num]++;\n}\n// 3. \u904d\u5386 counter \uff0c\u5c06\u5404\u5143\u7d20\u586b\u5165\u539f\u6570\u7ec4 nums\nlet i = 0;\nfor (let num = 0; num &lt; m + 1; num++) {\nfor (let j = 0; j &lt; counter[num]; j++, i++) {\nnums[i] = num;\n}\n}\n}\n</code></pre> counting_sort.ts<pre><code>/* \u8ba1\u6570\u6392\u5e8f */\n// \u7b80\u5355\u5b9e\u73b0\uff0c\u65e0\u6cd5\u7528\u4e8e\u6392\u5e8f\u5bf9\u8c61\nfunction countingSortNaive(nums: number[]): void {\n// 1. \u7edf\u8ba1\u6570\u7ec4\u6700\u5927\u5143\u7d20 m\nlet m = 0;\nfor (const num of nums) {\nm = Math.max(m, num);\n}\n// 2. \u7edf\u8ba1\u5404\u6570\u5b57\u7684\u51fa\u73b0\u6b21\u6570\n// counter[num] \u4ee3\u8868 num \u7684\u51fa\u73b0\u6b21\u6570\nconst counter: number[] = new Array&lt;number&gt;(m + 1).fill(0);\nfor (const num of nums) {\ncounter[num]++;\n}\n// 3. \u904d\u5386 counter \uff0c\u5c06\u5404\u5143\u7d20\u586b\u5165\u539f\u6570\u7ec4 nums\nlet i = 0;\nfor (let num = 0; num &lt; m + 1; num++) {\nfor (let j = 0; j &lt; counter[num]; j++, i++) {\nnums[i] = num;\n}\n}\n}\n</code></pre> counting_sort.c<pre><code>/* \u8ba1\u6570\u6392\u5e8f */\n// \u7b80\u5355\u5b9e\u73b0\uff0c\u65e0\u6cd5\u7528\u4e8e\u6392\u5e8f\u5bf9\u8c61\nvoid countingSortNaive(int nums[], int size) {\n// 1. \u7edf\u8ba1\u6570\u7ec4\u6700\u5927\u5143\u7d20 m\nint m = 0;\nfor (int i = 0; i &lt; size; i++) {\nif (nums[i] &gt; m) {\nm = nums[i];\n}\n}\n// 2. \u7edf\u8ba1\u5404\u6570\u5b57\u7684\u51fa\u73b0\u6b21\u6570\n// counter[num] \u4ee3\u8868 num \u7684\u51fa\u73b0\u6b21\u6570\nint *counter = malloc(sizeof(int) * m);\nfor (int i = 0; i &lt; size; i++) {\ncounter[nums[i]]++;\n}\n// 3. \u904d\u5386 counter \uff0c\u5c06\u5404\u5143\u7d20\u586b\u5165\u539f\u6570\u7ec4 nums\nint i = 0;\nfor (int num = 0; num &lt; m + 1; num++) {\nfor (int j = 0; j &lt; counter[num]; j++, i++) {\nnums[i] = num;\n}\n}\n}\n</code></pre> counting_sort.cs<pre><code>/* \u8ba1\u6570\u6392\u5e8f */\n// \u7b80\u5355\u5b9e\u73b0\uff0c\u65e0\u6cd5\u7528\u4e8e\u6392\u5e8f\u5bf9\u8c61\nvoid countingSortNaive(int[] nums) {\n// 1. \u7edf\u8ba1\u6570\u7ec4\u6700\u5927\u5143\u7d20 m\nint m = 0;\nforeach (int num in nums) {\nm = Math.Max(m, num);\n}\n// 2. \u7edf\u8ba1\u5404\u6570\u5b57\u7684\u51fa\u73b0\u6b21\u6570\n// counter[num] \u4ee3\u8868 num \u7684\u51fa\u73b0\u6b21\u6570\nint[] counter = new int[m + 1];\nforeach (int num in nums) {\ncounter[num]++;\n}\n// 3. \u904d\u5386 counter \uff0c\u5c06\u5404\u5143\u7d20\u586b\u5165\u539f\u6570\u7ec4 nums\nint i = 0;\nfor (int num = 0; num &lt; m + 1; num++) {\nfor (int j = 0; j &lt; counter[num]; j++, i++) {\nnums[i] = num;\n}\n}\n}\n</code></pre> counting_sort.swift<pre><code>/* \u8ba1\u6570\u6392\u5e8f */\n// \u7b80\u5355\u5b9e\u73b0\uff0c\u65e0\u6cd5\u7528\u4e8e\u6392\u5e8f\u5bf9\u8c61\nfunc countingSortNaive(nums: inout [Int]) {\n// 1. \u7edf\u8ba1\u6570\u7ec4\u6700\u5927\u5143\u7d20 m\nlet m = nums.max()!\n// 2. \u7edf\u8ba1\u5404\u6570\u5b57\u7684\u51fa\u73b0\u6b21\u6570\n// counter[num] \u4ee3\u8868 num \u7684\u51fa\u73b0\u6b21\u6570\nvar counter = Array(repeating: 0, count: m + 1)\nfor num in nums {\ncounter[num] += 1\n}\n// 3. \u904d\u5386 counter \uff0c\u5c06\u5404\u5143\u7d20\u586b\u5165\u539f\u6570\u7ec4 nums\nvar i = 0\nfor num in stride(from: 0, to: m + 1, by: 1) {\nfor _ in stride(from: 0, to: counter[num], by: 1) {\nnums[i] = num\ni += 1\n}\n}\n}\n</code></pre> counting_sort.zig<pre><code>[class]{}-[func]{countingSortNaive}\n</code></pre> counting_sort.dart<pre><code>/* \u8ba1\u6570\u6392\u5e8f */\n// \u7b80\u5355\u5b9e\u73b0\uff0c\u65e0\u6cd5\u7528\u4e8e\u6392\u5e8f\u5bf9\u8c61\nvoid countingSortNaive(List&lt;int&gt; nums) {\n// 1. \u7edf\u8ba1\u6570\u7ec4\u6700\u5927\u5143\u7d20 m\nint m = 0;\nfor (int num in nums) {\nm = max(m, num);\n}\n// 2. \u7edf\u8ba1\u5404\u6570\u5b57\u7684\u51fa\u73b0\u6b21\u6570\n// counter[num] \u4ee3\u8868 num \u7684\u51fa\u73b0\u6b21\u6570\nList&lt;int&gt; counter = List.filled(m + 1, 0);\nfor (int num in nums) {\ncounter[num]++;\n}\n// 3. \u904d\u5386 counter \uff0c\u5c06\u5404\u5143\u7d20\u586b\u5165\u539f\u6570\u7ec4 nums\nint i = 0;\nfor (int num = 0; num &lt; m + 1; num++) {\nfor (int j = 0; j &lt; counter[num]; j++, i++) {\nnums[i] = num;\n}\n}\n}\n</code></pre> <p>\u8ba1\u6570\u6392\u5e8f\u4e0e\u6876\u6392\u5e8f\u7684\u8054\u7cfb</p> <p>\u4ece\u6876\u6392\u5e8f\u7684\u89d2\u5ea6\u770b\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u8ba1\u6570\u6392\u5e8f\u4e2d\u7684\u8ba1\u6570\u6570\u7ec4 <code>counter</code> \u7684\u6bcf\u4e2a\u7d22\u5f15\u89c6\u4e3a\u4e00\u4e2a\u6876\uff0c\u5c06\u7edf\u8ba1\u6570\u91cf\u7684\u8fc7\u7a0b\u770b\u4f5c\u662f\u5c06\u5404\u4e2a\u5143\u7d20\u5206\u914d\u5230\u5bf9\u5e94\u7684\u6876\u4e2d\u3002\u672c\u8d28\u4e0a\uff0c\u8ba1\u6570\u6392\u5e8f\u662f\u6876\u6392\u5e8f\u5728\u6574\u578b\u6570\u636e\u4e0b\u7684\u4e00\u4e2a\u7279\u4f8b\u3002</p>"},{"location":"chapter_sorting/counting_sort/#1192","title":"11.9.2. \u00a0 \u5b8c\u6574\u5b9e\u73b0","text":"<p>\u7ec6\u5fc3\u7684\u540c\u5b66\u53ef\u80fd\u53d1\u73b0\uff0c\u5982\u679c\u8f93\u5165\u6570\u636e\u662f\u5bf9\u8c61\uff0c\u4e0a\u8ff0\u6b65\u9aa4 <code>3.</code> \u5c31\u5931\u6548\u4e86\u3002\u4f8b\u5982\uff0c\u8f93\u5165\u6570\u636e\u662f\u5546\u54c1\u5bf9\u8c61\uff0c\u6211\u4eec\u60f3\u8981\u6309\u7167\u5546\u54c1\u4ef7\u683c\uff08\u7c7b\u7684\u6210\u5458\u53d8\u91cf\uff09\u5bf9\u5546\u54c1\u8fdb\u884c\u6392\u5e8f\uff0c\u800c\u4e0a\u8ff0\u7b97\u6cd5\u53ea\u80fd\u7ed9\u51fa\u4ef7\u683c\u7684\u6392\u5e8f\u7ed3\u679c\u3002</p> <p>\u90a3\u4e48\u5982\u4f55\u624d\u80fd\u5f97\u5230\u539f\u6570\u636e\u7684\u6392\u5e8f\u7ed3\u679c\u5462\uff1f\u6211\u4eec\u9996\u5148\u8ba1\u7b97 <code>counter</code> \u7684\u300c\u524d\u7f00\u548c\u300d\u3002\u987e\u540d\u601d\u4e49\uff0c\u7d22\u5f15 <code>i</code> \u5904\u7684\u524d\u7f00\u548c <code>prefix[i]</code> \u7b49\u4e8e\u6570\u7ec4\u524d <code>i</code> \u4e2a\u5143\u7d20\u4e4b\u548c\uff0c\u5373</p> \\[ \\text{prefix}[i] = \\sum_{j=0}^i \\text{counter[j]} \\] <p>\u524d\u7f00\u548c\u5177\u6709\u660e\u786e\u7684\u610f\u4e49\uff0c<code>prefix[num] - 1</code> \u4ee3\u8868\u5143\u7d20 <code>num</code> \u5728\u7ed3\u679c\u6570\u7ec4 <code>res</code> \u4e2d\u6700\u540e\u4e00\u6b21\u51fa\u73b0\u7684\u7d22\u5f15\u3002\u8fd9\u4e2a\u4fe1\u606f\u975e\u5e38\u5173\u952e\uff0c\u56e0\u4e3a\u5b83\u544a\u8bc9\u6211\u4eec\u5404\u4e2a\u5143\u7d20\u5e94\u8be5\u51fa\u73b0\u5728\u7ed3\u679c\u6570\u7ec4\u7684\u54ea\u4e2a\u4f4d\u7f6e\u3002\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u5012\u5e8f\u904d\u5386\u539f\u6570\u7ec4 <code>nums</code> \u7684\u6bcf\u4e2a\u5143\u7d20 <code>num</code> \uff0c\u5728\u6bcf\u8f6e\u8fed\u4ee3\u4e2d\u6267\u884c\uff1a</p> <ol> <li>\u5c06 <code>num</code> \u586b\u5165\u6570\u7ec4 <code>res</code> \u7684\u7d22\u5f15 <code>prefix[num] - 1</code> \u5904\uff1b</li> <li>\u4ee4\u524d\u7f00\u548c <code>prefix[num]</code> \u51cf\u5c0f \\(1\\) \uff0c\u4ece\u800c\u5f97\u5230\u4e0b\u6b21\u653e\u7f6e <code>num</code> \u7684\u7d22\u5f15\uff1b</li> </ol> <p>\u904d\u5386\u5b8c\u6210\u540e\uff0c\u6570\u7ec4 <code>res</code> \u4e2d\u5c31\u662f\u6392\u5e8f\u597d\u7684\u7ed3\u679c\uff0c\u6700\u540e\u4f7f\u7528 <code>res</code> \u8986\u76d6\u539f\u6570\u7ec4 <code>nums</code> \u5373\u53ef\u3002</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p>\u8ba1\u6570\u6392\u5e8f\u7684\u5b9e\u73b0\u4ee3\u7801\u5982\u4e0b\u6240\u793a\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart counting_sort.java<pre><code>/* \u8ba1\u6570\u6392\u5e8f */\n// \u5b8c\u6574\u5b9e\u73b0\uff0c\u53ef\u6392\u5e8f\u5bf9\u8c61\uff0c\u5e76\u4e14\u662f\u7a33\u5b9a\u6392\u5e8f\nvoid countingSort(int[] nums) {\n// 1. \u7edf\u8ba1\u6570\u7ec4\u6700\u5927\u5143\u7d20 m\nint m = 0;\nfor (int num : nums) {\nm = Math.max(m, num);\n}\n// 2. \u7edf\u8ba1\u5404\u6570\u5b57\u7684\u51fa\u73b0\u6b21\u6570\n// counter[num] \u4ee3\u8868 num \u7684\u51fa\u73b0\u6b21\u6570\nint[] counter = new int[m + 1];\nfor (int num : nums) {\ncounter[num]++;\n}\n// 3. \u6c42 counter \u7684\u524d\u7f00\u548c\uff0c\u5c06\u201c\u51fa\u73b0\u6b21\u6570\u201d\u8f6c\u6362\u4e3a\u201c\u5c3e\u7d22\u5f15\u201d\n// \u5373 counter[num]-1 \u662f num \u5728 res \u4e2d\u6700\u540e\u4e00\u6b21\u51fa\u73b0\u7684\u7d22\u5f15\nfor (int i = 0; i &lt; m; i++) {\ncounter[i + 1] += counter[i];\n}\n// 4. \u5012\u5e8f\u904d\u5386 nums \uff0c\u5c06\u5404\u5143\u7d20\u586b\u5165\u7ed3\u679c\u6570\u7ec4 res\n// \u521d\u59cb\u5316\u6570\u7ec4 res \u7528\u4e8e\u8bb0\u5f55\u7ed3\u679c\nint n = nums.length;\nint[] res = new int[n];\nfor (int i = n - 1; i &gt;= 0; i--) {\nint num = nums[i];\nres[counter[num] - 1] = num; // \u5c06 num \u653e\u7f6e\u5230\u5bf9\u5e94\u7d22\u5f15\u5904\ncounter[num]--; // \u4ee4\u524d\u7f00\u548c\u81ea\u51cf 1 \uff0c\u5f97\u5230\u4e0b\u6b21\u653e\u7f6e num \u7684\u7d22\u5f15\n}\n// \u4f7f\u7528\u7ed3\u679c\u6570\u7ec4 res \u8986\u76d6\u539f\u6570\u7ec4 nums\nfor (int i = 0; i &lt; n; i++) {\nnums[i] = res[i];\n}\n}\n</code></pre> counting_sort.cpp<pre><code>/* \u8ba1\u6570\u6392\u5e8f */\n// \u5b8c\u6574\u5b9e\u73b0\uff0c\u53ef\u6392\u5e8f\u5bf9\u8c61\uff0c\u5e76\u4e14\u662f\u7a33\u5b9a\u6392\u5e8f\nvoid countingSort(vector&lt;int&gt; &amp;nums) {\n// 1. \u7edf\u8ba1\u6570\u7ec4\u6700\u5927\u5143\u7d20 m\nint m = 0;\nfor (int num : nums) {\nm = max(m, num);\n}\n// 2. \u7edf\u8ba1\u5404\u6570\u5b57\u7684\u51fa\u73b0\u6b21\u6570\n// counter[num] \u4ee3\u8868 num \u7684\u51fa\u73b0\u6b21\u6570\nvector&lt;int&gt; counter(m + 1, 0);\nfor (int num : nums) {\ncounter[num]++;\n}\n// 3. \u6c42 counter \u7684\u524d\u7f00\u548c\uff0c\u5c06\u201c\u51fa\u73b0\u6b21\u6570\u201d\u8f6c\u6362\u4e3a\u201c\u5c3e\u7d22\u5f15\u201d\n// \u5373 counter[num]-1 \u662f num \u5728 res \u4e2d\u6700\u540e\u4e00\u6b21\u51fa\u73b0\u7684\u7d22\u5f15\nfor (int i = 0; i &lt; m; i++) {\ncounter[i + 1] += counter[i];\n}\n// 4. \u5012\u5e8f\u904d\u5386 nums \uff0c\u5c06\u5404\u5143\u7d20\u586b\u5165\u7ed3\u679c\u6570\u7ec4 res\n// \u521d\u59cb\u5316\u6570\u7ec4 res \u7528\u4e8e\u8bb0\u5f55\u7ed3\u679c\nint n = nums.size();\nvector&lt;int&gt; res(n);\nfor (int i = n - 1; i &gt;= 0; i--) {\nint num = nums[i];\nres[counter[num] - 1] = num; // \u5c06 num \u653e\u7f6e\u5230\u5bf9\u5e94\u7d22\u5f15\u5904\ncounter[num]--;              // \u4ee4\u524d\u7f00\u548c\u81ea\u51cf 1 \uff0c\u5f97\u5230\u4e0b\u6b21\u653e\u7f6e num \u7684\u7d22\u5f15\n}\n// \u4f7f\u7528\u7ed3\u679c\u6570\u7ec4 res \u8986\u76d6\u539f\u6570\u7ec4 nums\nnums = res;\n}\n</code></pre> counting_sort.py<pre><code>def counting_sort(nums: list[int]) -&gt; None:\n\"\"\"\u8ba1\u6570\u6392\u5e8f\"\"\"\n# \u5b8c\u6574\u5b9e\u73b0\uff0c\u53ef\u6392\u5e8f\u5bf9\u8c61\uff0c\u5e76\u4e14\u662f\u7a33\u5b9a\u6392\u5e8f\n# 1. \u7edf\u8ba1\u6570\u7ec4\u6700\u5927\u5143\u7d20 m\nm = max(nums)\n# 2. \u7edf\u8ba1\u5404\u6570\u5b57\u7684\u51fa\u73b0\u6b21\u6570\n# counter[num] \u4ee3\u8868 num \u7684\u51fa\u73b0\u6b21\u6570\ncounter = [0] * (m + 1)\nfor num in nums:\ncounter[num] += 1\n# 3. \u6c42 counter \u7684\u524d\u7f00\u548c\uff0c\u5c06\u201c\u51fa\u73b0\u6b21\u6570\u201d\u8f6c\u6362\u4e3a\u201c\u5c3e\u7d22\u5f15\u201d\n# \u5373 counter[num]-1 \u662f num \u5728 res \u4e2d\u6700\u540e\u4e00\u6b21\u51fa\u73b0\u7684\u7d22\u5f15\nfor i in range(m):\ncounter[i + 1] += counter[i]\n# 4. \u5012\u5e8f\u904d\u5386 nums \uff0c\u5c06\u5404\u5143\u7d20\u586b\u5165\u7ed3\u679c\u6570\u7ec4 res\n# \u521d\u59cb\u5316\u6570\u7ec4 res \u7528\u4e8e\u8bb0\u5f55\u7ed3\u679c\nn = len(nums)\nres = [0] * n\nfor i in range(n - 1, -1, -1):\nnum = nums[i]\nres[counter[num] - 1] = num  # \u5c06 num \u653e\u7f6e\u5230\u5bf9\u5e94\u7d22\u5f15\u5904\ncounter[num] -= 1  # \u4ee4\u524d\u7f00\u548c\u81ea\u51cf 1 \uff0c\u5f97\u5230\u4e0b\u6b21\u653e\u7f6e num \u7684\u7d22\u5f15\n# \u4f7f\u7528\u7ed3\u679c\u6570\u7ec4 res \u8986\u76d6\u539f\u6570\u7ec4 nums\nfor i in range(n):\nnums[i] = res[i]\n</code></pre> counting_sort.go<pre><code>/* \u8ba1\u6570\u6392\u5e8f */\n// \u5b8c\u6574\u5b9e\u73b0\uff0c\u53ef\u6392\u5e8f\u5bf9\u8c61\uff0c\u5e76\u4e14\u662f\u7a33\u5b9a\u6392\u5e8f\nfunc countingSort(nums []int) {\n// 1. \u7edf\u8ba1\u6570\u7ec4\u6700\u5927\u5143\u7d20 m\nm := 0\nfor _, num := range nums {\nif num &gt; m {\nm = num\n}\n}\n// 2. \u7edf\u8ba1\u5404\u6570\u5b57\u7684\u51fa\u73b0\u6b21\u6570\n// counter[num] \u4ee3\u8868 num \u7684\u51fa\u73b0\u6b21\u6570\ncounter := make([]int, m+1)\nfor _, num := range nums {\ncounter[num]++\n}\n// 3. \u6c42 counter \u7684\u524d\u7f00\u548c\uff0c\u5c06\u201c\u51fa\u73b0\u6b21\u6570\u201d\u8f6c\u6362\u4e3a\u201c\u5c3e\u7d22\u5f15\u201d\n// \u5373 counter[num]-1 \u662f num \u5728 res \u4e2d\u6700\u540e\u4e00\u6b21\u51fa\u73b0\u7684\u7d22\u5f15\nfor i := 0; i &lt; m; i++ {\ncounter[i+1] += counter[i]\n}\n// 4. \u5012\u5e8f\u904d\u5386 nums \uff0c\u5c06\u5404\u5143\u7d20\u586b\u5165\u7ed3\u679c\u6570\u7ec4 res\n// \u521d\u59cb\u5316\u6570\u7ec4 res \u7528\u4e8e\u8bb0\u5f55\u7ed3\u679c\nn := len(nums)\nres := make([]int, n)\nfor i := n - 1; i &gt;= 0; i-- {\nnum := nums[i]\n// \u5c06 num \u653e\u7f6e\u5230\u5bf9\u5e94\u7d22\u5f15\u5904\nres[counter[num]-1] = num\n// \u4ee4\u524d\u7f00\u548c\u81ea\u51cf 1 \uff0c\u5f97\u5230\u4e0b\u6b21\u653e\u7f6e num \u7684\u7d22\u5f15\ncounter[num]--\n}\n// \u4f7f\u7528\u7ed3\u679c\u6570\u7ec4 res \u8986\u76d6\u539f\u6570\u7ec4 nums\ncopy(nums, res)\n}\n</code></pre> counting_sort.js<pre><code>/* \u8ba1\u6570\u6392\u5e8f */\n// \u5b8c\u6574\u5b9e\u73b0\uff0c\u53ef\u6392\u5e8f\u5bf9\u8c61\uff0c\u5e76\u4e14\u662f\u7a33\u5b9a\u6392\u5e8f\nfunction countingSort(nums) {\n// 1. \u7edf\u8ba1\u6570\u7ec4\u6700\u5927\u5143\u7d20 m\nlet m = 0;\nfor (const num of nums) {\nm = Math.max(m, num);\n}\n// 2. \u7edf\u8ba1\u5404\u6570\u5b57\u7684\u51fa\u73b0\u6b21\u6570\n// counter[num] \u4ee3\u8868 num \u7684\u51fa\u73b0\u6b21\u6570\nconst counter = new Array(m + 1).fill(0);\nfor (const num of nums) {\ncounter[num]++;\n}\n// 3. \u6c42 counter \u7684\u524d\u7f00\u548c\uff0c\u5c06\u201c\u51fa\u73b0\u6b21\u6570\u201d\u8f6c\u6362\u4e3a\u201c\u5c3e\u7d22\u5f15\u201d\n// \u5373 counter[num]-1 \u662f num \u5728 res \u4e2d\u6700\u540e\u4e00\u6b21\u51fa\u73b0\u7684\u7d22\u5f15\nfor (let i = 0; i &lt; m; i++) {\ncounter[i + 1] += counter[i];\n}\n// 4. \u5012\u5e8f\u904d\u5386 nums \uff0c\u5c06\u5404\u5143\u7d20\u586b\u5165\u7ed3\u679c\u6570\u7ec4 res\n// \u521d\u59cb\u5316\u6570\u7ec4 res \u7528\u4e8e\u8bb0\u5f55\u7ed3\u679c\nconst n = nums.length;\nconst res = new Array(n);\nfor (let i = n - 1; i &gt;= 0; i--) {\nconst num = nums[i];\nres[counter[num] - 1] = num; // \u5c06 num \u653e\u7f6e\u5230\u5bf9\u5e94\u7d22\u5f15\u5904\ncounter[num]--; // \u4ee4\u524d\u7f00\u548c\u81ea\u51cf 1 \uff0c\u5f97\u5230\u4e0b\u6b21\u653e\u7f6e num \u7684\u7d22\u5f15\n}\n// \u4f7f\u7528\u7ed3\u679c\u6570\u7ec4 res \u8986\u76d6\u539f\u6570\u7ec4 nums\nfor (let i = 0; i &lt; n; i++) {\nnums[i] = res[i];\n}\n}\n</code></pre> counting_sort.ts<pre><code>/* \u8ba1\u6570\u6392\u5e8f */\n// \u5b8c\u6574\u5b9e\u73b0\uff0c\u53ef\u6392\u5e8f\u5bf9\u8c61\uff0c\u5e76\u4e14\u662f\u7a33\u5b9a\u6392\u5e8f\nfunction countingSort(nums: number[]): void {\n// 1. \u7edf\u8ba1\u6570\u7ec4\u6700\u5927\u5143\u7d20 m\nlet m = 0;\nfor (const num of nums) {\nm = Math.max(m, num);\n}\n// 2. \u7edf\u8ba1\u5404\u6570\u5b57\u7684\u51fa\u73b0\u6b21\u6570\n// counter[num] \u4ee3\u8868 num \u7684\u51fa\u73b0\u6b21\u6570\nconst counter: number[] = new Array&lt;number&gt;(m + 1).fill(0);\nfor (const num of nums) {\ncounter[num]++;\n}\n// 3. \u6c42 counter \u7684\u524d\u7f00\u548c\uff0c\u5c06\u201c\u51fa\u73b0\u6b21\u6570\u201d\u8f6c\u6362\u4e3a\u201c\u5c3e\u7d22\u5f15\u201d\n// \u5373 counter[num]-1 \u662f num \u5728 res \u4e2d\u6700\u540e\u4e00\u6b21\u51fa\u73b0\u7684\u7d22\u5f15\nfor (let i = 0; i &lt; m; i++) {\ncounter[i + 1] += counter[i];\n}\n// 4. \u5012\u5e8f\u904d\u5386 nums \uff0c\u5c06\u5404\u5143\u7d20\u586b\u5165\u7ed3\u679c\u6570\u7ec4 res\n// \u521d\u59cb\u5316\u6570\u7ec4 res \u7528\u4e8e\u8bb0\u5f55\u7ed3\u679c\nconst n = nums.length;\nconst res: number[] = new Array&lt;number&gt;(n);\nfor (let i = n - 1; i &gt;= 0; i--) {\nconst num = nums[i];\nres[counter[num] - 1] = num; // \u5c06 num \u653e\u7f6e\u5230\u5bf9\u5e94\u7d22\u5f15\u5904\ncounter[num]--; // \u4ee4\u524d\u7f00\u548c\u81ea\u51cf 1 \uff0c\u5f97\u5230\u4e0b\u6b21\u653e\u7f6e num \u7684\u7d22\u5f15\n}\n// \u4f7f\u7528\u7ed3\u679c\u6570\u7ec4 res \u8986\u76d6\u539f\u6570\u7ec4 nums\nfor (let i = 0; i &lt; n; i++) {\nnums[i] = res[i];\n}\n}\n</code></pre> counting_sort.c<pre><code>/* \u8ba1\u6570\u6392\u5e8f */\n// \u5b8c\u6574\u5b9e\u73b0\uff0c\u53ef\u6392\u5e8f\u5bf9\u8c61\uff0c\u5e76\u4e14\u662f\u7a33\u5b9a\u6392\u5e8f\nvoid countingSort(int nums[], int size) {\n// 1. \u7edf\u8ba1\u6570\u7ec4\u6700\u5927\u5143\u7d20 m\nint m = 0;\nfor (int i = 0; i &lt; size; i++) {\nif (nums[i] &gt; m) {\nm = nums[i];\n}\n}\n// 2. \u7edf\u8ba1\u5404\u6570\u5b57\u7684\u51fa\u73b0\u6b21\u6570\n// counter[num] \u4ee3\u8868 num \u7684\u51fa\u73b0\u6b21\u6570\nint *counter = malloc(sizeof(int) * m);\nfor (int i = 0; i &lt; size; i++) {\ncounter[nums[i]]++;\n}\n// 3. \u6c42 counter \u7684\u524d\u7f00\u548c\uff0c\u5c06\u201c\u51fa\u73b0\u6b21\u6570\u201d\u8f6c\u6362\u4e3a\u201c\u5c3e\u7d22\u5f15\u201d\n// \u5373 counter[num]-1 \u662f num \u5728 res \u4e2d\u6700\u540e\u4e00\u6b21\u51fa\u73b0\u7684\u7d22\u5f15\nfor (int i = 0; i &lt; m; i++) {\ncounter[i + 1] += counter[i];\n}\n// 4. \u5012\u5e8f\u904d\u5386 nums \uff0c\u5c06\u5404\u5143\u7d20\u586b\u5165\u7ed3\u679c\u6570\u7ec4 res\n// \u521d\u59cb\u5316\u6570\u7ec4 res \u7528\u4e8e\u8bb0\u5f55\u7ed3\u679c\nint *res = malloc(sizeof(int) * size);\nfor (int i = size - 1; i &gt;= 0; i--) {\nint num = nums[i];\nres[counter[num] - 1] = num; // \u5c06 num \u653e\u7f6e\u5230\u5bf9\u5e94\u7d22\u5f15\u5904\ncounter[num]--;              // \u4ee4\u524d\u7f00\u548c\u81ea\u51cf 1 \uff0c\u5f97\u5230\u4e0b\u6b21\u653e\u7f6e num \u7684\u7d22\u5f15\n}\n// \u4f7f\u7528\u7ed3\u679c\u6570\u7ec4 res \u8986\u76d6\u539f\u6570\u7ec4 nums\nmemcpy(nums, res, size * sizeof(int));\n}\n</code></pre> counting_sort.cs<pre><code>/* \u8ba1\u6570\u6392\u5e8f */\n// \u5b8c\u6574\u5b9e\u73b0\uff0c\u53ef\u6392\u5e8f\u5bf9\u8c61\uff0c\u5e76\u4e14\u662f\u7a33\u5b9a\u6392\u5e8f\nvoid countingSort(int[] nums) {\n// 1. \u7edf\u8ba1\u6570\u7ec4\u6700\u5927\u5143\u7d20 m\nint m = 0;\nforeach (int num in nums) {\nm = Math.Max(m, num);\n}\n// 2. \u7edf\u8ba1\u5404\u6570\u5b57\u7684\u51fa\u73b0\u6b21\u6570\n// counter[num] \u4ee3\u8868 num \u7684\u51fa\u73b0\u6b21\u6570\nint[] counter = new int[m + 1];\nforeach (int num in nums) {\ncounter[num]++;\n}\n// 3. \u6c42 counter \u7684\u524d\u7f00\u548c\uff0c\u5c06\u201c\u51fa\u73b0\u6b21\u6570\u201d\u8f6c\u6362\u4e3a\u201c\u5c3e\u7d22\u5f15\u201d\n// \u5373 counter[num]-1 \u662f num \u5728 res \u4e2d\u6700\u540e\u4e00\u6b21\u51fa\u73b0\u7684\u7d22\u5f15\nfor (int i = 0; i &lt; m; i++) {\ncounter[i + 1] += counter[i];\n}\n// 4. \u5012\u5e8f\u904d\u5386 nums \uff0c\u5c06\u5404\u5143\u7d20\u586b\u5165\u7ed3\u679c\u6570\u7ec4 res\n// \u521d\u59cb\u5316\u6570\u7ec4 res \u7528\u4e8e\u8bb0\u5f55\u7ed3\u679c\nint n = nums.Length;\nint[] res = new int[n];\nfor (int i = n - 1; i &gt;= 0; i--) {\nint num = nums[i];\nres[counter[num] - 1] = num; // \u5c06 num \u653e\u7f6e\u5230\u5bf9\u5e94\u7d22\u5f15\u5904\ncounter[num]--; // \u4ee4\u524d\u7f00\u548c\u81ea\u51cf 1 \uff0c\u5f97\u5230\u4e0b\u6b21\u653e\u7f6e num \u7684\u7d22\u5f15\n}\n// \u4f7f\u7528\u7ed3\u679c\u6570\u7ec4 res \u8986\u76d6\u539f\u6570\u7ec4 nums\nfor (int i = 0; i &lt; n; i++) {\nnums[i] = res[i];\n}\n}\n</code></pre> counting_sort.swift<pre><code>/* \u8ba1\u6570\u6392\u5e8f */\n// \u5b8c\u6574\u5b9e\u73b0\uff0c\u53ef\u6392\u5e8f\u5bf9\u8c61\uff0c\u5e76\u4e14\u662f\u7a33\u5b9a\u6392\u5e8f\nfunc countingSort(nums: inout [Int]) {\n// 1. \u7edf\u8ba1\u6570\u7ec4\u6700\u5927\u5143\u7d20 m\nlet m = nums.max()!\n// 2. \u7edf\u8ba1\u5404\u6570\u5b57\u7684\u51fa\u73b0\u6b21\u6570\n// counter[num] \u4ee3\u8868 num \u7684\u51fa\u73b0\u6b21\u6570\nvar counter = Array(repeating: 0, count: m + 1)\nfor num in nums {\ncounter[num] += 1\n}\n// 3. \u6c42 counter \u7684\u524d\u7f00\u548c\uff0c\u5c06\u201c\u51fa\u73b0\u6b21\u6570\u201d\u8f6c\u6362\u4e3a\u201c\u5c3e\u7d22\u5f15\u201d\n// \u5373 counter[num]-1 \u662f num \u5728 res \u4e2d\u6700\u540e\u4e00\u6b21\u51fa\u73b0\u7684\u7d22\u5f15\nfor i in stride(from: 0, to: m, by: 1) {\ncounter[i + 1] += counter[i]\n}\n// 4. \u5012\u5e8f\u904d\u5386 nums \uff0c\u5c06\u5404\u5143\u7d20\u586b\u5165\u7ed3\u679c\u6570\u7ec4 res\n// \u521d\u59cb\u5316\u6570\u7ec4 res \u7528\u4e8e\u8bb0\u5f55\u7ed3\u679c\nvar res = Array(repeating: 0, count: nums.count)\nfor i in stride(from: nums.count - 1, through: 0, by: -1) {\nlet num = nums[i]\nres[counter[num] - 1] = num // \u5c06 num \u653e\u7f6e\u5230\u5bf9\u5e94\u7d22\u5f15\u5904\ncounter[num] -= 1 // \u4ee4\u524d\u7f00\u548c\u81ea\u51cf 1 \uff0c\u5f97\u5230\u4e0b\u6b21\u653e\u7f6e num \u7684\u7d22\u5f15\n}\n// \u4f7f\u7528\u7ed3\u679c\u6570\u7ec4 res \u8986\u76d6\u539f\u6570\u7ec4 nums\nfor i in stride(from: 0, to: nums.count, by: 1) {\nnums[i] = res[i]\n}\n}\n</code></pre> counting_sort.zig<pre><code>[class]{}-[func]{countingSort}\n</code></pre> counting_sort.dart<pre><code>/* \u8ba1\u6570\u6392\u5e8f */\n// \u5b8c\u6574\u5b9e\u73b0\uff0c\u53ef\u6392\u5e8f\u5bf9\u8c61\uff0c\u5e76\u4e14\u662f\u7a33\u5b9a\u6392\u5e8f\nvoid countingSort(List&lt;int&gt; nums) {\n// 1. \u7edf\u8ba1\u6570\u7ec4\u6700\u5927\u5143\u7d20 m\nint m = 0;\nfor (int num in nums) {\nm = max(m, num);\n}\n// 2. \u7edf\u8ba1\u5404\u6570\u5b57\u7684\u51fa\u73b0\u6b21\u6570\n// counter[num] \u4ee3\u8868 num \u7684\u51fa\u73b0\u6b21\u6570\nList&lt;int&gt; counter = List.filled(m + 1, 0);\nfor (int num in nums) {\ncounter[num]++;\n}\n// 3. \u6c42 counter \u7684\u524d\u7f00\u548c\uff0c\u5c06\u201c\u51fa\u73b0\u6b21\u6570\u201d\u8f6c\u6362\u4e3a\u201c\u5c3e\u7d22\u5f15\u201d\n// \u5373 counter[num]-1 \u662f num \u5728 res \u4e2d\u6700\u540e\u4e00\u6b21\u51fa\u73b0\u7684\u7d22\u5f15\nfor (int i = 0; i &lt; m; i++) {\ncounter[i + 1] += counter[i];\n}\n// 4. \u5012\u5e8f\u904d\u5386 nums \uff0c\u5c06\u5404\u5143\u7d20\u586b\u5165\u7ed3\u679c\u6570\u7ec4 res\n// \u521d\u59cb\u5316\u6570\u7ec4 res \u7528\u4e8e\u8bb0\u5f55\u7ed3\u679c\nint n = nums.length;\nList&lt;int&gt; res = List.filled(n, 0);\nfor (int i = n - 1; i &gt;= 0; i--) {\nint num = nums[i];\nres[counter[num] - 1] = num; // \u5c06 num \u653e\u7f6e\u5230\u5bf9\u5e94\u7d22\u5f15\u5904\ncounter[num]--;              // \u4ee4\u524d\u7f00\u548c\u81ea\u51cf 1 \uff0c\u5f97\u5230\u4e0b\u6b21\u653e\u7f6e num \u7684\u7d22\u5f15\n}\n// \u4f7f\u7528\u7ed3\u679c\u6570\u7ec4 res \u8986\u76d6\u539f\u6570\u7ec4 nums\nnums.setAll(0, res);\n}\n</code></pre>"},{"location":"chapter_sorting/counting_sort/#1193","title":"11.9.3. \u00a0 \u7b97\u6cd5\u7279\u6027","text":"<ul> <li>\u65f6\u95f4\u590d\u6742\u5ea6 \\(O(n + m)\\) \uff1a\u6d89\u53ca\u904d\u5386 <code>nums</code> \u548c\u904d\u5386 <code>counter</code> \uff0c\u90fd\u4f7f\u7528\u7ebf\u6027\u65f6\u95f4\u3002\u4e00\u822c\u60c5\u51b5\u4e0b \\(n \\gg m\\) \uff0c\u65f6\u95f4\u590d\u6742\u5ea6\u8d8b\u4e8e \\(O(n)\\) \u3002</li> <li>\u7a7a\u95f4\u590d\u6742\u5ea6 \\(O(n + m)\\) \u3001\u975e\u539f\u5730\u6392\u5e8f \uff1a\u501f\u52a9\u4e86\u957f\u5ea6\u5206\u522b\u4e3a \\(n\\) \u548c \\(m\\) \u7684\u6570\u7ec4 <code>res</code> \u548c <code>counter</code> \u3002</li> <li>\u7a33\u5b9a\u6392\u5e8f\uff1a\u7531\u4e8e\u5411 <code>res</code> \u4e2d\u586b\u5145\u5143\u7d20\u7684\u987a\u5e8f\u662f\u201c\u4ece\u53f3\u5411\u5de6\u201d\u7684\uff0c\u56e0\u6b64\u5012\u5e8f\u904d\u5386 <code>nums</code> \u53ef\u4ee5\u907f\u514d\u6539\u53d8\u76f8\u7b49\u5143\u7d20\u4e4b\u95f4\u7684\u76f8\u5bf9\u4f4d\u7f6e\uff0c\u4ece\u800c\u5b9e\u73b0\u7a33\u5b9a\u6392\u5e8f\u3002\u5b9e\u9645\u4e0a\uff0c\u6b63\u5e8f\u904d\u5386 <code>nums</code> \u4e5f\u53ef\u4ee5\u5f97\u5230\u6b63\u786e\u7684\u6392\u5e8f\u7ed3\u679c\uff0c\u4f46\u7ed3\u679c\u662f\u975e\u7a33\u5b9a\u7684\u3002</li> </ul>"},{"location":"chapter_sorting/counting_sort/#1194","title":"11.9.4. \u00a0 \u5c40\u9650\u6027","text":"<p>\u770b\u5230\u8fd9\u91cc\uff0c\u4f60\u4e5f\u8bb8\u4f1a\u89c9\u5f97\u8ba1\u6570\u6392\u5e8f\u975e\u5e38\u5de7\u5999\uff0c\u4ec5\u901a\u8fc7\u7edf\u8ba1\u6570\u91cf\u5c31\u53ef\u4ee5\u5b9e\u73b0\u9ad8\u6548\u7684\u6392\u5e8f\u5de5\u4f5c\u3002\u7136\u800c\uff0c\u4f7f\u7528\u8ba1\u6570\u6392\u5e8f\u7684\u524d\u7f6e\u6761\u4ef6\u76f8\u5bf9\u8f83\u4e3a\u4e25\u683c\u3002</p> <p>\u8ba1\u6570\u6392\u5e8f\u53ea\u9002\u7528\u4e8e\u975e\u8d1f\u6574\u6570\u3002\u82e5\u60f3\u8981\u5c06\u5176\u7528\u4e8e\u5176\u4ed6\u7c7b\u578b\u7684\u6570\u636e\uff0c\u9700\u8981\u786e\u4fdd\u8fd9\u4e9b\u6570\u636e\u53ef\u4ee5\u88ab\u8f6c\u6362\u4e3a\u975e\u8d1f\u6574\u6570\uff0c\u5e76\u4e14\u5728\u8f6c\u6362\u8fc7\u7a0b\u4e2d\u4e0d\u80fd\u6539\u53d8\u5404\u4e2a\u5143\u7d20\u4e4b\u95f4\u7684\u76f8\u5bf9\u5927\u5c0f\u5173\u7cfb\u3002\u4f8b\u5982\uff0c\u5bf9\u4e8e\u5305\u542b\u8d1f\u6570\u7684\u6574\u6570\u6570\u7ec4\uff0c\u53ef\u4ee5\u5148\u7ed9\u6240\u6709\u6570\u5b57\u52a0\u4e0a\u4e00\u4e2a\u5e38\u6570\uff0c\u5c06\u5168\u90e8\u6570\u5b57\u8f6c\u5316\u4e3a\u6b63\u6570\uff0c\u6392\u5e8f\u5b8c\u6210\u540e\u518d\u8f6c\u6362\u56de\u53bb\u5373\u53ef\u3002</p> <p>\u8ba1\u6570\u6392\u5e8f\u9002\u7528\u4e8e\u6570\u636e\u91cf\u5927\u4f46\u6570\u636e\u8303\u56f4\u8f83\u5c0f\u7684\u60c5\u51b5\u3002\u6bd4\u5982\uff0c\u5728\u4e0a\u8ff0\u793a\u4f8b\u4e2d \\(m\\) \u4e0d\u80fd\u592a\u5927\uff0c\u5426\u5219\u4f1a\u5360\u7528\u8fc7\u591a\u7a7a\u95f4\u3002\u800c\u5f53 \\(n \\ll m\\) \u65f6\uff0c\u8ba1\u6570\u6392\u5e8f\u4f7f\u7528 \\(O(m)\\) \u65f6\u95f4\uff0c\u53ef\u80fd\u6bd4 \\(O(n \\log n)\\) \u7684\u6392\u5e8f\u7b97\u6cd5\u8fd8\u8981\u6162\u3002</p>"},{"location":"chapter_sorting/heap_sort/","title":"11.7. \u00a0 \u5806\u6392\u5e8f","text":"<p>Tip</p> <p>\u9605\u8bfb\u672c\u8282\u524d\uff0c\u8bf7\u786e\u4fdd\u5df2\u5b66\u5b8c\u300c\u5806\u300d\u7ae0\u8282\u3002</p> <p>\u300c\u5806\u6392\u5e8f Heap Sort\u300d\u662f\u4e00\u79cd\u57fa\u4e8e\u5806\u6570\u636e\u7ed3\u6784\u5b9e\u73b0\u7684\u9ad8\u6548\u6392\u5e8f\u7b97\u6cd5\u3002\u6211\u4eec\u53ef\u4ee5\u5229\u7528\u5df2\u7ecf\u5b66\u8fc7\u7684\u201c\u5efa\u5806\u64cd\u4f5c\u201d\u548c\u201c\u5143\u7d20\u51fa\u5806\u64cd\u4f5c\u201d\u5b9e\u73b0\u5806\u6392\u5e8f\uff1a</p> <ol> <li>\u8f93\u5165\u6570\u7ec4\u5e76\u5efa\u7acb\u5c0f\u9876\u5806\uff0c\u6b64\u65f6\u6700\u5c0f\u5143\u7d20\u4f4d\u4e8e\u5806\u9876\u3002</li> <li>\u4e0d\u65ad\u6267\u884c\u51fa\u5806\u64cd\u4f5c\uff0c\u4f9d\u6b21\u8bb0\u5f55\u51fa\u5806\u5143\u7d20\uff0c\u5373\u53ef\u5f97\u5230\u4ece\u5c0f\u5230\u5927\u6392\u5e8f\u7684\u5e8f\u5217\u3002</li> </ol> <p>\u4ee5\u4e0a\u65b9\u6cd5\u867d\u7136\u53ef\u884c\uff0c\u4f46\u9700\u8981\u501f\u52a9\u4e00\u4e2a\u989d\u5916\u6570\u7ec4\u6765\u4fdd\u5b58\u5f39\u51fa\u7684\u5143\u7d20\uff0c\u6bd4\u8f83\u6d6a\u8d39\u7a7a\u95f4\u3002\u5728\u5b9e\u9645\u4e2d\uff0c\u6211\u4eec\u901a\u5e38\u4f7f\u7528\u4e00\u79cd\u66f4\u52a0\u4f18\u96c5\u7684\u5b9e\u73b0\u65b9\u5f0f\u3002</p>"},{"location":"chapter_sorting/heap_sort/#1171","title":"11.7.1. \u00a0 \u7b97\u6cd5\u6d41\u7a0b","text":"<p>\u8bbe\u6570\u7ec4\u7684\u957f\u5ea6\u4e3a \\(n\\) \uff0c\u5806\u6392\u5e8f\u7684\u6d41\u7a0b\u5982\u4e0b\uff1a</p> <ol> <li>\u8f93\u5165\u6570\u7ec4\u5e76\u5efa\u7acb\u5927\u9876\u5806\u3002\u5b8c\u6210\u540e\uff0c\u6700\u5927\u5143\u7d20\u4f4d\u4e8e\u5806\u9876\u3002</li> <li>\u5c06\u5806\u9876\u5143\u7d20\uff08\u7b2c\u4e00\u4e2a\u5143\u7d20\uff09\u4e0e\u5806\u5e95\u5143\u7d20\uff08\u6700\u540e\u4e00\u4e2a\u5143\u7d20\uff09\u4ea4\u6362\u3002\u5b8c\u6210\u4ea4\u6362\u540e\uff0c\u5806\u7684\u957f\u5ea6\u51cf \\(1\\) \uff0c\u5df2\u6392\u5e8f\u5143\u7d20\u6570\u91cf\u52a0 \\(1\\) \u3002</li> <li>\u4ece\u5806\u9876\u5143\u7d20\u5f00\u59cb\uff0c\u4ece\u9876\u5230\u5e95\u6267\u884c\u5806\u5316\u64cd\u4f5c\uff08Sift Down\uff09\u3002\u5b8c\u6210\u5806\u5316\u540e\uff0c\u5806\u7684\u6027\u8d28\u5f97\u5230\u4fee\u590d\u3002</li> <li>\u5faa\u73af\u6267\u884c\u7b2c <code>2.</code> \u548c <code>3.</code> \u6b65\u3002\u5faa\u73af \\(n - 1\\) \u8f6e\u540e\uff0c\u5373\u53ef\u5b8c\u6210\u6570\u7ec4\u6392\u5e8f\u3002</li> </ol> <p>\u5b9e\u9645\u4e0a\uff0c\u5143\u7d20\u51fa\u5806\u64cd\u4f5c\u4e2d\u4e5f\u5305\u542b\u7b2c <code>2.</code> \u548c <code>3.</code> \u6b65\uff0c\u53ea\u662f\u591a\u4e86\u4e00\u4e2a\u5f39\u51fa\u5143\u7d20\u7684\u6b65\u9aa4\u3002</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt;&lt;11&gt;&lt;12&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p>\u5728\u4ee3\u7801\u5b9e\u73b0\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528\u4e86\u4e0e\u5806\u7ae0\u8282\u76f8\u540c\u7684\u4ece\u9876\u81f3\u5e95\u5806\u5316\uff08Sift Down\uff09\u7684\u51fd\u6570\u3002\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u7531\u4e8e\u5806\u7684\u957f\u5ea6\u4f1a\u968f\u7740\u63d0\u53d6\u6700\u5927\u5143\u7d20\u800c\u51cf\u5c0f\uff0c\u56e0\u6b64\u6211\u4eec\u9700\u8981\u7ed9 Sift Down \u51fd\u6570\u6dfb\u52a0\u4e00\u4e2a\u957f\u5ea6\u53c2\u6570 \\(n\\) \uff0c\u7528\u4e8e\u6307\u5b9a\u5806\u7684\u5f53\u524d\u6709\u6548\u957f\u5ea6\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart heap_sort.java<pre><code>/* \u5806\u7684\u957f\u5ea6\u4e3a n \uff0c\u4ece\u8282\u70b9 i \u5f00\u59cb\uff0c\u4ece\u9876\u81f3\u5e95\u5806\u5316 */\nvoid siftDown(int[] nums, int n, int i) {\nwhile (true) {\n// \u5224\u65ad\u8282\u70b9 i, l, r \u4e2d\u503c\u6700\u5927\u7684\u8282\u70b9\uff0c\u8bb0\u4e3a ma\nint l = 2 * i + 1;\nint r = 2 * i + 2;\nint ma = i;\nif (l &lt; n &amp;&amp; nums[l] &gt; nums[ma])\nma = l;\nif (r &lt; n &amp;&amp; nums[r] &gt; nums[ma])\nma = r;\n// \u82e5\u8282\u70b9 i \u6700\u5927\u6216\u7d22\u5f15 l, r \u8d8a\u754c\uff0c\u5219\u65e0\u9700\u7ee7\u7eed\u5806\u5316\uff0c\u8df3\u51fa\nif (ma == i)\nbreak;\n// \u4ea4\u6362\u4e24\u8282\u70b9\nint temp = nums[i];\nnums[i] = nums[ma];\nnums[ma] = temp;\n// \u5faa\u73af\u5411\u4e0b\u5806\u5316\ni = ma;\n}\n}\n/* \u5806\u6392\u5e8f */\nvoid heapSort(int[] nums) {\n// \u5efa\u5806\u64cd\u4f5c\uff1a\u5806\u5316\u9664\u53f6\u8282\u70b9\u4ee5\u5916\u7684\u5176\u4ed6\u6240\u6709\u8282\u70b9\nfor (int i = nums.length / 2 - 1; i &gt;= 0; i--) {\nsiftDown(nums, nums.length, i);\n}\n// \u4ece\u5806\u4e2d\u63d0\u53d6\u6700\u5927\u5143\u7d20\uff0c\u5faa\u73af n-1 \u8f6e\nfor (int i = nums.length - 1; i &gt; 0; i--) {\n// \u4ea4\u6362\u6839\u8282\u70b9\u4e0e\u6700\u53f3\u53f6\u8282\u70b9\uff08\u5373\u4ea4\u6362\u9996\u5143\u7d20\u4e0e\u5c3e\u5143\u7d20\uff09\nint tmp = nums[0];\nnums[0] = nums[i];\nnums[i] = tmp;\n// \u4ee5\u6839\u8282\u70b9\u4e3a\u8d77\u70b9\uff0c\u4ece\u9876\u81f3\u5e95\u8fdb\u884c\u5806\u5316\nsiftDown(nums, i, 0);\n}\n}\n</code></pre> heap_sort.cpp<pre><code>/* \u5806\u7684\u957f\u5ea6\u4e3a n \uff0c\u4ece\u8282\u70b9 i \u5f00\u59cb\uff0c\u4ece\u9876\u81f3\u5e95\u5806\u5316 */\nvoid siftDown(vector&lt;int&gt; &amp;nums, int n, int i) {\nwhile (true) {\n// \u5224\u65ad\u8282\u70b9 i, l, r \u4e2d\u503c\u6700\u5927\u7684\u8282\u70b9\uff0c\u8bb0\u4e3a ma\nint l = 2 * i + 1;\nint r = 2 * i + 2;\nint ma = i;\nif (l &lt; n &amp;&amp; nums[l] &gt; nums[ma])\nma = l;\nif (r &lt; n &amp;&amp; nums[r] &gt; nums[ma])\nma = r;\n// \u82e5\u8282\u70b9 i \u6700\u5927\u6216\u7d22\u5f15 l, r \u8d8a\u754c\uff0c\u5219\u65e0\u9700\u7ee7\u7eed\u5806\u5316\uff0c\u8df3\u51fa\nif (ma == i) {\nbreak;\n}\n// \u4ea4\u6362\u4e24\u8282\u70b9\nswap(nums[i], nums[ma]);\n// \u5faa\u73af\u5411\u4e0b\u5806\u5316\ni = ma;\n}\n}\n/* \u5806\u6392\u5e8f */\nvoid heapSort(vector&lt;int&gt; &amp;nums) {\n// \u5efa\u5806\u64cd\u4f5c\uff1a\u5806\u5316\u9664\u53f6\u8282\u70b9\u4ee5\u5916\u7684\u5176\u4ed6\u6240\u6709\u8282\u70b9\nfor (int i = nums.size() / 2 - 1; i &gt;= 0; --i) {\nsiftDown(nums, nums.size(), i);\n}\n// \u4ece\u5806\u4e2d\u63d0\u53d6\u6700\u5927\u5143\u7d20\uff0c\u5faa\u73af n-1 \u8f6e\nfor (int i = nums.size() - 1; i &gt; 0; --i) {\n// \u4ea4\u6362\u6839\u8282\u70b9\u4e0e\u6700\u53f3\u53f6\u8282\u70b9\uff08\u5373\u4ea4\u6362\u9996\u5143\u7d20\u4e0e\u5c3e\u5143\u7d20\uff09\nswap(nums[0], nums[i]);\n// \u4ee5\u6839\u8282\u70b9\u4e3a\u8d77\u70b9\uff0c\u4ece\u9876\u81f3\u5e95\u8fdb\u884c\u5806\u5316\nsiftDown(nums, i, 0);\n}\n}\n</code></pre> heap_sort.py<pre><code>def sift_down(nums: list[int], n: int, i: int):\n\"\"\"\u5806\u7684\u957f\u5ea6\u4e3a n \uff0c\u4ece\u8282\u70b9 i \u5f00\u59cb\uff0c\u4ece\u9876\u81f3\u5e95\u5806\u5316\"\"\"\nwhile True:\n# \u5224\u65ad\u8282\u70b9 i, l, r \u4e2d\u503c\u6700\u5927\u7684\u8282\u70b9\uff0c\u8bb0\u4e3a ma\nl = 2 * i + 1\nr = 2 * i + 2\nma = i\nif l &lt; n and nums[l] &gt; nums[ma]:\nma = l\nif r &lt; n and nums[r] &gt; nums[ma]:\nma = r\n# \u82e5\u8282\u70b9 i \u6700\u5927\u6216\u7d22\u5f15 l, r \u8d8a\u754c\uff0c\u5219\u65e0\u9700\u7ee7\u7eed\u5806\u5316\uff0c\u8df3\u51fa\nif ma == i:\nbreak\n# \u4ea4\u6362\u4e24\u8282\u70b9\nnums[i], nums[ma] = nums[ma], nums[i]\n# \u5faa\u73af\u5411\u4e0b\u5806\u5316\ni = ma\ndef heap_sort(nums: list[int]):\n\"\"\"\u5806\u6392\u5e8f\"\"\"\n# \u5efa\u5806\u64cd\u4f5c\uff1a\u5806\u5316\u9664\u53f6\u8282\u70b9\u4ee5\u5916\u7684\u5176\u4ed6\u6240\u6709\u8282\u70b9\nfor i in range(len(nums) // 2 - 1, -1, -1):\nsift_down(nums, len(nums), i)\n# \u4ece\u5806\u4e2d\u63d0\u53d6\u6700\u5927\u5143\u7d20\uff0c\u5faa\u73af n-1 \u8f6e\nfor i in range(len(nums) - 1, 0, -1):\n# \u4ea4\u6362\u6839\u8282\u70b9\u4e0e\u6700\u53f3\u53f6\u8282\u70b9\uff08\u5373\u4ea4\u6362\u9996\u5143\u7d20\u4e0e\u5c3e\u5143\u7d20\uff09\nnums[0], nums[i] = nums[i], nums[0]\n# \u4ee5\u6839\u8282\u70b9\u4e3a\u8d77\u70b9\uff0c\u4ece\u9876\u81f3\u5e95\u8fdb\u884c\u5806\u5316\nsift_down(nums, i, 0)\n</code></pre> heap_sort.go<pre><code>/* \u5806\u7684\u957f\u5ea6\u4e3a n \uff0c\u4ece\u8282\u70b9 i \u5f00\u59cb\uff0c\u4ece\u9876\u81f3\u5e95\u5806\u5316 */\nfunc siftDown(nums *[]int, n, i int) {\nfor true {\n// \u5224\u65ad\u8282\u70b9 i, l, r \u4e2d\u503c\u6700\u5927\u7684\u8282\u70b9\uff0c\u8bb0\u4e3a ma\nl := 2*i + 1\nr := 2*i + 2\nma := i\nif l &lt; n &amp;&amp; (*nums)[l] &gt; (*nums)[ma] {\nma = l\n}\nif r &lt; n &amp;&amp; (*nums)[r] &gt; (*nums)[ma] {\nma = r\n}\n// \u82e5\u8282\u70b9 i \u6700\u5927\u6216\u7d22\u5f15 l, r \u8d8a\u754c\uff0c\u5219\u65e0\u9700\u7ee7\u7eed\u5806\u5316\uff0c\u8df3\u51fa\nif ma == i {\nbreak\n}\n// \u4ea4\u6362\u4e24\u8282\u70b9\n(*nums)[i], (*nums)[ma] = (*nums)[ma], (*nums)[i]\n// \u5faa\u73af\u5411\u4e0b\u5806\u5316\ni = ma\n}\n}\n/* \u5806\u6392\u5e8f */\nfunc heapSort(nums *[]int) {\n// \u5efa\u5806\u64cd\u4f5c\uff1a\u5806\u5316\u9664\u53f6\u8282\u70b9\u4ee5\u5916\u7684\u5176\u4ed6\u6240\u6709\u8282\u70b9\nfor i := len(*nums)/2 - 1; i &gt;= 0; i-- {\nsiftDown(nums, len(*nums), i)\n}\n// \u4ece\u5806\u4e2d\u63d0\u53d6\u6700\u5927\u5143\u7d20\uff0c\u5faa\u73af n-1 \u8f6e\nfor i := len(*nums) - 1; i &gt; 0; i-- {\n// \u4ea4\u6362\u6839\u8282\u70b9\u4e0e\u6700\u53f3\u53f6\u8282\u70b9\uff08\u5373\u4ea4\u6362\u9996\u5143\u7d20\u4e0e\u5c3e\u5143\u7d20\uff09\n(*nums)[0], (*nums)[i] = (*nums)[i], (*nums)[0]\n// \u4ee5\u6839\u8282\u70b9\u4e3a\u8d77\u70b9\uff0c\u4ece\u9876\u81f3\u5e95\u8fdb\u884c\u5806\u5316\nsiftDown(nums, i, 0)\n}\n}\n</code></pre> heap_sort.js<pre><code>/* \u5806\u7684\u957f\u5ea6\u4e3a n \uff0c\u4ece\u8282\u70b9 i \u5f00\u59cb\uff0c\u4ece\u9876\u81f3\u5e95\u5806\u5316 */\nfunction siftDown(nums, n, i) {\nwhile (true) {\n// \u5224\u65ad\u8282\u70b9 i, l, r \u4e2d\u503c\u6700\u5927\u7684\u8282\u70b9\uff0c\u8bb0\u4e3a ma\nlet l = 2 * i + 1;\nlet r = 2 * i + 2;\nlet ma = i;\nif (l &lt; n &amp;&amp; nums[l] &gt; nums[ma]) {\nma = l;\n}\nif (r &lt; n &amp;&amp; nums[r] &gt; nums[ma]) {\nma = r;\n}\n// \u82e5\u8282\u70b9 i \u6700\u5927\u6216\u7d22\u5f15 l, r \u8d8a\u754c\uff0c\u5219\u65e0\u9700\u7ee7\u7eed\u5806\u5316\uff0c\u8df3\u51fa\nif (ma === i) {\nbreak;\n}\n// \u4ea4\u6362\u4e24\u8282\u70b9\n[nums[i], nums[ma]] = [nums[ma], nums[i]];\n// \u5faa\u73af\u5411\u4e0b\u5806\u5316\ni = ma;\n}\n}\n/* \u5806\u6392\u5e8f */\nfunction heapSort(nums) {\n// \u5efa\u5806\u64cd\u4f5c\uff1a\u5806\u5316\u9664\u53f6\u8282\u70b9\u4ee5\u5916\u7684\u5176\u4ed6\u6240\u6709\u8282\u70b9\nfor (let i = Math.floor(nums.length / 2) - 1; i &gt;= 0; i--) {\nsiftDown(nums, nums.length, i);\n}\n// \u4ece\u5806\u4e2d\u63d0\u53d6\u6700\u5927\u5143\u7d20\uff0c\u5faa\u73af n-1 \u8f6e\nfor (let i = nums.length - 1; i &gt; 0; i--) {\n// \u4ea4\u6362\u6839\u8282\u70b9\u4e0e\u6700\u53f3\u53f6\u8282\u70b9\uff08\u5373\u4ea4\u6362\u9996\u5143\u7d20\u4e0e\u5c3e\u5143\u7d20\uff09\n[nums[0], nums[i]] = [nums[i], nums[0]];\n// \u4ee5\u6839\u8282\u70b9\u4e3a\u8d77\u70b9\uff0c\u4ece\u9876\u81f3\u5e95\u8fdb\u884c\u5806\u5316\nsiftDown(nums, i, 0);\n}\n}\n</code></pre> heap_sort.ts<pre><code>/* \u5806\u7684\u957f\u5ea6\u4e3a n \uff0c\u4ece\u8282\u70b9 i \u5f00\u59cb\uff0c\u4ece\u9876\u81f3\u5e95\u5806\u5316 */\nfunction siftDown(nums: number[], n: number, i: number): void {\nwhile (true) {\n// \u5224\u65ad\u8282\u70b9 i, l, r \u4e2d\u503c\u6700\u5927\u7684\u8282\u70b9\uff0c\u8bb0\u4e3a ma\nlet l = 2 * i + 1;\nlet r = 2 * i + 2;\nlet ma = i;\nif (l &lt; n &amp;&amp; nums[l] &gt; nums[ma]) {\nma = l;\n}\nif (r &lt; n &amp;&amp; nums[r] &gt; nums[ma]) {\nma = r;\n}\n// \u82e5\u8282\u70b9 i \u6700\u5927\u6216\u7d22\u5f15 l, r \u8d8a\u754c\uff0c\u5219\u65e0\u9700\u7ee7\u7eed\u5806\u5316\uff0c\u8df3\u51fa\nif (ma === i) {\nbreak;\n}\n// \u4ea4\u6362\u4e24\u8282\u70b9\n[nums[i], nums[ma]] = [nums[ma], nums[i]];\n// \u5faa\u73af\u5411\u4e0b\u5806\u5316\ni = ma;\n}\n}\n/* \u5806\u6392\u5e8f */\nfunction heapSort(nums: number[]): void {\n// \u5efa\u5806\u64cd\u4f5c\uff1a\u5806\u5316\u9664\u53f6\u8282\u70b9\u4ee5\u5916\u7684\u5176\u4ed6\u6240\u6709\u8282\u70b9\nfor (let i = Math.floor(nums.length / 2) - 1; i &gt;= 0; i--) {\nsiftDown(nums, nums.length, i);\n}\n// \u4ece\u5806\u4e2d\u63d0\u53d6\u6700\u5927\u5143\u7d20\uff0c\u5faa\u73af n-1 \u8f6e\nfor (let i = nums.length - 1; i &gt; 0; i--) {\n// \u4ea4\u6362\u6839\u8282\u70b9\u4e0e\u6700\u53f3\u53f6\u8282\u70b9\uff08\u5373\u4ea4\u6362\u9996\u5143\u7d20\u4e0e\u5c3e\u5143\u7d20\uff09\n[nums[0], nums[i]] = [nums[i], nums[0]];\n// \u4ee5\u6839\u8282\u70b9\u4e3a\u8d77\u70b9\uff0c\u4ece\u9876\u81f3\u5e95\u8fdb\u884c\u5806\u5316\nsiftDown(nums, i, 0);\n}\n}\n</code></pre> heap_sort.c<pre><code>/* \u5806\u7684\u957f\u5ea6\u4e3a n \uff0c\u4ece\u8282\u70b9 i \u5f00\u59cb\uff0c\u4ece\u9876\u81f3\u5e95\u5806\u5316 */\nvoid siftDown(int nums[], int n, int i) {\nwhile (1) {\n// \u5224\u65ad\u8282\u70b9 i, l, r \u4e2d\u503c\u6700\u5927\u7684\u8282\u70b9\uff0c\u8bb0\u4e3a ma\nint l = 2 * i + 1;\nint r = 2 * i + 2;\nint ma = i;\nif (l &lt; n &amp;&amp; nums[l] &gt; nums[ma])\nma = l;\nif (r &lt; n &amp;&amp; nums[r] &gt; nums[ma])\nma = r;\n// \u82e5\u8282\u70b9 i \u6700\u5927\u6216\u7d22\u5f15 l, r \u8d8a\u754c\uff0c\u5219\u65e0\u9700\u7ee7\u7eed\u5806\u5316\uff0c\u8df3\u51fa\nif (ma == i) {\nbreak;\n}\n// \u4ea4\u6362\u4e24\u8282\u70b9\nint temp = nums[i];\nnums[i] = nums[ma];\nnums[ma] = temp;\n// \u5faa\u73af\u5411\u4e0b\u5806\u5316\ni = ma;\n}\n}\n/* \u5806\u6392\u5e8f */\nvoid heapSort(int nums[], int n) {\n// \u5efa\u5806\u64cd\u4f5c\uff1a\u5806\u5316\u9664\u53f6\u8282\u70b9\u4ee5\u5916\u7684\u5176\u4ed6\u6240\u6709\u8282\u70b9\nfor (int i = n / 2 - 1; i &gt;= 0; --i) {\nsiftDown(nums, n, i);\n}\n// \u4ece\u5806\u4e2d\u63d0\u53d6\u6700\u5927\u5143\u7d20\uff0c\u5faa\u73af n-1 \u8f6e\nfor (int i = n - 1; i &gt; 0; --i) {\n// \u4ea4\u6362\u6839\u8282\u70b9\u4e0e\u6700\u53f3\u53f6\u8282\u70b9\uff08\u5373\u4ea4\u6362\u9996\u5143\u7d20\u4e0e\u5c3e\u5143\u7d20\uff09\nint tmp = nums[0];\nnums[0] = nums[i];\nnums[i] = tmp;\n// \u4ee5\u6839\u8282\u70b9\u4e3a\u8d77\u70b9\uff0c\u4ece\u9876\u81f3\u5e95\u8fdb\u884c\u5806\u5316\nsiftDown(nums, i, 0);\n}\n}\n</code></pre> heap_sort.cs<pre><code>/* \u5806\u7684\u957f\u5ea6\u4e3a n \uff0c\u4ece\u8282\u70b9 i \u5f00\u59cb\uff0c\u4ece\u9876\u81f3\u5e95\u5806\u5316 */\nvoid siftDown(int[] nums, int n, int i) {\nwhile (true) {\n// \u5224\u65ad\u8282\u70b9 i, l, r \u4e2d\u503c\u6700\u5927\u7684\u8282\u70b9\uff0c\u8bb0\u4e3a ma\nint l = 2 * i + 1;\nint r = 2 * i + 2;\nint ma = i;\nif (l &lt; n &amp;&amp; nums[l] &gt; nums[ma])\nma = l;\nif (r &lt; n &amp;&amp; nums[r] &gt; nums[ma])\nma = r;\n// \u82e5\u8282\u70b9 i \u6700\u5927\u6216\u7d22\u5f15 l, r \u8d8a\u754c\uff0c\u5219\u65e0\u9700\u7ee7\u7eed\u5806\u5316\uff0c\u8df3\u51fa\nif (ma == i)\nbreak;\n// \u4ea4\u6362\u4e24\u8282\u70b9\n(nums[ma], nums[i]) = (nums[i], nums[ma]);\n// \u5faa\u73af\u5411\u4e0b\u5806\u5316\ni = ma;\n}\n}\n/* \u5806\u6392\u5e8f */\nvoid heapSort(int[] nums) {\n// \u5efa\u5806\u64cd\u4f5c\uff1a\u5806\u5316\u9664\u53f6\u8282\u70b9\u4ee5\u5916\u7684\u5176\u4ed6\u6240\u6709\u8282\u70b9\nfor (int i = nums.Length / 2 - 1; i &gt;= 0; i--) {\nsiftDown(nums, nums.Length, i);\n}\n// \u4ece\u5806\u4e2d\u63d0\u53d6\u6700\u5927\u5143\u7d20\uff0c\u5faa\u73af n-1 \u8f6e\nfor (int i = nums.Length - 1; i &gt; 0; i--) {\n// \u4ea4\u6362\u6839\u8282\u70b9\u4e0e\u6700\u53f3\u53f6\u8282\u70b9\uff08\u5373\u4ea4\u6362\u9996\u5143\u7d20\u4e0e\u5c3e\u5143\u7d20\uff09\n(nums[i], nums[0]) = (nums[0], nums[i]);\n// \u4ee5\u6839\u8282\u70b9\u4e3a\u8d77\u70b9\uff0c\u4ece\u9876\u81f3\u5e95\u8fdb\u884c\u5806\u5316\nsiftDown(nums, i, 0);\n}\n}\n</code></pre> heap_sort.swift<pre><code>/* \u5806\u7684\u957f\u5ea6\u4e3a n \uff0c\u4ece\u8282\u70b9 i \u5f00\u59cb\uff0c\u4ece\u9876\u81f3\u5e95\u5806\u5316 */\nfunc siftDown(nums: inout [Int], n: Int, i: Int) {\nvar i = i\nwhile true {\n// \u5224\u65ad\u8282\u70b9 i, l, r \u4e2d\u503c\u6700\u5927\u7684\u8282\u70b9\uff0c\u8bb0\u4e3a ma\nlet l = 2 * i + 1\nlet r = 2 * i + 2\nvar ma = i\nif l &lt; n, nums[l] &gt; nums[ma] {\nma = l\n}\nif r &lt; n, nums[r] &gt; nums[ma] {\nma = r\n}\n// \u82e5\u8282\u70b9 i \u6700\u5927\u6216\u7d22\u5f15 l, r \u8d8a\u754c\uff0c\u5219\u65e0\u9700\u7ee7\u7eed\u5806\u5316\uff0c\u8df3\u51fa\nif ma == i {\nbreak\n}\n// \u4ea4\u6362\u4e24\u8282\u70b9\nnums.swapAt(i, ma)\n// \u5faa\u73af\u5411\u4e0b\u5806\u5316\ni = ma\n}\n}\n/* \u5806\u6392\u5e8f */\nfunc heapSort(nums: inout [Int]) {\n// \u5efa\u5806\u64cd\u4f5c\uff1a\u5806\u5316\u9664\u53f6\u8282\u70b9\u4ee5\u5916\u7684\u5176\u4ed6\u6240\u6709\u8282\u70b9\nfor i in stride(from: nums.count / 2 - 1, through: 0, by: -1) {\nsiftDown(nums: &amp;nums, n: nums.count, i: i)\n}\n// \u4ece\u5806\u4e2d\u63d0\u53d6\u6700\u5927\u5143\u7d20\uff0c\u5faa\u73af n-1 \u8f6e\nfor i in stride(from: nums.count - 1, to: 0, by: -1) {\n// \u4ea4\u6362\u6839\u8282\u70b9\u4e0e\u6700\u53f3\u53f6\u8282\u70b9\uff08\u5373\u4ea4\u6362\u9996\u5143\u7d20\u4e0e\u5c3e\u5143\u7d20\uff09\nnums.swapAt(0, i)\n// \u4ee5\u6839\u8282\u70b9\u4e3a\u8d77\u70b9\uff0c\u4ece\u9876\u81f3\u5e95\u8fdb\u884c\u5806\u5316\nsiftDown(nums: &amp;nums, n: i, i: 0)\n}\n}\n</code></pre> heap_sort.zig<pre><code>[class]{}-[func]{siftDown}\n[class]{}-[func]{heapSort}\n</code></pre> heap_sort.dart<pre><code>/* \u5806\u7684\u957f\u5ea6\u4e3a n \uff0c\u4ece\u8282\u70b9 i \u5f00\u59cb\uff0c\u4ece\u9876\u81f3\u5e95\u5806\u5316 */\nvoid siftDown(List&lt;int&gt; nums, int n, int i) {\nwhile (true) {\n// \u5224\u65ad\u8282\u70b9 i, l, r \u4e2d\u503c\u6700\u5927\u7684\u8282\u70b9\uff0c\u8bb0\u4e3a ma\nint l = 2 * i + 1;\nint r = 2 * i + 2;\nint ma = i;\nif (l &lt; n &amp;&amp; nums[l] &gt; nums[ma]) ma = l;\nif (r &lt; n &amp;&amp; nums[r] &gt; nums[ma]) ma = r;\n// \u82e5\u8282\u70b9 i \u6700\u5927\u6216\u7d22\u5f15 l, r \u8d8a\u754c\uff0c\u5219\u65e0\u9700\u7ee7\u7eed\u5806\u5316\uff0c\u8df3\u51fa\nif (ma == i) break;\n// \u4ea4\u6362\u4e24\u8282\u70b9\nint temp = nums[i];\nnums[i] = nums[ma];\nnums[ma] = temp;\n// \u5faa\u73af\u5411\u4e0b\u5806\u5316\ni = ma;\n}\n}\n/* \u5806\u6392\u5e8f */\nvoid heapSort(List&lt;int&gt; nums) {\n// \u5efa\u5806\u64cd\u4f5c\uff1a\u5806\u5316\u9664\u53f6\u8282\u70b9\u4ee5\u5916\u7684\u5176\u4ed6\u6240\u6709\u8282\u70b9\nfor (int i = nums.length ~/ 2 - 1; i &gt;= 0; i--) {\nsiftDown(nums, nums.length, i);\n}\n// \u4ece\u5806\u4e2d\u63d0\u53d6\u6700\u5927\u5143\u7d20\uff0c\u5faa\u73af n-1 \u8f6e\nfor (int i = nums.length - 1; i &gt; 0; i--) {\n// \u4ea4\u6362\u6839\u8282\u70b9\u4e0e\u6700\u53f3\u53f6\u8282\u70b9\uff08\u5373\u4ea4\u6362\u9996\u5143\u7d20\u4e0e\u5c3e\u5143\u7d20\uff09\nint tmp = nums[0];\nnums[0] = nums[i];\nnums[i] = tmp;\n// \u4ee5\u6839\u8282\u70b9\u4e3a\u8d77\u70b9\uff0c\u4ece\u9876\u81f3\u5e95\u8fdb\u884c\u5806\u5316\nsiftDown(nums, i, 0);\n}\n}\n</code></pre>"},{"location":"chapter_sorting/heap_sort/#1172","title":"11.7.2. \u00a0 \u7b97\u6cd5\u7279\u6027","text":"<ul> <li>\u65f6\u95f4\u590d\u6742\u5ea6 \\(O(n \\log n)\\) \u3001\u975e\u81ea\u9002\u5e94\u6392\u5e8f \uff1a\u5efa\u5806\u64cd\u4f5c\u4f7f\u7528 \\(O(n)\\) \u65f6\u95f4\u3002\u4ece\u5806\u4e2d\u63d0\u53d6\u6700\u5927\u5143\u7d20\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(\\log n)\\) \uff0c\u5171\u5faa\u73af \\(n - 1\\) \u8f6e\u3002</li> <li>\u7a7a\u95f4\u590d\u6742\u5ea6 \\(O(1)\\) \u3001\u539f\u5730\u6392\u5e8f \uff1a\u51e0\u4e2a\u6307\u9488\u53d8\u91cf\u4f7f\u7528 \\(O(1)\\) \u7a7a\u95f4\u3002\u5143\u7d20\u4ea4\u6362\u548c\u5806\u5316\u64cd\u4f5c\u90fd\u662f\u5728\u539f\u6570\u7ec4\u4e0a\u8fdb\u884c\u7684\u3002</li> <li>\u975e\u7a33\u5b9a\u6392\u5e8f\uff1a\u5728\u4ea4\u6362\u5806\u9876\u5143\u7d20\u548c\u5806\u5e95\u5143\u7d20\u65f6\uff0c\u76f8\u7b49\u5143\u7d20\u7684\u76f8\u5bf9\u4f4d\u7f6e\u53ef\u80fd\u53d1\u751f\u53d8\u5316\u3002</li> </ul>"},{"location":"chapter_sorting/insertion_sort/","title":"11.4. \u00a0 \u63d2\u5165\u6392\u5e8f","text":"<p>\u300c\u63d2\u5165\u6392\u5e8f Insertion Sort\u300d\u662f\u4e00\u79cd\u7b80\u5355\u7684\u6392\u5e8f\u7b97\u6cd5\uff0c\u5b83\u7684\u5de5\u4f5c\u539f\u7406\u4e0e\u624b\u52a8\u6574\u7406\u4e00\u526f\u724c\u7684\u8fc7\u7a0b\u975e\u5e38\u76f8\u4f3c\u3002</p> <p>\u5177\u4f53\u6765\u8bf4\uff0c\u6211\u4eec\u5728\u672a\u6392\u5e8f\u533a\u95f4\u9009\u62e9\u4e00\u4e2a\u57fa\u51c6\u5143\u7d20\uff0c\u5c06\u8be5\u5143\u7d20\u4e0e\u5176\u5de6\u4fa7\u5df2\u6392\u5e8f\u533a\u95f4\u7684\u5143\u7d20\u9010\u4e00\u6bd4\u8f83\u5927\u5c0f\uff0c\u5e76\u5c06\u8be5\u5143\u7d20\u63d2\u5165\u5230\u6b63\u786e\u7684\u4f4d\u7f6e\u3002</p> <p>\u56de\u5fc6\u6570\u7ec4\u7684\u5143\u7d20\u63d2\u5165\u64cd\u4f5c\uff0c\u8bbe\u57fa\u51c6\u5143\u7d20\u4e3a <code>base</code> \uff0c\u6211\u4eec\u9700\u8981\u5c06\u4ece\u76ee\u6807\u7d22\u5f15\u5230 <code>base</code> \u4e4b\u95f4\u7684\u6240\u6709\u5143\u7d20\u5411\u53f3\u79fb\u52a8\u4e00\u4f4d\uff0c\u7136\u540e\u518d\u5c06 <code>base</code> \u8d4b\u503c\u7ed9\u76ee\u6807\u7d22\u5f15\u3002</p> <p></p> <p> Fig. \u5355\u6b21\u63d2\u5165\u64cd\u4f5c </p>"},{"location":"chapter_sorting/insertion_sort/#1141","title":"11.4.1. \u00a0 \u7b97\u6cd5\u6d41\u7a0b","text":"<p>\u63d2\u5165\u6392\u5e8f\u7684\u6574\u4f53\u6d41\u7a0b\u5982\u4e0b\uff1a</p> <ol> <li>\u521d\u59cb\u72b6\u6001\u4e0b\uff0c\u6570\u7ec4\u7684\u7b2c 1 \u4e2a\u5143\u7d20\u5df2\u5b8c\u6210\u6392\u5e8f\u3002</li> <li>\u9009\u53d6\u6570\u7ec4\u7684\u7b2c 2 \u4e2a\u5143\u7d20\u4f5c\u4e3a <code>base</code> \uff0c\u5c06\u5176\u63d2\u5165\u5230\u6b63\u786e\u4f4d\u7f6e\u540e\uff0c\u6570\u7ec4\u7684\u524d 2 \u4e2a\u5143\u7d20\u5df2\u6392\u5e8f\u3002</li> <li>\u9009\u53d6\u7b2c 3 \u4e2a\u5143\u7d20\u4f5c\u4e3a <code>base</code> \uff0c\u5c06\u5176\u63d2\u5165\u5230\u6b63\u786e\u4f4d\u7f6e\u540e\uff0c\u6570\u7ec4\u7684\u524d 3 \u4e2a\u5143\u7d20\u5df2\u6392\u5e8f\u3002</li> <li>\u4ee5\u6b64\u7c7b\u63a8\uff0c\u5728\u6700\u540e\u4e00\u8f6e\u4e2d\uff0c\u9009\u53d6\u6700\u540e\u4e00\u4e2a\u5143\u7d20\u4f5c\u4e3a <code>base</code> \uff0c\u5c06\u5176\u63d2\u5165\u5230\u6b63\u786e\u4f4d\u7f6e\u540e\uff0c\u6240\u6709\u5143\u7d20\u5747\u5df2\u6392\u5e8f\u3002</li> </ol> <p></p> <p> Fig. \u63d2\u5165\u6392\u5e8f\u6d41\u7a0b </p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart insertion_sort.java<pre><code>/* \u63d2\u5165\u6392\u5e8f */\nvoid insertionSort(int[] nums) {\n// \u5916\u5faa\u73af\uff1a\u5df2\u6392\u5e8f\u5143\u7d20\u6570\u91cf\u4e3a 1, 2, ..., n\nfor (int i = 1; i &lt; nums.length; i++) {\nint base = nums[i], j = i - 1;\n// \u5185\u5faa\u73af\uff1a\u5c06 base \u63d2\u5165\u5230\u5df2\u6392\u5e8f\u90e8\u5206\u7684\u6b63\u786e\u4f4d\u7f6e\nwhile (j &gt;= 0 &amp;&amp; nums[j] &gt; base) {\nnums[j + 1] = nums[j]; // \u5c06 nums[j] \u5411\u53f3\u79fb\u52a8\u4e00\u4f4d\nj--;\n}\nnums[j + 1] = base;        // \u5c06 base \u8d4b\u503c\u5230\u6b63\u786e\u4f4d\u7f6e\n}\n}\n</code></pre> insertion_sort.cpp<pre><code>/* \u63d2\u5165\u6392\u5e8f */\nvoid insertionSort(vector&lt;int&gt; &amp;nums) {\n// \u5916\u5faa\u73af\uff1a\u5df2\u6392\u5e8f\u5143\u7d20\u6570\u91cf\u4e3a 1, 2, ..., n\nfor (int i = 1; i &lt; nums.size(); i++) {\nint base = nums[i], j = i - 1;\n// \u5185\u5faa\u73af\uff1a\u5c06 base \u63d2\u5165\u5230\u5df2\u6392\u5e8f\u90e8\u5206\u7684\u6b63\u786e\u4f4d\u7f6e\nwhile (j &gt;= 0 &amp;&amp; nums[j] &gt; base) {\nnums[j + 1] = nums[j]; // \u5c06 nums[j] \u5411\u53f3\u79fb\u52a8\u4e00\u4f4d\nj--;\n}\nnums[j + 1] = base; // \u5c06 base \u8d4b\u503c\u5230\u6b63\u786e\u4f4d\u7f6e\n}\n}\n</code></pre> insertion_sort.py<pre><code>def insertion_sort(nums: list[int]) -&gt; None:\n\"\"\"\u63d2\u5165\u6392\u5e8f\"\"\"\n# \u5916\u5faa\u73af\uff1a\u5df2\u6392\u5e8f\u533a\u95f4\u4e3a [0, i-1]\nfor i in range(1, len(nums)):\nbase = nums[i]\nj = i - 1\n# \u5185\u5faa\u73af\uff1a\u5c06 base \u63d2\u5165\u5230\u5df2\u6392\u5e8f\u533a\u95f4 [0, i-1] \u4e2d\u7684\u6b63\u786e\u4f4d\u7f6e\nwhile j &gt;= 0 and nums[j] &gt; base:\nnums[j + 1] = nums[j]  # \u5c06 nums[j] \u5411\u53f3\u79fb\u52a8\u4e00\u4f4d\nj -= 1\nnums[j + 1] = base  # \u5c06 base \u8d4b\u503c\u5230\u6b63\u786e\u4f4d\u7f6e\n</code></pre> insertion_sort.go<pre><code>/* \u63d2\u5165\u6392\u5e8f */\nfunc insertionSort(nums []int) {\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [0, i]\nfor i := 1; i &lt; len(nums); i++ {\nbase := nums[i]\nj := i - 1\n// \u5185\u5faa\u73af\uff1a\u5c06 base \u63d2\u5165\u5230\u5df2\u6392\u5e8f\u90e8\u5206\u7684\u6b63\u786e\u4f4d\u7f6e\nfor j &gt;= 0 &amp;&amp; nums[j] &gt; base {\nnums[j+1] = nums[j] // \u5c06 nums[j] \u5411\u53f3\u79fb\u52a8\u4e00\u4f4d\nj--\n}\nnums[j+1] = base // \u5c06 base \u8d4b\u503c\u5230\u6b63\u786e\u4f4d\u7f6e\n}\n}\n</code></pre> insertion_sort.js<pre><code>/* \u63d2\u5165\u6392\u5e8f */\nfunction insertionSort(nums) {\n// \u5916\u5faa\u73af\uff1a\u5df2\u6392\u5e8f\u5143\u7d20\u6570\u91cf\u4e3a 1, 2, ..., n\nfor (let i = 1; i &lt; nums.length; i++) {\nlet base = nums[i],\nj = i - 1;\n// \u5185\u5faa\u73af\uff1a\u5c06 base \u63d2\u5165\u5230\u5df2\u6392\u5e8f\u90e8\u5206\u7684\u6b63\u786e\u4f4d\u7f6e\nwhile (j &gt;= 0 &amp;&amp; nums[j] &gt; base) {\nnums[j + 1] = nums[j]; // \u5c06 nums[j] \u5411\u53f3\u79fb\u52a8\u4e00\u4f4d\nj--;\n}\nnums[j + 1] = base; // \u5c06 base \u8d4b\u503c\u5230\u6b63\u786e\u4f4d\u7f6e\n}\n}\n</code></pre> insertion_sort.ts<pre><code>/* \u63d2\u5165\u6392\u5e8f */\nfunction insertionSort(nums: number[]): void {\n// \u5916\u5faa\u73af\uff1a\u5df2\u6392\u5e8f\u5143\u7d20\u6570\u91cf\u4e3a 1, 2, ..., n\nfor (let i = 1; i &lt; nums.length; i++) {\nconst base = nums[i];\nlet j = i - 1;\n// \u5185\u5faa\u73af\uff1a\u5c06 base \u63d2\u5165\u5230\u5df2\u6392\u5e8f\u90e8\u5206\u7684\u6b63\u786e\u4f4d\u7f6e\nwhile (j &gt;= 0 &amp;&amp; nums[j] &gt; base) {\nnums[j + 1] = nums[j]; // \u5c06 nums[j] \u5411\u53f3\u79fb\u52a8\u4e00\u4f4d\nj--;\n}\nnums[j + 1] = base; // \u5c06 base \u8d4b\u503c\u5230\u6b63\u786e\u4f4d\u7f6e\n}\n}\n</code></pre> insertion_sort.c<pre><code>/* \u63d2\u5165\u6392\u5e8f */\nvoid insertionSort(int nums[], int size) {\n// \u5916\u5faa\u73af\uff1a\u5df2\u6392\u5e8f\u5143\u7d20\u6570\u91cf\u4e3a 1, 2, ..., n\nfor (int i = 1; i &lt; size; i++) {\nint base = nums[i], j = i - 1;\n// \u5185\u5faa\u73af\uff1a\u5c06 base \u63d2\u5165\u5230\u5df2\u6392\u5e8f\u90e8\u5206\u7684\u6b63\u786e\u4f4d\u7f6e\nwhile (j &gt;= 0 &amp;&amp; nums[j] &gt; base) {\n// \u5c06 nums[j] \u5411\u53f3\u79fb\u52a8\u4e00\u4f4d\nnums[j + 1] = nums[j];\nj--;\n}\n// \u5c06 base \u8d4b\u503c\u5230\u6b63\u786e\u4f4d\u7f6e\nnums[j + 1] = base;\n}\n}\n</code></pre> insertion_sort.cs<pre><code>/* \u63d2\u5165\u6392\u5e8f */\nvoid insertionSort(int[] nums) {\n// \u5916\u5faa\u73af\uff1a\u5df2\u6392\u5e8f\u5143\u7d20\u6570\u91cf\u4e3a 1, 2, ..., n\nfor (int i = 1; i &lt; nums.Length; i++) {\nint bas = nums[i], j = i - 1;\n// \u5185\u5faa\u73af\uff1a\u5c06 base \u63d2\u5165\u5230\u5df2\u6392\u5e8f\u90e8\u5206\u7684\u6b63\u786e\u4f4d\u7f6e\nwhile (j &gt;= 0 &amp;&amp; nums[j] &gt; bas) {\nnums[j + 1] = nums[j]; // \u5c06 nums[j] \u5411\u53f3\u79fb\u52a8\u4e00\u4f4d\nj--;\n}\nnums[j + 1] = bas;         // \u5c06 base \u8d4b\u503c\u5230\u6b63\u786e\u4f4d\u7f6e\n}\n}\n</code></pre> insertion_sort.swift<pre><code>/* \u63d2\u5165\u6392\u5e8f */\nfunc insertionSort(nums: inout [Int]) {\n// \u5916\u5faa\u73af\uff1a\u5df2\u6392\u5e8f\u5143\u7d20\u6570\u91cf\u4e3a 1, 2, ..., n\nfor i in stride(from: 1, to: nums.count, by: 1) {\nlet base = nums[i]\nvar j = i - 1\n// \u5185\u5faa\u73af\uff1a\u5c06 base \u63d2\u5165\u5230\u5df2\u6392\u5e8f\u90e8\u5206\u7684\u6b63\u786e\u4f4d\u7f6e\nwhile j &gt;= 0, nums[j] &gt; base {\nnums[j + 1] = nums[j] // \u5c06 nums[j] \u5411\u53f3\u79fb\u52a8\u4e00\u4f4d\nj -= 1\n}\nnums[j + 1] = base // \u5c06 base \u8d4b\u503c\u5230\u6b63\u786e\u4f4d\u7f6e\n}\n}\n</code></pre> insertion_sort.zig<pre><code>// \u63d2\u5165\u6392\u5e8f\nfn insertionSort(nums: []i32) void {\n// \u5916\u5faa\u73af\uff1a\u5df2\u6392\u5e8f\u5143\u7d20\u6570\u91cf\u4e3a 1, 2, ..., n\nvar i: usize = 1;\nwhile (i &lt; nums.len) : (i += 1) {\nvar base = nums[i];\nvar j: usize = i;\n// \u5185\u5faa\u73af\uff1a\u5c06 base \u63d2\u5165\u5230\u5df2\u6392\u5e8f\u90e8\u5206\u7684\u6b63\u786e\u4f4d\u7f6e\nwhile (j &gt;= 1 and nums[j - 1] &gt; base) : (j -= 1) {\nnums[j] = nums[j - 1];  // \u5c06 nums[j] \u5411\u53f3\u79fb\u52a8\u4e00\u4f4d\n}\nnums[j] = base;             // \u5c06 base \u8d4b\u503c\u5230\u6b63\u786e\u4f4d\u7f6e\n}\n}\n</code></pre> insertion_sort.dart<pre><code>/* \u63d2\u5165\u6392\u5e8f */\nvoid insertionSort(List&lt;int&gt; nums) {\n// \u5916\u5faa\u73af\uff1a\u5df2\u6392\u5e8f\u5143\u7d20\u6570\u91cf\u4e3a 1, 2, ..., n\nfor (int i = 1; i &lt; nums.length; i++) {\nint base = nums[i], j = i - 1;\n// \u5185\u5faa\u73af\uff1a\u5c06 base \u63d2\u5165\u5230\u5df2\u6392\u5e8f\u90e8\u5206\u7684\u6b63\u786e\u4f4d\u7f6e\nwhile (j &gt;= 0 &amp;&amp; nums[j] &gt; base) {\nnums[j + 1] = nums[j]; // \u5c06 nums[j] \u5411\u53f3\u79fb\u52a8\u4e00\u4f4d\nj--;\n}\nnums[j + 1] = base; // \u5c06 base \u8d4b\u503c\u5230\u6b63\u786e\u4f4d\u7f6e\n}\n}\n</code></pre>"},{"location":"chapter_sorting/insertion_sort/#1142","title":"11.4.2. \u00a0 \u7b97\u6cd5\u7279\u6027","text":"<ul> <li>\u65f6\u95f4\u590d\u6742\u5ea6 \\(O(n^2)\\) \u3001\u81ea\u9002\u5e94\u6392\u5e8f \uff1a\u6700\u5dee\u60c5\u51b5\u4e0b\uff0c\u6bcf\u6b21\u63d2\u5165\u64cd\u4f5c\u5206\u522b\u9700\u8981\u5faa\u73af \\(n - 1\\) , \\(n-2\\) , \\(\\cdots\\) , \\(2\\) , \\(1\\) \u6b21\uff0c\u6c42\u548c\u5f97\u5230 \\(\\frac{(n - 1) n}{2}\\) \uff0c\u56e0\u6b64\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(n^2)\\) \u3002\u5728\u9047\u5230\u6709\u5e8f\u6570\u636e\u65f6\uff0c\u63d2\u5165\u64cd\u4f5c\u4f1a\u63d0\u524d\u7ec8\u6b62\u3002\u5f53\u8f93\u5165\u6570\u7ec4\u5b8c\u5168\u6709\u5e8f\u65f6\uff0c\u63d2\u5165\u6392\u5e8f\u8fbe\u5230\u6700\u4f73\u65f6\u95f4\u590d\u6742\u5ea6 \\(O(n)\\) \u3002</li> <li>\u7a7a\u95f4\u590d\u6742\u5ea6 \\(O(1)\\) \u3001\u539f\u5730\u6392\u5e8f \uff1a\u6307\u9488 \\(i\\) , \\(j\\) \u4f7f\u7528\u5e38\u6570\u5927\u5c0f\u7684\u989d\u5916\u7a7a\u95f4\u3002</li> <li>\u7a33\u5b9a\u6392\u5e8f\uff1a\u5728\u63d2\u5165\u64cd\u4f5c\u8fc7\u7a0b\u4e2d\uff0c\u6211\u4eec\u4f1a\u5c06\u5143\u7d20\u63d2\u5165\u5230\u76f8\u7b49\u5143\u7d20\u7684\u53f3\u4fa7\uff0c\u4e0d\u4f1a\u6539\u53d8\u5b83\u4eec\u7684\u987a\u5e8f\u3002</li> </ul>"},{"location":"chapter_sorting/insertion_sort/#1143","title":"11.4.3. \u00a0 \u63d2\u5165\u6392\u5e8f\u4f18\u52bf","text":"<p>\u63d2\u5165\u6392\u5e8f\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(n^2)\\) \uff0c\u800c\u6211\u4eec\u5373\u5c06\u5b66\u4e60\u7684\u5feb\u901f\u6392\u5e8f\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(n \\log n)\\) \u3002\u5c3d\u7ba1\u63d2\u5165\u6392\u5e8f\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u76f8\u6bd4\u5feb\u901f\u6392\u5e8f\u66f4\u9ad8\uff0c\u4f46\u5728\u6570\u636e\u91cf\u8f83\u5c0f\u7684\u60c5\u51b5\u4e0b\uff0c\u63d2\u5165\u6392\u5e8f\u901a\u5e38\u66f4\u5feb\u3002</p> <p>\u8fd9\u4e2a\u7ed3\u8bba\u4e0e\u7ebf\u6027\u67e5\u627e\u548c\u4e8c\u5206\u67e5\u627e\u7684\u9002\u7528\u60c5\u51b5\u7684\u7ed3\u8bba\u7c7b\u4f3c\u3002\u5feb\u901f\u6392\u5e8f\u8fd9\u7c7b \\(O(n \\log n)\\) \u7684\u7b97\u6cd5\u5c5e\u4e8e\u57fa\u4e8e\u5206\u6cbb\u7684\u6392\u5e8f\u7b97\u6cd5\uff0c\u5f80\u5f80\u5305\u542b\u66f4\u591a\u5355\u5143\u8ba1\u7b97\u64cd\u4f5c\u3002\u800c\u5728\u6570\u636e\u91cf\u8f83\u5c0f\u65f6\uff0c\\(n^2\\) \u548c \\(n \\log n\\) \u7684\u6570\u503c\u6bd4\u8f83\u63a5\u8fd1\uff0c\u590d\u6742\u5ea6\u4e0d\u5360\u4e3b\u5bfc\u4f5c\u7528\uff1b\u6bcf\u8f6e\u4e2d\u7684\u5355\u5143\u8ba1\u7b97\u64cd\u4f5c\u6570\u91cf\u8d77\u5230\u51b3\u5b9a\u6027\u56e0\u7d20\u3002</p> <p>\u5b9e\u9645\u4e0a\uff0c\u8bb8\u591a\u7f16\u7a0b\u8bed\u8a00\uff08\u4f8b\u5982 Java\uff09\u7684\u5185\u7f6e\u6392\u5e8f\u51fd\u6570\u90fd\u91c7\u7528\u4e86\u63d2\u5165\u6392\u5e8f\uff0c\u5927\u81f4\u601d\u8def\u4e3a\uff1a\u5bf9\u4e8e\u957f\u6570\u7ec4\uff0c\u91c7\u7528\u57fa\u4e8e\u5206\u6cbb\u7684\u6392\u5e8f\u7b97\u6cd5\uff0c\u4f8b\u5982\u5feb\u901f\u6392\u5e8f\uff1b\u5bf9\u4e8e\u77ed\u6570\u7ec4\uff0c\u76f4\u63a5\u4f7f\u7528\u63d2\u5165\u6392\u5e8f\u3002</p> <p>\u867d\u7136\u5192\u6ce1\u6392\u5e8f\u3001\u9009\u62e9\u6392\u5e8f\u548c\u63d2\u5165\u6392\u5e8f\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u90fd\u4e3a \\(O(n^2)\\) \uff0c\u4f46\u5728\u5b9e\u9645\u60c5\u51b5\u4e2d\uff0c\u63d2\u5165\u6392\u5e8f\u7684\u4f7f\u7528\u9891\u7387\u663e\u8457\u9ad8\u4e8e\u5192\u6ce1\u6392\u5e8f\u548c\u9009\u62e9\u6392\u5e8f\u3002\u8fd9\u662f\u56e0\u4e3a\uff1a</p> <ul> <li>\u5192\u6ce1\u6392\u5e8f\u57fa\u4e8e\u5143\u7d20\u4ea4\u6362\u5b9e\u73b0\uff0c\u9700\u8981\u501f\u52a9\u4e00\u4e2a\u4e34\u65f6\u53d8\u91cf\uff0c\u5171\u6d89\u53ca 3 \u4e2a\u5355\u5143\u64cd\u4f5c\uff1b\u63d2\u5165\u6392\u5e8f\u57fa\u4e8e\u5143\u7d20\u8d4b\u503c\u5b9e\u73b0\uff0c\u4ec5\u9700 1 \u4e2a\u5355\u5143\u64cd\u4f5c\u3002\u56e0\u6b64\uff0c\u5192\u6ce1\u6392\u5e8f\u7684\u8ba1\u7b97\u5f00\u9500\u901a\u5e38\u6bd4\u63d2\u5165\u6392\u5e8f\u66f4\u9ad8\u3002</li> <li>\u9009\u62e9\u6392\u5e8f\u5728\u4efb\u4f55\u60c5\u51b5\u4e0b\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u90fd\u4e3a \\(O(n^2)\\) \u3002\u5982\u679c\u7ed9\u5b9a\u4e00\u7ec4\u90e8\u5206\u6709\u5e8f\u7684\u6570\u636e\uff0c\u63d2\u5165\u6392\u5e8f\u901a\u5e38\u6bd4\u9009\u62e9\u6392\u5e8f\u6548\u7387\u66f4\u9ad8\u3002</li> <li>\u9009\u62e9\u6392\u5e8f\u4e0d\u7a33\u5b9a\uff0c\u65e0\u6cd5\u5e94\u7528\u4e8e\u591a\u7ea7\u6392\u5e8f\u3002</li> </ul>"},{"location":"chapter_sorting/merge_sort/","title":"11.6. \u00a0 \u5f52\u5e76\u6392\u5e8f","text":"<p>\u300c\u5f52\u5e76\u6392\u5e8f Merge Sort\u300d\u57fa\u4e8e\u5206\u6cbb\u601d\u60f3\u5b9e\u73b0\u6392\u5e8f\uff0c\u5305\u542b\u201c\u5212\u5206\u201d\u548c\u201c\u5408\u5e76\u201d\u4e24\u4e2a\u9636\u6bb5\uff1a</p> <ol> <li>\u5212\u5206\u9636\u6bb5\uff1a\u901a\u8fc7\u9012\u5f52\u4e0d\u65ad\u5730\u5c06\u6570\u7ec4\u4ece\u4e2d\u70b9\u5904\u5206\u5f00\uff0c\u5c06\u957f\u6570\u7ec4\u7684\u6392\u5e8f\u95ee\u9898\u8f6c\u6362\u4e3a\u77ed\u6570\u7ec4\u7684\u6392\u5e8f\u95ee\u9898\uff1b</li> <li>\u5408\u5e76\u9636\u6bb5\uff1a\u5f53\u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a 1 \u65f6\u7ec8\u6b62\u5212\u5206\uff0c\u5f00\u59cb\u5408\u5e76\uff0c\u6301\u7eed\u5730\u5c06\u5de6\u53f3\u4e24\u4e2a\u8f83\u77ed\u7684\u6709\u5e8f\u6570\u7ec4\u5408\u5e76\u4e3a\u4e00\u4e2a\u8f83\u957f\u7684\u6709\u5e8f\u6570\u7ec4\uff0c\u76f4\u81f3\u7ed3\u675f\uff1b</li> </ol> <p></p> <p> Fig. \u5f52\u5e76\u6392\u5e8f\u7684\u5212\u5206\u4e0e\u5408\u5e76\u9636\u6bb5 </p>"},{"location":"chapter_sorting/merge_sort/#1161","title":"11.6.1. \u00a0 \u7b97\u6cd5\u6d41\u7a0b","text":"<p>\u201c\u5212\u5206\u9636\u6bb5\u201d\u4ece\u9876\u81f3\u5e95\u9012\u5f52\u5730\u5c06\u6570\u7ec4\u4ece\u4e2d\u70b9\u5207\u4e3a\u4e24\u4e2a\u5b50\u6570\u7ec4\uff0c\u76f4\u81f3\u957f\u5ea6\u4e3a 1 \uff1b</p> <ol> <li>\u8ba1\u7b97\u6570\u7ec4\u4e2d\u70b9 <code>mid</code> \uff0c\u9012\u5f52\u5212\u5206\u5de6\u5b50\u6570\u7ec4\uff08\u533a\u95f4 <code>[left, mid]</code> \uff09\u548c\u53f3\u5b50\u6570\u7ec4\uff08\u533a\u95f4 <code>[mid + 1, right]</code> \uff09\uff1b</li> <li>\u9012\u5f52\u6267\u884c\u6b65\u9aa4 <code>1.</code> \uff0c\u76f4\u81f3\u5b50\u6570\u7ec4\u533a\u95f4\u957f\u5ea6\u4e3a 1 \u65f6\uff0c\u7ec8\u6b62\u9012\u5f52\u5212\u5206\uff1b</li> </ol> <p>\u201c\u5408\u5e76\u9636\u6bb5\u201d\u4ece\u5e95\u81f3\u9876\u5730\u5c06\u5de6\u5b50\u6570\u7ec4\u548c\u53f3\u5b50\u6570\u7ec4\u5408\u5e76\u4e3a\u4e00\u4e2a\u6709\u5e8f\u6570\u7ec4\u3002\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u4ece\u957f\u5ea6\u4e3a 1 \u7684\u5b50\u6570\u7ec4\u5f00\u59cb\u5408\u5e76\uff0c\u5408\u5e76\u9636\u6bb5\u4e2d\u7684\u6bcf\u4e2a\u5b50\u6570\u7ec4\u90fd\u662f\u6709\u5e8f\u7684\u3002</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p>\u89c2\u5bdf\u53d1\u73b0\uff0c\u5f52\u5e76\u6392\u5e8f\u7684\u9012\u5f52\u987a\u5e8f\u4e0e\u4e8c\u53c9\u6811\u7684\u540e\u5e8f\u904d\u5386\u76f8\u540c\uff0c\u5177\u4f53\u6765\u770b\uff1a</p> <ul> <li>\u540e\u5e8f\u904d\u5386\uff1a\u5148\u9012\u5f52\u5de6\u5b50\u6811\uff0c\u518d\u9012\u5f52\u53f3\u5b50\u6811\uff0c\u6700\u540e\u5904\u7406\u6839\u8282\u70b9\u3002</li> <li>\u5f52\u5e76\u6392\u5e8f\uff1a\u5148\u9012\u5f52\u5de6\u5b50\u6570\u7ec4\uff0c\u518d\u9012\u5f52\u53f3\u5b50\u6570\u7ec4\uff0c\u6700\u540e\u5904\u7406\u5408\u5e76\u3002</li> </ul> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart merge_sort.java<pre><code>/* \u5408\u5e76\u5de6\u5b50\u6570\u7ec4\u548c\u53f3\u5b50\u6570\u7ec4 */\n// \u5de6\u5b50\u6570\u7ec4\u533a\u95f4 [left, mid]\n// \u53f3\u5b50\u6570\u7ec4\u533a\u95f4 [mid + 1, right]\nvoid merge(int[] nums, int left, int mid, int right) {\n// \u521d\u59cb\u5316\u8f85\u52a9\u6570\u7ec4\nint[] tmp = Arrays.copyOfRange(nums, left, right + 1);\n// \u5de6\u5b50\u6570\u7ec4\u7684\u8d77\u59cb\u7d22\u5f15\u548c\u7ed3\u675f\u7d22\u5f15\nint leftStart = left - left, leftEnd = mid - left;\n// \u53f3\u5b50\u6570\u7ec4\u7684\u8d77\u59cb\u7d22\u5f15\u548c\u7ed3\u675f\u7d22\u5f15\nint rightStart = mid + 1 - left, rightEnd = right - left;\n// i, j \u5206\u522b\u6307\u5411\u5de6\u5b50\u6570\u7ec4\u3001\u53f3\u5b50\u6570\u7ec4\u7684\u9996\u5143\u7d20\nint i = leftStart, j = rightStart;\n// \u901a\u8fc7\u8986\u76d6\u539f\u6570\u7ec4 nums \u6765\u5408\u5e76\u5de6\u5b50\u6570\u7ec4\u548c\u53f3\u5b50\u6570\u7ec4\nfor (int k = left; k &lt;= right; k++) {\n// \u82e5\u201c\u5de6\u5b50\u6570\u7ec4\u5df2\u5168\u90e8\u5408\u5e76\u5b8c\u201d\uff0c\u5219\u9009\u53d6\u53f3\u5b50\u6570\u7ec4\u5143\u7d20\uff0c\u5e76\u4e14 j++\nif (i &gt; leftEnd)\nnums[k] = tmp[j++];\n// \u5426\u5219\uff0c\u82e5\u201c\u53f3\u5b50\u6570\u7ec4\u5df2\u5168\u90e8\u5408\u5e76\u5b8c\u201d\u6216\u201c\u5de6\u5b50\u6570\u7ec4\u5143\u7d20 &lt;= \u53f3\u5b50\u6570\u7ec4\u5143\u7d20\u201d\uff0c\u5219\u9009\u53d6\u5de6\u5b50\u6570\u7ec4\u5143\u7d20\uff0c\u5e76\u4e14 i++\nelse if (j &gt; rightEnd || tmp[i] &lt;= tmp[j])\nnums[k] = tmp[i++];\n// \u5426\u5219\uff0c\u82e5\u201c\u5de6\u53f3\u5b50\u6570\u7ec4\u90fd\u672a\u5168\u90e8\u5408\u5e76\u5b8c\u201d\u4e14\u201c\u5de6\u5b50\u6570\u7ec4\u5143\u7d20 &gt; \u53f3\u5b50\u6570\u7ec4\u5143\u7d20\u201d\uff0c\u5219\u9009\u53d6\u53f3\u5b50\u6570\u7ec4\u5143\u7d20\uff0c\u5e76\u4e14 j++\nelse\nnums[k] = tmp[j++];\n}\n}\n/* \u5f52\u5e76\u6392\u5e8f */\nvoid mergeSort(int[] nums, int left, int right) {\n// \u7ec8\u6b62\u6761\u4ef6\nif (left &gt;= right)\nreturn;                      // \u5f53\u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a 1 \u65f6\u7ec8\u6b62\u9012\u5f52\n// \u5212\u5206\u9636\u6bb5\nint mid = (left + right) / 2;    // \u8ba1\u7b97\u4e2d\u70b9\nmergeSort(nums, left, mid);      // \u9012\u5f52\u5de6\u5b50\u6570\u7ec4\nmergeSort(nums, mid + 1, right); // \u9012\u5f52\u53f3\u5b50\u6570\u7ec4\n// \u5408\u5e76\u9636\u6bb5\nmerge(nums, left, mid, right);\n}\n</code></pre> merge_sort.cpp<pre><code>/* \u5408\u5e76\u5de6\u5b50\u6570\u7ec4\u548c\u53f3\u5b50\u6570\u7ec4 */\n// \u5de6\u5b50\u6570\u7ec4\u533a\u95f4 [left, mid]\n// \u53f3\u5b50\u6570\u7ec4\u533a\u95f4 [mid + 1, right]\nvoid merge(vector&lt;int&gt; &amp;nums, int left, int mid, int right) {\n// \u521d\u59cb\u5316\u8f85\u52a9\u6570\u7ec4\nvector&lt;int&gt; tmp(nums.begin() + left, nums.begin() + right + 1);\n// \u5de6\u5b50\u6570\u7ec4\u7684\u8d77\u59cb\u7d22\u5f15\u548c\u7ed3\u675f\u7d22\u5f15\nint leftStart = left - left, leftEnd = mid - left;\n// \u53f3\u5b50\u6570\u7ec4\u7684\u8d77\u59cb\u7d22\u5f15\u548c\u7ed3\u675f\u7d22\u5f15\nint rightStart = mid + 1 - left, rightEnd = right - left;\n// i, j \u5206\u522b\u6307\u5411\u5de6\u5b50\u6570\u7ec4\u3001\u53f3\u5b50\u6570\u7ec4\u7684\u9996\u5143\u7d20\nint i = leftStart, j = rightStart;\n// \u901a\u8fc7\u8986\u76d6\u539f\u6570\u7ec4 nums \u6765\u5408\u5e76\u5de6\u5b50\u6570\u7ec4\u548c\u53f3\u5b50\u6570\u7ec4\nfor (int k = left; k &lt;= right; k++) {\n// \u82e5\u201c\u5de6\u5b50\u6570\u7ec4\u5df2\u5168\u90e8\u5408\u5e76\u5b8c\u201d\uff0c\u5219\u9009\u53d6\u53f3\u5b50\u6570\u7ec4\u5143\u7d20\uff0c\u5e76\u4e14 j++\nif (i &gt; leftEnd)\nnums[k] = tmp[j++];\n// \u5426\u5219\uff0c\u82e5\u201c\u53f3\u5b50\u6570\u7ec4\u5df2\u5168\u90e8\u5408\u5e76\u5b8c\u201d\u6216\u201c\u5de6\u5b50\u6570\u7ec4\u5143\u7d20 &lt;= \u53f3\u5b50\u6570\u7ec4\u5143\u7d20\u201d\uff0c\u5219\u9009\u53d6\u5de6\u5b50\u6570\u7ec4\u5143\u7d20\uff0c\u5e76\u4e14 i++\nelse if (j &gt; rightEnd || tmp[i] &lt;= tmp[j])\nnums[k] = tmp[i++];\n// \u5426\u5219\uff0c\u82e5\u201c\u5de6\u53f3\u5b50\u6570\u7ec4\u90fd\u672a\u5168\u90e8\u5408\u5e76\u5b8c\u201d\u4e14\u201c\u5de6\u5b50\u6570\u7ec4\u5143\u7d20 &gt; \u53f3\u5b50\u6570\u7ec4\u5143\u7d20\u201d\uff0c\u5219\u9009\u53d6\u53f3\u5b50\u6570\u7ec4\u5143\u7d20\uff0c\u5e76\u4e14 j++\nelse\nnums[k] = tmp[j++];\n}\n}\n/* \u5f52\u5e76\u6392\u5e8f */\nvoid mergeSort(vector&lt;int&gt; &amp;nums, int left, int right) {\n// \u7ec8\u6b62\u6761\u4ef6\nif (left &gt;= right)\nreturn; // \u5f53\u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a 1 \u65f6\u7ec8\u6b62\u9012\u5f52\n// \u5212\u5206\u9636\u6bb5\nint mid = (left + right) / 2;    // \u8ba1\u7b97\u4e2d\u70b9\nmergeSort(nums, left, mid);      // \u9012\u5f52\u5de6\u5b50\u6570\u7ec4\nmergeSort(nums, mid + 1, right); // \u9012\u5f52\u53f3\u5b50\u6570\u7ec4\n// \u5408\u5e76\u9636\u6bb5\nmerge(nums, left, mid, right);\n}\n</code></pre> merge_sort.py<pre><code>def merge(nums: list[int], left: int, mid: int, right: int) -&gt; None:\n\"\"\"\u5408\u5e76\u5de6\u5b50\u6570\u7ec4\u548c\u53f3\u5b50\u6570\u7ec4\"\"\"\n# \u5de6\u5b50\u6570\u7ec4\u533a\u95f4 [left, mid]\n# \u53f3\u5b50\u6570\u7ec4\u533a\u95f4 [mid + 1, right]\n# \u521d\u59cb\u5316\u8f85\u52a9\u6570\u7ec4\ntmp = list(nums[left : right + 1])\n# \u5de6\u5b50\u6570\u7ec4\u7684\u8d77\u59cb\u7d22\u5f15\u548c\u7ed3\u675f\u7d22\u5f15\nleft_start = 0\nleft_end = mid - left\n# \u53f3\u5b50\u6570\u7ec4\u7684\u8d77\u59cb\u7d22\u5f15\u548c\u7ed3\u675f\u7d22\u5f15\nright_start = mid + 1 - left\nright_end = right - left\n# i, j \u5206\u522b\u6307\u5411\u5de6\u5b50\u6570\u7ec4\u3001\u53f3\u5b50\u6570\u7ec4\u7684\u9996\u5143\u7d20\ni = left_start\nj = right_start\n# \u901a\u8fc7\u8986\u76d6\u539f\u6570\u7ec4 nums \u6765\u5408\u5e76\u5de6\u5b50\u6570\u7ec4\u548c\u53f3\u5b50\u6570\u7ec4\nfor k in range(left, right + 1):\n# \u82e5\u201c\u5de6\u5b50\u6570\u7ec4\u5df2\u5168\u90e8\u5408\u5e76\u5b8c\u201d\uff0c\u5219\u9009\u53d6\u53f3\u5b50\u6570\u7ec4\u5143\u7d20\uff0c\u5e76\u4e14 j++\nif i &gt; left_end:\nnums[k] = tmp[j]\nj += 1\n# \u5426\u5219\uff0c\u82e5\u201c\u53f3\u5b50\u6570\u7ec4\u5df2\u5168\u90e8\u5408\u5e76\u5b8c\u201d\u6216\u201c\u5de6\u5b50\u6570\u7ec4\u5143\u7d20 &lt;= \u53f3\u5b50\u6570\u7ec4\u5143\u7d20\u201d\uff0c\u5219\u9009\u53d6\u5de6\u5b50\u6570\u7ec4\u5143\u7d20\uff0c\u5e76\u4e14 i++\nelif j &gt; right_end or tmp[i] &lt;= tmp[j]:\nnums[k] = tmp[i]\ni += 1\n# \u5426\u5219\uff0c\u82e5\u201c\u5de6\u53f3\u5b50\u6570\u7ec4\u90fd\u672a\u5168\u90e8\u5408\u5e76\u5b8c\u201d\u4e14\u201c\u5de6\u5b50\u6570\u7ec4\u5143\u7d20 &gt; \u53f3\u5b50\u6570\u7ec4\u5143\u7d20\u201d\uff0c\u5219\u9009\u53d6\u53f3\u5b50\u6570\u7ec4\u5143\u7d20\uff0c\u5e76\u4e14 j++\nelse:\nnums[k] = tmp[j]\nj += 1\ndef merge_sort(nums: list[int], left: int, right: int) -&gt; None:\n\"\"\"\u5f52\u5e76\u6392\u5e8f\"\"\"\n# \u7ec8\u6b62\u6761\u4ef6\nif left &gt;= right:\nreturn  # \u5f53\u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a 1 \u65f6\u7ec8\u6b62\u9012\u5f52\n# \u5212\u5206\u9636\u6bb5\nmid = (left + right) // 2  # \u8ba1\u7b97\u4e2d\u70b9\nmerge_sort(nums, left, mid)  # \u9012\u5f52\u5de6\u5b50\u6570\u7ec4\nmerge_sort(nums, mid + 1, right)  # \u9012\u5f52\u53f3\u5b50\u6570\u7ec4\n# \u5408\u5e76\u9636\u6bb5\nmerge(nums, left, mid, right)\n</code></pre> merge_sort.go<pre><code>/* \u5408\u5e76\u5de6\u5b50\u6570\u7ec4\u548c\u53f3\u5b50\u6570\u7ec4 */\n// \u5de6\u5b50\u6570\u7ec4\u533a\u95f4 [left, mid]\n// \u53f3\u5b50\u6570\u7ec4\u533a\u95f4 [mid + 1, right]\nfunc merge(nums []int, left, mid, right int) {\n// \u521d\u59cb\u5316\u8f85\u52a9\u6570\u7ec4 \u501f\u52a9 copy \u6a21\u5757\ntmp := make([]int, right-left+1)\nfor i := left; i &lt;= right; i++ {\ntmp[i-left] = nums[i]\n}\n// \u5de6\u5b50\u6570\u7ec4\u7684\u8d77\u59cb\u7d22\u5f15\u548c\u7ed3\u675f\u7d22\u5f15\nleftStart, leftEnd := left-left, mid-left\n// \u53f3\u5b50\u6570\u7ec4\u7684\u8d77\u59cb\u7d22\u5f15\u548c\u7ed3\u675f\u7d22\u5f15\nrightStart, rightEnd := mid+1-left, right-left\n// i, j \u5206\u522b\u6307\u5411\u5de6\u5b50\u6570\u7ec4\u3001\u53f3\u5b50\u6570\u7ec4\u7684\u9996\u5143\u7d20\ni, j := leftStart, rightStart\n// \u901a\u8fc7\u8986\u76d6\u539f\u6570\u7ec4 nums \u6765\u5408\u5e76\u5de6\u5b50\u6570\u7ec4\u548c\u53f3\u5b50\u6570\u7ec4\nfor k := left; k &lt;= right; k++ {\n// \u82e5\u201c\u5de6\u5b50\u6570\u7ec4\u5df2\u5168\u90e8\u5408\u5e76\u5b8c\u201d\uff0c\u5219\u9009\u53d6\u53f3\u5b50\u6570\u7ec4\u5143\u7d20\uff0c\u5e76\u4e14 j++\nif i &gt; leftEnd {\nnums[k] = tmp[j]\nj++\n// \u5426\u5219\uff0c\u82e5\u201c\u53f3\u5b50\u6570\u7ec4\u5df2\u5168\u90e8\u5408\u5e76\u5b8c\u201d\u6216\u201c\u5de6\u5b50\u6570\u7ec4\u5143\u7d20 &lt;= \u53f3\u5b50\u6570\u7ec4\u5143\u7d20\u201d\uff0c\u5219\u9009\u53d6\u5de6\u5b50\u6570\u7ec4\u5143\u7d20\uff0c\u5e76\u4e14 i++\n} else if j &gt; rightEnd || tmp[i] &lt;= tmp[j] {\nnums[k] = tmp[i]\ni++\n// \u5426\u5219\uff0c\u82e5\u201c\u5de6\u53f3\u5b50\u6570\u7ec4\u90fd\u672a\u5168\u90e8\u5408\u5e76\u5b8c\u201d\u4e14\u201c\u5de6\u5b50\u6570\u7ec4\u5143\u7d20 &gt; \u53f3\u5b50\u6570\u7ec4\u5143\u7d20\u201d\uff0c\u5219\u9009\u53d6\u53f3\u5b50\u6570\u7ec4\u5143\u7d20\uff0c\u5e76\u4e14 j++\n} else {\nnums[k] = tmp[j]\nj++\n}\n}\n}\n/* \u5f52\u5e76\u6392\u5e8f */\nfunc mergeSort(nums []int, left, right int) {\n// \u7ec8\u6b62\u6761\u4ef6\nif left &gt;= right {\nreturn\n}\n// \u5212\u5206\u9636\u6bb5\nmid := (left + right) / 2\nmergeSort(nums, left, mid)\nmergeSort(nums, mid+1, right)\n// \u5408\u5e76\u9636\u6bb5\nmerge(nums, left, mid, right)\n}\n</code></pre> merge_sort.js<pre><code>/* \u5408\u5e76\u5de6\u5b50\u6570\u7ec4\u548c\u53f3\u5b50\u6570\u7ec4 */\n// \u5de6\u5b50\u6570\u7ec4\u533a\u95f4 [left, mid]\n// \u53f3\u5b50\u6570\u7ec4\u533a\u95f4 [mid + 1, right]\nfunction merge(nums, left, mid, right) {\n// \u521d\u59cb\u5316\u8f85\u52a9\u6570\u7ec4\nlet tmp = nums.slice(left, right + 1);\n// \u5de6\u5b50\u6570\u7ec4\u7684\u8d77\u59cb\u7d22\u5f15\u548c\u7ed3\u675f\u7d22\u5f15\nlet leftStart = left - left,\nleftEnd = mid - left;\n// \u53f3\u5b50\u6570\u7ec4\u7684\u8d77\u59cb\u7d22\u5f15\u548c\u7ed3\u675f\u7d22\u5f15\nlet rightStart = mid + 1 - left,\nrightEnd = right - left;\n// i, j \u5206\u522b\u6307\u5411\u5de6\u5b50\u6570\u7ec4\u3001\u53f3\u5b50\u6570\u7ec4\u7684\u9996\u5143\u7d20\nlet i = leftStart,\nj = rightStart;\n// \u901a\u8fc7\u8986\u76d6\u539f\u6570\u7ec4 nums \u6765\u5408\u5e76\u5de6\u5b50\u6570\u7ec4\u548c\u53f3\u5b50\u6570\u7ec4\nfor (let k = left; k &lt;= right; k++) {\nif (i &gt; leftEnd) {\n// \u82e5\u201c\u5de6\u5b50\u6570\u7ec4\u5df2\u5168\u90e8\u5408\u5e76\u5b8c\u201d\uff0c\u5219\u9009\u53d6\u53f3\u5b50\u6570\u7ec4\u5143\u7d20\uff0c\u5e76\u4e14 j++\nnums[k] = tmp[j++];\n} else if (j &gt; rightEnd || tmp[i] &lt;= tmp[j]) {\n// \u5426\u5219\uff0c\u82e5\u201c\u53f3\u5b50\u6570\u7ec4\u5df2\u5168\u90e8\u5408\u5e76\u5b8c\u201d\u6216\u201c\u5de6\u5b50\u6570\u7ec4\u5143\u7d20 &lt;= \u53f3\u5b50\u6570\u7ec4\u5143\u7d20\u201d\uff0c\u5219\u9009\u53d6\u5de6\u5b50\u6570\u7ec4\u5143\u7d20\uff0c\u5e76\u4e14 i++\nnums[k] = tmp[i++];\n} else {\n// \u5426\u5219\uff0c\u82e5\u201c\u5de6\u53f3\u5b50\u6570\u7ec4\u90fd\u672a\u5168\u90e8\u5408\u5e76\u5b8c\u201d\u4e14\u201c\u5de6\u5b50\u6570\u7ec4\u5143\u7d20 &gt; \u53f3\u5b50\u6570\u7ec4\u5143\u7d20\u201d\uff0c\u5219\u9009\u53d6\u53f3\u5b50\u6570\u7ec4\u5143\u7d20\uff0c\u5e76\u4e14 j++\nnums[k] = tmp[j++];\n}\n}\n}\n/* \u5f52\u5e76\u6392\u5e8f */\nfunction mergeSort(nums, left, right) {\n// \u7ec8\u6b62\u6761\u4ef6\nif (left &gt;= right) return; // \u5f53\u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a 1 \u65f6\u7ec8\u6b62\u9012\u5f52\n// \u5212\u5206\u9636\u6bb5\nlet mid = Math.floor((left + right) / 2); // \u8ba1\u7b97\u4e2d\u70b9\nmergeSort(nums, left, mid); // \u9012\u5f52\u5de6\u5b50\u6570\u7ec4\nmergeSort(nums, mid + 1, right); // \u9012\u5f52\u53f3\u5b50\u6570\u7ec4\n// \u5408\u5e76\u9636\u6bb5\nmerge(nums, left, mid, right);\n}\n</code></pre> merge_sort.ts<pre><code>/* \u5408\u5e76\u5de6\u5b50\u6570\u7ec4\u548c\u53f3\u5b50\u6570\u7ec4 */\n// \u5de6\u5b50\u6570\u7ec4\u533a\u95f4 [left, mid]\n// \u53f3\u5b50\u6570\u7ec4\u533a\u95f4 [mid + 1, right]\nfunction merge(nums: number[], left: number, mid: number, right: number): void {\n// \u521d\u59cb\u5316\u8f85\u52a9\u6570\u7ec4\nlet tmp = nums.slice(left, right + 1);\n// \u5de6\u5b50\u6570\u7ec4\u7684\u8d77\u59cb\u7d22\u5f15\u548c\u7ed3\u675f\u7d22\u5f15\nlet leftStart = left - left,\nleftEnd = mid - left;\n// \u53f3\u5b50\u6570\u7ec4\u7684\u8d77\u59cb\u7d22\u5f15\u548c\u7ed3\u675f\u7d22\u5f15\nlet rightStart = mid + 1 - left,\nrightEnd = right - left;\n// i, j \u5206\u522b\u6307\u5411\u5de6\u5b50\u6570\u7ec4\u3001\u53f3\u5b50\u6570\u7ec4\u7684\u9996\u5143\u7d20\nlet i = leftStart,\nj = rightStart;\n// \u901a\u8fc7\u8986\u76d6\u539f\u6570\u7ec4 nums \u6765\u5408\u5e76\u5de6\u5b50\u6570\u7ec4\u548c\u53f3\u5b50\u6570\u7ec4\nfor (let k = left; k &lt;= right; k++) {\nif (i &gt; leftEnd) {\n// \u82e5\u201c\u5de6\u5b50\u6570\u7ec4\u5df2\u5168\u90e8\u5408\u5e76\u5b8c\u201d\uff0c\u5219\u9009\u53d6\u53f3\u5b50\u6570\u7ec4\u5143\u7d20\uff0c\u5e76\u4e14 j++\nnums[k] = tmp[j++];\n// \u5426\u5219\uff0c\u82e5\u201c\u53f3\u5b50\u6570\u7ec4\u5df2\u5168\u90e8\u5408\u5e76\u5b8c\u201d\u6216\u201c\u5de6\u5b50\u6570\u7ec4\u5143\u7d20 &lt;= \u53f3\u5b50\u6570\u7ec4\u5143\u7d20\u201d\uff0c\u5219\u9009\u53d6\u5de6\u5b50\u6570\u7ec4\u5143\u7d20\uff0c\u5e76\u4e14 i++\n} else if (j &gt; rightEnd || tmp[i] &lt;= tmp[j]) {\nnums[k] = tmp[i++];\n// \u5426\u5219\uff0c\u82e5\u201c\u5de6\u53f3\u5b50\u6570\u7ec4\u90fd\u672a\u5168\u90e8\u5408\u5e76\u5b8c\u201d\u4e14\u201c\u5de6\u5b50\u6570\u7ec4\u5143\u7d20 &gt; \u53f3\u5b50\u6570\u7ec4\u5143\u7d20\u201d\uff0c\u5219\u9009\u53d6\u53f3\u5b50\u6570\u7ec4\u5143\u7d20\uff0c\u5e76\u4e14 j++\n} else {\nnums[k] = tmp[j++];\n}\n}\n}\n/* \u5f52\u5e76\u6392\u5e8f */\nfunction mergeSort(nums: number[], left: number, right: number): void {\n// \u7ec8\u6b62\u6761\u4ef6\nif (left &gt;= right) return; // \u5f53\u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a 1 \u65f6\u7ec8\u6b62\u9012\u5f52\n// \u5212\u5206\u9636\u6bb5\nlet mid = Math.floor((left + right) / 2); // \u8ba1\u7b97\u4e2d\u70b9\nmergeSort(nums, left, mid); // \u9012\u5f52\u5de6\u5b50\u6570\u7ec4\nmergeSort(nums, mid + 1, right); // \u9012\u5f52\u53f3\u5b50\u6570\u7ec4\n// \u5408\u5e76\u9636\u6bb5\nmerge(nums, left, mid, right);\n}\n</code></pre> merge_sort.c<pre><code>/* \u5408\u5e76\u5de6\u5b50\u6570\u7ec4\u548c\u53f3\u5b50\u6570\u7ec4 */\n// \u5de6\u5b50\u6570\u7ec4\u533a\u95f4 [left, mid]\n// \u53f3\u5b50\u6570\u7ec4\u533a\u95f4 [mid + 1, right]\nvoid merge(int *nums, int left, int mid, int right) {\nint index;\n// \u521d\u59cb\u5316\u8f85\u52a9\u6570\u7ec4\nint tmp[right + 1 - left];\nfor (index = left; index &lt; right + 1; index++) {\ntmp[index - left] = nums[index];\n}\n// \u5de6\u5b50\u6570\u7ec4\u7684\u8d77\u59cb\u7d22\u5f15\u548c\u7ed3\u675f\u7d22\u5f15\nint leftStart = left - left, leftEnd = mid - left;\n// \u53f3\u5b50\u6570\u7ec4\u7684\u8d77\u59cb\u7d22\u5f15\u548c\u7ed3\u675f\u7d22\u5f15\nint rightStart = mid + 1 - left, rightEnd = right - left;\n// i, j \u5206\u522b\u6307\u5411\u5de6\u5b50\u6570\u7ec4\u3001\u53f3\u5b50\u6570\u7ec4\u7684\u9996\u5143\u7d20\nint i = leftStart, j = rightStart;\n// \u901a\u8fc7\u8986\u76d6\u539f\u6570\u7ec4 nums \u6765\u5408\u5e76\u5de6\u5b50\u6570\u7ec4\u548c\u53f3\u5b50\u6570\u7ec4\nfor (int k = left; k &lt;= right; k++) {\n// \u82e5\u201c\u5de6\u5b50\u6570\u7ec4\u5df2\u5168\u90e8\u5408\u5e76\u5b8c\u201d\uff0c\u5219\u9009\u53d6\u53f3\u5b50\u6570\u7ec4\u5143\u7d20\uff0c\u5e76\u4e14 j++\nif (i &gt; leftEnd)\nnums[k] = tmp[j++];\n// \u5426\u5219\uff0c\u82e5\u201c\u53f3\u5b50\u6570\u7ec4\u5df2\u5168\u90e8\u5408\u5e76\u5b8c\u201d\u6216\u201c\u5de6\u5b50\u6570\u7ec4\u5143\u7d20 &lt;= \u53f3\u5b50\u6570\u7ec4\u5143\u7d20\u201d\uff0c\u5219\u9009\u53d6\u5de6\u5b50\u6570\u7ec4\u5143\u7d20\uff0c\u5e76\u4e14 i++\nelse if (j &gt; rightEnd || tmp[i] &lt;= tmp[j])\nnums[k] = tmp[i++];\n// \u5426\u5219\uff0c\u82e5\u201c\u5de6\u53f3\u5b50\u6570\u7ec4\u90fd\u672a\u5168\u90e8\u5408\u5e76\u5b8c\u201d\u4e14\u201c\u5de6\u5b50\u6570\u7ec4\u5143\u7d20 &gt; \u53f3\u5b50\u6570\u7ec4\u5143\u7d20\u201d\uff0c\u5219\u9009\u53d6\u53f3\u5b50\u6570\u7ec4\u5143\u7d20\uff0c\u5e76\u4e14 j++\nelse\nnums[k] = tmp[j++];\n}\n}\n/* \u5f52\u5e76\u6392\u5e8f */\nvoid mergeSort(int *nums, int left, int right) {\n// \u7ec8\u6b62\u6761\u4ef6\nif (left &gt;= right)\nreturn; // \u5f53\u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a 1 \u65f6\u7ec8\u6b62\u9012\u5f52\n// \u5212\u5206\u9636\u6bb5\nint mid = (left + right) / 2;    // \u8ba1\u7b97\u4e2d\u70b9\nmergeSort(nums, left, mid);      // \u9012\u5f52\u5de6\u5b50\u6570\u7ec4\nmergeSort(nums, mid + 1, right); // \u9012\u5f52\u53f3\u5b50\u6570\u7ec4\n// \u5408\u5e76\u9636\u6bb5\nmerge(nums, left, mid, right);\n}\n</code></pre> merge_sort.cs<pre><code>/* \u5408\u5e76\u5de6\u5b50\u6570\u7ec4\u548c\u53f3\u5b50\u6570\u7ec4 */\n// \u5de6\u5b50\u6570\u7ec4\u533a\u95f4 [left, mid]\n// \u53f3\u5b50\u6570\u7ec4\u533a\u95f4 [mid + 1, right]\nvoid merge(int[] nums, int left, int mid, int right) {\n// \u521d\u59cb\u5316\u8f85\u52a9\u6570\u7ec4\nint[] tmp = nums[left..(right + 1)];\n// \u5de6\u5b50\u6570\u7ec4\u7684\u8d77\u59cb\u7d22\u5f15\u548c\u7ed3\u675f\u7d22\u5f15  \nint leftStart = left - left, leftEnd = mid - left;\n// \u53f3\u5b50\u6570\u7ec4\u7684\u8d77\u59cb\u7d22\u5f15\u548c\u7ed3\u675f\u7d22\u5f15       \nint rightStart = mid + 1 - left, rightEnd = right - left;\n// i, j \u5206\u522b\u6307\u5411\u5de6\u5b50\u6570\u7ec4\u3001\u53f3\u5b50\u6570\u7ec4\u7684\u9996\u5143\u7d20\nint i = leftStart, j = rightStart;\n// \u901a\u8fc7\u8986\u76d6\u539f\u6570\u7ec4 nums \u6765\u5408\u5e76\u5de6\u5b50\u6570\u7ec4\u548c\u53f3\u5b50\u6570\u7ec4\nfor (int k = left; k &lt;= right; k++) {\n// \u82e5\u201c\u5de6\u5b50\u6570\u7ec4\u5df2\u5168\u90e8\u5408\u5e76\u5b8c\u201d\uff0c\u5219\u9009\u53d6\u53f3\u5b50\u6570\u7ec4\u5143\u7d20\uff0c\u5e76\u4e14 j++\nif (i &gt; leftEnd)\nnums[k] = tmp[j++];\n// \u5426\u5219\uff0c\u82e5\u201c\u53f3\u5b50\u6570\u7ec4\u5df2\u5168\u90e8\u5408\u5e76\u5b8c\u201d\u6216\u201c\u5de6\u5b50\u6570\u7ec4\u5143\u7d20 &lt;= \u53f3\u5b50\u6570\u7ec4\u5143\u7d20\u201d\uff0c\u5219\u9009\u53d6\u5de6\u5b50\u6570\u7ec4\u5143\u7d20\uff0c\u5e76\u4e14 i++\nelse if (j &gt; rightEnd || tmp[i] &lt;= tmp[j])\nnums[k] = tmp[i++];\n// \u5426\u5219\uff0c\u82e5\u201c\u5de6\u53f3\u5b50\u6570\u7ec4\u90fd\u672a\u5168\u90e8\u5408\u5e76\u5b8c\u201d\u4e14\u201c\u5de6\u5b50\u6570\u7ec4\u5143\u7d20 &gt; \u53f3\u5b50\u6570\u7ec4\u5143\u7d20\u201d\uff0c\u5219\u9009\u53d6\u53f3\u5b50\u6570\u7ec4\u5143\u7d20\uff0c\u5e76\u4e14 j++\nelse\nnums[k] = tmp[j++];\n}\n}\n/* \u5f52\u5e76\u6392\u5e8f */\nvoid mergeSort(int[] nums, int left, int right) {\n// \u7ec8\u6b62\u6761\u4ef6\nif (left &gt;= right) return;       // \u5f53\u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a 1 \u65f6\u7ec8\u6b62\u9012\u5f52\n// \u5212\u5206\u9636\u6bb5\nint mid = (left + right) / 2;    // \u8ba1\u7b97\u4e2d\u70b9\nmergeSort(nums, left, mid);      // \u9012\u5f52\u5de6\u5b50\u6570\u7ec4\nmergeSort(nums, mid + 1, right); // \u9012\u5f52\u53f3\u5b50\u6570\u7ec4\n// \u5408\u5e76\u9636\u6bb5\nmerge(nums, left, mid, right);\n}\n</code></pre> merge_sort.swift<pre><code>/* \u5408\u5e76\u5de6\u5b50\u6570\u7ec4\u548c\u53f3\u5b50\u6570\u7ec4 */\n// \u5de6\u5b50\u6570\u7ec4\u533a\u95f4 [left, mid]\n// \u53f3\u5b50\u6570\u7ec4\u533a\u95f4 [mid + 1, right]\nfunc merge(nums: inout [Int], left: Int, mid: Int, right: Int) {\n// \u521d\u59cb\u5316\u8f85\u52a9\u6570\u7ec4\nlet tmp = Array(nums[left ..&lt; (right + 1)])\n// \u5de6\u5b50\u6570\u7ec4\u7684\u8d77\u59cb\u7d22\u5f15\u548c\u7ed3\u675f\u7d22\u5f15\nlet leftStart = left - left\nlet leftEnd = mid - left\n// \u53f3\u5b50\u6570\u7ec4\u7684\u8d77\u59cb\u7d22\u5f15\u548c\u7ed3\u675f\u7d22\u5f15\nlet rightStart = mid + 1 - left\nlet rightEnd = right - left\n// i, j \u5206\u522b\u6307\u5411\u5de6\u5b50\u6570\u7ec4\u3001\u53f3\u5b50\u6570\u7ec4\u7684\u9996\u5143\u7d20\nvar i = leftStart\nvar j = rightStart\n// \u901a\u8fc7\u8986\u76d6\u539f\u6570\u7ec4 nums \u6765\u5408\u5e76\u5de6\u5b50\u6570\u7ec4\u548c\u53f3\u5b50\u6570\u7ec4\nfor k in left ... right {\n// \u82e5\u201c\u5de6\u5b50\u6570\u7ec4\u5df2\u5168\u90e8\u5408\u5e76\u5b8c\u201d\uff0c\u5219\u9009\u53d6\u53f3\u5b50\u6570\u7ec4\u5143\u7d20\uff0c\u5e76\u4e14 j++\nif i &gt; leftEnd {\nnums[k] = tmp[j]\nj += 1\n}\n// \u5426\u5219\uff0c\u82e5\u201c\u53f3\u5b50\u6570\u7ec4\u5df2\u5168\u90e8\u5408\u5e76\u5b8c\u201d\u6216\u201c\u5de6\u5b50\u6570\u7ec4\u5143\u7d20 &lt;= \u53f3\u5b50\u6570\u7ec4\u5143\u7d20\u201d\uff0c\u5219\u9009\u53d6\u5de6\u5b50\u6570\u7ec4\u5143\u7d20\uff0c\u5e76\u4e14 i++\nelse if j &gt; rightEnd || tmp[i] &lt;= tmp[j] {\nnums[k] = tmp[i]\ni += 1\n}\n// \u5426\u5219\uff0c\u82e5\u201c\u5de6\u53f3\u5b50\u6570\u7ec4\u90fd\u672a\u5168\u90e8\u5408\u5e76\u5b8c\u201d\u4e14\u201c\u5de6\u5b50\u6570\u7ec4\u5143\u7d20 &gt; \u53f3\u5b50\u6570\u7ec4\u5143\u7d20\u201d\uff0c\u5219\u9009\u53d6\u53f3\u5b50\u6570\u7ec4\u5143\u7d20\uff0c\u5e76\u4e14 j++\nelse {\nnums[k] = tmp[j]\nj += 1\n}\n}\n}\n/* \u5f52\u5e76\u6392\u5e8f */\nfunc mergeSort(nums: inout [Int], left: Int, right: Int) {\n// \u7ec8\u6b62\u6761\u4ef6\nif left &gt;= right { // \u5f53\u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a 1 \u65f6\u7ec8\u6b62\u9012\u5f52\nreturn\n}\n// \u5212\u5206\u9636\u6bb5\nlet mid = (left + right) / 2 // \u8ba1\u7b97\u4e2d\u70b9\nmergeSort(nums: &amp;nums, left: left, right: mid) // \u9012\u5f52\u5de6\u5b50\u6570\u7ec4\nmergeSort(nums: &amp;nums, left: mid + 1, right: right) // \u9012\u5f52\u53f3\u5b50\u6570\u7ec4\n// \u5408\u5e76\u9636\u6bb5\nmerge(nums: &amp;nums, left: left, mid: mid, right: right)\n}\n</code></pre> merge_sort.zig<pre><code>// \u5408\u5e76\u5de6\u5b50\u6570\u7ec4\u548c\u53f3\u5b50\u6570\u7ec4\n// \u5de6\u5b50\u6570\u7ec4\u533a\u95f4 [left, mid]\n// \u53f3\u5b50\u6570\u7ec4\u533a\u95f4 [mid + 1, right]\nfn merge(nums: []i32, left: usize, mid: usize, right: usize) !void {\n// \u521d\u59cb\u5316\u8f85\u52a9\u6570\u7ec4\nvar mem_arena = std.heap.ArenaAllocator.init(std.heap.page_allocator);\ndefer mem_arena.deinit();\nconst mem_allocator = mem_arena.allocator();\nvar tmp = try mem_allocator.alloc(i32, right + 1 - left);\nstd.mem.copy(i32, tmp, nums[left..right+1]);\n// \u5de6\u5b50\u6570\u7ec4\u7684\u8d77\u59cb\u7d22\u5f15\u548c\u7ed3\u675f\u7d22\u5f15  \nvar leftStart = left - left;\nvar leftEnd = mid - left;\n// \u53f3\u5b50\u6570\u7ec4\u7684\u8d77\u59cb\u7d22\u5f15\u548c\u7ed3\u675f\u7d22\u5f15       \nvar rightStart = mid + 1 - left;\nvar rightEnd = right - left;\n// i, j \u5206\u522b\u6307\u5411\u5de6\u5b50\u6570\u7ec4\u3001\u53f3\u5b50\u6570\u7ec4\u7684\u9996\u5143\u7d20\nvar i = leftStart;\nvar j = rightStart;\n// \u901a\u8fc7\u8986\u76d6\u539f\u6570\u7ec4 nums \u6765\u5408\u5e76\u5de6\u5b50\u6570\u7ec4\u548c\u53f3\u5b50\u6570\u7ec4\nvar k = left;\nwhile (k &lt;= right) : (k += 1) {\n// \u82e5\u201c\u5de6\u5b50\u6570\u7ec4\u5df2\u5168\u90e8\u5408\u5e76\u5b8c\u201d\uff0c\u5219\u9009\u53d6\u53f3\u5b50\u6570\u7ec4\u5143\u7d20\uff0c\u5e76\u4e14 j++\nif (i &gt; leftEnd) {\nnums[k] = tmp[j];\nj += 1;\n// \u5426\u5219\uff0c\u82e5\u201c\u53f3\u5b50\u6570\u7ec4\u5df2\u5168\u90e8\u5408\u5e76\u5b8c\u201d\u6216\u201c\u5de6\u5b50\u6570\u7ec4\u5143\u7d20 &lt;= \u53f3\u5b50\u6570\u7ec4\u5143\u7d20\u201d\uff0c\u5219\u9009\u53d6\u5de6\u5b50\u6570\u7ec4\u5143\u7d20\uff0c\u5e76\u4e14 i++\n} else if  (j &gt; rightEnd or tmp[i] &lt;= tmp[j]) {\nnums[k] = tmp[i];\ni += 1;\n// \u5426\u5219\uff0c\u82e5\u201c\u5de6\u53f3\u5b50\u6570\u7ec4\u90fd\u672a\u5168\u90e8\u5408\u5e76\u5b8c\u201d\u4e14\u201c\u5de6\u5b50\u6570\u7ec4\u5143\u7d20 &gt; \u53f3\u5b50\u6570\u7ec4\u5143\u7d20\u201d\uff0c\u5219\u9009\u53d6\u53f3\u5b50\u6570\u7ec4\u5143\u7d20\uff0c\u5e76\u4e14 j++\n} else {\nnums[k] = tmp[j];\nj += 1;\n}\n}\n}\n// \u5f52\u5e76\u6392\u5e8f\nfn mergeSort(nums: []i32, left: usize, right: usize) !void {\n// \u7ec8\u6b62\u6761\u4ef6\nif (left &gt;= right) return;              // \u5f53\u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a 1 \u65f6\u7ec8\u6b62\u9012\u5f52\n// \u5212\u5206\u9636\u6bb5\nvar mid = (left + right) / 2;           // \u8ba1\u7b97\u4e2d\u70b9\ntry mergeSort(nums, left, mid);         // \u9012\u5f52\u5de6\u5b50\u6570\u7ec4\ntry mergeSort(nums, mid + 1, right);    // \u9012\u5f52\u53f3\u5b50\u6570\u7ec4\n// \u5408\u5e76\u9636\u6bb5\ntry merge(nums, left, mid, right);\n}\n</code></pre> merge_sort.dart<pre><code>/* \u5408\u5e76\u5de6\u5b50\u6570\u7ec4\u548c\u53f3\u5b50\u6570\u7ec4 */\n// \u5de6\u5b50\u6570\u7ec4\u533a\u95f4 [left, mid]\n// \u53f3\u5b50\u6570\u7ec4\u533a\u95f4 [mid + 1, right]\nvoid merge(List&lt;int&gt; nums, int left, int mid, int right) {\n// \u521d\u59cb\u5316\u8f85\u52a9\u6570\u7ec4\nList&lt;int&gt; tmp = nums.sublist(left, right + 1);\n// \u5de6\u5b50\u6570\u7ec4\u7684\u8d77\u59cb\u7d22\u5f15\u548c\u7ed3\u675f\u7d22\u5f15\nint leftStart = left - left, leftEnd = mid - left;\n// \u53f3\u5b50\u6570\u7ec4\u7684\u8d77\u59cb\u7d22\u5f15\u548c\u7ed3\u675f\u7d22\u5f15\nint rightStart = mid + 1 - left, rightEnd = right - left;\n// i, j \u5206\u522b\u6307\u5411\u5de6\u5b50\u6570\u7ec4\u3001\u53f3\u5b50\u6570\u7ec4\u7684\u9996\u5143\u7d20\nint i = leftStart, j = rightStart;\n// \u901a\u8fc7\u8986\u76d6\u539f\u6570\u7ec4 nums \u6765\u5408\u5e76\u5de6\u5b50\u6570\u7ec4\u548c\u53f3\u5b50\u6570\u7ec4\nfor (int k = left; k &lt;= right; k++) {\n// \u82e5\u201c\u5de6\u5b50\u6570\u7ec4\u5df2\u5168\u90e8\u5408\u5e76\u5b8c\u201d\uff0c\u5219\u9009\u53d6\u53f3\u5b50\u6570\u7ec4\u5143\u7d20\uff0c\u5e76\u4e14 j++\nif (i &gt; leftEnd)\nnums[k] = tmp[j++];\n// \u5426\u5219\uff0c\u82e5\u201c\u53f3\u5b50\u6570\u7ec4\u5df2\u5168\u90e8\u5408\u5e76\u5b8c\u201d\u6216\u201c\u5de6\u5b50\u6570\u7ec4\u5143\u7d20 &lt;= \u53f3\u5b50\u6570\u7ec4\u5143\u7d20\u201d\uff0c\u5219\u9009\u53d6\u5de6\u5b50\u6570\u7ec4\u5143\u7d20\uff0c\u5e76\u4e14 i++\nelse if (j &gt; rightEnd || tmp[i] &lt;= tmp[j])\nnums[k] = tmp[i++];\n// \u5426\u5219\uff0c\u82e5\u201c\u5de6\u53f3\u5b50\u6570\u7ec4\u90fd\u672a\u5168\u90e8\u5408\u5e76\u5b8c\u201d\u4e14\u201c\u5de6\u5b50\u6570\u7ec4\u5143\u7d20 &gt; \u53f3\u5b50\u6570\u7ec4\u5143\u7d20\u201d\uff0c\u5219\u9009\u53d6\u53f3\u5b50\u6570\u7ec4\u5143\u7d20\uff0c\u5e76\u4e14 j++\nelse\nnums[k] = tmp[j++];\n}\n}\n/* \u5f52\u5e76\u6392\u5e8f */\nvoid mergeSort(List&lt;int&gt; nums, int left, int right) {\n// \u7ec8\u6b62\u6761\u4ef6\nif (left &gt;= right) return; // \u5f53\u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a 1 \u65f6\u7ec8\u6b62\u9012\u5f52\n// \u5212\u5206\u9636\u6bb5\nint mid = (left + right) ~/ 2; // \u8ba1\u7b97\u4e2d\u70b9\nmergeSort(nums, left, mid); // \u9012\u5f52\u5de6\u5b50\u6570\u7ec4\nmergeSort(nums, mid + 1, right); // \u9012\u5f52\u53f3\u5b50\u6570\u7ec4\n// \u5408\u5e76\u9636\u6bb5\nmerge(nums, left, mid, right);\n}\n</code></pre> <p>\u5408\u5e76\u65b9\u6cd5 <code>merge()</code> \u4ee3\u7801\u4e2d\u7684\u96be\u70b9\u5305\u62ec\uff1a</p> <ul> <li>\u5728\u9605\u8bfb\u4ee3\u7801\u65f6\uff0c\u9700\u8981\u7279\u522b\u6ce8\u610f\u5404\u4e2a\u53d8\u91cf\u7684\u542b\u4e49\u3002<code>nums</code> \u7684\u5f85\u5408\u5e76\u533a\u95f4\u4e3a <code>[left, right]</code> \uff0c\u4f46\u7531\u4e8e <code>tmp</code> \u4ec5\u590d\u5236\u4e86 <code>nums</code> \u8be5\u533a\u95f4\u7684\u5143\u7d20\uff0c\u56e0\u6b64 <code>tmp</code> \u5bf9\u5e94\u533a\u95f4\u4e3a <code>[0, right - left]</code> \u3002</li> <li>\u5728\u6bd4\u8f83 <code>tmp[i]</code> \u548c <code>tmp[j]</code> \u7684\u5927\u5c0f\u65f6\uff0c\u8fd8\u9700\u8003\u8651\u5b50\u6570\u7ec4\u904d\u5386\u5b8c\u6210\u540e\u7684\u7d22\u5f15\u8d8a\u754c\u95ee\u9898\uff0c\u5373 <code>i &gt; leftEnd</code> \u548c <code>j &gt; rightEnd</code> \u7684\u60c5\u51b5\u3002\u7d22\u5f15\u8d8a\u754c\u7684\u4f18\u5148\u7ea7\u662f\u6700\u9ad8\u7684\uff0c\u5982\u679c\u5de6\u5b50\u6570\u7ec4\u5df2\u7ecf\u88ab\u5408\u5e76\u5b8c\u4e86\uff0c\u90a3\u4e48\u4e0d\u9700\u8981\u7ee7\u7eed\u6bd4\u8f83\uff0c\u76f4\u63a5\u5408\u5e76\u53f3\u5b50\u6570\u7ec4\u5143\u7d20\u5373\u53ef\u3002</li> </ul>"},{"location":"chapter_sorting/merge_sort/#1162","title":"11.6.2. \u00a0 \u7b97\u6cd5\u7279\u6027","text":"<ul> <li>\u65f6\u95f4\u590d\u6742\u5ea6 \\(O(n \\log n)\\) \u3001\u975e\u81ea\u9002\u5e94\u6392\u5e8f \uff1a\u5212\u5206\u4ea7\u751f\u9ad8\u5ea6\u4e3a \\(\\log n\\) \u7684\u9012\u5f52\u6811\uff0c\u6bcf\u5c42\u5408\u5e76\u7684\u603b\u64cd\u4f5c\u6570\u91cf\u4e3a \\(n\\) \uff0c\u56e0\u6b64\u603b\u4f53\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(n \\log n)\\) \u3002</li> <li>\u7a7a\u95f4\u590d\u6742\u5ea6 \\(O(n)\\) \u3001\u975e\u539f\u5730\u6392\u5e8f \uff1a\u9012\u5f52\u6df1\u5ea6\u4e3a \\(\\log n\\) \uff0c\u4f7f\u7528 \\(O(\\log n)\\) \u5927\u5c0f\u7684\u6808\u5e27\u7a7a\u95f4\u3002\u5408\u5e76\u64cd\u4f5c\u9700\u8981\u501f\u52a9\u8f85\u52a9\u6570\u7ec4\u5b9e\u73b0\uff0c\u4f7f\u7528 \\(O(n)\\) \u5927\u5c0f\u7684\u989d\u5916\u7a7a\u95f4\u3002</li> <li>\u7a33\u5b9a\u6392\u5e8f\uff1a\u5728\u5408\u5e76\u8fc7\u7a0b\u4e2d\uff0c\u76f8\u7b49\u5143\u7d20\u7684\u6b21\u5e8f\u4fdd\u6301\u4e0d\u53d8\u3002</li> </ul>"},{"location":"chapter_sorting/merge_sort/#1163","title":"11.6.3. \u00a0 \u94fe\u8868\u6392\u5e8f *","text":"<p>\u5f52\u5e76\u6392\u5e8f\u5728\u6392\u5e8f\u94fe\u8868\u65f6\u5177\u6709\u663e\u8457\u4f18\u52bf\uff0c\u7a7a\u95f4\u590d\u6742\u5ea6\u53ef\u4ee5\u4f18\u5316\u81f3 \\(O(1)\\) \uff0c\u539f\u56e0\u5982\u4e0b\uff1a</p> <ul> <li>\u7531\u4e8e\u94fe\u8868\u4ec5\u9700\u6539\u53d8\u6307\u9488\u5c31\u53ef\u5b9e\u73b0\u8282\u70b9\u7684\u589e\u5220\u64cd\u4f5c\uff0c\u56e0\u6b64\u5408\u5e76\u9636\u6bb5\uff08\u5c06\u4e24\u4e2a\u77ed\u6709\u5e8f\u94fe\u8868\u5408\u5e76\u4e3a\u4e00\u4e2a\u957f\u6709\u5e8f\u94fe\u8868\uff09\u65e0\u9700\u521b\u5efa\u8f85\u52a9\u94fe\u8868\u3002</li> <li>\u901a\u8fc7\u4f7f\u7528\u201c\u8fed\u4ee3\u5212\u5206\u201d\u66ff\u4ee3\u201c\u9012\u5f52\u5212\u5206\u201d\uff0c\u53ef\u7701\u53bb\u9012\u5f52\u4f7f\u7528\u7684\u6808\u5e27\u7a7a\u95f4\uff1b</li> </ul> <p>\u5177\u4f53\u5b9e\u73b0\u7ec6\u8282\u6bd4\u8f83\u590d\u6742\uff0c\u6709\u5174\u8da3\u7684\u540c\u5b66\u53ef\u4ee5\u67e5\u9605\u76f8\u5173\u8d44\u6599\u8fdb\u884c\u5b66\u4e60\u3002</p>"},{"location":"chapter_sorting/quick_sort/","title":"11.5. \u00a0 \u5feb\u901f\u6392\u5e8f","text":"<p>\u300c\u5feb\u901f\u6392\u5e8f Quick Sort\u300d\u662f\u4e00\u79cd\u57fa\u4e8e\u5206\u6cbb\u601d\u60f3\u7684\u6392\u5e8f\u7b97\u6cd5\uff0c\u8fd0\u884c\u9ad8\u6548\uff0c\u5e94\u7528\u5e7f\u6cdb\u3002</p> <p>\u5feb\u901f\u6392\u5e8f\u7684\u6838\u5fc3\u64cd\u4f5c\u662f\u300c\u54e8\u5175\u5212\u5206\u300d\uff0c\u5176\u76ee\u6807\u662f\uff1a\u9009\u62e9\u6570\u7ec4\u4e2d\u7684\u67d0\u4e2a\u5143\u7d20\u4f5c\u4e3a\u201c\u57fa\u51c6\u6570\u201d\uff0c\u5c06\u6240\u6709\u5c0f\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\u79fb\u5230\u5176\u5de6\u4fa7\uff0c\u800c\u5927\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\u79fb\u5230\u5176\u53f3\u4fa7\u3002\u5177\u4f53\u6765\u8bf4\uff0c\u54e8\u5175\u5212\u5206\u7684\u6d41\u7a0b\u4e3a\uff1a</p> <ol> <li>\u9009\u53d6\u6570\u7ec4\u6700\u5de6\u7aef\u5143\u7d20\u4f5c\u4e3a\u57fa\u51c6\u6570\uff0c\u521d\u59cb\u5316\u4e24\u4e2a\u6307\u9488 <code>i</code> \u548c <code>j</code> \u5206\u522b\u6307\u5411\u6570\u7ec4\u7684\u4e24\u7aef\uff1b</li> <li>\u8bbe\u7f6e\u4e00\u4e2a\u5faa\u73af\uff0c\u5728\u6bcf\u8f6e\u4e2d\u4f7f\u7528 <code>i</code>\uff08<code>j</code>\uff09\u5206\u522b\u5bfb\u627e\u7b2c\u4e00\u4e2a\u6bd4\u57fa\u51c6\u6570\u5927\uff08\u5c0f\uff09\u7684\u5143\u7d20\uff0c\u7136\u540e\u4ea4\u6362\u8fd9\u4e24\u4e2a\u5143\u7d20\uff1b</li> <li>\u5faa\u73af\u6267\u884c\u6b65\u9aa4 <code>2.</code> \uff0c\u76f4\u5230 <code>i</code> \u548c <code>j</code> \u76f8\u9047\u65f6\u505c\u6b62\uff0c\u6700\u540e\u5c06\u57fa\u51c6\u6570\u4ea4\u6362\u81f3\u4e24\u4e2a\u5b50\u6570\u7ec4\u7684\u5206\u754c\u7ebf\uff1b</li> </ol> <p>\u54e8\u5175\u5212\u5206\u5b8c\u6210\u540e\uff0c\u539f\u6570\u7ec4\u88ab\u5212\u5206\u6210\u4e09\u90e8\u5206\uff1a\u5de6\u5b50\u6570\u7ec4\u3001\u57fa\u51c6\u6570\u3001\u53f3\u5b50\u6570\u7ec4\uff0c\u4e14\u6ee1\u8db3\u201c\u5de6\u5b50\u6570\u7ec4\u4efb\u610f\u5143\u7d20 \\(\\leq\\) \u57fa\u51c6\u6570 \\(\\leq\\) \u53f3\u5b50\u6570\u7ec4\u4efb\u610f\u5143\u7d20\u201d\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u63a5\u4e0b\u6765\u53ea\u9700\u5bf9\u8fd9\u4e24\u4e2a\u5b50\u6570\u7ec4\u8fdb\u884c\u6392\u5e8f\u3002</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p>\u5feb\u901f\u6392\u5e8f\u7684\u5206\u6cbb\u601d\u60f3</p> <p>\u54e8\u5175\u5212\u5206\u7684\u5b9e\u8d28\u662f\u5c06\u4e00\u4e2a\u8f83\u957f\u6570\u7ec4\u7684\u6392\u5e8f\u95ee\u9898\u7b80\u5316\u4e3a\u4e24\u4e2a\u8f83\u77ed\u6570\u7ec4\u7684\u6392\u5e8f\u95ee\u9898\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart quick_sort.java<pre><code>/* \u5143\u7d20\u4ea4\u6362 */\nvoid swap(int[] nums, int i, int j) {\nint tmp = nums[i];\nnums[i] = nums[j];\nnums[j] = tmp;\n}\n/* \u54e8\u5175\u5212\u5206 */\nint partition(int[] nums, int left, int right) {\n// \u4ee5 nums[left] \u4f5c\u4e3a\u57fa\u51c6\u6570\nint i = left, j = right;\nwhile (i &lt; j) {\nwhile (i &lt; j &amp;&amp; nums[j] &gt;= nums[left])\nj--;          // \u4ece\u53f3\u5411\u5de6\u627e\u9996\u4e2a\u5c0f\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\nwhile (i &lt; j &amp;&amp; nums[i] &lt;= nums[left])\ni++;          // \u4ece\u5de6\u5411\u53f3\u627e\u9996\u4e2a\u5927\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\nswap(nums, i, j); // \u4ea4\u6362\u8fd9\u4e24\u4e2a\u5143\u7d20\n}\nswap(nums, i, left);  // \u5c06\u57fa\u51c6\u6570\u4ea4\u6362\u81f3\u4e24\u5b50\u6570\u7ec4\u7684\u5206\u754c\u7ebf\nreturn i;             // \u8fd4\u56de\u57fa\u51c6\u6570\u7684\u7d22\u5f15\n}\n</code></pre> quick_sort.cpp<pre><code>/* \u5143\u7d20\u4ea4\u6362 */\nvoid swap(vector&lt;int&gt; &amp;nums, int i, int j) {\nint tmp = nums[i];\nnums[i] = nums[j];\nnums[j] = tmp;\n}\n/* \u54e8\u5175\u5212\u5206 */\nint partition(vector&lt;int&gt; &amp;nums, int left, int right) {\n// \u4ee5 nums[left] \u4f5c\u4e3a\u57fa\u51c6\u6570\nint i = left, j = right;\nwhile (i &lt; j) {\nwhile (i &lt; j &amp;&amp; nums[j] &gt;= nums[left])\nj--; // \u4ece\u53f3\u5411\u5de6\u627e\u9996\u4e2a\u5c0f\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\nwhile (i &lt; j &amp;&amp; nums[i] &lt;= nums[left])\ni++;          // \u4ece\u5de6\u5411\u53f3\u627e\u9996\u4e2a\u5927\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\nswap(nums, i, j); // \u4ea4\u6362\u8fd9\u4e24\u4e2a\u5143\u7d20\n}\nswap(nums, i, left); // \u5c06\u57fa\u51c6\u6570\u4ea4\u6362\u81f3\u4e24\u5b50\u6570\u7ec4\u7684\u5206\u754c\u7ebf\nreturn i;            // \u8fd4\u56de\u57fa\u51c6\u6570\u7684\u7d22\u5f15\n}\n</code></pre> quick_sort.py<pre><code>def partition(self, nums: list[int], left: int, right: int) -&gt; int:\n\"\"\"\u54e8\u5175\u5212\u5206\"\"\"\n# \u4ee5 nums[left] \u4f5c\u4e3a\u57fa\u51c6\u6570\ni, j = left, right\nwhile i &lt; j:\nwhile i &lt; j and nums[j] &gt;= nums[left]:\nj -= 1  # \u4ece\u53f3\u5411\u5de6\u627e\u9996\u4e2a\u5c0f\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\nwhile i &lt; j and nums[i] &lt;= nums[left]:\ni += 1  # \u4ece\u5de6\u5411\u53f3\u627e\u9996\u4e2a\u5927\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\n# \u5143\u7d20\u4ea4\u6362\nnums[i], nums[j] = nums[j], nums[i]\n# \u5c06\u57fa\u51c6\u6570\u4ea4\u6362\u81f3\u4e24\u5b50\u6570\u7ec4\u7684\u5206\u754c\u7ebf\nnums[i], nums[left] = nums[left], nums[i]\nreturn i  # \u8fd4\u56de\u57fa\u51c6\u6570\u7684\u7d22\u5f15\n</code></pre> quick_sort.go<pre><code>/* \u54e8\u5175\u5212\u5206 */\nfunc (q *quickSort) partition(nums []int, left, right int) int {\n// \u4ee5 nums[left] \u4f5c\u4e3a\u57fa\u51c6\u6570\ni, j := left, right\nfor i &lt; j {\nfor i &lt; j &amp;&amp; nums[j] &gt;= nums[left] {\nj-- // \u4ece\u53f3\u5411\u5de6\u627e\u9996\u4e2a\u5c0f\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\n}\nfor i &lt; j &amp;&amp; nums[i] &lt;= nums[left] {\ni++ // \u4ece\u5de6\u5411\u53f3\u627e\u9996\u4e2a\u5927\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\n}\n// \u5143\u7d20\u4ea4\u6362\nnums[i], nums[j] = nums[j], nums[i]\n}\n// \u5c06\u57fa\u51c6\u6570\u4ea4\u6362\u81f3\u4e24\u5b50\u6570\u7ec4\u7684\u5206\u754c\u7ebf\nnums[i], nums[left] = nums[left], nums[i]\nreturn i // \u8fd4\u56de\u57fa\u51c6\u6570\u7684\u7d22\u5f15\n}\n</code></pre> quick_sort.js<pre><code>/* \u5143\u7d20\u4ea4\u6362 */\nswap(nums, i, j) {\nlet tmp = nums[i];\nnums[i] = nums[j];\nnums[j] = tmp;\n}\n/* \u54e8\u5175\u5212\u5206 */\npartition(nums, left, right) {\n// \u4ee5 nums[left] \u4f5c\u4e3a\u57fa\u51c6\u6570\nlet i = left,\nj = right;\nwhile (i &lt; j) {\nwhile (i &lt; j &amp;&amp; nums[j] &gt;= nums[left]) {\nj -= 1; // \u4ece\u53f3\u5411\u5de6\u627e\u9996\u4e2a\u5c0f\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\n}\nwhile (i &lt; j &amp;&amp; nums[i] &lt;= nums[left]) {\ni += 1; // \u4ece\u5de6\u5411\u53f3\u627e\u9996\u4e2a\u5927\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\n}\n// \u5143\u7d20\u4ea4\u6362\nthis.swap(nums, i, j); // \u4ea4\u6362\u8fd9\u4e24\u4e2a\u5143\u7d20\n}\nthis.swap(nums, i, left); // \u5c06\u57fa\u51c6\u6570\u4ea4\u6362\u81f3\u4e24\u5b50\u6570\u7ec4\u7684\u5206\u754c\u7ebf\nreturn i; // \u8fd4\u56de\u57fa\u51c6\u6570\u7684\u7d22\u5f15\n}\n</code></pre> quick_sort.ts<pre><code>/* \u5143\u7d20\u4ea4\u6362 */\nswap(nums: number[], i: number, j: number): void {\nlet tmp = nums[i];\nnums[i] = nums[j];\nnums[j] = tmp;\n}\n/* \u54e8\u5175\u5212\u5206 */\npartition(nums: number[], left: number, right: number): number {\n// \u4ee5 nums[left] \u4f5c\u4e3a\u57fa\u51c6\u6570\nlet i = left,\nj = right;\nwhile (i &lt; j) {\nwhile (i &lt; j &amp;&amp; nums[j] &gt;= nums[left]) {\nj -= 1; // \u4ece\u53f3\u5411\u5de6\u627e\u9996\u4e2a\u5c0f\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\n}\nwhile (i &lt; j &amp;&amp; nums[i] &lt;= nums[left]) {\ni += 1; // \u4ece\u5de6\u5411\u53f3\u627e\u9996\u4e2a\u5927\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\n}\n// \u5143\u7d20\u4ea4\u6362\nthis.swap(nums, i, j); // \u4ea4\u6362\u8fd9\u4e24\u4e2a\u5143\u7d20\n}\nthis.swap(nums, i, left); // \u5c06\u57fa\u51c6\u6570\u4ea4\u6362\u81f3\u4e24\u5b50\u6570\u7ec4\u7684\u5206\u754c\u7ebf\nreturn i; // \u8fd4\u56de\u57fa\u51c6\u6570\u7684\u7d22\u5f15\n}\n</code></pre> quick_sort.c<pre><code>/* \u5143\u7d20\u4ea4\u6362 */\nvoid swap(int nums[], int i, int j) {\nint tmp = nums[i];\nnums[i] = nums[j];\nnums[j] = tmp;\n}\n/* \u5feb\u901f\u6392\u5e8f\u7c7b */\n// \u5feb\u901f\u6392\u5e8f\u7c7b-\u54e8\u5175\u5212\u5206\nint partition(int nums[], int left, int right) {\n// \u4ee5 nums[left] \u4f5c\u4e3a\u57fa\u51c6\u6570\nint i = left, j = right;\nwhile (i &lt; j) {\nwhile (i &lt; j &amp;&amp; nums[j] &gt;= nums[left]) {\n// \u4ece\u53f3\u5411\u5de6\u627e\u9996\u4e2a\u5c0f\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\nj--;\n}\nwhile (i &lt; j &amp;&amp; nums[i] &lt;= nums[left]) {\n// \u4ece\u5de6\u5411\u53f3\u627e\u9996\u4e2a\u5927\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\ni++;\n}\n// \u4ea4\u6362\u8fd9\u4e24\u4e2a\u5143\u7d20\nswap(nums, i, j);\n}\n// \u5c06\u57fa\u51c6\u6570\u4ea4\u6362\u81f3\u4e24\u5b50\u6570\u7ec4\u7684\u5206\u754c\u7ebf\nswap(nums, i, left);\n// \u8fd4\u56de\u57fa\u51c6\u6570\u7684\u7d22\u5f15\nreturn i;\n}\n</code></pre> quick_sort.cs<pre><code>/* \u5143\u7d20\u4ea4\u6362 */\nvoid swap(int[] nums, int i, int j) {\nint tmp = nums[i];\nnums[i] = nums[j];\nnums[j] = tmp;\n}\n/* \u54e8\u5175\u5212\u5206 */\nint partition(int[] nums, int left, int right) {\n// \u4ee5 nums[left] \u4f5c\u4e3a\u57fa\u51c6\u6570\nint i = left, j = right;\nwhile (i &lt; j) {\nwhile (i &lt; j &amp;&amp; nums[j] &gt;= nums[left])\nj--;          // \u4ece\u53f3\u5411\u5de6\u627e\u9996\u4e2a\u5c0f\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\nwhile (i &lt; j &amp;&amp; nums[i] &lt;= nums[left])\ni++;          // \u4ece\u5de6\u5411\u53f3\u627e\u9996\u4e2a\u5927\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\nswap(nums, i, j); // \u4ea4\u6362\u8fd9\u4e24\u4e2a\u5143\u7d20\n}\nswap(nums, i, left);  // \u5c06\u57fa\u51c6\u6570\u4ea4\u6362\u81f3\u4e24\u5b50\u6570\u7ec4\u7684\u5206\u754c\u7ebf\nreturn i;             // \u8fd4\u56de\u57fa\u51c6\u6570\u7684\u7d22\u5f15\n}\n</code></pre> quick_sort.swift<pre><code>/* \u5143\u7d20\u4ea4\u6362 */\nfunc swap(nums: inout [Int], i: Int, j: Int) {\nlet tmp = nums[i]\nnums[i] = nums[j]\nnums[j] = tmp\n}\n/* \u54e8\u5175\u5212\u5206 */\nfunc partition(nums: inout [Int], left: Int, right: Int) -&gt; Int {\n// \u4ee5 nums[left] \u4f5c\u4e3a\u57fa\u51c6\u6570\nvar i = left\nvar j = right\nwhile i &lt; j {\nwhile i &lt; j, nums[j] &gt;= nums[left] {\nj -= 1 // \u4ece\u53f3\u5411\u5de6\u627e\u9996\u4e2a\u5c0f\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\n}\nwhile i &lt; j, nums[i] &lt;= nums[left] {\ni += 1 // \u4ece\u5de6\u5411\u53f3\u627e\u9996\u4e2a\u5927\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\n}\nswap(nums: &amp;nums, i: i, j: j) // \u4ea4\u6362\u8fd9\u4e24\u4e2a\u5143\u7d20\n}\nswap(nums: &amp;nums, i: i, j: left) // \u5c06\u57fa\u51c6\u6570\u4ea4\u6362\u81f3\u4e24\u5b50\u6570\u7ec4\u7684\u5206\u754c\u7ebf\nreturn i // \u8fd4\u56de\u57fa\u51c6\u6570\u7684\u7d22\u5f15\n}\n</code></pre> quick_sort.zig<pre><code>// \u5143\u7d20\u4ea4\u6362\nfn swap(nums: []i32, i: usize, j: usize) void {\nvar tmp = nums[i];\nnums[i] = nums[j];\nnums[j] = tmp;\n}\n// \u54e8\u5175\u5212\u5206\nfn partition(nums: []i32, left: usize, right: usize) usize {\n// \u4ee5 nums[left] \u4f5c\u4e3a\u57fa\u51c6\u6570\nvar i = left;\nvar j = right;\nwhile (i &lt; j) {\nwhile (i &lt; j and nums[j] &gt;= nums[left]) j -= 1; // \u4ece\u53f3\u5411\u5de6\u627e\u9996\u4e2a\u5c0f\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\nwhile (i &lt; j and nums[i] &lt;= nums[left]) i += 1; // \u4ece\u5de6\u5411\u53f3\u627e\u9996\u4e2a\u5927\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\nswap(nums, i, j);   // \u4ea4\u6362\u8fd9\u4e24\u4e2a\u5143\u7d20\n}\nswap(nums, i, left);    // \u5c06\u57fa\u51c6\u6570\u4ea4\u6362\u81f3\u4e24\u5b50\u6570\u7ec4\u7684\u5206\u754c\u7ebf\nreturn i;               // \u8fd4\u56de\u57fa\u51c6\u6570\u7684\u7d22\u5f15\n}\n</code></pre> quick_sort.dart<pre><code>/* \u5143\u7d20\u4ea4\u6362 */\nvoid _swap(List&lt;int&gt; nums, int i, int j) {\nint tmp = nums[i];\nnums[i] = nums[j];\nnums[j] = tmp;\n}\n/* \u54e8\u5175\u5212\u5206 */\nint _partition(List&lt;int&gt; nums, int left, int right) {\n// \u4ee5 nums[left] \u4f5c\u4e3a\u57fa\u51c6\u6570\nint i = left, j = right;\nwhile (i &lt; j) {\nwhile (i &lt; j &amp;&amp; nums[j] &gt;= nums[left]) j--; // \u4ece\u53f3\u5411\u5de6\u627e\u9996\u4e2a\u5c0f\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\nwhile (i &lt; j &amp;&amp; nums[i] &lt;= nums[left]) i++; // \u4ece\u5de6\u5411\u53f3\u627e\u9996\u4e2a\u5927\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\n_swap(nums, i, j); // \u4ea4\u6362\u8fd9\u4e24\u4e2a\u5143\u7d20\n}\n_swap(nums, i, left); // \u5c06\u57fa\u51c6\u6570\u4ea4\u6362\u81f3\u4e24\u5b50\u6570\u7ec4\u7684\u5206\u754c\u7ebf\nreturn i; // \u8fd4\u56de\u57fa\u51c6\u6570\u7684\u7d22\u5f15\n}\n</code></pre>"},{"location":"chapter_sorting/quick_sort/#1151","title":"11.5.1. \u00a0 \u7b97\u6cd5\u6d41\u7a0b","text":"<ol> <li>\u9996\u5148\uff0c\u5bf9\u539f\u6570\u7ec4\u6267\u884c\u4e00\u6b21\u300c\u54e8\u5175\u5212\u5206\u300d\uff0c\u5f97\u5230\u672a\u6392\u5e8f\u7684\u5de6\u5b50\u6570\u7ec4\u548c\u53f3\u5b50\u6570\u7ec4\uff1b</li> <li>\u7136\u540e\uff0c\u5bf9\u5de6\u5b50\u6570\u7ec4\u548c\u53f3\u5b50\u6570\u7ec4\u5206\u522b\u9012\u5f52\u6267\u884c\u300c\u54e8\u5175\u5212\u5206\u300d\uff1b</li> <li>\u6301\u7eed\u9012\u5f52\uff0c\u76f4\u81f3\u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a 1 \u65f6\u7ec8\u6b62\uff0c\u4ece\u800c\u5b8c\u6210\u6574\u4e2a\u6570\u7ec4\u7684\u6392\u5e8f\uff1b</li> </ol> <p> Fig. \u5feb\u901f\u6392\u5e8f\u6d41\u7a0b </p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart quick_sort.java<pre><code>/* \u5feb\u901f\u6392\u5e8f */\nvoid quickSort(int[] nums, int left, int right) {\n// \u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a 1 \u65f6\u7ec8\u6b62\u9012\u5f52\nif (left &gt;= right)\nreturn;\n// \u54e8\u5175\u5212\u5206\nint pivot = partition(nums, left, right);\n// \u9012\u5f52\u5de6\u5b50\u6570\u7ec4\u3001\u53f3\u5b50\u6570\u7ec4\nquickSort(nums, left, pivot - 1);\nquickSort(nums, pivot + 1, right);\n}\n</code></pre> quick_sort.cpp<pre><code>/* \u5feb\u901f\u6392\u5e8f */\nvoid quickSort(vector&lt;int&gt; &amp;nums, int left, int right) {\n// \u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a 1 \u65f6\u7ec8\u6b62\u9012\u5f52\nif (left &gt;= right)\nreturn;\n// \u54e8\u5175\u5212\u5206\nint pivot = partition(nums, left, right);\n// \u9012\u5f52\u5de6\u5b50\u6570\u7ec4\u3001\u53f3\u5b50\u6570\u7ec4\nquickSort(nums, left, pivot - 1);\nquickSort(nums, pivot + 1, right);\n}\n</code></pre> quick_sort.py<pre><code>def quick_sort(self, nums: list[int], left: int, right: int) -&gt; None:\n\"\"\"\u5feb\u901f\u6392\u5e8f\"\"\"\n# \u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a 1 \u65f6\u7ec8\u6b62\u9012\u5f52\nif left &gt;= right:\nreturn\n# \u54e8\u5175\u5212\u5206\npivot = self.partition(nums, left, right)\n# \u9012\u5f52\u5de6\u5b50\u6570\u7ec4\u3001\u53f3\u5b50\u6570\u7ec4\nself.quick_sort(nums, left, pivot - 1)\nself.quick_sort(nums, pivot + 1, right)\n</code></pre> quick_sort.go<pre><code>/* \u5feb\u901f\u6392\u5e8f */\nfunc (q *quickSort) quickSort(nums []int, left, right int) {\n// \u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a 1 \u65f6\u7ec8\u6b62\u9012\u5f52\nif left &gt;= right {\nreturn\n}\n// \u54e8\u5175\u5212\u5206\npivot := q.partition(nums, left, right)\n// \u9012\u5f52\u5de6\u5b50\u6570\u7ec4\u3001\u53f3\u5b50\u6570\u7ec4\nq.quickSort(nums, left, pivot-1)\nq.quickSort(nums, pivot+1, right)\n}\n</code></pre> quick_sort.js<pre><code>/* \u5feb\u901f\u6392\u5e8f */\nquickSort(nums, left, right) {\n// \u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a 1 \u65f6\u7ec8\u6b62\u9012\u5f52\nif (left &gt;= right) return;\n// \u54e8\u5175\u5212\u5206\nconst pivot = this.partition(nums, left, right);\n// \u9012\u5f52\u5de6\u5b50\u6570\u7ec4\u3001\u53f3\u5b50\u6570\u7ec4\nthis.quickSort(nums, left, pivot - 1);\nthis.quickSort(nums, pivot + 1, right);\n}\n</code></pre> quick_sort.ts<pre><code>/* \u5feb\u901f\u6392\u5e8f */\nquickSort(nums: number[], left: number, right: number): void {\n// \u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a 1 \u65f6\u7ec8\u6b62\u9012\u5f52\nif (left &gt;= right) {\nreturn;\n}\n// \u54e8\u5175\u5212\u5206\nconst pivot = this.partition(nums, left, right);\n// \u9012\u5f52\u5de6\u5b50\u6570\u7ec4\u3001\u53f3\u5b50\u6570\u7ec4\nthis.quickSort(nums, left, pivot - 1);\nthis.quickSort(nums, pivot + 1, right);\n}\n</code></pre> quick_sort.c<pre><code>/* \u5feb\u901f\u6392\u5e8f\u7c7b */\n// \u5feb\u901f\u6392\u5e8f\u7c7b-\u54e8\u5175\u5212\u5206\nint partition(int nums[], int left, int right) {\n// \u4ee5 nums[left] \u4f5c\u4e3a\u57fa\u51c6\u6570\nint i = left, j = right;\nwhile (i &lt; j) {\nwhile (i &lt; j &amp;&amp; nums[j] &gt;= nums[left]) {\n// \u4ece\u53f3\u5411\u5de6\u627e\u9996\u4e2a\u5c0f\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\nj--;\n}\nwhile (i &lt; j &amp;&amp; nums[i] &lt;= nums[left]) {\n// \u4ece\u5de6\u5411\u53f3\u627e\u9996\u4e2a\u5927\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\ni++;\n}\n// \u4ea4\u6362\u8fd9\u4e24\u4e2a\u5143\u7d20\nswap(nums, i, j);\n}\n// \u5c06\u57fa\u51c6\u6570\u4ea4\u6362\u81f3\u4e24\u5b50\u6570\u7ec4\u7684\u5206\u754c\u7ebf\nswap(nums, i, left);\n// \u8fd4\u56de\u57fa\u51c6\u6570\u7684\u7d22\u5f15\nreturn i;\n}\n// \u5feb\u901f\u6392\u5e8f\u7c7b-\u5feb\u901f\u6392\u5e8f\nvoid quickSort(int nums[], int left, int right) {\n// \u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a 1 \u65f6\u7ec8\u6b62\u9012\u5f52\nif (left &gt;= right) {\nreturn;\n}\n// \u54e8\u5175\u5212\u5206\nint pivot = partition(nums, left, right);\n// \u9012\u5f52\u5de6\u5b50\u6570\u7ec4\u3001\u53f3\u5b50\u6570\u7ec4\nquickSort(nums, left, pivot - 1);\nquickSort(nums, pivot + 1, right);\n}\n</code></pre> quick_sort.cs<pre><code>/* \u5feb\u901f\u6392\u5e8f */\nvoid quickSort(int[] nums, int left, int right) {\n// \u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a 1 \u65f6\u7ec8\u6b62\u9012\u5f52\nif (left &gt;= right)\nreturn;\n// \u54e8\u5175\u5212\u5206\nint pivot = partition(nums, left, right);\n// \u9012\u5f52\u5de6\u5b50\u6570\u7ec4\u3001\u53f3\u5b50\u6570\u7ec4\nquickSort(nums, left, pivot - 1);\nquickSort(nums, pivot + 1, right);\n}\n</code></pre> quick_sort.swift<pre><code>/* \u5feb\u901f\u6392\u5e8f */\nfunc quickSort(nums: inout [Int], left: Int, right: Int) {\n// \u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a 1 \u65f6\u7ec8\u6b62\u9012\u5f52\nif left &gt;= right {\nreturn\n}\n// \u54e8\u5175\u5212\u5206\nlet pivot = partition(nums: &amp;nums, left: left, right: right)\n// \u9012\u5f52\u5de6\u5b50\u6570\u7ec4\u3001\u53f3\u5b50\u6570\u7ec4\nquickSort(nums: &amp;nums, left: left, right: pivot - 1)\nquickSort(nums: &amp;nums, left: pivot + 1, right: right)\n}\n</code></pre> quick_sort.zig<pre><code>// \u5feb\u901f\u6392\u5e8f\nfn quickSort(nums: []i32, left: usize, right: usize) void {\n// \u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a 1 \u65f6\u7ec8\u6b62\u9012\u5f52\nif (left &gt;= right) return;\n// \u54e8\u5175\u5212\u5206\nvar pivot = partition(nums, left, right);\n// \u9012\u5f52\u5de6\u5b50\u6570\u7ec4\u3001\u53f3\u5b50\u6570\u7ec4\nquickSort(nums, left, pivot - 1);\nquickSort(nums, pivot + 1, right);\n}\n</code></pre> quick_sort.dart<pre><code>/* \u5feb\u901f\u6392\u5e8f */\nvoid quickSort(List&lt;int&gt; nums, int left, int right) {\n// \u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a 1 \u65f6\u7ec8\u6b62\u9012\u5f52\nif (left &gt;= right) return;\n// \u54e8\u5175\u5212\u5206\nint pivot = _partition(nums, left, right);\n// \u9012\u5f52\u5de6\u5b50\u6570\u7ec4\u3001\u53f3\u5b50\u6570\u7ec4\nquickSort(nums, left, pivot - 1);\nquickSort(nums, pivot + 1, right);\n}\n</code></pre>"},{"location":"chapter_sorting/quick_sort/#1152","title":"11.5.2. \u00a0 \u7b97\u6cd5\u7279\u6027","text":"<ul> <li>\u65f6\u95f4\u590d\u6742\u5ea6 \\(O(n \\log n)\\) \u3001\u81ea\u9002\u5e94\u6392\u5e8f \uff1a\u5728\u5e73\u5747\u60c5\u51b5\u4e0b\uff0c\u54e8\u5175\u5212\u5206\u7684\u9012\u5f52\u5c42\u6570\u4e3a \\(\\log n\\) \uff0c\u6bcf\u5c42\u4e2d\u7684\u603b\u5faa\u73af\u6570\u4e3a \\(n\\) \uff0c\u603b\u4f53\u4f7f\u7528 \\(O(n \\log n)\\) \u65f6\u95f4\u3002\u5728\u6700\u5dee\u60c5\u51b5\u4e0b\uff0c\u6bcf\u8f6e\u54e8\u5175\u5212\u5206\u64cd\u4f5c\u90fd\u5c06\u957f\u5ea6\u4e3a \\(n\\) \u7684\u6570\u7ec4\u5212\u5206\u4e3a\u957f\u5ea6\u4e3a \\(0\\) \u548c \\(n - 1\\) \u7684\u4e24\u4e2a\u5b50\u6570\u7ec4\uff0c\u6b64\u65f6\u9012\u5f52\u5c42\u6570\u8fbe\u5230 \\(n\\) \u5c42\uff0c\u6bcf\u5c42\u4e2d\u7684\u5faa\u73af\u6570\u4e3a \\(n\\) \uff0c\u603b\u4f53\u4f7f\u7528 \\(O(n^2)\\) \u65f6\u95f4\u3002</li> <li>\u7a7a\u95f4\u590d\u6742\u5ea6 \\(O(n)\\) \u3001\u539f\u5730\u6392\u5e8f \uff1a\u5728\u8f93\u5165\u6570\u7ec4\u5b8c\u5168\u5012\u5e8f\u7684\u60c5\u51b5\u4e0b\uff0c\u8fbe\u5230\u6700\u5dee\u9012\u5f52\u6df1\u5ea6 \\(n\\) \uff0c\u4f7f\u7528 \\(O(n)\\) \u6808\u5e27\u7a7a\u95f4\u3002\u6392\u5e8f\u64cd\u4f5c\u662f\u5728\u539f\u6570\u7ec4\u4e0a\u8fdb\u884c\u7684\uff0c\u672a\u501f\u52a9\u989d\u5916\u6570\u7ec4\u3002</li> <li>\u975e\u7a33\u5b9a\u6392\u5e8f\uff1a\u5728\u54e8\u5175\u5212\u5206\u7684\u6700\u540e\u4e00\u6b65\uff0c\u57fa\u51c6\u6570\u53ef\u80fd\u4f1a\u88ab\u4ea4\u6362\u81f3\u76f8\u7b49\u5143\u7d20\u7684\u53f3\u4fa7\u3002</li> </ul>"},{"location":"chapter_sorting/quick_sort/#1153","title":"11.5.3. \u00a0 \u5feb\u6392\u4e3a\u4ec0\u4e48\u5feb\uff1f","text":"<p>\u4ece\u540d\u79f0\u4e0a\u5c31\u80fd\u770b\u51fa\uff0c\u5feb\u901f\u6392\u5e8f\u5728\u6548\u7387\u65b9\u9762\u5e94\u8be5\u5177\u6709\u4e00\u5b9a\u7684\u4f18\u52bf\u3002\u5c3d\u7ba1\u5feb\u901f\u6392\u5e8f\u7684\u5e73\u5747\u65f6\u95f4\u590d\u6742\u5ea6\u4e0e\u300c\u5f52\u5e76\u6392\u5e8f\u300d\u548c\u300c\u5806\u6392\u5e8f\u300d\u76f8\u540c\uff0c\u4f46\u901a\u5e38\u5feb\u901f\u6392\u5e8f\u7684\u6548\u7387\u66f4\u9ad8\uff0c\u539f\u56e0\u5982\u4e0b\uff1a</p> <ul> <li>\u51fa\u73b0\u6700\u5dee\u60c5\u51b5\u7684\u6982\u7387\u5f88\u4f4e\uff1a\u867d\u7136\u5feb\u901f\u6392\u5e8f\u7684\u6700\u5dee\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(n^2)\\) \uff0c\u6ca1\u6709\u5f52\u5e76\u6392\u5e8f\u7a33\u5b9a\uff0c\u4f46\u5728\u7edd\u5927\u591a\u6570\u60c5\u51b5\u4e0b\uff0c\u5feb\u901f\u6392\u5e8f\u80fd\u5728 \\(O(n \\log n)\\) \u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e0b\u8fd0\u884c\u3002</li> <li>\u7f13\u5b58\u4f7f\u7528\u6548\u7387\u9ad8\uff1a\u5728\u6267\u884c\u54e8\u5175\u5212\u5206\u64cd\u4f5c\u65f6\uff0c\u7cfb\u7edf\u53ef\u5c06\u6574\u4e2a\u5b50\u6570\u7ec4\u52a0\u8f7d\u5230\u7f13\u5b58\uff0c\u56e0\u6b64\u8bbf\u95ee\u5143\u7d20\u7684\u6548\u7387\u8f83\u9ad8\u3002\u800c\u50cf\u300c\u5806\u6392\u5e8f\u300d\u8fd9\u7c7b\u7b97\u6cd5\u9700\u8981\u8df3\u8dc3\u5f0f\u8bbf\u95ee\u5143\u7d20\uff0c\u4ece\u800c\u7f3a\u4e4f\u8fd9\u4e00\u7279\u6027\u3002</li> <li>\u590d\u6742\u5ea6\u7684\u5e38\u6570\u7cfb\u6570\u4f4e\uff1a\u5728\u4e0a\u8ff0\u4e09\u79cd\u7b97\u6cd5\u4e2d\uff0c\u5feb\u901f\u6392\u5e8f\u7684\u6bd4\u8f83\u3001\u8d4b\u503c\u3001\u4ea4\u6362\u7b49\u64cd\u4f5c\u7684\u603b\u6570\u91cf\u6700\u5c11\u3002\u8fd9\u4e0e\u300c\u63d2\u5165\u6392\u5e8f\u300d\u6bd4\u300c\u5192\u6ce1\u6392\u5e8f\u300d\u66f4\u5feb\u7684\u539f\u56e0\u7c7b\u4f3c\u3002</li> </ul>"},{"location":"chapter_sorting/quick_sort/#1154","title":"11.5.4. \u00a0 \u57fa\u51c6\u6570\u4f18\u5316","text":"<p>\u5feb\u901f\u6392\u5e8f\u5728\u67d0\u4e9b\u8f93\u5165\u4e0b\u7684\u65f6\u95f4\u6548\u7387\u53ef\u80fd\u964d\u4f4e\u3002\u4e3e\u4e00\u4e2a\u6781\u7aef\u4f8b\u5b50\uff0c\u5047\u8bbe\u8f93\u5165\u6570\u7ec4\u662f\u5b8c\u5168\u5012\u5e8f\u7684\uff0c\u7531\u4e8e\u6211\u4eec\u9009\u62e9\u6700\u5de6\u7aef\u5143\u7d20\u4f5c\u4e3a\u57fa\u51c6\u6570\uff0c\u90a3\u4e48\u5728\u54e8\u5175\u5212\u5206\u5b8c\u6210\u540e\uff0c\u57fa\u51c6\u6570\u88ab\u4ea4\u6362\u81f3\u6570\u7ec4\u6700\u53f3\u7aef\uff0c\u5bfc\u81f4\u5de6\u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a \\(n - 1\\) \u3001\u53f3\u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a \\(0\\) \u3002\u5982\u6b64\u9012\u5f52\u4e0b\u53bb\uff0c\u6bcf\u8f6e\u54e8\u5175\u5212\u5206\u540e\u7684\u53f3\u5b50\u6570\u7ec4\u957f\u5ea6\u90fd\u4e3a \\(0\\) \uff0c\u5206\u6cbb\u7b56\u7565\u5931\u6548\uff0c\u5feb\u901f\u6392\u5e8f\u9000\u5316\u4e3a\u300c\u5192\u6ce1\u6392\u5e8f\u300d\u3002</p> <p>\u4e3a\u4e86\u5c3d\u91cf\u907f\u514d\u8fd9\u79cd\u60c5\u51b5\u53d1\u751f\uff0c\u6211\u4eec\u53ef\u4ee5\u4f18\u5316\u54e8\u5175\u5212\u5206\u4e2d\u7684\u57fa\u51c6\u6570\u7684\u9009\u53d6\u7b56\u7565\u3002\u4f8b\u5982\uff0c\u6211\u4eec\u53ef\u4ee5\u968f\u673a\u9009\u53d6\u4e00\u4e2a\u5143\u7d20\u4f5c\u4e3a\u57fa\u51c6\u6570\u3002\u7136\u800c\uff0c\u5982\u679c\u8fd0\u6c14\u4e0d\u4f73\uff0c\u6bcf\u6b21\u90fd\u9009\u5230\u4e0d\u7406\u60f3\u7684\u57fa\u51c6\u6570\uff0c\u6548\u7387\u4ecd\u7136\u4e0d\u5c3d\u5982\u4eba\u610f\u3002</p> <p>\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u7f16\u7a0b\u8bed\u8a00\u901a\u5e38\u751f\u6210\u7684\u662f\u201c\u4f2a\u968f\u673a\u6570\u201d\u3002\u5982\u679c\u6211\u4eec\u9488\u5bf9\u4f2a\u968f\u673a\u6570\u5e8f\u5217\u6784\u5efa\u4e00\u4e2a\u7279\u5b9a\u7684\u6d4b\u8bd5\u6837\u4f8b\uff0c\u90a3\u4e48\u5feb\u901f\u6392\u5e8f\u7684\u6548\u7387\u4ecd\u7136\u53ef\u80fd\u52a3\u5316\u3002</p> <p>\u4e3a\u4e86\u8fdb\u4e00\u6b65\u6539\u8fdb\uff0c\u6211\u4eec\u53ef\u4ee5\u5728\u6570\u7ec4\u4e2d\u9009\u53d6\u4e09\u4e2a\u5019\u9009\u5143\u7d20\uff08\u901a\u5e38\u4e3a\u6570\u7ec4\u7684\u9996\u3001\u5c3e\u3001\u4e2d\u70b9\u5143\u7d20\uff09\uff0c\u5e76\u5c06\u8fd9\u4e09\u4e2a\u5019\u9009\u5143\u7d20\u7684\u4e2d\u4f4d\u6570\u4f5c\u4e3a\u57fa\u51c6\u6570\u3002\u8fd9\u6837\u4e00\u6765\uff0c\u57fa\u51c6\u6570\u201c\u65e2\u4e0d\u592a\u5c0f\u4e5f\u4e0d\u592a\u5927\u201d\u7684\u6982\u7387\u5c06\u5927\u5e45\u63d0\u5347\u3002\u5f53\u7136\uff0c\u6211\u4eec\u8fd8\u53ef\u4ee5\u9009\u53d6\u66f4\u591a\u5019\u9009\u5143\u7d20\uff0c\u4ee5\u8fdb\u4e00\u6b65\u63d0\u9ad8\u7b97\u6cd5\u7684\u7a33\u5065\u6027\u3002\u91c7\u7528\u8fd9\u79cd\u65b9\u6cd5\u540e\uff0c\u65f6\u95f4\u590d\u6742\u5ea6\u52a3\u5316\u81f3 \\(O(n^2)\\) \u7684\u6982\u7387\u5927\u5927\u964d\u4f4e\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart quick_sort.java<pre><code>/* \u9009\u53d6\u4e09\u4e2a\u5143\u7d20\u7684\u4e2d\u4f4d\u6570 */\nint medianThree(int[] nums, int left, int mid, int right) {\n// \u6b64\u5904\u4f7f\u7528\u5f02\u6216\u8fd0\u7b97\u6765\u7b80\u5316\u4ee3\u7801\n// \u5f02\u6216\u89c4\u5219\u4e3a 0 ^ 0 = 1 ^ 1 = 0, 0 ^ 1 = 1 ^ 0 = 1\nif ((nums[left] &lt; nums[mid]) ^ (nums[left] &lt; nums[right]))\nreturn left;\nelse if ((nums[mid] &lt; nums[left]) ^ (nums[mid] &lt; nums[right]))\nreturn mid;\nelse\nreturn right;\n}\n/* \u54e8\u5175\u5212\u5206\uff08\u4e09\u6570\u53d6\u4e2d\u503c\uff09 */\nint partition(int[] nums, int left, int right) {\n// \u9009\u53d6\u4e09\u4e2a\u5019\u9009\u5143\u7d20\u7684\u4e2d\u4f4d\u6570\nint med = medianThree(nums, left, (left + right) / 2, right);\n// \u5c06\u4e2d\u4f4d\u6570\u4ea4\u6362\u81f3\u6570\u7ec4\u6700\u5de6\u7aef\nswap(nums, left, med);\n// \u4ee5 nums[left] \u4f5c\u4e3a\u57fa\u51c6\u6570\nint i = left, j = right;\nwhile (i &lt; j) {\nwhile (i &lt; j &amp;&amp; nums[j] &gt;= nums[left])\nj--;          // \u4ece\u53f3\u5411\u5de6\u627e\u9996\u4e2a\u5c0f\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\nwhile (i &lt; j &amp;&amp; nums[i] &lt;= nums[left])\ni++;          // \u4ece\u5de6\u5411\u53f3\u627e\u9996\u4e2a\u5927\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\nswap(nums, i, j); // \u4ea4\u6362\u8fd9\u4e24\u4e2a\u5143\u7d20\n}\nswap(nums, i, left);  // \u5c06\u57fa\u51c6\u6570\u4ea4\u6362\u81f3\u4e24\u5b50\u6570\u7ec4\u7684\u5206\u754c\u7ebf\nreturn i;             // \u8fd4\u56de\u57fa\u51c6\u6570\u7684\u7d22\u5f15\n}\n</code></pre> quick_sort.cpp<pre><code>/* \u9009\u53d6\u4e09\u4e2a\u5143\u7d20\u7684\u4e2d\u4f4d\u6570 */\nint medianThree(vector&lt;int&gt; &amp;nums, int left, int mid, int right) {\n// \u6b64\u5904\u4f7f\u7528\u5f02\u6216\u8fd0\u7b97\u6765\u7b80\u5316\u4ee3\u7801\n// \u5f02\u6216\u89c4\u5219\u4e3a 0 ^ 0 = 1 ^ 1 = 0, 0 ^ 1 = 1 ^ 0 = 1\nif ((nums[left] &lt; nums[mid]) ^ (nums[left] &lt; nums[right]))\nreturn left;\nelse if ((nums[mid] &lt; nums[left]) ^ (nums[mid] &lt; nums[right]))\nreturn mid;\nelse\nreturn right;\n}\n/* \u54e8\u5175\u5212\u5206\uff08\u4e09\u6570\u53d6\u4e2d\u503c\uff09 */\nint partition(vector&lt;int&gt; &amp;nums, int left, int right) {\n// \u9009\u53d6\u4e09\u4e2a\u5019\u9009\u5143\u7d20\u7684\u4e2d\u4f4d\u6570\nint med = medianThree(nums, left, (left + right) / 2, right);\n// \u5c06\u4e2d\u4f4d\u6570\u4ea4\u6362\u81f3\u6570\u7ec4\u6700\u5de6\u7aef\nswap(nums, left, med);\n// \u4ee5 nums[left] \u4f5c\u4e3a\u57fa\u51c6\u6570\nint i = left, j = right;\nwhile (i &lt; j) {\nwhile (i &lt; j &amp;&amp; nums[j] &gt;= nums[left])\nj--; // \u4ece\u53f3\u5411\u5de6\u627e\u9996\u4e2a\u5c0f\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\nwhile (i &lt; j &amp;&amp; nums[i] &lt;= nums[left])\ni++;          // \u4ece\u5de6\u5411\u53f3\u627e\u9996\u4e2a\u5927\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\nswap(nums, i, j); // \u4ea4\u6362\u8fd9\u4e24\u4e2a\u5143\u7d20\n}\nswap(nums, i, left); // \u5c06\u57fa\u51c6\u6570\u4ea4\u6362\u81f3\u4e24\u5b50\u6570\u7ec4\u7684\u5206\u754c\u7ebf\nreturn i;            // \u8fd4\u56de\u57fa\u51c6\u6570\u7684\u7d22\u5f15\n}\n</code></pre> quick_sort.py<pre><code>def median_three(self, nums: list[int], left: int, mid: int, right: int) -&gt; int:\n\"\"\"\u9009\u53d6\u4e09\u4e2a\u5143\u7d20\u7684\u4e2d\u4f4d\u6570\"\"\"\n# \u6b64\u5904\u4f7f\u7528\u5f02\u6216\u8fd0\u7b97\u6765\u7b80\u5316\u4ee3\u7801\n# \u5f02\u6216\u89c4\u5219\u4e3a 0 ^ 0 = 1 ^ 1 = 0, 0 ^ 1 = 1 ^ 0 = 1\nif (nums[left] &lt; nums[mid]) ^ (nums[left] &lt; nums[right]):\nreturn left\nelif (nums[mid] &lt; nums[left]) ^ (nums[mid] &lt; nums[right]):\nreturn mid\nreturn right\ndef partition(self, nums: list[int], left: int, right: int) -&gt; int:\n\"\"\"\u54e8\u5175\u5212\u5206\uff08\u4e09\u6570\u53d6\u4e2d\u503c\uff09\"\"\"\n# \u4ee5 nums[left] \u4f5c\u4e3a\u57fa\u51c6\u6570\nmed = self.median_three(nums, left, (left + right) // 2, right)\n# \u5c06\u4e2d\u4f4d\u6570\u4ea4\u6362\u81f3\u6570\u7ec4\u6700\u5de6\u7aef\nnums[left], nums[med] = nums[med], nums[left]\n# \u4ee5 nums[left] \u4f5c\u4e3a\u57fa\u51c6\u6570\ni, j = left, right\nwhile i &lt; j:\nwhile i &lt; j and nums[j] &gt;= nums[left]:\nj -= 1  # \u4ece\u53f3\u5411\u5de6\u627e\u9996\u4e2a\u5c0f\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\nwhile i &lt; j and nums[i] &lt;= nums[left]:\ni += 1  # \u4ece\u5de6\u5411\u53f3\u627e\u9996\u4e2a\u5927\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\n# \u5143\u7d20\u4ea4\u6362\nnums[i], nums[j] = nums[j], nums[i]\n# \u5c06\u57fa\u51c6\u6570\u4ea4\u6362\u81f3\u4e24\u5b50\u6570\u7ec4\u7684\u5206\u754c\u7ebf\nnums[i], nums[left] = nums[left], nums[i]\nreturn i  # \u8fd4\u56de\u57fa\u51c6\u6570\u7684\u7d22\u5f15\n</code></pre> quick_sort.go<pre><code>/* \u9009\u53d6\u4e09\u4e2a\u5143\u7d20\u7684\u4e2d\u4f4d\u6570 */\nfunc (q *quickSortMedian) medianThree(nums []int, left, mid, right int) int {\n// \u6b64\u5904\u4f7f\u7528\u5f02\u6216\u8fd0\u7b97\u6765\u7b80\u5316\u4ee3\u7801\uff08!= \u5728\u8fd9\u91cc\u8d77\u5230\u5f02\u6216\u7684\u4f5c\u7528\uff09\n// \u5f02\u6216\u89c4\u5219\u4e3a 0 ^ 0 = 1 ^ 1 = 0, 0 ^ 1 = 1 ^ 0 = 1\nif (nums[left] &lt; nums[mid]) != (nums[left] &lt; nums[right]) {\nreturn left\n} else if (nums[mid] &lt; nums[left]) != (nums[mid] &lt; nums[right]) {\nreturn mid\n}\nreturn right\n}\n/* \u54e8\u5175\u5212\u5206\uff08\u4e09\u6570\u53d6\u4e2d\u503c\uff09*/\nfunc (q *quickSortMedian) partition(nums []int, left, right int) int {\n// \u4ee5 nums[left] \u4f5c\u4e3a\u57fa\u51c6\u6570\nmed := q.medianThree(nums, left, (left+right)/2, right)\n// \u5c06\u4e2d\u4f4d\u6570\u4ea4\u6362\u81f3\u6570\u7ec4\u6700\u5de6\u7aef\nnums[left], nums[med] = nums[med], nums[left]\n// \u4ee5 nums[left] \u4f5c\u4e3a\u57fa\u51c6\u6570\ni, j := left, right\nfor i &lt; j {\nfor i &lt; j &amp;&amp; nums[j] &gt;= nums[left] {\nj-- //\u4ece\u53f3\u5411\u5de6\u627e\u9996\u4e2a\u5c0f\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\n}\nfor i &lt; j &amp;&amp; nums[i] &lt;= nums[left] {\ni++ //\u4ece\u5de6\u5411\u53f3\u627e\u9996\u4e2a\u5927\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\n}\n//\u5143\u7d20\u4ea4\u6362\nnums[i], nums[j] = nums[j], nums[i]\n}\n//\u5c06\u57fa\u51c6\u6570\u4ea4\u6362\u81f3\u4e24\u5b50\u6570\u7ec4\u7684\u5206\u754c\u7ebf\nnums[i], nums[left] = nums[left], nums[i]\nreturn i //\u8fd4\u56de\u57fa\u51c6\u6570\u7684\u7d22\u5f15\n}\n</code></pre> quick_sort.js<pre><code>/* \u9009\u53d6\u4e09\u4e2a\u5143\u7d20\u7684\u4e2d\u4f4d\u6570 */\nmedianThree(nums, left, mid, right) {\n// \u6b64\u5904\u4f7f\u7528\u5f02\u6216\u8fd0\u7b97\u6765\u7b80\u5316\u4ee3\u7801\n// \u5f02\u6216\u89c4\u5219\u4e3a 0 ^ 0 = 1 ^ 1 = 0, 0 ^ 1 = 1 ^ 0 = 1\nif ((nums[left] &lt; nums[mid]) ^ (nums[left] &lt; nums[right])) return left;\nelse if ((nums[mid] &lt; nums[left]) ^ (nums[mid] &lt; nums[right]))\nreturn mid;\nelse return right;\n}\n/* \u54e8\u5175\u5212\u5206\uff08\u4e09\u6570\u53d6\u4e2d\u503c\uff09 */\npartition(nums, left, right) {\n// \u9009\u53d6\u4e09\u4e2a\u5019\u9009\u5143\u7d20\u7684\u4e2d\u4f4d\u6570\nlet med = this.medianThree(\nnums,\nleft,\nMath.floor((left + right) / 2),\nright\n);\n// \u5c06\u4e2d\u4f4d\u6570\u4ea4\u6362\u81f3\u6570\u7ec4\u6700\u5de6\u7aef\nthis.swap(nums, left, med);\n// \u4ee5 nums[left] \u4f5c\u4e3a\u57fa\u51c6\u6570\nlet i = left,\nj = right;\nwhile (i &lt; j) {\nwhile (i &lt; j &amp;&amp; nums[j] &gt;= nums[left]) j--; // \u4ece\u53f3\u5411\u5de6\u627e\u9996\u4e2a\u5c0f\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\nwhile (i &lt; j &amp;&amp; nums[i] &lt;= nums[left]) i++; // \u4ece\u5de6\u5411\u53f3\u627e\u9996\u4e2a\u5927\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\nthis.swap(nums, i, j); // \u4ea4\u6362\u8fd9\u4e24\u4e2a\u5143\u7d20\n}\nthis.swap(nums, i, left); // \u5c06\u57fa\u51c6\u6570\u4ea4\u6362\u81f3\u4e24\u5b50\u6570\u7ec4\u7684\u5206\u754c\u7ebf\nreturn i; // \u8fd4\u56de\u57fa\u51c6\u6570\u7684\u7d22\u5f15\n}\n</code></pre> quick_sort.ts<pre><code>/* \u9009\u53d6\u4e09\u4e2a\u5143\u7d20\u7684\u4e2d\u4f4d\u6570 */\nmedianThree(\nnums: number[],\nleft: number,\nmid: number,\nright: number\n): number {\n// \u6b64\u5904\u4f7f\u7528\u5f02\u6216\u8fd0\u7b97\u6765\u7b80\u5316\u4ee3\u7801\n// \u5f02\u6216\u89c4\u5219\u4e3a 0 ^ 0 = 1 ^ 1 = 0, 0 ^ 1 = 1 ^ 0 = 1\nif (Number(nums[left] &lt; nums[mid]) ^ Number(nums[left] &lt; nums[right])) {\nreturn left;\n} else if (\nNumber(nums[mid] &lt; nums[left]) ^ Number(nums[mid] &lt; nums[right])\n) {\nreturn mid;\n} else {\nreturn right;\n}\n}\n/* \u54e8\u5175\u5212\u5206\uff08\u4e09\u6570\u53d6\u4e2d\u503c\uff09 */\npartition(nums: number[], left: number, right: number): number {\n// \u9009\u53d6\u4e09\u4e2a\u5019\u9009\u5143\u7d20\u7684\u4e2d\u4f4d\u6570\nlet med = this.medianThree(\nnums,\nleft,\nMath.floor((left + right) / 2),\nright\n);\n// \u5c06\u4e2d\u4f4d\u6570\u4ea4\u6362\u81f3\u6570\u7ec4\u6700\u5de6\u7aef\nthis.swap(nums, left, med);\n// \u4ee5 nums[left] \u4f5c\u4e3a\u57fa\u51c6\u6570\nlet i = left,\nj = right;\nwhile (i &lt; j) {\nwhile (i &lt; j &amp;&amp; nums[j] &gt;= nums[left]) {\nj--; // \u4ece\u53f3\u5411\u5de6\u627e\u9996\u4e2a\u5c0f\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\n}\nwhile (i &lt; j &amp;&amp; nums[i] &lt;= nums[left]) {\ni++; // \u4ece\u5de6\u5411\u53f3\u627e\u9996\u4e2a\u5927\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\n}\nthis.swap(nums, i, j); // \u4ea4\u6362\u8fd9\u4e24\u4e2a\u5143\u7d20\n}\nthis.swap(nums, i, left); // \u5c06\u57fa\u51c6\u6570\u4ea4\u6362\u81f3\u4e24\u5b50\u6570\u7ec4\u7684\u5206\u754c\u7ebf\nreturn i; // \u8fd4\u56de\u57fa\u51c6\u6570\u7684\u7d22\u5f15\n}\n</code></pre> quick_sort.c<pre><code>/* \u5feb\u901f\u6392\u5e8f\u7c7b\uff08\u4e2d\u4f4d\u57fa\u51c6\u6570\u4f18\u5316\uff09 */\n// \u9009\u53d6\u4e09\u4e2a\u5143\u7d20\u7684\u4e2d\u4f4d\u6570\nint medianThree(int nums[], int left, int mid, int right) {\n// \u6b64\u5904\u4f7f\u7528\u5f02\u6216\u8fd0\u7b97\u6765\u7b80\u5316\u4ee3\u7801\n// \u5f02\u6216\u89c4\u5219\u4e3a 0 ^ 0 = 1 ^ 1 = 0, 0 ^ 1 = 1 ^ 0 = 1\nif ((nums[left] &lt; nums[mid]) ^ (nums[left] &lt; nums[right]))\nreturn left;\nelse if ((nums[mid] &lt; nums[left]) ^ (nums[mid] &lt; nums[right]))\nreturn mid;\nelse\nreturn right;\n}\n/* \u5feb\u901f\u6392\u5e8f\u7c7b\uff08\u4e2d\u4f4d\u57fa\u51c6\u6570\u4f18\u5316\uff09 */\n// \u9009\u53d6\u4e09\u4e2a\u5143\u7d20\u7684\u4e2d\u4f4d\u6570\nint medianThree(int nums[], int left, int mid, int right) {\n// \u6b64\u5904\u4f7f\u7528\u5f02\u6216\u8fd0\u7b97\u6765\u7b80\u5316\u4ee3\u7801\n// \u5f02\u6216\u89c4\u5219\u4e3a 0 ^ 0 = 1 ^ 1 = 0, 0 ^ 1 = 1 ^ 0 = 1\nif ((nums[left] &lt; nums[mid]) ^ (nums[left] &lt; nums[right]))\nreturn left;\nelse if ((nums[mid] &lt; nums[left]) ^ (nums[mid] &lt; nums[right]))\nreturn mid;\nelse\nreturn right;\n}\n// \u54e8\u5175\u5212\u5206\uff08\u4e09\u6570\u53d6\u4e2d\u503c\uff09\nint partitionMedian(int nums[], int left, int right) {\n// \u9009\u53d6\u4e09\u4e2a\u5019\u9009\u5143\u7d20\u7684\u4e2d\u4f4d\u6570\nint med = medianThree(nums, left, (left + right) / 2, right);\n// \u5c06\u4e2d\u4f4d\u6570\u4ea4\u6362\u81f3\u6570\u7ec4\u6700\u5de6\u7aef\nswap(nums, left, med);\n// \u4ee5 nums[left] \u4f5c\u4e3a\u57fa\u51c6\u6570\nint i = left, j = right;\nwhile (i &lt; j) {\nwhile (i &lt; j &amp;&amp; nums[j] &gt;= nums[left])\nj--; // \u4ece\u53f3\u5411\u5de6\u627e\u9996\u4e2a\u5c0f\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\nwhile (i &lt; j &amp;&amp; nums[i] &lt;= nums[left])\ni++;          // \u4ece\u5de6\u5411\u53f3\u627e\u9996\u4e2a\u5927\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\nswap(nums, i, j); // \u4ea4\u6362\u8fd9\u4e24\u4e2a\u5143\u7d20\n}\nswap(nums, i, left); // \u5c06\u57fa\u51c6\u6570\u4ea4\u6362\u81f3\u4e24\u5b50\u6570\u7ec4\u7684\u5206\u754c\u7ebf\nreturn i;            // \u8fd4\u56de\u57fa\u51c6\u6570\u7684\u7d22\u5f15\n}\n</code></pre> quick_sort.cs<pre><code>/* \u9009\u53d6\u4e09\u4e2a\u5143\u7d20\u7684\u4e2d\u4f4d\u6570 */\nint medianThree(int[] nums, int left, int mid, int right) {\n// \u6b64\u5904\u4f7f\u7528\u5f02\u6216\u8fd0\u7b97\u6765\u7b80\u5316\u4ee3\u7801\n// \u5f02\u6216\u89c4\u5219\u4e3a 0 ^ 0 = 1 ^ 1 = 0, 0 ^ 1 = 1 ^ 0 = 1\nif ((nums[left] &lt; nums[mid]) ^ (nums[left] &lt; nums[right]))\nreturn left;\nelse if ((nums[mid] &lt; nums[left]) ^ (nums[mid] &lt; nums[right]))\nreturn mid;\nelse\nreturn right;\n}\n/* \u54e8\u5175\u5212\u5206\uff08\u4e09\u6570\u53d6\u4e2d\u503c\uff09 */\nint partition(int[] nums, int left, int right) {\n// \u9009\u53d6\u4e09\u4e2a\u5019\u9009\u5143\u7d20\u7684\u4e2d\u4f4d\u6570\nint med = medianThree(nums, left, (left + right) / 2, right);\n// \u5c06\u4e2d\u4f4d\u6570\u4ea4\u6362\u81f3\u6570\u7ec4\u6700\u5de6\u7aef\nswap(nums, left, med);\n// \u4ee5 nums[left] \u4f5c\u4e3a\u57fa\u51c6\u6570\nint i = left, j = right;\nwhile (i &lt; j) {\nwhile (i &lt; j &amp;&amp; nums[j] &gt;= nums[left])\nj--;          // \u4ece\u53f3\u5411\u5de6\u627e\u9996\u4e2a\u5c0f\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\nwhile (i &lt; j &amp;&amp; nums[i] &lt;= nums[left])\ni++;          // \u4ece\u5de6\u5411\u53f3\u627e\u9996\u4e2a\u5927\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\nswap(nums, i, j); // \u4ea4\u6362\u8fd9\u4e24\u4e2a\u5143\u7d20\n}\nswap(nums, i, left);  // \u5c06\u57fa\u51c6\u6570\u4ea4\u6362\u81f3\u4e24\u5b50\u6570\u7ec4\u7684\u5206\u754c\u7ebf\nreturn i;             // \u8fd4\u56de\u57fa\u51c6\u6570\u7684\u7d22\u5f15\n}\n</code></pre> quick_sort.swift<pre><code>/* \u9009\u53d6\u4e09\u4e2a\u5143\u7d20\u7684\u4e2d\u4f4d\u6570 */\nfunc medianThree(nums: [Int], left: Int, mid: Int, right: Int) -&gt; Int {\nif (nums[left] &lt; nums[mid]) != (nums[left] &lt; nums[right]) {\nreturn left\n} else if (nums[mid] &lt; nums[left]) != (nums[mid] &lt; nums[right]) {\nreturn mid\n} else {\nreturn right\n}\n}\n/* \u54e8\u5175\u5212\u5206\uff08\u4e09\u6570\u53d6\u4e2d\u503c\uff09 */\nfunc partitionMedian(nums: inout [Int], left: Int, right: Int) -&gt; Int {\n// \u9009\u53d6\u4e09\u4e2a\u5019\u9009\u5143\u7d20\u7684\u4e2d\u4f4d\u6570\nlet med = medianThree(nums: nums, left: left, mid: (left + right) / 2, right: right)\n// \u5c06\u4e2d\u4f4d\u6570\u4ea4\u6362\u81f3\u6570\u7ec4\u6700\u5de6\u7aef\nswap(nums: &amp;nums, i: left, j: med)\nreturn partition(nums: &amp;nums, left: left, right: right)\n}\n</code></pre> quick_sort.zig<pre><code>// \u9009\u53d6\u4e09\u4e2a\u5143\u7d20\u7684\u4e2d\u4f4d\u6570\nfn medianThree(nums: []i32, left: usize, mid: usize, right: usize) usize {\n// \u6b64\u5904\u4f7f\u7528\u5f02\u6216\u8fd0\u7b97\u6765\u7b80\u5316\u4ee3\u7801\n// \u5f02\u6216\u89c4\u5219\u4e3a 0 ^ 0 = 1 ^ 1 = 0, 0 ^ 1 = 1 ^ 0 = 1\nif ((nums[left] &lt; nums[mid]) != (nums[left] &lt; nums[right])) {\nreturn left;\n} else if ((nums[mid] &lt; nums[left]) != (nums[mid] &lt; nums[right])) {\nreturn mid;\n} else {\nreturn right;\n}\n}\n// \u54e8\u5175\u5212\u5206\uff08\u4e09\u6570\u53d6\u4e2d\u503c\uff09\nfn partition(nums: []i32, left: usize, right: usize) usize {\n// \u9009\u53d6\u4e09\u4e2a\u5019\u9009\u5143\u7d20\u7684\u4e2d\u4f4d\u6570\nvar med = medianThree(nums, left, (left + right) / 2, right);\n// \u5c06\u4e2d\u4f4d\u6570\u4ea4\u6362\u81f3\u6570\u7ec4\u6700\u5de6\u7aef\nswap(nums, left, med);\n// \u4ee5 nums[left] \u4f5c\u4e3a\u57fa\u51c6\u6570\nvar i = left;\nvar j = right;\nwhile (i &lt; j) {\nwhile (i &lt; j and nums[j] &gt;= nums[left]) j -= 1; // \u4ece\u53f3\u5411\u5de6\u627e\u9996\u4e2a\u5c0f\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\nwhile (i &lt; j and nums[i] &lt;= nums[left]) i += 1; // \u4ece\u5de6\u5411\u53f3\u627e\u9996\u4e2a\u5927\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\nswap(nums, i, j);   // \u4ea4\u6362\u8fd9\u4e24\u4e2a\u5143\u7d20\n}\nswap(nums, i, left);    // \u5c06\u57fa\u51c6\u6570\u4ea4\u6362\u81f3\u4e24\u5b50\u6570\u7ec4\u7684\u5206\u754c\u7ebf\nreturn i;               // \u8fd4\u56de\u57fa\u51c6\u6570\u7684\u7d22\u5f15\n}\n</code></pre> quick_sort.dart<pre><code>/* \u9009\u53d6\u4e09\u4e2a\u5143\u7d20\u7684\u4e2d\u4f4d\u6570 */\nint _medianThree(List&lt;int&gt; nums, int left, int mid, int right) {\n// \u6b64\u5904\u4f7f\u7528\u5f02\u6216\u8fd0\u7b97\u6765\u7b80\u5316\u4ee3\u7801\n// \u5f02\u6216\u89c4\u5219\u4e3a 0 ^ 0 = 1 ^ 1 = 0, 0 ^ 1 = 1 ^ 0 = 1\nif ((nums[left] &lt; nums[mid]) ^ (nums[left] &lt; nums[right]))\nreturn left;\nelse if ((nums[mid] &lt; nums[left]) ^ (nums[mid] &lt; nums[right]))\nreturn mid;\nelse\nreturn right;\n}\n/* \u54e8\u5175\u5212\u5206\uff08\u4e09\u6570\u53d6\u4e2d\u503c\uff09 */\nint _partition(List&lt;int&gt; nums, int left, int right) {\n// \u9009\u53d6\u4e09\u4e2a\u5019\u9009\u5143\u7d20\u7684\u4e2d\u4f4d\u6570\nint med = _medianThree(nums, left, (left + right) ~/ 2, right);\n// \u5c06\u4e2d\u4f4d\u6570\u4ea4\u6362\u81f3\u6570\u7ec4\u6700\u5de6\u7aef\n_swap(nums, left, med);\n// \u4ee5 nums[left] \u4f5c\u4e3a\u57fa\u51c6\u6570\nint i = left, j = right;\nwhile (i &lt; j) {\nwhile (i &lt; j &amp;&amp; nums[j] &gt;= nums[left]) j--; // \u4ece\u53f3\u5411\u5de6\u627e\u9996\u4e2a\u5c0f\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\nwhile (i &lt; j &amp;&amp; nums[i] &lt;= nums[left]) i++; // \u4ece\u5de6\u5411\u53f3\u627e\u9996\u4e2a\u5927\u4e8e\u57fa\u51c6\u6570\u7684\u5143\u7d20\n_swap(nums, i, j); // \u4ea4\u6362\u8fd9\u4e24\u4e2a\u5143\u7d20\n}\n_swap(nums, i, left); // \u5c06\u57fa\u51c6\u6570\u4ea4\u6362\u81f3\u4e24\u5b50\u6570\u7ec4\u7684\u5206\u754c\u7ebf\nreturn i; // \u8fd4\u56de\u57fa\u51c6\u6570\u7684\u7d22\u5f15\n}\n</code></pre>"},{"location":"chapter_sorting/quick_sort/#1155","title":"11.5.5. \u00a0 \u5c3e\u9012\u5f52\u4f18\u5316","text":"<p>\u5728\u67d0\u4e9b\u8f93\u5165\u4e0b\uff0c\u5feb\u901f\u6392\u5e8f\u53ef\u80fd\u5360\u7528\u7a7a\u95f4\u8f83\u591a\u3002\u4ee5\u5b8c\u5168\u5012\u5e8f\u7684\u8f93\u5165\u6570\u7ec4\u4e3a\u4f8b\uff0c\u7531\u4e8e\u6bcf\u8f6e\u54e8\u5175\u5212\u5206\u540e\u53f3\u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a \\(0\\) \uff0c\u9012\u5f52\u6811\u7684\u9ad8\u5ea6\u4f1a\u8fbe\u5230 \\(n - 1\\) \uff0c\u6b64\u65f6\u9700\u8981\u5360\u7528 \\(O(n)\\) \u5927\u5c0f\u7684\u6808\u5e27\u7a7a\u95f4\u3002</p> <p>\u4e3a\u4e86\u9632\u6b62\u6808\u5e27\u7a7a\u95f4\u7684\u7d2f\u79ef\uff0c\u6211\u4eec\u53ef\u4ee5\u5728\u6bcf\u8f6e\u54e8\u5175\u6392\u5e8f\u5b8c\u6210\u540e\uff0c\u6bd4\u8f83\u4e24\u4e2a\u5b50\u6570\u7ec4\u7684\u957f\u5ea6\uff0c\u4ec5\u5bf9\u8f83\u77ed\u7684\u5b50\u6570\u7ec4\u8fdb\u884c\u9012\u5f52\u3002\u7531\u4e8e\u8f83\u77ed\u5b50\u6570\u7ec4\u7684\u957f\u5ea6\u4e0d\u4f1a\u8d85\u8fc7 \\(\\frac{n}{2}\\) \uff0c\u56e0\u6b64\u8fd9\u79cd\u65b9\u6cd5\u80fd\u786e\u4fdd\u9012\u5f52\u6df1\u5ea6\u4e0d\u8d85\u8fc7 \\(\\log n\\) \uff0c\u4ece\u800c\u5c06\u6700\u5dee\u7a7a\u95f4\u590d\u6742\u5ea6\u4f18\u5316\u81f3 \\(O(\\log n)\\) \u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart quick_sort.java<pre><code>/* \u5feb\u901f\u6392\u5e8f\uff08\u5c3e\u9012\u5f52\u4f18\u5316\uff09 */\nvoid quickSort(int[] nums, int left, int right) {\n// \u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a 1 \u65f6\u7ec8\u6b62\nwhile (left &lt; right) {\n// \u54e8\u5175\u5212\u5206\u64cd\u4f5c\nint pivot = partition(nums, left, right);\n// \u5bf9\u4e24\u4e2a\u5b50\u6570\u7ec4\u4e2d\u8f83\u77ed\u7684\u90a3\u4e2a\u6267\u884c\u5feb\u6392\nif (pivot - left &lt; right - pivot) {\nquickSort(nums, left, pivot - 1); // \u9012\u5f52\u6392\u5e8f\u5de6\u5b50\u6570\u7ec4\nleft = pivot + 1; // \u5269\u4f59\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [pivot + 1, right]\n} else {\nquickSort(nums, pivot + 1, right); // \u9012\u5f52\u6392\u5e8f\u53f3\u5b50\u6570\u7ec4\nright = pivot - 1; // \u5269\u4f59\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [left, pivot - 1]\n}\n}\n}\n</code></pre> quick_sort.cpp<pre><code>/* \u5feb\u901f\u6392\u5e8f\uff08\u5c3e\u9012\u5f52\u4f18\u5316\uff09 */\nvoid quickSort(vector&lt;int&gt; &amp;nums, int left, int right) {\n// \u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a 1 \u65f6\u7ec8\u6b62\nwhile (left &lt; right) {\n// \u54e8\u5175\u5212\u5206\u64cd\u4f5c\nint pivot = partition(nums, left, right);\n// \u5bf9\u4e24\u4e2a\u5b50\u6570\u7ec4\u4e2d\u8f83\u77ed\u7684\u90a3\u4e2a\u6267\u884c\u5feb\u6392\nif (pivot - left &lt; right - pivot) {\nquickSort(nums, left, pivot - 1); // \u9012\u5f52\u6392\u5e8f\u5de6\u5b50\u6570\u7ec4\nleft = pivot + 1;                 // \u5269\u4f59\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [pivot + 1, right]\n} else {\nquickSort(nums, pivot + 1, right); // \u9012\u5f52\u6392\u5e8f\u53f3\u5b50\u6570\u7ec4\nright = pivot - 1;                 // \u5269\u4f59\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [left, pivot - 1]\n}\n}\n}\n</code></pre> quick_sort.py<pre><code>def quick_sort(self, nums: list[int], left: int, right: int) -&gt; None:\n\"\"\"\u5feb\u901f\u6392\u5e8f\uff08\u5c3e\u9012\u5f52\u4f18\u5316\uff09\"\"\"\n# \u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a 1 \u65f6\u7ec8\u6b62\nwhile left &lt; right:\n# \u54e8\u5175\u5212\u5206\u64cd\u4f5c\npivot = self.partition(nums, left, right)\n# \u5bf9\u4e24\u4e2a\u5b50\u6570\u7ec4\u4e2d\u8f83\u77ed\u7684\u90a3\u4e2a\u6267\u884c\u5feb\u6392\nif pivot - left &lt; right - pivot:\nself.quick_sort(nums, left, pivot - 1)  # \u9012\u5f52\u6392\u5e8f\u5de6\u5b50\u6570\u7ec4\nleft = pivot + 1  # \u5269\u4f59\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [pivot + 1, right]\nelse:\nself.quick_sort(nums, pivot + 1, right)  # \u9012\u5f52\u6392\u5e8f\u53f3\u5b50\u6570\u7ec4\nright = pivot - 1  # \u5269\u4f59\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [left, pivot - 1]\n</code></pre> quick_sort.go<pre><code>/* \u5feb\u901f\u6392\u5e8f\uff08\u5c3e\u9012\u5f52\u4f18\u5316\uff09*/\nfunc (q *quickSortTailCall) quickSort(nums []int, left, right int) {\n// \u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a 1 \u65f6\u7ec8\u6b62\nfor left &lt; right {\n// \u54e8\u5175\u5212\u5206\u64cd\u4f5c\npivot := q.partition(nums, left, right)\n// \u5bf9\u4e24\u4e2a\u5b50\u6570\u7ec4\u4e2d\u8f83\u77ed\u7684\u90a3\u4e2a\u6267\u884c\u5feb\u6392\nif pivot-left &lt; right-pivot {\nq.quickSort(nums, left, pivot-1) // \u9012\u5f52\u6392\u5e8f\u5de6\u5b50\u6570\u7ec4\nleft = pivot + 1                 // \u5269\u4f59\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [pivot + 1, right]\n} else {\nq.quickSort(nums, pivot+1, right) // \u9012\u5f52\u6392\u5e8f\u53f3\u5b50\u6570\u7ec4\nright = pivot - 1                 // \u5269\u4f59\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [left, pivot - 1]\n}\n}\n}\n</code></pre> quick_sort.js<pre><code>/* \u5feb\u901f\u6392\u5e8f\uff08\u5c3e\u9012\u5f52\u4f18\u5316\uff09 */\nquickSort(nums, left, right) {\n// \u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a 1 \u65f6\u7ec8\u6b62\nwhile (left &lt; right) {\n// \u54e8\u5175\u5212\u5206\u64cd\u4f5c\nlet pivot = this.partition(nums, left, right);\n// \u5bf9\u4e24\u4e2a\u5b50\u6570\u7ec4\u4e2d\u8f83\u77ed\u7684\u90a3\u4e2a\u6267\u884c\u5feb\u6392\nif (pivot - left &lt; right - pivot) {\nthis.quickSort(nums, left, pivot - 1); // \u9012\u5f52\u6392\u5e8f\u5de6\u5b50\u6570\u7ec4\nleft = pivot + 1; // \u5269\u4f59\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [pivot + 1, right]\n} else {\nthis.quickSort(nums, pivot + 1, right); // \u9012\u5f52\u6392\u5e8f\u53f3\u5b50\u6570\u7ec4\nright = pivot - 1; // \u5269\u4f59\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [left, pivot - 1]\n}\n}\n}\n</code></pre> quick_sort.ts<pre><code>/* \u5feb\u901f\u6392\u5e8f\uff08\u5c3e\u9012\u5f52\u4f18\u5316\uff09 */\nquickSort(nums: number[], left: number, right: number): void {\n// \u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a 1 \u65f6\u7ec8\u6b62\nwhile (left &lt; right) {\n// \u54e8\u5175\u5212\u5206\u64cd\u4f5c\nlet pivot = this.partition(nums, left, right);\n// \u5bf9\u4e24\u4e2a\u5b50\u6570\u7ec4\u4e2d\u8f83\u77ed\u7684\u90a3\u4e2a\u6267\u884c\u5feb\u6392\nif (pivot - left &lt; right - pivot) {\nthis.quickSort(nums, left, pivot - 1); // \u9012\u5f52\u6392\u5e8f\u5de6\u5b50\u6570\u7ec4\nleft = pivot + 1; // \u5269\u4f59\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [pivot + 1, right]\n} else {\nthis.quickSort(nums, pivot + 1, right); // \u9012\u5f52\u6392\u5e8f\u53f3\u5b50\u6570\u7ec4\nright = pivot - 1; // \u5269\u4f59\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [left, pivot - 1]\n}\n}\n}\n</code></pre> quick_sort.c<pre><code>/* \u5feb\u901f\u6392\u5e8f\u7c7b\uff08\u5c3e\u9012\u5f52\u4f18\u5316\uff09 */\n// \u5feb\u901f\u6392\u5e8f\uff08\u5c3e\u9012\u5f52\u4f18\u5316\uff09\nvoid quickSortTailCall(int nums[], int left, int right) {\n// \u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a 1 \u65f6\u7ec8\u6b62\nwhile (left &lt; right) {\n// \u54e8\u5175\u5212\u5206\u64cd\u4f5c\nint pivot = partition(nums, left, right);\n// \u5bf9\u4e24\u4e2a\u5b50\u6570\u7ec4\u4e2d\u8f83\u77ed\u7684\u90a3\u4e2a\u6267\u884c\u5feb\u6392\nif (pivot - left &lt; right - pivot) {\nquickSortTailCall(nums, left, pivot - 1); // \u9012\u5f52\u6392\u5e8f\u5de6\u5b50\u6570\u7ec4\nleft = pivot + 1;                         // \u5269\u4f59\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [pivot + 1, right]\n} else {\nquickSortTailCall(nums, pivot + 1, right); // \u9012\u5f52\u6392\u5e8f\u53f3\u5b50\u6570\u7ec4\nright = pivot - 1;                         // \u5269\u4f59\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [left, pivot - 1]\n}\n}\n}\n</code></pre> quick_sort.cs<pre><code>/* \u5feb\u901f\u6392\u5e8f\uff08\u5c3e\u9012\u5f52\u4f18\u5316\uff09 */\nvoid quickSort(int[] nums, int left, int right) {\n// \u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a 1 \u65f6\u7ec8\u6b62\nwhile (left &lt; right) {\n// \u54e8\u5175\u5212\u5206\u64cd\u4f5c\nint pivot = partition(nums, left, right);\n// \u5bf9\u4e24\u4e2a\u5b50\u6570\u7ec4\u4e2d\u8f83\u77ed\u7684\u90a3\u4e2a\u6267\u884c\u5feb\u6392\nif (pivot - left &lt; right - pivot) {\nquickSort(nums, left, pivot - 1);  // \u9012\u5f52\u6392\u5e8f\u5de6\u5b50\u6570\u7ec4\nleft = pivot + 1;  // \u5269\u4f59\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [pivot + 1, right]\n} else {\nquickSort(nums, pivot + 1, right); // \u9012\u5f52\u6392\u5e8f\u53f3\u5b50\u6570\u7ec4\nright = pivot - 1; // \u5269\u4f59\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [left, pivot - 1]\n}\n}\n}\n</code></pre> quick_sort.swift<pre><code>/* \u5feb\u901f\u6392\u5e8f\uff08\u5c3e\u9012\u5f52\u4f18\u5316\uff09 */\nfunc quickSortTailCall(nums: inout [Int], left: Int, right: Int) {\nvar left = left\nvar right = right\n// \u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a 1 \u65f6\u7ec8\u6b62\nwhile left &lt; right {\n// \u54e8\u5175\u5212\u5206\u64cd\u4f5c\nlet pivot = partition(nums: &amp;nums, left: left, right: right)\n// \u5bf9\u4e24\u4e2a\u5b50\u6570\u7ec4\u4e2d\u8f83\u77ed\u7684\u90a3\u4e2a\u6267\u884c\u5feb\u6392\nif (pivot - left) &lt; (right - pivot) {\nquickSortTailCall(nums: &amp;nums, left: left, right: pivot - 1) // \u9012\u5f52\u6392\u5e8f\u5de6\u5b50\u6570\u7ec4\nleft = pivot + 1 // \u5269\u4f59\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [pivot + 1, right]\n} else {\nquickSortTailCall(nums: &amp;nums, left: pivot + 1, right: right) // \u9012\u5f52\u6392\u5e8f\u53f3\u5b50\u6570\u7ec4\nright = pivot - 1 // \u5269\u4f59\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [left, pivot - 1]\n}\n}\n}\n</code></pre> quick_sort.zig<pre><code>// \u5feb\u901f\u6392\u5e8f\uff08\u5c3e\u9012\u5f52\u4f18\u5316\uff09\nfn quickSort(nums: []i32, left_: usize, right_: usize) void {\nvar left = left_;\nvar right = right_;\n// \u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a 1 \u65f6\u7ec8\u6b62\u9012\u5f52\nwhile (left &lt; right) {\n// \u54e8\u5175\u5212\u5206\u64cd\u4f5c\nvar pivot = partition(nums, left, right);\n// \u5bf9\u4e24\u4e2a\u5b50\u6570\u7ec4\u4e2d\u8f83\u77ed\u7684\u90a3\u4e2a\u6267\u884c\u5feb\u6392\nif (pivot - left &lt; right - pivot) {\nquickSort(nums, left, pivot - 1);   // \u9012\u5f52\u6392\u5e8f\u5de6\u5b50\u6570\u7ec4\nleft = pivot + 1;                   // \u5269\u4f59\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [pivot + 1, right]\n} else {\nquickSort(nums, pivot + 1, right);  // \u9012\u5f52\u6392\u5e8f\u53f3\u5b50\u6570\u7ec4\nright = pivot - 1;                  // \u5269\u4f59\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [left, pivot - 1]\n}\n}\n}\n</code></pre> quick_sort.dart<pre><code>/* \u5feb\u901f\u6392\u5e8f\uff08\u5c3e\u9012\u5f52\u4f18\u5316\uff09 */\nvoid quickSort(List&lt;int&gt; nums, int left, int right) {\n// \u5b50\u6570\u7ec4\u957f\u5ea6\u4e3a 1 \u65f6\u7ec8\u6b62\nwhile (left &lt; right) {\n// \u54e8\u5175\u5212\u5206\u64cd\u4f5c\nint pivot = _partition(nums, left, right);\n// \u5bf9\u4e24\u4e2a\u5b50\u6570\u7ec4\u4e2d\u8f83\u77ed\u7684\u90a3\u4e2a\u6267\u884c\u5feb\u6392\nif (pivot - left &lt; right - pivot) {\nquickSort(nums, left, pivot - 1); // \u9012\u5f52\u6392\u5e8f\u5de6\u5b50\u6570\u7ec4\nleft = pivot + 1; // \u5269\u4f59\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [pivot + 1, right]\n} else {\nquickSort(nums, pivot + 1, right); // \u9012\u5f52\u6392\u5e8f\u53f3\u5b50\u6570\u7ec4\nright = pivot - 1; // \u5269\u4f59\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [left, pivot - 1]\n}\n}\n}\n</code></pre>"},{"location":"chapter_sorting/radix_sort/","title":"11.10. \u00a0 \u57fa\u6570\u6392\u5e8f","text":"<p>\u4e0a\u4e00\u8282\u6211\u4eec\u4ecb\u7ecd\u4e86\u8ba1\u6570\u6392\u5e8f\uff0c\u5b83\u9002\u7528\u4e8e\u6570\u636e\u91cf \\(n\\) \u8f83\u5927\u4f46\u6570\u636e\u8303\u56f4 \\(m\\) \u8f83\u5c0f\u7684\u60c5\u51b5\u3002\u5047\u8bbe\u6211\u4eec\u9700\u8981\u5bf9 \\(n = 10^6\\) \u4e2a\u5b66\u53f7\u8fdb\u884c\u6392\u5e8f\uff0c\u800c\u5b66\u53f7\u662f\u4e00\u4e2a \\(8\\) \u4f4d\u6570\u5b57\uff0c\u8fd9\u610f\u5473\u7740\u6570\u636e\u8303\u56f4 \\(m = 10^8\\) \u975e\u5e38\u5927\uff0c\u4f7f\u7528\u8ba1\u6570\u6392\u5e8f\u9700\u8981\u5206\u914d\u5927\u91cf\u5185\u5b58\u7a7a\u95f4\uff0c\u800c\u57fa\u6570\u6392\u5e8f\u53ef\u4ee5\u907f\u514d\u8fd9\u79cd\u60c5\u51b5\u3002</p> <p>\u300c\u57fa\u6570\u6392\u5e8f Radix Sort\u300d\u7684\u6838\u5fc3\u601d\u60f3\u4e0e\u8ba1\u6570\u6392\u5e8f\u4e00\u81f4\uff0c\u4e5f\u901a\u8fc7\u7edf\u8ba1\u4e2a\u6570\u6765\u5b9e\u73b0\u6392\u5e8f\u3002\u5728\u6b64\u57fa\u7840\u4e0a\uff0c\u57fa\u6570\u6392\u5e8f\u5229\u7528\u6570\u5b57\u5404\u4f4d\u4e4b\u95f4\u7684\u9012\u8fdb\u5173\u7cfb\uff0c\u4f9d\u6b21\u5bf9\u6bcf\u4e00\u4f4d\u8fdb\u884c\u6392\u5e8f\uff0c\u4ece\u800c\u5f97\u5230\u6700\u7ec8\u7684\u6392\u5e8f\u7ed3\u679c\u3002</p>"},{"location":"chapter_sorting/radix_sort/#11101","title":"11.10.1. \u00a0 \u7b97\u6cd5\u6d41\u7a0b","text":"<p>\u4ee5\u5b66\u53f7\u6570\u636e\u4e3a\u4f8b\uff0c\u5047\u8bbe\u6570\u5b57\u7684\u6700\u4f4e\u4f4d\u662f\u7b2c \\(1\\) \u4f4d\uff0c\u6700\u9ad8\u4f4d\u662f\u7b2c \\(8\\) \u4f4d\uff0c\u57fa\u6570\u6392\u5e8f\u7684\u6b65\u9aa4\u5982\u4e0b\uff1a</p> <ol> <li>\u521d\u59cb\u5316\u4f4d\u6570 \\(k = 1\\) \uff1b</li> <li>\u5bf9\u5b66\u53f7\u7684\u7b2c \\(k\\) \u4f4d\u6267\u884c\u300c\u8ba1\u6570\u6392\u5e8f\u300d\u3002\u5b8c\u6210\u540e\uff0c\u6570\u636e\u4f1a\u6839\u636e\u7b2c \\(k\\) \u4f4d\u4ece\u5c0f\u5230\u5927\u6392\u5e8f\uff1b</li> <li>\u5c06 \\(k\\) \u589e\u52a0 \\(1\\) \uff0c\u7136\u540e\u8fd4\u56de\u6b65\u9aa4 <code>2.</code> \u7ee7\u7eed\u8fed\u4ee3\uff0c\u76f4\u5230\u6240\u6709\u4f4d\u90fd\u6392\u5e8f\u5b8c\u6210\u540e\u7ed3\u675f\uff1b</li> </ol> <p></p> <p> Fig. \u57fa\u6570\u6392\u5e8f\u7b97\u6cd5\u6d41\u7a0b </p> <p>\u4e0b\u9762\u6765\u5256\u6790\u4ee3\u7801\u5b9e\u73b0\u3002\u5bf9\u4e8e\u4e00\u4e2a \\(d\\) \u8fdb\u5236\u7684\u6570\u5b57 \\(x\\) \uff0c\u8981\u83b7\u53d6\u5176\u7b2c \\(k\\) \u4f4d \\(x_k\\) \uff0c\u53ef\u4ee5\u4f7f\u7528\u4ee5\u4e0b\u8ba1\u7b97\u516c\u5f0f\uff1a</p> \\[ x_k = \\lfloor\\frac{x}{d^{k-1}}\\rfloor \\bmod d \\] <p>\u5176\u4e2d \\(\\lfloor a \\rfloor\\) \u8868\u793a\u5bf9\u6d6e\u70b9\u6570 \\(a\\) \u5411\u4e0b\u53d6\u6574\uff0c\u800c \\(\\bmod \\space d\\) \u8868\u793a\u5bf9 \\(d\\) \u53d6\u4f59\u3002\u5bf9\u4e8e\u5b66\u53f7\u6570\u636e\uff0c\\(d = 10\\) \u4e14 \\(k \\in [1, 8]\\) \u3002</p> <p>\u6b64\u5916\uff0c\u6211\u4eec\u9700\u8981\u5c0f\u5e45\u6539\u52a8\u8ba1\u6570\u6392\u5e8f\u4ee3\u7801\uff0c\u4f7f\u4e4b\u53ef\u4ee5\u6839\u636e\u6570\u5b57\u7684\u7b2c \\(k\\) \u4f4d\u8fdb\u884c\u6392\u5e8f\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart radix_sort.java<pre><code>/* \u83b7\u53d6\u5143\u7d20 num \u7684\u7b2c k \u4f4d\uff0c\u5176\u4e2d exp = 10^(k-1) */\nint digit(int num, int exp) {\n// \u4f20\u5165 exp \u800c\u975e k \u53ef\u4ee5\u907f\u514d\u5728\u6b64\u91cd\u590d\u6267\u884c\u6602\u8d35\u7684\u6b21\u65b9\u8ba1\u7b97\nreturn (num / exp) % 10;\n}\n/* \u8ba1\u6570\u6392\u5e8f\uff08\u6839\u636e nums \u7b2c k \u4f4d\u6392\u5e8f\uff09 */\nvoid countingSortDigit(int[] nums, int exp) {\n// \u5341\u8fdb\u5236\u7684\u4f4d\u8303\u56f4\u4e3a 0~9 \uff0c\u56e0\u6b64\u9700\u8981\u957f\u5ea6\u4e3a 10 \u7684\u6876\nint[] counter = new int[10];\nint n = nums.length;\n// \u7edf\u8ba1 0~9 \u5404\u6570\u5b57\u7684\u51fa\u73b0\u6b21\u6570\nfor (int i = 0; i &lt; n; i++) {\nint d = digit(nums[i], exp); // \u83b7\u53d6 nums[i] \u7b2c k \u4f4d\uff0c\u8bb0\u4e3a d\ncounter[d]++;                // \u7edf\u8ba1\u6570\u5b57 d \u7684\u51fa\u73b0\u6b21\u6570\n}\n// \u6c42\u524d\u7f00\u548c\uff0c\u5c06\u201c\u51fa\u73b0\u4e2a\u6570\u201d\u8f6c\u6362\u4e3a\u201c\u6570\u7ec4\u7d22\u5f15\u201d\nfor (int i = 1; i &lt; 10; i++) {\ncounter[i] += counter[i - 1];\n}\n// \u5012\u5e8f\u904d\u5386\uff0c\u6839\u636e\u6876\u5185\u7edf\u8ba1\u7ed3\u679c\uff0c\u5c06\u5404\u5143\u7d20\u586b\u5165 res\nint[] res = new int[n];\nfor (int i = n - 1; i &gt;= 0; i--) {\nint d = digit(nums[i], exp);\nint j = counter[d] - 1; // \u83b7\u53d6 d \u5728\u6570\u7ec4\u4e2d\u7684\u7d22\u5f15 j\nres[j] = nums[i];       // \u5c06\u5f53\u524d\u5143\u7d20\u586b\u5165\u7d22\u5f15 j\ncounter[d]--;           // \u5c06 d \u7684\u6570\u91cf\u51cf 1\n}\n// \u4f7f\u7528\u7ed3\u679c\u8986\u76d6\u539f\u6570\u7ec4 nums\nfor (int i = 0; i &lt; n; i++)\nnums[i] = res[i];\n}\n/* \u57fa\u6570\u6392\u5e8f */\nvoid radixSort(int[] nums) {\n// \u83b7\u53d6\u6570\u7ec4\u7684\u6700\u5927\u5143\u7d20\uff0c\u7528\u4e8e\u5224\u65ad\u6700\u5927\u4f4d\u6570\nint m = Integer.MIN_VALUE;\nfor (int num : nums)\nif (num &gt; m)\nm = num;\n// \u6309\u7167\u4ece\u4f4e\u4f4d\u5230\u9ad8\u4f4d\u7684\u987a\u5e8f\u904d\u5386\nfor (int exp = 1; exp &lt;= m; exp *= 10)\n// \u5bf9\u6570\u7ec4\u5143\u7d20\u7684\u7b2c k \u4f4d\u6267\u884c\u8ba1\u6570\u6392\u5e8f\n// k = 1 -&gt; exp = 1\n// k = 2 -&gt; exp = 10\n// \u5373 exp = 10^(k-1)\ncountingSortDigit(nums, exp);\n}\n</code></pre> radix_sort.cpp<pre><code>/* \u83b7\u53d6\u5143\u7d20 num \u7684\u7b2c k \u4f4d\uff0c\u5176\u4e2d exp = 10^(k-1) */\nint digit(int num, int exp) {\n// \u4f20\u5165 exp \u800c\u975e k \u53ef\u4ee5\u907f\u514d\u5728\u6b64\u91cd\u590d\u6267\u884c\u6602\u8d35\u7684\u6b21\u65b9\u8ba1\u7b97\nreturn (num / exp) % 10;\n}\n/* \u8ba1\u6570\u6392\u5e8f\uff08\u6839\u636e nums \u7b2c k \u4f4d\u6392\u5e8f\uff09 */\nvoid countingSortDigit(vector&lt;int&gt; &amp;nums, int exp) {\n// \u5341\u8fdb\u5236\u7684\u4f4d\u8303\u56f4\u4e3a 0~9 \uff0c\u56e0\u6b64\u9700\u8981\u957f\u5ea6\u4e3a 10 \u7684\u6876\nvector&lt;int&gt; counter(10, 0);\nint n = nums.size();\n// \u7edf\u8ba1 0~9 \u5404\u6570\u5b57\u7684\u51fa\u73b0\u6b21\u6570\nfor (int i = 0; i &lt; n; i++) {\nint d = digit(nums[i], exp); // \u83b7\u53d6 nums[i] \u7b2c k \u4f4d\uff0c\u8bb0\u4e3a d\ncounter[d]++;                // \u7edf\u8ba1\u6570\u5b57 d \u7684\u51fa\u73b0\u6b21\u6570\n}\n// \u6c42\u524d\u7f00\u548c\uff0c\u5c06\u201c\u51fa\u73b0\u4e2a\u6570\u201d\u8f6c\u6362\u4e3a\u201c\u6570\u7ec4\u7d22\u5f15\u201d\nfor (int i = 1; i &lt; 10; i++) {\ncounter[i] += counter[i - 1];\n}\n// \u5012\u5e8f\u904d\u5386\uff0c\u6839\u636e\u6876\u5185\u7edf\u8ba1\u7ed3\u679c\uff0c\u5c06\u5404\u5143\u7d20\u586b\u5165 res\nvector&lt;int&gt; res(n, 0);\nfor (int i = n - 1; i &gt;= 0; i--) {\nint d = digit(nums[i], exp);\nint j = counter[d] - 1; // \u83b7\u53d6 d \u5728\u6570\u7ec4\u4e2d\u7684\u7d22\u5f15 j\nres[j] = nums[i];       // \u5c06\u5f53\u524d\u5143\u7d20\u586b\u5165\u7d22\u5f15 j\ncounter[d]--;           // \u5c06 d \u7684\u6570\u91cf\u51cf 1\n}\n// \u4f7f\u7528\u7ed3\u679c\u8986\u76d6\u539f\u6570\u7ec4 nums\nfor (int i = 0; i &lt; n; i++)\nnums[i] = res[i];\n}\n/* \u57fa\u6570\u6392\u5e8f */\nvoid radixSort(vector&lt;int&gt; &amp;nums) {\n// \u83b7\u53d6\u6570\u7ec4\u7684\u6700\u5927\u5143\u7d20\uff0c\u7528\u4e8e\u5224\u65ad\u6700\u5927\u4f4d\u6570\nint m = *max_element(nums.begin(), nums.end());\n// \u6309\u7167\u4ece\u4f4e\u4f4d\u5230\u9ad8\u4f4d\u7684\u987a\u5e8f\u904d\u5386\nfor (int exp = 1; exp &lt;= m; exp *= 10)\n// \u5bf9\u6570\u7ec4\u5143\u7d20\u7684\u7b2c k \u4f4d\u6267\u884c\u8ba1\u6570\u6392\u5e8f\n// k = 1 -&gt; exp = 1\n// k = 2 -&gt; exp = 10\n// \u5373 exp = 10^(k-1)\ncountingSortDigit(nums, exp);\n}\n</code></pre> radix_sort.py<pre><code>def digit(num: int, exp: int) -&gt; int:\n\"\"\"\u83b7\u53d6\u5143\u7d20 num \u7684\u7b2c k \u4f4d\uff0c\u5176\u4e2d exp = 10^(k-1)\"\"\"\n# \u4f20\u5165 exp \u800c\u975e k \u53ef\u4ee5\u907f\u514d\u5728\u6b64\u91cd\u590d\u6267\u884c\u6602\u8d35\u7684\u6b21\u65b9\u8ba1\u7b97\nreturn (num // exp) % 10\ndef counting_sort_digit(nums: list[int], exp: int) -&gt; None:\n\"\"\"\u8ba1\u6570\u6392\u5e8f\uff08\u6839\u636e nums \u7b2c k \u4f4d\u6392\u5e8f\uff09\"\"\"\n# \u5341\u8fdb\u5236\u7684\u4f4d\u8303\u56f4\u4e3a 0~9 \uff0c\u56e0\u6b64\u9700\u8981\u957f\u5ea6\u4e3a 10 \u7684\u6876\ncounter = [0] * 10\nn = len(nums)\n# \u7edf\u8ba1 0~9 \u5404\u6570\u5b57\u7684\u51fa\u73b0\u6b21\u6570\nfor i in range(n):\nd = digit(nums[i], exp)  # \u83b7\u53d6 nums[i] \u7b2c k \u4f4d\uff0c\u8bb0\u4e3a d\ncounter[d] += 1  # \u7edf\u8ba1\u6570\u5b57 d \u7684\u51fa\u73b0\u6b21\u6570\n# \u6c42\u524d\u7f00\u548c\uff0c\u5c06\u201c\u51fa\u73b0\u4e2a\u6570\u201d\u8f6c\u6362\u4e3a\u201c\u6570\u7ec4\u7d22\u5f15\u201d\nfor i in range(1, 10):\ncounter[i] += counter[i - 1]\n# \u5012\u5e8f\u904d\u5386\uff0c\u6839\u636e\u6876\u5185\u7edf\u8ba1\u7ed3\u679c\uff0c\u5c06\u5404\u5143\u7d20\u586b\u5165 res\nres = [0] * n\nfor i in range(n - 1, -1, -1):\nd = digit(nums[i], exp)\nj = counter[d] - 1  # \u83b7\u53d6 d \u5728\u6570\u7ec4\u4e2d\u7684\u7d22\u5f15 j\nres[j] = nums[i]  # \u5c06\u5f53\u524d\u5143\u7d20\u586b\u5165\u7d22\u5f15 j\ncounter[d] -= 1  # \u5c06 d \u7684\u6570\u91cf\u51cf 1\n# \u4f7f\u7528\u7ed3\u679c\u8986\u76d6\u539f\u6570\u7ec4 nums\nfor i in range(n):\nnums[i] = res[i]\ndef radix_sort(nums: list[int]) -&gt; None:\n\"\"\"\u57fa\u6570\u6392\u5e8f\"\"\"\n# \u83b7\u53d6\u6570\u7ec4\u7684\u6700\u5927\u5143\u7d20\uff0c\u7528\u4e8e\u5224\u65ad\u6700\u5927\u4f4d\u6570\nm = max(nums)\n# \u6309\u7167\u4ece\u4f4e\u4f4d\u5230\u9ad8\u4f4d\u7684\u987a\u5e8f\u904d\u5386\nexp = 1\nwhile exp &lt;= m:\n# \u5bf9\u6570\u7ec4\u5143\u7d20\u7684\u7b2c k \u4f4d\u6267\u884c\u8ba1\u6570\u6392\u5e8f\n# k = 1 -&gt; exp = 1\n# k = 2 -&gt; exp = 10\n# \u5373 exp = 10^(k-1)\ncounting_sort_digit(nums, exp)\nexp *= 10\n</code></pre> radix_sort.go<pre><code>/* \u83b7\u53d6\u5143\u7d20 num \u7684\u7b2c k \u4f4d\uff0c\u5176\u4e2d exp = 10^(k-1) */\nfunc digit(num, exp int) int {\n// \u4f20\u5165 exp \u800c\u975e k \u53ef\u4ee5\u907f\u514d\u5728\u6b64\u91cd\u590d\u6267\u884c\u6602\u8d35\u7684\u6b21\u65b9\u8ba1\u7b97\nreturn (num / exp) % 10\n}\n/* \u8ba1\u6570\u6392\u5e8f\uff08\u6839\u636e nums \u7b2c k \u4f4d\u6392\u5e8f\uff09 */\nfunc countingSortDigit(nums []int, exp int) {\n// \u5341\u8fdb\u5236\u7684\u4f4d\u8303\u56f4\u4e3a 0~9 \uff0c\u56e0\u6b64\u9700\u8981\u957f\u5ea6\u4e3a 10 \u7684\u6876\ncounter := make([]int, 10)\nn := len(nums)\n// \u7edf\u8ba1 0~9 \u5404\u6570\u5b57\u7684\u51fa\u73b0\u6b21\u6570\nfor i := 0; i &lt; n; i++ {\nd := digit(nums[i], exp) // \u83b7\u53d6 nums[i] \u7b2c k \u4f4d\uff0c\u8bb0\u4e3a d\ncounter[d]++             // \u7edf\u8ba1\u6570\u5b57 d \u7684\u51fa\u73b0\u6b21\u6570\n}\n// \u6c42\u524d\u7f00\u548c\uff0c\u5c06\u201c\u51fa\u73b0\u4e2a\u6570\u201d\u8f6c\u6362\u4e3a\u201c\u6570\u7ec4\u7d22\u5f15\u201d\nfor i := 1; i &lt; 10; i++ {\ncounter[i] += counter[i-1]\n}\n// \u5012\u5e8f\u904d\u5386\uff0c\u6839\u636e\u6876\u5185\u7edf\u8ba1\u7ed3\u679c\uff0c\u5c06\u5404\u5143\u7d20\u586b\u5165 res\nres := make([]int, n)\nfor i := n - 1; i &gt;= 0; i-- {\nd := digit(nums[i], exp)\nj := counter[d] - 1 // \u83b7\u53d6 d \u5728\u6570\u7ec4\u4e2d\u7684\u7d22\u5f15 j\nres[j] = nums[i]    // \u5c06\u5f53\u524d\u5143\u7d20\u586b\u5165\u7d22\u5f15 j\ncounter[d]--        // \u5c06 d \u7684\u6570\u91cf\u51cf 1\n}\n// \u4f7f\u7528\u7ed3\u679c\u8986\u76d6\u539f\u6570\u7ec4 nums\nfor i := 0; i &lt; n; i++ {\nnums[i] = res[i]\n}\n}\n/* \u57fa\u6570\u6392\u5e8f */\nfunc radixSort(nums []int) {\n// \u83b7\u53d6\u6570\u7ec4\u7684\u6700\u5927\u5143\u7d20\uff0c\u7528\u4e8e\u5224\u65ad\u6700\u5927\u4f4d\u6570\nmax := math.MinInt\nfor _, num := range nums {\nif num &gt; max {\nmax = num\n}\n}\n// \u6309\u7167\u4ece\u4f4e\u4f4d\u5230\u9ad8\u4f4d\u7684\u987a\u5e8f\u904d\u5386\nfor exp := 1; max &gt;= exp; exp *= 10 {\n// \u5bf9\u6570\u7ec4\u5143\u7d20\u7684\u7b2c k \u4f4d\u6267\u884c\u8ba1\u6570\u6392\u5e8f\n// k = 1 -&gt; exp = 1\n// k = 2 -&gt; exp = 10\n// \u5373 exp = 10^(k-1)\ncountingSortDigit(nums, exp)\n}\n}\n</code></pre> radix_sort.js<pre><code>/* \u83b7\u53d6\u5143\u7d20 num \u7684\u7b2c k \u4f4d\uff0c\u5176\u4e2d exp = 10^(k-1) */\nfunction digit(num, exp) {\n// \u4f20\u5165 exp \u800c\u975e k \u53ef\u4ee5\u907f\u514d\u5728\u6b64\u91cd\u590d\u6267\u884c\u6602\u8d35\u7684\u6b21\u65b9\u8ba1\u7b97\nreturn Math.floor(num / exp) % 10;\n}\n/* \u8ba1\u6570\u6392\u5e8f\uff08\u6839\u636e nums \u7b2c k \u4f4d\u6392\u5e8f\uff09 */\nfunction countingSortDigit(nums, exp) {\n// \u5341\u8fdb\u5236\u7684\u4f4d\u8303\u56f4\u4e3a 0~9 \uff0c\u56e0\u6b64\u9700\u8981\u957f\u5ea6\u4e3a 10 \u7684\u6876\nconst counter = new Array(10).fill(0);\nconst n = nums.length;\n// \u7edf\u8ba1 0~9 \u5404\u6570\u5b57\u7684\u51fa\u73b0\u6b21\u6570\nfor (let i = 0; i &lt; n; i++) {\nconst d = digit(nums[i], exp); // \u83b7\u53d6 nums[i] \u7b2c k \u4f4d\uff0c\u8bb0\u4e3a d\ncounter[d]++; // \u7edf\u8ba1\u6570\u5b57 d \u7684\u51fa\u73b0\u6b21\u6570\n}\n// \u6c42\u524d\u7f00\u548c\uff0c\u5c06\u201c\u51fa\u73b0\u4e2a\u6570\u201d\u8f6c\u6362\u4e3a\u201c\u6570\u7ec4\u7d22\u5f15\u201d\nfor (let i = 1; i &lt; 10; i++) {\ncounter[i] += counter[i - 1];\n}\n// \u5012\u5e8f\u904d\u5386\uff0c\u6839\u636e\u6876\u5185\u7edf\u8ba1\u7ed3\u679c\uff0c\u5c06\u5404\u5143\u7d20\u586b\u5165 res\nconst res = new Array(n).fill(0);\nfor (let i = n - 1; i &gt;= 0; i--) {\nconst d = digit(nums[i], exp);\nconst j = counter[d] - 1; // \u83b7\u53d6 d \u5728\u6570\u7ec4\u4e2d\u7684\u7d22\u5f15 j\nres[j] = nums[i]; // \u5c06\u5f53\u524d\u5143\u7d20\u586b\u5165\u7d22\u5f15 j\ncounter[d]--; // \u5c06 d \u7684\u6570\u91cf\u51cf 1\n}\n// \u4f7f\u7528\u7ed3\u679c\u8986\u76d6\u539f\u6570\u7ec4 nums\nfor (let i = 0; i &lt; n; i++) {\nnums[i] = res[i];\n}\n}\n/* \u57fa\u6570\u6392\u5e8f */\nfunction radixSort(nums) {\n// \u83b7\u53d6\u6570\u7ec4\u7684\u6700\u5927\u5143\u7d20\uff0c\u7528\u4e8e\u5224\u65ad\u6700\u5927\u4f4d\u6570\nlet m = Number.MIN_VALUE;\nfor (const num of nums) {\nif (num &gt; m) {\nm = num;\n}\n}\n// \u6309\u7167\u4ece\u4f4e\u4f4d\u5230\u9ad8\u4f4d\u7684\u987a\u5e8f\u904d\u5386\nfor (let exp = 1; exp &lt;= m; exp *= 10) {\n// \u5bf9\u6570\u7ec4\u5143\u7d20\u7684\u7b2c k \u4f4d\u6267\u884c\u8ba1\u6570\u6392\u5e8f\n// k = 1 -&gt; exp = 1\n// k = 2 -&gt; exp = 10\n// \u5373 exp = 10^(k-1)\ncountingSortDigit(nums, exp);\n}\n}\n</code></pre> radix_sort.ts<pre><code>/* \u83b7\u53d6\u5143\u7d20 num \u7684\u7b2c k \u4f4d\uff0c\u5176\u4e2d exp = 10^(k-1) */\nfunction digit(num: number, exp: number): number {\n// \u4f20\u5165 exp \u800c\u975e k \u53ef\u4ee5\u907f\u514d\u5728\u6b64\u91cd\u590d\u6267\u884c\u6602\u8d35\u7684\u6b21\u65b9\u8ba1\u7b97\nreturn Math.floor(num / exp) % 10;\n}\n/* \u8ba1\u6570\u6392\u5e8f\uff08\u6839\u636e nums \u7b2c k \u4f4d\u6392\u5e8f\uff09 */\nfunction countingSortDigit(nums: number[], exp: number): void {\n// \u5341\u8fdb\u5236\u7684\u4f4d\u8303\u56f4\u4e3a 0~9 \uff0c\u56e0\u6b64\u9700\u8981\u957f\u5ea6\u4e3a 10 \u7684\u6876\nconst counter = new Array(10).fill(0);\nconst n = nums.length;\n// \u7edf\u8ba1 0~9 \u5404\u6570\u5b57\u7684\u51fa\u73b0\u6b21\u6570\nfor (let i = 0; i &lt; n; i++) {\nconst d = digit(nums[i], exp); // \u83b7\u53d6 nums[i] \u7b2c k \u4f4d\uff0c\u8bb0\u4e3a d\ncounter[d]++; // \u7edf\u8ba1\u6570\u5b57 d \u7684\u51fa\u73b0\u6b21\u6570\n}\n// \u6c42\u524d\u7f00\u548c\uff0c\u5c06\u201c\u51fa\u73b0\u4e2a\u6570\u201d\u8f6c\u6362\u4e3a\u201c\u6570\u7ec4\u7d22\u5f15\u201d\nfor (let i = 1; i &lt; 10; i++) {\ncounter[i] += counter[i - 1];\n}\n// \u5012\u5e8f\u904d\u5386\uff0c\u6839\u636e\u6876\u5185\u7edf\u8ba1\u7ed3\u679c\uff0c\u5c06\u5404\u5143\u7d20\u586b\u5165 res\nconst res = new Array(n).fill(0);\nfor (let i = n - 1; i &gt;= 0; i--) {\nconst d = digit(nums[i], exp);\nconst j = counter[d] - 1; // \u83b7\u53d6 d \u5728\u6570\u7ec4\u4e2d\u7684\u7d22\u5f15 j\nres[j] = nums[i]; // \u5c06\u5f53\u524d\u5143\u7d20\u586b\u5165\u7d22\u5f15 j\ncounter[d]--; // \u5c06 d \u7684\u6570\u91cf\u51cf 1\n}\n// \u4f7f\u7528\u7ed3\u679c\u8986\u76d6\u539f\u6570\u7ec4 nums\nfor (let i = 0; i &lt; n; i++) {\nnums[i] = res[i];\n}\n}\n/* \u57fa\u6570\u6392\u5e8f */\nfunction radixSort(nums: number[]): void {\n// \u83b7\u53d6\u6570\u7ec4\u7684\u6700\u5927\u5143\u7d20\uff0c\u7528\u4e8e\u5224\u65ad\u6700\u5927\u4f4d\u6570\nlet m = Number.MIN_VALUE;\nfor (const num of nums) {\nif (num &gt; m) {\nm = num;\n}\n}\n// \u6309\u7167\u4ece\u4f4e\u4f4d\u5230\u9ad8\u4f4d\u7684\u987a\u5e8f\u904d\u5386\nfor (let exp = 1; exp &lt;= m; exp *= 10) {\n// \u5bf9\u6570\u7ec4\u5143\u7d20\u7684\u7b2c k \u4f4d\u6267\u884c\u8ba1\u6570\u6392\u5e8f\n// k = 1 -&gt; exp = 1\n// k = 2 -&gt; exp = 10\n// \u5373 exp = 10^(k-1)\ncountingSortDigit(nums, exp);\n}\n}\n</code></pre> radix_sort.c<pre><code>/* \u83b7\u53d6\u5143\u7d20 num \u7684\u7b2c k \u4f4d\uff0c\u5176\u4e2d exp = 10^(k-1) */\nint digit(int num, int exp) {\n// \u4f20\u5165 exp \u800c\u975e k \u53ef\u4ee5\u907f\u514d\u5728\u6b64\u91cd\u590d\u6267\u884c\u6602\u8d35\u7684\u6b21\u65b9\u8ba1\u7b97\nreturn (num / exp) % 10;\n}\n/* \u8ba1\u6570\u6392\u5e8f\uff08\u6839\u636e nums \u7b2c k \u4f4d\u6392\u5e8f\uff09 */\nvoid countingSortDigit(int nums[], int size, int exp) {\n// \u5341\u8fdb\u5236\u7684\u4f4d\u8303\u56f4\u4e3a 0~9 \uff0c\u56e0\u6b64\u9700\u8981\u957f\u5ea6\u4e3a 10 \u7684\u6876\nint *counter = (int *)malloc((sizeof(int) * 10));\n// \u7edf\u8ba1 0~9 \u5404\u6570\u5b57\u7684\u51fa\u73b0\u6b21\u6570\nfor (int i = 0; i &lt; size; i++) {\n// \u83b7\u53d6 nums[i] \u7b2c k \u4f4d\uff0c\u8bb0\u4e3a d\nint d = digit(nums[i], exp);\n// \u7edf\u8ba1\u6570\u5b57 d \u7684\u51fa\u73b0\u6b21\u6570\ncounter[d]++;\n}\n// \u6c42\u524d\u7f00\u548c\uff0c\u5c06\u201c\u51fa\u73b0\u4e2a\u6570\u201d\u8f6c\u6362\u4e3a\u201c\u6570\u7ec4\u7d22\u5f15\u201d\nfor (int i = 1; i &lt; 10; i++) {\ncounter[i] += counter[i - 1];\n}\n// \u5012\u5e8f\u904d\u5386\uff0c\u6839\u636e\u6876\u5185\u7edf\u8ba1\u7ed3\u679c\uff0c\u5c06\u5404\u5143\u7d20\u586b\u5165 res\nint *res = (int *)malloc(sizeof(int) * size);\nfor (int i = size - 1; i &gt;= 0; i--) {\nint d = digit(nums[i], exp);\nint j = counter[d] - 1; // \u83b7\u53d6 d \u5728\u6570\u7ec4\u4e2d\u7684\u7d22\u5f15 j\nres[j] = nums[i];       // \u5c06\u5f53\u524d\u5143\u7d20\u586b\u5165\u7d22\u5f15 j\ncounter[d]--;           // \u5c06 d \u7684\u6570\u91cf\u51cf 1\n}\n// \u4f7f\u7528\u7ed3\u679c\u8986\u76d6\u539f\u6570\u7ec4 nums\nfor (int i = 0; i &lt; size; i++) {\nnums[i] = res[i];\n}\n}\n/* \u57fa\u6570\u6392\u5e8f */\nvoid radixSort(int nums[], int size) {\n// \u83b7\u53d6\u6570\u7ec4\u7684\u6700\u5927\u5143\u7d20\uff0c\u7528\u4e8e\u5224\u65ad\u6700\u5927\u4f4d\u6570\nint max = INT32_MIN;\nfor (size_t i = 0; i &lt; size - 1; i++) {\nif (nums[i] &gt; max) {\nmax = nums[i];\n}\n}\n// \u6309\u7167\u4ece\u4f4e\u4f4d\u5230\u9ad8\u4f4d\u7684\u987a\u5e8f\u904d\u5386\nfor (int exp = 1; max &gt;= exp; exp *= 10)\n// \u5bf9\u6570\u7ec4\u5143\u7d20\u7684\u7b2c k \u4f4d\u6267\u884c\u8ba1\u6570\u6392\u5e8f\n// k = 1 -&gt; exp = 1\n// k = 2 -&gt; exp = 10\n// \u5373 exp = 10^(k-1)\ncountingSortDigit(nums, size, exp);\n}\n</code></pre> radix_sort.cs<pre><code>/* \u83b7\u53d6\u5143\u7d20 num \u7684\u7b2c k \u4f4d\uff0c\u5176\u4e2d exp = 10^(k-1) */\nint digit(int num, int exp) {\n// \u4f20\u5165 exp \u800c\u975e k \u53ef\u4ee5\u907f\u514d\u5728\u6b64\u91cd\u590d\u6267\u884c\u6602\u8d35\u7684\u6b21\u65b9\u8ba1\u7b97\nreturn (num / exp) % 10;\n}\n/* \u8ba1\u6570\u6392\u5e8f\uff08\u6839\u636e nums \u7b2c k \u4f4d\u6392\u5e8f\uff09 */\nvoid countingSortDigit(int[] nums, int exp) {\n// \u5341\u8fdb\u5236\u7684\u4f4d\u8303\u56f4\u4e3a 0~9 \uff0c\u56e0\u6b64\u9700\u8981\u957f\u5ea6\u4e3a 10 \u7684\u6876\nint[] counter = new int[10];\nint n = nums.Length;\n// \u7edf\u8ba1 0~9 \u5404\u6570\u5b57\u7684\u51fa\u73b0\u6b21\u6570\nfor (int i = 0; i &lt; n; i++) {\nint d = digit(nums[i], exp); // \u83b7\u53d6 nums[i] \u7b2c k \u4f4d\uff0c\u8bb0\u4e3a d\ncounter[d]++;                // \u7edf\u8ba1\u6570\u5b57 d \u7684\u51fa\u73b0\u6b21\u6570\n}\n// \u6c42\u524d\u7f00\u548c\uff0c\u5c06\u201c\u51fa\u73b0\u4e2a\u6570\u201d\u8f6c\u6362\u4e3a\u201c\u6570\u7ec4\u7d22\u5f15\u201d\nfor (int i = 1; i &lt; 10; i++) {\ncounter[i] += counter[i - 1];\n}\n// \u5012\u5e8f\u904d\u5386\uff0c\u6839\u636e\u6876\u5185\u7edf\u8ba1\u7ed3\u679c\uff0c\u5c06\u5404\u5143\u7d20\u586b\u5165 res\nint[] res = new int[n];\nfor (int i = n - 1; i &gt;= 0; i--) {\nint d = digit(nums[i], exp);\nint j = counter[d] - 1; // \u83b7\u53d6 d \u5728\u6570\u7ec4\u4e2d\u7684\u7d22\u5f15 j\nres[j] = nums[i];       // \u5c06\u5f53\u524d\u5143\u7d20\u586b\u5165\u7d22\u5f15 j\ncounter[d]--;           // \u5c06 d \u7684\u6570\u91cf\u51cf 1\n}\n// \u4f7f\u7528\u7ed3\u679c\u8986\u76d6\u539f\u6570\u7ec4 nums\nfor (int i = 0; i &lt; n; i++) {\nnums[i] = res[i];\n}\n}\n/* \u57fa\u6570\u6392\u5e8f */\nvoid radixSort(int[] nums) {\n// \u83b7\u53d6\u6570\u7ec4\u7684\u6700\u5927\u5143\u7d20\uff0c\u7528\u4e8e\u5224\u65ad\u6700\u5927\u4f4d\u6570\nint m = int.MinValue;\nforeach (int num in nums) {\nif (num &gt; m) m = num;\n}\n// \u6309\u7167\u4ece\u4f4e\u4f4d\u5230\u9ad8\u4f4d\u7684\u987a\u5e8f\u904d\u5386\nfor (int exp = 1; exp &lt;= m; exp *= 10) {\n// \u5bf9\u6570\u7ec4\u5143\u7d20\u7684\u7b2c k \u4f4d\u6267\u884c\u8ba1\u6570\u6392\u5e8f\n// k = 1 -&gt; exp = 1\n// k = 2 -&gt; exp = 10\n// \u5373 exp = 10^(k-1)\ncountingSortDigit(nums, exp);\n}\n}\n</code></pre> radix_sort.swift<pre><code>/* \u83b7\u53d6\u5143\u7d20 num \u7684\u7b2c k \u4f4d\uff0c\u5176\u4e2d exp = 10^(k-1) */\nfunc digit(num: Int, exp: Int) -&gt; Int {\n// \u4f20\u5165 exp \u800c\u975e k \u53ef\u4ee5\u907f\u514d\u5728\u6b64\u91cd\u590d\u6267\u884c\u6602\u8d35\u7684\u6b21\u65b9\u8ba1\u7b97\n(num / exp) % 10\n}\n/* \u8ba1\u6570\u6392\u5e8f\uff08\u6839\u636e nums \u7b2c k \u4f4d\u6392\u5e8f\uff09 */\nfunc countingSortDigit(nums: inout [Int], exp: Int) {\n// \u5341\u8fdb\u5236\u7684\u4f4d\u8303\u56f4\u4e3a 0~9 \uff0c\u56e0\u6b64\u9700\u8981\u957f\u5ea6\u4e3a 10 \u7684\u6876\nvar counter = Array(repeating: 0, count: 10)\nlet n = nums.count\n// \u7edf\u8ba1 0~9 \u5404\u6570\u5b57\u7684\u51fa\u73b0\u6b21\u6570\nfor i in nums.indices {\nlet d = digit(num: nums[i], exp: exp) // \u83b7\u53d6 nums[i] \u7b2c k \u4f4d\uff0c\u8bb0\u4e3a d\ncounter[d] += 1 // \u7edf\u8ba1\u6570\u5b57 d \u7684\u51fa\u73b0\u6b21\u6570\n}\n// \u6c42\u524d\u7f00\u548c\uff0c\u5c06\u201c\u51fa\u73b0\u4e2a\u6570\u201d\u8f6c\u6362\u4e3a\u201c\u6570\u7ec4\u7d22\u5f15\u201d\nfor i in 1 ..&lt; 10 {\ncounter[i] += counter[i - 1]\n}\n// \u5012\u5e8f\u904d\u5386\uff0c\u6839\u636e\u6876\u5185\u7edf\u8ba1\u7ed3\u679c\uff0c\u5c06\u5404\u5143\u7d20\u586b\u5165 res\nvar res = Array(repeating: 0, count: n)\nfor i in stride(from: n - 1, through: 0, by: -1) {\nlet d = digit(num: nums[i], exp: exp)\nlet j = counter[d] - 1 // \u83b7\u53d6 d \u5728\u6570\u7ec4\u4e2d\u7684\u7d22\u5f15 j\nres[j] = nums[i] // \u5c06\u5f53\u524d\u5143\u7d20\u586b\u5165\u7d22\u5f15 j\ncounter[d] -= 1 // \u5c06 d \u7684\u6570\u91cf\u51cf 1\n}\n// \u4f7f\u7528\u7ed3\u679c\u8986\u76d6\u539f\u6570\u7ec4 nums\nfor i in nums.indices {\nnums[i] = res[i]\n}\n}\n/* \u57fa\u6570\u6392\u5e8f */\nfunc radixSort(nums: inout [Int]) {\n// \u83b7\u53d6\u6570\u7ec4\u7684\u6700\u5927\u5143\u7d20\uff0c\u7528\u4e8e\u5224\u65ad\u6700\u5927\u4f4d\u6570\nvar m = Int.min\nfor num in nums {\nif num &gt; m {\nm = num\n}\n}\n// \u6309\u7167\u4ece\u4f4e\u4f4d\u5230\u9ad8\u4f4d\u7684\u987a\u5e8f\u904d\u5386\nfor exp in sequence(first: 1, next: { m &gt;= ($0 * 10) ? $0 * 10 : nil }) {\n// \u5bf9\u6570\u7ec4\u5143\u7d20\u7684\u7b2c k \u4f4d\u6267\u884c\u8ba1\u6570\u6392\u5e8f\n// k = 1 -&gt; exp = 1\n// k = 2 -&gt; exp = 10\n// \u5373 exp = 10^(k-1)\ncountingSortDigit(nums: &amp;nums, exp: exp)\n}\n}\n</code></pre> radix_sort.zig<pre><code>// \u83b7\u53d6\u5143\u7d20 num \u7684\u7b2c k \u4f4d\uff0c\u5176\u4e2d exp = 10^(k-1)\nfn digit(num: i32, exp: i32) i32 {\n// \u4f20\u5165 exp \u800c\u975e k \u53ef\u4ee5\u907f\u514d\u5728\u6b64\u91cd\u590d\u6267\u884c\u6602\u8d35\u7684\u6b21\u65b9\u8ba1\u7b97\nreturn @mod(@divFloor(num, exp), 10);\n}\n// \u8ba1\u6570\u6392\u5e8f\uff08\u6839\u636e nums \u7b2c k \u4f4d\u6392\u5e8f\uff09\nfn countingSortDigit(nums: []i32, exp: i32) !void {\n// \u5341\u8fdb\u5236\u7684\u4f4d\u8303\u56f4\u4e3a 0~9 \uff0c\u56e0\u6b64\u9700\u8981\u957f\u5ea6\u4e3a 10 \u7684\u6876\nvar mem_arena = std.heap.ArenaAllocator.init(std.heap.page_allocator);\n// defer mem_arena.deinit();\nconst mem_allocator = mem_arena.allocator();\nvar counter = try mem_allocator.alloc(usize, 10);\nstd.mem.set(usize, counter, 0);\nvar n = nums.len;\n// \u7edf\u8ba1 0~9 \u5404\u6570\u5b57\u7684\u51fa\u73b0\u6b21\u6570\nfor (nums) |num| {\nvar d = @bitCast(u32, digit(num, exp)); // \u83b7\u53d6 nums[i] \u7b2c k \u4f4d\uff0c\u8bb0\u4e3a d\ncounter[d] += 1; // \u7edf\u8ba1\u6570\u5b57 d \u7684\u51fa\u73b0\u6b21\u6570\n}\n// \u6c42\u524d\u7f00\u548c\uff0c\u5c06\u201c\u51fa\u73b0\u4e2a\u6570\u201d\u8f6c\u6362\u4e3a\u201c\u6570\u7ec4\u7d22\u5f15\u201d\nvar i: usize = 1;\nwhile (i &lt; 10) : (i += 1) {\ncounter[i] += counter[i - 1];\n}\n// \u5012\u5e8f\u904d\u5386\uff0c\u6839\u636e\u6876\u5185\u7edf\u8ba1\u7ed3\u679c\uff0c\u5c06\u5404\u5143\u7d20\u586b\u5165 res\nvar res = try mem_allocator.alloc(i32, n);\ni = n - 1;\nwhile (i &gt;= 0) : (i -= 1) {\nvar d = @bitCast(u32, digit(nums[i], exp));\nvar j = counter[d] - 1; // \u83b7\u53d6 d \u5728\u6570\u7ec4\u4e2d\u7684\u7d22\u5f15 j\nres[j] = nums[i];       // \u5c06\u5f53\u524d\u5143\u7d20\u586b\u5165\u7d22\u5f15 j\ncounter[d] -= 1;        // \u5c06 d \u7684\u6570\u91cf\u51cf 1\nif (i == 0) break;\n}\n// \u4f7f\u7528\u7ed3\u679c\u8986\u76d6\u539f\u6570\u7ec4 nums\ni = 0;\nwhile (i &lt; n) : (i += 1) {\nnums[i] = res[i];\n}\n}\n// \u57fa\u6570\u6392\u5e8f\nfn radixSort(nums: []i32) !void {\n// \u83b7\u53d6\u6570\u7ec4\u7684\u6700\u5927\u5143\u7d20\uff0c\u7528\u4e8e\u5224\u65ad\u6700\u5927\u4f4d\u6570\nvar m: i32 = std.math.minInt(i32);\nfor (nums) |num| {\nif (num &gt; m) m = num;\n}\n// \u6309\u7167\u4ece\u4f4e\u4f4d\u5230\u9ad8\u4f4d\u7684\u987a\u5e8f\u904d\u5386\nvar exp: i32 = 1;\nwhile (exp &lt;= m) : (exp *= 10) {\n// \u5bf9\u6570\u7ec4\u5143\u7d20\u7684\u7b2c k \u4f4d\u6267\u884c\u8ba1\u6570\u6392\u5e8f\n// k = 1 -&gt; exp = 1\n// k = 2 -&gt; exp = 10\n// \u5373 exp = 10^(k-1)\ntry countingSortDigit(nums, exp);    }\n} </code></pre> radix_sort.dart<pre><code>/* \u83b7\u53d6\u5143\u7d20 num \u7684\u7b2c k \u4f4d\uff0c\u5176\u4e2d exp = 10^(k-1) */\nint digit(int num, int exp) {\n// \u4f20\u5165 exp \u800c\u975e k \u53ef\u4ee5\u907f\u514d\u5728\u6b64\u91cd\u590d\u6267\u884c\u6602\u8d35\u7684\u6b21\u65b9\u8ba1\u7b97\nreturn (num ~/ exp) % 10;\n}\n/* \u8ba1\u6570\u6392\u5e8f\uff08\u6839\u636e nums \u7b2c k \u4f4d\u6392\u5e8f\uff09 */\nvoid countingSortDigit(List&lt;int&gt; nums, int exp) {\n// \u5341\u8fdb\u5236\u7684\u4f4d\u8303\u56f4\u4e3a 0~9 \uff0c\u56e0\u6b64\u9700\u8981\u957f\u5ea6\u4e3a 10 \u7684\u6876\nList&lt;int&gt; counter = List&lt;int&gt;.filled(10, 0);\nint n = nums.length;\n// \u7edf\u8ba1 0~9 \u5404\u6570\u5b57\u7684\u51fa\u73b0\u6b21\u6570\nfor (int i = 0; i &lt; n; i++) {\nint d = digit(nums[i], exp); // \u83b7\u53d6 nums[i] \u7b2c k \u4f4d\uff0c\u8bb0\u4e3a d\ncounter[d]++; // \u7edf\u8ba1\u6570\u5b57 d \u7684\u51fa\u73b0\u6b21\u6570\n}\n// \u6c42\u524d\u7f00\u548c\uff0c\u5c06\u201c\u51fa\u73b0\u4e2a\u6570\u201d\u8f6c\u6362\u4e3a\u201c\u6570\u7ec4\u7d22\u5f15\u201d\nfor (int i = 1; i &lt; 10; i++) {\ncounter[i] += counter[i - 1];\n}\n// \u5012\u5e8f\u904d\u5386\uff0c\u6839\u636e\u6876\u5185\u7edf\u8ba1\u7ed3\u679c\uff0c\u5c06\u5404\u5143\u7d20\u586b\u5165 res\nList&lt;int&gt; res = List&lt;int&gt;.filled(n, 0);\nfor (int i = n - 1; i &gt;= 0; i--) {\nint d = digit(nums[i], exp);\nint j = counter[d] - 1; // \u83b7\u53d6 d \u5728\u6570\u7ec4\u4e2d\u7684\u7d22\u5f15 j\nres[j] = nums[i]; // \u5c06\u5f53\u524d\u5143\u7d20\u586b\u5165\u7d22\u5f15 j\ncounter[d]--; // \u5c06 d \u7684\u6570\u91cf\u51cf 1\n}\n// \u4f7f\u7528\u7ed3\u679c\u8986\u76d6\u539f\u6570\u7ec4 nums\nfor (int i = 0; i &lt; n; i++) nums[i] = res[i];\n}\n/* \u57fa\u6570\u6392\u5e8f */\nvoid radixSort(List&lt;int&gt; nums) {\n// \u83b7\u53d6\u6570\u7ec4\u7684\u6700\u5927\u5143\u7d20\uff0c\u7528\u4e8e\u5224\u65ad\u6700\u5927\u4f4d\u6570\n// dart \u4e2d int \u7684\u957f\u5ea6\u662f 64 \u4f4d\u7684\nint m = -1 &lt;&lt; 63; for (int num in nums) if (num &gt; m) m = num;\n// \u6309\u7167\u4ece\u4f4e\u4f4d\u5230\u9ad8\u4f4d\u7684\u987a\u5e8f\u904d\u5386\nfor (int exp = 1; exp &lt;= m; exp *= 10)\n// \u5bf9\u6570\u7ec4\u5143\u7d20\u7684\u7b2c k \u4f4d\u6267\u884c\u8ba1\u6570\u6392\u5e8f\n// k = 1 -&gt; exp = 1\n// k = 2 -&gt; exp = 10\n// \u5373 exp = 10^(k-1)\ncountingSortDigit(nums, exp);\n}\n</code></pre> <p>\u4e3a\u4ec0\u4e48\u4ece\u6700\u4f4e\u4f4d\u5f00\u59cb\u6392\u5e8f\uff1f</p> <p>\u5728\u8fde\u7eed\u7684\u6392\u5e8f\u8f6e\u6b21\u4e2d\uff0c\u540e\u4e00\u8f6e\u6392\u5e8f\u4f1a\u8986\u76d6\u524d\u4e00\u8f6e\u6392\u5e8f\u7684\u7ed3\u679c\u3002\u4e3e\u4f8b\u6765\u8bf4\uff0c\u5982\u679c\u7b2c\u4e00\u8f6e\u6392\u5e8f\u7ed3\u679c \\(a &lt; b\\) \uff0c\u800c\u7b2c\u4e8c\u8f6e\u6392\u5e8f\u7ed3\u679c \\(a &gt; b\\) \uff0c\u90a3\u4e48\u7b2c\u4e8c\u8f6e\u7684\u7ed3\u679c\u5c06\u53d6\u4ee3\u7b2c\u4e00\u8f6e\u7684\u7ed3\u679c\u3002\u7531\u4e8e\u6570\u5b57\u7684\u9ad8\u4f4d\u4f18\u5148\u7ea7\u9ad8\u4e8e\u4f4e\u4f4d\uff0c\u6211\u4eec\u5e94\u8be5\u5148\u6392\u5e8f\u4f4e\u4f4d\u518d\u6392\u5e8f\u9ad8\u4f4d\u3002</p>"},{"location":"chapter_sorting/radix_sort/#11102","title":"11.10.2. \u00a0 \u7b97\u6cd5\u7279\u6027","text":"<p>\u76f8\u8f83\u4e8e\u8ba1\u6570\u6392\u5e8f\uff0c\u57fa\u6570\u6392\u5e8f\u9002\u7528\u4e8e\u6570\u503c\u8303\u56f4\u8f83\u5927\u7684\u60c5\u51b5\uff0c\u4f46\u524d\u63d0\u662f\u6570\u636e\u5fc5\u987b\u53ef\u4ee5\u8868\u793a\u4e3a\u56fa\u5b9a\u4f4d\u6570\u7684\u683c\u5f0f\uff0c\u4e14\u4f4d\u6570\u4e0d\u80fd\u8fc7\u5927\u3002\u4f8b\u5982\uff0c\u6d6e\u70b9\u6570\u4e0d\u9002\u5408\u4f7f\u7528\u57fa\u6570\u6392\u5e8f\uff0c\u56e0\u4e3a\u5176\u4f4d\u6570 \\(k\\) \u8fc7\u5927\uff0c\u53ef\u80fd\u5bfc\u81f4\u65f6\u95f4\u590d\u6742\u5ea6 \\(O(nk) \\gg O(n^2)\\) \u3002</p> <ul> <li>\u65f6\u95f4\u590d\u6742\u5ea6 \\(O(nk)\\) \uff1a\u8bbe\u6570\u636e\u91cf\u4e3a \\(n\\) \u3001\u6570\u636e\u4e3a \\(d\\) \u8fdb\u5236\u3001\u6700\u5927\u4f4d\u6570\u4e3a \\(k\\) \uff0c\u5219\u5bf9\u67d0\u4e00\u4f4d\u6267\u884c\u8ba1\u6570\u6392\u5e8f\u4f7f\u7528 \\(O(n + d)\\) \u65f6\u95f4\uff0c\u6392\u5e8f\u6240\u6709 \\(k\\) \u4f4d\u4f7f\u7528 \\(O((n + d)k)\\) \u65f6\u95f4\u3002\u901a\u5e38\u60c5\u51b5\u4e0b\uff0c\\(d\\) \u548c \\(k\\) \u90fd\u76f8\u5bf9\u8f83\u5c0f\uff0c\u65f6\u95f4\u590d\u6742\u5ea6\u8d8b\u5411 \\(O(n)\\) \u3002</li> <li>\u7a7a\u95f4\u590d\u6742\u5ea6 \\(O(n + d)\\) \u3001\u975e\u539f\u5730\u6392\u5e8f \uff1a\u4e0e\u8ba1\u6570\u6392\u5e8f\u76f8\u540c\uff0c\u57fa\u6570\u6392\u5e8f\u9700\u8981\u501f\u52a9\u957f\u5ea6\u4e3a \\(n\\) \u548c \\(d\\) \u7684\u6570\u7ec4 <code>res</code> \u548c <code>counter</code> \u3002</li> <li>\u7a33\u5b9a\u6392\u5e8f\uff1a\u4e0e\u8ba1\u6570\u6392\u5e8f\u76f8\u540c\u3002</li> </ul>"},{"location":"chapter_sorting/selection_sort/","title":"11.2. \u00a0 \u9009\u62e9\u6392\u5e8f","text":"<p>\u300c\u9009\u62e9\u6392\u5e8f Selection Sort\u300d\u7684\u5de5\u4f5c\u539f\u7406\u975e\u5e38\u76f4\u63a5\uff1a\u5f00\u542f\u4e00\u4e2a\u5faa\u73af\uff0c\u6bcf\u8f6e\u4ece\u672a\u6392\u5e8f\u533a\u95f4\u9009\u62e9\u6700\u5c0f\u7684\u5143\u7d20\uff0c\u5c06\u5176\u653e\u5230\u5df2\u6392\u5e8f\u533a\u95f4\u7684\u672b\u5c3e\u3002</p> <p>\u8bbe\u6570\u7ec4\u7684\u957f\u5ea6\u4e3a \\(n\\) \uff0c\u9009\u62e9\u6392\u5e8f\u7684\u7b97\u6cd5\u6d41\u7a0b\u5982\u4e0b\uff1a</p> <ol> <li>\u521d\u59cb\u72b6\u6001\u4e0b\uff0c\u6240\u6709\u5143\u7d20\u672a\u6392\u5e8f\uff0c\u5373\u672a\u6392\u5e8f\uff08\u7d22\u5f15\uff09\u533a\u95f4\u4e3a \\([0, n-1]\\) \u3002</li> <li>\u9009\u53d6\u533a\u95f4 \\([0, n-1]\\) \u4e2d\u7684\u6700\u5c0f\u5143\u7d20\uff0c\u5c06\u5176\u4e0e\u7d22\u5f15 \\(0\\) \u5904\u5143\u7d20\u4ea4\u6362\u3002\u5b8c\u6210\u540e\uff0c\u6570\u7ec4\u524d 1 \u4e2a\u5143\u7d20\u5df2\u6392\u5e8f\u3002</li> <li>\u9009\u53d6\u533a\u95f4 \\([1, n-1]\\) \u4e2d\u7684\u6700\u5c0f\u5143\u7d20\uff0c\u5c06\u5176\u4e0e\u7d22\u5f15 \\(1\\) \u5904\u5143\u7d20\u4ea4\u6362\u3002\u5b8c\u6210\u540e\uff0c\u6570\u7ec4\u524d 2 \u4e2a\u5143\u7d20\u5df2\u6392\u5e8f\u3002</li> <li>\u4ee5\u6b64\u7c7b\u63a8\u3002\u7ecf\u8fc7 \\(n - 1\\) \u8f6e\u9009\u62e9\u4e0e\u4ea4\u6362\u540e\uff0c\u6570\u7ec4\u524d \\(n - 1\\) \u4e2a\u5143\u7d20\u5df2\u6392\u5e8f\u3002</li> <li>\u4ec5\u5269\u7684\u4e00\u4e2a\u5143\u7d20\u5fc5\u5b9a\u662f\u6700\u5927\u5143\u7d20\uff0c\u65e0\u9700\u6392\u5e8f\uff0c\u56e0\u6b64\u6570\u7ec4\u6392\u5e8f\u5b8c\u6210\u3002</li> </ol> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt;&lt;11&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p>\u5728\u4ee3\u7801\u4e2d\uff0c\u6211\u4eec\u7528 \\(k\\) \u6765\u8bb0\u5f55\u672a\u6392\u5e8f\u533a\u95f4\u5185\u7684\u6700\u5c0f\u5143\u7d20\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart selection_sort.java<pre><code>/* \u9009\u62e9\u6392\u5e8f */\nvoid selectionSort(int[] nums) {\nint n = nums.length;\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [i, n-1]\nfor (int i = 0; i &lt; n - 1; i++) {\n// \u5185\u5faa\u73af\uff1a\u627e\u5230\u672a\u6392\u5e8f\u533a\u95f4\u5185\u7684\u6700\u5c0f\u5143\u7d20\nint k = i;\nfor (int j = i + 1; j &lt; n; j++) {\nif (nums[j] &lt; nums[k])\nk = j; // \u8bb0\u5f55\u6700\u5c0f\u5143\u7d20\u7684\u7d22\u5f15\n}\n// \u5c06\u8be5\u6700\u5c0f\u5143\u7d20\u4e0e\u672a\u6392\u5e8f\u533a\u95f4\u7684\u9996\u4e2a\u5143\u7d20\u4ea4\u6362\nint temp = nums[i];\nnums[i] = nums[k];\nnums[k] = temp;\n}\n}\n</code></pre> selection_sort.cpp<pre><code>/* \u9009\u62e9\u6392\u5e8f */\nvoid selectionSort(vector&lt;int&gt; &amp;nums) {\nint n = nums.size();\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [i, n-1]\nfor (int i = 0; i &lt; n - 1; i++) {\n// \u5185\u5faa\u73af\uff1a\u627e\u5230\u672a\u6392\u5e8f\u533a\u95f4\u5185\u7684\u6700\u5c0f\u5143\u7d20\nint k = i;\nfor (int j = i + 1; j &lt; n; j++) {\nif (nums[j] &lt; nums[k])\nk = j; // \u8bb0\u5f55\u6700\u5c0f\u5143\u7d20\u7684\u7d22\u5f15\n}\n// \u5c06\u8be5\u6700\u5c0f\u5143\u7d20\u4e0e\u672a\u6392\u5e8f\u533a\u95f4\u7684\u9996\u4e2a\u5143\u7d20\u4ea4\u6362\nswap(nums[i], nums[k]);\n}\n}\n</code></pre> selection_sort.py<pre><code>def selection_sort(nums: list[int]):\n\"\"\"\u9009\u62e9\u6392\u5e8f\"\"\"\nn = len(nums)\n# \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [i, n-1]\nfor i in range(n - 1):\n# \u5185\u5faa\u73af\uff1a\u627e\u5230\u672a\u6392\u5e8f\u533a\u95f4\u5185\u7684\u6700\u5c0f\u5143\u7d20\nk = i\nfor j in range(i + 1, n):\nif nums[j] &lt; nums[k]:\nk = j  # \u8bb0\u5f55\u6700\u5c0f\u5143\u7d20\u7684\u7d22\u5f15\n# \u5c06\u8be5\u6700\u5c0f\u5143\u7d20\u4e0e\u672a\u6392\u5e8f\u533a\u95f4\u7684\u9996\u4e2a\u5143\u7d20\u4ea4\u6362\nnums[i], nums[k] = nums[k], nums[i]\n</code></pre> selection_sort.go<pre><code>/* \u9009\u62e9\u6392\u5e8f */\nfunc selectionSort(nums []int) {\nn := len(nums)\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [i, n-1]\nfor i := 0; i &lt; n-1; i++ {\n// \u5185\u5faa\u73af\uff1a\u627e\u5230\u672a\u6392\u5e8f\u533a\u95f4\u5185\u7684\u6700\u5c0f\u5143\u7d20\nk := i\nfor j := i + 1; j &lt; n; j++ {\nif nums[j] &lt; nums[k] {\n// \u8bb0\u5f55\u6700\u5c0f\u5143\u7d20\u7684\u7d22\u5f15\nk = j\n}\n}\n// \u5c06\u8be5\u6700\u5c0f\u5143\u7d20\u4e0e\u672a\u6392\u5e8f\u533a\u95f4\u7684\u9996\u4e2a\u5143\u7d20\u4ea4\u6362\nnums[i], nums[k] = nums[k], nums[i]\n}\n}\n</code></pre> selection_sort.js<pre><code>/* \u9009\u62e9\u6392\u5e8f */\nfunction selectionSort(nums) {\nlet n = nums.length;\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [i, n-1]\nfor (let i = 0; i &lt; n - 1; i++) {\n// \u5185\u5faa\u73af\uff1a\u627e\u5230\u672a\u6392\u5e8f\u533a\u95f4\u5185\u7684\u6700\u5c0f\u5143\u7d20\nlet k = i;\nfor (let j = i + 1; j &lt; n; j++) {\nif (nums[j] &lt; nums[k]) {\nk = j; // \u8bb0\u5f55\u6700\u5c0f\u5143\u7d20\u7684\u7d22\u5f15\n}\n}\n// \u5c06\u8be5\u6700\u5c0f\u5143\u7d20\u4e0e\u672a\u6392\u5e8f\u533a\u95f4\u7684\u9996\u4e2a\u5143\u7d20\u4ea4\u6362\n[nums[i], nums[k]] = [nums[k], nums[i]];\n}\n}\n</code></pre> selection_sort.ts<pre><code>/* \u9009\u62e9\u6392\u5e8f */\nfunction selectionSort(nums: number[]): void {\nlet n = nums.length;\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [i, n-1]\nfor (let i = 0; i &lt; n - 1; i++) {\n// \u5185\u5faa\u73af\uff1a\u627e\u5230\u672a\u6392\u5e8f\u533a\u95f4\u5185\u7684\u6700\u5c0f\u5143\u7d20\nlet k = i;\nfor (let j = i + 1; j &lt; n; j++) {\nif (nums[j] &lt; nums[k]) {\nk = j; // \u8bb0\u5f55\u6700\u5c0f\u5143\u7d20\u7684\u7d22\u5f15\n}\n}\n// \u5c06\u8be5\u6700\u5c0f\u5143\u7d20\u4e0e\u672a\u6392\u5e8f\u533a\u95f4\u7684\u9996\u4e2a\u5143\u7d20\u4ea4\u6362\n[nums[i], nums[k]] = [nums[k], nums[i]];\n}\n}\n</code></pre> selection_sort.c<pre><code>/* \u9009\u62e9\u6392\u5e8f */\nvoid selectionSort(int nums[], int n) {\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [i, n-1]\nfor (int i = 0; i &lt; n - 1; i++) {\n// \u5185\u5faa\u73af\uff1a\u627e\u5230\u672a\u6392\u5e8f\u533a\u95f4\u5185\u7684\u6700\u5c0f\u5143\u7d20\nint k = i;\nfor (int j = i + 1; j &lt; n; j++) {\nif (nums[j] &lt; nums[k])\nk = j;  // \u8bb0\u5f55\u6700\u5c0f\u5143\u7d20\u7684\u7d22\u5f15\n}\n// \u5c06\u8be5\u6700\u5c0f\u5143\u7d20\u4e0e\u672a\u6392\u5e8f\u533a\u95f4\u7684\u9996\u4e2a\u5143\u7d20\u4ea4\u6362\nint temp = nums[i];\nnums[i] = nums[k];\nnums[k] = temp;\n}\n}\n</code></pre> selection_sort.cs<pre><code>/* \u9009\u62e9\u6392\u5e8f */\nvoid selectionSort(int[] nums) {\nint n = nums.Length;\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [i, n-1]\nfor (int i = 0; i &lt; n - 1; i++) {\n// \u5185\u5faa\u73af\uff1a\u627e\u5230\u672a\u6392\u5e8f\u533a\u95f4\u5185\u7684\u6700\u5c0f\u5143\u7d20\nint k = i;\nfor (int j = i + 1; j &lt; n; j++) {\nif (nums[j] &lt; nums[k])\nk = j; // \u8bb0\u5f55\u6700\u5c0f\u5143\u7d20\u7684\u7d22\u5f15\n}\n// \u5c06\u8be5\u6700\u5c0f\u5143\u7d20\u4e0e\u672a\u6392\u5e8f\u533a\u95f4\u7684\u9996\u4e2a\u5143\u7d20\u4ea4\u6362\n(nums[k], nums[i]) = (nums[i], nums[k]);\n}\n}\n</code></pre> selection_sort.swift<pre><code>/* \u9009\u62e9\u6392\u5e8f */\nfunc selectionSort(nums: inout [Int]) {\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [i, n-1]\nfor i in nums.indices.dropLast() {\n// \u5185\u5faa\u73af\uff1a\u627e\u5230\u672a\u6392\u5e8f\u533a\u95f4\u5185\u7684\u6700\u5c0f\u5143\u7d20\nvar k = i\nfor j in nums.indices.dropFirst(i + 1) {\nif nums[j] &lt; nums[k] {\nk = j // \u8bb0\u5f55\u6700\u5c0f\u5143\u7d20\u7684\u7d22\u5f15\n}\n}\n// \u5c06\u8be5\u6700\u5c0f\u5143\u7d20\u4e0e\u672a\u6392\u5e8f\u533a\u95f4\u7684\u9996\u4e2a\u5143\u7d20\u4ea4\u6362\nnums.swapAt(i, k)\n}\n}\n</code></pre> selection_sort.zig<pre><code>[class]{}-[func]{selectionSort}\n</code></pre> selection_sort.dart<pre><code>/* \u9009\u62e9\u6392\u5e8f */\nvoid selectionSort(List&lt;int&gt; nums) {\nint n = nums.length;\n// \u5916\u5faa\u73af\uff1a\u672a\u6392\u5e8f\u533a\u95f4\u4e3a [i, n-1]\nfor (int i = 0; i &lt; n - 1; i++) {\n// \u5185\u5faa\u73af\uff1a\u627e\u5230\u672a\u6392\u5e8f\u533a\u95f4\u5185\u7684\u6700\u5c0f\u5143\u7d20\nint k = i;\nfor (int j = i + 1; j &lt; n; j++) {\nif (nums[j] &lt; nums[k]) k = j; // \u8bb0\u5f55\u6700\u5c0f\u5143\u7d20\u7684\u7d22\u5f15\n}\n// \u5c06\u8be5\u6700\u5c0f\u5143\u7d20\u4e0e\u672a\u6392\u5e8f\u533a\u95f4\u7684\u9996\u4e2a\u5143\u7d20\u4ea4\u6362\nint temp = nums[i];\nnums[i] = nums[k];\nnums[k] = temp;\n}\n}\n</code></pre>"},{"location":"chapter_sorting/selection_sort/#1121","title":"11.2.1. \u00a0 \u7b97\u6cd5\u7279\u6027","text":"<ul> <li>\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(n^2)\\) \u3001\u975e\u81ea\u9002\u5e94\u6392\u5e8f\uff1a\u5916\u5faa\u73af\u5171 \\(n - 1\\) \u8f6e\uff0c\u7b2c\u4e00\u8f6e\u7684\u672a\u6392\u5e8f\u533a\u95f4\u957f\u5ea6\u4e3a \\(n\\) \uff0c\u6700\u540e\u4e00\u8f6e\u7684\u672a\u6392\u5e8f\u533a\u95f4\u957f\u5ea6\u4e3a \\(2\\) \uff0c\u5373\u5404\u8f6e\u5916\u5faa\u73af\u5206\u522b\u5305\u542b \\(n\\) , \\(n - 1\\) , \\(\\cdots\\) , \\(2\\) \u8f6e\u5185\u5faa\u73af\uff0c\u6c42\u548c\u4e3a \\(\\frac{(n - 1)(n + 2)}{2}\\) \u3002</li> <li>\u7a7a\u95f4\u590d\u6742\u5ea6 \\(O(1)\\) \u3001\u539f\u5730\u6392\u5e8f\uff1a\u6307\u9488 \\(i\\) , \\(j\\) \u4f7f\u7528\u5e38\u6570\u5927\u5c0f\u7684\u989d\u5916\u7a7a\u95f4\u3002</li> <li>\u975e\u7a33\u5b9a\u6392\u5e8f\uff1a\u5728\u4ea4\u6362\u5143\u7d20\u65f6\uff0c\u6709\u53ef\u80fd\u5c06 <code>nums[i]</code> \u4ea4\u6362\u81f3\u5176\u76f8\u7b49\u5143\u7d20\u7684\u53f3\u8fb9\uff0c\u5bfc\u81f4\u4e24\u8005\u7684\u76f8\u5bf9\u987a\u5e8f\u53d1\u751f\u6539\u53d8\u3002</li> </ul> <p> Fig. \u9009\u62e9\u6392\u5e8f\u975e\u7a33\u5b9a\u793a\u4f8b </p>"},{"location":"chapter_sorting/sorting_algorithm/","title":"11.1. \u00a0 \u6392\u5e8f\u7b97\u6cd5","text":"<p>\u300c\u6392\u5e8f\u7b97\u6cd5 Sorting Algorithm\u300d\u7528\u4e8e\u5bf9\u4e00\u7ec4\u6570\u636e\u6309\u7167\u7279\u5b9a\u987a\u5e8f\u8fdb\u884c\u6392\u5217\u3002\u6392\u5e8f\u7b97\u6cd5\u6709\u7740\u5e7f\u6cdb\u7684\u5e94\u7528\uff0c\u56e0\u4e3a\u6709\u5e8f\u6570\u636e\u901a\u5e38\u80fd\u591f\u88ab\u66f4\u6709\u6548\u5730\u67e5\u627e\u3001\u5206\u6790\u548c\u5904\u7406\u3002</p> <p>\u5728\u6392\u5e8f\u7b97\u6cd5\u4e2d\uff0c\u6570\u636e\u7c7b\u578b\u53ef\u4ee5\u662f\u6574\u6570\u3001\u6d6e\u70b9\u6570\u3001\u5b57\u7b26\u6216\u5b57\u7b26\u4e32\u7b49\uff1b\u987a\u5e8f\u7684\u5224\u65ad\u89c4\u5219\u53ef\u6839\u636e\u9700\u6c42\u8bbe\u5b9a\uff0c\u5982\u6570\u5b57\u5927\u5c0f\u3001\u5b57\u7b26 ASCII \u7801\u987a\u5e8f\u6216\u81ea\u5b9a\u4e49\u89c4\u5219\u3002</p> <p></p> <p> Fig. \u6570\u636e\u7c7b\u578b\u548c\u5224\u65ad\u89c4\u5219\u793a\u4f8b </p>"},{"location":"chapter_sorting/sorting_algorithm/#1111","title":"11.1.1. \u00a0 \u8bc4\u4ef7\u7ef4\u5ea6","text":"<p>\u8fd0\u884c\u6548\u7387\uff1a\u6211\u4eec\u671f\u671b\u6392\u5e8f\u7b97\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u5c3d\u91cf\u4f4e\uff0c\u4e14\u603b\u4f53\u64cd\u4f5c\u6570\u91cf\u8f83\u5c11\uff08\u5373\u65f6\u95f4\u590d\u6742\u5ea6\u4e2d\u7684\u5e38\u6570\u9879\u964d\u4f4e\uff09\u3002\u5bf9\u4e8e\u5927\u6570\u636e\u91cf\u60c5\u51b5\uff0c\u8fd0\u884c\u6548\u7387\u663e\u5f97\u5c24\u4e3a\u91cd\u8981\u3002</p> <p>\u5c31\u5730\u6027\uff1a\u987e\u540d\u601d\u4e49\uff0c\u300c\u539f\u5730\u6392\u5e8f\u300d\u901a\u8fc7\u5728\u539f\u6570\u7ec4\u4e0a\u76f4\u63a5\u64cd\u4f5c\u5b9e\u73b0\u6392\u5e8f\uff0c\u65e0\u9700\u501f\u52a9\u989d\u5916\u7684\u8f85\u52a9\u6570\u7ec4\uff0c\u4ece\u800c\u8282\u7701\u5185\u5b58\u3002\u901a\u5e38\u60c5\u51b5\u4e0b\uff0c\u539f\u5730\u6392\u5e8f\u7684\u6570\u636e\u642c\u8fd0\u64cd\u4f5c\u8f83\u5c11\uff0c\u8fd0\u884c\u901f\u5ea6\u4e5f\u66f4\u5feb\u3002</p> <p>\u7a33\u5b9a\u6027\uff1a\u300c\u7a33\u5b9a\u6392\u5e8f\u300d\u5728\u5b8c\u6210\u6392\u5e8f\u540e\uff0c\u76f8\u7b49\u5143\u7d20\u5728\u6570\u7ec4\u4e2d\u7684\u76f8\u5bf9\u987a\u5e8f\u4e0d\u53d1\u751f\u6539\u53d8\u3002\u7a33\u5b9a\u6392\u5e8f\u662f\u4f18\u826f\u7279\u6027\uff0c\u4e5f\u662f\u591a\u7ea7\u6392\u5e8f\u573a\u666f\u7684\u5fc5\u8981\u6761\u4ef6\u3002</p> <p>\u5047\u8bbe\u6211\u4eec\u6709\u4e00\u4e2a\u5b58\u50a8\u5b66\u751f\u4fe1\u606f\u7684\u8868\u683c\uff0c\u7b2c 1, 2 \u5217\u5206\u522b\u662f\u59d3\u540d\u548c\u5e74\u9f84\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u300c\u975e\u7a33\u5b9a\u6392\u5e8f\u300d\u53ef\u80fd\u5bfc\u81f4\u8f93\u5165\u6570\u636e\u7684\u6709\u5e8f\u6027\u4e27\u5931\u3002</p> <pre><code># \u8f93\u5165\u6570\u636e\u662f\u6309\u7167\u59d3\u540d\u6392\u5e8f\u597d\u7684\n# (name, age)\n('A', 19)\n('B', 18)\n('C', 21)\n('D', 19)\n('E', 23)\n# \u5047\u8bbe\u4f7f\u7528\u975e\u7a33\u5b9a\u6392\u5e8f\u7b97\u6cd5\u6309\u5e74\u9f84\u6392\u5e8f\u5217\u8868\uff0c\n# \u7ed3\u679c\u4e2d ('D', 19) \u548c ('A', 19) \u7684\u76f8\u5bf9\u4f4d\u7f6e\u6539\u53d8\uff0c\n# \u8f93\u5165\u6570\u636e\u6309\u59d3\u540d\u6392\u5e8f\u7684\u6027\u8d28\u4e22\u5931\n('B', 18)\n('D', 19)\n('A', 19)\n('C', 21)\n('E', 23)\n</code></pre> <p>\u81ea\u9002\u5e94\u6027\uff1a\u300c\u81ea\u9002\u5e94\u6392\u5e8f\u300d\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4f1a\u53d7\u8f93\u5165\u6570\u636e\u7684\u5f71\u54cd\uff0c\u5373\u6700\u4f73\u3001\u6700\u5dee\u3001\u5e73\u5747\u65f6\u95f4\u590d\u6742\u5ea6\u5e76\u4e0d\u5b8c\u5168\u76f8\u7b49\u3002</p> <p>\u81ea\u9002\u5e94\u6027\u9700\u8981\u6839\u636e\u5177\u4f53\u60c5\u51b5\u6765\u8bc4\u4f30\u3002\u5982\u679c\u6700\u5dee\u65f6\u95f4\u590d\u6742\u5ea6\u5dee\u4e8e\u5e73\u5747\u65f6\u95f4\u590d\u6742\u5ea6\uff0c\u8bf4\u660e\u6392\u5e8f\u7b97\u6cd5\u5728\u67d0\u4e9b\u6570\u636e\u4e0b\u6027\u80fd\u53ef\u80fd\u52a3\u5316\uff0c\u56e0\u6b64\u88ab\u89c6\u4e3a\u8d1f\u9762\u5c5e\u6027\uff1b\u800c\u5982\u679c\u6700\u4f73\u65f6\u95f4\u590d\u6742\u5ea6\u4f18\u4e8e\u5e73\u5747\u65f6\u95f4\u590d\u6742\u5ea6\uff0c\u5219\u88ab\u89c6\u4e3a\u6b63\u9762\u5c5e\u6027\u3002</p> <p>\u662f\u5426\u57fa\u4e8e\u6bd4\u8f83\uff1a\u300c\u57fa\u4e8e\u6bd4\u8f83\u7684\u6392\u5e8f\u300d\u4f9d\u8d56\u4e8e\u6bd4\u8f83\u8fd0\u7b97\u7b26\uff08\\(&lt;\\) , \\(=\\) , \\(&gt;\\)\uff09\u6765\u5224\u65ad\u5143\u7d20\u7684\u76f8\u5bf9\u987a\u5e8f\uff0c\u4ece\u800c\u6392\u5e8f\u6574\u4e2a\u6570\u7ec4\uff0c\u7406\u8bba\u6700\u4f18\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(n \\log n)\\) \u3002\u800c\u300c\u975e\u6bd4\u8f83\u6392\u5e8f\u300d\u4e0d\u4f7f\u7528\u6bd4\u8f83\u8fd0\u7b97\u7b26\uff0c\u65f6\u95f4\u590d\u6742\u5ea6\u53ef\u8fbe \\(O(n)\\) \uff0c\u4f46\u5176\u901a\u7528\u6027\u76f8\u5bf9\u8f83\u5dee\u3002</p>"},{"location":"chapter_sorting/sorting_algorithm/#1112","title":"11.1.2. \u00a0 \u7406\u60f3\u6392\u5e8f\u7b97\u6cd5","text":"<p>\u8fd0\u884c\u5feb\u3001\u539f\u5730\u3001\u7a33\u5b9a\u3001\u6b63\u5411\u81ea\u9002\u5e94\u3001\u901a\u7528\u6027\u597d\u3002\u663e\u7136\uff0c\u8fc4\u4eca\u4e3a\u6b62\u5c1a\u672a\u53d1\u73b0\u517c\u5177\u4ee5\u4e0a\u6240\u6709\u7279\u6027\u7684\u6392\u5e8f\u7b97\u6cd5\u3002\u56e0\u6b64\uff0c\u5728\u9009\u62e9\u6392\u5e8f\u7b97\u6cd5\u65f6\uff0c\u9700\u8981\u6839\u636e\u5177\u4f53\u7684\u6570\u636e\u7279\u70b9\u548c\u95ee\u9898\u9700\u6c42\u6765\u51b3\u5b9a\u3002</p> <p>\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u5c06\u5171\u540c\u5b66\u4e60\u5404\u79cd\u6392\u5e8f\u7b97\u6cd5\uff0c\u5e76\u57fa\u4e8e\u4e0a\u8ff0\u8bc4\u4ef7\u7ef4\u5ea6\u5bf9\u5404\u4e2a\u6392\u5e8f\u7b97\u6cd5\u7684\u4f18\u7f3a\u70b9\u8fdb\u884c\u5206\u6790\u3002</p>"},{"location":"chapter_sorting/summary/","title":"11.11. \u00a0 \u5c0f\u7ed3","text":"<ul> <li>\u5192\u6ce1\u6392\u5e8f\u901a\u8fc7\u4ea4\u6362\u76f8\u90bb\u5143\u7d20\u6765\u5b9e\u73b0\u6392\u5e8f\u3002\u901a\u8fc7\u6dfb\u52a0\u4e00\u4e2a\u6807\u5fd7\u4f4d\u6765\u5b9e\u73b0\u63d0\u524d\u8fd4\u56de\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u5192\u6ce1\u6392\u5e8f\u7684\u6700\u4f73\u65f6\u95f4\u590d\u6742\u5ea6\u4f18\u5316\u5230 \\(O(n)\\) \u3002</li> <li>\u63d2\u5165\u6392\u5e8f\u6bcf\u8f6e\u5c06\u672a\u6392\u5e8f\u533a\u95f4\u5185\u7684\u5143\u7d20\u63d2\u5165\u5230\u5df2\u6392\u5e8f\u533a\u95f4\u7684\u6b63\u786e\u4f4d\u7f6e\uff0c\u4ece\u800c\u5b8c\u6210\u6392\u5e8f\u3002\u867d\u7136\u63d2\u5165\u6392\u5e8f\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(n^2)\\) \uff0c\u4f46\u7531\u4e8e\u5355\u5143\u64cd\u4f5c\u76f8\u5bf9\u8f83\u5c11\uff0c\u5b83\u5728\u5c0f\u6570\u636e\u91cf\u7684\u6392\u5e8f\u4efb\u52a1\u4e2d\u975e\u5e38\u53d7\u6b22\u8fce\u3002</li> <li>\u5feb\u901f\u6392\u5e8f\u57fa\u4e8e\u54e8\u5175\u5212\u5206\u64cd\u4f5c\u5b9e\u73b0\u6392\u5e8f\u3002\u5728\u54e8\u5175\u5212\u5206\u4e2d\uff0c\u6709\u53ef\u80fd\u6bcf\u6b21\u90fd\u9009\u53d6\u5230\u6700\u5dee\u7684\u57fa\u51c6\u6570\uff0c\u5bfc\u81f4\u65f6\u95f4\u590d\u6742\u5ea6\u52a3\u5316\u81f3 \\(O(n^2)\\) \u3002\u5f15\u5165\u4e2d\u4f4d\u6570\u57fa\u51c6\u6570\u6216\u968f\u673a\u57fa\u51c6\u6570\u53ef\u4ee5\u964d\u4f4e\u8fd9\u79cd\u52a3\u5316\u7684\u6982\u7387\u3002\u5c3e\u9012\u5f52\u65b9\u6cd5\u53ef\u4ee5\u6709\u6548\u5730\u51cf\u5c11\u9012\u5f52\u6df1\u5ea6\uff0c\u5c06\u7a7a\u95f4\u590d\u6742\u5ea6\u4f18\u5316\u5230 \\(O(\\log n)\\) \u3002</li> <li>\u5f52\u5e76\u6392\u5e8f\u5305\u62ec\u5212\u5206\u548c\u5408\u5e76\u4e24\u4e2a\u9636\u6bb5\uff0c\u5178\u578b\u5730\u4f53\u73b0\u4e86\u5206\u6cbb\u7b56\u7565\u3002\u5728\u5f52\u5e76\u6392\u5e8f\u4e2d\uff0c\u6392\u5e8f\u6570\u7ec4\u9700\u8981\u521b\u5efa\u8f85\u52a9\u6570\u7ec4\uff0c\u7a7a\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(n)\\) \uff1b\u7136\u800c\u6392\u5e8f\u94fe\u8868\u7684\u7a7a\u95f4\u590d\u6742\u5ea6\u53ef\u4ee5\u4f18\u5316\u81f3 \\(O(1)\\) \u3002</li> <li>\u6876\u6392\u5e8f\u5305\u542b\u4e09\u4e2a\u6b65\u9aa4\uff1a\u6570\u636e\u5206\u6876\u3001\u6876\u5185\u6392\u5e8f\u548c\u5408\u5e76\u7ed3\u679c\u3002\u5b83\u540c\u6837\u4f53\u73b0\u4e86\u5206\u6cbb\u7b56\u7565\uff0c\u9002\u7528\u4e8e\u6570\u636e\u4f53\u91cf\u5f88\u5927\u7684\u60c5\u51b5\u3002\u6876\u6392\u5e8f\u7684\u5173\u952e\u5728\u4e8e\u5bf9\u6570\u636e\u8fdb\u884c\u5e73\u5747\u5206\u914d\u3002</li> <li>\u8ba1\u6570\u6392\u5e8f\u662f\u6876\u6392\u5e8f\u7684\u4e00\u4e2a\u7279\u4f8b\uff0c\u5b83\u901a\u8fc7\u7edf\u8ba1\u6570\u636e\u51fa\u73b0\u7684\u6b21\u6570\u6765\u5b9e\u73b0\u6392\u5e8f\u3002\u8ba1\u6570\u6392\u5e8f\u9002\u7528\u4e8e\u6570\u636e\u91cf\u5927\u4f46\u6570\u636e\u8303\u56f4\u6709\u9650\u7684\u60c5\u51b5\uff0c\u5e76\u4e14\u8981\u6c42\u6570\u636e\u80fd\u591f\u8f6c\u6362\u4e3a\u6b63\u6574\u6570\u3002</li> <li>\u57fa\u6570\u6392\u5e8f\u901a\u8fc7\u9010\u4f4d\u6392\u5e8f\u6765\u5b9e\u73b0\u6570\u636e\u6392\u5e8f\uff0c\u8981\u6c42\u6570\u636e\u80fd\u591f\u8868\u793a\u4e3a\u56fa\u5b9a\u4f4d\u6570\u7684\u6570\u5b57\u3002</li> </ul> <p> Fig. \u6392\u5e8f\u7b97\u6cd5\u5bf9\u6bd4 </p> <ul> <li>\u603b\u7684\u6765\u8bf4\uff0c\u6211\u4eec\u5e0c\u671b\u627e\u5230\u4e00\u79cd\u6392\u5e8f\u7b97\u6cd5\uff0c\u5177\u6709\u9ad8\u6548\u7387\u3001\u7a33\u5b9a\u3001\u539f\u5730\u4ee5\u53ca\u6b63\u5411\u81ea\u9002\u5e94\u6027\u7b49\u4f18\u70b9\u3002\u7136\u800c\uff0c\u6b63\u5982\u5176\u4ed6\u6570\u636e\u7ed3\u6784\u548c\u7b97\u6cd5\u4e00\u6837\uff0c\u6ca1\u6709\u4e00\u79cd\u6392\u5e8f\u7b97\u6cd5\u80fd\u591f\u540c\u65f6\u6ee1\u8db3\u6240\u6709\u8fd9\u4e9b\u6761\u4ef6\u3002\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u6211\u4eec\u9700\u8981\u6839\u636e\u6570\u636e\u7684\u7279\u6027\u6765\u9009\u62e9\u5408\u9002\u7684\u6392\u5e8f\u7b97\u6cd5\u3002</li> </ul>"},{"location":"chapter_sorting/summary/#11111-q-a","title":"11.11.1. \u00a0 Q &amp; A","text":"<p>\u54e8\u5175\u5212\u5206\u4e2d\u201c\u4ece\u53f3\u5f80\u5de6\u67e5\u627e\u201d\u4e0e\u201c\u4ece\u5de6\u5f80\u53f3\u67e5\u627e\u201d\u7684\u987a\u5e8f\u53ef\u4ee5\u4ea4\u6362\u5417\uff1f</p> <p>\u4e0d\u884c\uff0c\u5f53\u6211\u4eec\u4ee5\u6700\u5de6\u7aef\u5143\u7d20\u4e3a\u57fa\u51c6\u6570\u65f6\uff0c\u5fc5\u987b\u5148\u201c\u4ece\u53f3\u5f80\u5de6\u67e5\u627e\u201d\u518d\u201c\u4ece\u5de6\u5f80\u53f3\u67e5\u627e\u201d\u3002\u8fd9\u4e2a\u7ed3\u8bba\u6709\u4e9b\u53cd\u76f4\u89c9\uff0c\u6211\u4eec\u6765\u5256\u6790\u4e00\u4e0b\u539f\u56e0\u3002</p> <p>\u54e8\u5175\u5212\u5206 <code>partition()</code> \u7684\u6700\u540e\u4e00\u6b65\u662f\u4ea4\u6362 <code>nums[left]</code> \u548c <code>nums[i]</code> \u3002\u5b8c\u6210\u4ea4\u6362\u540e\uff0c\u57fa\u51c6\u6570\u5de6\u8fb9\u7684\u5143\u7d20\u90fd <code>&lt;=</code> \u57fa\u51c6\u6570\uff0c\u8fd9\u5c31\u8981\u6c42\u6700\u540e\u4e00\u6b65\u4ea4\u6362\u524d <code>nums[left] &gt;= nums[i]</code> \u5fc5\u987b\u6210\u7acb\u3002\u5047\u8bbe\u6211\u4eec\u5148\u201c\u4ece\u5de6\u5f80\u53f3\u67e5\u627e\u201d\uff0c\u90a3\u4e48\u5982\u679c\u627e\u4e0d\u5230\u6bd4\u57fa\u51c6\u6570\u66f4\u5c0f\u7684\u5143\u7d20\uff0c\u5219\u4f1a\u5728 <code>i == j</code> \u65f6\u8df3\u51fa\u5faa\u73af\uff0c\u6b64\u65f6\u53ef\u80fd <code>nums[j] == nums[i] &gt; nums[left]</code>\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u6b64\u65f6\u6700\u540e\u4e00\u6b65\u4ea4\u6362\u64cd\u4f5c\u4f1a\u628a\u4e00\u4e2a\u6bd4\u57fa\u51c6\u6570\u66f4\u5927\u7684\u5143\u7d20\u4ea4\u6362\u81f3\u6570\u7ec4\u6700\u5de6\u7aef\uff0c\u5bfc\u81f4\u54e8\u5175\u5212\u5206\u5931\u8d25\u3002</p> <p>\u4e3e\u4e2a\u4f8b\u5b50\uff0c\u7ed9\u5b9a\u6570\u7ec4 <code>[0, 0, 0, 0, 1]</code> \uff0c\u5982\u679c\u5148\u201c\u4ece\u5de6\u5411\u53f3\u67e5\u627e\u201d\uff0c\u54e8\u5175\u5212\u5206\u540e\u6570\u7ec4\u4e3a <code>[1, 0, 0, 0, 0]</code> \uff0c\u8fd9\u4e2a\u7ed3\u679c\u662f\u4e0d\u6b63\u786e\u7684\u3002</p> <p>\u518d\u6df1\u5165\u601d\u8003\u4e00\u4e0b\uff0c\u5982\u679c\u6211\u4eec\u9009\u62e9 <code>nums[right]</code> \u4e3a\u57fa\u51c6\u6570\uff0c\u90a3\u4e48\u6b63\u597d\u53cd\u8fc7\u6765\uff0c\u5fc5\u987b\u5148\u201c\u4ece\u5de6\u5f80\u53f3\u67e5\u627e\u201d\u3002</p>"},{"location":"chapter_stack_and_queue/","title":"5. \u00a0 \u6808\u4e0e\u961f\u5217","text":""},{"location":"chapter_stack_and_queue/deque/","title":"5.3. \u00a0 \u53cc\u5411\u961f\u5217","text":"<p>\u5bf9\u4e8e\u961f\u5217\uff0c\u6211\u4eec\u4ec5\u80fd\u5728\u5934\u90e8\u5220\u9664\u6216\u5728\u5c3e\u90e8\u6dfb\u52a0\u5143\u7d20\u3002\u7136\u800c\uff0c\u300c\u53cc\u5411\u961f\u5217 Deque\u300d\u63d0\u4f9b\u4e86\u66f4\u9ad8\u7684\u7075\u6d3b\u6027\uff0c\u5141\u8bb8\u5728\u5934\u90e8\u548c\u5c3e\u90e8\u6267\u884c\u5143\u7d20\u7684\u6dfb\u52a0\u6216\u5220\u9664\u64cd\u4f5c\u3002</p> <p></p> <p> Fig. \u53cc\u5411\u961f\u5217\u7684\u64cd\u4f5c </p>"},{"location":"chapter_stack_and_queue/deque/#531","title":"5.3.1. \u00a0 \u53cc\u5411\u961f\u5217\u5e38\u7528\u64cd\u4f5c","text":"<p>\u53cc\u5411\u961f\u5217\u7684\u5e38\u7528\u64cd\u4f5c\u5982\u4e0b\u8868\u6240\u793a\uff0c\u5177\u4f53\u7684\u65b9\u6cd5\u540d\u79f0\u9700\u8981\u6839\u636e\u6240\u4f7f\u7528\u7684\u7f16\u7a0b\u8bed\u8a00\u6765\u786e\u5b9a\u3002</p> \u65b9\u6cd5\u540d \u63cf\u8ff0 \u65f6\u95f4\u590d\u6742\u5ea6 pushFirst() \u5c06\u5143\u7d20\u6dfb\u52a0\u81f3\u961f\u9996 \\(O(1)\\) pushLast() \u5c06\u5143\u7d20\u6dfb\u52a0\u81f3\u961f\u5c3e \\(O(1)\\) popFirst() \u5220\u9664\u961f\u9996\u5143\u7d20 \\(O(1)\\) popLast() \u5220\u9664\u961f\u5c3e\u5143\u7d20 \\(O(1)\\) peekFirst() \u8bbf\u95ee\u961f\u9996\u5143\u7d20 \\(O(1)\\) peekLast() \u8bbf\u95ee\u961f\u5c3e\u5143\u7d20 \\(O(1)\\) <p>\u540c\u6837\u5730\uff0c\u6211\u4eec\u53ef\u4ee5\u76f4\u63a5\u4f7f\u7528\u7f16\u7a0b\u8bed\u8a00\u4e2d\u5df2\u5b9e\u73b0\u7684\u53cc\u5411\u961f\u5217\u7c7b\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart deque.java<pre><code>/* \u521d\u59cb\u5316\u53cc\u5411\u961f\u5217 */\nDeque&lt;Integer&gt; deque = new LinkedList&lt;&gt;();\n/* \u5143\u7d20\u5165\u961f */\ndeque.offerLast(2);   // \u6dfb\u52a0\u81f3\u961f\u5c3e\ndeque.offerLast(5);\ndeque.offerLast(4);\ndeque.offerFirst(3);  // \u6dfb\u52a0\u81f3\u961f\u9996\ndeque.offerFirst(1);\n/* \u8bbf\u95ee\u5143\u7d20 */\nint peekFirst = deque.peekFirst();  // \u961f\u9996\u5143\u7d20\nint peekLast = deque.peekLast();    // \u961f\u5c3e\u5143\u7d20\n/* \u5143\u7d20\u51fa\u961f */\nint popFirst = deque.pollFirst();  // \u961f\u9996\u5143\u7d20\u51fa\u961f\nint popLast = deque.pollLast();    // \u961f\u5c3e\u5143\u7d20\u51fa\u961f\n/* \u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6 */\nint size = deque.size();\n/* \u5224\u65ad\u53cc\u5411\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nboolean isEmpty = deque.isEmpty();\n</code></pre> deque.cpp<pre><code>/* \u521d\u59cb\u5316\u53cc\u5411\u961f\u5217 */\ndeque&lt;int&gt; deque;\n/* \u5143\u7d20\u5165\u961f */\ndeque.push_back(2);   // \u6dfb\u52a0\u81f3\u961f\u5c3e\ndeque.push_back(5);\ndeque.push_back(4);\ndeque.push_front(3);  // \u6dfb\u52a0\u81f3\u961f\u9996\ndeque.push_front(1);\n/* \u8bbf\u95ee\u5143\u7d20 */\nint front = deque.front(); // \u961f\u9996\u5143\u7d20\nint back = deque.back();   // \u961f\u5c3e\u5143\u7d20\n/* \u5143\u7d20\u51fa\u961f */\ndeque.pop_front();  // \u961f\u9996\u5143\u7d20\u51fa\u961f\ndeque.pop_back();   // \u961f\u5c3e\u5143\u7d20\u51fa\u961f\n/* \u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6 */\nint size = deque.size();\n/* \u5224\u65ad\u53cc\u5411\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nbool empty = deque.empty();\n</code></pre> deque.py<pre><code># \u521d\u59cb\u5316\u53cc\u5411\u961f\u5217\ndeque: Deque[int] = collections.deque()\n# \u5143\u7d20\u5165\u961f\ndeque.append(2)      # \u6dfb\u52a0\u81f3\u961f\u5c3e\ndeque.append(5)\ndeque.append(4)\ndeque.appendleft(3)  # \u6dfb\u52a0\u81f3\u961f\u9996\ndeque.appendleft(1)\n# \u8bbf\u95ee\u5143\u7d20\nfront: int = deque[0]  # \u961f\u9996\u5143\u7d20\nrear: int = deque[-1]  # \u961f\u5c3e\u5143\u7d20\n# \u5143\u7d20\u51fa\u961f\npop_front: int = deque.popleft()  # \u961f\u9996\u5143\u7d20\u51fa\u961f\npop_rear: int = deque.pop()       # \u961f\u5c3e\u5143\u7d20\u51fa\u961f\n# \u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6\nsize: int = len(deque)\n# \u5224\u65ad\u53cc\u5411\u961f\u5217\u662f\u5426\u4e3a\u7a7a\nis_empty: bool = len(deque) == 0\n</code></pre> deque_test.go<pre><code>/* \u521d\u59cb\u5316\u53cc\u5411\u961f\u5217 */\n// \u5728 Go \u4e2d\uff0c\u5c06 list \u4f5c\u4e3a\u53cc\u5411\u961f\u5217\u4f7f\u7528\ndeque := list.New()\n/* \u5143\u7d20\u5165\u961f */\ndeque.PushBack(2)      // \u6dfb\u52a0\u81f3\u961f\u5c3e\ndeque.PushBack(5)\ndeque.PushBack(4)\ndeque.PushFront(3)     // \u6dfb\u52a0\u81f3\u961f\u9996\ndeque.PushFront(1)\n/* \u8bbf\u95ee\u5143\u7d20 */\nfront := deque.Front() // \u961f\u9996\u5143\u7d20\nrear := deque.Back()   // \u961f\u5c3e\u5143\u7d20\n/* \u5143\u7d20\u51fa\u961f */\ndeque.Remove(front)    // \u961f\u9996\u5143\u7d20\u51fa\u961f\ndeque.Remove(rear)     // \u961f\u5c3e\u5143\u7d20\u51fa\u961f\n/* \u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6 */\nsize := deque.Len()\n/* \u5224\u65ad\u53cc\u5411\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nisEmpty := deque.Len() == 0\n</code></pre> deque.js<pre><code>/* \u521d\u59cb\u5316\u53cc\u5411\u961f\u5217 */\n// JavaScript \u6ca1\u6709\u5185\u7f6e\u7684\u53cc\u7aef\u961f\u5217\uff0c\u53ea\u80fd\u628a Array \u5f53\u4f5c\u53cc\u7aef\u961f\u5217\u6765\u4f7f\u7528\nconst deque = [];\n/* \u5143\u7d20\u5165\u961f */\ndeque.push(2);\ndeque.push(5);\ndeque.push(4);\n// \u8bf7\u6ce8\u610f\uff0c\u7531\u4e8e\u662f\u6570\u7ec4\uff0cunshift() \u65b9\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a O(n)\ndeque.unshift(3);\ndeque.unshift(1);\nconsole.log(\"\u53cc\u5411\u961f\u5217 deque = \", deque);\n/* \u8bbf\u95ee\u5143\u7d20 */\nconst peekFirst = deque[0];\nconsole.log(\"\u961f\u9996\u5143\u7d20 peekFirst = \" + peekFirst);\nconst peekLast = deque[deque.length - 1];\nconsole.log(\"\u961f\u5c3e\u5143\u7d20 peekLast = \" + peekLast);\n/* \u5143\u7d20\u51fa\u961f */\n// \u8bf7\u6ce8\u610f\uff0c\u7531\u4e8e\u662f\u6570\u7ec4\uff0cshift() \u65b9\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a O(n)\nconst popFront = deque.shift();\nconsole.log(\"\u961f\u9996\u51fa\u961f\u5143\u7d20 popFront = \" + popFront + \"\uff0c\u961f\u9996\u51fa\u961f\u540e deque = \" + deque);\nconst popBack = deque.pop();\nconsole.log(\"\u961f\u5c3e\u51fa\u961f\u5143\u7d20 popBack = \" + popBack + \"\uff0c\u961f\u5c3e\u51fa\u961f\u540e deque = \" + deque);\n/* \u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6 */\nconst size = deque.length;\nconsole.log(\"\u53cc\u5411\u961f\u5217\u957f\u5ea6 size = \" + size);\n/* \u5224\u65ad\u53cc\u5411\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nconst isEmpty = size === 0;\nconsole.log(\"\u53cc\u5411\u961f\u5217\u662f\u5426\u4e3a\u7a7a = \" + isEmpty);\n</code></pre> deque.ts<pre><code>/* \u521d\u59cb\u5316\u53cc\u5411\u961f\u5217 */\n// TypeScript \u6ca1\u6709\u5185\u7f6e\u7684\u53cc\u7aef\u961f\u5217\uff0c\u53ea\u80fd\u628a Array \u5f53\u4f5c\u53cc\u7aef\u961f\u5217\u6765\u4f7f\u7528\nconst deque: number[] = [];\n/* \u5143\u7d20\u5165\u961f */\ndeque.push(2);\ndeque.push(5);\ndeque.push(4);\n// \u8bf7\u6ce8\u610f\uff0c\u7531\u4e8e\u662f\u6570\u7ec4\uff0cunshift() \u65b9\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a O(n)\ndeque.unshift(3);\ndeque.unshift(1);\nconsole.log(\"\u53cc\u5411\u961f\u5217 deque = \", deque);\n/* \u8bbf\u95ee\u5143\u7d20 */\nconst peekFirst: number = deque[0];\nconsole.log(\"\u961f\u9996\u5143\u7d20 peekFirst = \" + peekFirst);\nconst peekLast: number = deque[deque.length - 1];\nconsole.log(\"\u961f\u5c3e\u5143\u7d20 peekLast = \" + peekLast);\n/* \u5143\u7d20\u51fa\u961f */\n// \u8bf7\u6ce8\u610f\uff0c\u7531\u4e8e\u662f\u6570\u7ec4\uff0cshift() \u65b9\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a O(n)\nconst popFront: number = deque.shift() as number;\nconsole.log(\"\u961f\u9996\u51fa\u961f\u5143\u7d20 popFront = \" + popFront + \"\uff0c\u961f\u9996\u51fa\u961f\u540e deque = \" + deque);\nconst popBack: number = deque.pop() as number;\nconsole.log(\"\u961f\u5c3e\u51fa\u961f\u5143\u7d20 popBack = \" + popBack + \"\uff0c\u961f\u5c3e\u51fa\u961f\u540e deque = \" + deque);\n/* \u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6 */\nconst size: number = deque.length;\nconsole.log(\"\u53cc\u5411\u961f\u5217\u957f\u5ea6 size = \" + size);\n/* \u5224\u65ad\u53cc\u5411\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nconst isEmpty: boolean = size === 0;\nconsole.log(\"\u53cc\u5411\u961f\u5217\u662f\u5426\u4e3a\u7a7a = \" + isEmpty);\n</code></pre> deque.c<pre><code>// C \u672a\u63d0\u4f9b\u5185\u7f6e\u53cc\u5411\u961f\u5217\n</code></pre> deque.cs<pre><code>/* \u521d\u59cb\u5316\u53cc\u5411\u961f\u5217 */\n// \u5728 C# \u4e2d\uff0c\u5c06\u94fe\u8868 LinkedList \u770b\u4f5c\u53cc\u5411\u961f\u5217\u6765\u4f7f\u7528\nLinkedList&lt;int&gt; deque = new LinkedList&lt;int&gt;();\n/* \u5143\u7d20\u5165\u961f */\ndeque.AddLast(2);   // \u6dfb\u52a0\u81f3\u961f\u5c3e\ndeque.AddLast(5);\ndeque.AddLast(4);\ndeque.AddFirst(3);  // \u6dfb\u52a0\u81f3\u961f\u9996\ndeque.AddFirst(1);\n/* \u8bbf\u95ee\u5143\u7d20 */\nint peekFirst = deque.First.Value;  // \u961f\u9996\u5143\u7d20\nint peekLast = deque.Last.Value;    // \u961f\u5c3e\u5143\u7d20\n/* \u5143\u7d20\u51fa\u961f */\ndeque.RemoveFirst();  // \u961f\u9996\u5143\u7d20\u51fa\u961f\ndeque.RemoveLast();   // \u961f\u5c3e\u5143\u7d20\u51fa\u961f\n/* \u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6 */\nint size = deque.Count;\n/* \u5224\u65ad\u53cc\u5411\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nbool isEmpty = deque.Count == 0;\n</code></pre> deque.swift<pre><code>/* \u521d\u59cb\u5316\u53cc\u5411\u961f\u5217 */\n// Swift \u6ca1\u6709\u5185\u7f6e\u7684\u53cc\u5411\u961f\u5217\u7c7b\uff0c\u53ef\u4ee5\u628a Array \u5f53\u4f5c\u53cc\u5411\u961f\u5217\u6765\u4f7f\u7528\nvar deque: [Int] = []\n/* \u5143\u7d20\u5165\u961f */\ndeque.append(2) // \u6dfb\u52a0\u81f3\u961f\u5c3e\ndeque.append(5)\ndeque.append(4)\ndeque.insert(3, at: 0) // \u6dfb\u52a0\u81f3\u961f\u9996\ndeque.insert(1, at: 0)\n/* \u8bbf\u95ee\u5143\u7d20 */\nlet peekFirst = deque.first! // \u961f\u9996\u5143\u7d20\nlet peekLast = deque.last! // \u961f\u5c3e\u5143\u7d20\n/* \u5143\u7d20\u51fa\u961f */\n// \u4f7f\u7528 Array \u6a21\u62df\u65f6 popFirst \u7684\u590d\u6742\u5ea6\u4e3a O(n)\nlet popFirst = deque.removeFirst() // \u961f\u9996\u5143\u7d20\u51fa\u961f\nlet popLast = deque.removeLast() // \u961f\u5c3e\u5143\u7d20\u51fa\u961f\n/* \u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6 */\nlet size = deque.count\n/* \u5224\u65ad\u53cc\u5411\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nlet isEmpty = deque.isEmpty\n</code></pre> deque.zig<pre><code>\n</code></pre> deque.dart<pre><code>/* \u521d\u59cb\u5316\u53cc\u5411\u961f\u5217 */\n// \u5728 Dart \u4e2d\uff0cQueue \u88ab\u5b9a\u4e49\u4e3a\u53cc\u5411\u961f\u5217\nQueue&lt;int&gt; deque = Queue&lt;int&gt;();\n/* \u5143\u7d20\u5165\u961f */\ndeque.addLast(2);  // \u6dfb\u52a0\u81f3\u961f\u5c3e\ndeque.addLast(5);\ndeque.addLast(4);\ndeque.addFirst(3); // \u6dfb\u52a0\u81f3\u961f\u9996\ndeque.addFirst(1);\n/* \u8bbf\u95ee\u5143\u7d20 */\nint peekFirst = deque.first; // \u961f\u9996\u5143\u7d20\nint peekLast = deque.last;   // \u961f\u5c3e\u5143\u7d20\n/* \u5143\u7d20\u51fa\u961f */\nint popFirst = deque.removeFirst(); // \u961f\u9996\u5143\u7d20\u51fa\u961f\nint popLast = deque.removeLast();   // \u961f\u5c3e\u5143\u7d20\u51fa\u961f\n/* \u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6 */\nint size = deque.length;\n/* \u5224\u65ad\u53cc\u5411\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nbool isEmpty = deque.isEmpty;W\n</code></pre>"},{"location":"chapter_stack_and_queue/deque/#532","title":"5.3.2. \u00a0 \u53cc\u5411\u961f\u5217\u5b9e\u73b0 *","text":"<p>\u53cc\u5411\u961f\u5217\u7684\u5b9e\u73b0\u4e0e\u961f\u5217\u7c7b\u4f3c\uff0c\u53ef\u4ee5\u9009\u62e9\u94fe\u8868\u6216\u6570\u7ec4\u4f5c\u4e3a\u5e95\u5c42\u6570\u636e\u7ed3\u6784\u3002</p>"},{"location":"chapter_stack_and_queue/deque/#_1","title":"\u57fa\u4e8e\u53cc\u5411\u94fe\u8868\u7684\u5b9e\u73b0","text":"<p>\u56de\u987e\u4e0a\u4e00\u8282\u5185\u5bb9\uff0c\u6211\u4eec\u4f7f\u7528\u666e\u901a\u5355\u5411\u94fe\u8868\u6765\u5b9e\u73b0\u961f\u5217\uff0c\u56e0\u4e3a\u5b83\u53ef\u4ee5\u65b9\u4fbf\u5730\u5220\u9664\u5934\u8282\u70b9\uff08\u5bf9\u5e94\u51fa\u961f\u64cd\u4f5c\uff09\u548c\u5728\u5c3e\u8282\u70b9\u540e\u6dfb\u52a0\u65b0\u8282\u70b9\uff08\u5bf9\u5e94\u5165\u961f\u64cd\u4f5c\uff09\u3002</p> <p>\u5bf9\u4e8e\u53cc\u5411\u961f\u5217\u800c\u8a00\uff0c\u5934\u90e8\u548c\u5c3e\u90e8\u90fd\u53ef\u4ee5\u6267\u884c\u5165\u961f\u548c\u51fa\u961f\u64cd\u4f5c\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u53cc\u5411\u961f\u5217\u9700\u8981\u5b9e\u73b0\u53e6\u4e00\u4e2a\u5bf9\u79f0\u65b9\u5411\u7684\u64cd\u4f5c\u3002\u4e3a\u6b64\uff0c\u6211\u4eec\u91c7\u7528\u300c\u53cc\u5411\u94fe\u8868\u300d\u4f5c\u4e3a\u53cc\u5411\u961f\u5217\u7684\u5e95\u5c42\u6570\u636e\u7ed3\u6784\u3002</p> <p>\u6211\u4eec\u5c06\u53cc\u5411\u94fe\u8868\u7684\u5934\u8282\u70b9\u548c\u5c3e\u8282\u70b9\u89c6\u4e3a\u53cc\u5411\u961f\u5217\u7684\u961f\u9996\u548c\u961f\u5c3e\uff0c\u540c\u65f6\u5b9e\u73b0\u5728\u4e24\u7aef\u6dfb\u52a0\u548c\u5220\u9664\u8282\u70b9\u7684\u529f\u80fd\u3002</p> LinkedListDequepushLast()pushFirst()popLast()popFirst() <p></p> <p></p> <p></p> <p></p> <p></p> <p>\u4ee5\u4e0b\u662f\u5177\u4f53\u5b9e\u73b0\u4ee3\u7801\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart linkedlist_deque.java<pre><code>/* \u53cc\u5411\u94fe\u8868\u8282\u70b9 */\nclass ListNode {\nint val; // \u8282\u70b9\u503c\nListNode next; // \u540e\u7ee7\u8282\u70b9\u5f15\u7528\uff08\u6307\u9488\uff09\nListNode prev; // \u524d\u9a71\u8282\u70b9\u5f15\u7528\uff08\u6307\u9488\uff09\nListNode(int val) {\nthis.val = val;\nprev = next = null;\n}\n}\n/* \u57fa\u4e8e\u53cc\u5411\u94fe\u8868\u5b9e\u73b0\u7684\u53cc\u5411\u961f\u5217 */\nclass LinkedListDeque {\nprivate ListNode front, rear; // \u5934\u8282\u70b9 front \uff0c\u5c3e\u8282\u70b9 rear\nprivate int queSize = 0; // \u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6\npublic LinkedListDeque() {\nfront = rear = null;\n}\n/* \u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6 */\npublic int size() {\nreturn queSize;\n}\n/* \u5224\u65ad\u53cc\u5411\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\npublic boolean isEmpty() {\nreturn size() == 0;\n}\n/* \u5165\u961f\u64cd\u4f5c */\nprivate void push(int num, boolean isFront) {\nListNode node = new ListNode(num);\n// \u82e5\u94fe\u8868\u4e3a\u7a7a\uff0c\u5219\u4ee4 front, rear \u90fd\u6307\u5411 node\nif (isEmpty())\nfront = rear = node;\n// \u961f\u9996\u5165\u961f\u64cd\u4f5c\nelse if (isFront) {\n// \u5c06 node \u6dfb\u52a0\u81f3\u94fe\u8868\u5934\u90e8\nfront.prev = node;\nnode.next = front;\nfront = node; // \u66f4\u65b0\u5934\u8282\u70b9\n// \u961f\u5c3e\u5165\u961f\u64cd\u4f5c\n} else {\n// \u5c06 node \u6dfb\u52a0\u81f3\u94fe\u8868\u5c3e\u90e8\nrear.next = node;\nnode.prev = rear;\nrear = node; // \u66f4\u65b0\u5c3e\u8282\u70b9\n}\nqueSize++; // \u66f4\u65b0\u961f\u5217\u957f\u5ea6\n}\n/* \u961f\u9996\u5165\u961f */\npublic void pushFirst(int num) {\npush(num, true);\n}\n/* \u961f\u5c3e\u5165\u961f */\npublic void pushLast(int num) {\npush(num, false);\n}\n/* \u51fa\u961f\u64cd\u4f5c */\nprivate Integer pop(boolean isFront) {\n// \u82e5\u961f\u5217\u4e3a\u7a7a\uff0c\u76f4\u63a5\u8fd4\u56de null\nif (isEmpty())\nreturn null;\nint val;\n// \u961f\u9996\u51fa\u961f\u64cd\u4f5c\nif (isFront) {\nval = front.val; // \u6682\u5b58\u5934\u8282\u70b9\u503c\n// \u5220\u9664\u5934\u8282\u70b9\nListNode fNext = front.next;\nif (fNext != null) {\nfNext.prev = null;\nfront.next = null;\n}\nfront = fNext; // \u66f4\u65b0\u5934\u8282\u70b9\n// \u961f\u5c3e\u51fa\u961f\u64cd\u4f5c\n} else {\nval = rear.val; // \u6682\u5b58\u5c3e\u8282\u70b9\u503c\n// \u5220\u9664\u5c3e\u8282\u70b9\nListNode rPrev = rear.prev;\nif (rPrev != null) {\nrPrev.next = null;\nrear.prev = null;\n}\nrear = rPrev; // \u66f4\u65b0\u5c3e\u8282\u70b9\n}\nqueSize--; // \u66f4\u65b0\u961f\u5217\u957f\u5ea6\nreturn val;\n}\n/* \u961f\u9996\u51fa\u961f */\npublic Integer popFirst() {\nreturn pop(true);\n}\n/* \u961f\u5c3e\u51fa\u961f */\npublic Integer popLast() {\nreturn pop(false);\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\npublic Integer peekFirst() {\nreturn isEmpty() ? null : front.val;\n}\n/* \u8bbf\u95ee\u961f\u5c3e\u5143\u7d20 */\npublic Integer peekLast() {\nreturn isEmpty() ? null : rear.val;\n}\n/* \u8fd4\u56de\u6570\u7ec4\u7528\u4e8e\u6253\u5370 */\npublic int[] toArray() {\nListNode node = front;\nint[] res = new int[size()];\nfor (int i = 0; i &lt; res.length; i++) {\nres[i] = node.val;\nnode = node.next;\n}\nreturn res;\n}\n}\n</code></pre> linkedlist_deque.cpp<pre><code>/* \u53cc\u5411\u94fe\u8868\u8282\u70b9 */\nstruct DoublyListNode {\nint val;              // \u8282\u70b9\u503c\nDoublyListNode *next; // \u540e\u7ee7\u8282\u70b9\u6307\u9488\nDoublyListNode *prev; // \u524d\u9a71\u8282\u70b9\u6307\u9488\nDoublyListNode(int val) : val(val), prev(nullptr), next(nullptr) {\n}\n};\n/* \u57fa\u4e8e\u53cc\u5411\u94fe\u8868\u5b9e\u73b0\u7684\u53cc\u5411\u961f\u5217 */\nclass LinkedListDeque {\nprivate:\nDoublyListNode *front, *rear; // \u5934\u8282\u70b9 front \uff0c\u5c3e\u8282\u70b9 rear\nint queSize = 0;              // \u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6\npublic:\n/* \u6784\u9020\u65b9\u6cd5 */\nLinkedListDeque() : front(nullptr), rear(nullptr) {\n}\n/* \u6790\u6784\u65b9\u6cd5 */\n~LinkedListDeque() {\n// \u904d\u5386\u94fe\u8868\u5220\u9664\u8282\u70b9\uff0c\u91ca\u653e\u5185\u5b58\nDoublyListNode *pre, *cur = front;\nwhile (cur != nullptr) {\npre = cur;\ncur = cur-&gt;next;\ndelete pre;\n}\n}\n/* \u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6 */\nint size() {\nreturn queSize;\n}\n/* \u5224\u65ad\u53cc\u5411\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nbool isEmpty() {\nreturn size() == 0;\n}\n/* \u5165\u961f\u64cd\u4f5c */\nvoid push(int num, bool isFront) {\nDoublyListNode *node = new DoublyListNode(num);\n// \u82e5\u94fe\u8868\u4e3a\u7a7a\uff0c\u5219\u4ee4 front, rear \u90fd\u6307\u5411 node\nif (isEmpty())\nfront = rear = node;\n// \u961f\u9996\u5165\u961f\u64cd\u4f5c\nelse if (isFront) {\n// \u5c06 node \u6dfb\u52a0\u81f3\u94fe\u8868\u5934\u90e8\nfront-&gt;prev = node;\nnode-&gt;next = front;\nfront = node; // \u66f4\u65b0\u5934\u8282\u70b9\n// \u961f\u5c3e\u5165\u961f\u64cd\u4f5c\n} else {\n// \u5c06 node \u6dfb\u52a0\u81f3\u94fe\u8868\u5c3e\u90e8\nrear-&gt;next = node;\nnode-&gt;prev = rear;\nrear = node; // \u66f4\u65b0\u5c3e\u8282\u70b9\n}\nqueSize++; // \u66f4\u65b0\u961f\u5217\u957f\u5ea6\n}\n/* \u961f\u9996\u5165\u961f */\nvoid pushFirst(int num) {\npush(num, true);\n}\n/* \u961f\u5c3e\u5165\u961f */\nvoid pushLast(int num) {\npush(num, false);\n}\n/* \u51fa\u961f\u64cd\u4f5c */\nint pop(bool isFront) {\n// \u82e5\u961f\u5217\u4e3a\u7a7a\uff0c\u76f4\u63a5\u8fd4\u56de -1\nif (isEmpty())\nreturn -1;\nint val;\n// \u961f\u9996\u51fa\u961f\u64cd\u4f5c\nif (isFront) {\nval = front-&gt;val; // \u6682\u5b58\u5934\u8282\u70b9\u503c\n// \u5220\u9664\u5934\u8282\u70b9\nDoublyListNode *fNext = front-&gt;next;\nif (fNext != nullptr) {\nfNext-&gt;prev = nullptr;\nfront-&gt;next = nullptr;\ndelete front;\n}\nfront = fNext; // \u66f4\u65b0\u5934\u8282\u70b9\n// \u961f\u5c3e\u51fa\u961f\u64cd\u4f5c\n} else {\nval = rear-&gt;val; // \u6682\u5b58\u5c3e\u8282\u70b9\u503c\n// \u5220\u9664\u5c3e\u8282\u70b9\nDoublyListNode *rPrev = rear-&gt;prev;\nif (rPrev != nullptr) {\nrPrev-&gt;next = nullptr;\nrear-&gt;prev = nullptr;\ndelete rear;\n}\nrear = rPrev; // \u66f4\u65b0\u5c3e\u8282\u70b9\n}\nqueSize--; // \u66f4\u65b0\u961f\u5217\u957f\u5ea6\nreturn val;\n}\n/* \u961f\u9996\u51fa\u961f */\nint popFirst() {\nreturn pop(true);\n}\n/* \u961f\u5c3e\u51fa\u961f */\nint popLast() {\nreturn pop(false);\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\nint peekFirst() {\nreturn isEmpty() ? -1 : front-&gt;val;\n}\n/* \u8bbf\u95ee\u961f\u5c3e\u5143\u7d20 */\nint peekLast() {\nreturn isEmpty() ? -1 : rear-&gt;val;\n}\n/* \u8fd4\u56de\u6570\u7ec4\u7528\u4e8e\u6253\u5370 */\nvector&lt;int&gt; toVector() {\nDoublyListNode *node = front;\nvector&lt;int&gt; res(size());\nfor (int i = 0; i &lt; res.size(); i++) {\nres[i] = node-&gt;val;\nnode = node-&gt;next;\n}\nreturn res;\n}\n};\n</code></pre> linkedlist_deque.py<pre><code>class ListNode:\n\"\"\"\u53cc\u5411\u94fe\u8868\u8282\u70b9\"\"\"\ndef __init__(self, val: int) -&gt; None:\n\"\"\"\u6784\u9020\u65b9\u6cd5\"\"\"\nself.val: int = val\nself.next: ListNode | None = None  # \u540e\u7ee7\u8282\u70b9\u5f15\u7528\uff08\u6307\u9488\uff09\nself.prev: ListNode | None = None  # \u524d\u9a71\u8282\u70b9\u5f15\u7528\uff08\u6307\u9488\uff09\nclass LinkedListDeque:\n\"\"\"\u57fa\u4e8e\u53cc\u5411\u94fe\u8868\u5b9e\u73b0\u7684\u53cc\u5411\u961f\u5217\"\"\"\ndef __init__(self) -&gt; None:\n\"\"\"\u6784\u9020\u65b9\u6cd5\"\"\"\nself.front: ListNode | None = None  # \u5934\u8282\u70b9 front\nself.rear: ListNode | None = None  # \u5c3e\u8282\u70b9 rear\nself.__size: int = 0  # \u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6\ndef size(self) -&gt; int:\n\"\"\"\u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6\"\"\"\nreturn self.__size\ndef is_empty(self) -&gt; bool:\n\"\"\"\u5224\u65ad\u53cc\u5411\u961f\u5217\u662f\u5426\u4e3a\u7a7a\"\"\"\nreturn self.size() == 0\ndef push(self, num: int, is_front: bool) -&gt; None:\n\"\"\"\u5165\u961f\u64cd\u4f5c\"\"\"\nnode = ListNode(num)\n# \u82e5\u94fe\u8868\u4e3a\u7a7a\uff0c\u5219\u4ee4 front, rear \u90fd\u6307\u5411 node\nif self.is_empty():\nself.front = self.rear = node\n# \u961f\u9996\u5165\u961f\u64cd\u4f5c\nelif is_front:\n# \u5c06 node \u6dfb\u52a0\u81f3\u94fe\u8868\u5934\u90e8\nself.front.prev = node\nnode.next = self.front\nself.front = node  # \u66f4\u65b0\u5934\u8282\u70b9\n# \u961f\u5c3e\u5165\u961f\u64cd\u4f5c\nelse:\n# \u5c06 node \u6dfb\u52a0\u81f3\u94fe\u8868\u5c3e\u90e8\nself.rear.next = node\nnode.prev = self.rear\nself.rear = node  # \u66f4\u65b0\u5c3e\u8282\u70b9\nself.__size += 1  # \u66f4\u65b0\u961f\u5217\u957f\u5ea6\ndef push_first(self, num: int) -&gt; None:\n\"\"\"\u961f\u9996\u5165\u961f\"\"\"\nself.push(num, True)\ndef push_last(self, num: int) -&gt; None:\n\"\"\"\u961f\u5c3e\u5165\u961f\"\"\"\nself.push(num, False)\ndef pop(self, is_front: bool) -&gt; int:\n\"\"\"\u51fa\u961f\u64cd\u4f5c\"\"\"\n# \u82e5\u961f\u5217\u4e3a\u7a7a\uff0c\u76f4\u63a5\u8fd4\u56de None\nif self.is_empty():\nreturn None\n# \u961f\u9996\u51fa\u961f\u64cd\u4f5c\nif is_front:\nval: int = self.front.val  # \u6682\u5b58\u5934\u8282\u70b9\u503c\n# \u5220\u9664\u5934\u8282\u70b9\nfnext: ListNode | None = self.front.next\nif fnext != None:\nfnext.prev = None\nself.front.next = None\nself.front = fnext  # \u66f4\u65b0\u5934\u8282\u70b9\n# \u961f\u5c3e\u51fa\u961f\u64cd\u4f5c\nelse:\nval: int = self.rear.val  # \u6682\u5b58\u5c3e\u8282\u70b9\u503c\n# \u5220\u9664\u5c3e\u8282\u70b9\nrprev: ListNode | None = self.rear.prev\nif rprev != None:\nrprev.next = None\nself.rear.prev = None\nself.rear = rprev  # \u66f4\u65b0\u5c3e\u8282\u70b9\nself.__size -= 1  # \u66f4\u65b0\u961f\u5217\u957f\u5ea6\nreturn val\ndef pop_first(self) -&gt; int:\n\"\"\"\u961f\u9996\u51fa\u961f\"\"\"\nreturn self.pop(True)\ndef pop_last(self) -&gt; int:\n\"\"\"\u961f\u5c3e\u51fa\u961f\"\"\"\nreturn self.pop(False)\ndef peek_first(self) -&gt; int:\n\"\"\"\u8bbf\u95ee\u961f\u9996\u5143\u7d20\"\"\"\nreturn None if self.is_empty() else self.front.val\ndef peek_last(self) -&gt; int:\n\"\"\"\u8bbf\u95ee\u961f\u5c3e\u5143\u7d20\"\"\"\nreturn None if self.is_empty() else self.rear.val\ndef to_array(self) -&gt; list[int]:\n\"\"\"\u8fd4\u56de\u6570\u7ec4\u7528\u4e8e\u6253\u5370\"\"\"\nnode = self.front\nres = [0] * self.size()\nfor i in range(self.size()):\nres[i] = node.val\nnode = node.next\nreturn res\n</code></pre> linkedlist_deque.go<pre><code>/* \u57fa\u4e8e\u53cc\u5411\u94fe\u8868\u5b9e\u73b0\u7684\u53cc\u5411\u961f\u5217 */\ntype linkedListDeque struct {\n// \u4f7f\u7528\u5185\u7f6e\u5305 list\ndata *list.List\n}\n/* \u521d\u59cb\u5316\u53cc\u7aef\u961f\u5217 */\nfunc newLinkedListDeque() *linkedListDeque {\nreturn &amp;linkedListDeque{\ndata: list.New(),\n}\n}\n/* \u961f\u9996\u5143\u7d20\u5165\u961f */\nfunc (s *linkedListDeque) pushFirst(value any) {\ns.data.PushFront(value)\n}\n/* \u961f\u5c3e\u5143\u7d20\u5165\u961f */\nfunc (s *linkedListDeque) pushLast(value any) {\ns.data.PushBack(value)\n}\n/* \u961f\u9996\u5143\u7d20\u51fa\u961f */\nfunc (s *linkedListDeque) popFirst() any {\nif s.isEmpty() {\nreturn nil\n}\ne := s.data.Front()\ns.data.Remove(e)\nreturn e.Value\n}\n/* \u961f\u5c3e\u5143\u7d20\u51fa\u961f */\nfunc (s *linkedListDeque) popLast() any {\nif s.isEmpty() {\nreturn nil\n}\ne := s.data.Back()\ns.data.Remove(e)\nreturn e.Value\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\nfunc (s *linkedListDeque) peekFirst() any {\nif s.isEmpty() {\nreturn nil\n}\ne := s.data.Front()\nreturn e.Value\n}\n/* \u8bbf\u95ee\u961f\u5c3e\u5143\u7d20 */\nfunc (s *linkedListDeque) peekLast() any {\nif s.isEmpty() {\nreturn nil\n}\ne := s.data.Back()\nreturn e.Value\n}\n/* \u83b7\u53d6\u961f\u5217\u7684\u957f\u5ea6 */\nfunc (s *linkedListDeque) size() int {\nreturn s.data.Len()\n}\n/* \u5224\u65ad\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nfunc (s *linkedListDeque) isEmpty() bool {\nreturn s.data.Len() == 0\n}\n/* \u83b7\u53d6 List \u7528\u4e8e\u6253\u5370 */\nfunc (s *linkedListDeque) toList() *list.List {\nreturn s.data\n}\n</code></pre> linkedlist_deque.js<pre><code>/* \u53cc\u5411\u94fe\u8868\u8282\u70b9 */\nclass ListNode {\nprev; // \u524d\u9a71\u8282\u70b9\u5f15\u7528 (\u6307\u9488)\nnext; // \u540e\u7ee7\u8282\u70b9\u5f15\u7528 (\u6307\u9488)\nval; // \u8282\u70b9\u503c\nconstructor(val) {\nthis.val = val;\nthis.next = null;\nthis.prev = null;\n}\n}\n/* \u57fa\u4e8e\u53cc\u5411\u94fe\u8868\u5b9e\u73b0\u7684\u53cc\u5411\u961f\u5217 */\nclass LinkedListDeque {\n#front; // \u5934\u8282\u70b9 front\n#rear; // \u5c3e\u8282\u70b9 rear\n#queSize; // \u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6\nconstructor() {\nthis.#front = null;\nthis.#rear = null;\nthis.#queSize = 0;\n}\n/* \u961f\u5c3e\u5165\u961f\u64cd\u4f5c */\npushLast(val) {\nconst node = new ListNode(val);\n// \u82e5\u94fe\u8868\u4e3a\u7a7a\uff0c\u5219\u4ee4 front, rear \u90fd\u6307\u5411 node\nif (this.#queSize === 0) {\nthis.#front = node;\nthis.#rear = node;\n} else {\n// \u5c06 node \u6dfb\u52a0\u81f3\u94fe\u8868\u5c3e\u90e8\nthis.#rear.next = node;\nnode.prev = this.#rear;\nthis.#rear = node; // \u66f4\u65b0\u5c3e\u8282\u70b9\n}\nthis.#queSize++;\n}\n/* \u961f\u9996\u5165\u961f\u64cd\u4f5c */\npushFirst(val) {\nconst node = new ListNode(val);\n// \u82e5\u94fe\u8868\u4e3a\u7a7a\uff0c\u5219\u4ee4 front, rear \u90fd\u6307\u5411 node\nif (this.#queSize === 0) {\nthis.#front = node;\nthis.#rear = node;\n} else {\n// \u5c06 node \u6dfb\u52a0\u81f3\u94fe\u8868\u5934\u90e8\nthis.#front.prev = node;\nnode.next = this.#front;\nthis.#front = node; // \u66f4\u65b0\u5934\u8282\u70b9\n}\nthis.#queSize++;\n}\n/* \u961f\u5c3e\u51fa\u961f\u64cd\u4f5c */\npopLast() {\nif (this.#queSize === 0) {\nreturn null;\n}\nconst value = this.#rear.val; // \u5b58\u50a8\u5c3e\u8282\u70b9\u503c\n// \u5220\u9664\u5c3e\u8282\u70b9\nlet temp = this.#rear.prev;\nif (temp !== null) {\ntemp.next = null;\nthis.#rear.prev = null;\n}\nthis.#rear = temp; // \u66f4\u65b0\u5c3e\u8282\u70b9\nthis.#queSize--;\nreturn value;\n}\n/* \u961f\u9996\u51fa\u961f\u64cd\u4f5c */\npopFirst() {\nif (this.#queSize === 0) {\nreturn null;\n}\nconst value = this.#front.val; // \u5b58\u50a8\u5c3e\u8282\u70b9\u503c\n// \u5220\u9664\u5934\u8282\u70b9\nlet temp = this.#front.next;\nif (temp !== null) {\ntemp.prev = null;\nthis.#front.next = null;\n}\nthis.#front = temp; // \u66f4\u65b0\u5934\u8282\u70b9\nthis.#queSize--;\nreturn value;\n}\n/* \u8bbf\u95ee\u961f\u5c3e\u5143\u7d20 */\npeekLast() {\nreturn this.#queSize === 0 ? null : this.#rear.val;\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\npeekFirst() {\nreturn this.#queSize === 0 ? null : this.#front.val;\n}\n/* \u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6 */\nsize() {\nreturn this.#queSize;\n}\n/* \u5224\u65ad\u53cc\u5411\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nisEmpty() {\nreturn this.#queSize === 0;\n}\n/* \u6253\u5370\u53cc\u5411\u961f\u5217 */\nprint() {\nconst arr = [];\nlet temp = this.#front;\nwhile (temp !== null) {\narr.push(temp.val);\ntemp = temp.next;\n}\nconsole.log('[' + arr.join(', ') + ']');\n}\n}\n</code></pre> linkedlist_deque.ts<pre><code>/* \u53cc\u5411\u94fe\u8868\u8282\u70b9 */\nclass ListNode {\nprev: ListNode; // \u524d\u9a71\u8282\u70b9\u5f15\u7528 (\u6307\u9488)\nnext: ListNode; // \u540e\u7ee7\u8282\u70b9\u5f15\u7528 (\u6307\u9488)\nval: number; // \u8282\u70b9\u503c\nconstructor(val: number) {\nthis.val = val;\nthis.next = null;\nthis.prev = null;\n}\n}\n/* \u57fa\u4e8e\u53cc\u5411\u94fe\u8868\u5b9e\u73b0\u7684\u53cc\u5411\u961f\u5217 */\nclass LinkedListDeque {\nprivate front: ListNode; // \u5934\u8282\u70b9 front\nprivate rear: ListNode; // \u5c3e\u8282\u70b9 rear\nprivate queSize: number; // \u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6\nconstructor() {\nthis.front = null;\nthis.rear = null;\nthis.queSize = 0;\n}\n/* \u961f\u5c3e\u5165\u961f\u64cd\u4f5c */\npushLast(val: number): void {\nconst node: ListNode = new ListNode(val);\n// \u82e5\u94fe\u8868\u4e3a\u7a7a\uff0c\u5219\u4ee4 front, rear \u90fd\u6307\u5411 node\nif (this.queSize === 0) {\nthis.front = node;\nthis.rear = node;\n} else {\n// \u5c06 node \u6dfb\u52a0\u81f3\u94fe\u8868\u5c3e\u90e8\nthis.rear.next = node;\nnode.prev = this.rear;\nthis.rear = node; // \u66f4\u65b0\u5c3e\u8282\u70b9\n}\nthis.queSize++;\n}\n/* \u961f\u9996\u5165\u961f\u64cd\u4f5c */\npushFirst(val: number): void {\nconst node: ListNode = new ListNode(val);\n// \u82e5\u94fe\u8868\u4e3a\u7a7a\uff0c\u5219\u4ee4 front, rear \u90fd\u6307\u5411 node\nif (this.queSize === 0) {\nthis.front = node;\nthis.rear = node;\n} else {\n// \u5c06 node \u6dfb\u52a0\u81f3\u94fe\u8868\u5934\u90e8\nthis.front.prev = node;\nnode.next = this.front;\nthis.front = node; // \u66f4\u65b0\u5934\u8282\u70b9\n}\nthis.queSize++;\n}\n/* \u961f\u5c3e\u51fa\u961f\u64cd\u4f5c */\npopLast(): number {\nif (this.queSize === 0) {\nreturn null;\n}\nconst value: number = this.rear.val; // \u5b58\u50a8\u5c3e\u8282\u70b9\u503c\n// \u5220\u9664\u5c3e\u8282\u70b9\nlet temp: ListNode = this.rear.prev;\nif (temp !== null) {\ntemp.next = null;\nthis.rear.prev = null;\n}\nthis.rear = temp; // \u66f4\u65b0\u5c3e\u8282\u70b9\nthis.queSize--;\nreturn value;\n}\n/* \u961f\u9996\u51fa\u961f\u64cd\u4f5c */\npopFirst(): number {\nif (this.queSize === 0) {\nreturn null;\n}\nconst value: number = this.front.val; // \u5b58\u50a8\u5c3e\u8282\u70b9\u503c\n// \u5220\u9664\u5934\u8282\u70b9\nlet temp: ListNode = this.front.next;\nif (temp !== null) {\ntemp.prev = null;\nthis.front.next = null;\n}\nthis.front = temp; // \u66f4\u65b0\u5934\u8282\u70b9\nthis.queSize--;\nreturn value;\n}\n/* \u8bbf\u95ee\u961f\u5c3e\u5143\u7d20 */\npeekLast(): number {\nreturn this.queSize === 0 ? null : this.rear.val;\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\npeekFirst(): number {\nreturn this.queSize === 0 ? null : this.front.val;\n}\n/* \u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6 */\nsize(): number {\nreturn this.queSize;\n}\n/* \u5224\u65ad\u53cc\u5411\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nisEmpty(): boolean {\nreturn this.queSize === 0;\n}\n/* \u6253\u5370\u53cc\u5411\u961f\u5217 */\nprint(): void {\nconst arr: number[] = [];\nlet temp: ListNode = this.front;\nwhile (temp !== null) {\narr.push(temp.val);\ntemp = temp.next;\n}\nconsole.log('[' + arr.join(', ') + ']');\n}\n}\n</code></pre> linkedlist_deque.c<pre><code>/* \u53cc\u5411\u94fe\u8868\u8282\u70b9 */\nstruct doublyListNode {\nint val;                     // \u8282\u70b9\u503c\nstruct doublyListNode *next; // \u540e\u7ee7\u8282\u70b9\nstruct doublyListNode *prev; // \u524d\u9a71\u8282\u70b9\n};\ntypedef struct doublyListNode doublyListNode;\n/* \u6784\u9020\u51fd\u6570 */\ndoublyListNode *newDoublyListNode(int num) {\ndoublyListNode *new = (doublyListNode *)malloc(sizeof(doublyListNode));\nnew-&gt;val = num;\nnew-&gt;next = NULL;\nnew-&gt;prev = NULL;\nreturn new;\n}\n/* \u6790\u6784\u51fd\u6570 */\nvoid delDoublyListNode(doublyListNode *node) {\nfree(node);\n}\n/* \u57fa\u4e8e\u53cc\u5411\u94fe\u8868\u5b9e\u73b0\u7684\u53cc\u5411\u961f\u5217 */\nstruct linkedListDeque {\ndoublyListNode *front, *rear; // \u5934\u8282\u70b9 front \uff0c\u5c3e\u8282\u70b9 rear\nint queSize;                  // \u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6\n};\ntypedef struct linkedListDeque linkedListDeque;\n/* \u6784\u9020\u51fd\u6570 */\nlinkedListDeque *newLinkedListDeque() {\nlinkedListDeque *deque = (linkedListDeque *)malloc(sizeof(linkedListDeque));\ndeque-&gt;front = NULL;\ndeque-&gt;rear = NULL;\ndeque-&gt;queSize = 0;\nreturn deque;\n}\n/* \u6790\u6784\u51fd\u6570 */\nvoid delLinkedListdeque(linkedListDeque *deque) {\n// \u91ca\u653e\u6240\u6709\u8282\u70b9\nfor (int i = 0; i &lt; deque-&gt;queSize &amp;&amp; deque-&gt;front != NULL; i++) {\ndoublyListNode *tmp = deque-&gt;front;\ndeque-&gt;front = deque-&gt;front-&gt;next;\nfree(tmp);\n}\n// \u91ca\u653e deque \u7ed3\u6784\u4f53\nfree(deque);\n}\n/* \u83b7\u53d6\u961f\u5217\u7684\u957f\u5ea6 */\nint size(linkedListDeque *deque) {\nreturn deque-&gt;queSize;\n}\n/* \u5224\u65ad\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nbool empty(linkedListDeque *deque) {\nreturn (size(deque) == 0);\n}\n/* \u5165\u961f */\nvoid push(linkedListDeque *deque, int num, bool isFront) {\ndoublyListNode *node = newDoublyListNode(num);\n// \u82e5\u94fe\u8868\u4e3a\u7a7a\uff0c\u5219\u4ee4 front, rear \u90fd\u6307\u5411node\nif (empty(deque)) {\ndeque-&gt;front = deque-&gt;rear = node;\n}\n// \u961f\u9996\u5165\u961f\u64cd\u4f5c\nelse if (isFront) {\n// \u5c06 node \u6dfb\u52a0\u81f3\u94fe\u8868\u5934\u90e8\ndeque-&gt;front-&gt;prev = node;\nnode-&gt;next = deque-&gt;front;\ndeque-&gt;front = node; // \u66f4\u65b0\u5934\u8282\u70b9\n}\n// \u5bf9\u5c3e\u5165\u961f\u64cd\u4f5c\nelse {\n// \u5c06 node \u6dfb\u52a0\u81f3\u94fe\u8868\u5c3e\u90e8\ndeque-&gt;rear-&gt;next = node;\nnode-&gt;prev = deque-&gt;rear;\ndeque-&gt;rear = node;\n}\ndeque-&gt;queSize++; // \u66f4\u65b0\u961f\u5217\u957f\u5ea6\n}\n/* \u961f\u9996\u5165\u961f */\nvoid pushFirst(linkedListDeque *deque, int num) {\npush(deque, num, true);\n}\n/* \u961f\u5c3e\u5165\u961f */\nvoid pushLast(linkedListDeque *deque, int num) {\npush(deque, num, false);\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\nint peekFirst(linkedListDeque *deque) {\nassert(size(deque) &amp;&amp; deque-&gt;front);\nreturn deque-&gt;front-&gt;val;\n}\n/* \u8bbf\u95ee\u961f\u5c3e\u5143\u7d20 */\nint peekLast(linkedListDeque *deque) {\nassert(size(deque) &amp;&amp; deque-&gt;rear);\nreturn deque-&gt;rear-&gt;val;\n}\n/* \u51fa\u961f */\nint pop(linkedListDeque *deque, bool isFront) {\nif (empty(deque))\nreturn -1;\nint val;\n// \u961f\u9996\u51fa\u961f\u64cd\u4f5c\nif (isFront) {\nval = peekFirst(deque); // \u6682\u5b58\u5934\u8282\u70b9\u503c\ndoublyListNode *fNext = deque-&gt;front-&gt;next;\nif (fNext) {\nfNext-&gt;prev = NULL;\ndeque-&gt;front-&gt;next = NULL;\ndelDoublyListNode(deque-&gt;front);\n}\ndeque-&gt;front = fNext; // \u66f4\u65b0\u5934\u8282\u70b9\n}\n// \u961f\u5c3e\u51fa\u961f\u64cd\u4f5c\nelse {\nval = peekLast(deque); // \u6682\u5b58\u5c3e\u8282\u70b9\u503c\ndoublyListNode *rPrev = deque-&gt;rear-&gt;prev;\nif (rPrev) {\nrPrev-&gt;next = NULL;\ndeque-&gt;rear-&gt;prev = NULL;\ndelDoublyListNode(deque-&gt;rear);\n}\ndeque-&gt;rear = rPrev; // \u66f4\u65b0\u5c3e\u8282\u70b9\n}\ndeque-&gt;queSize--; // \u66f4\u65b0\u961f\u5217\u957f\u5ea6\nreturn val;\n}\n/* \u961f\u9996\u51fa\u961f */\nint popFirst(linkedListDeque *deque) {\nreturn pop(deque, true);\n}\n/* \u961f\u5c3e\u51fa\u961f */\nint popLast(linkedListDeque *deque) {\nreturn pop(deque, false);\n}\n/* \u6253\u5370\u961f\u5217 */\nvoid printLinkedListDeque(linkedListDeque *deque) {\nint arr[deque-&gt;queSize];\n// \u62f7\u8d1d\u94fe\u8868\u4e2d\u7684\u6570\u636e\u5230\u6570\u7ec4\nint i;\ndoublyListNode *node;\nfor (i = 0, node = deque-&gt;front; i &lt; deque-&gt;queSize; i++) {\narr[i] = node-&gt;val;\nnode = node-&gt;next;\n}\nprintArray(arr, deque-&gt;queSize);\n}\n</code></pre> linkedlist_deque.cs<pre><code>/* \u53cc\u5411\u94fe\u8868\u8282\u70b9 */\nclass ListNode {\npublic int val;       // \u8282\u70b9\u503c\npublic ListNode? next; // \u540e\u7ee7\u8282\u70b9\u5f15\u7528\uff08\u6307\u9488\uff09\npublic ListNode? prev; // \u524d\u9a71\u8282\u70b9\u5f15\u7528\uff08\u6307\u9488\uff09\npublic ListNode(int val) {\nthis.val = val;\nprev = null;\nnext = null;\n}\n}\n/* \u57fa\u4e8e\u53cc\u5411\u94fe\u8868\u5b9e\u73b0\u7684\u53cc\u5411\u961f\u5217 */\nclass LinkedListDeque {\nprivate ListNode? front, rear; // \u5934\u8282\u70b9 front, \u5c3e\u8282\u70b9 rear\nprivate int queSize = 0;      // \u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6\npublic LinkedListDeque() {\nfront = null;\nrear = null;\n}\n/* \u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6 */\npublic int size() {\nreturn queSize;\n}\n/* \u5224\u65ad\u53cc\u5411\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\npublic bool isEmpty() {\nreturn size() == 0;\n}\n/* \u5165\u961f\u64cd\u4f5c */\nprivate void push(int num, bool isFront) {\nListNode node = new ListNode(num);\n// \u82e5\u94fe\u8868\u4e3a\u7a7a\uff0c\u5219\u4ee4 front, rear \u90fd\u6307\u5411 node\nif (isEmpty()) {\nfront = node;\nrear = node;\n}\n// \u961f\u9996\u5165\u961f\u64cd\u4f5c\nelse if (isFront) {\n// \u5c06 node \u6dfb\u52a0\u81f3\u94fe\u8868\u5934\u90e8\nfront.prev = node;\nnode.next = front;\nfront = node; // \u66f4\u65b0\u5934\u8282\u70b9                           \n}\n// \u961f\u5c3e\u5165\u961f\u64cd\u4f5c\nelse {\n// \u5c06 node \u6dfb\u52a0\u81f3\u94fe\u8868\u5c3e\u90e8\nrear.next = node;\nnode.prev = rear;\nrear = node;  // \u66f4\u65b0\u5c3e\u8282\u70b9\n}\nqueSize++; // \u66f4\u65b0\u961f\u5217\u957f\u5ea6\n}\n/* \u961f\u9996\u5165\u961f */\npublic void pushFirst(int num) {\npush(num, true);\n}\n/* \u961f\u5c3e\u5165\u961f */\npublic void pushLast(int num) {\npush(num, false);\n}\n/* \u51fa\u961f\u64cd\u4f5c */\nprivate int? pop(bool isFront) {\n// \u82e5\u961f\u5217\u4e3a\u7a7a\uff0c\u76f4\u63a5\u8fd4\u56de null\nif (isEmpty()) {\nreturn null;\n}\nint val;\n// \u961f\u9996\u51fa\u961f\u64cd\u4f5c\nif (isFront) {\nval = front.val; // \u6682\u5b58\u5934\u8282\u70b9\u503c\n// \u5220\u9664\u5934\u8282\u70b9\nListNode fNext = front.next;\nif (fNext != null) {\nfNext.prev = null;\nfront.next = null;\n}\nfront = fNext;   // \u66f4\u65b0\u5934\u8282\u70b9\n}\n// \u961f\u5c3e\u51fa\u961f\u64cd\u4f5c\nelse {\nval = rear.val;  // \u6682\u5b58\u5c3e\u8282\u70b9\u503c\n// \u5220\u9664\u5c3e\u8282\u70b9\nListNode rPrev = rear.prev;\nif (rPrev != null) {\nrPrev.next = null;\nrear.prev = null;\n}\nrear = rPrev;    // \u66f4\u65b0\u5c3e\u8282\u70b9\n}\nqueSize--; // \u66f4\u65b0\u961f\u5217\u957f\u5ea6\nreturn val;\n}\n/* \u961f\u9996\u51fa\u961f */\npublic int? popFirst() {\nreturn pop(true);\n}\n/* \u961f\u5c3e\u51fa\u961f */\npublic int? popLast() {\nreturn pop(false);\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\npublic int? peekFirst() {\nreturn isEmpty() ? null : front.val;\n}\n/* \u8bbf\u95ee\u961f\u5c3e\u5143\u7d20 */\npublic int? peekLast() {\nreturn isEmpty() ? null : rear.val;\n}\n/* \u8fd4\u56de\u6570\u7ec4\u7528\u4e8e\u6253\u5370 */\npublic int[] toArray() {\nListNode node = front;\nint[] res = new int[size()];\nfor (int i = 0; i &lt; res.Length; i++) {\nres[i] = node.val;\nnode = node.next;\n}\nreturn res;\n}\n}\n</code></pre> linkedlist_deque.swift<pre><code>/* \u53cc\u5411\u94fe\u8868\u8282\u70b9 */\nclass ListNode {\nvar val: Int // \u8282\u70b9\u503c\nvar next: ListNode? // \u540e\u7ee7\u8282\u70b9\u5f15\u7528\uff08\u6307\u9488\uff09\nvar prev: ListNode? // \u524d\u9a71\u8282\u70b9\u5f15\u7528\uff08\u6307\u9488\uff09\ninit(val: Int) {\nself.val = val\n}\n}\n/* \u57fa\u4e8e\u53cc\u5411\u94fe\u8868\u5b9e\u73b0\u7684\u53cc\u5411\u961f\u5217 */\nclass LinkedListDeque {\nprivate var front: ListNode? // \u5934\u8282\u70b9 front\nprivate var rear: ListNode? // \u5c3e\u8282\u70b9 rear\nprivate var queSize: Int // \u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6\ninit() {\nqueSize = 0\n}\n/* \u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6 */\nfunc size() -&gt; Int {\nqueSize\n}\n/* \u5224\u65ad\u53cc\u5411\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nfunc isEmpty() -&gt; Bool {\nsize() == 0\n}\n/* \u5165\u961f\u64cd\u4f5c */\nprivate func push(num: Int, isFront: Bool) {\nlet node = ListNode(val: num)\n// \u82e5\u94fe\u8868\u4e3a\u7a7a\uff0c\u5219\u4ee4 front, rear \u90fd\u6307\u5411 node\nif isEmpty() {\nfront = node\nrear = node\n}\n// \u961f\u9996\u5165\u961f\u64cd\u4f5c\nelse if isFront {\n// \u5c06 node \u6dfb\u52a0\u81f3\u94fe\u8868\u5934\u90e8\nfront?.prev = node\nnode.next = front\nfront = node // \u66f4\u65b0\u5934\u8282\u70b9\n}\n// \u961f\u5c3e\u5165\u961f\u64cd\u4f5c\nelse {\n// \u5c06 node \u6dfb\u52a0\u81f3\u94fe\u8868\u5c3e\u90e8\nrear?.next = node\nnode.prev = rear\nrear = node // \u66f4\u65b0\u5c3e\u8282\u70b9\n}\nqueSize += 1 // \u66f4\u65b0\u961f\u5217\u957f\u5ea6\n}\n/* \u961f\u9996\u5165\u961f */\nfunc pushFirst(num: Int) {\npush(num: num, isFront: true)\n}\n/* \u961f\u5c3e\u5165\u961f */\nfunc pushLast(num: Int) {\npush(num: num, isFront: false)\n}\n/* \u51fa\u961f\u64cd\u4f5c */\nprivate func pop(isFront: Bool) -&gt; Int {\nif isEmpty() {\nfatalError(\"\u53cc\u5411\u961f\u5217\u4e3a\u7a7a\")\n}\nlet val: Int\n// \u961f\u9996\u51fa\u961f\u64cd\u4f5c\nif isFront {\nval = front!.val // \u6682\u5b58\u5934\u8282\u70b9\u503c\n// \u5220\u9664\u5934\u8282\u70b9\nlet fNext = front?.next\nif fNext != nil {\nfNext?.prev = nil\nfront?.next = nil\n}\nfront = fNext // \u66f4\u65b0\u5934\u8282\u70b9\n}\n// \u961f\u5c3e\u51fa\u961f\u64cd\u4f5c\nelse {\nval = rear!.val // \u6682\u5b58\u5c3e\u8282\u70b9\u503c\n// \u5220\u9664\u5c3e\u8282\u70b9\nlet rPrev = rear?.prev\nif rPrev != nil {\nrPrev?.next = nil\nrear?.prev = nil\n}\nrear = rPrev // \u66f4\u65b0\u5c3e\u8282\u70b9\n}\nqueSize -= 1 // \u66f4\u65b0\u961f\u5217\u957f\u5ea6\nreturn val\n}\n/* \u961f\u9996\u51fa\u961f */\nfunc popFirst() -&gt; Int {\npop(isFront: true)\n}\n/* \u961f\u5c3e\u51fa\u961f */\nfunc popLast() -&gt; Int {\npop(isFront: false)\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\nfunc peekFirst() -&gt; Int? {\nisEmpty() ? nil : front?.val\n}\n/* \u8bbf\u95ee\u961f\u5c3e\u5143\u7d20 */\nfunc peekLast() -&gt; Int? {\nisEmpty() ? nil : rear?.val\n}\n/* \u8fd4\u56de\u6570\u7ec4\u7528\u4e8e\u6253\u5370 */\nfunc toArray() -&gt; [Int] {\nvar node = front\nvar res = Array(repeating: 0, count: size())\nfor i in res.indices {\nres[i] = node!.val\nnode = node?.next\n}\nreturn res\n}\n}\n</code></pre> linkedlist_deque.zig<pre><code>// \u53cc\u5411\u94fe\u8868\u8282\u70b9\nfn ListNode(comptime T: type) type {\nreturn struct {\nconst Self = @This();\nval: T = undefined,     // \u8282\u70b9\u503c\nnext: ?*Self = null,    // \u540e\u7ee7\u8282\u70b9\u5f15\u7528\uff08\u6307\u9488\uff09\nprev: ?*Self = null,    // \u524d\u9a71\u8282\u70b9\u5f15\u7528\uff08\u6307\u9488\uff09\n// Initialize a list node with specific value\npub fn init(self: *Self, x: i32) void {\nself.val = x;\nself.next = null;\nself.prev = null;\n}\n};\n}\n// \u57fa\u4e8e\u53cc\u5411\u94fe\u8868\u5b9e\u73b0\u7684\u53cc\u5411\u961f\u5217\nfn LinkedListDeque(comptime T: type) type {\nreturn struct {\nconst Self = @This();\nfront: ?*ListNode(T) = null,                    // \u5934\u8282\u70b9 front\nrear: ?*ListNode(T) = null,                     // \u5c3e\u8282\u70b9 rear\nque_size: usize = 0,                             // \u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6\nmem_arena: ?std.heap.ArenaAllocator = null,\nmem_allocator: std.mem.Allocator = undefined,   // \u5185\u5b58\u5206\u914d\u5668\n// \u6784\u9020\u65b9\u6cd5\uff08\u5206\u914d\u5185\u5b58+\u521d\u59cb\u5316\u961f\u5217\uff09\npub fn init(self: *Self, allocator: std.mem.Allocator) !void {\nif (self.mem_arena == null) {\nself.mem_arena = std.heap.ArenaAllocator.init(allocator);\nself.mem_allocator = self.mem_arena.?.allocator();\n}\nself.front = null;\nself.rear = null;\nself.que_size = 0;\n}\n// \u6790\u6784\u65b9\u6cd5\uff08\u91ca\u653e\u5185\u5b58\uff09\npub fn deinit(self: *Self) void {\nif (self.mem_arena == null) return;\nself.mem_arena.?.deinit();\n}\n// \u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6\npub fn size(self: *Self) usize {\nreturn self.que_size;\n}\n// \u5224\u65ad\u53cc\u5411\u961f\u5217\u662f\u5426\u4e3a\u7a7a\npub fn isEmpty(self: *Self) bool {\nreturn self.size() == 0;\n}\n// \u5165\u961f\u64cd\u4f5c\npub fn push(self: *Self, num: T, is_front: bool) !void {\nvar node = try self.mem_allocator.create(ListNode(T));\nnode.init(num);\n// \u82e5\u94fe\u8868\u4e3a\u7a7a\uff0c\u5219\u4ee4 front, rear \u90fd\u6307\u5411 node\nif (self.isEmpty()) {\nself.front = node;\nself.rear = node;\n// \u961f\u9996\u5165\u961f\u64cd\u4f5c\n} else if (is_front) {\n// \u5c06 node \u6dfb\u52a0\u81f3\u94fe\u8868\u5934\u90e8\nself.front.?.prev = node;\nnode.next = self.front;\nself.front = node;  // \u66f4\u65b0\u5934\u8282\u70b9\n// \u961f\u5c3e\u5165\u961f\u64cd\u4f5c\n} else {\n// \u5c06 node \u6dfb\u52a0\u81f3\u94fe\u8868\u5c3e\u90e8\nself.rear.?.next = node;\nnode.prev = self.rear;\nself.rear = node;   // \u66f4\u65b0\u5c3e\u8282\u70b9\n}\nself.que_size += 1;      // \u66f4\u65b0\u961f\u5217\u957f\u5ea6\n} // \u961f\u9996\u5165\u961f\npub fn pushFirst(self: *Self, num: T) !void {\ntry self.push(num, true);\n} // \u961f\u5c3e\u5165\u961f\npub fn pushLast(self: *Self, num: T) !void {\ntry self.push(num, false);\n} // \u51fa\u961f\u64cd\u4f5c\npub fn pop(self: *Self, is_front: bool) T {\nif (self.isEmpty()) @panic(\"\u53cc\u5411\u961f\u5217\u4e3a\u7a7a\");\nvar val: T = undefined;\n// \u961f\u9996\u51fa\u961f\u64cd\u4f5c\nif (is_front) {\nval = self.front.?.val;     // \u6682\u5b58\u5934\u8282\u70b9\u503c\n// \u5220\u9664\u5934\u8282\u70b9\nvar fNext = self.front.?.next;\nif (fNext != null) {\nfNext.?.prev = null;\nself.front.?.next = null;\n}\nself.front = fNext;         // \u66f4\u65b0\u5934\u8282\u70b9\n// \u961f\u5c3e\u51fa\u961f\u64cd\u4f5c\n} else {\nval = self.rear.?.val;      // \u6682\u5b58\u5c3e\u8282\u70b9\u503c\n// \u5220\u9664\u5c3e\u8282\u70b9\nvar rPrev = self.rear.?.prev;\nif (rPrev != null) {\nrPrev.?.next = null;\nself.rear.?.prev = null;\n}\nself.rear = rPrev;          // \u66f4\u65b0\u5c3e\u8282\u70b9\n}\nself.que_size -= 1;              // \u66f4\u65b0\u961f\u5217\u957f\u5ea6\nreturn val;\n} // \u961f\u9996\u51fa\u961f\npub fn popFirst(self: *Self) T {\nreturn self.pop(true);\n} // \u961f\u5c3e\u51fa\u961f\npub fn popLast(self: *Self) T {\nreturn self.pop(false);\n} // \u8bbf\u95ee\u961f\u9996\u5143\u7d20\npub fn peekFirst(self: *Self) T {\nif (self.isEmpty()) @panic(\"\u53cc\u5411\u961f\u5217\u4e3a\u7a7a\");\nreturn self.front.?.val;\n}  // \u8bbf\u95ee\u961f\u5c3e\u5143\u7d20\npub fn peekLast(self: *Self) T {\nif (self.isEmpty()) @panic(\"\u53cc\u5411\u961f\u5217\u4e3a\u7a7a\");\nreturn self.rear.?.val;\n}\n// \u8fd4\u56de\u6570\u7ec4\u7528\u4e8e\u6253\u5370\npub fn toArray(self: *Self) ![]T {\nvar node = self.front;\nvar res = try self.mem_allocator.alloc(T, self.size());\nstd.mem.set(T, res, @as(T, 0));\nvar i: usize = 0;\nwhile (i &lt; res.len) : (i += 1) {\nres[i] = node.?.val;\nnode = node.?.next;\n}\nreturn res;\n}\n};\n}\n</code></pre> linkedlist_deque.dart<pre><code>/* \u53cc\u5411\u94fe\u8868\u8282\u70b9 */\nclass ListNode {\nint val; // \u8282\u70b9\u503c\nListNode? next; // \u540e\u7ee7\u8282\u70b9\u5f15\u7528\uff08\u6307\u9488\uff09\nListNode? prev; // \u524d\u9a71\u8282\u70b9\u5f15\u7528\uff08\u6307\u9488\uff09\nListNode(this.val, {this.next, this.prev});\n}\n/* \u57fa\u4e8e\u53cc\u5411\u94fe\u8868\u5b9e\u73b0\u7684\u53cc\u5411\u5bf9\u5217 */\nclass LinkedListDeque {\nlate ListNode? _front; // \u5934\u8282\u70b9 _front\nlate ListNode? _rear; // \u5c3e\u8282\u70b9 _rear\nint _queSize = 0; // \u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6\nLinkedListDeque() {\nthis._front = null;\nthis._rear = null;\n}\n/* \u83b7\u53d6\u53cc\u5411\u961f\u5217\u957f\u5ea6 */\nint size() {\nreturn this._queSize;\n}\n/* \u5224\u65ad\u53cc\u5411\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nbool isEmpty() {\nreturn size() == 0;\n}\n/* \u5165\u961f\u64cd\u4f5c */\nvoid push(int num, bool isFront) {\nfinal ListNode node = ListNode(num);\nif (isEmpty()) {\n// \u82e5\u94fe\u8868\u4e3a\u7a7a\uff0c\u5219\u4ee4 _front\uff0c_rear \u90fd\u6307\u5411 node\n_front = _rear = node;\n} else if (isFront) {\n// \u961f\u9996\u5165\u961f\u64cd\u4f5c\n// \u5c06 node \u6dfb\u52a0\u81f3\u94fe\u8868\u5934\u90e8\n_front!.prev = node;\nnode.next = _front;\n_front = node; // \u66f4\u65b0\u5934\u8282\u70b9\n} else {\n// \u961f\u5c3e\u5165\u961f\u64cd\u4f5c\n// \u5c06 node \u6dfb\u52a0\u81f3\u94fe\u8868\u5c3e\u90e8\n_rear!.next = node;\nnode.prev = _rear;\n_rear = node; // \u66f4\u65b0\u5c3e\u8282\u70b9\n}\n_queSize++; // \u66f4\u65b0\u961f\u5217\u957f\u5ea6\n}\n/* \u961f\u9996\u5165\u961f */\nvoid pushFirst(int num) {\npush(num, true);\n}\n/* \u961f\u5c3e\u5165\u961f */\nvoid pushLast(int num) {\npush(num, false);\n}\n/* \u51fa\u961f\u64cd\u4f5c */\nint? pop(bool isFront) {\n// \u82e5\u961f\u5217\u4e3a\u7a7a\uff0c\u76f4\u63a5\u8fd4\u56de null\nif (isEmpty()) {\nreturn null;\n}\nfinal int val;\nif (isFront) {\n// \u961f\u9996\u51fa\u961f\u64cd\u4f5c\nval = _front!.val; // \u6682\u5b58\u5934\u8282\u70b9\u503c\n// \u5220\u9664\u5934\u8282\u70b9\nListNode? fNext = _front!.next;\nif (fNext != null) {\nfNext.prev = null;\n_front!.next = null;\n}\n_front = fNext; // \u66f4\u65b0\u5934\u8282\u70b9\n} else {\n// \u961f\u5c3e\u51fa\u961f\u64cd\u4f5c\nval = _rear!.val; // \u6682\u5b58\u5c3e\u8282\u70b9\u503c\n// \u5220\u9664\u5c3e\u8282\u70b9\nListNode? rPrev = _rear!.prev;\nif (rPrev != null) {\nrPrev.next = null;\n_rear!.prev = null;\n}\n_rear = rPrev; // \u66f4\u65b0\u5c3e\u8282\u70b9\n}\n_queSize--; // \u66f4\u65b0\u961f\u5217\u957f\u5ea6\nreturn val;\n}\n/* \u961f\u9996\u51fa\u961f */\nint? popFirst() {\nreturn pop(true);\n}\n/* \u961f\u5c3e\u51fa\u961f */\nint? popLast() {\nreturn pop(false);\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\nint? peekFirst() {\nreturn _front?.val;\n}\n/* \u8bbf\u95ee\u961f\u5c3e\u5143\u7d20 */\nint? peekLast() {\nreturn _rear?.val;\n}\n/* \u8fd4\u56de\u6570\u7ec4\u7528\u4e8e\u6253\u5370 */\nList&lt;int&gt; toArray() {\nListNode? node = _front;\nfinal List&lt;int&gt; res = [];\nfor (int i = 0; i &lt; _queSize; i++) {\nres.add(node!.val);\nnode = node.next;\n}\nreturn res;\n}\n}\n</code></pre>"},{"location":"chapter_stack_and_queue/deque/#_2","title":"\u57fa\u4e8e\u6570\u7ec4\u7684\u5b9e\u73b0","text":"<p>\u4e0e\u57fa\u4e8e\u6570\u7ec4\u5b9e\u73b0\u961f\u5217\u7c7b\u4f3c\uff0c\u6211\u4eec\u4e5f\u53ef\u4ee5\u4f7f\u7528\u73af\u5f62\u6570\u7ec4\u6765\u5b9e\u73b0\u53cc\u5411\u961f\u5217\u3002\u5728\u961f\u5217\u7684\u5b9e\u73b0\u57fa\u7840\u4e0a\uff0c\u4ec5\u9700\u589e\u52a0\u201c\u961f\u9996\u5165\u961f\u201d\u548c\u201c\u961f\u5c3e\u51fa\u961f\u201d\u7684\u65b9\u6cd5\u3002</p> ArrayDequepushLast()pushFirst()popLast()popFirst() <p></p> <p></p> <p></p> <p></p> <p></p> <p>\u4ee5\u4e0b\u662f\u5177\u4f53\u5b9e\u73b0\u4ee3\u7801\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart array_deque.java<pre><code>/* \u57fa\u4e8e\u73af\u5f62\u6570\u7ec4\u5b9e\u73b0\u7684\u53cc\u5411\u961f\u5217 */\nclass ArrayDeque {\nprivate int[] nums; // \u7528\u4e8e\u5b58\u50a8\u53cc\u5411\u961f\u5217\u5143\u7d20\u7684\u6570\u7ec4\nprivate int front; // \u961f\u9996\u6307\u9488\uff0c\u6307\u5411\u961f\u9996\u5143\u7d20\nprivate int queSize; // \u53cc\u5411\u961f\u5217\u957f\u5ea6\n/* \u6784\u9020\u65b9\u6cd5 */\npublic ArrayDeque(int capacity) {\nthis.nums = new int[capacity];\nfront = queSize = 0;\n}\n/* \u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u5bb9\u91cf */\npublic int capacity() {\nreturn nums.length;\n}\n/* \u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6 */\npublic int size() {\nreturn queSize;\n}\n/* \u5224\u65ad\u53cc\u5411\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\npublic boolean isEmpty() {\nreturn queSize == 0;\n}\n/* \u8ba1\u7b97\u73af\u5f62\u6570\u7ec4\u7d22\u5f15 */\nprivate int index(int i) {\n// \u901a\u8fc7\u53d6\u4f59\u64cd\u4f5c\u5b9e\u73b0\u6570\u7ec4\u9996\u5c3e\u76f8\u8fde\n// \u5f53 i \u8d8a\u8fc7\u6570\u7ec4\u5c3e\u90e8\u540e\uff0c\u56de\u5230\u5934\u90e8\n// \u5f53 i \u8d8a\u8fc7\u6570\u7ec4\u5934\u90e8\u540e\uff0c\u56de\u5230\u5c3e\u90e8\nreturn (i + capacity()) % capacity();\n}\n/* \u961f\u9996\u5165\u961f */\npublic void pushFirst(int num) {\nif (queSize == capacity()) {\nSystem.out.println(\"\u53cc\u5411\u961f\u5217\u5df2\u6ee1\");\nreturn;\n}\n// \u961f\u9996\u6307\u9488\u5411\u5de6\u79fb\u52a8\u4e00\u4f4d\n// \u901a\u8fc7\u53d6\u4f59\u64cd\u4f5c\uff0c\u5b9e\u73b0 front \u8d8a\u8fc7\u6570\u7ec4\u5934\u90e8\u540e\u56de\u5230\u5c3e\u90e8\nfront = index(front - 1);\n// \u5c06 num \u6dfb\u52a0\u81f3\u961f\u9996\nnums[front] = num;\nqueSize++;\n}\n/* \u961f\u5c3e\u5165\u961f */\npublic void pushLast(int num) {\nif (queSize == capacity()) {\nSystem.out.println(\"\u53cc\u5411\u961f\u5217\u5df2\u6ee1\");\nreturn;\n}\n// \u8ba1\u7b97\u5c3e\u6307\u9488\uff0c\u6307\u5411\u961f\u5c3e\u7d22\u5f15 + 1\nint rear = index(front + queSize);\n// \u5c06 num \u6dfb\u52a0\u81f3\u961f\u5c3e\nnums[rear] = num;\nqueSize++;\n}\n/* \u961f\u9996\u51fa\u961f */\npublic int popFirst() {\nint num = peekFirst();\n// \u961f\u9996\u6307\u9488\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\nfront = index(front + 1);\nqueSize--;\nreturn num;\n}\n/* \u961f\u5c3e\u51fa\u961f */\npublic int popLast() {\nint num = peekLast();\nqueSize--;\nreturn num;\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\npublic int peekFirst() {\nif (isEmpty())\nthrow new IndexOutOfBoundsException();\nreturn nums[front];\n}\n/* \u8bbf\u95ee\u961f\u5c3e\u5143\u7d20 */\npublic int peekLast() {\nif (isEmpty())\nthrow new IndexOutOfBoundsException();\n// \u8ba1\u7b97\u5c3e\u5143\u7d20\u7d22\u5f15\nint last = index(front + queSize - 1);\nreturn nums[last];\n}\n/* \u8fd4\u56de\u6570\u7ec4\u7528\u4e8e\u6253\u5370 */\npublic int[] toArray() {\n// \u4ec5\u8f6c\u6362\u6709\u6548\u957f\u5ea6\u8303\u56f4\u5185\u7684\u5217\u8868\u5143\u7d20\nint[] res = new int[queSize];\nfor (int i = 0, j = front; i &lt; queSize; i++, j++) {\nres[i] = nums[index(j)];\n}\nreturn res;\n}\n}\n</code></pre> array_deque.cpp<pre><code>/* \u57fa\u4e8e\u73af\u5f62\u6570\u7ec4\u5b9e\u73b0\u7684\u53cc\u5411\u961f\u5217 */\nclass ArrayDeque {\nprivate:\nvector&lt;int&gt; nums; // \u7528\u4e8e\u5b58\u50a8\u53cc\u5411\u961f\u5217\u5143\u7d20\u7684\u6570\u7ec4\nint front;        // \u961f\u9996\u6307\u9488\uff0c\u6307\u5411\u961f\u9996\u5143\u7d20\nint queSize;      // \u53cc\u5411\u961f\u5217\u957f\u5ea6\npublic:\n/* \u6784\u9020\u65b9\u6cd5 */\nArrayDeque(int capacity) {\nnums.resize(capacity);\nfront = queSize = 0;\n}\n/* \u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u5bb9\u91cf */\nint capacity() {\nreturn nums.size();\n}\n/* \u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6 */\nint size() {\nreturn queSize;\n}\n/* \u5224\u65ad\u53cc\u5411\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nbool isEmpty() {\nreturn queSize == 0;\n}\n/* \u8ba1\u7b97\u73af\u5f62\u6570\u7ec4\u7d22\u5f15 */\nint index(int i) {\n// \u901a\u8fc7\u53d6\u4f59\u64cd\u4f5c\u5b9e\u73b0\u6570\u7ec4\u9996\u5c3e\u76f8\u8fde\n// \u5f53 i \u8d8a\u8fc7\u6570\u7ec4\u5c3e\u90e8\u540e\uff0c\u56de\u5230\u5934\u90e8\n// \u5f53 i \u8d8a\u8fc7\u6570\u7ec4\u5934\u90e8\u540e\uff0c\u56de\u5230\u5c3e\u90e8\nreturn (i + capacity()) % capacity();\n}\n/* \u961f\u9996\u5165\u961f */\nvoid pushFirst(int num) {\nif (queSize == capacity()) {\ncout &lt;&lt; \"\u53cc\u5411\u961f\u5217\u5df2\u6ee1\" &lt;&lt; endl;\nreturn;\n}\n// \u961f\u9996\u6307\u9488\u5411\u5de6\u79fb\u52a8\u4e00\u4f4d\n// \u901a\u8fc7\u53d6\u4f59\u64cd\u4f5c\uff0c\u5b9e\u73b0 front \u8d8a\u8fc7\u6570\u7ec4\u5934\u90e8\u540e\u56de\u5230\u5c3e\u90e8\nfront = index(front - 1);\n// \u5c06 num \u6dfb\u52a0\u81f3\u961f\u9996\nnums[front] = num;\nqueSize++;\n}\n/* \u961f\u5c3e\u5165\u961f */\nvoid pushLast(int num) {\nif (queSize == capacity()) {\ncout &lt;&lt; \"\u53cc\u5411\u961f\u5217\u5df2\u6ee1\" &lt;&lt; endl;\nreturn;\n}\n// \u8ba1\u7b97\u5c3e\u6307\u9488\uff0c\u6307\u5411\u961f\u5c3e\u7d22\u5f15 + 1\nint rear = index(front + queSize);\n// \u5c06 num \u6dfb\u52a0\u81f3\u961f\u5c3e\nnums[rear] = num;\nqueSize++;\n}\n/* \u961f\u9996\u51fa\u961f */\nint popFirst() {\nint num = peekFirst();\n// \u961f\u9996\u6307\u9488\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\nfront = index(front + 1);\nqueSize--;\nreturn num;\n}\n/* \u961f\u5c3e\u51fa\u961f */\nint popLast() {\nint num = peekLast();\nqueSize--;\nreturn num;\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\nint peekFirst() {\nif (isEmpty())\nthrow out_of_range(\"\u53cc\u5411\u961f\u5217\u4e3a\u7a7a\");\nreturn nums[front];\n}\n/* \u8bbf\u95ee\u961f\u5c3e\u5143\u7d20 */\nint peekLast() {\nif (isEmpty())\nthrow out_of_range(\"\u53cc\u5411\u961f\u5217\u4e3a\u7a7a\");\n// \u8ba1\u7b97\u5c3e\u5143\u7d20\u7d22\u5f15\nint last = index(front + queSize - 1);\nreturn nums[last];\n}\n/* \u8fd4\u56de\u6570\u7ec4\u7528\u4e8e\u6253\u5370 */\nvector&lt;int&gt; toVector() {\n// \u4ec5\u8f6c\u6362\u6709\u6548\u957f\u5ea6\u8303\u56f4\u5185\u7684\u5217\u8868\u5143\u7d20\nvector&lt;int&gt; res(queSize);\nfor (int i = 0, j = front; i &lt; queSize; i++, j++) {\nres[i] = nums[index(j)];\n}\nreturn res;\n}\n};\n</code></pre> array_deque.py<pre><code>class ArrayDeque:\n\"\"\"\u57fa\u4e8e\u73af\u5f62\u6570\u7ec4\u5b9e\u73b0\u7684\u53cc\u5411\u961f\u5217\"\"\"\ndef __init__(self, capacity: int) -&gt; None:\n\"\"\"\u6784\u9020\u65b9\u6cd5\"\"\"\nself.__nums: list[int] = [0] * capacity\nself.__front: int = 0\nself.__size: int = 0\ndef capacity(self) -&gt; int:\n\"\"\"\u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u5bb9\u91cf\"\"\"\nreturn len(self.__nums)\ndef size(self) -&gt; int:\n\"\"\"\u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6\"\"\"\nreturn self.__size\ndef is_empty(self) -&gt; bool:\n\"\"\"\u5224\u65ad\u53cc\u5411\u961f\u5217\u662f\u5426\u4e3a\u7a7a\"\"\"\nreturn self.__size == 0\ndef index(self, i: int) -&gt; int:\n\"\"\"\u8ba1\u7b97\u73af\u5f62\u6570\u7ec4\u7d22\u5f15\"\"\"\n# \u901a\u8fc7\u53d6\u4f59\u64cd\u4f5c\u5b9e\u73b0\u6570\u7ec4\u9996\u5c3e\u76f8\u8fde\n# \u5f53 i \u8d8a\u8fc7\u6570\u7ec4\u5c3e\u90e8\u540e\uff0c\u56de\u5230\u5934\u90e8\n# \u5f53 i \u8d8a\u8fc7\u6570\u7ec4\u5934\u90e8\u540e\uff0c\u56de\u5230\u5c3e\u90e8\nreturn (i + self.capacity()) % self.capacity()\ndef push_first(self, num: int) -&gt; None:\n\"\"\"\u961f\u9996\u5165\u961f\"\"\"\nif self.__size == self.capacity():\nprint(\"\u53cc\u5411\u961f\u5217\u5df2\u6ee1\")\nreturn\n# \u961f\u9996\u6307\u9488\u5411\u5de6\u79fb\u52a8\u4e00\u4f4d\n# \u901a\u8fc7\u53d6\u4f59\u64cd\u4f5c\uff0c\u5b9e\u73b0 front \u8d8a\u8fc7\u6570\u7ec4\u5934\u90e8\u540e\u56de\u5230\u5c3e\u90e8\nself.__front = self.index(self.__front - 1)\n# \u5c06 num \u6dfb\u52a0\u81f3\u961f\u9996\nself.__nums[self.__front] = num\nself.__size += 1\ndef push_last(self, num: int) -&gt; None:\n\"\"\"\u961f\u5c3e\u5165\u961f\"\"\"\nif self.__size == self.capacity():\nprint(\"\u53cc\u5411\u961f\u5217\u5df2\u6ee1\")\nreturn\n# \u8ba1\u7b97\u5c3e\u6307\u9488\uff0c\u6307\u5411\u961f\u5c3e\u7d22\u5f15 + 1\nrear = self.index(self.__front + self.__size)\n# \u5c06 num \u6dfb\u52a0\u81f3\u961f\u5c3e\nself.__nums[rear] = num\nself.__size += 1\ndef pop_first(self) -&gt; int:\n\"\"\"\u961f\u9996\u51fa\u961f\"\"\"\nnum = self.peek_first()\n# \u961f\u9996\u6307\u9488\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\nself.__front = self.index(self.__front + 1)\nself.__size -= 1\nreturn num\ndef pop_last(self) -&gt; int:\n\"\"\"\u961f\u5c3e\u51fa\u961f\"\"\"\nnum = self.peek_last()\nself.__size -= 1\nreturn num\ndef peek_first(self) -&gt; int:\n\"\"\"\u8bbf\u95ee\u961f\u9996\u5143\u7d20\"\"\"\nif self.is_empty():\nraise IndexError(\"\u53cc\u5411\u961f\u5217\u4e3a\u7a7a\")\nreturn self.__nums[self.__front]\ndef peek_last(self) -&gt; int:\n\"\"\"\u8bbf\u95ee\u961f\u5c3e\u5143\u7d20\"\"\"\nif self.is_empty():\nraise IndexError(\"\u53cc\u5411\u961f\u5217\u4e3a\u7a7a\")\n# \u8ba1\u7b97\u5c3e\u5143\u7d20\u7d22\u5f15\nlast = self.index(self.__front + self.__size - 1)\nreturn self.__nums[last]\ndef to_array(self) -&gt; list[int]:\n\"\"\"\u8fd4\u56de\u6570\u7ec4\u7528\u4e8e\u6253\u5370\"\"\"\n# \u4ec5\u8f6c\u6362\u6709\u6548\u957f\u5ea6\u8303\u56f4\u5185\u7684\u5217\u8868\u5143\u7d20\nres = []\nfor i in range(self.__size):\nres.append(self.__nums[self.index(self.__front + i)])\nreturn res\n</code></pre> array_deque.go<pre><code>/* \u57fa\u4e8e\u73af\u5f62\u6570\u7ec4\u5b9e\u73b0\u7684\u53cc\u5411\u961f\u5217 */\ntype arrayDeque struct {\nnums        []int // \u7528\u4e8e\u5b58\u50a8\u53cc\u5411\u961f\u5217\u5143\u7d20\u7684\u6570\u7ec4\nfront       int   // \u961f\u9996\u6307\u9488\uff0c\u6307\u5411\u961f\u9996\u5143\u7d20\nqueSize     int   // \u53cc\u5411\u961f\u5217\u957f\u5ea6\nqueCapacity int   // \u961f\u5217\u5bb9\u91cf\uff08\u5373\u6700\u5927\u5bb9\u7eb3\u5143\u7d20\u6570\u91cf\uff09\n}\n/* \u521d\u59cb\u5316\u961f\u5217 */\nfunc newArrayDeque(queCapacity int) *arrayDeque {\nreturn &amp;arrayDeque{\nnums:        make([]int, queCapacity),\nqueCapacity: queCapacity,\nfront:       0,\nqueSize:     0,\n}\n}\n/* \u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6 */\nfunc (q *arrayDeque) size() int {\nreturn q.queSize\n}\n/* \u5224\u65ad\u53cc\u5411\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nfunc (q *arrayDeque) isEmpty() bool {\nreturn q.queSize == 0\n}\n/* \u8ba1\u7b97\u73af\u5f62\u6570\u7ec4\u7d22\u5f15 */\nfunc (q *arrayDeque) index(i int) int {\n// \u901a\u8fc7\u53d6\u4f59\u64cd\u4f5c\u5b9e\u73b0\u6570\u7ec4\u9996\u5c3e\u76f8\u8fde\n// \u5f53 i \u8d8a\u8fc7\u6570\u7ec4\u5c3e\u90e8\u540e\uff0c\u56de\u5230\u5934\u90e8\n// \u5f53 i \u8d8a\u8fc7\u6570\u7ec4\u5934\u90e8\u540e\uff0c\u56de\u5230\u5c3e\u90e8\nreturn (i + q.queCapacity) % q.queCapacity\n}\n/* \u961f\u9996\u5165\u961f */\nfunc (q *arrayDeque) pushFirst(num int) {\nif q.queSize == q.queCapacity {\nfmt.Println(\"\u53cc\u5411\u961f\u5217\u5df2\u6ee1\")\nreturn\n}\n// \u961f\u9996\u6307\u9488\u5411\u5de6\u79fb\u52a8\u4e00\u4f4d\n// \u901a\u8fc7\u53d6\u4f59\u64cd\u4f5c\uff0c\u5b9e\u73b0 front \u8d8a\u8fc7\u6570\u7ec4\u5934\u90e8\u540e\u56de\u5230\u5c3e\u90e8\nq.front = q.index(q.front - 1)\n// \u5c06 num \u6dfb\u52a0\u81f3\u961f\u9996\nq.nums[q.front] = num\nq.queSize++\n}\n/* \u961f\u5c3e\u5165\u961f */\nfunc (q *arrayDeque) pushLast(num int) {\nif q.queSize == q.queCapacity {\nfmt.Println(\"\u53cc\u5411\u961f\u5217\u5df2\u6ee1\")\nreturn\n}\n// \u8ba1\u7b97\u5c3e\u6307\u9488\uff0c\u6307\u5411\u961f\u5c3e\u7d22\u5f15 + 1\nrear := q.index(q.front + q.queSize)\n// \u5c06 num \u6dfb\u52a0\u81f3\u961f\u9996\nq.nums[rear] = num\nq.queSize++\n}\n/* \u961f\u9996\u51fa\u961f */\nfunc (q *arrayDeque) popFirst() any {\nnum := q.peekFirst()\n// \u961f\u9996\u6307\u9488\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\nq.front = q.index(q.front + 1)\nq.queSize--\nreturn num\n}\n/* \u961f\u5c3e\u51fa\u961f */\nfunc (q *arrayDeque) popLast() any {\nnum := q.peekLast()\nq.queSize--\nreturn num\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\nfunc (q *arrayDeque) peekFirst() any {\nif q.isEmpty() {\nreturn nil\n}\nreturn q.nums[q.front]\n}\n/* \u8bbf\u95ee\u961f\u5c3e\u5143\u7d20 */\nfunc (q *arrayDeque) peekLast() any {\nif q.isEmpty() {\nreturn nil\n}\n// \u8ba1\u7b97\u5c3e\u5143\u7d20\u7d22\u5f15\nlast := q.index(q.front + q.queSize - 1)\nreturn q.nums[last]\n}\n/* \u83b7\u53d6 Slice \u7528\u4e8e\u6253\u5370 */\nfunc (q *arrayDeque) toSlice() []int {\n// \u4ec5\u8f6c\u6362\u6709\u6548\u957f\u5ea6\u8303\u56f4\u5185\u7684\u5217\u8868\u5143\u7d20\nres := make([]int, q.queSize)\nfor i, j := 0, q.front; i &lt; q.queSize; i++ {\nres[i] = q.nums[q.index(j)]\nj++\n}\nreturn res\n}\n</code></pre> array_deque.js<pre><code>/* \u57fa\u4e8e\u73af\u5f62\u6570\u7ec4\u5b9e\u73b0\u7684\u53cc\u5411\u961f\u5217 */\nclass ArrayDeque {\n#nums; // \u7528\u4e8e\u5b58\u50a8\u53cc\u5411\u961f\u5217\u5143\u7d20\u7684\u6570\u7ec4\n#front; // \u961f\u9996\u6307\u9488\uff0c\u6307\u5411\u961f\u9996\u5143\u7d20\n#queSize; // \u53cc\u5411\u961f\u5217\u957f\u5ea6\n/* \u6784\u9020\u65b9\u6cd5 */\nconstructor(capacity) {\nthis.#nums = new Array(capacity);\nthis.#front = 0;\nthis.#queSize = 0;\n}\n/* \u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u5bb9\u91cf */\ncapacity() {\nreturn this.#nums.length;\n}\n/* \u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6 */\nsize() {\nreturn this.#queSize;\n}\n/* \u5224\u65ad\u53cc\u5411\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nisEmpty() {\nreturn this.#queSize === 0;\n}\n/* \u8ba1\u7b97\u73af\u5f62\u6570\u7ec4\u7d22\u5f15 */\nindex(i) {\n// \u901a\u8fc7\u53d6\u4f59\u64cd\u4f5c\u5b9e\u73b0\u6570\u7ec4\u9996\u5c3e\u76f8\u8fde\n// \u5f53 i \u8d8a\u8fc7\u6570\u7ec4\u5c3e\u90e8\u540e\uff0c\u56de\u5230\u5934\u90e8\n// \u5f53 i \u8d8a\u8fc7\u6570\u7ec4\u5934\u90e8\u540e\uff0c\u56de\u5230\u5c3e\u90e8\nreturn (i + this.capacity()) % this.capacity();\n}\n/* \u961f\u9996\u5165\u961f */\npushFirst(num) {\nif (this.#queSize === this.capacity()) {\nconsole.log('\u53cc\u5411\u961f\u5217\u5df2\u6ee1');\nreturn;\n}\n// \u961f\u9996\u6307\u9488\u5411\u5de6\u79fb\u52a8\u4e00\u4f4d\n// \u901a\u8fc7\u53d6\u4f59\u64cd\u4f5c\uff0c\u5b9e\u73b0 front \u8d8a\u8fc7\u6570\u7ec4\u5934\u90e8\u540e\u56de\u5230\u5c3e\u90e8\nthis.#front = this.index(this.#front - 1);\n// \u5c06 num \u6dfb\u52a0\u81f3\u961f\u9996\nthis.#nums[this.#front] = num;\nthis.#queSize++;\n}\n/* \u961f\u5c3e\u5165\u961f */\npushLast(num) {\nif (this.#queSize === this.capacity()) {\nconsole.log('\u53cc\u5411\u961f\u5217\u5df2\u6ee1');\nreturn;\n}\n// \u8ba1\u7b97\u5c3e\u6307\u9488\uff0c\u6307\u5411\u961f\u5c3e\u7d22\u5f15 + 1\nconst rear = this.index(this.#front + this.#queSize);\n// \u5c06 num \u6dfb\u52a0\u81f3\u961f\u5c3e\nthis.#nums[rear] = num;\nthis.#queSize++;\n}\n/* \u961f\u9996\u51fa\u961f */\npopFirst() {\nconst num = this.peekFirst();\n// \u961f\u9996\u6307\u9488\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\nthis.#front = this.index(this.#front + 1);\nthis.#queSize--;\nreturn num;\n}\n/* \u961f\u5c3e\u51fa\u961f */\npopLast() {\nconst num = this.peekLast();\nthis.#queSize--;\nreturn num;\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\npeekFirst() {\nif (this.isEmpty()) throw new Error('The Deque Is Empty.');\nreturn this.#nums[this.#front];\n}\n/* \u8bbf\u95ee\u961f\u5c3e\u5143\u7d20 */\npeekLast() {\nif (this.isEmpty()) throw new Error('The Deque Is Empty.');\n// \u8ba1\u7b97\u5c3e\u5143\u7d20\u7d22\u5f15\nconst last = this.index(this.#front + this.#queSize - 1);\nreturn this.#nums[last];\n}\n/* \u8fd4\u56de\u6570\u7ec4\u7528\u4e8e\u6253\u5370 */\ntoArray() {\n// \u4ec5\u8f6c\u6362\u6709\u6548\u957f\u5ea6\u8303\u56f4\u5185\u7684\u5217\u8868\u5143\u7d20\nconst res = [];\nfor (let i = 0, j = this.#front; i &lt; this.#queSize; i++, j++) {\nres[i] = this.#nums[this.index(j)];\n}\nreturn res;\n}\n}\n</code></pre> array_deque.ts<pre><code>/* \u57fa\u4e8e\u73af\u5f62\u6570\u7ec4\u5b9e\u73b0\u7684\u53cc\u5411\u961f\u5217 */\nclass ArrayDeque {\nprivate nums: number[]; // \u7528\u4e8e\u5b58\u50a8\u53cc\u5411\u961f\u5217\u5143\u7d20\u7684\u6570\u7ec4\nprivate front: number; // \u961f\u9996\u6307\u9488\uff0c\u6307\u5411\u961f\u9996\u5143\u7d20\nprivate queSize: number; // \u53cc\u5411\u961f\u5217\u957f\u5ea6\n/* \u6784\u9020\u65b9\u6cd5 */\nconstructor(capacity: number) {\nthis.nums = new Array(capacity);\nthis.front = 0;\nthis.queSize = 0;\n}\n/* \u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u5bb9\u91cf */\ncapacity(): number {\nreturn this.nums.length;\n}\n/* \u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6 */\nsize(): number {\nreturn this.queSize;\n}\n/* \u5224\u65ad\u53cc\u5411\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nisEmpty(): boolean {\nreturn this.queSize === 0;\n}\n/* \u8ba1\u7b97\u73af\u5f62\u6570\u7ec4\u7d22\u5f15 */\nindex(i: number): number {\n// \u901a\u8fc7\u53d6\u4f59\u64cd\u4f5c\u5b9e\u73b0\u6570\u7ec4\u9996\u5c3e\u76f8\u8fde\n// \u5f53 i \u8d8a\u8fc7\u6570\u7ec4\u5c3e\u90e8\u540e\uff0c\u56de\u5230\u5934\u90e8\n// \u5f53 i \u8d8a\u8fc7\u6570\u7ec4\u5934\u90e8\u540e\uff0c\u56de\u5230\u5c3e\u90e8\nreturn (i + this.capacity()) % this.capacity();\n}\n/* \u961f\u9996\u5165\u961f */\npushFirst(num: number): void {\nif (this.queSize === this.capacity()) {\nconsole.log('\u53cc\u5411\u961f\u5217\u5df2\u6ee1');\nreturn;\n}\n// \u961f\u9996\u6307\u9488\u5411\u5de6\u79fb\u52a8\u4e00\u4f4d\n// \u901a\u8fc7\u53d6\u4f59\u64cd\u4f5c\uff0c\u5b9e\u73b0 front \u8d8a\u8fc7\u6570\u7ec4\u5934\u90e8\u540e\u56de\u5230\u5c3e\u90e8\nthis.front = this.index(this.front - 1);\n// \u5c06 num \u6dfb\u52a0\u81f3\u961f\u9996\nthis.nums[this.front] = num;\nthis.queSize++;\n}\n/* \u961f\u5c3e\u5165\u961f */\npushLast(num: number): void {\nif (this.queSize === this.capacity()) {\nconsole.log('\u53cc\u5411\u961f\u5217\u5df2\u6ee1');\nreturn;\n}\n// \u8ba1\u7b97\u5c3e\u6307\u9488\uff0c\u6307\u5411\u961f\u5c3e\u7d22\u5f15 + 1\nconst rear: number = this.index(this.front + this.queSize);\n// \u5c06 num \u6dfb\u52a0\u81f3\u961f\u5c3e\nthis.nums[rear] = num;\nthis.queSize++;\n}\n/* \u961f\u9996\u51fa\u961f */\npopFirst(): number {\nconst num: number = this.peekFirst();\n// \u961f\u9996\u6307\u9488\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\nthis.front = this.index(this.front + 1);\nthis.queSize--;\nreturn num;\n}\n/* \u961f\u5c3e\u51fa\u961f */\npopLast(): number {\nconst num: number = this.peekLast();\nthis.queSize--;\nreturn num;\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\npeekFirst(): number {\nif (this.isEmpty()) throw new Error('The Deque Is Empty.');\nreturn this.nums[this.front];\n}\n/* \u8bbf\u95ee\u961f\u5c3e\u5143\u7d20 */\npeekLast(): number {\nif (this.isEmpty()) throw new Error('The Deque Is Empty.');\n// \u8ba1\u7b97\u5c3e\u5143\u7d20\u7d22\u5f15\nconst last = this.index(this.front + this.queSize - 1);\nreturn this.nums[last];\n}\n/* \u8fd4\u56de\u6570\u7ec4\u7528\u4e8e\u6253\u5370 */\ntoArray(): number[] {\n// \u4ec5\u8f6c\u6362\u6709\u6548\u957f\u5ea6\u8303\u56f4\u5185\u7684\u5217\u8868\u5143\u7d20\nconst res: number[] = [];\nfor (let i = 0, j = this.front; i &lt; this.queSize; i++, j++) {\nres[i] = this.nums[this.index(j)];\n}\nreturn res;\n}\n}\n</code></pre> array_deque.c<pre><code>/* \u57fa\u4e8e\u73af\u5f62\u6570\u7ec4\u5b9e\u73b0\u7684\u53cc\u5411\u961f\u5217 */\nstruct arrayDeque {\nint *nums;       // \u7528\u4e8e\u5b58\u50a8\u961f\u5217\u5143\u7d20\u7684\u6570\u7ec4\nint front;       // \u961f\u9996\u6307\u9488\uff0c\u6307\u5411\u961f\u9996\u5143\u7d20\nint queSize;     // \u5c3e\u6307\u9488\uff0c\u6307\u5411\u961f\u5c3e + 1\nint queCapacity; // \u961f\u5217\u5bb9\u91cf\n};\ntypedef struct arrayDeque arrayDeque;\n/* \u6784\u9020\u51fd\u6570 */\narrayDeque *newArrayDeque(int capacity) {\narrayDeque *deque = (arrayDeque *)malloc(sizeof(arrayDeque));\n// \u521d\u59cb\u5316\u6570\u7ec4\ndeque-&gt;queCapacity = capacity;\ndeque-&gt;nums = (int *)malloc(sizeof(int) * deque-&gt;queCapacity);\ndeque-&gt;front = deque-&gt;queSize = 0;\nreturn deque;\n}\n/* \u6790\u6784\u51fd\u6570 */\nvoid delArrayDeque(arrayDeque *deque) {\nfree(deque-&gt;nums);\ndeque-&gt;queCapacity = 0;\n}\n/* \u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u5bb9\u91cf */\nint capacity(arrayDeque *deque) {\nreturn deque-&gt;queCapacity;\n}\n/* \u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6 */\nint size(arrayDeque *deque) {\nreturn deque-&gt;queSize;\n}\n/* \u5224\u65ad\u53cc\u5411\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nbool empty(arrayDeque *deque) {\nreturn deque-&gt;queSize == 0;\n}\n/* \u8ba1\u7b97\u73af\u5f62\u6570\u7ec4\u7d22\u5f15 */\nint dequeIndex(arrayDeque *deque, int i) {\n// \u901a\u8fc7\u53d6\u4f59\u64cd\u4f5c\u5b9e\u73b0\u6570\u7ec4\u9996\u5c3e\u76f8\u8fde\n// \u5f53 i \u8d8a\u8fc7\u6570\u7ec4\u5c3e\u90e8\u65f6\uff0c\u56de\u5230\u5934\u90e8\n// \u5f53 i \u8d8a\u8fc7\u6570\u7ec4\u5934\u90e8\u540e\uff0c\u56de\u5230\u5c3e\u90e8\nreturn ((i + capacity(deque)) % capacity(deque));\n}\n/* \u961f\u9996\u5165\u961f */\nvoid pushFirst(arrayDeque *deque, int num) {\nif (deque-&gt;queSize == capacity(deque)) {\nprintf(\"\u53cc\u5411\u961f\u5217\u5df2\u6ee1\\r\\n\");\nreturn;\n}\n// \u961f\u9996\u6307\u9488\u5411\u5de6\u79fb\u52a8\u4e00\u4f4d\n// \u901a\u8fc7\u53d6\u4f59\u64cd\u4f5c\uff0c\u5b9e\u73b0 front \u8d8a\u8fc7\u6570\u7ec4\u5934\u90e8\u56de\u5230\u5c3e\u90e8\ndeque-&gt;front = dequeIndex(deque, deque-&gt;front - 1);\n// \u5c06 num \u6dfb\u52a0\u5230\u961f\u9996\ndeque-&gt;nums[deque-&gt;front] = num;\ndeque-&gt;queSize++;\n}\n/* \u961f\u5c3e\u5165\u961f */\nvoid pushLast(arrayDeque *deque, int num) {\nif (deque-&gt;queSize == capacity(deque)) {\nprintf(\"\u53cc\u5411\u961f\u5217\u5df2\u6ee1\\r\\n\");\nreturn;\n}\n// \u8ba1\u7b97\u5c3e\u6307\u9488\uff0c\u6307\u5411\u961f\u5c3e\u7d22\u5f15 + 1\nint rear = dequeIndex(deque, deque-&gt;front + deque-&gt;queSize);\n// \u5c06 num \u6dfb\u52a0\u81f3\u961f\u5c3e\ndeque-&gt;nums[rear] = num;\ndeque-&gt;queSize++;\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\nint peekFirst(arrayDeque *deque) {\n// \u8bbf\u95ee\u5f02\u5e38\uff1a\u53cc\u5411\u961f\u5217\u4e3a\u7a7a\nassert(empty(deque) == 0);\nreturn deque-&gt;nums[deque-&gt;front];\n}\n/* \u8bbf\u95ee\u961f\u5c3e\u5143\u7d20 */\nint peekLast(arrayDeque *deque) {\n// \u8bbf\u95ee\u5f02\u5e38\uff1a\u53cc\u5411\u961f\u5217\u4e3a\u7a7a\nassert(empty(deque) == 0);\nint last = dequeIndex(deque, deque-&gt;front + deque-&gt;queSize - 1);\nreturn deque-&gt;nums[last];\n}\n/* \u961f\u9996\u51fa\u961f */\nint popFirst(arrayDeque *deque) {\nint num = peekFirst(deque);\n// \u961f\u9996\u6307\u9488\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\ndeque-&gt;front = dequeIndex(deque, deque-&gt;front + 1);\ndeque-&gt;queSize--;\nreturn num;\n}\n/* \u961f\u5c3e\u51fa\u961f */\nint popLast(arrayDeque *deque) {\nint num = peekLast(deque);\ndeque-&gt;queSize--;\nreturn num;\n}\n/* \u6253\u5370\u961f\u5217 */\nvoid printArrayDeque(arrayDeque *deque) {\nint arr[deque-&gt;queSize];\n// \u62f7\u8d1d\nfor (int i = 0, j = deque-&gt;front; i &lt; deque-&gt;queSize; i++, j++) {\narr[i] = deque-&gt;nums[j % deque-&gt;queCapacity];\n}\nprintArray(arr, deque-&gt;queSize);\n}\n</code></pre> array_deque.cs<pre><code>/* \u57fa\u4e8e\u73af\u5f62\u6570\u7ec4\u5b9e\u73b0\u7684\u53cc\u5411\u961f\u5217 */\nclass ArrayDeque {\nprivate readonly int[] nums;  // \u7528\u4e8e\u5b58\u50a8\u53cc\u5411\u961f\u5217\u5143\u7d20\u7684\u6570\u7ec4\nprivate int front;   // \u961f\u9996\u6307\u9488\uff0c\u6307\u5411\u961f\u9996\u5143\u7d20\nprivate int queSize; // \u53cc\u5411\u961f\u5217\u957f\u5ea6\n/* \u6784\u9020\u65b9\u6cd5 */\npublic ArrayDeque(int capacity) {\nthis.nums = new int[capacity];\nfront = queSize = 0;\n}\n/* \u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u5bb9\u91cf */\npublic int capacity() {\nreturn nums.Length;\n}\n/* \u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6 */\npublic int size() {\nreturn queSize;\n}\n/* \u5224\u65ad\u53cc\u5411\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\npublic bool isEmpty() {\nreturn queSize == 0;\n}\n/* \u8ba1\u7b97\u73af\u5f62\u6570\u7ec4\u7d22\u5f15 */\nprivate int index(int i) {\n// \u901a\u8fc7\u53d6\u4f59\u64cd\u4f5c\u5b9e\u73b0\u6570\u7ec4\u9996\u5c3e\u76f8\u8fde\n// \u5f53 i \u8d8a\u8fc7\u6570\u7ec4\u5c3e\u90e8\u540e\uff0c\u56de\u5230\u5934\u90e8\n// \u5f53 i \u8d8a\u8fc7\u6570\u7ec4\u5934\u90e8\u540e\uff0c\u56de\u5230\u5c3e\u90e8\nreturn (i + capacity()) % capacity();\n}\n/* \u961f\u9996\u5165\u961f */\npublic void pushFirst(int num) {\nif (queSize == capacity()) {\nConsole.WriteLine(\"\u53cc\u5411\u961f\u5217\u5df2\u6ee1\");\nreturn;\n}\n// \u961f\u9996\u6307\u9488\u5411\u5de6\u79fb\u52a8\u4e00\u4f4d\n// \u901a\u8fc7\u53d6\u4f59\u64cd\u4f5c\uff0c\u5b9e\u73b0 front \u8d8a\u8fc7\u6570\u7ec4\u5934\u90e8\u540e\u56de\u5230\u5c3e\u90e8\nfront = index(front - 1);\n// \u5c06 num \u6dfb\u52a0\u81f3\u961f\u9996\nnums[front] = num;\nqueSize++;\n}\n/* \u961f\u5c3e\u5165\u961f */\npublic void pushLast(int num) {\nif (queSize == capacity()) {\nConsole.WriteLine(\"\u53cc\u5411\u961f\u5217\u5df2\u6ee1\");\nreturn;\n}\n// \u8ba1\u7b97\u5c3e\u6307\u9488\uff0c\u6307\u5411\u961f\u5c3e\u7d22\u5f15 + 1\nint rear = index(front + queSize);\n// \u5c06 num \u6dfb\u52a0\u81f3\u961f\u5c3e\nnums[rear] = num;\nqueSize++;\n}\n/* \u961f\u9996\u51fa\u961f */\npublic int popFirst() {\nint num = peekFirst();\n// \u961f\u9996\u6307\u9488\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\nfront = index(front + 1);\nqueSize--;\nreturn num;\n}\n/* \u961f\u5c3e\u51fa\u961f */\npublic int popLast() {\nint num = peekLast();\nqueSize--;\nreturn num;\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\npublic int peekFirst() {\nif (isEmpty()) {\nthrow new InvalidOperationException();\n}\nreturn nums[front];\n}\n/* \u8bbf\u95ee\u961f\u5c3e\u5143\u7d20 */\npublic int peekLast() {\nif (isEmpty()) {\nthrow new InvalidOperationException();\n}\n// \u8ba1\u7b97\u5c3e\u5143\u7d20\u7d22\u5f15\nint last = index(front + queSize - 1);\nreturn nums[last];\n}\n/* \u8fd4\u56de\u6570\u7ec4\u7528\u4e8e\u6253\u5370 */\npublic int[] toArray() {\n// \u4ec5\u8f6c\u6362\u6709\u6548\u957f\u5ea6\u8303\u56f4\u5185\u7684\u5217\u8868\u5143\u7d20\nint[] res = new int[queSize];\nfor (int i = 0, j = front; i &lt; queSize; i++, j++) {\nres[i] = nums[index(j)];\n}\nreturn res;\n}\n}\n</code></pre> array_deque.swift<pre><code>/* \u57fa\u4e8e\u73af\u5f62\u6570\u7ec4\u5b9e\u73b0\u7684\u53cc\u5411\u961f\u5217 */\nclass ArrayDeque {\nprivate var nums: [Int] // \u7528\u4e8e\u5b58\u50a8\u53cc\u5411\u961f\u5217\u5143\u7d20\u7684\u6570\u7ec4\nprivate var front: Int // \u961f\u9996\u6307\u9488\uff0c\u6307\u5411\u961f\u9996\u5143\u7d20\nprivate var queSize: Int // \u53cc\u5411\u961f\u5217\u957f\u5ea6\n/* \u6784\u9020\u65b9\u6cd5 */\ninit(capacity: Int) {\nnums = Array(repeating: 0, count: capacity)\nfront = 0\nqueSize = 0\n}\n/* \u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u5bb9\u91cf */\nfunc capacity() -&gt; Int {\nnums.count\n}\n/* \u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6 */\nfunc size() -&gt; Int {\nqueSize\n}\n/* \u5224\u65ad\u53cc\u5411\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nfunc isEmpty() -&gt; Bool {\nsize() == 0\n}\n/* \u8ba1\u7b97\u73af\u5f62\u6570\u7ec4\u7d22\u5f15 */\nprivate func index(i: Int) -&gt; Int {\n// \u901a\u8fc7\u53d6\u4f59\u64cd\u4f5c\u5b9e\u73b0\u6570\u7ec4\u9996\u5c3e\u76f8\u8fde\n// \u5f53 i \u8d8a\u8fc7\u6570\u7ec4\u5c3e\u90e8\u540e\uff0c\u56de\u5230\u5934\u90e8\n// \u5f53 i \u8d8a\u8fc7\u6570\u7ec4\u5934\u90e8\u540e\uff0c\u56de\u5230\u5c3e\u90e8\n(i + capacity()) % capacity()\n}\n/* \u961f\u9996\u5165\u961f */\nfunc pushFirst(num: Int) {\nif size() == capacity() {\nprint(\"\u53cc\u5411\u961f\u5217\u5df2\u6ee1\")\nreturn\n}\n// \u961f\u9996\u6307\u9488\u5411\u5de6\u79fb\u52a8\u4e00\u4f4d\n// \u901a\u8fc7\u53d6\u4f59\u64cd\u4f5c\uff0c\u5b9e\u73b0 front \u8d8a\u8fc7\u6570\u7ec4\u5934\u90e8\u540e\u56de\u5230\u5c3e\u90e8\nfront = index(i: front - 1)\n// \u5c06 num \u6dfb\u52a0\u81f3\u961f\u9996\nnums[front] = num\nqueSize += 1\n}\n/* \u961f\u5c3e\u5165\u961f */\nfunc pushLast(num: Int) {\nif size() == capacity() {\nprint(\"\u53cc\u5411\u961f\u5217\u5df2\u6ee1\")\nreturn\n}\n// \u8ba1\u7b97\u5c3e\u6307\u9488\uff0c\u6307\u5411\u961f\u5c3e\u7d22\u5f15 + 1\nlet rear = index(i: front + size())\n// \u5c06 num \u6dfb\u52a0\u81f3\u961f\u5c3e\nnums[rear] = num\nqueSize += 1\n}\n/* \u961f\u9996\u51fa\u961f */\nfunc popFirst() -&gt; Int {\nlet num = peekFirst()\n// \u961f\u9996\u6307\u9488\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\nfront = index(i: front + 1)\nqueSize -= 1\nreturn num\n}\n/* \u961f\u5c3e\u51fa\u961f */\nfunc popLast() -&gt; Int {\nlet num = peekLast()\nqueSize -= 1\nreturn num\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\nfunc peekFirst() -&gt; Int {\nif isEmpty() {\nfatalError(\"\u53cc\u5411\u961f\u5217\u4e3a\u7a7a\")\n}\nreturn nums[front]\n}\n/* \u8bbf\u95ee\u961f\u5c3e\u5143\u7d20 */\nfunc peekLast() -&gt; Int {\nif isEmpty() {\nfatalError(\"\u53cc\u5411\u961f\u5217\u4e3a\u7a7a\")\n}\n// \u8ba1\u7b97\u5c3e\u5143\u7d20\u7d22\u5f15\nlet last = index(i: front + size() - 1)\nreturn nums[last]\n}\n/* \u8fd4\u56de\u6570\u7ec4\u7528\u4e8e\u6253\u5370 */\nfunc toArray() -&gt; [Int] {\n// \u4ec5\u8f6c\u6362\u6709\u6548\u957f\u5ea6\u8303\u56f4\u5185\u7684\u5217\u8868\u5143\u7d20\nvar res = Array(repeating: 0, count: size())\nfor (i, j) in sequence(first: (0, front), next: { $0 &lt; self.size() - 1 ? ($0 + 1, $1 + 1) : nil }) {\nres[i] = nums[index(i: j)]\n}\nreturn res\n}\n}\n</code></pre> array_deque.zig<pre><code>[class]{ArrayDeque}-[func]{}\n</code></pre> array_deque.dart<pre><code>/* \u57fa\u4e8e\u73af\u5f62\u6570\u7ec4\u5b9e\u73b0\u7684\u53cc\u5411\u961f\u5217 */\nclass ArrayDeque {\nlate List&lt;int&gt; _nums; // \u7528\u4e8e\u5b58\u50a8\u53cc\u5411\u961f\u5217\u5143\u7d20\u7684\u6570\u7ec4\nlate int _front; // \u961f\u9996\u6307\u9488\uff0c\u6307\u5411\u961f\u9996\u5143\u7d20\nlate int _queSize; // \u53cc\u5411\u961f\u5217\u957f\u5ea6\n/* \u6784\u9020\u65b9\u6cd5 */\nArrayDeque(int capacity) {\nthis._nums = List.filled(capacity, 0);\nthis._front = this._queSize = 0;\n}\n/* \u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u5bb9\u91cf */\nint capacity() {\nreturn _nums.length;\n}\n/* \u83b7\u53d6\u53cc\u5411\u961f\u5217\u7684\u957f\u5ea6 */\nint size() {\nreturn _queSize;\n}\n/* \u5224\u65ad\u53cc\u5411\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nbool isEmpty() {\nreturn _queSize == 0;\n}\n/* \u8ba1\u7b97\u73af\u5f62\u6570\u7ec4\u7d22\u5f15 */\nint index(int i) {\n// \u901a\u8fc7\u53d6\u4f59\u64cd\u4f5c\u5b9e\u73b0\u6570\u7ec4\u9996\u5c3e\u76f8\u8fde\n// \u5f53 i \u8d8a\u8fc7\u6570\u7ec4\u5c3e\u90e8\u540e\uff0c\u56de\u5230\u5934\u90e8\n// \u5f53 i \u8d8a\u8fc7\u6570\u7ec4\u5934\u90e8\u540e\uff0c\u56de\u5230\u5c3e\u90e8\nreturn (i + capacity()) % capacity();\n}\n/* \u961f\u9996\u5165\u961f */\nvoid pushFirst(int num) {\nif (_queSize == capacity()) {\nthrow Exception(\"\u53cc\u5411\u961f\u5217\u5df2\u6ee1\");\n}\n// \u961f\u9996\u6307\u9488\u5411\u5de6\u79fb\u52a8\u4e00\u4f4d\n// \u901a\u8fc7\u53d6\u4f59\u64cd\u4f5c\uff0c\u5b9e\u73b0 _front \u8d8a\u8fc7\u6570\u7ec4\u5934\u90e8\u540e\u56de\u5230\u5c3e\u90e8\n_front = index(_front - 1);\n// \u5c06 num \u6dfb\u52a0\u81f3\u961f\u9996\n_nums[_front] = num;\n_queSize++;\n}\n/* \u961f\u5c3e\u5165\u961f */\nvoid pushLast(int num) {\nif (_queSize == capacity()) {\nthrow Exception(\"\u53cc\u5411\u961f\u5217\u5df2\u6ee1\");\n}\n// \u8ba1\u7b97\u5c3e\u6307\u9488\uff0c\u6307\u5411\u961f\u5c3e\u7d22\u5f15 + 1\nint rear = index(_front + _queSize);\n// \u5c06 num \u6dfb\u52a0\u81f3\u961f\u5c3e\n_nums[rear] = num;\n_queSize++;\n}\n/* \u961f\u9996\u51fa\u961f */\nint popFirst() {\nint num = peekFirst();\n// \u961f\u9996\u6307\u9488\u5411\u53f3\u79fb\u52a8\u4e00\u4f4d\n_front = index(_front + 1);\n_queSize--;\nreturn num;\n}\n/* \u961f\u5c3e\u51fa\u961f */\nint popLast() {\nint num = peekLast();\n_queSize--;\nreturn num;\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\nint peekFirst() {\nif (isEmpty()) {\nthrow Exception(\"\u53cc\u5411\u961f\u5217\u4e3a\u7a7a\");\n}\nreturn _nums[_front];\n}\n/* \u8bbf\u95ee\u961f\u5c3e\u5143\u7d20 */\nint peekLast() {\nif (isEmpty()) {\nthrow Exception(\"\u53cc\u5411\u961f\u5217\u4e3a\u7a7a\");\n}\n// \u8ba1\u7b97\u5c3e\u5143\u7d20\u7d22\u5f15\nint last = index(_front + _queSize - 1);\nreturn _nums[last];\n}\n/* \u8fd4\u56de\u6570\u7ec4\u7528\u4e8e\u6253\u5370 */\nList&lt;int&gt; toArray() {\n// \u4ec5\u8f6c\u6362\u6709\u6548\u957f\u5ea6\u8303\u56f4\u5185\u7684\u5217\u8868\u5143\u7d20\nList&lt;int&gt; res = List.filled(_queSize, 0);\nfor (int i = 0, j = _front; i &lt; _queSize; i++, j++) {\nres[i] = _nums[index(j)];\n}\nreturn res;\n}\n}\n</code></pre>"},{"location":"chapter_stack_and_queue/deque/#533","title":"5.3.3. \u00a0 \u53cc\u5411\u961f\u5217\u5e94\u7528","text":"<p>\u53cc\u5411\u961f\u5217\u517c\u5177\u6808\u4e0e\u961f\u5217\u7684\u903b\u8f91\uff0c\u56e0\u6b64\u5b83\u53ef\u4ee5\u5b9e\u73b0\u8fd9\u4e24\u8005\u7684\u6240\u6709\u5e94\u7528\u573a\u666f\uff0c\u540c\u65f6\u63d0\u4f9b\u66f4\u9ad8\u7684\u81ea\u7531\u5ea6\u3002</p> <p>\u6211\u4eec\u77e5\u9053\uff0c\u8f6f\u4ef6\u7684\u201c\u64a4\u9500\u201d\u529f\u80fd\u901a\u5e38\u4f7f\u7528\u6808\u6765\u5b9e\u73b0\uff1a\u7cfb\u7edf\u5c06\u6bcf\u6b21\u66f4\u6539\u64cd\u4f5c <code>push</code> \u5230\u6808\u4e2d\uff0c\u7136\u540e\u901a\u8fc7 <code>pop</code> \u5b9e\u73b0\u64a4\u9500\u3002\u7136\u800c\uff0c\u8003\u8651\u5230\u7cfb\u7edf\u8d44\u6e90\u7684\u9650\u5236\uff0c\u8f6f\u4ef6\u901a\u5e38\u4f1a\u9650\u5236\u64a4\u9500\u7684\u6b65\u6570\uff08\u4f8b\u5982\u4ec5\u5141\u8bb8\u4fdd\u5b58 \\(50\\) \u6b65\uff09\u3002\u5f53\u6808\u7684\u957f\u5ea6\u8d85\u8fc7 \\(50\\) \u65f6\uff0c\u8f6f\u4ef6\u9700\u8981\u5728\u6808\u5e95\uff08\u5373\u961f\u9996\uff09\u6267\u884c\u5220\u9664\u64cd\u4f5c\u3002\u4f46\u6808\u65e0\u6cd5\u5b9e\u73b0\u8be5\u529f\u80fd\uff0c\u6b64\u65f6\u5c31\u9700\u8981\u4f7f\u7528\u53cc\u5411\u961f\u5217\u6765\u66ff\u4ee3\u6808\u3002\u8bf7\u6ce8\u610f\uff0c\u201c\u64a4\u9500\u201d\u7684\u6838\u5fc3\u903b\u8f91\u4ecd\u7136\u9075\u5faa\u6808\u7684\u5148\u5165\u540e\u51fa\u539f\u5219\uff0c\u53ea\u662f\u53cc\u5411\u961f\u5217\u80fd\u591f\u66f4\u52a0\u7075\u6d3b\u5730\u5b9e\u73b0\u4e00\u4e9b\u989d\u5916\u903b\u8f91\u3002</p>"},{"location":"chapter_stack_and_queue/queue/","title":"5.2. \u00a0 \u961f\u5217","text":"<p>\u300c\u961f\u5217 Queue\u300d\u662f\u4e00\u79cd\u9075\u5faa\u5148\u5165\u5148\u51fa\uff08First In, First Out\uff09\u89c4\u5219\u7684\u7ebf\u6027\u6570\u636e\u7ed3\u6784\u3002\u987e\u540d\u601d\u4e49\uff0c\u961f\u5217\u6a21\u62df\u4e86\u6392\u961f\u73b0\u8c61\uff0c\u5373\u65b0\u6765\u7684\u4eba\u4e0d\u65ad\u52a0\u5165\u961f\u5217\u7684\u5c3e\u90e8\uff0c\u800c\u4f4d\u4e8e\u961f\u5217\u5934\u90e8\u7684\u4eba\u9010\u4e2a\u79bb\u5f00\u3002</p> <p>\u6211\u4eec\u628a\u961f\u5217\u7684\u5934\u90e8\u79f0\u4e3a\u300c\u961f\u9996\u300d\uff0c\u5c3e\u90e8\u79f0\u4e3a\u300c\u961f\u5c3e\u300d\uff0c\u628a\u5c06\u5143\u7d20\u52a0\u5165\u961f\u5c3e\u7684\u64cd\u4f5c\u79f0\u4e3a\u300c\u5165\u961f\u300d\uff0c\u5220\u9664\u961f\u9996\u5143\u7d20\u7684\u64cd\u4f5c\u79f0\u4e3a\u300c\u51fa\u961f\u300d\u3002</p> <p></p> <p> Fig. \u961f\u5217\u7684\u5148\u5165\u5148\u51fa\u89c4\u5219 </p>"},{"location":"chapter_stack_and_queue/queue/#521","title":"5.2.1. \u00a0 \u961f\u5217\u5e38\u7528\u64cd\u4f5c","text":"<p>\u961f\u5217\u7684\u5e38\u89c1\u64cd\u4f5c\u5982\u4e0b\u8868\u6240\u793a\u3002\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u4e0d\u540c\u7f16\u7a0b\u8bed\u8a00\u7684\u65b9\u6cd5\u540d\u79f0\u53ef\u80fd\u4f1a\u6709\u6240\u4e0d\u540c\u3002\u6211\u4eec\u5728\u6b64\u91c7\u7528\u4e0e\u6808\u76f8\u540c\u7684\u65b9\u6cd5\u547d\u540d\u3002</p> \u65b9\u6cd5\u540d \u63cf\u8ff0 \u65f6\u95f4\u590d\u6742\u5ea6 push() \u5143\u7d20\u5165\u961f\uff0c\u5373\u5c06\u5143\u7d20\u6dfb\u52a0\u81f3\u961f\u5c3e \\(O(1)\\) pop() \u961f\u9996\u5143\u7d20\u51fa\u961f \\(O(1)\\) peek() \u8bbf\u95ee\u961f\u9996\u5143\u7d20 \\(O(1)\\) <p>\u6211\u4eec\u53ef\u4ee5\u76f4\u63a5\u4f7f\u7528\u7f16\u7a0b\u8bed\u8a00\u4e2d\u73b0\u6210\u7684\u961f\u5217\u7c7b\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart queue.java<pre><code>/* \u521d\u59cb\u5316\u961f\u5217 */\nQueue&lt;Integer&gt; queue = new LinkedList&lt;&gt;();\n/* \u5143\u7d20\u5165\u961f */\nqueue.offer(1);\nqueue.offer(3);\nqueue.offer(2);\nqueue.offer(5);\nqueue.offer(4);\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\nint peek = queue.peek();\n/* \u5143\u7d20\u51fa\u961f */\nint pop = queue.poll();\n/* \u83b7\u53d6\u961f\u5217\u7684\u957f\u5ea6 */\nint size = queue.size();\n/* \u5224\u65ad\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nboolean isEmpty = queue.isEmpty();\n</code></pre> queue.cpp<pre><code>/* \u521d\u59cb\u5316\u961f\u5217 */\nqueue&lt;int&gt; queue;\n/* \u5143\u7d20\u5165\u961f */\nqueue.push(1);\nqueue.push(3);\nqueue.push(2);\nqueue.push(5);\nqueue.push(4);\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\nint front = queue.front();\n/* \u5143\u7d20\u51fa\u961f */\nqueue.pop();\n/* \u83b7\u53d6\u961f\u5217\u7684\u957f\u5ea6 */\nint size = queue.size();\n/* \u5224\u65ad\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nbool empty = queue.empty();\n</code></pre> queue.py<pre><code># \u521d\u59cb\u5316\u961f\u5217\n# \u5728 Python \u4e2d\uff0c\u6211\u4eec\u4e00\u822c\u5c06\u53cc\u5411\u961f\u5217\u7c7b deque \u770b\u4f5c\u961f\u5217\u4f7f\u7528\n# \u867d\u7136 queue.Queue() \u662f\u7eaf\u6b63\u7684\u961f\u5217\u7c7b\uff0c\u4f46\u4e0d\u592a\u597d\u7528\uff0c\u56e0\u6b64\u4e0d\u5efa\u8bae\nque: Deque[int] = collections.deque()\n# \u5143\u7d20\u5165\u961f\nque.append(1)\nque.append(3)\nque.append(2)\nque.append(5)\nque.append(4)\n# \u8bbf\u95ee\u961f\u9996\u5143\u7d20\nfront: int = que[0];\n# \u5143\u7d20\u51fa\u961f\npop: int = que.popleft()\n# \u83b7\u53d6\u961f\u5217\u7684\u957f\u5ea6\nsize: int = len(que)\n# \u5224\u65ad\u961f\u5217\u662f\u5426\u4e3a\u7a7a\nis_empty: bool = len(que) == 0\n</code></pre> queue_test.go<pre><code>/* \u521d\u59cb\u5316\u961f\u5217 */\n// \u5728 Go \u4e2d\uff0c\u5c06 list \u4f5c\u4e3a\u961f\u5217\u6765\u4f7f\u7528\nqueue := list.New()\n/* \u5143\u7d20\u5165\u961f */\nqueue.PushBack(1)\nqueue.PushBack(3)\nqueue.PushBack(2)\nqueue.PushBack(5)\nqueue.PushBack(4)\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\npeek := queue.Front()\n/* \u5143\u7d20\u51fa\u961f */\npop := queue.Front()\nqueue.Remove(pop)\n/* \u83b7\u53d6\u961f\u5217\u7684\u957f\u5ea6 */\nsize := queue.Len()\n/* \u5224\u65ad\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nisEmpty := queue.Len() == 0\n</code></pre> queue.js<pre><code>/* \u521d\u59cb\u5316\u961f\u5217 */\n// JavaScript \u6ca1\u6709\u5185\u7f6e\u7684\u961f\u5217\uff0c\u53ef\u4ee5\u628a Array \u5f53\u4f5c\u961f\u5217\u6765\u4f7f\u7528\nconst queue = [];\n/* \u5143\u7d20\u5165\u961f */\nqueue.push(1);\nqueue.push(3);\nqueue.push(2);\nqueue.push(5);\nqueue.push(4);\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\nconst peek = queue[0];\n/* \u5143\u7d20\u51fa\u961f */\n// \u5e95\u5c42\u662f\u6570\u7ec4\uff0c\u56e0\u6b64 shift() \u65b9\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a O(n)\nconst pop = queue.shift();\n/* \u83b7\u53d6\u961f\u5217\u7684\u957f\u5ea6 */\nconst size = queue.length;\n/* \u5224\u65ad\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nconst empty = queue.length === 0;\n</code></pre> queue.ts<pre><code>/* \u521d\u59cb\u5316\u961f\u5217 */\n// TypeScript \u6ca1\u6709\u5185\u7f6e\u7684\u961f\u5217\uff0c\u53ef\u4ee5\u628a Array \u5f53\u4f5c\u961f\u5217\u6765\u4f7f\u7528 \nconst queue: number[] = [];\n/* \u5143\u7d20\u5165\u961f */\nqueue.push(1);\nqueue.push(3);\nqueue.push(2);\nqueue.push(5);\nqueue.push(4);\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\nconst peek = queue[0];\n/* \u5143\u7d20\u51fa\u961f */\n// \u5e95\u5c42\u662f\u6570\u7ec4\uff0c\u56e0\u6b64 shift() \u65b9\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a O(n)\nconst pop = queue.shift();\n/* \u83b7\u53d6\u961f\u5217\u7684\u957f\u5ea6 */\nconst size = queue.length;\n/* \u5224\u65ad\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nconst empty = queue.length === 0;\n</code></pre> queue.c<pre><code>// C \u672a\u63d0\u4f9b\u5185\u7f6e\u961f\u5217\n</code></pre> queue.cs<pre><code>/* \u521d\u59cb\u5316\u961f\u5217 */\nQueue&lt;int&gt; queue = new();\n/* \u5143\u7d20\u5165\u961f */\nqueue.Enqueue(1);\nqueue.Enqueue(3);\nqueue.Enqueue(2);\nqueue.Enqueue(5);\nqueue.Enqueue(4);\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\nint peek = queue.Peek();\n/* \u5143\u7d20\u51fa\u961f */\nint pop = queue.Dequeue();\n/* \u83b7\u53d6\u961f\u5217\u7684\u957f\u5ea6 */\nint size = queue.Count();\n/* \u5224\u65ad\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nbool isEmpty = queue.Count() == 0;\n</code></pre> queue.swift<pre><code>/* \u521d\u59cb\u5316\u961f\u5217 */\n// Swift \u6ca1\u6709\u5185\u7f6e\u7684\u961f\u5217\u7c7b\uff0c\u53ef\u4ee5\u628a Array \u5f53\u4f5c\u961f\u5217\u6765\u4f7f\u7528\nvar queue: [Int] = []\n/* \u5143\u7d20\u5165\u961f */\nqueue.append(1)\nqueue.append(3)\nqueue.append(2)\nqueue.append(5)\nqueue.append(4)\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\nlet peek = queue.first!\n/* \u5143\u7d20\u51fa\u961f */\n// \u7531\u4e8e\u662f\u6570\u7ec4\uff0c\u56e0\u6b64 removeFirst \u7684\u590d\u6742\u5ea6\u4e3a O(n)\nlet pool = queue.removeFirst()\n/* \u83b7\u53d6\u961f\u5217\u7684\u957f\u5ea6 */\nlet size = queue.count\n/* \u5224\u65ad\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nlet isEmpty = queue.isEmpty\n</code></pre> queue.zig<pre><code>\n</code></pre> queue.dart<pre><code>/* \u521d\u59cb\u5316\u961f\u5217 */\n// \u5728 Dart \u4e2d\uff0c\u961f\u5217\u7c7b Qeque \u662f\u53cc\u5411\u961f\u5217\uff0c\u4e5f\u53ef\u4f5c\u4e3a\u961f\u5217\u4f7f\u7528\nQueue&lt;int&gt; queue = Queue();\n/* \u5143\u7d20\u5165\u961f */\nqueue.add(1);\nqueue.add(3);\nqueue.add(2);\nqueue.add(5);\nqueue.add(4);\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\nint peek = queue.first;\n/* \u5143\u7d20\u51fa\u961f */\nint pop = queue.removeFirst();\n/* \u83b7\u53d6\u961f\u5217\u7684\u957f\u5ea6 */\nint size = queue.length;\n/* \u5224\u65ad\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nbool isEmpty = queue.isEmpty;\n</code></pre>"},{"location":"chapter_stack_and_queue/queue/#522","title":"5.2.2. \u00a0 \u961f\u5217\u5b9e\u73b0","text":"<p>\u4e3a\u4e86\u5b9e\u73b0\u961f\u5217\uff0c\u6211\u4eec\u9700\u8981\u4e00\u79cd\u6570\u636e\u7ed3\u6784\uff0c\u53ef\u4ee5\u5728\u4e00\u7aef\u6dfb\u52a0\u5143\u7d20\uff0c\u5e76\u5728\u53e6\u4e00\u7aef\u5220\u9664\u5143\u7d20\u3002\u56e0\u6b64\uff0c\u94fe\u8868\u548c\u6570\u7ec4\u90fd\u53ef\u4ee5\u7528\u6765\u5b9e\u73b0\u961f\u5217\u3002</p>"},{"location":"chapter_stack_and_queue/queue/#_1","title":"\u57fa\u4e8e\u94fe\u8868\u7684\u5b9e\u73b0","text":"<p>\u5bf9\u4e8e\u94fe\u8868\u5b9e\u73b0\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u94fe\u8868\u7684\u300c\u5934\u8282\u70b9\u300d\u548c\u300c\u5c3e\u8282\u70b9\u300d\u5206\u522b\u89c6\u4e3a\u961f\u9996\u548c\u961f\u5c3e\uff0c\u89c4\u5b9a\u961f\u5c3e\u4ec5\u53ef\u6dfb\u52a0\u8282\u70b9\uff0c\u800c\u961f\u9996\u4ec5\u53ef\u5220\u9664\u8282\u70b9\u3002</p> LinkedListQueuepush()pop() <p></p> <p></p> <p></p> <p>\u4ee5\u4e0b\u662f\u7528\u94fe\u8868\u5b9e\u73b0\u961f\u5217\u7684\u793a\u4f8b\u4ee3\u7801\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart linkedlist_queue.java<pre><code>/* \u57fa\u4e8e\u94fe\u8868\u5b9e\u73b0\u7684\u961f\u5217 */\nclass LinkedListQueue {\nprivate ListNode front, rear; // \u5934\u8282\u70b9 front \uff0c\u5c3e\u8282\u70b9 rear\nprivate int queSize = 0;\npublic LinkedListQueue() {\nfront = null;\nrear = null;\n}\n/* \u83b7\u53d6\u961f\u5217\u7684\u957f\u5ea6 */\npublic int size() {\nreturn queSize;\n}\n/* \u5224\u65ad\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\npublic boolean isEmpty() {\nreturn size() == 0;\n}\n/* \u5165\u961f */\npublic void push(int num) {\n// \u5c3e\u8282\u70b9\u540e\u6dfb\u52a0 num\nListNode node = new ListNode(num);\n// \u5982\u679c\u961f\u5217\u4e3a\u7a7a\uff0c\u5219\u4ee4\u5934\u3001\u5c3e\u8282\u70b9\u90fd\u6307\u5411\u8be5\u8282\u70b9\nif (front == null) {\nfront = node;\nrear = node;\n// \u5982\u679c\u961f\u5217\u4e0d\u4e3a\u7a7a\uff0c\u5219\u5c06\u8be5\u8282\u70b9\u6dfb\u52a0\u5230\u5c3e\u8282\u70b9\u540e\n} else {\nrear.next = node;\nrear = node;\n}\nqueSize++;\n}\n/* \u51fa\u961f */\npublic int pop() {\nint num = peek();\n// \u5220\u9664\u5934\u8282\u70b9\nfront = front.next;\nqueSize--;\nreturn num;\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\npublic int peek() {\nif (size() == 0)\nthrow new IndexOutOfBoundsException();\nreturn front.val;\n}\n/* \u5c06\u94fe\u8868\u8f6c\u5316\u4e3a Array \u5e76\u8fd4\u56de */\npublic int[] toArray() {\nListNode node = front;\nint[] res = new int[size()];\nfor (int i = 0; i &lt; res.length; i++) {\nres[i] = node.val;\nnode = node.next;\n}\nreturn res;\n}\n}\n</code></pre> linkedlist_queue.cpp<pre><code>/* \u57fa\u4e8e\u94fe\u8868\u5b9e\u73b0\u7684\u961f\u5217 */\nclass LinkedListQueue {\nprivate:\nListNode *front, *rear; // \u5934\u8282\u70b9 front \uff0c\u5c3e\u8282\u70b9 rear\nint queSize;\npublic:\nLinkedListQueue() {\nfront = nullptr;\nrear = nullptr;\nqueSize = 0;\n}\n~LinkedListQueue() {\n// \u904d\u5386\u94fe\u8868\u5220\u9664\u8282\u70b9\uff0c\u91ca\u653e\u5185\u5b58\nfreeMemoryLinkedList(front);\n}\n/* \u83b7\u53d6\u961f\u5217\u7684\u957f\u5ea6 */\nint size() {\nreturn queSize;\n}\n/* \u5224\u65ad\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nbool empty() {\nreturn queSize == 0;\n}\n/* \u5165\u961f */\nvoid push(int num) {\n// \u5c3e\u8282\u70b9\u540e\u6dfb\u52a0 num\nListNode *node = new ListNode(num);\n// \u5982\u679c\u961f\u5217\u4e3a\u7a7a\uff0c\u5219\u4ee4\u5934\u3001\u5c3e\u8282\u70b9\u90fd\u6307\u5411\u8be5\u8282\u70b9\nif (front == nullptr) {\nfront = node;\nrear = node;\n}\n// \u5982\u679c\u961f\u5217\u4e0d\u4e3a\u7a7a\uff0c\u5219\u5c06\u8be5\u8282\u70b9\u6dfb\u52a0\u5230\u5c3e\u8282\u70b9\u540e\nelse {\nrear-&gt;next = node;\nrear = node;\n}\nqueSize++;\n}\n/* \u51fa\u961f */\nvoid pop() {\nint num = peek();\n// \u5220\u9664\u5934\u8282\u70b9\nListNode *tmp = front;\nfront = front-&gt;next;\n// \u91ca\u653e\u5185\u5b58\ndelete tmp;\nqueSize--;\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\nint peek() {\nif (size() == 0)\nthrow out_of_range(\"\u961f\u5217\u4e3a\u7a7a\");\nreturn front-&gt;val;\n}\n/* \u5c06\u94fe\u8868\u8f6c\u5316\u4e3a Vector \u5e76\u8fd4\u56de */\nvector&lt;int&gt; toVector() {\nListNode *node = front;\nvector&lt;int&gt; res(size());\nfor (int i = 0; i &lt; res.size(); i++) {\nres[i] = node-&gt;val;\nnode = node-&gt;next;\n}\nreturn res;\n}\n};\n</code></pre> linkedlist_queue.py<pre><code>class LinkedListQueue:\n\"\"\"\u57fa\u4e8e\u94fe\u8868\u5b9e\u73b0\u7684\u961f\u5217\"\"\"\ndef __init__(self):\n\"\"\"\u6784\u9020\u65b9\u6cd5\"\"\"\nself.__front: ListNode | None = None  # \u5934\u8282\u70b9 front\nself.__rear: ListNode | None = None  # \u5c3e\u8282\u70b9 rear\nself.__size: int = 0\ndef size(self) -&gt; int:\n\"\"\"\u83b7\u53d6\u961f\u5217\u7684\u957f\u5ea6\"\"\"\nreturn self.__size\ndef is_empty(self) -&gt; bool:\n\"\"\"\u5224\u65ad\u961f\u5217\u662f\u5426\u4e3a\u7a7a\"\"\"\nreturn not self.__front\ndef push(self, num: int) -&gt; None:\n\"\"\"\u5165\u961f\"\"\"\n# \u5c3e\u8282\u70b9\u540e\u6dfb\u52a0 num\nnode = ListNode(num)\n# \u5982\u679c\u961f\u5217\u4e3a\u7a7a\uff0c\u5219\u4ee4\u5934\u3001\u5c3e\u8282\u70b9\u90fd\u6307\u5411\u8be5\u8282\u70b9\nif self.__front is None:\nself.__front = node\nself.__rear = node\n# \u5982\u679c\u961f\u5217\u4e0d\u4e3a\u7a7a\uff0c\u5219\u5c06\u8be5\u8282\u70b9\u6dfb\u52a0\u5230\u5c3e\u8282\u70b9\u540e\nelse:\nself.__rear.next = node\nself.__rear = node\nself.__size += 1\ndef pop(self) -&gt; int:\n\"\"\"\u51fa\u961f\"\"\"\nnum = self.peek()\n# \u5220\u9664\u5934\u8282\u70b9\nself.__front = self.__front.next\nself.__size -= 1\nreturn num\ndef peek(self) -&gt; int:\n\"\"\"\u8bbf\u95ee\u961f\u9996\u5143\u7d20\"\"\"\nif self.size() == 0:\nprint(\"\u961f\u5217\u4e3a\u7a7a\")\nreturn False\nreturn self.__front.val\ndef to_list(self) -&gt; list[int]:\n\"\"\"\u8f6c\u5316\u4e3a\u5217\u8868\u7528\u4e8e\u6253\u5370\"\"\"\nqueue = []\ntemp = self.__front\nwhile temp:\nqueue.append(temp.val)\ntemp = temp.next\nreturn queue\n</code></pre> linkedlist_queue.go<pre><code>/* \u57fa\u4e8e\u94fe\u8868\u5b9e\u73b0\u7684\u961f\u5217 */\ntype linkedListQueue struct {\n// \u4f7f\u7528\u5185\u7f6e\u5305 list \u6765\u5b9e\u73b0\u961f\u5217\ndata *list.List\n}\n/* \u521d\u59cb\u5316\u961f\u5217 */\nfunc newLinkedListQueue() *linkedListQueue {\nreturn &amp;linkedListQueue{\ndata: list.New(),\n}\n}\n/* \u5165\u961f */\nfunc (s *linkedListQueue) push(value any) {\ns.data.PushBack(value)\n}\n/* \u51fa\u961f */\nfunc (s *linkedListQueue) pop() any {\nif s.isEmpty() {\nreturn nil\n}\ne := s.data.Front()\ns.data.Remove(e)\nreturn e.Value\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\nfunc (s *linkedListQueue) peek() any {\nif s.isEmpty() {\nreturn nil\n}\ne := s.data.Front()\nreturn e.Value\n}\n/* \u83b7\u53d6\u961f\u5217\u7684\u957f\u5ea6 */\nfunc (s *linkedListQueue) size() int {\nreturn s.data.Len()\n}\n/* \u5224\u65ad\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nfunc (s *linkedListQueue) isEmpty() bool {\nreturn s.data.Len() == 0\n}\n/* \u83b7\u53d6 List \u7528\u4e8e\u6253\u5370 */\nfunc (s *linkedListQueue) toList() *list.List {\nreturn s.data\n}\n</code></pre> linkedlist_queue.js<pre><code>/* \u57fa\u4e8e\u94fe\u8868\u5b9e\u73b0\u7684\u961f\u5217 */\nclass LinkedListQueue {\n#front; // \u5934\u8282\u70b9 #front\n#rear; // \u5c3e\u8282\u70b9 #rear\n#queSize = 0;\nconstructor() {\nthis.#front = null;\nthis.#rear = null;\n}\n/* \u83b7\u53d6\u961f\u5217\u7684\u957f\u5ea6 */\nget size() {\nreturn this.#queSize;\n}\n/* \u5224\u65ad\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nisEmpty() {\nreturn this.size === 0;\n}\n/* \u5165\u961f */\npush(num) {\n// \u5c3e\u8282\u70b9\u540e\u6dfb\u52a0 num\nconst node = new ListNode(num);\n// \u5982\u679c\u961f\u5217\u4e3a\u7a7a\uff0c\u5219\u4ee4\u5934\u3001\u5c3e\u8282\u70b9\u90fd\u6307\u5411\u8be5\u8282\u70b9\nif (!this.#front) {\nthis.#front = node;\nthis.#rear = node;\n// \u5982\u679c\u961f\u5217\u4e0d\u4e3a\u7a7a\uff0c\u5219\u5c06\u8be5\u8282\u70b9\u6dfb\u52a0\u5230\u5c3e\u8282\u70b9\u540e\n} else {\nthis.#rear.next = node;\nthis.#rear = node;\n}\nthis.#queSize++;\n}\n/* \u51fa\u961f */\npop() {\nconst num = this.peek();\n// \u5220\u9664\u5934\u8282\u70b9\nthis.#front = this.#front.next;\nthis.#queSize--;\nreturn num;\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\npeek() {\nif (this.size === 0) throw new Error('\u961f\u5217\u4e3a\u7a7a');\nreturn this.#front.val;\n}\n/* \u5c06\u94fe\u8868\u8f6c\u5316\u4e3a Array \u5e76\u8fd4\u56de */\ntoArray() {\nlet node = this.#front;\nconst res = new Array(this.size);\nfor (let i = 0; i &lt; res.length; i++) {\nres[i] = node.val;\nnode = node.next;\n}\nreturn res;\n}\n}\n</code></pre> linkedlist_queue.ts<pre><code>/* \u57fa\u4e8e\u94fe\u8868\u5b9e\u73b0\u7684\u961f\u5217 */\nclass LinkedListQueue {\nprivate front: ListNode | null; // \u5934\u8282\u70b9 front\nprivate rear: ListNode | null; // \u5c3e\u8282\u70b9 rear\nprivate queSize: number = 0;\nconstructor() {\nthis.front = null;\nthis.rear = null;\n}\n/* \u83b7\u53d6\u961f\u5217\u7684\u957f\u5ea6 */\nget size(): number {\nreturn this.queSize;\n}\n/* \u5224\u65ad\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nisEmpty(): boolean {\nreturn this.size === 0;\n}\n/* \u5165\u961f */\npush(num: number): void {\n// \u5c3e\u8282\u70b9\u540e\u6dfb\u52a0 num\nconst node = new ListNode(num);\n// \u5982\u679c\u961f\u5217\u4e3a\u7a7a\uff0c\u5219\u4ee4\u5934\u3001\u5c3e\u8282\u70b9\u90fd\u6307\u5411\u8be5\u8282\u70b9\nif (!this.front) {\nthis.front = node;\nthis.rear = node;\n// \u5982\u679c\u961f\u5217\u4e0d\u4e3a\u7a7a\uff0c\u5219\u5c06\u8be5\u8282\u70b9\u6dfb\u52a0\u5230\u5c3e\u8282\u70b9\u540e\n} else {\nthis.rear!.next = node;\nthis.rear = node;\n}\nthis.queSize++;\n}\n/* \u51fa\u961f */\npop(): number {\nconst num = this.peek();\nif (!this.front) throw new Error('\u961f\u5217\u4e3a\u7a7a');\n// \u5220\u9664\u5934\u8282\u70b9\nthis.front = this.front.next;\nthis.queSize--;\nreturn num;\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\npeek(): number {\nif (this.size === 0) throw new Error('\u961f\u5217\u4e3a\u7a7a');\nreturn this.front!.val;\n}\n/* \u5c06\u94fe\u8868\u8f6c\u5316\u4e3a Array \u5e76\u8fd4\u56de */\ntoArray(): number[] {\nlet node = this.front;\nconst res = new Array&lt;number&gt;(this.size);\nfor (let i = 0; i &lt; res.length; i++) {\nres[i] = node!.val;\nnode = node!.next;\n}\nreturn res;\n}\n}\n</code></pre> linkedlist_queue.c<pre><code>/* \u57fa\u4e8e\u94fe\u8868\u5b9e\u73b0\u7684\u961f\u5217 */\nstruct linkedListQueue {\nListNode *front, *rear;\nint queSize;\n};\ntypedef struct linkedListQueue linkedListQueue;\n/* \u6784\u9020\u51fd\u6570 */\nlinkedListQueue *newLinkedListQueue() {\nlinkedListQueue *queue = (linkedListQueue *)malloc(sizeof(linkedListQueue));\nqueue-&gt;front = NULL;\nqueue-&gt;rear = NULL;\nqueue-&gt;queSize = 0;\nreturn queue;\n}\n/* \u6790\u6784\u51fd\u6570 */\nvoid delLinkedListQueue(linkedListQueue *queue) {\n// \u91ca\u653e\u6240\u6709\u8282\u70b9\nfor (int i = 0; i &lt; queue-&gt;queSize &amp;&amp; queue-&gt;front != NULL; i++) {\nListNode *tmp = queue-&gt;front;\nqueue-&gt;front = queue-&gt;front-&gt;next;\nfree(tmp);\n}\n// \u91ca\u653e queue \u7ed3\u6784\u4f53\nfree(queue);\n}\n/* \u83b7\u53d6\u961f\u5217\u7684\u957f\u5ea6 */\nint size(linkedListQueue *queue) {\nreturn queue-&gt;queSize;\n}\n/* \u5224\u65ad\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nbool empty(linkedListQueue *queue) {\nreturn (size(queue) == 0);\n}\n/* \u5165\u961f */\nvoid push(linkedListQueue *queue, int num) {\n// \u5c3e\u8282\u70b9\u5904\u6dfb\u52a0 node\nListNode *node = newListNode(num);\n// \u5982\u679c\u961f\u5217\u4e3a\u7a7a\uff0c\u5219\u4ee4\u5934\u3001\u5c3e\u8282\u70b9\u90fd\u6307\u5411\u8be5\u8282\u70b9\nif (queue-&gt;front == NULL) {\nqueue-&gt;front = node;\nqueue-&gt;rear = node;\n}\n// \u5982\u679c\u961f\u5217\u4e0d\u4e3a\u7a7a\uff0c\u5219\u5c06\u8be5\u8282\u70b9\u6dfb\u52a0\u5230\u5c3e\u8282\u70b9\u540e\nelse {\nqueue-&gt;rear-&gt;next = node;\nqueue-&gt;rear = node;\n}\nqueue-&gt;queSize++;\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\nint peek(linkedListQueue *queue) {\nassert(size(queue) &amp;&amp; queue-&gt;front);\nreturn queue-&gt;front-&gt;val;\n}\n/* \u51fa\u961f */\nvoid pop(linkedListQueue *queue) {\nint num = peek(queue);\nListNode *tmp = queue-&gt;front;\nqueue-&gt;front = queue-&gt;front-&gt;next;\nfree(tmp);\nqueue-&gt;queSize--;\n}\n/* \u6253\u5370\u961f\u5217 */\nvoid printLinkedListQueue(linkedListQueue *queue) {\nint arr[queue-&gt;queSize];\n// \u62f7\u8d1d\u94fe\u8868\u4e2d\u7684\u6570\u636e\u5230\u6570\u7ec4\nint i;\nListNode *node;\nfor (i = 0, node = queue-&gt;front; i &lt; queue-&gt;queSize &amp;&amp; queue-&gt;front != queue-&gt;rear; i++) {\narr[i] = node-&gt;val;\nnode = node-&gt;next;\n}\nprintArray(arr, queue-&gt;queSize);\n}\n</code></pre> linkedlist_queue.cs<pre><code>/* \u57fa\u4e8e\u94fe\u8868\u5b9e\u73b0\u7684\u961f\u5217 */\nclass LinkedListQueue {\nprivate ListNode? front, rear;  // \u5934\u8282\u70b9 front \uff0c\u5c3e\u8282\u70b9 rear \nprivate int queSize = 0;\npublic LinkedListQueue() {\nfront = null;\nrear = null;\n}\n/* \u83b7\u53d6\u961f\u5217\u7684\u957f\u5ea6 */\npublic int size() {\nreturn queSize;\n}\n/* \u5224\u65ad\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\npublic bool isEmpty() {\nreturn size() == 0;\n}\n/* \u5165\u961f */\npublic void push(int num) {\n// \u5c3e\u8282\u70b9\u540e\u6dfb\u52a0 num\nListNode node = new ListNode(num);\n// \u5982\u679c\u961f\u5217\u4e3a\u7a7a\uff0c\u5219\u4ee4\u5934\u3001\u5c3e\u8282\u70b9\u90fd\u6307\u5411\u8be5\u8282\u70b9\nif (front == null) {\nfront = node;\nrear = node;\n// \u5982\u679c\u961f\u5217\u4e0d\u4e3a\u7a7a\uff0c\u5219\u5c06\u8be5\u8282\u70b9\u6dfb\u52a0\u5230\u5c3e\u8282\u70b9\u540e\n} else if (rear != null) {\nrear.next = node;\nrear = node;\n}\nqueSize++;\n}\n/* \u51fa\u961f */\npublic int pop() {\nint num = peek();\n// \u5220\u9664\u5934\u8282\u70b9\nfront = front?.next;\nqueSize--;\nreturn num;\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\npublic int peek() {\nif (size() == 0 || front == null)\nthrow new Exception();\nreturn front.val;\n}\n/* \u5c06\u94fe\u8868\u8f6c\u5316\u4e3a Array \u5e76\u8fd4\u56de */\npublic int[] toArray() {\nif (front == null)\nreturn Array.Empty&lt;int&gt;();\nListNode node = front;\nint[] res = new int[size()];\nfor (int i = 0; i &lt; res.Length; i++) {\nres[i] = node.val;\nnode = node.next;\n}\nreturn res;\n}\n}\n</code></pre> linkedlist_queue.swift<pre><code>/* \u57fa\u4e8e\u94fe\u8868\u5b9e\u73b0\u7684\u961f\u5217 */\nclass LinkedListQueue {\nprivate var front: ListNode? // \u5934\u8282\u70b9\nprivate var rear: ListNode? // \u5c3e\u8282\u70b9\nprivate var _size = 0\ninit() {}\n/* \u83b7\u53d6\u961f\u5217\u7684\u957f\u5ea6 */\nfunc size() -&gt; Int {\n_size\n}\n/* \u5224\u65ad\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nfunc isEmpty() -&gt; Bool {\nsize() == 0\n}\n/* \u5165\u961f */\nfunc push(num: Int) {\n// \u5c3e\u8282\u70b9\u540e\u6dfb\u52a0 num\nlet node = ListNode(x: num)\n// \u5982\u679c\u961f\u5217\u4e3a\u7a7a\uff0c\u5219\u4ee4\u5934\u3001\u5c3e\u8282\u70b9\u90fd\u6307\u5411\u8be5\u8282\u70b9\nif front == nil {\nfront = node\nrear = node\n}\n// \u5982\u679c\u961f\u5217\u4e0d\u4e3a\u7a7a\uff0c\u5219\u5c06\u8be5\u8282\u70b9\u6dfb\u52a0\u5230\u5c3e\u8282\u70b9\u540e\nelse {\nrear?.next = node\nrear = node\n}\n_size += 1\n}\n/* \u51fa\u961f */\n@discardableResult\nfunc pop() -&gt; Int {\nlet num = peek()\n// \u5220\u9664\u5934\u8282\u70b9\nfront = front?.next\n_size -= 1\nreturn num\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\nfunc peek() -&gt; Int {\nif isEmpty() {\nfatalError(\"\u961f\u5217\u4e3a\u7a7a\")\n}\nreturn front!.val\n}\n/* \u5c06\u94fe\u8868\u8f6c\u5316\u4e3a Array \u5e76\u8fd4\u56de */\nfunc toArray() -&gt; [Int] {\nvar node = front\nvar res = Array(repeating: 0, count: size())\nfor i in res.indices {\nres[i] = node!.val\nnode = node?.next\n}\nreturn res\n}\n}\n</code></pre> linkedlist_queue.zig<pre><code>// \u57fa\u4e8e\u94fe\u8868\u5b9e\u73b0\u7684\u961f\u5217\nfn LinkedListQueue(comptime T: type) type {\nreturn struct {\nconst Self = @This();\nfront: ?*inc.ListNode(T) = null,                // \u5934\u8282\u70b9 front\nrear: ?*inc.ListNode(T) = null,                 // \u5c3e\u8282\u70b9 rear\nque_size: usize = 0,                             // \u961f\u5217\u7684\u957f\u5ea6\nmem_arena: ?std.heap.ArenaAllocator = null,\nmem_allocator: std.mem.Allocator = undefined,   // \u5185\u5b58\u5206\u914d\u5668\n// \u6784\u9020\u65b9\u6cd5\uff08\u5206\u914d\u5185\u5b58+\u521d\u59cb\u5316\u961f\u5217\uff09\npub fn init(self: *Self, allocator: std.mem.Allocator) !void {\nif (self.mem_arena == null) {\nself.mem_arena = std.heap.ArenaAllocator.init(allocator);\nself.mem_allocator = self.mem_arena.?.allocator();\n}\nself.front = null;\nself.rear = null;\nself.que_size = 0;\n}\n// \u6790\u6784\u65b9\u6cd5\uff08\u91ca\u653e\u5185\u5b58\uff09\npub fn deinit(self: *Self) void {\nif (self.mem_arena == null) return;\nself.mem_arena.?.deinit();\n}\n// \u83b7\u53d6\u961f\u5217\u7684\u957f\u5ea6\npub fn size(self: *Self) usize {\nreturn self.que_size;\n}\n// \u5224\u65ad\u961f\u5217\u662f\u5426\u4e3a\u7a7a\npub fn isEmpty(self: *Self) bool {\nreturn self.size() == 0;\n}\n// \u8bbf\u95ee\u961f\u9996\u5143\u7d20\npub fn peek(self: *Self) T {\nif (self.size() == 0) @panic(\"\u961f\u5217\u4e3a\u7a7a\");\nreturn self.front.?.val;\n}  // \u5165\u961f\npub fn push(self: *Self, num: T) !void {\n// \u5c3e\u8282\u70b9\u540e\u6dfb\u52a0 num\nvar node = try self.mem_allocator.create(inc.ListNode(T));\nnode.init(num);\n// \u5982\u679c\u961f\u5217\u4e3a\u7a7a\uff0c\u5219\u4ee4\u5934\u3001\u5c3e\u8282\u70b9\u90fd\u6307\u5411\u8be5\u8282\u70b9\nif (self.front == null) {\nself.front = node;\nself.rear = node;\n// \u5982\u679c\u961f\u5217\u4e0d\u4e3a\u7a7a\uff0c\u5219\u5c06\u8be5\u8282\u70b9\u6dfb\u52a0\u5230\u5c3e\u8282\u70b9\u540e\n} else {\nself.rear.?.next = node;\nself.rear = node;\n}\nself.que_size += 1;\n} // \u51fa\u961f\npub fn pop(self: *Self) T {\nvar num = self.peek();\n// \u5220\u9664\u5934\u8282\u70b9\nself.front = self.front.?.next;\nself.que_size -= 1;\nreturn num;\n} // \u5c06\u94fe\u8868\u8f6c\u6362\u4e3a\u6570\u7ec4\npub fn toArray(self: *Self) ![]T {\nvar node = self.front;\nvar res = try self.mem_allocator.alloc(T, self.size());\nstd.mem.set(T, res, @as(T, 0));\nvar i: usize = 0;\nwhile (i &lt; res.len) : (i += 1) {\nres[i] = node.?.val;\nnode = node.?.next;\n}\nreturn res;\n}\n};\n}\n</code></pre> linkedlist_queue.dart<pre><code>/* \u57fa\u4e8e\u94fe\u8868\u5b9e\u73b0\u7684\u961f\u5217 */\nclass LinkedListQueue {\nListNode? _front; // \u5934\u8282\u70b9 _front\nListNode? _rear; // \u5c3e\u8282\u70b9 _rear\nint _queSize = 0; // \u961f\u5217\u957f\u5ea6\nLinkedListQueue() {\n_front = null;\n_rear = null;\n}\n/* \u83b7\u53d6\u961f\u5217\u7684\u957f\u5ea6 */\nint size() {\nreturn _queSize;\n}\n/* \u5224\u65ad\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nbool isEmpty() {\nreturn _queSize == 0;\n}\n/* \u5165\u961f */\nvoid push(int num) {\n// \u5c3e\u8282\u70b9\u540e\u6dfb\u52a0 num\nfinal node = ListNode(num);\n// \u5982\u679c\u961f\u5217\u4e3a\u7a7a\uff0c\u5219\u4ee4\u5934\u3001\u5c3e\u8282\u70b9\u90fd\u6307\u5411\u8be5\u8282\u70b9\nif (_front == null) {\n_front = node;\n_rear = node;\n} else {\n// \u5982\u679c\u961f\u5217\u4e0d\u4e3a\u7a7a\uff0c\u5219\u5c06\u8be5\u8282\u70b9\u6dfb\u52a0\u5230\u5c3e\u8282\u70b9\u540e\n_rear!.next = node;\n_rear = node;\n}\n_queSize++;\n}\n/* \u51fa\u961f */\nint pop() {\nfinal int num = peek();\n// \u5220\u9664\u5934\u8282\u70b9\n_front = _front!.next;\n_queSize--;\nreturn num;\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\nint peek() {\nif (_queSize == 0) {\nthrow Exception('\u961f\u5217\u4e3a\u7a7a');\n}\nreturn _front!.val;\n}\n/* \u5c06\u94fe\u8868\u8f6c\u5316\u4e3a Array \u5e76\u8fd4\u56de */\nList&lt;int&gt; toArray() {\nListNode? node = _front;\nfinal List&lt;int&gt; queue = [];\nwhile (node != null) {\nqueue.add(node.val);\nnode = node.next;\n}\nreturn queue;\n}\n}\n</code></pre>"},{"location":"chapter_stack_and_queue/queue/#_2","title":"\u57fa\u4e8e\u6570\u7ec4\u7684\u5b9e\u73b0","text":"<p>\u7531\u4e8e\u6570\u7ec4\u5220\u9664\u9996\u5143\u7d20\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(n)\\) \uff0c\u8fd9\u4f1a\u5bfc\u81f4\u51fa\u961f\u64cd\u4f5c\u6548\u7387\u8f83\u4f4e\u3002\u7136\u800c\uff0c\u6211\u4eec\u53ef\u4ee5\u91c7\u7528\u4ee5\u4e0b\u5de7\u5999\u65b9\u6cd5\u6765\u907f\u514d\u8fd9\u4e2a\u95ee\u9898\u3002</p> <p>\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u4e00\u4e2a\u53d8\u91cf <code>front</code> \u6307\u5411\u961f\u9996\u5143\u7d20\u7684\u7d22\u5f15\uff0c\u5e76\u7ef4\u62a4\u4e00\u4e2a\u53d8\u91cf <code>queSize</code> \u7528\u4e8e\u8bb0\u5f55\u961f\u5217\u957f\u5ea6\u3002\u5b9a\u4e49 <code>rear = front + queSize</code> \uff0c\u8fd9\u4e2a\u516c\u5f0f\u8ba1\u7b97\u51fa\u7684 <code>rear</code> \u6307\u5411\u961f\u5c3e\u5143\u7d20\u4e4b\u540e\u7684\u4e0b\u4e00\u4e2a\u4f4d\u7f6e\u3002</p> <p>\u57fa\u4e8e\u6b64\u8bbe\u8ba1\uff0c\u6570\u7ec4\u4e2d\u5305\u542b\u5143\u7d20\u7684\u6709\u6548\u533a\u95f4\u4e3a [front, rear - 1]\uff0c\u8fdb\u800c\uff1a</p> <ul> <li>\u5bf9\u4e8e\u5165\u961f\u64cd\u4f5c\uff0c\u5c06\u8f93\u5165\u5143\u7d20\u8d4b\u503c\u7ed9 <code>rear</code> \u7d22\u5f15\u5904\uff0c\u5e76\u5c06 <code>queSize</code> \u589e\u52a0 1 \uff1b</li> <li>\u5bf9\u4e8e\u51fa\u961f\u64cd\u4f5c\uff0c\u53ea\u9700\u5c06 <code>front</code> \u589e\u52a0 1 \uff0c\u5e76\u5c06 <code>queSize</code> \u51cf\u5c11 1 \uff1b</li> </ul> <p>\u53ef\u4ee5\u770b\u5230\uff0c\u5165\u961f\u548c\u51fa\u961f\u64cd\u4f5c\u90fd\u53ea\u9700\u8fdb\u884c\u4e00\u6b21\u64cd\u4f5c\uff0c\u65f6\u95f4\u590d\u6742\u5ea6\u5747\u4e3a \\(O(1)\\) \u3002</p> ArrayQueuepush()pop() <p></p> <p></p> <p></p> <p>\u4f60\u53ef\u80fd\u4f1a\u53d1\u73b0\u4e00\u4e2a\u95ee\u9898\uff1a\u5728\u4e0d\u65ad\u8fdb\u884c\u5165\u961f\u548c\u51fa\u961f\u7684\u8fc7\u7a0b\u4e2d\uff0c<code>front</code> \u548c <code>rear</code> \u90fd\u5728\u5411\u53f3\u79fb\u52a8\uff0c\u5f53\u5b83\u4eec\u5230\u8fbe\u6570\u7ec4\u5c3e\u90e8\u65f6\u5c31\u65e0\u6cd5\u7ee7\u7eed\u79fb\u52a8\u4e86\u3002\u4e3a\u89e3\u51b3\u6b64\u95ee\u9898\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u6570\u7ec4\u89c6\u4e3a\u9996\u5c3e\u76f8\u63a5\u7684\u300c\u73af\u5f62\u6570\u7ec4\u300d\u3002</p> <p>\u5bf9\u4e8e\u73af\u5f62\u6570\u7ec4\uff0c\u6211\u4eec\u9700\u8981\u8ba9 <code>front</code> \u6216 <code>rear</code> \u5728\u8d8a\u8fc7\u6570\u7ec4\u5c3e\u90e8\u65f6\uff0c\u76f4\u63a5\u56de\u5230\u6570\u7ec4\u5934\u90e8\u7ee7\u7eed\u904d\u5386\u3002\u8fd9\u79cd\u5468\u671f\u6027\u89c4\u5f8b\u53ef\u4ee5\u901a\u8fc7\u201c\u53d6\u4f59\u64cd\u4f5c\u201d\u6765\u5b9e\u73b0\uff0c\u4ee3\u7801\u5982\u4e0b\u6240\u793a\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart array_queue.java<pre><code>/* \u57fa\u4e8e\u73af\u5f62\u6570\u7ec4\u5b9e\u73b0\u7684\u961f\u5217 */\nclass ArrayQueue {\nprivate int[] nums; // \u7528\u4e8e\u5b58\u50a8\u961f\u5217\u5143\u7d20\u7684\u6570\u7ec4\nprivate int front; // \u961f\u9996\u6307\u9488\uff0c\u6307\u5411\u961f\u9996\u5143\u7d20\nprivate int queSize; // \u961f\u5217\u957f\u5ea6\npublic ArrayQueue(int capacity) {\nnums = new int[capacity];\nfront = queSize = 0;\n}\n/* \u83b7\u53d6\u961f\u5217\u7684\u5bb9\u91cf */\npublic int capacity() {\nreturn nums.length;\n}\n/* \u83b7\u53d6\u961f\u5217\u7684\u957f\u5ea6 */\npublic int size() {\nreturn queSize;\n}\n/* \u5224\u65ad\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\npublic boolean isEmpty() {\nreturn queSize == 0;\n}\n/* \u5165\u961f */\npublic void push(int num) {\nif (queSize == capacity()) {\nSystem.out.println(\"\u961f\u5217\u5df2\u6ee1\");\nreturn;\n}\n// \u8ba1\u7b97\u5c3e\u6307\u9488\uff0c\u6307\u5411\u961f\u5c3e\u7d22\u5f15 + 1\n// \u901a\u8fc7\u53d6\u4f59\u64cd\u4f5c\uff0c\u5b9e\u73b0 rear \u8d8a\u8fc7\u6570\u7ec4\u5c3e\u90e8\u540e\u56de\u5230\u5934\u90e8\nint rear = (front + queSize) % capacity();\n// \u5c06 num \u6dfb\u52a0\u81f3\u961f\u5c3e\nnums[rear] = num;\nqueSize++;\n}\n/* \u51fa\u961f */\npublic int pop() {\nint num = peek();\n// \u961f\u9996\u6307\u9488\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\uff0c\u82e5\u8d8a\u8fc7\u5c3e\u90e8\u5219\u8fd4\u56de\u5230\u6570\u7ec4\u5934\u90e8\nfront = (front + 1) % capacity();\nqueSize--;\nreturn num;\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\npublic int peek() {\nif (isEmpty())\nthrow new IndexOutOfBoundsException();\nreturn nums[front];\n}\n/* \u8fd4\u56de\u6570\u7ec4 */\npublic int[] toArray() {\n// \u4ec5\u8f6c\u6362\u6709\u6548\u957f\u5ea6\u8303\u56f4\u5185\u7684\u5217\u8868\u5143\u7d20\nint[] res = new int[queSize];\nfor (int i = 0, j = front; i &lt; queSize; i++, j++) {\nres[i] = nums[j % capacity()];\n}\nreturn res;\n}\n}\n</code></pre> array_queue.cpp<pre><code>/* \u57fa\u4e8e\u73af\u5f62\u6570\u7ec4\u5b9e\u73b0\u7684\u961f\u5217 */\nclass ArrayQueue {\nprivate:\nint *nums;       // \u7528\u4e8e\u5b58\u50a8\u961f\u5217\u5143\u7d20\u7684\u6570\u7ec4\nint front;       // \u961f\u9996\u6307\u9488\uff0c\u6307\u5411\u961f\u9996\u5143\u7d20\nint queSize;     // \u961f\u5217\u957f\u5ea6\nint queCapacity; // \u961f\u5217\u5bb9\u91cf\npublic:\nArrayQueue(int capacity) {\n// \u521d\u59cb\u5316\u6570\u7ec4\nnums = new int[capacity];\nqueCapacity = capacity;\nfront = queSize = 0;\n}\n~ArrayQueue() {\ndelete[] nums;\n}\n/* \u83b7\u53d6\u961f\u5217\u7684\u5bb9\u91cf */\nint capacity() {\nreturn queCapacity;\n}\n/* \u83b7\u53d6\u961f\u5217\u7684\u957f\u5ea6 */\nint size() {\nreturn queSize;\n}\n/* \u5224\u65ad\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nbool empty() {\nreturn size() == 0;\n}\n/* \u5165\u961f */\nvoid push(int num) {\nif (queSize == queCapacity) {\ncout &lt;&lt; \"\u961f\u5217\u5df2\u6ee1\" &lt;&lt; endl;\nreturn;\n}\n// \u8ba1\u7b97\u961f\u5c3e\u6307\u9488\uff0c\u6307\u5411\u961f\u5c3e\u7d22\u5f15 + 1\n// \u901a\u8fc7\u53d6\u4f59\u64cd\u4f5c\uff0c\u5b9e\u73b0 rear \u8d8a\u8fc7\u6570\u7ec4\u5c3e\u90e8\u540e\u56de\u5230\u5934\u90e8\nint rear = (front + queSize) % queCapacity;\n// \u5c06 num \u6dfb\u52a0\u81f3\u961f\u5c3e\nnums[rear] = num;\nqueSize++;\n}\n/* \u51fa\u961f */\nvoid pop() {\nint num = peek();\n// \u961f\u9996\u6307\u9488\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\uff0c\u82e5\u8d8a\u8fc7\u5c3e\u90e8\u5219\u8fd4\u56de\u5230\u6570\u7ec4\u5934\u90e8\nfront = (front + 1) % queCapacity;\nqueSize--;\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\nint peek() {\nif (empty())\nthrow out_of_range(\"\u961f\u5217\u4e3a\u7a7a\");\nreturn nums[front];\n}\n/* \u5c06\u6570\u7ec4\u8f6c\u5316\u4e3a Vector \u5e76\u8fd4\u56de */\nvector&lt;int&gt; toVector() {\n// \u4ec5\u8f6c\u6362\u6709\u6548\u957f\u5ea6\u8303\u56f4\u5185\u7684\u5217\u8868\u5143\u7d20\nvector&lt;int&gt; arr(queSize);\nfor (int i = 0, j = front; i &lt; queSize; i++, j++) {\narr[i] = nums[j % queCapacity];\n}\nreturn arr;\n}\n};\n</code></pre> array_queue.py<pre><code>class ArrayQueue:\n\"\"\"\u57fa\u4e8e\u73af\u5f62\u6570\u7ec4\u5b9e\u73b0\u7684\u961f\u5217\"\"\"\ndef __init__(self, size: int) -&gt; None:\n\"\"\"\u6784\u9020\u65b9\u6cd5\"\"\"\nself.__nums: list[int] = [0] * size  # \u7528\u4e8e\u5b58\u50a8\u961f\u5217\u5143\u7d20\u7684\u6570\u7ec4\nself.__front: int = 0  # \u961f\u9996\u6307\u9488\uff0c\u6307\u5411\u961f\u9996\u5143\u7d20\nself.__size: int = 0  # \u961f\u5217\u957f\u5ea6\ndef capacity(self) -&gt; int:\n\"\"\"\u83b7\u53d6\u961f\u5217\u7684\u5bb9\u91cf\"\"\"\nreturn len(self.__nums)\ndef size(self) -&gt; int:\n\"\"\"\u83b7\u53d6\u961f\u5217\u7684\u957f\u5ea6\"\"\"\nreturn self.__size\ndef is_empty(self) -&gt; bool:\n\"\"\"\u5224\u65ad\u961f\u5217\u662f\u5426\u4e3a\u7a7a\"\"\"\nreturn self.__size == 0\ndef push(self, num: int) -&gt; None:\n\"\"\"\u5165\u961f\"\"\"\nif self.__size == self.capacity():\nraise IndexError(\"\u961f\u5217\u5df2\u6ee1\")\n# \u8ba1\u7b97\u5c3e\u6307\u9488\uff0c\u6307\u5411\u961f\u5c3e\u7d22\u5f15 + 1\n# \u901a\u8fc7\u53d6\u4f59\u64cd\u4f5c\uff0c\u5b9e\u73b0 rear \u8d8a\u8fc7\u6570\u7ec4\u5c3e\u90e8\u540e\u56de\u5230\u5934\u90e8F\nrear: int = (self.__front + self.__size) % self.capacity()\n# \u5c06 num \u6dfb\u52a0\u81f3\u961f\u5c3e\nself.__nums[rear] = num\nself.__size += 1\ndef pop(self) -&gt; int:\n\"\"\"\u51fa\u961f\"\"\"\nnum: int = self.peek()\n# \u961f\u9996\u6307\u9488\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\uff0c\u82e5\u8d8a\u8fc7\u5c3e\u90e8\u5219\u8fd4\u56de\u5230\u6570\u7ec4\u5934\u90e8\nself.__front = (self.__front + 1) % self.capacity()\nself.__size -= 1\nreturn num\ndef peek(self) -&gt; int:\n\"\"\"\u8bbf\u95ee\u961f\u9996\u5143\u7d20\"\"\"\nif self.is_empty():\nraise IndexError(\"\u961f\u5217\u4e3a\u7a7a\")\nreturn self.__nums[self.__front]\ndef to_list(self) -&gt; list[int]:\n\"\"\"\u8fd4\u56de\u5217\u8868\u7528\u4e8e\u6253\u5370\"\"\"\nres = [0] * self.size()\nj: int = self.__front\nfor i in range(self.size()):\nres[i] = self.__nums[(j % self.capacity())]\nj += 1\nreturn res\n</code></pre> array_queue.go<pre><code>/* \u57fa\u4e8e\u73af\u5f62\u6570\u7ec4\u5b9e\u73b0\u7684\u961f\u5217 */\ntype arrayQueue struct {\nnums        []int // \u7528\u4e8e\u5b58\u50a8\u961f\u5217\u5143\u7d20\u7684\u6570\u7ec4\nfront       int   // \u961f\u9996\u6307\u9488\uff0c\u6307\u5411\u961f\u9996\u5143\u7d20\nqueSize     int   // \u961f\u5217\u957f\u5ea6\nqueCapacity int   // \u961f\u5217\u5bb9\u91cf\uff08\u5373\u6700\u5927\u5bb9\u7eb3\u5143\u7d20\u6570\u91cf\uff09\n}\n/* \u521d\u59cb\u5316\u961f\u5217 */\nfunc newArrayQueue(queCapacity int) *arrayQueue {\nreturn &amp;arrayQueue{\nnums:        make([]int, queCapacity),\nqueCapacity: queCapacity,\nfront:       0,\nqueSize:     0,\n}\n}\n/* \u83b7\u53d6\u961f\u5217\u7684\u957f\u5ea6 */\nfunc (q *arrayQueue) size() int {\nreturn q.queSize\n}\n/* \u5224\u65ad\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nfunc (q *arrayQueue) isEmpty() bool {\nreturn q.queSize == 0\n}\n/* \u5165\u961f */\nfunc (q *arrayQueue) push(num int) {\n// \u5f53 rear == queCapacity \u8868\u793a\u961f\u5217\u5df2\u6ee1\nif q.queSize == q.queCapacity {\nreturn\n}\n// \u8ba1\u7b97\u5c3e\u6307\u9488\uff0c\u6307\u5411\u961f\u5c3e\u7d22\u5f15 + 1\n// \u901a\u8fc7\u53d6\u4f59\u64cd\u4f5c\uff0c\u5b9e\u73b0 rear \u8d8a\u8fc7\u6570\u7ec4\u5c3e\u90e8\u540e\u56de\u5230\u5934\u90e8\nrear := (q.front + q.queSize) % q.queCapacity\n// \u5c06 num \u6dfb\u52a0\u81f3\u961f\u5c3e\nq.nums[rear] = num\nq.queSize++\n}\n/* \u51fa\u961f */\nfunc (q *arrayQueue) pop() any {\nnum := q.peek()\n// \u961f\u9996\u6307\u9488\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\uff0c\u82e5\u8d8a\u8fc7\u5c3e\u90e8\u5219\u8fd4\u56de\u5230\u6570\u7ec4\u5934\u90e8\nq.front = (q.front + 1) % q.queCapacity\nq.queSize--\nreturn num\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\nfunc (q *arrayQueue) peek() any {\nif q.isEmpty() {\nreturn nil\n}\nreturn q.nums[q.front]\n}\n/* \u83b7\u53d6 Slice \u7528\u4e8e\u6253\u5370 */\nfunc (q *arrayQueue) toSlice() []int {\nrear := (q.front + q.queSize)\nif rear &gt;= q.queCapacity {\nrear %= q.queCapacity\nreturn append(q.nums[q.front:], q.nums[:rear]...)\n}\nreturn q.nums[q.front:rear]\n}\n</code></pre> array_queue.js<pre><code>/* \u57fa\u4e8e\u73af\u5f62\u6570\u7ec4\u5b9e\u73b0\u7684\u961f\u5217 */\nclass ArrayQueue {\n#nums; // \u7528\u4e8e\u5b58\u50a8\u961f\u5217\u5143\u7d20\u7684\u6570\u7ec4\n#front = 0; // \u961f\u9996\u6307\u9488\uff0c\u6307\u5411\u961f\u9996\u5143\u7d20\n#queSize = 0; // \u961f\u5217\u957f\u5ea6\nconstructor(capacity) {\nthis.#nums = new Array(capacity);\n}\n/* \u83b7\u53d6\u961f\u5217\u7684\u5bb9\u91cf */\nget capacity() {\nreturn this.#nums.length;\n}\n/* \u83b7\u53d6\u961f\u5217\u7684\u957f\u5ea6 */\nget size() {\nreturn this.#queSize;\n}\n/* \u5224\u65ad\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nempty() {\nreturn this.#queSize == 0;\n}\n/* \u5165\u961f */\npush(num) {\nif (this.size == this.capacity) {\nconsole.log('\u961f\u5217\u5df2\u6ee1');\nreturn;\n}\n// \u8ba1\u7b97\u5c3e\u6307\u9488\uff0c\u6307\u5411\u961f\u5c3e\u7d22\u5f15 + 1\n// \u901a\u8fc7\u53d6\u4f59\u64cd\u4f5c\uff0c\u5b9e\u73b0 rear \u8d8a\u8fc7\u6570\u7ec4\u5c3e\u90e8\u540e\u56de\u5230\u5934\u90e8\nconst rear = (this.#front + this.size) % this.capacity;\n// \u5c06 num \u6dfb\u52a0\u81f3\u961f\u5c3e\nthis.#nums[rear] = num;\nthis.#queSize++;\n}\n/* \u51fa\u961f */\npop() {\nconst num = this.peek();\n// \u961f\u9996\u6307\u9488\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\uff0c\u82e5\u8d8a\u8fc7\u5c3e\u90e8\u5219\u8fd4\u56de\u5230\u6570\u7ec4\u5934\u90e8\nthis.#front = (this.#front + 1) % this.capacity;\nthis.#queSize--;\nreturn num;\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\npeek() {\nif (this.empty()) throw new Error('\u961f\u5217\u4e3a\u7a7a');\nreturn this.#nums[this.#front];\n}\n/* \u8fd4\u56de Array */\ntoArray() {\n// \u4ec5\u8f6c\u6362\u6709\u6548\u957f\u5ea6\u8303\u56f4\u5185\u7684\u5217\u8868\u5143\u7d20\nconst arr = new Array(this.size);\nfor (let i = 0, j = this.#front; i &lt; this.size; i++, j++) {\narr[i] = this.#nums[j % this.capacity];\n}\nreturn arr;\n}\n}\n</code></pre> array_queue.ts<pre><code>/* \u57fa\u4e8e\u73af\u5f62\u6570\u7ec4\u5b9e\u73b0\u7684\u961f\u5217 */\nclass ArrayQueue {\nprivate nums: number[]; // \u7528\u4e8e\u5b58\u50a8\u961f\u5217\u5143\u7d20\u7684\u6570\u7ec4\nprivate front: number; // \u961f\u9996\u6307\u9488\uff0c\u6307\u5411\u961f\u9996\u5143\u7d20\nprivate queSize: number; // \u961f\u5217\u957f\u5ea6\nconstructor(capacity: number) {\nthis.nums = new Array(capacity);\nthis.front = this.queSize = 0;\n}\n/* \u83b7\u53d6\u961f\u5217\u7684\u5bb9\u91cf */\nget capacity(): number {\nreturn this.nums.length;\n}\n/* \u83b7\u53d6\u961f\u5217\u7684\u957f\u5ea6 */\nget size(): number {\nreturn this.queSize;\n}\n/* \u5224\u65ad\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nempty(): boolean {\nreturn this.queSize == 0;\n}\n/* \u5165\u961f */\npush(num: number): void {\nif (this.size == this.capacity) {\nconsole.log('\u961f\u5217\u5df2\u6ee1');\nreturn;\n}\n// \u8ba1\u7b97\u5c3e\u6307\u9488\uff0c\u6307\u5411\u961f\u5c3e\u7d22\u5f15 + 1\n// \u901a\u8fc7\u53d6\u4f59\u64cd\u4f5c\uff0c\u5b9e\u73b0 rear \u8d8a\u8fc7\u6570\u7ec4\u5c3e\u90e8\u540e\u56de\u5230\u5934\u90e8\nconst rear = (this.front + this.queSize) % this.capacity;\n// \u5c06 num \u6dfb\u52a0\u81f3\u961f\u5c3e\nthis.nums[rear] = num;\nthis.queSize++;\n}\n/* \u51fa\u961f */\npop(): number {\nconst num = this.peek();\n// \u961f\u9996\u6307\u9488\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\uff0c\u82e5\u8d8a\u8fc7\u5c3e\u90e8\u5219\u8fd4\u56de\u5230\u6570\u7ec4\u5934\u90e8\nthis.front = (this.front + 1) % this.capacity;\nthis.queSize--;\nreturn num;\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\npeek(): number {\nif (this.empty()) throw new Error('\u961f\u5217\u4e3a\u7a7a');\nreturn this.nums[this.front];\n}\n/* \u8fd4\u56de Array */\ntoArray(): number[] {\n// \u4ec5\u8f6c\u6362\u6709\u6548\u957f\u5ea6\u8303\u56f4\u5185\u7684\u5217\u8868\u5143\u7d20\nconst arr = new Array(this.size);\nfor (let i = 0, j = this.front; i &lt; this.size; i++, j++) {\narr[i] = this.nums[j % this.capacity];\n}\nreturn arr;\n}\n}\n</code></pre> array_queue.c<pre><code>/* \u57fa\u4e8e\u73af\u5f62\u6570\u7ec4\u5b9e\u73b0\u7684\u961f\u5217 */\nstruct arrayQueue {\nint *nums;       // \u7528\u4e8e\u5b58\u50a8\u961f\u5217\u5143\u7d20\u7684\u6570\u7ec4\nint front;       // \u961f\u9996\u6307\u9488\uff0c\u6307\u5411\u961f\u9996\u5143\u7d20\nint queSize;     // \u5c3e\u6307\u9488\uff0c\u6307\u5411\u961f\u5c3e + 1\nint queCapacity; // \u961f\u5217\u5bb9\u91cf\n};\ntypedef struct arrayQueue arrayQueue;\n/* \u6784\u9020\u51fd\u6570 */\narrayQueue *newArrayQueue(int capacity) {\narrayQueue *queue = (arrayQueue *)malloc(sizeof(arrayQueue));\n// \u521d\u59cb\u5316\u6570\u7ec4\nqueue-&gt;queCapacity = capacity;\nqueue-&gt;nums = (int *)malloc(sizeof(int) * queue-&gt;queCapacity);\nqueue-&gt;front = queue-&gt;queSize = 0;\nreturn queue;\n}\n/* \u6790\u6784\u51fd\u6570 */\nvoid delArrayQueue(arrayQueue *queue) {\nfree(queue-&gt;nums);\nqueue-&gt;queCapacity = 0;\n}\n/* \u83b7\u53d6\u961f\u5217\u7684\u5bb9\u91cf */\nint capacity(arrayQueue *queue) {\nreturn queue-&gt;queCapacity;\n}\n/* \u83b7\u53d6\u961f\u5217\u7684\u957f\u5ea6 */\nint size(arrayQueue *queue) {\nreturn queue-&gt;queSize;\n}\n/* \u5224\u65ad\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nbool empty(arrayQueue *queue) {\nreturn queue-&gt;queSize == 0;\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\nint peek(arrayQueue *queue) {\nassert(size(queue) != 0);\nreturn queue-&gt;nums[queue-&gt;front];\n}\n/* \u5165\u961f */\nvoid push(arrayQueue *queue, int num) {\nif (size(queue) == capacity(queue)) {\nprintf(\"\u961f\u5217\u5df2\u6ee1\\r\\n\");\nreturn;\n}\n// \u8ba1\u7b97\u961f\u5c3e\u6307\u9488\uff0c\u6307\u5411\u961f\u5c3e\u7d22\u5f15 + 1\n// \u901a\u8fc7\u53d6\u4f59\u64cd\u4f5c\uff0c\u5b9e\u73b0 rear \u8d8a\u8fc7\u6570\u7ec4\u5c3e\u90e8\u540e\u56de\u5230\u5934\u90e8\nint rear = (queue-&gt;front + queue-&gt;queSize) % queue-&gt;queCapacity;\n// \u5c06 num \u6dfb\u52a0\u81f3\u961f\u5c3e\nqueue-&gt;nums[rear] = num;\nqueue-&gt;queSize++;\n}\n/* \u51fa\u961f */\nvoid pop(arrayQueue *queue) {\nint num = peek(queue);\n// \u961f\u9996\u6307\u9488\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\uff0c\u82e5\u8d8a\u8fc7\u5c3e\u90e8\u5219\u8fd4\u56de\u5230\u6570\u7ec4\u5934\u90e8\nqueue-&gt;front = (queue-&gt;front + 1) % queue-&gt;queCapacity;\nqueue-&gt;queSize--;\n}\n/* \u6253\u5370\u961f\u5217 */\nvoid printArrayQueue(arrayQueue *queue) {\nint arr[queue-&gt;queSize];\n// \u62f7\u8d1d\nfor (int i = 0, j = queue-&gt;front; i &lt; queue-&gt;queSize; i++, j++) {\narr[i] = queue-&gt;nums[j % queue-&gt;queCapacity];\n}\nprintArray(arr, queue-&gt;queSize);\n}\n</code></pre> array_queue.cs<pre><code>/* \u57fa\u4e8e\u73af\u5f62\u6570\u7ec4\u5b9e\u73b0\u7684\u961f\u5217 */\nclass ArrayQueue {\nprivate int[] nums;  // \u7528\u4e8e\u5b58\u50a8\u961f\u5217\u5143\u7d20\u7684\u6570\u7ec4\nprivate int front;   // \u961f\u9996\u6307\u9488\uff0c\u6307\u5411\u961f\u9996\u5143\u7d20\nprivate int queSize; // \u961f\u5217\u957f\u5ea6\npublic ArrayQueue(int capacity) {\nnums = new int[capacity];\nfront = queSize = 0;\n}\n/* \u83b7\u53d6\u961f\u5217\u7684\u5bb9\u91cf */\npublic int capacity() {\nreturn nums.Length;\n}\n/* \u83b7\u53d6\u961f\u5217\u7684\u957f\u5ea6 */\npublic int size() {\nreturn queSize;\n}\n/* \u5224\u65ad\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\npublic bool isEmpty() {\nreturn queSize == 0;\n}\n/* \u5165\u961f */\npublic void push(int num) {\nif (queSize == capacity()) {\nConsole.WriteLine(\"\u961f\u5217\u5df2\u6ee1\");\nreturn;\n}\n// \u8ba1\u7b97\u5c3e\u6307\u9488\uff0c\u6307\u5411\u961f\u5c3e\u7d22\u5f15 + 1\n// \u901a\u8fc7\u53d6\u4f59\u64cd\u4f5c\uff0c\u5b9e\u73b0 rear \u8d8a\u8fc7\u6570\u7ec4\u5c3e\u90e8\u540e\u56de\u5230\u5934\u90e8\nint rear = (front + queSize) % capacity();\n// \u5c06 num \u6dfb\u52a0\u81f3\u961f\u5c3e\nnums[rear] = num;\nqueSize++;\n}\n/* \u51fa\u961f */\npublic int pop() {\nint num = peek();\n// \u961f\u9996\u6307\u9488\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\uff0c\u82e5\u8d8a\u8fc7\u5c3e\u90e8\u5219\u8fd4\u56de\u5230\u6570\u7ec4\u5934\u90e8\nfront = (front + 1) % capacity();\nqueSize--;\nreturn num;\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\npublic int peek() {\nif (isEmpty())\nthrow new Exception();\nreturn nums[front];\n}\n/* \u8fd4\u56de\u6570\u7ec4 */\npublic int[] toArray() {\n// \u4ec5\u8f6c\u6362\u6709\u6548\u957f\u5ea6\u8303\u56f4\u5185\u7684\u5217\u8868\u5143\u7d20\nint[] res = new int[queSize];\nfor (int i = 0, j = front; i &lt; queSize; i++, j++) {\nres[i] = nums[j % this.capacity()];\n}\nreturn res;\n}\n}\n</code></pre> array_queue.swift<pre><code>/* \u57fa\u4e8e\u73af\u5f62\u6570\u7ec4\u5b9e\u73b0\u7684\u961f\u5217 */\nclass ArrayQueue {\nprivate var nums: [Int] // \u7528\u4e8e\u5b58\u50a8\u961f\u5217\u5143\u7d20\u7684\u6570\u7ec4\nprivate var front = 0 // \u961f\u9996\u6307\u9488\uff0c\u6307\u5411\u961f\u9996\u5143\u7d20\nprivate var queSize = 0 // \u961f\u5217\u957f\u5ea6\ninit(capacity: Int) {\n// \u521d\u59cb\u5316\u6570\u7ec4\nnums = Array(repeating: 0, count: capacity)\n}\n/* \u83b7\u53d6\u961f\u5217\u7684\u5bb9\u91cf */\nfunc capacity() -&gt; Int {\nnums.count\n}\n/* \u83b7\u53d6\u961f\u5217\u7684\u957f\u5ea6 */\nfunc size() -&gt; Int {\nqueSize\n}\n/* \u5224\u65ad\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nfunc isEmpty() -&gt; Bool {\nqueSize == 0\n}\n/* \u5165\u961f */\nfunc push(num: Int) {\nif size() == capacity() {\nprint(\"\u961f\u5217\u5df2\u6ee1\")\nreturn\n}\n// \u8ba1\u7b97\u5c3e\u6307\u9488\uff0c\u6307\u5411\u961f\u5c3e\u7d22\u5f15 + 1\n// \u901a\u8fc7\u53d6\u4f59\u64cd\u4f5c\uff0c\u5b9e\u73b0 rear \u8d8a\u8fc7\u6570\u7ec4\u5c3e\u90e8\u540e\u56de\u5230\u5934\u90e8\nlet rear = (front + queSize) % capacity()\n// \u5c06 num \u6dfb\u52a0\u81f3\u961f\u5c3e\nnums[rear] = num\nqueSize += 1\n}\n/* \u51fa\u961f */\n@discardableResult\nfunc pop() -&gt; Int {\nlet num = peek()\n// \u961f\u9996\u6307\u9488\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\uff0c\u82e5\u8d8a\u8fc7\u5c3e\u90e8\u5219\u8fd4\u56de\u5230\u6570\u7ec4\u5934\u90e8\nfront = (front + 1) % capacity()\nqueSize -= 1\nreturn num\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\nfunc peek() -&gt; Int {\nif isEmpty() {\nfatalError(\"\u961f\u5217\u4e3a\u7a7a\")\n}\nreturn nums[front]\n}\n/* \u8fd4\u56de\u6570\u7ec4 */\nfunc toArray() -&gt; [Int] {\n// \u4ec5\u8f6c\u6362\u6709\u6548\u957f\u5ea6\u8303\u56f4\u5185\u7684\u5217\u8868\u5143\u7d20\nvar res = Array(repeating: 0, count: queSize)\nfor (i, j) in sequence(first: (0, front), next: { $0 &lt; self.queSize - 1 ? ($0 + 1, $1 + 1) : nil }) {\nres[i] = nums[j % capacity()]\n}\nreturn res\n}\n}\n</code></pre> array_queue.zig<pre><code>// \u57fa\u4e8e\u73af\u5f62\u6570\u7ec4\u5b9e\u73b0\u7684\u961f\u5217\nfn ArrayQueue(comptime T: type) type {\nreturn struct {\nconst Self = @This();\nnums: []T = undefined,                          // \u7528\u4e8e\u5b58\u50a8\u961f\u5217\u5143\u7d20\u7684\u6570\u7ec4     \ncap: usize = 0,                                 // \u961f\u5217\u5bb9\u91cf\nfront: usize = 0,                               // \u961f\u9996\u6307\u9488\uff0c\u6307\u5411\u961f\u9996\u5143\u7d20\nque_size: usize = 0,                             // \u5c3e\u6307\u9488\uff0c\u6307\u5411\u961f\u5c3e + 1\nmem_arena: ?std.heap.ArenaAllocator = null,\nmem_allocator: std.mem.Allocator = undefined,   // \u5185\u5b58\u5206\u914d\u5668\n// \u6784\u9020\u65b9\u6cd5\uff08\u5206\u914d\u5185\u5b58+\u521d\u59cb\u5316\u6570\u7ec4\uff09\npub fn init(self: *Self, allocator: std.mem.Allocator, cap: usize) !void {\nif (self.mem_arena == null) {\nself.mem_arena = std.heap.ArenaAllocator.init(allocator);\nself.mem_allocator = self.mem_arena.?.allocator();\n}\nself.cap = cap;\nself.nums = try self.mem_allocator.alloc(T, self.cap);\nstd.mem.set(T, self.nums, @as(T, 0));\n}\n// \u6790\u6784\u65b9\u6cd5\uff08\u91ca\u653e\u5185\u5b58\uff09\npub fn deinit(self: *Self) void {\nif (self.mem_arena == null) return;\nself.mem_arena.?.deinit();\n}\n// \u83b7\u53d6\u961f\u5217\u7684\u5bb9\u91cf\npub fn capacity(self: *Self) usize {\nreturn self.cap;\n}\n// \u83b7\u53d6\u961f\u5217\u7684\u957f\u5ea6\npub fn size(self: *Self) usize {\nreturn self.que_size;\n}\n// \u5224\u65ad\u961f\u5217\u662f\u5426\u4e3a\u7a7a\npub fn isEmpty(self: *Self) bool {\nreturn self.que_size == 0;\n}\n// \u5165\u961f\npub fn push(self: *Self, num: T) !void {\nif (self.size() == self.capacity()) {\nstd.debug.print(\"\u961f\u5217\u5df2\u6ee1\\n\", .{});\nreturn;\n}\n// \u8ba1\u7b97\u5c3e\u6307\u9488\uff0c\u6307\u5411\u961f\u5c3e\u7d22\u5f15 + 1\n// \u901a\u8fc7\u53d6\u4f59\u64cd\u4f5c\uff0c\u5b9e\u73b0 rear \u8d8a\u8fc7\u6570\u7ec4\u5c3e\u90e8\u540e\u56de\u5230\u5934\u90e8\nvar rear = (self.front + self.que_size) % self.capacity();\n// \u5c06 num \u6dfb\u52a0\u81f3\u961f\u5c3e\nself.nums[rear] = num;\nself.que_size += 1;\n} // \u51fa\u961f\npub fn pop(self: *Self) T {\nvar num = self.peek();\n// \u961f\u9996\u6307\u9488\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\uff0c\u82e5\u8d8a\u8fc7\u5c3e\u90e8\u5219\u8fd4\u56de\u5230\u6570\u7ec4\u5934\u90e8\nself.front = (self.front + 1) % self.capacity();\nself.que_size -= 1;\nreturn num;\n} // \u8bbf\u95ee\u961f\u9996\u5143\u7d20\npub fn peek(self: *Self) T {\nif (self.isEmpty()) @panic(\"\u961f\u5217\u4e3a\u7a7a\");\nreturn self.nums[self.front];\n} // \u8fd4\u56de\u6570\u7ec4\npub fn toArray(self: *Self) ![]T {\n// \u4ec5\u8f6c\u6362\u6709\u6548\u957f\u5ea6\u8303\u56f4\u5185\u7684\u5217\u8868\u5143\u7d20\nvar res = try self.mem_allocator.alloc(T, self.size());\nstd.mem.set(T, res, @as(T, 0));\nvar i: usize = 0;\nvar j: usize = self.front;\nwhile (i &lt; self.size()) : ({ i += 1; j += 1; }) {\nres[i] = self.nums[j % self.capacity()];\n}\nreturn res;\n}\n};\n}\n</code></pre> array_queue.dart<pre><code>/* \u57fa\u4e8e\u73af\u5f62\u6570\u7ec4\u5b9e\u73b0\u7684\u961f\u5217 */\nclass ArrayQueue {\nlate List&lt;int&gt; _nums; // \u7528\u4e8e\u50a8\u5b58\u961f\u5217\u5143\u7d20\u7684\u6570\u7ec4\nlate int _front; // \u961f\u9996\u6307\u9488\uff0c\u6307\u5411\u961f\u9996\u5143\u7d20\nlate int _queSize; // \u961f\u5217\u957f\u5ea6\nArrayQueue(int capacity) {\n_nums = List.filled(capacity, 0);\n_front = _queSize = 0;\n}\n/* \u83b7\u53d6\u961f\u5217\u7684\u5bb9\u91cf */\nint capaCity() {\nreturn _nums.length;\n}\n/* \u83b7\u53d6\u961f\u5217\u7684\u957f\u5ea6 */\nint size() {\nreturn _queSize;\n}\n/* \u5224\u65ad\u961f\u5217\u662f\u5426\u4e3a\u7a7a */\nbool isEmpty() {\nreturn _queSize == 0;\n}\n/* \u5165\u961f */\nvoid push(int num) {\nif (_queSize == capaCity()) {\nthrow Exception(\"\u961f\u5217\u5df2\u6ee1\");\n}\n// \u8ba1\u7b97\u5c3e\u6307\u9488\uff0c\u6307\u5411\u961f\u5c3e\u7d22\u5f15 + 1\n// \u901a\u8fc7\u53d6\u4f59\u64cd\u4f5c\uff0c\u5b9e\u73b0 rear \u8d8a\u8fc7\u6570\u7ec4\u5c3e\u90e8\u540e\u56de\u5230\u5934\u90e8\nint rear = (_front + _queSize) % capaCity();\n// \u5c06 num \u6dfb\u52a0\u81f3\u961f\u5c3e\n_nums[rear] = num;\n_queSize++;\n}\n/* \u51fa\u961f */\nint pop() {\nint num = peek();\n// \u961f\u9996\u6307\u9488\u5411\u540e\u79fb\u52a8\u4e00\u4f4d\uff0c\u82e5\u8d8a\u8fc7\u5c3e\u90e8\u5219\u8fd4\u56de\u5230\u6570\u7ec4\u5934\u90e8\n_front = (_front + 1) % capaCity();\n_queSize--;\nreturn num;\n}\n/* \u8bbf\u95ee\u961f\u9996\u5143\u7d20 */\nint peek() {\nif (isEmpty()) {\nthrow Exception(\"\u961f\u5217\u4e3a\u7a7a\");\n}\nreturn _nums[_front];\n}\n/* \u8fd4\u56de Array */\nList&lt;int&gt; toArray() {\n// \u4ec5\u8f6c\u6362\u6709\u6548\u957f\u5ea6\u8303\u56f4\u5185\u7684\u5217\u8868\u5143\u7d20\nfinal List&lt;int&gt; res = List.filled(_queSize, 0);\nfor (int i = 0, j = _front; i &lt; _queSize; i++, j++) {\nres[i] = _nums[j % capaCity()];\n}\nreturn res;\n}\n}\n</code></pre> <p>\u4ee5\u4e0a\u5b9e\u73b0\u7684\u961f\u5217\u4ecd\u7136\u5177\u6709\u5c40\u9650\u6027\uff0c\u5373\u5176\u957f\u5ea6\u4e0d\u53ef\u53d8\u3002\u7136\u800c\uff0c\u8fd9\u4e2a\u95ee\u9898\u4e0d\u96be\u89e3\u51b3\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u6570\u7ec4\u66ff\u6362\u4e3a\u52a8\u6001\u6570\u7ec4\uff0c\u4ece\u800c\u5f15\u5165\u6269\u5bb9\u673a\u5236\u3002\u6709\u5174\u8da3\u7684\u540c\u5b66\u53ef\u4ee5\u5c1d\u8bd5\u81ea\u884c\u5b9e\u73b0\u3002</p> <p>\u4e24\u79cd\u5b9e\u73b0\u7684\u5bf9\u6bd4\u7ed3\u8bba\u4e0e\u6808\u4e00\u81f4\uff0c\u5728\u6b64\u4e0d\u518d\u8d58\u8ff0\u3002</p>"},{"location":"chapter_stack_and_queue/queue/#523","title":"5.2.3. \u00a0 \u961f\u5217\u5178\u578b\u5e94\u7528","text":"<ul> <li>\u6dd8\u5b9d\u8ba2\u5355\u3002\u8d2d\u7269\u8005\u4e0b\u5355\u540e\uff0c\u8ba2\u5355\u5c06\u52a0\u5165\u961f\u5217\u4e2d\uff0c\u7cfb\u7edf\u968f\u540e\u4f1a\u6839\u636e\u987a\u5e8f\u4f9d\u6b21\u5904\u7406\u961f\u5217\u4e2d\u7684\u8ba2\u5355\u3002\u5728\u53cc\u5341\u4e00\u671f\u95f4\uff0c\u77ed\u65f6\u95f4\u5185\u4f1a\u4ea7\u751f\u6d77\u91cf\u8ba2\u5355\uff0c\u9ad8\u5e76\u53d1\u6210\u4e3a\u5de5\u7a0b\u5e08\u4eec\u9700\u8981\u91cd\u70b9\u653b\u514b\u7684\u95ee\u9898\u3002</li> <li>\u5404\u7c7b\u5f85\u529e\u4e8b\u9879\u3002\u4efb\u4f55\u9700\u8981\u5b9e\u73b0\u201c\u5148\u6765\u540e\u5230\u201d\u529f\u80fd\u7684\u573a\u666f\uff0c\u4f8b\u5982\u6253\u5370\u673a\u7684\u4efb\u52a1\u961f\u5217\u3001\u9910\u5385\u7684\u51fa\u9910\u961f\u5217\u7b49\u3002\u961f\u5217\u5728\u8fd9\u4e9b\u573a\u666f\u4e2d\u53ef\u4ee5\u6709\u6548\u5730\u7ef4\u62a4\u5904\u7406\u987a\u5e8f\u3002</li> </ul>"},{"location":"chapter_stack_and_queue/stack/","title":"5.1. \u00a0 \u6808","text":"<p>\u300c\u6808 Stack\u300d\u662f\u4e00\u79cd\u9075\u5faa\u5148\u5165\u540e\u51fa\uff08First In, Last Out\uff09\u539f\u5219\u7684\u7ebf\u6027\u6570\u636e\u7ed3\u6784\u3002</p> <p>\u6211\u4eec\u53ef\u4ee5\u5c06\u6808\u7c7b\u6bd4\u4e3a\u684c\u9762\u4e0a\u7684\u4e00\u645e\u76d8\u5b50\uff0c\u5982\u679c\u9700\u8981\u62ff\u51fa\u5e95\u90e8\u7684\u76d8\u5b50\uff0c\u5219\u9700\u8981\u5148\u5c06\u4e0a\u9762\u7684\u76d8\u5b50\u4f9d\u6b21\u53d6\u51fa\u3002\u6211\u4eec\u5c06\u76d8\u5b50\u66ff\u6362\u4e3a\u5404\u79cd\u7c7b\u578b\u7684\u5143\u7d20\uff08\u5982\u6574\u6570\u3001\u5b57\u7b26\u3001\u5bf9\u8c61\u7b49\uff09\uff0c\u5c31\u5f97\u5230\u4e86\u6808\u6570\u636e\u7ed3\u6784\u3002</p> <p>\u5728\u6808\u4e2d\uff0c\u6211\u4eec\u628a\u5806\u53e0\u5143\u7d20\u7684\u9876\u90e8\u79f0\u4e3a\u300c\u6808\u9876\u300d\uff0c\u5e95\u90e8\u79f0\u4e3a\u300c\u6808\u5e95\u300d\u3002\u5c06\u628a\u5143\u7d20\u6dfb\u52a0\u5230\u6808\u9876\u7684\u64cd\u4f5c\u53eb\u505a\u300c\u5165\u6808\u300d\uff0c\u800c\u5220\u9664\u6808\u9876\u5143\u7d20\u7684\u64cd\u4f5c\u53eb\u505a\u300c\u51fa\u6808\u300d\u3002</p> <p></p> <p> Fig. \u6808\u7684\u5148\u5165\u540e\u51fa\u89c4\u5219 </p>"},{"location":"chapter_stack_and_queue/stack/#511","title":"5.1.1. \u00a0 \u6808\u5e38\u7528\u64cd\u4f5c","text":"<p>\u6808\u7684\u5e38\u7528\u64cd\u4f5c\u5982\u4e0b\u8868\u6240\u793a\uff0c\u5177\u4f53\u7684\u65b9\u6cd5\u540d\u9700\u8981\u6839\u636e\u6240\u4f7f\u7528\u7684\u7f16\u7a0b\u8bed\u8a00\u6765\u786e\u5b9a\u3002\u5728\u6b64\uff0c\u6211\u4eec\u4ee5\u5e38\u89c1\u7684 <code>push()</code> , <code>pop()</code> , <code>peek()</code> \u547d\u540d\u4e3a\u4f8b\u3002</p> \u65b9\u6cd5 \u63cf\u8ff0 \u65f6\u95f4\u590d\u6742\u5ea6 push() \u5143\u7d20\u5165\u6808\uff08\u6dfb\u52a0\u81f3\u6808\u9876\uff09 \\(O(1)\\) pop() \u6808\u9876\u5143\u7d20\u51fa\u6808 \\(O(1)\\) peek() \u8bbf\u95ee\u6808\u9876\u5143\u7d20 \\(O(1)\\) <p>\u901a\u5e38\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u53ef\u4ee5\u76f4\u63a5\u4f7f\u7528\u7f16\u7a0b\u8bed\u8a00\u5185\u7f6e\u7684\u6808\u7c7b\u3002\u7136\u800c\uff0c\u67d0\u4e9b\u8bed\u8a00\u53ef\u80fd\u6ca1\u6709\u4e13\u95e8\u63d0\u4f9b\u6808\u7c7b\uff0c\u8fd9\u65f6\u6211\u4eec\u53ef\u4ee5\u5c06\u8be5\u8bed\u8a00\u7684\u300c\u6570\u7ec4\u300d\u6216\u300c\u94fe\u8868\u300d\u89c6\u4f5c\u6808\u6765\u4f7f\u7528\uff0c\u5e76\u901a\u8fc7\u201c\u8111\u8865\u201d\u6765\u5ffd\u7565\u4e0e\u6808\u65e0\u5173\u7684\u64cd\u4f5c\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart stack.java<pre><code>/* \u521d\u59cb\u5316\u6808 */\nStack&lt;Integer&gt; stack = new Stack&lt;&gt;();\n/* \u5143\u7d20\u5165\u6808 */\nstack.push(1);\nstack.push(3);\nstack.push(2);\nstack.push(5);\nstack.push(4);\n/* \u8bbf\u95ee\u6808\u9876\u5143\u7d20 */\nint peek = stack.peek();\n/* \u5143\u7d20\u51fa\u6808 */\nint pop = stack.pop();\n/* \u83b7\u53d6\u6808\u7684\u957f\u5ea6 */\nint size = stack.size();\n/* \u5224\u65ad\u662f\u5426\u4e3a\u7a7a */\nboolean isEmpty = stack.isEmpty();\n</code></pre> stack.cpp<pre><code>/* \u521d\u59cb\u5316\u6808 */\nstack&lt;int&gt; stack;\n/* \u5143\u7d20\u5165\u6808 */\nstack.push(1);\nstack.push(3);\nstack.push(2);\nstack.push(5);\nstack.push(4);\n/* \u8bbf\u95ee\u6808\u9876\u5143\u7d20 */\nint top = stack.top();\n/* \u5143\u7d20\u51fa\u6808 */\nstack.pop(); // \u65e0\u8fd4\u56de\u503c\n/* \u83b7\u53d6\u6808\u7684\u957f\u5ea6 */\nint size = stack.size();\n/* \u5224\u65ad\u662f\u5426\u4e3a\u7a7a */\nbool empty = stack.empty();\n</code></pre> stack.py<pre><code># \u521d\u59cb\u5316\u6808\n# Python \u6ca1\u6709\u5185\u7f6e\u7684\u6808\u7c7b\uff0c\u53ef\u4ee5\u628a List \u5f53\u4f5c\u6808\u6765\u4f7f\u7528 \nstack: List[int] = []\n# \u5143\u7d20\u5165\u6808\nstack.append(1)\nstack.append(3)\nstack.append(2)\nstack.append(5)\nstack.append(4)\n# \u8bbf\u95ee\u6808\u9876\u5143\u7d20\npeek: int = stack[-1]\n# \u5143\u7d20\u51fa\u6808\npop: int = stack.pop()\n# \u83b7\u53d6\u6808\u7684\u957f\u5ea6\nsize: int = len(stack)\n# \u5224\u65ad\u662f\u5426\u4e3a\u7a7a\nis_empty: bool = len(stack) == 0\n</code></pre> stack_test.go<pre><code>/* \u521d\u59cb\u5316\u6808 */\n// \u5728 Go \u4e2d\uff0c\u63a8\u8350\u5c06 Slice \u5f53\u4f5c\u6808\u6765\u4f7f\u7528\nvar stack []int\n/* \u5143\u7d20\u5165\u6808 */\nstack = append(stack, 1)\nstack = append(stack, 3)\nstack = append(stack, 2)\nstack = append(stack, 5)\nstack = append(stack, 4)\n/* \u8bbf\u95ee\u6808\u9876\u5143\u7d20 */\npeek := stack[len(stack)-1]\n/* \u5143\u7d20\u51fa\u6808 */\npop := stack[len(stack)-1]\nstack = stack[:len(stack)-1]\n/* \u83b7\u53d6\u6808\u7684\u957f\u5ea6 */\nsize := len(stack)\n/* \u5224\u65ad\u662f\u5426\u4e3a\u7a7a */\nisEmpty := len(stack) == 0\n</code></pre> stack.js<pre><code>/* \u521d\u59cb\u5316\u6808 */\n// Javascript \u6ca1\u6709\u5185\u7f6e\u7684\u6808\u7c7b\uff0c\u53ef\u4ee5\u628a Array \u5f53\u4f5c\u6808\u6765\u4f7f\u7528 \nconst stack = [];\n/* \u5143\u7d20\u5165\u6808 */\nstack.push(1);\nstack.push(3);\nstack.push(2);\nstack.push(5);\nstack.push(4);\n/* \u8bbf\u95ee\u6808\u9876\u5143\u7d20 */\nconst peek = stack[stack.length-1];\n/* \u5143\u7d20\u51fa\u6808 */\nconst pop = stack.pop();\n/* \u83b7\u53d6\u6808\u7684\u957f\u5ea6 */\nconst size = stack.length;\n/* \u5224\u65ad\u662f\u5426\u4e3a\u7a7a */\nconst is_empty = stack.length === 0;\n</code></pre> stack.ts<pre><code>/* \u521d\u59cb\u5316\u6808 */\n// Typescript \u6ca1\u6709\u5185\u7f6e\u7684\u6808\u7c7b\uff0c\u53ef\u4ee5\u628a Array \u5f53\u4f5c\u6808\u6765\u4f7f\u7528 \nconst stack: number[] = [];\n/* \u5143\u7d20\u5165\u6808 */\nstack.push(1);\nstack.push(3);\nstack.push(2);\nstack.push(5);\nstack.push(4);\n/* \u8bbf\u95ee\u6808\u9876\u5143\u7d20 */\nconst peek = stack[stack.length - 1];\n/* \u5143\u7d20\u51fa\u6808 */\nconst pop = stack.pop();\n/* \u83b7\u53d6\u6808\u7684\u957f\u5ea6 */\nconst size = stack.length;\n/* \u5224\u65ad\u662f\u5426\u4e3a\u7a7a */\nconst is_empty = stack.length === 0;\n</code></pre> stack.c<pre><code>// C \u672a\u63d0\u4f9b\u5185\u7f6e\u6808\n</code></pre> stack.cs<pre><code>/* \u521d\u59cb\u5316\u6808 */\nStack&lt;int&gt; stack = new ();\n/* \u5143\u7d20\u5165\u6808 */\nstack.Push(1);\nstack.Push(3);\nstack.Push(2);\nstack.Push(5);\nstack.Push(4);\n/* \u8bbf\u95ee\u6808\u9876\u5143\u7d20 */\nint peek = stack.Peek();\n/* \u5143\u7d20\u51fa\u6808 */\nint pop = stack.Pop();\n/* \u83b7\u53d6\u6808\u7684\u957f\u5ea6 */\nint size = stack.Count();\n/* \u5224\u65ad\u662f\u5426\u4e3a\u7a7a */\nbool isEmpty = stack.Count()==0;\n</code></pre> stack.swift<pre><code>/* \u521d\u59cb\u5316\u6808 */\n// Swift \u6ca1\u6709\u5185\u7f6e\u7684\u6808\u7c7b\uff0c\u53ef\u4ee5\u628a Array \u5f53\u4f5c\u6808\u6765\u4f7f\u7528\nvar stack: [Int] = []\n/* \u5143\u7d20\u5165\u6808 */\nstack.append(1)\nstack.append(3)\nstack.append(2)\nstack.append(5)\nstack.append(4)\n/* \u8bbf\u95ee\u6808\u9876\u5143\u7d20 */\nlet peek = stack.last!\n/* \u5143\u7d20\u51fa\u6808 */\nlet pop = stack.removeLast()\n/* \u83b7\u53d6\u6808\u7684\u957f\u5ea6 */\nlet size = stack.count\n/* \u5224\u65ad\u662f\u5426\u4e3a\u7a7a */\nlet isEmpty = stack.isEmpty\n</code></pre> stack.zig<pre><code>\n</code></pre> stack.dart<pre><code>/* \u521d\u59cb\u5316\u6808 */\n// Dart \u6ca1\u6709\u5185\u7f6e\u7684\u6808\u7c7b\uff0c\u53ef\u4ee5\u628a List \u5f53\u4f5c\u6808\u6765\u4f7f\u7528\nList&lt;int&gt; stack = [];\n/* \u5143\u7d20\u5165\u6808 */\nstack.add(1);\nstack.add(3);\nstack.add(2);\nstack.add(5);\nstack.add(4);\n/* \u8bbf\u95ee\u6808\u9876\u5143\u7d20 */\nint peek = stack.last;\n/* \u5143\u7d20\u51fa\u6808 */\nint pop = stack.removeLast();\n/* \u83b7\u53d6\u6808\u7684\u957f\u5ea6 */\nint size = stack.length;\n/* \u5224\u65ad\u662f\u5426\u4e3a\u7a7a */\nbool isEmpty = stack.isEmpty;\n</code></pre>"},{"location":"chapter_stack_and_queue/stack/#512","title":"5.1.2. \u00a0 \u6808\u7684\u5b9e\u73b0","text":"<p>\u4e3a\u4e86\u6df1\u5165\u4e86\u89e3\u6808\u7684\u8fd0\u884c\u673a\u5236\uff0c\u6211\u4eec\u6765\u5c1d\u8bd5\u81ea\u5df1\u5b9e\u73b0\u4e00\u4e2a\u6808\u7c7b\u3002</p> <p>\u6808\u9075\u5faa\u5148\u5165\u540e\u51fa\u7684\u539f\u5219\uff0c\u56e0\u6b64\u6211\u4eec\u53ea\u80fd\u5728\u6808\u9876\u6dfb\u52a0\u6216\u5220\u9664\u5143\u7d20\u3002\u7136\u800c\uff0c\u6570\u7ec4\u548c\u94fe\u8868\u90fd\u53ef\u4ee5\u5728\u4efb\u610f\u4f4d\u7f6e\u6dfb\u52a0\u548c\u5220\u9664\u5143\u7d20\uff0c\u56e0\u6b64\u6808\u53ef\u4ee5\u88ab\u89c6\u4e3a\u4e00\u79cd\u53d7\u9650\u5236\u7684\u6570\u7ec4\u6216\u94fe\u8868\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u6211\u4eec\u53ef\u4ee5\u201c\u5c4f\u853d\u201d\u6570\u7ec4\u6216\u94fe\u8868\u7684\u90e8\u5206\u65e0\u5173\u64cd\u4f5c\uff0c\u4f7f\u5176\u5bf9\u5916\u8868\u73b0\u7684\u903b\u8f91\u7b26\u5408\u6808\u7684\u7279\u6027\u3002</p>"},{"location":"chapter_stack_and_queue/stack/#_1","title":"\u57fa\u4e8e\u94fe\u8868\u7684\u5b9e\u73b0","text":"<p>\u4f7f\u7528\u94fe\u8868\u6765\u5b9e\u73b0\u6808\u65f6\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u94fe\u8868\u7684\u5934\u8282\u70b9\u89c6\u4e3a\u6808\u9876\uff0c\u5c3e\u8282\u70b9\u89c6\u4e3a\u6808\u5e95\u3002</p> <p>\u5bf9\u4e8e\u5165\u6808\u64cd\u4f5c\uff0c\u6211\u4eec\u53ea\u9700\u5c06\u5143\u7d20\u63d2\u5165\u94fe\u8868\u5934\u90e8\uff0c\u8fd9\u79cd\u8282\u70b9\u63d2\u5165\u65b9\u6cd5\u88ab\u79f0\u4e3a\u201c\u5934\u63d2\u6cd5\u201d\u3002\u800c\u5bf9\u4e8e\u51fa\u6808\u64cd\u4f5c\uff0c\u53ea\u9700\u5c06\u5934\u8282\u70b9\u4ece\u94fe\u8868\u4e2d\u5220\u9664\u5373\u53ef\u3002</p> LinkedListStackpush()pop() <p></p> <p></p> <p></p> <p>\u4ee5\u4e0b\u662f\u57fa\u4e8e\u94fe\u8868\u5b9e\u73b0\u6808\u7684\u793a\u4f8b\u4ee3\u7801\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart linkedlist_stack.java<pre><code>/* \u57fa\u4e8e\u94fe\u8868\u5b9e\u73b0\u7684\u6808 */\nclass LinkedListStack {\nprivate ListNode stackPeek; // \u5c06\u5934\u8282\u70b9\u4f5c\u4e3a\u6808\u9876\nprivate int stkSize = 0; // \u6808\u7684\u957f\u5ea6\npublic LinkedListStack() {\nstackPeek = null;\n}\n/* \u83b7\u53d6\u6808\u7684\u957f\u5ea6 */\npublic int size() {\nreturn stkSize;\n}\n/* \u5224\u65ad\u6808\u662f\u5426\u4e3a\u7a7a */\npublic boolean isEmpty() {\nreturn size() == 0;\n}\n/* \u5165\u6808 */\npublic void push(int num) {\nListNode node = new ListNode(num);\nnode.next = stackPeek;\nstackPeek = node;\nstkSize++;\n}\n/* \u51fa\u6808 */\npublic int pop() {\nint num = peek();\nstackPeek = stackPeek.next;\nstkSize--;\nreturn num;\n}\n/* \u8bbf\u95ee\u6808\u9876\u5143\u7d20 */\npublic int peek() {\nif (size() == 0)\nthrow new IndexOutOfBoundsException();\nreturn stackPeek.val;\n}\n/* \u5c06 List \u8f6c\u5316\u4e3a Array \u5e76\u8fd4\u56de */\npublic int[] toArray() {\nListNode node = stackPeek;\nint[] res = new int[size()];\nfor (int i = res.length - 1; i &gt;= 0; i--) {\nres[i] = node.val;\nnode = node.next;\n}\nreturn res;\n}\n}\n</code></pre> linkedlist_stack.cpp<pre><code>/* \u57fa\u4e8e\u94fe\u8868\u5b9e\u73b0\u7684\u6808 */\nclass LinkedListStack {\nprivate:\nListNode *stackTop; // \u5c06\u5934\u8282\u70b9\u4f5c\u4e3a\u6808\u9876\nint stkSize;        // \u6808\u7684\u957f\u5ea6\npublic:\nLinkedListStack() {\nstackTop = nullptr;\nstkSize = 0;\n}\n~LinkedListStack() {\n// \u904d\u5386\u94fe\u8868\u5220\u9664\u8282\u70b9\uff0c\u91ca\u653e\u5185\u5b58\nfreeMemoryLinkedList(stackTop);\n}\n/* \u83b7\u53d6\u6808\u7684\u957f\u5ea6 */\nint size() {\nreturn stkSize;\n}\n/* \u5224\u65ad\u6808\u662f\u5426\u4e3a\u7a7a */\nbool empty() {\nreturn size() == 0;\n}\n/* \u5165\u6808 */\nvoid push(int num) {\nListNode *node = new ListNode(num);\nnode-&gt;next = stackTop;\nstackTop = node;\nstkSize++;\n}\n/* \u51fa\u6808 */\nvoid pop() {\nint num = top();\nListNode *tmp = stackTop;\nstackTop = stackTop-&gt;next;\n// \u91ca\u653e\u5185\u5b58\ndelete tmp;\nstkSize--;\n}\n/* \u8bbf\u95ee\u6808\u9876\u5143\u7d20 */\nint top() {\nif (size() == 0)\nthrow out_of_range(\"\u6808\u4e3a\u7a7a\");\nreturn stackTop-&gt;val;\n}\n/* \u5c06 List \u8f6c\u5316\u4e3a Array \u5e76\u8fd4\u56de */\nvector&lt;int&gt; toVector() {\nListNode *node = stackTop;\nvector&lt;int&gt; res(size());\nfor (int i = res.size() - 1; i &gt;= 0; i--) {\nres[i] = node-&gt;val;\nnode = node-&gt;next;\n}\nreturn res;\n}\n};\n</code></pre> linkedlist_stack.py<pre><code>class LinkedListStack:\n\"\"\"\u57fa\u4e8e\u94fe\u8868\u5b9e\u73b0\u7684\u6808\"\"\"\ndef __init__(self):\n\"\"\"\u6784\u9020\u65b9\u6cd5\"\"\"\nself.__peek: ListNode | None = None\nself.__size: int = 0\ndef size(self) -&gt; int:\n\"\"\"\u83b7\u53d6\u6808\u7684\u957f\u5ea6\"\"\"\nreturn self.__size\ndef is_empty(self) -&gt; bool:\n\"\"\"\u5224\u65ad\u6808\u662f\u5426\u4e3a\u7a7a\"\"\"\nreturn not self.__peek\ndef push(self, val: int) -&gt; None:\n\"\"\"\u5165\u6808\"\"\"\nnode = ListNode(val)\nnode.next = self.__peek\nself.__peek = node\nself.__size += 1\ndef pop(self) -&gt; int:\n\"\"\"\u51fa\u6808\"\"\"\nnum: int = self.peek()\nself.__peek = self.__peek.next\nself.__size -= 1\nreturn num\ndef peek(self) -&gt; int:\n\"\"\"\u8bbf\u95ee\u6808\u9876\u5143\u7d20\"\"\"\n# \u5224\u7a7a\u5904\u7406\nif not self.__peek:\nreturn None\nreturn self.__peek.val\ndef to_list(self) -&gt; list[int]:\n\"\"\"\u8f6c\u5316\u4e3a\u5217\u8868\u7528\u4e8e\u6253\u5370\"\"\"\narr = []\nnode = self.__peek\nwhile node:\narr.append(node.val)\nnode = node.next\narr.reverse()\nreturn arr\n</code></pre> linkedlist_stack.go<pre><code>/* \u57fa\u4e8e\u94fe\u8868\u5b9e\u73b0\u7684\u6808 */\ntype linkedListStack struct {\n// \u4f7f\u7528\u5185\u7f6e\u5305 list \u6765\u5b9e\u73b0\u6808\ndata *list.List\n}\n/* \u521d\u59cb\u5316\u6808 */\nfunc newLinkedListStack() *linkedListStack {\nreturn &amp;linkedListStack{\ndata: list.New(),\n}\n}\n/* \u5165\u6808 */\nfunc (s *linkedListStack) push(value int) {\ns.data.PushBack(value)\n}\n/* \u51fa\u6808 */\nfunc (s *linkedListStack) pop() any {\nif s.isEmpty() {\nreturn nil\n}\ne := s.data.Back()\ns.data.Remove(e)\nreturn e.Value\n}\n/* \u8bbf\u95ee\u6808\u9876\u5143\u7d20 */\nfunc (s *linkedListStack) peek() any {\nif s.isEmpty() {\nreturn nil\n}\ne := s.data.Back()\nreturn e.Value\n}\n/* \u83b7\u53d6\u6808\u7684\u957f\u5ea6 */\nfunc (s *linkedListStack) size() int {\nreturn s.data.Len()\n}\n/* \u5224\u65ad\u6808\u662f\u5426\u4e3a\u7a7a */\nfunc (s *linkedListStack) isEmpty() bool {\nreturn s.data.Len() == 0\n}\n/* \u83b7\u53d6 List \u7528\u4e8e\u6253\u5370 */\nfunc (s *linkedListStack) toList() *list.List {\nreturn s.data\n}\n</code></pre> linkedlist_stack.js<pre><code>/* \u57fa\u4e8e\u94fe\u8868\u5b9e\u73b0\u7684\u6808 */\nclass LinkedListStack {\n#stackPeek; // \u5c06\u5934\u8282\u70b9\u4f5c\u4e3a\u6808\u9876\n#stkSize = 0; // \u6808\u7684\u957f\u5ea6\nconstructor() {\nthis.#stackPeek = null;\n}\n/* \u83b7\u53d6\u6808\u7684\u957f\u5ea6 */\nget size() {\nreturn this.#stkSize;\n}\n/* \u5224\u65ad\u6808\u662f\u5426\u4e3a\u7a7a */\nisEmpty() {\nreturn this.size == 0;\n}\n/* \u5165\u6808 */\npush(num) {\nconst node = new ListNode(num);\nnode.next = this.#stackPeek;\nthis.#stackPeek = node;\nthis.#stkSize++;\n}\n/* \u51fa\u6808 */\npop() {\nconst num = this.peek();\nthis.#stackPeek = this.#stackPeek.next;\nthis.#stkSize--;\nreturn num;\n}\n/* \u8bbf\u95ee\u6808\u9876\u5143\u7d20 */\npeek() {\nif (!this.#stackPeek) throw new Error('\u6808\u4e3a\u7a7a');\nreturn this.#stackPeek.val;\n}\n/* \u5c06\u94fe\u8868\u8f6c\u5316\u4e3a Array \u5e76\u8fd4\u56de */\ntoArray() {\nlet node = this.#stackPeek;\nconst res = new Array(this.size);\nfor (let i = res.length - 1; i &gt;= 0; i--) {\nres[i] = node.val;\nnode = node.next;\n}\nreturn res;\n}\n}\n</code></pre> linkedlist_stack.ts<pre><code>/* \u57fa\u4e8e\u94fe\u8868\u5b9e\u73b0\u7684\u6808 */\nclass LinkedListStack {\nprivate stackPeek: ListNode | null; // \u5c06\u5934\u8282\u70b9\u4f5c\u4e3a\u6808\u9876\nprivate stkSize: number = 0; // \u6808\u7684\u957f\u5ea6\nconstructor() {\nthis.stackPeek = null;\n}\n/* \u83b7\u53d6\u6808\u7684\u957f\u5ea6 */\nget size(): number {\nreturn this.stkSize;\n}\n/* \u5224\u65ad\u6808\u662f\u5426\u4e3a\u7a7a */\nisEmpty(): boolean {\nreturn this.size == 0;\n}\n/* \u5165\u6808 */\npush(num: number): void {\nconst node = new ListNode(num);\nnode.next = this.stackPeek;\nthis.stackPeek = node;\nthis.stkSize++;\n}\n/* \u51fa\u6808 */\npop(): number {\nconst num = this.peek();\nif (!this.stackPeek) throw new Error('\u6808\u4e3a\u7a7a');\nthis.stackPeek = this.stackPeek.next;\nthis.stkSize--;\nreturn num;\n}\n/* \u8bbf\u95ee\u6808\u9876\u5143\u7d20 */\npeek(): number {\nif (!this.stackPeek) throw new Error('\u6808\u4e3a\u7a7a');\nreturn this.stackPeek.val;\n}\n/* \u5c06\u94fe\u8868\u8f6c\u5316\u4e3a Array \u5e76\u8fd4\u56de */\ntoArray(): number[] {\nlet node = this.stackPeek;\nconst res = new Array&lt;number&gt;(this.size);\nfor (let i = res.length - 1; i &gt;= 0; i--) {\nres[i] = node!.val;\nnode = node!.next;\n}\nreturn res;\n}\n}\n</code></pre> linkedlist_stack.c<pre><code>/* \u57fa\u4e8e\u94fe\u8868\u5b9e\u73b0\u7684\u6808 */\nstruct linkedListStack {\nListNode *top; // \u5c06\u5934\u8282\u70b9\u4f5c\u4e3a\u6808\u9876\nint size;      // \u6808\u7684\u957f\u5ea6\n};\ntypedef struct linkedListStack linkedListStack;\n/* \u6784\u9020\u51fd\u6570 */\nlinkedListStack *newLinkedListStack() {\nlinkedListStack *s = malloc(sizeof(linkedListStack));\ns-&gt;top = NULL;\ns-&gt;size = 0;\nreturn s;\n}\n/* \u6790\u6784\u51fd\u6570 */\nvoid delLinkedListStack(linkedListStack *s) {\nwhile (s-&gt;top) {\nListNode *n = s-&gt;top-&gt;next;\nfree(s-&gt;top);\ns-&gt;top = n;\n}\nfree(s);\n}\n/* \u83b7\u53d6\u6808\u7684\u957f\u5ea6 */\nint size(linkedListStack *s) {\nassert(s);\nreturn s-&gt;size;\n}\n/* \u5224\u65ad\u6808\u662f\u5426\u4e3a\u7a7a */\nbool isEmpty(linkedListStack *s) {\nassert(s);\nreturn size(s) == 0;\n}\n/* \u8bbf\u95ee\u6808\u9876\u5143\u7d20 */\nint peek(linkedListStack *s) {\nassert(s);\nassert(size(s) != 0);\nreturn s-&gt;top-&gt;val;\n}\n/* \u5165\u6808 */\nvoid push(linkedListStack *s, int num) {\nassert(s);\nListNode *node = (ListNode *)malloc(sizeof(ListNode));\nnode-&gt;next = s-&gt;top; // \u66f4\u65b0\u65b0\u52a0\u8282\u70b9\u6307\u9488\u57df\nnode-&gt;val = num;     // \u66f4\u65b0\u65b0\u52a0\u8282\u70b9\u6570\u636e\u57df\ns-&gt;top = node;       // \u66f4\u65b0\u6808\u9876\ns-&gt;size++;           // \u66f4\u65b0\u6808\u5927\u5c0f\n}\n/* \u51fa\u6808 */\nint pop(linkedListStack *s) {\nif (s-&gt;size == 0) {\nprintf(\"stack is empty.\\n\");\nreturn INT_MAX;\n}\nassert(s);\nint val = peek(s);\nListNode *tmp = s-&gt;top;\ns-&gt;top = s-&gt;top-&gt;next;\n// \u91ca\u653e\u5185\u5b58\nfree(tmp);\ns-&gt;size--;\nreturn val;\n}\n</code></pre> linkedlist_stack.cs<pre><code>/* \u57fa\u4e8e\u94fe\u8868\u5b9e\u73b0\u7684\u6808 */\nclass LinkedListStack {\nprivate ListNode? stackPeek;  // \u5c06\u5934\u8282\u70b9\u4f5c\u4e3a\u6808\u9876\nprivate int stkSize = 0;   // \u6808\u7684\u957f\u5ea6\npublic LinkedListStack() {\nstackPeek = null;\n}\n/* \u83b7\u53d6\u6808\u7684\u957f\u5ea6 */\npublic int size() {\nreturn stkSize;\n}\n/* \u5224\u65ad\u6808\u662f\u5426\u4e3a\u7a7a */\npublic bool isEmpty() {\nreturn size() == 0;\n}\n/* \u5165\u6808 */\npublic void push(int num) {\nListNode node = new ListNode(num);\nnode.next = stackPeek;\nstackPeek = node;\nstkSize++;\n}\n/* \u51fa\u6808 */\npublic int pop() {\nif (stackPeek == null)\nthrow new Exception();\nint num = peek();\nstackPeek = stackPeek.next;\nstkSize--;\nreturn num;\n}\n/* \u8bbf\u95ee\u6808\u9876\u5143\u7d20 */\npublic int peek() {\nif (size() == 0 || stackPeek == null)\nthrow new Exception();\nreturn stackPeek.val;\n}\n/* \u5c06 List \u8f6c\u5316\u4e3a Array \u5e76\u8fd4\u56de */\npublic int[] toArray() {\nif (stackPeek == null)\nreturn Array.Empty&lt;int&gt;();\nListNode node = stackPeek;\nint[] res = new int[size()];\nfor (int i = res.Length - 1; i &gt;= 0; i--) {\nres[i] = node.val;\nnode = node.next;\n}\nreturn res;\n}\n}\n</code></pre> linkedlist_stack.swift<pre><code>/* \u57fa\u4e8e\u94fe\u8868\u5b9e\u73b0\u7684\u6808 */\nclass LinkedListStack {\nprivate var _peek: ListNode? // \u5c06\u5934\u8282\u70b9\u4f5c\u4e3a\u6808\u9876\nprivate var _size = 0 // \u6808\u7684\u957f\u5ea6\ninit() {}\n/* \u83b7\u53d6\u6808\u7684\u957f\u5ea6 */\nfunc size() -&gt; Int {\n_size\n}\n/* \u5224\u65ad\u6808\u662f\u5426\u4e3a\u7a7a */\nfunc isEmpty() -&gt; Bool {\nsize() == 0\n}\n/* \u5165\u6808 */\nfunc push(num: Int) {\nlet node = ListNode(x: num)\nnode.next = _peek\n_peek = node\n_size += 1\n}\n/* \u51fa\u6808 */\n@discardableResult\nfunc pop() -&gt; Int {\nlet num = peek()\n_peek = _peek?.next\n_size -= 1\nreturn num\n}\n/* \u8bbf\u95ee\u6808\u9876\u5143\u7d20 */\nfunc peek() -&gt; Int {\nif isEmpty() {\nfatalError(\"\u6808\u4e3a\u7a7a\")\n}\nreturn _peek!.val\n}\n/* \u5c06 List \u8f6c\u5316\u4e3a Array \u5e76\u8fd4\u56de */\nfunc toArray() -&gt; [Int] {\nvar node = _peek\nvar res = Array(repeating: 0, count: _size)\nfor i in sequence(first: res.count - 1, next: { $0 &gt;= 0 + 1 ? $0 - 1 : nil }) {\nres[i] = node!.val\nnode = node?.next\n}\nreturn res\n}\n}\n</code></pre> linkedlist_stack.zig<pre><code>// \u57fa\u4e8e\u94fe\u8868\u5b9e\u73b0\u7684\u6808\nfn LinkedListStack(comptime T: type) type {\nreturn struct {\nconst Self = @This();\nstack_top: ?*inc.ListNode(T) = null,             // \u5c06\u5934\u8282\u70b9\u4f5c\u4e3a\u6808\u9876\nstk_size: usize = 0,                             // \u6808\u7684\u957f\u5ea6\nmem_arena: ?std.heap.ArenaAllocator = null,\nmem_allocator: std.mem.Allocator = undefined,   // \u5185\u5b58\u5206\u914d\u5668\n// \u6784\u9020\u65b9\u6cd5\uff08\u5206\u914d\u5185\u5b58+\u521d\u59cb\u5316\u6808\uff09\npub fn init(self: *Self, allocator: std.mem.Allocator) !void {\nif (self.mem_arena == null) {\nself.mem_arena = std.heap.ArenaAllocator.init(allocator);\nself.mem_allocator = self.mem_arena.?.allocator();\n}\nself.stack_top = null;\nself.stk_size = 0;\n}\n// \u6790\u6784\u65b9\u6cd5\uff08\u91ca\u653e\u5185\u5b58\uff09\npub fn deinit(self: *Self) void {\nif (self.mem_arena == null) return;\nself.mem_arena.?.deinit();\n}\n// \u83b7\u53d6\u6808\u7684\u957f\u5ea6\npub fn size(self: *Self) usize {\nreturn self.stk_size;\n}\n// \u5224\u65ad\u6808\u662f\u5426\u4e3a\u7a7a\npub fn isEmpty(self: *Self) bool {\nreturn self.size() == 0;\n}\n// \u8bbf\u95ee\u6808\u9876\u5143\u7d20\npub fn peek(self: *Self) T {\nif (self.size() == 0) @panic(\"\u6808\u4e3a\u7a7a\");\nreturn self.stack_top.?.val;\n}  // \u5165\u6808\npub fn push(self: *Self, num: T) !void {\nvar node = try self.mem_allocator.create(inc.ListNode(T));\nnode.init(num);\nnode.next = self.stack_top;\nself.stack_top = node;\nself.stk_size += 1;\n} // \u51fa\u6808\npub fn pop(self: *Self) T {\nvar num = self.peek();\nself.stack_top = self.stack_top.?.next;\nself.stk_size -= 1;\nreturn num;\n} // \u5c06\u6808\u8f6c\u6362\u4e3a\u6570\u7ec4\npub fn toArray(self: *Self) ![]T {\nvar node = self.stack_top;\nvar res = try self.mem_allocator.alloc(T, self.size());\nstd.mem.set(T, res, @as(T, 0));\nvar i: usize = 0;\nwhile (i &lt; res.len) : (i += 1) {\nres[res.len - i - 1] = node.?.val;\nnode = node.?.next;\n}\nreturn res;\n}\n};\n}\n</code></pre> linkedlist_stack.dart<pre><code>/* \u57fa\u4e8e\u94fe\u8868\u7c7b\u5b9e\u73b0\u7684\u6808 */\nclass LinkedListStack {\nListNode? _stackPeek; // \u5c06\u5934\u8282\u70b9\u4f5c\u4e3a\u6808\u9876\nint _stkSize = 0; // \u6808\u7684\u957f\u5ea6\nLinkedListStack() {\n_stackPeek = null;\n}\n/* \u83b7\u53d6\u6808\u7684\u957f\u5ea6 */\nint size() {\nreturn _stkSize;\n}\n/* \u5224\u65ad\u6808\u662f\u5426\u4e3a\u7a7a */\nbool isEmpty() {\nreturn _stkSize == 0;\n}\n/* \u5165\u6808 */\nvoid push(int num) {\nfinal ListNode node = ListNode(num);\nnode.next = _stackPeek;\n_stackPeek = node;\n_stkSize++;\n}\n/* \u51fa\u6808 */\nint pop() {\nfinal int num = peek();\n_stackPeek = _stackPeek!.next;\n_stkSize--;\nreturn num;\n}\n/* \u8bbf\u95ee\u6808\u9876\u5143\u7d20 */\nint peek() {\nif (_stackPeek == null) {\nthrow Exception(\"\u6808\u4e3a\u7a7a\");\n}\nreturn _stackPeek!.val;\n}\n/* \u5c06\u94fe\u8868\u8f6c\u5316\u4e3a List \u5e76\u8fd4\u56de */\nList&lt;int&gt; toList() {\nListNode? node = _stackPeek;\nList&lt;int&gt; list = [];\nwhile (node != null) {\nlist.add(node.val);\nnode = node.next;\n}\nlist = list.reversed.toList();\nreturn list;\n}\n}\n</code></pre>"},{"location":"chapter_stack_and_queue/stack/#_2","title":"\u57fa\u4e8e\u6570\u7ec4\u7684\u5b9e\u73b0","text":"<p>\u5728\u57fa\u4e8e\u300c\u6570\u7ec4\u300d\u5b9e\u73b0\u6808\u65f6\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u6570\u7ec4\u7684\u5c3e\u90e8\u4f5c\u4e3a\u6808\u9876\u3002\u5728\u8fd9\u6837\u7684\u8bbe\u8ba1\u4e0b\uff0c\u5165\u6808\u4e0e\u51fa\u6808\u64cd\u4f5c\u5c31\u5206\u522b\u5bf9\u5e94\u5728\u6570\u7ec4\u5c3e\u90e8\u6dfb\u52a0\u5143\u7d20\u4e0e\u5220\u9664\u5143\u7d20\uff0c\u65f6\u95f4\u590d\u6742\u5ea6\u90fd\u4e3a \\(O(1)\\) \u3002</p> ArrayStackpush()pop() <p></p> <p></p> <p></p> <p>\u7531\u4e8e\u5165\u6808\u7684\u5143\u7d20\u53ef\u80fd\u4f1a\u6e90\u6e90\u4e0d\u65ad\u5730\u589e\u52a0\uff0c\u56e0\u6b64\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u52a8\u6001\u6570\u7ec4\uff0c\u8fd9\u6837\u5c31\u65e0\u9700\u81ea\u884c\u5904\u7406\u6570\u7ec4\u6269\u5bb9\u95ee\u9898\u3002\u4ee5\u4e0b\u4e3a\u793a\u4f8b\u4ee3\u7801\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart array_stack.java<pre><code>/* \u57fa\u4e8e\u6570\u7ec4\u5b9e\u73b0\u7684\u6808 */\nclass ArrayStack {\nprivate ArrayList&lt;Integer&gt; stack;\npublic ArrayStack() {\n// \u521d\u59cb\u5316\u5217\u8868\uff08\u52a8\u6001\u6570\u7ec4\uff09\nstack = new ArrayList&lt;&gt;();\n}\n/* \u83b7\u53d6\u6808\u7684\u957f\u5ea6 */\npublic int size() {\nreturn stack.size();\n}\n/* \u5224\u65ad\u6808\u662f\u5426\u4e3a\u7a7a */\npublic boolean isEmpty() {\nreturn size() == 0;\n}\n/* \u5165\u6808 */\npublic void push(int num) {\nstack.add(num);\n}\n/* \u51fa\u6808 */\npublic int pop() {\nif (isEmpty())\nthrow new IndexOutOfBoundsException();\nreturn stack.remove(size() - 1);\n}\n/* \u8bbf\u95ee\u6808\u9876\u5143\u7d20 */\npublic int peek() {\nif (isEmpty())\nthrow new IndexOutOfBoundsException();\nreturn stack.get(size() - 1);\n}\n/* \u5c06 List \u8f6c\u5316\u4e3a Array \u5e76\u8fd4\u56de */\npublic Object[] toArray() {\nreturn stack.toArray();\n}\n}\n</code></pre> array_stack.cpp<pre><code>/* \u57fa\u4e8e\u6570\u7ec4\u5b9e\u73b0\u7684\u6808 */\nclass ArrayStack {\nprivate:\nvector&lt;int&gt; stack;\npublic:\n/* \u83b7\u53d6\u6808\u7684\u957f\u5ea6 */\nint size() {\nreturn stack.size();\n}\n/* \u5224\u65ad\u6808\u662f\u5426\u4e3a\u7a7a */\nbool empty() {\nreturn stack.empty();\n}\n/* \u5165\u6808 */\nvoid push(int num) {\nstack.push_back(num);\n}\n/* \u51fa\u6808 */\nvoid pop() {\nint oldTop = top();\nstack.pop_back();\n}\n/* \u8bbf\u95ee\u6808\u9876\u5143\u7d20 */\nint top() {\nif (empty())\nthrow out_of_range(\"\u6808\u4e3a\u7a7a\");\nreturn stack.back();\n}\n/* \u8fd4\u56de Vector */\nvector&lt;int&gt; toVector() {\nreturn stack;\n}\n};\n</code></pre> array_stack.py<pre><code>class ArrayStack:\n\"\"\"\u57fa\u4e8e\u6570\u7ec4\u5b9e\u73b0\u7684\u6808\"\"\"\ndef __init__(self) -&gt; None:\n\"\"\"\u6784\u9020\u65b9\u6cd5\"\"\"\nself.__stack: list[int] = []\ndef size(self) -&gt; int:\n\"\"\"\u83b7\u53d6\u6808\u7684\u957f\u5ea6\"\"\"\nreturn len(self.__stack)\ndef is_empty(self) -&gt; bool:\n\"\"\"\u5224\u65ad\u6808\u662f\u5426\u4e3a\u7a7a\"\"\"\nreturn self.__stack == []\ndef push(self, item: int) -&gt; None:\n\"\"\"\u5165\u6808\"\"\"\nself.__stack.append(item)\ndef pop(self) -&gt; int:\n\"\"\"\u51fa\u6808\"\"\"\nif self.is_empty():\nraise IndexError(\"\u6808\u4e3a\u7a7a\")\nreturn self.__stack.pop()\ndef peek(self) -&gt; int:\n\"\"\"\u8bbf\u95ee\u6808\u9876\u5143\u7d20\"\"\"\nif self.is_empty():\nraise IndexError(\"\u6808\u4e3a\u7a7a\")\nreturn self.__stack[-1]\ndef to_list(self) -&gt; list[int]:\n\"\"\"\u8fd4\u56de\u5217\u8868\u7528\u4e8e\u6253\u5370\"\"\"\nreturn self.__stack\n</code></pre> array_stack.go<pre><code>/* \u57fa\u4e8e\u6570\u7ec4\u5b9e\u73b0\u7684\u6808 */\ntype arrayStack struct {\ndata []int // \u6570\u636e\n}\n/* \u521d\u59cb\u5316\u6808 */\nfunc newArrayStack() *arrayStack {\nreturn &amp;arrayStack{\n// \u8bbe\u7f6e\u6808\u7684\u957f\u5ea6\u4e3a 0\uff0c\u5bb9\u91cf\u4e3a 16\ndata: make([]int, 0, 16),\n}\n}\n/* \u6808\u7684\u957f\u5ea6 */\nfunc (s *arrayStack) size() int {\nreturn len(s.data)\n}\n/* \u6808\u662f\u5426\u4e3a\u7a7a */\nfunc (s *arrayStack) isEmpty() bool {\nreturn s.size() == 0\n}\n/* \u5165\u6808 */\nfunc (s *arrayStack) push(v int) {\n// \u5207\u7247\u4f1a\u81ea\u52a8\u6269\u5bb9\ns.data = append(s.data, v)\n}\n/* \u51fa\u6808 */\nfunc (s *arrayStack) pop() any {\nval := s.peek()\ns.data = s.data[:len(s.data)-1]\nreturn val\n}\n/* \u83b7\u53d6\u6808\u9876\u5143\u7d20 */\nfunc (s *arrayStack) peek() any {\nif s.isEmpty() {\nreturn nil\n}\nval := s.data[len(s.data)-1]\nreturn val\n}\n/* \u83b7\u53d6 Slice \u7528\u4e8e\u6253\u5370 */\nfunc (s *arrayStack) toSlice() []int {\nreturn s.data\n}\n</code></pre> array_stack.js<pre><code>/* \u57fa\u4e8e\u6570\u7ec4\u5b9e\u73b0\u7684\u6808 */\nclass ArrayStack {\n#stack;\nconstructor() {\nthis.#stack = [];\n}\n/* \u83b7\u53d6\u6808\u7684\u957f\u5ea6 */\nget size() {\nreturn this.#stack.length;\n}\n/* \u5224\u65ad\u6808\u662f\u5426\u4e3a\u7a7a */\nempty() {\nreturn this.#stack.length === 0;\n}\n/* \u5165\u6808 */\npush(num) {\nthis.#stack.push(num);\n}\n/* \u51fa\u6808 */\npop() {\nif (this.empty()) throw new Error('\u6808\u4e3a\u7a7a');\nreturn this.#stack.pop();\n}\n/* \u8bbf\u95ee\u6808\u9876\u5143\u7d20 */\ntop() {\nif (this.empty()) throw new Error('\u6808\u4e3a\u7a7a');\nreturn this.#stack[this.#stack.length - 1];\n}\n/* \u8fd4\u56de Array */\ntoArray() {\nreturn this.#stack;\n}\n}\n</code></pre> array_stack.ts<pre><code>/* \u57fa\u4e8e\u6570\u7ec4\u5b9e\u73b0\u7684\u6808 */\nclass ArrayStack {\nprivate stack: number[];\nconstructor() {\nthis.stack = [];\n}\n/* \u83b7\u53d6\u6808\u7684\u957f\u5ea6 */\nget size(): number {\nreturn this.stack.length;\n}\n/* \u5224\u65ad\u6808\u662f\u5426\u4e3a\u7a7a */\nempty(): boolean {\nreturn this.stack.length === 0;\n}\n/* \u5165\u6808 */\npush(num: number): void {\nthis.stack.push(num);\n}\n/* \u51fa\u6808 */\npop(): number | undefined {\nif (this.empty()) throw new Error('\u6808\u4e3a\u7a7a');\nreturn this.stack.pop();\n}\n/* \u8bbf\u95ee\u6808\u9876\u5143\u7d20 */\ntop(): number | undefined {\nif (this.empty()) throw new Error('\u6808\u4e3a\u7a7a');\nreturn this.stack[this.stack.length - 1];\n}\n/* \u8fd4\u56de Array */\ntoArray() {\nreturn this.stack;\n}\n}\n</code></pre> array_stack.c<pre><code>/* \u57fa\u4e8e\u6570\u7ec4\u5b9e\u73b0\u7684\u6808 */\nstruct arrayStack {\nint *data;\nint size;\n};\ntypedef struct arrayStack arrayStack;\n/* \u6784\u9020\u51fd\u6570 */\narrayStack *newArrayStack() {\narrayStack *s = malloc(sizeof(arrayStack));\n// \u521d\u59cb\u5316\u4e00\u4e2a\u5927\u5bb9\u91cf\uff0c\u907f\u514d\u6269\u5bb9\ns-&gt;data = malloc(sizeof(int) * MAX_SIZE);\ns-&gt;size = 0;\nreturn s;\n}\n/* \u83b7\u53d6\u6808\u7684\u957f\u5ea6 */\nint size(arrayStack *s) {\nreturn s-&gt;size;\n}\n/* \u5224\u65ad\u6808\u662f\u5426\u4e3a\u7a7a */\nbool isEmpty(arrayStack *s) {\nreturn s-&gt;size == 0;\n}\n/* \u5165\u6808 */\nvoid push(arrayStack *s, int num) {\nif (s-&gt;size == MAX_SIZE) {\nprintf(\"stack is full.\\n\");\nreturn;\n}\ns-&gt;data[s-&gt;size] = num;\ns-&gt;size++;\n}\n/* \u8bbf\u95ee\u6808\u9876\u5143\u7d20 */\nint peek(arrayStack *s) {\nif (s-&gt;size == 0) {\nprintf(\"stack is empty.\\n\");\nreturn INT_MAX;\n}\nreturn s-&gt;data[s-&gt;size - 1];\n}\n/* \u51fa\u6808 */\nint pop(arrayStack *s) {\nif (s-&gt;size == 0) {\nprintf(\"stack is empty.\\n\");\nreturn INT_MAX;\n}\nint val = peek(s);\ns-&gt;size--;\nreturn val;\n}\n</code></pre> array_stack.cs<pre><code>/* \u57fa\u4e8e\u6570\u7ec4\u5b9e\u73b0\u7684\u6808 */\nclass ArrayStack {\nprivate List&lt;int&gt; stack;\npublic ArrayStack() {\n// \u521d\u59cb\u5316\u5217\u8868\uff08\u52a8\u6001\u6570\u7ec4\uff09\nstack = new();\n}\n/* \u83b7\u53d6\u6808\u7684\u957f\u5ea6 */\npublic int size() {\nreturn stack.Count();\n}\n/* \u5224\u65ad\u6808\u662f\u5426\u4e3a\u7a7a */\npublic bool isEmpty() {\nreturn size() == 0;\n}\n/* \u5165\u6808 */\npublic void push(int num) {\nstack.Add(num);\n}\n/* \u51fa\u6808 */\npublic int pop() {\nif (isEmpty())\nthrow new Exception();\nvar val = peek();\nstack.RemoveAt(size() - 1);\nreturn val;\n}\n/* \u8bbf\u95ee\u6808\u9876\u5143\u7d20 */\npublic int peek() {\nif (isEmpty())\nthrow new Exception();\nreturn stack[size() - 1];\n}\n/* \u5c06 List \u8f6c\u5316\u4e3a Array \u5e76\u8fd4\u56de */\npublic int[] toArray() {\nreturn stack.ToArray();\n}\n}\n</code></pre> array_stack.swift<pre><code>/* \u57fa\u4e8e\u6570\u7ec4\u5b9e\u73b0\u7684\u6808 */\nclass ArrayStack {\nprivate var stack: [Int]\ninit() {\n// \u521d\u59cb\u5316\u5217\u8868\uff08\u52a8\u6001\u6570\u7ec4\uff09\nstack = []\n}\n/* \u83b7\u53d6\u6808\u7684\u957f\u5ea6 */\nfunc size() -&gt; Int {\nstack.count\n}\n/* \u5224\u65ad\u6808\u662f\u5426\u4e3a\u7a7a */\nfunc isEmpty() -&gt; Bool {\nstack.isEmpty\n}\n/* \u5165\u6808 */\nfunc push(num: Int) {\nstack.append(num)\n}\n/* \u51fa\u6808 */\n@discardableResult\nfunc pop() -&gt; Int {\nif isEmpty() {\nfatalError(\"\u6808\u4e3a\u7a7a\")\n}\nreturn stack.removeLast()\n}\n/* \u8bbf\u95ee\u6808\u9876\u5143\u7d20 */\nfunc peek() -&gt; Int {\nif isEmpty() {\nfatalError(\"\u6808\u4e3a\u7a7a\")\n}\nreturn stack.last!\n}\n/* \u5c06 List \u8f6c\u5316\u4e3a Array \u5e76\u8fd4\u56de */\nfunc toArray() -&gt; [Int] {\nstack\n}\n}\n</code></pre> array_stack.zig<pre><code>// \u57fa\u4e8e\u6570\u7ec4\u5b9e\u73b0\u7684\u6808\nfn ArrayStack(comptime T: type) type {\nreturn struct {\nconst Self = @This();\nstack: ?std.ArrayList(T) = null,     // \u6784\u9020\u65b9\u6cd5\uff08\u5206\u914d\u5185\u5b58+\u521d\u59cb\u5316\u6808\uff09\npub fn init(self: *Self, allocator: std.mem.Allocator) void {\nif (self.stack == null) {\nself.stack = std.ArrayList(T).init(allocator);\n}\n}\n// \u6790\u6784\u65b9\u6cd5\uff08\u91ca\u653e\u5185\u5b58\uff09\npub fn deinit(self: *Self) void {\nif (self.stack == null) return;\nself.stack.?.deinit();\n}\n// \u83b7\u53d6\u6808\u7684\u957f\u5ea6\npub fn size(self: *Self) usize {\nreturn self.stack.?.items.len;\n}\n// \u5224\u65ad\u6808\u662f\u5426\u4e3a\u7a7a\npub fn isEmpty(self: *Self) bool {\nreturn self.size() == 0;\n}\n// \u8bbf\u95ee\u6808\u9876\u5143\u7d20\npub fn peek(self: *Self) T {\nif (self.isEmpty()) @panic(\"\u6808\u4e3a\u7a7a\");\nreturn self.stack.?.items[self.size() - 1];\n}  // \u5165\u6808\npub fn push(self: *Self, num: T) !void {\ntry self.stack.?.append(num);\n} // \u51fa\u6808\npub fn pop(self: *Self) T {\nvar num = self.stack.?.pop();\nreturn num;\n} // \u8fd4\u56de ArrayList\npub fn toList(self: *Self) std.ArrayList(T) {\nreturn self.stack.?;\n}\n};\n}\n</code></pre> array_stack.dart<pre><code>/* \u57fa\u4e8e\u6570\u7ec4\u5b9e\u73b0\u7684\u6808 */\nclass ArrayStack {\nlate List&lt;int&gt; _stack;\nArrayStack() {\n_stack = [];\n}\n/* \u83b7\u53d6\u6808\u7684\u957f\u5ea6 */\nint size() {\nreturn _stack.length;\n}\n/* \u5224\u65ad\u6808\u662f\u5426\u4e3a\u7a7a */\nbool isEmpty() {\nreturn _stack.isEmpty;\n}\n/* \u5165\u6808 */\nvoid push(int num) {\n_stack.add(num);\n}\n/* \u51fa\u6808 */\nint pop() {\nif (isEmpty()) {\nthrow Exception(\"\u6808\u4e3a\u7a7a\");\n}\nreturn _stack.removeLast();\n}\n/* \u8bbf\u95ee\u6808\u9876\u5143\u7d20 */\nint peek() {\nif (isEmpty()) {\nthrow Exception(\"\u6808\u4e3a\u7a7a\");\n}\nreturn _stack.last;\n}\n/* \u5c06\u6808\u8f6c\u5316\u4e3a Array \u5e76\u8fd4\u56de */\nList&lt;int&gt; toArray() =&gt; _stack;\n}\n</code></pre>"},{"location":"chapter_stack_and_queue/stack/#513","title":"5.1.3. \u00a0 \u4e24\u79cd\u5b9e\u73b0\u5bf9\u6bd4","text":""},{"location":"chapter_stack_and_queue/stack/#_3","title":"\u652f\u6301\u64cd\u4f5c","text":"<p>\u4e24\u79cd\u5b9e\u73b0\u90fd\u652f\u6301\u6808\u5b9a\u4e49\u4e2d\u7684\u5404\u9879\u64cd\u4f5c\u3002\u6570\u7ec4\u5b9e\u73b0\u989d\u5916\u652f\u6301\u968f\u673a\u8bbf\u95ee\uff0c\u4f46\u8fd9\u5df2\u8d85\u51fa\u4e86\u6808\u7684\u5b9a\u4e49\u8303\u7574\uff0c\u56e0\u6b64\u4e00\u822c\u4e0d\u4f1a\u7528\u5230\u3002</p>"},{"location":"chapter_stack_and_queue/stack/#_4","title":"\u65f6\u95f4\u6548\u7387","text":"<p>\u5728\u57fa\u4e8e\u6570\u7ec4\u7684\u5b9e\u73b0\u4e2d\uff0c\u5165\u6808\u548c\u51fa\u6808\u64cd\u4f5c\u90fd\u662f\u5728\u9884\u5148\u5206\u914d\u597d\u7684\u8fde\u7eed\u5185\u5b58\u4e2d\u8fdb\u884c\uff0c\u5177\u6709\u5f88\u597d\u7684\u7f13\u5b58\u672c\u5730\u6027\uff0c\u56e0\u6b64\u6548\u7387\u8f83\u9ad8\u3002\u7136\u800c\uff0c\u5982\u679c\u5165\u6808\u65f6\u8d85\u51fa\u6570\u7ec4\u5bb9\u91cf\uff0c\u4f1a\u89e6\u53d1\u6269\u5bb9\u673a\u5236\uff0c\u5bfc\u81f4\u8be5\u6b21\u5165\u6808\u64cd\u4f5c\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u53d8\u4e3a \\(O(n)\\) \u3002</p> <p>\u5728\u94fe\u8868\u5b9e\u73b0\u4e2d\uff0c\u94fe\u8868\u7684\u6269\u5bb9\u975e\u5e38\u7075\u6d3b\uff0c\u4e0d\u5b58\u5728\u4e0a\u8ff0\u6570\u7ec4\u6269\u5bb9\u65f6\u6548\u7387\u964d\u4f4e\u7684\u95ee\u9898\u3002\u4f46\u662f\uff0c\u5165\u6808\u64cd\u4f5c\u9700\u8981\u521d\u59cb\u5316\u8282\u70b9\u5bf9\u8c61\u5e76\u4fee\u6539\u6307\u9488\uff0c\u56e0\u6b64\u6548\u7387\u76f8\u5bf9\u8f83\u4f4e\u3002\u4e0d\u8fc7\uff0c\u5982\u679c\u5165\u6808\u5143\u7d20\u672c\u8eab\u5c31\u662f\u8282\u70b9\u5bf9\u8c61\uff0c\u90a3\u4e48\u53ef\u4ee5\u7701\u53bb\u521d\u59cb\u5316\u6b65\u9aa4\uff0c\u4ece\u800c\u63d0\u9ad8\u6548\u7387\u3002</p> <p>\u7efc\u4e0a\u6240\u8ff0\uff0c\u5f53\u5165\u6808\u4e0e\u51fa\u6808\u64cd\u4f5c\u7684\u5143\u7d20\u662f\u57fa\u672c\u6570\u636e\u7c7b\u578b\uff08\u5982 <code>int</code> , <code>double</code> \uff09\u65f6\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u51fa\u4ee5\u4e0b\u7ed3\u8bba\uff1a</p> <ul> <li>\u57fa\u4e8e\u6570\u7ec4\u5b9e\u73b0\u7684\u6808\u5728\u89e6\u53d1\u6269\u5bb9\u65f6\u6548\u7387\u4f1a\u964d\u4f4e\uff0c\u4f46\u7531\u4e8e\u6269\u5bb9\u662f\u4f4e\u9891\u64cd\u4f5c\uff0c\u56e0\u6b64\u5e73\u5747\u6548\u7387\u66f4\u9ad8\uff1b</li> <li>\u57fa\u4e8e\u94fe\u8868\u5b9e\u73b0\u7684\u6808\u53ef\u4ee5\u63d0\u4f9b\u66f4\u52a0\u7a33\u5b9a\u7684\u6548\u7387\u8868\u73b0\uff1b</li> </ul>"},{"location":"chapter_stack_and_queue/stack/#_5","title":"\u7a7a\u95f4\u6548\u7387","text":"<p>\u5728\u521d\u59cb\u5316\u5217\u8868\u65f6\uff0c\u7cfb\u7edf\u4f1a\u4e3a\u5217\u8868\u5206\u914d\u201c\u521d\u59cb\u5bb9\u91cf\u201d\uff0c\u8be5\u5bb9\u91cf\u53ef\u80fd\u8d85\u8fc7\u5b9e\u9645\u9700\u6c42\u3002\u5e76\u4e14\uff0c\u6269\u5bb9\u673a\u5236\u901a\u5e38\u662f\u6309\u7167\u7279\u5b9a\u500d\u7387\uff08\u4f8b\u5982 2 \u500d\uff09\u8fdb\u884c\u6269\u5bb9\uff0c\u6269\u5bb9\u540e\u7684\u5bb9\u91cf\u4e5f\u53ef\u80fd\u8d85\u51fa\u5b9e\u9645\u9700\u6c42\u3002\u56e0\u6b64\uff0c\u57fa\u4e8e\u6570\u7ec4\u5b9e\u73b0\u7684\u6808\u53ef\u80fd\u9020\u6210\u4e00\u5b9a\u7684\u7a7a\u95f4\u6d6a\u8d39\u3002</p> <p>\u7136\u800c\uff0c\u7531\u4e8e\u94fe\u8868\u8282\u70b9\u9700\u8981\u989d\u5916\u5b58\u50a8\u6307\u9488\uff0c\u56e0\u6b64\u94fe\u8868\u8282\u70b9\u5360\u7528\u7684\u7a7a\u95f4\u76f8\u5bf9\u8f83\u5927\u3002</p> <p>\u7efc\u4e0a\uff0c\u6211\u4eec\u4e0d\u80fd\u7b80\u5355\u5730\u786e\u5b9a\u54ea\u79cd\u5b9e\u73b0\u66f4\u52a0\u8282\u7701\u5185\u5b58\uff0c\u9700\u8981\u9488\u5bf9\u5177\u4f53\u60c5\u51b5\u8fdb\u884c\u5206\u6790\u3002</p>"},{"location":"chapter_stack_and_queue/stack/#514","title":"5.1.4. \u00a0 \u6808\u5178\u578b\u5e94\u7528","text":"<ul> <li>\u6d4f\u89c8\u5668\u4e2d\u7684\u540e\u9000\u4e0e\u524d\u8fdb\u3001\u8f6f\u4ef6\u4e2d\u7684\u64a4\u9500\u4e0e\u53cd\u64a4\u9500\u3002\u6bcf\u5f53\u6211\u4eec\u6253\u5f00\u65b0\u7684\u7f51\u9875\uff0c\u6d4f\u89c8\u5668\u5c31\u4f1a\u5c06\u4e0a\u4e00\u4e2a\u7f51\u9875\u6267\u884c\u5165\u6808\uff0c\u8fd9\u6837\u6211\u4eec\u5c31\u53ef\u4ee5\u901a\u8fc7\u300c\u540e\u9000\u300d\u64cd\u4f5c\u56de\u5230\u4e0a\u4e00\u9875\u9762\u3002\u540e\u9000\u64cd\u4f5c\u5b9e\u9645\u4e0a\u662f\u5728\u6267\u884c\u51fa\u6808\u3002\u5982\u679c\u8981\u540c\u65f6\u652f\u6301\u540e\u9000\u548c\u524d\u8fdb\uff0c\u90a3\u4e48\u9700\u8981\u4e24\u4e2a\u6808\u6765\u914d\u5408\u5b9e\u73b0\u3002</li> <li>\u7a0b\u5e8f\u5185\u5b58\u7ba1\u7406\u3002\u6bcf\u6b21\u8c03\u7528\u51fd\u6570\u65f6\uff0c\u7cfb\u7edf\u90fd\u4f1a\u5728\u6808\u9876\u6dfb\u52a0\u4e00\u4e2a\u6808\u5e27\uff0c\u7528\u4e8e\u8bb0\u5f55\u51fd\u6570\u7684\u4e0a\u4e0b\u6587\u4fe1\u606f\u3002\u5728\u9012\u5f52\u51fd\u6570\u4e2d\uff0c\u5411\u4e0b\u9012\u63a8\u9636\u6bb5\u4f1a\u4e0d\u65ad\u6267\u884c\u5165\u6808\u64cd\u4f5c\uff0c\u800c\u5411\u4e0a\u56de\u6eaf\u9636\u6bb5\u5219\u4f1a\u6267\u884c\u51fa\u6808\u64cd\u4f5c\u3002</li> </ul>"},{"location":"chapter_stack_and_queue/summary/","title":"5.4. \u00a0 \u5c0f\u7ed3","text":"<ul> <li>\u6808\u662f\u4e00\u79cd\u9075\u5faa\u5148\u5165\u540e\u51fa\u539f\u5219\u7684\u6570\u636e\u7ed3\u6784\uff0c\u53ef\u901a\u8fc7\u6570\u7ec4\u6216\u94fe\u8868\u6765\u5b9e\u73b0\u3002</li> <li>\u4ece\u65f6\u95f4\u6548\u7387\u89d2\u5ea6\u770b\uff0c\u6808\u7684\u6570\u7ec4\u5b9e\u73b0\u5177\u6709\u8f83\u9ad8\u7684\u5e73\u5747\u6548\u7387\uff0c\u4f46\u5728\u6269\u5bb9\u8fc7\u7a0b\u4e2d\uff0c\u5355\u6b21\u5165\u6808\u64cd\u4f5c\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4f1a\u964d\u4f4e\u81f3 \\(O(n)\\) \u3002\u76f8\u6bd4\u4e4b\u4e0b\uff0c\u57fa\u4e8e\u94fe\u8868\u5b9e\u73b0\u7684\u6808\u5177\u6709\u66f4\u4e3a\u7a33\u5b9a\u7684\u6548\u7387\u8868\u73b0\u3002</li> <li>\u5728\u7a7a\u95f4\u6548\u7387\u65b9\u9762\uff0c\u6808\u7684\u6570\u7ec4\u5b9e\u73b0\u53ef\u80fd\u5bfc\u81f4\u4e00\u5b9a\u7a0b\u5ea6\u7684\u7a7a\u95f4\u6d6a\u8d39\u3002\u4f46\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u94fe\u8868\u8282\u70b9\u6240\u5360\u7528\u7684\u5185\u5b58\u7a7a\u95f4\u6bd4\u6570\u7ec4\u5143\u7d20\u66f4\u5927\u3002</li> <li>\u961f\u5217\u662f\u4e00\u79cd\u9075\u5faa\u5148\u5165\u5148\u51fa\u539f\u5219\u7684\u6570\u636e\u7ed3\u6784\uff0c\u540c\u6837\u53ef\u4ee5\u901a\u8fc7\u6570\u7ec4\u6216\u94fe\u8868\u6765\u5b9e\u73b0\u3002\u5728\u65f6\u95f4\u6548\u7387\u548c\u7a7a\u95f4\u6548\u7387\u7684\u5bf9\u6bd4\u4e0a\uff0c\u961f\u5217\u7684\u7ed3\u8bba\u4e0e\u524d\u8ff0\u6808\u7684\u7ed3\u8bba\u76f8\u4f3c\u3002</li> <li>\u53cc\u5411\u961f\u5217\u662f\u4e00\u79cd\u5177\u6709\u66f4\u9ad8\u81ea\u7531\u5ea6\u7684\u961f\u5217\uff0c\u5b83\u5141\u8bb8\u5728\u4e24\u7aef\u8fdb\u884c\u5143\u7d20\u7684\u6dfb\u52a0\u548c\u5220\u9664\u64cd\u4f5c\u3002</li> </ul>"},{"location":"chapter_stack_and_queue/summary/#541-q-a","title":"5.4.1. \u00a0 Q &amp; A","text":"<p>\u6d4f\u89c8\u5668\u7684\u524d\u8fdb\u540e\u9000\u662f\u5426\u662f\u53cc\u5411\u94fe\u8868\u5b9e\u73b0\uff1f</p> <p>\u6d4f\u89c8\u5668\u7684\u524d\u8fdb\u540e\u9000\u529f\u80fd\u672c\u8d28\u4e0a\u662f\u201c\u6808\u201d\u7684\u4f53\u73b0\u3002\u5f53\u7528\u6237\u8bbf\u95ee\u4e00\u4e2a\u65b0\u9875\u9762\u65f6\uff0c\u8be5\u9875\u9762\u4f1a\u88ab\u6dfb\u52a0\u5230\u6808\u9876\uff1b\u5f53\u7528\u6237\u70b9\u51fb\u540e\u9000\u6309\u94ae\u65f6\uff0c\u8be5\u9875\u9762\u4f1a\u4ece\u6808\u9876\u5f39\u51fa\u3002\u4f7f\u7528\u53cc\u5411\u961f\u5217\u53ef\u4ee5\u65b9\u4fbf\u5b9e\u73b0\u4e00\u4e9b\u989d\u5916\u64cd\u4f5c\uff0c\u8fd9\u4e2a\u5728\u53cc\u5411\u961f\u5217\u7ae0\u8282\u6709\u63d0\u5230\u3002</p> <p>\u5728\u51fa\u6808\u540e\uff0c\u662f\u5426\u9700\u8981\u91ca\u653e\u51fa\u6808\u8282\u70b9\u7684\u5185\u5b58\uff1f</p> <p>\u5982\u679c\u540e\u7eed\u4ecd\u9700\u8981\u4f7f\u7528\u5f39\u51fa\u8282\u70b9\uff0c\u5219\u4e0d\u9700\u8981\u91ca\u653e\u5185\u5b58\u3002\u82e5\u4e4b\u540e\u4e0d\u9700\u8981\u7528\u5230\uff0c<code>Java</code> \u548c <code>Python</code> \u7b49\u8bed\u8a00\u62e5\u6709\u81ea\u52a8\u5783\u573e\u56de\u6536\u673a\u5236\uff0c\u56e0\u6b64\u4e0d\u9700\u8981\u624b\u52a8\u91ca\u653e\u5185\u5b58\uff1b\u5728 <code>C</code> \u548c <code>C++</code> \u4e2d\u9700\u8981\u624b\u52a8\u91ca\u653e\u5185\u5b58\u3002</p> <p>\u53cc\u5411\u961f\u5217\u50cf\u662f\u4e24\u4e2a\u6808\u62fc\u63a5\u5728\u4e86\u4e00\u8d77\uff0c\u5b83\u7684\u7528\u9014\u662f\u4ec0\u4e48\uff1f</p> <p>\u53cc\u5411\u961f\u5217\u5c31\u50cf\u662f\u6808\u548c\u961f\u5217\u7684\u7ec4\u5408\uff0c\u6216\u8005\u662f\u4e24\u4e2a\u6808\u62fc\u5728\u4e86\u4e00\u8d77\u3002\u5b83\u8868\u73b0\u7684\u662f\u6808 + \u961f\u5217\u7684\u903b\u8f91\uff0c\u56e0\u6b64\u53ef\u4ee5\u5b9e\u73b0\u6808\u4e0e\u961f\u5217\u7684\u6240\u6709\u5e94\u7528\uff0c\u5e76\u4e14\u66f4\u52a0\u7075\u6d3b\u3002</p>"},{"location":"chapter_tree/","title":"7. \u00a0 \u6811","text":""},{"location":"chapter_tree/array_representation_of_tree/","title":"7.3. \u00a0 \u4e8c\u53c9\u6811\u6570\u7ec4\u8868\u793a","text":"<p>\u5728\u94fe\u8868\u8868\u793a\u4e0b\uff0c\u4e8c\u53c9\u6811\u7684\u5b58\u50a8\u5355\u5143\u4e3a\u8282\u70b9 <code>TreeNode</code> \uff0c\u8282\u70b9\u4e4b\u95f4\u901a\u8fc7\u6307\u9488\u76f8\u8fde\u63a5\u3002\u5728\u4e0a\u8282\u4e2d\uff0c\u6211\u4eec\u5b66\u4e60\u4e86\u5728\u94fe\u8868\u8868\u793a\u4e0b\u7684\u4e8c\u53c9\u6811\u7684\u5404\u9879\u57fa\u672c\u64cd\u4f5c\u3002</p> <p>\u90a3\u4e48\uff0c\u80fd\u5426\u7528\u300c\u6570\u7ec4\u300d\u6765\u8868\u793a\u4e8c\u53c9\u6811\u5462\uff1f\u7b54\u6848\u662f\u80af\u5b9a\u7684\u3002</p>"},{"location":"chapter_tree/array_representation_of_tree/#731","title":"7.3.1. \u00a0 \u8868\u793a\u5b8c\u7f8e\u4e8c\u53c9\u6811","text":"<p>\u5148\u5206\u6790\u4e00\u4e2a\u7b80\u5355\u6848\u4f8b\uff0c\u7ed9\u5b9a\u4e00\u4e2a\u5b8c\u7f8e\u4e8c\u53c9\u6811\uff0c\u6211\u4eec\u5c06\u8282\u70b9\u6309\u7167\u5c42\u5e8f\u904d\u5386\u7684\u987a\u5e8f\u7f16\u53f7\uff08\u4ece \\(0\\) \u5f00\u59cb\uff09\uff0c\u6b64\u65f6\u6bcf\u4e2a\u8282\u70b9\u90fd\u5bf9\u5e94\u552f\u4e00\u7684\u7d22\u5f15\u3002</p> <p>\u6839\u636e\u5c42\u5e8f\u904d\u5386\u7684\u7279\u6027\uff0c\u6211\u4eec\u53ef\u4ee5\u63a8\u5bfc\u51fa\u7236\u8282\u70b9\u7d22\u5f15\u4e0e\u5b50\u8282\u70b9\u7d22\u5f15\u4e4b\u95f4\u7684\u201c\u6620\u5c04\u516c\u5f0f\u201d\uff1a\u82e5\u8282\u70b9\u7684\u7d22\u5f15\u4e3a \\(i\\) \uff0c\u5219\u8be5\u8282\u70b9\u7684\u5de6\u5b50\u8282\u70b9\u7d22\u5f15\u4e3a \\(2i + 1\\) \uff0c\u53f3\u5b50\u8282\u70b9\u7d22\u5f15\u4e3a \\(2i + 2\\) \u3002</p> <p></p> <p> Fig. \u5b8c\u7f8e\u4e8c\u53c9\u6811\u7684\u6570\u7ec4\u8868\u793a </p> <p>\u6620\u5c04\u516c\u5f0f\u7684\u4f5c\u7528\u76f8\u5f53\u4e8e\u94fe\u8868\u4e2d\u7684\u6307\u9488\u3002\u5982\u679c\u6211\u4eec\u5c06\u8282\u70b9\u6309\u7167\u5c42\u5e8f\u904d\u5386\u7684\u987a\u5e8f\u5b58\u50a8\u5728\u4e00\u4e2a\u6570\u7ec4\u4e2d\uff0c\u90a3\u4e48\u5bf9\u4e8e\u6570\u7ec4\u4e2d\u7684\u4efb\u610f\u8282\u70b9\uff0c\u6211\u4eec\u90fd\u53ef\u4ee5\u901a\u8fc7\u6620\u5c04\u516c\u5f0f\u6765\u8bbf\u95ee\u5176\u5b50\u8282\u70b9\u3002</p>"},{"location":"chapter_tree/array_representation_of_tree/#732","title":"7.3.2. \u00a0 \u8868\u793a\u4efb\u610f\u4e8c\u53c9\u6811","text":"<p>\u7136\u800c\uff0c\u5b8c\u7f8e\u4e8c\u53c9\u6811\u53ea\u662f\u4e00\u4e2a\u7279\u4f8b\u3002\u5728\u4e8c\u53c9\u6811\u7684\u4e2d\u95f4\u5c42\uff0c\u901a\u5e38\u5b58\u5728\u8bb8\u591a \\(\\text{null}\\) \uff0c\u800c\u5c42\u5e8f\u904d\u5386\u5e8f\u5217\u5e76\u4e0d\u5305\u542b\u8fd9\u4e9b \\(\\text{null}\\) \u3002\u6211\u4eec\u65e0\u6cd5\u4ec5\u51ed\u8be5\u5e8f\u5217\u6765\u63a8\u6d4b \\(\\text{null}\\) \u7684\u6570\u91cf\u548c\u5206\u5e03\u4f4d\u7f6e\uff0c\u8fd9\u610f\u5473\u7740\u5b58\u5728\u591a\u79cd\u4e8c\u53c9\u6811\u7ed3\u6784\u90fd\u7b26\u5408\u8be5\u5c42\u5e8f\u904d\u5386\u5e8f\u5217\u3002\u663e\u7136\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u4e0a\u8ff0\u7684\u6570\u7ec4\u8868\u793a\u65b9\u6cd5\u5df2\u7ecf\u5931\u6548\u3002</p> <p></p> <p> Fig. \u5c42\u5e8f\u904d\u5386\u5e8f\u5217\u5bf9\u5e94\u591a\u79cd\u4e8c\u53c9\u6811\u53ef\u80fd\u6027 </p> <p>\u4e3a\u4e86\u89e3\u51b3\u6b64\u95ee\u9898\uff0c\u6211\u4eec\u53ef\u4ee5\u8003\u8651\u5728\u5c42\u5e8f\u904d\u5386\u5e8f\u5217\u4e2d\u663e\u5f0f\u5730\u5199\u51fa\u6240\u6709 \\(\\text{null}\\)\u3002\u5982\u4e0b\u56fe\u6240\u793a\uff0c\u8fd9\u6837\u5904\u7406\u540e\uff0c\u5c42\u5e8f\u904d\u5386\u5e8f\u5217\u5c31\u53ef\u4ee5\u552f\u4e00\u8868\u793a\u4e8c\u53c9\u6811\u4e86\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart <pre><code>/* \u4e8c\u53c9\u6811\u7684\u6570\u7ec4\u8868\u793a */\n// \u4f7f\u7528 int \u7684\u5305\u88c5\u7c7b Integer \uff0c\u5c31\u53ef\u4ee5\u4f7f\u7528 null \u6765\u6807\u8bb0\u7a7a\u4f4d\nInteger[] tree = { 1, 2, 3, 4, null, 6, 7, 8, 9, null, null, 12, null, null, 15 };\n</code></pre> <pre><code>/* \u4e8c\u53c9\u6811\u7684\u6570\u7ec4\u8868\u793a */\n// \u4f7f\u7528 int \u6700\u5927\u503c\u6807\u8bb0\u7a7a\u4f4d\uff0c\u56e0\u6b64\u8981\u6c42\u8282\u70b9\u503c\u4e0d\u80fd\u4e3a INT_MAX\nvector&lt;int&gt; tree = {1, 2, 3, 4, INT_MAX, 6, 7, 8, 9, INT_MAX, INT_MAX, 12, INT_MAX, INT_MAX, 15};\n</code></pre> <pre><code># \u4e8c\u53c9\u6811\u7684\u6570\u7ec4\u8868\u793a\n# \u76f4\u63a5\u4f7f\u7528 None \u6765\u8868\u793a\u7a7a\u4f4d\ntree = [1, 2, 3, 4, None, 6, 7, 8, 9, None, None, 12, None, None, 15]\n</code></pre> <pre><code>/* \u4e8c\u53c9\u6811\u7684\u6570\u7ec4\u8868\u793a */\n// \u4f7f\u7528 any \u7c7b\u578b\u7684\u5207\u7247, \u5c31\u53ef\u4ee5\u4f7f\u7528 nil \u6765\u6807\u8bb0\u7a7a\u4f4d\ntree := []any{1, 2, 3, 4, nil, 6, 7, 8, 9, nil, nil, 12, nil, nil, 15}\n</code></pre> <pre><code>/* \u4e8c\u53c9\u6811\u7684\u6570\u7ec4\u8868\u793a */\n// \u76f4\u63a5\u4f7f\u7528 null \u6765\u8868\u793a\u7a7a\u4f4d\nlet tree = [1, 2, 3, 4, null, 6, 7, 8, 9, null, null, 12, null, null, 15];\n</code></pre> <pre><code>/* \u4e8c\u53c9\u6811\u7684\u6570\u7ec4\u8868\u793a */\n// \u76f4\u63a5\u4f7f\u7528 null \u6765\u8868\u793a\u7a7a\u4f4d\nlet tree: (number | null)[] = [1, 2, 3, 4, null, 6, 7, 8, 9, null, null, 12, null, null, 15];\n</code></pre> <pre><code>/* \u4e8c\u53c9\u6811\u7684\u6570\u7ec4\u8868\u793a */\n// \u4f7f\u7528 int \u6700\u5927\u503c\u6807\u8bb0\u7a7a\u4f4d\uff0c\u56e0\u6b64\u8981\u6c42\u8282\u70b9\u503c\u4e0d\u80fd\u4e3a INT_MAX\nint tree[] = {1, 2, 3, 4, INT_MAX, 6, 7, 8, 9, INT_MAX, INT_MAX, 12, INT_MAX, INT_MAX, 15};\n</code></pre> <pre><code>/* \u4e8c\u53c9\u6811\u7684\u6570\u7ec4\u8868\u793a */\n// \u4f7f\u7528 int? \u53ef\u7a7a\u7c7b\u578b \uff0c\u5c31\u53ef\u4ee5\u4f7f\u7528 null \u6765\u6807\u8bb0\u7a7a\u4f4d\nint?[] tree = { 1, 2, 3, 4, null, 6, 7, 8, 9, null, null, 12, null, null, 15 };\n</code></pre> <pre><code>/* \u4e8c\u53c9\u6811\u7684\u6570\u7ec4\u8868\u793a */\n// \u4f7f\u7528 Int? \u53ef\u7a7a\u7c7b\u578b \uff0c\u5c31\u53ef\u4ee5\u4f7f\u7528 nil \u6765\u6807\u8bb0\u7a7a\u4f4d\nlet tree: [Int?] = [1, 2, 3, 4, nil, 6, 7, 8, 9, nil, nil, 12, nil, nil, 15]\n</code></pre> <pre><code>\n</code></pre> <pre><code>/* \u4e8c\u53c9\u6811\u7684\u6570\u7ec4\u8868\u793a */\n// \u4f7f\u7528 int? \u53ef\u7a7a\u7c7b\u578b \uff0c\u5c31\u53ef\u4ee5\u4f7f\u7528 null \u6765\u6807\u8bb0\u7a7a\u4f4d\nList&lt;int?&gt; tree = [1, 2, 3, 4, null, 6, 7, 8, 9, null, null, 12, null, null, 15];\n</code></pre> <p></p> <p> Fig. \u4efb\u610f\u7c7b\u578b\u4e8c\u53c9\u6811\u7684\u6570\u7ec4\u8868\u793a </p>"},{"location":"chapter_tree/array_representation_of_tree/#733","title":"7.3.3. \u00a0 \u4f18\u52bf\u4e0e\u5c40\u9650\u6027","text":"<p>\u4e8c\u53c9\u6811\u7684\u6570\u7ec4\u8868\u793a\u5b58\u5728\u4ee5\u4e0b\u4f18\u70b9\uff1a</p> <ul> <li>\u6570\u7ec4\u5b58\u50a8\u5728\u8fde\u7eed\u7684\u5185\u5b58\u7a7a\u95f4\u4e2d\uff0c\u7f13\u5b58\u53cb\u597d\uff0c\u8bbf\u95ee\u4e0e\u904d\u5386\u901f\u5ea6\u8f83\u5feb\uff1b</li> <li>\u4e0d\u9700\u8981\u5b58\u50a8\u6307\u9488\uff0c\u6bd4\u8f83\u8282\u7701\u7a7a\u95f4\uff1b</li> <li>\u5141\u8bb8\u968f\u673a\u8bbf\u95ee\u8282\u70b9\uff1b</li> </ul> <p>\u7136\u800c\uff0c\u6570\u7ec4\u8868\u793a\u4e5f\u5177\u6709\u4e00\u4e9b\u5c40\u9650\u6027\uff1a</p> <ul> <li>\u6570\u7ec4\u5b58\u50a8\u9700\u8981\u8fde\u7eed\u5185\u5b58\u7a7a\u95f4\uff0c\u56e0\u6b64\u4e0d\u9002\u5408\u5b58\u50a8\u6570\u636e\u91cf\u8fc7\u5927\u7684\u6811\u3002</li> <li>\u589e\u5220\u8282\u70b9\u9700\u8981\u901a\u8fc7\u6570\u7ec4\u63d2\u5165\u4e0e\u5220\u9664\u64cd\u4f5c\u5b9e\u73b0\uff0c\u6548\u7387\u8f83\u4f4e\uff1b</li> <li>\u5f53\u4e8c\u53c9\u6811\u4e2d\u5b58\u5728\u5927\u91cf \\(\\text{null}\\) \u65f6\uff0c\u6570\u7ec4\u4e2d\u5305\u542b\u7684\u8282\u70b9\u6570\u636e\u6bd4\u91cd\u8f83\u4f4e\uff0c\u7a7a\u95f4\u5229\u7528\u7387\u8f83\u4f4e\u3002</li> </ul> <p>\u5b8c\u5168\u4e8c\u53c9\u6811\u975e\u5e38\u9002\u5408\u4f7f\u7528\u6570\u7ec4\u6765\u8868\u793a\u3002\u56de\u987e\u5b8c\u5168\u4e8c\u53c9\u6811\u7684\u5b9a\u4e49\uff0c\\(\\text{null}\\) \u53ea\u51fa\u73b0\u5728\u6700\u5e95\u5c42\u4e14\u9760\u53f3\u7684\u4f4d\u7f6e\uff0c\u8fd9\u610f\u5473\u7740\u6240\u6709 \\(\\text{null}\\) \u4e00\u5b9a\u51fa\u73b0\u5728\u5c42\u5e8f\u904d\u5386\u5e8f\u5217\u7684\u672b\u5c3e\u3002\u56e0\u6b64\uff0c\u5728\u4f7f\u7528\u6570\u7ec4\u8868\u793a\u5b8c\u5168\u4e8c\u53c9\u6811\u65f6\uff0c\u53ef\u4ee5\u7701\u7565\u5b58\u50a8\u6240\u6709 \\(\\text{null}\\) \u3002</p> <p></p> <p> Fig. \u5b8c\u5168\u4e8c\u53c9\u6811\u7684\u6570\u7ec4\u8868\u793a </p>"},{"location":"chapter_tree/avl_tree/","title":"7.5. \u00a0 AVL \u6811 *","text":"<p>\u5728\u4e8c\u53c9\u641c\u7d22\u6811\u7ae0\u8282\u4e2d\uff0c\u6211\u4eec\u63d0\u5230\u4e86\u5728\u591a\u6b21\u63d2\u5165\u548c\u5220\u9664\u64cd\u4f5c\u540e\uff0c\u4e8c\u53c9\u641c\u7d22\u6811\u53ef\u80fd\u9000\u5316\u4e3a\u94fe\u8868\u3002\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u6240\u6709\u64cd\u4f5c\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u5c06\u4ece \\(O(\\log n)\\) \u6076\u5316\u4e3a \\(O(n)\\)\u3002</p> <p>\u5982\u4e0b\u56fe\u6240\u793a\uff0c\u7ecf\u8fc7\u4e24\u6b21\u5220\u9664\u8282\u70b9\u64cd\u4f5c\uff0c\u8fd9\u4e2a\u4e8c\u53c9\u641c\u7d22\u6811\u4fbf\u4f1a\u9000\u5316\u4e3a\u94fe\u8868\u3002</p> <p></p> <p> Fig. AVL \u6811\u5728\u5220\u9664\u8282\u70b9\u540e\u53d1\u751f\u9000\u5316 </p> <p>\u518d\u4f8b\u5982\uff0c\u5728\u4ee5\u4e0b\u5b8c\u7f8e\u4e8c\u53c9\u6811\u4e2d\u63d2\u5165\u4e24\u4e2a\u8282\u70b9\u540e\uff0c\u6811\u5c06\u4e25\u91cd\u5411\u5de6\u503e\u659c\uff0c\u67e5\u627e\u64cd\u4f5c\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e5f\u968f\u4e4b\u6076\u5316\u3002</p> <p></p> <p> Fig. AVL \u6811\u5728\u63d2\u5165\u8282\u70b9\u540e\u53d1\u751f\u9000\u5316 </p> <p>G. M. Adelson-Velsky \u548c E. M. Landis \u5728\u5176 1962 \u5e74\u53d1\u8868\u7684\u8bba\u6587 \"An algorithm for the organization of information\" \u4e2d\u63d0\u51fa\u4e86\u300cAVL \u6811\u300d\u3002\u8bba\u6587\u4e2d\u8be6\u7ec6\u63cf\u8ff0\u4e86\u4e00\u7cfb\u5217\u64cd\u4f5c\uff0c\u786e\u4fdd\u5728\u6301\u7eed\u6dfb\u52a0\u548c\u5220\u9664\u8282\u70b9\u540e\uff0cAVL \u6811\u4e0d\u4f1a\u9000\u5316\uff0c\u4ece\u800c\u4f7f\u5f97\u5404\u79cd\u64cd\u4f5c\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4fdd\u6301\u5728 \\(O(\\log n)\\) \u7ea7\u522b\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u5728\u9700\u8981\u9891\u7e41\u8fdb\u884c\u589e\u5220\u67e5\u6539\u64cd\u4f5c\u7684\u573a\u666f\u4e2d\uff0cAVL \u6811\u80fd\u59cb\u7ec8\u4fdd\u6301\u9ad8\u6548\u7684\u6570\u636e\u64cd\u4f5c\u6027\u80fd\uff0c\u5177\u6709\u5f88\u597d\u7684\u5e94\u7528\u4ef7\u503c\u3002</p>"},{"location":"chapter_tree/avl_tree/#751-avl","title":"7.5.1. \u00a0 AVL \u6811\u5e38\u89c1\u672f\u8bed","text":"<p>\u300cAVL \u6811\u300d\u65e2\u662f\u4e8c\u53c9\u641c\u7d22\u6811\u4e5f\u662f\u5e73\u8861\u4e8c\u53c9\u6811\uff0c\u540c\u65f6\u6ee1\u8db3\u8fd9\u4e24\u7c7b\u4e8c\u53c9\u6811\u7684\u6240\u6709\u6027\u8d28\uff0c\u56e0\u6b64\u4e5f\u88ab\u79f0\u4e3a\u300c\u5e73\u8861\u4e8c\u53c9\u641c\u7d22\u6811\u300d\u3002</p>"},{"location":"chapter_tree/avl_tree/#_1","title":"\u8282\u70b9\u9ad8\u5ea6","text":"<p>\u5728\u64cd\u4f5c AVL \u6811\u65f6\uff0c\u6211\u4eec\u9700\u8981\u83b7\u53d6\u8282\u70b9\u7684\u9ad8\u5ea6\uff0c\u56e0\u6b64\u9700\u8981\u4e3a AVL \u6811\u7684\u8282\u70b9\u7c7b\u6dfb\u52a0 <code>height</code> \u53d8\u91cf\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart <pre><code>/* AVL \u6811\u8282\u70b9\u7c7b */\nclass TreeNode {\npublic int val;        // \u8282\u70b9\u503c\npublic int height;     // \u8282\u70b9\u9ad8\u5ea6\npublic TreeNode left;  // \u5de6\u5b50\u8282\u70b9\npublic TreeNode right; // \u53f3\u5b50\u8282\u70b9\npublic TreeNode(int x) { val = x; }\n}\n</code></pre> <pre><code>/* AVL \u6811\u8282\u70b9\u7c7b */\nstruct TreeNode {\nint val{};          // \u8282\u70b9\u503c\nint height = 0;     // \u8282\u70b9\u9ad8\u5ea6\nTreeNode *left{};   // \u5de6\u5b50\u8282\u70b9\nTreeNode *right{};  // \u53f3\u5b50\u8282\u70b9\nTreeNode() = default;\nexplicit TreeNode(int x) : val(x){}\n};\n</code></pre> <pre><code>class TreeNode:\n\"\"\"AVL \u6811\u8282\u70b9\u7c7b\"\"\"\ndef __init__(self, val: int):\nself.val: int = val                    # \u8282\u70b9\u503c\nself.height: int = 0                   # \u8282\u70b9\u9ad8\u5ea6\nself.left: Optional[TreeNode] = None   # \u5de6\u5b50\u8282\u70b9\u5f15\u7528\nself.right: Optional[TreeNode] = None  # \u53f3\u5b50\u8282\u70b9\u5f15\u7528\n</code></pre> <pre><code>/* AVL \u6811\u8282\u70b9\u7ed3\u6784\u4f53 */\ntype TreeNode struct {\nVal    int       // \u8282\u70b9\u503c\nHeight int       // \u8282\u70b9\u9ad8\u5ea6\nLeft   *TreeNode // \u5de6\u5b50\u8282\u70b9\u5f15\u7528\nRight  *TreeNode // \u53f3\u5b50\u8282\u70b9\u5f15\u7528\n}\n</code></pre> <pre><code>/* AVL \u6811\u8282\u70b9\u7c7b */\nclass TreeNode {\nval; // \u8282\u70b9\u503c\nheight; //\u8282\u70b9\u9ad8\u5ea6\nleft; // \u5de6\u5b50\u8282\u70b9\u6307\u9488\nright; // \u53f3\u5b50\u8282\u70b9\u6307\u9488\nconstructor(val, left, right, height) {\nthis.val = val === undefined ? 0 : val;\nthis.height = height === undefined ? 0 : height;\nthis.left = left === undefined ? null : left;\nthis.right = right === undefined ? null : right;\n}\n}\n</code></pre> <pre><code>/* AVL \u6811\u8282\u70b9\u7c7b */\nclass TreeNode {\nval: number;            // \u8282\u70b9\u503c\nheight: number;         // \u8282\u70b9\u9ad8\u5ea6\nleft: TreeNode | null;  // \u5de6\u5b50\u8282\u70b9\u6307\u9488\nright: TreeNode | null; // \u53f3\u5b50\u8282\u70b9\u6307\u9488\nconstructor(val?: number, height?: number, left?: TreeNode | null, right?: TreeNode | null) {\nthis.val = val === undefined ? 0 : val;\nthis.height = height === undefined ? 0 : height; this.left = left === undefined ? null : left; this.right = right === undefined ? null : right; }\n}\n</code></pre> <pre><code>/* AVL \u6811\u8282\u70b9\u7ed3\u6784\u4f53 */\nstruct TreeNode {\nint val;\nint height;\nstruct TreeNode *left;\nstruct TreeNode *right;\n};\ntypedef struct TreeNode TreeNode;\n/* \u6784\u9020\u51fd\u6570 */\nTreeNode *newTreeNode(int val) {\nTreeNode *node;\nnode = (TreeNode *)malloc(sizeof(TreeNode));\nnode-&gt;val = val;\nnode-&gt;height = 0;\nnode-&gt;left = NULL;\nnode-&gt;right = NULL;\nreturn node;\n}\n</code></pre> <pre><code>/* AVL \u6811\u8282\u70b9\u7c7b */\nclass TreeNode {\npublic int val;          // \u8282\u70b9\u503c\npublic int height;       // \u8282\u70b9\u9ad8\u5ea6\npublic TreeNode? left;   // \u5de6\u5b50\u8282\u70b9\npublic TreeNode? right;  // \u53f3\u5b50\u8282\u70b9\npublic TreeNode(int x) { val = x; }\n}\n</code></pre> <pre><code>/* AVL \u6811\u8282\u70b9\u7c7b */\nclass TreeNode {\nvar val: Int // \u8282\u70b9\u503c\nvar height: Int // \u8282\u70b9\u9ad8\u5ea6\nvar left: TreeNode? // \u5de6\u5b50\u8282\u70b9\nvar right: TreeNode? // \u53f3\u5b50\u8282\u70b9\ninit(x: Int) {\nval = x\nheight = 0\n}\n}\n</code></pre> <pre><code>\n</code></pre> <pre><code>/* AVL \u6811\u8282\u70b9\u7c7b */\nclass TreeNode {\nint val;         // \u8282\u70b9\u503c\nint height;      // \u8282\u70b9\u9ad8\u5ea6\nTreeNode? left;  // \u5de6\u5b50\u8282\u70b9\nTreeNode? right; // \u53f3\u5b50\u8282\u70b9\nTreeNode(this.val, [this.height = 0, this.left, this.right]);\n}\n</code></pre> <p>\u300c\u8282\u70b9\u9ad8\u5ea6\u300d\u662f\u6307\u4ece\u8be5\u8282\u70b9\u5230\u6700\u8fdc\u53f6\u8282\u70b9\u7684\u8ddd\u79bb\uff0c\u5373\u6240\u7ecf\u8fc7\u7684\u201c\u8fb9\u201d\u7684\u6570\u91cf\u3002\u9700\u8981\u7279\u522b\u6ce8\u610f\u7684\u662f\uff0c\u53f6\u8282\u70b9\u7684\u9ad8\u5ea6\u4e3a 0 \uff0c\u800c\u7a7a\u8282\u70b9\u7684\u9ad8\u5ea6\u4e3a -1 \u3002\u6211\u4eec\u5c06\u521b\u5efa\u4e24\u4e2a\u5de5\u5177\u51fd\u6570\uff0c\u5206\u522b\u7528\u4e8e\u83b7\u53d6\u548c\u66f4\u65b0\u8282\u70b9\u7684\u9ad8\u5ea6\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart avl_tree.java<pre><code>/* \u83b7\u53d6\u8282\u70b9\u9ad8\u5ea6 */\nint height(TreeNode node) {\n// \u7a7a\u8282\u70b9\u9ad8\u5ea6\u4e3a -1 \uff0c\u53f6\u8282\u70b9\u9ad8\u5ea6\u4e3a 0\nreturn node == null ? -1 : node.height;\n}\n/* \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6 */\nvoid updateHeight(TreeNode node) {\n// \u8282\u70b9\u9ad8\u5ea6\u7b49\u4e8e\u6700\u9ad8\u5b50\u6811\u9ad8\u5ea6 + 1\nnode.height = Math.max(height(node.left), height(node.right)) + 1;\n}\n</code></pre> avl_tree.cpp<pre><code>/* \u83b7\u53d6\u8282\u70b9\u9ad8\u5ea6 */\nint height(TreeNode *node) {\n// \u7a7a\u8282\u70b9\u9ad8\u5ea6\u4e3a -1 \uff0c\u53f6\u8282\u70b9\u9ad8\u5ea6\u4e3a 0\nreturn node == nullptr ? -1 : node-&gt;height;\n}\n/* \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6 */\nvoid updateHeight(TreeNode *node) {\n// \u8282\u70b9\u9ad8\u5ea6\u7b49\u4e8e\u6700\u9ad8\u5b50\u6811\u9ad8\u5ea6 + 1\nnode-&gt;height = max(height(node-&gt;left), height(node-&gt;right)) + 1;\n}\n</code></pre> avl_tree.py<pre><code>def height(self, node: TreeNode | None) -&gt; int:\n\"\"\"\u83b7\u53d6\u8282\u70b9\u9ad8\u5ea6\"\"\"\n# \u7a7a\u8282\u70b9\u9ad8\u5ea6\u4e3a -1 \uff0c\u53f6\u8282\u70b9\u9ad8\u5ea6\u4e3a 0\nif node is not None:\nreturn node.height\nreturn -1\ndef __update_height(self, node: TreeNode | None):\n\"\"\"\u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\"\"\"\n# \u8282\u70b9\u9ad8\u5ea6\u7b49\u4e8e\u6700\u9ad8\u5b50\u6811\u9ad8\u5ea6 + 1\nnode.height = max([self.height(node.left), self.height(node.right)]) + 1\n</code></pre> avl_tree.go<pre><code>/* \u83b7\u53d6\u8282\u70b9\u9ad8\u5ea6 */\nfunc (t *aVLTree) height(node *TreeNode) int {\n// \u7a7a\u8282\u70b9\u9ad8\u5ea6\u4e3a -1 \uff0c\u53f6\u8282\u70b9\u9ad8\u5ea6\u4e3a 0\nif node != nil {\nreturn node.Height\n}\nreturn -1\n}\n/* \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6 */\nfunc (t *aVLTree) updateHeight(node *TreeNode) {\nlh := t.height(node.Left)\nrh := t.height(node.Right)\n// \u8282\u70b9\u9ad8\u5ea6\u7b49\u4e8e\u6700\u9ad8\u5b50\u6811\u9ad8\u5ea6 + 1\nif lh &gt; rh {\nnode.Height = lh + 1\n} else {\nnode.Height = rh + 1\n}\n}\n</code></pre> avl_tree.js<pre><code>/* \u83b7\u53d6\u8282\u70b9\u9ad8\u5ea6 */\nheight(node) {\n// \u7a7a\u8282\u70b9\u9ad8\u5ea6\u4e3a -1 \uff0c\u53f6\u8282\u70b9\u9ad8\u5ea6\u4e3a 0\nreturn node === null ? -1 : node.height;\n}\n/* \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6 */\n#updateHeight(node) {\n// \u8282\u70b9\u9ad8\u5ea6\u7b49\u4e8e\u6700\u9ad8\u5b50\u6811\u9ad8\u5ea6 + 1\nnode.height =\nMath.max(this.height(node.left), this.height(node.right)) + 1;\n}\n</code></pre> avl_tree.ts<pre><code>/* \u83b7\u53d6\u8282\u70b9\u9ad8\u5ea6 */\nheight(node: TreeNode): number {\n// \u7a7a\u8282\u70b9\u9ad8\u5ea6\u4e3a -1 \uff0c\u53f6\u8282\u70b9\u9ad8\u5ea6\u4e3a 0\nreturn node === null ? -1 : node.height;\n}\n/* \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6 */\nupdateHeight(node: TreeNode): void {\n// \u8282\u70b9\u9ad8\u5ea6\u7b49\u4e8e\u6700\u9ad8\u5b50\u6811\u9ad8\u5ea6 + 1\nnode.height =\nMath.max(this.height(node.left), this.height(node.right)) + 1;\n}\n</code></pre> avl_tree.c<pre><code>/* \u83b7\u53d6\u8282\u70b9\u9ad8\u5ea6 */\nint height(TreeNode *node) {\n// \u7a7a\u8282\u70b9\u9ad8\u5ea6\u4e3a -1 \uff0c\u53f6\u8282\u70b9\u9ad8\u5ea6\u4e3a 0\nif (node != NULL) {\nreturn node-&gt;height;\n}\nreturn -1;\n}\n/* \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6 */\nvoid updateHeight(TreeNode *node) {\nint lh = height(node-&gt;left);\nint rh = height(node-&gt;right);\n// \u8282\u70b9\u9ad8\u5ea6\u7b49\u4e8e\u6700\u9ad8\u5b50\u6811\u9ad8\u5ea6 + 1\nif (lh &gt; rh) {\nnode-&gt;height = lh + 1;\n} else {\nnode-&gt;height = rh + 1;\n}\n}\n</code></pre> avl_tree.cs<pre><code>/* \u83b7\u53d6\u8282\u70b9\u9ad8\u5ea6 */\nint height(TreeNode? node) {\n// \u7a7a\u8282\u70b9\u9ad8\u5ea6\u4e3a -1 \uff0c\u53f6\u8282\u70b9\u9ad8\u5ea6\u4e3a 0\nreturn node == null ? -1 : node.height;\n}\n/* \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6 */\nvoid updateHeight(TreeNode node) {\n// \u8282\u70b9\u9ad8\u5ea6\u7b49\u4e8e\u6700\u9ad8\u5b50\u6811\u9ad8\u5ea6 + 1\nnode.height = Math.Max(height(node.left), height(node.right)) + 1;\n}\n</code></pre> avl_tree.swift<pre><code>/* \u83b7\u53d6\u8282\u70b9\u9ad8\u5ea6 */\nfunc height(node: TreeNode?) -&gt; Int {\n// \u7a7a\u8282\u70b9\u9ad8\u5ea6\u4e3a -1 \uff0c\u53f6\u8282\u70b9\u9ad8\u5ea6\u4e3a 0\nnode == nil ? -1 : node!.height\n}\n/* \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6 */\nfunc updateHeight(node: TreeNode?) {\n// \u8282\u70b9\u9ad8\u5ea6\u7b49\u4e8e\u6700\u9ad8\u5b50\u6811\u9ad8\u5ea6 + 1\nnode?.height = max(height(node: node?.left), height(node: node?.right)) + 1\n}\n</code></pre> avl_tree.zig<pre><code>// \u83b7\u53d6\u8282\u70b9\u9ad8\u5ea6\nfn height(self: *Self, node: ?*inc.TreeNode(T)) i32 {\n_ = self;\n// \u7a7a\u8282\u70b9\u9ad8\u5ea6\u4e3a -1 \uff0c\u53f6\u8282\u70b9\u9ad8\u5ea6\u4e3a 0\nreturn if (node == null) -1 else node.?.height;\n}\n// \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\nfn updateHeight(self: *Self, node: ?*inc.TreeNode(T)) void {\n// \u8282\u70b9\u9ad8\u5ea6\u7b49\u4e8e\u6700\u9ad8\u5b50\u6811\u9ad8\u5ea6 + 1\nnode.?.height = std.math.max(self.height(node.?.left), self.height(node.?.right)) + 1;\n}\n</code></pre> avl_tree.dart<pre><code>/* \u83b7\u53d6\u8282\u70b9\u9ad8\u5ea6 */\nint height(TreeNode? node) {\nreturn node == null ? -1 : node.height;\n}\n/* \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6 */\nvoid updateHeight(TreeNode? node) {\n// \u8282\u70b9\u9ad8\u5ea6\u7b49\u4e8e\u6700\u9ad8\u5b50\u6811\u9ad8\u5ea6 + 1\nnode!.height = max(height(node.left), height(node.right)) + 1;\n}\n</code></pre>"},{"location":"chapter_tree/avl_tree/#_2","title":"\u8282\u70b9\u5e73\u8861\u56e0\u5b50","text":"<p>\u8282\u70b9\u7684\u300c\u5e73\u8861\u56e0\u5b50 Balance Factor\u300d\u5b9a\u4e49\u4e3a\u8282\u70b9\u5de6\u5b50\u6811\u7684\u9ad8\u5ea6\u51cf\u53bb\u53f3\u5b50\u6811\u7684\u9ad8\u5ea6\uff0c\u540c\u65f6\u89c4\u5b9a\u7a7a\u8282\u70b9\u7684\u5e73\u8861\u56e0\u5b50\u4e3a 0 \u3002\u6211\u4eec\u540c\u6837\u5c06\u83b7\u53d6\u8282\u70b9\u5e73\u8861\u56e0\u5b50\u7684\u529f\u80fd\u5c01\u88c5\u6210\u51fd\u6570\uff0c\u65b9\u4fbf\u540e\u7eed\u4f7f\u7528\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart avl_tree.java<pre><code>/* \u83b7\u53d6\u5e73\u8861\u56e0\u5b50 */\nint balanceFactor(TreeNode node) {\n// \u7a7a\u8282\u70b9\u5e73\u8861\u56e0\u5b50\u4e3a 0\nif (node == null)\nreturn 0;\n// \u8282\u70b9\u5e73\u8861\u56e0\u5b50 = \u5de6\u5b50\u6811\u9ad8\u5ea6 - \u53f3\u5b50\u6811\u9ad8\u5ea6\nreturn height(node.left) - height(node.right);\n}\n</code></pre> avl_tree.cpp<pre><code>/* \u83b7\u53d6\u5e73\u8861\u56e0\u5b50 */\nint balanceFactor(TreeNode *node) {\n// \u7a7a\u8282\u70b9\u5e73\u8861\u56e0\u5b50\u4e3a 0\nif (node == nullptr)\nreturn 0;\n// \u8282\u70b9\u5e73\u8861\u56e0\u5b50 = \u5de6\u5b50\u6811\u9ad8\u5ea6 - \u53f3\u5b50\u6811\u9ad8\u5ea6\nreturn height(node-&gt;left) - height(node-&gt;right);\n}\n</code></pre> avl_tree.py<pre><code>def balance_factor(self, node: TreeNode | None) -&gt; int:\n\"\"\"\u83b7\u53d6\u5e73\u8861\u56e0\u5b50\"\"\"\n# \u7a7a\u8282\u70b9\u5e73\u8861\u56e0\u5b50\u4e3a 0\nif node is None:\nreturn 0\n# \u8282\u70b9\u5e73\u8861\u56e0\u5b50 = \u5de6\u5b50\u6811\u9ad8\u5ea6 - \u53f3\u5b50\u6811\u9ad8\u5ea6\nreturn self.height(node.left) - self.height(node.right)\n</code></pre> avl_tree.go<pre><code>/* \u83b7\u53d6\u5e73\u8861\u56e0\u5b50 */\nfunc (t *aVLTree) balanceFactor(node *TreeNode) int {\n// \u7a7a\u8282\u70b9\u5e73\u8861\u56e0\u5b50\u4e3a 0\nif node == nil {\nreturn 0\n}\n// \u8282\u70b9\u5e73\u8861\u56e0\u5b50 = \u5de6\u5b50\u6811\u9ad8\u5ea6 - \u53f3\u5b50\u6811\u9ad8\u5ea6\nreturn t.height(node.Left) - t.height(node.Right)\n}\n</code></pre> avl_tree.js<pre><code>/* \u83b7\u53d6\u5e73\u8861\u56e0\u5b50 */\nbalanceFactor(node) {\n// \u7a7a\u8282\u70b9\u5e73\u8861\u56e0\u5b50\u4e3a 0\nif (node === null) return 0;\n// \u8282\u70b9\u5e73\u8861\u56e0\u5b50 = \u5de6\u5b50\u6811\u9ad8\u5ea6 - \u53f3\u5b50\u6811\u9ad8\u5ea6\nreturn this.height(node.left) - this.height(node.right);\n}\n</code></pre> avl_tree.ts<pre><code>/* \u83b7\u53d6\u5e73\u8861\u56e0\u5b50 */\nbalanceFactor(node: TreeNode): number {\n// \u7a7a\u8282\u70b9\u5e73\u8861\u56e0\u5b50\u4e3a 0\nif (node === null) return 0;\n// \u8282\u70b9\u5e73\u8861\u56e0\u5b50 = \u5de6\u5b50\u6811\u9ad8\u5ea6 - \u53f3\u5b50\u6811\u9ad8\u5ea6\nreturn this.height(node.left) - this.height(node.right);\n}\n</code></pre> avl_tree.c<pre><code>/* \u83b7\u53d6\u5e73\u8861\u56e0\u5b50 */\nint balanceFactor(TreeNode *node) {\n// \u7a7a\u8282\u70b9\u5e73\u8861\u56e0\u5b50\u4e3a 0\nif (node == NULL) {\nreturn 0;\n}\n// \u8282\u70b9\u5e73\u8861\u56e0\u5b50 = \u5de6\u5b50\u6811\u9ad8\u5ea6 - \u53f3\u5b50\u6811\u9ad8\u5ea6\nreturn height(node-&gt;left) - height(node-&gt;right);\n}\n</code></pre> avl_tree.cs<pre><code>/* \u83b7\u53d6\u5e73\u8861\u56e0\u5b50 */\nint balanceFactor(TreeNode? node) {\n// \u7a7a\u8282\u70b9\u5e73\u8861\u56e0\u5b50\u4e3a 0\nif (node == null) return 0;\n// \u8282\u70b9\u5e73\u8861\u56e0\u5b50 = \u5de6\u5b50\u6811\u9ad8\u5ea6 - \u53f3\u5b50\u6811\u9ad8\u5ea6\nreturn height(node.left) - height(node.right);\n}\n</code></pre> avl_tree.swift<pre><code>/* \u83b7\u53d6\u5e73\u8861\u56e0\u5b50 */\nfunc balanceFactor(node: TreeNode?) -&gt; Int {\n// \u7a7a\u8282\u70b9\u5e73\u8861\u56e0\u5b50\u4e3a 0\nguard let node = node else { return 0 }\n// \u8282\u70b9\u5e73\u8861\u56e0\u5b50 = \u5de6\u5b50\u6811\u9ad8\u5ea6 - \u53f3\u5b50\u6811\u9ad8\u5ea6\nreturn height(node: node.left) - height(node: node.right)\n}\n</code></pre> avl_tree.zig<pre><code>// \u83b7\u53d6\u5e73\u8861\u56e0\u5b50\nfn balanceFactor(self: *Self, node: ?*inc.TreeNode(T)) i32 {\n// \u7a7a\u8282\u70b9\u5e73\u8861\u56e0\u5b50\u4e3a 0\nif (node == null) return 0;\n// \u8282\u70b9\u5e73\u8861\u56e0\u5b50 = \u5de6\u5b50\u6811\u9ad8\u5ea6 - \u53f3\u5b50\u6811\u9ad8\u5ea6\nreturn self.height(node.?.left) - self.height(node.?.right);\n}\n</code></pre> avl_tree.dart<pre><code>/* \u83b7\u53d6\u5e73\u8861\u56e0\u5b50 */\nint balanceFactor(TreeNode? node) {\n// \u7a7a\u8282\u70b9\u5e73\u8861\u56e0\u5b50\u4e3a 0\nif (node == null) return 0;\n// \u8282\u70b9\u5e73\u8861\u56e0\u5b50 = \u5de6\u5b50\u6811\u9ad8\u5ea6 - \u53f3\u5b50\u6811\u9ad8\u5ea6\nreturn height(node.left) - height(node.right);\n}\n</code></pre> <p>Note</p> <p>\u8bbe\u5e73\u8861\u56e0\u5b50\u4e3a \\(f\\) \uff0c\u5219\u4e00\u68f5 AVL \u6811\u7684\u4efb\u610f\u8282\u70b9\u7684\u5e73\u8861\u56e0\u5b50\u7686\u6ee1\u8db3 \\(-1 \\le f \\le 1\\) \u3002</p>"},{"location":"chapter_tree/avl_tree/#752-avl","title":"7.5.2. \u00a0 AVL \u6811\u65cb\u8f6c","text":"<p>AVL \u6811\u7684\u7279\u70b9\u5728\u4e8e\u300c\u65cb\u8f6c Rotation\u300d\u64cd\u4f5c\uff0c\u5b83\u80fd\u591f\u5728\u4e0d\u5f71\u54cd\u4e8c\u53c9\u6811\u7684\u4e2d\u5e8f\u904d\u5386\u5e8f\u5217\u7684\u524d\u63d0\u4e0b\uff0c\u4f7f\u5931\u8861\u8282\u70b9\u91cd\u65b0\u6062\u590d\u5e73\u8861\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u65cb\u8f6c\u64cd\u4f5c\u65e2\u80fd\u4fdd\u6301\u6811\u7684\u300c\u4e8c\u53c9\u641c\u7d22\u6811\u300d\u5c5e\u6027\uff0c\u4e5f\u80fd\u4f7f\u6811\u91cd\u65b0\u53d8\u4e3a\u300c\u5e73\u8861\u4e8c\u53c9\u6811\u300d\u3002</p> <p>\u6211\u4eec\u5c06\u5e73\u8861\u56e0\u5b50\u7edd\u5bf9\u503c \\(&gt; 1\\) \u7684\u8282\u70b9\u79f0\u4e3a\u300c\u5931\u8861\u8282\u70b9\u300d\u3002\u6839\u636e\u8282\u70b9\u5931\u8861\u60c5\u51b5\u7684\u4e0d\u540c\uff0c\u65cb\u8f6c\u64cd\u4f5c\u5206\u4e3a\u56db\u79cd\uff1a\u53f3\u65cb\u3001\u5de6\u65cb\u3001\u5148\u53f3\u65cb\u540e\u5de6\u65cb\u3001\u5148\u5de6\u65cb\u540e\u53f3\u65cb\u3002\u4e0b\u9762\u6211\u4eec\u5c06\u8be6\u7ec6\u4ecb\u7ecd\u8fd9\u4e9b\u65cb\u8f6c\u64cd\u4f5c\u3002</p>"},{"location":"chapter_tree/avl_tree/#_3","title":"\u53f3\u65cb","text":"<p>\u5982\u4e0b\u56fe\u6240\u793a\uff0c\u8282\u70b9\u4e0b\u65b9\u4e3a\u5e73\u8861\u56e0\u5b50\u3002\u4ece\u5e95\u81f3\u9876\u770b\uff0c\u4e8c\u53c9\u6811\u4e2d\u9996\u4e2a\u5931\u8861\u8282\u70b9\u662f\u201c\u8282\u70b9 3\u201d\u3002\u6211\u4eec\u5173\u6ce8\u4ee5\u8be5\u5931\u8861\u8282\u70b9\u4e3a\u6839\u8282\u70b9\u7684\u5b50\u6811\uff0c\u5c06\u8be5\u8282\u70b9\u8bb0\u4e3a <code>node</code> \uff0c\u5176\u5de6\u5b50\u8282\u70b9\u8bb0\u4e3a <code>child</code> \uff0c\u6267\u884c\u300c\u53f3\u65cb\u300d\u64cd\u4f5c\u3002\u5b8c\u6210\u53f3\u65cb\u540e\uff0c\u5b50\u6811\u5df2\u7ecf\u6062\u590d\u5e73\u8861\uff0c\u5e76\u4e14\u4ecd\u7136\u4fdd\u6301\u4e8c\u53c9\u641c\u7d22\u6811\u7684\u7279\u6027\u3002</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt; <p></p> <p></p> <p></p> <p></p> <p>\u6b64\u5916\uff0c\u5982\u679c\u8282\u70b9 <code>child</code> \u672c\u8eab\u6709\u53f3\u5b50\u8282\u70b9\uff08\u8bb0\u4e3a <code>grandChild</code> \uff09\uff0c\u5219\u9700\u8981\u5728\u300c\u53f3\u65cb\u300d\u4e2d\u6dfb\u52a0\u4e00\u6b65\uff1a\u5c06 <code>grandChild</code> \u4f5c\u4e3a <code>node</code> \u7684\u5de6\u5b50\u8282\u70b9\u3002</p> <p></p> <p> Fig. \u6709 grandChild \u7684\u53f3\u65cb\u64cd\u4f5c </p> <p>\u201c\u5411\u53f3\u65cb\u8f6c\u201d\u662f\u4e00\u79cd\u5f62\u8c61\u5316\u7684\u8bf4\u6cd5\uff0c\u5b9e\u9645\u4e0a\u9700\u8981\u901a\u8fc7\u4fee\u6539\u8282\u70b9\u6307\u9488\u6765\u5b9e\u73b0\uff0c\u4ee3\u7801\u5982\u4e0b\u6240\u793a\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart avl_tree.java<pre><code>/* \u53f3\u65cb\u64cd\u4f5c */\nTreeNode rightRotate(TreeNode node) {\nTreeNode child = node.left;\nTreeNode grandChild = child.right;\n// \u4ee5 child \u4e3a\u539f\u70b9\uff0c\u5c06 node \u5411\u53f3\u65cb\u8f6c\nchild.right = node;\nnode.left = grandChild;\n// \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\nupdateHeight(node);\nupdateHeight(child);\n// \u8fd4\u56de\u65cb\u8f6c\u540e\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn child;\n}\n</code></pre> avl_tree.cpp<pre><code>/* \u53f3\u65cb\u64cd\u4f5c */\nTreeNode *rightRotate(TreeNode *node) {\nTreeNode *child = node-&gt;left;\nTreeNode *grandChild = child-&gt;right;\n// \u4ee5 child \u4e3a\u539f\u70b9\uff0c\u5c06 node \u5411\u53f3\u65cb\u8f6c\nchild-&gt;right = node;\nnode-&gt;left = grandChild;\n// \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\nupdateHeight(node);\nupdateHeight(child);\n// \u8fd4\u56de\u65cb\u8f6c\u540e\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn child;\n}\n</code></pre> avl_tree.py<pre><code>def __right_rotate(self, node: TreeNode | None) -&gt; TreeNode | None:\n\"\"\"\u53f3\u65cb\u64cd\u4f5c\"\"\"\nchild = node.left\ngrand_child = child.right\n# \u4ee5 child \u4e3a\u539f\u70b9\uff0c\u5c06 node \u5411\u53f3\u65cb\u8f6c\nchild.right = node\nnode.left = grand_child\n# \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\nself.__update_height(node)\nself.__update_height(child)\n# \u8fd4\u56de\u65cb\u8f6c\u540e\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn child\n</code></pre> avl_tree.go<pre><code>/* \u53f3\u65cb\u64cd\u4f5c */\nfunc (t *aVLTree) rightRotate(node *TreeNode) *TreeNode {\nchild := node.Left\ngrandChild := child.Right\n// \u4ee5 child \u4e3a\u539f\u70b9\uff0c\u5c06 node \u5411\u53f3\u65cb\u8f6c\nchild.Right = node\nnode.Left = grandChild\n// \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\nt.updateHeight(node)\nt.updateHeight(child)\n// \u8fd4\u56de\u65cb\u8f6c\u540e\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn child\n}\n</code></pre> avl_tree.js<pre><code>/* \u53f3\u65cb\u64cd\u4f5c */\n#rightRotate(node) {\nconst child = node.left;\nconst grandChild = child.right;\n// \u4ee5 child \u4e3a\u539f\u70b9\uff0c\u5c06 node \u5411\u53f3\u65cb\u8f6c\nchild.right = node;\nnode.left = grandChild;\n// \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\nthis.#updateHeight(node);\nthis.#updateHeight(child);\n// \u8fd4\u56de\u65cb\u8f6c\u540e\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn child;\n}\n</code></pre> avl_tree.ts<pre><code>/* \u53f3\u65cb\u64cd\u4f5c */\nrightRotate(node: TreeNode): TreeNode {\nconst child = node.left;\nconst grandChild = child.right;\n// \u4ee5 child \u4e3a\u539f\u70b9\uff0c\u5c06 node \u5411\u53f3\u65cb\u8f6c\nchild.right = node;\nnode.left = grandChild;\n// \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\nthis.updateHeight(node);\nthis.updateHeight(child);\n// \u8fd4\u56de\u65cb\u8f6c\u540e\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn child;\n}\n</code></pre> avl_tree.c<pre><code>/* \u53f3\u65cb\u64cd\u4f5c */\nTreeNode *rightRotate(TreeNode *node) {\nTreeNode *child, *grandChild;\nchild = node-&gt;left;\ngrandChild = child-&gt;right;\n// \u4ee5 child \u4e3a\u539f\u70b9\uff0c\u5c06 node \u5411\u53f3\u65cb\u8f6c\nchild-&gt;right = node;\nnode-&gt;left = grandChild;\n// \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\nupdateHeight(node);\nupdateHeight(child);\n// \u8fd4\u56de\u65cb\u8f6c\u540e\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn child;\n}\n</code></pre> avl_tree.cs<pre><code>/* \u53f3\u65cb\u64cd\u4f5c */\nTreeNode? rightRotate(TreeNode? node) {\nTreeNode? child = node.left;\nTreeNode? grandChild = child?.right;\n// \u4ee5 child \u4e3a\u539f\u70b9\uff0c\u5c06 node \u5411\u53f3\u65cb\u8f6c\nchild.right = node;\nnode.left = grandChild;\n// \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\nupdateHeight(node);\nupdateHeight(child);\n// \u8fd4\u56de\u65cb\u8f6c\u540e\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn child;\n}\n</code></pre> avl_tree.swift<pre><code>/* \u53f3\u65cb\u64cd\u4f5c */\nfunc rightRotate(node: TreeNode?) -&gt; TreeNode? {\nlet child = node?.left\nlet grandChild = child?.right\n// \u4ee5 child \u4e3a\u539f\u70b9\uff0c\u5c06 node \u5411\u53f3\u65cb\u8f6c\nchild?.right = node\nnode?.left = grandChild\n// \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\nupdateHeight(node: node)\nupdateHeight(node: child)\n// \u8fd4\u56de\u65cb\u8f6c\u540e\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn child\n}\n</code></pre> avl_tree.zig<pre><code>// \u53f3\u65cb\u64cd\u4f5c\nfn rightRotate(self: *Self, node: ?*inc.TreeNode(T)) ?*inc.TreeNode(T) {\nvar child = node.?.left;\nvar grandChild = child.?.right;\n// \u4ee5 child \u4e3a\u539f\u70b9\uff0c\u5c06 node \u5411\u53f3\u65cb\u8f6c\nchild.?.right = node;\nnode.?.left = grandChild;\n// \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\nself.updateHeight(node);\nself.updateHeight(child);\n// \u8fd4\u56de\u65cb\u8f6c\u540e\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn child;\n}\n</code></pre> avl_tree.dart<pre><code>/* \u53f3\u65cb\u64cd\u4f5c */\nTreeNode? rightRotate(TreeNode? node) {\nTreeNode? child = node!.left;\nTreeNode? grandChild = child!.right;\n// \u4ee5 child \u4e3a\u539f\u70b9\uff0c\u5c06 node \u5411\u53f3\u65cb\u8f6c\nchild.right = node;\nnode.left = grandChild;\n// \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\nupdateHeight(node);\nupdateHeight(child);\n// \u8fd4\u56de\u65cb\u8f6c\u540e\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn child;\n}\n</code></pre>"},{"location":"chapter_tree/avl_tree/#_4","title":"\u5de6\u65cb","text":"<p>\u76f8\u5e94\u7684\uff0c\u5982\u679c\u8003\u8651\u4e0a\u8ff0\u5931\u8861\u4e8c\u53c9\u6811\u7684\u201c\u955c\u50cf\u201d\uff0c\u5219\u9700\u8981\u6267\u884c\u300c\u5de6\u65cb\u300d\u64cd\u4f5c\u3002</p> <p></p> <p> Fig. \u5de6\u65cb\u64cd\u4f5c </p> <p>\u540c\u7406\uff0c\u82e5\u8282\u70b9 <code>child</code> \u672c\u8eab\u6709\u5de6\u5b50\u8282\u70b9\uff08\u8bb0\u4e3a <code>grandChild</code> \uff09\uff0c\u5219\u9700\u8981\u5728\u300c\u5de6\u65cb\u300d\u4e2d\u6dfb\u52a0\u4e00\u6b65\uff1a\u5c06 <code>grandChild</code> \u4f5c\u4e3a <code>node</code> \u7684\u53f3\u5b50\u8282\u70b9\u3002</p> <p></p> <p> Fig. \u6709 grandChild \u7684\u5de6\u65cb\u64cd\u4f5c </p> <p>\u53ef\u4ee5\u89c2\u5bdf\u5230\uff0c\u53f3\u65cb\u548c\u5de6\u65cb\u64cd\u4f5c\u5728\u903b\u8f91\u4e0a\u662f\u955c\u50cf\u5bf9\u79f0\u7684\uff0c\u5b83\u4eec\u5206\u522b\u89e3\u51b3\u7684\u4e24\u79cd\u5931\u8861\u60c5\u51b5\u4e5f\u662f\u5bf9\u79f0\u7684\u3002\u57fa\u4e8e\u5bf9\u79f0\u6027\uff0c\u6211\u4eec\u53ef\u4ee5\u8f7b\u677e\u5730\u4ece\u53f3\u65cb\u7684\u4ee3\u7801\u63a8\u5bfc\u51fa\u5de6\u65cb\u7684\u4ee3\u7801\u3002\u5177\u4f53\u5730\uff0c\u53ea\u9700\u5c06\u300c\u53f3\u65cb\u300d\u4ee3\u7801\u4e2d\u7684\u628a\u6240\u6709\u7684 <code>left</code> \u66ff\u6362\u4e3a <code>right</code> \uff0c\u5c06\u6240\u6709\u7684 <code>right</code> \u66ff\u6362\u4e3a <code>left</code> \uff0c\u5373\u53ef\u5f97\u5230\u300c\u5de6\u65cb\u300d\u4ee3\u7801\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart avl_tree.java<pre><code>/* \u5de6\u65cb\u64cd\u4f5c */\nTreeNode leftRotate(TreeNode node) {\nTreeNode child = node.right;\nTreeNode grandChild = child.left;\n// \u4ee5 child \u4e3a\u539f\u70b9\uff0c\u5c06 node \u5411\u5de6\u65cb\u8f6c\nchild.left = node;\nnode.right = grandChild;\n// \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\nupdateHeight(node);\nupdateHeight(child);\n// \u8fd4\u56de\u65cb\u8f6c\u540e\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn child;\n}\n</code></pre> avl_tree.cpp<pre><code>/* \u5de6\u65cb\u64cd\u4f5c */\nTreeNode *leftRotate(TreeNode *node) {\nTreeNode *child = node-&gt;right;\nTreeNode *grandChild = child-&gt;left;\n// \u4ee5 child \u4e3a\u539f\u70b9\uff0c\u5c06 node \u5411\u5de6\u65cb\u8f6c\nchild-&gt;left = node;\nnode-&gt;right = grandChild;\n// \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\nupdateHeight(node);\nupdateHeight(child);\n// \u8fd4\u56de\u65cb\u8f6c\u540e\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn child;\n}\n</code></pre> avl_tree.py<pre><code>def __left_rotate(self, node: TreeNode | None) -&gt; TreeNode | None:\n\"\"\"\u5de6\u65cb\u64cd\u4f5c\"\"\"\nchild = node.right\ngrand_child = child.left\n# \u4ee5 child \u4e3a\u539f\u70b9\uff0c\u5c06 node \u5411\u5de6\u65cb\u8f6c\nchild.left = node\nnode.right = grand_child\n# \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\nself.__update_height(node)\nself.__update_height(child)\n# \u8fd4\u56de\u65cb\u8f6c\u540e\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn child\n</code></pre> avl_tree.go<pre><code>/* \u5de6\u65cb\u64cd\u4f5c */\nfunc (t *aVLTree) leftRotate(node *TreeNode) *TreeNode {\nchild := node.Right\ngrandChild := child.Left\n// \u4ee5 child \u4e3a\u539f\u70b9\uff0c\u5c06 node \u5411\u5de6\u65cb\u8f6c\nchild.Left = node\nnode.Right = grandChild\n// \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\nt.updateHeight(node)\nt.updateHeight(child)\n// \u8fd4\u56de\u65cb\u8f6c\u540e\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn child\n}\n</code></pre> avl_tree.js<pre><code>/* \u5de6\u65cb\u64cd\u4f5c */\n#leftRotate(node) {\nconst child = node.right;\nconst grandChild = child.left;\n// \u4ee5 child \u4e3a\u539f\u70b9\uff0c\u5c06 node \u5411\u5de6\u65cb\u8f6c\nchild.left = node;\nnode.right = grandChild;\n// \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\nthis.#updateHeight(node);\nthis.#updateHeight(child);\n// \u8fd4\u56de\u65cb\u8f6c\u540e\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn child;\n}\n</code></pre> avl_tree.ts<pre><code>/* \u5de6\u65cb\u64cd\u4f5c */\nleftRotate(node: TreeNode): TreeNode {\nconst child = node.right;\nconst grandChild = child.left;\n// \u4ee5 child \u4e3a\u539f\u70b9\uff0c\u5c06 node \u5411\u5de6\u65cb\u8f6c\nchild.left = node;\nnode.right = grandChild;\n// \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\nthis.updateHeight(node);\nthis.updateHeight(child);\n// \u8fd4\u56de\u65cb\u8f6c\u540e\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn child;\n}\n</code></pre> avl_tree.c<pre><code>/* \u5de6\u65cb\u64cd\u4f5c */\nTreeNode *leftRotate(TreeNode *node) {\nTreeNode *child, *grandChild;\nchild = node-&gt;right;\ngrandChild = child-&gt;left;\n// \u4ee5 child \u4e3a\u539f\u70b9\uff0c\u5c06 node \u5411\u5de6\u65cb\u8f6c\nchild-&gt;left = node;\nnode-&gt;right = grandChild;\n// \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\nupdateHeight(node);\nupdateHeight(child);\n// \u8fd4\u56de\u65cb\u8f6c\u540e\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn child;\n}\n</code></pre> avl_tree.cs<pre><code>/* \u5de6\u65cb\u64cd\u4f5c */\nTreeNode? leftRotate(TreeNode? node) {\nTreeNode? child = node.right;\nTreeNode? grandChild = child?.left;\n// \u4ee5 child \u4e3a\u539f\u70b9\uff0c\u5c06 node \u5411\u5de6\u65cb\u8f6c\nchild.left = node;\nnode.right = grandChild;\n// \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\nupdateHeight(node);\nupdateHeight(child);\n// \u8fd4\u56de\u65cb\u8f6c\u540e\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn child;\n}\n</code></pre> avl_tree.swift<pre><code>/* \u5de6\u65cb\u64cd\u4f5c */\nfunc leftRotate(node: TreeNode?) -&gt; TreeNode? {\nlet child = node?.right\nlet grandChild = child?.left\n// \u4ee5 child \u4e3a\u539f\u70b9\uff0c\u5c06 node \u5411\u5de6\u65cb\u8f6c\nchild?.left = node\nnode?.right = grandChild\n// \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\nupdateHeight(node: node)\nupdateHeight(node: child)\n// \u8fd4\u56de\u65cb\u8f6c\u540e\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn child\n}\n</code></pre> avl_tree.zig<pre><code>// \u5de6\u65cb\u64cd\u4f5c\nfn leftRotate(self: *Self, node: ?*inc.TreeNode(T)) ?*inc.TreeNode(T) {\nvar child = node.?.right;\nvar grandChild = child.?.left;\n// \u4ee5 child \u4e3a\u539f\u70b9\uff0c\u5c06 node \u5411\u5de6\u65cb\u8f6c\nchild.?.left = node;\nnode.?.right = grandChild;\n// \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\nself.updateHeight(node);\nself.updateHeight(child);\n// \u8fd4\u56de\u65cb\u8f6c\u540e\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn child;\n}\n</code></pre> avl_tree.dart<pre><code>/* \u5de6\u65cb\u64cd\u4f5c */\nTreeNode? leftRotate(TreeNode? node) {\nTreeNode? child = node!.right;\nTreeNode? grandChild = child!.left;\n// \u4ee5 child \u4e3a\u539f\u70b9\uff0c\u5c06 node \u5411\u5de6\u65cb\u8f6c\nchild.left = node;\nnode.right = grandChild;\n// \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\nupdateHeight(node);\nupdateHeight(child);\n// \u8fd4\u56de\u65cb\u8f6c\u540e\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn child;\n}\n</code></pre>"},{"location":"chapter_tree/avl_tree/#_5","title":"\u5148\u5de6\u65cb\u540e\u53f3\u65cb","text":"<p>\u5bf9\u4e8e\u4e0b\u56fe\u4e2d\u7684\u5931\u8861\u8282\u70b9 3\uff0c\u4ec5\u4f7f\u7528\u5de6\u65cb\u6216\u53f3\u65cb\u90fd\u65e0\u6cd5\u4f7f\u5b50\u6811\u6062\u590d\u5e73\u8861\u3002\u6b64\u65f6\u9700\u8981\u5148\u5de6\u65cb\u540e\u53f3\u65cb\uff0c\u5373\u5148\u5bf9 <code>child</code> \u6267\u884c\u300c\u5de6\u65cb\u300d\uff0c\u518d\u5bf9 <code>node</code> \u6267\u884c\u300c\u53f3\u65cb\u300d\u3002</p> <p></p> <p> Fig. \u5148\u5de6\u65cb\u540e\u53f3\u65cb </p>"},{"location":"chapter_tree/avl_tree/#_6","title":"\u5148\u53f3\u65cb\u540e\u5de6\u65cb","text":"<p>\u540c\u7406\uff0c\u5bf9\u4e8e\u4e0a\u8ff0\u5931\u8861\u4e8c\u53c9\u6811\u7684\u955c\u50cf\u60c5\u51b5\uff0c\u9700\u8981\u5148\u53f3\u65cb\u540e\u5de6\u65cb\uff0c\u5373\u5148\u5bf9 <code>child</code> \u6267\u884c\u300c\u53f3\u65cb\u300d\uff0c\u7136\u540e\u5bf9 <code>node</code> \u6267\u884c\u300c\u5de6\u65cb\u300d\u3002</p> <p></p> <p> Fig. \u5148\u53f3\u65cb\u540e\u5de6\u65cb </p>"},{"location":"chapter_tree/avl_tree/#_7","title":"\u65cb\u8f6c\u7684\u9009\u62e9","text":"<p>\u4e0b\u56fe\u5c55\u793a\u7684\u56db\u79cd\u5931\u8861\u60c5\u51b5\u4e0e\u4e0a\u8ff0\u6848\u4f8b\u9010\u4e2a\u5bf9\u5e94\uff0c\u5206\u522b\u9700\u8981\u91c7\u7528\u53f3\u65cb\u3001\u5de6\u65cb\u3001\u5148\u53f3\u540e\u5de6\u3001\u5148\u5de6\u540e\u53f3\u7684\u65cb\u8f6c\u64cd\u4f5c\u3002</p> <p></p> <p> Fig. AVL \u6811\u7684\u56db\u79cd\u65cb\u8f6c\u60c5\u51b5 </p> <p>\u5728\u4ee3\u7801\u4e2d\uff0c\u6211\u4eec\u901a\u8fc7\u5224\u65ad\u5931\u8861\u8282\u70b9\u7684\u5e73\u8861\u56e0\u5b50\u4ee5\u53ca\u8f83\u9ad8\u4e00\u4fa7\u5b50\u8282\u70b9\u7684\u5e73\u8861\u56e0\u5b50\u7684\u6b63\u8d1f\u53f7\uff0c\u6765\u786e\u5b9a\u5931\u8861\u8282\u70b9\u5c5e\u4e8e\u4e0a\u56fe\u4e2d\u7684\u54ea\u79cd\u60c5\u51b5\u3002</p> \u5931\u8861\u8282\u70b9\u7684\u5e73\u8861\u56e0\u5b50 \u5b50\u8282\u70b9\u7684\u5e73\u8861\u56e0\u5b50 \u5e94\u91c7\u7528\u7684\u65cb\u8f6c\u65b9\u6cd5 \\(&gt;0\\) \uff08\u5373\u5de6\u504f\u6811\uff09 \\(\\geq 0\\) \u53f3\u65cb \\(&gt;0\\) \uff08\u5373\u5de6\u504f\u6811\uff09 \\(&lt;0\\) \u5148\u5de6\u65cb\u540e\u53f3\u65cb \\(&lt;0\\) \uff08\u5373\u53f3\u504f\u6811\uff09 \\(\\leq 0\\) \u5de6\u65cb \\(&lt;0\\) \uff08\u5373\u53f3\u504f\u6811\uff09 \\(&gt;0\\) \u5148\u53f3\u65cb\u540e\u5de6\u65cb <p>\u4e3a\u4e86\u4fbf\u4e8e\u4f7f\u7528\uff0c\u6211\u4eec\u5c06\u65cb\u8f6c\u64cd\u4f5c\u5c01\u88c5\u6210\u4e00\u4e2a\u51fd\u6570\u3002\u6709\u4e86\u8fd9\u4e2a\u51fd\u6570\uff0c\u6211\u4eec\u5c31\u80fd\u5bf9\u5404\u79cd\u5931\u8861\u60c5\u51b5\u8fdb\u884c\u65cb\u8f6c\uff0c\u4f7f\u5931\u8861\u8282\u70b9\u91cd\u65b0\u6062\u590d\u5e73\u8861\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart avl_tree.java<pre><code>/* \u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u8be5\u5b50\u6811\u91cd\u65b0\u6062\u590d\u5e73\u8861 */\nTreeNode rotate(TreeNode node) {\n// \u83b7\u53d6\u8282\u70b9 node \u7684\u5e73\u8861\u56e0\u5b50\nint balanceFactor = balanceFactor(node);\n// \u5de6\u504f\u6811\nif (balanceFactor &gt; 1) {\nif (balanceFactor(node.left) &gt;= 0) {\n// \u53f3\u65cb\nreturn rightRotate(node);\n} else {\n// \u5148\u5de6\u65cb\u540e\u53f3\u65cb\nnode.left = leftRotate(node.left);\nreturn rightRotate(node);\n}\n}\n// \u53f3\u504f\u6811\nif (balanceFactor &lt; -1) {\nif (balanceFactor(node.right) &lt;= 0) {\n// \u5de6\u65cb\nreturn leftRotate(node);\n} else {\n// \u5148\u53f3\u65cb\u540e\u5de6\u65cb\nnode.right = rightRotate(node.right);\nreturn leftRotate(node);\n}\n}\n// \u5e73\u8861\u6811\uff0c\u65e0\u9700\u65cb\u8f6c\uff0c\u76f4\u63a5\u8fd4\u56de\nreturn node;\n}\n</code></pre> avl_tree.cpp<pre><code>/* \u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u8be5\u5b50\u6811\u91cd\u65b0\u6062\u590d\u5e73\u8861 */\nTreeNode *rotate(TreeNode *node) {\n// \u83b7\u53d6\u8282\u70b9 node \u7684\u5e73\u8861\u56e0\u5b50\nint _balanceFactor = balanceFactor(node);\n// \u5de6\u504f\u6811\nif (_balanceFactor &gt; 1) {\nif (balanceFactor(node-&gt;left) &gt;= 0) {\n// \u53f3\u65cb\nreturn rightRotate(node);\n} else {\n// \u5148\u5de6\u65cb\u540e\u53f3\u65cb\nnode-&gt;left = leftRotate(node-&gt;left);\nreturn rightRotate(node);\n}\n}\n// \u53f3\u504f\u6811\nif (_balanceFactor &lt; -1) {\nif (balanceFactor(node-&gt;right) &lt;= 0) {\n// \u5de6\u65cb\nreturn leftRotate(node);\n} else {\n// \u5148\u53f3\u65cb\u540e\u5de6\u65cb\nnode-&gt;right = rightRotate(node-&gt;right);\nreturn leftRotate(node);\n}\n}\n// \u5e73\u8861\u6811\uff0c\u65e0\u9700\u65cb\u8f6c\uff0c\u76f4\u63a5\u8fd4\u56de\nreturn node;\n}\n</code></pre> avl_tree.py<pre><code>def __rotate(self, node: TreeNode | None) -&gt; TreeNode | None:\n\"\"\"\u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u8be5\u5b50\u6811\u91cd\u65b0\u6062\u590d\u5e73\u8861\"\"\"\n# \u83b7\u53d6\u8282\u70b9 node \u7684\u5e73\u8861\u56e0\u5b50\nbalance_factor = self.balance_factor(node)\n# \u5de6\u504f\u6811\nif balance_factor &gt; 1:\nif self.balance_factor(node.left) &gt;= 0:\n# \u53f3\u65cb\nreturn self.__right_rotate(node)\nelse:\n# \u5148\u5de6\u65cb\u540e\u53f3\u65cb\nnode.left = self.__left_rotate(node.left)\nreturn self.__right_rotate(node)\n# \u53f3\u504f\u6811\nelif balance_factor &lt; -1:\nif self.balance_factor(node.right) &lt;= 0:\n# \u5de6\u65cb\nreturn self.__left_rotate(node)\nelse:\n# \u5148\u53f3\u65cb\u540e\u5de6\u65cb\nnode.right = self.__right_rotate(node.right)\nreturn self.__left_rotate(node)\n# \u5e73\u8861\u6811\uff0c\u65e0\u9700\u65cb\u8f6c\uff0c\u76f4\u63a5\u8fd4\u56de\nreturn node\n</code></pre> avl_tree.go<pre><code>/* \u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u8be5\u5b50\u6811\u91cd\u65b0\u6062\u590d\u5e73\u8861 */\nfunc (t *aVLTree) rotate(node *TreeNode) *TreeNode {\n// \u83b7\u53d6\u8282\u70b9 node \u7684\u5e73\u8861\u56e0\u5b50\n// Go \u63a8\u8350\u77ed\u53d8\u91cf\uff0c\u8fd9\u91cc bf \u6307\u4ee3 t.balanceFactor\nbf := t.balanceFactor(node)\n// \u5de6\u504f\u6811\nif bf &gt; 1 {\nif t.balanceFactor(node.Left) &gt;= 0 {\n// \u53f3\u65cb\nreturn t.rightRotate(node)\n} else {\n// \u5148\u5de6\u65cb\u540e\u53f3\u65cb\nnode.Left = t.leftRotate(node.Left)\nreturn t.rightRotate(node)\n}\n}\n// \u53f3\u504f\u6811\nif bf &lt; -1 {\nif t.balanceFactor(node.Right) &lt;= 0 {\n// \u5de6\u65cb\nreturn t.leftRotate(node)\n} else {\n// \u5148\u53f3\u65cb\u540e\u5de6\u65cb\nnode.Right = t.rightRotate(node.Right)\nreturn t.leftRotate(node)\n}\n}\n// \u5e73\u8861\u6811\uff0c\u65e0\u9700\u65cb\u8f6c\uff0c\u76f4\u63a5\u8fd4\u56de\nreturn node\n}\n</code></pre> avl_tree.js<pre><code>/* \u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u8be5\u5b50\u6811\u91cd\u65b0\u6062\u590d\u5e73\u8861 */\n#rotate(node) {\n// \u83b7\u53d6\u8282\u70b9 node \u7684\u5e73\u8861\u56e0\u5b50\nconst balanceFactor = this.balanceFactor(node);\n// \u5de6\u504f\u6811\nif (balanceFactor &gt; 1) {\nif (this.balanceFactor(node.left) &gt;= 0) {\n// \u53f3\u65cb\nreturn this.#rightRotate(node);\n} else {\n// \u5148\u5de6\u65cb\u540e\u53f3\u65cb\nnode.left = this.#leftRotate(node.left);\nreturn this.#rightRotate(node);\n}\n}\n// \u53f3\u504f\u6811\nif (balanceFactor &lt; -1) {\nif (this.balanceFactor(node.right) &lt;= 0) {\n// \u5de6\u65cb\nreturn this.#leftRotate(node);\n} else {\n// \u5148\u53f3\u65cb\u540e\u5de6\u65cb\nnode.right = this.#rightRotate(node.right);\nreturn this.#leftRotate(node);\n}\n}\n// \u5e73\u8861\u6811\uff0c\u65e0\u9700\u65cb\u8f6c\uff0c\u76f4\u63a5\u8fd4\u56de\nreturn node;\n}\n</code></pre> avl_tree.ts<pre><code>/* \u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u8be5\u5b50\u6811\u91cd\u65b0\u6062\u590d\u5e73\u8861 */\nrotate(node: TreeNode): TreeNode {\n// \u83b7\u53d6\u8282\u70b9 node \u7684\u5e73\u8861\u56e0\u5b50\nconst balanceFactor = this.balanceFactor(node);\n// \u5de6\u504f\u6811\nif (balanceFactor &gt; 1) {\nif (this.balanceFactor(node.left) &gt;= 0) {\n// \u53f3\u65cb\nreturn this.rightRotate(node);\n} else {\n// \u5148\u5de6\u65cb\u540e\u53f3\u65cb\nnode.left = this.leftRotate(node.left);\nreturn this.rightRotate(node);\n}\n}\n// \u53f3\u504f\u6811\nif (balanceFactor &lt; -1) {\nif (this.balanceFactor(node.right) &lt;= 0) {\n// \u5de6\u65cb\nreturn this.leftRotate(node);\n} else {\n// \u5148\u53f3\u65cb\u540e\u5de6\u65cb\nnode.right = this.rightRotate(node.right);\nreturn this.leftRotate(node);\n}\n}\n// \u5e73\u8861\u6811\uff0c\u65e0\u9700\u65cb\u8f6c\uff0c\u76f4\u63a5\u8fd4\u56de\nreturn node;\n}\n</code></pre> avl_tree.c<pre><code>/* \u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u8be5\u5b50\u6811\u91cd\u65b0\u6062\u590d\u5e73\u8861 */\nTreeNode *rotate(TreeNode *node) {\n// \u83b7\u53d6\u8282\u70b9 node \u7684\u5e73\u8861\u56e0\u5b50\nint bf = balanceFactor(node);\n// \u5de6\u504f\u6811\nif (bf &gt; 1) {\nif (balanceFactor(node-&gt;left) &gt;= 0) {\n// \u53f3\u65cb\nreturn rightRotate(node);\n} else {\n// \u5148\u5de6\u65cb\u540e\u53f3\u65cb\nnode-&gt;left = leftRotate(node-&gt;left);\nreturn rightRotate(node);\n}\n}\n// \u53f3\u504f\u6811\nif (bf &lt; -1) {\nif (balanceFactor(node-&gt;right) &lt;= 0) {\n// \u5de6\u65cb\nreturn leftRotate(node);\n} else {\n// \u5148\u53f3\u65cb\u540e\u5de6\u65cb\nnode-&gt;right = rightRotate(node-&gt;right);\nreturn leftRotate(node);\n}\n}\n// \u5e73\u8861\u6811\uff0c\u65e0\u9700\u65cb\u8f6c\uff0c\u76f4\u63a5\u8fd4\u56de\nreturn node;\n}\n</code></pre> avl_tree.cs<pre><code>/* \u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u8be5\u5b50\u6811\u91cd\u65b0\u6062\u590d\u5e73\u8861 */\nTreeNode? rotate(TreeNode? node) {\n// \u83b7\u53d6\u8282\u70b9 node \u7684\u5e73\u8861\u56e0\u5b50\nint balanceFactorInt = balanceFactor(node);\n// \u5de6\u504f\u6811\nif (balanceFactorInt &gt; 1) {\nif (balanceFactor(node.left) &gt;= 0) {\n// \u53f3\u65cb\nreturn rightRotate(node);\n} else {\n// \u5148\u5de6\u65cb\u540e\u53f3\u65cb\nnode.left = leftRotate(node?.left);\nreturn rightRotate(node);\n}\n}\n// \u53f3\u504f\u6811\nif (balanceFactorInt &lt; -1) {\nif (balanceFactor(node.right) &lt;= 0) {\n// \u5de6\u65cb\nreturn leftRotate(node);\n} else {\n// \u5148\u53f3\u65cb\u540e\u5de6\u65cb\nnode.right = rightRotate(node?.right);\nreturn leftRotate(node);\n}\n}\n// \u5e73\u8861\u6811\uff0c\u65e0\u9700\u65cb\u8f6c\uff0c\u76f4\u63a5\u8fd4\u56de\nreturn node;\n}\n</code></pre> avl_tree.swift<pre><code>/* \u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u8be5\u5b50\u6811\u91cd\u65b0\u6062\u590d\u5e73\u8861 */\nfunc rotate(node: TreeNode?) -&gt; TreeNode? {\n// \u83b7\u53d6\u8282\u70b9 node \u7684\u5e73\u8861\u56e0\u5b50\nlet balanceFactor = balanceFactor(node: node)\n// \u5de6\u504f\u6811\nif balanceFactor &gt; 1 {\nif self.balanceFactor(node: node?.left) &gt;= 0 {\n// \u53f3\u65cb\nreturn rightRotate(node: node)\n} else {\n// \u5148\u5de6\u65cb\u540e\u53f3\u65cb\nnode?.left = leftRotate(node: node?.left)\nreturn rightRotate(node: node)\n}\n}\n// \u53f3\u504f\u6811\nif balanceFactor &lt; -1 {\nif self.balanceFactor(node: node?.right) &lt;= 0 {\n// \u5de6\u65cb\nreturn leftRotate(node: node)\n} else {\n// \u5148\u53f3\u65cb\u540e\u5de6\u65cb\nnode?.right = rightRotate(node: node?.right)\nreturn leftRotate(node: node)\n}\n}\n// \u5e73\u8861\u6811\uff0c\u65e0\u9700\u65cb\u8f6c\uff0c\u76f4\u63a5\u8fd4\u56de\nreturn node\n}\n</code></pre> avl_tree.zig<pre><code>// \u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u8be5\u5b50\u6811\u91cd\u65b0\u6062\u590d\u5e73\u8861\nfn rotate(self: *Self, node: ?*inc.TreeNode(T)) ?*inc.TreeNode(T) {\n// \u83b7\u53d6\u8282\u70b9 node \u7684\u5e73\u8861\u56e0\u5b50\nvar balance_factor = self.balanceFactor(node);\n// \u5de6\u504f\u6811\nif (balance_factor &gt; 1) {\nif (self.balanceFactor(node.?.left) &gt;= 0) {\n// \u53f3\u65cb\nreturn self.rightRotate(node);\n} else {\n// \u5148\u5de6\u65cb\u540e\u53f3\u65cb\nnode.?.left = self.leftRotate(node.?.left);\nreturn self.rightRotate(node);\n}\n}\n// \u53f3\u504f\u6811\nif (balance_factor &lt; -1) {\nif (self.balanceFactor(node.?.right) &lt;= 0) {\n// \u5de6\u65cb\nreturn self.leftRotate(node);\n} else {\n// \u5148\u53f3\u65cb\u540e\u5de6\u65cb\nnode.?.right = self.rightRotate(node.?.right);\nreturn self.leftRotate(node);\n}\n}\n// \u5e73\u8861\u6811\uff0c\u65e0\u9700\u65cb\u8f6c\uff0c\u76f4\u63a5\u8fd4\u56de\nreturn node;\n}\n</code></pre> avl_tree.dart<pre><code>/* \u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u8be5\u5b50\u6811\u91cd\u65b0\u6062\u590d\u5e73\u8861 */\nTreeNode? rotate(TreeNode? node) {\n// \u83b7\u53d6\u8282\u70b9 node \u7684\u5e73\u8861\u56e0\u5b50\nint factor = balanceFactor(node);\n// \u5de6\u504f\u6811\nif (factor &gt; 1) {\nif (balanceFactor(node!.left) &gt;= 0) {\n// \u53f3\u65cb\nreturn rightRotate(node);\n} else {\n// \u5148\u5de6\u65cb\u540e\u53f3\u65cb\nnode.left = leftRotate(node.left);\nreturn rightRotate(node);\n}\n}\n// \u53f3\u504f\u6811\nif (factor &lt; -1) {\nif (balanceFactor(node!.right) &lt;= 0) {\n// \u5de6\u65cb\nreturn leftRotate(node);\n} else {\n// \u5148\u53f3\u65cb\u540e\u5de6\u65cb\nnode.right = rightRotate(node.right);\nreturn leftRotate(node);\n}\n}\n// \u5e73\u8861\u6811\uff0c\u65e0\u9700\u65cb\u8f6c\uff0c\u76f4\u63a5\u8fd4\u56de\nreturn node;\n}\n</code></pre>"},{"location":"chapter_tree/avl_tree/#753-avl","title":"7.5.3. \u00a0 AVL \u6811\u5e38\u7528\u64cd\u4f5c","text":""},{"location":"chapter_tree/avl_tree/#_8","title":"\u63d2\u5165\u8282\u70b9","text":"<p>\u300cAVL \u6811\u300d\u7684\u8282\u70b9\u63d2\u5165\u64cd\u4f5c\u4e0e\u300c\u4e8c\u53c9\u641c\u7d22\u6811\u300d\u5728\u4e3b\u4f53\u4e0a\u7c7b\u4f3c\u3002\u552f\u4e00\u7684\u533a\u522b\u5728\u4e8e\uff0c\u5728 AVL \u6811\u4e2d\u63d2\u5165\u8282\u70b9\u540e\uff0c\u4ece\u8be5\u8282\u70b9\u5230\u6839\u8282\u70b9\u7684\u8def\u5f84\u4e0a\u53ef\u80fd\u4f1a\u51fa\u73b0\u4e00\u7cfb\u5217\u5931\u8861\u8282\u70b9\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u9700\u8981\u4ece\u8fd9\u4e2a\u8282\u70b9\u5f00\u59cb\uff0c\u81ea\u5e95\u5411\u4e0a\u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u6240\u6709\u5931\u8861\u8282\u70b9\u6062\u590d\u5e73\u8861\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart avl_tree.java<pre><code>/* \u63d2\u5165\u8282\u70b9 */\nvoid insert(int val) {\nroot = insertHelper(root, val);\n}\n/* \u9012\u5f52\u63d2\u5165\u8282\u70b9\uff08\u8f85\u52a9\u65b9\u6cd5\uff09 */\nTreeNode insertHelper(TreeNode node, int val) {\nif (node == null)\nreturn new TreeNode(val);\n/* 1. \u67e5\u627e\u63d2\u5165\u4f4d\u7f6e\uff0c\u5e76\u63d2\u5165\u8282\u70b9 */\nif (val &lt; node.val)\nnode.left = insertHelper(node.left, val);\nelse if (val &gt; node.val)\nnode.right = insertHelper(node.right, val);\nelse\nreturn node; // \u91cd\u590d\u8282\u70b9\u4e0d\u63d2\u5165\uff0c\u76f4\u63a5\u8fd4\u56de\nupdateHeight(node); // \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\n/* 2. \u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u8be5\u5b50\u6811\u91cd\u65b0\u6062\u590d\u5e73\u8861 */\nnode = rotate(node);\n// \u8fd4\u56de\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn node;\n}\n</code></pre> avl_tree.cpp<pre><code>/* \u63d2\u5165\u8282\u70b9 */\nvoid insert(int val) {\nroot = insertHelper(root, val);\n}\n/* \u9012\u5f52\u63d2\u5165\u8282\u70b9\uff08\u8f85\u52a9\u65b9\u6cd5\uff09 */\nTreeNode *insertHelper(TreeNode *node, int val) {\nif (node == nullptr)\nreturn new TreeNode(val);\n/* 1. \u67e5\u627e\u63d2\u5165\u4f4d\u7f6e\uff0c\u5e76\u63d2\u5165\u8282\u70b9 */\nif (val &lt; node-&gt;val)\nnode-&gt;left = insertHelper(node-&gt;left, val);\nelse if (val &gt; node-&gt;val)\nnode-&gt;right = insertHelper(node-&gt;right, val);\nelse\nreturn node;    // \u91cd\u590d\u8282\u70b9\u4e0d\u63d2\u5165\uff0c\u76f4\u63a5\u8fd4\u56de\nupdateHeight(node); // \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\n/* 2. \u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u8be5\u5b50\u6811\u91cd\u65b0\u6062\u590d\u5e73\u8861 */\nnode = rotate(node);\n// \u8fd4\u56de\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn node;\n}\n</code></pre> avl_tree.py<pre><code>def insert(self, val) -&gt; None:\n\"\"\"\u63d2\u5165\u8282\u70b9\"\"\"\nself.__root = self.__insert_helper(self.__root, val)\ndef __insert_helper(self, node: TreeNode | None, val: int) -&gt; TreeNode:\n\"\"\"\u9012\u5f52\u63d2\u5165\u8282\u70b9\uff08\u8f85\u52a9\u65b9\u6cd5\uff09\"\"\"\nif node is None:\nreturn TreeNode(val)\n# 1. \u67e5\u627e\u63d2\u5165\u4f4d\u7f6e\uff0c\u5e76\u63d2\u5165\u8282\u70b9\nif val &lt; node.val:\nnode.left = self.__insert_helper(node.left, val)\nelif val &gt; node.val:\nnode.right = self.__insert_helper(node.right, val)\nelse:\n# \u91cd\u590d\u8282\u70b9\u4e0d\u63d2\u5165\uff0c\u76f4\u63a5\u8fd4\u56de\nreturn node\n# \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\nself.__update_height(node)\n# 2. \u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u8be5\u5b50\u6811\u91cd\u65b0\u6062\u590d\u5e73\u8861\nreturn self.__rotate(node)\n</code></pre> avl_tree.go<pre><code>/* \u63d2\u5165\u8282\u70b9 */\nfunc (t *aVLTree) insert(val int) {\nt.root = t.insertHelper(t.root, val)\n}\n/* \u9012\u5f52\u63d2\u5165\u8282\u70b9\uff08\u8f85\u52a9\u65b9\u6cd5\uff09 */\nfunc (t *aVLTree) insertHelper(node *TreeNode, val int) *TreeNode {\nif node == nil {\nreturn NewTreeNode(val)\n}\n/* 1. \u67e5\u627e\u63d2\u5165\u4f4d\u7f6e\uff0c\u5e76\u63d2\u5165\u8282\u70b9 */\nif val &lt; node.Val {\nnode.Left = t.insertHelper(node.Left, val)\n} else if val &gt; node.Val {\nnode.Right = t.insertHelper(node.Right, val)\n} else {\n// \u91cd\u590d\u8282\u70b9\u4e0d\u63d2\u5165\uff0c\u76f4\u63a5\u8fd4\u56de\nreturn node\n}\n// \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\nt.updateHeight(node)\n/* 2. \u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u8be5\u5b50\u6811\u91cd\u65b0\u6062\u590d\u5e73\u8861 */\nnode = t.rotate(node)\n// \u8fd4\u56de\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn node\n}\n</code></pre> avl_tree.js<pre><code>/* \u63d2\u5165\u8282\u70b9 */\ninsert(val) {\nthis.root = this.#insertHelper(this.root, val);\n}\n/* \u9012\u5f52\u63d2\u5165\u8282\u70b9\uff08\u8f85\u52a9\u65b9\u6cd5\uff09 */\n#insertHelper(node, val) {\nif (node === null) return new TreeNode(val);\n/* 1. \u67e5\u627e\u63d2\u5165\u4f4d\u7f6e\uff0c\u5e76\u63d2\u5165\u8282\u70b9 */\nif (val &lt; node.val) node.left = this.#insertHelper(node.left, val);\nelse if (val &gt; node.val)\nnode.right = this.#insertHelper(node.right, val);\nelse return node; // \u91cd\u590d\u8282\u70b9\u4e0d\u63d2\u5165\uff0c\u76f4\u63a5\u8fd4\u56de\nthis.#updateHeight(node); // \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\n/* 2. \u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u8be5\u5b50\u6811\u91cd\u65b0\u6062\u590d\u5e73\u8861 */\nnode = this.#rotate(node);\n// \u8fd4\u56de\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn node;\n}\n</code></pre> avl_tree.ts<pre><code>/* \u63d2\u5165\u8282\u70b9 */\ninsert(val: number): void {\nthis.root = this.insertHelper(this.root, val);\n}\n/* \u9012\u5f52\u63d2\u5165\u8282\u70b9\uff08\u8f85\u52a9\u65b9\u6cd5\uff09 */\ninsertHelper(node: TreeNode, val: number): TreeNode {\nif (node === null) return new TreeNode(val);\n/* 1. \u67e5\u627e\u63d2\u5165\u4f4d\u7f6e\uff0c\u5e76\u63d2\u5165\u8282\u70b9 */\nif (val &lt; node.val) {\nnode.left = this.insertHelper(node.left, val);\n} else if (val &gt; node.val) {\nnode.right = this.insertHelper(node.right, val);\n} else {\nreturn node; // \u91cd\u590d\u8282\u70b9\u4e0d\u63d2\u5165\uff0c\u76f4\u63a5\u8fd4\u56de\n}\nthis.updateHeight(node); // \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\n/* 2. \u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u8be5\u5b50\u6811\u91cd\u65b0\u6062\u590d\u5e73\u8861 */\nnode = this.rotate(node);\n// \u8fd4\u56de\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn node;\n}\n</code></pre> avl_tree.c<pre><code>/* \u63d2\u5165\u8282\u70b9 */\nvoid insert(aVLTree *tree, int val) {\ntree-&gt;root = insertHelper(tree-&gt;root, val);\n}\n/* \u9012\u5f52\u63d2\u5165\u8282\u70b9\uff08\u8f85\u52a9\u65b9\u6cd5\uff09 */\nTreeNode *insertHelper(TreeNode *node, int val) {\nif (node == NULL) {\nreturn newTreeNode(val);\n}\n/* 1. \u67e5\u627e\u63d2\u5165\u4f4d\u7f6e\uff0c\u5e76\u63d2\u5165\u8282\u70b9 */\nif (val &lt; node-&gt;val) {\nnode-&gt;left = insertHelper(node-&gt;left, val);\n} else if (val &gt; node-&gt;val) {\nnode-&gt;right = insertHelper(node-&gt;right, val);\n} else {\n// \u91cd\u590d\u8282\u70b9\u4e0d\u63d2\u5165\uff0c\u76f4\u63a5\u8fd4\u56de\nreturn node;\n}\n// \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\nupdateHeight(node);\n/* 2. \u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u8be5\u5b50\u6811\u91cd\u65b0\u6062\u590d\u5e73\u8861 */\nnode = rotate(node);\n// \u8fd4\u56de\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn node;\n}\n</code></pre> avl_tree.cs<pre><code>/* \u63d2\u5165\u8282\u70b9 */\nvoid insert(int val) {\nroot = insertHelper(root, val);\n}\n/* \u9012\u5f52\u63d2\u5165\u8282\u70b9\uff08\u8f85\u52a9\u65b9\u6cd5\uff09 */\nTreeNode? insertHelper(TreeNode? node, int val) {\nif (node == null) return new TreeNode(val);\n/* 1. \u67e5\u627e\u63d2\u5165\u4f4d\u7f6e\uff0c\u5e76\u63d2\u5165\u8282\u70b9 */\nif (val &lt; node.val)\nnode.left = insertHelper(node.left, val);\nelse if (val &gt; node.val)\nnode.right = insertHelper(node.right, val);\nelse\nreturn node;     // \u91cd\u590d\u8282\u70b9\u4e0d\u63d2\u5165\uff0c\u76f4\u63a5\u8fd4\u56de\nupdateHeight(node);  // \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\n/* 2. \u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u8be5\u5b50\u6811\u91cd\u65b0\u6062\u590d\u5e73\u8861 */\nnode = rotate(node);\n// \u8fd4\u56de\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn node;\n}\n</code></pre> avl_tree.swift<pre><code>/* \u63d2\u5165\u8282\u70b9 */\n@discardableResult\nfunc insert(val: Int) {\nroot = insertHelper(node: root, val: val)\n}\n/* \u9012\u5f52\u63d2\u5165\u8282\u70b9\uff08\u8f85\u52a9\u65b9\u6cd5\uff09 */\nfunc insertHelper(node: TreeNode?, val: Int) -&gt; TreeNode? {\nvar node = node\nif node == nil {\nreturn TreeNode(x: val)\n}\n/* 1. \u67e5\u627e\u63d2\u5165\u4f4d\u7f6e\uff0c\u5e76\u63d2\u5165\u8282\u70b9 */\nif val &lt; node!.val {\nnode?.left = insertHelper(node: node?.left, val: val)\n} else if val &gt; node!.val {\nnode?.right = insertHelper(node: node?.right, val: val)\n} else {\nreturn node // \u91cd\u590d\u8282\u70b9\u4e0d\u63d2\u5165\uff0c\u76f4\u63a5\u8fd4\u56de\n}\nupdateHeight(node: node) // \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\n/* 2. \u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u8be5\u5b50\u6811\u91cd\u65b0\u6062\u590d\u5e73\u8861 */\nnode = rotate(node: node)\n// \u8fd4\u56de\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn node\n}\n</code></pre> avl_tree.zig<pre><code>// \u63d2\u5165\u8282\u70b9\nfn insert(self: *Self, val: T) void {\nself.root = try self.insertHelper(self.root, val);\n}\n// \u9012\u5f52\u63d2\u5165\u8282\u70b9\uff08\u8f85\u52a9\u65b9\u6cd5\uff09\nfn insertHelper(self: *Self, node_: ?*inc.TreeNode(T), val: T) !?*inc.TreeNode(T) {\nvar node = node_;\nif (node == null) {\nvar tmp_node = try self.mem_allocator.create(inc.TreeNode(T));\ntmp_node.init(val);\nreturn tmp_node;\n}\n// 1. \u67e5\u627e\u63d2\u5165\u4f4d\u7f6e\uff0c\u5e76\u63d2\u5165\u8282\u70b9\nif (val &lt; node.?.val) {\nnode.?.left = try self.insertHelper(node.?.left, val);\n} else if (val &gt; node.?.val) {\nnode.?.right = try self.insertHelper(node.?.right, val);\n} else {\nreturn node;            // \u91cd\u590d\u8282\u70b9\u4e0d\u63d2\u5165\uff0c\u76f4\u63a5\u8fd4\u56de\n}\nself.updateHeight(node);    // \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\n// 2. \u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u8be5\u5b50\u6811\u91cd\u65b0\u6062\u590d\u5e73\u8861\nnode = self.rotate(node);\n// \u8fd4\u56de\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn node;\n}\n</code></pre> avl_tree.dart<pre><code>/* \u63d2\u5165\u8282\u70b9 */\nvoid insert(int val) {\nroot = insertHelper(root, val);\n}\n/* \u9012\u5f52\u63d2\u5165\u8282\u70b9\uff08\u8f85\u52a9\u65b9\u6cd5\uff09 */\nTreeNode? insertHelper(TreeNode? node, int val) {\nif (node == null) return TreeNode(val);\n/* 1. \u67e5\u627e\u63d2\u5165\u4f4d\u7f6e\uff0c\u5e76\u63d2\u5165\u8282\u70b9 */\nif (val &lt; node.val)\nnode.left = insertHelper(node.left, val);\nelse if (val &gt; node.val)\nnode.right = insertHelper(node.right, val);\nelse\nreturn node; // \u91cd\u590d\u8282\u70b9\u4e0d\u63d2\u5165\uff0c\u76f4\u63a5\u8fd4\u56de\nupdateHeight(node); // \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\n/* 2. \u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u8be5\u5b50\u6811\u91cd\u65b0\u6062\u590d\u5e73\u8861 */\nnode = rotate(node);\n// \u8fd4\u56de\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn node;\n}\n</code></pre>"},{"location":"chapter_tree/avl_tree/#_9","title":"\u5220\u9664\u8282\u70b9","text":"<p>\u7c7b\u4f3c\u5730\uff0c\u5728\u4e8c\u53c9\u641c\u7d22\u6811\u7684\u5220\u9664\u8282\u70b9\u65b9\u6cd5\u7684\u57fa\u7840\u4e0a\uff0c\u9700\u8981\u4ece\u5e95\u81f3\u9876\u5730\u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u6240\u6709\u5931\u8861\u8282\u70b9\u6062\u590d\u5e73\u8861\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart avl_tree.java<pre><code>/* \u5220\u9664\u8282\u70b9 */\nvoid remove(int val) {\nroot = removeHelper(root, val);\n}\n/* \u9012\u5f52\u5220\u9664\u8282\u70b9\uff08\u8f85\u52a9\u65b9\u6cd5\uff09 */\nTreeNode removeHelper(TreeNode node, int val) {\nif (node == null)\nreturn null;\n/* 1. \u67e5\u627e\u8282\u70b9\uff0c\u5e76\u5220\u9664\u4e4b */\nif (val &lt; node.val)\nnode.left = removeHelper(node.left, val);\nelse if (val &gt; node.val)\nnode.right = removeHelper(node.right, val);\nelse {\nif (node.left == null || node.right == null) {\nTreeNode child = node.left != null ? node.left : node.right;\n// \u5b50\u8282\u70b9\u6570\u91cf = 0 \uff0c\u76f4\u63a5\u5220\u9664 node \u5e76\u8fd4\u56de\nif (child == null)\nreturn null;\n// \u5b50\u8282\u70b9\u6570\u91cf = 1 \uff0c\u76f4\u63a5\u5220\u9664 node\nelse\nnode = child;\n} else {\n// \u5b50\u8282\u70b9\u6570\u91cf = 2 \uff0c\u5219\u5c06\u4e2d\u5e8f\u904d\u5386\u7684\u4e0b\u4e2a\u8282\u70b9\u5220\u9664\uff0c\u5e76\u7528\u8be5\u8282\u70b9\u66ff\u6362\u5f53\u524d\u8282\u70b9\nTreeNode temp = node.right;\nwhile (temp.left != null) {\ntemp = temp.left;\n}\nnode.right = removeHelper(node.right, temp.val);\nnode.val = temp.val;\n}\n}\nupdateHeight(node); // \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\n/* 2. \u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u8be5\u5b50\u6811\u91cd\u65b0\u6062\u590d\u5e73\u8861 */\nnode = rotate(node);\n// \u8fd4\u56de\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn node;\n}\n</code></pre> avl_tree.cpp<pre><code>/* \u5220\u9664\u8282\u70b9 */\nvoid remove(int val) {\nroot = removeHelper(root, val);\n}\n/* \u9012\u5f52\u5220\u9664\u8282\u70b9\uff08\u8f85\u52a9\u65b9\u6cd5\uff09 */\nTreeNode *removeHelper(TreeNode *node, int val) {\nif (node == nullptr)\nreturn nullptr;\n/* 1. \u67e5\u627e\u8282\u70b9\uff0c\u5e76\u5220\u9664\u4e4b */\nif (val &lt; node-&gt;val)\nnode-&gt;left = removeHelper(node-&gt;left, val);\nelse if (val &gt; node-&gt;val)\nnode-&gt;right = removeHelper(node-&gt;right, val);\nelse {\nif (node-&gt;left == nullptr || node-&gt;right == nullptr) {\nTreeNode *child = node-&gt;left != nullptr ? node-&gt;left : node-&gt;right;\n// \u5b50\u8282\u70b9\u6570\u91cf = 0 \uff0c\u76f4\u63a5\u5220\u9664 node \u5e76\u8fd4\u56de\nif (child == nullptr) {\ndelete node;\nreturn nullptr;\n}\n// \u5b50\u8282\u70b9\u6570\u91cf = 1 \uff0c\u76f4\u63a5\u5220\u9664 node\nelse {\ndelete node;\nnode = child;\n}\n} else {\n// \u5b50\u8282\u70b9\u6570\u91cf = 2 \uff0c\u5219\u5c06\u4e2d\u5e8f\u904d\u5386\u7684\u4e0b\u4e2a\u8282\u70b9\u5220\u9664\uff0c\u5e76\u7528\u8be5\u8282\u70b9\u66ff\u6362\u5f53\u524d\u8282\u70b9\nTreeNode *temp = node-&gt;right;\nwhile (temp-&gt;left != nullptr) {\ntemp = temp-&gt;left;\n}\nint tempVal = temp-&gt;val;\nnode-&gt;right = removeHelper(node-&gt;right, temp-&gt;val);\nnode-&gt;val = tempVal;\n}\n}\nupdateHeight(node); // \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\n/* 2. \u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u8be5\u5b50\u6811\u91cd\u65b0\u6062\u590d\u5e73\u8861 */\nnode = rotate(node);\n// \u8fd4\u56de\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn node;\n}\n</code></pre> avl_tree.py<pre><code>def remove(self, val: int) -&gt; None:\n\"\"\"\u5220\u9664\u8282\u70b9\"\"\"\nself.__root = self.__remove_helper(self.__root, val)\ndef __remove_helper(self, node: TreeNode | None, val: int) -&gt; TreeNode | None:\n\"\"\"\u9012\u5f52\u5220\u9664\u8282\u70b9\uff08\u8f85\u52a9\u65b9\u6cd5\uff09\"\"\"\nif node is None:\nreturn None\n# 1. \u67e5\u627e\u8282\u70b9\uff0c\u5e76\u5220\u9664\u4e4b\nif val &lt; node.val:\nnode.left = self.__remove_helper(node.left, val)\nelif val &gt; node.val:\nnode.right = self.__remove_helper(node.right, val)\nelse:\nif node.left is None or node.right is None:\nchild = node.left or node.right\n# \u5b50\u8282\u70b9\u6570\u91cf = 0 \uff0c\u76f4\u63a5\u5220\u9664 node \u5e76\u8fd4\u56de\nif child is None:\nreturn None\n# \u5b50\u8282\u70b9\u6570\u91cf = 1 \uff0c\u76f4\u63a5\u5220\u9664 node\nelse:\nnode = child\nelse:\n# \u5b50\u8282\u70b9\u6570\u91cf = 2 \uff0c\u5219\u5c06\u4e2d\u5e8f\u904d\u5386\u7684\u4e0b\u4e2a\u8282\u70b9\u5220\u9664\uff0c\u5e76\u7528\u8be5\u8282\u70b9\u66ff\u6362\u5f53\u524d\u8282\u70b9\ntemp = node.right\nwhile temp.left is not None:\ntemp = temp.left\nnode.right = self.__remove_helper(node.right, temp.val)\nnode.val = temp.val\n# \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\nself.__update_height(node)\n# 2. \u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u8be5\u5b50\u6811\u91cd\u65b0\u6062\u590d\u5e73\u8861\nreturn self.__rotate(node)\n</code></pre> avl_tree.go<pre><code>/* \u5220\u9664\u8282\u70b9 */\nfunc (t *aVLTree) remove(val int) {\nt.root = t.removeHelper(t.root, val)\n}\n/* \u9012\u5f52\u5220\u9664\u8282\u70b9\uff08\u8f85\u52a9\u65b9\u6cd5\uff09 */\nfunc (t *aVLTree) removeHelper(node *TreeNode, val int) *TreeNode {\nif node == nil {\nreturn nil\n}\n/* 1. \u67e5\u627e\u8282\u70b9\uff0c\u5e76\u5220\u9664\u4e4b */\nif val &lt; node.Val {\nnode.Left = t.removeHelper(node.Left, val)\n} else if val &gt; node.Val {\nnode.Right = t.removeHelper(node.Right, val)\n} else {\nif node.Left == nil || node.Right == nil {\nchild := node.Left\nif node.Right != nil {\nchild = node.Right\n}\nif child == nil {\n// \u5b50\u8282\u70b9\u6570\u91cf = 0 \uff0c\u76f4\u63a5\u5220\u9664 node \u5e76\u8fd4\u56de\nreturn nil\n} else {\n// \u5b50\u8282\u70b9\u6570\u91cf = 1 \uff0c\u76f4\u63a5\u5220\u9664 node\nnode = child\n}\n} else {\n// \u5b50\u8282\u70b9\u6570\u91cf = 2 \uff0c\u5219\u5c06\u4e2d\u5e8f\u904d\u5386\u7684\u4e0b\u4e2a\u8282\u70b9\u5220\u9664\uff0c\u5e76\u7528\u8be5\u8282\u70b9\u66ff\u6362\u5f53\u524d\u8282\u70b9\ntemp := node.Right\nfor temp.Left != nil {\ntemp = temp.Left\n}\nnode.Right = t.removeHelper(node.Right, temp.Val)\nnode.Val = temp.Val\n}\n}\n// \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\nt.updateHeight(node)\n/* 2. \u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u8be5\u5b50\u6811\u91cd\u65b0\u6062\u590d\u5e73\u8861 */\nnode = t.rotate(node)\n// \u8fd4\u56de\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn node\n}\n</code></pre> avl_tree.js<pre><code>/* \u5220\u9664\u8282\u70b9 */\nremove(val) {\nthis.root = this.#removeHelper(this.root, val);\n}\n/* \u9012\u5f52\u5220\u9664\u8282\u70b9\uff08\u8f85\u52a9\u65b9\u6cd5\uff09 */\n#removeHelper(node, val) {\nif (node === null) return null;\n/* 1. \u67e5\u627e\u8282\u70b9\uff0c\u5e76\u5220\u9664\u4e4b */\nif (val &lt; node.val) node.left = this.#removeHelper(node.left, val);\nelse if (val &gt; node.val)\nnode.right = this.#removeHelper(node.right, val);\nelse {\nif (node.left === null || node.right === null) {\nconst child = node.left !== null ? node.left : node.right;\n// \u5b50\u8282\u70b9\u6570\u91cf = 0 \uff0c\u76f4\u63a5\u5220\u9664 node \u5e76\u8fd4\u56de\nif (child === null) return null;\n// \u5b50\u8282\u70b9\u6570\u91cf = 1 \uff0c\u76f4\u63a5\u5220\u9664 node\nelse node = child;\n} else {\n// \u5b50\u8282\u70b9\u6570\u91cf = 2 \uff0c\u5219\u5c06\u4e2d\u5e8f\u904d\u5386\u7684\u4e0b\u4e2a\u8282\u70b9\u5220\u9664\uff0c\u5e76\u7528\u8be5\u8282\u70b9\u66ff\u6362\u5f53\u524d\u8282\u70b9\nlet temp = node.right;\nwhile (temp.left !== null) {\ntemp = temp.left;\n}\nnode.right = this.#removeHelper(node.right, temp.val);\nnode.val = temp.val;\n}\n}\nthis.#updateHeight(node); // \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\n/* 2. \u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u8be5\u5b50\u6811\u91cd\u65b0\u6062\u590d\u5e73\u8861 */\nnode = this.#rotate(node);\n// \u8fd4\u56de\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn node;\n}\n</code></pre> avl_tree.ts<pre><code>/* \u5220\u9664\u8282\u70b9 */\nremove(val: number): void {\nthis.root = this.removeHelper(this.root, val);\n}\n/* \u9012\u5f52\u5220\u9664\u8282\u70b9\uff08\u8f85\u52a9\u65b9\u6cd5\uff09 */\nremoveHelper(node: TreeNode, val: number): TreeNode {\nif (node === null) return null;\n/* 1. \u67e5\u627e\u8282\u70b9\uff0c\u5e76\u5220\u9664\u4e4b */\nif (val &lt; node.val) {\nnode.left = this.removeHelper(node.left, val);\n} else if (val &gt; node.val) {\nnode.right = this.removeHelper(node.right, val);\n} else {\nif (node.left === null || node.right === null) {\nconst child = node.left !== null ? node.left : node.right;\n// \u5b50\u8282\u70b9\u6570\u91cf = 0 \uff0c\u76f4\u63a5\u5220\u9664 node \u5e76\u8fd4\u56de\nif (child === null) {\nreturn null;\n} else {\n// \u5b50\u8282\u70b9\u6570\u91cf = 1 \uff0c\u76f4\u63a5\u5220\u9664 node\nnode = child;\n}\n} else {\n// \u5b50\u8282\u70b9\u6570\u91cf = 2 \uff0c\u5219\u5c06\u4e2d\u5e8f\u904d\u5386\u7684\u4e0b\u4e2a\u8282\u70b9\u5220\u9664\uff0c\u5e76\u7528\u8be5\u8282\u70b9\u66ff\u6362\u5f53\u524d\u8282\u70b9\nlet temp = node.right;\nwhile (temp.left !== null) {\ntemp = temp.left;\n}\nnode.right = this.removeHelper(node.right, temp.val);\nnode.val = temp.val;\n}\n}\nthis.updateHeight(node); // \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\n/* 2. \u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u8be5\u5b50\u6811\u91cd\u65b0\u6062\u590d\u5e73\u8861 */\nnode = this.rotate(node);\n// \u8fd4\u56de\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn node;\n}\n</code></pre> avl_tree.c<pre><code>/* \u5220\u9664\u8282\u70b9 */\n// \u7531\u4e8e\u5f15\u5165\u4e86 stdio.h \uff0c\u6b64\u5904\u65e0\u6cd5\u4f7f\u7528 remove \u5173\u952e\u8bcd\nvoid removeNode(aVLTree *tree, int val) {\nTreeNode *root = removeHelper(tree-&gt;root, val);\n}\n/* \u9012\u5f52\u5220\u9664\u8282\u70b9\uff08\u8f85\u52a9\u65b9\u6cd5\uff09 */\nTreeNode *removeHelper(TreeNode *node, int val) {\nTreeNode *child, *grandChild;\nif (node == NULL) {\nreturn NULL;\n}\n/* 1. \u67e5\u627e\u8282\u70b9\uff0c\u5e76\u5220\u9664\u4e4b */\nif (val &lt; node-&gt;val) {\nnode-&gt;left = removeHelper(node-&gt;left, val);\n} else if (val &gt; node-&gt;val) {\nnode-&gt;right = removeHelper(node-&gt;right, val);\n} else {\nif (node-&gt;left == NULL || node-&gt;right == NULL) {\nchild = node-&gt;left;\nif (node-&gt;right != NULL) {\nchild = node-&gt;right;\n}\n// \u5b50\u8282\u70b9\u6570\u91cf = 0 \uff0c\u76f4\u63a5\u5220\u9664 node \u5e76\u8fd4\u56de\nif (child == NULL) {\nreturn NULL;\n} else {\n// \u5b50\u8282\u70b9\u6570\u91cf = 1 \uff0c\u76f4\u63a5\u5220\u9664 node\nnode = child;\n}\n} else {\n// \u5b50\u8282\u70b9\u6570\u91cf = 2 \uff0c\u5219\u5c06\u4e2d\u5e8f\u904d\u5386\u7684\u4e0b\u4e2a\u8282\u70b9\u5220\u9664\uff0c\u5e76\u7528\u8be5\u8282\u70b9\u66ff\u6362\u5f53\u524d\u8282\u70b9\nTreeNode *temp = node-&gt;right;\nwhile (temp-&gt;left != NULL) {\ntemp = temp-&gt;left;\n}\nint tempVal = temp-&gt;val;\nnode-&gt;right = removeHelper(node-&gt;right, temp-&gt;val);\nnode-&gt;val = tempVal;\n}\n}\n// \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\nupdateHeight(node);\n/* 2. \u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u8be5\u5b50\u6811\u91cd\u65b0\u6062\u590d\u5e73\u8861 */\nnode = rotate(node);\n// \u8fd4\u56de\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn node;\n}\n</code></pre> avl_tree.cs<pre><code>/* \u5220\u9664\u8282\u70b9 */\nvoid remove(int val) {\nroot = removeHelper(root, val);\n}\n/* \u9012\u5f52\u5220\u9664\u8282\u70b9\uff08\u8f85\u52a9\u65b9\u6cd5\uff09 */\nTreeNode? removeHelper(TreeNode? node, int val) {\nif (node == null) return null;\n/* 1. \u67e5\u627e\u8282\u70b9\uff0c\u5e76\u5220\u9664\u4e4b */\nif (val &lt; node.val)\nnode.left = removeHelper(node.left, val);\nelse if (val &gt; node.val)\nnode.right = removeHelper(node.right, val);\nelse {\nif (node.left == null || node.right == null) {\nTreeNode? child = node.left != null ? node.left : node.right;\n// \u5b50\u8282\u70b9\u6570\u91cf = 0 \uff0c\u76f4\u63a5\u5220\u9664 node \u5e76\u8fd4\u56de\nif (child == null)\nreturn null;\n// \u5b50\u8282\u70b9\u6570\u91cf = 1 \uff0c\u76f4\u63a5\u5220\u9664 node\nelse\nnode = child;\n} else {\n// \u5b50\u8282\u70b9\u6570\u91cf = 2 \uff0c\u5219\u5c06\u4e2d\u5e8f\u904d\u5386\u7684\u4e0b\u4e2a\u8282\u70b9\u5220\u9664\uff0c\u5e76\u7528\u8be5\u8282\u70b9\u66ff\u6362\u5f53\u524d\u8282\u70b9\nTreeNode? temp = node.right;\nwhile (temp.left != null) {\ntemp = temp.left;\n}\nnode.right = removeHelper(node.right, temp.val);\nnode.val = temp.val;\n}\n}\nupdateHeight(node);  // \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\n/* 2. \u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u8be5\u5b50\u6811\u91cd\u65b0\u6062\u590d\u5e73\u8861 */\nnode = rotate(node);\n// \u8fd4\u56de\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn node;\n}\n</code></pre> avl_tree.swift<pre><code>/* \u5220\u9664\u8282\u70b9 */\n@discardableResult\nfunc remove(val: Int) {\nroot = removeHelper(node: root, val: val)\n}\n/* \u9012\u5f52\u5220\u9664\u8282\u70b9\uff08\u8f85\u52a9\u65b9\u6cd5\uff09 */\nfunc removeHelper(node: TreeNode?, val: Int) -&gt; TreeNode? {\nvar node = node\nif node == nil {\nreturn nil\n}\n/* 1. \u67e5\u627e\u8282\u70b9\uff0c\u5e76\u5220\u9664\u4e4b */\nif val &lt; node!.val {\nnode?.left = removeHelper(node: node?.left, val: val)\n} else if val &gt; node!.val {\nnode?.right = removeHelper(node: node?.right, val: val)\n} else {\nif node?.left == nil || node?.right == nil {\nlet child = node?.left != nil ? node?.left : node?.right\n// \u5b50\u8282\u70b9\u6570\u91cf = 0 \uff0c\u76f4\u63a5\u5220\u9664 node \u5e76\u8fd4\u56de\nif child == nil {\nreturn nil\n}\n// \u5b50\u8282\u70b9\u6570\u91cf = 1 \uff0c\u76f4\u63a5\u5220\u9664 node\nelse {\nnode = child\n}\n} else {\n// \u5b50\u8282\u70b9\u6570\u91cf = 2 \uff0c\u5219\u5c06\u4e2d\u5e8f\u904d\u5386\u7684\u4e0b\u4e2a\u8282\u70b9\u5220\u9664\uff0c\u5e76\u7528\u8be5\u8282\u70b9\u66ff\u6362\u5f53\u524d\u8282\u70b9\nvar temp = node?.right\nwhile temp?.left != nil {\ntemp = temp?.left\n}\nnode?.right = removeHelper(node: node?.right, val: temp!.val)\nnode?.val = temp!.val\n}\n}\nupdateHeight(node: node) // \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\n/* 2. \u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u8be5\u5b50\u6811\u91cd\u65b0\u6062\u590d\u5e73\u8861 */\nnode = rotate(node: node)\n// \u8fd4\u56de\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn node\n}\n</code></pre> avl_tree.zig<pre><code>// \u5220\u9664\u8282\u70b9\nfn remove(self: *Self, val: T) void {\nself.root = self.removeHelper(self.root, val);\n}\n// \u9012\u5f52\u5220\u9664\u8282\u70b9\uff08\u8f85\u52a9\u65b9\u6cd5\uff09\nfn removeHelper(self: *Self, node_: ?*inc.TreeNode(T), val: T) ?*inc.TreeNode(T) {\nvar node = node_;\nif (node == null) return null;\n// 1. \u67e5\u627e\u8282\u70b9\uff0c\u5e76\u5220\u9664\u4e4b\nif (val &lt; node.?.val) {\nnode.?.left = self.removeHelper(node.?.left, val);\n} else if (val &gt; node.?.val) {\nnode.?.right = self.removeHelper(node.?.right, val);\n} else {\nif (node.?.left == null or node.?.right == null) {\nvar child = if (node.?.left != null) node.?.left else node.?.right;\n// \u5b50\u8282\u70b9\u6570\u91cf = 0 \uff0c\u76f4\u63a5\u5220\u9664 node \u5e76\u8fd4\u56de\nif (child == null) {\nreturn null;\n// \u5b50\u8282\u70b9\u6570\u91cf = 1 \uff0c\u76f4\u63a5\u5220\u9664 node\n} else {\nnode = child;\n}\n} else {\n// \u5b50\u8282\u70b9\u6570\u91cf = 2 \uff0c\u5219\u5c06\u4e2d\u5e8f\u904d\u5386\u7684\u4e0b\u4e2a\u8282\u70b9\u5220\u9664\uff0c\u5e76\u7528\u8be5\u8282\u70b9\u66ff\u6362\u5f53\u524d\u8282\u70b9\nvar temp = node.?.right;\nwhile (temp.?.left != null) {\ntemp = temp.?.left;\n}\nnode.?.right = self.removeHelper(node.?.right, temp.?.val);\nnode.?.val = temp.?.val;\n}\n}\nself.updateHeight(node); // \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\n// 2. \u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u8be5\u5b50\u6811\u91cd\u65b0\u6062\u590d\u5e73\u8861\nnode = self.rotate(node);\n// \u8fd4\u56de\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn node;\n}\n</code></pre> avl_tree.dart<pre><code>/* \u5220\u9664\u8282\u70b9 */\nvoid remove(int val) {\nroot = removeHelper(root, val);\n}\n/* \u9012\u5f52\u5220\u9664\u8282\u70b9\uff08\u8f85\u52a9\u65b9\u6cd5\uff09 */\nTreeNode? removeHelper(TreeNode? node, int val) {\nif (node == null) return null;\n/* 1. \u67e5\u627e\u8282\u70b9\uff0c\u5e76\u5220\u9664\u4e4b */\nif (val &lt; node.val)\nnode.left = removeHelper(node.left, val);\nelse if (val &gt; node.val)\nnode.right = removeHelper(node.right, val);\nelse {\nif (node.left == null || node.right == null) {\nTreeNode? child = node.left ?? node.right;\n// \u5b50\u8282\u70b9\u6570\u91cf = 0 \uff0c\u76f4\u63a5\u5220\u9664 node \u5e76\u8fd4\u56de\nif (child == null)\nreturn null;\n// \u5b50\u8282\u70b9\u6570\u91cf = 1 \uff0c\u76f4\u63a5\u5220\u9664 node\nelse\nnode = child;\n} else {\n// \u5b50\u8282\u70b9\u6570\u91cf = 2 \uff0c\u5219\u5c06\u4e2d\u5e8f\u904d\u5386\u7684\u4e0b\u4e2a\u8282\u70b9\u5220\u9664\uff0c\u5e76\u7528\u8be5\u8282\u70b9\u66ff\u6362\u5f53\u524d\u8282\u70b9\nTreeNode? temp = node.right;\nwhile (temp!.left != null) {\ntemp = temp.left;\n}\nnode.right = removeHelper(node.right, temp.val);\nnode.val = temp.val;\n}\n}\nupdateHeight(node); // \u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\n/* 2. \u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u8be5\u5b50\u6811\u91cd\u65b0\u6062\u590d\u5e73\u8861 */\nnode = rotate(node);\n// \u8fd4\u56de\u5b50\u6811\u7684\u6839\u8282\u70b9\nreturn node;\n}\n</code></pre>"},{"location":"chapter_tree/avl_tree/#_10","title":"\u67e5\u627e\u8282\u70b9","text":"<p>AVL \u6811\u7684\u8282\u70b9\u67e5\u627e\u64cd\u4f5c\u4e0e\u4e8c\u53c9\u641c\u7d22\u6811\u4e00\u81f4\uff0c\u5728\u6b64\u4e0d\u518d\u8d58\u8ff0\u3002</p>"},{"location":"chapter_tree/avl_tree/#754-avl","title":"7.5.4. \u00a0 AVL \u6811\u5178\u578b\u5e94\u7528","text":"<ul> <li>\u7ec4\u7ec7\u548c\u5b58\u50a8\u5927\u578b\u6570\u636e\uff0c\u9002\u7528\u4e8e\u9ad8\u9891\u67e5\u627e\u3001\u4f4e\u9891\u589e\u5220\u7684\u573a\u666f\uff1b</li> <li>\u7528\u4e8e\u6784\u5efa\u6570\u636e\u5e93\u4e2d\u7684\u7d22\u5f15\u7cfb\u7edf\uff1b</li> </ul> <p>\u4e3a\u4ec0\u4e48\u7ea2\u9ed1\u6811\u6bd4 AVL \u6811\u66f4\u53d7\u6b22\u8fce\uff1f</p> <p>\u7ea2\u9ed1\u6811\u7684\u5e73\u8861\u6761\u4ef6\u76f8\u5bf9\u5bbd\u677e\uff0c\u56e0\u6b64\u5728\u7ea2\u9ed1\u6811\u4e2d\u63d2\u5165\u4e0e\u5220\u9664\u8282\u70b9\u6240\u9700\u7684\u65cb\u8f6c\u64cd\u4f5c\u76f8\u5bf9\u8f83\u5c11\uff0c\u5728\u8282\u70b9\u589e\u5220\u64cd\u4f5c\u4e0a\u7684\u5e73\u5747\u6548\u7387\u9ad8\u4e8e AVL \u6811\u3002</p>"},{"location":"chapter_tree/binary_search_tree/","title":"7.4. \u00a0 \u4e8c\u53c9\u641c\u7d22\u6811","text":"<p>\u300c\u4e8c\u53c9\u641c\u7d22\u6811 Binary Search Tree\u300d\u6ee1\u8db3\u4ee5\u4e0b\u6761\u4ef6\uff1a</p> <ol> <li>\u5bf9\u4e8e\u6839\u8282\u70b9\uff0c\u5de6\u5b50\u6811\u4e2d\u6240\u6709\u8282\u70b9\u7684\u503c \\(&lt;\\) \u6839\u8282\u70b9\u7684\u503c \\(&lt;\\) \u53f3\u5b50\u6811\u4e2d\u6240\u6709\u8282\u70b9\u7684\u503c\uff1b</li> <li>\u4efb\u610f\u8282\u70b9\u7684\u5de6\u3001\u53f3\u5b50\u6811\u4e5f\u662f\u4e8c\u53c9\u641c\u7d22\u6811\uff0c\u5373\u540c\u6837\u6ee1\u8db3\u6761\u4ef6 <code>1.</code> \uff1b</li> </ol> <p></p> <p> Fig. \u4e8c\u53c9\u641c\u7d22\u6811 </p>"},{"location":"chapter_tree/binary_search_tree/#741","title":"7.4.1. \u00a0 \u4e8c\u53c9\u641c\u7d22\u6811\u7684\u64cd\u4f5c","text":""},{"location":"chapter_tree/binary_search_tree/#_1","title":"\u67e5\u627e\u8282\u70b9","text":"<p>\u7ed9\u5b9a\u76ee\u6807\u8282\u70b9\u503c <code>num</code> \uff0c\u53ef\u4ee5\u6839\u636e\u4e8c\u53c9\u641c\u7d22\u6811\u7684\u6027\u8d28\u6765\u67e5\u627e\u3002\u6211\u4eec\u58f0\u660e\u4e00\u4e2a\u8282\u70b9 <code>cur</code> \uff0c\u4ece\u4e8c\u53c9\u6811\u7684\u6839\u8282\u70b9 <code>root</code> \u51fa\u53d1\uff0c\u5faa\u73af\u6bd4\u8f83\u8282\u70b9\u503c <code>cur.val</code> \u548c <code>num</code> \u4e4b\u95f4\u7684\u5927\u5c0f\u5173\u7cfb</p> <ul> <li>\u82e5 <code>cur.val &lt; num</code> \uff0c\u8bf4\u660e\u76ee\u6807\u8282\u70b9\u5728 <code>cur</code> \u7684\u53f3\u5b50\u6811\u4e2d\uff0c\u56e0\u6b64\u6267\u884c <code>cur = cur.right</code> \uff1b</li> <li>\u82e5 <code>cur.val &gt; num</code> \uff0c\u8bf4\u660e\u76ee\u6807\u8282\u70b9\u5728 <code>cur</code> \u7684\u5de6\u5b50\u6811\u4e2d\uff0c\u56e0\u6b64\u6267\u884c <code>cur = cur.left</code> \uff1b</li> <li>\u82e5 <code>cur.val = num</code> \uff0c\u8bf4\u660e\u627e\u5230\u76ee\u6807\u8282\u70b9\uff0c\u8df3\u51fa\u5faa\u73af\u5e76\u8fd4\u56de\u8be5\u8282\u70b9\uff1b</li> </ul> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt; <p></p> <p></p> <p></p> <p></p> <p>\u4e8c\u53c9\u641c\u7d22\u6811\u7684\u67e5\u627e\u64cd\u4f5c\u4e0e\u4e8c\u5206\u67e5\u627e\u7b97\u6cd5\u7684\u5de5\u4f5c\u539f\u7406\u4e00\u81f4\uff0c\u90fd\u662f\u6bcf\u8f6e\u6392\u9664\u4e00\u534a\u60c5\u51b5\u3002\u5faa\u73af\u6b21\u6570\u6700\u591a\u4e3a\u4e8c\u53c9\u6811\u7684\u9ad8\u5ea6\uff0c\u5f53\u4e8c\u53c9\u6811\u5e73\u8861\u65f6\uff0c\u4f7f\u7528 \\(O(\\log n)\\) \u65f6\u95f4\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart binary_search_tree.java<pre><code>/* \u67e5\u627e\u8282\u70b9 */\nTreeNode search(int num) {\nTreeNode cur = root;\n// \u5faa\u73af\u67e5\u627e\uff0c\u8d8a\u8fc7\u53f6\u8282\u70b9\u540e\u8df3\u51fa\nwhile (cur != null) {\n// \u76ee\u6807\u8282\u70b9\u5728 cur \u7684\u53f3\u5b50\u6811\u4e2d\nif (cur.val &lt; num)\ncur = cur.right;\n// \u76ee\u6807\u8282\u70b9\u5728 cur \u7684\u5de6\u5b50\u6811\u4e2d\nelse if (cur.val &gt; num)\ncur = cur.left;\n// \u627e\u5230\u76ee\u6807\u8282\u70b9\uff0c\u8df3\u51fa\u5faa\u73af\nelse\nbreak;\n}\n// \u8fd4\u56de\u76ee\u6807\u8282\u70b9\nreturn cur;\n}\n</code></pre> binary_search_tree.cpp<pre><code>/* \u67e5\u627e\u8282\u70b9 */\nTreeNode *search(int num) {\nTreeNode *cur = root;\n// \u5faa\u73af\u67e5\u627e\uff0c\u8d8a\u8fc7\u53f6\u8282\u70b9\u540e\u8df3\u51fa\nwhile (cur != nullptr) {\n// \u76ee\u6807\u8282\u70b9\u5728 cur \u7684\u53f3\u5b50\u6811\u4e2d\nif (cur-&gt;val &lt; num)\ncur = cur-&gt;right;\n// \u76ee\u6807\u8282\u70b9\u5728 cur \u7684\u5de6\u5b50\u6811\u4e2d\nelse if (cur-&gt;val &gt; num)\ncur = cur-&gt;left;\n// \u627e\u5230\u76ee\u6807\u8282\u70b9\uff0c\u8df3\u51fa\u5faa\u73af\nelse\nbreak;\n}\n// \u8fd4\u56de\u76ee\u6807\u8282\u70b9\nreturn cur;\n}\n</code></pre> binary_search_tree.py<pre><code>def search(self, num: int) -&gt; TreeNode | None:\n\"\"\"\u67e5\u627e\u8282\u70b9\"\"\"\ncur: TreeNode | None = self.root\n# \u5faa\u73af\u67e5\u627e\uff0c\u8d8a\u8fc7\u53f6\u8282\u70b9\u540e\u8df3\u51fa\nwhile cur is not None:\n# \u76ee\u6807\u8282\u70b9\u5728 cur \u7684\u53f3\u5b50\u6811\u4e2d\nif cur.val &lt; num:\ncur = cur.right\n# \u76ee\u6807\u8282\u70b9\u5728 cur \u7684\u5de6\u5b50\u6811\u4e2d\nelif cur.val &gt; num:\ncur = cur.left\n# \u627e\u5230\u76ee\u6807\u8282\u70b9\uff0c\u8df3\u51fa\u5faa\u73af\nelse:\nbreak\nreturn cur\n</code></pre> binary_search_tree.go<pre><code>/* \u67e5\u627e\u8282\u70b9 */\nfunc (bst *binarySearchTree) search(num int) *TreeNode {\nnode := bst.root\n// \u5faa\u73af\u67e5\u627e\uff0c\u8d8a\u8fc7\u53f6\u8282\u70b9\u540e\u8df3\u51fa\nfor node != nil {\nif node.Val &lt; num {\n// \u76ee\u6807\u8282\u70b9\u5728 cur \u7684\u53f3\u5b50\u6811\u4e2d\nnode = node.Right\n} else if node.Val &gt; num {\n// \u76ee\u6807\u8282\u70b9\u5728 cur \u7684\u5de6\u5b50\u6811\u4e2d\nnode = node.Left\n} else {\n// \u627e\u5230\u76ee\u6807\u8282\u70b9\uff0c\u8df3\u51fa\u5faa\u73af\nbreak\n}\n}\n// \u8fd4\u56de\u76ee\u6807\u8282\u70b9\nreturn node\n}\n</code></pre> binary_search_tree.js<pre><code>/* \u67e5\u627e\u8282\u70b9 */\nfunction search(num) {\nlet cur = root;\n// \u5faa\u73af\u67e5\u627e\uff0c\u8d8a\u8fc7\u53f6\u8282\u70b9\u540e\u8df3\u51fa\nwhile (cur !== null) {\n// \u76ee\u6807\u8282\u70b9\u5728 cur \u7684\u53f3\u5b50\u6811\u4e2d\nif (cur.val &lt; num) cur = cur.right;\n// \u76ee\u6807\u8282\u70b9\u5728 cur \u7684\u5de6\u5b50\u6811\u4e2d\nelse if (cur.val &gt; num) cur = cur.left;\n// \u627e\u5230\u76ee\u6807\u8282\u70b9\uff0c\u8df3\u51fa\u5faa\u73af\nelse break;\n}\n// \u8fd4\u56de\u76ee\u6807\u8282\u70b9\nreturn cur;\n}\n</code></pre> binary_search_tree.ts<pre><code>/* \u67e5\u627e\u8282\u70b9 */\nfunction search(num: number): TreeNode | null {\nlet cur = root;\n// \u5faa\u73af\u67e5\u627e\uff0c\u8d8a\u8fc7\u53f6\u8282\u70b9\u540e\u8df3\u51fa\nwhile (cur !== null) {\nif (cur.val &lt; num) {\ncur = cur.right; // \u76ee\u6807\u8282\u70b9\u5728 cur \u7684\u53f3\u5b50\u6811\u4e2d\n} else if (cur.val &gt; num) {\ncur = cur.left; // \u76ee\u6807\u8282\u70b9\u5728 cur \u7684\u5de6\u5b50\u6811\u4e2d\n} else {\nbreak; // \u627e\u5230\u76ee\u6807\u8282\u70b9\uff0c\u8df3\u51fa\u5faa\u73af\n}\n}\n// \u8fd4\u56de\u76ee\u6807\u8282\u70b9\nreturn cur;\n}\n</code></pre> binary_search_tree.c<pre><code>/* \u67e5\u627e\u8282\u70b9 */\nTreeNode *search(binarySearchTree *bst, int num) {\nTreeNode *cur = bst-&gt;root;\n// \u5faa\u73af\u67e5\u627e\uff0c\u8d8a\u8fc7\u53f6\u8282\u70b9\u540e\u8df3\u51fa\nwhile (cur != NULL) {\nif (cur-&gt;val &lt; num) {\n// \u76ee\u6807\u8282\u70b9\u5728 cur \u7684\u53f3\u5b50\u6811\u4e2d\ncur = cur-&gt;right;\n} else if (cur-&gt;val &gt; num) {\n// \u76ee\u6807\u8282\u70b9\u5728 cur \u7684\u5de6\u5b50\u6811\u4e2d\ncur = cur-&gt;left;\n} else {\n// \u627e\u5230\u76ee\u6807\u8282\u70b9\uff0c\u8df3\u51fa\u5faa\u73af\nbreak;\n}\n}\n// \u8fd4\u56de\u76ee\u6807\u8282\u70b9\nreturn cur;\n}\n</code></pre> binary_search_tree.cs<pre><code>/* \u67e5\u627e\u8282\u70b9 */\nTreeNode? search(int num) {\nTreeNode? cur = root;\n// \u5faa\u73af\u67e5\u627e\uff0c\u8d8a\u8fc7\u53f6\u8282\u70b9\u540e\u8df3\u51fa\nwhile (cur != null) {\n// \u76ee\u6807\u8282\u70b9\u5728 cur \u7684\u53f3\u5b50\u6811\u4e2d\nif (cur.val &lt; num) cur =\ncur.right;\n// \u76ee\u6807\u8282\u70b9\u5728 cur \u7684\u5de6\u5b50\u6811\u4e2d\nelse if (cur.val &gt; num)\ncur = cur.left;\n// \u627e\u5230\u76ee\u6807\u8282\u70b9\uff0c\u8df3\u51fa\u5faa\u73af\nelse\nbreak;\n}\n// \u8fd4\u56de\u76ee\u6807\u8282\u70b9\nreturn cur;\n}\n</code></pre> binary_search_tree.swift<pre><code>/* \u67e5\u627e\u8282\u70b9 */\nfunc search(num: Int) -&gt; TreeNode? {\nvar cur = root\n// \u5faa\u73af\u67e5\u627e\uff0c\u8d8a\u8fc7\u53f6\u8282\u70b9\u540e\u8df3\u51fa\nwhile cur != nil {\n// \u76ee\u6807\u8282\u70b9\u5728 cur \u7684\u53f3\u5b50\u6811\u4e2d\nif cur!.val &lt; num {\ncur = cur?.right\n}\n// \u76ee\u6807\u8282\u70b9\u5728 cur \u7684\u5de6\u5b50\u6811\u4e2d\nelse if cur!.val &gt; num {\ncur = cur?.left\n}\n// \u627e\u5230\u76ee\u6807\u8282\u70b9\uff0c\u8df3\u51fa\u5faa\u73af\nelse {\nbreak\n}\n}\n// \u8fd4\u56de\u76ee\u6807\u8282\u70b9\nreturn cur\n}\n</code></pre> binary_search_tree.zig<pre><code>// \u67e5\u627e\u8282\u70b9\nfn search(self: *Self, num: T) ?*inc.TreeNode(T) {\nvar cur = self.root;\n// \u5faa\u73af\u67e5\u627e\uff0c\u8d8a\u8fc7\u53f6\u8282\u70b9\u540e\u8df3\u51fa\nwhile (cur != null) {\n// \u76ee\u6807\u8282\u70b9\u5728 cur \u7684\u53f3\u5b50\u6811\u4e2d\nif (cur.?.val &lt; num) {\ncur = cur.?.right;\n// \u76ee\u6807\u8282\u70b9\u5728 cur \u7684\u5de6\u5b50\u6811\u4e2d\n} else if (cur.?.val &gt; num) {\ncur = cur.?.left;\n// \u627e\u5230\u76ee\u6807\u8282\u70b9\uff0c\u8df3\u51fa\u5faa\u73af\n} else {\nbreak;\n}\n}\n// \u8fd4\u56de\u76ee\u6807\u8282\u70b9\nreturn cur;\n}\n</code></pre> binary_search_tree.dart<pre><code>[class]{BinarySearchTree}-[func]{search}\n</code></pre>"},{"location":"chapter_tree/binary_search_tree/#_2","title":"\u63d2\u5165\u8282\u70b9","text":"<p>\u7ed9\u5b9a\u4e00\u4e2a\u5f85\u63d2\u5165\u5143\u7d20 <code>num</code> \uff0c\u4e3a\u4e86\u4fdd\u6301\u4e8c\u53c9\u641c\u7d22\u6811\u201c\u5de6\u5b50\u6811 &lt; \u6839\u8282\u70b9 &lt; \u53f3\u5b50\u6811\u201d\u7684\u6027\u8d28\uff0c\u63d2\u5165\u64cd\u4f5c\u5206\u4e3a\u4e24\u6b65\uff1a</p> <ol> <li>\u67e5\u627e\u63d2\u5165\u4f4d\u7f6e\uff1a\u4e0e\u67e5\u627e\u64cd\u4f5c\u76f8\u4f3c\uff0c\u4ece\u6839\u8282\u70b9\u51fa\u53d1\uff0c\u6839\u636e\u5f53\u524d\u8282\u70b9\u503c\u548c <code>num</code> \u7684\u5927\u5c0f\u5173\u7cfb\u5faa\u73af\u5411\u4e0b\u641c\u7d22\uff0c\u76f4\u5230\u8d8a\u8fc7\u53f6\u8282\u70b9\uff08\u904d\u5386\u81f3 \\(\\text{null}\\) \uff09\u65f6\u8df3\u51fa\u5faa\u73af\uff1b</li> <li>\u5728\u8be5\u4f4d\u7f6e\u63d2\u5165\u8282\u70b9\uff1a\u521d\u59cb\u5316\u8282\u70b9 <code>num</code> \uff0c\u5c06\u8be5\u8282\u70b9\u7f6e\u4e8e \\(\\text{null}\\) \u7684\u4f4d\u7f6e\uff1b</li> </ol> <p>\u4e8c\u53c9\u641c\u7d22\u6811\u4e0d\u5141\u8bb8\u5b58\u5728\u91cd\u590d\u8282\u70b9\uff0c\u5426\u5219\u5c06\u8fdd\u53cd\u5176\u5b9a\u4e49\u3002\u56e0\u6b64\uff0c\u82e5\u5f85\u63d2\u5165\u8282\u70b9\u5728\u6811\u4e2d\u5df2\u5b58\u5728\uff0c\u5219\u4e0d\u6267\u884c\u63d2\u5165\uff0c\u76f4\u63a5\u8fd4\u56de\u3002</p> <p></p> <p> Fig. \u5728\u4e8c\u53c9\u641c\u7d22\u6811\u4e2d\u63d2\u5165\u8282\u70b9 </p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart binary_search_tree.java<pre><code>/* \u63d2\u5165\u8282\u70b9 */\nvoid insert(int num) {\n// \u82e5\u6811\u4e3a\u7a7a\uff0c\u76f4\u63a5\u63d0\u524d\u8fd4\u56de\nif (root == null)\nreturn;\nTreeNode cur = root, pre = null;\n// \u5faa\u73af\u67e5\u627e\uff0c\u8d8a\u8fc7\u53f6\u8282\u70b9\u540e\u8df3\u51fa\nwhile (cur != null) {\n// \u627e\u5230\u91cd\u590d\u8282\u70b9\uff0c\u76f4\u63a5\u8fd4\u56de\nif (cur.val == num)\nreturn;\npre = cur;\n// \u63d2\u5165\u4f4d\u7f6e\u5728 cur \u7684\u53f3\u5b50\u6811\u4e2d\nif (cur.val &lt; num)\ncur = cur.right;\n// \u63d2\u5165\u4f4d\u7f6e\u5728 cur \u7684\u5de6\u5b50\u6811\u4e2d\nelse\ncur = cur.left;\n}\n// \u63d2\u5165\u8282\u70b9\nTreeNode node = new TreeNode(num);\nif (pre.val &lt; num)\npre.right = node;\nelse\npre.left = node;\n}\n</code></pre> binary_search_tree.cpp<pre><code>/* \u63d2\u5165\u8282\u70b9 */\nvoid insert(int num) {\n// \u82e5\u6811\u4e3a\u7a7a\uff0c\u76f4\u63a5\u63d0\u524d\u8fd4\u56de\nif (root == nullptr)\nreturn;\nTreeNode *cur = root, *pre = nullptr;\n// \u5faa\u73af\u67e5\u627e\uff0c\u8d8a\u8fc7\u53f6\u8282\u70b9\u540e\u8df3\u51fa\nwhile (cur != nullptr) {\n// \u627e\u5230\u91cd\u590d\u8282\u70b9\uff0c\u76f4\u63a5\u8fd4\u56de\nif (cur-&gt;val == num)\nreturn;\npre = cur;\n// \u63d2\u5165\u4f4d\u7f6e\u5728 cur \u7684\u53f3\u5b50\u6811\u4e2d\nif (cur-&gt;val &lt; num)\ncur = cur-&gt;right;\n// \u63d2\u5165\u4f4d\u7f6e\u5728 cur \u7684\u5de6\u5b50\u6811\u4e2d\nelse\ncur = cur-&gt;left;\n}\n// \u63d2\u5165\u8282\u70b9\nTreeNode *node = new TreeNode(num);\nif (pre-&gt;val &lt; num)\npre-&gt;right = node;\nelse\npre-&gt;left = node;\n}\n</code></pre> binary_search_tree.py<pre><code>def insert(self, num: int) -&gt; None:\n\"\"\"\u63d2\u5165\u8282\u70b9\"\"\"\n# \u82e5\u6811\u4e3a\u7a7a\uff0c\u76f4\u63a5\u63d0\u524d\u8fd4\u56de\nif self.root is None:\nreturn\n# \u5faa\u73af\u67e5\u627e\uff0c\u8d8a\u8fc7\u53f6\u8282\u70b9\u540e\u8df3\u51fa\ncur, pre = self.root, None\nwhile cur is not None:\n# \u627e\u5230\u91cd\u590d\u8282\u70b9\uff0c\u76f4\u63a5\u8fd4\u56de\nif cur.val == num:\nreturn\npre = cur\n# \u63d2\u5165\u4f4d\u7f6e\u5728 cur \u7684\u53f3\u5b50\u6811\u4e2d\nif cur.val &lt; num:\ncur = cur.right\n# \u63d2\u5165\u4f4d\u7f6e\u5728 cur \u7684\u5de6\u5b50\u6811\u4e2d\nelse:\ncur = cur.left\n# \u63d2\u5165\u8282\u70b9\nnode = TreeNode(num)\nif pre.val &lt; num:\npre.right = node\nelse:\npre.left = node\n</code></pre> binary_search_tree.go<pre><code>/* \u63d2\u5165\u8282\u70b9 */\nfunc (bst *binarySearchTree) insert(num int) {\ncur := bst.root\n// \u82e5\u6811\u4e3a\u7a7a\uff0c\u76f4\u63a5\u63d0\u524d\u8fd4\u56de\nif cur == nil {\nreturn\n}\n// \u5f85\u63d2\u5165\u8282\u70b9\u4e4b\u524d\u7684\u8282\u70b9\u4f4d\u7f6e\nvar pre *TreeNode = nil\n// \u5faa\u73af\u67e5\u627e\uff0c\u8d8a\u8fc7\u53f6\u8282\u70b9\u540e\u8df3\u51fa\nfor cur != nil {\nif cur.Val == num {\nreturn\n}\npre = cur\nif cur.Val &lt; num {\ncur = cur.Right\n} else {\ncur = cur.Left\n}\n}\n// \u63d2\u5165\u8282\u70b9\nnode := NewTreeNode(num)\nif pre.Val &lt; num {\npre.Right = node\n} else {\npre.Left = node\n}\n}\n</code></pre> binary_search_tree.js<pre><code>/* \u63d2\u5165\u8282\u70b9 */\nfunction insert(num) {\n// \u82e5\u6811\u4e3a\u7a7a\uff0c\u76f4\u63a5\u63d0\u524d\u8fd4\u56de\nif (root === null) return;\nlet cur = root,\npre = null;\n// \u5faa\u73af\u67e5\u627e\uff0c\u8d8a\u8fc7\u53f6\u8282\u70b9\u540e\u8df3\u51fa\nwhile (cur !== null) {\n// \u627e\u5230\u91cd\u590d\u8282\u70b9\uff0c\u76f4\u63a5\u8fd4\u56de\nif (cur.val === num) return;\npre = cur;\n// \u63d2\u5165\u4f4d\u7f6e\u5728 cur \u7684\u53f3\u5b50\u6811\u4e2d\nif (cur.val &lt; num) cur = cur.right;\n// \u63d2\u5165\u4f4d\u7f6e\u5728 cur \u7684\u5de6\u5b50\u6811\u4e2d\nelse cur = cur.left;\n}\n// \u63d2\u5165\u8282\u70b9\nlet node = new TreeNode(num);\nif (pre.val &lt; num) pre.right = node;\nelse pre.left = node;\n}\n</code></pre> binary_search_tree.ts<pre><code>/* \u63d2\u5165\u8282\u70b9 */\nfunction insert(num: number): void {\n// \u82e5\u6811\u4e3a\u7a7a\uff0c\u76f4\u63a5\u63d0\u524d\u8fd4\u56de\nif (root === null) {\nreturn;\n}\nlet cur = root,\npre: TreeNode | null = null;\n// \u5faa\u73af\u67e5\u627e\uff0c\u8d8a\u8fc7\u53f6\u8282\u70b9\u540e\u8df3\u51fa\nwhile (cur !== null) {\nif (cur.val === num) {\nreturn; // \u627e\u5230\u91cd\u590d\u8282\u70b9\uff0c\u76f4\u63a5\u8fd4\u56de\n}\npre = cur;\nif (cur.val &lt; num) {\ncur = cur.right as TreeNode; // \u63d2\u5165\u4f4d\u7f6e\u5728 cur \u7684\u53f3\u5b50\u6811\u4e2d\n} else {\ncur = cur.left as TreeNode; // \u63d2\u5165\u4f4d\u7f6e\u5728 cur \u7684\u5de6\u5b50\u6811\u4e2d\n}\n}\n// \u63d2\u5165\u8282\u70b9\nlet node = new TreeNode(num);\nif (pre!.val &lt; num) {\npre!.right = node;\n} else {\npre!.left = node;\n}\n}\n</code></pre> binary_search_tree.c<pre><code>/* \u63d2\u5165\u8282\u70b9 */\nvoid insert(binarySearchTree *bst, int num) {\n// \u82e5\u6811\u4e3a\u7a7a\uff0c\u76f4\u63a5\u63d0\u524d\u8fd4\u56de\nif (bst-&gt;root == NULL)\nreturn;\nTreeNode *cur = bst-&gt;root, *pre = NULL;\n// \u5faa\u73af\u67e5\u627e\uff0c\u8d8a\u8fc7\u53f6\u8282\u70b9\u540e\u8df3\u51fa\nwhile (cur != NULL) {\n// \u627e\u5230\u91cd\u590d\u8282\u70b9\uff0c\u76f4\u63a5\u8fd4\u56de\nif (cur-&gt;val == num) {\nreturn;\n}\npre = cur;\nif (cur-&gt;val &lt; num) {\n// \u63d2\u5165\u4f4d\u7f6e\u5728 cur \u7684\u53f3\u5b50\u6811\u4e2d\ncur = cur-&gt;right;\n} else {\n// \u63d2\u5165\u4f4d\u7f6e\u5728 cur \u7684\u5de6\u5b50\u6811\u4e2d\ncur = cur-&gt;left;\n}\n}\n// \u63d2\u5165\u8282\u70b9\nTreeNode *node = newTreeNode(num);\nif (pre-&gt;val &lt; num) {\npre-&gt;right = node;\n} else {\npre-&gt;left = node;\n}\n}\n</code></pre> binary_search_tree.cs<pre><code>/* \u63d2\u5165\u8282\u70b9 */\nvoid insert(int num) {\n// \u82e5\u6811\u4e3a\u7a7a\uff0c\u76f4\u63a5\u63d0\u524d\u8fd4\u56de\nif (root == null)\nreturn;\nTreeNode? cur = root, pre = null;\n// \u5faa\u73af\u67e5\u627e\uff0c\u8d8a\u8fc7\u53f6\u8282\u70b9\u540e\u8df3\u51fa\nwhile (cur != null) {\n// \u627e\u5230\u91cd\u590d\u8282\u70b9\uff0c\u76f4\u63a5\u8fd4\u56de\nif (cur.val == num)\nreturn;\npre = cur;\n// \u63d2\u5165\u4f4d\u7f6e\u5728 cur \u7684\u53f3\u5b50\u6811\u4e2d\nif (cur.val &lt; num)\ncur = cur.right;\n// \u63d2\u5165\u4f4d\u7f6e\u5728 cur \u7684\u5de6\u5b50\u6811\u4e2d\nelse\ncur = cur.left;\n}\n// \u63d2\u5165\u8282\u70b9\nTreeNode node = new TreeNode(num);\nif (pre != null) {\nif (pre.val &lt; num)\npre.right = node;\nelse\npre.left = node;\n}\n}\n</code></pre> binary_search_tree.swift<pre><code>/* \u63d2\u5165\u8282\u70b9 */\nfunc insert(num: Int) {\n// \u82e5\u6811\u4e3a\u7a7a\uff0c\u76f4\u63a5\u63d0\u524d\u8fd4\u56de\nif root == nil {\nreturn\n}\nvar cur = root\nvar pre: TreeNode?\n// \u5faa\u73af\u67e5\u627e\uff0c\u8d8a\u8fc7\u53f6\u8282\u70b9\u540e\u8df3\u51fa\nwhile cur != nil {\n// \u627e\u5230\u91cd\u590d\u8282\u70b9\uff0c\u76f4\u63a5\u8fd4\u56de\nif cur!.val == num {\nreturn\n}\npre = cur\n// \u63d2\u5165\u4f4d\u7f6e\u5728 cur \u7684\u53f3\u5b50\u6811\u4e2d\nif cur!.val &lt; num {\ncur = cur?.right\n}\n// \u63d2\u5165\u4f4d\u7f6e\u5728 cur \u7684\u5de6\u5b50\u6811\u4e2d\nelse {\ncur = cur?.left\n}\n}\n// \u63d2\u5165\u8282\u70b9\nlet node = TreeNode(x: num)\nif pre!.val &lt; num {\npre?.right = node\n} else {\npre?.left = node\n}\n}\n</code></pre> binary_search_tree.zig<pre><code>// \u63d2\u5165\u8282\u70b9\nfn insert(self: *Self, num: T) !void {\n// \u82e5\u6811\u4e3a\u7a7a\uff0c\u76f4\u63a5\u63d0\u524d\u8fd4\u56de\nif (self.root == null) return;\nvar cur = self.root;\nvar pre: ?*inc.TreeNode(T) = null;\n// \u5faa\u73af\u67e5\u627e\uff0c\u8d8a\u8fc7\u53f6\u8282\u70b9\u540e\u8df3\u51fa\nwhile (cur != null) {\n// \u627e\u5230\u91cd\u590d\u8282\u70b9\uff0c\u76f4\u63a5\u8fd4\u56de\nif (cur.?.val == num) return;\npre = cur;\n// \u63d2\u5165\u4f4d\u7f6e\u5728 cur \u7684\u53f3\u5b50\u6811\u4e2d\nif (cur.?.val &lt; num) {\ncur = cur.?.right;\n// \u63d2\u5165\u4f4d\u7f6e\u5728 cur \u7684\u5de6\u5b50\u6811\u4e2d\n} else {\ncur = cur.?.left;\n}\n}\n// \u63d2\u5165\u8282\u70b9\nvar node = try self.mem_allocator.create(inc.TreeNode(T));\nnode.init(num);\nif (pre.?.val &lt; num) {\npre.?.right = node;\n} else {\npre.?.left = node;\n}\n}\n</code></pre> binary_search_tree.dart<pre><code>[class]{BinarySearchTree}-[func]{insert}\n</code></pre> <p>\u4e3a\u4e86\u63d2\u5165\u8282\u70b9\uff0c\u6211\u4eec\u9700\u8981\u5229\u7528\u8f85\u52a9\u8282\u70b9 <code>pre</code> \u4fdd\u5b58\u4e0a\u4e00\u8f6e\u5faa\u73af\u7684\u8282\u70b9\uff0c\u8fd9\u6837\u5728\u904d\u5386\u81f3 \\(\\text{null}\\) \u65f6\uff0c\u6211\u4eec\u53ef\u4ee5\u83b7\u53d6\u5230\u5176\u7236\u8282\u70b9\uff0c\u4ece\u800c\u5b8c\u6210\u8282\u70b9\u63d2\u5165\u64cd\u4f5c\u3002</p> <p>\u4e0e\u67e5\u627e\u8282\u70b9\u76f8\u540c\uff0c\u63d2\u5165\u8282\u70b9\u4f7f\u7528 \\(O(\\log n)\\) \u65f6\u95f4\u3002</p>"},{"location":"chapter_tree/binary_search_tree/#_3","title":"\u5220\u9664\u8282\u70b9","text":"<p>\u4e0e\u63d2\u5165\u8282\u70b9\u7c7b\u4f3c\uff0c\u6211\u4eec\u9700\u8981\u5728\u5220\u9664\u64cd\u4f5c\u540e\u7ef4\u6301\u4e8c\u53c9\u641c\u7d22\u6811\u7684\u201c\u5de6\u5b50\u6811 &lt; \u6839\u8282\u70b9 &lt; \u53f3\u5b50\u6811\u201d\u7684\u6027\u8d28\u3002\u9996\u5148\uff0c\u6211\u4eec\u9700\u8981\u5728\u4e8c\u53c9\u6811\u4e2d\u6267\u884c\u67e5\u627e\u64cd\u4f5c\uff0c\u83b7\u53d6\u5f85\u5220\u9664\u8282\u70b9\u3002\u63a5\u4e0b\u6765\uff0c\u6839\u636e\u5f85\u5220\u9664\u8282\u70b9\u7684\u5b50\u8282\u70b9\u6570\u91cf\uff0c\u5220\u9664\u64cd\u4f5c\u9700\u5206\u4e3a\u4e09\u79cd\u60c5\u51b5\uff1a</p> <p>\u5f53\u5f85\u5220\u9664\u8282\u70b9\u7684\u5b50\u8282\u70b9\u6570\u91cf \\(= 0\\) \u65f6\uff0c\u8868\u793a\u5f85\u5220\u9664\u8282\u70b9\u662f\u53f6\u8282\u70b9\uff0c\u53ef\u4ee5\u76f4\u63a5\u5220\u9664\u3002</p> <p></p> <p> Fig. \u5728\u4e8c\u53c9\u641c\u7d22\u6811\u4e2d\u5220\u9664\u8282\u70b9\uff08\u5ea6\u4e3a 0\uff09 </p> <p>\u5f53\u5f85\u5220\u9664\u8282\u70b9\u7684\u5b50\u8282\u70b9\u6570\u91cf \\(= 1\\) \u65f6\uff0c\u5c06\u5f85\u5220\u9664\u8282\u70b9\u66ff\u6362\u4e3a\u5176\u5b50\u8282\u70b9\u5373\u53ef\u3002</p> <p></p> <p> Fig. \u5728\u4e8c\u53c9\u641c\u7d22\u6811\u4e2d\u5220\u9664\u8282\u70b9\uff08\u5ea6\u4e3a 1\uff09 </p> <p>\u5f53\u5f85\u5220\u9664\u8282\u70b9\u7684\u5b50\u8282\u70b9\u6570\u91cf \\(= 2\\) \u65f6\uff0c\u5220\u9664\u64cd\u4f5c\u5206\u4e3a\u4e09\u6b65\uff1a</p> <ol> <li>\u627e\u5230\u5f85\u5220\u9664\u8282\u70b9\u5728\u201c\u4e2d\u5e8f\u904d\u5386\u5e8f\u5217\u201d\u4e2d\u7684\u4e0b\u4e00\u4e2a\u8282\u70b9\uff0c\u8bb0\u4e3a <code>tmp</code> \uff1b</li> <li>\u5728\u6811\u4e2d\u9012\u5f52\u5220\u9664\u8282\u70b9 <code>tmp</code> \uff1b</li> <li>\u7528 <code>tmp</code> \u7684\u503c\u8986\u76d6\u5f85\u5220\u9664\u8282\u70b9\u7684\u503c\uff1b</li> </ol> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt; <p></p> <p></p> <p></p> <p></p> <p>\u5220\u9664\u8282\u70b9\u64cd\u4f5c\u540c\u6837\u4f7f\u7528 \\(O(\\log n)\\) \u65f6\u95f4\uff0c\u5176\u4e2d\u67e5\u627e\u5f85\u5220\u9664\u8282\u70b9\u9700\u8981 \\(O(\\log n)\\) \u65f6\u95f4\uff0c\u83b7\u53d6\u4e2d\u5e8f\u904d\u5386\u540e\u7ee7\u8282\u70b9\u9700\u8981 \\(O(\\log n)\\) \u65f6\u95f4\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart binary_search_tree.java<pre><code>/* \u5220\u9664\u8282\u70b9 */\nvoid remove(int num) {\n// \u82e5\u6811\u4e3a\u7a7a\uff0c\u76f4\u63a5\u63d0\u524d\u8fd4\u56de\nif (root == null)\nreturn;\nTreeNode cur = root, pre = null;\n// \u5faa\u73af\u67e5\u627e\uff0c\u8d8a\u8fc7\u53f6\u8282\u70b9\u540e\u8df3\u51fa\nwhile (cur != null) {\n// \u627e\u5230\u5f85\u5220\u9664\u8282\u70b9\uff0c\u8df3\u51fa\u5faa\u73af\nif (cur.val == num)\nbreak;\npre = cur;\n// \u5f85\u5220\u9664\u8282\u70b9\u5728 cur \u7684\u53f3\u5b50\u6811\u4e2d\nif (cur.val &lt; num)\ncur = cur.right;\n// \u5f85\u5220\u9664\u8282\u70b9\u5728 cur \u7684\u5de6\u5b50\u6811\u4e2d\nelse\ncur = cur.left;\n}\n// \u82e5\u65e0\u5f85\u5220\u9664\u8282\u70b9\uff0c\u5219\u76f4\u63a5\u8fd4\u56de\nif (cur == null)\nreturn;\n// \u5b50\u8282\u70b9\u6570\u91cf = 0 or 1\nif (cur.left == null || cur.right == null) {\n// \u5f53\u5b50\u8282\u70b9\u6570\u91cf = 0 / 1 \u65f6\uff0c child = null / \u8be5\u5b50\u8282\u70b9\nTreeNode child = cur.left != null ? cur.left : cur.right;\n// \u5220\u9664\u8282\u70b9 cur\nif (cur != root) {\nif (pre.left == cur)\npre.left = child;\nelse\npre.right = child;\n} else {\n// \u82e5\u5220\u9664\u8282\u70b9\u4e3a\u6839\u8282\u70b9\uff0c\u5219\u91cd\u65b0\u6307\u5b9a\u6839\u8282\u70b9\nroot = child;\n}\n}\n// \u5b50\u8282\u70b9\u6570\u91cf = 2\nelse {\n// \u83b7\u53d6\u4e2d\u5e8f\u904d\u5386\u4e2d cur \u7684\u4e0b\u4e00\u4e2a\u8282\u70b9\nTreeNode tmp = cur.right;\nwhile (tmp.left != null) {\ntmp = tmp.left;\n}\n// \u9012\u5f52\u5220\u9664\u8282\u70b9 tmp\nremove(tmp.val);\n// \u7528 tmp \u8986\u76d6 cur\ncur.val = tmp.val;\n}\n}\n</code></pre> binary_search_tree.cpp<pre><code>/* \u5220\u9664\u8282\u70b9 */\nvoid remove(int num) {\n// \u82e5\u6811\u4e3a\u7a7a\uff0c\u76f4\u63a5\u63d0\u524d\u8fd4\u56de\nif (root == nullptr)\nreturn;\nTreeNode *cur = root, *pre = nullptr;\n// \u5faa\u73af\u67e5\u627e\uff0c\u8d8a\u8fc7\u53f6\u8282\u70b9\u540e\u8df3\u51fa\nwhile (cur != nullptr) {\n// \u627e\u5230\u5f85\u5220\u9664\u8282\u70b9\uff0c\u8df3\u51fa\u5faa\u73af\nif (cur-&gt;val == num)\nbreak;\npre = cur;\n// \u5f85\u5220\u9664\u8282\u70b9\u5728 cur \u7684\u53f3\u5b50\u6811\u4e2d\nif (cur-&gt;val &lt; num)\ncur = cur-&gt;right;\n// \u5f85\u5220\u9664\u8282\u70b9\u5728 cur \u7684\u5de6\u5b50\u6811\u4e2d\nelse\ncur = cur-&gt;left;\n}\n// \u82e5\u65e0\u5f85\u5220\u9664\u8282\u70b9\uff0c\u5219\u76f4\u63a5\u8fd4\u56de\nif (cur == nullptr)\nreturn;\n// \u5b50\u8282\u70b9\u6570\u91cf = 0 or 1\nif (cur-&gt;left == nullptr || cur-&gt;right == nullptr) {\n// \u5f53\u5b50\u8282\u70b9\u6570\u91cf = 0 / 1 \u65f6\uff0c child = nullptr / \u8be5\u5b50\u8282\u70b9\nTreeNode *child = cur-&gt;left != nullptr ? cur-&gt;left : cur-&gt;right;\n// \u5220\u9664\u8282\u70b9 cur\nif (cur != root) {\nif (pre-&gt;left == cur)\npre-&gt;left = child;\nelse\npre-&gt;right = child;\n} else {\n// \u82e5\u5220\u9664\u8282\u70b9\u4e3a\u6839\u8282\u70b9\uff0c\u5219\u91cd\u65b0\u6307\u5b9a\u6839\u8282\u70b9\nroot = child;\n}\n// \u91ca\u653e\u5185\u5b58\ndelete cur;\n}\n// \u5b50\u8282\u70b9\u6570\u91cf = 2\nelse {\n// \u83b7\u53d6\u4e2d\u5e8f\u904d\u5386\u4e2d cur \u7684\u4e0b\u4e00\u4e2a\u8282\u70b9\nTreeNode *tmp = cur-&gt;right;\nwhile (tmp-&gt;left != nullptr) {\ntmp = tmp-&gt;left;\n}\nint tmpVal = tmp-&gt;val;\n// \u9012\u5f52\u5220\u9664\u8282\u70b9 tmp\nremove(tmp-&gt;val);\n// \u7528 tmp \u8986\u76d6 cur\ncur-&gt;val = tmpVal;\n}\n}\n</code></pre> binary_search_tree.py<pre><code>def remove(self, num: int) -&gt; None:\n\"\"\"\u5220\u9664\u8282\u70b9\"\"\"\n# \u82e5\u6811\u4e3a\u7a7a\uff0c\u76f4\u63a5\u63d0\u524d\u8fd4\u56de\nif self.root is None:\nreturn\n# \u5faa\u73af\u67e5\u627e\uff0c\u8d8a\u8fc7\u53f6\u8282\u70b9\u540e\u8df3\u51fa\ncur, pre = self.root, None\nwhile cur is not None:\n# \u627e\u5230\u5f85\u5220\u9664\u8282\u70b9\uff0c\u8df3\u51fa\u5faa\u73af\nif cur.val == num:\nbreak\npre = cur\n# \u5f85\u5220\u9664\u8282\u70b9\u5728 cur \u7684\u53f3\u5b50\u6811\u4e2d\nif cur.val &lt; num:\ncur = cur.right\n# \u5f85\u5220\u9664\u8282\u70b9\u5728 cur \u7684\u5de6\u5b50\u6811\u4e2d\nelse:\ncur = cur.left\n# \u82e5\u65e0\u5f85\u5220\u9664\u8282\u70b9\uff0c\u5219\u76f4\u63a5\u8fd4\u56de\nif cur is None:\nreturn\n# \u5b50\u8282\u70b9\u6570\u91cf = 0 or 1\nif cur.left is None or cur.right is None:\n# \u5f53\u5b50\u8282\u70b9\u6570\u91cf = 0 / 1 \u65f6\uff0c child = null / \u8be5\u5b50\u8282\u70b9\nchild = cur.left or cur.right\n# \u5220\u9664\u8282\u70b9 cur\nif cur != self.root:\nif pre.left == cur:\npre.left = child\nelse:\npre.right = child\nelse:\n# \u82e5\u5220\u9664\u8282\u70b9\u4e3a\u6839\u8282\u70b9\uff0c\u5219\u91cd\u65b0\u6307\u5b9a\u6839\u8282\u70b9\nself.__root = cur\n# \u5b50\u8282\u70b9\u6570\u91cf = 2\nelse:\n# \u83b7\u53d6\u4e2d\u5e8f\u904d\u5386\u4e2d cur \u7684\u4e0b\u4e00\u4e2a\u8282\u70b9\ntmp: TreeNode = cur.right\nwhile tmp.left is not None:\ntmp = tmp.left\n# \u9012\u5f52\u5220\u9664\u8282\u70b9 tmp\nself.remove(tmp.val)\n# \u7528 tmp \u8986\u76d6 cur\ncur.val = tmp.val\n</code></pre> binary_search_tree.go<pre><code>/* \u5220\u9664\u8282\u70b9 */\nfunc (bst *binarySearchTree) remove(num int) {\ncur := bst.root\n// \u82e5\u6811\u4e3a\u7a7a\uff0c\u76f4\u63a5\u63d0\u524d\u8fd4\u56de\nif cur == nil {\nreturn\n}\n// \u5f85\u5220\u9664\u8282\u70b9\u4e4b\u524d\u7684\u8282\u70b9\u4f4d\u7f6e\nvar pre *TreeNode = nil\n// \u5faa\u73af\u67e5\u627e\uff0c\u8d8a\u8fc7\u53f6\u8282\u70b9\u540e\u8df3\u51fa\nfor cur != nil {\nif cur.Val == num {\nbreak\n}\npre = cur\nif cur.Val &lt; num {\n// \u5f85\u5220\u9664\u8282\u70b9\u5728\u53f3\u5b50\u6811\u4e2d\ncur = cur.Right\n} else {\n// \u5f85\u5220\u9664\u8282\u70b9\u5728\u5de6\u5b50\u6811\u4e2d\ncur = cur.Left\n}\n}\n// \u82e5\u65e0\u5f85\u5220\u9664\u8282\u70b9\uff0c\u5219\u76f4\u63a5\u8fd4\u56de\nif cur == nil {\nreturn\n}\n// \u5b50\u8282\u70b9\u6570\u4e3a 0 \u6216 1\nif cur.Left == nil || cur.Right == nil {\nvar child *TreeNode = nil\n// \u53d6\u51fa\u5f85\u5220\u9664\u8282\u70b9\u7684\u5b50\u8282\u70b9\nif cur.Left != nil {\nchild = cur.Left\n} else {\nchild = cur.Right\n}\n// \u5220\u9664\u8282\u70b9 cur\nif cur != bst.root {\nif pre.Left == cur {\npre.Left = child\n} else {\npre.Right = child\n}\n} else {\n// \u82e5\u5220\u9664\u8282\u70b9\u4e3a\u6839\u8282\u70b9\uff0c\u5219\u91cd\u65b0\u6307\u5b9a\u6839\u8282\u70b9\nbst.root = child\n}\n// \u5b50\u8282\u70b9\u6570\u4e3a 2\n} else {\n// \u83b7\u53d6\u4e2d\u5e8f\u904d\u5386\u4e2d\u5f85\u5220\u9664\u8282\u70b9 cur \u7684\u4e0b\u4e00\u4e2a\u8282\u70b9\ntmp := cur.Right\nfor tmp.Left != nil {\ntmp = tmp.Left\n}\n// \u9012\u5f52\u5220\u9664\u8282\u70b9 tmp\nbst.remove(tmp.Val)\n// \u7528 tmp \u8986\u76d6 cur\ncur.Val = tmp.Val\n}\n}\n</code></pre> binary_search_tree.js<pre><code>/* \u5220\u9664\u8282\u70b9 */\nfunction remove(num) {\n// \u82e5\u6811\u4e3a\u7a7a\uff0c\u76f4\u63a5\u63d0\u524d\u8fd4\u56de\nif (root === null) return;\nlet cur = root,\npre = null;\n// \u5faa\u73af\u67e5\u627e\uff0c\u8d8a\u8fc7\u53f6\u8282\u70b9\u540e\u8df3\u51fa\nwhile (cur !== null) {\n// \u627e\u5230\u5f85\u5220\u9664\u8282\u70b9\uff0c\u8df3\u51fa\u5faa\u73af\nif (cur.val === num) break;\npre = cur;\n// \u5f85\u5220\u9664\u8282\u70b9\u5728 cur \u7684\u53f3\u5b50\u6811\u4e2d\nif (cur.val &lt; num) cur = cur.right;\n// \u5f85\u5220\u9664\u8282\u70b9\u5728 cur \u7684\u5de6\u5b50\u6811\u4e2d\nelse cur = cur.left;\n}\n// \u82e5\u65e0\u5f85\u5220\u9664\u8282\u70b9\uff0c\u5219\u76f4\u63a5\u8fd4\u56de\nif (cur === null) return;\n// \u5b50\u8282\u70b9\u6570\u91cf = 0 or 1\nif (cur.left === null || cur.right === null) {\n// \u5f53\u5b50\u8282\u70b9\u6570\u91cf = 0 / 1 \u65f6\uff0c child = null / \u8be5\u5b50\u8282\u70b9\nlet child = cur.left !== null ? cur.left : cur.right;\n// \u5220\u9664\u8282\u70b9 cur\nif (cur != root) {\nif (pre.left === cur) pre.left = child;\nelse pre.right = child;\n} else {\n// \u82e5\u5220\u9664\u8282\u70b9\u4e3a\u6839\u8282\u70b9\uff0c\u5219\u91cd\u65b0\u6307\u5b9a\u6839\u8282\u70b9\nroot = child;\n}\n}\n// \u5b50\u8282\u70b9\u6570\u91cf = 2\nelse {\n// \u83b7\u53d6\u4e2d\u5e8f\u904d\u5386\u4e2d cur \u7684\u4e0b\u4e00\u4e2a\u8282\u70b9\nlet tmp = cur.right;\nwhile (tmp.left !== null) {\ntmp = tmp.left;\n}\n// \u9012\u5f52\u5220\u9664\u8282\u70b9 tmp\nremove(tmp.val);\n// \u7528 tmp \u8986\u76d6 cur\ncur.val = tmp.val;\n}\n}\n</code></pre> binary_search_tree.ts<pre><code>/* \u5220\u9664\u8282\u70b9 */\nfunction remove(num: number): void {\n// \u82e5\u6811\u4e3a\u7a7a\uff0c\u76f4\u63a5\u63d0\u524d\u8fd4\u56de\nif (root === null) {\nreturn;\n}\nlet cur = root,\npre: TreeNode | null = null;\n// \u5faa\u73af\u67e5\u627e\uff0c\u8d8a\u8fc7\u53f6\u8282\u70b9\u540e\u8df3\u51fa\nwhile (cur !== null) {\n// \u627e\u5230\u5f85\u5220\u9664\u8282\u70b9\uff0c\u8df3\u51fa\u5faa\u73af\nif (cur.val === num) {\nbreak;\n}\npre = cur;\nif (cur.val &lt; num) {\ncur = cur.right as TreeNode; // \u5f85\u5220\u9664\u8282\u70b9\u5728 cur \u7684\u53f3\u5b50\u6811\u4e2d\n} else {\ncur = cur.left as TreeNode; // \u5f85\u5220\u9664\u8282\u70b9\u5728 cur \u7684\u5de6\u5b50\u6811\u4e2d\n}\n}\n// \u82e5\u65e0\u5f85\u5220\u9664\u8282\u70b9\uff0c\u5219\u76f4\u63a5\u8fd4\u56de\nif (cur === null) {\nreturn;\n}\n// \u5b50\u8282\u70b9\u6570\u91cf = 0 or 1\nif (cur.left === null || cur.right === null) {\n// \u5f53\u5b50\u8282\u70b9\u6570\u91cf = 0 / 1 \u65f6\uff0c child = null / \u8be5\u5b50\u8282\u70b9\nlet child = cur.left !== null ? cur.left : cur.right;\n// \u5220\u9664\u8282\u70b9 cur\nif (cur != root) {\nif (pre!.left === cur) {\npre!.left = child;\n} else {\npre!.right = child;\n}\n} else {\n// \u82e5\u5220\u9664\u8282\u70b9\u4e3a\u6839\u8282\u70b9\uff0c\u5219\u91cd\u65b0\u6307\u5b9a\u6839\u8282\u70b9\nroot = child;\n}\n}\n// \u5b50\u8282\u70b9\u6570\u91cf = 2\nelse {\n// \u83b7\u53d6\u4e2d\u5e8f\u904d\u5386\u4e2d cur \u7684\u4e0b\u4e00\u4e2a\u8282\u70b9\nlet tmp = cur.right;\nwhile (tmp.left !== null) {\ntmp = tmp.left;\n}\n// \u9012\u5f52\u5220\u9664\u8282\u70b9 tmp\nremove(tmp!.val);\n// \u7528 tmp \u8986\u76d6 cur\ncur.val = tmp.val;\n}\n}\n</code></pre> binary_search_tree.c<pre><code>/* \u5220\u9664\u8282\u70b9 */\n// \u7531\u4e8e\u5f15\u5165\u4e86 stdio.h \uff0c\u6b64\u5904\u65e0\u6cd5\u4f7f\u7528 remove \u5173\u952e\u8bcd\nvoid removeNode(binarySearchTree *bst, int num) {\n// \u82e5\u6811\u4e3a\u7a7a\uff0c\u76f4\u63a5\u63d0\u524d\u8fd4\u56de\nif (bst-&gt;root == NULL)\nreturn;\nTreeNode *cur = bst-&gt;root, *pre = NULL;\n// \u5faa\u73af\u67e5\u627e\uff0c\u8d8a\u8fc7\u53f6\u8282\u70b9\u540e\u8df3\u51fa\nwhile (cur != NULL) {\n// \u627e\u5230\u5f85\u5220\u9664\u8282\u70b9\uff0c\u8df3\u51fa\u5faa\u73af\nif (cur-&gt;val == num)\nbreak;\npre = cur;\nif (cur-&gt;val &lt; num) {\n// \u5f85\u5220\u9664\u8282\u70b9\u5728 root \u7684\u53f3\u5b50\u6811\u4e2d\ncur = cur-&gt;right;\n} else {\n// \u5f85\u5220\u9664\u8282\u70b9\u5728 root \u7684\u5de6\u5b50\u6811\u4e2d\ncur = cur-&gt;left;\n}\n}\n// \u82e5\u65e0\u5f85\u5220\u9664\u8282\u70b9\uff0c\u5219\u76f4\u63a5\u8fd4\u56de\nif (cur == NULL)\nreturn;\n// \u5224\u65ad\u5f85\u5220\u9664\u8282\u70b9\u662f\u5426\u5b58\u5728\u5b50\u8282\u70b9\nif (cur-&gt;left == NULL || cur-&gt;right == NULL) {\n/* \u5b50\u8282\u70b9\u6570\u91cf = 0 or 1 */\n// \u5f53\u5b50\u8282\u70b9\u6570\u91cf = 0 / 1 \u65f6\uff0c child = nullptr / \u8be5\u5b50\u8282\u70b9\nTreeNode *child = cur-&gt;left != NULL ? cur-&gt;left : cur-&gt;right;\n// \u5220\u9664\u8282\u70b9 cur\nif (pre-&gt;left == cur) {\npre-&gt;left = child;\n} else {\npre-&gt;right = child;\n}\n} else {\n/* \u5b50\u8282\u70b9\u6570\u91cf = 2 */\n// \u83b7\u53d6\u4e2d\u5e8f\u904d\u5386\u4e2d cur \u7684\u4e0b\u4e00\u4e2a\u8282\u70b9\nTreeNode *tmp = cur-&gt;right;\nwhile (tmp-&gt;left != NULL) {\ntmp = tmp-&gt;left;\n}\nint tmpVal = tmp-&gt;val;\n// \u9012\u5f52\u5220\u9664\u8282\u70b9 tmp\nremoveNode(bst, tmp-&gt;val);\n// \u7528 tmp \u8986\u76d6 cur\ncur-&gt;val = tmpVal;\n}\n}\n</code></pre> binary_search_tree.cs<pre><code>/* \u5220\u9664\u8282\u70b9 */\nvoid remove(int num) {\n// \u82e5\u6811\u4e3a\u7a7a\uff0c\u76f4\u63a5\u63d0\u524d\u8fd4\u56de\nif (root == null)\nreturn;\nTreeNode? cur = root, pre = null;\n// \u5faa\u73af\u67e5\u627e\uff0c\u8d8a\u8fc7\u53f6\u8282\u70b9\u540e\u8df3\u51fa\nwhile (cur != null) {\n// \u627e\u5230\u5f85\u5220\u9664\u8282\u70b9\uff0c\u8df3\u51fa\u5faa\u73af\nif (cur.val == num)\nbreak;\npre = cur;\n// \u5f85\u5220\u9664\u8282\u70b9\u5728 cur \u7684\u53f3\u5b50\u6811\u4e2d\nif (cur.val &lt; num)\ncur = cur.right;\n// \u5f85\u5220\u9664\u8282\u70b9\u5728 cur \u7684\u5de6\u5b50\u6811\u4e2d\nelse\ncur = cur.left;\n}\n// \u82e5\u65e0\u5f85\u5220\u9664\u8282\u70b9\uff0c\u5219\u76f4\u63a5\u8fd4\u56de\nif (cur == null || pre == null)\nreturn;\n// \u5b50\u8282\u70b9\u6570\u91cf = 0 or 1\nif (cur.left == null || cur.right == null) {\n// \u5f53\u5b50\u8282\u70b9\u6570\u91cf = 0 / 1 \u65f6\uff0c child = null / \u8be5\u5b50\u8282\u70b9\nTreeNode? child = cur.left != null ? cur.left : cur.right;\n// \u5220\u9664\u8282\u70b9 cur\nif (cur != root) {\nif (pre.left == cur)\npre.left = child;\nelse\npre.right = child;\n} else {\n// \u82e5\u5220\u9664\u8282\u70b9\u4e3a\u6839\u8282\u70b9\uff0c\u5219\u91cd\u65b0\u6307\u5b9a\u6839\u8282\u70b9\nroot = child;\n}\n}\n// \u5b50\u8282\u70b9\u6570\u91cf = 2\nelse {\n// \u83b7\u53d6\u4e2d\u5e8f\u904d\u5386\u4e2d cur \u7684\u4e0b\u4e00\u4e2a\u8282\u70b9\nTreeNode? tmp = cur.right;\nwhile (tmp.left != null) {\ntmp = tmp.left;\n}\n// \u9012\u5f52\u5220\u9664\u8282\u70b9 tmp\nremove(tmp.val);\n// \u7528 tmp \u8986\u76d6 cur\ncur.val = tmp.val;\n}\n}\n</code></pre> binary_search_tree.swift<pre><code>/* \u5220\u9664\u8282\u70b9 */\n@discardableResult\nfunc remove(num: Int) {\n// \u82e5\u6811\u4e3a\u7a7a\uff0c\u76f4\u63a5\u63d0\u524d\u8fd4\u56de\nif root == nil {\nreturn\n}\nvar cur = root\nvar pre: TreeNode?\n// \u5faa\u73af\u67e5\u627e\uff0c\u8d8a\u8fc7\u53f6\u8282\u70b9\u540e\u8df3\u51fa\nwhile cur != nil {\n// \u627e\u5230\u5f85\u5220\u9664\u8282\u70b9\uff0c\u8df3\u51fa\u5faa\u73af\nif cur!.val == num {\nbreak\n}\npre = cur\n// \u5f85\u5220\u9664\u8282\u70b9\u5728 cur \u7684\u53f3\u5b50\u6811\u4e2d\nif cur!.val &lt; num {\ncur = cur?.right\n}\n// \u5f85\u5220\u9664\u8282\u70b9\u5728 cur \u7684\u5de6\u5b50\u6811\u4e2d\nelse {\ncur = cur?.left\n}\n}\n// \u82e5\u65e0\u5f85\u5220\u9664\u8282\u70b9\uff0c\u5219\u76f4\u63a5\u8fd4\u56de\nif cur == nil {\nreturn\n}\n// \u5b50\u8282\u70b9\u6570\u91cf = 0 or 1\nif cur?.left == nil || cur?.right == nil {\n// \u5f53\u5b50\u8282\u70b9\u6570\u91cf = 0 / 1 \u65f6\uff0c child = null / \u8be5\u5b50\u8282\u70b9\nlet child = cur?.left != nil ? cur?.left : cur?.right\n// \u5220\u9664\u8282\u70b9 cur\nif cur != root {\nif pre?.left === cur {\npre?.left = child\n} else {\npre?.right = child\n}\n} else {\n// \u82e5\u5220\u9664\u8282\u70b9\u4e3a\u6839\u8282\u70b9\uff0c\u5219\u91cd\u65b0\u6307\u5b9a\u6839\u8282\u70b9\nroot = cur;\n}\n}\n// \u5b50\u8282\u70b9\u6570\u91cf = 2\nelse {\n// \u83b7\u53d6\u4e2d\u5e8f\u904d\u5386\u4e2d cur \u7684\u4e0b\u4e00\u4e2a\u8282\u70b9\nvar tmp = cur?.right\nwhile tmp?.left != nil {\ntmp = tmp?.left\n}\n// \u9012\u5f52\u5220\u9664\u8282\u70b9 tmp\nremove(num: tmp!.val)\n// \u7528 tmp \u8986\u76d6 cur\ncur?.val = tmp!.val\n}\n}\n</code></pre> binary_search_tree.zig<pre><code>// \u5220\u9664\u8282\u70b9\nfn remove(self: *Self, num: T) !void {\n// \u82e5\u6811\u4e3a\u7a7a\uff0c\u76f4\u63a5\u63d0\u524d\u8fd4\u56de\nif (self.root == null) return;\nvar cur = self.root;\nvar pre: ?*inc.TreeNode(T) = null;\n// \u5faa\u73af\u67e5\u627e\uff0c\u8d8a\u8fc7\u53f6\u8282\u70b9\u540e\u8df3\u51fa\nwhile (cur != null) {\n// \u627e\u5230\u5f85\u5220\u9664\u8282\u70b9\uff0c\u8df3\u51fa\u5faa\u73af\nif (cur.?.val == num) break;\npre = cur;\n// \u5f85\u5220\u9664\u8282\u70b9\u5728 cur \u7684\u53f3\u5b50\u6811\u4e2d\nif (cur.?.val &lt; num) {\ncur = cur.?.right;\n// \u5f85\u5220\u9664\u8282\u70b9\u5728 cur \u7684\u5de6\u5b50\u6811\u4e2d\n} else {\ncur = cur.?.left;\n}\n}\n// \u82e5\u65e0\u5f85\u5220\u9664\u8282\u70b9\uff0c\u5219\u76f4\u63a5\u8fd4\u56de\nif (cur == null) return;\n// \u5b50\u8282\u70b9\u6570\u91cf = 0 or 1\nif (cur.?.left == null or cur.?.right == null) {\n// \u5f53\u5b50\u8282\u70b9\u6570\u91cf = 0 / 1 \u65f6\uff0c child = null / \u8be5\u5b50\u8282\u70b9\nvar child = if (cur.?.left != null) cur.?.left else cur.?.right;\n// \u5220\u9664\u8282\u70b9 cur\nif (pre.?.left == cur) {\npre.?.left = child;\n} else {\npre.?.right = child;\n}\n// \u5b50\u8282\u70b9\u6570\u91cf = 2\n} else {\n// \u83b7\u53d6\u4e2d\u5e8f\u904d\u5386\u4e2d cur \u7684\u4e0b\u4e00\u4e2a\u8282\u70b9\nvar tmp = cur.?.right;\nwhile (tmp.?.left != null) {\ntmp = tmp.?.left;\n}\nvar tmpVal = tmp.?.val;\n// \u9012\u5f52\u5220\u9664\u8282\u70b9 tmp\n_ = self.remove(tmp.?.val);\n// \u7528 tmp \u8986\u76d6 cur\ncur.?.val = tmpVal;\n}\n}\n</code></pre> binary_search_tree.dart<pre><code>[class]{BinarySearchTree}-[func]{remove}\n</code></pre>"},{"location":"chapter_tree/binary_search_tree/#_4","title":"\u6392\u5e8f","text":"<p>\u6211\u4eec\u77e5\u9053\uff0c\u4e8c\u53c9\u6811\u7684\u4e2d\u5e8f\u904d\u5386\u9075\u5faa\u201c\u5de6 \\(\\rightarrow\\) \u6839 \\(\\rightarrow\\) \u53f3\u201d\u7684\u904d\u5386\u987a\u5e8f\uff0c\u800c\u4e8c\u53c9\u641c\u7d22\u6811\u6ee1\u8db3\u201c\u5de6\u5b50\u8282\u70b9 \\(&lt;\\) \u6839\u8282\u70b9 \\(&lt;\\) \u53f3\u5b50\u8282\u70b9\u201d\u7684\u5927\u5c0f\u5173\u7cfb\u3002\u56e0\u6b64\uff0c\u5728\u4e8c\u53c9\u641c\u7d22\u6811\u4e2d\u8fdb\u884c\u4e2d\u5e8f\u904d\u5386\u65f6\uff0c\u603b\u662f\u4f1a\u4f18\u5148\u904d\u5386\u4e0b\u4e00\u4e2a\u6700\u5c0f\u8282\u70b9\uff0c\u4ece\u800c\u5f97\u51fa\u4e00\u4e2a\u91cd\u8981\u6027\u8d28\uff1a\u4e8c\u53c9\u641c\u7d22\u6811\u7684\u4e2d\u5e8f\u904d\u5386\u5e8f\u5217\u662f\u5347\u5e8f\u7684\u3002</p> <p>\u5229\u7528\u4e2d\u5e8f\u904d\u5386\u5347\u5e8f\u7684\u6027\u8d28\uff0c\u6211\u4eec\u5728\u4e8c\u53c9\u641c\u7d22\u6811\u4e2d\u83b7\u53d6\u6709\u5e8f\u6570\u636e\u4ec5\u9700 \\(O(n)\\) \u65f6\u95f4\uff0c\u65e0\u9700\u989d\u5916\u6392\u5e8f\uff0c\u975e\u5e38\u9ad8\u6548\u3002</p> <p></p> <p> Fig. \u4e8c\u53c9\u641c\u7d22\u6811\u7684\u4e2d\u5e8f\u904d\u5386\u5e8f\u5217 </p>"},{"location":"chapter_tree/binary_search_tree/#742","title":"7.4.2. \u00a0 \u4e8c\u53c9\u641c\u7d22\u6811\u7684\u6548\u7387","text":"<p>\u7ed9\u5b9a\u4e00\u7ec4\u6570\u636e\uff0c\u6211\u4eec\u8003\u8651\u4f7f\u7528\u6570\u7ec4\u6216\u4e8c\u53c9\u641c\u7d22\u6811\u5b58\u50a8\u3002</p> <p>\u89c2\u5bdf\u53ef\u77e5\uff0c\u4e8c\u53c9\u641c\u7d22\u6811\u7684\u5404\u9879\u64cd\u4f5c\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u90fd\u662f\u5bf9\u6570\u9636\uff0c\u5177\u6709\u7a33\u5b9a\u4e14\u9ad8\u6548\u7684\u6027\u80fd\u8868\u73b0\u3002\u53ea\u6709\u5728\u9ad8\u9891\u6dfb\u52a0\u3001\u4f4e\u9891\u67e5\u627e\u5220\u9664\u7684\u6570\u636e\u9002\u7528\u573a\u666f\u4e0b\uff0c\u6570\u7ec4\u6bd4\u4e8c\u53c9\u641c\u7d22\u6811\u7684\u6548\u7387\u66f4\u9ad8\u3002</p> \u65e0\u5e8f\u6570\u7ec4 \u4e8c\u53c9\u641c\u7d22\u6811 \u67e5\u627e\u5143\u7d20 \\(O(n)\\) \\(O(\\log n)\\) \u63d2\u5165\u5143\u7d20 \\(O(1)\\) \\(O(\\log n)\\) \u5220\u9664\u5143\u7d20 \\(O(n)\\) \\(O(\\log n)\\) <p>\u5728\u7406\u60f3\u60c5\u51b5\u4e0b\uff0c\u4e8c\u53c9\u641c\u7d22\u6811\u662f\u201c\u5e73\u8861\u201d\u7684\uff0c\u8fd9\u6837\u5c31\u53ef\u4ee5\u5728 \\(\\log n\\) \u8f6e\u5faa\u73af\u5185\u67e5\u627e\u4efb\u610f\u8282\u70b9\u3002</p> <p>\u7136\u800c\uff0c\u5982\u679c\u6211\u4eec\u5728\u4e8c\u53c9\u641c\u7d22\u6811\u4e2d\u4e0d\u65ad\u5730\u63d2\u5165\u548c\u5220\u9664\u8282\u70b9\uff0c\u53ef\u80fd\u5bfc\u81f4\u4e8c\u53c9\u6811\u9000\u5316\u4e3a\u94fe\u8868\uff0c\u8fd9\u65f6\u5404\u79cd\u64cd\u4f5c\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e5f\u4f1a\u9000\u5316\u4e3a \\(O(n)\\) \u3002</p> <p></p> <p> Fig. \u4e8c\u53c9\u641c\u7d22\u6811\u7684\u5e73\u8861\u4e0e\u9000\u5316 </p>"},{"location":"chapter_tree/binary_search_tree/#743","title":"7.4.3. \u00a0 \u4e8c\u53c9\u641c\u7d22\u6811\u5e38\u89c1\u5e94\u7528","text":"<ul> <li>\u7528\u4f5c\u7cfb\u7edf\u4e2d\u7684\u591a\u7ea7\u7d22\u5f15\uff0c\u5b9e\u73b0\u9ad8\u6548\u7684\u67e5\u627e\u3001\u63d2\u5165\u3001\u5220\u9664\u64cd\u4f5c\u3002</li> <li>\u4f5c\u4e3a\u67d0\u4e9b\u641c\u7d22\u7b97\u6cd5\u7684\u5e95\u5c42\u6570\u636e\u7ed3\u6784\u3002</li> <li>\u7528\u4e8e\u5b58\u50a8\u6570\u636e\u6d41\uff0c\u4ee5\u4fdd\u6301\u5176\u6709\u5e8f\u72b6\u6001\u3002</li> </ul>"},{"location":"chapter_tree/binary_tree/","title":"7.1. \u00a0 \u4e8c\u53c9\u6811","text":"<p>\u300c\u4e8c\u53c9\u6811 Binary Tree\u300d\u662f\u4e00\u79cd\u975e\u7ebf\u6027\u6570\u636e\u7ed3\u6784\uff0c\u4ee3\u8868\u7740\u7956\u5148\u4e0e\u540e\u4ee3\u4e4b\u95f4\u7684\u6d3e\u751f\u5173\u7cfb\uff0c\u4f53\u73b0\u7740\u201c\u4e00\u5206\u4e3a\u4e8c\u201d\u7684\u5206\u6cbb\u903b\u8f91\u3002\u4e0e\u94fe\u8868\u7c7b\u4f3c\uff0c\u4e8c\u53c9\u6811\u7684\u57fa\u672c\u5355\u5143\u662f\u8282\u70b9\uff0c\u6bcf\u4e2a\u8282\u70b9\u5305\u542b\u4e00\u4e2a\u300c\u503c\u300d\u548c\u4e24\u4e2a\u300c\u6307\u9488\u300d\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart <pre><code>/* \u4e8c\u53c9\u6811\u8282\u70b9\u7c7b */\nclass TreeNode {\nint val;         // \u8282\u70b9\u503c\nTreeNode left;   // \u5de6\u5b50\u8282\u70b9\u6307\u9488\nTreeNode right;  // \u53f3\u5b50\u8282\u70b9\u6307\u9488\nTreeNode(int x) { val = x; }\n}\n</code></pre> <pre><code>/* \u4e8c\u53c9\u6811\u8282\u70b9\u7ed3\u6784\u4f53 */\nstruct TreeNode {\nint val;          // \u8282\u70b9\u503c\nTreeNode *left;   // \u5de6\u5b50\u8282\u70b9\u6307\u9488\nTreeNode *right;  // \u53f3\u5b50\u8282\u70b9\u6307\u9488\nTreeNode(int x) : val(x), left(nullptr), right(nullptr) {}\n};\n</code></pre> <pre><code>class TreeNode:\n\"\"\"\u4e8c\u53c9\u6811\u8282\u70b9\u7c7b\"\"\"\ndef __init__(self, val: int):\nself.val: int = val                   # \u8282\u70b9\u503c\nself.left: Optional[TreeNode] = None  # \u5de6\u5b50\u8282\u70b9\u6307\u9488\nself.right: Optional[TreeNode] = None # \u53f3\u5b50\u8282\u70b9\u6307\u9488\n</code></pre> <pre><code>/* \u4e8c\u53c9\u6811\u8282\u70b9\u7ed3\u6784\u4f53 */\ntype TreeNode struct {\nVal   int\nLeft  *TreeNode\nRight *TreeNode\n}\n/* \u8282\u70b9\u521d\u59cb\u5316\u65b9\u6cd5 */\nfunc NewTreeNode(v int) *TreeNode {\nreturn &amp;TreeNode{\nLeft:  nil,\nRight: nil,\nVal:   v,\n}\n}\n</code></pre> <pre><code>/* \u4e8c\u53c9\u6811\u8282\u70b9\u7c7b */\nfunction TreeNode(val, left, right) {\nthis.val = (val === undefined ? 0 : val); // \u8282\u70b9\u503c\nthis.left = (left === undefined ? null : left); // \u5de6\u5b50\u8282\u70b9\u6307\u9488\nthis.right = (right === undefined ? null : right); // \u53f3\u5b50\u8282\u70b9\u6307\u9488\n}\n</code></pre> <pre><code>/* \u4e8c\u53c9\u6811\u8282\u70b9\u7c7b */\nclass TreeNode {\nval: number;\nleft: TreeNode | null;\nright: TreeNode | null;\nconstructor(val?: number, left?: TreeNode | null, right?: TreeNode | null) {\nthis.val = val === undefined ? 0 : val; // \u8282\u70b9\u503c\nthis.left = left === undefined ? null : left; // \u5de6\u5b50\u8282\u70b9\u6307\u9488\nthis.right = right === undefined ? null : right; // \u53f3\u5b50\u8282\u70b9\u6307\u9488\n}\n}\n</code></pre> <pre><code>/* \u4e8c\u53c9\u6811\u8282\u70b9\u7ed3\u6784\u4f53 */\nstruct TreeNode {\nint val;                // \u8282\u70b9\u503c\nint height;             // \u8282\u70b9\u9ad8\u5ea6\nstruct TreeNode *left;  // \u5de6\u5b50\u8282\u70b9\u6307\u9488\nstruct TreeNode *right; // \u53f3\u5b50\u8282\u70b9\u6307\u9488\n};\ntypedef struct TreeNode TreeNode;\n/* \u6784\u9020\u51fd\u6570 */\nTreeNode *newTreeNode(int val) {\nTreeNode *node;\nnode = (TreeNode *)malloc(sizeof(TreeNode));\nnode-&gt;val = val;\nnode-&gt;height = 0;\nnode-&gt;left = NULL;\nnode-&gt;right = NULL;\nreturn node;\n}\n</code></pre> <pre><code>/* \u4e8c\u53c9\u6811\u8282\u70b9\u7c7b */\nclass TreeNode {\nint val;          // \u8282\u70b9\u503c\nTreeNode? left;   // \u5de6\u5b50\u8282\u70b9\u6307\u9488\nTreeNode? right;  // \u53f3\u5b50\u8282\u70b9\u6307\u9488\nTreeNode(int x) { val = x; }\n}\n</code></pre> <pre><code>/* \u4e8c\u53c9\u6811\u8282\u70b9\u7c7b */\nclass TreeNode {\nvar val: Int // \u8282\u70b9\u503c\nvar left: TreeNode? // \u5de6\u5b50\u8282\u70b9\u6307\u9488\nvar right: TreeNode? // \u53f3\u5b50\u8282\u70b9\u6307\u9488\ninit(x: Int) {\nval = x\n}\n}\n</code></pre> <pre><code>\n</code></pre> <pre><code>/* \u4e8c\u53c9\u6811\u8282\u70b9\u7c7b */\nclass TreeNode {\nint val;         // \u8282\u70b9\u503c\nTreeNode? left;  // \u5de6\u5b50\u8282\u70b9\u6307\u9488\nTreeNode? right; // \u53f3\u5b50\u8282\u70b9\u6307\u9488\nTreeNode(this.val, [this.left, this.right]);\n}\n</code></pre> <p>\u8282\u70b9\u7684\u4e24\u4e2a\u6307\u9488\u5206\u522b\u6307\u5411\u300c\u5de6\u5b50\u8282\u70b9\u300d\u548c\u300c\u53f3\u5b50\u8282\u70b9\u300d\uff0c\u540c\u65f6\u8be5\u8282\u70b9\u88ab\u79f0\u4e3a\u8fd9\u4e24\u4e2a\u5b50\u8282\u70b9\u7684\u300c\u7236\u8282\u70b9\u300d\u3002\u5f53\u7ed9\u5b9a\u4e00\u4e2a\u4e8c\u53c9\u6811\u7684\u8282\u70b9\u65f6\uff0c\u6211\u4eec\u5c06\u8be5\u8282\u70b9\u7684\u5de6\u5b50\u8282\u70b9\u53ca\u5176\u4ee5\u4e0b\u8282\u70b9\u5f62\u6210\u7684\u6811\u79f0\u4e3a\u8be5\u8282\u70b9\u7684\u300c\u5de6\u5b50\u6811\u300d\uff0c\u540c\u7406\u53ef\u5f97\u300c\u53f3\u5b50\u6811\u300d\u3002</p> <p>\u5728\u4e8c\u53c9\u6811\u4e2d\uff0c\u9664\u53f6\u8282\u70b9\u5916\uff0c\u5176\u4ed6\u6240\u6709\u8282\u70b9\u90fd\u5305\u542b\u5b50\u8282\u70b9\u548c\u975e\u7a7a\u5b50\u6811\u3002\u4f8b\u5982\uff0c\u5728\u4ee5\u4e0b\u793a\u4f8b\u4e2d\uff0c\u82e5\u5c06\u201c\u8282\u70b9 2\u201d\u89c6\u4e3a\u7236\u8282\u70b9\uff0c\u5219\u5176\u5de6\u5b50\u8282\u70b9\u548c\u53f3\u5b50\u8282\u70b9\u5206\u522b\u662f\u201c\u8282\u70b9 4\u201d\u548c\u201c\u8282\u70b9 5\u201d\uff0c\u5de6\u5b50\u6811\u662f\u201c\u8282\u70b9 4 \u53ca\u5176\u4ee5\u4e0b\u8282\u70b9\u5f62\u6210\u7684\u6811\u201d\uff0c\u53f3\u5b50\u6811\u662f\u201c\u8282\u70b9 5 \u53ca\u5176\u4ee5\u4e0b\u8282\u70b9\u5f62\u6210\u7684\u6811\u201d\u3002</p> <p></p> <p> Fig. \u7236\u8282\u70b9\u3001\u5b50\u8282\u70b9\u3001\u5b50\u6811 </p>"},{"location":"chapter_tree/binary_tree/#711","title":"7.1.1. \u00a0 \u4e8c\u53c9\u6811\u5e38\u89c1\u672f\u8bed","text":"<p>\u4e8c\u53c9\u6811\u6d89\u53ca\u7684\u672f\u8bed\u8f83\u591a\uff0c\u5efa\u8bae\u5c3d\u91cf\u7406\u89e3\u5e76\u8bb0\u4f4f\u3002</p> <ul> <li>\u300c\u6839\u8282\u70b9 Root Node\u300d\uff1a\u4f4d\u4e8e\u4e8c\u53c9\u6811\u9876\u5c42\u7684\u8282\u70b9\uff0c\u6ca1\u6709\u7236\u8282\u70b9\uff1b</li> <li>\u300c\u53f6\u8282\u70b9 Leaf Node\u300d\uff1a\u6ca1\u6709\u5b50\u8282\u70b9\u7684\u8282\u70b9\uff0c\u5176\u4e24\u4e2a\u6307\u9488\u5747\u6307\u5411 \\(\\text{null}\\) \uff1b</li> <li>\u8282\u70b9\u7684\u300c\u5c42 Level\u300d\uff1a\u4ece\u9876\u81f3\u5e95\u9012\u589e\uff0c\u6839\u8282\u70b9\u6240\u5728\u5c42\u4e3a 1 \uff1b</li> <li>\u8282\u70b9\u7684\u300c\u5ea6 Degree\u300d\uff1a\u8282\u70b9\u7684\u5b50\u8282\u70b9\u7684\u6570\u91cf\u3002\u5728\u4e8c\u53c9\u6811\u4e2d\uff0c\u5ea6\u7684\u8303\u56f4\u662f 0, 1, 2 \uff1b</li> <li>\u300c\u8fb9 Edge\u300d\uff1a\u8fde\u63a5\u4e24\u4e2a\u8282\u70b9\u7684\u7ebf\u6bb5\uff0c\u5373\u8282\u70b9\u6307\u9488\uff1b</li> <li>\u4e8c\u53c9\u6811\u7684\u300c\u9ad8\u5ea6\u300d\uff1a\u4ece\u6839\u8282\u70b9\u5230\u6700\u8fdc\u53f6\u8282\u70b9\u6240\u7ecf\u8fc7\u7684\u8fb9\u7684\u6570\u91cf\uff1b</li> <li>\u8282\u70b9\u7684\u300c\u6df1\u5ea6 Depth\u300d \uff1a\u4ece\u6839\u8282\u70b9\u5230\u8be5\u8282\u70b9\u6240\u7ecf\u8fc7\u7684\u8fb9\u7684\u6570\u91cf\uff1b</li> <li>\u8282\u70b9\u7684\u300c\u9ad8\u5ea6 Height\u300d\uff1a\u4ece\u6700\u8fdc\u53f6\u8282\u70b9\u5230\u8be5\u8282\u70b9\u6240\u7ecf\u8fc7\u7684\u8fb9\u7684\u6570\u91cf\uff1b</li> </ul> <p></p> <p> Fig. \u4e8c\u53c9\u6811\u7684\u5e38\u7528\u672f\u8bed </p> <p>\u9ad8\u5ea6\u4e0e\u6df1\u5ea6\u7684\u5b9a\u4e49</p> <p>\u8bf7\u6ce8\u610f\uff0c\u6211\u4eec\u901a\u5e38\u5c06\u300c\u9ad8\u5ea6\u300d\u548c\u300c\u6df1\u5ea6\u300d\u5b9a\u4e49\u4e3a\u201c\u8d70\u8fc7\u8fb9\u7684\u6570\u91cf\u201d\uff0c\u4f46\u6709\u4e9b\u9898\u76ee\u6216\u6559\u6750\u53ef\u80fd\u4f1a\u5c06\u5176\u5b9a\u4e49\u4e3a\u201c\u8d70\u8fc7\u8282\u70b9\u7684\u6570\u91cf\u201d\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u9ad8\u5ea6\u548c\u6df1\u5ea6\u90fd\u9700\u8981\u52a0 1 \u3002</p>"},{"location":"chapter_tree/binary_tree/#712","title":"7.1.2. \u00a0 \u4e8c\u53c9\u6811\u57fa\u672c\u64cd\u4f5c","text":"<p>\u521d\u59cb\u5316\u4e8c\u53c9\u6811\u3002\u4e0e\u94fe\u8868\u7c7b\u4f3c\uff0c\u9996\u5148\u521d\u59cb\u5316\u8282\u70b9\uff0c\u7136\u540e\u6784\u5efa\u5f15\u7528\u6307\u5411\uff08\u5373\u6307\u9488\uff09\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart binary_tree.java<pre><code>// \u521d\u59cb\u5316\u8282\u70b9\nTreeNode n1 = new TreeNode(1);\nTreeNode n2 = new TreeNode(2);\nTreeNode n3 = new TreeNode(3);\nTreeNode n4 = new TreeNode(4);\nTreeNode n5 = new TreeNode(5);\n// \u6784\u5efa\u5f15\u7528\u6307\u5411\uff08\u5373\u6307\u9488\uff09\nn1.left = n2;\nn1.right = n3;\nn2.left = n4;\nn2.right = n5;\n</code></pre> binary_tree.cpp<pre><code>/* \u521d\u59cb\u5316\u4e8c\u53c9\u6811 */\n// \u521d\u59cb\u5316\u8282\u70b9\nTreeNode* n1 = new TreeNode(1);\nTreeNode* n2 = new TreeNode(2);\nTreeNode* n3 = new TreeNode(3);\nTreeNode* n4 = new TreeNode(4);\nTreeNode* n5 = new TreeNode(5);\n// \u6784\u5efa\u5f15\u7528\u6307\u5411\uff08\u5373\u6307\u9488\uff09\nn1-&gt;left = n2;\nn1-&gt;right = n3;\nn2-&gt;left = n4;\nn2-&gt;right = n5;\n</code></pre> binary_tree.py<pre><code># \u521d\u59cb\u5316\u4e8c\u53c9\u6811\n# \u521d\u59cb\u5316\u8282\u70b9\nn1 = TreeNode(val=1)\nn2 = TreeNode(val=2)\nn3 = TreeNode(val=3)\nn4 = TreeNode(val=4)\nn5 = TreeNode(val=5)\n# \u6784\u5efa\u5f15\u7528\u6307\u5411\uff08\u5373\u6307\u9488\uff09\nn1.left = n2\nn1.right = n3\nn2.left = n4\nn2.right = n5\n</code></pre> binary_tree.go<pre><code>/* \u521d\u59cb\u5316\u4e8c\u53c9\u6811 */\n// \u521d\u59cb\u5316\u8282\u70b9\nn1 := NewTreeNode(1)\nn2 := NewTreeNode(2)\nn3 := NewTreeNode(3)\nn4 := NewTreeNode(4)\nn5 := NewTreeNode(5)\n// \u6784\u5efa\u5f15\u7528\u6307\u5411\uff08\u5373\u6307\u9488\uff09\nn1.Left = n2\nn1.Right = n3\nn2.Left = n4\nn2.Right = n5\n</code></pre> binary_tree.js<pre><code>/* \u521d\u59cb\u5316\u4e8c\u53c9\u6811 */\n// \u521d\u59cb\u5316\u8282\u70b9\nlet n1 = new TreeNode(1),\nn2 = new TreeNode(2),\nn3 = new TreeNode(3),\nn4 = new TreeNode(4),\nn5 = new TreeNode(5);\n// \u6784\u5efa\u5f15\u7528\u6307\u5411\uff08\u5373\u6307\u9488\uff09\nn1.left = n2;\nn1.right = n3;\nn2.left = n4;\nn2.right = n5;\n</code></pre> binary_tree.ts<pre><code>/* \u521d\u59cb\u5316\u4e8c\u53c9\u6811 */\n// \u521d\u59cb\u5316\u8282\u70b9\nlet n1 = new TreeNode(1),\nn2 = new TreeNode(2),\nn3 = new TreeNode(3),\nn4 = new TreeNode(4),\nn5 = new TreeNode(5);\n// \u6784\u5efa\u5f15\u7528\u6307\u5411\uff08\u5373\u6307\u9488\uff09\nn1.left = n2;\nn1.right = n3;\nn2.left = n4;\nn2.right = n5;\n</code></pre> binary_tree.c<pre><code>/* \u521d\u59cb\u5316\u4e8c\u53c9\u6811 */\n// \u521d\u59cb\u5316\u8282\u70b9\nTreeNode *n1 = newTreeNode(1);\nTreeNode *n2 = newTreeNode(2);\nTreeNode *n3 = newTreeNode(3);\nTreeNode *n4 = newTreeNode(4);\nTreeNode *n5 = newTreeNode(5);\n// \u6784\u5efa\u5f15\u7528\u6307\u5411\uff08\u5373\u6307\u9488\uff09\nn1-&gt;left = n2;\nn1-&gt;right = n3;\nn2-&gt;left = n4;\nn2-&gt;right = n5;\n</code></pre> binary_tree.cs<pre><code>/* \u521d\u59cb\u5316\u4e8c\u53c9\u6811 */\n// \u521d\u59cb\u5316\u8282\u70b9\nTreeNode n1 = new TreeNode(1);\nTreeNode n2 = new TreeNode(2);\nTreeNode n3 = new TreeNode(3);\nTreeNode n4 = new TreeNode(4);\nTreeNode n5 = new TreeNode(5);\n// \u6784\u5efa\u5f15\u7528\u6307\u5411\uff08\u5373\u6307\u9488\uff09\nn1.left = n2;\nn1.right = n3;\nn2.left = n4;\nn2.right = n5;\n</code></pre> binary_tree.swift<pre><code>// \u521d\u59cb\u5316\u8282\u70b9\nlet n1 = TreeNode(x: 1)\nlet n2 = TreeNode(x: 2)\nlet n3 = TreeNode(x: 3)\nlet n4 = TreeNode(x: 4)\nlet n5 = TreeNode(x: 5)\n// \u6784\u5efa\u5f15\u7528\u6307\u5411\uff08\u5373\u6307\u9488\uff09\nn1.left = n2\nn1.right = n3\nn2.left = n4\nn2.right = n5\n</code></pre> binary_tree.zig<pre><code>\n</code></pre> binary_tree.dart<pre><code>/* \u521d\u59cb\u5316\u4e8c\u53c9\u6811 */\n// \u521d\u59cb\u5316\u8282\u70b9\nTreeNode n1 = new TreeNode(1);\nTreeNode n2 = new TreeNode(2);\nTreeNode n3 = new TreeNode(3);\nTreeNode n4 = new TreeNode(4);\nTreeNode n5 = new TreeNode(5);\n// \u6784\u5efa\u5f15\u7528\u6307\u5411\uff08\u5373\u6307\u9488\uff09\nn1.left = n2;\nn1.right = n3;\nn2.left = n4;\nn2.right = n5;\n</code></pre> <p>\u63d2\u5165\u4e0e\u5220\u9664\u8282\u70b9\u3002\u4e0e\u94fe\u8868\u7c7b\u4f3c\uff0c\u901a\u8fc7\u4fee\u6539\u6307\u9488\u6765\u5b9e\u73b0\u63d2\u5165\u4e0e\u5220\u9664\u8282\u70b9\u3002</p> <p></p> <p> Fig. \u5728\u4e8c\u53c9\u6811\u4e2d\u63d2\u5165\u4e0e\u5220\u9664\u8282\u70b9 </p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart binary_tree.java<pre><code>TreeNode P = new TreeNode(0);\n// \u5728 n1 -&gt; n2 \u4e2d\u95f4\u63d2\u5165\u8282\u70b9 P\nn1.left = P;\nP.left = n2;\n// \u5220\u9664\u8282\u70b9 P\nn1.left = n2;\n</code></pre> binary_tree.cpp<pre><code>/* \u63d2\u5165\u4e0e\u5220\u9664\u8282\u70b9 */\nTreeNode* P = new TreeNode(0);\n// \u5728 n1 -&gt; n2 \u4e2d\u95f4\u63d2\u5165\u8282\u70b9 P\nn1-&gt;left = P;\nP-&gt;left = n2;\n// \u5220\u9664\u8282\u70b9 P\nn1-&gt;left = n2;\n</code></pre> binary_tree.py<pre><code># \u63d2\u5165\u4e0e\u5220\u9664\u8282\u70b9\np = TreeNode(0)\n# \u5728 n1 -&gt; n2 \u4e2d\u95f4\u63d2\u5165\u8282\u70b9 P\nn1.left = p\np.left = n2\n# \u5220\u9664\u8282\u70b9 P\nn1.left = n2\n</code></pre> binary_tree.go<pre><code>/* \u63d2\u5165\u4e0e\u5220\u9664\u8282\u70b9 */\n// \u5728 n1 -&gt; n2 \u4e2d\u95f4\u63d2\u5165\u8282\u70b9 P\np := NewTreeNode(0)\nn1.Left = p\np.Left = n2\n// \u5220\u9664\u8282\u70b9 P\nn1.Left = n2\n</code></pre> binary_tree.js<pre><code>/* \u63d2\u5165\u4e0e\u5220\u9664\u8282\u70b9 */\nlet P = new TreeNode(0);\n// \u5728 n1 -&gt; n2 \u4e2d\u95f4\u63d2\u5165\u8282\u70b9 P\nn1.left = P;\nP.left = n2;\n// \u5220\u9664\u8282\u70b9 P\nn1.left = n2;\n</code></pre> binary_tree.ts<pre><code>/* \u63d2\u5165\u4e0e\u5220\u9664\u8282\u70b9 */\nconst P = new TreeNode(0);\n// \u5728 n1 -&gt; n2 \u4e2d\u95f4\u63d2\u5165\u8282\u70b9 P\nn1.left = P;\nP.left = n2;\n// \u5220\u9664\u8282\u70b9 P\nn1.left = n2;\n</code></pre> binary_tree.c<pre><code>/* \u63d2\u5165\u4e0e\u5220\u9664\u8282\u70b9 */\nTreeNode *P = newTreeNode(0);\n// \u5728 n1 -&gt; n2 \u4e2d\u95f4\u63d2\u5165\u8282\u70b9 P\nn1-&gt;left = P;\nP-&gt;left = n2;\n// \u5220\u9664\u8282\u70b9 P\nn1-&gt;left = n2;\n</code></pre> binary_tree.cs<pre><code>/* \u63d2\u5165\u4e0e\u5220\u9664\u8282\u70b9 */\nTreeNode P = new TreeNode(0);\n// \u5728 n1 -&gt; n2 \u4e2d\u95f4\u63d2\u5165\u8282\u70b9 P\nn1.left = P;\nP.left = n2;\n// \u5220\u9664\u8282\u70b9 P\nn1.left = n2;\n</code></pre> binary_tree.swift<pre><code>let P = TreeNode(x: 0)\n// \u5728 n1 -&gt; n2 \u4e2d\u95f4\u63d2\u5165\u8282\u70b9 P\nn1.left = P\nP.left = n2\n// \u5220\u9664\u8282\u70b9 P\nn1.left = n2\n</code></pre> binary_tree.zig<pre><code>\n</code></pre> binary_tree.dart<pre><code>/* \u63d2\u5165\u4e0e\u5220\u9664\u8282\u70b9 */\nTreeNode P = new TreeNode(0);\n// \u5728 n1 -&gt; n2 \u4e2d\u95f4\u63d2\u5165\u8282\u70b9 P\nn1.left = P;\nP.left = n2;\n// \u5220\u9664\u8282\u70b9 P\nn1.left = n2;\n</code></pre> <p>Note</p> <p>\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u63d2\u5165\u8282\u70b9\u53ef\u80fd\u4f1a\u6539\u53d8\u4e8c\u53c9\u6811\u7684\u539f\u6709\u903b\u8f91\u7ed3\u6784\uff0c\u800c\u5220\u9664\u8282\u70b9\u901a\u5e38\u610f\u5473\u7740\u5220\u9664\u8be5\u8282\u70b9\u53ca\u5176\u6240\u6709\u5b50\u6811\u3002\u56e0\u6b64\uff0c\u5728\u4e8c\u53c9\u6811\u4e2d\uff0c\u63d2\u5165\u4e0e\u5220\u9664\u64cd\u4f5c\u901a\u5e38\u662f\u7531\u4e00\u5957\u64cd\u4f5c\u914d\u5408\u5b8c\u6210\u7684\uff0c\u4ee5\u5b9e\u73b0\u6709\u5b9e\u9645\u610f\u4e49\u7684\u64cd\u4f5c\u3002</p>"},{"location":"chapter_tree/binary_tree/#713","title":"7.1.3. \u00a0 \u5e38\u89c1\u4e8c\u53c9\u6811\u7c7b\u578b","text":""},{"location":"chapter_tree/binary_tree/#_1","title":"\u5b8c\u7f8e\u4e8c\u53c9\u6811","text":"<p>\u300c\u5b8c\u7f8e\u4e8c\u53c9\u6811 Perfect Binary Tree\u300d\u9664\u4e86\u6700\u5e95\u5c42\u5916\uff0c\u5176\u4f59\u6240\u6709\u5c42\u7684\u8282\u70b9\u90fd\u88ab\u5b8c\u5168\u586b\u6ee1\u3002\u5728\u5b8c\u7f8e\u4e8c\u53c9\u6811\u4e2d\uff0c\u53f6\u8282\u70b9\u7684\u5ea6\u4e3a \\(0\\) \uff0c\u5176\u4f59\u6240\u6709\u8282\u70b9\u7684\u5ea6\u90fd\u4e3a \\(2\\) \uff1b\u82e5\u6811\u9ad8\u5ea6\u4e3a \\(h\\) \uff0c\u5219\u8282\u70b9\u603b\u6570\u4e3a \\(2^{h+1} - 1\\) \uff0c\u5448\u73b0\u6807\u51c6\u7684\u6307\u6570\u7ea7\u5173\u7cfb\uff0c\u53cd\u6620\u4e86\u81ea\u7136\u754c\u4e2d\u5e38\u89c1\u7684\u7ec6\u80de\u5206\u88c2\u73b0\u8c61\u3002</p> <p>Tip</p> <p>\u5728\u4e2d\u6587\u793e\u533a\u4e2d\uff0c\u5b8c\u7f8e\u4e8c\u53c9\u6811\u5e38\u88ab\u79f0\u4e3a\u300c\u6ee1\u4e8c\u53c9\u6811\u300d\uff0c\u8bf7\u6ce8\u610f\u533a\u5206\u3002</p> <p></p> <p> Fig. \u5b8c\u7f8e\u4e8c\u53c9\u6811 </p>"},{"location":"chapter_tree/binary_tree/#_2","title":"\u5b8c\u5168\u4e8c\u53c9\u6811","text":"<p>\u300c\u5b8c\u5168\u4e8c\u53c9\u6811 Complete Binary Tree\u300d\u53ea\u6709\u6700\u5e95\u5c42\u7684\u8282\u70b9\u672a\u88ab\u586b\u6ee1\uff0c\u4e14\u6700\u5e95\u5c42\u8282\u70b9\u5c3d\u91cf\u9760\u5de6\u586b\u5145\u3002</p> <p></p> <p> Fig. \u5b8c\u5168\u4e8c\u53c9\u6811 </p>"},{"location":"chapter_tree/binary_tree/#_3","title":"\u5b8c\u6ee1\u4e8c\u53c9\u6811","text":"<p>\u300c\u5b8c\u6ee1\u4e8c\u53c9\u6811 Full Binary Tree\u300d\u9664\u4e86\u53f6\u8282\u70b9\u4e4b\u5916\uff0c\u5176\u4f59\u6240\u6709\u8282\u70b9\u90fd\u6709\u4e24\u4e2a\u5b50\u8282\u70b9\u3002</p> <p></p> <p> Fig. \u5b8c\u6ee1\u4e8c\u53c9\u6811 </p>"},{"location":"chapter_tree/binary_tree/#_4","title":"\u5e73\u8861\u4e8c\u53c9\u6811","text":"<p>\u300c\u5e73\u8861\u4e8c\u53c9\u6811 Balanced Binary Tree\u300d\u4e2d\u4efb\u610f\u8282\u70b9\u7684\u5de6\u5b50\u6811\u548c\u53f3\u5b50\u6811\u7684\u9ad8\u5ea6\u4e4b\u5dee\u7684\u7edd\u5bf9\u503c\u4e0d\u8d85\u8fc7 1 \u3002</p> <p></p> <p> Fig. \u5e73\u8861\u4e8c\u53c9\u6811 </p>"},{"location":"chapter_tree/binary_tree/#714","title":"7.1.4. \u00a0 \u4e8c\u53c9\u6811\u7684\u9000\u5316","text":"<p>\u5f53\u4e8c\u53c9\u6811\u7684\u6bcf\u5c42\u8282\u70b9\u90fd\u88ab\u586b\u6ee1\u65f6\uff0c\u8fbe\u5230\u300c\u5b8c\u7f8e\u4e8c\u53c9\u6811\u300d\uff1b\u800c\u5f53\u6240\u6709\u8282\u70b9\u90fd\u504f\u5411\u4e00\u4fa7\u65f6\uff0c\u4e8c\u53c9\u6811\u9000\u5316\u4e3a\u300c\u94fe\u8868\u300d\u3002</p> <ul> <li>\u5b8c\u7f8e\u4e8c\u53c9\u6811\u662f\u7406\u60f3\u60c5\u51b5\uff0c\u53ef\u4ee5\u5145\u5206\u53d1\u6325\u4e8c\u53c9\u6811\u201c\u5206\u6cbb\u201d\u7684\u4f18\u52bf\uff1b</li> <li>\u94fe\u8868\u5219\u662f\u53e6\u4e00\u4e2a\u6781\u7aef\uff0c\u5404\u9879\u64cd\u4f5c\u90fd\u53d8\u4e3a\u7ebf\u6027\u64cd\u4f5c\uff0c\u65f6\u95f4\u590d\u6742\u5ea6\u9000\u5316\u81f3 \\(O(n)\\) \uff1b</li> </ul> <p></p> <p> Fig. \u4e8c\u53c9\u6811\u7684\u6700\u4f73\u4e0e\u6700\u5dee\u7ed3\u6784 </p> <p>\u5982\u4e0b\u8868\u6240\u793a\uff0c\u5728\u6700\u4f73\u548c\u6700\u5dee\u7ed3\u6784\u4e0b\uff0c\u4e8c\u53c9\u6811\u7684\u53f6\u8282\u70b9\u6570\u91cf\u3001\u8282\u70b9\u603b\u6570\u3001\u9ad8\u5ea6\u7b49\u8fbe\u5230\u6781\u5927\u6216\u6781\u5c0f\u503c\u3002</p> \u5b8c\u7f8e\u4e8c\u53c9\u6811 \u94fe\u8868 \u7b2c \\(i\\) \u5c42\u7684\u8282\u70b9\u6570\u91cf \\(2^{i-1}\\) \\(1\\) \u6811\u7684\u9ad8\u5ea6\u4e3a \\(h\\) \u65f6\u7684\u53f6\u8282\u70b9\u6570\u91cf \\(2^h\\) \\(1\\) \u6811\u7684\u9ad8\u5ea6\u4e3a \\(h\\) \u65f6\u7684\u8282\u70b9\u603b\u6570 \\(2^{h+1} - 1\\) \\(h + 1\\) \u6811\u7684\u8282\u70b9\u603b\u6570\u4e3a \\(n\\) \u65f6\u7684\u9ad8\u5ea6 \\(\\log_2 (n+1) - 1\\) \\(n - 1\\)"},{"location":"chapter_tree/binary_tree_traversal/","title":"7.2. \u00a0 \u4e8c\u53c9\u6811\u904d\u5386","text":"<p>\u4ece\u7269\u7406\u7ed3\u6784\u7684\u89d2\u5ea6\u6765\u770b\uff0c\u6811\u662f\u4e00\u79cd\u57fa\u4e8e\u94fe\u8868\u7684\u6570\u636e\u7ed3\u6784\uff0c\u56e0\u6b64\u5176\u904d\u5386\u65b9\u5f0f\u662f\u901a\u8fc7\u6307\u9488\u9010\u4e2a\u8bbf\u95ee\u8282\u70b9\u3002\u7136\u800c\uff0c\u6811\u662f\u4e00\u79cd\u975e\u7ebf\u6027\u6570\u636e\u7ed3\u6784\uff0c\u8fd9\u4f7f\u5f97\u904d\u5386\u6811\u6bd4\u904d\u5386\u94fe\u8868\u66f4\u52a0\u590d\u6742\uff0c\u9700\u8981\u501f\u52a9\u641c\u7d22\u7b97\u6cd5\u6765\u5b9e\u73b0\u3002</p> <p>\u4e8c\u53c9\u6811\u5e38\u89c1\u7684\u904d\u5386\u65b9\u5f0f\u5305\u62ec\u5c42\u5e8f\u904d\u5386\u3001\u524d\u5e8f\u904d\u5386\u3001\u4e2d\u5e8f\u904d\u5386\u548c\u540e\u5e8f\u904d\u5386\u7b49\u3002</p>"},{"location":"chapter_tree/binary_tree_traversal/#721","title":"7.2.1. \u00a0 \u5c42\u5e8f\u904d\u5386","text":"<p>\u300c\u5c42\u5e8f\u904d\u5386 Level-Order Traversal\u300d\u4ece\u9876\u90e8\u5230\u5e95\u90e8\u9010\u5c42\u904d\u5386\u4e8c\u53c9\u6811\uff0c\u5e76\u5728\u6bcf\u4e00\u5c42\u6309\u7167\u4ece\u5de6\u5230\u53f3\u7684\u987a\u5e8f\u8bbf\u95ee\u8282\u70b9\u3002</p> <p>\u5c42\u5e8f\u904d\u5386\u672c\u8d28\u4e0a\u5c5e\u4e8e\u300c\u5e7f\u5ea6\u4f18\u5148\u641c\u7d22 Breadth-First Traversal\u300d\uff0c\u5b83\u4f53\u73b0\u4e86\u4e00\u79cd\u201c\u4e00\u5708\u4e00\u5708\u5411\u5916\u6269\u5c55\u201d\u7684\u9010\u5c42\u641c\u7d22\u65b9\u5f0f\u3002</p> <p></p> <p> Fig. \u4e8c\u53c9\u6811\u7684\u5c42\u5e8f\u904d\u5386 </p>"},{"location":"chapter_tree/binary_tree_traversal/#_1","title":"\u7b97\u6cd5\u5b9e\u73b0","text":"<p>\u5e7f\u5ea6\u4f18\u5148\u904d\u5386\u901a\u5e38\u501f\u52a9\u300c\u961f\u5217\u300d\u6765\u5b9e\u73b0\u3002\u961f\u5217\u9075\u5faa\u201c\u5148\u8fdb\u5148\u51fa\u201d\u7684\u89c4\u5219\uff0c\u800c\u5e7f\u5ea6\u4f18\u5148\u904d\u5386\u5219\u9075\u5faa\u201c\u9010\u5c42\u63a8\u8fdb\u201d\u7684\u89c4\u5219\uff0c\u4e24\u8005\u80cc\u540e\u7684\u601d\u60f3\u662f\u4e00\u81f4\u7684\u3002</p> JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart binary_tree_bfs.java<pre><code>/* \u5c42\u5e8f\u904d\u5386 */\nList&lt;Integer&gt; levelOrder(TreeNode root) {\n// \u521d\u59cb\u5316\u961f\u5217\uff0c\u52a0\u5165\u6839\u8282\u70b9\nQueue&lt;TreeNode&gt; queue = new LinkedList&lt;&gt;() {{ add(root); }};\n// \u521d\u59cb\u5316\u4e00\u4e2a\u5217\u8868\uff0c\u7528\u4e8e\u4fdd\u5b58\u904d\u5386\u5e8f\u5217\nList&lt;Integer&gt; list = new ArrayList&lt;&gt;();\nwhile (!queue.isEmpty()) {\nTreeNode node = queue.poll(); // \u961f\u5217\u51fa\u961f\nlist.add(node.val);           // \u4fdd\u5b58\u8282\u70b9\u503c\nif (node.left != null)\nqueue.offer(node.left);   // \u5de6\u5b50\u8282\u70b9\u5165\u961f\nif (node.right != null)\nqueue.offer(node.right);  // \u53f3\u5b50\u8282\u70b9\u5165\u961f\n}\nreturn list;\n}\n</code></pre> binary_tree_bfs.cpp<pre><code>/* \u5c42\u5e8f\u904d\u5386 */\nvector&lt;int&gt; levelOrder(TreeNode *root) {\n// \u521d\u59cb\u5316\u961f\u5217\uff0c\u52a0\u5165\u6839\u8282\u70b9\nqueue&lt;TreeNode *&gt; queue;\nqueue.push(root);\n// \u521d\u59cb\u5316\u4e00\u4e2a\u5217\u8868\uff0c\u7528\u4e8e\u4fdd\u5b58\u904d\u5386\u5e8f\u5217\nvector&lt;int&gt; vec;\nwhile (!queue.empty()) {\nTreeNode *node = queue.front();\nqueue.pop();              // \u961f\u5217\u51fa\u961f\nvec.push_back(node-&gt;val); // \u4fdd\u5b58\u8282\u70b9\u503c\nif (node-&gt;left != nullptr)\nqueue.push(node-&gt;left); // \u5de6\u5b50\u8282\u70b9\u5165\u961f\nif (node-&gt;right != nullptr)\nqueue.push(node-&gt;right); // \u53f3\u5b50\u8282\u70b9\u5165\u961f\n}\nreturn vec;\n}\n</code></pre> binary_tree_bfs.py<pre><code>def level_order(root: TreeNode | None) -&gt; list[int]:\n\"\"\"\u5c42\u5e8f\u904d\u5386\"\"\"\n# \u521d\u59cb\u5316\u961f\u5217\uff0c\u52a0\u5165\u6839\u8282\u70b9\nqueue: deque[TreeNode] = deque()\nqueue.append(root)\n# \u521d\u59cb\u5316\u4e00\u4e2a\u5217\u8868\uff0c\u7528\u4e8e\u4fdd\u5b58\u904d\u5386\u5e8f\u5217\nres = []\nwhile queue:\nnode: TreeNode = queue.popleft()  # \u961f\u5217\u51fa\u961f\nres.append(node.val)  # \u4fdd\u5b58\u8282\u70b9\u503c\nif node.left is not None:\nqueue.append(node.left)  # \u5de6\u5b50\u8282\u70b9\u5165\u961f\nif node.right is not None:\nqueue.append(node.right)  # \u53f3\u5b50\u8282\u70b9\u5165\u961f\nreturn res\n</code></pre> binary_tree_bfs.go<pre><code>/* \u5c42\u5e8f\u904d\u5386 */\nfunc levelOrder(root *TreeNode) []int {\n// \u521d\u59cb\u5316\u961f\u5217\uff0c\u52a0\u5165\u6839\u8282\u70b9\nqueue := list.New()\nqueue.PushBack(root)\n// \u521d\u59cb\u5316\u4e00\u4e2a\u5207\u7247\uff0c\u7528\u4e8e\u4fdd\u5b58\u904d\u5386\u5e8f\u5217\nnums := make([]int, 0)\nfor queue.Len() &gt; 0 {\n// \u961f\u5217\u51fa\u961f\nnode := queue.Remove(queue.Front()).(*TreeNode)\n// \u4fdd\u5b58\u8282\u70b9\u503c\nnums = append(nums, node.Val)\nif node.Left != nil {\n// \u5de6\u5b50\u8282\u70b9\u5165\u961f\nqueue.PushBack(node.Left)\n}\nif node.Right != nil {\n// \u53f3\u5b50\u8282\u70b9\u5165\u961f\nqueue.PushBack(node.Right)\n}\n}\nreturn nums\n}\n</code></pre> binary_tree_bfs.js<pre><code>/* \u5c42\u5e8f\u904d\u5386 */\nfunction levelOrder(root) {\n// \u521d\u59cb\u5316\u961f\u5217\uff0c\u52a0\u5165\u6839\u8282\u70b9\nconst queue = [root];\n// \u521d\u59cb\u5316\u4e00\u4e2a\u5217\u8868\uff0c\u7528\u4e8e\u4fdd\u5b58\u904d\u5386\u5e8f\u5217\nconst list = [];\nwhile (queue.length) {\nlet node = queue.shift(); // \u961f\u5217\u51fa\u961f\nlist.push(node.val); // \u4fdd\u5b58\u8282\u70b9\u503c\nif (node.left) queue.push(node.left); // \u5de6\u5b50\u8282\u70b9\u5165\u961f\nif (node.right) queue.push(node.right); // \u53f3\u5b50\u8282\u70b9\u5165\u961f\n}\nreturn list;\n}\n</code></pre> binary_tree_bfs.ts<pre><code>/* \u5c42\u5e8f\u904d\u5386 */\nfunction levelOrder(root: TreeNode | null): number[] {\n// \u521d\u59cb\u5316\u961f\u5217\uff0c\u52a0\u5165\u6839\u8282\u70b9\nconst queue = [root];\n// \u521d\u59cb\u5316\u4e00\u4e2a\u5217\u8868\uff0c\u7528\u4e8e\u4fdd\u5b58\u904d\u5386\u5e8f\u5217\nconst list: number[] = [];\nwhile (queue.length) {\nlet node = queue.shift() as TreeNode; // \u961f\u5217\u51fa\u961f\nlist.push(node.val); // \u4fdd\u5b58\u8282\u70b9\u503c\nif (node.left) {\nqueue.push(node.left); // \u5de6\u5b50\u8282\u70b9\u5165\u961f\n}\nif (node.right) {\nqueue.push(node.right); // \u53f3\u5b50\u8282\u70b9\u5165\u961f\n}\n}\nreturn list;\n}\n</code></pre> binary_tree_bfs.c<pre><code>/* \u5c42\u5e8f\u904d\u5386 */\nint *levelOrder(TreeNode *root, int *size) {\n/* \u8f85\u52a9\u961f\u5217 */\nint front, rear;\nint index, *arr;\nTreeNode *node;\nTreeNode **queue;\n/* \u8f85\u52a9\u961f\u5217 */\nqueue = (TreeNode **)malloc(sizeof(TreeNode *) * MAX_NODE_SIZE);\n// \u961f\u5217\u6307\u9488\nfront = 0, rear = 0;\n// \u52a0\u5165\u6839\u8282\u70b9\nqueue[rear++] = root;\n// \u521d\u59cb\u5316\u4e00\u4e2a\u5217\u8868\uff0c\u7528\u4e8e\u4fdd\u5b58\u904d\u5386\u5e8f\u5217\n/* \u8f85\u52a9\u6570\u7ec4 */\narr = (int *)malloc(sizeof(int) * MAX_NODE_SIZE);\n// \u6570\u7ec4\u6307\u9488\nindex = 0;\nwhile (front &lt; rear) {\n// \u961f\u5217\u51fa\u961f\nnode = queue[front++];\n// \u4fdd\u5b58\u8282\u70b9\u503c\narr[index++] = node-&gt;val;\nif (node-&gt;left != NULL) {\n// \u5de6\u5b50\u8282\u70b9\u5165\u961f\nqueue[rear++] = node-&gt;left;\n}\nif (node-&gt;right != NULL) {\n// \u53f3\u5b50\u8282\u70b9\u5165\u961f\nqueue[rear++] = node-&gt;right;\n}\n}\n// \u66f4\u65b0\u6570\u7ec4\u957f\u5ea6\u7684\u503c\n*size = index;\narr = realloc(arr, sizeof(int) * (*size));\n// \u91ca\u653e\u8f85\u52a9\u6570\u7ec4\u7a7a\u95f4\nfree(queue);\nreturn arr;\n}\n</code></pre> binary_tree_bfs.cs<pre><code>/* \u5c42\u5e8f\u904d\u5386 */\nList&lt;int&gt; levelOrder(TreeNode root) {\n// \u521d\u59cb\u5316\u961f\u5217\uff0c\u52a0\u5165\u6839\u8282\u70b9\nQueue&lt;TreeNode&gt; queue = new();\nqueue.Enqueue(root);\n// \u521d\u59cb\u5316\u4e00\u4e2a\u5217\u8868\uff0c\u7528\u4e8e\u4fdd\u5b58\u904d\u5386\u5e8f\u5217\nList&lt;int&gt; list = new();\nwhile (queue.Count != 0) {\nTreeNode node = queue.Dequeue(); // \u961f\u5217\u51fa\u961f\nlist.Add(node.val);              // \u4fdd\u5b58\u8282\u70b9\u503c\nif (node.left != null)\nqueue.Enqueue(node.left);    // \u5de6\u5b50\u8282\u70b9\u5165\u961f\nif (node.right != null)\nqueue.Enqueue(node.right);   // \u53f3\u5b50\u8282\u70b9\u5165\u961f\n}\nreturn list;\n}\n</code></pre> binary_tree_bfs.swift<pre><code>/* \u5c42\u5e8f\u904d\u5386 */\nfunc levelOrder(root: TreeNode) -&gt; [Int] {\n// \u521d\u59cb\u5316\u961f\u5217\uff0c\u52a0\u5165\u6839\u8282\u70b9\nvar queue: [TreeNode] = [root]\n// \u521d\u59cb\u5316\u4e00\u4e2a\u5217\u8868\uff0c\u7528\u4e8e\u4fdd\u5b58\u904d\u5386\u5e8f\u5217\nvar list: [Int] = []\nwhile !queue.isEmpty {\nlet node = queue.removeFirst() // \u961f\u5217\u51fa\u961f\nlist.append(node.val) // \u4fdd\u5b58\u8282\u70b9\u503c\nif let left = node.left {\nqueue.append(left) // \u5de6\u5b50\u8282\u70b9\u5165\u961f\n}\nif let right = node.right {\nqueue.append(right) // \u53f3\u5b50\u8282\u70b9\u5165\u961f\n}\n}\nreturn list\n}\n</code></pre> binary_tree_bfs.zig<pre><code>// \u5c42\u5e8f\u904d\u5386\nfn levelOrder(comptime T: type, mem_allocator: std.mem.Allocator, root: *inc.TreeNode(T)) !std.ArrayList(T) {\n// \u521d\u59cb\u5316\u961f\u5217\uff0c\u52a0\u5165\u6839\u8282\u70b9\nconst L = std.TailQueue(*inc.TreeNode(T));\nvar queue = L{};\nvar root_node = try mem_allocator.create(L.Node);\nroot_node.data = root;\nqueue.append(root_node); // \u521d\u59cb\u5316\u4e00\u4e2a\u5217\u8868\uff0c\u7528\u4e8e\u4fdd\u5b58\u904d\u5386\u5e8f\u5217\nvar list = std.ArrayList(T).init(std.heap.page_allocator);\nwhile (queue.len &gt; 0) {\nvar queue_node = queue.popFirst().?;    // \u961f\u5217\u51fa\u961f\nvar node = queue_node.data;\ntry list.append(node.val);              // \u4fdd\u5b58\u8282\u70b9\u503c\nif (node.left != null) {\nvar tmp_node = try mem_allocator.create(L.Node);\ntmp_node.data = node.left.?;\nqueue.append(tmp_node);             // \u5de6\u5b50\u8282\u70b9\u5165\u961f\n}\nif (node.right != null) {\nvar tmp_node = try mem_allocator.create(L.Node);\ntmp_node.data = node.right.?;\nqueue.append(tmp_node);             // \u53f3\u5b50\u8282\u70b9\u5165\u961f\n}        }\nreturn list;\n}\n</code></pre> binary_tree_bfs.dart<pre><code>/* \u5c42\u5e8f\u904d\u5386 */\nList&lt;int&gt; levelOrder(TreeNode? root) {\n// \u521d\u59cb\u5316\u961f\u5217\uff0c\u52a0\u5165\u6839\u8282\u70b9\nQueue&lt;TreeNode?&gt; queue = Queue();\nqueue.add(root);\n// \u521d\u59cb\u5316\u4e00\u4e2a\u5217\u8868\uff0c\u7528\u4e8e\u4fdd\u5b58\u904d\u5386\u5e8f\u5217\nList&lt;int&gt; res = [];\nwhile (queue.isNotEmpty) {\nTreeNode? node = queue.removeFirst(); // \u961f\u5217\u51fa\u961f\nres.add(node!.val); // \u4fdd\u5b58\u8282\u70b9\u503c\nif (node.left != null) queue.add(node.left); // \u5de6\u5b50\u8282\u70b9\u5165\u961f\nif (node.right != null) queue.add(node.right); // \u53f3\u5b50\u8282\u70b9\u5165\u961f\n}\nreturn res;\n}\n</code></pre>"},{"location":"chapter_tree/binary_tree_traversal/#_2","title":"\u590d\u6742\u5ea6\u5206\u6790","text":"<p>\u65f6\u95f4\u590d\u6742\u5ea6\uff1a\u6240\u6709\u8282\u70b9\u88ab\u8bbf\u95ee\u4e00\u6b21\uff0c\u4f7f\u7528 \\(O(n)\\) \u65f6\u95f4\uff0c\u5176\u4e2d \\(n\\) \u4e3a\u8282\u70b9\u6570\u91cf\u3002</p> <p>\u7a7a\u95f4\u590d\u6742\u5ea6\uff1a\u5728\u6700\u5dee\u60c5\u51b5\u4e0b\uff0c\u5373\u6ee1\u4e8c\u53c9\u6811\u65f6\uff0c\u904d\u5386\u5230\u6700\u5e95\u5c42\u4e4b\u524d\uff0c\u961f\u5217\u4e2d\u6700\u591a\u540c\u65f6\u5b58\u5728 \\(\\frac{n + 1}{2}\\) \u4e2a\u8282\u70b9\uff0c\u5360\u7528 \\(O(n)\\) \u7a7a\u95f4\u3002</p>"},{"location":"chapter_tree/binary_tree_traversal/#722","title":"7.2.2. \u00a0 \u524d\u5e8f\u3001\u4e2d\u5e8f\u3001\u540e\u5e8f\u904d\u5386","text":"<p>\u76f8\u5e94\u5730\uff0c\u524d\u5e8f\u3001\u4e2d\u5e8f\u548c\u540e\u5e8f\u904d\u5386\u90fd\u5c5e\u4e8e\u300c\u6df1\u5ea6\u4f18\u5148\u904d\u5386 Depth-First Traversal\u300d\uff0c\u5b83\u4f53\u73b0\u4e86\u4e00\u79cd\u201c\u5148\u8d70\u5230\u5c3d\u5934\uff0c\u518d\u56de\u6eaf\u7ee7\u7eed\u201d\u7684\u904d\u5386\u65b9\u5f0f\u3002</p> <p>\u5982\u4e0b\u56fe\u6240\u793a\uff0c\u5de6\u4fa7\u662f\u6df1\u5ea6\u4f18\u5148\u904d\u5386\u7684\u793a\u610f\u56fe\uff0c\u53f3\u4e0a\u65b9\u662f\u5bf9\u5e94\u7684\u9012\u5f52\u5b9e\u73b0\u4ee3\u7801\u3002\u6df1\u5ea6\u4f18\u5148\u904d\u5386\u5c31\u50cf\u662f\u7ed5\u7740\u6574\u4e2a\u4e8c\u53c9\u6811\u7684\u5916\u56f4\u201c\u8d70\u201d\u4e00\u5708\uff0c\u5728\u8fd9\u4e2a\u8fc7\u7a0b\u4e2d\uff0c\u5728\u6bcf\u4e2a\u8282\u70b9\u90fd\u4f1a\u9047\u5230\u4e09\u4e2a\u4f4d\u7f6e\uff0c\u5206\u522b\u5bf9\u5e94\u524d\u5e8f\u904d\u5386\u3001\u4e2d\u5e8f\u904d\u5386\u548c\u540e\u5e8f\u904d\u5386\u3002</p> <p></p> <p> Fig. \u4e8c\u53c9\u641c\u7d22\u6811\u7684\u524d\u3001\u4e2d\u3001\u540e\u5e8f\u904d\u5386 </p> \u4f4d\u7f6e \u542b\u4e49 \u6b64\u5904\u8bbf\u95ee\u8282\u70b9\u65f6\u5bf9\u5e94 \u6a59\u8272\u5706\u5708\u5904 \u521a\u8fdb\u5165\u6b64\u8282\u70b9\uff0c\u5373\u5c06\u8bbf\u95ee\u8be5\u8282\u70b9\u7684\u5de6\u5b50\u6811 \u524d\u5e8f\u904d\u5386 Pre-Order Traversal \u84dd\u8272\u5706\u5708\u5904 \u5df2\u8bbf\u95ee\u5b8c\u5de6\u5b50\u6811\uff0c\u5373\u5c06\u8bbf\u95ee\u53f3\u5b50\u6811 \u4e2d\u5e8f\u904d\u5386 In-Order Traversal \u7d2b\u8272\u5706\u5708\u5904 \u5df2\u8bbf\u95ee\u5b8c\u5de6\u5b50\u6811\u548c\u53f3\u5b50\u6811\uff0c\u5373\u5c06\u8fd4\u56de \u540e\u5e8f\u904d\u5386 Post-Order Traversal"},{"location":"chapter_tree/binary_tree_traversal/#_3","title":"\u7b97\u6cd5\u5b9e\u73b0","text":"JavaC++PythonGoJavaScriptTypeScriptCC#SwiftZigDart binary_tree_dfs.java<pre><code>/* \u524d\u5e8f\u904d\u5386 */\nvoid preOrder(TreeNode root) {\nif (root == null)\nreturn;\n// \u8bbf\u95ee\u4f18\u5148\u7ea7\uff1a\u6839\u8282\u70b9 -&gt; \u5de6\u5b50\u6811 -&gt; \u53f3\u5b50\u6811\nlist.add(root.val);\npreOrder(root.left);\npreOrder(root.right);\n}\n/* \u4e2d\u5e8f\u904d\u5386 */\nvoid inOrder(TreeNode root) {\nif (root == null)\nreturn;\n// \u8bbf\u95ee\u4f18\u5148\u7ea7\uff1a\u5de6\u5b50\u6811 -&gt; \u6839\u8282\u70b9 -&gt; \u53f3\u5b50\u6811\ninOrder(root.left);\nlist.add(root.val);\ninOrder(root.right);\n}\n/* \u540e\u5e8f\u904d\u5386 */\nvoid postOrder(TreeNode root) {\nif (root == null)\nreturn;\n// \u8bbf\u95ee\u4f18\u5148\u7ea7\uff1a\u5de6\u5b50\u6811 -&gt; \u53f3\u5b50\u6811 -&gt; \u6839\u8282\u70b9\npostOrder(root.left);\npostOrder(root.right);\nlist.add(root.val);\n}\n</code></pre> binary_tree_dfs.cpp<pre><code>/* \u524d\u5e8f\u904d\u5386 */\nvoid preOrder(TreeNode *root) {\nif (root == nullptr)\nreturn;\n// \u8bbf\u95ee\u4f18\u5148\u7ea7\uff1a\u6839\u8282\u70b9 -&gt; \u5de6\u5b50\u6811 -&gt; \u53f3\u5b50\u6811\nvec.push_back(root-&gt;val);\npreOrder(root-&gt;left);\npreOrder(root-&gt;right);\n}\n/* \u4e2d\u5e8f\u904d\u5386 */\nvoid inOrder(TreeNode *root) {\nif (root == nullptr)\nreturn;\n// \u8bbf\u95ee\u4f18\u5148\u7ea7\uff1a\u5de6\u5b50\u6811 -&gt; \u6839\u8282\u70b9 -&gt; \u53f3\u5b50\u6811\ninOrder(root-&gt;left);\nvec.push_back(root-&gt;val);\ninOrder(root-&gt;right);\n}\n/* \u540e\u5e8f\u904d\u5386 */\nvoid postOrder(TreeNode *root) {\nif (root == nullptr)\nreturn;\n// \u8bbf\u95ee\u4f18\u5148\u7ea7\uff1a\u5de6\u5b50\u6811 -&gt; \u53f3\u5b50\u6811 -&gt; \u6839\u8282\u70b9\npostOrder(root-&gt;left);\npostOrder(root-&gt;right);\nvec.push_back(root-&gt;val);\n}\n</code></pre> binary_tree_dfs.py<pre><code>def pre_order(root: TreeNode | None) -&gt; None:\n\"\"\"\u524d\u5e8f\u904d\u5386\"\"\"\nif root is None:\nreturn\n# \u8bbf\u95ee\u4f18\u5148\u7ea7\uff1a\u6839\u8282\u70b9 -&gt; \u5de6\u5b50\u6811 -&gt; \u53f3\u5b50\u6811\nres.append(root.val)\npre_order(root=root.left)\npre_order(root=root.right)\ndef in_order(root: TreeNode | None) -&gt; None:\n\"\"\"\u4e2d\u5e8f\u904d\u5386\"\"\"\nif root is None:\nreturn\n# \u8bbf\u95ee\u4f18\u5148\u7ea7\uff1a\u5de6\u5b50\u6811 -&gt; \u6839\u8282\u70b9 -&gt; \u53f3\u5b50\u6811\nin_order(root=root.left)\nres.append(root.val)\nin_order(root=root.right)\ndef post_order(root: TreeNode | None) -&gt; None:\n\"\"\"\u540e\u5e8f\u904d\u5386\"\"\"\nif root is None:\nreturn\n# \u8bbf\u95ee\u4f18\u5148\u7ea7\uff1a\u5de6\u5b50\u6811 -&gt; \u53f3\u5b50\u6811 -&gt; \u6839\u8282\u70b9\npost_order(root=root.left)\npost_order(root=root.right)\nres.append(root.val)\n</code></pre> binary_tree_dfs.go<pre><code>/* \u524d\u5e8f\u904d\u5386 */\nfunc preOrder(node *TreeNode) {\nif node == nil {\nreturn\n}\n// \u8bbf\u95ee\u4f18\u5148\u7ea7\uff1a\u6839\u8282\u70b9 -&gt; \u5de6\u5b50\u6811 -&gt; \u53f3\u5b50\u6811\nnums = append(nums, node.Val)\npreOrder(node.Left)\npreOrder(node.Right)\n}\n/* \u4e2d\u5e8f\u904d\u5386 */\nfunc inOrder(node *TreeNode) {\nif node == nil {\nreturn\n}\n// \u8bbf\u95ee\u4f18\u5148\u7ea7\uff1a\u5de6\u5b50\u6811 -&gt; \u6839\u8282\u70b9 -&gt; \u53f3\u5b50\u6811\ninOrder(node.Left)\nnums = append(nums, node.Val)\ninOrder(node.Right)\n}\n/* \u540e\u5e8f\u904d\u5386 */\nfunc postOrder(node *TreeNode) {\nif node == nil {\nreturn\n}\n// \u8bbf\u95ee\u4f18\u5148\u7ea7\uff1a\u5de6\u5b50\u6811 -&gt; \u53f3\u5b50\u6811 -&gt; \u6839\u8282\u70b9\npostOrder(node.Left)\npostOrder(node.Right)\nnums = append(nums, node.Val)\n}\n</code></pre> binary_tree_dfs.js<pre><code>/* \u524d\u5e8f\u904d\u5386 */\nfunction preOrder(root) {\nif (root === null) return;\n// \u8bbf\u95ee\u4f18\u5148\u7ea7\uff1a\u6839\u8282\u70b9 -&gt; \u5de6\u5b50\u6811 -&gt; \u53f3\u5b50\u6811\nlist.push(root.val);\npreOrder(root.left);\npreOrder(root.right);\n}\n/* \u4e2d\u5e8f\u904d\u5386 */\nfunction inOrder(root) {\nif (root === null) return;\n// \u8bbf\u95ee\u4f18\u5148\u7ea7\uff1a\u5de6\u5b50\u6811 -&gt; \u6839\u8282\u70b9 -&gt; \u53f3\u5b50\u6811\ninOrder(root.left);\nlist.push(root.val);\ninOrder(root.right);\n}\n/* \u540e\u5e8f\u904d\u5386 */\nfunction postOrder(root) {\nif (root === null) return;\n// \u8bbf\u95ee\u4f18\u5148\u7ea7\uff1a\u5de6\u5b50\u6811 -&gt; \u53f3\u5b50\u6811 -&gt; \u6839\u8282\u70b9\npostOrder(root.left);\npostOrder(root.right);\nlist.push(root.val);\n}\n</code></pre> binary_tree_dfs.ts<pre><code>/* \u524d\u5e8f\u904d\u5386 */\nfunction preOrder(root: TreeNode | null): void {\nif (root === null) {\nreturn;\n}\n// \u8bbf\u95ee\u4f18\u5148\u7ea7\uff1a\u6839\u8282\u70b9 -&gt; \u5de6\u5b50\u6811 -&gt; \u53f3\u5b50\u6811\nlist.push(root.val);\npreOrder(root.left);\npreOrder(root.right);\n}\n/* \u4e2d\u5e8f\u904d\u5386 */\nfunction inOrder(root: TreeNode | null): void {\nif (root === null) {\nreturn;\n}\n// \u8bbf\u95ee\u4f18\u5148\u7ea7\uff1a\u5de6\u5b50\u6811 -&gt; \u6839\u8282\u70b9 -&gt; \u53f3\u5b50\u6811\ninOrder(root.left);\nlist.push(root.val);\ninOrder(root.right);\n}\n/* \u540e\u5e8f\u904d\u5386 */\nfunction postOrder(root: TreeNode | null): void {\nif (root === null) {\nreturn;\n}\n// \u8bbf\u95ee\u4f18\u5148\u7ea7\uff1a\u5de6\u5b50\u6811 -&gt; \u53f3\u5b50\u6811 -&gt; \u6839\u8282\u70b9\npostOrder(root.left);\npostOrder(root.right);\nlist.push(root.val);\n}\n</code></pre> binary_tree_dfs.c<pre><code>/* \u524d\u5e8f\u904d\u5386 */\nvoid preOrder(TreeNode *root, int *size) {\nif (root == NULL)\nreturn;\n// \u8bbf\u95ee\u4f18\u5148\u7ea7\uff1a\u6839\u8282\u70b9 -&gt; \u5de6\u5b50\u6811 -&gt; \u53f3\u5b50\u6811\narr[(*size)++] = root-&gt;val;\npreOrder(root-&gt;left, size);\npreOrder(root-&gt;right, size);\n}\n/* \u4e2d\u5e8f\u904d\u5386 */\nvoid inOrder(TreeNode *root, int *size) {\nif (root == NULL)\nreturn;\n// \u8bbf\u95ee\u4f18\u5148\u7ea7\uff1a\u5de6\u5b50\u6811 -&gt; \u6839\u8282\u70b9 -&gt; \u53f3\u5b50\u6811\ninOrder(root-&gt;left, size);\narr[(*size)++] = root-&gt;val;\ninOrder(root-&gt;right, size);\n}\n/* \u540e\u5e8f\u904d\u5386 */\nvoid postOrder(TreeNode *root, int *size) {\nif (root == NULL)\nreturn;\n// \u8bbf\u95ee\u4f18\u5148\u7ea7\uff1a\u5de6\u5b50\u6811 -&gt; \u53f3\u5b50\u6811 -&gt; \u6839\u8282\u70b9\npostOrder(root-&gt;left, size);\npostOrder(root-&gt;right, size);\narr[(*size)++] = root-&gt;val;\n}\n</code></pre> binary_tree_dfs.cs<pre><code>/* \u524d\u5e8f\u904d\u5386 */\nvoid preOrder(TreeNode? root) {\nif (root == null) return;\n// \u8bbf\u95ee\u4f18\u5148\u7ea7\uff1a\u6839\u8282\u70b9 -&gt; \u5de6\u5b50\u6811 -&gt; \u53f3\u5b50\u6811\nlist.Add(root.val);\npreOrder(root.left);\npreOrder(root.right);\n}\n/* \u4e2d\u5e8f\u904d\u5386 */\nvoid inOrder(TreeNode? root) {\nif (root == null) return;\n// \u8bbf\u95ee\u4f18\u5148\u7ea7\uff1a\u5de6\u5b50\u6811 -&gt; \u6839\u8282\u70b9 -&gt; \u53f3\u5b50\u6811\ninOrder(root.left);\nlist.Add(root.val);\ninOrder(root.right);\n}\n/* \u540e\u5e8f\u904d\u5386 */\nvoid postOrder(TreeNode? root) {\nif (root == null) return;\n// \u8bbf\u95ee\u4f18\u5148\u7ea7\uff1a\u5de6\u5b50\u6811 -&gt; \u53f3\u5b50\u6811 -&gt; \u6839\u8282\u70b9\npostOrder(root.left);\npostOrder(root.right);\nlist.Add(root.val);\n}\n</code></pre> binary_tree_dfs.swift<pre><code>/* \u524d\u5e8f\u904d\u5386 */\nfunc preOrder(root: TreeNode?) {\nguard let root = root else {\nreturn\n}\n// \u8bbf\u95ee\u4f18\u5148\u7ea7\uff1a\u6839\u8282\u70b9 -&gt; \u5de6\u5b50\u6811 -&gt; \u53f3\u5b50\u6811\nlist.append(root.val)\npreOrder(root: root.left)\npreOrder(root: root.right)\n}\n/* \u4e2d\u5e8f\u904d\u5386 */\nfunc inOrder(root: TreeNode?) {\nguard let root = root else {\nreturn\n}\n// \u8bbf\u95ee\u4f18\u5148\u7ea7\uff1a\u5de6\u5b50\u6811 -&gt; \u6839\u8282\u70b9 -&gt; \u53f3\u5b50\u6811\ninOrder(root: root.left)\nlist.append(root.val)\ninOrder(root: root.right)\n}\n/* \u540e\u5e8f\u904d\u5386 */\nfunc postOrder(root: TreeNode?) {\nguard let root = root else {\nreturn\n}\n// \u8bbf\u95ee\u4f18\u5148\u7ea7\uff1a\u5de6\u5b50\u6811 -&gt; \u53f3\u5b50\u6811 -&gt; \u6839\u8282\u70b9\npostOrder(root: root.left)\npostOrder(root: root.right)\nlist.append(root.val)\n}\n</code></pre> binary_tree_dfs.zig<pre><code>// \u524d\u5e8f\u904d\u5386\nfn preOrder(comptime T: type, root: ?*inc.TreeNode(T)) !void {\nif (root == null) return;\n// \u8bbf\u95ee\u4f18\u5148\u7ea7\uff1a\u6839\u8282\u70b9 -&gt; \u5de6\u5b50\u6811 -&gt; \u53f3\u5b50\u6811\ntry list.append(root.?.val);\ntry preOrder(T, root.?.left);\ntry preOrder(T, root.?.right);\n}\n// \u4e2d\u5e8f\u904d\u5386\nfn inOrder(comptime T: type, root: ?*inc.TreeNode(T)) !void {\nif (root == null) return;\n// \u8bbf\u95ee\u4f18\u5148\u7ea7\uff1a\u5de6\u5b50\u6811 -&gt; \u6839\u8282\u70b9 -&gt; \u53f3\u5b50\u6811\ntry inOrder(T, root.?.left);\ntry list.append(root.?.val);\ntry inOrder(T, root.?.right);\n}\n// \u540e\u5e8f\u904d\u5386\nfn postOrder(comptime T: type, root: ?*inc.TreeNode(T)) !void {\nif (root == null) return;\n// \u8bbf\u95ee\u4f18\u5148\u7ea7\uff1a\u5de6\u5b50\u6811 -&gt; \u53f3\u5b50\u6811 -&gt; \u6839\u8282\u70b9\ntry postOrder(T, root.?.left);\ntry postOrder(T, root.?.right);\ntry list.append(root.?.val);\n}\n</code></pre> binary_tree_dfs.dart<pre><code>/* \u524d\u5e8f\u904d\u5386 */\nvoid preOrder(TreeNode? node) {\nif (node == null) return;\n// \u8bbf\u95ee\u4f18\u5148\u7ea7\uff1a\u6839\u8282\u70b9 -&gt; \u5de6\u5b50\u6811 -&gt; \u53f3\u5b50\u6811\nlist.add(node.val);\npreOrder(node.left);\npreOrder(node.right);\n}\n/* \u4e2d\u5e8f\u904d\u5386 */\nvoid inOrder(TreeNode? node) {\nif (node == null) return;\n// \u8bbf\u95ee\u4f18\u5148\u7ea7\uff1a\u5de6\u5b50\u6811 -&gt; \u6839\u8282\u70b9 -&gt; \u53f3\u5b50\u6811\ninOrder(node.left);\nlist.add(node.val);\ninOrder(node.right);\n}\n/* \u540e\u5e8f\u904d\u5386 */\nvoid postOrder(TreeNode? node) {\nif (node == null) return;\n// \u8bbf\u95ee\u4f18\u5148\u7ea7\uff1a\u5de6\u5b50\u6811 -&gt; \u53f3\u5b50\u6811 -&gt; \u6839\u8282\u70b9\npostOrder(node.left);\npostOrder(node.right);\nlist.add(node.val);\n}\n</code></pre> <p>Note</p> <p>\u6211\u4eec\u4e5f\u53ef\u4ee5\u4ec5\u57fa\u4e8e\u5faa\u73af\u5b9e\u73b0\u524d\u3001\u4e2d\u3001\u540e\u5e8f\u904d\u5386\uff0c\u6709\u5174\u8da3\u7684\u540c\u5b66\u53ef\u4ee5\u81ea\u884c\u5b9e\u73b0\u3002</p> <p>\u9012\u5f52\u8fc7\u7a0b\u53ef\u5206\u4e3a\u201c\u9012\u201d\u548c\u201c\u5f52\u201d\u4e24\u4e2a\u76f8\u53cd\u7684\u90e8\u5206\u3002\u201c\u9012\u201d\u8868\u793a\u5f00\u542f\u65b0\u65b9\u6cd5\uff0c\u7a0b\u5e8f\u5728\u6b64\u8fc7\u7a0b\u4e2d\u8bbf\u95ee\u4e0b\u4e00\u4e2a\u8282\u70b9\uff1b\u201c\u5f52\u201d\u8868\u793a\u51fd\u6570\u8fd4\u56de\uff0c\u4ee3\u8868\u8be5\u8282\u70b9\u5df2\u7ecf\u8bbf\u95ee\u5b8c\u6bd5\u3002\u5982\u4e0b\u56fe\u6240\u793a\uff0c\u4e3a\u524d\u5e8f\u904d\u5386\u4e8c\u53c9\u6811\u7684\u9012\u5f52\u8fc7\u7a0b\u3002</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt;&lt;11&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p>"},{"location":"chapter_tree/binary_tree_traversal/#_4","title":"\u590d\u6742\u5ea6\u5206\u6790","text":"<p>\u65f6\u95f4\u590d\u6742\u5ea6\uff1a\u6240\u6709\u8282\u70b9\u88ab\u8bbf\u95ee\u4e00\u6b21\uff0c\u4f7f\u7528 \\(O(n)\\) \u65f6\u95f4\uff0c\u5176\u4e2d \\(n\\) \u4e3a\u8282\u70b9\u6570\u91cf\u3002</p> <p>\u7a7a\u95f4\u590d\u6742\u5ea6\uff1a\u5728\u6700\u5dee\u60c5\u51b5\u4e0b\uff0c\u5373\u6811\u9000\u5316\u4e3a\u94fe\u8868\u65f6\uff0c\u9012\u5f52\u6df1\u5ea6\u8fbe\u5230 \\(n\\) \uff0c\u7cfb\u7edf\u5360\u7528 \\(O(n)\\) \u6808\u5e27\u7a7a\u95f4\u3002</p>"},{"location":"chapter_tree/summary/","title":"7.6. \u00a0 \u5c0f\u7ed3","text":"<ul> <li>\u4e8c\u53c9\u6811\u662f\u4e00\u79cd\u975e\u7ebf\u6027\u6570\u636e\u7ed3\u6784\uff0c\u4f53\u73b0\u201c\u4e00\u5206\u4e3a\u4e8c\u201d\u7684\u5206\u6cbb\u903b\u8f91\u3002\u6bcf\u4e2a\u4e8c\u53c9\u6811\u8282\u70b9\u5305\u542b\u4e00\u4e2a\u503c\u4ee5\u53ca\u4e24\u4e2a\u6307\u9488\uff0c\u5206\u522b\u6307\u5411\u5176\u5de6\u5b50\u8282\u70b9\u548c\u53f3\u5b50\u8282\u70b9\u3002</li> <li>\u5bf9\u4e8e\u4e8c\u53c9\u6811\u4e2d\u7684\u67d0\u4e2a\u8282\u70b9\uff0c\u5176\u5de6\uff08\u53f3\uff09\u5b50\u8282\u70b9\u53ca\u5176\u4ee5\u4e0b\u5f62\u6210\u7684\u6811\u88ab\u79f0\u4e3a\u8be5\u8282\u70b9\u7684\u5de6\uff08\u53f3\uff09\u5b50\u6811\u3002</li> <li>\u4e8c\u53c9\u6811\u7684\u76f8\u5173\u672f\u8bed\u5305\u62ec\u6839\u8282\u70b9\u3001\u53f6\u8282\u70b9\u3001\u5c42\u3001\u5ea6\u3001\u8fb9\u3001\u9ad8\u5ea6\u548c\u6df1\u5ea6\u7b49\u3002</li> <li>\u4e8c\u53c9\u6811\u7684\u521d\u59cb\u5316\u3001\u8282\u70b9\u63d2\u5165\u548c\u8282\u70b9\u5220\u9664\u64cd\u4f5c\u4e0e\u94fe\u8868\u64cd\u4f5c\u65b9\u6cd5\u7c7b\u4f3c\u3002</li> <li>\u5e38\u89c1\u7684\u4e8c\u53c9\u6811\u7c7b\u578b\u6709\u5b8c\u7f8e\u4e8c\u53c9\u6811\u3001\u5b8c\u5168\u4e8c\u53c9\u6811\u3001\u6ee1\u4e8c\u53c9\u6811\u548c\u5e73\u8861\u4e8c\u53c9\u6811\u3002\u5b8c\u7f8e\u4e8c\u53c9\u6811\u662f\u6700\u7406\u60f3\u7684\u72b6\u6001\uff0c\u800c\u94fe\u8868\u662f\u9000\u5316\u540e\u7684\u6700\u5dee\u72b6\u6001\u3002</li> <li>\u4e8c\u53c9\u6811\u53ef\u4ee5\u7528\u6570\u7ec4\u8868\u793a\uff0c\u65b9\u6cd5\u662f\u5c06\u8282\u70b9\u503c\u548c\u7a7a\u4f4d\u6309\u5c42\u5e8f\u904d\u5386\u987a\u5e8f\u6392\u5217\uff0c\u5e76\u6839\u636e\u7236\u8282\u70b9\u4e0e\u5b50\u8282\u70b9\u4e4b\u95f4\u7684\u7d22\u5f15\u6620\u5c04\u5173\u7cfb\u6765\u5b9e\u73b0\u6307\u9488\u3002</li> <li>\u4e8c\u53c9\u6811\u7684\u5c42\u5e8f\u904d\u5386\u662f\u4e00\u79cd\u5e7f\u5ea6\u4f18\u5148\u641c\u7d22\u65b9\u6cd5\uff0c\u5b83\u4f53\u73b0\u4e86\u201c\u4e00\u5708\u4e00\u5708\u5411\u5916\u201d\u7684\u5206\u5c42\u904d\u5386\u65b9\u5f0f\uff0c\u901a\u5e38\u901a\u8fc7\u961f\u5217\u6765\u5b9e\u73b0\u3002</li> <li>\u524d\u5e8f\u3001\u4e2d\u5e8f\u3001\u540e\u5e8f\u904d\u5386\u7686\u5c5e\u4e8e\u6df1\u5ea6\u4f18\u5148\u641c\u7d22\uff0c\u5b83\u4eec\u4f53\u73b0\u4e86\u201c\u8d70\u5230\u5c3d\u5934\uff0c\u518d\u56de\u5934\u7ee7\u7eed\u201d\u7684\u56de\u6eaf\u904d\u5386\u65b9\u5f0f\uff0c\u901a\u5e38\u4f7f\u7528\u9012\u5f52\u6765\u5b9e\u73b0\u3002</li> <li>\u4e8c\u53c9\u641c\u7d22\u6811\u662f\u4e00\u79cd\u9ad8\u6548\u7684\u5143\u7d20\u67e5\u627e\u6570\u636e\u7ed3\u6784\uff0c\u5176\u67e5\u627e\u3001\u63d2\u5165\u548c\u5220\u9664\u64cd\u4f5c\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u5747\u4e3a \\(O(\\log n)\\) \u3002\u5f53\u4e8c\u53c9\u641c\u7d22\u6811\u9000\u5316\u4e3a\u94fe\u8868\u65f6\uff0c\u5404\u9879\u65f6\u95f4\u590d\u6742\u5ea6\u4f1a\u52a3\u5316\u81f3 \\(O(n)\\) \u3002</li> <li>AVL \u6811\uff0c\u4e5f\u79f0\u4e3a\u5e73\u8861\u4e8c\u53c9\u641c\u7d22\u6811\uff0c\u5b83\u901a\u8fc7\u65cb\u8f6c\u64cd\u4f5c\uff0c\u786e\u4fdd\u5728\u4e0d\u65ad\u63d2\u5165\u548c\u5220\u9664\u8282\u70b9\u540e\uff0c\u6811\u4ecd\u7136\u4fdd\u6301\u5e73\u8861\u3002</li> <li>AVL \u6811\u7684\u65cb\u8f6c\u64cd\u4f5c\u5305\u62ec\u53f3\u65cb\u3001\u5de6\u65cb\u3001\u5148\u53f3\u65cb\u518d\u5de6\u65cb\u3001\u5148\u5de6\u65cb\u518d\u53f3\u65cb\u3002\u5728\u63d2\u5165\u6216\u5220\u9664\u8282\u70b9\u540e\uff0cAVL \u6811\u4f1a\u4ece\u5e95\u5411\u9876\u6267\u884c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4f7f\u6811\u91cd\u65b0\u6062\u590d\u5e73\u8861\u3002</li> </ul>"}]}
\ No newline at end of file
diff --git a/sitemap.xml b/sitemap.xml
index 11868b592..1f921c2e3 100644
--- a/sitemap.xml
+++ b/sitemap.xml
@@ -2,382 +2,382 @@
 <urlset xmlns="http://www.sitemaps.org/schemas/sitemap/0.9">
     <url>
          <loc>https://www.hello-algo.com/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_appendix/contribution/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_appendix/installation/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_array_and_linkedlist/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_array_and_linkedlist/array/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_array_and_linkedlist/linked_list/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_array_and_linkedlist/list/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_array_and_linkedlist/summary/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_backtracking/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_backtracking/backtracking_algorithm/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_backtracking/n_queens_problem/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_backtracking/permutations_problem/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_computational_complexity/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_computational_complexity/performance_evaluation/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_computational_complexity/space_complexity/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_computational_complexity/summary/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_computational_complexity/time_complexity/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_data_structure/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_data_structure/basic_data_types/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_data_structure/character_encoding/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_data_structure/classification_of_data_structure/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_data_structure/number_encoding/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_data_structure/summary/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_graph/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_graph/graph/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_graph/graph_operations/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_graph/graph_traversal/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_graph/summary/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_hashing/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_hashing/hash_collision/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_hashing/hash_map/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_hashing/summary/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_heap/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_heap/build_heap/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_heap/heap/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_heap/summary/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_heap/top_k/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_introduction/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_introduction/algorithms_are_everywhere/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_introduction/summary/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_introduction/what_is_dsa/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_preface/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_preface/about_the_book/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_preface/suggestions/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_preface/summary/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_reference/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_searching/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_searching/binary_search/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_searching/binary_search_edge/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_searching/replace_linear_by_hashing/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_searching/searching_algorithm_revisited/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_searching/summary/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_sorting/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_sorting/bubble_sort/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_sorting/bucket_sort/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_sorting/counting_sort/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_sorting/heap_sort/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_sorting/insertion_sort/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_sorting/merge_sort/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_sorting/quick_sort/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_sorting/radix_sort/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_sorting/selection_sort/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_sorting/sorting_algorithm/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_sorting/summary/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_stack_and_queue/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_stack_and_queue/deque/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_stack_and_queue/queue/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_stack_and_queue/stack/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_stack_and_queue/summary/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_tree/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_tree/array_representation_of_tree/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_tree/avl_tree/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_tree/binary_search_tree/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_tree/binary_tree/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_tree/binary_tree_traversal/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
     <url>
          <loc>https://www.hello-algo.com/chapter_tree/summary/</loc>
-         <lastmod>2023-06-13</lastmod>
+         <lastmod>2023-06-14</lastmod>
          <changefreq>daily</changefreq>
     </url>
 </urlset>
\ No newline at end of file
diff --git a/sitemap.xml.gz b/sitemap.xml.gz
index 38d42916a94d3e91087318d2495049d16e580de1..f681eeaa4d9862205f0a31f476519b401a3cf3e3 100644
GIT binary patch
delta 241
zcmV<N01p5A1^WemABzYG>;H*l0{?SqbY*Q}a4vXlYyj1o&63+741n+Z6q(!;XSbbB
z+exywK0$kCWUSasFgQr$=j{uQH$R6x^wL2-1W*{}1B8%(_4~QEvm*vF-fiZu%hh~_
zPW#5Vb~FF;``6<8{C)efj=>W0ELC>2nRm>?&#F3|PD?UDj6Dpr^r5Xtcd0<tB&=4;
zAM@?YEPc6wYi|73*6VF<g{EdYwAL@cwtlI7U#+WL;jumt_rBS_t=_&YR^Jw{Uy;C>
r4YV&bK<b6`8IfS*KZTQK0UrS)lZF8}0S~jk0W<*!#_PMcH#GnNRx5ie

delta 241
zcmV<N01p5A1^WemABzYGV9JPO0{?SqbY*Q}a4vXlYyj1o&5q+B41n+R6jkqSIy2I0
zchz=o`vkjZ<PbMOC6Hp%pSNE~GyOTtVJ|D3Ljf0|4=~0C)*t8I&W;$!c(<9qE?4sz
zI_(?d+RgmW?_Z1W^N;PzItEL~vsBs9X5KLmKdb6=IxWdTF!nIe(ucMp-K7FmldxJX
zf6TWpv-IT#uDS7BTd%jd6`Gpq&|1F$+xn&UeYLJ~g~$3p-1}zxwt9PCtiCN?-;uzX
r4YDsZK<b6`8IfS*zl4)!0UrS~lZF8}0Z+5P0W<*!@IA?iH#GnN(nxq%