2023-06-22 00:23:01 +08:00
<!doctype html>
< html lang = "zh" class = "no-js" >
< head >
< meta charset = "utf-8" >
< meta name = "viewport" content = "width=device-width,initial-scale=1" >
< meta name = "description" content = "动画图解、一键运行的数据结构与算法教程" >
< meta name = "author" content = "Krahets" >
< link rel = "canonical" href = "https://www.hello-algo.com/chapter_backtracking/summary/" >
< link rel = "prev" href = "../n_queens_problem/" >
2023-06-30 04:33:52 +08:00
< link rel = "next" href = "../../chapter_dynamic_programming/" >
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< link rel = "icon" href = "../../assets/images/favicon.png" >
2023-09-29 22:06:02 +08:00
< meta name = "generator" content = "mkdocs-1.5.3, mkdocs-material-9.4.1" >
2023-06-22 00:23:01 +08:00
2023-08-19 22:07:40 +08:00
< title > 13.5 < / title >
2023-06-22 00:23:01 +08:00
2023-09-29 22:06:02 +08:00
< link rel = "stylesheet" href = "../../assets/stylesheets/main.72749a73.min.css" >
2023-06-22 00:23:01 +08:00
2023-09-24 17:12:06 +08:00
< link rel = "stylesheet" href = "../../assets/stylesheets/palette.a5377069.min.css" >
2023-06-22 00:23:01 +08:00
2023-09-24 17:12:06 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< link rel = "preconnect" href = "https://fonts.gstatic.com" crossorigin >
< link rel = "stylesheet" href = "https://fonts.googleapis.com/css?family=Noto+Sans+SC:300,300i,400,400i,700,700i%7CFira+Code:400,400i,700,700i&display=fallback" >
< style > : root { --md-text-font : "Noto Sans SC" ; --md-code-font : "Fira Code" } < / style >
< link rel = "stylesheet" href = "../../stylesheets/extra.css" >
< script > _ _md _scope = new URL ( "../.." , location ) , _ _md _hash = e => [ ... e ] . reduce ( ( e , _ ) => ( e << 5 ) - e + _ . charCodeAt ( 0 ) , 0 ) , _ _md _get = ( e , _ = localStorage , t = _ _md _scope ) => JSON . parse ( _ . getItem ( t . pathname + "." + e ) ) , _ _md _set = ( e , _ , t = localStorage , a = _ _md _scope ) => { try { t . setItem ( a . pathname + "." + e , JSON . stringify ( _ ) ) } catch ( e ) { } } < / script >
2023-09-22 13:08:10 +08:00
< link href = "../../assets/stylesheets/glightbox.min.css" rel = "stylesheet" / > < style >
html.glightbox-open { overflow: initial; height: 100%; }
.gslide-title { margin-top: 0px; user-select: text; }
.gslide-desc { color: #666; user-select: text; }
.gslide-image img { background: white; }
.gscrollbar-fixer { padding-right: 15px; }
.gdesc-inner { font-size: 0.75rem; }
body[data-md-color-scheme="slate"] .gdesc-inner { background: var(--md-default-bg-color);}
body[data-md-color-scheme="slate"] .gslide-title { color: var(--md-default-fg-color);}
body[data-md-color-scheme="slate"] .gslide-desc { color: var(--md-default-fg-color);}
< / style > < script src = "../../assets/javascripts/glightbox.min.js" > < / script > < / head >
2023-06-22 00:23:01 +08:00
< body dir = "ltr" data-md-color-scheme = "default" data-md-color-primary = "white" data-md-color-accent = "indigo" >
< script > var palette = _ _md _get ( "__palette" ) ; if ( palette && "object" == typeof palette . color ) for ( var key of Object . keys ( palette . color ) ) document . body . setAttribute ( "data-md-color-" + key , palette . color [ key ] ) < / script >
< input class = "md-toggle" data-md-toggle = "drawer" type = "checkbox" id = "__drawer" autocomplete = "off" >
< input class = "md-toggle" data-md-toggle = "search" type = "checkbox" id = "__search" autocomplete = "off" >
< label class = "md-overlay" for = "__drawer" > < / label >
< div data-md-component = "skip" >
2023-07-16 04:19:01 +08:00
< a href = "#135" class = "md-skip" >
2023-06-22 00:23:01 +08:00
跳转至
< / a >
< / div >
< div data-md-component = "announce" >
< / div >
< header class = "md-header md-header--shadow" data-md-component = "header" >
< nav class = "md-header__inner md-grid" aria-label = "页眉" >
< a href = "../.." title = "Hello 算法" class = "md-header__button md-logo" aria-label = "Hello 算法" data-md-component = "logo" >
< img src = "../../assets/images/logo.png" alt = "logo" >
< / a >
< label class = "md-header__button md-icon" for = "__drawer" >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M3 6h18v2H3V6m0 5h18v2H3v-2m0 5h18v2H3v-2Z" / > < / svg >
< / label >
< div class = "md-header__title" data-md-component = "header-title" >
< div class = "md-header__ellipsis" >
< div class = "md-header__topic" >
< span class = "md-ellipsis" >
Hello 算法
< / span >
< / div >
< div class = "md-header__topic" data-md-component = "header-topic" >
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
13.5 小结
2023-06-22 00:23:01 +08:00
< / span >
< / div >
< / div >
< / div >
< form class = "md-header__option" data-md-component = "palette" >
2023-09-24 17:12:06 +08:00
< input class = "md-option" data-md-color-media = "" data-md-color-scheme = "default" data-md-color-primary = "white" data-md-color-accent = "indigo" aria-label = "Switch to dark mode" type = "radio" name = "__palette" id = "__palette_1" >
< label class = "md-header__button md-icon" title = "Switch to dark mode" for = "__palette_2" hidden >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M7.5 2c-1.79 1.15-3 3.18-3 5.5s1.21 4.35 3.03 5.5C4.46 13 2 10.54 2 7.5A5.5 5.5 0 0 1 7.5 2m11.57 1.5 1.43 1.43L4.93 20.5 3.5 19.07 19.07 3.5m-6.18 2.43L11.41 5 9.97 6l.42-1.7L9 3.24l1.75-.12.58-1.65L12 3.1l1.73.03-1.35 1.13.51 1.67m-3.3 3.61-1.16-.73-1.12.78.34-1.32-1.09-.83 1.36-.09.45-1.29.51 1.27 1.36.03-1.05.87.4 1.31M19 13.5a5.5 5.5 0 0 1-5.5 5.5c-1.22 0-2.35-.4-3.26-1.07l7.69-7.69c.67.91 1.07 2.04 1.07 3.26m-4.4 6.58 2.77-1.15-.24 3.35-2.53-2.2m4.33-2.7 1.15-2.77 2.2 2.54-3.35.23m1.15-4.96-1.14-2.78 3.34.24-2.2 2.54M9.63 18.93l2.77 1.15-2.53 2.19-.24-3.34Z" / > < / svg >
< / label >
< input class = "md-option" data-md-color-media = "" data-md-color-scheme = "slate" data-md-color-primary = "grey" data-md-color-accent = "indigo" aria-label = "Switch to light mode" type = "radio" name = "__palette" id = "__palette_2" >
< label class = "md-header__button md-icon" title = "Switch to light mode" for = "__palette_1" hidden >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M7.5 2c-1.79 1.15-3 3.18-3 5.5s1.21 4.35 3.03 5.5C4.46 13 2 10.54 2 7.5A5.5 5.5 0 0 1 7.5 2m11.57 1.5 1.43 1.43L4.93 20.5 3.5 19.07 19.07 3.5m-6.18 2.43L11.41 5 9.97 6l.42-1.7L9 3.24l1.75-.12.58-1.65L12 3.1l1.73.03-1.35 1.13.51 1.67m-3.3 3.61-1.16-.73-1.12.78.34-1.32-1.09-.83 1.36-.09.45-1.29.51 1.27 1.36.03-1.05.87.4 1.31M19 13.5a5.5 5.5 0 0 1-5.5 5.5c-1.22 0-2.35-.4-3.26-1.07l7.69-7.69c.67.91 1.07 2.04 1.07 3.26m-4.4 6.58 2.77-1.15-.24 3.35-2.53-2.2m4.33-2.7 1.15-2.77 2.2 2.54-3.35.23m1.15-4.96-1.14-2.78 3.34.24-2.2 2.54M9.63 18.93l2.77 1.15-2.53 2.19-.24-3.34Z" / > < / svg >
< / label >
< / form >
2023-06-22 00:23:01 +08:00
2023-10-06 13:31:31 +08:00
< div class = "md-header__option" >
< div class = "md-select" >
< button class = "md-header__button md-icon" aria-label = "选择当前语言" >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "m12.87 15.07-2.54-2.51.03-.03A17.52 17.52 0 0 0 14.07 6H17V4h-7V2H8v2H1v2h11.17C11.5 7.92 10.44 9.75 9 11.35 8.07 10.32 7.3 9.19 6.69 8h-2c.73 1.63 1.73 3.17 2.98 4.56l-5.09 5.02L4 19l5-5 3.11 3.11.76-2.04M18.5 10h-2L12 22h2l1.12-3h4.75L21 22h2l-4.5-12m-2.62 7 1.62-4.33L19.12 17h-3.24Z" / > < / svg >
< / button >
< div class = "md-select__inner" >
< ul class = "md-select__list" >
< li class = "md-select__item" >
< a href = "/" hreflang = "zh" class = "md-select__link" >
中文
< / a >
< / li >
< / ul >
< / div >
< / div >
< / div >
2023-06-22 00:23:01 +08:00
< label class = "md-header__button md-icon" for = "__search" >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M9.5 3A6.5 6.5 0 0 1 16 9.5c0 1.61-.59 3.09-1.56 4.23l.27.27h.79l5 5-1.5 1.5-5-5v-.79l-.27-.27A6.516 6.516 0 0 1 9.5 16 6.5 6.5 0 0 1 3 9.5 6.5 6.5 0 0 1 9.5 3m0 2C7 5 5 7 5 9.5S7 14 9.5 14 14 12 14 9.5 12 5 9.5 5Z" / > < / svg >
< / label >
< div class = "md-search" data-md-component = "search" role = "dialog" >
< label class = "md-search__overlay" for = "__search" > < / label >
< div class = "md-search__inner" role = "search" >
< form class = "md-search__form" name = "search" >
< input type = "text" class = "md-search__input" name = "query" aria-label = "搜索" placeholder = "搜索" autocapitalize = "off" autocorrect = "off" autocomplete = "off" spellcheck = "false" data-md-component = "search-query" required >
< label class = "md-search__icon md-icon" for = "__search" >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M9.5 3A6.5 6.5 0 0 1 16 9.5c0 1.61-.59 3.09-1.56 4.23l.27.27h.79l5 5-1.5 1.5-5-5v-.79l-.27-.27A6.516 6.516 0 0 1 9.5 16 6.5 6.5 0 0 1 3 9.5 6.5 6.5 0 0 1 9.5 3m0 2C7 5 5 7 5 9.5S7 14 9.5 14 14 12 14 9.5 12 5 9.5 5Z" / > < / svg >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M20 11v2H8l5.5 5.5-1.42 1.42L4.16 12l7.92-7.92L13.5 5.5 8 11h12Z" / > < / svg >
< / label >
< nav class = "md-search__options" aria-label = "查找" >
< a href = "javascript:void(0)" class = "md-search__icon md-icon" title = "分享" aria-label = "分享" data-clipboard data-clipboard-text = "" data-md-component = "search-share" tabindex = "-1" >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M18 16.08c-.76 0-1.44.3-1.96.77L8.91 12.7c.05-.23.09-.46.09-.7 0-.24-.04-.47-.09-.7l7.05-4.11c.54.5 1.25.81 2.04.81a3 3 0 0 0 3-3 3 3 0 0 0-3-3 3 3 0 0 0-3 3c0 .24.04.47.09.7L8.04 9.81C7.5 9.31 6.79 9 6 9a3 3 0 0 0-3 3 3 3 0 0 0 3 3c.79 0 1.5-.31 2.04-.81l7.12 4.15c-.05.21-.08.43-.08.66 0 1.61 1.31 2.91 2.92 2.91 1.61 0 2.92-1.3 2.92-2.91A2.92 2.92 0 0 0 18 16.08Z" / > < / svg >
< / a >
< button type = "reset" class = "md-search__icon md-icon" title = "清空当前内容" aria-label = "清空当前内容" tabindex = "-1" >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M19 6.41 17.59 5 12 10.59 6.41 5 5 6.41 10.59 12 5 17.59 6.41 19 12 13.41 17.59 19 19 17.59 13.41 12 19 6.41Z" / > < / svg >
< / button >
< / nav >
< div class = "md-search__suggest" data-md-component = "search-suggest" > < / div >
< / form >
< div class = "md-search__output" >
< div class = "md-search__scrollwrap" data-md-scrollfix >
< div class = "md-search-result" data-md-component = "search-result" >
< div class = "md-search-result__meta" >
正在初始化搜索引擎
< / div >
< ol class = "md-search-result__list" role = "presentation" > < / ol >
< / div >
< / div >
< / div >
< / div >
< / div >
< div class = "md-header__source" >
< a href = "https://github.com/krahets/hello-algo" title = "前往仓库" class = "md-source" data-md-component = "source" >
< div class = "md-source__icon md-icon" >
2023-09-24 17:12:06 +08:00
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 496 512" > <!-- ! Font Awesome Free 6.4.2 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc. --> < path d = "M165.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6zm-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3zm44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9zM244.8 8C106.1 8 0 113.3 0 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C428.2 457.8 496 362.9 496 252 496 113.3 383.5 8 244.8 8zM97.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1zm-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7zm32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1zm-11.4-14.7c-1.6 1-1.6 3.6 0 5.9 1.6 2.3 4.3 3.3 5.6 2.3 1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2z" / > < / svg >
2023-06-22 00:23:01 +08:00
< / div >
< div class = "md-source__repository" >
krahets/hello-algo
< / div >
< / a >
< / div >
< / nav >
< / header >
< div class = "md-container" data-md-component = "container" >
< main class = "md-main" data-md-component = "main" >
< div class = "md-main__inner md-grid" >
< div class = "md-sidebar md-sidebar--primary" data-md-component = "sidebar" data-md-type = "navigation" >
< div class = "md-sidebar__scrollwrap" >
< div class = "md-sidebar__inner" >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< nav class = "md-nav md-nav--primary" aria-label = "导航栏" data-md-level = "0" >
< label class = "md-nav__title" for = "__drawer" >
< a href = "../.." title = "Hello 算法" class = "md-nav__button md-logo" aria-label = "Hello 算法" data-md-component = "logo" >
< img src = "../../assets/images/logo.png" alt = "logo" >
< / a >
Hello 算法
< / label >
< div class = "md-nav__source" >
< a href = "https://github.com/krahets/hello-algo" title = "前往仓库" class = "md-source" data-md-component = "source" >
< div class = "md-source__icon md-icon" >
2023-09-24 17:12:06 +08:00
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 496 512" > <!-- ! Font Awesome Free 6.4.2 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc. --> < path d = "M165.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6zm-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3zm44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9zM244.8 8C106.1 8 0 113.3 0 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C428.2 457.8 496 362.9 496 252 496 113.3 383.5 8 244.8 8zM97.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1zm-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7zm32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1zm-11.4-14.7c-1.6 1-1.6 3.6 0 5.9 1.6 2.3 4.3 3.3 5.6 2.3 1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2z" / > < / svg >
2023-06-22 00:23:01 +08:00
< / div >
< div class = "md-source__repository" >
krahets/hello-algo
< / div >
< / a >
< / div >
< ul class = "md-nav__list" data-md-scrollfix >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
< li class = "md-nav__item md-nav__item--nested" >
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-09-29 22:06:02 +08:00
2023-07-17 17:51:12 +08:00
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_1" >
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_preface/" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M21 4H3a2 2 0 0 0-2 2v13a2 2 0 0 0 2 2h18a2 2 0 0 0 2-2V6a2 2 0 0 0-2-2M3 19V6h8v13H3m18 0h-8V6h8v13m-7-9.5h6V11h-6V9.5m0 2.5h6v1.5h-6V12m0 2.5h6V16h-6v-1.5Z" / > < / svg >
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
第 0 章 前言
2023-07-17 17:51:12 +08:00
< / span >
< / a >
2023-06-22 00:23:01 +08:00
2023-09-29 22:06:02 +08:00
< label class = "md-nav__link " for = "__nav_1" >
2023-07-17 17:51:12 +08:00
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_1_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_1" >
< span class = "md-nav__icon md-icon" > < / span >
2023-08-19 22:07:40 +08:00
第 0 章 前言
2023-07-17 17:51:12 +08:00
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_preface/about_the_book/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
0.1 关于本书
2023-07-17 17:51:12 +08:00
< / span >
2023-06-22 00:23:01 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_preface/suggestions/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
0.2 如何使用本书
2023-07-17 17:51:12 +08:00
< / span >
2023-06-22 00:23:01 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_preface/summary/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
0.3 小结
2023-07-17 17:51:12 +08:00
< / span >
2023-06-22 00:23:01 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
< / ul >
< / nav >
2023-06-22 00:23:01 +08:00
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
< li class = "md-nav__item md-nav__item--nested" >
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-09-29 22:06:02 +08:00
2023-07-17 17:51:12 +08:00
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_2" >
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_introduction/" class = "md-nav__link " >
2023-07-19 16:10:17 +08:00
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2m0 16H5V5h14v14M6.2 7.7h5v1.5h-5V7.7m6.8 8.1h5v1.5h-5v-1.5m0-2.6h5v1.5h-5v-1.5M8 18h1.5v-2h2v-1.5h-2v-2H8v2H6V16h2v2m6.1-7.1 1.4-1.4 1.4 1.4 1.1-1-1.4-1.4L18 7.1 16.9 6l-1.4 1.4L14.1 6 13 7.1l1.4 1.4L13 9.9l1.1 1Z" / > < / svg >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
第 1 章 初识算法
2023-07-17 17:51:12 +08:00
< / span >
< / a >
2023-06-22 00:23:01 +08:00
2023-09-29 22:06:02 +08:00
< label class = "md-nav__link " for = "__nav_2" >
2023-07-17 17:51:12 +08:00
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_2_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_2" >
< span class = "md-nav__icon md-icon" > < / span >
2023-08-19 22:07:40 +08:00
第 1 章 初识算法
2023-07-17 17:51:12 +08:00
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_introduction/algorithms_are_everywhere/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
1.1 算法无处不在
2023-07-17 17:51:12 +08:00
< / span >
2023-06-22 00:23:01 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_introduction/what_is_dsa/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
1.2 算法是什么
2023-07-17 17:51:12 +08:00
< / span >
2023-06-22 00:23:01 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_introduction/summary/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
1.3 小结
2023-07-17 17:51:12 +08:00
< / span >
2023-06-22 00:23:01 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
< / ul >
< / nav >
2023-06-22 00:23:01 +08:00
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-08-24 17:47:31 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
< li class = "md-nav__item md-nav__item--nested" >
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-09-29 22:06:02 +08:00
2023-07-17 17:51:12 +08:00
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_3" >
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_computational_complexity/" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z" / > < / svg >
< span class = "md-ellipsis" >
2023-08-28 04:36:05 +08:00
第 2 章 复杂度分析
2023-07-17 17:51:12 +08:00
< / span >
< / a >
2023-06-22 00:23:01 +08:00
2023-09-29 22:06:02 +08:00
< label class = "md-nav__link " for = "__nav_3" >
2023-07-17 17:51:12 +08:00
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_3_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_3" >
< span class = "md-nav__icon md-icon" > < / span >
2023-08-28 04:36:05 +08:00
第 2 章 复杂度分析
2023-07-17 17:51:12 +08:00
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_computational_complexity/performance_evaluation/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
2.1 算法效率评估
2023-07-17 17:51:12 +08:00
< / span >
2023-06-22 00:23:01 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_computational_complexity/iteration_and_recursion/" class = "md-nav__link" >
< span class = "md-ellipsis" >
2.2 迭代与递归
< / span >
< / a >
< / li >
2023-06-22 00:23:01 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_computational_complexity/time_complexity/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-24 17:47:31 +08:00
2.3 时间复杂度
2023-07-17 17:51:12 +08:00
< / span >
2023-06-22 00:23:01 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_computational_complexity/space_complexity/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-24 17:47:31 +08:00
2.4 空间复杂度
2023-07-17 17:51:12 +08:00
< / span >
2023-06-22 00:23:01 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_computational_complexity/summary/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-24 17:47:31 +08:00
2.5 小结
2023-07-17 17:51:12 +08:00
< / span >
2023-06-22 00:23:01 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
< / ul >
< / nav >
2023-06-22 00:23:01 +08:00
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
< li class = "md-nav__item md-nav__item--nested" >
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-09-29 22:06:02 +08:00
2023-07-17 17:51:12 +08:00
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_4" >
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_data_structure/" class = "md-nav__link " >
2023-06-22 00:23:01 +08:00
2023-07-19 16:10:17 +08:00
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z" / > < / svg >
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
第 3 章 数据结构
2023-07-17 17:51:12 +08:00
< / span >
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
< / a >
2023-06-22 00:23:01 +08:00
2023-09-29 22:06:02 +08:00
< label class = "md-nav__link " for = "__nav_4" >
2023-07-17 17:51:12 +08:00
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_4_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_4" >
< span class = "md-nav__icon md-icon" > < / span >
2023-08-19 22:07:40 +08:00
第 3 章 数据结构
2023-07-17 17:51:12 +08:00
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< li class = "md-nav__item" >
2023-07-17 17:51:12 +08:00
< a href = "../../chapter_data_structure/classification_of_data_structure/" class = "md-nav__link" >
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
3.1 数据结构分类
2023-07-17 17:51:12 +08:00
< / span >
2023-06-22 00:23:01 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_data_structure/basic_data_types/" class = "md-nav__link" >
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
3.2 基本数据类型
2023-07-17 17:51:12 +08:00
< / span >
< / a >
< / li >
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_data_structure/number_encoding/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
3.3 数字编码 *
2023-07-17 17:51:12 +08:00
< / span >
2023-06-22 00:23:01 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_data_structure/character_encoding/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
3.4 字符编码 *
2023-07-17 17:51:12 +08:00
< / span >
2023-06-22 00:23:01 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_data_structure/summary/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
3.5 小结
2023-07-17 17:51:12 +08:00
< / span >
2023-06-22 00:23:01 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
< / ul >
< / nav >
2023-06-22 00:23:01 +08:00
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
< li class = "md-nav__item md-nav__item--nested" >
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-09-29 22:06:02 +08:00
2023-07-17 17:51:12 +08:00
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_5" >
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_array_and_linkedlist/" class = "md-nav__link " >
2023-07-19 16:10:17 +08:00
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z" / > < / svg >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
第 4 章 数组与链表
2023-07-17 17:51:12 +08:00
< / span >
< / a >
2023-06-22 00:23:01 +08:00
2023-09-29 22:06:02 +08:00
< label class = "md-nav__link " for = "__nav_5" >
2023-07-17 17:51:12 +08:00
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_5_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_5" >
< span class = "md-nav__icon md-icon" > < / span >
2023-08-19 22:07:40 +08:00
第 4 章 数组与链表
2023-07-17 17:51:12 +08:00
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_array_and_linkedlist/array/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
4.1 数组
2023-07-17 17:51:12 +08:00
< / span >
2023-06-22 00:23:01 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_array_and_linkedlist/linked_list/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
4.2 链表
2023-07-17 17:51:12 +08:00
< / span >
2023-06-22 00:23:01 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_array_and_linkedlist/list/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
4.3 列表
2023-07-17 17:51:12 +08:00
< / span >
2023-06-22 00:23:01 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_array_and_linkedlist/summary/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
4.4 小结
2023-07-17 17:51:12 +08:00
< / span >
2023-06-22 00:23:01 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
< / ul >
< / nav >
2023-06-22 00:23:01 +08:00
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
< li class = "md-nav__item md-nav__item--nested" >
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-09-29 22:06:02 +08:00
2023-07-17 17:51:12 +08:00
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_6" >
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_stack_and_queue/" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z" / > < / svg >
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
第 5 章 栈与队列
2023-07-17 17:51:12 +08:00
< / span >
< / a >
2023-06-22 00:23:01 +08:00
2023-09-29 22:06:02 +08:00
< label class = "md-nav__link " for = "__nav_6" >
2023-07-17 17:51:12 +08:00
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_6_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_6" >
< span class = "md-nav__icon md-icon" > < / span >
2023-08-19 22:07:40 +08:00
第 5 章 栈与队列
2023-07-17 17:51:12 +08:00
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_stack_and_queue/stack/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
5.1 栈
2023-07-17 17:51:12 +08:00
< / span >
2023-06-22 00:23:01 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_stack_and_queue/queue/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
5.2 队列
2023-07-17 17:51:12 +08:00
< / span >
2023-06-22 00:23:01 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_stack_and_queue/deque/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
5.3 双向队列
2023-07-17 17:51:12 +08:00
< / span >
2023-06-22 00:23:01 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_stack_and_queue/summary/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
5.4 小结
2023-07-17 17:51:12 +08:00
< / span >
2023-06-22 00:23:01 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
< / ul >
< / nav >
2023-06-22 00:23:01 +08:00
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
< li class = "md-nav__item md-nav__item--nested" >
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-09-29 22:06:02 +08:00
2023-07-17 17:51:12 +08:00
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_7" >
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_hashing/" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z" / > < / svg >
< span class = "md-ellipsis" >
2023-08-21 03:56:52 +08:00
第 6 章 哈希表
2023-07-17 17:51:12 +08:00
< / span >
< / a >
2023-06-22 00:23:01 +08:00
2023-09-29 22:06:02 +08:00
< label class = "md-nav__link " for = "__nav_7" >
2023-07-17 17:51:12 +08:00
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_7_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_7" >
< span class = "md-nav__icon md-icon" > < / span >
2023-08-21 03:56:52 +08:00
第 6 章 哈希表
2023-07-17 17:51:12 +08:00
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_hashing/hash_map/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
6.1 哈希表
2023-07-17 17:51:12 +08:00
< / span >
2023-06-22 00:23:01 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_hashing/hash_collision/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
6.2 哈希冲突
2023-07-17 17:51:12 +08:00
< / span >
2023-06-22 00:23:01 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_hashing/hash_algorithm/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
6.3 哈希算法
2023-07-17 17:51:12 +08:00
< / span >
2023-06-22 00:23:01 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_hashing/summary/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
6.4 小结
2023-07-17 17:51:12 +08:00
< / span >
2023-06-22 00:23:01 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
< / ul >
< / nav >
2023-06-22 00:23:01 +08:00
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
< li class = "md-nav__item md-nav__item--nested" >
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-09-29 22:06:02 +08:00
2023-07-17 17:51:12 +08:00
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_8" >
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_tree/" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z" / > < / svg >
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
第 7 章 树
2023-07-17 17:51:12 +08:00
< / span >
< / a >
2023-06-22 00:23:01 +08:00
2023-09-29 22:06:02 +08:00
< label class = "md-nav__link " for = "__nav_8" >
2023-07-17 17:51:12 +08:00
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_8_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_8" >
< span class = "md-nav__icon md-icon" > < / span >
2023-08-19 22:07:40 +08:00
第 7 章 树
2023-07-17 17:51:12 +08:00
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_tree/binary_tree/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
7.1 二叉树
2023-07-17 17:51:12 +08:00
< / span >
2023-06-22 00:23:01 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_tree/binary_tree_traversal/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
7.2 二叉树遍历
2023-07-17 17:51:12 +08:00
< / span >
2023-06-22 00:23:01 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_tree/array_representation_of_tree/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
7.3 二叉树数组表示
2023-07-17 17:51:12 +08:00
< / span >
2023-06-22 00:23:01 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_tree/binary_search_tree/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
7.4 二叉搜索树
2023-07-17 17:51:12 +08:00
< / span >
2023-06-22 00:23:01 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_tree/avl_tree/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
7.5 AVL 树 *
2023-07-17 17:51:12 +08:00
< / span >
2023-06-22 00:23:01 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_tree/summary/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
7.6 小结
2023-07-17 17:51:12 +08:00
< / span >
2023-06-22 00:23:01 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
< / ul >
< / nav >
2023-06-22 00:23:01 +08:00
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
< li class = "md-nav__item md-nav__item--nested" >
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-09-29 22:06:02 +08:00
2023-07-17 17:51:12 +08:00
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_9" >
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_heap/" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z" / > < / svg >
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
第 8 章 堆
2023-07-17 17:51:12 +08:00
< / span >
< / a >
2023-06-22 00:23:01 +08:00
2023-09-29 22:06:02 +08:00
< label class = "md-nav__link " for = "__nav_9" >
2023-07-17 17:51:12 +08:00
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_9_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_9" >
< span class = "md-nav__icon md-icon" > < / span >
2023-08-19 22:07:40 +08:00
第 8 章 堆
2023-07-17 17:51:12 +08:00
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_heap/heap/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
8.1 堆
2023-07-17 17:51:12 +08:00
< / span >
2023-06-22 00:23:01 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_heap/build_heap/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
8.2 建堆操作
2023-07-17 17:51:12 +08:00
< / span >
2023-06-22 00:23:01 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_heap/top_k/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
8.3 Top-K 问题
2023-07-17 17:51:12 +08:00
< / span >
2023-06-22 00:23:01 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_heap/summary/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
8.4 小结
2023-07-17 17:51:12 +08:00
< / span >
2023-06-22 00:23:01 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
< / ul >
< / nav >
2023-06-22 00:23:01 +08:00
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
< li class = "md-nav__item md-nav__item--nested" >
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-09-29 22:06:02 +08:00
2023-07-17 17:51:12 +08:00
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_10" >
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_graph/" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z" / > < / svg >
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
第 9 章 图
2023-07-17 17:51:12 +08:00
< / span >
< / a >
2023-06-22 00:23:01 +08:00
2023-09-29 22:06:02 +08:00
< label class = "md-nav__link " for = "__nav_10" >
2023-07-17 17:51:12 +08:00
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_10_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_10" >
< span class = "md-nav__icon md-icon" > < / span >
2023-08-19 22:07:40 +08:00
第 9 章 图
2023-07-17 17:51:12 +08:00
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_graph/graph/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
9.1 图
2023-07-17 17:51:12 +08:00
< / span >
2023-06-22 00:23:01 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_graph/graph_operations/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
9.2 图基础操作
2023-07-17 17:51:12 +08:00
< / span >
2023-06-22 00:23:01 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_graph/graph_traversal/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
9.3 图的遍历
2023-07-17 17:51:12 +08:00
< / span >
2023-06-22 00:23:01 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_graph/summary/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
9.4 小结
2023-07-17 17:51:12 +08:00
< / span >
2023-06-22 00:23:01 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
< / ul >
< / nav >
2023-06-22 00:23:01 +08:00
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-08-04 05:25:00 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
< li class = "md-nav__item md-nav__item--nested" >
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-09-29 22:06:02 +08:00
2023-07-17 17:51:12 +08:00
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_11" >
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_searching/" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z" / > < / svg >
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
第 10 章 搜索
2023-07-17 17:51:12 +08:00
< / span >
< / a >
2023-06-22 00:23:01 +08:00
2023-09-29 22:06:02 +08:00
< label class = "md-nav__link " for = "__nav_11" >
2023-07-17 17:51:12 +08:00
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_11_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_11" >
< span class = "md-nav__icon md-icon" > < / span >
2023-08-19 22:07:40 +08:00
第 10 章 搜索
2023-07-17 17:51:12 +08:00
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_searching/binary_search/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
10.1 二分查找
2023-07-17 17:51:12 +08:00
< / span >
2023-06-22 00:23:01 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-08-04 05:25:00 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_searching/binary_search_insertion/" class = "md-nav__link" >
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
10.2 二分查找插入点
2023-08-04 05:25:00 +08:00
< / span >
< / a >
< / li >
2023-06-22 00:23:01 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_searching/binary_search_edge/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
10.3 二分查找边界
2023-07-17 17:51:12 +08:00
< / span >
2023-06-22 00:23:01 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_searching/replace_linear_by_hashing/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
10.4 哈希优化策略
2023-07-17 17:51:12 +08:00
< / span >
2023-06-22 00:23:01 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_searching/searching_algorithm_revisited/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
10.5 重识搜索算法
2023-07-17 17:51:12 +08:00
< / span >
2023-06-22 00:23:01 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_searching/summary/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
10.6 小结
2023-07-17 17:51:12 +08:00
< / span >
2023-06-22 00:23:01 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
< / ul >
< / nav >
2023-06-22 00:23:01 +08:00
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
< li class = "md-nav__item md-nav__item--nested" >
2023-06-22 00:23:01 +08:00
2023-09-29 22:06:02 +08:00
2023-07-17 17:51:12 +08:00
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_12" >
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_sorting/" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z" / > < / svg >
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
第 11 章 排序
2023-07-17 17:51:12 +08:00
< / span >
< / a >
2023-09-29 22:06:02 +08:00
< label class = "md-nav__link " for = "__nav_12" >
2023-07-17 17:51:12 +08:00
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_12_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_12" >
< span class = "md-nav__icon md-icon" > < / span >
2023-08-19 22:07:40 +08:00
第 11 章 排序
2023-07-17 17:51:12 +08:00
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_sorting/sorting_algorithm/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
11.1 排序算法
2023-07-17 17:51:12 +08:00
< / span >
2023-06-22 00:23:01 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_sorting/selection_sort/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
11.2 选择排序
2023-07-17 17:51:12 +08:00
< / span >
2023-06-22 00:23:01 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_sorting/bubble_sort/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
11.3 冒泡排序
2023-07-17 17:51:12 +08:00
< / span >
2023-06-22 00:23:01 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_sorting/insertion_sort/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
11.4 插入排序
2023-07-17 17:51:12 +08:00
< / span >
2023-06-22 00:23:01 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_sorting/quick_sort/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
11.5 快速排序
2023-07-17 17:51:12 +08:00
< / span >
2023-06-22 00:23:01 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_sorting/merge_sort/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
11.6 归并排序
2023-07-17 17:51:12 +08:00
< / span >
2023-06-22 00:23:01 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_sorting/heap_sort/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
11.7 堆排序
2023-07-17 17:51:12 +08:00
< / span >
2023-06-22 00:23:01 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_sorting/bucket_sort/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
11.8 桶排序
2023-07-17 17:51:12 +08:00
< / span >
2023-06-22 00:23:01 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_sorting/counting_sort/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
11.9 计数排序
2023-07-17 17:51:12 +08:00
< / span >
2023-06-22 00:23:01 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_sorting/radix_sort/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
11.10 基数排序
2023-07-17 17:51:12 +08:00
< / span >
2023-06-22 00:23:01 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_sorting/summary/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
11.11 小结
2023-07-17 17:51:12 +08:00
< / span >
2023-06-22 00:23:01 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
< / ul >
< / nav >
2023-06-22 00:23:01 +08:00
< / li >
2023-07-16 04:19:01 +08:00
2023-07-17 17:51:12 +08:00
2023-07-16 04:19:01 +08:00
2023-07-17 17:51:12 +08:00
2023-07-16 04:19:01 +08:00
2023-07-17 17:51:12 +08:00
2023-07-16 04:19:01 +08:00
2023-07-17 17:51:12 +08:00
2023-07-17 02:17:51 +08:00
2023-07-17 20:19:46 +08:00
2023-07-17 17:51:12 +08:00
2023-07-17 04:21:02 +08:00
2023-07-16 04:19:01 +08:00
2023-07-17 17:51:12 +08:00
< li class = "md-nav__item md-nav__item--nested" >
2023-07-16 04:19:01 +08:00
2023-07-17 17:51:12 +08:00
2023-09-29 22:06:02 +08:00
2023-07-17 17:51:12 +08:00
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_13" >
2023-07-16 04:19:01 +08:00
2023-07-17 17:51:12 +08:00
< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_divide_and_conquer/" class = "md-nav__link " >
2023-07-19 16:10:17 +08:00
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z" / > < / svg >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
第 12 章 分治
2023-07-17 17:51:12 +08:00
< / span >
< / a >
2023-07-16 04:19:01 +08:00
2023-09-29 22:06:02 +08:00
< label class = "md-nav__link " for = "__nav_13" >
2023-07-17 17:51:12 +08:00
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_13_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_13" >
< span class = "md-nav__icon md-icon" > < / span >
2023-08-19 22:07:40 +08:00
第 12 章 分治
2023-07-17 17:51:12 +08:00
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
2023-07-16 04:19:01 +08:00
2023-07-17 17:51:12 +08:00
2023-07-16 04:19:01 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_divide_and_conquer/divide_and_conquer/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
12.1 分治算法
2023-07-17 17:51:12 +08:00
< / span >
2023-07-16 04:19:01 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-07-16 04:19:01 +08:00
2023-07-17 17:51:12 +08:00
2023-07-16 04:19:01 +08:00
2023-07-17 04:21:02 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_divide_and_conquer/binary_search_recur/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
12.2 分治搜索策略
2023-07-17 17:51:12 +08:00
< / span >
2023-07-17 04:21:02 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-07-17 04:21:02 +08:00
2023-07-17 17:51:12 +08:00
2023-07-17 04:21:02 +08:00
2023-07-16 04:19:01 +08:00
< li class = "md-nav__item" >
2023-07-17 02:17:51 +08:00
< a href = "../../chapter_divide_and_conquer/build_binary_tree_problem/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
12.3 构建树问题
2023-07-17 17:51:12 +08:00
< / span >
2023-07-16 04:19:01 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-07-17 02:17:51 +08:00
2023-07-17 17:51:12 +08:00
2023-07-17 02:17:51 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_divide_and_conquer/hanota_problem/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
12.4 汉诺塔问题
2023-07-17 17:51:12 +08:00
< / span >
2023-07-17 02:17:51 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-07-17 02:17:51 +08:00
2023-07-17 20:19:46 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_divide_and_conquer/summary/" class = "md-nav__link" >
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
12.5 小结
2023-07-17 20:19:46 +08:00
< / span >
< / a >
< / li >
2023-07-17 17:51:12 +08:00
< / ul >
< / nav >
2023-07-16 04:19:01 +08:00
< / li >
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
< li class = "md-nav__item md-nav__item--active md-nav__item--nested" >
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-09-29 22:06:02 +08:00
2023-07-17 17:51:12 +08:00
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_14" checked >
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
< div class = "md-nav__link md-nav__container" >
< a href = "../" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z" / > < / svg >
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
第 13 章 回溯
2023-07-17 17:51:12 +08:00
< / span >
< / a >
2023-06-22 00:23:01 +08:00
2023-09-29 22:06:02 +08:00
< label class = "md-nav__link " for = "__nav_14" >
2023-07-17 17:51:12 +08:00
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_14_label" aria-expanded = "true" >
< label class = "md-nav__title" for = "__nav_14" >
< span class = "md-nav__icon md-icon" > < / span >
2023-08-19 22:07:40 +08:00
第 13 章 回溯
2023-07-17 17:51:12 +08:00
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< li class = "md-nav__item" >
< a href = "../backtracking_algorithm/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
13.1 回溯算法
2023-07-17 17:51:12 +08:00
< / span >
2023-06-22 00:23:01 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< li class = "md-nav__item" >
< a href = "../permutations_problem/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
13.2 全排列问题
2023-07-17 17:51:12 +08:00
< / span >
2023-06-22 00:23:01 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< li class = "md-nav__item" >
< a href = "../subset_sum_problem/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
13.3 子集和问题
2023-07-17 17:51:12 +08:00
< / span >
2023-06-22 00:23:01 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< li class = "md-nav__item" >
< a href = "../n_queens_problem/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
13.4 N 皇后问题
2023-07-17 17:51:12 +08:00
< / span >
2023-06-22 00:23:01 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< li class = "md-nav__item md-nav__item--active" >
< input class = "md-nav__toggle md-toggle" type = "checkbox" id = "__toc" >
2023-08-29 20:57:26 +08:00
< label class = "md-nav__link md-nav__link--active" for = "__toc" >
< span class = "md-ellipsis" >
13.5 小结
< / span >
< span class = "md-nav__icon md-icon" > < / span >
< / label >
2023-06-22 00:23:01 +08:00
< a href = "./" class = "md-nav__link md-nav__link--active" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
13.5 小结
2023-07-17 17:51:12 +08:00
< / span >
2023-06-22 00:23:01 +08:00
< / a >
2023-08-29 20:57:26 +08:00
< nav class = "md-nav md-nav--secondary" aria-label = "目录" >
< label class = "md-nav__title" for = "__toc" >
< span class = "md-nav__icon md-icon" > < / span >
目录
< / label >
< ul class = "md-nav__list" data-md-component = "toc" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "#1" class = "md-nav__link" >
1. 重点回顾
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "#2-q-a" class = "md-nav__link" >
2. Q & A
< / a >
< / li >
< / ul >
< / nav >
2023-06-22 00:23:01 +08:00
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
< / ul >
< / nav >
2023-06-22 00:23:01 +08:00
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-07-01 22:39:28 +08:00
2023-07-17 17:51:12 +08:00
2023-07-06 00:08:29 +08:00
2023-07-17 17:51:12 +08:00
2023-07-07 21:39:04 +08:00
2023-07-17 17:51:12 +08:00
2023-07-11 19:21:38 +08:00
2023-07-17 17:51:12 +08:00
2023-07-14 02:56:32 +08:00
2023-07-17 17:51:12 +08:00
2023-07-13 05:26:03 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
< li class = "md-nav__item md-nav__item--nested" >
2023-06-22 00:23:01 +08:00
2023-06-30 04:33:52 +08:00
2023-07-17 17:51:12 +08:00
2023-09-29 22:06:02 +08:00
2023-07-17 17:51:12 +08:00
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_15" >
2023-06-30 04:33:52 +08:00
2023-07-17 17:51:12 +08:00
< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_dynamic_programming/" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z" / > < / svg >
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
第 14 章 动态规划
2023-07-17 17:51:12 +08:00
< / span >
< / a >
2023-06-30 04:33:52 +08:00
2023-09-29 22:06:02 +08:00
< label class = "md-nav__link " for = "__nav_15" >
2023-07-17 17:51:12 +08:00
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_15_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_15" >
< span class = "md-nav__icon md-icon" > < / span >
2023-08-19 22:07:40 +08:00
第 14 章 动态规划
2023-07-17 17:51:12 +08:00
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
2023-06-30 04:33:52 +08:00
2023-07-17 17:51:12 +08:00
2023-06-30 04:33:52 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_dynamic_programming/intro_to_dynamic_programming/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
14.1 初探动态规划
2023-07-17 17:51:12 +08:00
< / span >
2023-07-01 22:39:28 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-07-01 22:39:28 +08:00
2023-07-17 17:51:12 +08:00
2023-07-01 22:39:28 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_dynamic_programming/dp_problem_features/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
14.2 DP 问题特性
2023-07-17 17:51:12 +08:00
< / span >
2023-06-30 04:33:52 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-07-06 00:08:29 +08:00
2023-07-17 17:51:12 +08:00
2023-07-06 00:08:29 +08:00
2023-07-07 21:39:04 +08:00
< li class = "md-nav__item" >
2023-07-09 03:02:15 +08:00
< a href = "../../chapter_dynamic_programming/dp_solution_pipeline/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
14.3 DP 解题思路
2023-07-17 17:51:12 +08:00
< / span >
2023-07-07 21:39:04 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-07-07 21:39:04 +08:00
2023-07-17 17:51:12 +08:00
2023-07-07 21:39:04 +08:00
2023-07-06 00:08:29 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_dynamic_programming/knapsack_problem/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
14.4 0-1 背包问题
2023-07-17 17:51:12 +08:00
< / span >
2023-07-06 00:08:29 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-07-11 19:21:38 +08:00
2023-07-17 17:51:12 +08:00
2023-07-11 19:21:38 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_dynamic_programming/unbounded_knapsack_problem/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
14.5 完全背包问题
2023-07-17 17:51:12 +08:00
< / span >
2023-07-11 19:21:38 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-07-13 05:26:03 +08:00
2023-07-17 17:51:12 +08:00
2023-07-13 05:26:03 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_dynamic_programming/edit_distance_problem/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
14.6 编辑距离问题
2023-07-17 17:51:12 +08:00
< / span >
2023-07-13 05:26:03 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-07-14 02:56:32 +08:00
2023-07-17 17:51:12 +08:00
2023-07-14 02:56:32 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_dynamic_programming/summary/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
14.7 小结
2023-07-17 17:51:12 +08:00
< / span >
2023-07-14 02:56:32 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-07-14 02:56:32 +08:00
2023-07-17 17:51:12 +08:00
< / ul >
< / nav >
2023-06-30 04:33:52 +08:00
< / li >
2023-07-17 17:51:12 +08:00
2023-06-30 04:33:52 +08:00
2023-07-17 17:51:12 +08:00
2023-06-30 04:33:52 +08:00
2023-07-17 17:51:12 +08:00
2023-07-21 21:53:15 +08:00
2023-07-21 22:50:40 +08:00
2023-07-21 15:14:51 +08:00
2023-06-30 04:33:52 +08:00
2023-07-17 17:51:12 +08:00
< li class = "md-nav__item md-nav__item--nested" >
2023-06-30 04:33:52 +08:00
2023-07-17 17:51:12 +08:00
2023-09-29 22:06:02 +08:00
2023-07-17 17:51:12 +08:00
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_16" >
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
< div class = "md-nav__link md-nav__container" >
2023-07-20 18:24:35 +08:00
< a href = "../../chapter_greedy/" class = "md-nav__link " >
2023-07-17 17:51:12 +08:00
2023-07-20 18:24:35 +08:00
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z" / > < / svg >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
第 15 章 贪心
2023-07-17 17:51:12 +08:00
< / span >
< / a >
2023-09-29 22:06:02 +08:00
< label class = "md-nav__link " for = "__nav_16" >
2023-07-17 17:51:12 +08:00
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_16_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_16" >
< span class = "md-nav__icon md-icon" > < / span >
2023-08-19 22:07:40 +08:00
第 15 章 贪心
2023-07-20 18:24:35 +08:00
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "../../chapter_greedy/greedy_algorithm/" class = "md-nav__link" >
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
15.1 贪心算法
2023-07-20 18:24:35 +08:00
< / span >
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_greedy/fractional_knapsack_problem/" class = "md-nav__link" >
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
15.2 分数背包问题
2023-07-20 18:24:35 +08:00
< / span >
< / a >
< / li >
2023-07-21 15:14:51 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_greedy/max_capacity_problem/" class = "md-nav__link" >
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
15.3 最大容量问题
2023-07-21 15:14:51 +08:00
< / span >
< / a >
< / li >
2023-07-21 21:53:15 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_greedy/max_product_cutting_problem/" class = "md-nav__link" >
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
15.4 最大切分乘积问题
2023-07-21 21:53:15 +08:00
< / span >
< / a >
< / li >
2023-07-21 22:50:40 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_greedy/summary/" class = "md-nav__link" >
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
15.5 小结
2023-07-21 22:50:40 +08:00
< / span >
< / a >
< / li >
2023-07-20 18:24:35 +08:00
< / ul >
< / nav >
< / li >
2023-10-30 04:59:19 +08:00
2023-07-20 18:24:35 +08:00
< li class = "md-nav__item md-nav__item--nested" >
2023-09-29 22:06:02 +08:00
2023-07-20 18:24:35 +08:00
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_17" >
< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_appendix/" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M11 18h2v-2h-2v2m1-16A10 10 0 0 0 2 12a10 10 0 0 0 10 10 10 10 0 0 0 10-10A10 10 0 0 0 12 2m0 18c-4.41 0-8-3.59-8-8s3.59-8 8-8 8 3.59 8 8-3.59 8-8 8m0-14a4 4 0 0 0-4 4h2a2 2 0 0 1 2-2 2 2 0 0 1 2 2c0 2-3 1.75-3 5h2c0-2.25 3-2.5 3-5a4 4 0 0 0-4-4Z" / > < / svg >
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
第 16 章 附录
2023-07-20 18:24:35 +08:00
< / span >
< / a >
2023-09-29 22:06:02 +08:00
< label class = "md-nav__link " for = "__nav_17" >
2023-07-20 18:24:35 +08:00
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_17_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_17" >
< span class = "md-nav__icon md-icon" > < / span >
2023-08-19 22:07:40 +08:00
第 16 章 附录
2023-07-17 17:51:12 +08:00
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_appendix/installation/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
16.1 编程环境安装
2023-07-17 17:51:12 +08:00
< / span >
2023-06-22 00:23:01 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_appendix/contribution/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-08-19 22:07:40 +08:00
16.2 一起参与创作
2023-07-17 17:51:12 +08:00
< / span >
2023-06-22 00:23:01 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-10-30 04:59:19 +08:00
< li class = "md-nav__item" >
2023-10-30 05:31:23 +08:00
< a href = "../../chapter_appendix/terminology/" class = "md-nav__link" >
2023-10-30 04:59:19 +08:00
< span class = "md-ellipsis" >
16.3 术语表
< / span >
< span class = "md-status md-status--new" title = "最近添加" >
< / span >
< / a >
< / li >
2023-07-17 17:51:12 +08:00
< / ul >
< / nav >
2023-06-22 00:23:01 +08:00
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
< li class = "md-nav__item md-nav__item--nested" >
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-09-29 22:06:02 +08:00
2023-07-20 18:24:35 +08:00
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_18" >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_reference/" class = "md-nav__link " >
< span class = "md-ellipsis" >
参考文献
< / span >
< / a >
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
< / div >
2023-07-20 18:24:35 +08:00
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_18_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_18" >
2023-07-17 17:51:12 +08:00
< span class = "md-nav__icon md-icon" > < / span >
参考文献
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< / ul >
< / nav >
2023-06-22 00:23:01 +08:00
< / li >
< / ul >
< / nav >
< / div >
< / div >
< / div >
< div class = "md-sidebar md-sidebar--secondary" data-md-component = "sidebar" data-md-type = "toc" >
< div class = "md-sidebar__scrollwrap" >
< div class = "md-sidebar__inner" >
< nav class = "md-nav md-nav--secondary" aria-label = "目录" >
2023-08-29 20:57:26 +08:00
< label class = "md-nav__title" for = "__toc" >
< span class = "md-nav__icon md-icon" > < / span >
目录
< / label >
< ul class = "md-nav__list" data-md-component = "toc" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "#1" class = "md-nav__link" >
1. 重点回顾
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "#2-q-a" class = "md-nav__link" >
2. Q & A
< / a >
< / li >
< / ul >
2023-06-22 00:23:01 +08:00
< / nav >
< / div >
< / div >
< / div >
< div class = "md-content" data-md-component = "content" >
< article class = "md-content__inner md-typeset" >
2023-09-21 20:44:52 +08:00
<!--
Copyright (c) 2016-2023 Martin Donath < martin.donath @ squidfunk . com >
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to
deal in the Software without restriction, including without limitation the
rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
sell copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in
all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
IN THE SOFTWARE.
-->
<!-- Tags -->
<!-- Actions -->
2023-06-22 00:23:01 +08:00
< a href = "https://github.com/krahets/hello-algo/tree/main/docs/chapter_backtracking/summary.md" title = "编辑此页" class = "md-content__button md-icon" >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M10 20H6V4h7v5h5v3.1l2-2V8l-6-6H6c-1.1 0-2 .9-2 2v16c0 1.1.9 2 2 2h4v-2m10.2-7c.1 0 .3.1.4.2l1.3 1.3c.2.2.2.6 0 .8l-1 1-2.1-2.1 1-1c.1-.1.2-.2.4-.2m0 3.9L14.1 23H12v-2.1l6.1-6.1 2.1 2.1Z" / > < / svg >
< / a >
2023-09-21 20:44:52 +08:00
<!--
Hack: check whether the content contains a h1 headline. If it doesn't, the
page title (or respectively site name) is used as the main headline.
-->
<!-- Page content -->
2023-08-19 22:07:40 +08:00
< h1 id = "135" > 13.5 小结< a class = "headerlink" href = "#135" title = "Permanent link" > ¶ < / a > < / h1 >
2023-08-29 20:57:26 +08:00
< h3 id = "1" > 1. 重点回顾< a class = "headerlink" href = "#1" title = "Permanent link" > ¶ < / a > < / h3 >
2023-06-22 00:23:01 +08:00
< ul >
< li > 回溯算法本质是穷举法，通过对解空间进行深度优先遍历来寻找符合条件的解。在搜索过程中，遇到满足条件的解则记录，直至找到所有解或遍历完成后结束。< / li >
< li > 回溯算法的搜索过程包括尝试与回退两个部分。它通过深度优先搜索来尝试各种选择，当遇到不满足约束条件的情况时，则撤销上一步的选择，退回到之前的状态，并继续尝试其他选择。尝试与回退是两个方向相反的操作。< / li >
< li > 回溯问题通常包含多个约束条件，它们可用于实现剪枝操作。剪枝可以提前结束不必要的搜索分支，大幅提升搜索效率。< / li >
< li > 回溯算法主要可用于解决搜索问题和约束满足问题。组合优化问题虽然可以用回溯算法解决，但往往存在更高效率或更好效果的解法。< / li >
< li > 全排列问题旨在搜索给定集合的所有可能的排列。我们借助一个数组来记录每个元素是否被选择，剪枝掉重复选择同一元素的搜索分支，确保每个元素只被选择一次。< / li >
< li > 在全排列问题中，如果集合中存在重复元素，则最终结果会出现重复排列。我们需要约束相等元素在每轮中只能被选择一次，这通常借助一个哈希表来实现。< / li >
< li > 子集和问题的目标是在给定集合中找到和为目标值的所有子集。集合不区分元素顺序，而搜索过程会输出所有顺序的结果，产生重复子集。我们在回溯前将数据进行排序，并设置一个变量来指示每一轮的遍历起点，从而将生成重复子集的搜索分支进行剪枝。< / li >
< li > 对于子集和问题，数组中的相等元素会产生重复集合。我们利用数组已排序的前置条件，通过判断相邻元素是否相等实现剪枝，从而确保相等元素在每轮中只能被选中一次。< / li >
< li > < span class = "arithmatex" > \(n\)< / span > 皇后旨在寻找将 < span class = "arithmatex" > \(n\)< / span > 个皇后放置到 < span class = "arithmatex" > \(n \times n\)< / span > 尺寸棋盘上的方案，要求所有皇后两两之间无法攻击对方。该问题的约束条件有行约束、列约束、主对角线和副对角线约束。为满足行约束，我们采用按行放置的策略，保证每一行放置一个皇后。< / li >
< li > 列约束和对角线约束的处理方式类似。对于列约束，我们利用一个数组来记录每一列是否有皇后，从而指示选中的格子是否合法。对于对角线约束，我们借助两个数组来分别记录该主、副对角线是否存在皇后；难点在于找处在到同一主（副）对角线上格子满足的行列索引规律。< / li >
< / ul >
2023-08-29 20:57:26 +08:00
< h3 id = "2-q-a" > 2. Q & A< a class = "headerlink" href = "#2-q-a" title = "Permanent link" > ¶ < / a > < / h3 >
< div class = "admonition question" >
< p class = "admonition-title" > 怎么理解回溯和递归的关系？< / p >
< p > 总的来看，回溯是一种“算法策略”，而递归更像是一个“工具”。< / p >
< ul >
< li > 回溯算法通常基于递归实现。然而，回溯是递归的应用场景之一，是递归在搜索问题中的应用。< / li >
< li > 递归的结构体现了“子问题分解”的解题范式，常用于解决分治、回溯、动态规划（记忆化递归）等问题。< / li >
< / ul >
< / div >
2023-06-22 00:23:01 +08:00
2023-09-21 20:44:52 +08:00
<!-- Source file information -->
2023-06-22 00:23:01 +08:00
2023-09-21 20:44:52 +08:00
<!-- Was this page helpful? -->
2023-06-22 00:23:01 +08:00
2023-09-21 20:44:52 +08:00
<!-- Previous and next pages link -->
< nav
class="md-footer__inner md-grid"
aria-label="页脚"
>
<!-- Link to previous page -->
< a
href="../n_queens_problem/"
class="md-footer__link md-footer__link--prev"
aria-label="上一页: 13.4 & nbsp; N 皇后问题"
rel="prev"
>
< div class = "md-footer__button md-icon" >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M20 11v2H8l5.5 5.5-1.42 1.42L4.16 12l7.92-7.92L13.5 5.5 8 11h12Z" / > < / svg >
< / div >
< div class = "md-footer__title" >
< span class = "md-footer__direction" >
上一页
< / span >
< div class = "md-ellipsis" >
13.4 N 皇后问题
< / div >
< / div >
< / a >
<!-- Link to next page -->
< a
href="../../chapter_dynamic_programming/"
class="md-footer__link md-footer__link--next"
aria-label="下一页: 第 14 章 & nbsp; 动态规划"
rel="next"
>
< div class = "md-footer__title" >
< span class = "md-footer__direction" >
下一页
< / span >
< div class = "md-ellipsis" >
第 14 章 动态规划
< / div >
< / div >
< div class = "md-footer__button md-icon" >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M4 11v2h12l-5.5 5.5 1.42 1.42L19.84 12l-7.92-7.92L10.5 5.5 16 11H4Z" / > < / svg >
< / div >
< / a >
< / nav >
<!-- Comment system -->
2023-10-06 13:31:31 +08:00
2023-10-09 18:19:36 +08:00
2023-09-22 13:41:28 +08:00
< h5 align = "center" id = "__comments" > 欢迎在评论区留下你的见解、疑惑或建议< / h5 >
2023-10-06 13:31:31 +08:00
2023-06-22 00:23:01 +08:00
<!-- Insert generated snippet here -->
< script
src="https://giscus.app/client.js"
data-repo="krahets/hello-algo"
data-repo-id="R_kgDOIXtSqw"
data-category="Announcements"
data-category-id="DIC_kwDOIXtSq84CSZk_"
data-mapping="pathname"
data-strict="1"
data-reactions-enabled="1"
data-emit-metadata="0"
data-input-position="top"
data-theme="preferred_color_scheme"
data-lang="zh-CN"
crossorigin="anonymous"
async
>
< / script >
<!-- Synchronize Giscus theme with palette -->
< script >
var giscus = document.querySelector("script[src*=giscus]")
/* Set palette on initial load */
var palette = __md_get("__palette")
if (palette & & typeof palette.color === "object") {
2023-09-12 03:15:25 +08:00
var theme = palette.color.scheme === "slate" ? "dark_dimmed" : "light"
2023-06-22 00:23:01 +08:00
giscus.setAttribute("data-theme", theme)
}
/* Register event handlers after documented loaded */
document.addEventListener("DOMContentLoaded", function() {
var ref = document.querySelector("[data-md-component=palette]")
ref.addEventListener("change", function() {
var palette = __md_get("__palette")
if (palette & & typeof palette.color === "object") {
2023-09-12 03:15:25 +08:00
var theme = palette.color.scheme === "slate" ? "dark_dimmed" : "light"
2023-06-22 00:23:01 +08:00
/* Instruct Giscus to change theme */
var frame = document.querySelector(".giscus-frame")
frame.contentWindow.postMessage(
{ giscus: { setConfig: { theme } } },
"https://giscus.app"
)
}
})
})
< / script >
< / article >
< / div >
< script > var tabs = _ _md _get ( "__tabs" ) ; if ( Array . isArray ( tabs ) ) e : for ( var set of document . querySelectorAll ( ".tabbed-set" ) ) { var tab , labels = set . querySelector ( ".tabbed-labels" ) ; for ( tab of tabs ) for ( var label of labels . getElementsByTagName ( "label" ) ) if ( label . innerText . trim ( ) === tab ) { var input = document . getElementById ( label . htmlFor ) ; input . checked = ! 0 ; continue e } } < / script >
< / div >
< button type = "button" class = "md-top md-icon" data-md-component = "top" hidden >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M13 20h-2V8l-5.5 5.5-1.42-1.42L12 4.16l7.92 7.92-1.42 1.42L13 8v12Z" / > < / svg >
回到页面顶部
< / button >
< / main >
2023-10-06 13:31:31 +08:00
< footer class = "md-footer" >
< nav class = "md-footer__inner md-grid" aria-label = "页脚" >
< a href = "../n_queens_problem/" class = "md-footer__link md-footer__link--prev" aria-label = "上一页: 13.4 &nbsp; N 皇后问题" rel = "prev" >
< div class = "md-footer__button md-icon" >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M20 11v2H8l5.5 5.5-1.42 1.42L4.16 12l7.92-7.92L13.5 5.5 8 11h12Z" / > < / svg >
< / div >
< div class = "md-footer__title" >
< span class = "md-footer__direction" >
上一页
< / span >
< div class = "md-ellipsis" >
13.4 N 皇后问题
< / div >
< / div >
< / a >
< a href = "../../chapter_dynamic_programming/" class = "md-footer__link md-footer__link--next" aria-label = "下一页: 第 14 章 &nbsp; 动态规划" rel = "next" >
< div class = "md-footer__title" >
< span class = "md-footer__direction" >
下一页
< / span >
< div class = "md-ellipsis" >
第 14 章 动态规划
< / div >
< / div >
< div class = "md-footer__button md-icon" >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M4 11v2h12l-5.5 5.5 1.42 1.42L19.84 12l-7.92-7.92L10.5 5.5 16 11H4Z" / > < / svg >
< / div >
< / a >
< / nav >
2023-06-22 00:23:01 +08:00
< div class = "md-footer-meta md-typeset" >
< div class = "md-footer-meta__inner md-grid" >
< div class = "md-copyright" >
< div class = "md-copyright__highlight" >
2023-09-22 13:08:10 +08:00
Copyright © 2022 - 2023 Krahets
2023-06-22 00:23:01 +08:00
< / div >
< / div >
< div class = "md-social" >
< a href = "https://github.com/krahets" target = "_blank" rel = "noopener" title = "github.com" class = "md-social__link" >
2023-09-24 17:12:06 +08:00
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 496 512" > <!-- ! Font Awesome Free 6.4.2 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc. --> < path d = "M165.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6zm-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3zm44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9zM244.8 8C106.1 8 0 113.3 0 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C428.2 457.8 496 362.9 496 252 496 113.3 383.5 8 244.8 8zM97.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1zm-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7zm32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1zm-11.4-14.7c-1.6 1-1.6 3.6 0 5.9 1.6 2.3 4.3 3.3 5.6 2.3 1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2z" / > < / svg >
2023-06-22 00:23:01 +08:00
< / a >
< a href = "https://twitter.com/krahets" target = "_blank" rel = "noopener" title = "twitter.com" class = "md-social__link" >
2023-09-24 17:12:06 +08:00
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 512 512" > <!-- ! Font Awesome Free 6.4.2 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc. --> < path d = "M459.37 151.716c.325 4.548.325 9.097.325 13.645 0 138.72-105.583 298.558-298.558 298.558-59.452 0-114.68-17.219-161.137-47.106 8.447.974 16.568 1.299 25.34 1.299 49.055 0 94.213-16.568 130.274-44.832-46.132-.975-84.792-31.188-98.112-72.772 6.498.974 12.995 1.624 19.818 1.624 9.421 0 18.843-1.3 27.614-3.573-48.081-9.747-84.143-51.98-84.143-102.985v-1.299c13.969 7.797 30.214 12.67 47.431 13.319-28.264-18.843-46.781-51.005-46.781-87.391 0-19.492 5.197-37.36 14.294-52.954 51.655 63.675 129.3 105.258 216.365 109.807-1.624-7.797-2.599-15.918-2.599-24.04 0-57.828 46.782-104.934 104.934-104.934 30.213 0 57.502 12.67 76.67 33.137 23.715-4.548 46.456-13.32 66.599-25.34-7.798 24.366-24.366 44.833-46.132 57.827 21.117-2.273 41.584-8.122 60.426-16.243-14.292 20.791-32.161 39.308-52.628 54.253z" / > < / svg >
2023-06-22 00:23:01 +08:00
< / a >
< a href = "https://leetcode.cn/u/jyd/" target = "_blank" rel = "noopener" title = "leetcode.cn" class = "md-social__link" >
2023-09-24 17:12:06 +08:00
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 640 512" > <!-- ! Font Awesome Free 6.4.2 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc. --> < path d = "M392.8 1.2c-17-4.9-34.7 5-39.6 22l-128 448c-4.9 17 5 34.7 22 39.6s34.7-5 39.6-22l128-448c4.9-17-5-34.7-22-39.6zm80.6 120.1c-12.5 12.5-12.5 32.8 0 45.3l89.3 89.4-89.4 89.4c-12.5 12.5-12.5 32.8 0 45.3s32.8 12.5 45.3 0l112-112c12.5-12.5 12.5-32.8 0-45.3l-112-112c-12.5-12.5-32.8-12.5-45.3 0zm-306.7 0c-12.5-12.5-32.8-12.5-45.3 0l-112 112c-12.5 12.5-12.5 32.8 0 45.3l112 112c12.5 12.5 32.8 12.5 45.3 0s12.5-32.8 0-45.3L77.3 256l89.4-89.4c12.5-12.5 12.5-32.8 0-45.3z" / > < / svg >
2023-06-22 00:23:01 +08:00
< / a >
< / div >
< / div >
< / div >
< / footer >
< / div >
< div class = "md-dialog" data-md-component = "dialog" >
< div class = "md-dialog__inner md-typeset" > < / div >
< / div >
2023-09-24 17:12:06 +08:00
< script id = "__config" type = "application/json" > { "base" : "../.." , "features" : [ "content.action.edit" , "content.code.annotate" , "content.code.copy" , "content.tabs.link" , "content.tooltips" , "navigation.indexes" , "navigation.instant" , "navigation.top" , "navigation.footer" , "navigation.tracking" , "search.highlight" , "search.share" , "search.suggest" , "toc.follow" ] , "search" : "../../assets/javascripts/workers/search.a264c092.min.js" , "translations" : { "clipboard.copied" : "\u5df2\u590d\u5236" , "clipboard.copy" : "\u590d\u5236" , "search.result.more.one" : "\u5728\u8be5\u9875\u4e0a\u8fd8\u6709 1 \u4e2a\u7b26\u5408\u6761\u4ef6\u7684\u7ed3\u679c" , "search.result.more.other" : "\u5728\u8be5\u9875\u4e0a\u8fd8\u6709 # \u4e2a\u7b26\u5408\u6761\u4ef6\u7684\u7ed3\u679c" , "search.result.none" : "\u6ca1\u6709\u627e\u5230\u7b26\u5408\u6761\u4ef6\u7684\u7ed3\u679c" , "search.result.one" : "\u627e\u5230 1 \u4e2a\u7b26\u5408\u6761\u4ef6\u7684\u7ed3\u679c" , "search.result.other" : "# \u4e2a\u7b26\u5408\u6761\u4ef6\u7684\u7ed3\u679c" , "search.result.placeholder" : "\u952e\u5165\u4ee5\u5f00\u59cb\u641c\u7d22" , "search.result.term.missing" : "\u7f3a\u5c11" , "select.version" : "\u9009\u62e9\u5f53\u524d\u7248\u672c" } } < / script >
2023-06-22 00:23:01 +08:00
2023-09-29 22:06:02 +08:00
< script src = "../../assets/javascripts/bundle.4e0fa4ba.min.js" > < / script >
2023-06-22 00:23:01 +08:00
2023-09-24 17:12:06 +08:00
< script src = "../../javascripts/mathjax.js" > < / script >
2023-06-22 00:23:01 +08:00
2023-09-24 17:12:06 +08:00
< script src = "https://polyfill.io/v3/polyfill.min.js?features=es6" > < / script >
2023-06-22 00:23:01 +08:00
2023-09-24 17:12:06 +08:00
< script src = "https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js" > < / script >
2023-06-22 00:23:01 +08:00
2023-09-22 13:08:10 +08:00
< script > document $ . subscribe ( ( ) => { const lightbox = GLightbox ( { "touchNavigation" : true , "loop" : false , "zoomable" : true , "draggable" : false , "openEffect" : "zoom" , "closeEffect" : "zoom" , "slideEffect" : "none" } ) ; } ) < / script > < / body >
2023-06-22 00:23:01 +08:00
< / html >
