mirror of
https://github.com/krahets/hello-algo.git
synced 2024-12-25 01:06:30 +08:00
deploy
This commit is contained in:
krahets
parent
1a7a8ac395
commit
6abac5a2e7
39 changed files with 1316 additions and 453 deletions
BIN
assets/avatar/avatar_khoaxuantu.jpg
Normal file
BIN
assets/avatar/avatar_khoaxuantu.jpg
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 9.5 KiB |
|
|
@ -3879,7 +3879,7 @@
|
|||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">preorder_traversal_i_compact.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* 前序遍历：例题一 */</span>
|
||||
<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">fn</span> <span class="nf">pre_order</span><span class="p">(</span><span class="n">res</span>: <span class="kp">&</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o"><</span><span class="n">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>>></span><span class="p">,</span><span class="w"> </span><span class="n">root</span>: <span class="nb">Option</span><span class="o"><</span><span class="n">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>>></span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">fn</span> <span class="nf">pre_order</span><span class="p">(</span><span class="n">res</span>: <span class="kp">&</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o"><</span><span class="n">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>>></span><span class="p">,</span><span class="w"> </span><span class="n">root</span>: <span class="nb">Option</span><span class="o"><&</span><span class="n">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>>></span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">root</span><span class="p">.</span><span class="n">is_none</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
|
||||
<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="w"> </span><span class="p">}</span>
|
||||
|
|
@ -3888,8 +3888,8 @@
|
|||
<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="w"> </span><span class="c1">// 记录解</span>
|
||||
<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
|
||||
<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="w"> </span><span class="n">pre_order</span><span class="p">(</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
|
||||
<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="w"> </span><span class="n">pre_order</span><span class="p">(</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
|
||||
<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="w"> </span><span class="n">pre_order</span><span class="p">(</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">as_ref</span><span class="p">());</span>
|
||||
<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="w"> </span><span class="n">pre_order</span><span class="p">(</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">as_ref</span><span class="p">());</span>
|
||||
<a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="p">}</span>
|
||||
</code></pre></div>
|
||||
|
|
@ -4144,7 +4144,7 @@
|
|||
<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a><span class="k">fn</span> <span class="nf">pre_order</span><span class="p">(</span>
|
||||
<a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="w"> </span><span class="n">res</span>: <span class="kp">&</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o"><</span><span class="nb">Vec</span><span class="o"><</span><span class="n">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>>>></span><span class="p">,</span>
|
||||
<a id="__codelineno-23-4" name="__codelineno-23-4" href="#__codelineno-23-4"></a><span class="w"> </span><span class="n">path</span>: <span class="kp">&</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o"><</span><span class="n">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>>></span><span class="p">,</span>
|
||||
<a id="__codelineno-23-5" name="__codelineno-23-5" href="#__codelineno-23-5"></a><span class="w"> </span><span class="n">root</span>: <span class="nb">Option</span><span class="o"><</span><span class="n">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>>></span><span class="p">,</span>
|
||||
<a id="__codelineno-23-5" name="__codelineno-23-5" href="#__codelineno-23-5"></a><span class="w"> </span><span class="n">root</span>: <span class="nb">Option</span><span class="o"><&</span><span class="n">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>>></span><span class="p">,</span>
|
||||
<a id="__codelineno-23-6" name="__codelineno-23-6" href="#__codelineno-23-6"></a><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-23-7" name="__codelineno-23-7" href="#__codelineno-23-7"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">root</span><span class="p">.</span><span class="n">is_none</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-23-8" name="__codelineno-23-8" href="#__codelineno-23-8"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
|
||||
|
|
@ -4156,10 +4156,10 @@
|
|||
<a id="__codelineno-23-14" name="__codelineno-23-14" href="#__codelineno-23-14"></a><span class="w"> </span><span class="c1">// 记录解</span>
|
||||
<a id="__codelineno-23-15" name="__codelineno-23-15" href="#__codelineno-23-15"></a><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">path</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
|
||||
<a id="__codelineno-23-16" name="__codelineno-23-16" href="#__codelineno-23-16"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-23-17" name="__codelineno-23-17" href="#__codelineno-23-17"></a><span class="w"> </span><span class="n">pre_order</span><span class="p">(</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">path</span><span class="p">,</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
|
||||
<a id="__codelineno-23-18" name="__codelineno-23-18" href="#__codelineno-23-18"></a><span class="w"> </span><span class="n">pre_order</span><span class="p">(</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">path</span><span class="p">,</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
|
||||
<a id="__codelineno-23-17" name="__codelineno-23-17" href="#__codelineno-23-17"></a><span class="w"> </span><span class="n">pre_order</span><span class="p">(</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">path</span><span class="p">,</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">as_ref</span><span class="p">());</span>
|
||||
<a id="__codelineno-23-18" name="__codelineno-23-18" href="#__codelineno-23-18"></a><span class="w"> </span><span class="n">pre_order</span><span class="p">(</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">path</span><span class="p">,</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">as_ref</span><span class="p">());</span>
|
||||
<a id="__codelineno-23-19" name="__codelineno-23-19" href="#__codelineno-23-19"></a><span class="w"> </span><span class="c1">// 回退</span>
|
||||
<a id="__codelineno-23-20" name="__codelineno-23-20" href="#__codelineno-23-20"></a><span class="w"> </span><span class="n">path</span><span class="p">.</span><span class="n">remove</span><span class="p">(</span><span class="n">path</span><span class="p">.</span><span class="n">len</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
|
||||
<a id="__codelineno-23-20" name="__codelineno-23-20" href="#__codelineno-23-20"></a><span class="w"> </span><span class="n">path</span><span class="p">.</span><span class="n">pop</span><span class="p">();</span>
|
||||
<a id="__codelineno-23-21" name="__codelineno-23-21" href="#__codelineno-23-21"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-23-22" name="__codelineno-23-22" href="#__codelineno-23-22"></a><span class="p">}</span>
|
||||
</code></pre></div>
|
||||
|
|
@ -4475,7 +4475,7 @@
|
|||
<a id="__codelineno-37-2" name="__codelineno-37-2" href="#__codelineno-37-2"></a><span class="k">fn</span> <span class="nf">pre_order</span><span class="p">(</span>
|
||||
<a id="__codelineno-37-3" name="__codelineno-37-3" href="#__codelineno-37-3"></a><span class="w"> </span><span class="n">res</span>: <span class="kp">&</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o"><</span><span class="nb">Vec</span><span class="o"><</span><span class="n">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>>>></span><span class="p">,</span>
|
||||
<a id="__codelineno-37-4" name="__codelineno-37-4" href="#__codelineno-37-4"></a><span class="w"> </span><span class="n">path</span>: <span class="kp">&</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o"><</span><span class="n">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>>></span><span class="p">,</span>
|
||||
<a id="__codelineno-37-5" name="__codelineno-37-5" href="#__codelineno-37-5"></a><span class="w"> </span><span class="n">root</span>: <span class="nb">Option</span><span class="o"><</span><span class="n">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>>></span><span class="p">,</span>
|
||||
<a id="__codelineno-37-5" name="__codelineno-37-5" href="#__codelineno-37-5"></a><span class="w"> </span><span class="n">root</span>: <span class="nb">Option</span><span class="o"><&</span><span class="n">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>>></span><span class="p">,</span>
|
||||
<a id="__codelineno-37-6" name="__codelineno-37-6" href="#__codelineno-37-6"></a><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-37-7" name="__codelineno-37-7" href="#__codelineno-37-7"></a><span class="w"> </span><span class="c1">// 剪枝</span>
|
||||
<a id="__codelineno-37-8" name="__codelineno-37-8" href="#__codelineno-37-8"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">root</span><span class="p">.</span><span class="n">is_none</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">root</span><span class="p">.</span><span class="n">as_ref</span><span class="p">().</span><span class="n">unwrap</span><span class="p">().</span><span class="n">borrow</span><span class="p">().</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">3</span><span class="w"> </span><span class="p">{</span>
|
||||
|
|
@ -4488,10 +4488,10 @@
|
|||
<a id="__codelineno-37-15" name="__codelineno-37-15" href="#__codelineno-37-15"></a><span class="w"> </span><span class="c1">// 记录解</span>
|
||||
<a id="__codelineno-37-16" name="__codelineno-37-16" href="#__codelineno-37-16"></a><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">path</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
|
||||
<a id="__codelineno-37-17" name="__codelineno-37-17" href="#__codelineno-37-17"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-37-18" name="__codelineno-37-18" href="#__codelineno-37-18"></a><span class="w"> </span><span class="n">pre_order</span><span class="p">(</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">path</span><span class="p">,</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
|
||||
<a id="__codelineno-37-19" name="__codelineno-37-19" href="#__codelineno-37-19"></a><span class="w"> </span><span class="n">pre_order</span><span class="p">(</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">path</span><span class="p">,</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
|
||||
<a id="__codelineno-37-18" name="__codelineno-37-18" href="#__codelineno-37-18"></a><span class="w"> </span><span class="n">pre_order</span><span class="p">(</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">path</span><span class="p">,</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">as_ref</span><span class="p">());</span>
|
||||
<a id="__codelineno-37-19" name="__codelineno-37-19" href="#__codelineno-37-19"></a><span class="w"> </span><span class="n">pre_order</span><span class="p">(</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">path</span><span class="p">,</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">as_ref</span><span class="p">());</span>
|
||||
<a id="__codelineno-37-20" name="__codelineno-37-20" href="#__codelineno-37-20"></a><span class="w"> </span><span class="c1">// 回退</span>
|
||||
<a id="__codelineno-37-21" name="__codelineno-37-21" href="#__codelineno-37-21"></a><span class="w"> </span><span class="n">path</span><span class="p">.</span><span class="n">remove</span><span class="p">(</span><span class="n">path</span><span class="p">.</span><span class="n">len</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
|
||||
<a id="__codelineno-37-21" name="__codelineno-37-21" href="#__codelineno-37-21"></a><span class="w"> </span><span class="n">path</span><span class="p">.</span><span class="n">pop</span><span class="p">();</span>
|
||||
<a id="__codelineno-37-22" name="__codelineno-37-22" href="#__codelineno-37-22"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-37-23" name="__codelineno-37-23" href="#__codelineno-37-23"></a><span class="p">}</span>
|
||||
</code></pre></div>
|
||||
|
|
@ -5334,7 +5334,7 @@
|
|||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">preorder_traversal_iii_template.rs</span><pre><span></span><code><a id="__codelineno-65-1" name="__codelineno-65-1" href="#__codelineno-65-1"></a><span class="cm">/* 判断当前状态是否为解 */</span>
|
||||
<a id="__codelineno-65-2" name="__codelineno-65-2" href="#__codelineno-65-2"></a><span class="k">fn</span> <span class="nf">is_solution</span><span class="p">(</span><span class="n">state</span>: <span class="kp">&</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o"><</span><span class="n">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>>></span><span class="p">)</span><span class="w"> </span>-> <span class="kt">bool</span> <span class="p">{</span>
|
||||
<a id="__codelineno-65-3" name="__codelineno-65-3" href="#__codelineno-65-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="o">!</span><span class="n">state</span><span class="p">.</span><span class="n">is_empty</span><span class="p">()</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">state</span><span class="p">.</span><span class="n">get</span><span class="p">(</span><span class="n">state</span><span class="p">.</span><span class="n">len</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">).</span><span class="n">unwrap</span><span class="p">().</span><span class="n">borrow</span><span class="p">().</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span><span class="p">;</span>
|
||||
<a id="__codelineno-65-3" name="__codelineno-65-3" href="#__codelineno-65-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="o">!</span><span class="n">state</span><span class="p">.</span><span class="n">is_empty</span><span class="p">()</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">state</span><span class="p">.</span><span class="n">last</span><span class="p">().</span><span class="n">unwrap</span><span class="p">().</span><span class="n">borrow</span><span class="p">().</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span><span class="p">;</span>
|
||||
<a id="__codelineno-65-4" name="__codelineno-65-4" href="#__codelineno-65-4"></a><span class="p">}</span>
|
||||
<a id="__codelineno-65-5" name="__codelineno-65-5" href="#__codelineno-65-5"></a>
|
||||
<a id="__codelineno-65-6" name="__codelineno-65-6" href="#__codelineno-65-6"></a><span class="cm">/* 记录解 */</span>
|
||||
|
|
@ -5346,8 +5346,8 @@
|
|||
<a id="__codelineno-65-12" name="__codelineno-65-12" href="#__codelineno-65-12"></a><span class="p">}</span>
|
||||
<a id="__codelineno-65-13" name="__codelineno-65-13" href="#__codelineno-65-13"></a>
|
||||
<a id="__codelineno-65-14" name="__codelineno-65-14" href="#__codelineno-65-14"></a><span class="cm">/* 判断在当前状态下，该选择是否合法 */</span>
|
||||
<a id="__codelineno-65-15" name="__codelineno-65-15" href="#__codelineno-65-15"></a><span class="k">fn</span> <span class="nf">is_valid</span><span class="p">(</span><span class="n">_</span>: <span class="kp">&</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o"><</span><span class="n">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>>></span><span class="p">,</span><span class="w"> </span><span class="n">choice</span>: <span class="nc">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>></span><span class="p">)</span><span class="w"> </span>-> <span class="kt">bool</span> <span class="p">{</span>
|
||||
<a id="__codelineno-65-16" name="__codelineno-65-16" href="#__codelineno-65-16"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">choice</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">val</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span>
|
||||
<a id="__codelineno-65-15" name="__codelineno-65-15" href="#__codelineno-65-15"></a><span class="k">fn</span> <span class="nf">is_valid</span><span class="p">(</span><span class="n">_</span>: <span class="kp">&</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o"><</span><span class="n">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>>></span><span class="p">,</span><span class="w"> </span><span class="n">choice</span>: <span class="nb">Option</span><span class="o"><&</span><span class="n">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>>></span><span class="p">)</span><span class="w"> </span>-> <span class="kt">bool</span> <span class="p">{</span>
|
||||
<a id="__codelineno-65-16" name="__codelineno-65-16" href="#__codelineno-65-16"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">choice</span><span class="p">.</span><span class="n">is_some</span><span class="p">()</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">choice</span><span class="p">.</span><span class="n">unwrap</span><span class="p">().</span><span class="n">borrow</span><span class="p">().</span><span class="n">val</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span>
|
||||
<a id="__codelineno-65-17" name="__codelineno-65-17" href="#__codelineno-65-17"></a><span class="p">}</span>
|
||||
<a id="__codelineno-65-18" name="__codelineno-65-18" href="#__codelineno-65-18"></a>
|
||||
<a id="__codelineno-65-19" name="__codelineno-65-19" href="#__codelineno-65-19"></a><span class="cm">/* 更新状态 */</span>
|
||||
|
|
@ -5357,13 +5357,13 @@
|
|||
<a id="__codelineno-65-23" name="__codelineno-65-23" href="#__codelineno-65-23"></a>
|
||||
<a id="__codelineno-65-24" name="__codelineno-65-24" href="#__codelineno-65-24"></a><span class="cm">/* 恢复状态 */</span>
|
||||
<a id="__codelineno-65-25" name="__codelineno-65-25" href="#__codelineno-65-25"></a><span class="k">fn</span> <span class="nf">undo_choice</span><span class="p">(</span><span class="n">state</span>: <span class="kp">&</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o"><</span><span class="n">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>>></span><span class="p">,</span><span class="w"> </span><span class="n">_</span>: <span class="nc">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>></span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-65-26" name="__codelineno-65-26" href="#__codelineno-65-26"></a><span class="w"> </span><span class="n">state</span><span class="p">.</span><span class="n">remove</span><span class="p">(</span><span class="n">state</span><span class="p">.</span><span class="n">len</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
|
||||
<a id="__codelineno-65-26" name="__codelineno-65-26" href="#__codelineno-65-26"></a><span class="w"> </span><span class="n">state</span><span class="p">.</span><span class="n">pop</span><span class="p">();</span>
|
||||
<a id="__codelineno-65-27" name="__codelineno-65-27" href="#__codelineno-65-27"></a><span class="p">}</span>
|
||||
<a id="__codelineno-65-28" name="__codelineno-65-28" href="#__codelineno-65-28"></a>
|
||||
<a id="__codelineno-65-29" name="__codelineno-65-29" href="#__codelineno-65-29"></a><span class="cm">/* 回溯算法：例题三 */</span>
|
||||
<a id="__codelineno-65-30" name="__codelineno-65-30" href="#__codelineno-65-30"></a><span class="k">fn</span> <span class="nf">backtrack</span><span class="p">(</span>
|
||||
<a id="__codelineno-65-31" name="__codelineno-65-31" href="#__codelineno-65-31"></a><span class="w"> </span><span class="n">state</span>: <span class="kp">&</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o"><</span><span class="n">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>>></span><span class="p">,</span>
|
||||
<a id="__codelineno-65-32" name="__codelineno-65-32" href="#__codelineno-65-32"></a><span class="w"> </span><span class="n">choices</span>: <span class="kp">&</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o"><</span><span class="n">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>>></span><span class="p">,</span>
|
||||
<a id="__codelineno-65-32" name="__codelineno-65-32" href="#__codelineno-65-32"></a><span class="w"> </span><span class="n">choices</span>: <span class="kp">&</span><span class="nb">Vec</span><span class="o"><</span><span class="nb">Option</span><span class="o"><&</span><span class="n">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>>>></span><span class="p">,</span>
|
||||
<a id="__codelineno-65-33" name="__codelineno-65-33" href="#__codelineno-65-33"></a><span class="w"> </span><span class="n">res</span>: <span class="kp">&</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o"><</span><span class="nb">Vec</span><span class="o"><</span><span class="n">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>>>></span><span class="p">,</span>
|
||||
<a id="__codelineno-65-34" name="__codelineno-65-34" href="#__codelineno-65-34"></a><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-65-35" name="__codelineno-65-35" href="#__codelineno-65-35"></a><span class="w"> </span><span class="c1">// 检查是否为解</span>
|
||||
|
|
@ -5372,22 +5372,22 @@
|
|||
<a id="__codelineno-65-38" name="__codelineno-65-38" href="#__codelineno-65-38"></a><span class="w"> </span><span class="n">record_solution</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
|
||||
<a id="__codelineno-65-39" name="__codelineno-65-39" href="#__codelineno-65-39"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-65-40" name="__codelineno-65-40" href="#__codelineno-65-40"></a><span class="w"> </span><span class="c1">// 遍历所有选择</span>
|
||||
<a id="__codelineno-65-41" name="__codelineno-65-41" href="#__codelineno-65-41"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">choices</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-65-41" name="__codelineno-65-41" href="#__codelineno-65-41"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="o">&</span><span class="n">choice</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">choices</span><span class="p">.</span><span class="n">iter</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-65-42" name="__codelineno-65-42" href="#__codelineno-65-42"></a><span class="w"> </span><span class="c1">// 剪枝：检查选择是否合法</span>
|
||||
<a id="__codelineno-65-43" name="__codelineno-65-43" href="#__codelineno-65-43"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">is_valid</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">.</span><span class="n">clone</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-65-43" name="__codelineno-65-43" href="#__codelineno-65-43"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">is_valid</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-65-44" name="__codelineno-65-44" href="#__codelineno-65-44"></a><span class="w"> </span><span class="c1">// 尝试：做出选择，更新状态</span>
|
||||
<a id="__codelineno-65-45" name="__codelineno-65-45" href="#__codelineno-65-45"></a><span class="w"> </span><span class="n">make_choice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
|
||||
<a id="__codelineno-65-45" name="__codelineno-65-45" href="#__codelineno-65-45"></a><span class="w"> </span><span class="n">make_choice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">.</span><span class="n">unwrap</span><span class="p">().</span><span class="n">clone</span><span class="p">());</span>
|
||||
<a id="__codelineno-65-46" name="__codelineno-65-46" href="#__codelineno-65-46"></a><span class="w"> </span><span class="c1">// 进行下一轮选择</span>
|
||||
<a id="__codelineno-65-47" name="__codelineno-65-47" href="#__codelineno-65-47"></a><span class="w"> </span><span class="n">backtrack</span><span class="p">(</span>
|
||||
<a id="__codelineno-65-48" name="__codelineno-65-48" href="#__codelineno-65-48"></a><span class="w"> </span><span class="n">state</span><span class="p">,</span>
|
||||
<a id="__codelineno-65-49" name="__codelineno-65-49" href="#__codelineno-65-49"></a><span class="w"> </span><span class="o">&</span><span class="k">mut</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span>
|
||||
<a id="__codelineno-65-50" name="__codelineno-65-50" href="#__codelineno-65-50"></a><span class="w"> </span><span class="n">choice</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">clone</span><span class="p">().</span><span class="n">unwrap</span><span class="p">(),</span>
|
||||
<a id="__codelineno-65-51" name="__codelineno-65-51" href="#__codelineno-65-51"></a><span class="w"> </span><span class="n">choice</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">clone</span><span class="p">().</span><span class="n">unwrap</span><span class="p">(),</span>
|
||||
<a id="__codelineno-65-49" name="__codelineno-65-49" href="#__codelineno-65-49"></a><span class="w"> </span><span class="o">&</span><span class="fm">vec!</span><span class="p">[</span>
|
||||
<a id="__codelineno-65-50" name="__codelineno-65-50" href="#__codelineno-65-50"></a><span class="w"> </span><span class="n">choice</span><span class="p">.</span><span class="n">unwrap</span><span class="p">().</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">as_ref</span><span class="p">(),</span>
|
||||
<a id="__codelineno-65-51" name="__codelineno-65-51" href="#__codelineno-65-51"></a><span class="w"> </span><span class="n">choice</span><span class="p">.</span><span class="n">unwrap</span><span class="p">().</span><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">as_ref</span><span class="p">(),</span>
|
||||
<a id="__codelineno-65-52" name="__codelineno-65-52" href="#__codelineno-65-52"></a><span class="w"> </span><span class="p">],</span>
|
||||
<a id="__codelineno-65-53" name="__codelineno-65-53" href="#__codelineno-65-53"></a><span class="w"> </span><span class="n">res</span><span class="p">,</span>
|
||||
<a id="__codelineno-65-54" name="__codelineno-65-54" href="#__codelineno-65-54"></a><span class="w"> </span><span class="p">);</span>
|
||||
<a id="__codelineno-65-55" name="__codelineno-65-55" href="#__codelineno-65-55"></a><span class="w"> </span><span class="c1">// 回退：撤销选择，恢复到之前的状态</span>
|
||||
<a id="__codelineno-65-56" name="__codelineno-65-56" href="#__codelineno-65-56"></a><span class="w"> </span><span class="n">undo_choice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
|
||||
<a id="__codelineno-65-56" name="__codelineno-65-56" href="#__codelineno-65-56"></a><span class="w"> </span><span class="n">undo_choice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">.</span><span class="n">unwrap</span><span class="p">().</span><span class="n">clone</span><span class="p">());</span>
|
||||
<a id="__codelineno-65-57" name="__codelineno-65-57" href="#__codelineno-65-57"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-65-58" name="__codelineno-65-58" href="#__codelineno-65-58"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-65-59" name="__codelineno-65-59" href="#__codelineno-65-59"></a><span class="p">}</span>
|
||||
|
|
|
|||
|
|
@ -3671,14 +3671,14 @@
|
|||
</ol>
|
||||
<p>也就是说，在能够解决问题的前提下，算法效率已成为衡量算法优劣的主要评价指标，它包括以下两个维度。</p>
|
||||
<ul>
|
||||
<li><strong>时间效率</strong>：算法运行速度的快慢。</li>
|
||||
<li><strong>时间效率</strong>：算法运行时间的长短。</li>
|
||||
<li><strong>空间效率</strong>：算法占用内存空间的大小。</li>
|
||||
</ul>
|
||||
<p>简而言之，<strong>我们的目标是设计“既快又省”的数据结构与算法</strong>。而有效地评估算法效率至关重要，因为只有这样，我们才能将各种算法进行对比，进而指导算法设计与优化过程。</p>
|
||||
<p>效率评估方法主要分为两种：实际测试、理论估算。</p>
|
||||
<h2 id="211">2.1.1 实际测试<a class="headerlink" href="#211" title="Permanent link">¶</a></h2>
|
||||
<p>假设我们现在有算法 <code>A</code> 和算法 <code>B</code> ，它们都能解决同一问题，现在需要对比这两个算法的效率。最直接的方法是找一台计算机，运行这两个算法，并监控记录它们的运行时间和内存占用情况。这种评估方式能够反映真实情况，但也存在较大的局限性。</p>
|
||||
<p>一方面，<strong>难以排除测试环境的干扰因素</strong>。硬件配置会影响算法的性能。比如在某台计算机中，算法 <code>A</code> 的运行时间比算法 <code>B</code> 短；但在另一台配置不同的计算机中，可能得到相反的测试结果。这意味着我们需要在各种机器上进行测试，统计平均效率，而这是不现实的。</p>
|
||||
<p>一方面，<strong>难以排除测试环境的干扰因素</strong>。硬件配置会影响算法的性能表现。比如一个算法的并行度较高，那么它就更适合在多核 CPU 上运行，一个算法的内存操作密集，那么它在高性能内存上的表现就会更好。也就是说，算法在不同的机器上的测试结果可能是不一致的。这意味着我们需要在各种机器上进行测试，统计平均效率，而这是不现实的。</p>
|
||||
<p>另一方面，<strong>展开完整测试非常耗费资源</strong>。随着输入数据量的变化，算法会表现出不同的效率。例如，在输入数据量较小时，算法 <code>A</code> 的运行时间比算法 <code>B</code> 短；而在输入数据量较大时，测试结果可能恰恰相反。因此，为了得到有说服力的结论，我们需要测试各种规模的输入数据，而这需要耗费大量的计算资源。</p>
|
||||
<h2 id="212">2.1.2 理论估算<a class="headerlink" href="#212" title="Permanent link">¶</a></h2>
|
||||
<p>由于实际测试具有较大的局限性，因此我们可以考虑仅通过一些计算来评估算法的效率。这种估算方法被称为<u>渐近复杂度分析（asymptotic complexity analysis）</u>，简称<u>复杂度分析</u>。</p>
|
||||
|
|
@ -3688,8 +3688,9 @@
|
|||
<li>“随着输入数据大小的增加”意味着复杂度反映了算法运行效率与输入数据体量之间的关系。</li>
|
||||
<li>“时间和空间的增长趋势”表示复杂度分析关注的不是运行时间或占用空间的具体值，而是时间或空间增长的“快慢”。</li>
|
||||
</ul>
|
||||
<p><strong>复杂度分析克服了实际测试方法的弊端</strong>，体现在以下两个方面。</p>
|
||||
<p><strong>复杂度分析克服了实际测试方法的弊端</strong>，体现在以下几个方面。</p>
|
||||
<ul>
|
||||
<li>它无需实际运行代码，更加绿色节能。</li>
|
||||
<li>它独立于测试环境，分析结果适用于所有运行平台。</li>
|
||||
<li>它可以体现不同数据量下的算法效率，尤其是在大数据量下的算法性能。</li>
|
||||
</ul>
|
||||
|
|
|
|||
|
|
@ -4383,7 +4383,7 @@
|
|||
<ul>
|
||||
<li><strong>时间复杂度能够有效评估算法效率</strong>。例如，算法 <code>B</code> 的运行时间呈线性增长，在 <span class="arithmatex">\(n > 1\)</span> 时比算法 <code>A</code> 更慢，在 <span class="arithmatex">\(n > 1000000\)</span> 时比算法 <code>C</code> 更慢。事实上，只要输入数据大小 <span class="arithmatex">\(n\)</span> 足够大，复杂度为“常数阶”的算法一定优于“线性阶”的算法，这正是时间增长趋势的含义。</li>
|
||||
<li><strong>时间复杂度的推算方法更简便</strong>。显然，运行平台和计算操作类型都与算法运行时间的增长趋势无关。因此在时间复杂度分析中，我们可以简单地将所有计算操作的执行时间视为相同的“单位时间”，从而将“计算操作运行时间统计”简化为“计算操作数量统计”，这样一来估算难度就大大降低了。</li>
|
||||
<li><strong>时间复杂度也存在一定的局限性</strong>。例如，尽管算法 <code>A</code> 和 <code>C</code> 的时间复杂度相同，但实际运行时间差别很大。同样，尽管算法 <code>B</code> 的时间复杂度比 <code>C</code> 高，但在输入数据大小 <span class="arithmatex">\(n\)</span> 较小时，算法 <code>B</code> 明显优于算法 <code>C</code> 。在这些情况下，我们很难仅凭时间复杂度判断算法效率的高低。当然，尽管存在上述问题，复杂度分析仍然是评判算法效率最有效且常用的方法。</li>
|
||||
<li><strong>时间复杂度也存在一定的局限性</strong>。例如，尽管算法 <code>A</code> 和 <code>C</code> 的时间复杂度相同，但实际运行时间差别很大。同样，尽管算法 <code>B</code> 的时间复杂度比 <code>C</code> 高，但在输入数据大小 <span class="arithmatex">\(n\)</span> 较小时，算法 <code>B</code> 明显优于算法 <code>C</code> 。对于此类情况，我们时常难以仅凭时间复杂度判断算法效率的高低。当然，尽管存在上述问题，复杂度分析仍然是评判算法效率最有效且常用的方法。</li>
|
||||
</ul>
|
||||
<h2 id="232">2.3.2 函数渐近上界<a class="headerlink" href="#232" title="Permanent link">¶</a></h2>
|
||||
<p>给定一个输入大小为 <span class="arithmatex">\(n\)</span> 的函数：</p>
|
||||
|
|
@ -6617,10 +6617,12 @@ O(\log_m n) = O(\log_k n / \log_k m) = O(\log_k n)
|
|||
<a id="__codelineno-182-2" name="__codelineno-182-2" href="#__codelineno-182-2"></a><span class="w"> </span><span class="sd">"""线性对数阶"""</span>
|
||||
<a id="__codelineno-182-3" name="__codelineno-182-3" href="#__codelineno-182-3"></a> <span class="k">if</span> <span class="n">n</span> <span class="o"><=</span> <span class="mi">1</span><span class="p">:</span>
|
||||
<a id="__codelineno-182-4" name="__codelineno-182-4" href="#__codelineno-182-4"></a> <span class="k">return</span> <span class="mi">1</span>
|
||||
<a id="__codelineno-182-5" name="__codelineno-182-5" href="#__codelineno-182-5"></a> <span class="n">count</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">linear_log_recur</span><span class="p">(</span><span class="n">n</span> <span class="o">//</span> <span class="mi">2</span><span class="p">)</span> <span class="o">+</span> <span class="n">linear_log_recur</span><span class="p">(</span><span class="n">n</span> <span class="o">//</span> <span class="mi">2</span><span class="p">)</span>
|
||||
<a id="__codelineno-182-6" name="__codelineno-182-6" href="#__codelineno-182-6"></a> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
|
||||
<a id="__codelineno-182-7" name="__codelineno-182-7" href="#__codelineno-182-7"></a> <span class="n">count</span> <span class="o">+=</span> <span class="mi">1</span>
|
||||
<a id="__codelineno-182-8" name="__codelineno-182-8" href="#__codelineno-182-8"></a> <span class="k">return</span> <span class="n">count</span>
|
||||
<a id="__codelineno-182-5" name="__codelineno-182-5" href="#__codelineno-182-5"></a> <span class="c1"># 一分为二，子问题的规模减小一半</span>
|
||||
<a id="__codelineno-182-6" name="__codelineno-182-6" href="#__codelineno-182-6"></a> <span class="n">count</span> <span class="o">=</span> <span class="n">linear_log_recur</span><span class="p">(</span><span class="n">n</span> <span class="o">//</span> <span class="mi">2</span><span class="p">)</span> <span class="o">+</span> <span class="n">linear_log_recur</span><span class="p">(</span><span class="n">n</span> <span class="o">//</span> <span class="mi">2</span><span class="p">)</span>
|
||||
<a id="__codelineno-182-7" name="__codelineno-182-7" href="#__codelineno-182-7"></a> <span class="c1"># 当前子问题包含 n 个操作</span>
|
||||
<a id="__codelineno-182-8" name="__codelineno-182-8" href="#__codelineno-182-8"></a> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
|
||||
<a id="__codelineno-182-9" name="__codelineno-182-9" href="#__codelineno-182-9"></a> <span class="n">count</span> <span class="o">+=</span> <span class="mi">1</span>
|
||||
<a id="__codelineno-182-10" name="__codelineno-182-10" href="#__codelineno-182-10"></a> <span class="k">return</span> <span class="n">count</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
|
|
|
|||
|
|
@ -3688,7 +3688,7 @@
|
|||
<p><strong>Q</strong>：在构建栈（队列）的时候，未指定它的大小，为什么它们是“静态数据结构”呢？</p>
|
||||
<p>在高级编程语言中，我们无须人工指定栈（队列）的初始容量，这个工作由类内部自动完成。例如，Java 的 <code>ArrayList</code> 的初始容量通常为 10。另外，扩容操作也是自动实现的。详见后续的“列表”章节。</p>
|
||||
<p><strong>Q</strong>：原码转补码的方法是“先取反后加 1”，那么补码转原码应该是逆运算“先减 1 后取反”，而补码转原码也一样可以通过“先取反后加 1”得到，这是为什么呢？</p>
|
||||
<p><strong>A</strong>：这是因为原码和补码的相互转换实际上是计算“补数”的过程。我们先给出补数的定义：假设 <span class="arithmatex">\(a + b = c\)</span> ，那么我们称 <span class="arithmatex">\(a\)</span> 是 <span class="arithmatex">\(b\)</span> 到 <span class="arithmatex">\(c\)</span> 的补数，反之也称 <span class="arithmatex">\(b\)</span> 是 <span class="arithmatex">\(a\)</span> 到 <span class="arithmatex">\(c\)</span> 的补数。</p>
|
||||
<p>这是因为原码和补码的相互转换实际上是计算“补数”的过程。我们先给出补数的定义：假设 <span class="arithmatex">\(a + b = c\)</span> ，那么我们称 <span class="arithmatex">\(a\)</span> 是 <span class="arithmatex">\(b\)</span> 到 <span class="arithmatex">\(c\)</span> 的补数，反之也称 <span class="arithmatex">\(b\)</span> 是 <span class="arithmatex">\(a\)</span> 到 <span class="arithmatex">\(c\)</span> 的补数。</p>
|
||||
<p>给定一个 <span class="arithmatex">\(n = 4\)</span> 位长度的二进制数 <span class="arithmatex">\(0010\)</span> ，如果将这个数字看作原码（不考虑符号位），那么它的补码需通过“先取反后加 1”得到：</p>
|
||||
<div class="arithmatex">\[
|
||||
0010 \rightarrow 1101 \rightarrow 1110
|
||||
|
|
@ -3705,7 +3705,7 @@
|
|||
\]</div>
|
||||
<p>总结来看，“先取反后加 1”和“先减 1 后取反”这两种运算都是在计算到 <span class="arithmatex">\(10000\)</span> 的补数，它们是等价的。</p>
|
||||
<p>本质上看，“取反”操作实际上是求到 <span class="arithmatex">\(1111\)</span> 的补数（因为恒有 <code>原码 + 反码 = 1111</code>）；而在反码基础上再加 1 得到的补码，就是到 <span class="arithmatex">\(10000\)</span> 的补数。</p>
|
||||
<p>上述 <span class="arithmatex">\(n = 4\)</span> 为例，其可推广至任意位数的二进制数。</p>
|
||||
<p>上述以 <span class="arithmatex">\(n = 4\)</span> 为例，其可被推广至任意位数的二进制数。</p>
|
||||
|
||||
<!-- Source file information -->
|
||||
|
||||
|
|
|
|||
|
|
@ -3929,7 +3929,18 @@ dp[i] = \min(dp[i-1], dp[i-2]) + cost[i]
|
|||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">min_cost_climbing_stairs_dp</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### 爬楼梯最小代价：动态规划 ###</span>
|
||||
<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">min_cost_climbing_stairs_dp</span><span class="p">(</span><span class="n">cost</span><span class="p">)</span>
|
||||
<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cost</span><span class="o">.</span><span class="n">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span>
|
||||
<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">cost</span><span class="o">[</span><span class="n">n</span><span class="o">]</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span>
|
||||
<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w"> </span><span class="c1"># 初始化 dp 表，用于存储子问题的解</span>
|
||||
<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
|
||||
<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w"> </span><span class="c1"># 初始状态：预设最小子问题的解</span>
|
||||
<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="mi">1</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="mi">2</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cost</span><span class="o">[</span><span class="mi">1</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">cost</span><span class="o">[</span><span class="mi">2</span><span class="o">]</span>
|
||||
<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w"> </span><span class="c1"># 状态转移：从较小子问题逐步求解较大子问题</span>
|
||||
<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w"> </span><span class="p">(</span><span class="mi">3</span><span class="o">...</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">))</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">i</span><span class="o">|</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="o">]].</span><span class="n">min</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">cost</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">n</span><span class="o">]</span>
|
||||
<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="k">end</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
|
|
@ -4167,7 +4178,27 @@ dp[i] = \min(dp[i-1], dp[i-2]) + cost[i]
|
|||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">min_cost_climbing_stairs_dp_comp</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="c1">### 爬楼梯最小代价：动态规划 ###</span>
|
||||
<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">min_cost_climbing_stairs_dp</span><span class="p">(</span><span class="n">cost</span><span class="p">)</span>
|
||||
<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cost</span><span class="o">.</span><span class="n">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span>
|
||||
<a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">cost</span><span class="o">[</span><span class="n">n</span><span class="o">]</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span>
|
||||
<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a><span class="w"> </span><span class="c1"># 初始化 dp 表，用于存储子问题的解</span>
|
||||
<a id="__codelineno-26-6" name="__codelineno-26-6" href="#__codelineno-26-6"></a><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
|
||||
<a id="__codelineno-26-7" name="__codelineno-26-7" href="#__codelineno-26-7"></a><span class="w"> </span><span class="c1"># 初始状态：预设最小子问题的解</span>
|
||||
<a id="__codelineno-26-8" name="__codelineno-26-8" href="#__codelineno-26-8"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="mi">1</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="mi">2</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cost</span><span class="o">[</span><span class="mi">1</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">cost</span><span class="o">[</span><span class="mi">2</span><span class="o">]</span>
|
||||
<a id="__codelineno-26-9" name="__codelineno-26-9" href="#__codelineno-26-9"></a><span class="w"> </span><span class="c1"># 状态转移：从较小子问题逐步求解较大子问题</span>
|
||||
<a id="__codelineno-26-10" name="__codelineno-26-10" href="#__codelineno-26-10"></a><span class="w"> </span><span class="p">(</span><span class="mi">3</span><span class="o">...</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">))</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">i</span><span class="o">|</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="o">]].</span><span class="n">min</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">cost</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-26-11" name="__codelineno-26-11" href="#__codelineno-26-11"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">n</span><span class="o">]</span>
|
||||
<a id="__codelineno-26-12" name="__codelineno-26-12" href="#__codelineno-26-12"></a><span class="k">end</span>
|
||||
<a id="__codelineno-26-13" name="__codelineno-26-13" href="#__codelineno-26-13"></a>
|
||||
<a id="__codelineno-26-14" name="__codelineno-26-14" href="#__codelineno-26-14"></a><span class="c1"># 爬楼梯最小代价：空间优化后的动态规划</span>
|
||||
<a id="__codelineno-26-15" name="__codelineno-26-15" href="#__codelineno-26-15"></a><span class="k">def</span><span class="w"> </span><span class="nf">min_cost_climbing_stairs_dp_comp</span><span class="p">(</span><span class="n">cost</span><span class="p">)</span>
|
||||
<a id="__codelineno-26-16" name="__codelineno-26-16" href="#__codelineno-26-16"></a><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cost</span><span class="o">.</span><span class="n">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span>
|
||||
<a id="__codelineno-26-17" name="__codelineno-26-17" href="#__codelineno-26-17"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">cost</span><span class="o">[</span><span class="n">n</span><span class="o">]</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span>
|
||||
<a id="__codelineno-26-18" name="__codelineno-26-18" href="#__codelineno-26-18"></a><span class="w"> </span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cost</span><span class="o">[</span><span class="mi">1</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">cost</span><span class="o">[</span><span class="mi">2</span><span class="o">]</span>
|
||||
<a id="__codelineno-26-19" name="__codelineno-26-19" href="#__codelineno-26-19"></a><span class="w"> </span><span class="p">(</span><span class="mi">3</span><span class="o">...</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">))</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">i</span><span class="o">|</span><span class="w"> </span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">b</span><span class="p">,</span><span class="w"> </span><span class="o">[</span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="n">b</span><span class="o">].</span><span class="n">min</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">cost</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-26-20" name="__codelineno-26-20" href="#__codelineno-26-20"></a><span class="w"> </span><span class="n">b</span>
|
||||
<a id="__codelineno-26-21" name="__codelineno-26-21" href="#__codelineno-26-21"></a><span class="k">end</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
|
|
@ -4497,7 +4528,23 @@ dp[i, 2] = dp[i-2, 1] + dp[i-2, 2]
|
|||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">climbing_stairs_constraint_dp.rb</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">climbing_stairs_constraint_dp</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">climbing_stairs_constraint_dp.rb</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="c1">### 带约束爬楼梯：动态规划 ###</span>
|
||||
<a id="__codelineno-40-2" name="__codelineno-40-2" href="#__codelineno-40-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">climbing_stairs_constraint_dp</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
|
||||
<a id="__codelineno-40-3" name="__codelineno-40-3" href="#__codelineno-40-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span>
|
||||
<a id="__codelineno-40-4" name="__codelineno-40-4" href="#__codelineno-40-4"></a>
|
||||
<a id="__codelineno-40-5" name="__codelineno-40-5" href="#__codelineno-40-5"></a><span class="w"> </span><span class="c1"># 初始化 dp 表，用于存储子问题的解</span>
|
||||
<a id="__codelineno-40-6" name="__codelineno-40-6" href="#__codelineno-40-6"></a><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-40-7" name="__codelineno-40-7" href="#__codelineno-40-7"></a><span class="w"> </span><span class="c1"># 初始状态：预设最小子问题的解</span>
|
||||
<a id="__codelineno-40-8" name="__codelineno-40-8" href="#__codelineno-40-8"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="mi">1</span><span class="o">][</span><span class="mi">1</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="mi">1</span><span class="o">][</span><span class="mi">2</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span>
|
||||
<a id="__codelineno-40-9" name="__codelineno-40-9" href="#__codelineno-40-9"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="mi">2</span><span class="o">][</span><span class="mi">1</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="mi">2</span><span class="o">][</span><span class="mi">2</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="mi">1</span>
|
||||
<a id="__codelineno-40-10" name="__codelineno-40-10" href="#__codelineno-40-10"></a><span class="w"> </span><span class="c1"># 状态转移：从较小子问题逐步求解较大子问题</span>
|
||||
<a id="__codelineno-40-11" name="__codelineno-40-11" href="#__codelineno-40-11"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">3</span><span class="o">...</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-40-12" name="__codelineno-40-12" href="#__codelineno-40-12"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="mi">2</span><span class="o">]</span>
|
||||
<a id="__codelineno-40-13" name="__codelineno-40-13" href="#__codelineno-40-13"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="mi">2</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="o">][</span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="o">][</span><span class="mi">2</span><span class="o">]</span>
|
||||
<a id="__codelineno-40-14" name="__codelineno-40-14" href="#__codelineno-40-14"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-40-15" name="__codelineno-40-15" href="#__codelineno-40-15"></a>
|
||||
<a id="__codelineno-40-16" name="__codelineno-40-16" href="#__codelineno-40-16"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">n</span><span class="o">][</span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">n</span><span class="o">][</span><span class="mi">2</span><span class="o">]</span>
|
||||
<a id="__codelineno-40-17" name="__codelineno-40-17" href="#__codelineno-40-17"></a><span class="k">end</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
|
|
|
|||
|
|
@ -4059,7 +4059,18 @@ dp[i, j] = \min(dp[i-1, j], dp[i, j-1]) + grid[i, j]
|
|||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">min_path_sum.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">min_path_sum_dfs</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">min_path_sum.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### 最小路径和：暴力搜索 ###</span>
|
||||
<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">min_path_sum_dfs</span><span class="p">(</span><span class="n">grid</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">)</span>
|
||||
<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w"> </span><span class="c1"># 若为左上角单元格，则终止搜索</span>
|
||||
<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span>
|
||||
<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w"> </span><span class="c1"># 若行列索引越界，则返回 +∞ 代价</span>
|
||||
<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nb">Float</span><span class="o">::</span><span class="no">INFINITY</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="mi">0</span>
|
||||
<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w"> </span><span class="c1"># 计算从左上角到 (i-1, j) 和 (i, j-1) 的最小路径代价</span>
|
||||
<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w"> </span><span class="n">up</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">min_path_sum_dfs</span><span class="p">(</span><span class="n">grid</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">)</span>
|
||||
<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">min_path_sum_dfs</span><span class="p">(</span><span class="n">grid</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w"> </span><span class="c1"># 返回从左上角到 (i, j) 的最小路径代价</span>
|
||||
<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="w"> </span><span class="o">[</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">up</span><span class="o">].</span><span class="n">min</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span>
|
||||
<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="k">end</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
|
|
@ -4396,7 +4407,20 @@ dp[i, j] = \min(dp[i-1, j], dp[i, j-1]) + grid[i, j]
|
|||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">min_path_sum.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">min_path_sum_dfs_mem</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">min_path_sum.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="c1">### 最小路径和：记忆化搜索 ###</span>
|
||||
<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">min_path_sum_dfs_mem</span><span class="p">(</span><span class="n">grid</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">)</span>
|
||||
<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a><span class="w"> </span><span class="c1"># 若为左上角单元格，则终止搜索</span>
|
||||
<a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="mi">0</span><span class="o">][</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span>
|
||||
<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a><span class="w"> </span><span class="c1"># 若行列索引越界，则返回 +∞ 代价</span>
|
||||
<a id="__codelineno-26-6" name="__codelineno-26-6" href="#__codelineno-26-6"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nb">Float</span><span class="o">::</span><span class="no">INFINITY</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="mi">0</span>
|
||||
<a id="__codelineno-26-7" name="__codelineno-26-7" href="#__codelineno-26-7"></a><span class="w"> </span><span class="c1"># 若已有记录，则直接返回</span>
|
||||
<a id="__codelineno-26-8" name="__codelineno-26-8" href="#__codelineno-26-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">mem</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">mem</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
|
||||
<a id="__codelineno-26-9" name="__codelineno-26-9" href="#__codelineno-26-9"></a><span class="w"> </span><span class="c1"># 左边和上边单元格的最小路径代价</span>
|
||||
<a id="__codelineno-26-10" name="__codelineno-26-10" href="#__codelineno-26-10"></a><span class="w"> </span><span class="n">up</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">min_path_sum_dfs_mem</span><span class="p">(</span><span class="n">grid</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">)</span>
|
||||
<a id="__codelineno-26-11" name="__codelineno-26-11" href="#__codelineno-26-11"></a><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">min_path_sum_dfs_mem</span><span class="p">(</span><span class="n">grid</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-26-12" name="__codelineno-26-12" href="#__codelineno-26-12"></a><span class="w"> </span><span class="c1"># 记录并返回左上角到 (i, j) 的最小路径代价</span>
|
||||
<a id="__codelineno-26-13" name="__codelineno-26-13" href="#__codelineno-26-13"></a><span class="w"> </span><span class="n">mem</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">up</span><span class="o">].</span><span class="n">min</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span>
|
||||
<a id="__codelineno-26-14" name="__codelineno-26-14" href="#__codelineno-26-14"></a><span class="k">end</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
|
|
@ -4753,7 +4777,24 @@ dp[i, j] = \min(dp[i-1, j], dp[i, j-1]) + grid[i, j]
|
|||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">min_path_sum.rb</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">min_path_sum_dp</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">min_path_sum.rb</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="c1">### 最小路径和：动态规划 ###</span>
|
||||
<a id="__codelineno-40-2" name="__codelineno-40-2" href="#__codelineno-40-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">min_path_sum_dp</span><span class="p">(</span><span class="n">grid</span><span class="p">)</span>
|
||||
<a id="__codelineno-40-3" name="__codelineno-40-3" href="#__codelineno-40-3"></a><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grid</span><span class="o">.</span><span class="n">length</span><span class="p">,</span><span class="w"> </span><span class="n">grid</span><span class="o">.</span><span class="n">first</span><span class="o">.</span><span class="n">length</span>
|
||||
<a id="__codelineno-40-4" name="__codelineno-40-4" href="#__codelineno-40-4"></a><span class="w"> </span><span class="c1"># 初始化 dp 表</span>
|
||||
<a id="__codelineno-40-5" name="__codelineno-40-5" href="#__codelineno-40-5"></a><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">m</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-40-6" name="__codelineno-40-6" href="#__codelineno-40-6"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="mi">0</span><span class="o">][</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="mi">0</span><span class="o">][</span><span class="mi">0</span><span class="o">]</span>
|
||||
<a id="__codelineno-40-7" name="__codelineno-40-7" href="#__codelineno-40-7"></a><span class="w"> </span><span class="c1"># 状态转移：首行</span>
|
||||
<a id="__codelineno-40-8" name="__codelineno-40-8" href="#__codelineno-40-8"></a><span class="w"> </span><span class="p">(</span><span class="mi">1</span><span class="o">...</span><span class="n">m</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">j</span><span class="o">|</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="mi">0</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="mi">0</span><span class="o">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="mi">0</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-40-9" name="__codelineno-40-9" href="#__codelineno-40-9"></a><span class="w"> </span><span class="c1"># 状态转移：首列</span>
|
||||
<a id="__codelineno-40-10" name="__codelineno-40-10" href="#__codelineno-40-10"></a><span class="w"> </span><span class="p">(</span><span class="mi">1</span><span class="o">...</span><span class="n">n</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">i</span><span class="o">|</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-40-11" name="__codelineno-40-11" href="#__codelineno-40-11"></a><span class="w"> </span><span class="c1"># 状态转移：其余行和列</span>
|
||||
<a id="__codelineno-40-12" name="__codelineno-40-12" href="#__codelineno-40-12"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="n">n</span>
|
||||
<a id="__codelineno-40-13" name="__codelineno-40-13" href="#__codelineno-40-13"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="n">m</span>
|
||||
<a id="__codelineno-40-14" name="__codelineno-40-14" href="#__codelineno-40-14"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">j</span><span class="o">]].</span><span class="n">min</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span>
|
||||
<a id="__codelineno-40-15" name="__codelineno-40-15" href="#__codelineno-40-15"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-40-16" name="__codelineno-40-16" href="#__codelineno-40-16"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-40-17" name="__codelineno-40-17" href="#__codelineno-40-17"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="o">][</span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="o">]</span>
|
||||
<a id="__codelineno-40-18" name="__codelineno-40-18" href="#__codelineno-40-18"></a><span class="k">end</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
|
|
@ -5128,7 +5169,23 @@ dp[i, j] = \min(dp[i-1, j], dp[i, j-1]) + grid[i, j]
|
|||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">min_path_sum.rb</span><pre><span></span><code><a id="__codelineno-54-1" name="__codelineno-54-1" href="#__codelineno-54-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">min_path_sum_dp_comp</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">min_path_sum.rb</span><pre><span></span><code><a id="__codelineno-54-1" name="__codelineno-54-1" href="#__codelineno-54-1"></a><span class="c1">### 最小路径和：空间优化后的动态规划 ###</span>
|
||||
<a id="__codelineno-54-2" name="__codelineno-54-2" href="#__codelineno-54-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">min_path_sum_dp_comp</span><span class="p">(</span><span class="n">grid</span><span class="p">)</span>
|
||||
<a id="__codelineno-54-3" name="__codelineno-54-3" href="#__codelineno-54-3"></a><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grid</span><span class="o">.</span><span class="n">length</span><span class="p">,</span><span class="w"> </span><span class="n">grid</span><span class="o">.</span><span class="n">first</span><span class="o">.</span><span class="n">length</span>
|
||||
<a id="__codelineno-54-4" name="__codelineno-54-4" href="#__codelineno-54-4"></a><span class="w"> </span><span class="c1"># 初始化 dp 表</span>
|
||||
<a id="__codelineno-54-5" name="__codelineno-54-5" href="#__codelineno-54-5"></a><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">m</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
|
||||
<a id="__codelineno-54-6" name="__codelineno-54-6" href="#__codelineno-54-6"></a><span class="w"> </span><span class="c1"># 状态转移：首行</span>
|
||||
<a id="__codelineno-54-7" name="__codelineno-54-7" href="#__codelineno-54-7"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="mi">0</span><span class="o">][</span><span class="mi">0</span><span class="o">]</span>
|
||||
<a id="__codelineno-54-8" name="__codelineno-54-8" href="#__codelineno-54-8"></a><span class="w"> </span><span class="p">(</span><span class="mi">1</span><span class="o">...</span><span class="n">m</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">j</span><span class="o">|</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="mi">0</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-54-9" name="__codelineno-54-9" href="#__codelineno-54-9"></a><span class="w"> </span><span class="c1"># 状态转移：其余行</span>
|
||||
<a id="__codelineno-54-10" name="__codelineno-54-10" href="#__codelineno-54-10"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="n">n</span>
|
||||
<a id="__codelineno-54-11" name="__codelineno-54-11" href="#__codelineno-54-11"></a><span class="w"> </span><span class="c1"># 状态转移：首列</span>
|
||||
<a id="__codelineno-54-12" name="__codelineno-54-12" href="#__codelineno-54-12"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="mi">0</span><span class="o">]</span>
|
||||
<a id="__codelineno-54-13" name="__codelineno-54-13" href="#__codelineno-54-13"></a><span class="w"> </span><span class="c1"># 状态转移：其余列</span>
|
||||
<a id="__codelineno-54-14" name="__codelineno-54-14" href="#__codelineno-54-14"></a><span class="w"> </span><span class="p">(</span><span class="mi">1</span><span class="o">...</span><span class="n">m</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">j</span><span class="o">|</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="o">]].</span><span class="n">min</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-54-15" name="__codelineno-54-15" href="#__codelineno-54-15"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-54-16" name="__codelineno-54-16" href="#__codelineno-54-16"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span>
|
||||
<a id="__codelineno-54-17" name="__codelineno-54-17" href="#__codelineno-54-17"></a><span class="k">end</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
|
|
|
|||
|
|
@ -4084,7 +4084,27 @@ dp[i, j] = dp[i-1, j-1]
|
|||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">edit_distance.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">edit_distance_dp</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">edit_distance.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### 编辑距离：动态规划 ###</span>
|
||||
<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">edit_distance_dp</span><span class="p">(</span><span class="n">s</span><span class="p">,</span><span class="w"> </span><span class="n">t</span><span class="p">)</span>
|
||||
<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">s</span><span class="o">.</span><span class="n">length</span><span class="p">,</span><span class="w"> </span><span class="n">t</span><span class="o">.</span><span class="n">length</span>
|
||||
<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w"> </span><span class="c1"># 状态转移：首行首列</span>
|
||||
<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w"> </span><span class="p">(</span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">))</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">i</span><span class="o">|</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w"> </span><span class="p">(</span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">))</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">j</span><span class="o">|</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="mi">0</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w"> </span><span class="c1"># 状态转移：其余行和列</span>
|
||||
<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">s</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">t</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span>
|
||||
<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="w"> </span><span class="c1"># 若两字符相等，则直接跳过此两字符</span>
|
||||
<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span>
|
||||
<a id="__codelineno-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a><span class="w"> </span><span class="k">else</span>
|
||||
<a id="__codelineno-12-15" name="__codelineno-12-15" href="#__codelineno-12-15"></a><span class="w"> </span><span class="c1"># 最少编辑步数 = 插入、删除、替换这三种操作的最少编辑步数 + 1</span>
|
||||
<a id="__codelineno-12-16" name="__codelineno-12-16" href="#__codelineno-12-16"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]].</span><span class="n">min</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
|
||||
<a id="__codelineno-12-17" name="__codelineno-12-17" href="#__codelineno-12-17"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-12-18" name="__codelineno-12-18" href="#__codelineno-12-18"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-12-19" name="__codelineno-12-19" href="#__codelineno-12-19"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-12-20" name="__codelineno-12-20" href="#__codelineno-12-20"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">n</span><span class="o">][</span><span class="n">m</span><span class="o">]</span>
|
||||
<a id="__codelineno-12-21" name="__codelineno-12-21" href="#__codelineno-12-21"></a><span class="k">end</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
|
|
@ -4555,7 +4575,32 @@ dp[i, j] = dp[i-1, j-1]
|
|||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">edit_distance.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">edit_distance_dp_comp</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">edit_distance.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="c1">### 编辑距离：空间优化后的动态规划 ###</span>
|
||||
<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">edit_distance_dp_comp</span><span class="p">(</span><span class="n">s</span><span class="p">,</span><span class="w"> </span><span class="n">t</span><span class="p">)</span>
|
||||
<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">s</span><span class="o">.</span><span class="n">length</span><span class="p">,</span><span class="w"> </span><span class="n">t</span><span class="o">.</span><span class="n">length</span>
|
||||
<a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
|
||||
<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a><span class="w"> </span><span class="c1"># 状态转移：首行</span>
|
||||
<a id="__codelineno-26-6" name="__codelineno-26-6" href="#__codelineno-26-6"></a><span class="w"> </span><span class="p">(</span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">))</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">j</span><span class="o">|</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-26-7" name="__codelineno-26-7" href="#__codelineno-26-7"></a><span class="w"> </span><span class="c1"># 状态转移：其余行</span>
|
||||
<a id="__codelineno-26-8" name="__codelineno-26-8" href="#__codelineno-26-8"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-26-9" name="__codelineno-26-9" href="#__codelineno-26-9"></a><span class="w"> </span><span class="c1"># 状态转移：首列</span>
|
||||
<a id="__codelineno-26-10" name="__codelineno-26-10" href="#__codelineno-26-10"></a><span class="w"> </span><span class="n">leftup</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">.</span><span class="n">first</span><span class="w"> </span><span class="c1"># 暂存 dp[i-1, j-1]</span>
|
||||
<a id="__codelineno-26-11" name="__codelineno-26-11" href="#__codelineno-26-11"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
|
||||
<a id="__codelineno-26-12" name="__codelineno-26-12" href="#__codelineno-26-12"></a><span class="w"> </span><span class="c1"># 状态转移：其余列</span>
|
||||
<a id="__codelineno-26-13" name="__codelineno-26-13" href="#__codelineno-26-13"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-26-14" name="__codelineno-26-14" href="#__codelineno-26-14"></a><span class="w"> </span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="o">]</span>
|
||||
<a id="__codelineno-26-15" name="__codelineno-26-15" href="#__codelineno-26-15"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">s</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">t</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span>
|
||||
<a id="__codelineno-26-16" name="__codelineno-26-16" href="#__codelineno-26-16"></a><span class="w"> </span><span class="c1"># 若两字符相等，则直接跳过此两字符</span>
|
||||
<a id="__codelineno-26-17" name="__codelineno-26-17" href="#__codelineno-26-17"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">leftup</span>
|
||||
<a id="__codelineno-26-18" name="__codelineno-26-18" href="#__codelineno-26-18"></a><span class="w"> </span><span class="k">else</span>
|
||||
<a id="__codelineno-26-19" name="__codelineno-26-19" href="#__codelineno-26-19"></a><span class="w"> </span><span class="c1"># 最少编辑步数 = 插入、删除、替换这三种操作的最少编辑步数 + 1</span>
|
||||
<a id="__codelineno-26-20" name="__codelineno-26-20" href="#__codelineno-26-20"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">leftup</span><span class="o">].</span><span class="n">min</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
|
||||
<a id="__codelineno-26-21" name="__codelineno-26-21" href="#__codelineno-26-21"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-26-22" name="__codelineno-26-22" href="#__codelineno-26-22"></a><span class="w"> </span><span class="n">leftup</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span><span class="w"> </span><span class="c1"># 更新为下一轮的 dp[i-1, j-1]</span>
|
||||
<a id="__codelineno-26-23" name="__codelineno-26-23" href="#__codelineno-26-23"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-26-24" name="__codelineno-26-24" href="#__codelineno-26-24"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-26-25" name="__codelineno-26-25" href="#__codelineno-26-25"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">m</span><span class="o">]</span>
|
||||
<a id="__codelineno-26-26" name="__codelineno-26-26" href="#__codelineno-26-26"></a><span class="k">end</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
|
|
|
|||
|
|
@ -4062,9 +4062,29 @@
|
|||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">climbing_stairs_backtrack.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">backtrack</span><span class="p">}</span>
|
||||
<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a>
|
||||
<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">climbing_stairs_backtrack</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">climbing_stairs_backtrack.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### 回溯 ###</span>
|
||||
<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
|
||||
<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w"> </span><span class="c1"># 当爬到第 n 阶时，方案数量加 1</span>
|
||||
<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w"> </span><span class="n">res</span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">state</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">n</span>
|
||||
<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w"> </span><span class="c1"># 遍历所有选择</span>
|
||||
<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">choices</span>
|
||||
<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w"> </span><span class="c1"># 剪枝：不允许越过第 n 阶</span>
|
||||
<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w"> </span><span class="k">next</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">state</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">n</span>
|
||||
<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a>
|
||||
<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w"> </span><span class="c1"># 尝试：做出选择，更新状态</span>
|
||||
<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="w"> </span><span class="n">backtrack</span><span class="p">(</span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">state</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">choice</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
|
||||
<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a><span class="w"> </span><span class="c1"># 回退</span>
|
||||
<a id="__codelineno-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a><span class="k">end</span>
|
||||
<a id="__codelineno-12-15" name="__codelineno-12-15" href="#__codelineno-12-15"></a>
|
||||
<a id="__codelineno-12-16" name="__codelineno-12-16" href="#__codelineno-12-16"></a><span class="c1">### 爬楼梯：回溯 ###</span>
|
||||
<a id="__codelineno-12-17" name="__codelineno-12-17" href="#__codelineno-12-17"></a><span class="k">def</span><span class="w"> </span><span class="nf">climbing_stairs_backtrack</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
|
||||
<a id="__codelineno-12-18" name="__codelineno-12-18" href="#__codelineno-12-18"></a><span class="w"> </span><span class="n">choices</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="o">]</span><span class="w"> </span><span class="c1"># 可选择向上爬 1 阶或 2 阶</span>
|
||||
<a id="__codelineno-12-19" name="__codelineno-12-19" href="#__codelineno-12-19"></a><span class="w"> </span><span class="n">state</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="c1"># 从第 0 阶开始爬</span>
|
||||
<a id="__codelineno-12-20" name="__codelineno-12-20" href="#__codelineno-12-20"></a><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="c1"># 使用 res[0] 记录方案数量</span>
|
||||
<a id="__codelineno-12-21" name="__codelineno-12-21" href="#__codelineno-12-21"></a><span class="w"> </span><span class="n">backtrack</span><span class="p">(</span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
|
||||
<a id="__codelineno-12-22" name="__codelineno-12-22" href="#__codelineno-12-22"></a><span class="w"> </span><span class="n">res</span><span class="o">.</span><span class="n">first</span>
|
||||
<a id="__codelineno-12-23" name="__codelineno-12-23" href="#__codelineno-12-23"></a><span class="k">end</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
|
|
@ -4326,9 +4346,18 @@ dp[i] = dp[i-1] + dp[i-2]
|
|||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">climbing_stairs_dfs.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">dfs</span><span class="p">}</span>
|
||||
<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a>
|
||||
<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">climbing_stairs_dfs</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">climbing_stairs_dfs.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="c1">### 搜索 ###</span>
|
||||
<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
|
||||
<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a><span class="w"> </span><span class="c1"># 已知 dp[1] 和 dp[2] ，返回之</span>
|
||||
<a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span>
|
||||
<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a><span class="w"> </span><span class="c1"># dp[i] = dp[i-1] + dp[i-2]</span>
|
||||
<a id="__codelineno-26-6" name="__codelineno-26-6" href="#__codelineno-26-6"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
|
||||
<a id="__codelineno-26-7" name="__codelineno-26-7" href="#__codelineno-26-7"></a><span class="k">end</span>
|
||||
<a id="__codelineno-26-8" name="__codelineno-26-8" href="#__codelineno-26-8"></a>
|
||||
<a id="__codelineno-26-9" name="__codelineno-26-9" href="#__codelineno-26-9"></a><span class="c1">### 爬楼梯：搜索 ###</span>
|
||||
<a id="__codelineno-26-10" name="__codelineno-26-10" href="#__codelineno-26-10"></a><span class="k">def</span><span class="w"> </span><span class="nf">climbing_stairs_dfs</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
|
||||
<a id="__codelineno-26-11" name="__codelineno-26-11" href="#__codelineno-26-11"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
|
||||
<a id="__codelineno-26-12" name="__codelineno-26-12" href="#__codelineno-26-12"></a><span class="k">end</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
|
|
@ -4667,9 +4696,25 @@ dp[i] = dp[i-1] + dp[i-2]
|
|||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">climbing_stairs_dfs_mem.rb</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">dfs</span><span class="p">}</span>
|
||||
<a id="__codelineno-40-2" name="__codelineno-40-2" href="#__codelineno-40-2"></a>
|
||||
<a id="__codelineno-40-3" name="__codelineno-40-3" href="#__codelineno-40-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">climbing_stairs_dfs_mem</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">climbing_stairs_dfs_mem.rb</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="c1">### 记忆化搜索 ###</span>
|
||||
<a id="__codelineno-40-2" name="__codelineno-40-2" href="#__codelineno-40-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">)</span>
|
||||
<a id="__codelineno-40-3" name="__codelineno-40-3" href="#__codelineno-40-3"></a><span class="w"> </span><span class="c1"># 已知 dp[1] 和 dp[2] ，返回之</span>
|
||||
<a id="__codelineno-40-4" name="__codelineno-40-4" href="#__codelineno-40-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span>
|
||||
<a id="__codelineno-40-5" name="__codelineno-40-5" href="#__codelineno-40-5"></a><span class="w"> </span><span class="c1"># 若存在记录 dp[i] ，则直接返回之</span>
|
||||
<a id="__codelineno-40-6" name="__codelineno-40-6" href="#__codelineno-40-6"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">mem</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">mem</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
|
||||
<a id="__codelineno-40-7" name="__codelineno-40-7" href="#__codelineno-40-7"></a>
|
||||
<a id="__codelineno-40-8" name="__codelineno-40-8" href="#__codelineno-40-8"></a><span class="w"> </span><span class="c1"># dp[i] = dp[i-1] + dp[i-2]</span>
|
||||
<a id="__codelineno-40-9" name="__codelineno-40-9" href="#__codelineno-40-9"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">)</span>
|
||||
<a id="__codelineno-40-10" name="__codelineno-40-10" href="#__codelineno-40-10"></a><span class="w"> </span><span class="c1"># 记录 dp[i]</span>
|
||||
<a id="__codelineno-40-11" name="__codelineno-40-11" href="#__codelineno-40-11"></a><span class="w"> </span><span class="n">mem</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">count</span>
|
||||
<a id="__codelineno-40-12" name="__codelineno-40-12" href="#__codelineno-40-12"></a><span class="k">end</span>
|
||||
<a id="__codelineno-40-13" name="__codelineno-40-13" href="#__codelineno-40-13"></a>
|
||||
<a id="__codelineno-40-14" name="__codelineno-40-14" href="#__codelineno-40-14"></a><span class="c1">### 爬楼梯：记忆化搜索 ###</span>
|
||||
<a id="__codelineno-40-15" name="__codelineno-40-15" href="#__codelineno-40-15"></a><span class="k">def</span><span class="w"> </span><span class="nf">climbing_stairs_dfs_mem</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
|
||||
<a id="__codelineno-40-16" name="__codelineno-40-16" href="#__codelineno-40-16"></a><span class="w"> </span><span class="c1"># mem[i] 记录爬到第 i 阶的方案总数，-1 代表无记录</span>
|
||||
<a id="__codelineno-40-17" name="__codelineno-40-17" href="#__codelineno-40-17"></a><span class="w"> </span><span class="n">mem</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-40-18" name="__codelineno-40-18" href="#__codelineno-40-18"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">)</span>
|
||||
<a id="__codelineno-40-19" name="__codelineno-40-19" href="#__codelineno-40-19"></a><span class="k">end</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
|
|
@ -4931,7 +4976,19 @@ dp[i] = dp[i-1] + dp[i-2]
|
|||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">climbing_stairs_dp.rb</span><pre><span></span><code><a id="__codelineno-54-1" name="__codelineno-54-1" href="#__codelineno-54-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">climbing_stairs_dp</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">climbing_stairs_dp.rb</span><pre><span></span><code><a id="__codelineno-54-1" name="__codelineno-54-1" href="#__codelineno-54-1"></a><span class="c1">### 爬楼梯：动态规划 ###</span>
|
||||
<a id="__codelineno-54-2" name="__codelineno-54-2" href="#__codelineno-54-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">climbing_stairs_dp</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
|
||||
<a id="__codelineno-54-3" name="__codelineno-54-3" href="#__codelineno-54-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span>
|
||||
<a id="__codelineno-54-4" name="__codelineno-54-4" href="#__codelineno-54-4"></a>
|
||||
<a id="__codelineno-54-5" name="__codelineno-54-5" href="#__codelineno-54-5"></a><span class="w"> </span><span class="c1"># 初始化 dp 表，用于存储子问题的解</span>
|
||||
<a id="__codelineno-54-6" name="__codelineno-54-6" href="#__codelineno-54-6"></a><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
|
||||
<a id="__codelineno-54-7" name="__codelineno-54-7" href="#__codelineno-54-7"></a><span class="w"> </span><span class="c1"># 初始状态：预设最小子问题的解</span>
|
||||
<a id="__codelineno-54-8" name="__codelineno-54-8" href="#__codelineno-54-8"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="mi">1</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="mi">2</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span>
|
||||
<a id="__codelineno-54-9" name="__codelineno-54-9" href="#__codelineno-54-9"></a><span class="w"> </span><span class="c1"># 状态转移：从较小子问题逐步求解较大子问题</span>
|
||||
<a id="__codelineno-54-10" name="__codelineno-54-10" href="#__codelineno-54-10"></a><span class="w"> </span><span class="p">(</span><span class="mi">3</span><span class="o">...</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">))</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">i</span><span class="o">|</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="o">]</span><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-54-11" name="__codelineno-54-11" href="#__codelineno-54-11"></a>
|
||||
<a id="__codelineno-54-12" name="__codelineno-54-12" href="#__codelineno-54-12"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">n</span><span class="o">]</span>
|
||||
<a id="__codelineno-54-13" name="__codelineno-54-13" href="#__codelineno-54-13"></a><span class="k">end</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
|
|
@ -5153,7 +5210,15 @@ dp[i] = dp[i-1] + dp[i-2]
|
|||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">climbing_stairs_dp.rb</span><pre><span></span><code><a id="__codelineno-68-1" name="__codelineno-68-1" href="#__codelineno-68-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">climbing_stairs_dp_comp</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">climbing_stairs_dp.rb</span><pre><span></span><code><a id="__codelineno-68-1" name="__codelineno-68-1" href="#__codelineno-68-1"></a><span class="c1">### 爬楼梯：空间优化后的动态规划 ###</span>
|
||||
<a id="__codelineno-68-2" name="__codelineno-68-2" href="#__codelineno-68-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">climbing_stairs_dp_comp</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
|
||||
<a id="__codelineno-68-3" name="__codelineno-68-3" href="#__codelineno-68-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span>
|
||||
<a id="__codelineno-68-4" name="__codelineno-68-4" href="#__codelineno-68-4"></a>
|
||||
<a id="__codelineno-68-5" name="__codelineno-68-5" href="#__codelineno-68-5"></a><span class="w"> </span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span>
|
||||
<a id="__codelineno-68-6" name="__codelineno-68-6" href="#__codelineno-68-6"></a><span class="w"> </span><span class="p">(</span><span class="mi">3</span><span class="o">...</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">))</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">b</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-68-7" name="__codelineno-68-7" href="#__codelineno-68-7"></a>
|
||||
<a id="__codelineno-68-8" name="__codelineno-68-8" href="#__codelineno-68-8"></a><span class="w"> </span><span class="n">b</span>
|
||||
<a id="__codelineno-68-9" name="__codelineno-68-9" href="#__codelineno-68-9"></a><span class="k">end</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
|
|
|
|||
|
|
@ -3977,7 +3977,18 @@ dp[i, c] = \max(dp[i-1, c], dp[i-1, c - wgt[i-1]] + val[i-1])
|
|||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">knapsack.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">knapsack_dfs</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">knapsack.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### 0-1 背包：暴力搜索 ###</span>
|
||||
<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">knapsack_dfs</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">)</span>
|
||||
<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w"> </span><span class="c1"># 若已选完所有物品或背包无剩余容量，则返回价值 0</span>
|
||||
<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span>
|
||||
<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w"> </span><span class="c1"># 若超过背包容量，则只能选择不放入背包</span>
|
||||
<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">knapsack_dfs</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">c</span>
|
||||
<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w"> </span><span class="c1"># 计算不放入和放入物品 i 的最大价值</span>
|
||||
<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w"> </span><span class="n">no</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">knapsack_dfs</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">)</span>
|
||||
<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w"> </span><span class="n">yes</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">knapsack_dfs</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span>
|
||||
<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w"> </span><span class="c1"># 返回两种方案中价值更大的那一个</span>
|
||||
<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="w"> </span><span class="o">[</span><span class="n">no</span><span class="p">,</span><span class="w"> </span><span class="n">yes</span><span class="o">].</span><span class="n">max</span>
|
||||
<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="k">end</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
|
|
@ -4323,7 +4334,20 @@ dp[i, c] = \max(dp[i-1, c], dp[i-1, c - wgt[i-1]] + val[i-1])
|
|||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">knapsack.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">knapsack_dfs_mem</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">knapsack.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="c1">### 0-1 背包：记忆化搜索 ###</span>
|
||||
<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">knapsack_dfs_mem</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">)</span>
|
||||
<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a><span class="w"> </span><span class="c1"># 若已选完所有物品或背包无剩余容量，则返回价值 0</span>
|
||||
<a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span>
|
||||
<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a><span class="w"> </span><span class="c1"># 若已有记录，则直接返回</span>
|
||||
<a id="__codelineno-26-6" name="__codelineno-26-6" href="#__codelineno-26-6"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">mem</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">mem</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
|
||||
<a id="__codelineno-26-7" name="__codelineno-26-7" href="#__codelineno-26-7"></a><span class="w"> </span><span class="c1"># 若超过背包容量，则只能选择不放入背包</span>
|
||||
<a id="__codelineno-26-8" name="__codelineno-26-8" href="#__codelineno-26-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">knapsack_dfs_mem</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">c</span>
|
||||
<a id="__codelineno-26-9" name="__codelineno-26-9" href="#__codelineno-26-9"></a><span class="w"> </span><span class="c1"># 计算不放入和放入物品 i 的最大价值</span>
|
||||
<a id="__codelineno-26-10" name="__codelineno-26-10" href="#__codelineno-26-10"></a><span class="w"> </span><span class="n">no</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">knapsack_dfs_mem</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">)</span>
|
||||
<a id="__codelineno-26-11" name="__codelineno-26-11" href="#__codelineno-26-11"></a><span class="w"> </span><span class="n">yes</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">knapsack_dfs_mem</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span>
|
||||
<a id="__codelineno-26-12" name="__codelineno-26-12" href="#__codelineno-26-12"></a><span class="w"> </span><span class="c1"># 记录并返回两种方案中价值更大的那一个</span>
|
||||
<a id="__codelineno-26-13" name="__codelineno-26-13" href="#__codelineno-26-13"></a><span class="w"> </span><span class="n">mem</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="n">no</span><span class="p">,</span><span class="w"> </span><span class="n">yes</span><span class="o">].</span><span class="n">max</span>
|
||||
<a id="__codelineno-26-14" name="__codelineno-26-14" href="#__codelineno-26-14"></a><span class="k">end</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
|
|
@ -4654,7 +4678,25 @@ dp[i, c] = \max(dp[i-1, c], dp[i-1, c - wgt[i-1]] + val[i-1])
|
|||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">knapsack.rb</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">knapsack_dp</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">knapsack.rb</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="c1">### 0-1 背包：动态规划 ###</span>
|
||||
<a id="__codelineno-40-2" name="__codelineno-40-2" href="#__codelineno-40-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">knapsack_dp</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">cap</span><span class="p">)</span>
|
||||
<a id="__codelineno-40-3" name="__codelineno-40-3" href="#__codelineno-40-3"></a><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">wgt</span><span class="o">.</span><span class="n">length</span>
|
||||
<a id="__codelineno-40-4" name="__codelineno-40-4" href="#__codelineno-40-4"></a><span class="w"> </span><span class="c1"># 初始化 dp 表</span>
|
||||
<a id="__codelineno-40-5" name="__codelineno-40-5" href="#__codelineno-40-5"></a><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-40-6" name="__codelineno-40-6" href="#__codelineno-40-6"></a><span class="w"> </span><span class="c1"># 状态转移</span>
|
||||
<a id="__codelineno-40-7" name="__codelineno-40-7" href="#__codelineno-40-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-40-8" name="__codelineno-40-8" href="#__codelineno-40-8"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-40-9" name="__codelineno-40-9" href="#__codelineno-40-9"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">c</span>
|
||||
<a id="__codelineno-40-10" name="__codelineno-40-10" href="#__codelineno-40-10"></a><span class="w"> </span><span class="c1"># 若超过背包容量，则不选物品 i</span>
|
||||
<a id="__codelineno-40-11" name="__codelineno-40-11" href="#__codelineno-40-11"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">c</span><span class="o">]</span>
|
||||
<a id="__codelineno-40-12" name="__codelineno-40-12" href="#__codelineno-40-12"></a><span class="w"> </span><span class="k">else</span>
|
||||
<a id="__codelineno-40-13" name="__codelineno-40-13" href="#__codelineno-40-13"></a><span class="w"> </span><span class="c1"># 不选和选物品 i 这两种方案的较大值</span>
|
||||
<a id="__codelineno-40-14" name="__codelineno-40-14" href="#__codelineno-40-14"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]].</span><span class="n">max</span>
|
||||
<a id="__codelineno-40-15" name="__codelineno-40-15" href="#__codelineno-40-15"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-40-16" name="__codelineno-40-16" href="#__codelineno-40-16"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-40-17" name="__codelineno-40-17" href="#__codelineno-40-17"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-40-18" name="__codelineno-40-18" href="#__codelineno-40-18"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">n</span><span class="o">][</span><span class="n">cap</span><span class="o">]</span>
|
||||
<a id="__codelineno-40-19" name="__codelineno-40-19" href="#__codelineno-40-19"></a><span class="k">end</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
|
|
@ -5020,7 +5062,26 @@ dp[i, c] = \max(dp[i-1, c], dp[i-1, c - wgt[i-1]] + val[i-1])
|
|||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">knapsack.rb</span><pre><span></span><code><a id="__codelineno-54-1" name="__codelineno-54-1" href="#__codelineno-54-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">knapsack_dp_comp</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">knapsack.rb</span><pre><span></span><code><a id="__codelineno-54-1" name="__codelineno-54-1" href="#__codelineno-54-1"></a><span class="c1">### 0-1 背包：空间优化后的动态规划 ###</span>
|
||||
<a id="__codelineno-54-2" name="__codelineno-54-2" href="#__codelineno-54-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">knapsack_dp_comp</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">cap</span><span class="p">)</span>
|
||||
<a id="__codelineno-54-3" name="__codelineno-54-3" href="#__codelineno-54-3"></a><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">wgt</span><span class="o">.</span><span class="n">length</span>
|
||||
<a id="__codelineno-54-4" name="__codelineno-54-4" href="#__codelineno-54-4"></a><span class="w"> </span><span class="c1"># 初始化 dp 表</span>
|
||||
<a id="__codelineno-54-5" name="__codelineno-54-5" href="#__codelineno-54-5"></a><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
|
||||
<a id="__codelineno-54-6" name="__codelineno-54-6" href="#__codelineno-54-6"></a><span class="w"> </span><span class="c1"># 状态转移</span>
|
||||
<a id="__codelineno-54-7" name="__codelineno-54-7" href="#__codelineno-54-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-54-8" name="__codelineno-54-8" href="#__codelineno-54-8"></a><span class="w"> </span><span class="c1"># 倒序遍历</span>
|
||||
<a id="__codelineno-54-9" name="__codelineno-54-9" href="#__codelineno-54-9"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">cap</span><span class="o">.</span><span class="n">downto</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-54-10" name="__codelineno-54-10" href="#__codelineno-54-10"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">c</span>
|
||||
<a id="__codelineno-54-11" name="__codelineno-54-11" href="#__codelineno-54-11"></a><span class="w"> </span><span class="c1"># 若超过背包容量，则不选物品 i</span>
|
||||
<a id="__codelineno-54-12" name="__codelineno-54-12" href="#__codelineno-54-12"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">c</span><span class="o">]</span>
|
||||
<a id="__codelineno-54-13" name="__codelineno-54-13" href="#__codelineno-54-13"></a><span class="w"> </span><span class="k">else</span>
|
||||
<a id="__codelineno-54-14" name="__codelineno-54-14" href="#__codelineno-54-14"></a><span class="w"> </span><span class="c1"># 不选和选物品 i 这两种方案的较大值</span>
|
||||
<a id="__codelineno-54-15" name="__codelineno-54-15" href="#__codelineno-54-15"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="n">dp</span><span class="o">[</span><span class="n">c</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]].</span><span class="n">max</span>
|
||||
<a id="__codelineno-54-16" name="__codelineno-54-16" href="#__codelineno-54-16"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-54-17" name="__codelineno-54-17" href="#__codelineno-54-17"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-54-18" name="__codelineno-54-18" href="#__codelineno-54-18"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-54-19" name="__codelineno-54-19" href="#__codelineno-54-19"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">cap</span><span class="o">]</span>
|
||||
<a id="__codelineno-54-20" name="__codelineno-54-20" href="#__codelineno-54-20"></a><span class="k">end</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
|
|
|
|||
|
|
@ -4194,7 +4194,25 @@ dp[i, c] = \max(dp[i-1, c], dp[i, c - wgt[i-1]] + val[i-1])
|
|||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">unbounded_knapsack.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">unbounded_knapsack_dp</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">unbounded_knapsack.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### 完全背包：动态规划 ###</span>
|
||||
<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">unbounded_knapsack_dp</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">cap</span><span class="p">)</span>
|
||||
<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">wgt</span><span class="o">.</span><span class="n">length</span>
|
||||
<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w"> </span><span class="c1"># 初始化 dp 表</span>
|
||||
<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w"> </span><span class="c1"># 状态转移</span>
|
||||
<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">c</span>
|
||||
<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w"> </span><span class="c1"># 若超过背包容量，则不选物品 i</span>
|
||||
<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">c</span><span class="o">]</span>
|
||||
<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="w"> </span><span class="k">else</span>
|
||||
<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a><span class="w"> </span><span class="c1"># 不选和选物品 i 这两种方案的较大值</span>
|
||||
<a id="__codelineno-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]].</span><span class="n">max</span>
|
||||
<a id="__codelineno-12-15" name="__codelineno-12-15" href="#__codelineno-12-15"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-12-16" name="__codelineno-12-16" href="#__codelineno-12-16"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-12-17" name="__codelineno-12-17" href="#__codelineno-12-17"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-12-18" name="__codelineno-12-18" href="#__codelineno-12-18"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">n</span><span class="o">][</span><span class="n">cap</span><span class="o">]</span>
|
||||
<a id="__codelineno-12-19" name="__codelineno-12-19" href="#__codelineno-12-19"></a><span class="k">end</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
|
|
@ -4529,7 +4547,46 @@ dp[i, c] = \max(dp[i-1, c], dp[i, c - wgt[i-1]] + val[i-1])
|
|||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">unbounded_knapsack.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">unbounded_knapsack_dp_comp</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">unbounded_knapsack.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="c1">### 完全背包：动态规划 ###</span>
|
||||
<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">unbounded_knapsack_dp</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">cap</span><span class="p">)</span>
|
||||
<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">wgt</span><span class="o">.</span><span class="n">length</span>
|
||||
<a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a><span class="w"> </span><span class="c1"># 初始化 dp 表</span>
|
||||
<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-26-6" name="__codelineno-26-6" href="#__codelineno-26-6"></a><span class="w"> </span><span class="c1"># 状态转移</span>
|
||||
<a id="__codelineno-26-7" name="__codelineno-26-7" href="#__codelineno-26-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-26-8" name="__codelineno-26-8" href="#__codelineno-26-8"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-26-9" name="__codelineno-26-9" href="#__codelineno-26-9"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">c</span>
|
||||
<a id="__codelineno-26-10" name="__codelineno-26-10" href="#__codelineno-26-10"></a><span class="w"> </span><span class="c1"># 若超过背包容量，则不选物品 i</span>
|
||||
<a id="__codelineno-26-11" name="__codelineno-26-11" href="#__codelineno-26-11"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">c</span><span class="o">]</span>
|
||||
<a id="__codelineno-26-12" name="__codelineno-26-12" href="#__codelineno-26-12"></a><span class="w"> </span><span class="k">else</span>
|
||||
<a id="__codelineno-26-13" name="__codelineno-26-13" href="#__codelineno-26-13"></a><span class="w"> </span><span class="c1"># 不选和选物品 i 这两种方案的较大值</span>
|
||||
<a id="__codelineno-26-14" name="__codelineno-26-14" href="#__codelineno-26-14"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]].</span><span class="n">max</span>
|
||||
<a id="__codelineno-26-15" name="__codelineno-26-15" href="#__codelineno-26-15"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-26-16" name="__codelineno-26-16" href="#__codelineno-26-16"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-26-17" name="__codelineno-26-17" href="#__codelineno-26-17"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-26-18" name="__codelineno-26-18" href="#__codelineno-26-18"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">n</span><span class="o">][</span><span class="n">cap</span><span class="o">]</span>
|
||||
<a id="__codelineno-26-19" name="__codelineno-26-19" href="#__codelineno-26-19"></a><span class="k">end</span>
|
||||
<a id="__codelineno-26-20" name="__codelineno-26-20" href="#__codelineno-26-20"></a>
|
||||
<a id="__codelineno-26-21" name="__codelineno-26-21" href="#__codelineno-26-21"></a><span class="c1">### 完全背包：空间优化后的动态规划 ##3</span>
|
||||
<a id="__codelineno-26-22" name="__codelineno-26-22" href="#__codelineno-26-22"></a><span class="k">def</span><span class="w"> </span><span class="nf">unbounded_knapsack_dp_comp</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">cap</span><span class="p">)</span>
|
||||
<a id="__codelineno-26-23" name="__codelineno-26-23" href="#__codelineno-26-23"></a><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">wgt</span><span class="o">.</span><span class="n">length</span>
|
||||
<a id="__codelineno-26-24" name="__codelineno-26-24" href="#__codelineno-26-24"></a><span class="w"> </span><span class="c1"># 初始化 dp 表</span>
|
||||
<a id="__codelineno-26-25" name="__codelineno-26-25" href="#__codelineno-26-25"></a><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
|
||||
<a id="__codelineno-26-26" name="__codelineno-26-26" href="#__codelineno-26-26"></a><span class="w"> </span><span class="c1"># 状态转移</span>
|
||||
<a id="__codelineno-26-27" name="__codelineno-26-27" href="#__codelineno-26-27"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-26-28" name="__codelineno-26-28" href="#__codelineno-26-28"></a><span class="w"> </span><span class="c1"># 正序遍历</span>
|
||||
<a id="__codelineno-26-29" name="__codelineno-26-29" href="#__codelineno-26-29"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-26-30" name="__codelineno-26-30" href="#__codelineno-26-30"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">c</span>
|
||||
<a id="__codelineno-26-31" name="__codelineno-26-31" href="#__codelineno-26-31"></a><span class="w"> </span><span class="c1"># 若超过背包容量，则不选物品 i</span>
|
||||
<a id="__codelineno-26-32" name="__codelineno-26-32" href="#__codelineno-26-32"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">c</span><span class="o">]</span>
|
||||
<a id="__codelineno-26-33" name="__codelineno-26-33" href="#__codelineno-26-33"></a><span class="w"> </span><span class="k">else</span>
|
||||
<a id="__codelineno-26-34" name="__codelineno-26-34" href="#__codelineno-26-34"></a><span class="w"> </span><span class="c1"># 不选和选物品 i 这两种方案的较大值</span>
|
||||
<a id="__codelineno-26-35" name="__codelineno-26-35" href="#__codelineno-26-35"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="n">dp</span><span class="o">[</span><span class="n">c</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]].</span><span class="n">max</span>
|
||||
<a id="__codelineno-26-36" name="__codelineno-26-36" href="#__codelineno-26-36"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-26-37" name="__codelineno-26-37" href="#__codelineno-26-37"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-26-38" name="__codelineno-26-38" href="#__codelineno-26-38"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-26-39" name="__codelineno-26-39" href="#__codelineno-26-39"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">cap</span><span class="o">]</span>
|
||||
<a id="__codelineno-26-40" name="__codelineno-26-40" href="#__codelineno-26-40"></a><span class="k">end</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
|
|
@ -4940,7 +4997,28 @@ dp[i, a] = \min(dp[i-1, a], dp[i, a - coins[i-1]] + 1)
|
|||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">coin_change.rb</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">coin_change_dp</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">coin_change.rb</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="c1">### 零钱兑换：动态规划 ###</span>
|
||||
<a id="__codelineno-40-2" name="__codelineno-40-2" href="#__codelineno-40-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">coin_change_dp</span><span class="p">(</span><span class="n">coins</span><span class="p">,</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span>
|
||||
<a id="__codelineno-40-3" name="__codelineno-40-3" href="#__codelineno-40-3"></a><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="o">.</span><span class="n">length</span>
|
||||
<a id="__codelineno-40-4" name="__codelineno-40-4" href="#__codelineno-40-4"></a><span class="w"> </span><span class="n">_MAX</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
|
||||
<a id="__codelineno-40-5" name="__codelineno-40-5" href="#__codelineno-40-5"></a><span class="w"> </span><span class="c1"># 初始化 dp 表</span>
|
||||
<a id="__codelineno-40-6" name="__codelineno-40-6" href="#__codelineno-40-6"></a><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-40-7" name="__codelineno-40-7" href="#__codelineno-40-7"></a><span class="w"> </span><span class="c1"># 状态转移：首行首列</span>
|
||||
<a id="__codelineno-40-8" name="__codelineno-40-8" href="#__codelineno-40-8"></a><span class="w"> </span><span class="p">(</span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">))</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">a</span><span class="o">|</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="mi">0</span><span class="o">][</span><span class="n">a</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_MAX</span><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-40-9" name="__codelineno-40-9" href="#__codelineno-40-9"></a><span class="w"> </span><span class="c1"># 状态转移：其余行和列</span>
|
||||
<a id="__codelineno-40-10" name="__codelineno-40-10" href="#__codelineno-40-10"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-40-11" name="__codelineno-40-11" href="#__codelineno-40-11"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-40-12" name="__codelineno-40-12" href="#__codelineno-40-12"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">coins</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">a</span>
|
||||
<a id="__codelineno-40-13" name="__codelineno-40-13" href="#__codelineno-40-13"></a><span class="w"> </span><span class="c1"># 若超过目标金额，则不选硬币 i</span>
|
||||
<a id="__codelineno-40-14" name="__codelineno-40-14" href="#__codelineno-40-14"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">a</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">a</span><span class="o">]</span>
|
||||
<a id="__codelineno-40-15" name="__codelineno-40-15" href="#__codelineno-40-15"></a><span class="w"> </span><span class="k">else</span>
|
||||
<a id="__codelineno-40-16" name="__codelineno-40-16" href="#__codelineno-40-16"></a><span class="w"> </span><span class="c1"># 不选和选硬币 i 这两种方案的较小值</span>
|
||||
<a id="__codelineno-40-17" name="__codelineno-40-17" href="#__codelineno-40-17"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">a</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">a</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">coins</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">].</span><span class="n">min</span>
|
||||
<a id="__codelineno-40-18" name="__codelineno-40-18" href="#__codelineno-40-18"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-40-19" name="__codelineno-40-19" href="#__codelineno-40-19"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-40-20" name="__codelineno-40-20" href="#__codelineno-40-20"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-40-21" name="__codelineno-40-21" href="#__codelineno-40-21"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">n</span><span class="o">][</span><span class="n">amt</span><span class="o">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">_MAX</span><span class="w"> </span><span class="p">?</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">n</span><span class="o">][</span><span class="n">amt</span><span class="o">]</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
|
||||
<a id="__codelineno-40-22" name="__codelineno-40-22" href="#__codelineno-40-22"></a><span class="k">end</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
|
|
@ -5344,7 +5422,28 @@ dp[i, a] = \min(dp[i-1, a], dp[i, a - coins[i-1]] + 1)
|
|||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">coin_change.rb</span><pre><span></span><code><a id="__codelineno-54-1" name="__codelineno-54-1" href="#__codelineno-54-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">coin_change_dp_comp</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">coin_change.rb</span><pre><span></span><code><a id="__codelineno-54-1" name="__codelineno-54-1" href="#__codelineno-54-1"></a><span class="c1">### 零钱兑换：空间优化后的动态规划 ###</span>
|
||||
<a id="__codelineno-54-2" name="__codelineno-54-2" href="#__codelineno-54-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">coin_change_dp_comp</span><span class="p">(</span><span class="n">coins</span><span class="p">,</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span>
|
||||
<a id="__codelineno-54-3" name="__codelineno-54-3" href="#__codelineno-54-3"></a><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="o">.</span><span class="n">length</span>
|
||||
<a id="__codelineno-54-4" name="__codelineno-54-4" href="#__codelineno-54-4"></a><span class="w"> </span><span class="n">_MAX</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
|
||||
<a id="__codelineno-54-5" name="__codelineno-54-5" href="#__codelineno-54-5"></a><span class="w"> </span><span class="c1"># 初始化 dp 表</span>
|
||||
<a id="__codelineno-54-6" name="__codelineno-54-6" href="#__codelineno-54-6"></a><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">_MAX</span><span class="p">)</span>
|
||||
<a id="__codelineno-54-7" name="__codelineno-54-7" href="#__codelineno-54-7"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
|
||||
<a id="__codelineno-54-8" name="__codelineno-54-8" href="#__codelineno-54-8"></a><span class="w"> </span><span class="c1"># 状态转移</span>
|
||||
<a id="__codelineno-54-9" name="__codelineno-54-9" href="#__codelineno-54-9"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-54-10" name="__codelineno-54-10" href="#__codelineno-54-10"></a><span class="w"> </span><span class="c1"># 正序遍历</span>
|
||||
<a id="__codelineno-54-11" name="__codelineno-54-11" href="#__codelineno-54-11"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-54-12" name="__codelineno-54-12" href="#__codelineno-54-12"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">coins</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">a</span>
|
||||
<a id="__codelineno-54-13" name="__codelineno-54-13" href="#__codelineno-54-13"></a><span class="w"> </span><span class="c1"># 若超过目标金额，则不选硬币 i</span>
|
||||
<a id="__codelineno-54-14" name="__codelineno-54-14" href="#__codelineno-54-14"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">a</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">a</span><span class="o">]</span>
|
||||
<a id="__codelineno-54-15" name="__codelineno-54-15" href="#__codelineno-54-15"></a><span class="w"> </span><span class="k">else</span>
|
||||
<a id="__codelineno-54-16" name="__codelineno-54-16" href="#__codelineno-54-16"></a><span class="w"> </span><span class="c1"># 不选和选硬币 i 这两种方案的较小值</span>
|
||||
<a id="__codelineno-54-17" name="__codelineno-54-17" href="#__codelineno-54-17"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">a</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="n">dp</span><span class="o">[</span><span class="n">a</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">coins</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">].</span><span class="n">min</span>
|
||||
<a id="__codelineno-54-18" name="__codelineno-54-18" href="#__codelineno-54-18"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-54-19" name="__codelineno-54-19" href="#__codelineno-54-19"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-54-20" name="__codelineno-54-20" href="#__codelineno-54-20"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-54-21" name="__codelineno-54-21" href="#__codelineno-54-21"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">amt</span><span class="o">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">_MAX</span><span class="w"> </span><span class="p">?</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">amt</span><span class="o">]</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
|
||||
<a id="__codelineno-54-22" name="__codelineno-54-22" href="#__codelineno-54-22"></a><span class="k">end</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
|
|
@ -5725,7 +5824,27 @@ dp[i, a] = dp[i-1, a] + dp[i, a - coins[i-1]]
|
|||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">coin_change_ii.rb</span><pre><span></span><code><a id="__codelineno-68-1" name="__codelineno-68-1" href="#__codelineno-68-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">coin_change_ii_dp</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">coin_change_ii.rb</span><pre><span></span><code><a id="__codelineno-68-1" name="__codelineno-68-1" href="#__codelineno-68-1"></a><span class="c1">### 零钱兑换 II：动态规划 ###</span>
|
||||
<a id="__codelineno-68-2" name="__codelineno-68-2" href="#__codelineno-68-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">coin_change_ii_dp</span><span class="p">(</span><span class="n">coins</span><span class="p">,</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span>
|
||||
<a id="__codelineno-68-3" name="__codelineno-68-3" href="#__codelineno-68-3"></a><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="o">.</span><span class="n">length</span>
|
||||
<a id="__codelineno-68-4" name="__codelineno-68-4" href="#__codelineno-68-4"></a><span class="w"> </span><span class="c1"># 初始化 dp 表</span>
|
||||
<a id="__codelineno-68-5" name="__codelineno-68-5" href="#__codelineno-68-5"></a><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-68-6" name="__codelineno-68-6" href="#__codelineno-68-6"></a><span class="w"> </span><span class="c1"># 初始化首列</span>
|
||||
<a id="__codelineno-68-7" name="__codelineno-68-7" href="#__codelineno-68-7"></a><span class="w"> </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">))</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">i</span><span class="o">|</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-68-8" name="__codelineno-68-8" href="#__codelineno-68-8"></a><span class="w"> </span><span class="c1"># 状态转移</span>
|
||||
<a id="__codelineno-68-9" name="__codelineno-68-9" href="#__codelineno-68-9"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-68-10" name="__codelineno-68-10" href="#__codelineno-68-10"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-68-11" name="__codelineno-68-11" href="#__codelineno-68-11"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">coins</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">a</span>
|
||||
<a id="__codelineno-68-12" name="__codelineno-68-12" href="#__codelineno-68-12"></a><span class="w"> </span><span class="c1"># 若超过目标金额，则不选硬币 i</span>
|
||||
<a id="__codelineno-68-13" name="__codelineno-68-13" href="#__codelineno-68-13"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">a</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">a</span><span class="o">]</span>
|
||||
<a id="__codelineno-68-14" name="__codelineno-68-14" href="#__codelineno-68-14"></a><span class="w"> </span><span class="k">else</span>
|
||||
<a id="__codelineno-68-15" name="__codelineno-68-15" href="#__codelineno-68-15"></a><span class="w"> </span><span class="c1"># 不选和选硬币 i 这两种方案之和</span>
|
||||
<a id="__codelineno-68-16" name="__codelineno-68-16" href="#__codelineno-68-16"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">a</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">a</span><span class="o">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">coins</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]]</span>
|
||||
<a id="__codelineno-68-17" name="__codelineno-68-17" href="#__codelineno-68-17"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-68-18" name="__codelineno-68-18" href="#__codelineno-68-18"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-68-19" name="__codelineno-68-19" href="#__codelineno-68-19"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-68-20" name="__codelineno-68-20" href="#__codelineno-68-20"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">n</span><span class="o">][</span><span class="n">amt</span><span class="o">]</span>
|
||||
<a id="__codelineno-68-21" name="__codelineno-68-21" href="#__codelineno-68-21"></a><span class="k">end</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
|
|
@ -6043,7 +6162,27 @@ dp[i, a] = dp[i-1, a] + dp[i, a - coins[i-1]]
|
|||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">coin_change_ii.rb</span><pre><span></span><code><a id="__codelineno-82-1" name="__codelineno-82-1" href="#__codelineno-82-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">coin_change_ii_dp_comp</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">coin_change_ii.rb</span><pre><span></span><code><a id="__codelineno-82-1" name="__codelineno-82-1" href="#__codelineno-82-1"></a><span class="c1">### 零钱兑换 II：空间优化后的动态规划 ###</span>
|
||||
<a id="__codelineno-82-2" name="__codelineno-82-2" href="#__codelineno-82-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">coin_change_ii_dp_comp</span><span class="p">(</span><span class="n">coins</span><span class="p">,</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span>
|
||||
<a id="__codelineno-82-3" name="__codelineno-82-3" href="#__codelineno-82-3"></a><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="o">.</span><span class="n">length</span>
|
||||
<a id="__codelineno-82-4" name="__codelineno-82-4" href="#__codelineno-82-4"></a><span class="w"> </span><span class="c1"># 初始化 dp 表</span>
|
||||
<a id="__codelineno-82-5" name="__codelineno-82-5" href="#__codelineno-82-5"></a><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
|
||||
<a id="__codelineno-82-6" name="__codelineno-82-6" href="#__codelineno-82-6"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span>
|
||||
<a id="__codelineno-82-7" name="__codelineno-82-7" href="#__codelineno-82-7"></a><span class="w"> </span><span class="c1"># 状态转移</span>
|
||||
<a id="__codelineno-82-8" name="__codelineno-82-8" href="#__codelineno-82-8"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-82-9" name="__codelineno-82-9" href="#__codelineno-82-9"></a><span class="w"> </span><span class="c1"># 正序遍历</span>
|
||||
<a id="__codelineno-82-10" name="__codelineno-82-10" href="#__codelineno-82-10"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-82-11" name="__codelineno-82-11" href="#__codelineno-82-11"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">coins</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">a</span>
|
||||
<a id="__codelineno-82-12" name="__codelineno-82-12" href="#__codelineno-82-12"></a><span class="w"> </span><span class="c1"># 若超过目标金额，则不选硬币 i</span>
|
||||
<a id="__codelineno-82-13" name="__codelineno-82-13" href="#__codelineno-82-13"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">a</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">a</span><span class="o">]</span>
|
||||
<a id="__codelineno-82-14" name="__codelineno-82-14" href="#__codelineno-82-14"></a><span class="w"> </span><span class="k">else</span>
|
||||
<a id="__codelineno-82-15" name="__codelineno-82-15" href="#__codelineno-82-15"></a><span class="w"> </span><span class="c1"># 不选和选硬币 i 这两种方案之和</span>
|
||||
<a id="__codelineno-82-16" name="__codelineno-82-16" href="#__codelineno-82-16"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">a</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">a</span><span class="o">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">coins</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]]</span>
|
||||
<a id="__codelineno-82-17" name="__codelineno-82-17" href="#__codelineno-82-17"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-82-18" name="__codelineno-82-18" href="#__codelineno-82-18"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-82-19" name="__codelineno-82-19" href="#__codelineno-82-19"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-82-20" name="__codelineno-82-20" href="#__codelineno-82-20"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">amt</span><span class="o">]</span>
|
||||
<a id="__codelineno-82-21" name="__codelineno-82-21" href="#__codelineno-82-21"></a><span class="k">end</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
|
|
|
|||
|
|
@ -3956,7 +3956,15 @@
|
|||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">my_heap.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">MaxHeap</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">__init__</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">my_heap.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### 构造方法，根据输入列表建堆 ###</span>
|
||||
<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">initialize</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
|
||||
<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w"> </span><span class="c1"># 将列表元素原封不动添加进堆</span>
|
||||
<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w"> </span><span class="vi">@max_heap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span>
|
||||
<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w"> </span><span class="c1"># 堆化除叶节点以外的其他所有节点</span>
|
||||
<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w"> </span><span class="n">parent</span><span class="p">(</span><span class="n">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="o">.</span><span class="n">downto</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="k">do</span><span class="w"> </span><span class="o">|</span><span class="n">i</span><span class="o">|</span>
|
||||
<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w"> </span><span class="n">sift_down</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
|
||||
<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="k">end</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
|
|
|
|||
|
|
@ -4172,7 +4172,7 @@
|
|||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">heap.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a>
|
||||
<div class="highlight"><span class="filename">heap.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1"># Ruby 未提供内置 Heap 类</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
|
|
|
|||
|
|
@ -3696,7 +3696,7 @@
|
|||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">my_heap.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">MaxHeap</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">__init__</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">my_heap.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">MaxHeap</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="kp">initialize</span><span class="p">}</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
|
|
|
|||
File diff suppressed because one or more lines are too long
210
en/sitemap.xml
210
en/sitemap.xml
|
|
@ -2,527 +2,527 @@
|
|||
<urlset xmlns="http://www.sitemaps.org/schemas/sitemap/0.9">
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_appendix/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_appendix/contribution/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_appendix/installation/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_appendix/terminology/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_array_and_linkedlist/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_array_and_linkedlist/array/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_array_and_linkedlist/linked_list/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_array_and_linkedlist/list/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_array_and_linkedlist/ram_and_cache/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_array_and_linkedlist/summary/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_backtracking/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_backtracking/backtracking_algorithm/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_backtracking/n_queens_problem/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_backtracking/permutations_problem/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_backtracking/subset_sum_problem/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_backtracking/summary/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_computational_complexity/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_computational_complexity/iteration_and_recursion/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_computational_complexity/performance_evaluation/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_computational_complexity/space_complexity/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_computational_complexity/summary/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_computational_complexity/time_complexity/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_data_structure/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_data_structure/basic_data_types/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_data_structure/character_encoding/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_data_structure/classification_of_data_structure/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_data_structure/number_encoding/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_data_structure/summary/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_divide_and_conquer/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_divide_and_conquer/binary_search_recur/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_divide_and_conquer/build_binary_tree_problem/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_divide_and_conquer/divide_and_conquer/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_divide_and_conquer/hanota_problem/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_divide_and_conquer/summary/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_dynamic_programming/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_dynamic_programming/dp_problem_features/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_dynamic_programming/dp_solution_pipeline/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_dynamic_programming/edit_distance_problem/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_dynamic_programming/intro_to_dynamic_programming/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_dynamic_programming/knapsack_problem/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_dynamic_programming/summary/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_dynamic_programming/unbounded_knapsack_problem/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_graph/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_graph/graph/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_graph/graph_operations/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_graph/graph_traversal/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_graph/summary/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_greedy/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_greedy/fractional_knapsack_problem/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_greedy/greedy_algorithm/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_greedy/max_capacity_problem/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_greedy/max_product_cutting_problem/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_greedy/summary/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_hashing/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_hashing/hash_algorithm/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_hashing/hash_collision/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_hashing/hash_map/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_hashing/summary/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_heap/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_heap/build_heap/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_heap/heap/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_heap/summary/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_heap/top_k/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_hello_algo/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_introduction/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_introduction/algorithms_are_everywhere/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_introduction/summary/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_introduction/what_is_dsa/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_preface/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_preface/about_the_book/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_preface/suggestions/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_preface/summary/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_reference/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_searching/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_searching/binary_search/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_searching/binary_search_edge/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_searching/binary_search_insertion/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_searching/replace_linear_by_hashing/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_searching/searching_algorithm_revisited/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_searching/summary/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_sorting/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_sorting/bubble_sort/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_sorting/bucket_sort/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_sorting/counting_sort/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_sorting/heap_sort/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_sorting/insertion_sort/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_sorting/merge_sort/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_sorting/quick_sort/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_sorting/radix_sort/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_sorting/selection_sort/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_sorting/sorting_algorithm/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_sorting/summary/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_stack_and_queue/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_stack_and_queue/deque/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_stack_and_queue/queue/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_stack_and_queue/stack/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_stack_and_queue/summary/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_tree/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_tree/array_representation_of_tree/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_tree/avl_tree/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_tree/binary_search_tree/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_tree/binary_tree/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_tree/binary_tree_traversal/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/en/chapter_tree/summary/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
</urlset>
|
||||
Binary file not shown.
|
|
@ -461,7 +461,7 @@ a:hover .text-button span {
|
|||
|
||||
.profile-cell {
|
||||
flex: 1; /* even distribution */
|
||||
flex-basis: 15%;
|
||||
flex-basis: 20%;
|
||||
margin: 1em 0.5em;
|
||||
text-align: center;
|
||||
}
|
||||
|
|
|
|||
13
index.html
13
index.html
|
|
@ -578,6 +578,19 @@
|
|||
</sub>
|
||||
</a>
|
||||
</div>
|
||||
<div class="profile-cell">
|
||||
<a href="https://github.com/khoaxuantu">
|
||||
<img alt="Reviewer: khoaxuantu" class="profile-img" src="assets/avatar/avatar_khoaxuantu.jpg"/>
|
||||
<br/>
|
||||
<b>
|
||||
khoaxuantu
|
||||
</b>
|
||||
<br/>
|
||||
<sub>
|
||||
Ruby
|
||||
</sub>
|
||||
</a>
|
||||
</div>
|
||||
<div class="profile-cell">
|
||||
<a href="https://github.com/krahets">
|
||||
<img alt="Reviewer: krahets" class="profile-img" src="assets/avatar/avatar_krahets.jpg"/>
|
||||
|
|
|
|||
File diff suppressed because one or more lines are too long
212
sitemap.xml
212
sitemap.xml
|
|
@ -2,532 +2,532 @@
|
|||
<urlset xmlns="http://www.sitemaps.org/schemas/sitemap/0.9">
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_appendix/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_appendix/contribution/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_appendix/installation/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_appendix/terminology/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_array_and_linkedlist/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_array_and_linkedlist/array/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_array_and_linkedlist/linked_list/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_array_and_linkedlist/list/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_array_and_linkedlist/ram_and_cache/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_array_and_linkedlist/summary/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_backtracking/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_backtracking/backtracking_algorithm/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_backtracking/n_queens_problem/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_backtracking/permutations_problem/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_backtracking/subset_sum_problem/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_backtracking/summary/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_computational_complexity/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_computational_complexity/iteration_and_recursion/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_computational_complexity/performance_evaluation/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_computational_complexity/space_complexity/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_computational_complexity/summary/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_computational_complexity/time_complexity/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_data_structure/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_data_structure/basic_data_types/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_data_structure/character_encoding/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_data_structure/classification_of_data_structure/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_data_structure/number_encoding/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_data_structure/summary/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_divide_and_conquer/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_divide_and_conquer/binary_search_recur/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_divide_and_conquer/build_binary_tree_problem/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_divide_and_conquer/divide_and_conquer/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_divide_and_conquer/hanota_problem/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_divide_and_conquer/summary/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_dynamic_programming/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_dynamic_programming/dp_problem_features/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_dynamic_programming/dp_solution_pipeline/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_dynamic_programming/edit_distance_problem/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_dynamic_programming/intro_to_dynamic_programming/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_dynamic_programming/knapsack_problem/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_dynamic_programming/summary/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_dynamic_programming/unbounded_knapsack_problem/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_graph/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_graph/graph/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_graph/graph_operations/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_graph/graph_traversal/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_graph/summary/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_greedy/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_greedy/fractional_knapsack_problem/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_greedy/greedy_algorithm/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_greedy/max_capacity_problem/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_greedy/max_product_cutting_problem/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_greedy/summary/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_hashing/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_hashing/hash_algorithm/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_hashing/hash_collision/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_hashing/hash_map/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_hashing/summary/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_heap/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_heap/build_heap/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_heap/heap/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_heap/summary/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_heap/top_k/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_hello_algo/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_introduction/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_introduction/algorithms_are_everywhere/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_introduction/summary/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_introduction/what_is_dsa/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_paperbook/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_preface/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_preface/about_the_book/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_preface/suggestions/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_preface/summary/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_reference/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_searching/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_searching/binary_search/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_searching/binary_search_edge/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_searching/binary_search_insertion/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_searching/replace_linear_by_hashing/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_searching/searching_algorithm_revisited/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_searching/summary/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_sorting/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_sorting/bubble_sort/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_sorting/bucket_sort/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_sorting/counting_sort/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_sorting/heap_sort/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_sorting/insertion_sort/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_sorting/merge_sort/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_sorting/quick_sort/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_sorting/radix_sort/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_sorting/selection_sort/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_sorting/sorting_algorithm/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_sorting/summary/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_stack_and_queue/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_stack_and_queue/deque/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_stack_and_queue/queue/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_stack_and_queue/stack/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_stack_and_queue/summary/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_tree/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_tree/array_representation_of_tree/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_tree/avl_tree/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_tree/binary_search_tree/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_tree/binary_tree/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_tree/binary_tree_traversal/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_tree/summary/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
</urlset>
|
||||
BIN
sitemap.xml.gz
BIN
sitemap.xml.gz
Binary file not shown.
|
|
@ -461,7 +461,7 @@ a:hover .text-button span {
|
|||
|
||||
.profile-cell {
|
||||
flex: 1; /* even distribution */
|
||||
flex-basis: 15%;
|
||||
flex-basis: 20%;
|
||||
margin: 1em 0.5em;
|
||||
text-align: center;
|
||||
}
|
||||
|
|
|
|||
|
|
@ -3814,7 +3814,7 @@
|
|||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">preorder_traversal_i_compact.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* 前序走訪：例題一 */</span>
|
||||
<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">fn</span> <span class="nf">pre_order</span><span class="p">(</span><span class="n">res</span>: <span class="kp">&</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o"><</span><span class="n">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>>></span><span class="p">,</span><span class="w"> </span><span class="n">root</span>: <span class="nb">Option</span><span class="o"><</span><span class="n">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>>></span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">fn</span> <span class="nf">pre_order</span><span class="p">(</span><span class="n">res</span>: <span class="kp">&</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o"><</span><span class="n">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>>></span><span class="p">,</span><span class="w"> </span><span class="n">root</span>: <span class="nb">Option</span><span class="o"><&</span><span class="n">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>>></span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">root</span><span class="p">.</span><span class="n">is_none</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
|
||||
<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="w"> </span><span class="p">}</span>
|
||||
|
|
@ -3823,8 +3823,8 @@
|
|||
<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="w"> </span><span class="c1">// 記錄解</span>
|
||||
<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
|
||||
<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="w"> </span><span class="n">pre_order</span><span class="p">(</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
|
||||
<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="w"> </span><span class="n">pre_order</span><span class="p">(</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
|
||||
<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="w"> </span><span class="n">pre_order</span><span class="p">(</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">as_ref</span><span class="p">());</span>
|
||||
<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="w"> </span><span class="n">pre_order</span><span class="p">(</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">as_ref</span><span class="p">());</span>
|
||||
<a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="p">}</span>
|
||||
</code></pre></div>
|
||||
|
|
@ -4079,7 +4079,7 @@
|
|||
<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a><span class="k">fn</span> <span class="nf">pre_order</span><span class="p">(</span>
|
||||
<a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="w"> </span><span class="n">res</span>: <span class="kp">&</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o"><</span><span class="nb">Vec</span><span class="o"><</span><span class="n">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>>>></span><span class="p">,</span>
|
||||
<a id="__codelineno-23-4" name="__codelineno-23-4" href="#__codelineno-23-4"></a><span class="w"> </span><span class="n">path</span>: <span class="kp">&</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o"><</span><span class="n">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>>></span><span class="p">,</span>
|
||||
<a id="__codelineno-23-5" name="__codelineno-23-5" href="#__codelineno-23-5"></a><span class="w"> </span><span class="n">root</span>: <span class="nb">Option</span><span class="o"><</span><span class="n">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>>></span><span class="p">,</span>
|
||||
<a id="__codelineno-23-5" name="__codelineno-23-5" href="#__codelineno-23-5"></a><span class="w"> </span><span class="n">root</span>: <span class="nb">Option</span><span class="o"><&</span><span class="n">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>>></span><span class="p">,</span>
|
||||
<a id="__codelineno-23-6" name="__codelineno-23-6" href="#__codelineno-23-6"></a><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-23-7" name="__codelineno-23-7" href="#__codelineno-23-7"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">root</span><span class="p">.</span><span class="n">is_none</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-23-8" name="__codelineno-23-8" href="#__codelineno-23-8"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
|
||||
|
|
@ -4091,10 +4091,10 @@
|
|||
<a id="__codelineno-23-14" name="__codelineno-23-14" href="#__codelineno-23-14"></a><span class="w"> </span><span class="c1">// 記錄解</span>
|
||||
<a id="__codelineno-23-15" name="__codelineno-23-15" href="#__codelineno-23-15"></a><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">path</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
|
||||
<a id="__codelineno-23-16" name="__codelineno-23-16" href="#__codelineno-23-16"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-23-17" name="__codelineno-23-17" href="#__codelineno-23-17"></a><span class="w"> </span><span class="n">pre_order</span><span class="p">(</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">path</span><span class="p">,</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
|
||||
<a id="__codelineno-23-18" name="__codelineno-23-18" href="#__codelineno-23-18"></a><span class="w"> </span><span class="n">pre_order</span><span class="p">(</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">path</span><span class="p">,</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
|
||||
<a id="__codelineno-23-17" name="__codelineno-23-17" href="#__codelineno-23-17"></a><span class="w"> </span><span class="n">pre_order</span><span class="p">(</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">path</span><span class="p">,</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">as_ref</span><span class="p">());</span>
|
||||
<a id="__codelineno-23-18" name="__codelineno-23-18" href="#__codelineno-23-18"></a><span class="w"> </span><span class="n">pre_order</span><span class="p">(</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">path</span><span class="p">,</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">as_ref</span><span class="p">());</span>
|
||||
<a id="__codelineno-23-19" name="__codelineno-23-19" href="#__codelineno-23-19"></a><span class="w"> </span><span class="c1">// 回退</span>
|
||||
<a id="__codelineno-23-20" name="__codelineno-23-20" href="#__codelineno-23-20"></a><span class="w"> </span><span class="n">path</span><span class="p">.</span><span class="n">remove</span><span class="p">(</span><span class="n">path</span><span class="p">.</span><span class="n">len</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
|
||||
<a id="__codelineno-23-20" name="__codelineno-23-20" href="#__codelineno-23-20"></a><span class="w"> </span><span class="n">path</span><span class="p">.</span><span class="n">pop</span><span class="p">();</span>
|
||||
<a id="__codelineno-23-21" name="__codelineno-23-21" href="#__codelineno-23-21"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-23-22" name="__codelineno-23-22" href="#__codelineno-23-22"></a><span class="p">}</span>
|
||||
</code></pre></div>
|
||||
|
|
@ -4410,7 +4410,7 @@
|
|||
<a id="__codelineno-37-2" name="__codelineno-37-2" href="#__codelineno-37-2"></a><span class="k">fn</span> <span class="nf">pre_order</span><span class="p">(</span>
|
||||
<a id="__codelineno-37-3" name="__codelineno-37-3" href="#__codelineno-37-3"></a><span class="w"> </span><span class="n">res</span>: <span class="kp">&</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o"><</span><span class="nb">Vec</span><span class="o"><</span><span class="n">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>>>></span><span class="p">,</span>
|
||||
<a id="__codelineno-37-4" name="__codelineno-37-4" href="#__codelineno-37-4"></a><span class="w"> </span><span class="n">path</span>: <span class="kp">&</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o"><</span><span class="n">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>>></span><span class="p">,</span>
|
||||
<a id="__codelineno-37-5" name="__codelineno-37-5" href="#__codelineno-37-5"></a><span class="w"> </span><span class="n">root</span>: <span class="nb">Option</span><span class="o"><</span><span class="n">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>>></span><span class="p">,</span>
|
||||
<a id="__codelineno-37-5" name="__codelineno-37-5" href="#__codelineno-37-5"></a><span class="w"> </span><span class="n">root</span>: <span class="nb">Option</span><span class="o"><&</span><span class="n">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>>></span><span class="p">,</span>
|
||||
<a id="__codelineno-37-6" name="__codelineno-37-6" href="#__codelineno-37-6"></a><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-37-7" name="__codelineno-37-7" href="#__codelineno-37-7"></a><span class="w"> </span><span class="c1">// 剪枝</span>
|
||||
<a id="__codelineno-37-8" name="__codelineno-37-8" href="#__codelineno-37-8"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">root</span><span class="p">.</span><span class="n">is_none</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">root</span><span class="p">.</span><span class="n">as_ref</span><span class="p">().</span><span class="n">unwrap</span><span class="p">().</span><span class="n">borrow</span><span class="p">().</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">3</span><span class="w"> </span><span class="p">{</span>
|
||||
|
|
@ -4423,10 +4423,10 @@
|
|||
<a id="__codelineno-37-15" name="__codelineno-37-15" href="#__codelineno-37-15"></a><span class="w"> </span><span class="c1">// 記錄解</span>
|
||||
<a id="__codelineno-37-16" name="__codelineno-37-16" href="#__codelineno-37-16"></a><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">path</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
|
||||
<a id="__codelineno-37-17" name="__codelineno-37-17" href="#__codelineno-37-17"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-37-18" name="__codelineno-37-18" href="#__codelineno-37-18"></a><span class="w"> </span><span class="n">pre_order</span><span class="p">(</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">path</span><span class="p">,</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
|
||||
<a id="__codelineno-37-19" name="__codelineno-37-19" href="#__codelineno-37-19"></a><span class="w"> </span><span class="n">pre_order</span><span class="p">(</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">path</span><span class="p">,</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
|
||||
<a id="__codelineno-37-18" name="__codelineno-37-18" href="#__codelineno-37-18"></a><span class="w"> </span><span class="n">pre_order</span><span class="p">(</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">path</span><span class="p">,</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">as_ref</span><span class="p">());</span>
|
||||
<a id="__codelineno-37-19" name="__codelineno-37-19" href="#__codelineno-37-19"></a><span class="w"> </span><span class="n">pre_order</span><span class="p">(</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">path</span><span class="p">,</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">as_ref</span><span class="p">());</span>
|
||||
<a id="__codelineno-37-20" name="__codelineno-37-20" href="#__codelineno-37-20"></a><span class="w"> </span><span class="c1">// 回退</span>
|
||||
<a id="__codelineno-37-21" name="__codelineno-37-21" href="#__codelineno-37-21"></a><span class="w"> </span><span class="n">path</span><span class="p">.</span><span class="n">remove</span><span class="p">(</span><span class="n">path</span><span class="p">.</span><span class="n">len</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
|
||||
<a id="__codelineno-37-21" name="__codelineno-37-21" href="#__codelineno-37-21"></a><span class="w"> </span><span class="n">path</span><span class="p">.</span><span class="n">pop</span><span class="p">();</span>
|
||||
<a id="__codelineno-37-22" name="__codelineno-37-22" href="#__codelineno-37-22"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-37-23" name="__codelineno-37-23" href="#__codelineno-37-23"></a><span class="p">}</span>
|
||||
</code></pre></div>
|
||||
|
|
@ -5269,7 +5269,7 @@
|
|||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">preorder_traversal_iii_template.rs</span><pre><span></span><code><a id="__codelineno-65-1" name="__codelineno-65-1" href="#__codelineno-65-1"></a><span class="cm">/* 判斷當前狀態是否為解 */</span>
|
||||
<a id="__codelineno-65-2" name="__codelineno-65-2" href="#__codelineno-65-2"></a><span class="k">fn</span> <span class="nf">is_solution</span><span class="p">(</span><span class="n">state</span>: <span class="kp">&</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o"><</span><span class="n">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>>></span><span class="p">)</span><span class="w"> </span>-> <span class="kt">bool</span> <span class="p">{</span>
|
||||
<a id="__codelineno-65-3" name="__codelineno-65-3" href="#__codelineno-65-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="o">!</span><span class="n">state</span><span class="p">.</span><span class="n">is_empty</span><span class="p">()</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">state</span><span class="p">.</span><span class="n">get</span><span class="p">(</span><span class="n">state</span><span class="p">.</span><span class="n">len</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">).</span><span class="n">unwrap</span><span class="p">().</span><span class="n">borrow</span><span class="p">().</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span><span class="p">;</span>
|
||||
<a id="__codelineno-65-3" name="__codelineno-65-3" href="#__codelineno-65-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="o">!</span><span class="n">state</span><span class="p">.</span><span class="n">is_empty</span><span class="p">()</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">state</span><span class="p">.</span><span class="n">last</span><span class="p">().</span><span class="n">unwrap</span><span class="p">().</span><span class="n">borrow</span><span class="p">().</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span><span class="p">;</span>
|
||||
<a id="__codelineno-65-4" name="__codelineno-65-4" href="#__codelineno-65-4"></a><span class="p">}</span>
|
||||
<a id="__codelineno-65-5" name="__codelineno-65-5" href="#__codelineno-65-5"></a>
|
||||
<a id="__codelineno-65-6" name="__codelineno-65-6" href="#__codelineno-65-6"></a><span class="cm">/* 記錄解 */</span>
|
||||
|
|
@ -5281,8 +5281,8 @@
|
|||
<a id="__codelineno-65-12" name="__codelineno-65-12" href="#__codelineno-65-12"></a><span class="p">}</span>
|
||||
<a id="__codelineno-65-13" name="__codelineno-65-13" href="#__codelineno-65-13"></a>
|
||||
<a id="__codelineno-65-14" name="__codelineno-65-14" href="#__codelineno-65-14"></a><span class="cm">/* 判斷在當前狀態下，該選擇是否合法 */</span>
|
||||
<a id="__codelineno-65-15" name="__codelineno-65-15" href="#__codelineno-65-15"></a><span class="k">fn</span> <span class="nf">is_valid</span><span class="p">(</span><span class="n">_</span>: <span class="kp">&</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o"><</span><span class="n">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>>></span><span class="p">,</span><span class="w"> </span><span class="n">choice</span>: <span class="nc">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>></span><span class="p">)</span><span class="w"> </span>-> <span class="kt">bool</span> <span class="p">{</span>
|
||||
<a id="__codelineno-65-16" name="__codelineno-65-16" href="#__codelineno-65-16"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">choice</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">val</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span>
|
||||
<a id="__codelineno-65-15" name="__codelineno-65-15" href="#__codelineno-65-15"></a><span class="k">fn</span> <span class="nf">is_valid</span><span class="p">(</span><span class="n">_</span>: <span class="kp">&</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o"><</span><span class="n">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>>></span><span class="p">,</span><span class="w"> </span><span class="n">choice</span>: <span class="nb">Option</span><span class="o"><&</span><span class="n">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>>></span><span class="p">)</span><span class="w"> </span>-> <span class="kt">bool</span> <span class="p">{</span>
|
||||
<a id="__codelineno-65-16" name="__codelineno-65-16" href="#__codelineno-65-16"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">choice</span><span class="p">.</span><span class="n">is_some</span><span class="p">()</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">choice</span><span class="p">.</span><span class="n">unwrap</span><span class="p">().</span><span class="n">borrow</span><span class="p">().</span><span class="n">val</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span>
|
||||
<a id="__codelineno-65-17" name="__codelineno-65-17" href="#__codelineno-65-17"></a><span class="p">}</span>
|
||||
<a id="__codelineno-65-18" name="__codelineno-65-18" href="#__codelineno-65-18"></a>
|
||||
<a id="__codelineno-65-19" name="__codelineno-65-19" href="#__codelineno-65-19"></a><span class="cm">/* 更新狀態 */</span>
|
||||
|
|
@ -5292,13 +5292,13 @@
|
|||
<a id="__codelineno-65-23" name="__codelineno-65-23" href="#__codelineno-65-23"></a>
|
||||
<a id="__codelineno-65-24" name="__codelineno-65-24" href="#__codelineno-65-24"></a><span class="cm">/* 恢復狀態 */</span>
|
||||
<a id="__codelineno-65-25" name="__codelineno-65-25" href="#__codelineno-65-25"></a><span class="k">fn</span> <span class="nf">undo_choice</span><span class="p">(</span><span class="n">state</span>: <span class="kp">&</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o"><</span><span class="n">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>>></span><span class="p">,</span><span class="w"> </span><span class="n">_</span>: <span class="nc">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>></span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-65-26" name="__codelineno-65-26" href="#__codelineno-65-26"></a><span class="w"> </span><span class="n">state</span><span class="p">.</span><span class="n">remove</span><span class="p">(</span><span class="n">state</span><span class="p">.</span><span class="n">len</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
|
||||
<a id="__codelineno-65-26" name="__codelineno-65-26" href="#__codelineno-65-26"></a><span class="w"> </span><span class="n">state</span><span class="p">.</span><span class="n">pop</span><span class="p">();</span>
|
||||
<a id="__codelineno-65-27" name="__codelineno-65-27" href="#__codelineno-65-27"></a><span class="p">}</span>
|
||||
<a id="__codelineno-65-28" name="__codelineno-65-28" href="#__codelineno-65-28"></a>
|
||||
<a id="__codelineno-65-29" name="__codelineno-65-29" href="#__codelineno-65-29"></a><span class="cm">/* 回溯演算法：例題三 */</span>
|
||||
<a id="__codelineno-65-30" name="__codelineno-65-30" href="#__codelineno-65-30"></a><span class="k">fn</span> <span class="nf">backtrack</span><span class="p">(</span>
|
||||
<a id="__codelineno-65-31" name="__codelineno-65-31" href="#__codelineno-65-31"></a><span class="w"> </span><span class="n">state</span>: <span class="kp">&</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o"><</span><span class="n">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>>></span><span class="p">,</span>
|
||||
<a id="__codelineno-65-32" name="__codelineno-65-32" href="#__codelineno-65-32"></a><span class="w"> </span><span class="n">choices</span>: <span class="kp">&</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o"><</span><span class="n">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>>></span><span class="p">,</span>
|
||||
<a id="__codelineno-65-32" name="__codelineno-65-32" href="#__codelineno-65-32"></a><span class="w"> </span><span class="n">choices</span>: <span class="kp">&</span><span class="nb">Vec</span><span class="o"><</span><span class="nb">Option</span><span class="o"><&</span><span class="n">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>>>></span><span class="p">,</span>
|
||||
<a id="__codelineno-65-33" name="__codelineno-65-33" href="#__codelineno-65-33"></a><span class="w"> </span><span class="n">res</span>: <span class="kp">&</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o"><</span><span class="nb">Vec</span><span class="o"><</span><span class="n">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>>>></span><span class="p">,</span>
|
||||
<a id="__codelineno-65-34" name="__codelineno-65-34" href="#__codelineno-65-34"></a><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-65-35" name="__codelineno-65-35" href="#__codelineno-65-35"></a><span class="w"> </span><span class="c1">// 檢查是否為解</span>
|
||||
|
|
@ -5307,22 +5307,22 @@
|
|||
<a id="__codelineno-65-38" name="__codelineno-65-38" href="#__codelineno-65-38"></a><span class="w"> </span><span class="n">record_solution</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
|
||||
<a id="__codelineno-65-39" name="__codelineno-65-39" href="#__codelineno-65-39"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-65-40" name="__codelineno-65-40" href="#__codelineno-65-40"></a><span class="w"> </span><span class="c1">// 走訪所有選擇</span>
|
||||
<a id="__codelineno-65-41" name="__codelineno-65-41" href="#__codelineno-65-41"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">choices</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-65-41" name="__codelineno-65-41" href="#__codelineno-65-41"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="o">&</span><span class="n">choice</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">choices</span><span class="p">.</span><span class="n">iter</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-65-42" name="__codelineno-65-42" href="#__codelineno-65-42"></a><span class="w"> </span><span class="c1">// 剪枝：檢查選擇是否合法</span>
|
||||
<a id="__codelineno-65-43" name="__codelineno-65-43" href="#__codelineno-65-43"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">is_valid</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">.</span><span class="n">clone</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-65-43" name="__codelineno-65-43" href="#__codelineno-65-43"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">is_valid</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-65-44" name="__codelineno-65-44" href="#__codelineno-65-44"></a><span class="w"> </span><span class="c1">// 嘗試：做出選擇，更新狀態</span>
|
||||
<a id="__codelineno-65-45" name="__codelineno-65-45" href="#__codelineno-65-45"></a><span class="w"> </span><span class="n">make_choice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
|
||||
<a id="__codelineno-65-45" name="__codelineno-65-45" href="#__codelineno-65-45"></a><span class="w"> </span><span class="n">make_choice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">.</span><span class="n">unwrap</span><span class="p">().</span><span class="n">clone</span><span class="p">());</span>
|
||||
<a id="__codelineno-65-46" name="__codelineno-65-46" href="#__codelineno-65-46"></a><span class="w"> </span><span class="c1">// 進行下一輪選擇</span>
|
||||
<a id="__codelineno-65-47" name="__codelineno-65-47" href="#__codelineno-65-47"></a><span class="w"> </span><span class="n">backtrack</span><span class="p">(</span>
|
||||
<a id="__codelineno-65-48" name="__codelineno-65-48" href="#__codelineno-65-48"></a><span class="w"> </span><span class="n">state</span><span class="p">,</span>
|
||||
<a id="__codelineno-65-49" name="__codelineno-65-49" href="#__codelineno-65-49"></a><span class="w"> </span><span class="o">&</span><span class="k">mut</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span>
|
||||
<a id="__codelineno-65-50" name="__codelineno-65-50" href="#__codelineno-65-50"></a><span class="w"> </span><span class="n">choice</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">clone</span><span class="p">().</span><span class="n">unwrap</span><span class="p">(),</span>
|
||||
<a id="__codelineno-65-51" name="__codelineno-65-51" href="#__codelineno-65-51"></a><span class="w"> </span><span class="n">choice</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">clone</span><span class="p">().</span><span class="n">unwrap</span><span class="p">(),</span>
|
||||
<a id="__codelineno-65-49" name="__codelineno-65-49" href="#__codelineno-65-49"></a><span class="w"> </span><span class="o">&</span><span class="fm">vec!</span><span class="p">[</span>
|
||||
<a id="__codelineno-65-50" name="__codelineno-65-50" href="#__codelineno-65-50"></a><span class="w"> </span><span class="n">choice</span><span class="p">.</span><span class="n">unwrap</span><span class="p">().</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">as_ref</span><span class="p">(),</span>
|
||||
<a id="__codelineno-65-51" name="__codelineno-65-51" href="#__codelineno-65-51"></a><span class="w"> </span><span class="n">choice</span><span class="p">.</span><span class="n">unwrap</span><span class="p">().</span><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">as_ref</span><span class="p">(),</span>
|
||||
<a id="__codelineno-65-52" name="__codelineno-65-52" href="#__codelineno-65-52"></a><span class="w"> </span><span class="p">],</span>
|
||||
<a id="__codelineno-65-53" name="__codelineno-65-53" href="#__codelineno-65-53"></a><span class="w"> </span><span class="n">res</span><span class="p">,</span>
|
||||
<a id="__codelineno-65-54" name="__codelineno-65-54" href="#__codelineno-65-54"></a><span class="w"> </span><span class="p">);</span>
|
||||
<a id="__codelineno-65-55" name="__codelineno-65-55" href="#__codelineno-65-55"></a><span class="w"> </span><span class="c1">// 回退：撤銷選擇，恢復到之前的狀態</span>
|
||||
<a id="__codelineno-65-56" name="__codelineno-65-56" href="#__codelineno-65-56"></a><span class="w"> </span><span class="n">undo_choice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
|
||||
<a id="__codelineno-65-56" name="__codelineno-65-56" href="#__codelineno-65-56"></a><span class="w"> </span><span class="n">undo_choice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">.</span><span class="n">unwrap</span><span class="p">().</span><span class="n">clone</span><span class="p">());</span>
|
||||
<a id="__codelineno-65-57" name="__codelineno-65-57" href="#__codelineno-65-57"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-65-58" name="__codelineno-65-58" href="#__codelineno-65-58"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-65-59" name="__codelineno-65-59" href="#__codelineno-65-59"></a><span class="p">}</span>
|
||||
|
|
|
|||
|
|
@ -3606,14 +3606,14 @@
|
|||
</ol>
|
||||
<p>也就是說，在能夠解決問題的前提下，演算法效率已成為衡量演算法優劣的主要評價指標，它包括以下兩個維度。</p>
|
||||
<ul>
|
||||
<li><strong>時間效率</strong>：演算法執行速度的快慢。</li>
|
||||
<li><strong>時間效率</strong>：演算法執行時間的長短。</li>
|
||||
<li><strong>空間效率</strong>：演算法佔用記憶體空間的大小。</li>
|
||||
</ul>
|
||||
<p>簡而言之，<strong>我們的目標是設計“既快又省”的資料結構與演算法</strong>。而有效地評估演算法效率至關重要，因為只有這樣，我們才能將各種演算法進行對比，進而指導演算法設計與最佳化過程。</p>
|
||||
<p>效率評估方法主要分為兩種：實際測試、理論估算。</p>
|
||||
<h2 id="211">2.1.1 實際測試<a class="headerlink" href="#211" title="Permanent link">¶</a></h2>
|
||||
<p>假設我們現在有演算法 <code>A</code> 和演算法 <code>B</code> ，它們都能解決同一問題，現在需要對比這兩個演算法的效率。最直接的方法是找一臺計算機，執行這兩個演算法，並監控記錄它們的執行時間和記憶體佔用情況。這種評估方式能夠反映真實情況，但也存在較大的侷限性。</p>
|
||||
<p>一方面，<strong>難以排除測試環境的干擾因素</strong>。硬體配置會影響演算法的效能。比如在某臺計算機中，演算法 <code>A</code> 的執行時間比演算法 <code>B</code> 短；但在另一臺配置不同的計算機中，可能得到相反的測試結果。這意味著我們需要在各種機器上進行測試，統計平均效率，而這是不現實的。</p>
|
||||
<p>一方面，<strong>難以排除測試環境的干擾因素</strong>。硬體配置會影響演算法的效能表現。比如一個演算法的並行度較高，那麼它就更適合在多核 CPU 上執行，一個演算法的記憶體操作密集，那麼它在高效能記憶體上的表現就會更好。也就是說，演算法在不同的機器上的測試結果可能是不一致的。這意味著我們需要在各種機器上進行測試，統計平均效率，而這是不現實的。</p>
|
||||
<p>另一方面，<strong>展開完整測試非常耗費資源</strong>。隨著輸入資料量的變化，演算法會表現出不同的效率。例如，在輸入資料量較小時，演算法 <code>A</code> 的執行時間比演算法 <code>B</code> 短；而在輸入資料量較大時，測試結果可能恰恰相反。因此，為了得到有說服力的結論，我們需要測試各種規模的輸入資料，而這需要耗費大量的計算資源。</p>
|
||||
<h2 id="212">2.1.2 理論估算<a class="headerlink" href="#212" title="Permanent link">¶</a></h2>
|
||||
<p>由於實際測試具有較大的侷限性，因此我們可以考慮僅透過一些計算來評估演算法的效率。這種估算方法被稱為<u>漸近複雜度分析（asymptotic complexity analysis）</u>，簡稱<u>複雜度分析</u>。</p>
|
||||
|
|
@ -3623,8 +3623,9 @@
|
|||
<li>“隨著輸入資料大小的增加”意味著複雜度反映了演算法執行效率與輸入資料體量之間的關係。</li>
|
||||
<li>“時間和空間的增長趨勢”表示複雜度分析關注的不是執行時間或佔用空間的具體值，而是時間或空間增長的“快慢”。</li>
|
||||
</ul>
|
||||
<p><strong>複雜度分析克服了實際測試方法的弊端</strong>，體現在以下兩個方面。</p>
|
||||
<p><strong>複雜度分析克服了實際測試方法的弊端</strong>，體現在以下幾個方面。</p>
|
||||
<ul>
|
||||
<li>它無需實際執行程式碼，更加綠色節能。</li>
|
||||
<li>它獨立於測試環境，分析結果適用於所有執行平臺。</li>
|
||||
<li>它可以體現不同資料量下的演算法效率，尤其是在大資料量下的演算法效能。</li>
|
||||
</ul>
|
||||
|
|
|
|||
|
|
@ -4318,7 +4318,7 @@
|
|||
<ul>
|
||||
<li><strong>時間複雜度能夠有效評估演算法效率</strong>。例如，演算法 <code>B</code> 的執行時間呈線性增長，在 <span class="arithmatex">\(n > 1\)</span> 時比演算法 <code>A</code> 更慢，在 <span class="arithmatex">\(n > 1000000\)</span> 時比演算法 <code>C</code> 更慢。事實上，只要輸入資料大小 <span class="arithmatex">\(n\)</span> 足夠大，複雜度為“常數階”的演算法一定優於“線性階”的演算法，這正是時間增長趨勢的含義。</li>
|
||||
<li><strong>時間複雜度的推算方法更簡便</strong>。顯然，執行平臺和計算操作型別都與演算法執行時間的增長趨勢無關。因此在時間複雜度分析中，我們可以簡單地將所有計算操作的執行時間視為相同的“單位時間”，從而將“計算操作執行時間統計”簡化為“計算操作數量統計”，這樣一來估算難度就大大降低了。</li>
|
||||
<li><strong>時間複雜度也存在一定的侷限性</strong>。例如，儘管演算法 <code>A</code> 和 <code>C</code> 的時間複雜度相同，但實際執行時間差別很大。同樣，儘管演算法 <code>B</code> 的時間複雜度比 <code>C</code> 高，但在輸入資料大小 <span class="arithmatex">\(n\)</span> 較小時，演算法 <code>B</code> 明顯優於演算法 <code>C</code> 。在這些情況下，我們很難僅憑時間複雜度判斷演算法效率的高低。當然，儘管存在上述問題，複雜度分析仍然是評判演算法效率最有效且常用的方法。</li>
|
||||
<li><strong>時間複雜度也存在一定的侷限性</strong>。例如，儘管演算法 <code>A</code> 和 <code>C</code> 的時間複雜度相同，但實際執行時間差別很大。同樣，儘管演算法 <code>B</code> 的時間複雜度比 <code>C</code> 高，但在輸入資料大小 <span class="arithmatex">\(n\)</span> 較小時，演算法 <code>B</code> 明顯優於演算法 <code>C</code> 。對於此類情況，我們時常難以僅憑時間複雜度判斷演算法效率的高低。當然，儘管存在上述問題，複雜度分析仍然是評判演算法效率最有效且常用的方法。</li>
|
||||
</ul>
|
||||
<h2 id="232">2.3.2 函式漸近上界<a class="headerlink" href="#232" title="Permanent link">¶</a></h2>
|
||||
<p>給定一個輸入大小為 <span class="arithmatex">\(n\)</span> 的函式：</p>
|
||||
|
|
@ -6552,10 +6552,12 @@ O(\log_m n) = O(\log_k n / \log_k m) = O(\log_k n)
|
|||
<a id="__codelineno-182-2" name="__codelineno-182-2" href="#__codelineno-182-2"></a><span class="w"> </span><span class="sd">"""線性對數階"""</span>
|
||||
<a id="__codelineno-182-3" name="__codelineno-182-3" href="#__codelineno-182-3"></a> <span class="k">if</span> <span class="n">n</span> <span class="o"><=</span> <span class="mi">1</span><span class="p">:</span>
|
||||
<a id="__codelineno-182-4" name="__codelineno-182-4" href="#__codelineno-182-4"></a> <span class="k">return</span> <span class="mi">1</span>
|
||||
<a id="__codelineno-182-5" name="__codelineno-182-5" href="#__codelineno-182-5"></a> <span class="n">count</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">linear_log_recur</span><span class="p">(</span><span class="n">n</span> <span class="o">//</span> <span class="mi">2</span><span class="p">)</span> <span class="o">+</span> <span class="n">linear_log_recur</span><span class="p">(</span><span class="n">n</span> <span class="o">//</span> <span class="mi">2</span><span class="p">)</span>
|
||||
<a id="__codelineno-182-6" name="__codelineno-182-6" href="#__codelineno-182-6"></a> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
|
||||
<a id="__codelineno-182-7" name="__codelineno-182-7" href="#__codelineno-182-7"></a> <span class="n">count</span> <span class="o">+=</span> <span class="mi">1</span>
|
||||
<a id="__codelineno-182-8" name="__codelineno-182-8" href="#__codelineno-182-8"></a> <span class="k">return</span> <span class="n">count</span>
|
||||
<a id="__codelineno-182-5" name="__codelineno-182-5" href="#__codelineno-182-5"></a> <span class="c1"># 一分為二，子問題的規模減小一半</span>
|
||||
<a id="__codelineno-182-6" name="__codelineno-182-6" href="#__codelineno-182-6"></a> <span class="n">count</span> <span class="o">=</span> <span class="n">linear_log_recur</span><span class="p">(</span><span class="n">n</span> <span class="o">//</span> <span class="mi">2</span><span class="p">)</span> <span class="o">+</span> <span class="n">linear_log_recur</span><span class="p">(</span><span class="n">n</span> <span class="o">//</span> <span class="mi">2</span><span class="p">)</span>
|
||||
<a id="__codelineno-182-7" name="__codelineno-182-7" href="#__codelineno-182-7"></a> <span class="c1"># 當前子問題包含 n 個操作</span>
|
||||
<a id="__codelineno-182-8" name="__codelineno-182-8" href="#__codelineno-182-8"></a> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
|
||||
<a id="__codelineno-182-9" name="__codelineno-182-9" href="#__codelineno-182-9"></a> <span class="n">count</span> <span class="o">+=</span> <span class="mi">1</span>
|
||||
<a id="__codelineno-182-10" name="__codelineno-182-10" href="#__codelineno-182-10"></a> <span class="k">return</span> <span class="n">count</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
|
|
|
|||
|
|
@ -3623,7 +3623,7 @@
|
|||
<p><strong>Q</strong>：在構建堆疊（佇列）的時候，未指定它的大小，為什麼它們是“靜態資料結構”呢？</p>
|
||||
<p>在高階程式語言中，我們無須人工指定堆疊（佇列）的初始容量，這個工作由類別內部自動完成。例如，Java 的 <code>ArrayList</code> 的初始容量通常為 10。另外，擴容操作也是自動實現的。詳見後續的“串列”章節。</p>
|
||||
<p><strong>Q</strong>：原碼轉二補數的方法是“先取反後加 1”，那麼二補數轉原碼應該是逆運算“先減 1 後取反”，而二補數轉原碼也一樣可以透過“先取反後加 1”得到，這是為什麼呢？</p>
|
||||
<p><strong>A</strong>：這是因為原碼和二補數的相互轉換實際上是計算“補數”的過程。我們先給出補數的定義：假設 <span class="arithmatex">\(a + b = c\)</span> ，那麼我們稱 <span class="arithmatex">\(a\)</span> 是 <span class="arithmatex">\(b\)</span> 到 <span class="arithmatex">\(c\)</span> 的補數，反之也稱 <span class="arithmatex">\(b\)</span> 是 <span class="arithmatex">\(a\)</span> 到 <span class="arithmatex">\(c\)</span> 的補數。</p>
|
||||
<p>這是因為原碼和二補數的相互轉換實際上是計算“補數”的過程。我們先給出補數的定義：假設 <span class="arithmatex">\(a + b = c\)</span> ，那麼我們稱 <span class="arithmatex">\(a\)</span> 是 <span class="arithmatex">\(b\)</span> 到 <span class="arithmatex">\(c\)</span> 的補數，反之也稱 <span class="arithmatex">\(b\)</span> 是 <span class="arithmatex">\(a\)</span> 到 <span class="arithmatex">\(c\)</span> 的補數。</p>
|
||||
<p>給定一個 <span class="arithmatex">\(n = 4\)</span> 位長度的二進位制數 <span class="arithmatex">\(0010\)</span> ，如果將這個數字看作原碼（不考慮符號位），那麼它的二補數需透過“先取反後加 1”得到：</p>
|
||||
<div class="arithmatex">\[
|
||||
0010 \rightarrow 1101 \rightarrow 1110
|
||||
|
|
@ -3640,7 +3640,7 @@
|
|||
\]</div>
|
||||
<p>總結來看，“先取反後加 1”和“先減 1 後取反”這兩種運算都是在計算到 <span class="arithmatex">\(10000\)</span> 的補數，它們是等價的。</p>
|
||||
<p>本質上看，“取反”操作實際上是求到 <span class="arithmatex">\(1111\)</span> 的補數（因為恆有 <code>原碼 + 一補數 = 1111</code>）；而在一補數基礎上再加 1 得到的二補數，就是到 <span class="arithmatex">\(10000\)</span> 的補數。</p>
|
||||
<p>上述 <span class="arithmatex">\(n = 4\)</span> 為例，其可推廣至任意位數的二進位制數。</p>
|
||||
<p>上述以 <span class="arithmatex">\(n = 4\)</span> 為例，其可被推廣至任意位數的二進位制數。</p>
|
||||
|
||||
<!-- Source file information -->
|
||||
|
||||
|
|
|
|||
|
|
@ -3864,7 +3864,18 @@ dp[i] = \min(dp[i-1], dp[i-2]) + cost[i]
|
|||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">min_cost_climbing_stairs_dp</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### 爬樓梯最小代價：動態規劃 ###</span>
|
||||
<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">min_cost_climbing_stairs_dp</span><span class="p">(</span><span class="n">cost</span><span class="p">)</span>
|
||||
<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cost</span><span class="o">.</span><span class="n">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span>
|
||||
<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">cost</span><span class="o">[</span><span class="n">n</span><span class="o">]</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span>
|
||||
<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w"> </span><span class="c1"># 初始化 dp 表，用於儲存子問題的解</span>
|
||||
<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
|
||||
<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w"> </span><span class="c1"># 初始狀態：預設最小子問題的解</span>
|
||||
<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="mi">1</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="mi">2</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cost</span><span class="o">[</span><span class="mi">1</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">cost</span><span class="o">[</span><span class="mi">2</span><span class="o">]</span>
|
||||
<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w"> </span><span class="c1"># 狀態轉移：從較小子問題逐步求解較大子問題</span>
|
||||
<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w"> </span><span class="p">(</span><span class="mi">3</span><span class="o">...</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">))</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">i</span><span class="o">|</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="o">]].</span><span class="n">min</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">cost</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">n</span><span class="o">]</span>
|
||||
<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="k">end</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
|
|
@ -4102,7 +4113,27 @@ dp[i] = \min(dp[i-1], dp[i-2]) + cost[i]
|
|||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">min_cost_climbing_stairs_dp_comp</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="c1">### 爬樓梯最小代價：動態規劃 ###</span>
|
||||
<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">min_cost_climbing_stairs_dp</span><span class="p">(</span><span class="n">cost</span><span class="p">)</span>
|
||||
<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cost</span><span class="o">.</span><span class="n">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span>
|
||||
<a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">cost</span><span class="o">[</span><span class="n">n</span><span class="o">]</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span>
|
||||
<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a><span class="w"> </span><span class="c1"># 初始化 dp 表，用於儲存子問題的解</span>
|
||||
<a id="__codelineno-26-6" name="__codelineno-26-6" href="#__codelineno-26-6"></a><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
|
||||
<a id="__codelineno-26-7" name="__codelineno-26-7" href="#__codelineno-26-7"></a><span class="w"> </span><span class="c1"># 初始狀態：預設最小子問題的解</span>
|
||||
<a id="__codelineno-26-8" name="__codelineno-26-8" href="#__codelineno-26-8"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="mi">1</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="mi">2</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cost</span><span class="o">[</span><span class="mi">1</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">cost</span><span class="o">[</span><span class="mi">2</span><span class="o">]</span>
|
||||
<a id="__codelineno-26-9" name="__codelineno-26-9" href="#__codelineno-26-9"></a><span class="w"> </span><span class="c1"># 狀態轉移：從較小子問題逐步求解較大子問題</span>
|
||||
<a id="__codelineno-26-10" name="__codelineno-26-10" href="#__codelineno-26-10"></a><span class="w"> </span><span class="p">(</span><span class="mi">3</span><span class="o">...</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">))</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">i</span><span class="o">|</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="o">]].</span><span class="n">min</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">cost</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-26-11" name="__codelineno-26-11" href="#__codelineno-26-11"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">n</span><span class="o">]</span>
|
||||
<a id="__codelineno-26-12" name="__codelineno-26-12" href="#__codelineno-26-12"></a><span class="k">end</span>
|
||||
<a id="__codelineno-26-13" name="__codelineno-26-13" href="#__codelineno-26-13"></a>
|
||||
<a id="__codelineno-26-14" name="__codelineno-26-14" href="#__codelineno-26-14"></a><span class="c1"># 爬樓梯最小代價：空間最佳化後的動態規劃</span>
|
||||
<a id="__codelineno-26-15" name="__codelineno-26-15" href="#__codelineno-26-15"></a><span class="k">def</span><span class="w"> </span><span class="nf">min_cost_climbing_stairs_dp_comp</span><span class="p">(</span><span class="n">cost</span><span class="p">)</span>
|
||||
<a id="__codelineno-26-16" name="__codelineno-26-16" href="#__codelineno-26-16"></a><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cost</span><span class="o">.</span><span class="n">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span>
|
||||
<a id="__codelineno-26-17" name="__codelineno-26-17" href="#__codelineno-26-17"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">cost</span><span class="o">[</span><span class="n">n</span><span class="o">]</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span>
|
||||
<a id="__codelineno-26-18" name="__codelineno-26-18" href="#__codelineno-26-18"></a><span class="w"> </span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cost</span><span class="o">[</span><span class="mi">1</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">cost</span><span class="o">[</span><span class="mi">2</span><span class="o">]</span>
|
||||
<a id="__codelineno-26-19" name="__codelineno-26-19" href="#__codelineno-26-19"></a><span class="w"> </span><span class="p">(</span><span class="mi">3</span><span class="o">...</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">))</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">i</span><span class="o">|</span><span class="w"> </span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">b</span><span class="p">,</span><span class="w"> </span><span class="o">[</span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="n">b</span><span class="o">].</span><span class="n">min</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">cost</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-26-20" name="__codelineno-26-20" href="#__codelineno-26-20"></a><span class="w"> </span><span class="n">b</span>
|
||||
<a id="__codelineno-26-21" name="__codelineno-26-21" href="#__codelineno-26-21"></a><span class="k">end</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
|
|
@ -4432,7 +4463,23 @@ dp[i, 2] = dp[i-2, 1] + dp[i-2, 2]
|
|||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">climbing_stairs_constraint_dp.rb</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">climbing_stairs_constraint_dp</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">climbing_stairs_constraint_dp.rb</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="c1">### 帶約束爬樓梯：動態規劃 ###</span>
|
||||
<a id="__codelineno-40-2" name="__codelineno-40-2" href="#__codelineno-40-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">climbing_stairs_constraint_dp</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
|
||||
<a id="__codelineno-40-3" name="__codelineno-40-3" href="#__codelineno-40-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span>
|
||||
<a id="__codelineno-40-4" name="__codelineno-40-4" href="#__codelineno-40-4"></a>
|
||||
<a id="__codelineno-40-5" name="__codelineno-40-5" href="#__codelineno-40-5"></a><span class="w"> </span><span class="c1"># 初始化 dp 表，用於儲存子問題的解</span>
|
||||
<a id="__codelineno-40-6" name="__codelineno-40-6" href="#__codelineno-40-6"></a><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-40-7" name="__codelineno-40-7" href="#__codelineno-40-7"></a><span class="w"> </span><span class="c1"># 初始狀態：預設最小子問題的解</span>
|
||||
<a id="__codelineno-40-8" name="__codelineno-40-8" href="#__codelineno-40-8"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="mi">1</span><span class="o">][</span><span class="mi">1</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="mi">1</span><span class="o">][</span><span class="mi">2</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span>
|
||||
<a id="__codelineno-40-9" name="__codelineno-40-9" href="#__codelineno-40-9"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="mi">2</span><span class="o">][</span><span class="mi">1</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="mi">2</span><span class="o">][</span><span class="mi">2</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="mi">1</span>
|
||||
<a id="__codelineno-40-10" name="__codelineno-40-10" href="#__codelineno-40-10"></a><span class="w"> </span><span class="c1"># 狀態轉移：從較小子問題逐步求解較大子問題</span>
|
||||
<a id="__codelineno-40-11" name="__codelineno-40-11" href="#__codelineno-40-11"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">3</span><span class="o">...</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-40-12" name="__codelineno-40-12" href="#__codelineno-40-12"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="mi">2</span><span class="o">]</span>
|
||||
<a id="__codelineno-40-13" name="__codelineno-40-13" href="#__codelineno-40-13"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="mi">2</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="o">][</span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="o">][</span><span class="mi">2</span><span class="o">]</span>
|
||||
<a id="__codelineno-40-14" name="__codelineno-40-14" href="#__codelineno-40-14"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-40-15" name="__codelineno-40-15" href="#__codelineno-40-15"></a>
|
||||
<a id="__codelineno-40-16" name="__codelineno-40-16" href="#__codelineno-40-16"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">n</span><span class="o">][</span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">n</span><span class="o">][</span><span class="mi">2</span><span class="o">]</span>
|
||||
<a id="__codelineno-40-17" name="__codelineno-40-17" href="#__codelineno-40-17"></a><span class="k">end</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
|
|
|
|||
|
|
@ -3994,7 +3994,18 @@ dp[i, j] = \min(dp[i-1, j], dp[i, j-1]) + grid[i, j]
|
|||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">min_path_sum.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">min_path_sum_dfs</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">min_path_sum.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### 最小路徑和：暴力搜尋 ###</span>
|
||||
<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">min_path_sum_dfs</span><span class="p">(</span><span class="n">grid</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">)</span>
|
||||
<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w"> </span><span class="c1"># 若為左上角單元格，則終止搜尋</span>
|
||||
<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span>
|
||||
<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w"> </span><span class="c1"># 若行列索引越界，則返回 +∞ 代價</span>
|
||||
<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nb">Float</span><span class="o">::</span><span class="no">INFINITY</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="mi">0</span>
|
||||
<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w"> </span><span class="c1"># 計算從左上角到 (i-1, j) 和 (i, j-1) 的最小路徑代價</span>
|
||||
<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w"> </span><span class="n">up</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">min_path_sum_dfs</span><span class="p">(</span><span class="n">grid</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">)</span>
|
||||
<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">min_path_sum_dfs</span><span class="p">(</span><span class="n">grid</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w"> </span><span class="c1"># 返回從左上角到 (i, j) 的最小路徑代價</span>
|
||||
<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="w"> </span><span class="o">[</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">up</span><span class="o">].</span><span class="n">min</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span>
|
||||
<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="k">end</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
|
|
@ -4331,7 +4342,20 @@ dp[i, j] = \min(dp[i-1, j], dp[i, j-1]) + grid[i, j]
|
|||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">min_path_sum.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">min_path_sum_dfs_mem</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">min_path_sum.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="c1">### 最小路徑和：記憶化搜尋 ###</span>
|
||||
<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">min_path_sum_dfs_mem</span><span class="p">(</span><span class="n">grid</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">)</span>
|
||||
<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a><span class="w"> </span><span class="c1"># 若為左上角單元格，則終止搜尋</span>
|
||||
<a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="mi">0</span><span class="o">][</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span>
|
||||
<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a><span class="w"> </span><span class="c1"># 若行列索引越界，則返回 +∞ 代價</span>
|
||||
<a id="__codelineno-26-6" name="__codelineno-26-6" href="#__codelineno-26-6"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nb">Float</span><span class="o">::</span><span class="no">INFINITY</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="mi">0</span>
|
||||
<a id="__codelineno-26-7" name="__codelineno-26-7" href="#__codelineno-26-7"></a><span class="w"> </span><span class="c1"># 若已有記錄，則直接返回</span>
|
||||
<a id="__codelineno-26-8" name="__codelineno-26-8" href="#__codelineno-26-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">mem</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">mem</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
|
||||
<a id="__codelineno-26-9" name="__codelineno-26-9" href="#__codelineno-26-9"></a><span class="w"> </span><span class="c1"># 左邊和上邊單元格的最小路徑代價</span>
|
||||
<a id="__codelineno-26-10" name="__codelineno-26-10" href="#__codelineno-26-10"></a><span class="w"> </span><span class="n">up</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">min_path_sum_dfs_mem</span><span class="p">(</span><span class="n">grid</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">)</span>
|
||||
<a id="__codelineno-26-11" name="__codelineno-26-11" href="#__codelineno-26-11"></a><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">min_path_sum_dfs_mem</span><span class="p">(</span><span class="n">grid</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-26-12" name="__codelineno-26-12" href="#__codelineno-26-12"></a><span class="w"> </span><span class="c1"># 記錄並返回左上角到 (i, j) 的最小路徑代價</span>
|
||||
<a id="__codelineno-26-13" name="__codelineno-26-13" href="#__codelineno-26-13"></a><span class="w"> </span><span class="n">mem</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">up</span><span class="o">].</span><span class="n">min</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span>
|
||||
<a id="__codelineno-26-14" name="__codelineno-26-14" href="#__codelineno-26-14"></a><span class="k">end</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
|
|
@ -4688,7 +4712,24 @@ dp[i, j] = \min(dp[i-1, j], dp[i, j-1]) + grid[i, j]
|
|||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">min_path_sum.rb</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">min_path_sum_dp</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">min_path_sum.rb</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="c1">### 最小路徑和：動態規劃 ###</span>
|
||||
<a id="__codelineno-40-2" name="__codelineno-40-2" href="#__codelineno-40-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">min_path_sum_dp</span><span class="p">(</span><span class="n">grid</span><span class="p">)</span>
|
||||
<a id="__codelineno-40-3" name="__codelineno-40-3" href="#__codelineno-40-3"></a><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grid</span><span class="o">.</span><span class="n">length</span><span class="p">,</span><span class="w"> </span><span class="n">grid</span><span class="o">.</span><span class="n">first</span><span class="o">.</span><span class="n">length</span>
|
||||
<a id="__codelineno-40-4" name="__codelineno-40-4" href="#__codelineno-40-4"></a><span class="w"> </span><span class="c1"># 初始化 dp 表</span>
|
||||
<a id="__codelineno-40-5" name="__codelineno-40-5" href="#__codelineno-40-5"></a><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">m</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-40-6" name="__codelineno-40-6" href="#__codelineno-40-6"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="mi">0</span><span class="o">][</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="mi">0</span><span class="o">][</span><span class="mi">0</span><span class="o">]</span>
|
||||
<a id="__codelineno-40-7" name="__codelineno-40-7" href="#__codelineno-40-7"></a><span class="w"> </span><span class="c1"># 狀態轉移：首行</span>
|
||||
<a id="__codelineno-40-8" name="__codelineno-40-8" href="#__codelineno-40-8"></a><span class="w"> </span><span class="p">(</span><span class="mi">1</span><span class="o">...</span><span class="n">m</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">j</span><span class="o">|</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="mi">0</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="mi">0</span><span class="o">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="mi">0</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-40-9" name="__codelineno-40-9" href="#__codelineno-40-9"></a><span class="w"> </span><span class="c1"># 狀態轉移：首列</span>
|
||||
<a id="__codelineno-40-10" name="__codelineno-40-10" href="#__codelineno-40-10"></a><span class="w"> </span><span class="p">(</span><span class="mi">1</span><span class="o">...</span><span class="n">n</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">i</span><span class="o">|</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-40-11" name="__codelineno-40-11" href="#__codelineno-40-11"></a><span class="w"> </span><span class="c1"># 狀態轉移：其餘行和列</span>
|
||||
<a id="__codelineno-40-12" name="__codelineno-40-12" href="#__codelineno-40-12"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="n">n</span>
|
||||
<a id="__codelineno-40-13" name="__codelineno-40-13" href="#__codelineno-40-13"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="n">m</span>
|
||||
<a id="__codelineno-40-14" name="__codelineno-40-14" href="#__codelineno-40-14"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">j</span><span class="o">]].</span><span class="n">min</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span>
|
||||
<a id="__codelineno-40-15" name="__codelineno-40-15" href="#__codelineno-40-15"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-40-16" name="__codelineno-40-16" href="#__codelineno-40-16"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-40-17" name="__codelineno-40-17" href="#__codelineno-40-17"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="o">][</span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="o">]</span>
|
||||
<a id="__codelineno-40-18" name="__codelineno-40-18" href="#__codelineno-40-18"></a><span class="k">end</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
|
|
@ -5063,7 +5104,23 @@ dp[i, j] = \min(dp[i-1, j], dp[i, j-1]) + grid[i, j]
|
|||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">min_path_sum.rb</span><pre><span></span><code><a id="__codelineno-54-1" name="__codelineno-54-1" href="#__codelineno-54-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">min_path_sum_dp_comp</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">min_path_sum.rb</span><pre><span></span><code><a id="__codelineno-54-1" name="__codelineno-54-1" href="#__codelineno-54-1"></a><span class="c1">### 最小路徑和：空間最佳化後的動態規劃 ###</span>
|
||||
<a id="__codelineno-54-2" name="__codelineno-54-2" href="#__codelineno-54-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">min_path_sum_dp_comp</span><span class="p">(</span><span class="n">grid</span><span class="p">)</span>
|
||||
<a id="__codelineno-54-3" name="__codelineno-54-3" href="#__codelineno-54-3"></a><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grid</span><span class="o">.</span><span class="n">length</span><span class="p">,</span><span class="w"> </span><span class="n">grid</span><span class="o">.</span><span class="n">first</span><span class="o">.</span><span class="n">length</span>
|
||||
<a id="__codelineno-54-4" name="__codelineno-54-4" href="#__codelineno-54-4"></a><span class="w"> </span><span class="c1"># 初始化 dp 表</span>
|
||||
<a id="__codelineno-54-5" name="__codelineno-54-5" href="#__codelineno-54-5"></a><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">m</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
|
||||
<a id="__codelineno-54-6" name="__codelineno-54-6" href="#__codelineno-54-6"></a><span class="w"> </span><span class="c1"># 狀態轉移：首行</span>
|
||||
<a id="__codelineno-54-7" name="__codelineno-54-7" href="#__codelineno-54-7"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="mi">0</span><span class="o">][</span><span class="mi">0</span><span class="o">]</span>
|
||||
<a id="__codelineno-54-8" name="__codelineno-54-8" href="#__codelineno-54-8"></a><span class="w"> </span><span class="p">(</span><span class="mi">1</span><span class="o">...</span><span class="n">m</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">j</span><span class="o">|</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="mi">0</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-54-9" name="__codelineno-54-9" href="#__codelineno-54-9"></a><span class="w"> </span><span class="c1"># 狀態轉移：其餘行</span>
|
||||
<a id="__codelineno-54-10" name="__codelineno-54-10" href="#__codelineno-54-10"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="n">n</span>
|
||||
<a id="__codelineno-54-11" name="__codelineno-54-11" href="#__codelineno-54-11"></a><span class="w"> </span><span class="c1"># 狀態轉移：首列</span>
|
||||
<a id="__codelineno-54-12" name="__codelineno-54-12" href="#__codelineno-54-12"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="mi">0</span><span class="o">]</span>
|
||||
<a id="__codelineno-54-13" name="__codelineno-54-13" href="#__codelineno-54-13"></a><span class="w"> </span><span class="c1"># 狀態轉移：其餘列</span>
|
||||
<a id="__codelineno-54-14" name="__codelineno-54-14" href="#__codelineno-54-14"></a><span class="w"> </span><span class="p">(</span><span class="mi">1</span><span class="o">...</span><span class="n">m</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">j</span><span class="o">|</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="o">]].</span><span class="n">min</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-54-15" name="__codelineno-54-15" href="#__codelineno-54-15"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-54-16" name="__codelineno-54-16" href="#__codelineno-54-16"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span>
|
||||
<a id="__codelineno-54-17" name="__codelineno-54-17" href="#__codelineno-54-17"></a><span class="k">end</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
|
|
|
|||
|
|
@ -4019,7 +4019,27 @@ dp[i, j] = dp[i-1, j-1]
|
|||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">edit_distance.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">edit_distance_dp</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">edit_distance.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### 編輯距離：動態規劃 ###</span>
|
||||
<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">edit_distance_dp</span><span class="p">(</span><span class="n">s</span><span class="p">,</span><span class="w"> </span><span class="n">t</span><span class="p">)</span>
|
||||
<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">s</span><span class="o">.</span><span class="n">length</span><span class="p">,</span><span class="w"> </span><span class="n">t</span><span class="o">.</span><span class="n">length</span>
|
||||
<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w"> </span><span class="c1"># 狀態轉移：首行首列</span>
|
||||
<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w"> </span><span class="p">(</span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">))</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">i</span><span class="o">|</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w"> </span><span class="p">(</span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">))</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">j</span><span class="o">|</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="mi">0</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w"> </span><span class="c1"># 狀態轉移：其餘行和列</span>
|
||||
<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">s</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">t</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span>
|
||||
<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="w"> </span><span class="c1"># 若兩字元相等，則直接跳過此兩字元</span>
|
||||
<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span>
|
||||
<a id="__codelineno-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a><span class="w"> </span><span class="k">else</span>
|
||||
<a id="__codelineno-12-15" name="__codelineno-12-15" href="#__codelineno-12-15"></a><span class="w"> </span><span class="c1"># 最少編輯步數 = 插入、刪除、替換這三種操作的最少編輯步數 + 1</span>
|
||||
<a id="__codelineno-12-16" name="__codelineno-12-16" href="#__codelineno-12-16"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]].</span><span class="n">min</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
|
||||
<a id="__codelineno-12-17" name="__codelineno-12-17" href="#__codelineno-12-17"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-12-18" name="__codelineno-12-18" href="#__codelineno-12-18"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-12-19" name="__codelineno-12-19" href="#__codelineno-12-19"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-12-20" name="__codelineno-12-20" href="#__codelineno-12-20"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">n</span><span class="o">][</span><span class="n">m</span><span class="o">]</span>
|
||||
<a id="__codelineno-12-21" name="__codelineno-12-21" href="#__codelineno-12-21"></a><span class="k">end</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
|
|
@ -4490,7 +4510,32 @@ dp[i, j] = dp[i-1, j-1]
|
|||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">edit_distance.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">edit_distance_dp_comp</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">edit_distance.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="c1">### 編輯距離：空間最佳化後的動態規劃 ###</span>
|
||||
<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">edit_distance_dp_comp</span><span class="p">(</span><span class="n">s</span><span class="p">,</span><span class="w"> </span><span class="n">t</span><span class="p">)</span>
|
||||
<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">s</span><span class="o">.</span><span class="n">length</span><span class="p">,</span><span class="w"> </span><span class="n">t</span><span class="o">.</span><span class="n">length</span>
|
||||
<a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
|
||||
<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a><span class="w"> </span><span class="c1"># 狀態轉移：首行</span>
|
||||
<a id="__codelineno-26-6" name="__codelineno-26-6" href="#__codelineno-26-6"></a><span class="w"> </span><span class="p">(</span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">))</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">j</span><span class="o">|</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-26-7" name="__codelineno-26-7" href="#__codelineno-26-7"></a><span class="w"> </span><span class="c1"># 狀態轉移：其餘行</span>
|
||||
<a id="__codelineno-26-8" name="__codelineno-26-8" href="#__codelineno-26-8"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-26-9" name="__codelineno-26-9" href="#__codelineno-26-9"></a><span class="w"> </span><span class="c1"># 狀態轉移：首列</span>
|
||||
<a id="__codelineno-26-10" name="__codelineno-26-10" href="#__codelineno-26-10"></a><span class="w"> </span><span class="n">leftup</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">.</span><span class="n">first</span><span class="w"> </span><span class="c1"># 暫存 dp[i-1, j-1]</span>
|
||||
<a id="__codelineno-26-11" name="__codelineno-26-11" href="#__codelineno-26-11"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
|
||||
<a id="__codelineno-26-12" name="__codelineno-26-12" href="#__codelineno-26-12"></a><span class="w"> </span><span class="c1"># 狀態轉移：其餘列</span>
|
||||
<a id="__codelineno-26-13" name="__codelineno-26-13" href="#__codelineno-26-13"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-26-14" name="__codelineno-26-14" href="#__codelineno-26-14"></a><span class="w"> </span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="o">]</span>
|
||||
<a id="__codelineno-26-15" name="__codelineno-26-15" href="#__codelineno-26-15"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">s</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">t</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span>
|
||||
<a id="__codelineno-26-16" name="__codelineno-26-16" href="#__codelineno-26-16"></a><span class="w"> </span><span class="c1"># 若兩字元相等，則直接跳過此兩字元</span>
|
||||
<a id="__codelineno-26-17" name="__codelineno-26-17" href="#__codelineno-26-17"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">leftup</span>
|
||||
<a id="__codelineno-26-18" name="__codelineno-26-18" href="#__codelineno-26-18"></a><span class="w"> </span><span class="k">else</span>
|
||||
<a id="__codelineno-26-19" name="__codelineno-26-19" href="#__codelineno-26-19"></a><span class="w"> </span><span class="c1"># 最少編輯步數 = 插入、刪除、替換這三種操作的最少編輯步數 + 1</span>
|
||||
<a id="__codelineno-26-20" name="__codelineno-26-20" href="#__codelineno-26-20"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">leftup</span><span class="o">].</span><span class="n">min</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
|
||||
<a id="__codelineno-26-21" name="__codelineno-26-21" href="#__codelineno-26-21"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-26-22" name="__codelineno-26-22" href="#__codelineno-26-22"></a><span class="w"> </span><span class="n">leftup</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span><span class="w"> </span><span class="c1"># 更新為下一輪的 dp[i-1, j-1]</span>
|
||||
<a id="__codelineno-26-23" name="__codelineno-26-23" href="#__codelineno-26-23"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-26-24" name="__codelineno-26-24" href="#__codelineno-26-24"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-26-25" name="__codelineno-26-25" href="#__codelineno-26-25"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">m</span><span class="o">]</span>
|
||||
<a id="__codelineno-26-26" name="__codelineno-26-26" href="#__codelineno-26-26"></a><span class="k">end</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
|
|
|
|||
|
|
@ -3997,9 +3997,29 @@
|
|||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">climbing_stairs_backtrack.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">backtrack</span><span class="p">}</span>
|
||||
<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a>
|
||||
<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">climbing_stairs_backtrack</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">climbing_stairs_backtrack.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### 回溯 ###</span>
|
||||
<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
|
||||
<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w"> </span><span class="c1"># 當爬到第 n 階時，方案數量加 1</span>
|
||||
<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w"> </span><span class="n">res</span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">state</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">n</span>
|
||||
<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w"> </span><span class="c1"># 走訪所有選擇</span>
|
||||
<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">choices</span>
|
||||
<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w"> </span><span class="c1"># 剪枝：不允許越過第 n 階</span>
|
||||
<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w"> </span><span class="k">next</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">state</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">n</span>
|
||||
<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a>
|
||||
<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w"> </span><span class="c1"># 嘗試：做出選擇，更新狀態</span>
|
||||
<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="w"> </span><span class="n">backtrack</span><span class="p">(</span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">state</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">choice</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
|
||||
<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a><span class="w"> </span><span class="c1"># 回退</span>
|
||||
<a id="__codelineno-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a><span class="k">end</span>
|
||||
<a id="__codelineno-12-15" name="__codelineno-12-15" href="#__codelineno-12-15"></a>
|
||||
<a id="__codelineno-12-16" name="__codelineno-12-16" href="#__codelineno-12-16"></a><span class="c1">### 爬樓梯：回溯 ###</span>
|
||||
<a id="__codelineno-12-17" name="__codelineno-12-17" href="#__codelineno-12-17"></a><span class="k">def</span><span class="w"> </span><span class="nf">climbing_stairs_backtrack</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
|
||||
<a id="__codelineno-12-18" name="__codelineno-12-18" href="#__codelineno-12-18"></a><span class="w"> </span><span class="n">choices</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="o">]</span><span class="w"> </span><span class="c1"># 可選擇向上爬 1 階或 2 階</span>
|
||||
<a id="__codelineno-12-19" name="__codelineno-12-19" href="#__codelineno-12-19"></a><span class="w"> </span><span class="n">state</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="c1"># 從第 0 階開始爬</span>
|
||||
<a id="__codelineno-12-20" name="__codelineno-12-20" href="#__codelineno-12-20"></a><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="c1"># 使用 res[0] 記錄方案數量</span>
|
||||
<a id="__codelineno-12-21" name="__codelineno-12-21" href="#__codelineno-12-21"></a><span class="w"> </span><span class="n">backtrack</span><span class="p">(</span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
|
||||
<a id="__codelineno-12-22" name="__codelineno-12-22" href="#__codelineno-12-22"></a><span class="w"> </span><span class="n">res</span><span class="o">.</span><span class="n">first</span>
|
||||
<a id="__codelineno-12-23" name="__codelineno-12-23" href="#__codelineno-12-23"></a><span class="k">end</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
|
|
@ -4261,9 +4281,18 @@ dp[i] = dp[i-1] + dp[i-2]
|
|||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">climbing_stairs_dfs.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">dfs</span><span class="p">}</span>
|
||||
<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a>
|
||||
<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">climbing_stairs_dfs</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">climbing_stairs_dfs.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="c1">### 搜尋 ###</span>
|
||||
<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
|
||||
<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a><span class="w"> </span><span class="c1"># 已知 dp[1] 和 dp[2] ，返回之</span>
|
||||
<a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span>
|
||||
<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a><span class="w"> </span><span class="c1"># dp[i] = dp[i-1] + dp[i-2]</span>
|
||||
<a id="__codelineno-26-6" name="__codelineno-26-6" href="#__codelineno-26-6"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
|
||||
<a id="__codelineno-26-7" name="__codelineno-26-7" href="#__codelineno-26-7"></a><span class="k">end</span>
|
||||
<a id="__codelineno-26-8" name="__codelineno-26-8" href="#__codelineno-26-8"></a>
|
||||
<a id="__codelineno-26-9" name="__codelineno-26-9" href="#__codelineno-26-9"></a><span class="c1">### 爬樓梯：搜尋 ###</span>
|
||||
<a id="__codelineno-26-10" name="__codelineno-26-10" href="#__codelineno-26-10"></a><span class="k">def</span><span class="w"> </span><span class="nf">climbing_stairs_dfs</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
|
||||
<a id="__codelineno-26-11" name="__codelineno-26-11" href="#__codelineno-26-11"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
|
||||
<a id="__codelineno-26-12" name="__codelineno-26-12" href="#__codelineno-26-12"></a><span class="k">end</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
|
|
@ -4602,9 +4631,25 @@ dp[i] = dp[i-1] + dp[i-2]
|
|||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">climbing_stairs_dfs_mem.rb</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">dfs</span><span class="p">}</span>
|
||||
<a id="__codelineno-40-2" name="__codelineno-40-2" href="#__codelineno-40-2"></a>
|
||||
<a id="__codelineno-40-3" name="__codelineno-40-3" href="#__codelineno-40-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">climbing_stairs_dfs_mem</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">climbing_stairs_dfs_mem.rb</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="c1">### 記憶化搜尋 ###</span>
|
||||
<a id="__codelineno-40-2" name="__codelineno-40-2" href="#__codelineno-40-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">)</span>
|
||||
<a id="__codelineno-40-3" name="__codelineno-40-3" href="#__codelineno-40-3"></a><span class="w"> </span><span class="c1"># 已知 dp[1] 和 dp[2] ，返回之</span>
|
||||
<a id="__codelineno-40-4" name="__codelineno-40-4" href="#__codelineno-40-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span>
|
||||
<a id="__codelineno-40-5" name="__codelineno-40-5" href="#__codelineno-40-5"></a><span class="w"> </span><span class="c1"># 若存在記錄 dp[i] ，則直接返回之</span>
|
||||
<a id="__codelineno-40-6" name="__codelineno-40-6" href="#__codelineno-40-6"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">mem</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">mem</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
|
||||
<a id="__codelineno-40-7" name="__codelineno-40-7" href="#__codelineno-40-7"></a>
|
||||
<a id="__codelineno-40-8" name="__codelineno-40-8" href="#__codelineno-40-8"></a><span class="w"> </span><span class="c1"># dp[i] = dp[i-1] + dp[i-2]</span>
|
||||
<a id="__codelineno-40-9" name="__codelineno-40-9" href="#__codelineno-40-9"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">)</span>
|
||||
<a id="__codelineno-40-10" name="__codelineno-40-10" href="#__codelineno-40-10"></a><span class="w"> </span><span class="c1"># 記錄 dp[i]</span>
|
||||
<a id="__codelineno-40-11" name="__codelineno-40-11" href="#__codelineno-40-11"></a><span class="w"> </span><span class="n">mem</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">count</span>
|
||||
<a id="__codelineno-40-12" name="__codelineno-40-12" href="#__codelineno-40-12"></a><span class="k">end</span>
|
||||
<a id="__codelineno-40-13" name="__codelineno-40-13" href="#__codelineno-40-13"></a>
|
||||
<a id="__codelineno-40-14" name="__codelineno-40-14" href="#__codelineno-40-14"></a><span class="c1">### 爬樓梯：記憶化搜尋 ###</span>
|
||||
<a id="__codelineno-40-15" name="__codelineno-40-15" href="#__codelineno-40-15"></a><span class="k">def</span><span class="w"> </span><span class="nf">climbing_stairs_dfs_mem</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
|
||||
<a id="__codelineno-40-16" name="__codelineno-40-16" href="#__codelineno-40-16"></a><span class="w"> </span><span class="c1"># mem[i] 記錄爬到第 i 階的方案總數，-1 代表無記錄</span>
|
||||
<a id="__codelineno-40-17" name="__codelineno-40-17" href="#__codelineno-40-17"></a><span class="w"> </span><span class="n">mem</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-40-18" name="__codelineno-40-18" href="#__codelineno-40-18"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">)</span>
|
||||
<a id="__codelineno-40-19" name="__codelineno-40-19" href="#__codelineno-40-19"></a><span class="k">end</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
|
|
@ -4866,7 +4911,19 @@ dp[i] = dp[i-1] + dp[i-2]
|
|||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">climbing_stairs_dp.rb</span><pre><span></span><code><a id="__codelineno-54-1" name="__codelineno-54-1" href="#__codelineno-54-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">climbing_stairs_dp</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">climbing_stairs_dp.rb</span><pre><span></span><code><a id="__codelineno-54-1" name="__codelineno-54-1" href="#__codelineno-54-1"></a><span class="c1">### 爬樓梯：動態規劃 ###</span>
|
||||
<a id="__codelineno-54-2" name="__codelineno-54-2" href="#__codelineno-54-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">climbing_stairs_dp</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
|
||||
<a id="__codelineno-54-3" name="__codelineno-54-3" href="#__codelineno-54-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span>
|
||||
<a id="__codelineno-54-4" name="__codelineno-54-4" href="#__codelineno-54-4"></a>
|
||||
<a id="__codelineno-54-5" name="__codelineno-54-5" href="#__codelineno-54-5"></a><span class="w"> </span><span class="c1"># 初始化 dp 表，用於儲存子問題的解</span>
|
||||
<a id="__codelineno-54-6" name="__codelineno-54-6" href="#__codelineno-54-6"></a><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
|
||||
<a id="__codelineno-54-7" name="__codelineno-54-7" href="#__codelineno-54-7"></a><span class="w"> </span><span class="c1"># 初始狀態：預設最小子問題的解</span>
|
||||
<a id="__codelineno-54-8" name="__codelineno-54-8" href="#__codelineno-54-8"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="mi">1</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="mi">2</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span>
|
||||
<a id="__codelineno-54-9" name="__codelineno-54-9" href="#__codelineno-54-9"></a><span class="w"> </span><span class="c1"># 狀態轉移：從較小子問題逐步求解較大子問題</span>
|
||||
<a id="__codelineno-54-10" name="__codelineno-54-10" href="#__codelineno-54-10"></a><span class="w"> </span><span class="p">(</span><span class="mi">3</span><span class="o">...</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">))</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">i</span><span class="o">|</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="o">]</span><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-54-11" name="__codelineno-54-11" href="#__codelineno-54-11"></a>
|
||||
<a id="__codelineno-54-12" name="__codelineno-54-12" href="#__codelineno-54-12"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">n</span><span class="o">]</span>
|
||||
<a id="__codelineno-54-13" name="__codelineno-54-13" href="#__codelineno-54-13"></a><span class="k">end</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
|
|
@ -5088,7 +5145,15 @@ dp[i] = dp[i-1] + dp[i-2]
|
|||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">climbing_stairs_dp.rb</span><pre><span></span><code><a id="__codelineno-68-1" name="__codelineno-68-1" href="#__codelineno-68-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">climbing_stairs_dp_comp</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">climbing_stairs_dp.rb</span><pre><span></span><code><a id="__codelineno-68-1" name="__codelineno-68-1" href="#__codelineno-68-1"></a><span class="c1">### 爬樓梯：空間最佳化後的動態規劃 ###</span>
|
||||
<a id="__codelineno-68-2" name="__codelineno-68-2" href="#__codelineno-68-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">climbing_stairs_dp_comp</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
|
||||
<a id="__codelineno-68-3" name="__codelineno-68-3" href="#__codelineno-68-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span>
|
||||
<a id="__codelineno-68-4" name="__codelineno-68-4" href="#__codelineno-68-4"></a>
|
||||
<a id="__codelineno-68-5" name="__codelineno-68-5" href="#__codelineno-68-5"></a><span class="w"> </span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span>
|
||||
<a id="__codelineno-68-6" name="__codelineno-68-6" href="#__codelineno-68-6"></a><span class="w"> </span><span class="p">(</span><span class="mi">3</span><span class="o">...</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">))</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">b</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-68-7" name="__codelineno-68-7" href="#__codelineno-68-7"></a>
|
||||
<a id="__codelineno-68-8" name="__codelineno-68-8" href="#__codelineno-68-8"></a><span class="w"> </span><span class="n">b</span>
|
||||
<a id="__codelineno-68-9" name="__codelineno-68-9" href="#__codelineno-68-9"></a><span class="k">end</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
|
|
|
|||
|
|
@ -3912,7 +3912,18 @@ dp[i, c] = \max(dp[i-1, c], dp[i-1, c - wgt[i-1]] + val[i-1])
|
|||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">knapsack.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">knapsack_dfs</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">knapsack.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### 0-1 背包：暴力搜尋 ###</span>
|
||||
<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">knapsack_dfs</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">)</span>
|
||||
<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w"> </span><span class="c1"># 若已選完所有物品或背包無剩餘容量，則返回價值 0</span>
|
||||
<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span>
|
||||
<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w"> </span><span class="c1"># 若超過背包容量，則只能選擇不放入背包</span>
|
||||
<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">knapsack_dfs</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">c</span>
|
||||
<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w"> </span><span class="c1"># 計算不放入和放入物品 i 的最大價值</span>
|
||||
<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w"> </span><span class="n">no</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">knapsack_dfs</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">)</span>
|
||||
<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w"> </span><span class="n">yes</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">knapsack_dfs</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span>
|
||||
<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w"> </span><span class="c1"># 返回兩種方案中價值更大的那一個</span>
|
||||
<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="w"> </span><span class="o">[</span><span class="n">no</span><span class="p">,</span><span class="w"> </span><span class="n">yes</span><span class="o">].</span><span class="n">max</span>
|
||||
<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="k">end</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
|
|
@ -4258,7 +4269,20 @@ dp[i, c] = \max(dp[i-1, c], dp[i-1, c - wgt[i-1]] + val[i-1])
|
|||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">knapsack.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">knapsack_dfs_mem</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">knapsack.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="c1">### 0-1 背包：記憶化搜尋 ###</span>
|
||||
<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">knapsack_dfs_mem</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">)</span>
|
||||
<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a><span class="w"> </span><span class="c1"># 若已選完所有物品或背包無剩餘容量，則返回價值 0</span>
|
||||
<a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span>
|
||||
<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a><span class="w"> </span><span class="c1"># 若已有記錄，則直接返回</span>
|
||||
<a id="__codelineno-26-6" name="__codelineno-26-6" href="#__codelineno-26-6"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">mem</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">mem</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
|
||||
<a id="__codelineno-26-7" name="__codelineno-26-7" href="#__codelineno-26-7"></a><span class="w"> </span><span class="c1"># 若超過背包容量，則只能選擇不放入背包</span>
|
||||
<a id="__codelineno-26-8" name="__codelineno-26-8" href="#__codelineno-26-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">knapsack_dfs_mem</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">c</span>
|
||||
<a id="__codelineno-26-9" name="__codelineno-26-9" href="#__codelineno-26-9"></a><span class="w"> </span><span class="c1"># 計算不放入和放入物品 i 的最大價值</span>
|
||||
<a id="__codelineno-26-10" name="__codelineno-26-10" href="#__codelineno-26-10"></a><span class="w"> </span><span class="n">no</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">knapsack_dfs_mem</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">)</span>
|
||||
<a id="__codelineno-26-11" name="__codelineno-26-11" href="#__codelineno-26-11"></a><span class="w"> </span><span class="n">yes</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">knapsack_dfs_mem</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span>
|
||||
<a id="__codelineno-26-12" name="__codelineno-26-12" href="#__codelineno-26-12"></a><span class="w"> </span><span class="c1"># 記錄並返回兩種方案中價值更大的那一個</span>
|
||||
<a id="__codelineno-26-13" name="__codelineno-26-13" href="#__codelineno-26-13"></a><span class="w"> </span><span class="n">mem</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="n">no</span><span class="p">,</span><span class="w"> </span><span class="n">yes</span><span class="o">].</span><span class="n">max</span>
|
||||
<a id="__codelineno-26-14" name="__codelineno-26-14" href="#__codelineno-26-14"></a><span class="k">end</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
|
|
@ -4589,7 +4613,25 @@ dp[i, c] = \max(dp[i-1, c], dp[i-1, c - wgt[i-1]] + val[i-1])
|
|||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">knapsack.rb</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">knapsack_dp</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">knapsack.rb</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="c1">### 0-1 背包：動態規劃 ###</span>
|
||||
<a id="__codelineno-40-2" name="__codelineno-40-2" href="#__codelineno-40-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">knapsack_dp</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">cap</span><span class="p">)</span>
|
||||
<a id="__codelineno-40-3" name="__codelineno-40-3" href="#__codelineno-40-3"></a><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">wgt</span><span class="o">.</span><span class="n">length</span>
|
||||
<a id="__codelineno-40-4" name="__codelineno-40-4" href="#__codelineno-40-4"></a><span class="w"> </span><span class="c1"># 初始化 dp 表</span>
|
||||
<a id="__codelineno-40-5" name="__codelineno-40-5" href="#__codelineno-40-5"></a><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-40-6" name="__codelineno-40-6" href="#__codelineno-40-6"></a><span class="w"> </span><span class="c1"># 狀態轉移</span>
|
||||
<a id="__codelineno-40-7" name="__codelineno-40-7" href="#__codelineno-40-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-40-8" name="__codelineno-40-8" href="#__codelineno-40-8"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-40-9" name="__codelineno-40-9" href="#__codelineno-40-9"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">c</span>
|
||||
<a id="__codelineno-40-10" name="__codelineno-40-10" href="#__codelineno-40-10"></a><span class="w"> </span><span class="c1"># 若超過背包容量，則不選物品 i</span>
|
||||
<a id="__codelineno-40-11" name="__codelineno-40-11" href="#__codelineno-40-11"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">c</span><span class="o">]</span>
|
||||
<a id="__codelineno-40-12" name="__codelineno-40-12" href="#__codelineno-40-12"></a><span class="w"> </span><span class="k">else</span>
|
||||
<a id="__codelineno-40-13" name="__codelineno-40-13" href="#__codelineno-40-13"></a><span class="w"> </span><span class="c1"># 不選和選物品 i 這兩種方案的較大值</span>
|
||||
<a id="__codelineno-40-14" name="__codelineno-40-14" href="#__codelineno-40-14"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]].</span><span class="n">max</span>
|
||||
<a id="__codelineno-40-15" name="__codelineno-40-15" href="#__codelineno-40-15"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-40-16" name="__codelineno-40-16" href="#__codelineno-40-16"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-40-17" name="__codelineno-40-17" href="#__codelineno-40-17"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-40-18" name="__codelineno-40-18" href="#__codelineno-40-18"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">n</span><span class="o">][</span><span class="n">cap</span><span class="o">]</span>
|
||||
<a id="__codelineno-40-19" name="__codelineno-40-19" href="#__codelineno-40-19"></a><span class="k">end</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
|
|
@ -4955,7 +4997,26 @@ dp[i, c] = \max(dp[i-1, c], dp[i-1, c - wgt[i-1]] + val[i-1])
|
|||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">knapsack.rb</span><pre><span></span><code><a id="__codelineno-54-1" name="__codelineno-54-1" href="#__codelineno-54-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">knapsack_dp_comp</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">knapsack.rb</span><pre><span></span><code><a id="__codelineno-54-1" name="__codelineno-54-1" href="#__codelineno-54-1"></a><span class="c1">### 0-1 背包：空間最佳化後的動態規劃 ###</span>
|
||||
<a id="__codelineno-54-2" name="__codelineno-54-2" href="#__codelineno-54-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">knapsack_dp_comp</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">cap</span><span class="p">)</span>
|
||||
<a id="__codelineno-54-3" name="__codelineno-54-3" href="#__codelineno-54-3"></a><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">wgt</span><span class="o">.</span><span class="n">length</span>
|
||||
<a id="__codelineno-54-4" name="__codelineno-54-4" href="#__codelineno-54-4"></a><span class="w"> </span><span class="c1"># 初始化 dp 表</span>
|
||||
<a id="__codelineno-54-5" name="__codelineno-54-5" href="#__codelineno-54-5"></a><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
|
||||
<a id="__codelineno-54-6" name="__codelineno-54-6" href="#__codelineno-54-6"></a><span class="w"> </span><span class="c1"># 狀態轉移</span>
|
||||
<a id="__codelineno-54-7" name="__codelineno-54-7" href="#__codelineno-54-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-54-8" name="__codelineno-54-8" href="#__codelineno-54-8"></a><span class="w"> </span><span class="c1"># 倒序走訪</span>
|
||||
<a id="__codelineno-54-9" name="__codelineno-54-9" href="#__codelineno-54-9"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">cap</span><span class="o">.</span><span class="n">downto</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-54-10" name="__codelineno-54-10" href="#__codelineno-54-10"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">c</span>
|
||||
<a id="__codelineno-54-11" name="__codelineno-54-11" href="#__codelineno-54-11"></a><span class="w"> </span><span class="c1"># 若超過背包容量，則不選物品 i</span>
|
||||
<a id="__codelineno-54-12" name="__codelineno-54-12" href="#__codelineno-54-12"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">c</span><span class="o">]</span>
|
||||
<a id="__codelineno-54-13" name="__codelineno-54-13" href="#__codelineno-54-13"></a><span class="w"> </span><span class="k">else</span>
|
||||
<a id="__codelineno-54-14" name="__codelineno-54-14" href="#__codelineno-54-14"></a><span class="w"> </span><span class="c1"># 不選和選物品 i 這兩種方案的較大值</span>
|
||||
<a id="__codelineno-54-15" name="__codelineno-54-15" href="#__codelineno-54-15"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="n">dp</span><span class="o">[</span><span class="n">c</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]].</span><span class="n">max</span>
|
||||
<a id="__codelineno-54-16" name="__codelineno-54-16" href="#__codelineno-54-16"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-54-17" name="__codelineno-54-17" href="#__codelineno-54-17"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-54-18" name="__codelineno-54-18" href="#__codelineno-54-18"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-54-19" name="__codelineno-54-19" href="#__codelineno-54-19"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">cap</span><span class="o">]</span>
|
||||
<a id="__codelineno-54-20" name="__codelineno-54-20" href="#__codelineno-54-20"></a><span class="k">end</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
|
|
|
|||
|
|
@ -4129,7 +4129,25 @@ dp[i, c] = \max(dp[i-1, c], dp[i, c - wgt[i-1]] + val[i-1])
|
|||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">unbounded_knapsack.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">unbounded_knapsack_dp</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">unbounded_knapsack.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### 完全背包：動態規劃 ###</span>
|
||||
<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">unbounded_knapsack_dp</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">cap</span><span class="p">)</span>
|
||||
<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">wgt</span><span class="o">.</span><span class="n">length</span>
|
||||
<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w"> </span><span class="c1"># 初始化 dp 表</span>
|
||||
<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w"> </span><span class="c1"># 狀態轉移</span>
|
||||
<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">c</span>
|
||||
<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w"> </span><span class="c1"># 若超過背包容量，則不選物品 i</span>
|
||||
<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">c</span><span class="o">]</span>
|
||||
<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="w"> </span><span class="k">else</span>
|
||||
<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a><span class="w"> </span><span class="c1"># 不選和選物品 i 這兩種方案的較大值</span>
|
||||
<a id="__codelineno-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]].</span><span class="n">max</span>
|
||||
<a id="__codelineno-12-15" name="__codelineno-12-15" href="#__codelineno-12-15"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-12-16" name="__codelineno-12-16" href="#__codelineno-12-16"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-12-17" name="__codelineno-12-17" href="#__codelineno-12-17"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-12-18" name="__codelineno-12-18" href="#__codelineno-12-18"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">n</span><span class="o">][</span><span class="n">cap</span><span class="o">]</span>
|
||||
<a id="__codelineno-12-19" name="__codelineno-12-19" href="#__codelineno-12-19"></a><span class="k">end</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
|
|
@ -4464,7 +4482,46 @@ dp[i, c] = \max(dp[i-1, c], dp[i, c - wgt[i-1]] + val[i-1])
|
|||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">unbounded_knapsack.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">unbounded_knapsack_dp_comp</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">unbounded_knapsack.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="c1">### 完全背包：動態規劃 ###</span>
|
||||
<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">unbounded_knapsack_dp</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">cap</span><span class="p">)</span>
|
||||
<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">wgt</span><span class="o">.</span><span class="n">length</span>
|
||||
<a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a><span class="w"> </span><span class="c1"># 初始化 dp 表</span>
|
||||
<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-26-6" name="__codelineno-26-6" href="#__codelineno-26-6"></a><span class="w"> </span><span class="c1"># 狀態轉移</span>
|
||||
<a id="__codelineno-26-7" name="__codelineno-26-7" href="#__codelineno-26-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-26-8" name="__codelineno-26-8" href="#__codelineno-26-8"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-26-9" name="__codelineno-26-9" href="#__codelineno-26-9"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">c</span>
|
||||
<a id="__codelineno-26-10" name="__codelineno-26-10" href="#__codelineno-26-10"></a><span class="w"> </span><span class="c1"># 若超過背包容量，則不選物品 i</span>
|
||||
<a id="__codelineno-26-11" name="__codelineno-26-11" href="#__codelineno-26-11"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">c</span><span class="o">]</span>
|
||||
<a id="__codelineno-26-12" name="__codelineno-26-12" href="#__codelineno-26-12"></a><span class="w"> </span><span class="k">else</span>
|
||||
<a id="__codelineno-26-13" name="__codelineno-26-13" href="#__codelineno-26-13"></a><span class="w"> </span><span class="c1"># 不選和選物品 i 這兩種方案的較大值</span>
|
||||
<a id="__codelineno-26-14" name="__codelineno-26-14" href="#__codelineno-26-14"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]].</span><span class="n">max</span>
|
||||
<a id="__codelineno-26-15" name="__codelineno-26-15" href="#__codelineno-26-15"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-26-16" name="__codelineno-26-16" href="#__codelineno-26-16"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-26-17" name="__codelineno-26-17" href="#__codelineno-26-17"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-26-18" name="__codelineno-26-18" href="#__codelineno-26-18"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">n</span><span class="o">][</span><span class="n">cap</span><span class="o">]</span>
|
||||
<a id="__codelineno-26-19" name="__codelineno-26-19" href="#__codelineno-26-19"></a><span class="k">end</span>
|
||||
<a id="__codelineno-26-20" name="__codelineno-26-20" href="#__codelineno-26-20"></a>
|
||||
<a id="__codelineno-26-21" name="__codelineno-26-21" href="#__codelineno-26-21"></a><span class="c1">### 完全背包：空間最佳化後的動態規劃 ##3</span>
|
||||
<a id="__codelineno-26-22" name="__codelineno-26-22" href="#__codelineno-26-22"></a><span class="k">def</span><span class="w"> </span><span class="nf">unbounded_knapsack_dp_comp</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">cap</span><span class="p">)</span>
|
||||
<a id="__codelineno-26-23" name="__codelineno-26-23" href="#__codelineno-26-23"></a><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">wgt</span><span class="o">.</span><span class="n">length</span>
|
||||
<a id="__codelineno-26-24" name="__codelineno-26-24" href="#__codelineno-26-24"></a><span class="w"> </span><span class="c1"># 初始化 dp 表</span>
|
||||
<a id="__codelineno-26-25" name="__codelineno-26-25" href="#__codelineno-26-25"></a><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
|
||||
<a id="__codelineno-26-26" name="__codelineno-26-26" href="#__codelineno-26-26"></a><span class="w"> </span><span class="c1"># 狀態轉移</span>
|
||||
<a id="__codelineno-26-27" name="__codelineno-26-27" href="#__codelineno-26-27"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-26-28" name="__codelineno-26-28" href="#__codelineno-26-28"></a><span class="w"> </span><span class="c1"># 正序走訪</span>
|
||||
<a id="__codelineno-26-29" name="__codelineno-26-29" href="#__codelineno-26-29"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-26-30" name="__codelineno-26-30" href="#__codelineno-26-30"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">c</span>
|
||||
<a id="__codelineno-26-31" name="__codelineno-26-31" href="#__codelineno-26-31"></a><span class="w"> </span><span class="c1"># 若超過背包容量，則不選物品 i</span>
|
||||
<a id="__codelineno-26-32" name="__codelineno-26-32" href="#__codelineno-26-32"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">c</span><span class="o">]</span>
|
||||
<a id="__codelineno-26-33" name="__codelineno-26-33" href="#__codelineno-26-33"></a><span class="w"> </span><span class="k">else</span>
|
||||
<a id="__codelineno-26-34" name="__codelineno-26-34" href="#__codelineno-26-34"></a><span class="w"> </span><span class="c1"># 不選和選物品 i 這兩種方案的較大值</span>
|
||||
<a id="__codelineno-26-35" name="__codelineno-26-35" href="#__codelineno-26-35"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="n">dp</span><span class="o">[</span><span class="n">c</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]].</span><span class="n">max</span>
|
||||
<a id="__codelineno-26-36" name="__codelineno-26-36" href="#__codelineno-26-36"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-26-37" name="__codelineno-26-37" href="#__codelineno-26-37"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-26-38" name="__codelineno-26-38" href="#__codelineno-26-38"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-26-39" name="__codelineno-26-39" href="#__codelineno-26-39"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">cap</span><span class="o">]</span>
|
||||
<a id="__codelineno-26-40" name="__codelineno-26-40" href="#__codelineno-26-40"></a><span class="k">end</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
|
|
@ -4875,7 +4932,28 @@ dp[i, a] = \min(dp[i-1, a], dp[i, a - coins[i-1]] + 1)
|
|||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">coin_change.rb</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">coin_change_dp</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">coin_change.rb</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="c1">### 零錢兌換：動態規劃 ###</span>
|
||||
<a id="__codelineno-40-2" name="__codelineno-40-2" href="#__codelineno-40-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">coin_change_dp</span><span class="p">(</span><span class="n">coins</span><span class="p">,</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span>
|
||||
<a id="__codelineno-40-3" name="__codelineno-40-3" href="#__codelineno-40-3"></a><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="o">.</span><span class="n">length</span>
|
||||
<a id="__codelineno-40-4" name="__codelineno-40-4" href="#__codelineno-40-4"></a><span class="w"> </span><span class="n">_MAX</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
|
||||
<a id="__codelineno-40-5" name="__codelineno-40-5" href="#__codelineno-40-5"></a><span class="w"> </span><span class="c1"># 初始化 dp 表</span>
|
||||
<a id="__codelineno-40-6" name="__codelineno-40-6" href="#__codelineno-40-6"></a><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-40-7" name="__codelineno-40-7" href="#__codelineno-40-7"></a><span class="w"> </span><span class="c1"># 狀態轉移：首行首列</span>
|
||||
<a id="__codelineno-40-8" name="__codelineno-40-8" href="#__codelineno-40-8"></a><span class="w"> </span><span class="p">(</span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">))</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">a</span><span class="o">|</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="mi">0</span><span class="o">][</span><span class="n">a</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_MAX</span><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-40-9" name="__codelineno-40-9" href="#__codelineno-40-9"></a><span class="w"> </span><span class="c1"># 狀態轉移：其餘行和列</span>
|
||||
<a id="__codelineno-40-10" name="__codelineno-40-10" href="#__codelineno-40-10"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-40-11" name="__codelineno-40-11" href="#__codelineno-40-11"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-40-12" name="__codelineno-40-12" href="#__codelineno-40-12"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">coins</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">a</span>
|
||||
<a id="__codelineno-40-13" name="__codelineno-40-13" href="#__codelineno-40-13"></a><span class="w"> </span><span class="c1"># 若超過目標金額，則不選硬幣 i</span>
|
||||
<a id="__codelineno-40-14" name="__codelineno-40-14" href="#__codelineno-40-14"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">a</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">a</span><span class="o">]</span>
|
||||
<a id="__codelineno-40-15" name="__codelineno-40-15" href="#__codelineno-40-15"></a><span class="w"> </span><span class="k">else</span>
|
||||
<a id="__codelineno-40-16" name="__codelineno-40-16" href="#__codelineno-40-16"></a><span class="w"> </span><span class="c1"># 不選和選硬幣 i 這兩種方案的較小值</span>
|
||||
<a id="__codelineno-40-17" name="__codelineno-40-17" href="#__codelineno-40-17"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">a</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">a</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">coins</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">].</span><span class="n">min</span>
|
||||
<a id="__codelineno-40-18" name="__codelineno-40-18" href="#__codelineno-40-18"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-40-19" name="__codelineno-40-19" href="#__codelineno-40-19"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-40-20" name="__codelineno-40-20" href="#__codelineno-40-20"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-40-21" name="__codelineno-40-21" href="#__codelineno-40-21"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">n</span><span class="o">][</span><span class="n">amt</span><span class="o">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">_MAX</span><span class="w"> </span><span class="p">?</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">n</span><span class="o">][</span><span class="n">amt</span><span class="o">]</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
|
||||
<a id="__codelineno-40-22" name="__codelineno-40-22" href="#__codelineno-40-22"></a><span class="k">end</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
|
|
@ -5279,7 +5357,28 @@ dp[i, a] = \min(dp[i-1, a], dp[i, a - coins[i-1]] + 1)
|
|||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">coin_change.rb</span><pre><span></span><code><a id="__codelineno-54-1" name="__codelineno-54-1" href="#__codelineno-54-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">coin_change_dp_comp</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">coin_change.rb</span><pre><span></span><code><a id="__codelineno-54-1" name="__codelineno-54-1" href="#__codelineno-54-1"></a><span class="c1">### 零錢兌換：空間最佳化後的動態規劃 ###</span>
|
||||
<a id="__codelineno-54-2" name="__codelineno-54-2" href="#__codelineno-54-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">coin_change_dp_comp</span><span class="p">(</span><span class="n">coins</span><span class="p">,</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span>
|
||||
<a id="__codelineno-54-3" name="__codelineno-54-3" href="#__codelineno-54-3"></a><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="o">.</span><span class="n">length</span>
|
||||
<a id="__codelineno-54-4" name="__codelineno-54-4" href="#__codelineno-54-4"></a><span class="w"> </span><span class="n">_MAX</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
|
||||
<a id="__codelineno-54-5" name="__codelineno-54-5" href="#__codelineno-54-5"></a><span class="w"> </span><span class="c1"># 初始化 dp 表</span>
|
||||
<a id="__codelineno-54-6" name="__codelineno-54-6" href="#__codelineno-54-6"></a><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">_MAX</span><span class="p">)</span>
|
||||
<a id="__codelineno-54-7" name="__codelineno-54-7" href="#__codelineno-54-7"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
|
||||
<a id="__codelineno-54-8" name="__codelineno-54-8" href="#__codelineno-54-8"></a><span class="w"> </span><span class="c1"># 狀態轉移</span>
|
||||
<a id="__codelineno-54-9" name="__codelineno-54-9" href="#__codelineno-54-9"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-54-10" name="__codelineno-54-10" href="#__codelineno-54-10"></a><span class="w"> </span><span class="c1"># 正序走訪</span>
|
||||
<a id="__codelineno-54-11" name="__codelineno-54-11" href="#__codelineno-54-11"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-54-12" name="__codelineno-54-12" href="#__codelineno-54-12"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">coins</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">a</span>
|
||||
<a id="__codelineno-54-13" name="__codelineno-54-13" href="#__codelineno-54-13"></a><span class="w"> </span><span class="c1"># 若超過目標金額，則不選硬幣 i</span>
|
||||
<a id="__codelineno-54-14" name="__codelineno-54-14" href="#__codelineno-54-14"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">a</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">a</span><span class="o">]</span>
|
||||
<a id="__codelineno-54-15" name="__codelineno-54-15" href="#__codelineno-54-15"></a><span class="w"> </span><span class="k">else</span>
|
||||
<a id="__codelineno-54-16" name="__codelineno-54-16" href="#__codelineno-54-16"></a><span class="w"> </span><span class="c1"># 不選和選硬幣 i 這兩種方案的較小值</span>
|
||||
<a id="__codelineno-54-17" name="__codelineno-54-17" href="#__codelineno-54-17"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">a</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="n">dp</span><span class="o">[</span><span class="n">a</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">coins</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">].</span><span class="n">min</span>
|
||||
<a id="__codelineno-54-18" name="__codelineno-54-18" href="#__codelineno-54-18"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-54-19" name="__codelineno-54-19" href="#__codelineno-54-19"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-54-20" name="__codelineno-54-20" href="#__codelineno-54-20"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-54-21" name="__codelineno-54-21" href="#__codelineno-54-21"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">amt</span><span class="o">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">_MAX</span><span class="w"> </span><span class="p">?</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">amt</span><span class="o">]</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
|
||||
<a id="__codelineno-54-22" name="__codelineno-54-22" href="#__codelineno-54-22"></a><span class="k">end</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
|
|
@ -5660,7 +5759,27 @@ dp[i, a] = dp[i-1, a] + dp[i, a - coins[i-1]]
|
|||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">coin_change_ii.rb</span><pre><span></span><code><a id="__codelineno-68-1" name="__codelineno-68-1" href="#__codelineno-68-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">coin_change_ii_dp</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">coin_change_ii.rb</span><pre><span></span><code><a id="__codelineno-68-1" name="__codelineno-68-1" href="#__codelineno-68-1"></a><span class="c1">### 零錢兌換 II：動態規劃 ###</span>
|
||||
<a id="__codelineno-68-2" name="__codelineno-68-2" href="#__codelineno-68-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">coin_change_ii_dp</span><span class="p">(</span><span class="n">coins</span><span class="p">,</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span>
|
||||
<a id="__codelineno-68-3" name="__codelineno-68-3" href="#__codelineno-68-3"></a><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="o">.</span><span class="n">length</span>
|
||||
<a id="__codelineno-68-4" name="__codelineno-68-4" href="#__codelineno-68-4"></a><span class="w"> </span><span class="c1"># 初始化 dp 表</span>
|
||||
<a id="__codelineno-68-5" name="__codelineno-68-5" href="#__codelineno-68-5"></a><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-68-6" name="__codelineno-68-6" href="#__codelineno-68-6"></a><span class="w"> </span><span class="c1"># 初始化首列</span>
|
||||
<a id="__codelineno-68-7" name="__codelineno-68-7" href="#__codelineno-68-7"></a><span class="w"> </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">))</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">i</span><span class="o">|</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-68-8" name="__codelineno-68-8" href="#__codelineno-68-8"></a><span class="w"> </span><span class="c1"># 狀態轉移</span>
|
||||
<a id="__codelineno-68-9" name="__codelineno-68-9" href="#__codelineno-68-9"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-68-10" name="__codelineno-68-10" href="#__codelineno-68-10"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-68-11" name="__codelineno-68-11" href="#__codelineno-68-11"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">coins</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">a</span>
|
||||
<a id="__codelineno-68-12" name="__codelineno-68-12" href="#__codelineno-68-12"></a><span class="w"> </span><span class="c1"># 若超過目標金額，則不選硬幣 i</span>
|
||||
<a id="__codelineno-68-13" name="__codelineno-68-13" href="#__codelineno-68-13"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">a</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">a</span><span class="o">]</span>
|
||||
<a id="__codelineno-68-14" name="__codelineno-68-14" href="#__codelineno-68-14"></a><span class="w"> </span><span class="k">else</span>
|
||||
<a id="__codelineno-68-15" name="__codelineno-68-15" href="#__codelineno-68-15"></a><span class="w"> </span><span class="c1"># 不選和選硬幣 i 這兩種方案之和</span>
|
||||
<a id="__codelineno-68-16" name="__codelineno-68-16" href="#__codelineno-68-16"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">a</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">a</span><span class="o">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">coins</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]]</span>
|
||||
<a id="__codelineno-68-17" name="__codelineno-68-17" href="#__codelineno-68-17"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-68-18" name="__codelineno-68-18" href="#__codelineno-68-18"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-68-19" name="__codelineno-68-19" href="#__codelineno-68-19"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-68-20" name="__codelineno-68-20" href="#__codelineno-68-20"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">n</span><span class="o">][</span><span class="n">amt</span><span class="o">]</span>
|
||||
<a id="__codelineno-68-21" name="__codelineno-68-21" href="#__codelineno-68-21"></a><span class="k">end</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
|
|
@ -5978,7 +6097,27 @@ dp[i, a] = dp[i-1, a] + dp[i, a - coins[i-1]]
|
|||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">coin_change_ii.rb</span><pre><span></span><code><a id="__codelineno-82-1" name="__codelineno-82-1" href="#__codelineno-82-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">coin_change_ii_dp_comp</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">coin_change_ii.rb</span><pre><span></span><code><a id="__codelineno-82-1" name="__codelineno-82-1" href="#__codelineno-82-1"></a><span class="c1">### 零錢兌換 II：空間最佳化後的動態規劃 ###</span>
|
||||
<a id="__codelineno-82-2" name="__codelineno-82-2" href="#__codelineno-82-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">coin_change_ii_dp_comp</span><span class="p">(</span><span class="n">coins</span><span class="p">,</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span>
|
||||
<a id="__codelineno-82-3" name="__codelineno-82-3" href="#__codelineno-82-3"></a><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="o">.</span><span class="n">length</span>
|
||||
<a id="__codelineno-82-4" name="__codelineno-82-4" href="#__codelineno-82-4"></a><span class="w"> </span><span class="c1"># 初始化 dp 表</span>
|
||||
<a id="__codelineno-82-5" name="__codelineno-82-5" href="#__codelineno-82-5"></a><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
|
||||
<a id="__codelineno-82-6" name="__codelineno-82-6" href="#__codelineno-82-6"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span>
|
||||
<a id="__codelineno-82-7" name="__codelineno-82-7" href="#__codelineno-82-7"></a><span class="w"> </span><span class="c1"># 狀態轉移</span>
|
||||
<a id="__codelineno-82-8" name="__codelineno-82-8" href="#__codelineno-82-8"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-82-9" name="__codelineno-82-9" href="#__codelineno-82-9"></a><span class="w"> </span><span class="c1"># 正序走訪</span>
|
||||
<a id="__codelineno-82-10" name="__codelineno-82-10" href="#__codelineno-82-10"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-82-11" name="__codelineno-82-11" href="#__codelineno-82-11"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">coins</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">a</span>
|
||||
<a id="__codelineno-82-12" name="__codelineno-82-12" href="#__codelineno-82-12"></a><span class="w"> </span><span class="c1"># 若超過目標金額，則不選硬幣 i</span>
|
||||
<a id="__codelineno-82-13" name="__codelineno-82-13" href="#__codelineno-82-13"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">a</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">a</span><span class="o">]</span>
|
||||
<a id="__codelineno-82-14" name="__codelineno-82-14" href="#__codelineno-82-14"></a><span class="w"> </span><span class="k">else</span>
|
||||
<a id="__codelineno-82-15" name="__codelineno-82-15" href="#__codelineno-82-15"></a><span class="w"> </span><span class="c1"># 不選和選硬幣 i 這兩種方案之和</span>
|
||||
<a id="__codelineno-82-16" name="__codelineno-82-16" href="#__codelineno-82-16"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">a</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">a</span><span class="o">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">coins</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]]</span>
|
||||
<a id="__codelineno-82-17" name="__codelineno-82-17" href="#__codelineno-82-17"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-82-18" name="__codelineno-82-18" href="#__codelineno-82-18"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-82-19" name="__codelineno-82-19" href="#__codelineno-82-19"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-82-20" name="__codelineno-82-20" href="#__codelineno-82-20"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">amt</span><span class="o">]</span>
|
||||
<a id="__codelineno-82-21" name="__codelineno-82-21" href="#__codelineno-82-21"></a><span class="k">end</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
|
|
|
|||
|
|
@ -3891,7 +3891,15 @@
|
|||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">my_heap.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">MaxHeap</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">__init__</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">my_heap.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### 建構子，根據輸入串列建堆積 ###</span>
|
||||
<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">initialize</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
|
||||
<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w"> </span><span class="c1"># 將串列元素原封不動新增進堆積</span>
|
||||
<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w"> </span><span class="vi">@max_heap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span>
|
||||
<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w"> </span><span class="c1"># 堆積化除葉節點以外的其他所有節點</span>
|
||||
<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w"> </span><span class="n">parent</span><span class="p">(</span><span class="n">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="o">.</span><span class="n">downto</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="k">do</span><span class="w"> </span><span class="o">|</span><span class="n">i</span><span class="o">|</span>
|
||||
<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w"> </span><span class="n">sift_down</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
|
||||
<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="k">end</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
|
|
|
|||
|
|
@ -4107,7 +4107,7 @@
|
|||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">heap.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a>
|
||||
<div class="highlight"><span class="filename">heap.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1"># Ruby 未提供內建 Heap 類別</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
|
|
|
|||
File diff suppressed because one or more lines are too long
|
|
@ -2,527 +2,527 @@
|
|||
<urlset xmlns="http://www.sitemaps.org/schemas/sitemap/0.9">
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_appendix/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_appendix/contribution/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_appendix/installation/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_appendix/terminology/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_array_and_linkedlist/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_array_and_linkedlist/array/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_array_and_linkedlist/linked_list/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_array_and_linkedlist/list/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_array_and_linkedlist/ram_and_cache/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_array_and_linkedlist/summary/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_backtracking/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_backtracking/backtracking_algorithm/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_backtracking/n_queens_problem/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_backtracking/permutations_problem/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_backtracking/subset_sum_problem/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_backtracking/summary/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_computational_complexity/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_computational_complexity/iteration_and_recursion/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_computational_complexity/performance_evaluation/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_computational_complexity/space_complexity/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_computational_complexity/summary/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_computational_complexity/time_complexity/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_data_structure/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_data_structure/basic_data_types/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_data_structure/character_encoding/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_data_structure/classification_of_data_structure/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_data_structure/number_encoding/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_data_structure/summary/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_divide_and_conquer/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_divide_and_conquer/binary_search_recur/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_divide_and_conquer/build_binary_tree_problem/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_divide_and_conquer/divide_and_conquer/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_divide_and_conquer/hanota_problem/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_divide_and_conquer/summary/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_dynamic_programming/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_dynamic_programming/dp_problem_features/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_dynamic_programming/dp_solution_pipeline/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_dynamic_programming/edit_distance_problem/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_dynamic_programming/intro_to_dynamic_programming/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_dynamic_programming/knapsack_problem/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_dynamic_programming/summary/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_dynamic_programming/unbounded_knapsack_problem/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_graph/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_graph/graph/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_graph/graph_operations/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_graph/graph_traversal/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_graph/summary/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_greedy/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_greedy/fractional_knapsack_problem/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_greedy/greedy_algorithm/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_greedy/max_capacity_problem/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_greedy/max_product_cutting_problem/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_greedy/summary/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_hashing/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_hashing/hash_algorithm/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_hashing/hash_collision/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_hashing/hash_map/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_hashing/summary/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_heap/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_heap/build_heap/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_heap/heap/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_heap/summary/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_heap/top_k/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_hello_algo/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_introduction/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_introduction/algorithms_are_everywhere/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_introduction/summary/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_introduction/what_is_dsa/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_preface/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_preface/about_the_book/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_preface/suggestions/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_preface/summary/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_reference/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_searching/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_searching/binary_search/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_searching/binary_search_edge/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_searching/binary_search_insertion/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_searching/replace_linear_by_hashing/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_searching/searching_algorithm_revisited/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_searching/summary/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_sorting/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_sorting/bubble_sort/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_sorting/bucket_sort/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_sorting/counting_sort/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_sorting/heap_sort/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_sorting/insertion_sort/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_sorting/merge_sort/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_sorting/quick_sort/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_sorting/radix_sort/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_sorting/selection_sort/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_sorting/sorting_algorithm/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_sorting/summary/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_stack_and_queue/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_stack_and_queue/deque/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_stack_and_queue/queue/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_stack_and_queue/stack/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_stack_and_queue/summary/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_tree/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_tree/array_representation_of_tree/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_tree/avl_tree/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_tree/binary_search_tree/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_tree/binary_tree/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_tree/binary_tree_traversal/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/zh-hant/chapter_tree/summary/</loc>
|
||||
<lastmod>2024-05-24</lastmod>
|
||||
<lastmod>2024-05-31</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
</urlset>
|
||||
Binary file not shown.
|
|
@ -461,7 +461,7 @@ a:hover .text-button span {
|
|||
|
||||
.profile-cell {
|
||||
flex: 1; /* even distribution */
|
||||
flex-basis: 15%;
|
||||
flex-basis: 20%;
|
||||
margin: 1em 0.5em;
|
||||
text-align: center;
|
||||
}
|
||||
|
|
|
|||
Loading…
Reference in a new issue