deploy

chapter_sorting/bubble_sort/index.html

@@ -1801,7 +1801,7 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">bubble_sort.py</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="k">def</span> <span class="nf">bubble_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="n">List</span><span class="p">[</span><span class="nb">int</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
+<div class="highlight"><span class="filename">bubble_sort.py</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="k">def</span> <span class="nf">bubble_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
 <a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot; 冒泡排序 &quot;&quot;&quot;</span>
 <a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a>    <span class="n">n</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
 <a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a>    <span class="c1"># 外循环：待排序元素数量为 n-1, n-2, ..., 1</span>
@@ -1984,7 +1984,7 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">bubble_sort.py</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="k">def</span> <span class="nf">bubble_sort_with_flag</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="n">List</span><span class="p">[</span><span class="nb">int</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
+<div class="highlight"><span class="filename">bubble_sort.py</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="k">def</span> <span class="nf">bubble_sort_with_flag</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
 <a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot; 冒泡排序（标志优化） &quot;&quot;&quot;</span>
 <a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a>    <span class="n">n</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
 <a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a>    <span class="c1"># 外循环：待排序元素数量为 n-1, n-2, ..., 1</span>

chapter_sorting/bucket_sort/index.html

@@ -21,7 +21,7 @@
     
     
       
-        <title>Bucket sort - Hello 算法</title>
+        <title>桶排序 - Hello 算法</title>
       
     
     
@@ -109,7 +109,7 @@
         <div class="md-header__topic" data-md-component="header-topic">
           <span class="md-ellipsis">
             
-              Bucket sort
+              桶排序
             
           </span>
         </div>
@@ -1607,21 +1607,8 @@
   
   
   
+    
   
-    <label class="md-nav__title" for="__toc">
-      <span class="md-nav__icon md-icon"></span>
-      目录
-    </label>
-    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
-      
-        <li class="md-nav__item">
-  <a href="#_1" class="md-nav__link">
-    拓展到桶排序
-  </a>
-  
-</li>
-      
-    </ul>
   
 </nav>
                   </div>
@@ -1644,19 +1631,21 @@
   
 
 
-  <h1>Bucket sort</h1>
-
-<h2 id="_1">拓展到桶排序<a class="headerlink" href="#_1" title="Permanent link">&para;</a></h2>
-<p>如果我们把上述 <code>bucket</code> 中的每个索引想象成一个桶，那么可以将计数排序理解为把 <span class="arithmatex">\(n\)</span> 个元素分配到对应的桶中，再根据桶与桶之间天然的有序性来实现排序。</p>
-<p>以上解读便是「桶排序 Bucket Sort」的核心思想。具体地，桶排序考虑将 <span class="arithmatex">\(n\)</span> 个元素根据大小范围均匀地分配到 <span class="arithmatex">\(k\)</span> 个桶中，由于桶之间是有序的，<strong>因此仅需在每个桶内部执行排序</strong>，最终按照桶之间的大小关系将元素依次排列，即可得到排序结果。</p>
-<p>假设使用「快速排序」来排序各个桶内的元素，每个桶内元素数量为 <span class="arithmatex">\(\frac{n}{k}\)</span> ，则排序单个桶使用 <span class="arithmatex">\(O(\frac{n}{k} \log\frac{n}{k})\)</span> 时间，排序所有桶使用 <span class="arithmatex">\(O(n \log\frac{n}{k})\)</span> 时间。<strong>当桶数量 <span class="arithmatex">\(k\)</span> 接近 <span class="arithmatex">\(n\)</span> 时，时间复杂度则趋向于 <span class="arithmatex">\(O(n)\)</span></strong> 。</p>
+<h1 id="_1">桶排序<a class="headerlink" href="#_1" title="Permanent link">&para;</a></h1>
+<p>「桶排序 Bucket Sort」考虑设置 <span class="arithmatex">\(k\)</span> 个桶，并将 <span class="arithmatex">\(n\)</span> 个元素根据大小分配到 <span class="arithmatex">\(k\)</span> 个桶中，<strong>并在每个桶内部分别执行排序</strong>，由于桶之间的大小关系的确定的，因此最后按照桶之间的顺序将元素依次展开即可。</p>
+<p>假设元素平均分布在各个桶内，则每个桶内元素数量为 <span class="arithmatex">\(\frac{n}{k}\)</span> ；如果使用「快速排序」来实现桶内排序，则排序单个桶使用 <span class="arithmatex">\(O(\frac{n}{k} \log\frac{n}{k})\)</span> 时间，排序所有桶使用 <span class="arithmatex">\(O(n \log\frac{n}{k})\)</span> 时间。<strong>当桶数量 <span class="arithmatex">\(k\)</span> 比较大时，时间复杂度则趋向于 <span class="arithmatex">\(O(n)\)</span></strong> 。</p>
+<div class="admonition note 计数排序与桶排序的关系">
+<p class="admonition-title">Note</p>
+<p><strong>计数排序可以看作是桶排序的一种特例</strong>。我们可以把计数排序中 <code>counter</code> 的每个索引想象成一个桶，将统计数量的过程想象成把 <span class="arithmatex">\(n\)</span> 个元素分配到对应的桶中，再根据桶之间的有序性输出结果，从而实现排序。</p>
+</div>
 <p>（图）</p>
-<p>理论上桶排序的时间复杂度是 <span class="arithmatex">\(O(n)\)</span> ，<strong>但前提是需要将元素均匀分配到各个桶中</strong>，而这是不太容易做到的。假设我们要把淘宝中的 <span class="arithmatex">\(100\)</span> 万件商品根据价格范围平均分配到 <span class="arithmatex">\(100\)</span> 个桶中，由于商品价格不是均匀分布的，比如 <span class="arithmatex">\(1\)</span> ~ <span class="arithmatex">\(100\)</span> 元的商品非常多、<span class="arithmatex">\(1\)</span> 万元以上的商品非常少等，因此难以简单地设定各个桶的价格分界线。解决方案有：</p>
+<p>理论上桶排序的时间复杂度是 <span class="arithmatex">\(O(n)\)</span> ，<strong>但前提是需要将元素均匀分配到各个桶中</strong>，而这并不容易做到。假设想要把淘宝的 <span class="arithmatex">\(100\)</span> 万件商品根据价格范围平均分配到 <span class="arithmatex">\(100\)</span> 个桶中，而商品价格不是均匀分布的，例如 <span class="arithmatex">\(100\)</span> 元以下的商品非常多、<span class="arithmatex">\(1000\)</span> 元以上的商品非常少等。如果我们将价格区间平均划分为 <span class="arithmatex">\(100\)</span> 份，那么各个桶内的商品数量差距会非常大。为了实现平均分配，我们一般这样做：</p>
 <ul>
-<li>先初步设置一个分界线，将元素分配完后，<strong>把元素较多的桶继续划分为多个桶</strong>，直至每个桶内元素数量合理为止；该做法一般使用递归实现；</li>
-<li>如果我们提前知道商品价格的概率分布，<strong>则可以根据已知分布来设置每个桶的价格分界线</strong>；值得说明的是，数据分布不一定需要 case-by-case 地统计，有时可以采用一些常见分布来近似，例如自然界的正态分布；</li>
+<li>先粗略设置分界线，将元素分配完后，<strong>把元素较多的桶继续划分为多个桶</strong>，直至所有桶内元素数量合理为止；该做法本质上是一个递归树；</li>
+<li>如果我们提前知道商品价格的概率分布，<strong>则可以根据已知分布来设置每个桶的价格分界线</strong>；值得说明的是，数据分布不一定需要特意统计，也可以根据数据特点采用某种常见概率模型来近似，例如自然界的正态分布等；</li>
 </ul>
 <p>（图）</p>
+<p>另外，排序桶内元素需要选择一种合适的排序算法，比如快速排序。</p>
 
 
 

chapter_sorting/counting_sort/index.html

@@ -1801,7 +1801,7 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">counting_sort.py</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="k">def</span> <span class="nf">counting_sort_naive</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="n">List</span><span class="p">[</span><span class="nb">int</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
+<div class="highlight"><span class="filename">counting_sort.py</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="k">def</span> <span class="nf">counting_sort_naive</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
 <a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot; 计数排序 &quot;&quot;&quot;</span>
 <a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a>    <span class="c1"># 简单实现，无法用于排序对象</span>
 <a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a>    <span class="c1"># 1. 统计数组最大元素 m</span>
@@ -2007,7 +2007,7 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">counting_sort.py</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="k">def</span> <span class="nf">counting_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="n">List</span><span class="p">[</span><span class="nb">int</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
+<div class="highlight"><span class="filename">counting_sort.py</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="k">def</span> <span class="nf">counting_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
 <a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot; 计数排序 &quot;&quot;&quot;</span>
 <a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a>    <span class="c1"># 完整实现，可排序对象，并且是稳定排序</span>
 <a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a>    <span class="c1"># 1. 统计数组最大元素 m</span>

chapter_sorting/insertion_sort/index.html

@@ -1772,7 +1772,7 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">insertion_sort.py</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="k">def</span> <span class="nf">insertion_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="n">List</span><span class="p">[</span><span class="nb">int</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
+<div class="highlight"><span class="filename">insertion_sort.py</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="k">def</span> <span class="nf">insertion_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
 <a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot; 插入排序 &quot;&quot;&quot;</span>
 <a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a>    <span class="c1"># 外循环：base = nums[1], nums[2], ..., nums[n-1]   </span>
 <a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)):</span>

chapter_sorting/merge_sort/index.html

@@ -1860,12 +1860,12 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">merge_sort.py</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="k">def</span> <span class="nf">merge</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="n">List</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">left</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">mid</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">right</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
+<div class="highlight"><span class="filename">merge_sort.py</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="k">def</span> <span class="nf">merge</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">left</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">mid</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">right</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
 <a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot; 合并左子数组和右子数组 &quot;&quot;&quot;</span>
 <a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a>    <span class="c1"># 左子数组区间 [left, mid]</span>
 <a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a>    <span class="c1"># 右子数组区间 [mid + 1, right]</span>
-<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a>    <span class="c1"># 初始化辅助数组 借助 copy模块</span>
-<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a>    <span class="n">tmp</span><span class="p">:</span> <span class="n">List</span><span class="p">[</span><span class="nb">int</span><span class="p">]</span> <span class="o">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">left</span><span class="p">:</span><span class="n">right</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">copy</span><span class="p">()</span>
+<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a>    <span class="c1"># 初始化辅助数组</span>
+<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a>    <span class="n">tmp</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">left</span><span class="p">:</span><span class="n">right</span> <span class="o">+</span> <span class="mi">1</span><span class="p">])</span>
 <a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a>    <span class="c1"># 左子数组的起始索引和结束索引</span>
 <a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a>    <span class="n">left_start</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">0</span>
 <a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a>    <span class="n">left_end</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">mid</span> <span class="o">-</span> <span class="n">left</span>
@@ -1890,7 +1890,7 @@
 <a id="__codelineno-2-28" name="__codelineno-2-28" href="#__codelineno-2-28"></a>            <span class="n">nums</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="o">=</span> <span class="n">tmp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span>
 <a id="__codelineno-2-29" name="__codelineno-2-29" href="#__codelineno-2-29"></a>            <span class="n">j</span> <span class="o">+=</span> <span class="mi">1</span>
 <a id="__codelineno-2-30" name="__codelineno-2-30" href="#__codelineno-2-30"></a>
-<a id="__codelineno-2-31" name="__codelineno-2-31" href="#__codelineno-2-31"></a><span class="k">def</span> <span class="nf">merge_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="n">List</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">left</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">right</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
+<a id="__codelineno-2-31" name="__codelineno-2-31" href="#__codelineno-2-31"></a><span class="k">def</span> <span class="nf">merge_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">left</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">right</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
 <a id="__codelineno-2-32" name="__codelineno-2-32" href="#__codelineno-2-32"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot; 归并排序 &quot;&quot;&quot;</span>
 <a id="__codelineno-2-33" name="__codelineno-2-33" href="#__codelineno-2-33"></a>    <span class="c1"># 终止条件</span>
 <a id="__codelineno-2-34" name="__codelineno-2-34" href="#__codelineno-2-34"></a>    <span class="k">if</span> <span class="n">left</span> <span class="o">&gt;=</span> <span class="n">right</span><span class="p">:</span>

chapter_sorting/quick_sort/index.html

@@ -1844,7 +1844,7 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">quick_sort.py</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="k">def</span> <span class="nf">partition</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">nums</span><span class="p">:</span> <span class="n">List</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">left</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">right</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<div class="highlight"><span class="filename">quick_sort.py</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="k">def</span> <span class="nf">partition</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">left</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">right</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
 <a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot; 哨兵划分 &quot;&quot;&quot;</span>
 <a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a>    <span class="c1"># 以 nums[left] 作为基准数</span>
 <a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a>    <span class="n">i</span><span class="p">,</span> <span class="n">j</span> <span class="o">=</span> <span class="n">left</span><span class="p">,</span> <span class="n">right</span>
@@ -2066,7 +2066,7 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">quick_sort.py</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="k">def</span> <span class="nf">quick_sort</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">nums</span><span class="p">:</span> <span class="n">List</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">left</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">right</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
+<div class="highlight"><span class="filename">quick_sort.py</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="k">def</span> <span class="nf">quick_sort</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">left</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">right</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
 <a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot; 快速排序 &quot;&quot;&quot;</span>
 <a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a>    <span class="c1"># 子数组长度为 1 时终止递归</span>
 <a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a>    <span class="k">if</span> <span class="n">left</span> <span class="o">&gt;=</span> <span class="n">right</span><span class="p">:</span>
@@ -2257,7 +2257,7 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">quick_sort.py</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="k">def</span> <span class="nf">median_three</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">nums</span><span class="p">:</span> <span class="n">List</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">left</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">mid</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">right</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<div class="highlight"><span class="filename">quick_sort.py</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="k">def</span> <span class="nf">median_three</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">left</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">mid</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">right</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
 <a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot; 选取三个元素的中位数 &quot;&quot;&quot;</span>
 <a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a>    <span class="c1"># 此处使用异或运算来简化代码</span>
 <a id="__codelineno-22-4" name="__codelineno-22-4" href="#__codelineno-22-4"></a>    <span class="c1"># 异或规则为 0 ^ 0 = 1 ^ 1 = 0, 0 ^ 1 = 1 ^ 0 = 1</span>
@@ -2267,7 +2267,7 @@
 <a id="__codelineno-22-8" name="__codelineno-22-8" href="#__codelineno-22-8"></a>        <span class="k">return</span> <span class="n">mid</span>
 <a id="__codelineno-22-9" name="__codelineno-22-9" href="#__codelineno-22-9"></a>    <span class="k">return</span> <span class="n">right</span>
 <a id="__codelineno-22-10" name="__codelineno-22-10" href="#__codelineno-22-10"></a>
-<a id="__codelineno-22-11" name="__codelineno-22-11" href="#__codelineno-22-11"></a><span class="k">def</span> <span class="nf">partition</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">nums</span><span class="p">:</span> <span class="n">List</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">left</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">right</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-22-11" name="__codelineno-22-11" href="#__codelineno-22-11"></a><span class="k">def</span> <span class="nf">partition</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">left</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">right</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
 <a id="__codelineno-22-12" name="__codelineno-22-12" href="#__codelineno-22-12"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot; 哨兵划分（三数取中值） &quot;&quot;&quot;</span>
 <a id="__codelineno-22-13" name="__codelineno-22-13" href="#__codelineno-22-13"></a>    <span class="c1"># 以 nums[left] 作为基准数</span>
 <a id="__codelineno-22-14" name="__codelineno-22-14" href="#__codelineno-22-14"></a>    <span class="n">med</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">median_three</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span> <span class="n">left</span><span class="p">,</span> <span class="p">(</span><span class="n">left</span> <span class="o">+</span> <span class="n">right</span><span class="p">)</span> <span class="o">//</span> <span class="mi">2</span><span class="p">,</span> <span class="n">right</span><span class="p">)</span>
@@ -2531,7 +2531,7 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">quick_sort.py</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="k">def</span> <span class="nf">quick_sort</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">nums</span><span class="p">:</span> <span class="n">List</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">left</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">right</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
+<div class="highlight"><span class="filename">quick_sort.py</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="k">def</span> <span class="nf">quick_sort</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">left</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">right</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
 <a id="__codelineno-32-2" name="__codelineno-32-2" href="#__codelineno-32-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot; 快速排序（尾递归优化） &quot;&quot;&quot;</span>
 <a id="__codelineno-32-3" name="__codelineno-32-3" href="#__codelineno-32-3"></a>    <span class="c1"># 子数组长度为 1 时终止</span>
 <a id="__codelineno-32-4" name="__codelineno-32-4" href="#__codelineno-32-4"></a>    <span class="k">while</span> <span class="n">left</span> <span class="o">&lt;</span> <span class="n">right</span><span class="p">:</span>