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@@ -32,6 +32,8 @@
<link rel="alternate" href="/ru/chapter_sorting/heap_sort/" hreflang="ru">
<link rel="alternate" href="/ko/chapter_sorting/heap_sort/" hreflang="ko">
<link rel="icon" href="../../assets/images/favicon.png">
@@ -230,6 +232,12 @@
</a>
</li>
<li class="md-select__item">
<a href="/ko/chapter_sorting/heap_sort/" hreflang="ko" class="md-select__link">
한국어
</a>
</li>
</ul>
</div>
</div>
@@ -4793,7 +4801,7 @@
<div class="tabbed-content">
<div class="tabbed-block">
<div class="highlight"><span class="filename">heap_sort.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">sift_down</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">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;堆的长度为 n ，从节点 i 开始，从顶至底堆化&quot;&quot;&quot;</span>
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w"> </span><span class="sd">"""堆的长度为 n ，从节点 i 开始，从顶至底堆化"""</span>
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a> <span class="k">while</span> <span class="kc">True</span><span class="p">:</span>
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a> <span class="c1"># 判断节点 i, l, r 中值最大的节点，记为 ma</span>
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a> <span class="n">l</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">1</span>
@@ -4812,7 +4820,7 @@
<a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a> <span class="n">i</span> <span class="o">=</span> <span class="n">ma</span>
<a id="__codelineno-0-19" name="__codelineno-0-19" href="#__codelineno-0-19"></a>
<a id="__codelineno-0-20" name="__codelineno-0-20" href="#__codelineno-0-20"></a><span class="k">def</span><span class="w"> </span><span class="nf">heap_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>
<a id="__codelineno-0-21" name="__codelineno-0-21" href="#__codelineno-0-21"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;堆排序&quot;&quot;&quot;</span>
<a id="__codelineno-0-21" name="__codelineno-0-21" href="#__codelineno-0-21"></a><span class="w"> </span><span class="sd">"""堆排序"""</span>
<a id="__codelineno-0-22" name="__codelineno-0-22" href="#__codelineno-0-22"></a> <span class="c1"># 建堆操作：堆化除叶节点以外的其他所有节点</span>
<a id="__codelineno-0-23" name="__codelineno-0-23" href="#__codelineno-0-23"></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="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span> <span class="o">//</span> <span class="mi">2</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">):</span>
<a id="__codelineno-0-24" name="__codelineno-0-24" href="#__codelineno-0-24"></a> <span class="n">sift_down</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">),</span> <span class="n">i</span><span class="p">)</span>
@@ -4951,20 +4959,20 @@
<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w"> </span><span class="nx">l</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">2</span><span class="o">*</span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w"> </span><span class="nx">r</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">2</span><span class="o">*</span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">2</span>
<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w"> </span><span class="nx">ma</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">i</span>
<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">l</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">nums</span><span class="p">)[</span><span class="nx">l</span><span class="p">]</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">nums</span><span class="p">)[</span><span class="nx">ma</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w"> </span><span class="nx">ma</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">l</span>
<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">l</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">nums</span><span class="p">)[</span><span class="nx">l</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">nums</span><span class="p">)[</span><span class="nx">ma</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w"> </span><span class="nx">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">l</span>
<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">r</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">nums</span><span class="p">)[</span><span class="nx">r</span><span class="p">]</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">nums</span><span class="p">)[</span><span class="nx">ma</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="w"> </span><span class="nx">ma</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">r</span>
<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">r</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">nums</span><span class="p">)[</span><span class="nx">r</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">nums</span><span class="p">)[</span><span class="nx">ma</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="w"> </span><span class="nx">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">r</span>
<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="w"> </span><span class="c1">// 若节点 i 最大或索引 l, r 越界，则无须继续堆化，跳出</span>
<a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">ma</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-4-16" name="__codelineno-4-16" href="#__codelineno-4-16"></a><span class="w"> </span><span class="k">break</span>
<a id="__codelineno-4-17" name="__codelineno-4-17" href="#__codelineno-4-17"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-4-18" name="__codelineno-4-18" href="#__codelineno-4-18"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
<a id="__codelineno-4-19" name="__codelineno-4-19" href="#__codelineno-4-19"></a><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">nums</span><span class="p">)[</span><span class="nx">i</span><span class="p">],</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">nums</span><span class="p">)[</span><span class="nx">ma</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">nums</span><span class="p">)[</span><span class="nx">ma</span><span class="p">],</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">nums</span><span class="p">)[</span><span class="nx">i</span><span class="p">]</span>
<a id="__codelineno-4-19" name="__codelineno-4-19" href="#__codelineno-4-19"></a><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">nums</span><span class="p">)[</span><span class="nx">i</span><span class="p">],</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">nums</span><span class="p">)[</span><span class="nx">ma</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">nums</span><span class="p">)[</span><span class="nx">ma</span><span class="p">],</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">nums</span><span class="p">)[</span><span class="nx">i</span><span class="p">]</span>
<a id="__codelineno-4-20" name="__codelineno-4-20" href="#__codelineno-4-20"></a><span class="w"> </span><span class="c1">// 循环向下堆化</span>
<a id="__codelineno-4-21" name="__codelineno-4-21" href="#__codelineno-4-21"></a><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">ma</span>
<a id="__codelineno-4-21" name="__codelineno-4-21" href="#__codelineno-4-21"></a><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">ma</span>
<a id="__codelineno-4-22" name="__codelineno-4-22" href="#__codelineno-4-22"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-4-23" name="__codelineno-4-23" href="#__codelineno-4-23"></a><span class="p">}</span>
<a id="__codelineno-4-24" name="__codelineno-4-24" href="#__codelineno-4-24"></a>
@@ -4975,9 +4983,9 @@
<a id="__codelineno-4-29" name="__codelineno-4-29" href="#__codelineno-4-29"></a><span class="w"> </span><span class="nx">siftDown</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">nums</span><span class="p">),</span><span class="w"> </span><span class="nx">i</span><span class="p">)</span>
<a id="__codelineno-4-30" name="__codelineno-4-30" href="#__codelineno-4-30"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-4-31" name="__codelineno-4-31" href="#__codelineno-4-31"></a><span class="w"> </span><span class="c1">// 从堆中提取最大元素，循环 n-1 轮</span>
<a id="__codelineno-4-32" name="__codelineno-4-32" href="#__codelineno-4-32"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">nums</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="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">--</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-4-32" name="__codelineno-4-32" href="#__codelineno-4-32"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">nums</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="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">--</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-4-33" name="__codelineno-4-33" href="#__codelineno-4-33"></a><span class="w"> </span><span class="c1">// 交换根节点与最右叶节点（交换首元素与尾元素）</span>
<a id="__codelineno-4-34" name="__codelineno-4-34" href="#__codelineno-4-34"></a><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">nums</span><span class="p">)[</span><span class="mi">0</span><span class="p">],</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">nums</span><span class="p">)[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">nums</span><span class="p">)[</span><span class="nx">i</span><span class="p">],</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">nums</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
<a id="__codelineno-4-34" name="__codelineno-4-34" href="#__codelineno-4-34"></a><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">nums</span><span class="p">)[</span><span class="mi">0</span><span class="p">],</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">nums</span><span class="p">)[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">nums</span><span class="p">)[</span><span class="nx">i</span><span class="p">],</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">nums</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
<a id="__codelineno-4-35" name="__codelineno-4-35" href="#__codelineno-4-35"></a><span class="w"> </span><span class="c1">// 以根节点为起点，从顶至底进行堆化</span>
<a id="__codelineno-4-36" name="__codelineno-4-36" href="#__codelineno-4-36"></a><span class="w"> </span><span class="nx">siftDown</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
<a id="__codelineno-4-37" name="__codelineno-4-37" href="#__codelineno-4-37"></a><span class="w"> </span><span class="p">}</span>
@@ -5313,7 +5321,7 @@
</div>
<details class="pythontutor">
<summary>可视化运行</summary>
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</details>
<h2 id="1172">11.7.2 &nbsp; 算法特性<a class="headerlink" href="#1172" title="Permanent link">&para;</a></h2>
@@ -5430,6 +5438,8 @@ aria-label="页脚"
/* Set palette on initial load */
giscus.setAttribute("data-theme", getGiscusTheme())
/* Register event handlers after documented loaded */
document.addEventListener("DOMContentLoaded", function() {
var ref = document.querySelector("[data-md-component=palette]")
@@ -5527,7 +5537,7 @@ aria-label="页脚"
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