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第 8 章 &nbsp; 堆
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第 8 章 &nbsp; 堆
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8.1 &nbsp; 堆
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8.1 &nbsp; 堆
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8.1.1 &nbsp; 堆的常用操作
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8.1.2 &nbsp; 堆的实现
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1. &nbsp; 堆的存储与表示
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2. &nbsp; 访问堆顶元素
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3. &nbsp; 元素入堆
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4. &nbsp; 堆顶元素出堆
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8.1.3 &nbsp; 堆的常见应用
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8.2 &nbsp; 建堆操作
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8.3 &nbsp; Top-k 问题
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第 9 章 &nbsp; 图
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9.1 &nbsp; 图
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9.2 &nbsp; 图基础操作
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9.3 &nbsp; 图的遍历
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第 10 章 &nbsp; 搜索
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第 10 章 &nbsp; 搜索
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10.1 &nbsp; 二分查找
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10.2 &nbsp; 二分查找插入点
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10.3 &nbsp; 二分查找边界
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10.4 &nbsp; 哈希优化策略
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10.5 &nbsp; 重识搜索算法
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第 11 章 &nbsp; 排序
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11.1 &nbsp; 排序算法
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11.2 &nbsp; 选择排序
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11.3 &nbsp; 冒泡排序
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11.4 &nbsp; 插入排序
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11.5 &nbsp; 快速排序
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11.6 &nbsp; 归并排序
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11.7 &nbsp; 堆排序
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11.8 &nbsp; 桶排序
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11.9 &nbsp; 计数排序
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11.10 &nbsp; 基数排序
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11.11 &nbsp; 小结
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第 12 章 &nbsp; 分治
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12.1 &nbsp; 分治算法
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12.2 &nbsp; 分治搜索策略
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12.3 &nbsp; 构建树问题
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12.4 &nbsp; 汉诺塔问题
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12.5 &nbsp; 小结
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第 13 章 &nbsp; 回溯
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13.1 &nbsp; 回溯算法
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13.2 &nbsp; 全排列问题
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13.3 &nbsp; 子集和问题
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13.4 &nbsp; N 皇后问题
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第 14 章 &nbsp; 动态规划
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14.1 &nbsp; 初探动态规划
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<h1 id="81">8.1 &nbsp; 堆<a class="headerlink" href="#81" title="Permanent link">&para;</a></h1>
<p>「堆 heap」是一种满足特定条件的完全二叉树，主要可分为两种类型，如图 8-1 所示。</p>
<ul>
<li>「小顶堆 min heap」：任意节点的值 <span class="arithmatex">\(\leq\)</span> 其子节点的值。</li>
<li>「大顶堆 max heap」：任意节点的值 <span class="arithmatex">\(\geq\)</span> 其子节点的值。</li>
</ul>
<p><a class="glightbox" href="../heap.assets/min_heap_and_max_heap.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="小顶堆与大顶堆" class="animation-figure" src="../heap.assets/min_heap_and_max_heap.png" /></a></p>
<p align="center"> 图 8-1 &nbsp; 小顶堆与大顶堆 </p>
<p>堆作为完全二叉树的一个特例，具有以下特性。</p>
<ul>
<li>最底层节点靠左填充，其他层的节点都被填满。</li>
<li>我们将二叉树的根节点称为“堆顶”，将底层最靠右的节点称为“堆底”。</li>
<li>对于大顶堆（小顶堆），堆顶元素（根节点）的值是最大（最小）的。</li>
</ul>
<h2 id="811">8.1.1 &nbsp; 堆的常用操作<a class="headerlink" href="#811" title="Permanent link">&para;</a></h2>
<p>需要指出的是，许多编程语言提供的是「优先队列 priority queue」，这是一种抽象的数据结构，定义为具有优先级排序的队列。</p>
<p>实际上，<strong>堆通常用于实现优先队列，大顶堆相当于元素按从大到小的顺序出队的优先队列</strong>。从使用角度来看，我们可以将“优先队列”和“堆”看作等价的数据结构。因此，本书对两者不做特别区分，统一称作“堆”。</p>
<p>堆的常用操作见表 8-1 ，方法名需要根据编程语言来确定。</p>
<p align="center"> 表 8-1 &nbsp; 堆的操作效率 </p>
<div class="center-table">
<table>
<thead>
<tr>
<th>方法名</th>
<th>描述</th>
<th>时间复杂度</th>
</tr>
</thead>
<tbody>
<tr>
<td><code>push()</code></td>
<td>元素入堆</td>
<td><span class="arithmatex">\(O(\log n)\)</span></td>
</tr>
<tr>
<td><code>pop()</code></td>
<td>堆顶元素出堆</td>
<td><span class="arithmatex">\(O(\log n)\)</span></td>
</tr>
<tr>
<td><code>peek()</code></td>
<td>访问堆顶元素（对于大 / 小顶堆分别为最大 / 小值）</td>
<td><span class="arithmatex">\(O(1)\)</span></td>
</tr>
<tr>
<td><code>size()</code></td>
<td>获取堆的元素数量</td>
<td><span class="arithmatex">\(O(1)\)</span></td>
</tr>
<tr>
<td><code>isEmpty()</code></td>
<td>判断堆是否为空</td>
<td><span class="arithmatex">\(O(1)\)</span></td>
</tr>
</tbody>
</table>
</div>
<p>在实际应用中，我们可以直接使用编程语言提供的堆类（或优先队列类）。</p>
<p>类似于排序算法中的“从小到大排列”和“从大到小排列”，我们可以通过设置一个 <code>flag</code> 或修改 <code>Comparator</code> 实现“小顶堆”与“大顶堆”之间的转换。代码如下所示：</p>
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<div class="highlight"><span class="filename">heap.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="c1"># 初始化小顶堆</span>
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="n">min_heap</span><span class="p">,</span> <span class="n">flag</span> <span class="o">=</span> <span class="p">[],</span> <span class="mi">1</span>
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a><span class="c1"># 初始化大顶堆</span>
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a><span class="n">max_heap</span><span class="p">,</span> <span class="n">flag</span> <span class="o">=</span> <span class="p">[],</span> <span class="o">-</span><span class="mi">1</span>
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a><span class="c1"># Python 的 heapq 模块默认实现小顶堆</span>
<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a><span class="c1"># 考虑将“元素取负”后再入堆，这样就可以将大小关系颠倒，从而实现大顶堆</span>
<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a><span class="c1"># 在本示例中，flag = 1 时对应小顶堆，flag = -1 时对应大顶堆</span>
<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>
<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a><span class="c1"># 元素入堆</span>
<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a><span class="n">heapq</span><span class="o">.</span><span class="n">heappush</span><span class="p">(</span><span class="n">max_heap</span><span class="p">,</span> <span class="n">flag</span> <span class="o">*</span> <span class="mi">1</span><span class="p">)</span>
<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a><span class="n">heapq</span><span class="o">.</span><span class="n">heappush</span><span class="p">(</span><span class="n">max_heap</span><span class="p">,</span> <span class="n">flag</span> <span class="o">*</span> <span class="mi">3</span><span class="p">)</span>
<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a><span class="n">heapq</span><span class="o">.</span><span class="n">heappush</span><span class="p">(</span><span class="n">max_heap</span><span class="p">,</span> <span class="n">flag</span> <span class="o">*</span> <span class="mi">2</span><span class="p">)</span>
<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a><span class="n">heapq</span><span class="o">.</span><span class="n">heappush</span><span class="p">(</span><span class="n">max_heap</span><span class="p">,</span> <span class="n">flag</span> <span class="o">*</span> <span class="mi">5</span><span class="p">)</span>
<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a><span class="n">heapq</span><span class="o">.</span><span class="n">heappush</span><span class="p">(</span><span class="n">max_heap</span><span class="p">,</span> <span class="n">flag</span> <span class="o">*</span> <span class="mi">4</span><span class="p">)</span>
<a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a>
<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a><span class="c1"># 获取堆顶元素</span>
<a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a><span class="n">peek</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">flag</span> <span class="o">*</span> <span class="n">max_heap</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="c1"># 5</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="c1"># 堆顶元素出堆</span>
<a id="__codelineno-0-21" name="__codelineno-0-21" href="#__codelineno-0-21"></a><span class="c1"># 出堆元素会形成一个从大到小的序列</span>
<a id="__codelineno-0-22" name="__codelineno-0-22" href="#__codelineno-0-22"></a><span class="n">val</span> <span class="o">=</span> <span class="n">flag</span> <span class="o">*</span> <span class="n">heapq</span><span class="o">.</span><span class="n">heappop</span><span class="p">(</span><span class="n">max_heap</span><span class="p">)</span> <span class="c1"># 5</span>
<a id="__codelineno-0-23" name="__codelineno-0-23" href="#__codelineno-0-23"></a><span class="n">val</span> <span class="o">=</span> <span class="n">flag</span> <span class="o">*</span> <span class="n">heapq</span><span class="o">.</span><span class="n">heappop</span><span class="p">(</span><span class="n">max_heap</span><span class="p">)</span> <span class="c1"># 4</span>
<a id="__codelineno-0-24" name="__codelineno-0-24" href="#__codelineno-0-24"></a><span class="n">val</span> <span class="o">=</span> <span class="n">flag</span> <span class="o">*</span> <span class="n">heapq</span><span class="o">.</span><span class="n">heappop</span><span class="p">(</span><span class="n">max_heap</span><span class="p">)</span> <span class="c1"># 3</span>
<a id="__codelineno-0-25" name="__codelineno-0-25" href="#__codelineno-0-25"></a><span class="n">val</span> <span class="o">=</span> <span class="n">flag</span> <span class="o">*</span> <span class="n">heapq</span><span class="o">.</span><span class="n">heappop</span><span class="p">(</span><span class="n">max_heap</span><span class="p">)</span> <span class="c1"># 2</span>
<a id="__codelineno-0-26" name="__codelineno-0-26" href="#__codelineno-0-26"></a><span class="n">val</span> <span class="o">=</span> <span class="n">flag</span> <span class="o">*</span> <span class="n">heapq</span><span class="o">.</span><span class="n">heappop</span><span class="p">(</span><span class="n">max_heap</span><span class="p">)</span> <span class="c1"># 1</span>
<a id="__codelineno-0-27" name="__codelineno-0-27" href="#__codelineno-0-27"></a>
<a id="__codelineno-0-28" name="__codelineno-0-28" href="#__codelineno-0-28"></a><span class="c1"># 获取堆大小</span>
<a id="__codelineno-0-29" name="__codelineno-0-29" href="#__codelineno-0-29"></a><span class="n">size</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">max_heap</span><span class="p">)</span>
<a id="__codelineno-0-30" name="__codelineno-0-30" href="#__codelineno-0-30"></a>
<a id="__codelineno-0-31" name="__codelineno-0-31" href="#__codelineno-0-31"></a><span class="c1"># 判断堆是否为空</span>
<a id="__codelineno-0-32" name="__codelineno-0-32" href="#__codelineno-0-32"></a><span class="n">is_empty</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="ow">not</span> <span class="n">max_heap</span>
<a id="__codelineno-0-33" name="__codelineno-0-33" href="#__codelineno-0-33"></a>
<a id="__codelineno-0-34" name="__codelineno-0-34" href="#__codelineno-0-34"></a><span class="c1"># 输入列表并建堆</span>
<a id="__codelineno-0-35" name="__codelineno-0-35" href="#__codelineno-0-35"></a><span class="n">min_heap</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="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">4</span><span class="p">]</span>
<a id="__codelineno-0-36" name="__codelineno-0-36" href="#__codelineno-0-36"></a><span class="n">heapq</span><span class="o">.</span><span class="n">heapify</span><span class="p">(</span><span class="n">min_heap</span><span class="p">)</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">heap.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 初始化堆 */</span>
<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="c1">// 初始化小顶堆</span>
<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="n">priority_queue</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">greater</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">minHeap</span><span class="p">;</span>
<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="c1">// 初始化大顶堆</span>
<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="n">priority_queue</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">less</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">;</span>
<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a>
<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="cm">/* 元素入堆 */</span>
<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span>
<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span>
<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a>
<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="cm">/* 获取堆顶元素 */</span>
<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="kt">int</span><span class="w"> </span><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">top</span><span class="p">();</span><span class="w"> </span><span class="c1">// 5</span>
<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a>
<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="cm">/* 堆顶元素出堆 */</span>
<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="c1">// 出堆元素会形成一个从大到小的序列</span>
<a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">pop</span><span class="p">();</span><span class="w"> </span><span class="c1">// 5</span>
<a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">pop</span><span class="p">();</span><span class="w"> </span><span class="c1">// 4</span>
<a id="__codelineno-1-21" name="__codelineno-1-21" href="#__codelineno-1-21"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">pop</span><span class="p">();</span><span class="w"> </span><span class="c1">// 3</span>
<a id="__codelineno-1-22" name="__codelineno-1-22" href="#__codelineno-1-22"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">pop</span><span class="p">();</span><span class="w"> </span><span class="c1">// 2</span>
<a id="__codelineno-1-23" name="__codelineno-1-23" href="#__codelineno-1-23"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">pop</span><span class="p">();</span><span class="w"> </span><span class="c1">// 1</span>
<a id="__codelineno-1-24" name="__codelineno-1-24" href="#__codelineno-1-24"></a>
<a id="__codelineno-1-25" name="__codelineno-1-25" href="#__codelineno-1-25"></a><span class="cm">/* 获取堆大小 */</span>
<a id="__codelineno-1-26" name="__codelineno-1-26" href="#__codelineno-1-26"></a><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">size</span><span class="p">();</span>
<a id="__codelineno-1-27" name="__codelineno-1-27" href="#__codelineno-1-27"></a>
<a id="__codelineno-1-28" name="__codelineno-1-28" href="#__codelineno-1-28"></a><span class="cm">/* 判断堆是否为空 */</span>
<a id="__codelineno-1-29" name="__codelineno-1-29" href="#__codelineno-1-29"></a><span class="kt">bool</span><span class="w"> </span><span class="n">isEmpty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">empty</span><span class="p">();</span>
<a id="__codelineno-1-30" name="__codelineno-1-30" href="#__codelineno-1-30"></a>
<a id="__codelineno-1-31" name="__codelineno-1-31" href="#__codelineno-1-31"></a><span class="cm">/* 输入列表并建堆 */</span>
<a id="__codelineno-1-32" name="__codelineno-1-32" href="#__codelineno-1-32"></a><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">input</span><span class="p">{</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">5</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">};</span>
<a id="__codelineno-1-33" name="__codelineno-1-33" href="#__codelineno-1-33"></a><span class="n">priority_queue</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">greater</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">minHeap</span><span class="p">(</span><span class="n">input</span><span class="p">.</span><span class="n">begin</span><span class="p">(),</span><span class="w"> </span><span class="n">input</span><span class="p">.</span><span class="n">end</span><span class="p">());</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">heap.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 初始化堆 */</span>
<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="c1">// 初始化小顶堆</span>
<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="n">Queue</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">minHeap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">PriorityQueue</span><span class="o">&lt;&gt;</span><span class="p">();</span>
<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="c1">// 初始化大顶堆（使用 lambda 表达式修改 Comparator 即可）</span>
<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="n">Queue</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">maxHeap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">PriorityQueue</span><span class="o">&lt;&gt;</span><span class="p">((</span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="n">b</span><span class="p">)</span><span class="w"> </span><span class="o">-&gt;</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">a</span><span class="p">);</span>
<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a>
<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="cm">/* 元素入堆 */</span>
<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="n">maxHeap</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="n">maxHeap</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span>
<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="n">maxHeap</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span>
<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="n">maxHeap</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="n">maxHeap</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a>
<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="cm">/* 获取堆顶元素 */</span>
<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="kt">int</span><span class="w"> </span><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">peek</span><span class="p">();</span><span class="w"> </span><span class="c1">// 5</span>
<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a>
<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="cm">/* 堆顶元素出堆 */</span>
<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="c1">// 出堆元素会形成一个从大到小的序列</span>
<a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">poll</span><span class="p">();</span><span class="w"> </span><span class="c1">// 5</span>
<a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">poll</span><span class="p">();</span><span class="w"> </span><span class="c1">// 4</span>
<a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">poll</span><span class="p">();</span><span class="w"> </span><span class="c1">// 3</span>
<a id="__codelineno-2-22" name="__codelineno-2-22" href="#__codelineno-2-22"></a><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">poll</span><span class="p">();</span><span class="w"> </span><span class="c1">// 2</span>
<a id="__codelineno-2-23" name="__codelineno-2-23" href="#__codelineno-2-23"></a><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">poll</span><span class="p">();</span><span class="w"> </span><span class="c1">// 1</span>
<a id="__codelineno-2-24" name="__codelineno-2-24" href="#__codelineno-2-24"></a>
<a id="__codelineno-2-25" name="__codelineno-2-25" href="#__codelineno-2-25"></a><span class="cm">/* 获取堆大小 */</span>
<a id="__codelineno-2-26" name="__codelineno-2-26" href="#__codelineno-2-26"></a><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">size</span><span class="p">();</span>
<a id="__codelineno-2-27" name="__codelineno-2-27" href="#__codelineno-2-27"></a>
<a id="__codelineno-2-28" name="__codelineno-2-28" href="#__codelineno-2-28"></a><span class="cm">/* 判断堆是否为空 */</span>
<a id="__codelineno-2-29" name="__codelineno-2-29" href="#__codelineno-2-29"></a><span class="kt">boolean</span><span class="w"> </span><span class="n">isEmpty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">isEmpty</span><span class="p">();</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="cm">/* 输入列表并建堆 */</span>
<a id="__codelineno-2-32" name="__codelineno-2-32" href="#__codelineno-2-32"></a><span class="n">minHeap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">PriorityQueue</span><span class="o">&lt;&gt;</span><span class="p">(</span><span class="n">Arrays</span><span class="p">.</span><span class="na">asList</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">5</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">));</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">heap.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 初始化堆 */</span>
<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="c1">// 初始化小顶堆</span>
<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="n">PriorityQueue</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">minHeap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">();</span>
<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="c1">// 初始化大顶堆（使用 lambda 表达式修改 Comparator 即可）</span>
<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="n">PriorityQueue</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">maxHeap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">(</span><span class="n">Comparer</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="p">.</span><span class="n">Create</span><span class="p">((</span><span class="n">x</span><span class="p">,</span><span class="w"> </span><span class="n">y</span><span class="p">)</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="n">y</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">x</span><span class="p">));</span>
<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a>
<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="cm">/* 元素入堆 */</span>
<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">Enqueue</span><span class="p">(</span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="m">1</span><span class="p">);</span>
<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">Enqueue</span><span class="p">(</span><span class="m">3</span><span class="p">,</span><span class="w"> </span><span class="m">3</span><span class="p">);</span>
<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">Enqueue</span><span class="p">(</span><span class="m">2</span><span class="p">,</span><span class="w"> </span><span class="m">2</span><span class="p">);</span>
<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">Enqueue</span><span class="p">(</span><span class="m">5</span><span class="p">,</span><span class="w"> </span><span class="m">5</span><span class="p">);</span>
<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">Enqueue</span><span class="p">(</span><span class="m">4</span><span class="p">,</span><span class="w"> </span><span class="m">4</span><span class="p">);</span>
<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a>
<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="cm">/* 获取堆顶元素 */</span>
<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="kt">int</span><span class="w"> </span><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">Peek</span><span class="p">();</span><span class="c1">//5</span>
<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a>
<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="cm">/* 堆顶元素出堆 */</span>
<a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="c1">// 出堆元素会形成一个从大到小的序列</span>
<a id="__codelineno-3-19" name="__codelineno-3-19" href="#__codelineno-3-19"></a><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">Dequeue</span><span class="p">();</span><span class="w"> </span><span class="c1">// 5</span>
<a id="__codelineno-3-20" name="__codelineno-3-20" href="#__codelineno-3-20"></a><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">Dequeue</span><span class="p">();</span><span class="w"> </span><span class="c1">// 4</span>
<a id="__codelineno-3-21" name="__codelineno-3-21" href="#__codelineno-3-21"></a><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">Dequeue</span><span class="p">();</span><span class="w"> </span><span class="c1">// 3</span>
<a id="__codelineno-3-22" name="__codelineno-3-22" href="#__codelineno-3-22"></a><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">Dequeue</span><span class="p">();</span><span class="w"> </span><span class="c1">// 2</span>
<a id="__codelineno-3-23" name="__codelineno-3-23" href="#__codelineno-3-23"></a><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">Dequeue</span><span class="p">();</span><span class="w"> </span><span class="c1">// 1</span>
<a id="__codelineno-3-24" name="__codelineno-3-24" href="#__codelineno-3-24"></a>
<a id="__codelineno-3-25" name="__codelineno-3-25" href="#__codelineno-3-25"></a><span class="cm">/* 获取堆大小 */</span>
<a id="__codelineno-3-26" name="__codelineno-3-26" href="#__codelineno-3-26"></a><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">Count</span><span class="p">;</span>
<a id="__codelineno-3-27" name="__codelineno-3-27" href="#__codelineno-3-27"></a>
<a id="__codelineno-3-28" name="__codelineno-3-28" href="#__codelineno-3-28"></a><span class="cm">/* 判断堆是否为空 */</span>
<a id="__codelineno-3-29" name="__codelineno-3-29" href="#__codelineno-3-29"></a><span class="kt">bool</span><span class="w"> </span><span class="n">isEmpty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">Count</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
<a id="__codelineno-3-30" name="__codelineno-3-30" href="#__codelineno-3-30"></a>
<a id="__codelineno-3-31" name="__codelineno-3-31" href="#__codelineno-3-31"></a><span class="cm">/* 输入列表并建堆 */</span>
<a id="__codelineno-3-32" name="__codelineno-3-32" href="#__codelineno-3-32"></a><span class="n">minHeap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">PriorityQueue</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">&gt;</span><span class="p">([(</span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="m">1</span><span class="p">),</span><span class="w"> </span><span class="p">(</span><span class="m">3</span><span class="p">,</span><span class="w"> </span><span class="m">3</span><span class="p">),</span><span class="w"> </span><span class="p">(</span><span class="m">2</span><span class="p">,</span><span class="w"> </span><span class="m">2</span><span class="p">),</span><span class="w"> </span><span class="p">(</span><span class="m">5</span><span class="p">,</span><span class="w"> </span><span class="m">5</span><span class="p">),</span><span class="w"> </span><span class="p">(</span><span class="m">4</span><span class="p">,</span><span class="w"> </span><span class="m">4</span><span class="p">)]);</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">heap.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="c1">// Go 语言中可以通过实现 heap.Interface 来构建整数大顶堆</span>
<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="c1">// 实现 heap.Interface 需要同时实现 sort.Interface</span>
<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="kd">type</span><span class="w"> </span><span class="nx">intHeap</span><span class="w"> </span><span class="p">[]</span><span class="kt">any</span>
<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a>
<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="c1">// Push heap.Interface 的方法，实现推入元素到堆</span>
<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">intHeap</span><span class="p">)</span><span class="w"> </span><span class="nx">Push</span><span class="p">(</span><span class="nx">x</span><span class="w"> </span><span class="kt">any</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w"> </span><span class="c1">// Push 和 Pop 使用 pointer receiver 作为参数</span>
<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="w"> </span><span class="c1">// 因为它们不仅会对切片的内容进行调整，还会修改切片的长度。</span>
<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w"> </span><span class="o">*</span><span class="nx">h</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="o">*</span><span class="nx">h</span><span class="p">,</span><span class="w"> </span><span class="nx">x</span><span class="p">.(</span><span class="kt">int</span><span class="p">))</span>
<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="p">}</span>
<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a>
<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="c1">// Pop heap.Interface 的方法，实现弹出堆顶元素</span>
<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">intHeap</span><span class="p">)</span><span class="w"> </span><span class="nx">Pop</span><span class="p">()</span><span class="w"> </span><span class="kt">any</span><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">// 待出堆元素存放在最后</span>
<a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a><span class="w"> </span><span class="nx">last</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">h</span><span class="p">)[</span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">h</span><span class="p">)</span><span class="o">-</span><span class="mi">1</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="o">*</span><span class="nx">h</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">h</span><span class="p">)[:</span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">h</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
<a id="__codelineno-4-17" name="__codelineno-4-17" href="#__codelineno-4-17"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">last</span>
<a id="__codelineno-4-18" name="__codelineno-4-18" href="#__codelineno-4-18"></a><span class="p">}</span>
<a id="__codelineno-4-19" name="__codelineno-4-19" href="#__codelineno-4-19"></a>
<a id="__codelineno-4-20" name="__codelineno-4-20" href="#__codelineno-4-20"></a><span class="c1">// Len sort.Interface 的方法</span>
<a id="__codelineno-4-21" name="__codelineno-4-21" href="#__codelineno-4-21"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">intHeap</span><span class="p">)</span><span class="w"> </span><span class="nx">Len</span><span class="p">()</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-4-22" name="__codelineno-4-22" href="#__codelineno-4-22"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">h</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>
<a id="__codelineno-4-25" name="__codelineno-4-25" href="#__codelineno-4-25"></a><span class="c1">// Less sort.Interface 的方法</span>
<a id="__codelineno-4-26" name="__codelineno-4-26" href="#__codelineno-4-26"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">intHeap</span><span class="p">)</span><span class="w"> </span><span class="nx">Less</span><span class="p">(</span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">bool</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-4-27" name="__codelineno-4-27" href="#__codelineno-4-27"></a><span class="w"> </span><span class="c1">// 如果实现小顶堆，则需要调整为小于号</span>
<a id="__codelineno-4-28" name="__codelineno-4-28" href="#__codelineno-4-28"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">h</span><span class="p">)[</span><span class="nx">i</span><span class="p">].(</span><span class="kt">int</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">h</span><span class="p">)[</span><span class="nx">j</span><span class="p">].(</span><span class="kt">int</span><span class="p">)</span>
<a id="__codelineno-4-29" name="__codelineno-4-29" href="#__codelineno-4-29"></a><span class="p">}</span>
<a id="__codelineno-4-30" name="__codelineno-4-30" href="#__codelineno-4-30"></a>
<a id="__codelineno-4-31" name="__codelineno-4-31" href="#__codelineno-4-31"></a><span class="c1">// Swap sort.Interface 的方法</span>
<a id="__codelineno-4-32" name="__codelineno-4-32" href="#__codelineno-4-32"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">intHeap</span><span class="p">)</span><span class="w"> </span><span class="nx">Swap</span><span class="p">(</span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="kt">int</span><span class="p">)</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="p">(</span><span class="o">*</span><span class="nx">h</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">h</span><span class="p">)[</span><span class="nx">j</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">h</span><span class="p">)[</span><span class="nx">j</span><span class="p">],</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">h</span><span class="p">)[</span><span class="nx">i</span><span class="p">]</span>
<a id="__codelineno-4-34" name="__codelineno-4-34" href="#__codelineno-4-34"></a><span class="p">}</span>
<a id="__codelineno-4-35" name="__codelineno-4-35" href="#__codelineno-4-35"></a>
<a id="__codelineno-4-36" name="__codelineno-4-36" href="#__codelineno-4-36"></a><span class="c1">// Top 获取堆顶元素</span>
<a id="__codelineno-4-37" name="__codelineno-4-37" href="#__codelineno-4-37"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">intHeap</span><span class="p">)</span><span class="w"> </span><span class="nx">Top</span><span class="p">()</span><span class="w"> </span><span class="kt">any</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-4-38" name="__codelineno-4-38" href="#__codelineno-4-38"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">h</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
<a id="__codelineno-4-39" name="__codelineno-4-39" href="#__codelineno-4-39"></a><span class="p">}</span>
<a id="__codelineno-4-40" name="__codelineno-4-40" href="#__codelineno-4-40"></a>
<a id="__codelineno-4-41" name="__codelineno-4-41" href="#__codelineno-4-41"></a><span class="cm">/* Driver Code */</span>
<a id="__codelineno-4-42" name="__codelineno-4-42" href="#__codelineno-4-42"></a><span class="kd">func</span><span class="w"> </span><span class="nx">TestHeap</span><span class="p">(</span><span class="nx">t</span><span class="w"> </span><span class="o">*</span><span class="nx">testing</span><span class="p">.</span><span class="nx">T</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-4-43" name="__codelineno-4-43" href="#__codelineno-4-43"></a><span class="w"> </span><span class="cm">/* 初始化堆 */</span>
<a id="__codelineno-4-44" name="__codelineno-4-44" href="#__codelineno-4-44"></a><span class="w"> </span><span class="c1">// 初始化大顶堆</span>
<a id="__codelineno-4-45" name="__codelineno-4-45" href="#__codelineno-4-45"></a><span class="w"> </span><span class="nx">maxHeap</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="o">&amp;</span><span class="nx">intHeap</span><span class="p">{}</span>
<a id="__codelineno-4-46" name="__codelineno-4-46" href="#__codelineno-4-46"></a><span class="w"> </span><span class="nx">heap</span><span class="p">.</span><span class="nx">Init</span><span class="p">(</span><span class="nx">maxHeap</span><span class="p">)</span>
<a id="__codelineno-4-47" name="__codelineno-4-47" href="#__codelineno-4-47"></a><span class="w"> </span><span class="cm">/* 元素入堆 */</span>
<a id="__codelineno-4-48" name="__codelineno-4-48" href="#__codelineno-4-48"></a><span class="w"> </span><span class="c1">// 调用 heap.Interface 的方法，来添加元素</span>
<a id="__codelineno-4-49" name="__codelineno-4-49" href="#__codelineno-4-49"></a><span class="w"> </span><span class="nx">heap</span><span class="p">.</span><span class="nx">Push</span><span class="p">(</span><span class="nx">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
<a id="__codelineno-4-50" name="__codelineno-4-50" href="#__codelineno-4-50"></a><span class="w"> </span><span class="nx">heap</span><span class="p">.</span><span class="nx">Push</span><span class="p">(</span><span class="nx">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">)</span>
<a id="__codelineno-4-51" name="__codelineno-4-51" href="#__codelineno-4-51"></a><span class="w"> </span><span class="nx">heap</span><span class="p">.</span><span class="nx">Push</span><span class="p">(</span><span class="nx">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
<a id="__codelineno-4-52" name="__codelineno-4-52" href="#__codelineno-4-52"></a><span class="w"> </span><span class="nx">heap</span><span class="p">.</span><span class="nx">Push</span><span class="p">(</span><span class="nx">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">)</span>
<a id="__codelineno-4-53" name="__codelineno-4-53" href="#__codelineno-4-53"></a><span class="w"> </span><span class="nx">heap</span><span class="p">.</span><span class="nx">Push</span><span class="p">(</span><span class="nx">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="mi">5</span><span class="p">)</span>
<a id="__codelineno-4-54" name="__codelineno-4-54" href="#__codelineno-4-54"></a>
<a id="__codelineno-4-55" name="__codelineno-4-55" href="#__codelineno-4-55"></a><span class="w"> </span><span class="cm">/* 获取堆顶元素 */</span>
<a id="__codelineno-4-56" name="__codelineno-4-56" href="#__codelineno-4-56"></a><span class="w"> </span><span class="nx">top</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">maxHeap</span><span class="p">.</span><span class="nx">Top</span><span class="p">()</span>
<a id="__codelineno-4-57" name="__codelineno-4-57" href="#__codelineno-4-57"></a><span class="w"> </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Printf</span><span class="p">(</span><span class="s">&quot;堆顶元素为 %d\n&quot;</span><span class="p">,</span><span class="w"> </span><span class="nx">top</span><span class="p">)</span>
<a id="__codelineno-4-58" name="__codelineno-4-58" href="#__codelineno-4-58"></a>
<a id="__codelineno-4-59" name="__codelineno-4-59" href="#__codelineno-4-59"></a><span class="w"> </span><span class="cm">/* 堆顶元素出堆 */</span>
<a id="__codelineno-4-60" name="__codelineno-4-60" href="#__codelineno-4-60"></a><span class="w"> </span><span class="c1">// 调用 heap.Interface 的方法，来移除元素</span>
<a id="__codelineno-4-61" name="__codelineno-4-61" href="#__codelineno-4-61"></a><span class="w"> </span><span class="nx">heap</span><span class="p">.</span><span class="nx">Pop</span><span class="p">(</span><span class="nx">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="c1">// 5</span>
<a id="__codelineno-4-62" name="__codelineno-4-62" href="#__codelineno-4-62"></a><span class="w"> </span><span class="nx">heap</span><span class="p">.</span><span class="nx">Pop</span><span class="p">(</span><span class="nx">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="c1">// 4</span>
<a id="__codelineno-4-63" name="__codelineno-4-63" href="#__codelineno-4-63"></a><span class="w"> </span><span class="nx">heap</span><span class="p">.</span><span class="nx">Pop</span><span class="p">(</span><span class="nx">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="c1">// 3</span>
<a id="__codelineno-4-64" name="__codelineno-4-64" href="#__codelineno-4-64"></a><span class="w"> </span><span class="nx">heap</span><span class="p">.</span><span class="nx">Pop</span><span class="p">(</span><span class="nx">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="c1">// 2</span>
<a id="__codelineno-4-65" name="__codelineno-4-65" href="#__codelineno-4-65"></a><span class="w"> </span><span class="nx">heap</span><span class="p">.</span><span class="nx">Pop</span><span class="p">(</span><span class="nx">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="c1">// 1</span>
<a id="__codelineno-4-66" name="__codelineno-4-66" href="#__codelineno-4-66"></a>
<a id="__codelineno-4-67" name="__codelineno-4-67" href="#__codelineno-4-67"></a><span class="w"> </span><span class="cm">/* 获取堆大小 */</span>
<a id="__codelineno-4-68" name="__codelineno-4-68" href="#__codelineno-4-68"></a><span class="w"> </span><span class="nx">size</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">maxHeap</span><span class="p">)</span>
<a id="__codelineno-4-69" name="__codelineno-4-69" href="#__codelineno-4-69"></a><span class="w"> </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Printf</span><span class="p">(</span><span class="s">&quot;堆元素数量为 %d\n&quot;</span><span class="p">,</span><span class="w"> </span><span class="nx">size</span><span class="p">)</span>
<a id="__codelineno-4-70" name="__codelineno-4-70" href="#__codelineno-4-70"></a>
<a id="__codelineno-4-71" name="__codelineno-4-71" href="#__codelineno-4-71"></a><span class="w"> </span><span class="cm">/* 判断堆是否为空 */</span>
<a id="__codelineno-4-72" name="__codelineno-4-72" href="#__codelineno-4-72"></a><span class="w"> </span><span class="nx">isEmpty</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">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-4-73" name="__codelineno-4-73" href="#__codelineno-4-73"></a><span class="w"> </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Printf</span><span class="p">(</span><span class="s">&quot;堆是否为空 %t\n&quot;</span><span class="p">,</span><span class="w"> </span><span class="nx">isEmpty</span><span class="p">)</span>
<a id="__codelineno-4-74" name="__codelineno-4-74" href="#__codelineno-4-74"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">heap.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* 初始化堆 */</span>
<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="c1">// Swift 的 Heap 类型同时支持最大堆和最小堆，且需要引入 swift-collections</span>
<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="kd">var</span> <span class="nv">heap</span> <span class="p">=</span> <span class="n">Heap</span><span class="p">&lt;</span><span class="nb">Int</span><span class="p">&gt;()</span>
<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a>
<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="cm">/* 元素入堆 */</span>
<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="n">heap</span><span class="p">.</span><span class="bp">insert</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="n">heap</span><span class="p">.</span><span class="bp">insert</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>
<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="n">heap</span><span class="p">.</span><span class="bp">insert</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span>
<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="n">heap</span><span class="p">.</span><span class="bp">insert</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="n">heap</span><span class="p">.</span><span class="bp">insert</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span>
<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a>
<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="cm">/* 获取堆顶元素 */</span>
<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="kd">var</span> <span class="nv">peek</span> <span class="p">=</span> <span class="n">heap</span><span class="p">.</span><span class="bp">max</span><span class="p">()</span><span class="o">!</span>
<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a>
<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a><span class="cm">/* 堆顶元素出堆 */</span>
<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a><span class="n">peek</span> <span class="p">=</span> <span class="n">heap</span><span class="p">.</span><span class="n">removeMax</span><span class="p">()</span> <span class="c1">// 5</span>
<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a><span class="n">peek</span> <span class="p">=</span> <span class="n">heap</span><span class="p">.</span><span class="n">removeMax</span><span class="p">()</span> <span class="c1">// 4</span>
<a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a><span class="n">peek</span> <span class="p">=</span> <span class="n">heap</span><span class="p">.</span><span class="n">removeMax</span><span class="p">()</span> <span class="c1">// 3</span>
<a id="__codelineno-5-19" name="__codelineno-5-19" href="#__codelineno-5-19"></a><span class="n">peek</span> <span class="p">=</span> <span class="n">heap</span><span class="p">.</span><span class="n">removeMax</span><span class="p">()</span> <span class="c1">// 2</span>
<a id="__codelineno-5-20" name="__codelineno-5-20" href="#__codelineno-5-20"></a><span class="n">peek</span> <span class="p">=</span> <span class="n">heap</span><span class="p">.</span><span class="n">removeMax</span><span class="p">()</span> <span class="c1">// 1</span>
<a id="__codelineno-5-21" name="__codelineno-5-21" href="#__codelineno-5-21"></a>
<a id="__codelineno-5-22" name="__codelineno-5-22" href="#__codelineno-5-22"></a><span class="cm">/* 获取堆大小 */</span>
<a id="__codelineno-5-23" name="__codelineno-5-23" href="#__codelineno-5-23"></a><span class="kd">let</span> <span class="nv">size</span> <span class="p">=</span> <span class="n">heap</span><span class="p">.</span><span class="bp">count</span>
<a id="__codelineno-5-24" name="__codelineno-5-24" href="#__codelineno-5-24"></a>
<a id="__codelineno-5-25" name="__codelineno-5-25" href="#__codelineno-5-25"></a><span class="cm">/* 判断堆是否为空 */</span>
<a id="__codelineno-5-26" name="__codelineno-5-26" href="#__codelineno-5-26"></a><span class="kd">let</span> <span class="nv">isEmpty</span> <span class="p">=</span> <span class="n">heap</span><span class="p">.</span><span class="bp">isEmpty</span>
<a id="__codelineno-5-27" name="__codelineno-5-27" href="#__codelineno-5-27"></a>
<a id="__codelineno-5-28" name="__codelineno-5-28" href="#__codelineno-5-28"></a><span class="cm">/* 输入列表并建堆 */</span>
<a id="__codelineno-5-29" name="__codelineno-5-29" href="#__codelineno-5-29"></a><span class="kd">let</span> <span class="nv">heap2</span> <span class="p">=</span> <span class="n">Heap</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">4</span><span class="p">])</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">heap.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="c1">// JavaScript 未提供内置 Heap 类</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">heap.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="c1">// TypeScript 未提供内置 Heap 类</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">heap.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="c1">// Dart 未提供内置 Heap 类</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">heap.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="k">use</span><span class="w"> </span><span class="n">std</span>::<span class="n">collections</span>::<span class="n">BinaryHeap</span><span class="p">;</span>
<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">use</span><span class="w"> </span><span class="n">std</span>::<span class="n">cmp</span>::<span class="n">Reverse</span><span class="p">;</span>
<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a>
<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="cm">/* 初始化堆 */</span>
<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="c1">// 初始化小顶堆</span>
<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">min_heap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">BinaryHeap</span>::<span class="o">&lt;</span><span class="n">Reverse</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;&gt;</span>::<span class="n">new</span><span class="p">();</span>
<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="c1">// 初始化大顶堆</span>
<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">max_heap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">BinaryHeap</span>::<span class="n">new</span><span class="p">();</span>
<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a>
<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="cm">/* 元素入堆 */</span>
<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="n">max_heap</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="n">max_heap</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span>
<a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="n">max_heap</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span>
<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="n">max_heap</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
<a id="__codelineno-9-15" name="__codelineno-9-15" href="#__codelineno-9-15"></a><span class="n">max_heap</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
<a id="__codelineno-9-16" name="__codelineno-9-16" href="#__codelineno-9-16"></a>
<a id="__codelineno-9-17" name="__codelineno-9-17" href="#__codelineno-9-17"></a><span class="cm">/* 获取堆顶元素 */</span>
<a id="__codelineno-9-18" name="__codelineno-9-18" href="#__codelineno-9-18"></a><span class="kd">let</span><span class="w"> </span><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max_heap</span><span class="p">.</span><span class="n">peek</span><span class="p">().</span><span class="n">unwrap</span><span class="p">();</span><span class="w"> </span><span class="c1">// 5</span>
<a id="__codelineno-9-19" name="__codelineno-9-19" href="#__codelineno-9-19"></a>
<a id="__codelineno-9-20" name="__codelineno-9-20" href="#__codelineno-9-20"></a><span class="cm">/* 堆顶元素出堆 */</span>
<a id="__codelineno-9-21" name="__codelineno-9-21" href="#__codelineno-9-21"></a><span class="c1">// 出堆元素会形成一个从大到小的序列</span>
<a id="__codelineno-9-22" name="__codelineno-9-22" href="#__codelineno-9-22"></a><span class="kd">let</span><span class="w"> </span><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max_heap</span><span class="p">.</span><span class="n">pop</span><span class="p">().</span><span class="n">unwrap</span><span class="p">();</span><span class="w"> </span><span class="c1">// 5</span>
<a id="__codelineno-9-23" name="__codelineno-9-23" href="#__codelineno-9-23"></a><span class="kd">let</span><span class="w"> </span><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max_heap</span><span class="p">.</span><span class="n">pop</span><span class="p">().</span><span class="n">unwrap</span><span class="p">();</span><span class="w"> </span><span class="c1">// 4</span>
<a id="__codelineno-9-24" name="__codelineno-9-24" href="#__codelineno-9-24"></a><span class="kd">let</span><span class="w"> </span><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max_heap</span><span class="p">.</span><span class="n">pop</span><span class="p">().</span><span class="n">unwrap</span><span class="p">();</span><span class="w"> </span><span class="c1">// 3</span>
<a id="__codelineno-9-25" name="__codelineno-9-25" href="#__codelineno-9-25"></a><span class="kd">let</span><span class="w"> </span><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max_heap</span><span class="p">.</span><span class="n">pop</span><span class="p">().</span><span class="n">unwrap</span><span class="p">();</span><span class="w"> </span><span class="c1">// 2</span>
<a id="__codelineno-9-26" name="__codelineno-9-26" href="#__codelineno-9-26"></a><span class="kd">let</span><span class="w"> </span><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max_heap</span><span class="p">.</span><span class="n">pop</span><span class="p">().</span><span class="n">unwrap</span><span class="p">();</span><span class="w"> </span><span class="c1">// 1</span>
<a id="__codelineno-9-27" name="__codelineno-9-27" href="#__codelineno-9-27"></a>
<a id="__codelineno-9-28" name="__codelineno-9-28" href="#__codelineno-9-28"></a><span class="cm">/* 获取堆大小 */</span>
<a id="__codelineno-9-29" name="__codelineno-9-29" href="#__codelineno-9-29"></a><span class="kd">let</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max_heap</span><span class="p">.</span><span class="n">len</span><span class="p">();</span>
<a id="__codelineno-9-30" name="__codelineno-9-30" href="#__codelineno-9-30"></a>
<a id="__codelineno-9-31" name="__codelineno-9-31" href="#__codelineno-9-31"></a><span class="cm">/* 判断堆是否为空 */</span>
<a id="__codelineno-9-32" name="__codelineno-9-32" href="#__codelineno-9-32"></a><span class="kd">let</span><span class="w"> </span><span class="n">is_empty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max_heap</span><span class="p">.</span><span class="n">is_empty</span><span class="p">();</span>
<a id="__codelineno-9-33" name="__codelineno-9-33" href="#__codelineno-9-33"></a>
<a id="__codelineno-9-34" name="__codelineno-9-34" href="#__codelineno-9-34"></a><span class="cm">/* 输入列表并建堆 */</span>
<a id="__codelineno-9-35" name="__codelineno-9-35" href="#__codelineno-9-35"></a><span class="kd">let</span><span class="w"> </span><span class="n">min_heap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">BinaryHeap</span>::<span class="n">from</span><span class="p">(</span><span class="fm">vec!</span><span class="p">[</span><span class="n">Reverse</span><span class="p">(</span><span class="mi">1</span><span class="p">),</span><span class="w"> </span><span class="n">Reverse</span><span class="p">(</span><span class="mi">3</span><span class="p">),</span><span class="w"> </span><span class="n">Reverse</span><span class="p">(</span><span class="mi">2</span><span class="p">),</span><span class="w"> </span><span class="n">Reverse</span><span class="p">(</span><span class="mi">5</span><span class="p">),</span><span class="w"> </span><span class="n">Reverse</span><span class="p">(</span><span class="mi">4</span><span class="p">)]);</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">heap.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="c1">// C 未提供内置 Heap 类</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">heap.zig</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a>
</code></pre></div>
</div>
</div>
</div>
<details class="pythontutor">
<summary>可视化运行</summary>
<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=import%20heapq%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E5%B0%8F%E9%A1%B6%E5%A0%86%0A%20%20%20%20min_heap,%20flag%20%3D%20%5B%5D,%201%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E5%A4%A7%E9%A1%B6%E5%A0%86%0A%20%20%20%20max_heap,%20flag%20%3D%20%5B%5D,%20-1%0A%20%20%20%20%0A%20%20%20%20%23%20Python%20%E7%9A%84%20heapq%20%E6%A8%A1%E5%9D%97%E9%BB%98%E8%AE%A4%E5%AE%9E%E7%8E%B0%E5%B0%8F%E9%A1%B6%E5%A0%86%0A%20%20%20%20%23%20%E8%80%83%E8%99%91%E5%B0%86%E2%80%9C%E5%85%83%E7%B4%A0%E5%8F%96%E8%B4%9F%E2%80%9D%E5%90%8E%E5%86%8D%E5%85%A5%E5%A0%86%EF%BC%8C%E8%BF%99%E6%A0%B7%E5%B0%B1%E5%8F%AF%E4%BB%A5%E5%B0%86%E5%A4%A7%E5%B0%8F%E5%85%B3%E7%B3%BB%E9%A2%A0%E5%80%92%EF%BC%8C%E4%BB%8E%E8%80%8C%E5%AE%9E%E7%8E%B0%E5%A4%A7%E9%A1%B6%E5%A0%86%0A%20%20%20%20%23%20%E5%9C%A8%E6%9C%AC%E7%A4%BA%E4%BE%8B%E4%B8%AD%EF%BC%8Cflag%20%3D%201%20%E6%97%B6%E5%AF%B9%E5%BA%94%E5%B0%8F%E9%A1%B6%E5%A0%86%EF%BC%8Cflag%20%3D%20-1%20%E6%97%B6%E5%AF%B9%E5%BA%94%E5%A4%A7%E9%A1%B6%E5%A0%86%0A%20%20%20%20%0A%20%20%20%20%23%20%E5%85%83%E7%B4%A0%E5%85%A5%E5%A0%86%0A%20%20%20%20heapq.heappush%28max_heap,%20flag%20*%201%29%0A%20%20%20%20heapq.heappush%28max_heap,%20flag%20*%203%29%0A%20%20%20%20heapq.heappush%28max_heap,%20flag%20*%202%29%0A%20%20%20%20heapq.heappush%28max_heap,%20flag%20*%205%29%0A%20%20%20%20heapq.heappush%28max_heap,%20flag%20*%204%29%0A%20%20%20%20%0A%20%20%20%20%23%20%E8%8E%B7%E5%8F%96%E5%A0%86%E9%A1%B6%E5%85%83%E7%B4%A0%0A%20%20%20%20peek%20%3D%20flag%20*%20max_heap%5B0%5D%20%23%205%0A%20%20%20%20%0A%20%20%20%20%23%20%E5%A0%86%E9%A1%B6%E5%85%83%E7%B4%A0%E5%87%BA%E5%A0%86%0A%20%20%20%20%23%20%E5%87%BA%E5%A0%86%E5%85%83%E7%B4%A0%E4%BC%9A%E5%BD%A2%E6%88%90%E4%B8%80%E4%B8%AA%E4%BB%8E%E5%A4%A7%E5%88%B0%E5%B0%8F%E7%9A%84%E5%BA%8F%E5%88%97%0A%20%20%20%20val%20%3D%20flag%20*%20heapq.heappop%28max_heap%29%20%23%205%0A%20%20%20%20val%20%3D%20flag%20*%20heapq.heappop%28max_heap%29%20%23%204%0A%20%20%20%20val%20%3D%20flag%20*%20heapq.heappop%28max_heap%29%20%23%203%0A%20%20%20%20val%20%3D%20flag%20*%20heapq.heappop%28max_heap%29%20%23%202%0A%20%20%20%20val%20%3D%20flag%20*%20heapq.heappop%28max_heap%29%20%23%201%0A%20%20%20%20%0A%20%20%20%20%23%20%E8%8E%B7%E5%8F%96%E5%A0%86%E5%A4%A7%E5%B0%8F%0A%20%20%20%20size%20%3D%20len%28max_heap%29%0A%20%20%20%20%0A%20%20%20%20%23%20%E5%88%A4%E6%96%AD%E5%A0%86%E6%98%AF%E5%90%A6%E4%B8%BA%E7%A9%BA%0A%20%20%20%20is_empty%20%3D%20not%20max_heap%0A%20%20%20%20%0A%20%20%20%20%23%20%E8%BE%93%E5%85%A5%E5%88%97%E8%A1%A8%E5%B9%B6%E5%BB%BA%E5%A0%86%0A%20%20%20%20min_heap%20%3D%20%5B1,%203,%202,%205,%204%5D%0A%20%20%20%20heapq.heapify%28min_heap%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=import%20heapq%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E5%B0%8F%E9%A1%B6%E5%A0%86%0A%20%20%20%20min_heap,%20flag%20%3D%20%5B%5D,%201%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E5%A4%A7%E9%A1%B6%E5%A0%86%0A%20%20%20%20max_heap,%20flag%20%3D%20%5B%5D,%20-1%0A%20%20%20%20%0A%20%20%20%20%23%20Python%20%E7%9A%84%20heapq%20%E6%A8%A1%E5%9D%97%E9%BB%98%E8%AE%A4%E5%AE%9E%E7%8E%B0%E5%B0%8F%E9%A1%B6%E5%A0%86%0A%20%20%20%20%23%20%E8%80%83%E8%99%91%E5%B0%86%E2%80%9C%E5%85%83%E7%B4%A0%E5%8F%96%E8%B4%9F%E2%80%9D%E5%90%8E%E5%86%8D%E5%85%A5%E5%A0%86%EF%BC%8C%E8%BF%99%E6%A0%B7%E5%B0%B1%E5%8F%AF%E4%BB%A5%E5%B0%86%E5%A4%A7%E5%B0%8F%E5%85%B3%E7%B3%BB%E9%A2%A0%E5%80%92%EF%BC%8C%E4%BB%8E%E8%80%8C%E5%AE%9E%E7%8E%B0%E5%A4%A7%E9%A1%B6%E5%A0%86%0A%20%20%20%20%23%20%E5%9C%A8%E6%9C%AC%E7%A4%BA%E4%BE%8B%E4%B8%AD%EF%BC%8Cflag%20%3D%201%20%E6%97%B6%E5%AF%B9%E5%BA%94%E5%B0%8F%E9%A1%B6%E5%A0%86%EF%BC%8Cflag%20%3D%20-1%20%E6%97%B6%E5%AF%B9%E5%BA%94%E5%A4%A7%E9%A1%B6%E5%A0%86%0A%20%20%20%20%0A%20%20%20%20%23%20%E5%85%83%E7%B4%A0%E5%85%A5%E5%A0%86%0A%20%20%20%20heapq.heappush%28max_heap,%20flag%20*%201%29%0A%20%20%20%20heapq.heappush%28max_heap,%20flag%20*%203%29%0A%20%20%20%20heapq.heappush%28max_heap,%20flag%20*%202%29%0A%20%20%20%20heapq.heappush%28max_heap,%20flag%20*%205%29%0A%20%20%20%20heapq.heappush%28max_heap,%20flag%20*%204%29%0A%20%20%20%20%0A%20%20%20%20%23%20%E8%8E%B7%E5%8F%96%E5%A0%86%E9%A1%B6%E5%85%83%E7%B4%A0%0A%20%20%20%20peek%20%3D%20flag%20*%20max_heap%5B0%5D%20%23%205%0A%20%20%20%20%0A%20%20%20%20%23%20%E5%A0%86%E9%A1%B6%E5%85%83%E7%B4%A0%E5%87%BA%E5%A0%86%0A%20%20%20%20%23%20%E5%87%BA%E5%A0%86%E5%85%83%E7%B4%A0%E4%BC%9A%E5%BD%A2%E6%88%90%E4%B8%80%E4%B8%AA%E4%BB%8E%E5%A4%A7%E5%88%B0%E5%B0%8F%E7%9A%84%E5%BA%8F%E5%88%97%0A%20%20%20%20val%20%3D%20flag%20*%20heapq.heappop%28max_heap%29%20%23%205%0A%20%20%20%20val%20%3D%20flag%20*%20heapq.heappop%28max_heap%29%20%23%204%0A%20%20%20%20val%20%3D%20flag%20*%20heapq.heappop%28max_heap%29%20%23%203%0A%20%20%20%20val%20%3D%20flag%20*%20heapq.heappop%28max_heap%29%20%23%202%0A%20%20%20%20val%20%3D%20flag%20*%20heapq.heappop%28max_heap%29%20%23%201%0A%20%20%20%20%0A%20%20%20%20%23%20%E8%8E%B7%E5%8F%96%E5%A0%86%E5%A4%A7%E5%B0%8F%0A%20%20%20%20size%20%3D%20len%28max_heap%29%0A%20%20%20%20%0A%20%20%20%20%23%20%E5%88%A4%E6%96%AD%E5%A0%86%E6%98%AF%E5%90%A6%E4%B8%BA%E7%A9%BA%0A%20%20%20%20is_empty%20%3D%20not%20max_heap%0A%20%20%20%20%0A%20%20%20%20%23%20%E8%BE%93%E5%85%A5%E5%88%97%E8%A1%A8%E5%B9%B6%E5%BB%BA%E5%A0%86%0A%20%20%20%20min_heap%20%3D%20%5B1,%203,%202,%205,%204%5D%0A%20%20%20%20heapq.heapify%28min_heap%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全屏观看 &gt;</a></div></p>
</details>
<h2 id="812">8.1.2 &nbsp; 堆的实现<a class="headerlink" href="#812" title="Permanent link">&para;</a></h2>
<p>下文实现的是大顶堆。若要将其转换为小顶堆，只需将所有大小逻辑判断取逆（例如，将 <span class="arithmatex">\(\geq\)</span> 替换为 <span class="arithmatex">\(\leq\)</span> ）。感兴趣的读者可以自行实现。</p>
<h3 id="1">1. &nbsp; 堆的存储与表示<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
<p>“二叉树”章节讲过，完全二叉树非常适合用数组来表示。由于堆正是一种完全二叉树，<strong>因此我们将采用数组来存储堆</strong>。</p>
<p>当使用数组表示二叉树时，元素代表节点值，索引代表节点在二叉树中的位置。<strong>节点指针通过索引映射公式来实现</strong>。</p>
<p>如图 8-2 所示，给定索引 <span class="arithmatex">\(i\)</span> ，其左子节点的索引为 <span class="arithmatex">\(2i + 1\)</span> ，右子节点的索引为 <span class="arithmatex">\(2i + 2\)</span> ，父节点的索引为 <span class="arithmatex">\((i - 1) / 2\)</span>（向下整除）。当索引越界时，表示空节点或节点不存在。</p>
<p><a class="glightbox" href="../heap.assets/representation_of_heap.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="堆的表示与存储" class="animation-figure" src="../heap.assets/representation_of_heap.png" /></a></p>
<p align="center"> 图 8-2 &nbsp; 堆的表示与存储 </p>
<p>我们可以将索引映射公式封装成函数，方便后续使用：</p>
<div class="tabbed-set tabbed-alternate" data-tabs="2:12"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Zig</label></div>
<div class="tabbed-content">
<div class="tabbed-block">
<div class="highlight"><span class="filename">my_heap.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">left</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">i</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-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;获取左子节点的索引&quot;&quot;&quot;</span>
<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a> <span class="k">return</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">1</span>
<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a>
<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="k">def</span> <span class="nf">right</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">i</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-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;获取右子节点的索引&quot;&quot;&quot;</span>
<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a> <span class="k">return</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">2</span>
<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a>
<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="k">def</span> <span class="nf">parent</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">i</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-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;获取父节点的索引&quot;&quot;&quot;</span>
<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a> <span class="k">return</span> <span class="p">(</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">//</span> <span class="mi">2</span> <span class="c1"># 向下整除</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">my_heap.cpp</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="cm">/* 获取左子节点的索引 */</span>
<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">left</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">2</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">1</span><span class="p">;</span>
<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a><span class="p">}</span>
<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a>
<a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a><span class="cm">/* 获取右子节点的索引 */</span>
<a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a><span class="kt">int</span><span class="w"> </span><span class="nf">right</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">2</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><span class="p">;</span>
<a id="__codelineno-13-9" name="__codelineno-13-9" href="#__codelineno-13-9"></a><span class="p">}</span>
<a id="__codelineno-13-10" name="__codelineno-13-10" href="#__codelineno-13-10"></a>
<a id="__codelineno-13-11" name="__codelineno-13-11" href="#__codelineno-13-11"></a><span class="cm">/* 获取父节点的索引 */</span>
<a id="__codelineno-13-12" name="__codelineno-13-12" href="#__codelineno-13-12"></a><span class="kt">int</span><span class="w"> </span><span class="nf">parent</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-13-13" name="__codelineno-13-13" href="#__codelineno-13-13"></a><span class="w"> </span><span class="k">return</span><span class="w"> </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="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 向下整除</span>
<a id="__codelineno-13-14" name="__codelineno-13-14" href="#__codelineno-13-14"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">my_heap.java</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* 获取左子节点的索引 */</span>
<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">left</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">2</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">1</span><span class="p">;</span>
<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="p">}</span>
<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a>
<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="cm">/* 获取右子节点的索引 */</span>
<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="kt">int</span><span class="w"> </span><span class="nf">right</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">2</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><span class="p">;</span>
<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="p">}</span>
<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a>
<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a><span class="cm">/* 获取父节点的索引 */</span>
<a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a><span class="kt">int</span><span class="w"> </span><span class="nf">parent</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a><span class="w"> </span><span class="k">return</span><span class="w"> </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="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 向下整除</span>
<a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">my_heap.cs</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* 获取左子节点的索引 */</span>
<a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">Left</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="m">2</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="m">1</span><span class="p">;</span>
<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="p">}</span>
<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a>
<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="cm">/* 获取右子节点的索引 */</span>
<a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="kt">int</span><span class="w"> </span><span class="nf">Right</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="m">2</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="m">2</span><span class="p">;</span>
<a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="p">}</span>
<a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a>
<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="cm">/* 获取父节点的索引 */</span>
<a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a><span class="kt">int</span><span class="w"> </span><span class="nf">Parent</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-15-13" name="__codelineno-15-13" href="#__codelineno-15-13"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="m">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 向下整除</span>
<a id="__codelineno-15-14" name="__codelineno-15-14" href="#__codelineno-15-14"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">my_heap.go</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* 获取左子节点的索引 */</span>
<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="nx">left</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w"> </span><span class="k">return</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-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="p">}</span>
<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a>
<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="cm">/* 获取右子节点的索引 */</span>
<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="nx">right</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w"> </span><span class="k">return</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-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="p">}</span>
<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a>
<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="cm">/* 获取父节点的索引 */</span>
<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="nx">parent</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a><span class="w"> </span><span class="c1">// 向下整除</span>
<a id="__codelineno-16-14" name="__codelineno-16-14" href="#__codelineno-16-14"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="nx">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="mi">2</span>
<a id="__codelineno-16-15" name="__codelineno-16-15" href="#__codelineno-16-15"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">my_heap.swift</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="cm">/* 获取左子节点的索引 */</span>
<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a><span class="kd">func</span> <span class="nf">left</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">-&gt;</span> <span class="nb">Int</span> <span class="p">{</span>
<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a> <span class="mi">2</span> <span class="o">*</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">1</span>
<a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a><span class="p">}</span>
<a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a>
<a id="__codelineno-17-6" name="__codelineno-17-6" href="#__codelineno-17-6"></a><span class="cm">/* 获取右子节点的索引 */</span>
<a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a><span class="kd">func</span> <span class="nf">right</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">-&gt;</span> <span class="nb">Int</span> <span class="p">{</span>
<a id="__codelineno-17-8" name="__codelineno-17-8" href="#__codelineno-17-8"></a> <span class="mi">2</span> <span class="o">*</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">2</span>
<a id="__codelineno-17-9" name="__codelineno-17-9" href="#__codelineno-17-9"></a><span class="p">}</span>
<a id="__codelineno-17-10" name="__codelineno-17-10" href="#__codelineno-17-10"></a>
<a id="__codelineno-17-11" name="__codelineno-17-11" href="#__codelineno-17-11"></a><span class="cm">/* 获取父节点的索引 */</span>
<a id="__codelineno-17-12" name="__codelineno-17-12" href="#__codelineno-17-12"></a><span class="kd">func</span> <span class="nf">parent</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">-&gt;</span> <span class="nb">Int</span> <span class="p">{</span>
<a id="__codelineno-17-13" name="__codelineno-17-13" href="#__codelineno-17-13"></a> <span class="p">(</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">/</span> <span class="mi">2</span> <span class="c1">// 向下整除</span>
<a id="__codelineno-17-14" name="__codelineno-17-14" href="#__codelineno-17-14"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">my_heap.js</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="cm">/* 获取左子节点的索引 */</span>
<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a><span class="err">#</span><span class="nx">left</span><span class="p">(</span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
<a id="__codelineno-18-4" name="__codelineno-18-4" href="#__codelineno-18-4"></a><span class="p">}</span>
<a id="__codelineno-18-5" name="__codelineno-18-5" href="#__codelineno-18-5"></a>
<a id="__codelineno-18-6" name="__codelineno-18-6" href="#__codelineno-18-6"></a><span class="cm">/* 获取右子节点的索引 */</span>
<a id="__codelineno-18-7" name="__codelineno-18-7" href="#__codelineno-18-7"></a><span class="err">#</span><span class="nx">right</span><span class="p">(</span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-18-8" name="__codelineno-18-8" href="#__codelineno-18-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span>
<a id="__codelineno-18-9" name="__codelineno-18-9" href="#__codelineno-18-9"></a><span class="p">}</span>
<a id="__codelineno-18-10" name="__codelineno-18-10" href="#__codelineno-18-10"></a>
<a id="__codelineno-18-11" name="__codelineno-18-11" href="#__codelineno-18-11"></a><span class="cm">/* 获取父节点的索引 */</span>
<a id="__codelineno-18-12" name="__codelineno-18-12" href="#__codelineno-18-12"></a><span class="err">#</span><span class="nx">parent</span><span class="p">(</span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-18-13" name="__codelineno-18-13" href="#__codelineno-18-13"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">floor</span><span class="p">((</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">);</span><span class="w"> </span><span class="c1">// 向下整除</span>
<a id="__codelineno-18-14" name="__codelineno-18-14" href="#__codelineno-18-14"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">my_heap.ts</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="cm">/* 获取左子节点的索引 */</span>
<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a><span class="nx">left</span><span class="p">(</span><span class="nx">i</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
<a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a><span class="p">}</span>
<a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a>
<a id="__codelineno-19-6" name="__codelineno-19-6" href="#__codelineno-19-6"></a><span class="cm">/* 获取右子节点的索引 */</span>
<a id="__codelineno-19-7" name="__codelineno-19-7" href="#__codelineno-19-7"></a><span class="nx">right</span><span class="p">(</span><span class="nx">i</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-19-8" name="__codelineno-19-8" href="#__codelineno-19-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span>
<a id="__codelineno-19-9" name="__codelineno-19-9" href="#__codelineno-19-9"></a><span class="p">}</span>
<a id="__codelineno-19-10" name="__codelineno-19-10" href="#__codelineno-19-10"></a>
<a id="__codelineno-19-11" name="__codelineno-19-11" href="#__codelineno-19-11"></a><span class="cm">/* 获取父节点的索引 */</span>
<a id="__codelineno-19-12" name="__codelineno-19-12" href="#__codelineno-19-12"></a><span class="nx">parent</span><span class="p">(</span><span class="nx">i</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-19-13" name="__codelineno-19-13" href="#__codelineno-19-13"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">floor</span><span class="p">((</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">);</span><span class="w"> </span><span class="c1">// 向下整除</span>
<a id="__codelineno-19-14" name="__codelineno-19-14" href="#__codelineno-19-14"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">my_heap.dart</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="cm">/* 获取左子节点的索引 */</span>
<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">_left</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="m">2</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="m">1</span><span class="p">;</span>
<a id="__codelineno-20-4" name="__codelineno-20-4" href="#__codelineno-20-4"></a><span class="p">}</span>
<a id="__codelineno-20-5" name="__codelineno-20-5" href="#__codelineno-20-5"></a>
<a id="__codelineno-20-6" name="__codelineno-20-6" href="#__codelineno-20-6"></a><span class="cm">/* 获取右子节点的索引 */</span>
<a id="__codelineno-20-7" name="__codelineno-20-7" href="#__codelineno-20-7"></a><span class="kt">int</span><span class="w"> </span><span class="n">_right</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-20-8" name="__codelineno-20-8" href="#__codelineno-20-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="m">2</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="m">2</span><span class="p">;</span>
<a id="__codelineno-20-9" name="__codelineno-20-9" href="#__codelineno-20-9"></a><span class="p">}</span>
<a id="__codelineno-20-10" name="__codelineno-20-10" href="#__codelineno-20-10"></a>
<a id="__codelineno-20-11" name="__codelineno-20-11" href="#__codelineno-20-11"></a><span class="cm">/* 获取父节点的索引 */</span>
<a id="__codelineno-20-12" name="__codelineno-20-12" href="#__codelineno-20-12"></a><span class="kt">int</span><span class="w"> </span><span class="n">_parent</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-20-13" name="__codelineno-20-13" href="#__codelineno-20-13"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="o">~/</span><span class="w"> </span><span class="m">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 向下整除</span>
<a id="__codelineno-20-14" name="__codelineno-20-14" href="#__codelineno-20-14"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">my_heap.rs</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="cm">/* 获取左子节点的索引 */</span>
<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a><span class="k">fn</span> <span class="nf">left</span><span class="p">(</span><span class="n">i</span>: <span class="kt">usize</span><span class="p">)</span><span class="w"> </span>-&gt; <span class="kt">usize</span> <span class="p">{</span>
<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="w"> </span><span class="mi">2</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">1</span>
<a id="__codelineno-21-4" name="__codelineno-21-4" href="#__codelineno-21-4"></a><span class="p">}</span>
<a id="__codelineno-21-5" name="__codelineno-21-5" href="#__codelineno-21-5"></a>
<a id="__codelineno-21-6" name="__codelineno-21-6" href="#__codelineno-21-6"></a><span class="cm">/* 获取右子节点的索引 */</span>
<a id="__codelineno-21-7" name="__codelineno-21-7" href="#__codelineno-21-7"></a><span class="k">fn</span> <span class="nf">right</span><span class="p">(</span><span class="n">i</span>: <span class="kt">usize</span><span class="p">)</span><span class="w"> </span>-&gt; <span class="kt">usize</span> <span class="p">{</span>
<a id="__codelineno-21-8" name="__codelineno-21-8" href="#__codelineno-21-8"></a><span class="w"> </span><span class="mi">2</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-21-9" name="__codelineno-21-9" href="#__codelineno-21-9"></a><span class="p">}</span>
<a id="__codelineno-21-10" name="__codelineno-21-10" href="#__codelineno-21-10"></a>
<a id="__codelineno-21-11" name="__codelineno-21-11" href="#__codelineno-21-11"></a><span class="cm">/* 获取父节点的索引 */</span>
<a id="__codelineno-21-12" name="__codelineno-21-12" href="#__codelineno-21-12"></a><span class="k">fn</span> <span class="nf">parent</span><span class="p">(</span><span class="n">i</span>: <span class="kt">usize</span><span class="p">)</span><span class="w"> </span>-&gt; <span class="kt">usize</span> <span class="p">{</span>
<a id="__codelineno-21-13" name="__codelineno-21-13" href="#__codelineno-21-13"></a><span class="w"> </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="mi">2</span><span class="w"> </span><span class="c1">// 向下整除</span>
<a id="__codelineno-21-14" name="__codelineno-21-14" href="#__codelineno-21-14"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">my_heap.c</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="cm">/* 获取左子节点的索引 */</span>
<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">left</span><span class="p">(</span><span class="n">MaxHeap</span><span class="w"> </span><span class="o">*</span><span class="n">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">2</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">1</span><span class="p">;</span>
<a id="__codelineno-22-4" name="__codelineno-22-4" href="#__codelineno-22-4"></a><span class="p">}</span>
<a id="__codelineno-22-5" name="__codelineno-22-5" href="#__codelineno-22-5"></a>
<a id="__codelineno-22-6" name="__codelineno-22-6" href="#__codelineno-22-6"></a><span class="cm">/* 获取右子节点的索引 */</span>
<a id="__codelineno-22-7" name="__codelineno-22-7" href="#__codelineno-22-7"></a><span class="kt">int</span><span class="w"> </span><span class="nf">right</span><span class="p">(</span><span class="n">MaxHeap</span><span class="w"> </span><span class="o">*</span><span class="n">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-22-8" name="__codelineno-22-8" href="#__codelineno-22-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">2</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><span class="p">;</span>
<a id="__codelineno-22-9" name="__codelineno-22-9" href="#__codelineno-22-9"></a><span class="p">}</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="cm">/* 获取父节点的索引 */</span>
<a id="__codelineno-22-12" name="__codelineno-22-12" href="#__codelineno-22-12"></a><span class="kt">int</span><span class="w"> </span><span class="nf">parent</span><span class="p">(</span><span class="n">MaxHeap</span><span class="w"> </span><span class="o">*</span><span class="n">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-22-13" name="__codelineno-22-13" href="#__codelineno-22-13"></a><span class="w"> </span><span class="k">return</span><span class="w"> </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="mi">2</span><span class="p">;</span>
<a id="__codelineno-22-14" name="__codelineno-22-14" href="#__codelineno-22-14"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">my_heap.zig</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="c1">// 获取左子节点的索引</span>
<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a><span class="k">fn</span><span class="w"> </span><span class="n">left</span><span class="p">(</span><span class="n">i</span><span class="o">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="kt">usize</span><span class="w"> </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="k">return</span><span class="w"> </span><span class="mi">2</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">1</span><span class="p">;</span>
<a id="__codelineno-23-4" name="__codelineno-23-4" href="#__codelineno-23-4"></a><span class="p">}</span>
<a id="__codelineno-23-5" name="__codelineno-23-5" href="#__codelineno-23-5"></a>
<a id="__codelineno-23-6" name="__codelineno-23-6" href="#__codelineno-23-6"></a><span class="c1">// 获取右子节点的索引</span>
<a id="__codelineno-23-7" name="__codelineno-23-7" href="#__codelineno-23-7"></a><span class="k">fn</span><span class="w"> </span><span class="n">right</span><span class="p">(</span><span class="n">i</span><span class="o">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="kt">usize</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="w"> </span><span class="mi">2</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><span class="p">;</span>
<a id="__codelineno-23-9" name="__codelineno-23-9" href="#__codelineno-23-9"></a><span class="p">}</span>
<a id="__codelineno-23-10" name="__codelineno-23-10" href="#__codelineno-23-10"></a>
<a id="__codelineno-23-11" name="__codelineno-23-11" href="#__codelineno-23-11"></a><span class="c1">// 获取父节点的索引</span>
<a id="__codelineno-23-12" name="__codelineno-23-12" href="#__codelineno-23-12"></a><span class="k">fn</span><span class="w"> </span><span class="n">parent</span><span class="p">(</span><span class="n">i</span><span class="o">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="kt">usize</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-23-13" name="__codelineno-23-13" href="#__codelineno-23-13"></a><span class="w"> </span><span class="c1">// return (i - 1) / 2; // 向下整除</span>
<a id="__codelineno-23-14" name="__codelineno-23-14" href="#__codelineno-23-14"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nb">@divFloor</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="mi">2</span><span class="p">);</span>
<a id="__codelineno-23-15" name="__codelineno-23-15" href="#__codelineno-23-15"></a><span class="p">}</span>
</code></pre></div>
</div>
</div>
</div>
<h3 id="2">2. &nbsp; 访问堆顶元素<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
<p>堆顶元素即为二叉树的根节点，也就是列表的首个元素：</p>
<div class="tabbed-set tabbed-alternate" data-tabs="3:12"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><input id="__tabbed_3_12" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Python</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Java</label><label for="__tabbed_3_4">C#</label><label for="__tabbed_3_5">Go</label><label for="__tabbed_3_6">Swift</label><label for="__tabbed_3_7">JS</label><label for="__tabbed_3_8">TS</label><label for="__tabbed_3_9">Dart</label><label for="__tabbed_3_10">Rust</label><label for="__tabbed_3_11">C</label><label for="__tabbed_3_12">Zig</label></div>
<div class="tabbed-content">
<div class="tabbed-block">
<div class="highlight"><span class="filename">my_heap.py</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="k">def</span> <span class="nf">peek</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;访问堆顶元素&quot;&quot;&quot;</span>
<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a> <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">max_heap</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">my_heap.cpp</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="cm">/* 访问堆顶元素 */</span>
<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">peek</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="mi">0</span><span class="p">];</span>
<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">my_heap.java</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="cm">/* 访问堆顶元素 */</span>
<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">peek</span><span class="p">()</span><span class="w"> </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="k">return</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
<a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">my_heap.cs</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="cm">/* 访问堆顶元素 */</span>
<a id="__codelineno-27-2" name="__codelineno-27-2" href="#__codelineno-27-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">Peek</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-27-3" name="__codelineno-27-3" href="#__codelineno-27-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="m">0</span><span class="p">];</span>
<a id="__codelineno-27-4" name="__codelineno-27-4" href="#__codelineno-27-4"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">my_heap.go</span><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="cm">/* 访问堆顶元素 */</span>
<a id="__codelineno-28-2" name="__codelineno-28-2" href="#__codelineno-28-2"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="nx">peek</span><span class="p">()</span><span class="w"> </span><span class="kt">any</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-28-3" name="__codelineno-28-3" href="#__codelineno-28-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
<a id="__codelineno-28-4" name="__codelineno-28-4" href="#__codelineno-28-4"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">my_heap.swift</span><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="cm">/* 访问堆顶元素 */</span>
<a id="__codelineno-29-2" name="__codelineno-29-2" href="#__codelineno-29-2"></a><span class="kd">func</span> <span class="nf">peek</span><span class="p">()</span> <span class="p">-&gt;</span> <span class="nb">Int</span> <span class="p">{</span>
<a id="__codelineno-29-3" name="__codelineno-29-3" href="#__codelineno-29-3"></a> <span class="n">maxHeap</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
<a id="__codelineno-29-4" name="__codelineno-29-4" href="#__codelineno-29-4"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">my_heap.js</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="cm">/* 访问堆顶元素 */</span>
<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a><span class="nx">peek</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">maxHeap</span><span class="p">[</span><span class="mf">0</span><span class="p">];</span>
<a id="__codelineno-30-4" name="__codelineno-30-4" href="#__codelineno-30-4"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">my_heap.ts</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="cm">/* 访问堆顶元素 */</span>
<a id="__codelineno-31-2" name="__codelineno-31-2" href="#__codelineno-31-2"></a><span class="nx">peek</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-31-3" name="__codelineno-31-3" href="#__codelineno-31-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">maxHeap</span><span class="p">[</span><span class="mf">0</span><span class="p">];</span>
<a id="__codelineno-31-4" name="__codelineno-31-4" href="#__codelineno-31-4"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">my_heap.dart</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="cm">/* 访问堆顶元素 */</span>
<a id="__codelineno-32-2" name="__codelineno-32-2" href="#__codelineno-32-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">peek</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-32-3" name="__codelineno-32-3" href="#__codelineno-32-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">_maxHeap</span><span class="p">[</span><span class="m">0</span><span class="p">];</span>
<a id="__codelineno-32-4" name="__codelineno-32-4" href="#__codelineno-32-4"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">my_heap.rs</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="cm">/* 访问堆顶元素 */</span>
<a id="__codelineno-33-2" name="__codelineno-33-2" href="#__codelineno-33-2"></a><span class="k">fn</span> <span class="nf">peek</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">)</span><span class="w"> </span>-&gt; <span class="nb">Option</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-33-3" name="__codelineno-33-3" href="#__codelineno-33-3"></a><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">.</span><span class="n">first</span><span class="p">().</span><span class="n">copied</span><span class="p">()</span>
<a id="__codelineno-33-4" name="__codelineno-33-4" href="#__codelineno-33-4"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">my_heap.c</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="cm">/* 访问堆顶元素 */</span>
<a id="__codelineno-34-2" name="__codelineno-34-2" href="#__codelineno-34-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">peek</span><span class="p">(</span><span class="n">MaxHeap</span><span class="w"> </span><span class="o">*</span><span class="n">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-34-3" name="__codelineno-34-3" href="#__codelineno-34-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">maxHeap</span><span class="o">-&gt;</span><span class="n">data</span><span class="p">[</span><span class="mi">0</span><span class="p">];</span>
<a id="__codelineno-34-4" name="__codelineno-34-4" href="#__codelineno-34-4"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">my_heap.zig</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="c1">// 访问堆顶元素</span>
<a id="__codelineno-35-2" name="__codelineno-35-2" href="#__codelineno-35-2"></a><span class="k">fn</span><span class="w"> </span><span class="n">peek</span><span class="p">(</span><span class="n">self</span><span class="o">:</span><span class="w"> </span><span class="o">*</span><span class="n">Self</span><span class="p">)</span><span class="w"> </span><span class="n">T</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-35-3" name="__codelineno-35-3" href="#__codelineno-35-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">items</span><span class="p">[</span><span class="mi">0</span><span class="p">];</span>
<a id="__codelineno-35-4" name="__codelineno-35-4" href="#__codelineno-35-4"></a><span class="p">}</span><span class="w"> </span>
</code></pre></div>
</div>
</div>
</div>
<details class="pythontutor">
<summary>可视化运行</summary>
<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=class%20MaxHeap%3A%0A%20%20%20%20%22%22%22%E5%A4%A7%E9%A1%B6%E5%A0%86%22%22%22%0A%0A%20%20%20%20def%20__init__%28self,%20nums%3A%20list%5Bint%5D%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E6%9E%84%E9%80%A0%E6%96%B9%E6%B3%95%22%22%22%0A%20%20%20%20%20%20%20%20%23%20%E5%B0%86%E5%88%97%E8%A1%A8%E5%85%83%E7%B4%A0%E5%8E%9F%E5%B0%81%E4%B8%8D%E5%8A%A8%E6%B7%BB%E5%8A%A0%E8%BF%9B%E5%A0%86%0A%20%20%20%20%20%20%20%20self.max_heap%20%3D%20nums%0A%0A%20%20%20%20def%20left%28self,%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%8E%B7%E5%8F%96%E5%B7%A6%E5%AD%90%E8%8A%82%E7%82%B9%E7%9A%84%E7%B4%A2%E5%BC%95%22%22%22%0A%20%20%20%20%20%20%20%20return%202%20*%20i%20%2B%201%0A%0A%20%20%20%20def%20right%28self,%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%8E%B7%E5%8F%96%E5%8F%B3%E5%AD%90%E8%8A%82%E7%82%B9%E7%9A%84%E7%B4%A2%E5%BC%95%22%22%22%0A%20%20%20%20%20%20%20%20return%202%20*%20i%20%2B%202%0A%0A%20%20%20%20def%20parent%28self,%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%8E%B7%E5%8F%96%E7%88%B6%E8%8A%82%E7%82%B9%E7%9A%84%E7%B4%A2%E5%BC%95%22%22%22%0A%20%20%20%20%20%20%20%20return%20%28i%20-%201%29%20//%202%20%20%23%20%E5%90%91%E4%B8%8B%E6%95%B4%E9%99%A4%0A%0A%20%20%20%20def%20size%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%8E%B7%E5%8F%96%E5%A0%86%E5%A4%A7%E5%B0%8F%22%22%22%0A%20%20%20%20%20%20%20%20return%20len%28self.max_heap%29%0A%0A%20%20%20%20def%20is_empty%28self%29%20-%3E%20bool%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E5%88%A4%E6%96%AD%E5%A0%86%E6%98%AF%E5%90%A6%E4%B8%BA%E7%A9%BA%22%22%22%0A%20%20%20%20%20%20%20%20return%20self.size%28%29%20%3D%3D%200%0A%0A%20%20%20%20def%20peek%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%AE%BF%E9%97%AE%E5%A0%86%E9%A1%B6%E5%85%83%E7%B4%A0%22%22%22%0A%20%20%20%20%20%20%20%20return%20self.max_heap%5B0%5D%0A%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E5%A4%A7%E9%A1%B6%E5%A0%86%0A%20%20%20%20%23%20%E8%AF%B7%E6%B3%A8%E6%84%8F%EF%BC%8C%E8%BE%93%E5%85%A5%E6%95%B0%E7%BB%84%E5%B7%B2%E7%BB%8F%E6%98%AF%E4%B8%80%E4%B8%AA%E5%B7%B2%E7%BB%8F%E6%98%AF%E4%B8%80%E4%B8%AA%E5%90%88%E6%B3%95%E7%9A%84%E5%A0%86%20%0A%20%20%20%20max_heap%20%3D%20MaxHeap%28%5B9,%208,%206,%206,%207,%205,%202,%201,%204,%203,%206,%202%5D%29%0A%0A%20%20%20%20%23%20%E8%8E%B7%E5%8F%96%E5%A0%86%E9%A1%B6%E5%85%83%E7%B4%A0%0A%20%20%20%20peek%20%3D%20max_heap.peek%28%29%0A%20%20%20%20print%28f%22%5Cn%E5%A0%86%E9%A1%B6%E5%85%83%E7%B4%A0%E4%B8%BA%20%7Bpeek%7D%22%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=7&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=class%20MaxHeap%3A%0A%20%20%20%20%22%22%22%E5%A4%A7%E9%A1%B6%E5%A0%86%22%22%22%0A%0A%20%20%20%20def%20__init__%28self,%20nums%3A%20list%5Bint%5D%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E6%9E%84%E9%80%A0%E6%96%B9%E6%B3%95%22%22%22%0A%20%20%20%20%20%20%20%20%23%20%E5%B0%86%E5%88%97%E8%A1%A8%E5%85%83%E7%B4%A0%E5%8E%9F%E5%B0%81%E4%B8%8D%E5%8A%A8%E6%B7%BB%E5%8A%A0%E8%BF%9B%E5%A0%86%0A%20%20%20%20%20%20%20%20self.max_heap%20%3D%20nums%0A%0A%20%20%20%20def%20left%28self,%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%8E%B7%E5%8F%96%E5%B7%A6%E5%AD%90%E8%8A%82%E7%82%B9%E7%9A%84%E7%B4%A2%E5%BC%95%22%22%22%0A%20%20%20%20%20%20%20%20return%202%20*%20i%20%2B%201%0A%0A%20%20%20%20def%20right%28self,%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%8E%B7%E5%8F%96%E5%8F%B3%E5%AD%90%E8%8A%82%E7%82%B9%E7%9A%84%E7%B4%A2%E5%BC%95%22%22%22%0A%20%20%20%20%20%20%20%20return%202%20*%20i%20%2B%202%0A%0A%20%20%20%20def%20parent%28self,%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%8E%B7%E5%8F%96%E7%88%B6%E8%8A%82%E7%82%B9%E7%9A%84%E7%B4%A2%E5%BC%95%22%22%22%0A%20%20%20%20%20%20%20%20return%20%28i%20-%201%29%20//%202%20%20%23%20%E5%90%91%E4%B8%8B%E6%95%B4%E9%99%A4%0A%0A%20%20%20%20def%20size%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%8E%B7%E5%8F%96%E5%A0%86%E5%A4%A7%E5%B0%8F%22%22%22%0A%20%20%20%20%20%20%20%20return%20len%28self.max_heap%29%0A%0A%20%20%20%20def%20is_empty%28self%29%20-%3E%20bool%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E5%88%A4%E6%96%AD%E5%A0%86%E6%98%AF%E5%90%A6%E4%B8%BA%E7%A9%BA%22%22%22%0A%20%20%20%20%20%20%20%20return%20self.size%28%29%20%3D%3D%200%0A%0A%20%20%20%20def%20peek%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%AE%BF%E9%97%AE%E5%A0%86%E9%A1%B6%E5%85%83%E7%B4%A0%22%22%22%0A%20%20%20%20%20%20%20%20return%20self.max_heap%5B0%5D%0A%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E5%A4%A7%E9%A1%B6%E5%A0%86%0A%20%20%20%20%23%20%E8%AF%B7%E6%B3%A8%E6%84%8F%EF%BC%8C%E8%BE%93%E5%85%A5%E6%95%B0%E7%BB%84%E5%B7%B2%E7%BB%8F%E6%98%AF%E4%B8%80%E4%B8%AA%E5%B7%B2%E7%BB%8F%E6%98%AF%E4%B8%80%E4%B8%AA%E5%90%88%E6%B3%95%E7%9A%84%E5%A0%86%20%0A%20%20%20%20max_heap%20%3D%20MaxHeap%28%5B9,%208,%206,%206,%207,%205,%202,%201,%204,%203,%206,%202%5D%29%0A%0A%20%20%20%20%23%20%E8%8E%B7%E5%8F%96%E5%A0%86%E9%A1%B6%E5%85%83%E7%B4%A0%0A%20%20%20%20peek%20%3D%20max_heap.peek%28%29%0A%20%20%20%20print%28f%22%5Cn%E5%A0%86%E9%A1%B6%E5%85%83%E7%B4%A0%E4%B8%BA%20%7Bpeek%7D%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=7&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全屏观看 &gt;</a></div></p>
</details>
<h3 id="3">3. &nbsp; 元素入堆<a class="headerlink" href="#3" title="Permanent link">&para;</a></h3>
<p>给定元素 <code>val</code> ，我们首先将其添加到堆底。添加之后，由于 <code>val</code> 可能大于堆中其他元素，堆的成立条件可能已被破坏，<strong>因此需要修复从插入节点到根节点的路径上的各个节点</strong>，这个操作被称为「堆化 heapify」。</p>
<p>考虑从入堆节点开始，<strong>从底至顶执行堆化</strong>。如图 8-3 所示，我们比较插入节点与其父节点的值，如果插入节点更大，则将它们交换。然后继续执行此操作，从底至顶修复堆中的各个节点，直至越过根节点或遇到无须交换的节点时结束。</p>
<div class="tabbed-set tabbed-alternate" data-tabs="4:9"><input checked="checked" id="__tabbed_4_1" name="__tabbed_4" type="radio" /><input id="__tabbed_4_2" name="__tabbed_4" type="radio" /><input id="__tabbed_4_3" name="__tabbed_4" type="radio" /><input id="__tabbed_4_4" name="__tabbed_4" type="radio" /><input id="__tabbed_4_5" name="__tabbed_4" type="radio" /><input id="__tabbed_4_6" name="__tabbed_4" type="radio" /><input id="__tabbed_4_7" name="__tabbed_4" type="radio" /><input id="__tabbed_4_8" name="__tabbed_4" type="radio" /><input id="__tabbed_4_9" name="__tabbed_4" type="radio" /><div class="tabbed-labels"><label for="__tabbed_4_1">&lt;1&gt;</label><label for="__tabbed_4_2">&lt;2&gt;</label><label for="__tabbed_4_3">&lt;3&gt;</label><label for="__tabbed_4_4">&lt;4&gt;</label><label for="__tabbed_4_5">&lt;5&gt;</label><label for="__tabbed_4_6">&lt;6&gt;</label><label for="__tabbed_4_7">&lt;7&gt;</label><label for="__tabbed_4_8">&lt;8&gt;</label><label for="__tabbed_4_9">&lt;9&gt;</label></div>
<div class="tabbed-content">
<div class="tabbed-block">
<p><a class="glightbox" href="../heap.assets/heap_push_step1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="元素入堆步骤" class="animation-figure" src="../heap.assets/heap_push_step1.png" /></a></p>
</div>
<div class="tabbed-block">
<p><a class="glightbox" href="../heap.assets/heap_push_step2.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_push_step2" class="animation-figure" src="../heap.assets/heap_push_step2.png" /></a></p>
</div>
<div class="tabbed-block">
<p><a class="glightbox" href="../heap.assets/heap_push_step3.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_push_step3" class="animation-figure" src="../heap.assets/heap_push_step3.png" /></a></p>
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<p><a class="glightbox" href="../heap.assets/heap_push_step4.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_push_step4" class="animation-figure" src="../heap.assets/heap_push_step4.png" /></a></p>
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<p><a class="glightbox" href="../heap.assets/heap_push_step5.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_push_step5" class="animation-figure" src="../heap.assets/heap_push_step5.png" /></a></p>
</div>
<div class="tabbed-block">
<p><a class="glightbox" href="../heap.assets/heap_push_step6.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_push_step6" class="animation-figure" src="../heap.assets/heap_push_step6.png" /></a></p>
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<div class="tabbed-block">
<p><a class="glightbox" href="../heap.assets/heap_push_step7.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_push_step7" class="animation-figure" src="../heap.assets/heap_push_step7.png" /></a></p>
</div>
<div class="tabbed-block">
<p><a class="glightbox" href="../heap.assets/heap_push_step8.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_push_step8" class="animation-figure" src="../heap.assets/heap_push_step8.png" /></a></p>
</div>
<div class="tabbed-block">
<p><a class="glightbox" href="../heap.assets/heap_push_step9.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_push_step9" class="animation-figure" src="../heap.assets/heap_push_step9.png" /></a></p>
</div>
</div>
</div>
<p align="center"> 图 8-3 &nbsp; 元素入堆步骤 </p>
<p>设节点总数为 <span class="arithmatex">\(n\)</span> ，则树的高度为 <span class="arithmatex">\(O(\log n)\)</span> 。由此可知，堆化操作的循环轮数最多为 <span class="arithmatex">\(O(\log n)\)</span> ，<strong>元素入堆操作的时间复杂度为 <span class="arithmatex">\(O(\log n)\)</span></strong> 。代码如下所示：</p>
<div class="tabbed-set tabbed-alternate" data-tabs="5:12"><input checked="checked" id="__tabbed_5_1" name="__tabbed_5" type="radio" /><input id="__tabbed_5_2" name="__tabbed_5" type="radio" /><input id="__tabbed_5_3" name="__tabbed_5" type="radio" /><input id="__tabbed_5_4" name="__tabbed_5" type="radio" /><input id="__tabbed_5_5" name="__tabbed_5" type="radio" /><input id="__tabbed_5_6" name="__tabbed_5" type="radio" /><input id="__tabbed_5_7" name="__tabbed_5" type="radio" /><input id="__tabbed_5_8" name="__tabbed_5" type="radio" /><input id="__tabbed_5_9" name="__tabbed_5" type="radio" /><input id="__tabbed_5_10" name="__tabbed_5" type="radio" /><input id="__tabbed_5_11" name="__tabbed_5" type="radio" /><input id="__tabbed_5_12" name="__tabbed_5" type="radio" /><div class="tabbed-labels"><label for="__tabbed_5_1">Python</label><label for="__tabbed_5_2">C++</label><label for="__tabbed_5_3">Java</label><label for="__tabbed_5_4">C#</label><label for="__tabbed_5_5">Go</label><label for="__tabbed_5_6">Swift</label><label for="__tabbed_5_7">JS</label><label for="__tabbed_5_8">TS</label><label for="__tabbed_5_9">Dart</label><label for="__tabbed_5_10">Rust</label><label for="__tabbed_5_11">C</label><label for="__tabbed_5_12">Zig</label></div>
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<div class="highlight"><span class="filename">my_heap.py</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="k">def</span> <span class="nf">push</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
<a id="__codelineno-36-2" name="__codelineno-36-2" href="#__codelineno-36-2"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;元素入堆&quot;&quot;&quot;</span>
<a id="__codelineno-36-3" name="__codelineno-36-3" href="#__codelineno-36-3"></a> <span class="c1"># 添加节点</span>
<a id="__codelineno-36-4" name="__codelineno-36-4" href="#__codelineno-36-4"></a> <span class="bp">self</span><span class="o">.</span><span class="n">max_heap</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">val</span><span class="p">)</span>
<a id="__codelineno-36-5" name="__codelineno-36-5" href="#__codelineno-36-5"></a> <span class="c1"># 从底至顶堆化</span>
<a id="__codelineno-36-6" name="__codelineno-36-6" href="#__codelineno-36-6"></a> <span class="bp">self</span><span class="o">.</span><span class="n">sift_up</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">()</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
<a id="__codelineno-36-7" name="__codelineno-36-7" href="#__codelineno-36-7"></a>
<a id="__codelineno-36-8" name="__codelineno-36-8" href="#__codelineno-36-8"></a><span class="k">def</span> <span class="nf">sift_up</span><span class="p">(</span><span class="bp">self</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-36-9" name="__codelineno-36-9" href="#__codelineno-36-9"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;从节点 i 开始，从底至顶堆化&quot;&quot;&quot;</span>
<a id="__codelineno-36-10" name="__codelineno-36-10" href="#__codelineno-36-10"></a> <span class="k">while</span> <span class="kc">True</span><span class="p">:</span>
<a id="__codelineno-36-11" name="__codelineno-36-11" href="#__codelineno-36-11"></a> <span class="c1"># 获取节点 i 的父节点</span>
<a id="__codelineno-36-12" name="__codelineno-36-12" href="#__codelineno-36-12"></a> <span class="n">p</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">parent</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
<a id="__codelineno-36-13" name="__codelineno-36-13" href="#__codelineno-36-13"></a> <span class="c1"># 当“越过根节点”或“节点无须修复”时，结束堆化</span>
<a id="__codelineno-36-14" name="__codelineno-36-14" href="#__codelineno-36-14"></a> <span class="k">if</span> <span class="n">p</span> <span class="o">&lt;</span> <span class="mi">0</span> <span class="ow">or</span> <span class="bp">self</span><span class="o">.</span><span class="n">max_heap</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">&lt;=</span> <span class="bp">self</span><span class="o">.</span><span class="n">max_heap</span><span class="p">[</span><span class="n">p</span><span class="p">]:</span>
<a id="__codelineno-36-15" name="__codelineno-36-15" href="#__codelineno-36-15"></a> <span class="k">break</span>
<a id="__codelineno-36-16" name="__codelineno-36-16" href="#__codelineno-36-16"></a> <span class="c1"># 交换两节点</span>
<a id="__codelineno-36-17" name="__codelineno-36-17" href="#__codelineno-36-17"></a> <span class="bp">self</span><span class="o">.</span><span class="n">swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span> <span class="n">p</span><span class="p">)</span>
<a id="__codelineno-36-18" name="__codelineno-36-18" href="#__codelineno-36-18"></a> <span class="c1"># 循环向上堆化</span>
<a id="__codelineno-36-19" name="__codelineno-36-19" href="#__codelineno-36-19"></a> <span class="n">i</span> <span class="o">=</span> <span class="n">p</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">my_heap.cpp</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="cm">/* 元素入堆 */</span>
<a id="__codelineno-37-2" name="__codelineno-37-2" href="#__codelineno-37-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </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="c1">// 添加节点</span>
<a id="__codelineno-37-4" name="__codelineno-37-4" href="#__codelineno-37-4"></a><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">val</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="c1">// 从底至顶堆化</span>
<a id="__codelineno-37-6" name="__codelineno-37-6" href="#__codelineno-37-6"></a><span class="w"> </span><span class="n">siftUp</span><span class="p">(</span><span class="n">size</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-37-7" name="__codelineno-37-7" href="#__codelineno-37-7"></a><span class="p">}</span>
<a id="__codelineno-37-8" name="__codelineno-37-8" href="#__codelineno-37-8"></a>
<a id="__codelineno-37-9" name="__codelineno-37-9" href="#__codelineno-37-9"></a><span class="cm">/* 从节点 i 开始，从底至顶堆化 */</span>
<a id="__codelineno-37-10" name="__codelineno-37-10" href="#__codelineno-37-10"></a><span class="kt">void</span><span class="w"> </span><span class="nf">siftUp</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-37-11" name="__codelineno-37-11" href="#__codelineno-37-11"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nb">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-37-12" name="__codelineno-37-12" href="#__codelineno-37-12"></a><span class="w"> </span><span class="c1">// 获取节点 i 的父节点</span>
<a id="__codelineno-37-13" name="__codelineno-37-13" href="#__codelineno-37-13"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">p</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">parent</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
<a id="__codelineno-37-14" name="__codelineno-37-14" href="#__codelineno-37-14"></a><span class="w"> </span><span class="c1">// 当“越过根节点”或“节点无须修复”时，结束堆化</span>
<a id="__codelineno-37-15" name="__codelineno-37-15" href="#__codelineno-37-15"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">p</span><span class="w"> </span><span class="o">&lt;</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">maxHeap</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">p</span><span class="p">])</span>
<a id="__codelineno-37-16" name="__codelineno-37-16" href="#__codelineno-37-16"></a><span class="w"> </span><span class="k">break</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="c1">// 交换两节点</span>
<a id="__codelineno-37-18" name="__codelineno-37-18" href="#__codelineno-37-18"></a><span class="w"> </span><span class="n">swap</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">p</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="c1">// 循环向上堆化</span>
<a id="__codelineno-37-20" name="__codelineno-37-20" href="#__codelineno-37-20"></a><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">p</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="p">}</span>
<a id="__codelineno-37-22" name="__codelineno-37-22" href="#__codelineno-37-22"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">my_heap.java</span><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="cm">/* 元素入堆 */</span>
<a id="__codelineno-38-2" name="__codelineno-38-2" href="#__codelineno-38-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-38-3" name="__codelineno-38-3" href="#__codelineno-38-3"></a><span class="w"> </span><span class="c1">// 添加节点</span>
<a id="__codelineno-38-4" name="__codelineno-38-4" href="#__codelineno-38-4"></a><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
<a id="__codelineno-38-5" name="__codelineno-38-5" href="#__codelineno-38-5"></a><span class="w"> </span><span class="c1">// 从底至顶堆化</span>
<a id="__codelineno-38-6" name="__codelineno-38-6" href="#__codelineno-38-6"></a><span class="w"> </span><span class="n">siftUp</span><span class="p">(</span><span class="n">size</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-38-7" name="__codelineno-38-7" href="#__codelineno-38-7"></a><span class="p">}</span>
<a id="__codelineno-38-8" name="__codelineno-38-8" href="#__codelineno-38-8"></a>
<a id="__codelineno-38-9" name="__codelineno-38-9" href="#__codelineno-38-9"></a><span class="cm">/* 从节点 i 开始，从底至顶堆化 */</span>
<a id="__codelineno-38-10" name="__codelineno-38-10" href="#__codelineno-38-10"></a><span class="kt">void</span><span class="w"> </span><span class="nf">siftUp</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-38-11" name="__codelineno-38-11" href="#__codelineno-38-11"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="kc">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-38-12" name="__codelineno-38-12" href="#__codelineno-38-12"></a><span class="w"> </span><span class="c1">// 获取节点 i 的父节点</span>
<a id="__codelineno-38-13" name="__codelineno-38-13" href="#__codelineno-38-13"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">p</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">parent</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
<a id="__codelineno-38-14" name="__codelineno-38-14" href="#__codelineno-38-14"></a><span class="w"> </span><span class="c1">// 当“越过根节点”或“节点无须修复”时，结束堆化</span>
<a id="__codelineno-38-15" name="__codelineno-38-15" href="#__codelineno-38-15"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">p</span><span class="w"> </span><span class="o">&lt;</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">maxHeap</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">p</span><span class="p">))</span>
<a id="__codelineno-38-16" name="__codelineno-38-16" href="#__codelineno-38-16"></a><span class="w"> </span><span class="k">break</span><span class="p">;</span>
<a id="__codelineno-38-17" name="__codelineno-38-17" href="#__codelineno-38-17"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
<a id="__codelineno-38-18" name="__codelineno-38-18" href="#__codelineno-38-18"></a><span class="w"> </span><span class="n">swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">p</span><span class="p">);</span>
<a id="__codelineno-38-19" name="__codelineno-38-19" href="#__codelineno-38-19"></a><span class="w"> </span><span class="c1">// 循环向上堆化</span>
<a id="__codelineno-38-20" name="__codelineno-38-20" href="#__codelineno-38-20"></a><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">p</span><span class="p">;</span>
<a id="__codelineno-38-21" name="__codelineno-38-21" href="#__codelineno-38-21"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-38-22" name="__codelineno-38-22" href="#__codelineno-38-22"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">my_heap.cs</span><pre><span></span><code><a id="__codelineno-39-1" name="__codelineno-39-1" href="#__codelineno-39-1"></a><span class="cm">/* 元素入堆 */</span>
<a id="__codelineno-39-2" name="__codelineno-39-2" href="#__codelineno-39-2"></a><span class="k">void</span><span class="w"> </span><span class="nf">Push</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-39-3" name="__codelineno-39-3" href="#__codelineno-39-3"></a><span class="w"> </span><span class="c1">// 添加节点</span>
<a id="__codelineno-39-4" name="__codelineno-39-4" href="#__codelineno-39-4"></a><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
<a id="__codelineno-39-5" name="__codelineno-39-5" href="#__codelineno-39-5"></a><span class="w"> </span><span class="c1">// 从底至顶堆化</span>
<a id="__codelineno-39-6" name="__codelineno-39-6" href="#__codelineno-39-6"></a><span class="w"> </span><span class="n">SiftUp</span><span class="p">(</span><span class="n">Size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">);</span>
<a id="__codelineno-39-7" name="__codelineno-39-7" href="#__codelineno-39-7"></a><span class="p">}</span>
<a id="__codelineno-39-8" name="__codelineno-39-8" href="#__codelineno-39-8"></a>
<a id="__codelineno-39-9" name="__codelineno-39-9" href="#__codelineno-39-9"></a><span class="cm">/* 从节点 i 开始，从底至顶堆化 */</span>
<a id="__codelineno-39-10" name="__codelineno-39-10" href="#__codelineno-39-10"></a><span class="k">void</span><span class="w"> </span><span class="nf">SiftUp</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-39-11" name="__codelineno-39-11" href="#__codelineno-39-11"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="k">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-39-12" name="__codelineno-39-12" href="#__codelineno-39-12"></a><span class="w"> </span><span class="c1">// 获取节点 i 的父节点</span>
<a id="__codelineno-39-13" name="__codelineno-39-13" href="#__codelineno-39-13"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">p</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Parent</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
<a id="__codelineno-39-14" name="__codelineno-39-14" href="#__codelineno-39-14"></a><span class="w"> </span><span class="c1">// 若“越过根节点”或“节点无须修复”，则结束堆化</span>
<a id="__codelineno-39-15" name="__codelineno-39-15" href="#__codelineno-39-15"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">p</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">p</span><span class="p">])</span>
<a id="__codelineno-39-16" name="__codelineno-39-16" href="#__codelineno-39-16"></a><span class="w"> </span><span class="k">break</span><span class="p">;</span>
<a id="__codelineno-39-17" name="__codelineno-39-17" href="#__codelineno-39-17"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
<a id="__codelineno-39-18" name="__codelineno-39-18" href="#__codelineno-39-18"></a><span class="w"> </span><span class="n">Swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">p</span><span class="p">);</span>
<a id="__codelineno-39-19" name="__codelineno-39-19" href="#__codelineno-39-19"></a><span class="w"> </span><span class="c1">// 循环向上堆化</span>
<a id="__codelineno-39-20" name="__codelineno-39-20" href="#__codelineno-39-20"></a><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">p</span><span class="p">;</span>
<a id="__codelineno-39-21" name="__codelineno-39-21" href="#__codelineno-39-21"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-39-22" name="__codelineno-39-22" href="#__codelineno-39-22"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">my_heap.go</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="cm">/* 元素入堆 */</span>
<a id="__codelineno-40-2" name="__codelineno-40-2" href="#__codelineno-40-2"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="nx">push</span><span class="p">(</span><span class="nx">val</span><span class="w"> </span><span class="kt">any</span><span class="p">)</span><span class="w"> </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">// 添加节点</span>
<a id="__codelineno-40-4" name="__codelineno-40-4" href="#__codelineno-40-4"></a><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">)</span>
<a id="__codelineno-40-5" name="__codelineno-40-5" href="#__codelineno-40-5"></a><span class="w"> </span><span class="c1">// 从底至顶堆化</span>
<a id="__codelineno-40-6" name="__codelineno-40-6" href="#__codelineno-40-6"></a><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">siftUp</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="nx">h</span><span class="p">.</span><span class="nx">data</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-40-7" name="__codelineno-40-7" href="#__codelineno-40-7"></a><span class="p">}</span>
<a id="__codelineno-40-8" name="__codelineno-40-8" href="#__codelineno-40-8"></a>
<a id="__codelineno-40-9" name="__codelineno-40-9" href="#__codelineno-40-9"></a><span class="cm">/* 从节点 i 开始，从底至顶堆化 */</span>
<a id="__codelineno-40-10" name="__codelineno-40-10" href="#__codelineno-40-10"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="nx">siftUp</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="kt">int</span><span class="p">)</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="k">for</span><span class="w"> </span><span class="kc">true</span><span class="w"> </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="c1">// 获取节点 i 的父节点</span>
<a id="__codelineno-40-13" name="__codelineno-40-13" href="#__codelineno-40-13"></a><span class="w"> </span><span class="nx">p</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">parent</span><span class="p">(</span><span class="nx">i</span><span class="p">)</span>
<a id="__codelineno-40-14" name="__codelineno-40-14" href="#__codelineno-40-14"></a><span class="w"> </span><span class="c1">// 当“越过根节点”或“节点无须修复”时，结束堆化</span>
<a id="__codelineno-40-15" name="__codelineno-40-15" href="#__codelineno-40-15"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">p</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="p">[</span><span class="nx">i</span><span class="p">].(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="p">[</span><span class="nx">p</span><span class="p">].(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </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="k">break</span>
<a id="__codelineno-40-17" name="__codelineno-40-17" href="#__codelineno-40-17"></a><span class="w"> </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="c1">// 交换两节点</span>
<a id="__codelineno-40-19" name="__codelineno-40-19" href="#__codelineno-40-19"></a><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">swap</span><span class="p">(</span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">p</span><span class="p">)</span>
<a id="__codelineno-40-20" name="__codelineno-40-20" href="#__codelineno-40-20"></a><span class="w"> </span><span class="c1">// 循环向上堆化</span>
<a id="__codelineno-40-21" name="__codelineno-40-21" href="#__codelineno-40-21"></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">p</span>
<a id="__codelineno-40-22" name="__codelineno-40-22" href="#__codelineno-40-22"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-40-23" name="__codelineno-40-23" href="#__codelineno-40-23"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">my_heap.swift</span><pre><span></span><code><a id="__codelineno-41-1" name="__codelineno-41-1" href="#__codelineno-41-1"></a><span class="cm">/* 元素入堆 */</span>
<a id="__codelineno-41-2" name="__codelineno-41-2" href="#__codelineno-41-2"></a><span class="kd">func</span> <span class="nf">push</span><span class="p">(</span><span class="n">val</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">{</span>
<a id="__codelineno-41-3" name="__codelineno-41-3" href="#__codelineno-41-3"></a> <span class="c1">// 添加节点</span>
<a id="__codelineno-41-4" name="__codelineno-41-4" href="#__codelineno-41-4"></a> <span class="n">maxHeap</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">val</span><span class="p">)</span>
<a id="__codelineno-41-5" name="__codelineno-41-5" href="#__codelineno-41-5"></a> <span class="c1">// 从底至顶堆化</span>
<a id="__codelineno-41-6" name="__codelineno-41-6" href="#__codelineno-41-6"></a> <span class="n">siftUp</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="n">size</span><span class="p">()</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
<a id="__codelineno-41-7" name="__codelineno-41-7" href="#__codelineno-41-7"></a><span class="p">}</span>
<a id="__codelineno-41-8" name="__codelineno-41-8" href="#__codelineno-41-8"></a>
<a id="__codelineno-41-9" name="__codelineno-41-9" href="#__codelineno-41-9"></a><span class="cm">/* 从节点 i 开始，从底至顶堆化 */</span>
<a id="__codelineno-41-10" name="__codelineno-41-10" href="#__codelineno-41-10"></a><span class="kd">func</span> <span class="nf">siftUp</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">{</span>
<a id="__codelineno-41-11" name="__codelineno-41-11" href="#__codelineno-41-11"></a> <span class="kd">var</span> <span class="nv">i</span> <span class="p">=</span> <span class="n">i</span>
<a id="__codelineno-41-12" name="__codelineno-41-12" href="#__codelineno-41-12"></a> <span class="k">while</span> <span class="kc">true</span> <span class="p">{</span>
<a id="__codelineno-41-13" name="__codelineno-41-13" href="#__codelineno-41-13"></a> <span class="c1">// 获取节点 i 的父节点</span>
<a id="__codelineno-41-14" name="__codelineno-41-14" href="#__codelineno-41-14"></a> <span class="kd">let</span> <span class="nv">p</span> <span class="p">=</span> <span class="n">parent</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="n">i</span><span class="p">)</span>
<a id="__codelineno-41-15" name="__codelineno-41-15" href="#__codelineno-41-15"></a> <span class="c1">// 当“越过根节点”或“节点无须修复”时，结束堆化</span>
<a id="__codelineno-41-16" name="__codelineno-41-16" href="#__codelineno-41-16"></a> <span class="k">if</span> <span class="n">p</span> <span class="o">&lt;</span> <span class="mi">0</span> <span class="o">||</span> <span class="n">maxHeap</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">&lt;=</span> <span class="n">maxHeap</span><span class="p">[</span><span class="n">p</span><span class="p">]</span> <span class="p">{</span>
<a id="__codelineno-41-17" name="__codelineno-41-17" href="#__codelineno-41-17"></a> <span class="k">break</span>
<a id="__codelineno-41-18" name="__codelineno-41-18" href="#__codelineno-41-18"></a> <span class="p">}</span>
<a id="__codelineno-41-19" name="__codelineno-41-19" href="#__codelineno-41-19"></a> <span class="c1">// 交换两节点</span>
<a id="__codelineno-41-20" name="__codelineno-41-20" href="#__codelineno-41-20"></a> <span class="bp">swap</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">:</span> <span class="n">p</span><span class="p">)</span>
<a id="__codelineno-41-21" name="__codelineno-41-21" href="#__codelineno-41-21"></a> <span class="c1">// 循环向上堆化</span>
<a id="__codelineno-41-22" name="__codelineno-41-22" href="#__codelineno-41-22"></a> <span class="n">i</span> <span class="p">=</span> <span class="n">p</span>
<a id="__codelineno-41-23" name="__codelineno-41-23" href="#__codelineno-41-23"></a> <span class="p">}</span>
<a id="__codelineno-41-24" name="__codelineno-41-24" href="#__codelineno-41-24"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">my_heap.js</span><pre><span></span><code><a id="__codelineno-42-1" name="__codelineno-42-1" href="#__codelineno-42-1"></a><span class="cm">/* 元素入堆 */</span>
<a id="__codelineno-42-2" name="__codelineno-42-2" href="#__codelineno-42-2"></a><span class="nx">push</span><span class="p">(</span><span class="nx">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-42-3" name="__codelineno-42-3" href="#__codelineno-42-3"></a><span class="w"> </span><span class="c1">// 添加节点</span>
<a id="__codelineno-42-4" name="__codelineno-42-4" href="#__codelineno-42-4"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">maxHeap</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">val</span><span class="p">);</span>
<a id="__codelineno-42-5" name="__codelineno-42-5" href="#__codelineno-42-5"></a><span class="w"> </span><span class="c1">// 从底至顶堆化</span>
<a id="__codelineno-42-6" name="__codelineno-42-6" href="#__codelineno-42-6"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">siftUp</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
<a id="__codelineno-42-7" name="__codelineno-42-7" href="#__codelineno-42-7"></a><span class="p">}</span>
<a id="__codelineno-42-8" name="__codelineno-42-8" href="#__codelineno-42-8"></a>
<a id="__codelineno-42-9" name="__codelineno-42-9" href="#__codelineno-42-9"></a><span class="cm">/* 从节点 i 开始，从底至顶堆化 */</span>
<a id="__codelineno-42-10" name="__codelineno-42-10" href="#__codelineno-42-10"></a><span class="err">#</span><span class="nx">siftUp</span><span class="p">(</span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-42-11" name="__codelineno-42-11" href="#__codelineno-42-11"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="kc">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-42-12" name="__codelineno-42-12" href="#__codelineno-42-12"></a><span class="w"> </span><span class="c1">// 获取节点 i 的父节点</span>
<a id="__codelineno-42-13" name="__codelineno-42-13" href="#__codelineno-42-13"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">p</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">parent</span><span class="p">(</span><span class="nx">i</span><span class="p">);</span>
<a id="__codelineno-42-14" name="__codelineno-42-14" href="#__codelineno-42-14"></a><span class="w"> </span><span class="c1">// 当“越过根节点”或“节点无须修复”时，结束堆化</span>
<a id="__codelineno-42-15" name="__codelineno-42-15" href="#__codelineno-42-15"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">p</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">maxHeap</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">maxHeap</span><span class="p">[</span><span class="nx">p</span><span class="p">])</span><span class="w"> </span><span class="k">break</span><span class="p">;</span>
<a id="__codelineno-42-16" name="__codelineno-42-16" href="#__codelineno-42-16"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
<a id="__codelineno-42-17" name="__codelineno-42-17" href="#__codelineno-42-17"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">swap</span><span class="p">(</span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">p</span><span class="p">);</span>
<a id="__codelineno-42-18" name="__codelineno-42-18" href="#__codelineno-42-18"></a><span class="w"> </span><span class="c1">// 循环向上堆化</span>
<a id="__codelineno-42-19" name="__codelineno-42-19" href="#__codelineno-42-19"></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">p</span><span class="p">;</span>
<a id="__codelineno-42-20" name="__codelineno-42-20" href="#__codelineno-42-20"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-42-21" name="__codelineno-42-21" href="#__codelineno-42-21"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">my_heap.ts</span><pre><span></span><code><a id="__codelineno-43-1" name="__codelineno-43-1" href="#__codelineno-43-1"></a><span class="cm">/* 元素入堆 */</span>
<a id="__codelineno-43-2" name="__codelineno-43-2" href="#__codelineno-43-2"></a><span class="nx">push</span><span class="p">(</span><span class="nx">val</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-43-3" name="__codelineno-43-3" href="#__codelineno-43-3"></a><span class="w"> </span><span class="c1">// 添加节点</span>
<a id="__codelineno-43-4" name="__codelineno-43-4" href="#__codelineno-43-4"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">maxHeap</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">val</span><span class="p">);</span>
<a id="__codelineno-43-5" name="__codelineno-43-5" href="#__codelineno-43-5"></a><span class="w"> </span><span class="c1">// 从底至顶堆化</span>
<a id="__codelineno-43-6" name="__codelineno-43-6" href="#__codelineno-43-6"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">siftUp</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
<a id="__codelineno-43-7" name="__codelineno-43-7" href="#__codelineno-43-7"></a><span class="p">}</span>
<a id="__codelineno-43-8" name="__codelineno-43-8" href="#__codelineno-43-8"></a>
<a id="__codelineno-43-9" name="__codelineno-43-9" href="#__codelineno-43-9"></a><span class="cm">/* 从节点 i 开始，从底至顶堆化 */</span>
<a id="__codelineno-43-10" name="__codelineno-43-10" href="#__codelineno-43-10"></a><span class="nx">siftUp</span><span class="p">(</span><span class="nx">i</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-43-11" name="__codelineno-43-11" href="#__codelineno-43-11"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="kc">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-43-12" name="__codelineno-43-12" href="#__codelineno-43-12"></a><span class="w"> </span><span class="c1">// 获取节点 i 的父节点</span>
<a id="__codelineno-43-13" name="__codelineno-43-13" href="#__codelineno-43-13"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">p</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">parent</span><span class="p">(</span><span class="nx">i</span><span class="p">);</span>
<a id="__codelineno-43-14" name="__codelineno-43-14" href="#__codelineno-43-14"></a><span class="w"> </span><span class="c1">// 当“越过根节点”或“节点无须修复”时，结束堆化</span>
<a id="__codelineno-43-15" name="__codelineno-43-15" href="#__codelineno-43-15"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">p</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">maxHeap</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">maxHeap</span><span class="p">[</span><span class="nx">p</span><span class="p">])</span><span class="w"> </span><span class="k">break</span><span class="p">;</span>
<a id="__codelineno-43-16" name="__codelineno-43-16" href="#__codelineno-43-16"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
<a id="__codelineno-43-17" name="__codelineno-43-17" href="#__codelineno-43-17"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">swap</span><span class="p">(</span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">p</span><span class="p">);</span>
<a id="__codelineno-43-18" name="__codelineno-43-18" href="#__codelineno-43-18"></a><span class="w"> </span><span class="c1">// 循环向上堆化</span>
<a id="__codelineno-43-19" name="__codelineno-43-19" href="#__codelineno-43-19"></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">p</span><span class="p">;</span>
<a id="__codelineno-43-20" name="__codelineno-43-20" href="#__codelineno-43-20"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-43-21" name="__codelineno-43-21" href="#__codelineno-43-21"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">my_heap.dart</span><pre><span></span><code><a id="__codelineno-44-1" name="__codelineno-44-1" href="#__codelineno-44-1"></a><span class="cm">/* 元素入堆 */</span>
<a id="__codelineno-44-2" name="__codelineno-44-2" href="#__codelineno-44-2"></a><span class="kt">void</span><span class="w"> </span><span class="n">push</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-44-3" name="__codelineno-44-3" href="#__codelineno-44-3"></a><span class="w"> </span><span class="c1">// 添加节点</span>
<a id="__codelineno-44-4" name="__codelineno-44-4" href="#__codelineno-44-4"></a><span class="w"> </span><span class="n">_maxHeap</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
<a id="__codelineno-44-5" name="__codelineno-44-5" href="#__codelineno-44-5"></a><span class="w"> </span><span class="c1">// 从底至顶堆化</span>
<a id="__codelineno-44-6" name="__codelineno-44-6" href="#__codelineno-44-6"></a><span class="w"> </span><span class="n">siftUp</span><span class="p">(</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">);</span>
<a id="__codelineno-44-7" name="__codelineno-44-7" href="#__codelineno-44-7"></a><span class="p">}</span>
<a id="__codelineno-44-8" name="__codelineno-44-8" href="#__codelineno-44-8"></a>
<a id="__codelineno-44-9" name="__codelineno-44-9" href="#__codelineno-44-9"></a><span class="cm">/* 从节点 i 开始，从底至顶堆化 */</span>
<a id="__codelineno-44-10" name="__codelineno-44-10" href="#__codelineno-44-10"></a><span class="kt">void</span><span class="w"> </span><span class="n">siftUp</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-44-11" name="__codelineno-44-11" href="#__codelineno-44-11"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="kc">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-44-12" name="__codelineno-44-12" href="#__codelineno-44-12"></a><span class="w"> </span><span class="c1">// 获取节点 i 的父节点</span>
<a id="__codelineno-44-13" name="__codelineno-44-13" href="#__codelineno-44-13"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">p</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_parent</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
<a id="__codelineno-44-14" name="__codelineno-44-14" href="#__codelineno-44-14"></a><span class="w"> </span><span class="c1">// 当“越过根节点”或“节点无须修复”时，结束堆化</span>
<a id="__codelineno-44-15" name="__codelineno-44-15" href="#__codelineno-44-15"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">p</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">_maxHeap</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">_maxHeap</span><span class="p">[</span><span class="n">p</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-44-16" name="__codelineno-44-16" href="#__codelineno-44-16"></a><span class="w"> </span><span class="k">break</span><span class="p">;</span>
<a id="__codelineno-44-17" name="__codelineno-44-17" href="#__codelineno-44-17"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-44-18" name="__codelineno-44-18" href="#__codelineno-44-18"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
<a id="__codelineno-44-19" name="__codelineno-44-19" href="#__codelineno-44-19"></a><span class="w"> </span><span class="n">_swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">p</span><span class="p">);</span>
<a id="__codelineno-44-20" name="__codelineno-44-20" href="#__codelineno-44-20"></a><span class="w"> </span><span class="c1">// 循环向上堆化</span>
<a id="__codelineno-44-21" name="__codelineno-44-21" href="#__codelineno-44-21"></a><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">p</span><span class="p">;</span>
<a id="__codelineno-44-22" name="__codelineno-44-22" href="#__codelineno-44-22"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-44-23" name="__codelineno-44-23" href="#__codelineno-44-23"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">my_heap.rs</span><pre><span></span><code><a id="__codelineno-45-1" name="__codelineno-45-1" href="#__codelineno-45-1"></a><span class="cm">/* 元素入堆 */</span>
<a id="__codelineno-45-2" name="__codelineno-45-2" href="#__codelineno-45-2"></a><span class="k">fn</span> <span class="nf">push</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">val</span>: <span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-45-3" name="__codelineno-45-3" href="#__codelineno-45-3"></a><span class="w"> </span><span class="c1">// 添加节点</span>
<a id="__codelineno-45-4" name="__codelineno-45-4" href="#__codelineno-45-4"></a><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
<a id="__codelineno-45-5" name="__codelineno-45-5" href="#__codelineno-45-5"></a><span class="w"> </span><span class="c1">// 从底至顶堆化</span>
<a id="__codelineno-45-6" name="__codelineno-45-6" href="#__codelineno-45-6"></a><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">sift_up</span><span class="p">(</span><span class="bp">self</span><span class="p">.</span><span class="n">size</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-45-7" name="__codelineno-45-7" href="#__codelineno-45-7"></a><span class="p">}</span>
<a id="__codelineno-45-8" name="__codelineno-45-8" href="#__codelineno-45-8"></a>
<a id="__codelineno-45-9" name="__codelineno-45-9" href="#__codelineno-45-9"></a><span class="cm">/* 从节点 i 开始，从底至顶堆化 */</span>
<a id="__codelineno-45-10" name="__codelineno-45-10" href="#__codelineno-45-10"></a><span class="k">fn</span> <span class="nf">sift_up</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">i</span>: <span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-45-11" name="__codelineno-45-11" href="#__codelineno-45-11"></a><span class="w"> </span><span class="k">loop</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-45-12" name="__codelineno-45-12" href="#__codelineno-45-12"></a><span class="w"> </span><span class="c1">// 节点 i 已经是堆顶节点了，结束堆化</span>
<a id="__codelineno-45-13" name="__codelineno-45-13" href="#__codelineno-45-13"></a><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="p">{</span>
<a id="__codelineno-45-14" name="__codelineno-45-14" href="#__codelineno-45-14"></a><span class="w"> </span><span class="k">break</span><span class="p">;</span>
<a id="__codelineno-45-15" name="__codelineno-45-15" href="#__codelineno-45-15"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-45-16" name="__codelineno-45-16" href="#__codelineno-45-16"></a><span class="w"> </span><span class="c1">// 获取节点 i 的父节点</span>
<a id="__codelineno-45-17" name="__codelineno-45-17" href="#__codelineno-45-17"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">p</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">Self</span>::<span class="n">parent</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
<a id="__codelineno-45-18" name="__codelineno-45-18" href="#__codelineno-45-18"></a><span class="w"> </span><span class="c1">// 当“节点无须修复”时，结束堆化</span>
<a id="__codelineno-45-19" name="__codelineno-45-19" href="#__codelineno-45-19"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">[</span><span class="n">p</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-45-20" name="__codelineno-45-20" href="#__codelineno-45-20"></a><span class="w"> </span><span class="k">break</span><span class="p">;</span>
<a id="__codelineno-45-21" name="__codelineno-45-21" href="#__codelineno-45-21"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-45-22" name="__codelineno-45-22" href="#__codelineno-45-22"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
<a id="__codelineno-45-23" name="__codelineno-45-23" href="#__codelineno-45-23"></a><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">p</span><span class="p">);</span>
<a id="__codelineno-45-24" name="__codelineno-45-24" href="#__codelineno-45-24"></a><span class="w"> </span><span class="c1">// 循环向上堆化</span>
<a id="__codelineno-45-25" name="__codelineno-45-25" href="#__codelineno-45-25"></a><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">p</span><span class="p">;</span>
<a id="__codelineno-45-26" name="__codelineno-45-26" href="#__codelineno-45-26"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-45-27" name="__codelineno-45-27" href="#__codelineno-45-27"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">my_heap.c</span><pre><span></span><code><a id="__codelineno-46-1" name="__codelineno-46-1" href="#__codelineno-46-1"></a><span class="cm">/* 元素入堆 */</span>
<a id="__codelineno-46-2" name="__codelineno-46-2" href="#__codelineno-46-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="n">MaxHeap</span><span class="w"> </span><span class="o">*</span><span class="n">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-46-3" name="__codelineno-46-3" href="#__codelineno-46-3"></a><span class="w"> </span><span class="c1">// 默认情况下，不应该添加这么多节点</span>
<a id="__codelineno-46-4" name="__codelineno-46-4" href="#__codelineno-46-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">maxHeap</span><span class="o">-&gt;</span><span class="n">size</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">MAX_SIZE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-46-5" name="__codelineno-46-5" href="#__codelineno-46-5"></a><span class="w"> </span><span class="n">printf</span><span class="p">(</span><span class="s">&quot;heap is full!&quot;</span><span class="p">);</span>
<a id="__codelineno-46-6" name="__codelineno-46-6" href="#__codelineno-46-6"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
<a id="__codelineno-46-7" name="__codelineno-46-7" href="#__codelineno-46-7"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-46-8" name="__codelineno-46-8" href="#__codelineno-46-8"></a><span class="w"> </span><span class="c1">// 添加节点</span>
<a id="__codelineno-46-9" name="__codelineno-46-9" href="#__codelineno-46-9"></a><span class="w"> </span><span class="n">maxHeap</span><span class="o">-&gt;</span><span class="n">data</span><span class="p">[</span><span class="n">maxHeap</span><span class="o">-&gt;</span><span class="n">size</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
<a id="__codelineno-46-10" name="__codelineno-46-10" href="#__codelineno-46-10"></a><span class="w"> </span><span class="n">maxHeap</span><span class="o">-&gt;</span><span class="n">size</span><span class="o">++</span><span class="p">;</span>
<a id="__codelineno-46-11" name="__codelineno-46-11" href="#__codelineno-46-11"></a>
<a id="__codelineno-46-12" name="__codelineno-46-12" href="#__codelineno-46-12"></a><span class="w"> </span><span class="c1">// 从底至顶堆化</span>
<a id="__codelineno-46-13" name="__codelineno-46-13" href="#__codelineno-46-13"></a><span class="w"> </span><span class="n">siftUp</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="n">maxHeap</span><span class="o">-&gt;</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>
<a id="__codelineno-46-14" name="__codelineno-46-14" href="#__codelineno-46-14"></a><span class="p">}</span>
<a id="__codelineno-46-15" name="__codelineno-46-15" href="#__codelineno-46-15"></a>
<a id="__codelineno-46-16" name="__codelineno-46-16" href="#__codelineno-46-16"></a><span class="cm">/* 从节点 i 开始，从底至顶堆化 */</span>
<a id="__codelineno-46-17" name="__codelineno-46-17" href="#__codelineno-46-17"></a><span class="kt">void</span><span class="w"> </span><span class="nf">siftUp</span><span class="p">(</span><span class="n">MaxHeap</span><span class="w"> </span><span class="o">*</span><span class="n">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-46-18" name="__codelineno-46-18" href="#__codelineno-46-18"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nb">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-46-19" name="__codelineno-46-19" href="#__codelineno-46-19"></a><span class="w"> </span><span class="c1">// 获取节点 i 的父节点</span>
<a id="__codelineno-46-20" name="__codelineno-46-20" href="#__codelineno-46-20"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">p</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">parent</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
<a id="__codelineno-46-21" name="__codelineno-46-21" href="#__codelineno-46-21"></a><span class="w"> </span><span class="c1">// 当“越过根节点”或“节点无须修复”时，结束堆化</span>
<a id="__codelineno-46-22" name="__codelineno-46-22" href="#__codelineno-46-22"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">p</span><span class="w"> </span><span class="o">&lt;</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">maxHeap</span><span class="o">-&gt;</span><span class="n">data</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">maxHeap</span><span class="o">-&gt;</span><span class="n">data</span><span class="p">[</span><span class="n">p</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-46-23" name="__codelineno-46-23" href="#__codelineno-46-23"></a><span class="w"> </span><span class="k">break</span><span class="p">;</span>
<a id="__codelineno-46-24" name="__codelineno-46-24" href="#__codelineno-46-24"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-46-25" name="__codelineno-46-25" href="#__codelineno-46-25"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
<a id="__codelineno-46-26" name="__codelineno-46-26" href="#__codelineno-46-26"></a><span class="w"> </span><span class="n">swap</span><span class="p">(</span><span class="n">maxHeap</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">p</span><span class="p">);</span>
<a id="__codelineno-46-27" name="__codelineno-46-27" href="#__codelineno-46-27"></a><span class="w"> </span><span class="c1">// 循环向上堆化</span>
<a id="__codelineno-46-28" name="__codelineno-46-28" href="#__codelineno-46-28"></a><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">p</span><span class="p">;</span>
<a id="__codelineno-46-29" name="__codelineno-46-29" href="#__codelineno-46-29"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-46-30" name="__codelineno-46-30" href="#__codelineno-46-30"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">my_heap.zig</span><pre><span></span><code><a id="__codelineno-47-1" name="__codelineno-47-1" href="#__codelineno-47-1"></a><span class="c1">// 元素入堆</span>
<a id="__codelineno-47-2" name="__codelineno-47-2" href="#__codelineno-47-2"></a><span class="k">fn</span><span class="w"> </span><span class="n">push</span><span class="p">(</span><span class="n">self</span><span class="o">:</span><span class="w"> </span><span class="o">*</span><span class="n">Self</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="o">:</span><span class="w"> </span><span class="n">T</span><span class="p">)</span><span class="w"> </span><span class="o">!</span><span class="kt">void</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-47-3" name="__codelineno-47-3" href="#__codelineno-47-3"></a><span class="w"> </span><span class="c1">// 添加节点</span>
<a id="__codelineno-47-4" name="__codelineno-47-4" href="#__codelineno-47-4"></a><span class="w"> </span><span class="k">try</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
<a id="__codelineno-47-5" name="__codelineno-47-5" href="#__codelineno-47-5"></a><span class="w"> </span><span class="c1">// 从底至顶堆化</span>
<a id="__codelineno-47-6" name="__codelineno-47-6" href="#__codelineno-47-6"></a><span class="w"> </span><span class="k">try</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">siftUp</span><span class="p">(</span><span class="n">self</span><span class="p">.</span><span class="n">size</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-47-7" name="__codelineno-47-7" href="#__codelineno-47-7"></a><span class="p">}</span><span class="w"> </span>
<a id="__codelineno-47-8" name="__codelineno-47-8" href="#__codelineno-47-8"></a>
<a id="__codelineno-47-9" name="__codelineno-47-9" href="#__codelineno-47-9"></a><span class="c1">// 从节点 i 开始，从底至顶堆化</span>
<a id="__codelineno-47-10" name="__codelineno-47-10" href="#__codelineno-47-10"></a><span class="k">fn</span><span class="w"> </span><span class="n">siftUp</span><span class="p">(</span><span class="n">self</span><span class="o">:</span><span class="w"> </span><span class="o">*</span><span class="n">Self</span><span class="p">,</span><span class="w"> </span><span class="n">i_</span><span class="o">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="o">!</span><span class="kt">void</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-47-11" name="__codelineno-47-11" href="#__codelineno-47-11"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i_</span><span class="p">;</span>
<a id="__codelineno-47-12" name="__codelineno-47-12" href="#__codelineno-47-12"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="kc">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-47-13" name="__codelineno-47-13" href="#__codelineno-47-13"></a><span class="w"> </span><span class="c1">// 获取节点 i 的父节点</span>
<a id="__codelineno-47-14" name="__codelineno-47-14" href="#__codelineno-47-14"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">p</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">parent</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
<a id="__codelineno-47-15" name="__codelineno-47-15" href="#__codelineno-47-15"></a><span class="w"> </span><span class="c1">// 当“越过根节点”或“节点无须修复”时，结束堆化</span>
<a id="__codelineno-47-16" name="__codelineno-47-16" href="#__codelineno-47-16"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">p</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="k">or</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">items</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">items</span><span class="p">[</span><span class="n">p</span><span class="p">])</span><span class="w"> </span><span class="k">break</span><span class="p">;</span>
<a id="__codelineno-47-17" name="__codelineno-47-17" href="#__codelineno-47-17"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
<a id="__codelineno-47-18" name="__codelineno-47-18" href="#__codelineno-47-18"></a><span class="w"> </span><span class="k">try</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">p</span><span class="p">);</span>
<a id="__codelineno-47-19" name="__codelineno-47-19" href="#__codelineno-47-19"></a><span class="w"> </span><span class="c1">// 循环向上堆化</span>
<a id="__codelineno-47-20" name="__codelineno-47-20" href="#__codelineno-47-20"></a><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">p</span><span class="p">;</span>
<a id="__codelineno-47-21" name="__codelineno-47-21" href="#__codelineno-47-21"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-47-22" name="__codelineno-47-22" href="#__codelineno-47-22"></a><span class="p">}</span>
</code></pre></div>
</div>
</div>
</div>
<details class="pythontutor">
<summary>可视化运行</summary>
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</details>
<h3 id="4">4. &nbsp; 堆顶元素出堆<a class="headerlink" href="#4" title="Permanent link">&para;</a></h3>
<p>堆顶元素是二叉树的根节点，即列表首元素。如果我们直接从列表中删除首元素，那么二叉树中所有节点的索引都会发生变化，这将使得后续使用堆化进行修复变得困难。为了尽量减少元素索引的变动，我们采用以下操作步骤。</p>
<ol>
<li>交换堆顶元素与堆底元素（交换根节点与最右叶节点）。</li>
<li>交换完成后，将堆底从列表中删除（注意，由于已经交换，因此实际上删除的是原来的堆顶元素）。</li>
<li>从根节点开始，<strong>从顶至底执行堆化</strong>。</li>
</ol>
<p>如图 8-4 所示，<strong>“从顶至底堆化”的操作方向与“从底至顶堆化”相反</strong>，我们将根节点的值与其两个子节点的值进行比较，将最大的子节点与根节点交换。然后循环执行此操作，直到越过叶节点或遇到无须交换的节点时结束。</p>
<div class="tabbed-set tabbed-alternate" data-tabs="6:10"><input checked="checked" id="__tabbed_6_1" name="__tabbed_6" type="radio" /><input id="__tabbed_6_2" name="__tabbed_6" type="radio" /><input id="__tabbed_6_3" name="__tabbed_6" type="radio" /><input id="__tabbed_6_4" name="__tabbed_6" type="radio" /><input id="__tabbed_6_5" name="__tabbed_6" type="radio" /><input id="__tabbed_6_6" name="__tabbed_6" type="radio" /><input id="__tabbed_6_7" name="__tabbed_6" type="radio" /><input id="__tabbed_6_8" name="__tabbed_6" type="radio" /><input id="__tabbed_6_9" name="__tabbed_6" type="radio" /><input id="__tabbed_6_10" name="__tabbed_6" type="radio" /><div class="tabbed-labels"><label for="__tabbed_6_1">&lt;1&gt;</label><label for="__tabbed_6_2">&lt;2&gt;</label><label for="__tabbed_6_3">&lt;3&gt;</label><label for="__tabbed_6_4">&lt;4&gt;</label><label for="__tabbed_6_5">&lt;5&gt;</label><label for="__tabbed_6_6">&lt;6&gt;</label><label for="__tabbed_6_7">&lt;7&gt;</label><label for="__tabbed_6_8">&lt;8&gt;</label><label for="__tabbed_6_9">&lt;9&gt;</label><label for="__tabbed_6_10">&lt;10&gt;</label></div>
<div class="tabbed-content">
<div class="tabbed-block">
<p><a class="glightbox" href="../heap.assets/heap_pop_step1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="堆顶元素出堆步骤" class="animation-figure" src="../heap.assets/heap_pop_step1.png" /></a></p>
</div>
<div class="tabbed-block">
<p><a class="glightbox" href="../heap.assets/heap_pop_step2.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_pop_step2" class="animation-figure" src="../heap.assets/heap_pop_step2.png" /></a></p>
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<div class="tabbed-block">
<p><a class="glightbox" href="../heap.assets/heap_pop_step3.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_pop_step3" class="animation-figure" src="../heap.assets/heap_pop_step3.png" /></a></p>
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<p><a class="glightbox" href="../heap.assets/heap_pop_step4.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_pop_step4" class="animation-figure" src="../heap.assets/heap_pop_step4.png" /></a></p>
</div>
<div class="tabbed-block">
<p><a class="glightbox" href="../heap.assets/heap_pop_step5.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_pop_step5" class="animation-figure" src="../heap.assets/heap_pop_step5.png" /></a></p>
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<div class="tabbed-block">
<p><a class="glightbox" href="../heap.assets/heap_pop_step6.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_pop_step6" class="animation-figure" src="../heap.assets/heap_pop_step6.png" /></a></p>
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<div class="tabbed-block">
<p><a class="glightbox" href="../heap.assets/heap_pop_step7.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_pop_step7" class="animation-figure" src="../heap.assets/heap_pop_step7.png" /></a></p>
</div>
<div class="tabbed-block">
<p><a class="glightbox" href="../heap.assets/heap_pop_step8.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_pop_step8" class="animation-figure" src="../heap.assets/heap_pop_step8.png" /></a></p>
</div>
<div class="tabbed-block">
<p><a class="glightbox" href="../heap.assets/heap_pop_step9.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_pop_step9" class="animation-figure" src="../heap.assets/heap_pop_step9.png" /></a></p>
</div>
<div class="tabbed-block">
<p><a class="glightbox" href="../heap.assets/heap_pop_step10.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_pop_step10" class="animation-figure" src="../heap.assets/heap_pop_step10.png" /></a></p>
</div>
</div>
</div>
<p align="center"> 图 8-4 &nbsp; 堆顶元素出堆步骤 </p>
<p>与元素入堆操作相似，堆顶元素出堆操作的时间复杂度也为 <span class="arithmatex">\(O(\log n)\)</span> 。代码如下所示：</p>
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<div class="highlight"><span class="filename">my_heap.py</span><pre><span></span><code><a id="__codelineno-48-1" name="__codelineno-48-1" href="#__codelineno-48-1"></a><span class="k">def</span> <span class="nf">pop</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
<a id="__codelineno-48-2" name="__codelineno-48-2" href="#__codelineno-48-2"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;元素出堆&quot;&quot;&quot;</span>
<a id="__codelineno-48-3" name="__codelineno-48-3" href="#__codelineno-48-3"></a> <span class="c1"># 判空处理</span>
<a id="__codelineno-48-4" name="__codelineno-48-4" href="#__codelineno-48-4"></a> <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">is_empty</span><span class="p">():</span>
<a id="__codelineno-48-5" name="__codelineno-48-5" href="#__codelineno-48-5"></a> <span class="k">raise</span> <span class="ne">IndexError</span><span class="p">(</span><span class="s2">&quot;堆为空&quot;</span><span class="p">)</span>
<a id="__codelineno-48-6" name="__codelineno-48-6" href="#__codelineno-48-6"></a> <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-48-7" name="__codelineno-48-7" href="#__codelineno-48-7"></a> <span class="bp">self</span><span class="o">.</span><span class="n">swap</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">()</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
<a id="__codelineno-48-8" name="__codelineno-48-8" href="#__codelineno-48-8"></a> <span class="c1"># 删除节点</span>
<a id="__codelineno-48-9" name="__codelineno-48-9" href="#__codelineno-48-9"></a> <span class="n">val</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">max_heap</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>
<a id="__codelineno-48-10" name="__codelineno-48-10" href="#__codelineno-48-10"></a> <span class="c1"># 从顶至底堆化</span>
<a id="__codelineno-48-11" name="__codelineno-48-11" href="#__codelineno-48-11"></a> <span class="bp">self</span><span class="o">.</span><span class="n">sift_down</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<a id="__codelineno-48-12" name="__codelineno-48-12" href="#__codelineno-48-12"></a> <span class="c1"># 返回堆顶元素</span>
<a id="__codelineno-48-13" name="__codelineno-48-13" href="#__codelineno-48-13"></a> <span class="k">return</span> <span class="n">val</span>
<a id="__codelineno-48-14" name="__codelineno-48-14" href="#__codelineno-48-14"></a>
<a id="__codelineno-48-15" name="__codelineno-48-15" href="#__codelineno-48-15"></a><span class="k">def</span> <span class="nf">sift_down</span><span class="p">(</span><span class="bp">self</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-48-16" name="__codelineno-48-16" href="#__codelineno-48-16"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;从节点 i 开始，从顶至底堆化&quot;&quot;&quot;</span>
<a id="__codelineno-48-17" name="__codelineno-48-17" href="#__codelineno-48-17"></a> <span class="k">while</span> <span class="kc">True</span><span class="p">:</span>
<a id="__codelineno-48-18" name="__codelineno-48-18" href="#__codelineno-48-18"></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-48-19" name="__codelineno-48-19" href="#__codelineno-48-19"></a> <span class="n">l</span><span class="p">,</span> <span class="n">r</span><span class="p">,</span> <span class="n">ma</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">left</span><span class="p">(</span><span class="n">i</span><span class="p">),</span> <span class="bp">self</span><span class="o">.</span><span class="n">right</span><span class="p">(</span><span class="n">i</span><span class="p">),</span> <span class="n">i</span>
<a id="__codelineno-48-20" name="__codelineno-48-20" href="#__codelineno-48-20"></a> <span class="k">if</span> <span class="n">l</span> <span class="o">&lt;</span> <span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">()</span> <span class="ow">and</span> <span class="bp">self</span><span class="o">.</span><span class="n">max_heap</span><span class="p">[</span><span class="n">l</span><span class="p">]</span> <span class="o">&gt;</span> <span class="bp">self</span><span class="o">.</span><span class="n">max_heap</span><span class="p">[</span><span class="n">ma</span><span class="p">]:</span>
<a id="__codelineno-48-21" name="__codelineno-48-21" href="#__codelineno-48-21"></a> <span class="n">ma</span> <span class="o">=</span> <span class="n">l</span>
<a id="__codelineno-48-22" name="__codelineno-48-22" href="#__codelineno-48-22"></a> <span class="k">if</span> <span class="n">r</span> <span class="o">&lt;</span> <span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">()</span> <span class="ow">and</span> <span class="bp">self</span><span class="o">.</span><span class="n">max_heap</span><span class="p">[</span><span class="n">r</span><span class="p">]</span> <span class="o">&gt;</span> <span class="bp">self</span><span class="o">.</span><span class="n">max_heap</span><span class="p">[</span><span class="n">ma</span><span class="p">]:</span>
<a id="__codelineno-48-23" name="__codelineno-48-23" href="#__codelineno-48-23"></a> <span class="n">ma</span> <span class="o">=</span> <span class="n">r</span>
<a id="__codelineno-48-24" name="__codelineno-48-24" href="#__codelineno-48-24"></a> <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-48-25" name="__codelineno-48-25" href="#__codelineno-48-25"></a> <span class="k">if</span> <span class="n">ma</span> <span class="o">==</span> <span class="n">i</span><span class="p">:</span>
<a id="__codelineno-48-26" name="__codelineno-48-26" href="#__codelineno-48-26"></a> <span class="k">break</span>
<a id="__codelineno-48-27" name="__codelineno-48-27" href="#__codelineno-48-27"></a> <span class="c1"># 交换两节点</span>
<a id="__codelineno-48-28" name="__codelineno-48-28" href="#__codelineno-48-28"></a> <span class="bp">self</span><span class="o">.</span><span class="n">swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span> <span class="n">ma</span><span class="p">)</span>
<a id="__codelineno-48-29" name="__codelineno-48-29" href="#__codelineno-48-29"></a> <span class="c1"># 循环向下堆化</span>
<a id="__codelineno-48-30" name="__codelineno-48-30" href="#__codelineno-48-30"></a> <span class="n">i</span> <span class="o">=</span> <span class="n">ma</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">my_heap.cpp</span><pre><span></span><code><a id="__codelineno-49-1" name="__codelineno-49-1" href="#__codelineno-49-1"></a><span class="cm">/* 元素出堆 */</span>
<a id="__codelineno-49-2" name="__codelineno-49-2" href="#__codelineno-49-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">pop</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-49-3" name="__codelineno-49-3" href="#__codelineno-49-3"></a><span class="w"> </span><span class="c1">// 判空处理</span>
<a id="__codelineno-49-4" name="__codelineno-49-4" href="#__codelineno-49-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-49-5" name="__codelineno-49-5" href="#__codelineno-49-5"></a><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="n">out_of_range</span><span class="p">(</span><span class="s">&quot;堆为空&quot;</span><span class="p">);</span>
<a id="__codelineno-49-6" name="__codelineno-49-6" href="#__codelineno-49-6"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-49-7" name="__codelineno-49-7" href="#__codelineno-49-7"></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-49-8" name="__codelineno-49-8" href="#__codelineno-49-8"></a><span class="w"> </span><span class="n">swap</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">size</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-49-9" name="__codelineno-49-9" href="#__codelineno-49-9"></a><span class="w"> </span><span class="c1">// 删除节点</span>
<a id="__codelineno-49-10" name="__codelineno-49-10" href="#__codelineno-49-10"></a><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">pop_back</span><span class="p">();</span>
<a id="__codelineno-49-11" name="__codelineno-49-11" href="#__codelineno-49-11"></a><span class="w"> </span><span class="c1">// 从顶至底堆化</span>
<a id="__codelineno-49-12" name="__codelineno-49-12" href="#__codelineno-49-12"></a><span class="w"> </span><span class="n">siftDown</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
<a id="__codelineno-49-13" name="__codelineno-49-13" href="#__codelineno-49-13"></a><span class="p">}</span>
<a id="__codelineno-49-14" name="__codelineno-49-14" href="#__codelineno-49-14"></a>
<a id="__codelineno-49-15" name="__codelineno-49-15" href="#__codelineno-49-15"></a><span class="cm">/* 从节点 i 开始，从顶至底堆化 */</span>
<a id="__codelineno-49-16" name="__codelineno-49-16" href="#__codelineno-49-16"></a><span class="kt">void</span><span class="w"> </span><span class="nf">siftDown</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-49-17" name="__codelineno-49-17" href="#__codelineno-49-17"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nb">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-49-18" name="__codelineno-49-18" href="#__codelineno-49-18"></a><span class="w"> </span><span class="c1">// 判断节点 i, l, r 中值最大的节点，记为 ma</span>
<a id="__codelineno-49-19" name="__codelineno-49-19" href="#__codelineno-49-19"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">right</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
<a id="__codelineno-49-20" name="__codelineno-49-20" href="#__codelineno-49-20"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">l</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">l</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">ma</span><span class="p">])</span>
<a id="__codelineno-49-21" name="__codelineno-49-21" href="#__codelineno-49-21"></a><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">l</span><span class="p">;</span>
<a id="__codelineno-49-22" name="__codelineno-49-22" href="#__codelineno-49-22"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">r</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">ma</span><span class="p">])</span>
<a id="__codelineno-49-23" name="__codelineno-49-23" href="#__codelineno-49-23"></a><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">r</span><span class="p">;</span>
<a id="__codelineno-49-24" name="__codelineno-49-24" href="#__codelineno-49-24"></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-49-25" name="__codelineno-49-25" href="#__codelineno-49-25"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">ma</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">i</span><span class="p">)</span>
<a id="__codelineno-49-26" name="__codelineno-49-26" href="#__codelineno-49-26"></a><span class="w"> </span><span class="k">break</span><span class="p">;</span>
<a id="__codelineno-49-27" name="__codelineno-49-27" href="#__codelineno-49-27"></a><span class="w"> </span><span class="n">swap</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">ma</span><span class="p">]);</span>
<a id="__codelineno-49-28" name="__codelineno-49-28" href="#__codelineno-49-28"></a><span class="w"> </span><span class="c1">// 循环向下堆化</span>
<a id="__codelineno-49-29" name="__codelineno-49-29" href="#__codelineno-49-29"></a><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ma</span><span class="p">;</span>
<a id="__codelineno-49-30" name="__codelineno-49-30" href="#__codelineno-49-30"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-49-31" name="__codelineno-49-31" href="#__codelineno-49-31"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">my_heap.java</span><pre><span></span><code><a id="__codelineno-50-1" name="__codelineno-50-1" href="#__codelineno-50-1"></a><span class="cm">/* 元素出堆 */</span>
<a id="__codelineno-50-2" name="__codelineno-50-2" href="#__codelineno-50-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">pop</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-50-3" name="__codelineno-50-3" href="#__codelineno-50-3"></a><span class="w"> </span><span class="c1">// 判空处理</span>
<a id="__codelineno-50-4" name="__codelineno-50-4" href="#__codelineno-50-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
<a id="__codelineno-50-5" name="__codelineno-50-5" href="#__codelineno-50-5"></a><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">();</span>
<a id="__codelineno-50-6" name="__codelineno-50-6" href="#__codelineno-50-6"></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-50-7" name="__codelineno-50-7" href="#__codelineno-50-7"></a><span class="w"> </span><span class="n">swap</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">size</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-50-8" name="__codelineno-50-8" href="#__codelineno-50-8"></a><span class="w"> </span><span class="c1">// 删除节点</span>
<a id="__codelineno-50-9" name="__codelineno-50-9" href="#__codelineno-50-9"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">remove</span><span class="p">(</span><span class="n">size</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-50-10" name="__codelineno-50-10" href="#__codelineno-50-10"></a><span class="w"> </span><span class="c1">// 从顶至底堆化</span>
<a id="__codelineno-50-11" name="__codelineno-50-11" href="#__codelineno-50-11"></a><span class="w"> </span><span class="n">siftDown</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
<a id="__codelineno-50-12" name="__codelineno-50-12" href="#__codelineno-50-12"></a><span class="w"> </span><span class="c1">// 返回堆顶元素</span>
<a id="__codelineno-50-13" name="__codelineno-50-13" href="#__codelineno-50-13"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
<a id="__codelineno-50-14" name="__codelineno-50-14" href="#__codelineno-50-14"></a><span class="p">}</span>
<a id="__codelineno-50-15" name="__codelineno-50-15" href="#__codelineno-50-15"></a>
<a id="__codelineno-50-16" name="__codelineno-50-16" href="#__codelineno-50-16"></a><span class="cm">/* 从节点 i 开始，从顶至底堆化 */</span>
<a id="__codelineno-50-17" name="__codelineno-50-17" href="#__codelineno-50-17"></a><span class="kt">void</span><span class="w"> </span><span class="nf">siftDown</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-50-18" name="__codelineno-50-18" href="#__codelineno-50-18"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="kc">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-50-19" name="__codelineno-50-19" href="#__codelineno-50-19"></a><span class="w"> </span><span class="c1">// 判断节点 i, l, r 中值最大的节点，记为 ma</span>
<a id="__codelineno-50-20" name="__codelineno-50-20" href="#__codelineno-50-20"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">right</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
<a id="__codelineno-50-21" name="__codelineno-50-21" href="#__codelineno-50-21"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">l</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">l</span><span class="p">)</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">ma</span><span class="p">))</span>
<a id="__codelineno-50-22" name="__codelineno-50-22" href="#__codelineno-50-22"></a><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">l</span><span class="p">;</span>
<a id="__codelineno-50-23" name="__codelineno-50-23" href="#__codelineno-50-23"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">r</span><span class="p">)</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">ma</span><span class="p">))</span>
<a id="__codelineno-50-24" name="__codelineno-50-24" href="#__codelineno-50-24"></a><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">r</span><span class="p">;</span>
<a id="__codelineno-50-25" name="__codelineno-50-25" href="#__codelineno-50-25"></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-50-26" name="__codelineno-50-26" href="#__codelineno-50-26"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">ma</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">i</span><span class="p">)</span>
<a id="__codelineno-50-27" name="__codelineno-50-27" href="#__codelineno-50-27"></a><span class="w"> </span><span class="k">break</span><span class="p">;</span>
<a id="__codelineno-50-28" name="__codelineno-50-28" href="#__codelineno-50-28"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
<a id="__codelineno-50-29" name="__codelineno-50-29" href="#__codelineno-50-29"></a><span class="w"> </span><span class="n">swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">ma</span><span class="p">);</span>
<a id="__codelineno-50-30" name="__codelineno-50-30" href="#__codelineno-50-30"></a><span class="w"> </span><span class="c1">// 循环向下堆化</span>
<a id="__codelineno-50-31" name="__codelineno-50-31" href="#__codelineno-50-31"></a><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ma</span><span class="p">;</span>
<a id="__codelineno-50-32" name="__codelineno-50-32" href="#__codelineno-50-32"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-50-33" name="__codelineno-50-33" href="#__codelineno-50-33"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">my_heap.cs</span><pre><span></span><code><a id="__codelineno-51-1" name="__codelineno-51-1" href="#__codelineno-51-1"></a><span class="cm">/* 元素出堆 */</span>
<a id="__codelineno-51-2" name="__codelineno-51-2" href="#__codelineno-51-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">Pop</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-51-3" name="__codelineno-51-3" href="#__codelineno-51-3"></a><span class="w"> </span><span class="c1">// 判空处理</span>
<a id="__codelineno-51-4" name="__codelineno-51-4" href="#__codelineno-51-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">IsEmpty</span><span class="p">())</span>
<a id="__codelineno-51-5" name="__codelineno-51-5" href="#__codelineno-51-5"></a><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="nf">IndexOutOfRangeException</span><span class="p">();</span>
<a id="__codelineno-51-6" name="__codelineno-51-6" href="#__codelineno-51-6"></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-51-7" name="__codelineno-51-7" href="#__codelineno-51-7"></a><span class="w"> </span><span class="n">Swap</span><span class="p">(</span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="n">Size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">);</span>
<a id="__codelineno-51-8" name="__codelineno-51-8" href="#__codelineno-51-8"></a><span class="w"> </span><span class="c1">// 删除节点</span>
<a id="__codelineno-51-9" name="__codelineno-51-9" href="#__codelineno-51-9"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">Last</span><span class="p">();</span>
<a id="__codelineno-51-10" name="__codelineno-51-10" href="#__codelineno-51-10"></a><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">RemoveAt</span><span class="p">(</span><span class="n">Size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">);</span>
<a id="__codelineno-51-11" name="__codelineno-51-11" href="#__codelineno-51-11"></a><span class="w"> </span><span class="c1">// 从顶至底堆化</span>
<a id="__codelineno-51-12" name="__codelineno-51-12" href="#__codelineno-51-12"></a><span class="w"> </span><span class="n">SiftDown</span><span class="p">(</span><span class="m">0</span><span class="p">);</span>
<a id="__codelineno-51-13" name="__codelineno-51-13" href="#__codelineno-51-13"></a><span class="w"> </span><span class="c1">// 返回堆顶元素</span>
<a id="__codelineno-51-14" name="__codelineno-51-14" href="#__codelineno-51-14"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
<a id="__codelineno-51-15" name="__codelineno-51-15" href="#__codelineno-51-15"></a><span class="p">}</span>
<a id="__codelineno-51-16" name="__codelineno-51-16" href="#__codelineno-51-16"></a>
<a id="__codelineno-51-17" name="__codelineno-51-17" href="#__codelineno-51-17"></a><span class="cm">/* 从节点 i 开始，从顶至底堆化 */</span>
<a id="__codelineno-51-18" name="__codelineno-51-18" href="#__codelineno-51-18"></a><span class="k">void</span><span class="w"> </span><span class="nf">SiftDown</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-51-19" name="__codelineno-51-19" href="#__codelineno-51-19"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="k">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-51-20" name="__codelineno-51-20" href="#__codelineno-51-20"></a><span class="w"> </span><span class="c1">// 判断节点 i, l, r 中值最大的节点，记为 ma</span>
<a id="__codelineno-51-21" name="__codelineno-51-21" href="#__codelineno-51-21"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Left</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Right</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
<a id="__codelineno-51-22" name="__codelineno-51-22" href="#__codelineno-51-22"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">l</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">Size</span><span class="p">()</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">l</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">ma</span><span class="p">])</span>
<a id="__codelineno-51-23" name="__codelineno-51-23" href="#__codelineno-51-23"></a><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">l</span><span class="p">;</span>
<a id="__codelineno-51-24" name="__codelineno-51-24" href="#__codelineno-51-24"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">Size</span><span class="p">()</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">r</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">ma</span><span class="p">])</span>
<a id="__codelineno-51-25" name="__codelineno-51-25" href="#__codelineno-51-25"></a><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">r</span><span class="p">;</span>
<a id="__codelineno-51-26" name="__codelineno-51-26" href="#__codelineno-51-26"></a><span class="w"> </span><span class="c1">// 若“节点 i 最大”或“越过叶节点”，则结束堆化</span>
<a id="__codelineno-51-27" name="__codelineno-51-27" href="#__codelineno-51-27"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">ma</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="k">break</span><span class="p">;</span>
<a id="__codelineno-51-28" name="__codelineno-51-28" href="#__codelineno-51-28"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
<a id="__codelineno-51-29" name="__codelineno-51-29" href="#__codelineno-51-29"></a><span class="w"> </span><span class="n">Swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">ma</span><span class="p">);</span>
<a id="__codelineno-51-30" name="__codelineno-51-30" href="#__codelineno-51-30"></a><span class="w"> </span><span class="c1">// 循环向下堆化</span>
<a id="__codelineno-51-31" name="__codelineno-51-31" href="#__codelineno-51-31"></a><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ma</span><span class="p">;</span>
<a id="__codelineno-51-32" name="__codelineno-51-32" href="#__codelineno-51-32"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-51-33" name="__codelineno-51-33" href="#__codelineno-51-33"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">my_heap.go</span><pre><span></span><code><a id="__codelineno-52-1" name="__codelineno-52-1" href="#__codelineno-52-1"></a><span class="cm">/* 元素出堆 */</span>
<a id="__codelineno-52-2" name="__codelineno-52-2" href="#__codelineno-52-2"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="nx">pop</span><span class="p">()</span><span class="w"> </span><span class="kt">any</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-52-3" name="__codelineno-52-3" href="#__codelineno-52-3"></a><span class="w"> </span><span class="c1">// 判空处理</span>
<a id="__codelineno-52-4" name="__codelineno-52-4" href="#__codelineno-52-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-52-5" name="__codelineno-52-5" href="#__codelineno-52-5"></a><span class="w"> </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Println</span><span class="p">(</span><span class="s">&quot;error&quot;</span><span class="p">)</span>
<a id="__codelineno-52-6" name="__codelineno-52-6" href="#__codelineno-52-6"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="kc">nil</span>
<a id="__codelineno-52-7" name="__codelineno-52-7" href="#__codelineno-52-7"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-52-8" name="__codelineno-52-8" href="#__codelineno-52-8"></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-52-9" name="__codelineno-52-9" href="#__codelineno-52-9"></a><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">swap</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span>
<a id="__codelineno-52-10" name="__codelineno-52-10" href="#__codelineno-52-10"></a><span class="w"> </span><span class="c1">// 删除节点</span>
<a id="__codelineno-52-11" name="__codelineno-52-11" href="#__codelineno-52-11"></a><span class="w"> </span><span class="nx">val</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="p">[</span><span class="nb">len</span><span class="p">(</span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
<a id="__codelineno-52-12" name="__codelineno-52-12" href="#__codelineno-52-12"></a><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="p">[:</span><span class="nb">len</span><span class="p">(</span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
<a id="__codelineno-52-13" name="__codelineno-52-13" href="#__codelineno-52-13"></a><span class="w"> </span><span class="c1">// 从顶至底堆化</span>
<a id="__codelineno-52-14" name="__codelineno-52-14" href="#__codelineno-52-14"></a><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">siftDown</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<a id="__codelineno-52-15" name="__codelineno-52-15" href="#__codelineno-52-15"></a>
<a id="__codelineno-52-16" name="__codelineno-52-16" href="#__codelineno-52-16"></a><span class="w"> </span><span class="c1">// 返回堆顶元素</span>
<a id="__codelineno-52-17" name="__codelineno-52-17" href="#__codelineno-52-17"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">val</span>
<a id="__codelineno-52-18" name="__codelineno-52-18" href="#__codelineno-52-18"></a><span class="p">}</span>
<a id="__codelineno-52-19" name="__codelineno-52-19" href="#__codelineno-52-19"></a>
<a id="__codelineno-52-20" name="__codelineno-52-20" href="#__codelineno-52-20"></a><span class="cm">/* 从节点 i 开始，从顶至底堆化 */</span>
<a id="__codelineno-52-21" name="__codelineno-52-21" href="#__codelineno-52-21"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="nx">siftDown</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-52-22" name="__codelineno-52-22" href="#__codelineno-52-22"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="kc">true</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-52-23" name="__codelineno-52-23" href="#__codelineno-52-23"></a><span class="w"> </span><span class="c1">// 判断节点 i, l, r 中值最大的节点，记为 max</span>
<a id="__codelineno-52-24" name="__codelineno-52-24" href="#__codelineno-52-24"></a><span class="w"> </span><span class="nx">l</span><span class="p">,</span><span class="w"> </span><span class="nx">r</span><span class="p">,</span><span class="w"> </span><span class="nx">max</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">left</span><span class="p">(</span><span class="nx">i</span><span class="p">),</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">right</span><span class="p">(</span><span class="nx">i</span><span class="p">),</span><span class="w"> </span><span class="nx">i</span>
<a id="__codelineno-52-25" name="__codelineno-52-25" href="#__codelineno-52-25"></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">h</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="p">[</span><span class="nx">l</span><span class="p">].(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="p">[</span><span class="nx">max</span><span class="p">].(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-52-26" name="__codelineno-52-26" href="#__codelineno-52-26"></a><span class="w"> </span><span class="nx">max</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">l</span>
<a id="__codelineno-52-27" name="__codelineno-52-27" href="#__codelineno-52-27"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-52-28" name="__codelineno-52-28" href="#__codelineno-52-28"></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">h</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="p">[</span><span class="nx">r</span><span class="p">].(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="p">[</span><span class="nx">max</span><span class="p">].(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-52-29" name="__codelineno-52-29" href="#__codelineno-52-29"></a><span class="w"> </span><span class="nx">max</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">r</span>
<a id="__codelineno-52-30" name="__codelineno-52-30" href="#__codelineno-52-30"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-52-31" name="__codelineno-52-31" href="#__codelineno-52-31"></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-52-32" name="__codelineno-52-32" href="#__codelineno-52-32"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">max</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-52-33" name="__codelineno-52-33" href="#__codelineno-52-33"></a><span class="w"> </span><span class="k">break</span>
<a id="__codelineno-52-34" name="__codelineno-52-34" href="#__codelineno-52-34"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-52-35" name="__codelineno-52-35" href="#__codelineno-52-35"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
<a id="__codelineno-52-36" name="__codelineno-52-36" href="#__codelineno-52-36"></a><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">swap</span><span class="p">(</span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">max</span><span class="p">)</span>
<a id="__codelineno-52-37" name="__codelineno-52-37" href="#__codelineno-52-37"></a><span class="w"> </span><span class="c1">// 循环向下堆化</span>
<a id="__codelineno-52-38" name="__codelineno-52-38" href="#__codelineno-52-38"></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">max</span>
<a id="__codelineno-52-39" name="__codelineno-52-39" href="#__codelineno-52-39"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-52-40" name="__codelineno-52-40" href="#__codelineno-52-40"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">my_heap.swift</span><pre><span></span><code><a id="__codelineno-53-1" name="__codelineno-53-1" href="#__codelineno-53-1"></a><span class="cm">/* 元素出堆 */</span>
<a id="__codelineno-53-2" name="__codelineno-53-2" href="#__codelineno-53-2"></a><span class="kd">func</span> <span class="nf">pop</span><span class="p">()</span> <span class="p">-&gt;</span> <span class="nb">Int</span> <span class="p">{</span>
<a id="__codelineno-53-3" name="__codelineno-53-3" href="#__codelineno-53-3"></a> <span class="c1">// 判空处理</span>
<a id="__codelineno-53-4" name="__codelineno-53-4" href="#__codelineno-53-4"></a> <span class="k">if</span> <span class="bp">isEmpty</span><span class="p">()</span> <span class="p">{</span>
<a id="__codelineno-53-5" name="__codelineno-53-5" href="#__codelineno-53-5"></a> <span class="bp">fatalError</span><span class="p">(</span><span class="s">&quot;堆为空&quot;</span><span class="p">)</span>
<a id="__codelineno-53-6" name="__codelineno-53-6" href="#__codelineno-53-6"></a> <span class="p">}</span>
<a id="__codelineno-53-7" name="__codelineno-53-7" href="#__codelineno-53-7"></a> <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-53-8" name="__codelineno-53-8" href="#__codelineno-53-8"></a> <span class="bp">swap</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="n">j</span><span class="p">:</span> <span class="n">size</span><span class="p">()</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
<a id="__codelineno-53-9" name="__codelineno-53-9" href="#__codelineno-53-9"></a> <span class="c1">// 删除节点</span>
<a id="__codelineno-53-10" name="__codelineno-53-10" href="#__codelineno-53-10"></a> <span class="kd">let</span> <span class="nv">val</span> <span class="p">=</span> <span class="n">maxHeap</span><span class="p">.</span><span class="n">remove</span><span class="p">(</span><span class="n">at</span><span class="p">:</span> <span class="n">size</span><span class="p">()</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
<a id="__codelineno-53-11" name="__codelineno-53-11" href="#__codelineno-53-11"></a> <span class="c1">// 从顶至底堆化</span>
<a id="__codelineno-53-12" name="__codelineno-53-12" href="#__codelineno-53-12"></a> <span class="n">siftDown</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="mi">0</span><span class="p">)</span>
<a id="__codelineno-53-13" name="__codelineno-53-13" href="#__codelineno-53-13"></a> <span class="c1">// 返回堆顶元素</span>
<a id="__codelineno-53-14" name="__codelineno-53-14" href="#__codelineno-53-14"></a> <span class="k">return</span> <span class="n">val</span>
<a id="__codelineno-53-15" name="__codelineno-53-15" href="#__codelineno-53-15"></a><span class="p">}</span>
<a id="__codelineno-53-16" name="__codelineno-53-16" href="#__codelineno-53-16"></a>
<a id="__codelineno-53-17" name="__codelineno-53-17" href="#__codelineno-53-17"></a><span class="cm">/* 从节点 i 开始，从顶至底堆化 */</span>
<a id="__codelineno-53-18" name="__codelineno-53-18" href="#__codelineno-53-18"></a><span class="kd">func</span> <span class="nf">siftDown</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">{</span>
<a id="__codelineno-53-19" name="__codelineno-53-19" href="#__codelineno-53-19"></a> <span class="kd">var</span> <span class="nv">i</span> <span class="p">=</span> <span class="n">i</span>
<a id="__codelineno-53-20" name="__codelineno-53-20" href="#__codelineno-53-20"></a> <span class="k">while</span> <span class="kc">true</span> <span class="p">{</span>
<a id="__codelineno-53-21" name="__codelineno-53-21" href="#__codelineno-53-21"></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-53-22" name="__codelineno-53-22" href="#__codelineno-53-22"></a> <span class="kd">let</span> <span class="nv">l</span> <span class="p">=</span> <span class="kr">left</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="n">i</span><span class="p">)</span>
<a id="__codelineno-53-23" name="__codelineno-53-23" href="#__codelineno-53-23"></a> <span class="kd">let</span> <span class="nv">r</span> <span class="p">=</span> <span class="kr">right</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="n">i</span><span class="p">)</span>
<a id="__codelineno-53-24" name="__codelineno-53-24" href="#__codelineno-53-24"></a> <span class="kd">var</span> <span class="nv">ma</span> <span class="p">=</span> <span class="n">i</span>
<a id="__codelineno-53-25" name="__codelineno-53-25" href="#__codelineno-53-25"></a> <span class="k">if</span> <span class="n">l</span> <span class="o">&lt;</span> <span class="n">size</span><span class="p">(),</span> <span class="n">maxHeap</span><span class="p">[</span><span class="n">l</span><span class="p">]</span> <span class="o">&gt;</span> <span class="n">maxHeap</span><span class="p">[</span><span class="n">ma</span><span class="p">]</span> <span class="p">{</span>
<a id="__codelineno-53-26" name="__codelineno-53-26" href="#__codelineno-53-26"></a> <span class="n">ma</span> <span class="p">=</span> <span class="n">l</span>
<a id="__codelineno-53-27" name="__codelineno-53-27" href="#__codelineno-53-27"></a> <span class="p">}</span>
<a id="__codelineno-53-28" name="__codelineno-53-28" href="#__codelineno-53-28"></a> <span class="k">if</span> <span class="n">r</span> <span class="o">&lt;</span> <span class="n">size</span><span class="p">(),</span> <span class="n">maxHeap</span><span class="p">[</span><span class="n">r</span><span class="p">]</span> <span class="o">&gt;</span> <span class="n">maxHeap</span><span class="p">[</span><span class="n">ma</span><span class="p">]</span> <span class="p">{</span>
<a id="__codelineno-53-29" name="__codelineno-53-29" href="#__codelineno-53-29"></a> <span class="n">ma</span> <span class="p">=</span> <span class="n">r</span>
<a id="__codelineno-53-30" name="__codelineno-53-30" href="#__codelineno-53-30"></a> <span class="p">}</span>
<a id="__codelineno-53-31" name="__codelineno-53-31" href="#__codelineno-53-31"></a> <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-53-32" name="__codelineno-53-32" href="#__codelineno-53-32"></a> <span class="k">if</span> <span class="n">ma</span> <span class="p">==</span> <span class="n">i</span> <span class="p">{</span>
<a id="__codelineno-53-33" name="__codelineno-53-33" href="#__codelineno-53-33"></a> <span class="k">break</span>
<a id="__codelineno-53-34" name="__codelineno-53-34" href="#__codelineno-53-34"></a> <span class="p">}</span>
<a id="__codelineno-53-35" name="__codelineno-53-35" href="#__codelineno-53-35"></a> <span class="c1">// 交换两节点</span>
<a id="__codelineno-53-36" name="__codelineno-53-36" href="#__codelineno-53-36"></a> <span class="bp">swap</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">:</span> <span class="n">ma</span><span class="p">)</span>
<a id="__codelineno-53-37" name="__codelineno-53-37" href="#__codelineno-53-37"></a> <span class="c1">// 循环向下堆化</span>
<a id="__codelineno-53-38" name="__codelineno-53-38" href="#__codelineno-53-38"></a> <span class="n">i</span> <span class="p">=</span> <span class="n">ma</span>
<a id="__codelineno-53-39" name="__codelineno-53-39" href="#__codelineno-53-39"></a> <span class="p">}</span>
<a id="__codelineno-53-40" name="__codelineno-53-40" href="#__codelineno-53-40"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">my_heap.js</span><pre><span></span><code><a id="__codelineno-54-1" name="__codelineno-54-1" href="#__codelineno-54-1"></a><span class="cm">/* 元素出堆 */</span>
<a id="__codelineno-54-2" name="__codelineno-54-2" href="#__codelineno-54-2"></a><span class="nx">pop</span><span class="p">()</span><span class="w"> </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="c1">// 判空处理</span>
<a id="__codelineno-54-4" name="__codelineno-54-4" href="#__codelineno-54-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">isEmpty</span><span class="p">())</span><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="ne">Error</span><span class="p">(</span><span class="s1">&#39;堆为空&#39;</span><span class="p">);</span>
<a id="__codelineno-54-5" name="__codelineno-54-5" href="#__codelineno-54-5"></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-54-6" name="__codelineno-54-6" href="#__codelineno-54-6"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">swap</span><span class="p">(</span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</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">// 删除节点</span>
<a id="__codelineno-54-8" name="__codelineno-54-8" href="#__codelineno-54-8"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">maxHeap</span><span class="p">.</span><span class="nx">pop</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">// 从顶至底堆化</span>
<a id="__codelineno-54-10" name="__codelineno-54-10" href="#__codelineno-54-10"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">siftDown</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
<a id="__codelineno-54-11" name="__codelineno-54-11" href="#__codelineno-54-11"></a><span class="w"> </span><span class="c1">// 返回堆顶元素</span>
<a id="__codelineno-54-12" name="__codelineno-54-12" href="#__codelineno-54-12"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">val</span><span class="p">;</span>
<a id="__codelineno-54-13" name="__codelineno-54-13" href="#__codelineno-54-13"></a><span class="p">}</span>
<a id="__codelineno-54-14" name="__codelineno-54-14" href="#__codelineno-54-14"></a>
<a id="__codelineno-54-15" name="__codelineno-54-15" href="#__codelineno-54-15"></a><span class="cm">/* 从节点 i 开始，从顶至底堆化 */</span>
<a id="__codelineno-54-16" name="__codelineno-54-16" href="#__codelineno-54-16"></a><span class="err">#</span><span class="nx">siftDown</span><span class="p">(</span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-54-17" name="__codelineno-54-17" href="#__codelineno-54-17"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="kc">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-54-18" name="__codelineno-54-18" href="#__codelineno-54-18"></a><span class="w"> </span><span class="c1">// 判断节点 i, l, r 中值最大的节点，记为 ma</span>
<a id="__codelineno-54-19" name="__codelineno-54-19" href="#__codelineno-54-19"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">l</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">left</span><span class="p">(</span><span class="nx">i</span><span class="p">),</span>
<a id="__codelineno-54-20" name="__codelineno-54-20" href="#__codelineno-54-20"></a><span class="w"> </span><span class="nx">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">right</span><span class="p">(</span><span class="nx">i</span><span class="p">);</span>
<a id="__codelineno-54-21" name="__codelineno-54-21" href="#__codelineno-54-21"></a><span class="w"> </span><span class="kd">let</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="p">;</span>
<a id="__codelineno-54-22" name="__codelineno-54-22" href="#__codelineno-54-22"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">l</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">maxHeap</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="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">maxHeap</span><span class="p">[</span><span class="nx">ma</span><span class="p">])</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">l</span><span class="p">;</span>
<a id="__codelineno-54-23" name="__codelineno-54-23" href="#__codelineno-54-23"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">r</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">maxHeap</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="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">maxHeap</span><span class="p">[</span><span class="nx">ma</span><span class="p">])</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">r</span><span class="p">;</span>
<a id="__codelineno-54-24" name="__codelineno-54-24" href="#__codelineno-54-24"></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-54-25" name="__codelineno-54-25" href="#__codelineno-54-25"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</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="p">)</span><span class="w"> </span><span class="k">break</span><span class="p">;</span>
<a id="__codelineno-54-26" name="__codelineno-54-26" href="#__codelineno-54-26"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
<a id="__codelineno-54-27" name="__codelineno-54-27" href="#__codelineno-54-27"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">swap</span><span class="p">(</span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">ma</span><span class="p">);</span>
<a id="__codelineno-54-28" name="__codelineno-54-28" href="#__codelineno-54-28"></a><span class="w"> </span><span class="c1">// 循环向下堆化</span>
<a id="__codelineno-54-29" name="__codelineno-54-29" href="#__codelineno-54-29"></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><span class="p">;</span>
<a id="__codelineno-54-30" name="__codelineno-54-30" href="#__codelineno-54-30"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-54-31" name="__codelineno-54-31" href="#__codelineno-54-31"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">my_heap.ts</span><pre><span></span><code><a id="__codelineno-55-1" name="__codelineno-55-1" href="#__codelineno-55-1"></a><span class="cm">/* 元素出堆 */</span>
<a id="__codelineno-55-2" name="__codelineno-55-2" href="#__codelineno-55-2"></a><span class="nx">pop</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-55-3" name="__codelineno-55-3" href="#__codelineno-55-3"></a><span class="w"> </span><span class="c1">// 判空处理</span>
<a id="__codelineno-55-4" name="__codelineno-55-4" href="#__codelineno-55-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">isEmpty</span><span class="p">())</span><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="ne">RangeError</span><span class="p">(</span><span class="s1">&#39;Heap is empty.&#39;</span><span class="p">);</span>
<a id="__codelineno-55-5" name="__codelineno-55-5" href="#__codelineno-55-5"></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-55-6" name="__codelineno-55-6" href="#__codelineno-55-6"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">swap</span><span class="p">(</span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
<a id="__codelineno-55-7" name="__codelineno-55-7" href="#__codelineno-55-7"></a><span class="w"> </span><span class="c1">// 删除节点</span>
<a id="__codelineno-55-8" name="__codelineno-55-8" href="#__codelineno-55-8"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">maxHeap</span><span class="p">.</span><span class="nx">pop</span><span class="p">();</span>
<a id="__codelineno-55-9" name="__codelineno-55-9" href="#__codelineno-55-9"></a><span class="w"> </span><span class="c1">// 从顶至底堆化</span>
<a id="__codelineno-55-10" name="__codelineno-55-10" href="#__codelineno-55-10"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">siftDown</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
<a id="__codelineno-55-11" name="__codelineno-55-11" href="#__codelineno-55-11"></a><span class="w"> </span><span class="c1">// 返回堆顶元素</span>
<a id="__codelineno-55-12" name="__codelineno-55-12" href="#__codelineno-55-12"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">val</span><span class="p">;</span>
<a id="__codelineno-55-13" name="__codelineno-55-13" href="#__codelineno-55-13"></a><span class="p">}</span>
<a id="__codelineno-55-14" name="__codelineno-55-14" href="#__codelineno-55-14"></a>
<a id="__codelineno-55-15" name="__codelineno-55-15" href="#__codelineno-55-15"></a><span class="cm">/* 从节点 i 开始，从顶至底堆化 */</span>
<a id="__codelineno-55-16" name="__codelineno-55-16" href="#__codelineno-55-16"></a><span class="nx">siftDown</span><span class="p">(</span><span class="nx">i</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-55-17" name="__codelineno-55-17" href="#__codelineno-55-17"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="kc">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-55-18" name="__codelineno-55-18" href="#__codelineno-55-18"></a><span class="w"> </span><span class="c1">// 判断节点 i, l, r 中值最大的节点，记为 ma</span>
<a id="__codelineno-55-19" name="__codelineno-55-19" href="#__codelineno-55-19"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">l</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">left</span><span class="p">(</span><span class="nx">i</span><span class="p">),</span>
<a id="__codelineno-55-20" name="__codelineno-55-20" href="#__codelineno-55-20"></a><span class="w"> </span><span class="nx">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">right</span><span class="p">(</span><span class="nx">i</span><span class="p">);</span>
<a id="__codelineno-55-21" name="__codelineno-55-21" href="#__codelineno-55-21"></a><span class="w"> </span><span class="kd">let</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="p">;</span>
<a id="__codelineno-55-22" name="__codelineno-55-22" href="#__codelineno-55-22"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">l</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">maxHeap</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="k">this</span><span class="p">.</span><span class="nx">maxHeap</span><span class="p">[</span><span class="nx">ma</span><span class="p">])</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">l</span><span class="p">;</span>
<a id="__codelineno-55-23" name="__codelineno-55-23" href="#__codelineno-55-23"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">r</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">maxHeap</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="k">this</span><span class="p">.</span><span class="nx">maxHeap</span><span class="p">[</span><span class="nx">ma</span><span class="p">])</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">r</span><span class="p">;</span>
<a id="__codelineno-55-24" name="__codelineno-55-24" href="#__codelineno-55-24"></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-55-25" name="__codelineno-55-25" href="#__codelineno-55-25"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</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="p">)</span><span class="w"> </span><span class="k">break</span><span class="p">;</span>
<a id="__codelineno-55-26" name="__codelineno-55-26" href="#__codelineno-55-26"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
<a id="__codelineno-55-27" name="__codelineno-55-27" href="#__codelineno-55-27"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">swap</span><span class="p">(</span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">ma</span><span class="p">);</span>
<a id="__codelineno-55-28" name="__codelineno-55-28" href="#__codelineno-55-28"></a><span class="w"> </span><span class="c1">// 循环向下堆化</span>
<a id="__codelineno-55-29" name="__codelineno-55-29" href="#__codelineno-55-29"></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><span class="p">;</span>
<a id="__codelineno-55-30" name="__codelineno-55-30" href="#__codelineno-55-30"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-55-31" name="__codelineno-55-31" href="#__codelineno-55-31"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">my_heap.dart</span><pre><span></span><code><a id="__codelineno-56-1" name="__codelineno-56-1" href="#__codelineno-56-1"></a><span class="cm">/* 元素出堆 */</span>
<a id="__codelineno-56-2" name="__codelineno-56-2" href="#__codelineno-56-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">pop</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-56-3" name="__codelineno-56-3" href="#__codelineno-56-3"></a><span class="w"> </span><span class="c1">// 判空处理</span>
<a id="__codelineno-56-4" name="__codelineno-56-4" href="#__codelineno-56-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="n">Exception</span><span class="p">(</span><span class="s1">&#39;堆为空&#39;</span><span class="p">);</span>
<a id="__codelineno-56-5" name="__codelineno-56-5" href="#__codelineno-56-5"></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-56-6" name="__codelineno-56-6" href="#__codelineno-56-6"></a><span class="w"> </span><span class="n">_swap</span><span class="p">(</span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">);</span>
<a id="__codelineno-56-7" name="__codelineno-56-7" href="#__codelineno-56-7"></a><span class="w"> </span><span class="c1">// 删除节点</span>
<a id="__codelineno-56-8" name="__codelineno-56-8" href="#__codelineno-56-8"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_maxHeap</span><span class="p">.</span><span class="n">removeLast</span><span class="p">();</span>
<a id="__codelineno-56-9" name="__codelineno-56-9" href="#__codelineno-56-9"></a><span class="w"> </span><span class="c1">// 从顶至底堆化</span>
<a id="__codelineno-56-10" name="__codelineno-56-10" href="#__codelineno-56-10"></a><span class="w"> </span><span class="n">siftDown</span><span class="p">(</span><span class="m">0</span><span class="p">);</span>
<a id="__codelineno-56-11" name="__codelineno-56-11" href="#__codelineno-56-11"></a><span class="w"> </span><span class="c1">// 返回堆顶元素</span>
<a id="__codelineno-56-12" name="__codelineno-56-12" href="#__codelineno-56-12"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
<a id="__codelineno-56-13" name="__codelineno-56-13" href="#__codelineno-56-13"></a><span class="p">}</span>
<a id="__codelineno-56-14" name="__codelineno-56-14" href="#__codelineno-56-14"></a>
<a id="__codelineno-56-15" name="__codelineno-56-15" href="#__codelineno-56-15"></a><span class="cm">/* 从节点 i 开始，从顶至底堆化 */</span>
<a id="__codelineno-56-16" name="__codelineno-56-16" href="#__codelineno-56-16"></a><span class="kt">void</span><span class="w"> </span><span class="n">siftDown</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-56-17" name="__codelineno-56-17" href="#__codelineno-56-17"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="kc">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-56-18" name="__codelineno-56-18" href="#__codelineno-56-18"></a><span class="w"> </span><span class="c1">// 判断节点 i, l, r 中值最大的节点，记为 ma</span>
<a id="__codelineno-56-19" name="__codelineno-56-19" href="#__codelineno-56-19"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_left</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
<a id="__codelineno-56-20" name="__codelineno-56-20" href="#__codelineno-56-20"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_right</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
<a id="__codelineno-56-21" name="__codelineno-56-21" href="#__codelineno-56-21"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
<a id="__codelineno-56-22" name="__codelineno-56-22" href="#__codelineno-56-22"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">l</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">_maxHeap</span><span class="p">[</span><span class="n">l</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">_maxHeap</span><span class="p">[</span><span class="n">ma</span><span class="p">])</span><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">l</span><span class="p">;</span>
<a id="__codelineno-56-23" name="__codelineno-56-23" href="#__codelineno-56-23"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">_maxHeap</span><span class="p">[</span><span class="n">r</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">_maxHeap</span><span class="p">[</span><span class="n">ma</span><span class="p">])</span><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">r</span><span class="p">;</span>
<a id="__codelineno-56-24" name="__codelineno-56-24" href="#__codelineno-56-24"></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-56-25" name="__codelineno-56-25" href="#__codelineno-56-25"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">ma</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="k">break</span><span class="p">;</span>
<a id="__codelineno-56-26" name="__codelineno-56-26" href="#__codelineno-56-26"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
<a id="__codelineno-56-27" name="__codelineno-56-27" href="#__codelineno-56-27"></a><span class="w"> </span><span class="n">_swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">ma</span><span class="p">);</span>
<a id="__codelineno-56-28" name="__codelineno-56-28" href="#__codelineno-56-28"></a><span class="w"> </span><span class="c1">// 循环向下堆化</span>
<a id="__codelineno-56-29" name="__codelineno-56-29" href="#__codelineno-56-29"></a><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ma</span><span class="p">;</span>
<a id="__codelineno-56-30" name="__codelineno-56-30" href="#__codelineno-56-30"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-56-31" name="__codelineno-56-31" href="#__codelineno-56-31"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">my_heap.rs</span><pre><span></span><code><a id="__codelineno-57-1" name="__codelineno-57-1" href="#__codelineno-57-1"></a><span class="cm">/* 元素出堆 */</span>
<a id="__codelineno-57-2" name="__codelineno-57-2" href="#__codelineno-57-2"></a><span class="k">fn</span> <span class="nf">pop</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="bp">self</span><span class="p">)</span><span class="w"> </span>-&gt; <span class="kt">i32</span> <span class="p">{</span>
<a id="__codelineno-57-3" name="__codelineno-57-3" href="#__codelineno-57-3"></a><span class="w"> </span><span class="c1">// 判空处理</span>
<a id="__codelineno-57-4" name="__codelineno-57-4" href="#__codelineno-57-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">is_empty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-57-5" name="__codelineno-57-5" href="#__codelineno-57-5"></a><span class="w"> </span><span class="fm">panic!</span><span class="p">(</span><span class="s">&quot;index out of bounds&quot;</span><span class="p">);</span>
<a id="__codelineno-57-6" name="__codelineno-57-6" href="#__codelineno-57-6"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-57-7" name="__codelineno-57-7" href="#__codelineno-57-7"></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-57-8" name="__codelineno-57-8" href="#__codelineno-57-8"></a><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">swap</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">size</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-57-9" name="__codelineno-57-9" href="#__codelineno-57-9"></a><span class="w"> </span><span class="c1">// 删除节点</span>
<a id="__codelineno-57-10" name="__codelineno-57-10" href="#__codelineno-57-10"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">.</span><span class="n">remove</span><span class="p">(</span><span class="bp">self</span><span class="p">.</span><span class="n">size</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-57-11" name="__codelineno-57-11" href="#__codelineno-57-11"></a><span class="w"> </span><span class="c1">// 从顶至底堆化</span>
<a id="__codelineno-57-12" name="__codelineno-57-12" href="#__codelineno-57-12"></a><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">sift_down</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
<a id="__codelineno-57-13" name="__codelineno-57-13" href="#__codelineno-57-13"></a><span class="w"> </span><span class="c1">// 返回堆顶元素</span>
<a id="__codelineno-57-14" name="__codelineno-57-14" href="#__codelineno-57-14"></a><span class="w"> </span><span class="n">val</span>
<a id="__codelineno-57-15" name="__codelineno-57-15" href="#__codelineno-57-15"></a><span class="p">}</span>
<a id="__codelineno-57-16" name="__codelineno-57-16" href="#__codelineno-57-16"></a>
<a id="__codelineno-57-17" name="__codelineno-57-17" href="#__codelineno-57-17"></a><span class="cm">/* 从节点 i 开始，从顶至底堆化 */</span>
<a id="__codelineno-57-18" name="__codelineno-57-18" href="#__codelineno-57-18"></a><span class="k">fn</span> <span class="nf">sift_down</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">i</span>: <span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-57-19" name="__codelineno-57-19" href="#__codelineno-57-19"></a><span class="w"> </span><span class="k">loop</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-57-20" name="__codelineno-57-20" href="#__codelineno-57-20"></a><span class="w"> </span><span class="c1">// 判断节点 i, l, r 中值最大的节点，记为 ma</span>
<a id="__codelineno-57-21" name="__codelineno-57-21" href="#__codelineno-57-21"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="p">(</span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">r</span><span class="p">,</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">ma</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="bp">Self</span>::<span class="n">left</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="bp">Self</span>::<span class="n">right</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
<a id="__codelineno-57-22" name="__codelineno-57-22" href="#__codelineno-57-22"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">[</span><span class="n">l</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">[</span><span class="n">ma</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-57-23" name="__codelineno-57-23" href="#__codelineno-57-23"></a><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">l</span><span class="p">;</span>
<a id="__codelineno-57-24" name="__codelineno-57-24" href="#__codelineno-57-24"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-57-25" name="__codelineno-57-25" href="#__codelineno-57-25"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">[</span><span class="n">r</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">[</span><span class="n">ma</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-57-26" name="__codelineno-57-26" href="#__codelineno-57-26"></a><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">r</span><span class="p">;</span>
<a id="__codelineno-57-27" name="__codelineno-57-27" href="#__codelineno-57-27"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-57-28" name="__codelineno-57-28" href="#__codelineno-57-28"></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-57-29" name="__codelineno-57-29" href="#__codelineno-57-29"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">ma</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-57-30" name="__codelineno-57-30" href="#__codelineno-57-30"></a><span class="w"> </span><span class="k">break</span><span class="p">;</span>
<a id="__codelineno-57-31" name="__codelineno-57-31" href="#__codelineno-57-31"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-57-32" name="__codelineno-57-32" href="#__codelineno-57-32"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
<a id="__codelineno-57-33" name="__codelineno-57-33" href="#__codelineno-57-33"></a><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">ma</span><span class="p">);</span>
<a id="__codelineno-57-34" name="__codelineno-57-34" href="#__codelineno-57-34"></a><span class="w"> </span><span class="c1">// 循环向下堆化</span>
<a id="__codelineno-57-35" name="__codelineno-57-35" href="#__codelineno-57-35"></a><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ma</span><span class="p">;</span>
<a id="__codelineno-57-36" name="__codelineno-57-36" href="#__codelineno-57-36"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-57-37" name="__codelineno-57-37" href="#__codelineno-57-37"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">my_heap.c</span><pre><span></span><code><a id="__codelineno-58-1" name="__codelineno-58-1" href="#__codelineno-58-1"></a><span class="cm">/* 元素出堆 */</span>
<a id="__codelineno-58-2" name="__codelineno-58-2" href="#__codelineno-58-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">pop</span><span class="p">(</span><span class="n">MaxHeap</span><span class="w"> </span><span class="o">*</span><span class="n">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-58-3" name="__codelineno-58-3" href="#__codelineno-58-3"></a><span class="w"> </span><span class="c1">// 判空处理</span>
<a id="__codelineno-58-4" name="__codelineno-58-4" href="#__codelineno-58-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-58-5" name="__codelineno-58-5" href="#__codelineno-58-5"></a><span class="w"> </span><span class="n">printf</span><span class="p">(</span><span class="s">&quot;heap is empty!&quot;</span><span class="p">);</span>
<a id="__codelineno-58-6" name="__codelineno-58-6" href="#__codelineno-58-6"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">;</span>
<a id="__codelineno-58-7" name="__codelineno-58-7" href="#__codelineno-58-7"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-58-8" name="__codelineno-58-8" href="#__codelineno-58-8"></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-58-9" name="__codelineno-58-9" href="#__codelineno-58-9"></a><span class="w"> </span><span class="n">swap</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">size</span><span class="p">(</span><span class="n">maxHeap</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-58-10" name="__codelineno-58-10" href="#__codelineno-58-10"></a><span class="w"> </span><span class="c1">// 删除节点</span>
<a id="__codelineno-58-11" name="__codelineno-58-11" href="#__codelineno-58-11"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="o">-&gt;</span><span class="n">data</span><span class="p">[</span><span class="n">maxHeap</span><span class="o">-&gt;</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>
<a id="__codelineno-58-12" name="__codelineno-58-12" href="#__codelineno-58-12"></a><span class="w"> </span><span class="n">maxHeap</span><span class="o">-&gt;</span><span class="n">size</span><span class="o">--</span><span class="p">;</span>
<a id="__codelineno-58-13" name="__codelineno-58-13" href="#__codelineno-58-13"></a><span class="w"> </span><span class="c1">// 从顶至底堆化</span>
<a id="__codelineno-58-14" name="__codelineno-58-14" href="#__codelineno-58-14"></a><span class="w"> </span><span class="n">siftDown</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
<a id="__codelineno-58-15" name="__codelineno-58-15" href="#__codelineno-58-15"></a>
<a id="__codelineno-58-16" name="__codelineno-58-16" href="#__codelineno-58-16"></a><span class="w"> </span><span class="c1">// 返回堆顶元素</span>
<a id="__codelineno-58-17" name="__codelineno-58-17" href="#__codelineno-58-17"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
<a id="__codelineno-58-18" name="__codelineno-58-18" href="#__codelineno-58-18"></a><span class="p">}</span>
<a id="__codelineno-58-19" name="__codelineno-58-19" href="#__codelineno-58-19"></a>
<a id="__codelineno-58-20" name="__codelineno-58-20" href="#__codelineno-58-20"></a><span class="cm">/* 从节点 i 开始，从顶至底堆化 */</span>
<a id="__codelineno-58-21" name="__codelineno-58-21" href="#__codelineno-58-21"></a><span class="kt">void</span><span class="w"> </span><span class="nf">siftDown</span><span class="p">(</span><span class="n">MaxHeap</span><span class="w"> </span><span class="o">*</span><span class="n">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-58-22" name="__codelineno-58-22" href="#__codelineno-58-22"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nb">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-58-23" name="__codelineno-58-23" href="#__codelineno-58-23"></a><span class="w"> </span><span class="c1">// 判断节点 i, l, r 中值最大的节点，记为 max</span>
<a id="__codelineno-58-24" name="__codelineno-58-24" href="#__codelineno-58-24"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
<a id="__codelineno-58-25" name="__codelineno-58-25" href="#__codelineno-58-25"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">right</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
<a id="__codelineno-58-26" name="__codelineno-58-26" href="#__codelineno-58-26"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">max</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
<a id="__codelineno-58-27" name="__codelineno-58-27" href="#__codelineno-58-27"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">l</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">maxHeap</span><span class="o">-&gt;</span><span class="n">data</span><span class="p">[</span><span class="n">l</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">maxHeap</span><span class="o">-&gt;</span><span class="n">data</span><span class="p">[</span><span class="n">max</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-58-28" name="__codelineno-58-28" href="#__codelineno-58-28"></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">l</span><span class="p">;</span>
<a id="__codelineno-58-29" name="__codelineno-58-29" href="#__codelineno-58-29"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-58-30" name="__codelineno-58-30" href="#__codelineno-58-30"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">maxHeap</span><span class="o">-&gt;</span><span class="n">data</span><span class="p">[</span><span class="n">r</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">maxHeap</span><span class="o">-&gt;</span><span class="n">data</span><span class="p">[</span><span class="n">max</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-58-31" name="__codelineno-58-31" href="#__codelineno-58-31"></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">r</span><span class="p">;</span>
<a id="__codelineno-58-32" name="__codelineno-58-32" href="#__codelineno-58-32"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-58-33" name="__codelineno-58-33" href="#__codelineno-58-33"></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-58-34" name="__codelineno-58-34" href="#__codelineno-58-34"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">max</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-58-35" name="__codelineno-58-35" href="#__codelineno-58-35"></a><span class="w"> </span><span class="k">break</span><span class="p">;</span>
<a id="__codelineno-58-36" name="__codelineno-58-36" href="#__codelineno-58-36"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-58-37" name="__codelineno-58-37" href="#__codelineno-58-37"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
<a id="__codelineno-58-38" name="__codelineno-58-38" href="#__codelineno-58-38"></a><span class="w"> </span><span class="n">swap</span><span class="p">(</span><span class="n">maxHeap</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">max</span><span class="p">);</span>
<a id="__codelineno-58-39" name="__codelineno-58-39" href="#__codelineno-58-39"></a><span class="w"> </span><span class="c1">// 循环向下堆化</span>
<a id="__codelineno-58-40" name="__codelineno-58-40" href="#__codelineno-58-40"></a><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max</span><span class="p">;</span>
<a id="__codelineno-58-41" name="__codelineno-58-41" href="#__codelineno-58-41"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-58-42" name="__codelineno-58-42" href="#__codelineno-58-42"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">my_heap.zig</span><pre><span></span><code><a id="__codelineno-59-1" name="__codelineno-59-1" href="#__codelineno-59-1"></a><span class="c1">// 元素出堆</span>
<a id="__codelineno-59-2" name="__codelineno-59-2" href="#__codelineno-59-2"></a><span class="k">fn</span><span class="w"> </span><span class="n">pop</span><span class="p">(</span><span class="n">self</span><span class="o">:</span><span class="w"> </span><span class="o">*</span><span class="n">Self</span><span class="p">)</span><span class="w"> </span><span class="o">!</span><span class="n">T</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-59-3" name="__codelineno-59-3" href="#__codelineno-59-3"></a><span class="w"> </span><span class="c1">// 判断处理</span>
<a id="__codelineno-59-4" name="__codelineno-59-4" href="#__codelineno-59-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">self</span><span class="p">.</span><span class="n">isEmpty</span><span class="p">())</span><span class="w"> </span><span class="k">unreachable</span><span class="p">;</span>
<a id="__codelineno-59-5" name="__codelineno-59-5" href="#__codelineno-59-5"></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-59-6" name="__codelineno-59-6" href="#__codelineno-59-6"></a><span class="w"> </span><span class="k">try</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">swap</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">size</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-59-7" name="__codelineno-59-7" href="#__codelineno-59-7"></a><span class="w"> </span><span class="c1">// 删除节点</span>
<a id="__codelineno-59-8" name="__codelineno-59-8" href="#__codelineno-59-8"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">pop</span><span class="p">();</span>
<a id="__codelineno-59-9" name="__codelineno-59-9" href="#__codelineno-59-9"></a><span class="w"> </span><span class="c1">// 从顶至底堆化</span>
<a id="__codelineno-59-10" name="__codelineno-59-10" href="#__codelineno-59-10"></a><span class="w"> </span><span class="k">try</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">siftDown</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
<a id="__codelineno-59-11" name="__codelineno-59-11" href="#__codelineno-59-11"></a><span class="w"> </span><span class="c1">// 返回堆顶元素</span>
<a id="__codelineno-59-12" name="__codelineno-59-12" href="#__codelineno-59-12"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
<a id="__codelineno-59-13" name="__codelineno-59-13" href="#__codelineno-59-13"></a><span class="p">}</span><span class="w"> </span>
<a id="__codelineno-59-14" name="__codelineno-59-14" href="#__codelineno-59-14"></a>
<a id="__codelineno-59-15" name="__codelineno-59-15" href="#__codelineno-59-15"></a><span class="c1">// 从节点 i 开始，从顶至底堆化</span>
<a id="__codelineno-59-16" name="__codelineno-59-16" href="#__codelineno-59-16"></a><span class="k">fn</span><span class="w"> </span><span class="n">siftDown</span><span class="p">(</span><span class="n">self</span><span class="o">:</span><span class="w"> </span><span class="o">*</span><span class="n">Self</span><span class="p">,</span><span class="w"> </span><span class="n">i_</span><span class="o">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="o">!</span><span class="kt">void</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-59-17" name="__codelineno-59-17" href="#__codelineno-59-17"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i_</span><span class="p">;</span>
<a id="__codelineno-59-18" name="__codelineno-59-18" href="#__codelineno-59-18"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="kc">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-59-19" name="__codelineno-59-19" href="#__codelineno-59-19"></a><span class="w"> </span><span class="c1">// 判断节点 i, l, r 中值最大的节点，记为 ma</span>
<a id="__codelineno-59-20" name="__codelineno-59-20" href="#__codelineno-59-20"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
<a id="__codelineno-59-21" name="__codelineno-59-21" href="#__codelineno-59-21"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">right</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
<a id="__codelineno-59-22" name="__codelineno-59-22" href="#__codelineno-59-22"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
<a id="__codelineno-59-23" name="__codelineno-59-23" href="#__codelineno-59-23"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">l</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="k">and</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">items</span><span class="p">[</span><span class="n">l</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">items</span><span class="p">[</span><span class="n">ma</span><span class="p">])</span><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">l</span><span class="p">;</span>
<a id="__codelineno-59-24" name="__codelineno-59-24" href="#__codelineno-59-24"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="k">and</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">items</span><span class="p">[</span><span class="n">r</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">items</span><span class="p">[</span><span class="n">ma</span><span class="p">])</span><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">r</span><span class="p">;</span>
<a id="__codelineno-59-25" name="__codelineno-59-25" href="#__codelineno-59-25"></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-59-26" name="__codelineno-59-26" href="#__codelineno-59-26"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">ma</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="k">break</span><span class="p">;</span>
<a id="__codelineno-59-27" name="__codelineno-59-27" href="#__codelineno-59-27"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
<a id="__codelineno-59-28" name="__codelineno-59-28" href="#__codelineno-59-28"></a><span class="w"> </span><span class="k">try</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">ma</span><span class="p">);</span>
<a id="__codelineno-59-29" name="__codelineno-59-29" href="#__codelineno-59-29"></a><span class="w"> </span><span class="c1">// 循环向下堆化</span>
<a id="__codelineno-59-30" name="__codelineno-59-30" href="#__codelineno-59-30"></a><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ma</span><span class="p">;</span>
<a id="__codelineno-59-31" name="__codelineno-59-31" href="#__codelineno-59-31"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-59-32" name="__codelineno-59-32" href="#__codelineno-59-32"></a><span class="p">}</span>
</code></pre></div>
</div>
</div>
</div>
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<summary>可视化运行</summary>
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target="_blank" rel="noopener noreferrer">全屏观看 &gt;</a></div></p>
</details>
<h2 id="813">8.1.3 &nbsp; 堆的常见应用<a class="headerlink" href="#813" title="Permanent link">&para;</a></h2>
<ul>
<li><strong>优先队列</strong>：堆通常作为实现优先队列的首选数据结构，其入队和出队操作的时间复杂度均为 <span class="arithmatex">\(O(\log n)\)</span> ，而建队操作为 <span class="arithmatex">\(O(n)\)</span> ，这些操作都非常高效。</li>
<li><strong>堆排序</strong>：给定一组数据，我们可以用它们建立一个堆，然后不断地执行元素出堆操作，从而得到有序数据。然而，我们通常会使用一种更优雅的方式实现堆排序，详见“堆排序”章节。</li>
<li><strong>获取最大的 <span class="arithmatex">\(k\)</span> 个元素</strong>：这是一个经典的算法问题，同时也是一种典型应用，例如选择热度前 10 的新闻作为微博热搜，选取销量前 10 的商品等。</li>
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