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chapter_heap/build_heap/index.html
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<a href="../../chapter_hello_algo/" class="md-nav__link ">
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<span class="md-ellipsis">
序
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</a>
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序
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</nav>
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第 0 章 &nbsp; 前言
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第 1 章 &nbsp; 初识算法
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第 2 章 &nbsp; 复杂度分析
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第 3 章 &nbsp; 数据结构
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第 4 章 &nbsp; 数组与链表
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第 5 章 &nbsp; 栈与队列
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第 6 章 &nbsp; 哈希表
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第 7 章 &nbsp; 树
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第 8 章 &nbsp; 堆
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第 9 章 &nbsp; 图
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第 10 章 &nbsp; 搜索
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第 11 章 &nbsp; 排序
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第 12 章 &nbsp; 分治
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第 13 章 &nbsp; 回溯
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第 14 章 &nbsp; 动态规划
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第 15 章 &nbsp; 贪心
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第 16 章 &nbsp; 附录
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参考文献
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<a href="../../chapter_paperbook/" class="md-nav__link ">
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纸质书
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纸质书
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Copyright &copy; 2022-2024 krahets</br>The website content is licensed under <a href="https://creativecommons.org/licenses/by-nc-sa/4.0/">CC BY-NC-SA 4.0</a>
Copyright &copy; 2022-2024 krahets<br>The website content is licensed under <a href="https://creativecommons.org/licenses/by-nc-sa/4.0/">CC BY-NC-SA 4.0</a>
</div>
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序
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序
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第 0 章 &nbsp; 前言
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第 1 章 &nbsp; 初识算法
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第 2 章 &nbsp; 复杂度分析
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第 3 章 &nbsp; 数据结构
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第 4 章 &nbsp; 数组与链表
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第 5 章 &nbsp; 栈与队列
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第 6 章 &nbsp; 哈希表
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第 7 章 &nbsp; 树
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第 8 章 &nbsp; 堆
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第 9 章 &nbsp; 图
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第 10 章 &nbsp; 搜索
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第 11 章 &nbsp; 排序
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第 12 章 &nbsp; 分治
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第 13 章 &nbsp; 回溯
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第 14 章 &nbsp; 动态规划
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第 15 章 &nbsp; 贪心
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第 16 章 &nbsp; 附录
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参考文献
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<a href="../../chapter_paperbook/" class="md-nav__link ">
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纸质书
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<!-- Page content -->
<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>
<p><u>堆（heap）</u>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>
<li><u>小顶堆（min heap）</u>：任意节点的值 <span class="arithmatex">\(\leq\)</span> 其子节点的值。</li>
<li><u>大顶堆（max heap）</u>：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>
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<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>
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<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>需要指出的是，许多编程语言提供的是<u>优先队列（priority queue）</u>，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>
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</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>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<u>堆化（heapify）</u>。</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>
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第 0 章 &nbsp; 前言
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第 1 章 &nbsp; 初识算法
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第 11 章 &nbsp; 排序
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第 12 章 &nbsp; 分治
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第 13 章 &nbsp; 回溯
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第 14 章 &nbsp; 动态规划
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第 15 章 &nbsp; 贪心
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第 16 章 &nbsp; 附录
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参考文献
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纸质书
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纸质书
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Copyright &copy; 2022-2024 krahets</br>The website content is licensed under <a href="https://creativecommons.org/licenses/by-nc-sa/4.0/">CC BY-NC-SA 4.0</a>
Copyright &copy; 2022-2024 krahets<br>The website content is licensed under <a href="https://creativecommons.org/licenses/by-nc-sa/4.0/">CC BY-NC-SA 4.0</a>
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chapter_heap/summary/index.html
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序
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序
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第 0 章 &nbsp; 前言
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第 1 章 &nbsp; 初识算法
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第 2 章 &nbsp; 复杂度分析
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第 3 章 &nbsp; 数据结构
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第 4 章 &nbsp; 数组与链表
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第 5 章 &nbsp; 栈与队列
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第 6 章 &nbsp; 哈希表
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第 7 章 &nbsp; 树
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第 8 章 &nbsp; 堆
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第 9 章 &nbsp; 图
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第 10 章 &nbsp; 搜索
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第 11 章 &nbsp; 排序
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第 12 章 &nbsp; 分治
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第 13 章 &nbsp; 回溯
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第 14 章 &nbsp; 动态规划
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第 15 章 &nbsp; 贪心
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第 16 章 &nbsp; 附录
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参考文献
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纸质书
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纸质书
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Copyright &copy; 2022-2024 krahets</br>The website content is licensed under <a href="https://creativecommons.org/licenses/by-nc-sa/4.0/">CC BY-NC-SA 4.0</a>
Copyright &copy; 2022-2024 krahets<br>The website content is licensed under <a href="https://creativecommons.org/licenses/by-nc-sa/4.0/">CC BY-NC-SA 4.0</a>
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chapter_heap/top_k/index.html
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序
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序
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第 0 章 &nbsp; 前言
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第 1 章 &nbsp; 初识算法
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第 2 章 &nbsp; 复杂度分析
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第 3 章 &nbsp; 数据结构
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第 4 章 &nbsp; 数组与链表
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第 5 章 &nbsp; 栈与队列
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第 6 章 &nbsp; 哈希表
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第 7 章 &nbsp; 树
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第 8 章 &nbsp; 堆
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第 9 章 &nbsp; 图
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第 10 章 &nbsp; 搜索
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第 11 章 &nbsp; 排序
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第 12 章 &nbsp; 分治
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第 13 章 &nbsp; 回溯
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第 14 章 &nbsp; 动态规划
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第 15 章 &nbsp; 贪心
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第 16 章 &nbsp; 附录
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参考文献
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纸质书
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纸质书
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