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< title > 8.1. < / title >
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跳转至
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Hello 算法
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8.1. 堆
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正在初始化搜索引擎
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krahets/hello-algo
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Hello 算法
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0. 前言
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0. 前言
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0.1. 关于本书
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< a href = "../../chapter_preface/suggestions/" class = "md-nav__link" >
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0.2. 如何使用本书
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0.3. 小结
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< a href = "../../chapter_introduction/" class = "md-nav__link " >
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1. 初识算法
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1. 初识算法
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1.1. 算法无处不在
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1.2. 算法是什么
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1.3. 小结
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< a href = "../../chapter_computational_complexity/" class = "md-nav__link " >
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2. 复杂度
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2. 复杂度
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2.1. 算法效率评估
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2.2. 时间复杂度
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2.3. 空间复杂度
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2.4. 小结
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< a href = "../../chapter_data_structure/" class = "md-nav__link " >
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< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M12 3C7.58 3 4 4.79 4 7v10c0 2.21 3.59 4 8 4s8-1.79 8-4V7c0-2.21-3.58-4-8-4m6 14c0 .5-2.13 2-6 2s-6-1.5-6-2v-2.23c1.61.78 3.72 1.23 6 1.23s4.39-.45 6-1.23V17m0-4.55c-1.3.95-3.58 1.55-6 1.55s-4.7-.6-6-1.55V9.64c1.47.83 3.61 1.36 6 1.36s4.53-.53 6-1.36v2.81M12 9C8.13 9 6 7.5 6 7s2.13-2 6-2 6 1.5 6 2-2.13 2-6 2Z" / > < / svg >
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3. 数据结构
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3. 数据结构
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3.1. 数据结构分类
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3.2. 基本数据类型
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3.3. 数字编码 *
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3.4. 字符编码 *
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3.5. 小结
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< a href = "../../chapter_array_and_linkedlist/" class = "md-nav__link " >
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4. 数组与链表
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4. 数组与链表
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4.1. 数组
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4.2. 链表
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< li class = "md-nav__item" >
< a href = "../../chapter_array_and_linkedlist/list/" class = "md-nav__link" >
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4.3. 列表
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4.4. 小结
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< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_stack_and_queue/" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z" / > < / svg >
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5. 栈与队列
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< label class = "md-nav__title" for = "__nav_6" >
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5. 栈与队列
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< li class = "md-nav__item" >
< a href = "../../chapter_stack_and_queue/stack/" class = "md-nav__link" >
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5.1. 栈
< / span >
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< / a >
< / li >
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< li class = "md-nav__item" >
< a href = "../../chapter_stack_and_queue/queue/" class = "md-nav__link" >
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5.2. 队列
< / span >
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< / a >
< / li >
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< li class = "md-nav__item" >
< a href = "../../chapter_stack_and_queue/deque/" class = "md-nav__link" >
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5.3. 双向队列
< / span >
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< / a >
< / li >
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< li class = "md-nav__item" >
< a href = "../../chapter_stack_and_queue/summary/" class = "md-nav__link" >
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5.4. 小结
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< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_hashing/" class = "md-nav__link " >
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6. 散列表
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< / a >
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6. 散列表
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< a href = "../../chapter_hashing/hash_map/" class = "md-nav__link" >
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6.1. 哈希表
< / span >
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< / a >
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< li class = "md-nav__item" >
< a href = "../../chapter_hashing/hash_collision/" class = "md-nav__link" >
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6.2. 哈希冲突
< / span >
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< a href = "../../chapter_hashing/hash_algorithm/" class = "md-nav__link" >
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6.3. 哈希算法
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< a href = "../../chapter_hashing/summary/" class = "md-nav__link" >
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6.4. 小结
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< a href = "../../chapter_tree/" class = "md-nav__link " >
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7. 树
< / span >
< / a >
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< / label >
< / div >
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< span class = "md-nav__icon md-icon" > < / span >
7. 树
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< a href = "../../chapter_tree/binary_tree/" class = "md-nav__link" >
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7.1. 二叉树
< / span >
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< a href = "../../chapter_tree/binary_tree_traversal/" class = "md-nav__link" >
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7.2. 二叉树遍历
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< li class = "md-nav__item" >
< a href = "../../chapter_tree/array_representation_of_tree/" class = "md-nav__link" >
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7.3. 二叉树数组表示
< / span >
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< li class = "md-nav__item" >
< a href = "../../chapter_tree/binary_search_tree/" class = "md-nav__link" >
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7.4. 二叉搜索树
< / span >
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< li class = "md-nav__item" >
< a href = "../../chapter_tree/avl_tree/" class = "md-nav__link" >
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7.5. AVL 树 *
< / span >
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< a href = "../../chapter_tree/summary/" class = "md-nav__link" >
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7.6. 小结
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< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_9" checked >
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8. 堆
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8. 堆
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8.1. 堆
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< a href = "./" class = "md-nav__link md-nav__link--active" >
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8.1. 堆
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目录
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8.1.1. 堆常用操作
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8.1.2. 堆的实现
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< / a >
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< nav class = "md-nav" aria-label = "8.1.2. >
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< a href = "#_1" class = "md-nav__link" >
堆的存储与表示
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< a href = "#_2" class = "md-nav__link" >
访问堆顶元素
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< / li >
< li class = "md-nav__item" >
< a href = "#_3" class = "md-nav__link" >
元素入堆
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "#_4" class = "md-nav__link" >
堆顶元素出堆
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< li class = "md-nav__item" >
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< a href = "#813" class = "md-nav__link" >
8.1.3. 堆常见应用
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< li class = "md-nav__item" >
< a href = "../build_heap/" class = "md-nav__link" >
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< span class = "md-ellipsis" >
8.2. 建堆操作
< / span >
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< / a >
< / li >
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< li class = "md-nav__item" >
< a href = "../top_k/" class = "md-nav__link" >
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< span class = "md-ellipsis" >
8.3. Top-K 问题
< / span >
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< / a >
< / li >
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< li class = "md-nav__item" >
< a href = "../summary/" class = "md-nav__link" >
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< span class = "md-ellipsis" >
8.4. 小结
< / span >
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< / a >
< / li >
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< / ul >
< / nav >
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< / li >
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< li class = "md-nav__item md-nav__item--nested" >
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< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_10" >
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< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_graph/" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z" / > < / svg >
< span class = "md-ellipsis" >
9. 图
< / span >
< / a >
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< label class = "md-nav__link " for = "__nav_10" >
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_10_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_10" >
< span class = "md-nav__icon md-icon" > < / span >
9. 图
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
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< li class = "md-nav__item" >
< a href = "../../chapter_graph/graph/" class = "md-nav__link" >
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< span class = "md-ellipsis" >
9.1. 图
< / span >
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< / a >
< / li >
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< li class = "md-nav__item" >
< a href = "../../chapter_graph/graph_operations/" class = "md-nav__link" >
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< span class = "md-ellipsis" >
9.2. 图基础操作
< / span >
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< / a >
< / li >
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< li class = "md-nav__item" >
< a href = "../../chapter_graph/graph_traversal/" class = "md-nav__link" >
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< span class = "md-ellipsis" >
9.3. 图的遍历
< / span >
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< / a >
< / li >
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< li class = "md-nav__item" >
< a href = "../../chapter_graph/summary/" class = "md-nav__link" >
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< span class = "md-ellipsis" >
9.4. 小结
< / span >
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< / a >
< / li >
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< / ul >
< / nav >
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< / li >
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< li class = "md-nav__item md-nav__item--nested" >
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< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_11" >
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< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_searching/" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z" / > < / svg >
< span class = "md-ellipsis" >
10. 搜索
< / span >
< / a >
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< label class = "md-nav__link " for = "__nav_11" >
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_11_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_11" >
< span class = "md-nav__icon md-icon" > < / span >
10. 搜索
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
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< li class = "md-nav__item" >
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< a href = "../../chapter_searching/binary_search/" class = "md-nav__link" >
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< span class = "md-ellipsis" >
10.1. 二分查找
< / span >
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< / a >
< / li >
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< li class = "md-nav__item" >
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< a href = "../../chapter_searching/binary_search_edge/" class = "md-nav__link" >
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< span class = "md-ellipsis" >
10.2. 二分查找边界
< / span >
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< / a >
< / li >
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< li class = "md-nav__item" >
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< a href = "../../chapter_searching/replace_linear_by_hashing/" class = "md-nav__link" >
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< span class = "md-ellipsis" >
10.3. 哈希优化策略
< / span >
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< / a >
< / li >
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< li class = "md-nav__item" >
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< a href = "../../chapter_searching/searching_algorithm_revisited/" class = "md-nav__link" >
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< span class = "md-ellipsis" >
10.4. 重识搜索算法
< / span >
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< / a >
< / li >
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< li class = "md-nav__item" >
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< a href = "../../chapter_searching/summary/" class = "md-nav__link" >
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< span class = "md-ellipsis" >
10.5. 小结
< / span >
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< / a >
< / li >
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< / ul >
< / nav >
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< / li >
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< li class = "md-nav__item md-nav__item--nested" >
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< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_12" >
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< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_sorting/" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z" / > < / svg >
< span class = "md-ellipsis" >
11. 排序
< / span >
< / a >
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< label class = "md-nav__link " for = "__nav_12" >
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_12_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_12" >
< span class = "md-nav__icon md-icon" > < / span >
11. 排序
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
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< li class = "md-nav__item" >
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< a href = "../../chapter_sorting/sorting_algorithm/" class = "md-nav__link" >
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< span class = "md-ellipsis" >
11.1. 排序算法
< / span >
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< / a >
< / li >
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< li class = "md-nav__item" >
< a href = "../../chapter_sorting/selection_sort/" class = "md-nav__link" >
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< span class = "md-ellipsis" >
11.2. 选择排序
< / span >
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< / a >
< / li >
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< li class = "md-nav__item" >
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< a href = "../../chapter_sorting/bubble_sort/" class = "md-nav__link" >
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< span class = "md-ellipsis" >
11.3. 冒泡排序
< / span >
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< / a >
< / li >
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< li class = "md-nav__item" >
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< a href = "../../chapter_sorting/insertion_sort/" class = "md-nav__link" >
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< span class = "md-ellipsis" >
11.4. 插入排序
< / span >
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< / a >
< / li >
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< li class = "md-nav__item" >
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< a href = "../../chapter_sorting/quick_sort/" class = "md-nav__link" >
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< span class = "md-ellipsis" >
11.5. 快速排序
< / span >
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< / a >
< / li >
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< li class = "md-nav__item" >
< a href = "../../chapter_sorting/merge_sort/" class = "md-nav__link" >
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< span class = "md-ellipsis" >
11.6. 归并排序
< / span >
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< / a >
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< / li >
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< li class = "md-nav__item" >
< a href = "../../chapter_sorting/heap_sort/" class = "md-nav__link" >
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< span class = "md-ellipsis" >
11.7. 堆排序
< / span >
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< / a >
< / li >
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< li class = "md-nav__item" >
< a href = "../../chapter_sorting/bucket_sort/" class = "md-nav__link" >
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< span class = "md-ellipsis" >
11.8. 桶排序
< / span >
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< / a >
< / li >
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< li class = "md-nav__item" >
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< a href = "../../chapter_sorting/counting_sort/" class = "md-nav__link" >
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< span class = "md-ellipsis" >
11.9. 计数排序
< / span >
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< / a >
< / li >
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< li class = "md-nav__item" >
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< a href = "../../chapter_sorting/radix_sort/" class = "md-nav__link" >
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< span class = "md-ellipsis" >
11.10. 基数排序
< / span >
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< / a >
< / li >
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< li class = "md-nav__item" >
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< a href = "../../chapter_sorting/summary/" class = "md-nav__link" >
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< span class = "md-ellipsis" >
11.11. 小结
< / span >
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< / a >
< / li >
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< / ul >
< / nav >
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< / li >
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12.5. 小结
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13.3. 子集和问题
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14. 动态规划
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14.1. 初探动态规划
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14.2. DP 问题特性
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14.3. DP 解题思路
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14.4. 0-1 背包问题
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14.7. 小结
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目录
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8.1.1. 堆常用操作
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8.1.2. 堆的实现
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堆的存储与表示
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访问堆顶元素
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元素入堆
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堆顶元素出堆
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8.1.3. 堆常见应用
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< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M10 20H6V4h7v5h5v3.1l2-2V8l-6-6H6c-1.1 0-2 .9-2 2v16c0 1.1.9 2 2 2h4v-2m10.2-7c.1 0 .3.1.4.2l1.3 1.3c.2.2.2.6 0 .8l-1 1-2.1-2.1 1-1c.1-.1.2-.2.4-.2m0 3.9L14.1 23H12v-2.1l6.1-6.1 2.1 2.1Z" / > < / svg >
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< h1 id = "81" > 8.1. 堆< a class = "headerlink" href = "#81" title = "Permanent link" > ¶ < / a > < / h1 >
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< p > 「堆 Heap」是一种满足特定条件的完全二叉树， ： < / p >
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< ul >
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< li > 「大顶堆 Max Heap」， < span class = "arithmatex" > \(\geq\)< / span > 其子节点的值；< / li >
< li > 「小顶堆 Min Heap」， < span class = "arithmatex" > \(\leq\)< / span > 其子节点的值；< / li >
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< / ul >
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< p > < img alt = "小顶堆与大顶堆" src = "../heap.assets/min_heap_and_max_heap.png" / > < / p >
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< p align = "center" > Fig. 小顶堆与大顶堆 < / p >
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< p > 堆作为完全二叉树的一个特例，具有以下特性：< / p >
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< ul >
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< 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（即根节点）的值分别是最大（最小）的。< / li >
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< h2 id = "811" > 8.1.1. 堆常用操作< a class = "headerlink" href = "#811" title = "Permanent link" > ¶ < / a > < / h2 >
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< p > 需要指出的是，许多编程语言提供的是「优先队列 Priority Queue」， ， < / p >
< p > 实际上，< strong > 堆通常用作实现优先队列，大顶堆相当于元素按从大到小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，统一使用「堆」来命名。< / p >
< p > 堆的常用操作见下表，方法名需要根据编程语言来确定。< / p >
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< div class = "center-table" >
< table >
< thead >
< tr >
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< th > 方法名< / th >
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< th > 描述< / th >
< th > 时间复杂度< / th >
< / tr >
< / thead >
< tbody >
< tr >
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< td > push()< / td >
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< td > 元素入堆< / td >
< td > < span class = "arithmatex" > \(O(\log n)\)< / span > < / td >
< / tr >
< tr >
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< td > pop()< / td >
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< td > 堆顶元素出堆< / td >
< td > < span class = "arithmatex" > \(O(\log n)\)< / span > < / td >
< / tr >
< tr >
< td > peek()< / td >
< td > 访问堆顶元素（大 / 小顶堆分别为最大 / 小值）< / td >
< td > < span class = "arithmatex" > \(O(1)\)< / span > < / td >
< / tr >
< tr >
< td > size()< / td >
< td > 获取堆的元素数量< / td >
< td > < span class = "arithmatex" > \(O(1)\)< / span > < / td >
< / tr >
< tr >
< td > isEmpty()< / td >
< td > 判断堆是否为空< / td >
< td > < span class = "arithmatex" > \(O(1)\)< / span > < / td >
< / tr >
< / tbody >
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< 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 >
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< div class = "admonition tip" >
< p class = "admonition-title" > Tip< / p >
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< p > 类似于排序算法中的“从小到大排列”和“从大到小排列”，我们可以通过修改 Comparator 来实现“小顶堆”与“大顶堆”之间的转换。< / p >
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< / div >
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< div class = "tabbed-set tabbed-alternate" data-tabs = "1:11" > < input checked = "checked" id = "__tabbed_1_1" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_2" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_3" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_4" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_5" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_6" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_7" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_8" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_9" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_10" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_11" name = "__tabbed_1" type = "radio" / > < div class = "tabbed-labels" > < label for = "__tabbed_1_1" > Java< / label > < label for = "__tabbed_1_2" > C++< / label > < label for = "__tabbed_1_3" > Python< / label > < label for = "__tabbed_1_4" > Go< / label > < label for = "__tabbed_1_5" > JavaScript< / label > < label for = "__tabbed_1_6" > TypeScript< / label > < label for = "__tabbed_1_7" > C< / label > < label for = "__tabbed_1_8" > C#< / label > < label for = "__tabbed_1_9" > Swift< / label > < label for = "__tabbed_1_10" > Zig< / label > < label for = "__tabbed_1_11" > Dart< / label > < / div >
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< div class = "tabbed-content" >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > heap.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-0-1" name = "__codelineno-0-1" href = "#__codelineno-0-1" > < / a > < span class = "cm" > /* 初始化堆 */< / span >
< a id = "__codelineno-0-2" name = "__codelineno-0-2" href = "#__codelineno-0-2" > < / a > < span class = "c1" > // 初始化小顶堆< / span >
< a id = "__codelineno-0-3" name = "__codelineno-0-3" href = "#__codelineno-0-3" > < / a > < span class = "n" > Queue< / span > < span class = "o" > < < / span > < span class = "n" > Integer< / span > < span class = "o" > > < / 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" > < > < / span > < span class = "p" > ();< / span >
< a id = "__codelineno-0-4" name = "__codelineno-0-4" href = "#__codelineno-0-4" > < / a > < span class = "c1" > // 初始化大顶堆（使用 lambda 表达式修改 Comparator 即可）< / span >
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< a id = "__codelineno-0-5" name = "__codelineno-0-5" href = "#__codelineno-0-5" > < / a > < span class = "n" > Queue< / span > < span class = "o" > < < / span > < span class = "n" > Integer< / span > < span class = "o" > > < / 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" > < > < / 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" > -> < / 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 >
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< a id = "__codelineno-0-6" name = "__codelineno-0-6" href = "#__codelineno-0-6" > < / a >
< a id = "__codelineno-0-7" name = "__codelineno-0-7" href = "#__codelineno-0-7" > < / a > < span class = "cm" > /* 元素入堆 */< / span >
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< a id = "__codelineno-0-8" name = "__codelineno-0-8" href = "#__codelineno-0-8" > < / 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-0-9" name = "__codelineno-0-9" href = "#__codelineno-0-9" > < / 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-0-10" name = "__codelineno-0-10" href = "#__codelineno-0-10" > < / 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-0-11" name = "__codelineno-0-11" href = "#__codelineno-0-11" > < / 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-0-12" name = "__codelineno-0-12" href = "#__codelineno-0-12" > < / 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 >
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< a id = "__codelineno-0-13" name = "__codelineno-0-13" href = "#__codelineno-0-13" > < / a >
< a id = "__codelineno-0-14" name = "__codelineno-0-14" href = "#__codelineno-0-14" > < / a > < span class = "cm" > /* 获取堆顶元素 */< / span >
< a id = "__codelineno-0-15" name = "__codelineno-0-15" href = "#__codelineno-0-15" > < / 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-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 = "cm" > /* 堆顶元素出堆 */< / span >
< a id = "__codelineno-0-18" name = "__codelineno-0-18" href = "#__codelineno-0-18" > < / a > < span class = "c1" > // 出堆元素会形成一个从大到小的序列< / span >
< a id = "__codelineno-0-19" name = "__codelineno-0-19" href = "#__codelineno-0-19" > < / a > < span class = "n" > peek< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > heap< / 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-0-20" name = "__codelineno-0-20" href = "#__codelineno-0-20" > < / a > < span class = "n" > peek< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > heap< / 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-0-21" name = "__codelineno-0-21" href = "#__codelineno-0-21" > < / a > < span class = "n" > peek< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > heap< / 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-0-22" name = "__codelineno-0-22" href = "#__codelineno-0-22" > < / a > < span class = "n" > peek< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > heap< / 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-0-23" name = "__codelineno-0-23" href = "#__codelineno-0-23" > < / a > < span class = "n" > peek< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > heap< / 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-0-24" name = "__codelineno-0-24" href = "#__codelineno-0-24" > < / a >
< a id = "__codelineno-0-25" name = "__codelineno-0-25" href = "#__codelineno-0-25" > < / a > < span class = "cm" > /* 获取堆大小 */< / span >
< a id = "__codelineno-0-26" name = "__codelineno-0-26" href = "#__codelineno-0-26" > < / 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-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 = "cm" > /* 判断堆是否为空 */< / span >
< a id = "__codelineno-0-29" name = "__codelineno-0-29" href = "#__codelineno-0-29" > < / 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-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 = "cm" > /* 输入列表并建堆 */< / span >
< a id = "__codelineno-0-32" name = "__codelineno-0-32" href = "#__codelineno-0-32" > < / 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" > < > < / 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 >
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< 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" > < < / span > < span class = "kt" > int< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > greater< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > > < / 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" > < < / span > < span class = "kt" > int< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > less< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > > < / 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" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / 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" > < < / span > < span class = "kt" > int< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > greater< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > > < / 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 >
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2023-02-23 20:23:42 +08:00
< div class = "highlight" > < span class = "filename" > heap.py< / span > < pre > < span > < / span > < code > < a id = "__codelineno-2-1" name = "__codelineno-2-1" href = "#__codelineno-2-1" > < / a > < span class = "c1" > # 初始化小顶堆< / span >
< a id = "__codelineno-2-2" name = "__codelineno-2-2" href = "#__codelineno-2-2" > < / 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-2-3" name = "__codelineno-2-3" href = "#__codelineno-2-3" > < / a > < span class = "c1" > # 初始化大顶堆< / span >
< a id = "__codelineno-2-4" name = "__codelineno-2-4" href = "#__codelineno-2-4" > < / 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-2-5" name = "__codelineno-2-5" href = "#__codelineno-2-5" > < / a >
< a id = "__codelineno-2-6" name = "__codelineno-2-6" href = "#__codelineno-2-6" > < / a > < span class = "c1" > # Python 的 heapq 模块默认实现小顶堆< / span >
< a id = "__codelineno-2-7" name = "__codelineno-2-7" href = "#__codelineno-2-7" > < / 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-2-8" name = "__codelineno-2-8" href = "#__codelineno-2-8" > < / a > < span class = "c1" > # 在本示例中， ， < / span >
2023-04-09 05:30:54 +08:00
< a id = "__codelineno-2-9" name = "__codelineno-2-9" href = "#__codelineno-2-9" > < / a >
< a id = "__codelineno-2-10" name = "__codelineno-2-10" href = "#__codelineno-2-10" > < / a > < span class = "c1" > # 元素入堆< / span >
< a id = "__codelineno-2-11" name = "__codelineno-2-11" href = "#__codelineno-2-11" > < / 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-2-12" name = "__codelineno-2-12" href = "#__codelineno-2-12" > < / 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-2-13" name = "__codelineno-2-13" href = "#__codelineno-2-13" > < / 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-2-14" name = "__codelineno-2-14" href = "#__codelineno-2-14" > < / 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-2-15" name = "__codelineno-2-15" href = "#__codelineno-2-15" > < / 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-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 = "c1" > # 获取堆顶元素< / span >
< a id = "__codelineno-2-18" name = "__codelineno-2-18" href = "#__codelineno-2-18" > < / 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-2-19" name = "__codelineno-2-19" href = "#__codelineno-2-19" > < / a >
< a id = "__codelineno-2-20" name = "__codelineno-2-20" href = "#__codelineno-2-20" > < / a > < span class = "c1" > # 堆顶元素出堆< / span >
< a id = "__codelineno-2-21" name = "__codelineno-2-21" href = "#__codelineno-2-21" > < / a > < span class = "c1" > # 出堆元素会形成一个从大到小的序列< / span >
< a id = "__codelineno-2-22" name = "__codelineno-2-22" href = "#__codelineno-2-22" > < / 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-2-23" name = "__codelineno-2-23" href = "#__codelineno-2-23" > < / 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-2-24" name = "__codelineno-2-24" href = "#__codelineno-2-24" > < / 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-2-25" name = "__codelineno-2-25" href = "#__codelineno-2-25" > < / 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-2-26" name = "__codelineno-2-26" href = "#__codelineno-2-26" > < / 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-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 = "c1" > # 获取堆大小< / span >
< a id = "__codelineno-2-29" name = "__codelineno-2-29" href = "#__codelineno-2-29" > < / 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-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 = "c1" > # 判断堆是否为空< / span >
< a id = "__codelineno-2-32" name = "__codelineno-2-32" href = "#__codelineno-2-32" > < / 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-2-33" name = "__codelineno-2-33" href = "#__codelineno-2-33" > < / a >
< a id = "__codelineno-2-34" name = "__codelineno-2-34" href = "#__codelineno-2-34" > < / a > < span class = "c1" > # 输入列表并建堆< / span >
< a id = "__codelineno-2-35" name = "__codelineno-2-35" href = "#__codelineno-2-35" > < / a > < span class = "n" > min_heap< / span > < span class = "p" > :< / span > < span class = "n" > List< / span > < span class = "p" > [< / span > < span class = "nb" > int< / span > < span class = "p" > ]< / span > < span class = "o" > =< / span > < span class = "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-2-36" name = "__codelineno-2-36" href = "#__codelineno-2-36" > < / 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 >
2023-02-08 14:54:41 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > heap.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-3-1" name = "__codelineno-3-1" href = "#__codelineno-3-1" > < / 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-3-2" name = "__codelineno-3-2" href = "#__codelineno-3-2" > < / a > < span class = "c1" > // 实现 heap.Interface 需要同时实现 sort.Interface< / span >
< a id = "__codelineno-3-3" name = "__codelineno-3-3" href = "#__codelineno-3-3" > < / 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-3-4" name = "__codelineno-3-4" href = "#__codelineno-3-4" > < / a >
< a id = "__codelineno-3-5" name = "__codelineno-3-5" href = "#__codelineno-3-5" > < / a > < span class = "c1" > // Push heap.Interface 的方法，实现推入元素到堆< / span >
< a id = "__codelineno-3-6" name = "__codelineno-3-6" href = "#__codelineno-3-6" > < / 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-3-7" name = "__codelineno-3-7" href = "#__codelineno-3-7" > < / a > < span class = "w" > < / span > < span class = "c1" > // Push 和 Pop 使用 pointer receiver 作为参数< / span >
< a id = "__codelineno-3-8" name = "__codelineno-3-8" href = "#__codelineno-3-8" > < / 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-3-9" name = "__codelineno-3-9" href = "#__codelineno-3-9" > < / 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-3-10" name = "__codelineno-3-10" href = "#__codelineno-3-10" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-3-11" name = "__codelineno-3-11" href = "#__codelineno-3-11" > < / a >
< a id = "__codelineno-3-12" name = "__codelineno-3-12" href = "#__codelineno-3-12" > < / a > < span class = "c1" > // Pop heap.Interface 的方法，实现弹出堆顶元素< / span >
< a id = "__codelineno-3-13" name = "__codelineno-3-13" href = "#__codelineno-3-13" > < / 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-3-14" name = "__codelineno-3-14" href = "#__codelineno-3-14" > < / a > < span class = "w" > < / span > < span class = "c1" > // 待出堆元素存放在最后< / span >
< a id = "__codelineno-3-15" name = "__codelineno-3-15" href = "#__codelineno-3-15" > < / 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-3-16" name = "__codelineno-3-16" href = "#__codelineno-3-16" > < / 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-3-17" name = "__codelineno-3-17" href = "#__codelineno-3-17" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > last< / span >
< a id = "__codelineno-3-18" name = "__codelineno-3-18" href = "#__codelineno-3-18" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-3-19" name = "__codelineno-3-19" href = "#__codelineno-3-19" > < / a >
< a id = "__codelineno-3-20" name = "__codelineno-3-20" href = "#__codelineno-3-20" > < / a > < span class = "c1" > // Len sort.Interface 的方法< / span >
< a id = "__codelineno-3-21" name = "__codelineno-3-21" href = "#__codelineno-3-21" > < / 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-3-22" name = "__codelineno-3-22" href = "#__codelineno-3-22" > < / 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-3-23" name = "__codelineno-3-23" href = "#__codelineno-3-23" > < / a > < span class = "p" > }< / 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 = "c1" > // Less sort.Interface 的方法< / span >
< a id = "__codelineno-3-26" name = "__codelineno-3-26" href = "#__codelineno-3-26" > < / 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-3-27" name = "__codelineno-3-27" href = "#__codelineno-3-27" > < / 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-3-28" name = "__codelineno-3-28" href = "#__codelineno-3-28" > < / 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" > > < / 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-3-29" name = "__codelineno-3-29" href = "#__codelineno-3-29" > < / a > < 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 = "c1" > // Swap sort.Interface 的方法< / span >
< a id = "__codelineno-3-32" name = "__codelineno-3-32" href = "#__codelineno-3-32" > < / 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-3-33" name = "__codelineno-3-33" href = "#__codelineno-3-33" > < / 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-3-34" name = "__codelineno-3-34" href = "#__codelineno-3-34" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-3-35" name = "__codelineno-3-35" href = "#__codelineno-3-35" > < / a >
< a id = "__codelineno-3-36" name = "__codelineno-3-36" href = "#__codelineno-3-36" > < / a > < span class = "c1" > // Top 获取堆顶元素< / span >
< a id = "__codelineno-3-37" name = "__codelineno-3-37" href = "#__codelineno-3-37" > < / 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-3-38" name = "__codelineno-3-38" href = "#__codelineno-3-38" > < / 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-3-39" name = "__codelineno-3-39" href = "#__codelineno-3-39" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-3-40" name = "__codelineno-3-40" href = "#__codelineno-3-40" > < / a >
< a id = "__codelineno-3-41" name = "__codelineno-3-41" href = "#__codelineno-3-41" > < / a > < span class = "cm" > /* Driver Code */< / span >
< a id = "__codelineno-3-42" name = "__codelineno-3-42" href = "#__codelineno-3-42" > < / 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-3-43" name = "__codelineno-3-43" href = "#__codelineno-3-43" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 初始化堆 */< / span >
< a id = "__codelineno-3-44" name = "__codelineno-3-44" href = "#__codelineno-3-44" > < / a > < span class = "w" > < / span > < span class = "c1" > // 初始化大顶堆< / span >
< a id = "__codelineno-3-45" name = "__codelineno-3-45" href = "#__codelineno-3-45" > < / 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" > & < / span > < span class = "nx" > intHeap< / span > < span class = "p" > {}< / span >
< a id = "__codelineno-3-46" name = "__codelineno-3-46" href = "#__codelineno-3-46" > < / 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-3-47" name = "__codelineno-3-47" href = "#__codelineno-3-47" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 元素入堆 */< / span >
< a id = "__codelineno-3-48" name = "__codelineno-3-48" href = "#__codelineno-3-48" > < / a > < span class = "w" > < / span > < span class = "c1" > // 调用 heap.Interface 的方法，来添加元素< / span >
< a id = "__codelineno-3-49" name = "__codelineno-3-49" href = "#__codelineno-3-49" > < / 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-3-50" name = "__codelineno-3-50" href = "#__codelineno-3-50" > < / 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-3-51" name = "__codelineno-3-51" href = "#__codelineno-3-51" > < / 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-3-52" name = "__codelineno-3-52" href = "#__codelineno-3-52" > < / 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-3-53" name = "__codelineno-3-53" href = "#__codelineno-3-53" > < / 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-3-54" name = "__codelineno-3-54" href = "#__codelineno-3-54" > < / a >
< a id = "__codelineno-3-55" name = "__codelineno-3-55" href = "#__codelineno-3-55" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 获取堆顶元素 */< / span >
< a id = "__codelineno-3-56" name = "__codelineno-3-56" href = "#__codelineno-3-56" > < / 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-3-57" name = "__codelineno-3-57" href = "#__codelineno-3-57" > < / 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" > " 堆顶元素为 %d\n" < / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > top< / span > < span class = "p" > )< / span >
< a id = "__codelineno-3-58" name = "__codelineno-3-58" href = "#__codelineno-3-58" > < / a >
< a id = "__codelineno-3-59" name = "__codelineno-3-59" href = "#__codelineno-3-59" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 堆顶元素出堆 */< / span >
< a id = "__codelineno-3-60" name = "__codelineno-3-60" href = "#__codelineno-3-60" > < / a > < span class = "w" > < / span > < span class = "c1" > // 调用 heap.Interface 的方法，来移除元素< / span >
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< a id = "__codelineno-3-61" name = "__codelineno-3-61" href = "#__codelineno-3-61" > < / 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-3-62" name = "__codelineno-3-62" href = "#__codelineno-3-62" > < / 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-3-63" name = "__codelineno-3-63" href = "#__codelineno-3-63" > < / 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-3-64" name = "__codelineno-3-64" href = "#__codelineno-3-64" > < / 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-3-65" name = "__codelineno-3-65" href = "#__codelineno-3-65" > < / 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 >
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< a id = "__codelineno-3-66" name = "__codelineno-3-66" href = "#__codelineno-3-66" > < / a >
< a id = "__codelineno-3-67" name = "__codelineno-3-67" href = "#__codelineno-3-67" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 获取堆大小 */< / span >
< a id = "__codelineno-3-68" name = "__codelineno-3-68" href = "#__codelineno-3-68" > < / 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-3-69" name = "__codelineno-3-69" href = "#__codelineno-3-69" > < / 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" > " 堆元素数量为 %d\n" < / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > size< / span > < span class = "p" > )< / span >
< a id = "__codelineno-3-70" name = "__codelineno-3-70" href = "#__codelineno-3-70" > < / a >
< a id = "__codelineno-3-71" name = "__codelineno-3-71" href = "#__codelineno-3-71" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 判断堆是否为空 */< / span >
< a id = "__codelineno-3-72" name = "__codelineno-3-72" href = "#__codelineno-3-72" > < / 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-3-73" name = "__codelineno-3-73" href = "#__codelineno-3-73" > < / 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" > " 堆是否为空 %t\n" < / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > isEmpty< / span > < span class = "p" > )< / span >
< a id = "__codelineno-3-74" name = "__codelineno-3-74" href = "#__codelineno-3-74" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > heap.js< / span > < pre > < span > < / span > < code > < a id = "__codelineno-4-1" name = "__codelineno-4-1" href = "#__codelineno-4-1" > < / a > < span class = "c1" > // JavaScript 未提供内置 Heap 类< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > heap.ts< / span > < pre > < span > < / span > < code > < a id = "__codelineno-5-1" name = "__codelineno-5-1" href = "#__codelineno-5-1" > < / a > < span class = "c1" > // TypeScript 未提供内置 Heap 类< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > heap.c< / span > < pre > < span > < / span > < code > < a id = "__codelineno-6-1" name = "__codelineno-6-1" href = "#__codelineno-6-1" > < / a > < span class = "c1" > // C 未提供内置 Heap 类< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-02-15 21:48:29 +08:00
< div class = "highlight" > < span class = "filename" > heap.cs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-7-1" name = "__codelineno-7-1" href = "#__codelineno-7-1" > < / a > < span class = "cm" > /* 初始化堆 */< / span >
< a id = "__codelineno-7-2" name = "__codelineno-7-2" href = "#__codelineno-7-2" > < / a > < span class = "c1" > // 初始化小顶堆< / span >
< a id = "__codelineno-7-3" name = "__codelineno-7-3" href = "#__codelineno-7-3" > < / a > < span class = "n" > PriorityQueue< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "o" > > < / 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" > < < / span > < span class = "kt" > int< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "p" > ();< / span >
< a id = "__codelineno-7-4" name = "__codelineno-7-4" href = "#__codelineno-7-4" > < / 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-7-5" name = "__codelineno-7-5" href = "#__codelineno-7-5" > < / a > < span class = "n" > PriorityQueue< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "o" > > < / 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" > < < / span > < span class = "kt" > int< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "p" > (< / span > < span class = "n" > Comparer< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / 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" > => < / 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-7-6" name = "__codelineno-7-6" href = "#__codelineno-7-6" > < / a >
< a id = "__codelineno-7-7" name = "__codelineno-7-7" href = "#__codelineno-7-7" > < / a > < span class = "cm" > /* 元素入堆 */< / span >
< a id = "__codelineno-7-8" name = "__codelineno-7-8" href = "#__codelineno-7-8" > < / 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-7-9" name = "__codelineno-7-9" href = "#__codelineno-7-9" > < / 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-7-10" name = "__codelineno-7-10" href = "#__codelineno-7-10" > < / 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-7-11" name = "__codelineno-7-11" href = "#__codelineno-7-11" > < / 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-7-12" name = "__codelineno-7-12" href = "#__codelineno-7-12" > < / 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-7-13" name = "__codelineno-7-13" href = "#__codelineno-7-13" > < / a >
< a id = "__codelineno-7-14" name = "__codelineno-7-14" href = "#__codelineno-7-14" > < / a > < span class = "cm" > /* 获取堆顶元素 */< / span >
< a id = "__codelineno-7-15" name = "__codelineno-7-15" href = "#__codelineno-7-15" > < / 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-7-16" name = "__codelineno-7-16" href = "#__codelineno-7-16" > < / a >
< a id = "__codelineno-7-17" name = "__codelineno-7-17" href = "#__codelineno-7-17" > < / a > < span class = "cm" > /* 堆顶元素出堆 */< / span >
< a id = "__codelineno-7-18" name = "__codelineno-7-18" href = "#__codelineno-7-18" > < / a > < span class = "c1" > // 出堆元素会形成一个从大到小的序列< / span >
< a id = "__codelineno-7-19" name = "__codelineno-7-19" href = "#__codelineno-7-19" > < / 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-7-20" name = "__codelineno-7-20" href = "#__codelineno-7-20" > < / 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-7-21" name = "__codelineno-7-21" href = "#__codelineno-7-21" > < / 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-7-22" name = "__codelineno-7-22" href = "#__codelineno-7-22" > < / 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-7-23" name = "__codelineno-7-23" href = "#__codelineno-7-23" > < / 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-7-24" name = "__codelineno-7-24" href = "#__codelineno-7-24" > < / a >
< a id = "__codelineno-7-25" name = "__codelineno-7-25" href = "#__codelineno-7-25" > < / a > < span class = "cm" > /* 获取堆大小 */< / span >
< a id = "__codelineno-7-26" name = "__codelineno-7-26" href = "#__codelineno-7-26" > < / 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-7-27" name = "__codelineno-7-27" href = "#__codelineno-7-27" > < / a >
< a id = "__codelineno-7-28" name = "__codelineno-7-28" href = "#__codelineno-7-28" > < / a > < span class = "cm" > /* 判断堆是否为空 */< / span >
< a id = "__codelineno-7-29" name = "__codelineno-7-29" href = "#__codelineno-7-29" > < / 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-7-30" name = "__codelineno-7-30" href = "#__codelineno-7-30" > < / a >
< a id = "__codelineno-7-31" name = "__codelineno-7-31" href = "#__codelineno-7-31" > < / a > < span class = "cm" > /* 输入列表并建堆 */< / span >
< a id = "__codelineno-7-32" name = "__codelineno-7-32" href = "#__codelineno-7-32" > < / 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" > < < / span > < span class = "kt" > int< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "p" > (< / span > < span class = "k" > new< / span > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "p" > )< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "p" > {< / span > < span class = "w" > < / 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 > < span class = "w" > < / span > < span class = "p" > });< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > heap.swift< / span > < pre > < span > < / span > < code > < a id = "__codelineno-8-1" name = "__codelineno-8-1" href = "#__codelineno-8-1" > < / a > < span class = "c1" > // Swift 未提供内置 Heap 类< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > heap.zig< / span > < pre > < span > < / span > < code > < a id = "__codelineno-9-1" name = "__codelineno-9-1" href = "#__codelineno-9-1" > < / a >
< / code > < / pre > < / div >
< / div >
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< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > heap.dart< / span > < pre > < span > < / span > < code > < a id = "__codelineno-10-1" name = "__codelineno-10-1" href = "#__codelineno-10-1" > < / a > < span class = "c1" > // Dart 未提供内置 Heap 类< / span >
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< / code > < / pre > < / div >
< / div >
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< / div >
< / div >
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< h2 id = "812" > 8.1.2. 堆的实现< a class = "headerlink" href = "#812" title = "Permanent link" > ¶ < / a > < / h2 >
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< 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 >
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< h3 id = "_1" > 堆的存储与表示< a class = "headerlink" href = "#_1" title = "Permanent link" > ¶ < / a > < / h3 >
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< p > 我们在二叉树章节中学习到，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 > 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 > 具体而言，给定索引 < span class = "arithmatex" > \(i\)< / span > ，其左子节点索引为 < span class = "arithmatex" > \(2i + 1\)< / span > ，右子节点索引为 < span class = "arithmatex" > \(2i + 2\)< / span > ，父节点索引为 < span class = "arithmatex" > \((i - 1) / 2\)< / span > （向下取整）。当索引越界时，表示空节点或节点不存在。< / p >
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< p > < img alt = "堆的表示与存储" src = "../heap.assets/representation_of_heap.png" / > < / p >
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< p align = "center" > Fig. 堆的表示与存储 < / p >
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< p > 我们可以将索引映射公式封装成函数，方便后续使用。< / p >
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< div class = "tabbed-set tabbed-alternate" data-tabs = "2:11" > < 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" / > < div class = "tabbed-labels" > < label for = "__tabbed_2_1" > Java< / label > < label for = "__tabbed_2_2" > C++< / label > < label for = "__tabbed_2_3" > Python< / label > < label for = "__tabbed_2_4" > Go< / label > < label for = "__tabbed_2_5" > JavaScript< / label > < label for = "__tabbed_2_6" > TypeScript< / label > < label for = "__tabbed_2_7" > C< / label > < label for = "__tabbed_2_8" > C#< / label > < label for = "__tabbed_2_9" > Swift< / label > < label for = "__tabbed_2_10" > Zig< / label > < label for = "__tabbed_2_11" > Dart< / label > < / div >
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< div class = "tabbed-content" >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > my_heap.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-11-1" name = "__codelineno-11-1" href = "#__codelineno-11-1" > < / a > < span class = "cm" > /* 获取左子节点索引 */< / span >
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< a id = "__codelineno-11-2" name = "__codelineno-11-2" href = "#__codelineno-11-2" > < / 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-11-3" name = "__codelineno-11-3" href = "#__codelineno-11-3" > < / 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-11-4" name = "__codelineno-11-4" href = "#__codelineno-11-4" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-11-5" name = "__codelineno-11-5" href = "#__codelineno-11-5" > < / a >
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< a id = "__codelineno-11-6" name = "__codelineno-11-6" href = "#__codelineno-11-6" > < / a > < span class = "cm" > /* 获取右子节点索引 */< / span >
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< a id = "__codelineno-11-7" name = "__codelineno-11-7" href = "#__codelineno-11-7" > < / 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-11-8" name = "__codelineno-11-8" href = "#__codelineno-11-8" > < / 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 >
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< a id = "__codelineno-11-9" name = "__codelineno-11-9" href = "#__codelineno-11-9" > < / a > < span class = "p" > }< / span >
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< a id = "__codelineno-11-10" name = "__codelineno-11-10" href = "#__codelineno-11-10" > < / a >
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< a id = "__codelineno-11-11" name = "__codelineno-11-11" href = "#__codelineno-11-11" > < / a > < span class = "cm" > /* 获取父节点索引 */< / span >
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< a id = "__codelineno-11-12" name = "__codelineno-11-12" href = "#__codelineno-11-12" > < / 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 >
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< a id = "__codelineno-11-13" name = "__codelineno-11-13" href = "#__codelineno-11-13" > < / 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 >
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< a id = "__codelineno-11-14" name = "__codelineno-11-14" href = "#__codelineno-11-14" > < / a > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > my_heap.cpp< / span > < pre > < span > < / span > < code > < a id = "__codelineno-12-1" name = "__codelineno-12-1" href = "#__codelineno-12-1" > < / a > < span class = "cm" > /* 获取左子节点索引 */< / span >
< a id = "__codelineno-12-2" name = "__codelineno-12-2" href = "#__codelineno-12-2" > < / 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-12-3" name = "__codelineno-12-3" href = "#__codelineno-12-3" > < / 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-12-4" name = "__codelineno-12-4" href = "#__codelineno-12-4" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-12-5" name = "__codelineno-12-5" href = "#__codelineno-12-5" > < / a >
< a id = "__codelineno-12-6" name = "__codelineno-12-6" href = "#__codelineno-12-6" > < / a > < span class = "cm" > /* 获取右子节点索引 */< / span >
< a id = "__codelineno-12-7" name = "__codelineno-12-7" href = "#__codelineno-12-7" > < / 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-12-8" name = "__codelineno-12-8" href = "#__codelineno-12-8" > < / 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-12-9" name = "__codelineno-12-9" href = "#__codelineno-12-9" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-12-10" name = "__codelineno-12-10" href = "#__codelineno-12-10" > < / a >
< a id = "__codelineno-12-11" name = "__codelineno-12-11" href = "#__codelineno-12-11" > < / a > < span class = "cm" > /* 获取父节点索引 */< / span >
< a id = "__codelineno-12-12" name = "__codelineno-12-12" href = "#__codelineno-12-12" > < / 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-12-13" name = "__codelineno-12-13" href = "#__codelineno-12-13" > < / 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" > // 向下取整< / span >
< a id = "__codelineno-12-14" name = "__codelineno-12-14" href = "#__codelineno-12-14" > < / a > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > my_heap.py< / span > < pre > < span > < / span > < code > < a id = "__codelineno-13-1" name = "__codelineno-13-1" href = "#__codelineno-13-1" > < / 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" > -> < / span > < span class = "nb" > int< / span > < span class = "p" > :< / span >
< a id = "__codelineno-13-2" name = "__codelineno-13-2" href = "#__codelineno-13-2" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 获取左子节点索引" " " < / span >
< a id = "__codelineno-13-3" name = "__codelineno-13-3" href = "#__codelineno-13-3" > < / 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-13-4" name = "__codelineno-13-4" href = "#__codelineno-13-4" > < / a >
< a id = "__codelineno-13-5" name = "__codelineno-13-5" href = "#__codelineno-13-5" > < / 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" > -> < / span > < span class = "nb" > int< / span > < span class = "p" > :< / span >
< a id = "__codelineno-13-6" name = "__codelineno-13-6" href = "#__codelineno-13-6" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 获取右子节点索引" " " < / span >
< a id = "__codelineno-13-7" name = "__codelineno-13-7" href = "#__codelineno-13-7" > < / 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-13-8" name = "__codelineno-13-8" href = "#__codelineno-13-8" > < / a >
< a id = "__codelineno-13-9" name = "__codelineno-13-9" href = "#__codelineno-13-9" > < / 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" > -> < / span > < span class = "nb" > int< / span > < span class = "p" > :< / span >
< a id = "__codelineno-13-10" name = "__codelineno-13-10" href = "#__codelineno-13-10" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 获取父节点索引" " " < / span >
< a id = "__codelineno-13-11" name = "__codelineno-13-11" href = "#__codelineno-13-11" > < / 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 >
2023-02-08 14:54:41 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > my_heap.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-14-1" name = "__codelineno-14-1" href = "#__codelineno-14-1" > < / a > < span class = "cm" > /* 获取左子节点索引 */< / span >
< a id = "__codelineno-14-2" name = "__codelineno-14-2" href = "#__codelineno-14-2" > < / 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-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 = "o" > *< / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span >
2023-02-08 16:47:58 +08:00
< 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 >
2023-04-09 04:35:05 +08:00
< a id = "__codelineno-14-6" name = "__codelineno-14-6" href = "#__codelineno-14-6" > < / a > < span class = "cm" > /* 获取右子节点索引 */< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-14-7" name = "__codelineno-14-7" href = "#__codelineno-14-7" > < / 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-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 = "o" > *< / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "mi" > 2< / span >
2023-02-08 16:47:58 +08:00
< 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 >
2023-04-09 04:35:05 +08:00
< a id = "__codelineno-14-11" name = "__codelineno-14-11" href = "#__codelineno-14-11" > < / a > < span class = "cm" > /* 获取父节点索引 */< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-14-12" name = "__codelineno-14-12" href = "#__codelineno-14-12" > < / 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-14-13" name = "__codelineno-14-13" href = "#__codelineno-14-13" > < / a > < 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 = "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-14-15" name = "__codelineno-14-15" href = "#__codelineno-14-15" > < / a > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > my_heap.js< / span > < pre > < span > < / span > < code > < a id = "__codelineno-15-1" name = "__codelineno-15-1" href = "#__codelineno-15-1" > < / a > < span class = "cm" > /* 获取左子节点索引 */< / span >
< a id = "__codelineno-15-2" name = "__codelineno-15-2" href = "#__codelineno-15-2" > < / 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 >
2023-02-08 16:47:58 +08:00
< 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 = "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-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 >
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< a id = "__codelineno-15-6" name = "__codelineno-15-6" href = "#__codelineno-15-6" > < / a > < span class = "cm" > /* 获取右子节点索引 */< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-15-7" name = "__codelineno-15-7" href = "#__codelineno-15-7" > < / 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 >
2023-02-08 16:47:58 +08:00
< 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 = "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-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 >
2023-04-09 04:35:05 +08:00
< a id = "__codelineno-15-11" name = "__codelineno-15-11" href = "#__codelineno-15-11" > < / a > < span class = "cm" > /* 获取父节点索引 */< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-15-12" name = "__codelineno-15-12" href = "#__codelineno-15-12" > < / 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 >
2023-02-08 16:47:58 +08:00
< 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 = "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-15-14" name = "__codelineno-15-14" href = "#__codelineno-15-14" > < / a > < span class = "p" > }< / span >
2023-02-08 14:54:41 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-06-02 02:38:32 +08:00
< div class = "highlight" > < span class = "filename" > my_heap.ts< / span > < pre > < span > < / span > < code > < a id = "__codelineno-16-1" name = "__codelineno-16-1" href = "#__codelineno-16-1" > < / a > < span class = "cm" > /* 获取左子节点索引 */< / span >
< a id = "__codelineno-16-2" name = "__codelineno-16-2" href = "#__codelineno-16-2" > < / 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-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 = "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 >
2023-04-18 20:19:15 +08:00
< 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" > /* 获取右子节点索引 */< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-16-7" name = "__codelineno-16-7" href = "#__codelineno-16-7" > < / 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-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 = "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 >
2023-04-18 20:19:15 +08:00
< 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" > /* 获取父节点索引 */< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-16-12" name = "__codelineno-16-12" href = "#__codelineno-16-12" > < / 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-16-13" name = "__codelineno-16-13" href = "#__codelineno-16-13" > < / 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 >
2023-04-18 20:19:15 +08:00
< a id = "__codelineno-16-14" name = "__codelineno-16-14" href = "#__codelineno-16-14" > < / a > < span class = "p" > }< / span >
2023-02-08 14:54:41 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-06-02 02:38:32 +08:00
< div class = "highlight" > < span class = "filename" > my_heap.c< / span > < pre > < span > < / span > < code > < a id = "__codelineno-17-1" name = "__codelineno-17-1" href = "#__codelineno-17-1" > < / a > < span class = "cm" > /* 获取左子节点索引 */< / span >
< a id = "__codelineno-17-2" name = "__codelineno-17-2" href = "#__codelineno-17-2" > < / 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" > h< / 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-17-3" name = "__codelineno-17-3" href = "#__codelineno-17-3" > < / 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 >
2023-04-23 14:58:11 +08:00
< 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" > /* 获取右子节点索引 */< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-17-7" name = "__codelineno-17-7" href = "#__codelineno-17-7" > < / 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" > h< / 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-17-8" name = "__codelineno-17-8" href = "#__codelineno-17-8" > < / 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 >
2023-04-23 14:58:11 +08:00
< 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" > /* 获取父节点索引 */< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-17-12" name = "__codelineno-17-12" href = "#__codelineno-17-12" > < / 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" > h< / 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-17-13" name = "__codelineno-17-13" href = "#__codelineno-17-13" > < / 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 >
2023-04-23 14:58:11 +08:00
< a id = "__codelineno-17-14" name = "__codelineno-17-14" href = "#__codelineno-17-14" > < / a > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > my_heap.cs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-18-1" name = "__codelineno-18-1" href = "#__codelineno-18-1" > < / a > < span class = "cm" > /* 获取左子节点索引 */< / span >
< a id = "__codelineno-18-2" name = "__codelineno-18-2" href = "#__codelineno-18-2" > < / 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-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 = "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 >
2023-02-08 20:30:33 +08:00
< 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 >
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< a id = "__codelineno-18-6" name = "__codelineno-18-6" href = "#__codelineno-18-6" > < / a > < span class = "cm" > /* 获取右子节点索引 */< / span >
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< a id = "__codelineno-18-7" name = "__codelineno-18-7" href = "#__codelineno-18-7" > < / 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-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 = "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 >
2023-02-08 20:30:33 +08:00
< 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 >
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< a id = "__codelineno-18-11" name = "__codelineno-18-11" href = "#__codelineno-18-11" > < / a > < span class = "cm" > /* 获取父节点索引 */< / span >
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< a id = "__codelineno-18-12" name = "__codelineno-18-12" href = "#__codelineno-18-12" > < / 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-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 = "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 >
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< a id = "__codelineno-18-14" name = "__codelineno-18-14" href = "#__codelineno-18-14" > < / a > < span class = "p" > }< / span >
2023-02-08 14:54:41 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > my_heap.swift< / span > < pre > < span > < / span > < code > < a id = "__codelineno-19-1" name = "__codelineno-19-1" href = "#__codelineno-19-1" > < / a > < span class = "cm" > /* 获取左子节点索引 */< / span >
< a id = "__codelineno-19-2" name = "__codelineno-19-2" href = "#__codelineno-19-2" > < / 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" > -> < / span > < span class = "nb" > Int< / span > < span class = "p" > {< / span >
< a id = "__codelineno-19-3" name = "__codelineno-19-3" href = "#__codelineno-19-3" > < / a > < span class = "mi" > 2< / span > < span class = "o" > *< / span > < span class = "n" > i< / span > < span class = "o" > +< / span > < span class = "mi" > 1< / span >
2023-02-09 22:55:35 +08:00
< 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 >
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< a id = "__codelineno-19-6" name = "__codelineno-19-6" href = "#__codelineno-19-6" > < / a > < span class = "cm" > /* 获取右子节点索引 */< / span >
< a id = "__codelineno-19-7" name = "__codelineno-19-7" href = "#__codelineno-19-7" > < / 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" > -> < / span > < span class = "nb" > Int< / span > < span class = "p" > {< / span >
< a id = "__codelineno-19-8" name = "__codelineno-19-8" href = "#__codelineno-19-8" > < / a > < span class = "mi" > 2< / span > < span class = "o" > *< / span > < span class = "n" > i< / span > < span class = "o" > +< / span > < span class = "mi" > 2< / span >
2023-02-09 22:55:35 +08:00
< 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 >
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< a id = "__codelineno-19-11" name = "__codelineno-19-11" href = "#__codelineno-19-11" > < / a > < span class = "cm" > /* 获取父节点索引 */< / span >
< a id = "__codelineno-19-12" name = "__codelineno-19-12" href = "#__codelineno-19-12" > < / 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" > -> < / span > < span class = "nb" > Int< / span > < span class = "p" > {< / span >
< a id = "__codelineno-19-13" name = "__codelineno-19-13" href = "#__codelineno-19-13" > < / 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-19-14" name = "__codelineno-19-14" href = "#__codelineno-19-14" > < / a > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > my_heap.zig< / span > < pre > < span > < / span > < code > < a id = "__codelineno-20-1" name = "__codelineno-20-1" href = "#__codelineno-20-1" > < / a > < span class = "c1" > // 获取左子节点索引< / span >
< a id = "__codelineno-20-2" name = "__codelineno-20-2" href = "#__codelineno-20-2" > < / 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-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 = "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 >
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< a id = "__codelineno-20-4" name = "__codelineno-20-4" href = "#__codelineno-20-4" > < / a > < span class = "p" > }< / span >
2023-06-02 02:38:32 +08:00
< 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 = "c1" > // 获取右子节点索引< / span >
< a id = "__codelineno-20-7" name = "__codelineno-20-7" href = "#__codelineno-20-7" > < / 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-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 = "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-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 = "c1" > // 获取父节点索引< / span >
< a id = "__codelineno-20-12" name = "__codelineno-20-12" href = "#__codelineno-20-12" > < / 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-20-13" name = "__codelineno-20-13" href = "#__codelineno-20-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // return (i - 1) / 2; // 向下整除< / span >
< a id = "__codelineno-20-14" name = "__codelineno-20-14" href = "#__codelineno-20-14" > < / 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-20-15" name = "__codelineno-20-15" href = "#__codelineno-20-15" > < / a > < span class = "p" > }< / span >
2023-02-08 14:54:41 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > my_heap.dart< / span > < pre > < span > < / span > < code > < a id = "__codelineno-21-1" name = "__codelineno-21-1" href = "#__codelineno-21-1" > < / a > < span class = "cm" > /* 获取左子节点索引 */< / span >
< a id = "__codelineno-21-2" name = "__codelineno-21-2" href = "#__codelineno-21-2" > < / 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-21-3" name = "__codelineno-21-3" href = "#__codelineno-21-3" > < / 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 >
2023-02-08 14:54:41 +08:00
< a id = "__codelineno-21-4" name = "__codelineno-21-4" href = "#__codelineno-21-4" > < / a > < span class = "p" > }< / span >
2023-06-02 02:38:32 +08:00
< 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" > /* 获取右子节点索引 */< / span >
< a id = "__codelineno-21-7" name = "__codelineno-21-7" href = "#__codelineno-21-7" > < / 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-21-8" name = "__codelineno-21-8" href = "#__codelineno-21-8" > < / 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-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" > /* 获取父节点索引 */< / span >
< a id = "__codelineno-21-12" name = "__codelineno-21-12" href = "#__codelineno-21-12" > < / 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-21-13" name = "__codelineno-21-13" href = "#__codelineno-21-13" > < / 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-21-14" name = "__codelineno-21-14" href = "#__codelineno-21-14" > < / a > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
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< / div >
< / div >
< h3 id = "_2" > 访问堆顶元素< a class = "headerlink" href = "#_2" title = "Permanent link" > ¶ < / 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 = "3:11" > < 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" / > < div class = "tabbed-labels" > < label for = "__tabbed_3_1" > Java< / label > < label for = "__tabbed_3_2" > C++< / label > < label for = "__tabbed_3_3" > Python< / label > < label for = "__tabbed_3_4" > Go< / label > < label for = "__tabbed_3_5" > JavaScript< / label > < label for = "__tabbed_3_6" > TypeScript< / label > < label for = "__tabbed_3_7" > C< / label > < label for = "__tabbed_3_8" > C#< / label > < label for = "__tabbed_3_9" > Swift< / label > < label for = "__tabbed_3_10" > Zig< / label > < label for = "__tabbed_3_11" > Dart< / label > < / div >
< div class = "tabbed-content" >
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< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > my_heap.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-22-1" name = "__codelineno-22-1" href = "#__codelineno-22-1" > < / a > < span class = "cm" > /* 访问堆顶元素 */< / 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" > peek< / 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 = "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-22-4" name = "__codelineno-22-4" href = "#__codelineno-22-4" > < / a > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > my_heap.cpp< / span > < pre > < span > < / span > < code > < a id = "__codelineno-23-1" name = "__codelineno-23-1" href = "#__codelineno-23-1" > < / a > < span class = "cm" > /* 访问堆顶元素 */< / span >
< a id = "__codelineno-23-2" name = "__codelineno-23-2" href = "#__codelineno-23-2" > < / 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-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 = "n" > maxHeap< / span > < span class = "p" > [< / span > < span class = "mi" > 0< / span > < span class = "p" > ];< / span >
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< a id = "__codelineno-23-4" name = "__codelineno-23-4" href = "#__codelineno-23-4" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< 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" > -> < / 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" > " " " 访问堆顶元素" " " < / 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 >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > my_heap.go< / 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 = "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-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 = "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 >
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< 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" >
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< div class = "highlight" > < span class = "filename" > my_heap.js< / 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 = "nx" > 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 = "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 >
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< a id = "__codelineno-26-4" name = "__codelineno-26-4" href = "#__codelineno-26-4" > < / a > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > my_heap.ts< / 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 = "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-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 = "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 >
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< a id = "__codelineno-27-4" name = "__codelineno-27-4" href = "#__codelineno-27-4" > < / a > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > my_heap.c< / 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 = "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" > h< / span > < span class = "p" > )< / 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 = "n" > h< / span > < span class = "o" > -> < / span > < span class = "n" > data< / span > < span class = "p" > [< / span > < span class = "mi" > 0< / span > < span class = "p" > ];< / span >
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< 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" >
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< div class = "highlight" > < span class = "filename" > my_heap.cs< / 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 = "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-29-3" name = "__codelineno-29-3" href = "#__codelineno-29-3" > < / 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-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.swift< / 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 = "kd" > func< / span > < span class = "nf" > peek< / span > < span class = "p" > ()< / span > < span class = "p" > -> < / span > < span class = "nb" > Int< / span > < span class = "p" > {< / span >
< a id = "__codelineno-30-3" name = "__codelineno-30-3" href = "#__codelineno-30-3" > < / a > < span class = "n" > maxHeap< / span > < span class = "p" > [< / span > < span class = "mi" > 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.zig< / span > < pre > < span > < / span > < code > < a id = "__codelineno-31-1" name = "__codelineno-31-1" href = "#__codelineno-31-1" > < / a > < span class = "c1" > // 访问堆顶元素< / span >
< a id = "__codelineno-31-2" name = "__codelineno-31-2" href = "#__codelineno-31-2" > < / 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-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 = "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-31-4" name = "__codelineno-31-4" href = "#__codelineno-31-4" > < / a > < span class = "p" > }< / span > < span class = "w" > < / 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 >
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< / code > < / pre > < / div >
< / div >
< / div >
< / div >
< h3 id = "_3" > 元素入堆< a class = "headerlink" href = "#_3" title = "Permanent link" > ¶ < / a > < / h3 >
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< 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 val 可能大于堆中其他元素，堆的成立条件可能已被破坏。因此，< strong > 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 > 。具体来说，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需交换的节点时结束。< / p >
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< 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" > < 1> < / label > < label for = "__tabbed_4_2" > < 2> < / label > < label for = "__tabbed_4_3" > < 3> < / label > < label for = "__tabbed_4_4" > < 4> < / label > < label for = "__tabbed_4_5" > < 5> < / label > < label for = "__tabbed_4_6" > < 6> < / label > < label for = "__tabbed_4_7" > < 7> < / label > < label for = "__tabbed_4_8" > < 8> < / label > < label for = "__tabbed_4_9" > < 9> < / label > < / div >
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< div class = "tabbed-content" >
< div class = "tabbed-block" >
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< p > < img alt = "元素入堆步骤" src = "../heap.assets/heap_push_step1.png" / > < / p >
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< / div >
< div class = "tabbed-block" >
< p > < img alt = "heap_push_step2" src = "../heap.assets/heap_push_step2.png" / > < / p >
< / div >
< div class = "tabbed-block" >
< p > < img alt = "heap_push_step3" src = "../heap.assets/heap_push_step3.png" / > < / p >
< / div >
< div class = "tabbed-block" >
< p > < img alt = "heap_push_step4" src = "../heap.assets/heap_push_step4.png" / > < / p >
< / div >
< div class = "tabbed-block" >
< p > < img alt = "heap_push_step5" src = "../heap.assets/heap_push_step5.png" / > < / p >
< / div >
< div class = "tabbed-block" >
< p > < img alt = "heap_push_step6" src = "../heap.assets/heap_push_step6.png" / > < / p >
< / div >
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< div class = "tabbed-block" >
< p > < img alt = "heap_push_step7" src = "../heap.assets/heap_push_step7.png" / > < / p >
< / div >
< div class = "tabbed-block" >
< p > < img alt = "heap_push_step8" src = "../heap.assets/heap_push_step8.png" / > < / p >
< / div >
< div class = "tabbed-block" >
< p > < img alt = "heap_push_step9" src = "../heap.assets/heap_push_step9.png" / > < / p >
< / div >
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< / div >
< / div >
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< 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 > 。< / p >
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< div class = "tabbed-set tabbed-alternate" data-tabs = "5:11" > < 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" / > < div class = "tabbed-labels" > < label for = "__tabbed_5_1" > Java< / label > < label for = "__tabbed_5_2" > C++< / label > < label for = "__tabbed_5_3" > Python< / label > < label for = "__tabbed_5_4" > Go< / label > < label for = "__tabbed_5_5" > JavaScript< / label > < label for = "__tabbed_5_6" > TypeScript< / label > < label for = "__tabbed_5_7" > C< / label > < label for = "__tabbed_5_8" > C#< / label > < label for = "__tabbed_5_9" > Swift< / label > < label for = "__tabbed_5_10" > Zig< / label > < label for = "__tabbed_5_11" > Dart< / label > < / div >
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< div class = "tabbed-content" >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > my_heap.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-33-1" name = "__codelineno-33-1" href = "#__codelineno-33-1" > < / a > < span class = "cm" > /* 元素入堆 */< / span >
< a id = "__codelineno-33-2" name = "__codelineno-33-2" href = "#__codelineno-33-2" > < / 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 >
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< a id = "__codelineno-33-3" name = "__codelineno-33-3" href = "#__codelineno-33-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 添加节点< / span >
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< a id = "__codelineno-33-4" name = "__codelineno-33-4" href = "#__codelineno-33-4" > < / 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 >
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< a id = "__codelineno-33-5" name = "__codelineno-33-5" href = "#__codelineno-33-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 从底至顶堆化< / span >
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< a id = "__codelineno-33-6" name = "__codelineno-33-6" href = "#__codelineno-33-6" > < / 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 >
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< a id = "__codelineno-33-7" name = "__codelineno-33-7" href = "#__codelineno-33-7" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-33-8" name = "__codelineno-33-8" href = "#__codelineno-33-8" > < / a >
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< a id = "__codelineno-33-9" name = "__codelineno-33-9" href = "#__codelineno-33-9" > < / a > < span class = "cm" > /* 从节点 i 开始，从底至顶堆化 */< / span >
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< a id = "__codelineno-33-10" name = "__codelineno-33-10" href = "#__codelineno-33-10" > < / 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-33-11" name = "__codelineno-33-11" href = "#__codelineno-33-11" > < / 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 >
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< a id = "__codelineno-33-12" name = "__codelineno-33-12" href = "#__codelineno-33-12" > < / a > < span class = "w" > < / span > < span class = "c1" > // 获取节点 i 的父节点< / span >
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< a id = "__codelineno-33-13" name = "__codelineno-33-13" href = "#__codelineno-33-13" > < / 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 >
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< a id = "__codelineno-33-14" name = "__codelineno-33-14" href = "#__codelineno-33-14" > < / a > < span class = "w" > < / span > < span class = "c1" > // 当“越过根节点”或“节点无需修复”时，结束堆化< / span >
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< a id = "__codelineno-33-15" name = "__codelineno-33-15" href = "#__codelineno-33-15" > < / 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" > < < / 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" > < =< / 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-33-16" name = "__codelineno-33-16" href = "#__codelineno-33-16" > < / a > < span class = "w" > < / span > < span class = "k" > break< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-33-17" name = "__codelineno-33-17" href = "#__codelineno-33-17" > < / a > < span class = "w" > < / span > < span class = "c1" > // 交换两节点< / span >
< a id = "__codelineno-33-18" name = "__codelineno-33-18" href = "#__codelineno-33-18" > < / 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-33-19" name = "__codelineno-33-19" href = "#__codelineno-33-19" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环向上堆化< / span >
< a id = "__codelineno-33-20" name = "__codelineno-33-20" href = "#__codelineno-33-20" > < / 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-33-21" name = "__codelineno-33-21" href = "#__codelineno-33-21" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-33-22" name = "__codelineno-33-22" href = "#__codelineno-33-22" > < / a > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > my_heap.cpp< / span > < pre > < span > < / span > < code > < a id = "__codelineno-34-1" name = "__codelineno-34-1" href = "#__codelineno-34-1" > < / a > < span class = "cm" > /* 元素入堆 */< / span >
< a id = "__codelineno-34-2" name = "__codelineno-34-2" href = "#__codelineno-34-2" > < / 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 >
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< a id = "__codelineno-34-3" name = "__codelineno-34-3" href = "#__codelineno-34-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 添加节点< / span >
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< a id = "__codelineno-34-4" name = "__codelineno-34-4" href = "#__codelineno-34-4" > < / 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 >
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< a id = "__codelineno-34-5" name = "__codelineno-34-5" href = "#__codelineno-34-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 从底至顶堆化< / span >
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< a id = "__codelineno-34-6" name = "__codelineno-34-6" href = "#__codelineno-34-6" > < / 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 >
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< a id = "__codelineno-34-7" name = "__codelineno-34-7" href = "#__codelineno-34-7" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-34-8" name = "__codelineno-34-8" href = "#__codelineno-34-8" > < / a >
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< a id = "__codelineno-34-9" name = "__codelineno-34-9" href = "#__codelineno-34-9" > < / a > < span class = "cm" > /* 从节点 i 开始，从底至顶堆化 */< / span >
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< a id = "__codelineno-34-10" name = "__codelineno-34-10" href = "#__codelineno-34-10" > < / 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-34-11" name = "__codelineno-34-11" href = "#__codelineno-34-11" > < / 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 >
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< a id = "__codelineno-34-12" name = "__codelineno-34-12" href = "#__codelineno-34-12" > < / a > < span class = "w" > < / span > < span class = "c1" > // 获取节点 i 的父节点< / span >
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< a id = "__codelineno-34-13" name = "__codelineno-34-13" href = "#__codelineno-34-13" > < / 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 >
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< a id = "__codelineno-34-14" name = "__codelineno-34-14" href = "#__codelineno-34-14" > < / a > < span class = "w" > < / span > < span class = "c1" > // 当“越过根节点”或“节点无需修复”时，结束堆化< / span >
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< a id = "__codelineno-34-15" name = "__codelineno-34-15" href = "#__codelineno-34-15" > < / 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" > < < / 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" > < =< / 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-34-16" name = "__codelineno-34-16" href = "#__codelineno-34-16" > < / a > < span class = "w" > < / span > < span class = "k" > break< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-34-17" name = "__codelineno-34-17" href = "#__codelineno-34-17" > < / a > < span class = "w" > < / span > < span class = "c1" > // 交换两节点< / span >
< a id = "__codelineno-34-18" name = "__codelineno-34-18" href = "#__codelineno-34-18" > < / 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-34-19" name = "__codelineno-34-19" href = "#__codelineno-34-19" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环向上堆化< / span >
< a id = "__codelineno-34-20" name = "__codelineno-34-20" href = "#__codelineno-34-20" > < / 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-34-21" name = "__codelineno-34-21" href = "#__codelineno-34-21" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-34-22" name = "__codelineno-34-22" href = "#__codelineno-34-22" > < / a > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > my_heap.py< / span > < pre > < span > < / span > < code > < a id = "__codelineno-35-1" name = "__codelineno-35-1" href = "#__codelineno-35-1" > < / 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-35-2" name = "__codelineno-35-2" href = "#__codelineno-35-2" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 元素入堆" " " < / span >
< a id = "__codelineno-35-3" name = "__codelineno-35-3" href = "#__codelineno-35-3" > < / a > < span class = "c1" > # 添加节点< / span >
< a id = "__codelineno-35-4" name = "__codelineno-35-4" href = "#__codelineno-35-4" > < / 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-35-5" name = "__codelineno-35-5" href = "#__codelineno-35-5" > < / a > < span class = "c1" > # 从底至顶堆化< / span >
< a id = "__codelineno-35-6" name = "__codelineno-35-6" href = "#__codelineno-35-6" > < / 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-35-7" name = "__codelineno-35-7" href = "#__codelineno-35-7" > < / a >
< a id = "__codelineno-35-8" name = "__codelineno-35-8" href = "#__codelineno-35-8" > < / 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-35-9" name = "__codelineno-35-9" href = "#__codelineno-35-9" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 从节点 i 开始，从底至顶堆化" " " < / span >
< a id = "__codelineno-35-10" name = "__codelineno-35-10" href = "#__codelineno-35-10" > < / a > < span class = "k" > while< / span > < span class = "kc" > True< / span > < span class = "p" > :< / span >
< a id = "__codelineno-35-11" name = "__codelineno-35-11" href = "#__codelineno-35-11" > < / a > < span class = "c1" > # 获取节点 i 的父节点< / span >
< a id = "__codelineno-35-12" name = "__codelineno-35-12" href = "#__codelineno-35-12" > < / 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-35-13" name = "__codelineno-35-13" href = "#__codelineno-35-13" > < / a > < span class = "c1" > # 当“越过根节点”或“节点无需修复”时，结束堆化< / span >
< a id = "__codelineno-35-14" name = "__codelineno-35-14" href = "#__codelineno-35-14" > < / a > < span class = "k" > if< / span > < span class = "n" > p< / span > < span class = "o" > < < / 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" > < =< / 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-35-15" name = "__codelineno-35-15" href = "#__codelineno-35-15" > < / a > < span class = "k" > break< / span >
< a id = "__codelineno-35-16" name = "__codelineno-35-16" href = "#__codelineno-35-16" > < / a > < span class = "c1" > # 交换两节点< / span >
< a id = "__codelineno-35-17" name = "__codelineno-35-17" href = "#__codelineno-35-17" > < / 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-35-18" name = "__codelineno-35-18" href = "#__codelineno-35-18" > < / a > < span class = "c1" > # 循环向上堆化< / span >
< a id = "__codelineno-35-19" name = "__codelineno-35-19" href = "#__codelineno-35-19" > < / a > < span class = "n" > i< / span > < span class = "o" > =< / span > < span class = "n" > p< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > my_heap.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-36-1" name = "__codelineno-36-1" href = "#__codelineno-36-1" > < / a > < span class = "cm" > /* 元素入堆 */< / span >
< a id = "__codelineno-36-2" name = "__codelineno-36-2" href = "#__codelineno-36-2" > < / 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-36-3" name = "__codelineno-36-3" href = "#__codelineno-36-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 添加节点< / span >
< a id = "__codelineno-36-4" name = "__codelineno-36-4" href = "#__codelineno-36-4" > < / 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-36-5" name = "__codelineno-36-5" href = "#__codelineno-36-5" > < / a > < span class = "w" > < / span > < 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 = "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-36-7" name = "__codelineno-36-7" href = "#__codelineno-36-7" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-36-8" name = "__codelineno-36-8" href = "#__codelineno-36-8" > < / a >
< a id = "__codelineno-36-9" name = "__codelineno-36-9" href = "#__codelineno-36-9" > < / a > < span class = "cm" > /* 从节点 i 开始，从底至顶堆化 */< / span >
< a id = "__codelineno-36-10" name = "__codelineno-36-10" href = "#__codelineno-36-10" > < / 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-36-11" name = "__codelineno-36-11" href = "#__codelineno-36-11" > < / 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-36-12" name = "__codelineno-36-12" href = "#__codelineno-36-12" > < / a > < span class = "w" > < / span > < span class = "c1" > // 获取节点 i 的父节点< / span >
< a id = "__codelineno-36-13" name = "__codelineno-36-13" href = "#__codelineno-36-13" > < / 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-36-14" name = "__codelineno-36-14" href = "#__codelineno-36-14" > < / a > < span class = "w" > < / span > < span class = "c1" > // 当“越过根节点”或“节点无需修复”时，结束堆化< / span >
< a id = "__codelineno-36-15" name = "__codelineno-36-15" href = "#__codelineno-36-15" > < / 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" > < < / 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" > < =< / 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-36-16" name = "__codelineno-36-16" href = "#__codelineno-36-16" > < / a > < span class = "w" > < / span > < span class = "k" > break< / span >
< a id = "__codelineno-36-17" name = "__codelineno-36-17" href = "#__codelineno-36-17" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-36-18" name = "__codelineno-36-18" href = "#__codelineno-36-18" > < / a > < span class = "w" > < / span > < span class = "c1" > // 交换两节点< / span >
< a id = "__codelineno-36-19" name = "__codelineno-36-19" href = "#__codelineno-36-19" > < / 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-36-20" name = "__codelineno-36-20" href = "#__codelineno-36-20" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环向上堆化< / span >
< a id = "__codelineno-36-21" name = "__codelineno-36-21" href = "#__codelineno-36-21" > < / 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-36-22" name = "__codelineno-36-22" href = "#__codelineno-36-22" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-36-23" name = "__codelineno-36-23" href = "#__codelineno-36-23" > < / a > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > my_heap.js< / 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 = "nx" > push< / span > < span class = "p" > (< / span > < span class = "nx" > val< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
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< 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 >
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< a id = "__codelineno-37-4" name = "__codelineno-37-4" href = "#__codelineno-37-4" > < / 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 >
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< 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 >
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< a id = "__codelineno-37-6" name = "__codelineno-37-6" href = "#__codelineno-37-6" > < / 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 >
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< 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 >
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< a id = "__codelineno-37-10" name = "__codelineno-37-10" href = "#__codelineno-37-10" > < / 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-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 = "kc" > true< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
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< 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 >
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< a id = "__codelineno-37-13" name = "__codelineno-37-13" href = "#__codelineno-37-13" > < / 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-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“节点无需修复”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 = "nx" > p< / span > < span class = "w" > < / span > < span class = "o" > < < / 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" > < =< / 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-37-16" name = "__codelineno-37-16" href = "#__codelineno-37-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // 交换两节点< / span >
< a id = "__codelineno-37-17" name = "__codelineno-37-17" href = "#__codelineno-37-17" > < / 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-37-18" name = "__codelineno-37-18" href = "#__codelineno-37-18" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环向上堆化< / span >
< a id = "__codelineno-37-19" name = "__codelineno-37-19" href = "#__codelineno-37-19" > < / 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-37-20" name = "__codelineno-37-20" href = "#__codelineno-37-20" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-37-21" name = "__codelineno-37-21" href = "#__codelineno-37-21" > < / a > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > my_heap.ts< / 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 = "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-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 = "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-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 = "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 >
2023-02-08 14:54:41 +08:00
< 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 >
2023-04-09 04:35:05 +08:00
< 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 >
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< a id = "__codelineno-38-10" name = "__codelineno-38-10" href = "#__codelineno-38-10" > < / 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-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 = "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-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“节点无需修复”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 = "nx" > p< / span > < span class = "w" > < / span > < span class = "o" > < < / 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" > < =< / 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-38-16" name = "__codelineno-38-16" href = "#__codelineno-38-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // 交换两节点< / span >
< a id = "__codelineno-38-17" name = "__codelineno-38-17" href = "#__codelineno-38-17" > < / 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-38-18" name = "__codelineno-38-18" href = "#__codelineno-38-18" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环向上堆化< / span >
< a id = "__codelineno-38-19" name = "__codelineno-38-19" href = "#__codelineno-38-19" > < / 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-38-20" name = "__codelineno-38-20" href = "#__codelineno-38-20" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-38-21" name = "__codelineno-38-21" href = "#__codelineno-38-21" > < / a > < span class = "p" > }< / span >
2023-02-08 14:54:41 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > my_heap.c< / 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 = "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" > h< / 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-39-3" name = "__codelineno-39-3" href = "#__codelineno-39-3" > < / 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-39-4" name = "__codelineno-39-4" href = "#__codelineno-39-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > h< / span > < span class = "o" > -> < / 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-39-5" name = "__codelineno-39-5" href = "#__codelineno-39-5" > < / a > < span class = "w" > < / span > < span class = "n" > printf< / span > < span class = "p" > (< / span > < span class = "s" > " heap is full!" < / span > < span class = "p" > );< / span >
< a id = "__codelineno-39-6" name = "__codelineno-39-6" href = "#__codelineno-39-6" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-39-7" name = "__codelineno-39-7" href = "#__codelineno-39-7" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-39-8" name = "__codelineno-39-8" href = "#__codelineno-39-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 添加节点< / span >
< a id = "__codelineno-39-9" name = "__codelineno-39-9" href = "#__codelineno-39-9" > < / a > < span class = "w" > < / span > < span class = "n" > h< / span > < span class = "o" > -> < / span > < span class = "n" > data< / span > < span class = "p" > [< / span > < span class = "n" > h< / span > < span class = "o" > -> < / 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-39-10" name = "__codelineno-39-10" href = "#__codelineno-39-10" > < / a > < span class = "w" > < / span > < span class = "n" > h< / span > < span class = "o" > -> < / span > < span class = "n" > size< / span > < span class = "o" > ++< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-39-11" name = "__codelineno-39-11" href = "#__codelineno-39-11" > < / a >
< a id = "__codelineno-39-12" name = "__codelineno-39-12" href = "#__codelineno-39-12" > < / a > < span class = "w" > < / span > < span class = "c1" > // 从底至顶堆化< / span >
< a id = "__codelineno-39-13" name = "__codelineno-39-13" href = "#__codelineno-39-13" > < / a > < span class = "w" > < / span > < span class = "n" > siftUp< / span > < span class = "p" > (< / span > < span class = "n" > h< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > h< / span > < span class = "o" > -> < / 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-39-14" name = "__codelineno-39-14" href = "#__codelineno-39-14" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-39-15" name = "__codelineno-39-15" href = "#__codelineno-39-15" > < / a >
< a id = "__codelineno-39-16" name = "__codelineno-39-16" href = "#__codelineno-39-16" > < / a > < span class = "cm" > /* 从节点 i 开始，从底至顶堆化 */< / span >
< a id = "__codelineno-39-17" name = "__codelineno-39-17" href = "#__codelineno-39-17" > < / 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" > h< / 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-39-18" name = "__codelineno-39-18" href = "#__codelineno-39-18" > < / 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-39-19" name = "__codelineno-39-19" href = "#__codelineno-39-19" > < / a > < span class = "w" > < / span > < span class = "c1" > // 获取节点 i 的父节点< / span >
< a id = "__codelineno-39-20" name = "__codelineno-39-20" href = "#__codelineno-39-20" > < / 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" > h< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > i< / 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 = "c1" > // 当“越过根节点”或“节点无需修复”时，结束堆化< / span >
< a id = "__codelineno-39-22" name = "__codelineno-39-22" href = "#__codelineno-39-22" > < / 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" > < < / 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" > h< / span > < span class = "o" > -> < / 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" > < =< / span > < span class = "w" > < / span > < span class = "n" > h< / span > < span class = "o" > -> < / 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-39-23" name = "__codelineno-39-23" href = "#__codelineno-39-23" > < / a > < span class = "w" > < / span > < span class = "k" > break< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-39-24" name = "__codelineno-39-24" href = "#__codelineno-39-24" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-39-25" name = "__codelineno-39-25" href = "#__codelineno-39-25" > < / a > < span class = "w" > < / span > < span class = "c1" > // 交换两节点< / span >
< a id = "__codelineno-39-26" name = "__codelineno-39-26" href = "#__codelineno-39-26" > < / a > < span class = "w" > < / span > < span class = "n" > swap< / span > < span class = "p" > (< / span > < span class = "n" > h< / 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-39-27" name = "__codelineno-39-27" href = "#__codelineno-39-27" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环向上堆化< / span >
< a id = "__codelineno-39-28" name = "__codelineno-39-28" href = "#__codelineno-39-28" > < / 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-39-29" name = "__codelineno-39-29" href = "#__codelineno-39-29" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-39-30" name = "__codelineno-39-30" href = "#__codelineno-39-30" > < / 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-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 = "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-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 = "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-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 = "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-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 = "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-40-11" name = "__codelineno-40-11" href = "#__codelineno-40-11" > < / 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-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 = "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-40-14" name = "__codelineno-40-14" href = "#__codelineno-40-14" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若“越过根节点”或“节点无需修复”，则结束堆化< / 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 = "p" > (< / span > < span class = "n" > p< / span > < span class = "w" > < / span > < span class = "o" > < < / 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" > < =< / 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-40-16" name = "__codelineno-40-16" href = "#__codelineno-40-16" > < / a > < span class = "w" > < / span > < span class = "k" > break< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-40-17" name = "__codelineno-40-17" href = "#__codelineno-40-17" > < / a > < span class = "w" > < / span > < span class = "c1" > // 交换两节点< / span >
< a id = "__codelineno-40-18" name = "__codelineno-40-18" href = "#__codelineno-40-18" > < / 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-40-19" name = "__codelineno-40-19" href = "#__codelineno-40-19" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环向上堆化< / span >
< a id = "__codelineno-40-20" name = "__codelineno-40-20" href = "#__codelineno-40-20" > < / 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-40-21" name = "__codelineno-40-21" href = "#__codelineno-40-21" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-40-22" name = "__codelineno-40-22" href = "#__codelineno-40-22" > < / 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“节点无需修复”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" > < < / 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" > < =< / 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.zig< / span > < pre > < span > < / span > < code > < a id = "__codelineno-42-1" name = "__codelineno-42-1" href = "#__codelineno-42-1" > < / a > < span class = "c1" > // 元素入堆< / span >
< a id = "__codelineno-42-2" name = "__codelineno-42-2" href = "#__codelineno-42-2" > < / 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-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" > 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-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" > 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-42-7" name = "__codelineno-42-7" href = "#__codelineno-42-7" > < / a > < span class = "p" > }< / span > < span class = "w" > < / 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 = "c1" > // 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 = "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-42-11" name = "__codelineno-42-11" href = "#__codelineno-42-11" > < / 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-42-12" name = "__codelineno-42-12" href = "#__codelineno-42-12" > < / 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-42-13" name = "__codelineno-42-13" href = "#__codelineno-42-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 获取节点 i 的父节点< / span >
< a id = "__codelineno-42-14" name = "__codelineno-42-14" href = "#__codelineno-42-14" > < / 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-42-15" name = "__codelineno-42-15" href = "#__codelineno-42-15" > < / a > < span class = "w" > < / span > < span class = "c1" > // 当“越过根节点”或“节点无需修复”时，结束堆化< / span >
< a id = "__codelineno-42-16" name = "__codelineno-42-16" href = "#__codelineno-42-16" > < / 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" > < < / 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" > < =< / 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-42-17" name = "__codelineno-42-17" href = "#__codelineno-42-17" > < / a > < span class = "w" > < / span > < span class = "c1" > // 交换两节点< / span >
< a id = "__codelineno-42-18" name = "__codelineno-42-18" href = "#__codelineno-42-18" > < / 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-42-19" name = "__codelineno-42-19" href = "#__codelineno-42-19" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环向上堆化< / span >
< a id = "__codelineno-42-20" name = "__codelineno-42-20" href = "#__codelineno-42-20" > < / 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-42-21" name = "__codelineno-42-21" href = "#__codelineno-42-21" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-42-22" name = "__codelineno-42-22" href = "#__codelineno-42-22" > < / 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-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 = "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-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 = "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-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 = "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-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 = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{< / span > < span class = "n" > MaxHeap< / span > < span class = "p" > }< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > siftUp< / span > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
< / div >
< / div >
< h3 id = "_4" > 堆顶元素出堆< a class = "headerlink" href = "#_4" title = "Permanent link" > ¶ < / a > < / h3 >
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< 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修复变得困难。为了尽量减少元素索引的变动，我们采取以下操作步骤：< / p >
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< ol >
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< li > 交换堆顶元素与堆底元素（即交换根节点与最右叶节点）；< / li >
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< li > 交换完成后，将堆底从列表中删除（注意，由于已经交换，实际上删除的是原来的堆顶元素）；< / li >
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< li > 从根节点开始，< strong > 从顶至底执行堆化< / strong > ； < / li >
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< / ol >
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< p > 顾名思义，< 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需交换的节点时结束。< / p >
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< 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" > < 1> < / label > < label for = "__tabbed_6_2" > < 2> < / label > < label for = "__tabbed_6_3" > < 3> < / label > < label for = "__tabbed_6_4" > < 4> < / label > < label for = "__tabbed_6_5" > < 5> < / label > < label for = "__tabbed_6_6" > < 6> < / label > < label for = "__tabbed_6_7" > < 7> < / label > < label for = "__tabbed_6_8" > < 8> < / label > < label for = "__tabbed_6_9" > < 9> < / label > < label for = "__tabbed_6_10" > < 10> < / label > < / div >
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< div class = "tabbed-content" >
< div class = "tabbed-block" >
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< p > < img alt = "堆顶元素出堆步骤" src = "../heap.assets/heap_pop_step1.png" / > < / p >
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< / div >
< div class = "tabbed-block" >
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< p > < img alt = "heap_pop_step2" src = "../heap.assets/heap_pop_step2.png" / > < / p >
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< / div >
< div class = "tabbed-block" >
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< p > < img alt = "heap_pop_step3" src = "../heap.assets/heap_pop_step3.png" / > < / p >
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< / div >
< div class = "tabbed-block" >
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< p > < img alt = "heap_pop_step4" src = "../heap.assets/heap_pop_step4.png" / > < / p >
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< / div >
< div class = "tabbed-block" >
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< p > < img alt = "heap_pop_step5" src = "../heap.assets/heap_pop_step5.png" / > < / p >
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< / div >
< div class = "tabbed-block" >
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< p > < img alt = "heap_pop_step6" src = "../heap.assets/heap_pop_step6.png" / > < / p >
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< / div >
< div class = "tabbed-block" >
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< p > < img alt = "heap_pop_step7" src = "../heap.assets/heap_pop_step7.png" / > < / p >
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< / div >
< div class = "tabbed-block" >
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< p > < img alt = "heap_pop_step8" src = "../heap.assets/heap_pop_step8.png" / > < / p >
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< / div >
< div class = "tabbed-block" >
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< p > < img alt = "heap_pop_step9" src = "../heap.assets/heap_pop_step9.png" / > < / p >
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< / div >
< div class = "tabbed-block" >
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< p > < img alt = "heap_pop_step10" src = "../heap.assets/heap_pop_step10.png" / > < / p >
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< / div >
< / div >
< / div >
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< 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 > 。< / p >
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< div class = "tabbed-set tabbed-alternate" data-tabs = "7:11" > < input checked = "checked" id = "__tabbed_7_1" name = "__tabbed_7" type = "radio" / > < input id = "__tabbed_7_2" name = "__tabbed_7" type = "radio" / > < input id = "__tabbed_7_3" name = "__tabbed_7" type = "radio" / > < input id = "__tabbed_7_4" name = "__tabbed_7" type = "radio" / > < input id = "__tabbed_7_5" name = "__tabbed_7" type = "radio" / > < input id = "__tabbed_7_6" name = "__tabbed_7" type = "radio" / > < input id = "__tabbed_7_7" name = "__tabbed_7" type = "radio" / > < input id = "__tabbed_7_8" name = "__tabbed_7" type = "radio" / > < input id = "__tabbed_7_9" name = "__tabbed_7" type = "radio" / > < input id = "__tabbed_7_10" name = "__tabbed_7" type = "radio" / > < input id = "__tabbed_7_11" name = "__tabbed_7" type = "radio" / > < div class = "tabbed-labels" > < label for = "__tabbed_7_1" > Java< / label > < label for = "__tabbed_7_2" > C++< / label > < label for = "__tabbed_7_3" > Python< / label > < label for = "__tabbed_7_4" > Go< / label > < label for = "__tabbed_7_5" > JavaScript< / label > < label for = "__tabbed_7_6" > TypeScript< / label > < label for = "__tabbed_7_7" > C< / label > < label for = "__tabbed_7_8" > C#< / label > < label for = "__tabbed_7_9" > Swift< / label > < label for = "__tabbed_7_10" > Zig< / label > < label for = "__tabbed_7_11" > Dart< / label > < / div >
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< div class = "tabbed-content" >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > my_heap.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-44-1" name = "__codelineno-44-1" href = "#__codelineno-44-1" > < / a > < span class = "cm" > /* 元素出堆 */< / span >
< a id = "__codelineno-44-2" name = "__codelineno-44-2" href = "#__codelineno-44-2" > < / 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 >
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< a id = "__codelineno-44-3" name = "__codelineno-44-3" href = "#__codelineno-44-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 判空处理< / span >
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< a id = "__codelineno-44-4" name = "__codelineno-44-4" href = "#__codelineno-44-4" > < / 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-44-5" name = "__codelineno-44-5" href = "#__codelineno-44-5" > < / 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-44-6" name = "__codelineno-44-6" href = "#__codelineno-44-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 交换根节点与最右叶节点（即交换首元素与尾元素）< / span >
< a id = "__codelineno-44-7" name = "__codelineno-44-7" href = "#__codelineno-44-7" > < / 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-44-8" name = "__codelineno-44-8" href = "#__codelineno-44-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 删除节点< / span >
< a id = "__codelineno-44-9" name = "__codelineno-44-9" href = "#__codelineno-44-9" > < / 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-44-10" name = "__codelineno-44-10" href = "#__codelineno-44-10" > < / a > < span class = "w" > < / span > < span class = "c1" > // 从顶至底堆化< / span >
< a id = "__codelineno-44-11" name = "__codelineno-44-11" href = "#__codelineno-44-11" > < / 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-44-12" name = "__codelineno-44-12" href = "#__codelineno-44-12" > < / a > < span class = "w" > < / span > < span class = "c1" > // 返回堆顶元素< / span >
< a id = "__codelineno-44-13" name = "__codelineno-44-13" href = "#__codelineno-44-13" > < / 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-44-14" name = "__codelineno-44-14" href = "#__codelineno-44-14" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-44-15" name = "__codelineno-44-15" href = "#__codelineno-44-15" > < / a >
< a id = "__codelineno-44-16" name = "__codelineno-44-16" href = "#__codelineno-44-16" > < / a > < span class = "cm" > /* 从节点 i 开始，从顶至底堆化 */< / span >
< a id = "__codelineno-44-17" name = "__codelineno-44-17" href = "#__codelineno-44-17" > < / 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-44-18" name = "__codelineno-44-18" href = "#__codelineno-44-18" > < / 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-44-19" name = "__codelineno-44-19" href = "#__codelineno-44-19" > < / 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-44-20" name = "__codelineno-44-20" href = "#__codelineno-44-20" > < / 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-44-21" name = "__codelineno-44-21" href = "#__codelineno-44-21" > < / 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" > < < / 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 = "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" > > < / 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-44-22" name = "__codelineno-44-22" href = "#__codelineno-44-22" > < / 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-44-23" name = "__codelineno-44-23" href = "#__codelineno-44-23" > < / 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" > < < / 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 = "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" > > < / 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-44-24" name = "__codelineno-44-24" href = "#__codelineno-44-24" > < / 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-44-25" name = "__codelineno-44-25" href = "#__codelineno-44-25" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若节点 i 最大或索引 l, r 越界，则无需继续堆化，跳出< / span >
< a id = "__codelineno-44-26" name = "__codelineno-44-26" href = "#__codelineno-44-26" > < / 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-44-27" name = "__codelineno-44-27" href = "#__codelineno-44-27" > < / a > < span class = "w" > < / span > < span class = "k" > break< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-44-28" name = "__codelineno-44-28" href = "#__codelineno-44-28" > < / a > < span class = "w" > < / span > < span class = "c1" > // 交换两节点< / span >
< a id = "__codelineno-44-29" name = "__codelineno-44-29" href = "#__codelineno-44-29" > < / 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-44-30" name = "__codelineno-44-30" href = "#__codelineno-44-30" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环向下堆化< / span >
< a id = "__codelineno-44-31" name = "__codelineno-44-31" href = "#__codelineno-44-31" > < / 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-44-32" name = "__codelineno-44-32" href = "#__codelineno-44-32" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-44-33" name = "__codelineno-44-33" href = "#__codelineno-44-33" > < / a > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > my_heap.cpp< / span > < pre > < span > < / span > < code > < a id = "__codelineno-45-1" name = "__codelineno-45-1" href = "#__codelineno-45-1" > < / a > < span class = "cm" > /* 元素出堆 */< / span >
< a id = "__codelineno-45-2" name = "__codelineno-45-2" href = "#__codelineno-45-2" > < / 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 >
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< a id = "__codelineno-45-3" name = "__codelineno-45-3" href = "#__codelineno-45-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 判空处理< / span >
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< a id = "__codelineno-45-4" name = "__codelineno-45-4" href = "#__codelineno-45-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > empty< / span > < span class = "p" > ())< / span > < span class = "w" > < / 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 = "k" > throw< / span > < span class = "w" > < / span > < span class = "n" > out_of_range< / span > < span class = "p" > (< / span > < span class = "s" > " 堆为空" < / span > < span class = "p" > );< / span >
< a id = "__codelineno-45-6" name = "__codelineno-45-6" href = "#__codelineno-45-6" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-45-7" name = "__codelineno-45-7" href = "#__codelineno-45-7" > < / a > < span class = "w" > < / span > < span class = "c1" > // 交换根节点与最右叶节点（即交换首元素与尾元素）< / span >
< a id = "__codelineno-45-8" name = "__codelineno-45-8" href = "#__codelineno-45-8" > < / 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-45-9" name = "__codelineno-45-9" href = "#__codelineno-45-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 删除节点< / span >
< a id = "__codelineno-45-10" name = "__codelineno-45-10" href = "#__codelineno-45-10" > < / 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-45-11" name = "__codelineno-45-11" href = "#__codelineno-45-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 从顶至底堆化< / span >
< a id = "__codelineno-45-12" name = "__codelineno-45-12" href = "#__codelineno-45-12" > < / a > < span class = "w" > < / span > < span class = "n" > siftDown< / span > < span class = "p" > (< / span > < span class = "mi" > 0< / span > < span class = "p" > );< / span >
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< a id = "__codelineno-45-13" name = "__codelineno-45-13" href = "#__codelineno-45-13" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-45-14" name = "__codelineno-45-14" href = "#__codelineno-45-14" > < / a >
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< a id = "__codelineno-45-15" name = "__codelineno-45-15" href = "#__codelineno-45-15" > < / a > < span class = "cm" > /* 从节点 i 开始，从顶至底堆化 */< / span >
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< a id = "__codelineno-45-16" name = "__codelineno-45-16" href = "#__codelineno-45-16" > < / 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-45-17" name = "__codelineno-45-17" href = "#__codelineno-45-17" > < / 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 >
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< a id = "__codelineno-45-18" name = "__codelineno-45-18" href = "#__codelineno-45-18" > < / 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 >
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< a id = "__codelineno-45-19" name = "__codelineno-45-19" href = "#__codelineno-45-19" > < / 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-45-20" name = "__codelineno-45-20" href = "#__codelineno-45-20" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若节点 i 最大或索引 l, r 越界，则无需继续堆化，跳出< / span >
< a id = "__codelineno-45-21" name = "__codelineno-45-21" href = "#__codelineno-45-21" > < / 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" > < < / 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 = "n" > maxHeap< / span > < span class = "p" > [< / span > < span class = "n" > l< / span > < span class = "p" > ]< / 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" > ma< / 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 = "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-45-23" name = "__codelineno-45-23" href = "#__codelineno-45-23" > < / 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" > < < / 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 = "n" > maxHeap< / span > < span class = "p" > [< / span > < span class = "n" > r< / span > < span class = "p" > ]< / 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" > ma< / 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 = "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-45-25" name = "__codelineno-45-25" href = "#__codelineno-45-25" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若节点 i 最大或索引 l, r 越界，则无需继续堆化，跳出< / span >
< a id = "__codelineno-45-26" name = "__codelineno-45-26" href = "#__codelineno-45-26" > < / 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-45-27" name = "__codelineno-45-27" href = "#__codelineno-45-27" > < / a > < span class = "w" > < / span > < span class = "k" > break< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-45-28" name = "__codelineno-45-28" href = "#__codelineno-45-28" > < / 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-45-29" name = "__codelineno-45-29" href = "#__codelineno-45-29" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环向下堆化< / span >
< a id = "__codelineno-45-30" name = "__codelineno-45-30" href = "#__codelineno-45-30" > < / 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-45-31" name = "__codelineno-45-31" href = "#__codelineno-45-31" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-45-32" name = "__codelineno-45-32" href = "#__codelineno-45-32" > < / a > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > my_heap.py< / span > < pre > < span > < / span > < code > < a id = "__codelineno-46-1" name = "__codelineno-46-1" href = "#__codelineno-46-1" > < / 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" > -> < / span > < span class = "nb" > int< / span > < span class = "p" > :< / span >
< a id = "__codelineno-46-2" name = "__codelineno-46-2" href = "#__codelineno-46-2" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 元素出堆" " " < / span >
< a id = "__codelineno-46-3" name = "__codelineno-46-3" href = "#__codelineno-46-3" > < / a > < span class = "c1" > # 判空处理< / span >
< a id = "__codelineno-46-4" name = "__codelineno-46-4" href = "#__codelineno-46-4" > < / 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-46-5" name = "__codelineno-46-5" href = "#__codelineno-46-5" > < / a > < span class = "k" > raise< / span > < span class = "ne" > IndexError< / span > < span class = "p" > (< / span > < span class = "s2" > " 堆为空" < / span > < span class = "p" > )< / span >
< a id = "__codelineno-46-6" name = "__codelineno-46-6" href = "#__codelineno-46-6" > < / a > < span class = "c1" > # 交换根节点与最右叶节点（即交换首元素与尾元素）< / span >
< a id = "__codelineno-46-7" name = "__codelineno-46-7" href = "#__codelineno-46-7" > < / 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-46-8" name = "__codelineno-46-8" href = "#__codelineno-46-8" > < / a > < span class = "c1" > # 删除节点< / span >
< a id = "__codelineno-46-9" name = "__codelineno-46-9" href = "#__codelineno-46-9" > < / 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-46-10" name = "__codelineno-46-10" href = "#__codelineno-46-10" > < / a > < span class = "c1" > # 从顶至底堆化< / span >
< a id = "__codelineno-46-11" name = "__codelineno-46-11" href = "#__codelineno-46-11" > < / 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-46-12" name = "__codelineno-46-12" href = "#__codelineno-46-12" > < / a > < span class = "c1" > # 返回堆顶元素< / span >
< a id = "__codelineno-46-13" name = "__codelineno-46-13" href = "#__codelineno-46-13" > < / a > < span class = "k" > return< / span > < span class = "n" > val< / span >
< a id = "__codelineno-46-14" name = "__codelineno-46-14" href = "#__codelineno-46-14" > < / a >
< a id = "__codelineno-46-15" name = "__codelineno-46-15" href = "#__codelineno-46-15" > < / 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-46-16" name = "__codelineno-46-16" href = "#__codelineno-46-16" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 从节点 i 开始，从顶至底堆化" " " < / span >
< a id = "__codelineno-46-17" name = "__codelineno-46-17" href = "#__codelineno-46-17" > < / a > < span class = "k" > while< / span > < span class = "kc" > True< / span > < span class = "p" > :< / span >
< a id = "__codelineno-46-18" name = "__codelineno-46-18" href = "#__codelineno-46-18" > < / 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-46-19" name = "__codelineno-46-19" href = "#__codelineno-46-19" > < / 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-46-20" name = "__codelineno-46-20" href = "#__codelineno-46-20" > < / a > < span class = "k" > if< / span > < span class = "n" > l< / span > < span class = "o" > < < / 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" > > < / 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-46-21" name = "__codelineno-46-21" href = "#__codelineno-46-21" > < / a > < span class = "n" > ma< / span > < span class = "o" > =< / span > < span class = "n" > l< / span >
< a id = "__codelineno-46-22" name = "__codelineno-46-22" href = "#__codelineno-46-22" > < / a > < span class = "k" > if< / span > < span class = "n" > r< / span > < span class = "o" > < < / 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" > > < / 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-46-23" name = "__codelineno-46-23" href = "#__codelineno-46-23" > < / a > < span class = "n" > ma< / span > < span class = "o" > =< / span > < span class = "n" > r< / span >
< a id = "__codelineno-46-24" name = "__codelineno-46-24" href = "#__codelineno-46-24" > < / a > < span class = "c1" > # 若节点 i 最大或索引 l, r 越界，则无需继续堆化，跳出< / span >
< a id = "__codelineno-46-25" name = "__codelineno-46-25" href = "#__codelineno-46-25" > < / 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-46-26" name = "__codelineno-46-26" href = "#__codelineno-46-26" > < / a > < span class = "k" > break< / span >
< a id = "__codelineno-46-27" name = "__codelineno-46-27" href = "#__codelineno-46-27" > < / a > < span class = "c1" > # 交换两节点< / span >
< a id = "__codelineno-46-28" name = "__codelineno-46-28" href = "#__codelineno-46-28" > < / 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-46-29" name = "__codelineno-46-29" href = "#__codelineno-46-29" > < / a > < span class = "c1" > # 循环向下堆化< / span >
< a id = "__codelineno-46-30" name = "__codelineno-46-30" href = "#__codelineno-46-30" > < / a > < span class = "n" > i< / span > < span class = "o" > =< / span > < span class = "n" > ma< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > my_heap.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-47-1" name = "__codelineno-47-1" href = "#__codelineno-47-1" > < / a > < span class = "cm" > /* 元素出堆 */< / span >
< a id = "__codelineno-47-2" name = "__codelineno-47-2" href = "#__codelineno-47-2" > < / 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 >
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< a id = "__codelineno-47-3" name = "__codelineno-47-3" href = "#__codelineno-47-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 判空处理< / span >
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< a id = "__codelineno-47-4" name = "__codelineno-47-4" href = "#__codelineno-47-4" > < / 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-47-5" name = "__codelineno-47-5" href = "#__codelineno-47-5" > < / 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" > " error" < / span > < span class = "p" > )< / span >
< a id = "__codelineno-47-6" name = "__codelineno-47-6" href = "#__codelineno-47-6" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "kc" > nil< / span >
< a id = "__codelineno-47-7" name = "__codelineno-47-7" href = "#__codelineno-47-7" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-47-8" name = "__codelineno-47-8" href = "#__codelineno-47-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 交换根节点与最右叶节点（即交换首元素与尾元素）< / span >
< a id = "__codelineno-47-9" name = "__codelineno-47-9" href = "#__codelineno-47-9" > < / 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-47-10" name = "__codelineno-47-10" href = "#__codelineno-47-10" > < / a > < span class = "w" > < / span > < span class = "c1" > // 删除节点< / span >
< a id = "__codelineno-47-11" name = "__codelineno-47-11" href = "#__codelineno-47-11" > < / 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-47-12" name = "__codelineno-47-12" href = "#__codelineno-47-12" > < / 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-47-13" name = "__codelineno-47-13" href = "#__codelineno-47-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 从顶至底堆化< / span >
< a id = "__codelineno-47-14" name = "__codelineno-47-14" href = "#__codelineno-47-14" > < / 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-47-15" name = "__codelineno-47-15" href = "#__codelineno-47-15" > < / a >
< a id = "__codelineno-47-16" name = "__codelineno-47-16" href = "#__codelineno-47-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // 返回堆顶元素< / span >
< a id = "__codelineno-47-17" name = "__codelineno-47-17" href = "#__codelineno-47-17" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > val< / span >
< a id = "__codelineno-47-18" name = "__codelineno-47-18" href = "#__codelineno-47-18" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-47-19" name = "__codelineno-47-19" href = "#__codelineno-47-19" > < / a >
< a id = "__codelineno-47-20" name = "__codelineno-47-20" href = "#__codelineno-47-20" > < / a > < span class = "cm" > /* 从节点 i 开始，从顶至底堆化 */< / span >
< a id = "__codelineno-47-21" name = "__codelineno-47-21" href = "#__codelineno-47-21" > < / 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-47-22" name = "__codelineno-47-22" href = "#__codelineno-47-22" > < / 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-47-23" name = "__codelineno-47-23" href = "#__codelineno-47-23" > < / 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-47-24" name = "__codelineno-47-24" href = "#__codelineno-47-24" > < / 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-47-25" name = "__codelineno-47-25" href = "#__codelineno-47-25" > < / 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" > < < / 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" > & & < / 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" > > < / 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-47-26" name = "__codelineno-47-26" href = "#__codelineno-47-26" > < / 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-47-27" name = "__codelineno-47-27" href = "#__codelineno-47-27" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-47-28" name = "__codelineno-47-28" href = "#__codelineno-47-28" > < / 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" > < < / 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" > & & < / 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" > > < / 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-47-29" name = "__codelineno-47-29" href = "#__codelineno-47-29" > < / 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-47-30" name = "__codelineno-47-30" href = "#__codelineno-47-30" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-47-31" name = "__codelineno-47-31" href = "#__codelineno-47-31" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若节点 i 最大或索引 l, r 越界，则无需继续堆化，跳出< / span >
< a id = "__codelineno-47-32" name = "__codelineno-47-32" href = "#__codelineno-47-32" > < / 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-47-33" name = "__codelineno-47-33" href = "#__codelineno-47-33" > < / a > < span class = "w" > < / span > < span class = "k" > break< / span >
< a id = "__codelineno-47-34" name = "__codelineno-47-34" href = "#__codelineno-47-34" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-47-35" name = "__codelineno-47-35" href = "#__codelineno-47-35" > < / a > < span class = "w" > < / span > < span class = "c1" > // 交换两节点< / span >
< a id = "__codelineno-47-36" name = "__codelineno-47-36" href = "#__codelineno-47-36" > < / 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-47-37" name = "__codelineno-47-37" href = "#__codelineno-47-37" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环向下堆化< / span >
< a id = "__codelineno-47-38" name = "__codelineno-47-38" href = "#__codelineno-47-38" > < / 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-47-39" name = "__codelineno-47-39" href = "#__codelineno-47-39" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-47-40" name = "__codelineno-47-40" href = "#__codelineno-47-40" > < / a > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > my_heap.js< / span > < pre > < span > < / span > < code > < a id = "__codelineno-48-1" name = "__codelineno-48-1" href = "#__codelineno-48-1" > < / a > < span class = "cm" > /* 元素出堆 */< / span >
< a id = "__codelineno-48-2" name = "__codelineno-48-2" href = "#__codelineno-48-2" > < / a > < span class = "nx" > pop< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-48-3" name = "__codelineno-48-3" href = "#__codelineno-48-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 判空处理< / span >
< a id = "__codelineno-48-4" name = "__codelineno-48-4" href = "#__codelineno-48-4" > < / 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" > ' 堆为空' < / span > < span class = "p" > );< / span >
< a id = "__codelineno-48-5" name = "__codelineno-48-5" href = "#__codelineno-48-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 交换根节点与最右叶节点（即交换首元素与尾元素）< / span >
< a id = "__codelineno-48-6" name = "__codelineno-48-6" href = "#__codelineno-48-6" > < / 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-48-7" name = "__codelineno-48-7" href = "#__codelineno-48-7" > < / a > < span class = "w" > < / span > < span class = "c1" > // 删除节点< / span >
< a id = "__codelineno-48-8" name = "__codelineno-48-8" href = "#__codelineno-48-8" > < / 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-48-9" name = "__codelineno-48-9" href = "#__codelineno-48-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 从顶至底堆化< / span >
< a id = "__codelineno-48-10" name = "__codelineno-48-10" href = "#__codelineno-48-10" > < / 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-48-11" name = "__codelineno-48-11" href = "#__codelineno-48-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 返回堆顶元素< / span >
< a id = "__codelineno-48-12" name = "__codelineno-48-12" href = "#__codelineno-48-12" > < / 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-48-13" name = "__codelineno-48-13" href = "#__codelineno-48-13" > < / a > < span class = "p" > }< / 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 = "cm" > /* 从节点 i 开始，从顶至底堆化 */< / span >
< a id = "__codelineno-48-16" name = "__codelineno-48-16" href = "#__codelineno-48-16" > < / 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-48-17" name = "__codelineno-48-17" href = "#__codelineno-48-17" > < / 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-48-18" name = "__codelineno-48-18" href = "#__codelineno-48-18" > < / 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-48-19" name = "__codelineno-48-19" href = "#__codelineno-48-19" > < / 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-48-20" name = "__codelineno-48-20" href = "#__codelineno-48-20" > < / 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-48-21" name = "__codelineno-48-21" href = "#__codelineno-48-21" > < / 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-48-22" name = "__codelineno-48-22" href = "#__codelineno-48-22" > < / 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" > < < / 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 = "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" > > < / 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-48-23" name = "__codelineno-48-23" href = "#__codelineno-48-23" > < / 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" > < < / 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 = "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" > > < / 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-48-24" name = "__codelineno-48-24" href = "#__codelineno-48-24" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若节点 i 最大或索引 l, r 越界，则无需继续堆化，跳出< / span >
< a id = "__codelineno-48-25" name = "__codelineno-48-25" href = "#__codelineno-48-25" > < / 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-48-26" name = "__codelineno-48-26" href = "#__codelineno-48-26" > < / a > < span class = "w" > < / span > < span class = "c1" > // 交换两节点< / span >
< a id = "__codelineno-48-27" name = "__codelineno-48-27" href = "#__codelineno-48-27" > < / 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-48-28" name = "__codelineno-48-28" href = "#__codelineno-48-28" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环向下堆化< / span >
< a id = "__codelineno-48-29" name = "__codelineno-48-29" href = "#__codelineno-48-29" > < / 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-48-30" name = "__codelineno-48-30" href = "#__codelineno-48-30" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-48-31" name = "__codelineno-48-31" href = "#__codelineno-48-31" > < / a > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > my_heap.ts< / 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 = "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-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 = "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" > ' Heap is empty.' < / span > < span class = "p" > );< / span >
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< a id = "__codelineno-49-5" name = "__codelineno-49-5" href = "#__codelineno-49-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 交换根节点与最右叶节点（即交换首元素与尾元素）< / span >
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< a id = "__codelineno-49-6" name = "__codelineno-49-6" href = "#__codelineno-49-6" > < / 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 >
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< a id = "__codelineno-49-7" name = "__codelineno-49-7" href = "#__codelineno-49-7" > < / a > < span class = "w" > < / span > < span class = "c1" > // 删除节点< / span >
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< a id = "__codelineno-49-8" name = "__codelineno-49-8" href = "#__codelineno-49-8" > < / 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 >
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< a id = "__codelineno-49-9" name = "__codelineno-49-9" href = "#__codelineno-49-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 从顶至底堆化< / span >
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< a id = "__codelineno-49-10" name = "__codelineno-49-10" href = "#__codelineno-49-10" > < / 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 >
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< a id = "__codelineno-49-11" name = "__codelineno-49-11" href = "#__codelineno-49-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 返回堆顶元素< / span >
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< a id = "__codelineno-49-12" name = "__codelineno-49-12" href = "#__codelineno-49-12" > < / 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-49-13" name = "__codelineno-49-13" href = "#__codelineno-49-13" > < / a > < span class = "p" > }< / span >
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< a id = "__codelineno-49-14" name = "__codelineno-49-14" href = "#__codelineno-49-14" > < / a >
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< 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 = "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-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 = "kc" > 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 = "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-49-20" name = "__codelineno-49-20" href = "#__codelineno-49-20" > < / 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-49-21" name = "__codelineno-49-21" href = "#__codelineno-49-21" > < / 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-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 = "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" > size< / span > < span class = "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" > maxHeap< / span > < span class = "p" > [< / span > < span class = "nx" > l< / span > < span class = "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" > 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-49-23" name = "__codelineno-49-23" href = "#__codelineno-49-23" > < / 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" > < < / 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 = "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" > > < / 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-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，则无需继续堆化，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 = "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-49-26" name = "__codelineno-49-26" href = "#__codelineno-49-26" > < / a > < span class = "w" > < / span > < span class = "c1" > // 交换两节点< / span >
< a id = "__codelineno-49-27" name = "__codelineno-49-27" href = "#__codelineno-49-27" > < / 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-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 = "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-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.c< / 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 = "n" > maxHeap< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > h< / 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 > < span class = "n" > h< / span > < span class = "p" > ))< / span > < span class = "w" > < / 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 = "n" > printf< / span > < span class = "p" > (< / span > < span class = "s" > " heap is empty!" < / 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 = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > INT_MAX< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-50-7" name = "__codelineno-50-7" href = "#__codelineno-50-7" > < / a > < span class = "w" > < / 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" > // 交换根节点与最右叶节点（即交换首元素与尾元素）< / span >
< a id = "__codelineno-50-9" name = "__codelineno-50-9" href = "#__codelineno-50-9" > < / a > < span class = "w" > < / span > < span class = "n" > swap< / span > < span class = "p" > (< / span > < span class = "n" > h< / 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" > h< / 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" > // 删除节点< / span >
< a id = "__codelineno-50-11" name = "__codelineno-50-11" href = "#__codelineno-50-11" > < / 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" > h< / span > < span class = "o" > -> < / span > < span class = "n" > data< / span > < span class = "p" > [< / span > < span class = "n" > h< / span > < span class = "o" > -> < / 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-50-12" name = "__codelineno-50-12" href = "#__codelineno-50-12" > < / a > < span class = "w" > < / span > < span class = "n" > h< / span > < span class = "o" > -> < / span > < span class = "n" > size< / span > < span class = "o" > --< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-50-13" name = "__codelineno-50-13" href = "#__codelineno-50-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 从顶至底堆化< / span >
< a id = "__codelineno-50-14" name = "__codelineno-50-14" href = "#__codelineno-50-14" > < / a > < span class = "w" > < / span > < span class = "n" > siftDown< / span > < span class = "p" > (< / span > < span class = "n" > h< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < 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 = "w" > < / span > < span class = "c1" > // 返回堆顶元素< / span >
< a id = "__codelineno-50-17" name = "__codelineno-50-17" href = "#__codelineno-50-17" > < / 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-50-18" name = "__codelineno-50-18" href = "#__codelineno-50-18" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-50-19" name = "__codelineno-50-19" href = "#__codelineno-50-19" > < / a >
< a id = "__codelineno-50-20" name = "__codelineno-50-20" href = "#__codelineno-50-20" > < / a > < span class = "cm" > /* 从节点 i 开始，从顶至底堆化 */< / span >
< a id = "__codelineno-50-21" name = "__codelineno-50-21" href = "#__codelineno-50-21" > < / 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" > h< / 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-50-22" name = "__codelineno-50-22" href = "#__codelineno-50-22" > < / 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-50-23" name = "__codelineno-50-23" href = "#__codelineno-50-23" > < / 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-50-24" name = "__codelineno-50-24" href = "#__codelineno-50-24" > < / 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" > h< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > i< / 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 = "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" > h< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "p" > );< / span >
< a id = "__codelineno-50-26" name = "__codelineno-50-26" href = "#__codelineno-50-26" > < / 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-50-27" name = "__codelineno-50-27" href = "#__codelineno-50-27" > < / 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" > < < / span > < span class = "w" > < / span > < span class = "n" > size< / span > < span class = "p" > (< / span > < span class = "n" > h< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > & & < / span > < span class = "w" > < / span > < span class = "n" > h< / span > < span class = "o" > -> < / 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" > > < / span > < span class = "w" > < / span > < span class = "n" > h< / span > < span class = "o" > -> < / 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-50-28" name = "__codelineno-50-28" href = "#__codelineno-50-28" > < / 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-50-29" name = "__codelineno-50-29" href = "#__codelineno-50-29" > < / a > < span class = "w" > < / 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 = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > r< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "n" > size< / span > < span class = "p" > (< / span > < span class = "n" > h< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > & & < / span > < span class = "w" > < / span > < span class = "n" > h< / span > < span class = "o" > -> < / 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" > > < / span > < span class = "w" > < / span > < span class = "n" > h< / span > < span class = "o" > -> < / 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-50-31" name = "__codelineno-50-31" href = "#__codelineno-50-31" > < / 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-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 = "w" > < / span > < span class = "c1" > // 若节点 i 最大或索引 l, r 越界，则无需继续堆化，跳出< / span >
< a id = "__codelineno-50-34" name = "__codelineno-50-34" href = "#__codelineno-50-34" > < / 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-50-35" name = "__codelineno-50-35" href = "#__codelineno-50-35" > < / a > < span class = "w" > < / span > < span class = "k" > break< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-50-36" name = "__codelineno-50-36" href = "#__codelineno-50-36" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-50-37" name = "__codelineno-50-37" href = "#__codelineno-50-37" > < / a > < span class = "w" > < / span > < span class = "c1" > // 交换两节点< / span >
< a id = "__codelineno-50-38" name = "__codelineno-50-38" href = "#__codelineno-50-38" > < / a > < span class = "w" > < / span > < span class = "n" > swap< / span > < span class = "p" > (< / span > < span class = "n" > h< / 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-50-39" name = "__codelineno-50-39" href = "#__codelineno-50-39" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环向下堆化< / span >
< a id = "__codelineno-50-40" name = "__codelineno-50-40" href = "#__codelineno-50-40" > < / 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-50-41" name = "__codelineno-50-41" href = "#__codelineno-50-41" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-50-42" name = "__codelineno-50-42" href = "#__codelineno-50-42" > < / 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（即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" > < < / 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 = "n" > maxHeap< / span > < span class = "p" > [< / span > < span class = "n" > l< / span > < span class = "p" > ]< / 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" > 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" > < < / 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 = "n" > maxHeap< / span > < span class = "p" > [< / span > < span class = "n" > r< / span > < span class = "p" > ]< / 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" > 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.swift< / 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 = "nf" > pop< / span > < span class = "p" > ()< / span > < span class = "p" > -> < / span > < span class = "nb" > Int< / span > < span class = "p" > {< / span >
< a id = "__codelineno-52-3" name = "__codelineno-52-3" href = "#__codelineno-52-3" > < / a > < span class = "c1" > // 判空处理< / span >
< a id = "__codelineno-52-4" name = "__codelineno-52-4" href = "#__codelineno-52-4" > < / a > < span class = "k" > if< / span > < span class = "bp" > isEmpty< / span > < span class = "p" > ()< / span > < span class = "p" > {< / span >
< a id = "__codelineno-52-5" name = "__codelineno-52-5" href = "#__codelineno-52-5" > < / a > < span class = "bp" > fatalError< / span > < span class = "p" > (< / span > < span class = "s" > " 堆为空" < / span > < span class = "p" > )< / span >
< a id = "__codelineno-52-6" name = "__codelineno-52-6" href = "#__codelineno-52-6" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-52-7" name = "__codelineno-52-7" href = "#__codelineno-52-7" > < / a > < span class = "c1" > // 交换根节点与最右叶节点（即交换首元素与尾元素）< / span >
< a id = "__codelineno-52-8" name = "__codelineno-52-8" href = "#__codelineno-52-8" > < / 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-52-9" name = "__codelineno-52-9" href = "#__codelineno-52-9" > < / a > < span class = "c1" > // 删除节点< / span >
< a id = "__codelineno-52-10" name = "__codelineno-52-10" href = "#__codelineno-52-10" > < / 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-52-11" name = "__codelineno-52-11" href = "#__codelineno-52-11" > < / a > < span class = "c1" > // 从顶至底堆化< / span >
< a id = "__codelineno-52-12" name = "__codelineno-52-12" href = "#__codelineno-52-12" > < / 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-52-13" name = "__codelineno-52-13" href = "#__codelineno-52-13" > < / a > < span class = "c1" > // 返回堆顶元素< / span >
< a id = "__codelineno-52-14" name = "__codelineno-52-14" href = "#__codelineno-52-14" > < / a > < span class = "k" > return< / span > < span class = "n" > val< / span >
< a id = "__codelineno-52-15" name = "__codelineno-52-15" href = "#__codelineno-52-15" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-52-16" name = "__codelineno-52-16" href = "#__codelineno-52-16" > < / a >
< a id = "__codelineno-52-17" name = "__codelineno-52-17" href = "#__codelineno-52-17" > < / a > < span class = "cm" > /* 从节点 i 开始，从顶至底堆化 */< / span >
< a id = "__codelineno-52-18" name = "__codelineno-52-18" href = "#__codelineno-52-18" > < / 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-52-19" name = "__codelineno-52-19" href = "#__codelineno-52-19" > < / a > < span class = "kd" > var< / span > < span class = "nv" > i< / span > < span class = "p" > =< / span > < span class = "n" > i< / span >
< a id = "__codelineno-52-20" name = "__codelineno-52-20" href = "#__codelineno-52-20" > < / a > < span class = "k" > while< / span > < span class = "kc" > true< / span > < span class = "p" > {< / span >
< a id = "__codelineno-52-21" name = "__codelineno-52-21" href = "#__codelineno-52-21" > < / 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-52-22" name = "__codelineno-52-22" href = "#__codelineno-52-22" > < / 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-52-23" name = "__codelineno-52-23" href = "#__codelineno-52-23" > < / 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-52-24" name = "__codelineno-52-24" href = "#__codelineno-52-24" > < / a > < span class = "kd" > var< / span > < span class = "nv" > ma< / span > < span class = "p" > =< / span > < span class = "n" > i< / span >
< a id = "__codelineno-52-25" name = "__codelineno-52-25" href = "#__codelineno-52-25" > < / a > < span class = "k" > if< / span > < span class = "n" > l< / span > < span class = "o" > < < / 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" > > < / 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-52-26" name = "__codelineno-52-26" href = "#__codelineno-52-26" > < / a > < span class = "n" > ma< / span > < span class = "p" > =< / span > < span class = "n" > l< / span >
< a id = "__codelineno-52-27" name = "__codelineno-52-27" href = "#__codelineno-52-27" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-52-28" name = "__codelineno-52-28" href = "#__codelineno-52-28" > < / a > < span class = "k" > if< / span > < span class = "n" > r< / span > < span class = "o" > < < / 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" > > < / 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-52-29" name = "__codelineno-52-29" href = "#__codelineno-52-29" > < / a > < span class = "n" > ma< / span > < span class = "p" > =< / span > < span class = "n" > r< / span >
< a id = "__codelineno-52-30" name = "__codelineno-52-30" href = "#__codelineno-52-30" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-52-31" name = "__codelineno-52-31" href = "#__codelineno-52-31" > < / a > < span class = "c1" > // 若节点 i 最大或索引 l, r 越界，则无需继续堆化，跳出< / span >
< a id = "__codelineno-52-32" name = "__codelineno-52-32" href = "#__codelineno-52-32" > < / 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-52-33" name = "__codelineno-52-33" href = "#__codelineno-52-33" > < / a > < span class = "k" > break< / span >
< a id = "__codelineno-52-34" name = "__codelineno-52-34" href = "#__codelineno-52-34" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-52-35" name = "__codelineno-52-35" href = "#__codelineno-52-35" > < / a > < 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 = "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-52-37" name = "__codelineno-52-37" href = "#__codelineno-52-37" > < / a > < 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 = "n" > i< / span > < span class = "p" > =< / span > < span class = "n" > ma< / span >
< a id = "__codelineno-52-39" name = "__codelineno-52-39" href = "#__codelineno-52-39" > < / a > < 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.zig< / span > < pre > < span > < / span > < code > < a id = "__codelineno-53-1" name = "__codelineno-53-1" href = "#__codelineno-53-1" > < / a > < span class = "c1" > // 元素出堆< / span >
< a id = "__codelineno-53-2" name = "__codelineno-53-2" href = "#__codelineno-53-2" > < / 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-53-3" name = "__codelineno-53-3" href = "#__codelineno-53-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 判断处理< / span >
< a id = "__codelineno-53-4" name = "__codelineno-53-4" href = "#__codelineno-53-4" > < / 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-53-5" name = "__codelineno-53-5" href = "#__codelineno-53-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 交换根节点与最右叶节点（即交换首元素与尾元素）< / span >
< a id = "__codelineno-53-6" name = "__codelineno-53-6" href = "#__codelineno-53-6" > < / 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-53-7" name = "__codelineno-53-7" href = "#__codelineno-53-7" > < / a > < span class = "w" > < / span > < span class = "c1" > // 删除节点< / span >
< a id = "__codelineno-53-8" name = "__codelineno-53-8" href = "#__codelineno-53-8" > < / 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-53-9" name = "__codelineno-53-9" href = "#__codelineno-53-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 从顶至底堆化< / span >
< a id = "__codelineno-53-10" name = "__codelineno-53-10" href = "#__codelineno-53-10" > < / 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-53-11" name = "__codelineno-53-11" href = "#__codelineno-53-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 返回堆顶元素< / span >
< a id = "__codelineno-53-12" name = "__codelineno-53-12" href = "#__codelineno-53-12" > < / 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-53-13" name = "__codelineno-53-13" href = "#__codelineno-53-13" > < / a > < span class = "p" > }< / span > < span class = "w" > < / span >
< a id = "__codelineno-53-14" name = "__codelineno-53-14" href = "#__codelineno-53-14" > < / a >
< a id = "__codelineno-53-15" name = "__codelineno-53-15" href = "#__codelineno-53-15" > < / a > < span class = "c1" > // 从节点 i 开始，从顶至底堆化< / span >
< a id = "__codelineno-53-16" name = "__codelineno-53-16" href = "#__codelineno-53-16" > < / 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-53-17" name = "__codelineno-53-17" href = "#__codelineno-53-17" > < / 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-53-18" name = "__codelineno-53-18" href = "#__codelineno-53-18" > < / 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-53-19" name = "__codelineno-53-19" href = "#__codelineno-53-19" > < / 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-53-20" name = "__codelineno-53-20" href = "#__codelineno-53-20" > < / 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-53-21" name = "__codelineno-53-21" href = "#__codelineno-53-21" > < / 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-53-22" name = "__codelineno-53-22" href = "#__codelineno-53-22" > < / 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-53-23" name = "__codelineno-53-23" href = "#__codelineno-53-23" > < / 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" > < < / 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" > > < / 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-53-24" name = "__codelineno-53-24" href = "#__codelineno-53-24" > < / 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" > < < / 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" > > < / 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-53-25" name = "__codelineno-53-25" href = "#__codelineno-53-25" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若节点 i 最大或索引 l, r 越界，则无需继续堆化，跳出< / span >
< a id = "__codelineno-53-26" name = "__codelineno-53-26" href = "#__codelineno-53-26" > < / 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-53-27" name = "__codelineno-53-27" href = "#__codelineno-53-27" > < / a > < span class = "w" > < / span > < span class = "c1" > // 交换两节点< / span >
< a id = "__codelineno-53-28" name = "__codelineno-53-28" href = "#__codelineno-53-28" > < / 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-53-29" name = "__codelineno-53-29" href = "#__codelineno-53-29" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环向下堆化< / span >
< a id = "__codelineno-53-30" name = "__codelineno-53-30" href = "#__codelineno-53-30" > < / 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-53-31" name = "__codelineno-53-31" href = "#__codelineno-53-31" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-53-32" name = "__codelineno-53-32" href = "#__codelineno-53-32" > < / 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-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 = "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-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 = "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" > ' 堆为空' < / 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（即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 = "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-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 = "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-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 = "n" > _siftDown< / span > < span class = "p" > (< / span > < span class = "m" > 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 = "n" > 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 = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{< / span > < span class = "n" > MaxHeap< / span > < span class = "p" > }< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > siftDown< / span > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
< / div >
< / div >
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< h2 id = "813" > 8.1.3. 堆常见应用< a class = "headerlink" href = "#813" title = "Permanent link" > ¶ < / a > < / h2 >
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< ul >
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< 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 >
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< 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，详见后续的堆排序章节。< / li >
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< 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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