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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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0. 写在前面
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0. 写在前面
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0.1. 关于本书
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0.2. 如何使用本书
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0.3. 小结
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1. 引言
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1. 引言
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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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2. 复杂度分析
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2. 复杂度分析
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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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< a href = "../../chapter_computational_complexity/space_complexity/" class = "md-nav__link" >
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2.3. 空间复杂度
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< a href = "../../chapter_computational_complexity/space_time_tradeoff/" class = "md-nav__link" >
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2.4. 权衡时间与空间
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< a href = "../../chapter_computational_complexity/summary/" class = "md-nav__link" >
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2.5. 小结
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3. 数据结构简介
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3. 数据结构简介
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3.1. 数据与内存
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3.2. 数据结构分类
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3.3. 小结
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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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4.3. 列表
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4.4. 小结
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5. 栈与队列
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5. 栈与队列
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5.1. 栈
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< a href = "../../chapter_stack_and_queue/queue/" class = "md-nav__link" >
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5.2. 队列
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< a href = "../../chapter_stack_and_queue/deque/" class = "md-nav__link" >
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5.3. 双向队列
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5.4. 小结
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6. 散列表
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6. 散列表
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6.1. 哈希表
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< a href = "../../chapter_hashing/hash_collision/" class = "md-nav__link" >
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6.2. 哈希冲突处理
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6.3. 小结
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7. 树
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7. 树
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7.1. 二叉树
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7.2. 二叉树遍历
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< a href = "../../chapter_tree/binary_search_tree/" class = "md-nav__link" >
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7.3. 二叉搜索树
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< a href = "../../chapter_tree/avl_tree/" class = "md-nav__link" >
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7.4. AVL 树 *
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7.5. 小结
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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. 堆术语与性质
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8.1.2. 堆常用操作
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8.1.3. 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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8.1.4. 堆常见应用
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8.2. 建堆操作 *
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8.3. 小结
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9. 图
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9. 图
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9.1. 图
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< a href = "../../chapter_graph/graph_operations/" class = "md-nav__link" >
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9.2. 图基础操作
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< a href = "../../chapter_graph/graph_traversal/" class = "md-nav__link" >
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9.3. 图的遍历（ ）
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9.4. 小结
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10. 查找算法
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10. 查找算法
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10.1. 线性查找
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< a href = "../../chapter_searching/binary_search/" class = "md-nav__link" >
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10.2. 二分查找
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10.3. 哈希查找
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< a href = "../../chapter_searching/summary/" class = "md-nav__link" >
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10.4. 小结
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< label class = "md-nav__link" for = "__nav_12" id = "__nav_12_label" tabindex = "0" >
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11. 排序算法
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11. 排序算法
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11.1. 排序简介
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< li class = "md-nav__item" >
< a href = "../../chapter_sorting/bubble_sort/" class = "md-nav__link" >
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11.2. 冒泡排序
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< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_sorting/insertion_sort/" class = "md-nav__link" >
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11.3. 插入排序
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< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_sorting/quick_sort/" class = "md-nav__link" >
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11.4. 快速排序
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< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_sorting/merge_sort/" class = "md-nav__link" >
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11.5. 归并排序
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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" >
11.6. 桶排序（ ）
< / a >
< / li >
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< li class = "md-nav__item" >
< a href = "../../chapter_sorting/counting_sort/" class = "md-nav__link" >
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11.7. 计数排序（ ）
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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" >
11.8. 基数排序（ ）
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< / a >
< / li >
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< li class = "md-nav__item" >
< a href = "../../chapter_sorting/summary/" class = "md-nav__link" >
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11.9. 小结
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< / a >
< / li >
< / ul >
< / nav >
< / li >
< li class = "md-nav__item md-nav__item--section md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_13" >
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< label class = "md-nav__link" for = "__nav_13" id = "__nav_13_label" tabindex = "0" >
12. 附录
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_13_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_13" >
< span class = "md-nav__icon md-icon" > < / span >
12. 附录
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "../../chapter_appendix/installation/" class = "md-nav__link" >
12.1. 编程环境安装
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_appendix/contribution/" class = "md-nav__link" >
12.2. 一起参与创作
< / a >
< / li >
< / ul >
< / nav >
< / li >
< li class = "md-nav__item md-nav__item--section md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_14" >
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< div class = "md-nav__link md-nav__link--index " >
< a href = "../../chapter_reference/" > 参考文献< / a >
< / div >
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< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_14_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_14" >
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< span class = "md-nav__icon md-icon" > < / span >
参考文献
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< / ul >
< / nav >
< / li >
< / ul >
< / nav >
< / div >
< / div >
< / div >
< div class = "md-sidebar md-sidebar--secondary" data-md-component = "sidebar" data-md-type = "toc" >
< div class = "md-sidebar__scrollwrap" >
< div class = "md-sidebar__inner" >
< nav class = "md-nav md-nav--secondary" aria-label = "目录" >
< label class = "md-nav__title" for = "__toc" >
< span class = "md-nav__icon md-icon" > < / span >
目录
< / label >
< ul class = "md-nav__list" data-md-component = "toc" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "#811" class = "md-nav__link" >
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8.1.1. 堆术语与性质
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< / a >
< / li >
< li class = "md-nav__item" >
< a href = "#812" class = "md-nav__link" >
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8.1.2. 堆常用操作
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< / a >
< / li >
< li class = "md-nav__item" >
< a href = "#813" class = "md-nav__link" >
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8.1.3. 堆的实现
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< / a >
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< nav class = "md-nav" aria-label = "8.1.3. 堆的实现" >
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< ul class = "md-nav__list" >
< li class = "md-nav__item" >
< a href = "#_1" class = "md-nav__link" >
堆的存储与表示
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "#_2" class = "md-nav__link" >
访问堆顶元素
< / a >
< / 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
< / a >
< / li >
< / ul >
< / nav >
< / li >
< li class = "md-nav__item" >
< a href = "#814" class = "md-nav__link" >
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8.1.4. 堆常见应用
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< / a >
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< div class = "md-content" data-md-component = "content" >
< article class = "md-content__inner md-typeset" >
< a href = "https://github.com/krahets/hello-algo/tree/main/docs/chapter_heap/heap.md" title = "编辑此页" class = "md-content__button md-icon" >
< 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 >
< / a >
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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」是一棵限定条件下的「完全二叉树」。根据成立条件， ： < / p >
< ul >
< li > 「大顶堆 Max Heap」， < span class = "arithmatex" > \(\geq\)< / span > 其子结点的值；< / li >
< li > 「小顶堆 Min Heap」， < span class = "arithmatex" > \(\leq\)< / span > 其子结点的值；< / li >
< / 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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< h2 id = "811" > 8.1.1. 堆术语与性质< a class = "headerlink" href = "#811" title = "Permanent link" > ¶ < / a > < / h2 >
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< ul >
< li > 由于堆是完全二叉树，因此最底层结点靠左填充，其它层结点皆被填满。< / li >
< li > 二叉树中的根结点对应「堆顶」，底层最靠右结点对应「堆底」。< / li >
< li > 对于大顶堆 / 小顶堆，其堆顶元素（即根结点）的值最大 / 最小。< / li >
< / ul >
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< h2 id = "812" > 8.1.2. 堆常用操作< a class = "headerlink" href = "#812" title = "Permanent link" > ¶ < / a > < / h2 >
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< p > 值得说明的是，多数编程语言提供的是「优先队列 Priority Queue」， ， < strong > 定义为具有出队优先级的队列< / strong > 。< / p >
< p > 而恰好，< strong > 堆的定义与优先队列的操作逻辑完全吻合< / strong > ，大顶堆就是一个元素从大到小出队的优先队列。从使用角度看，我们可以将「优先队列」和「堆」理解为等价的数据结构。因此，本文与代码对两者不做特别区分，统一使用「堆」来命名。< / p >
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< p > 堆的常用操作见下表，方法名需根据编程语言确定。< / 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 >
< / table >
< / div >
< p > 我们可以直接使用编程语言提供的堆类（或优先队列类）。< / p >
< div class = "admonition tip" >
< p class = "admonition-title" > Tip< / p >
< p > 类似于排序中“从小到大排列”和“从大到小排列”，“大顶堆”和“小顶堆”可仅通过修改 Comparator 来互相转换。< / p >
< / div >
< div class = "tabbed-set tabbed-alternate" data-tabs = "1:10" > < 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" / > < 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 > < / div >
< 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 >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > heap.cpp< / span > < pre > < span > < / span > < code > < a id = "__codelineno-1-1" name = "__codelineno-1-1" href = "#__codelineno-1-1" > < / a > < span class = "cm" > /* 初始化堆 */< / span >
< a id = "__codelineno-1-2" name = "__codelineno-1-2" href = "#__codelineno-1-2" > < / a > < span class = "c1" > // 初始化小顶堆< / span >
< a id = "__codelineno-1-3" name = "__codelineno-1-3" href = "#__codelineno-1-3" > < / a > < span class = "n" > priority_queue< / span > < span class = "o" > < < / 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 >
< div class = "tabbed-block" >
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 >
< a id = "__codelineno-2-9" name = "__codelineno-2-9" href = "#__codelineno-2-9" > < / a > < span class = "sd" > " " " 元素入堆 " " " < / span >
< a id = "__codelineno-2-10" name = "__codelineno-2-10" href = "#__codelineno-2-10" > < / 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-2-11" 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" > 3< / 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" > 2< / 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" > 5< / 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" > 4< / span > < span class = "p" > )< / span >
< a id = "__codelineno-2-15" name = "__codelineno-2-15" href = "#__codelineno-2-15" > < / a >
< a id = "__codelineno-2-16" name = "__codelineno-2-16" href = "#__codelineno-2-16" > < / a > < span class = "sd" > " " " 获取堆顶元素 " " " < / span >
2023-03-12 18:46:10 +08:00
< a id = "__codelineno-2-17" name = "__codelineno-2-17" href = "#__codelineno-2-17" > < / 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 >
2023-02-23 20:23:42 +08:00
< a id = "__codelineno-2-18" name = "__codelineno-2-18" href = "#__codelineno-2-18" > < / a >
< a id = "__codelineno-2-19" name = "__codelineno-2-19" href = "#__codelineno-2-19" > < / a > < span class = "sd" > " " " 堆顶元素出堆 " " " < / span >
< a id = "__codelineno-2-20" name = "__codelineno-2-20" href = "#__codelineno-2-20" > < / a > < span class = "c1" > # 出堆元素会形成一个从大到小的序列< / span >
< a id = "__codelineno-2-21" name = "__codelineno-2-21" href = "#__codelineno-2-21" > < / 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-2-22" 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" > # 4< / 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" > # 3< / 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" > # 2< / 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" > # 1< / span >
< a id = "__codelineno-2-26" name = "__codelineno-2-26" href = "#__codelineno-2-26" > < / a >
< a id = "__codelineno-2-27" name = "__codelineno-2-27" href = "#__codelineno-2-27" > < / a > < span class = "sd" > " " " 获取堆大小 " " " < / span >
2023-03-12 18:46:10 +08:00
< a id = "__codelineno-2-28" name = "__codelineno-2-28" href = "#__codelineno-2-28" > < / 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 >
2023-02-23 20:23:42 +08:00
< a id = "__codelineno-2-29" name = "__codelineno-2-29" href = "#__codelineno-2-29" > < / a >
< a id = "__codelineno-2-30" name = "__codelineno-2-30" href = "#__codelineno-2-30" > < / a > < span class = "sd" > " " " 判断堆是否为空 " " " < / span >
2023-03-12 18:46:10 +08:00
< a id = "__codelineno-2-31" name = "__codelineno-2-31" href = "#__codelineno-2-31" > < / 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 >
2023-02-23 20:23:42 +08:00
< a id = "__codelineno-2-32" name = "__codelineno-2-32" href = "#__codelineno-2-32" > < / a >
< a id = "__codelineno-2-33" name = "__codelineno-2-33" href = "#__codelineno-2-33" > < / a > < span class = "sd" > " " " 输入列表并建堆 " " " < / span >
2023-03-12 18:46:10 +08:00
< a id = "__codelineno-2-34" name = "__codelineno-2-34" href = "#__codelineno-2-34" > < / 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 >
2023-02-23 20:23:42 +08:00
< a id = "__codelineno-2-35" name = "__codelineno-2-35" href = "#__codelineno-2-35" > < / 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" >
< 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 >
< / 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 >
< / div >
< / div >
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< h2 id = "813" > 8.1.3. 堆的实现< a class = "headerlink" href = "#813" title = "Permanent link" > ¶ < / a > < / h2 >
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< p > 下文实现的是「大顶堆」，若想转换为「小顶堆」，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 > ）即可，有兴趣的同学可自行实现。< / p >
< h3 id = "_1" > 堆的存储与表示< a class = "headerlink" href = "#_1" title = "Permanent link" > ¶ < / a > < / h3 >
< p > 在二叉树章节我们学过，「完全二叉树」非常适合使用「数组」来表示，而堆恰好是一棵完全二叉树，< strong > 因而我们采用「数组」来存储「堆」< / strong > 。< / p >
< p > < strong > 二叉树指针< / strong > 。使用数组表示二叉树时，元素代表结点值，索引代表结点在二叉树中的位置，< strong > 而结点指针通过索引映射公式来实现< / strong > 。< / p >
< p > 具体地，给定索引 < span class = "arithmatex" > \(i\)< / span > ，那么其左子结点索引为 < span class = "arithmatex" > \(2i + 1\)< / span > 、右子结点索引为 < span class = "arithmatex" > \(2i + 2\)< / span > 、父结点索引为 < span class = "arithmatex" > \((i - 1) / 2\)< / span > （向下整除）。当索引越界时，代表空结点或结点不存在。< / 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 > 我们将索引映射公式封装成函数，以便后续使用。< / p >
< div class = "tabbed-set tabbed-alternate" data-tabs = "2:10" > < 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" / > < 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 > < / div >
< div class = "tabbed-content" >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > my_heap.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-10-1" name = "__codelineno-10-1" href = "#__codelineno-10-1" > < / a > < span class = "cm" > /* 获取左子结点索引 */< / span >
< a id = "__codelineno-10-2" name = "__codelineno-10-2" href = "#__codelineno-10-2" > < / 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-10-3" name = "__codelineno-10-3" href = "#__codelineno-10-3" > < / 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-10-4" name = "__codelineno-10-4" href = "#__codelineno-10-4" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-10-5" name = "__codelineno-10-5" href = "#__codelineno-10-5" > < / a >
< a id = "__codelineno-10-6" name = "__codelineno-10-6" href = "#__codelineno-10-6" > < / a > < span class = "cm" > /* 获取右子结点索引 */< / span >
< a id = "__codelineno-10-7" name = "__codelineno-10-7" href = "#__codelineno-10-7" > < / 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-10-8" name = "__codelineno-10-8" href = "#__codelineno-10-8" > < / 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-10-9" name = "__codelineno-10-9" href = "#__codelineno-10-9" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-10-10" name = "__codelineno-10-10" href = "#__codelineno-10-10" > < / a >
< a id = "__codelineno-10-11" name = "__codelineno-10-11" href = "#__codelineno-10-11" > < / a > < span class = "cm" > /* 获取父结点索引 */< / span >
< a id = "__codelineno-10-12" name = "__codelineno-10-12" href = "#__codelineno-10-12" > < / 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-10-13" name = "__codelineno-10-13" href = "#__codelineno-10-13" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > /< / span > < span class = "w" > < / span > < span class = "mi" > 2< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 向下整除< / span >
< a id = "__codelineno-10-14" name = "__codelineno-10-14" href = "#__codelineno-10-14" > < / 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.cpp< / span > < pre > < span > < / span > < code > < a id = "__codelineno-11-1" name = "__codelineno-11-1" href = "#__codelineno-11-1" > < / a > < span class = "cm" > /* 获取左子结点索引 */< / span >
< 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 >
< a id = "__codelineno-11-6" name = "__codelineno-11-6" href = "#__codelineno-11-6" > < / a > < span class = "cm" > /* 获取右子结点索引 */< / span >
< 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 >
< a id = "__codelineno-11-9" name = "__codelineno-11-9" href = "#__codelineno-11-9" > < / a > < span class = "p" > }< / span > < span class = "w" > < / span >
< a id = "__codelineno-11-10" name = "__codelineno-11-10" href = "#__codelineno-11-10" > < / a >
< a id = "__codelineno-11-11" name = "__codelineno-11-11" href = "#__codelineno-11-11" > < / a > < span class = "cm" > /* 获取父结点索引 */< / span >
< 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 >
< 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" > // 向下取整< / span >
< 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.py< / span > < pre > < span > < / span > < code > < a id = "__codelineno-12-1" name = "__codelineno-12-1" href = "#__codelineno-12-1" > < / a > < span class = "k" > def< / span > < span class = "nf" > left< / span > < span class = "p" > (< / span > < span class = "bp" > self< / span > < span class = "p" > ,< / span > < span class = "n" > i< / span > < span class = "p" > :< / span > < span class = "nb" > int< / span > < span class = "p" > )< / span > < span class = "o" > -> < / span > < span class = "nb" > int< / span > < span class = "p" > :< / span >
< a id = "__codelineno-12-2" name = "__codelineno-12-2" href = "#__codelineno-12-2" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 获取左子结点索引 " " " < / span >
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< a id = "__codelineno-12-3" name = "__codelineno-12-3" href = "#__codelineno-12-3" > < / a > < span class = "k" > return< / span > < span class = "mi" > 2< / span > < span class = "o" > *< / span > < span class = "n" > i< / span > < span class = "o" > +< / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-12-4" name = "__codelineno-12-4" href = "#__codelineno-12-4" > < / a >
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< a id = "__codelineno-12-5" name = "__codelineno-12-5" href = "#__codelineno-12-5" > < / a > < span class = "k" > def< / span > < span class = "nf" > right< / span > < span class = "p" > (< / span > < span class = "bp" > self< / span > < span class = "p" > ,< / span > < span class = "n" > i< / span > < span class = "p" > :< / span > < span class = "nb" > int< / span > < span class = "p" > )< / span > < span class = "o" > -> < / span > < span class = "nb" > int< / span > < span class = "p" > :< / span >
< a id = "__codelineno-12-6" name = "__codelineno-12-6" href = "#__codelineno-12-6" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 获取右子结点索引 " " " < / span >
2023-02-23 20:23:42 +08:00
< a id = "__codelineno-12-7" name = "__codelineno-12-7" href = "#__codelineno-12-7" > < / a > < span class = "k" > return< / span > < span class = "mi" > 2< / span > < span class = "o" > *< / span > < span class = "n" > i< / span > < span class = "o" > +< / span > < span class = "mi" > 2< / span >
< a id = "__codelineno-12-8" name = "__codelineno-12-8" href = "#__codelineno-12-8" > < / a >
2023-03-03 02:46:43 +08:00
< a id = "__codelineno-12-9" name = "__codelineno-12-9" href = "#__codelineno-12-9" > < / a > < span class = "k" > def< / span > < span class = "nf" > parent< / span > < span class = "p" > (< / span > < span class = "bp" > self< / span > < span class = "p" > ,< / span > < span class = "n" > i< / span > < span class = "p" > :< / span > < span class = "nb" > int< / span > < span class = "p" > )< / span > < span class = "o" > -> < / span > < span class = "nb" > int< / span > < span class = "p" > :< / span >
< a id = "__codelineno-12-10" name = "__codelineno-12-10" href = "#__codelineno-12-10" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 获取父结点索引 " " " < / span >
2023-02-23 20:23:42 +08:00
< a id = "__codelineno-12-11" name = "__codelineno-12-11" href = "#__codelineno-12-11" > < / a > < span class = "k" > return< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span > < span class = "o" > //< / span > < span class = "mi" > 2< / span > < span class = "c1" > # 向下整除< / span >
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-13-1" name = "__codelineno-13-1" href = "#__codelineno-13-1" > < / a > < span class = "cm" > /* 获取左子结点索引 */< / span >
< a id = "__codelineno-13-2" name = "__codelineno-13-2" href = "#__codelineno-13-2" > < / 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-13-3" name = "__codelineno-13-3" href = "#__codelineno-13-3" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "mi" > 2< / span > < span class = "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 14:54:41 +08:00
< a id = "__codelineno-13-4" name = "__codelineno-13-4" href = "#__codelineno-13-4" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-13-5" name = "__codelineno-13-5" href = "#__codelineno-13-5" > < / a >
2023-02-09 04:43:20 +08:00
< a id = "__codelineno-13-6" name = "__codelineno-13-6" href = "#__codelineno-13-6" > < / a > < span class = "cm" > /* 获取右子结点索引 */< / span >
< a id = "__codelineno-13-7" name = "__codelineno-13-7" href = "#__codelineno-13-7" > < / 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-13-8" name = "__codelineno-13-8" href = "#__codelineno-13-8" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "mi" > 2< / span > < span class = "o" > *< / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "mi" > 2< / span >
< a id = "__codelineno-13-9" name = "__codelineno-13-9" href = "#__codelineno-13-9" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-13-10" name = "__codelineno-13-10" href = "#__codelineno-13-10" > < / a >
< a id = "__codelineno-13-11" name = "__codelineno-13-11" href = "#__codelineno-13-11" > < / a > < span class = "cm" > /* 获取父结点索引 */< / span >
< a id = "__codelineno-13-12" name = "__codelineno-13-12" href = "#__codelineno-13-12" > < / 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-13-13" name = "__codelineno-13-13" href = "#__codelineno-13-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 向下整除< / span >
< a id = "__codelineno-13-14" name = "__codelineno-13-14" href = "#__codelineno-13-14" > < / a > < span class = "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-13-15" name = "__codelineno-13-15" href = "#__codelineno-13-15" > < / a > < span class = "p" > }< / span >
2023-02-08 14:54:41 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-02-08 16:47:58 +08:00
< div class = "highlight" > < span class = "filename" > my_heap.js< / span > < pre > < span > < / span > < code > < a id = "__codelineno-14-1" name = "__codelineno-14-1" href = "#__codelineno-14-1" > < / a > < span class = "cm" > /* 获取左子结点索引 */< / span >
< a id = "__codelineno-14-2" name = "__codelineno-14-2" href = "#__codelineno-14-2" > < / a > < span class = "err" > #< / span > < span class = "nx" > left< / span > < span class = "p" > (< / span > < span class = "nx" > i< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-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 = "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-14-4" name = "__codelineno-14-4" href = "#__codelineno-14-4" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-14-5" name = "__codelineno-14-5" href = "#__codelineno-14-5" > < / a >
< a id = "__codelineno-14-6" name = "__codelineno-14-6" href = "#__codelineno-14-6" > < / a > < span class = "cm" > /* 获取右子结点索引 */< / span >
< a id = "__codelineno-14-7" name = "__codelineno-14-7" href = "#__codelineno-14-7" > < / a > < span class = "err" > #< / span > < span class = "nx" > right< / span > < span class = "p" > (< / span > < span class = "nx" > i< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-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 = "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-14-9" name = "__codelineno-14-9" href = "#__codelineno-14-9" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-14-10" name = "__codelineno-14-10" href = "#__codelineno-14-10" > < / a >
< a id = "__codelineno-14-11" name = "__codelineno-14-11" href = "#__codelineno-14-11" > < / a > < span class = "cm" > /* 获取父结点索引 */< / span >
< a id = "__codelineno-14-12" name = "__codelineno-14-12" href = "#__codelineno-14-12" > < / a > < span class = "err" > #< / span > < span class = "nx" > parent< / span > < span class = "p" > (< / span > < span class = "nx" > i< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-14-13" name = "__codelineno-14-13" href = "#__codelineno-14-13" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "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-14-14" name = "__codelineno-14-14" href = "#__codelineno-14-14" > < / a > < span class = "p" > }< / span >
2023-02-08 14:54:41 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-02-08 16:47:58 +08:00
< div class = "highlight" > < span class = "filename" > my_heap.ts< / span > < pre > < span > < / span > < code > < a id = "__codelineno-15-1" name = "__codelineno-15-1" href = "#__codelineno-15-1" > < / a > < span class = "cm" > /* 获取左子结点索引 */< / span >
< a id = "__codelineno-15-2" name = "__codelineno-15-2" href = "#__codelineno-15-2" > < / 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-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 >
< a id = "__codelineno-15-6" name = "__codelineno-15-6" href = "#__codelineno-15-6" > < / a > < span class = "cm" > /* 获取右子结点索引 */< / span >
< a id = "__codelineno-15-7" name = "__codelineno-15-7" href = "#__codelineno-15-7" > < / 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-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 >
< a id = "__codelineno-15-11" name = "__codelineno-15-11" href = "#__codelineno-15-11" > < / a > < span class = "cm" > /* 获取父结点索引 */< / span >
< a id = "__codelineno-15-12" name = "__codelineno-15-12" href = "#__codelineno-15-12" > < / 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-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" >
2023-02-11 18:21:51 +08:00
< div class = "highlight" > < span class = "filename" > my_heap.c< / span > < pre > < span > < / span > < code > < a id = "__codelineno-16-1" name = "__codelineno-16-1" href = "#__codelineno-16-1" > < / 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" > left< / span > < span class = "p" > }< / span >
< a id = "__codelineno-16-2" name = "__codelineno-16-2" href = "#__codelineno-16-2" > < / a >
< a id = "__codelineno-16-3" name = "__codelineno-16-3" href = "#__codelineno-16-3" > < / 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" > right< / span > < span class = "p" > }< / span >
< a id = "__codelineno-16-4" name = "__codelineno-16-4" href = "#__codelineno-16-4" > < / a >
< a id = "__codelineno-16-5" name = "__codelineno-16-5" href = "#__codelineno-16-5" > < / 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" > parent< / span > < span class = "p" > }< / span >
2023-02-08 14:54:41 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-02-15 21:48:29 +08:00
< div class = "highlight" > < span class = "filename" > my_heap.cs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-17-1" name = "__codelineno-17-1" href = "#__codelineno-17-1" > < / a > < span class = "cm" > /* 获取左子结点索引 */< / 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 = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "p" > )< / span >
< a id = "__codelineno-17-3" name = "__codelineno-17-3" href = "#__codelineno-17-3" > < / a > < span class = "p" > {< / span >
< a id = "__codelineno-17-4" name = "__codelineno-17-4" href = "#__codelineno-17-4" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "m" > 2< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-17-5" name = "__codelineno-17-5" href = "#__codelineno-17-5" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-17-6" name = "__codelineno-17-6" href = "#__codelineno-17-6" > < / a >
< a id = "__codelineno-17-7" name = "__codelineno-17-7" href = "#__codelineno-17-7" > < / a > < span class = "cm" > /* 获取右子结点索引 */< / span >
< a id = "__codelineno-17-8" name = "__codelineno-17-8" href = "#__codelineno-17-8" > < / 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 >
< 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 > < 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-17-11" name = "__codelineno-17-11" href = "#__codelineno-17-11" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-17-12" name = "__codelineno-17-12" href = "#__codelineno-17-12" > < / a >
< a id = "__codelineno-17-13" name = "__codelineno-17-13" href = "#__codelineno-17-13" > < / a > < span class = "cm" > /* 获取父结点索引 */< / span >
< a id = "__codelineno-17-14" name = "__codelineno-17-14" href = "#__codelineno-17-14" > < / 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 >
< a id = "__codelineno-17-15" name = "__codelineno-17-15" href = "#__codelineno-17-15" > < / a > < span class = "p" > {< / span >
< a id = "__codelineno-17-16" name = "__codelineno-17-16" href = "#__codelineno-17-16" > < / 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-17-17" name = "__codelineno-17-17" href = "#__codelineno-17-17" > < / a > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-02-08 20:30:33 +08:00
< div class = "highlight" > < span class = "filename" > my_heap.swift< / span > < pre > < span > < / span > < code > < a id = "__codelineno-18-1" name = "__codelineno-18-1" href = "#__codelineno-18-1" > < / a > < span class = "cm" > /* 获取左子结点索引 */< / span >
< a id = "__codelineno-18-2" name = "__codelineno-18-2" href = "#__codelineno-18-2" > < / 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-18-3" name = "__codelineno-18-3" href = "#__codelineno-18-3" > < / a > < span class = "mi" > 2< / span > < span class = "o" > *< / span > < span class = "n" > i< / span > < span class = "o" > +< / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-18-4" name = "__codelineno-18-4" href = "#__codelineno-18-4" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-18-5" name = "__codelineno-18-5" href = "#__codelineno-18-5" > < / a >
< a id = "__codelineno-18-6" name = "__codelineno-18-6" href = "#__codelineno-18-6" > < / a > < span class = "cm" > /* 获取右子结点索引 */< / span >
< a id = "__codelineno-18-7" name = "__codelineno-18-7" href = "#__codelineno-18-7" > < / 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-18-8" name = "__codelineno-18-8" href = "#__codelineno-18-8" > < / a > < span class = "mi" > 2< / span > < span class = "o" > *< / span > < span class = "n" > i< / span > < span class = "o" > +< / span > < span class = "mi" > 2< / span >
< a id = "__codelineno-18-9" name = "__codelineno-18-9" href = "#__codelineno-18-9" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-18-10" name = "__codelineno-18-10" href = "#__codelineno-18-10" > < / a >
< a id = "__codelineno-18-11" name = "__codelineno-18-11" href = "#__codelineno-18-11" > < / a > < span class = "cm" > /* 获取父结点索引 */< / span >
< a id = "__codelineno-18-12" name = "__codelineno-18-12" href = "#__codelineno-18-12" > < / 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-18-13" name = "__codelineno-18-13" href = "#__codelineno-18-13" > < / 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-18-14" name = "__codelineno-18-14" href = "#__codelineno-18-14" > < / a > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-02-09 22:55:35 +08:00
< div class = "highlight" > < span class = "filename" > my_heap.zig< / span > < pre > < span > < / span > < code > < a id = "__codelineno-19-1" name = "__codelineno-19-1" href = "#__codelineno-19-1" > < / a > < span class = "c1" > // 获取左子结点索引< / span >
< a id = "__codelineno-19-2" name = "__codelineno-19-2" href = "#__codelineno-19-2" > < / 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-19-3" name = "__codelineno-19-3" href = "#__codelineno-19-3" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "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-19-4" name = "__codelineno-19-4" href = "#__codelineno-19-4" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-19-5" name = "__codelineno-19-5" href = "#__codelineno-19-5" > < / a >
< a id = "__codelineno-19-6" name = "__codelineno-19-6" href = "#__codelineno-19-6" > < / a > < span class = "c1" > // 获取右子结点索引< / span >
< a id = "__codelineno-19-7" name = "__codelineno-19-7" href = "#__codelineno-19-7" > < / 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-19-8" name = "__codelineno-19-8" href = "#__codelineno-19-8" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "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-19-9" name = "__codelineno-19-9" href = "#__codelineno-19-9" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-19-10" name = "__codelineno-19-10" href = "#__codelineno-19-10" > < / a >
< a id = "__codelineno-19-11" name = "__codelineno-19-11" href = "#__codelineno-19-11" > < / a > < span class = "c1" > // 获取父结点索引< / span >
< a id = "__codelineno-19-12" name = "__codelineno-19-12" href = "#__codelineno-19-12" > < / 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-19-13" name = "__codelineno-19-13" href = "#__codelineno-19-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // return (i - 1) / 2; // 向下整除< / span >
< a id = "__codelineno-19-14" name = "__codelineno-19-14" href = "#__codelineno-19-14" > < / 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-19-15" name = "__codelineno-19-15" href = "#__codelineno-19-15" > < / a > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
< / div >
< / div >
< h3 id = "_2" > 访问堆顶元素< a class = "headerlink" href = "#_2" title = "Permanent link" > ¶ < / a > < / h3 >
< p > 堆顶元素是二叉树的根结点，即列表首元素。< / p >
< div class = "tabbed-set tabbed-alternate" data-tabs = "3:10" > < 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" / > < 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 > < / div >
< div class = "tabbed-content" >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > my_heap.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-20-1" name = "__codelineno-20-1" href = "#__codelineno-20-1" > < / a > < span class = "cm" > /* 访问堆顶元素 */< / span >
< a id = "__codelineno-20-2" name = "__codelineno-20-2" href = "#__codelineno-20-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > peek< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-20-3" name = "__codelineno-20-3" href = "#__codelineno-20-3" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "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-20-4" name = "__codelineno-20-4" href = "#__codelineno-20-4" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > my_heap.cpp< / span > < pre > < span > < / span > < code > < a id = "__codelineno-21-1" name = "__codelineno-21-1" href = "#__codelineno-21-1" > < / a > < span class = "cm" > /* 访问堆顶元素 */< / 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 = "nf" > peek< / 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 = "n" > maxHeap< / span > < span class = "p" > [< / span > < span class = "mi" > 0< / span > < span class = "p" > ];< / span >
< a id = "__codelineno-21-4" name = "__codelineno-21-4" href = "#__codelineno-21-4" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-03-03 02:46:43 +08:00
< div class = "highlight" > < span class = "filename" > my_heap.py< / span > < pre > < span > < / span > < code > < a id = "__codelineno-22-1" name = "__codelineno-22-1" href = "#__codelineno-22-1" > < / a > < span class = "k" > def< / span > < span class = "nf" > 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-22-2" name = "__codelineno-22-2" href = "#__codelineno-22-2" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 访问堆顶元素 " " " < / span >
2023-02-23 20:23:42 +08:00
< a id = "__codelineno-22-3" name = "__codelineno-22-3" href = "#__codelineno-22-3" > < / 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 >
2023-02-08 14:54:41 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > my_heap.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-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 = "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-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 = "nx" > h< / span > < span class = "p" > .< / span > < span class = "nx" > data< / span > < span class = "p" > [< / span > < span class = "mi" > 0< / span > < span class = "p" > ]< / span >
< a id = "__codelineno-23-4" name = "__codelineno-23-4" href = "#__codelineno-23-4" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > my_heap.js< / span > < pre > < span > < / span > < code > < a id = "__codelineno-24-1" name = "__codelineno-24-1" href = "#__codelineno-24-1" > < / a > < span class = "cm" > /* 访问堆顶元素 */< / span >
< a id = "__codelineno-24-2" name = "__codelineno-24-2" href = "#__codelineno-24-2" > < / a > < span class = "nx" > peek< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-24-3" name = "__codelineno-24-3" href = "#__codelineno-24-3" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "err" > #< / span > < span class = "nx" > maxHeap< / span > < span class = "p" > [< / span > < span class = "mf" > 0< / span > < span class = "p" > ];< / span >
< a id = "__codelineno-24-4" name = "__codelineno-24-4" href = "#__codelineno-24-4" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > my_heap.ts< / span > < pre > < span > < / span > < code > < a id = "__codelineno-25-1" name = "__codelineno-25-1" href = "#__codelineno-25-1" > < / a > < span class = "cm" > /* 访问堆顶元素 */< / span >
2023-02-08 16:47:58 +08:00
< a id = "__codelineno-25-2" name = "__codelineno-25-2" href = "#__codelineno-25-2" > < / 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 >
2023-02-08 14:54:41 +08:00
< 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 = "k" > this< / span > < span class = "p" > .< / span > < span class = "nx" > maxHeap< / span > < span class = "p" > [< / span > < span class = "mf" > 0< / span > < span class = "p" > ];< / span >
< a id = "__codelineno-25-4" name = "__codelineno-25-4" href = "#__codelineno-25-4" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-02-11 18:21:51 +08:00
< div class = "highlight" > < span class = "filename" > my_heap.c< / span > < pre > < span > < / span > < code > < a id = "__codelineno-26-1" name = "__codelineno-26-1" href = "#__codelineno-26-1" > < / 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" > peek< / span > < span class = "p" > }< / span >
2023-02-08 14:54:41 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-02-15 21:48:29 +08:00
< div class = "highlight" > < span class = "filename" > my_heap.cs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-27-1" name = "__codelineno-27-1" href = "#__codelineno-27-1" > < / a > < span class = "cm" > /* 访问堆顶元素 */< / span >
< a id = "__codelineno-27-2" name = "__codelineno-27-2" href = "#__codelineno-27-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > peek< / span > < span class = "p" > ()< / span >
< a id = "__codelineno-27-3" name = "__codelineno-27-3" href = "#__codelineno-27-3" > < / a > < span class = "p" > {< / span >
< a id = "__codelineno-27-4" name = "__codelineno-27-4" href = "#__codelineno-27-4" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > maxHeap< / span > < span class = "p" > [< / span > < span class = "m" > 0< / span > < span class = "p" > ];< / span >
< a id = "__codelineno-27-5" name = "__codelineno-27-5" href = "#__codelineno-27-5" > < / a > < 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" > my_heap.swift< / span > < pre > < span > < / span > < code > < a id = "__codelineno-28-1" name = "__codelineno-28-1" href = "#__codelineno-28-1" > < / a > < span class = "cm" > /* 访问堆顶元素 */< / span >
< a id = "__codelineno-28-2" name = "__codelineno-28-2" href = "#__codelineno-28-2" > < / a > < span class = "kd" > func< / span > < span class = "nf" > peek< / span > < span class = "p" > ()< / span > < span class = "p" > -> < / span > < span class = "nb" > Int< / span > < span class = "p" > {< / span >
< a id = "__codelineno-28-3" name = "__codelineno-28-3" href = "#__codelineno-28-3" > < / a > < span class = "n" > maxHeap< / span > < span class = "p" > [< / span > < span class = "mi" > 0< / span > < span class = "p" > ]< / span >
< a id = "__codelineno-28-4" name = "__codelineno-28-4" href = "#__codelineno-28-4" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-02-09 22:55:35 +08:00
< div class = "highlight" > < span class = "filename" > my_heap.zig< / span > < pre > < span > < / span > < code > < a id = "__codelineno-29-1" name = "__codelineno-29-1" href = "#__codelineno-29-1" > < / a > < span class = "c1" > // 访问堆顶元素< / span >
< a id = "__codelineno-29-2" name = "__codelineno-29-2" href = "#__codelineno-29-2" > < / 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 >
2023-03-15 03:13:04 +08:00
< 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" > 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 >
2023-02-09 22:55:35 +08:00
< a id = "__codelineno-29-4" name = "__codelineno-29-4" href = "#__codelineno-29-4" > < / a > < span class = "p" > }< / span > < span class = "w" > < / span >
2023-02-08 14:54:41 +08:00
< / code > < / pre > < / div >
< / div >
< / div >
< / div >
< h3 id = "_3" > 元素入堆< a class = "headerlink" href = "#_3" title = "Permanent link" > ¶ < / a > < / h3 >
< p > 给定元素 < code > val< / code > ，我们先将其添加到堆底。添加后，由于 < code > val< / code > 可能大于堆中其它元素，此时堆的成立条件可能已经被破坏，< strong > 因此需要修复从插入结点到根结点这条路径上的各个结点< / strong > ，该操作被称为「堆化 Heapify」。< / p >
< p > 考虑从入堆结点开始，< strong > 从底至顶执行堆化< / strong > 。具体地，比较插入结点与其父结点的值，若插入结点更大则将它们交换；并循环以上操作，从底至顶地修复堆中的各个结点；直至越过根结点时结束，或当遇到无需交换的结点时提前结束。< / p >
2023-02-22 00:57:11 +08:00
< div class = "tabbed-set tabbed-alternate" data-tabs = "4:6" > < 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" / > < 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 > < / div >
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< div class = "tabbed-content" >
< div class = "tabbed-block" >
2023-02-26 19:22:59 +08:00
< 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 >
< / div >
< / div >
< p > 设结点总数为 < span class = "arithmatex" > \(n\)< / span > ，则树的高度为 < span class = "arithmatex" > \(O(\log n)\)< / span > ，易得堆化操作的循环轮数最多为 < span class = "arithmatex" > \(O(\log n)\)< / span > ， < strong > 因而元素入堆操作的时间复杂度为 < span class = "arithmatex" > \(O(\log n)\)< / span > < / strong > 。< / p >
< div class = "tabbed-set tabbed-alternate" data-tabs = "5:10" > < 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" / > < 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 > < / div >
< div class = "tabbed-content" >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > my_heap.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-30-1" name = "__codelineno-30-1" href = "#__codelineno-30-1" > < / a > < span class = "cm" > /* 元素入堆 */< / span >
< a id = "__codelineno-30-2" name = "__codelineno-30-2" href = "#__codelineno-30-2" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "nf" > push< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > val< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-30-3" name = "__codelineno-30-3" href = "#__codelineno-30-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 添加结点< / span >
< a id = "__codelineno-30-4" name = "__codelineno-30-4" href = "#__codelineno-30-4" > < / a > < span class = "w" > < / span > < span class = "n" > maxHeap< / span > < span class = "p" > .< / span > < span class = "na" > add< / span > < span class = "p" > (< / span > < span class = "n" > val< / span > < span class = "p" > );< / span >
< a id = "__codelineno-30-5" name = "__codelineno-30-5" href = "#__codelineno-30-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 从底至顶堆化< / span >
< a id = "__codelineno-30-6" name = "__codelineno-30-6" href = "#__codelineno-30-6" > < / a > < span class = "w" > < / span > < span class = "n" > siftUp< / span > < span class = "p" > (< / span > < span class = "n" > size< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > );< / span >
< a id = "__codelineno-30-7" name = "__codelineno-30-7" href = "#__codelineno-30-7" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-30-8" name = "__codelineno-30-8" href = "#__codelineno-30-8" > < / a >
< a id = "__codelineno-30-9" name = "__codelineno-30-9" href = "#__codelineno-30-9" > < / a > < span class = "cm" > /* 从结点 i 开始，从底至顶堆化 */< / span >
< a id = "__codelineno-30-10" name = "__codelineno-30-10" href = "#__codelineno-30-10" > < / 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-30-11" name = "__codelineno-30-11" href = "#__codelineno-30-11" > < / 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-30-12" name = "__codelineno-30-12" href = "#__codelineno-30-12" > < / a > < span class = "w" > < / span > < span class = "c1" > // 获取结点 i 的父结点< / span >
< a id = "__codelineno-30-13" name = "__codelineno-30-13" href = "#__codelineno-30-13" > < / 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-30-14" name = "__codelineno-30-14" href = "#__codelineno-30-14" > < / a > < span class = "w" > < / span > < span class = "c1" > // 当“越过根结点”或“结点无需修复”时，结束堆化< / span >
< a id = "__codelineno-30-15" name = "__codelineno-30-15" href = "#__codelineno-30-15" > < / 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-30-16" name = "__codelineno-30-16" href = "#__codelineno-30-16" > < / a > < span class = "w" > < / span > < span class = "k" > break< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-30-17" name = "__codelineno-30-17" href = "#__codelineno-30-17" > < / a > < span class = "w" > < / span > < span class = "c1" > // 交换两结点< / span >
< a id = "__codelineno-30-18" name = "__codelineno-30-18" href = "#__codelineno-30-18" > < / 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-30-19" name = "__codelineno-30-19" href = "#__codelineno-30-19" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环向上堆化< / span >
< a id = "__codelineno-30-20" name = "__codelineno-30-20" href = "#__codelineno-30-20" > < / 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-30-21" name = "__codelineno-30-21" href = "#__codelineno-30-21" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-30-22" name = "__codelineno-30-22" href = "#__codelineno-30-22" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > my_heap.cpp< / span > < pre > < span > < / span > < code > < a id = "__codelineno-31-1" name = "__codelineno-31-1" href = "#__codelineno-31-1" > < / a > < span class = "cm" > /* 元素入堆 */< / span >
< a id = "__codelineno-31-2" name = "__codelineno-31-2" href = "#__codelineno-31-2" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "nf" > push< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > val< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-31-3" name = "__codelineno-31-3" href = "#__codelineno-31-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 添加结点< / span >
< a id = "__codelineno-31-4" name = "__codelineno-31-4" href = "#__codelineno-31-4" > < / a > < span class = "w" > < / span > < span class = "n" > maxHeap< / span > < span class = "p" > .< / span > < span class = "n" > push_back< / span > < span class = "p" > (< / span > < span class = "n" > val< / span > < span class = "p" > );< / span >
< a id = "__codelineno-31-5" name = "__codelineno-31-5" href = "#__codelineno-31-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 从底至顶堆化< / span >
< a id = "__codelineno-31-6" name = "__codelineno-31-6" href = "#__codelineno-31-6" > < / a > < span class = "w" > < / span > < span class = "n" > siftUp< / span > < span class = "p" > (< / span > < span class = "n" > size< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > );< / span >
< a id = "__codelineno-31-7" name = "__codelineno-31-7" href = "#__codelineno-31-7" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-31-8" name = "__codelineno-31-8" href = "#__codelineno-31-8" > < / a >
< a id = "__codelineno-31-9" name = "__codelineno-31-9" href = "#__codelineno-31-9" > < / a > < span class = "cm" > /* 从结点 i 开始，从底至顶堆化 */< / span >
< a id = "__codelineno-31-10" name = "__codelineno-31-10" href = "#__codelineno-31-10" > < / 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-31-11" name = "__codelineno-31-11" href = "#__codelineno-31-11" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nb" > true< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-31-12" name = "__codelineno-31-12" href = "#__codelineno-31-12" > < / a > < span class = "w" > < / span > < span class = "c1" > // 获取结点 i 的父结点< / span >
< a id = "__codelineno-31-13" name = "__codelineno-31-13" href = "#__codelineno-31-13" > < / 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-31-14" name = "__codelineno-31-14" href = "#__codelineno-31-14" > < / a > < span class = "w" > < / span > < span class = "c1" > // 当“越过根结点”或“结点无需修复”时，结束堆化< / span >
< a id = "__codelineno-31-15" name = "__codelineno-31-15" href = "#__codelineno-31-15" > < / 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-31-16" name = "__codelineno-31-16" href = "#__codelineno-31-16" > < / a > < span class = "w" > < / span > < span class = "k" > break< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-31-17" name = "__codelineno-31-17" href = "#__codelineno-31-17" > < / a > < span class = "w" > < / span > < span class = "c1" > // 交换两结点< / span >
< a id = "__codelineno-31-18" name = "__codelineno-31-18" href = "#__codelineno-31-18" > < / 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-31-19" name = "__codelineno-31-19" href = "#__codelineno-31-19" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环向上堆化< / span >
< a id = "__codelineno-31-20" name = "__codelineno-31-20" href = "#__codelineno-31-20" > < / 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-31-21" name = "__codelineno-31-21" href = "#__codelineno-31-21" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-31-22" name = "__codelineno-31-22" href = "#__codelineno-31-22" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-03-03 02:46:43 +08:00
< div class = "highlight" > < span class = "filename" > my_heap.py< / span > < pre > < span > < / span > < code > < a id = "__codelineno-32-1" name = "__codelineno-32-1" href = "#__codelineno-32-1" > < / a > < span class = "k" > def< / span > < span class = "nf" > 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-32-2" name = "__codelineno-32-2" href = "#__codelineno-32-2" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 元素入堆 " " " < / span >
2023-02-23 20:23:42 +08:00
< a id = "__codelineno-32-3" name = "__codelineno-32-3" href = "#__codelineno-32-3" > < / a > < span class = "c1" > # 添加结点< / span >
< a id = "__codelineno-32-4" name = "__codelineno-32-4" href = "#__codelineno-32-4" > < / 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-32-5" name = "__codelineno-32-5" href = "#__codelineno-32-5" > < / a > < span class = "c1" > # 从底至顶堆化< / span >
< a id = "__codelineno-32-6" name = "__codelineno-32-6" href = "#__codelineno-32-6" > < / 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-32-7" name = "__codelineno-32-7" href = "#__codelineno-32-7" > < / a >
2023-03-03 02:46:43 +08:00
< a id = "__codelineno-32-8" name = "__codelineno-32-8" href = "#__codelineno-32-8" > < / 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-32-9" name = "__codelineno-32-9" href = "#__codelineno-32-9" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 从结点 i 开始，从底至顶堆化 " " " < / span >
2023-02-23 20:23:42 +08:00
< a id = "__codelineno-32-10" name = "__codelineno-32-10" href = "#__codelineno-32-10" > < / a > < span class = "k" > while< / span > < span class = "kc" > True< / span > < span class = "p" > :< / span >
< a id = "__codelineno-32-11" name = "__codelineno-32-11" href = "#__codelineno-32-11" > < / a > < span class = "c1" > # 获取结点 i 的父结点< / span >
< a id = "__codelineno-32-12" name = "__codelineno-32-12" href = "#__codelineno-32-12" > < / 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-32-13" name = "__codelineno-32-13" href = "#__codelineno-32-13" > < / a > < span class = "c1" > # 当“越过根结点”或“结点无需修复”时，结束堆化< / span >
< a id = "__codelineno-32-14" name = "__codelineno-32-14" href = "#__codelineno-32-14" > < / 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-32-15" name = "__codelineno-32-15" href = "#__codelineno-32-15" > < / a > < span class = "k" > break< / span >
< a id = "__codelineno-32-16" name = "__codelineno-32-16" href = "#__codelineno-32-16" > < / a > < span class = "c1" > # 交换两结点< / span >
< a id = "__codelineno-32-17" name = "__codelineno-32-17" href = "#__codelineno-32-17" > < / 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-32-18" name = "__codelineno-32-18" href = "#__codelineno-32-18" > < / a > < span class = "c1" > # 循环向上堆化< / span >
< a id = "__codelineno-32-19" name = "__codelineno-32-19" href = "#__codelineno-32-19" > < / a > < span class = "n" > i< / span > < span class = "o" > =< / span > < span class = "n" > p< / span >
2023-02-08 14:54:41 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > my_heap.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-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 = "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-33-3" name = "__codelineno-33-3" href = "#__codelineno-33-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 添加结点< / span >
< a id = "__codelineno-33-4" name = "__codelineno-33-4" href = "#__codelineno-33-4" > < / 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-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 >
< a id = "__codelineno-33-6" name = "__codelineno-33-6" href = "#__codelineno-33-6" > < / 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-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 >
< a id = "__codelineno-33-9" name = "__codelineno-33-9" href = "#__codelineno-33-9" > < / a > < span class = "cm" > /* 从结点 i 开始，从底至顶堆化 */< / span >
< a id = "__codelineno-33-10" name = "__codelineno-33-10" href = "#__codelineno-33-10" > < / 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-33-11" name = "__codelineno-33-11" href = "#__codelineno-33-11" > < / 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-33-12" name = "__codelineno-33-12" href = "#__codelineno-33-12" > < / a > < span class = "w" > < / span > < span class = "c1" > // 获取结点 i 的父结点< / span >
< a id = "__codelineno-33-13" name = "__codelineno-33-13" href = "#__codelineno-33-13" > < / 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-33-14" name = "__codelineno-33-14" href = "#__codelineno-33-14" > < / a > < span class = "w" > < / span > < span class = "c1" > // 当“越过根结点”或“结点无需修复”时，结束堆化< / span >
< 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 = "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-33-16" name = "__codelineno-33-16" href = "#__codelineno-33-16" > < / a > < span class = "w" > < / span > < span class = "k" > break< / span >
< a id = "__codelineno-33-17" name = "__codelineno-33-17" href = "#__codelineno-33-17" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-33-18" name = "__codelineno-33-18" href = "#__codelineno-33-18" > < / a > < span class = "w" > < / span > < span class = "c1" > // 交换两结点< / span >
< a id = "__codelineno-33-19" name = "__codelineno-33-19" href = "#__codelineno-33-19" > < / 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-33-20" name = "__codelineno-33-20" href = "#__codelineno-33-20" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环向上堆化< / span >
< a id = "__codelineno-33-21" name = "__codelineno-33-21" href = "#__codelineno-33-21" > < / 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-33-22" name = "__codelineno-33-22" href = "#__codelineno-33-22" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-33-23" name = "__codelineno-33-23" href = "#__codelineno-33-23" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > my_heap.js< / span > < pre > < span > < / span > < code > < a id = "__codelineno-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 = "nx" > push< / span > < span class = "p" > (< / span > < span class = "nx" > val< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-34-3" name = "__codelineno-34-3" href = "#__codelineno-34-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 添加结点< / span >
< a id = "__codelineno-34-4" name = "__codelineno-34-4" href = "#__codelineno-34-4" > < / a > < span class = "w" > < / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "err" > #< / span > < span class = "nx" > maxHeap< / span > < span class = "p" > .< / span > < span class = "nx" > push< / span > < span class = "p" > (< / span > < span class = "nx" > val< / span > < span class = "p" > );< / span >
< a id = "__codelineno-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 >
< a id = "__codelineno-34-6" name = "__codelineno-34-6" href = "#__codelineno-34-6" > < / a > < span class = "w" > < / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "err" > #< / span > < span class = "nx" > siftUp< / span > < span class = "p" > (< / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "nx" > size< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "p" > );< / span >
< a id = "__codelineno-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 >
< a id = "__codelineno-34-9" name = "__codelineno-34-9" href = "#__codelineno-34-9" > < / a > < span class = "cm" > /* 从结点 i 开始，从底至顶堆化 */< / span >
< a id = "__codelineno-34-10" name = "__codelineno-34-10" href = "#__codelineno-34-10" > < / 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-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 = "kc" > true< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-34-12" name = "__codelineno-34-12" href = "#__codelineno-34-12" > < / a > < span class = "w" > < / span > < span class = "c1" > // 获取结点 i 的父结点< / span >
< a id = "__codelineno-34-13" name = "__codelineno-34-13" href = "#__codelineno-34-13" > < / 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-34-14" name = "__codelineno-34-14" href = "#__codelineno-34-14" > < / a > < span class = "w" > < / span > < span class = "c1" > // 当“越过根结点”或“结点无需修复”时，结束堆化< / span >
< 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 = "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-34-16" name = "__codelineno-34-16" href = "#__codelineno-34-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // 交换两结点< / span >
< a id = "__codelineno-34-17" name = "__codelineno-34-17" href = "#__codelineno-34-17" > < / 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-34-18" name = "__codelineno-34-18" href = "#__codelineno-34-18" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环向上堆化< / span >
< a id = "__codelineno-34-19" name = "__codelineno-34-19" href = "#__codelineno-34-19" > < / 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-34-20" name = "__codelineno-34-20" href = "#__codelineno-34-20" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-34-21" name = "__codelineno-34-21" href = "#__codelineno-34-21" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > my_heap.ts< / span > < pre > < span > < / span > < code > < a id = "__codelineno-35-1" name = "__codelineno-35-1" href = "#__codelineno-35-1" > < / a > < span class = "cm" > /* 元素入堆 */< / span >
2023-02-08 16:47:58 +08:00
< a id = "__codelineno-35-2" name = "__codelineno-35-2" href = "#__codelineno-35-2" > < / 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 >
2023-02-08 14:54:41 +08:00
< a id = "__codelineno-35-3" name = "__codelineno-35-3" href = "#__codelineno-35-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 添加结点< / span >
< a id = "__codelineno-35-4" name = "__codelineno-35-4" href = "#__codelineno-35-4" > < / 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-35-5" name = "__codelineno-35-5" href = "#__codelineno-35-5" > < / a > < span class = "w" > < / span > < 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 = "w" > < / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "nx" > siftUp< / span > < span class = "p" > (< / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "nx" > size< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "p" > );< / span >
< a id = "__codelineno-35-7" name = "__codelineno-35-7" href = "#__codelineno-35-7" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-35-8" name = "__codelineno-35-8" href = "#__codelineno-35-8" > < / a >
< a id = "__codelineno-35-9" name = "__codelineno-35-9" href = "#__codelineno-35-9" > < / a > < span class = "cm" > /* 从结点 i 开始，从底至顶堆化 */< / span >
2023-02-08 16:47:58 +08:00
< a id = "__codelineno-35-10" name = "__codelineno-35-10" href = "#__codelineno-35-10" > < / 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 >
2023-02-08 14:54:41 +08:00
< a id = "__codelineno-35-11" name = "__codelineno-35-11" href = "#__codelineno-35-11" > < / 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-35-12" name = "__codelineno-35-12" href = "#__codelineno-35-12" > < / a > < span class = "w" > < / span > < span class = "c1" > // 获取结点 i 的父结点< / span >
< a id = "__codelineno-35-13" name = "__codelineno-35-13" href = "#__codelineno-35-13" > < / 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-35-14" name = "__codelineno-35-14" href = "#__codelineno-35-14" > < / a > < span class = "w" > < / span > < span class = "c1" > // 当“越过根结点”或“结点无需修复”时，结束堆化< / span >
< a id = "__codelineno-35-15" name = "__codelineno-35-15" href = "#__codelineno-35-15" > < / 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-35-16" name = "__codelineno-35-16" href = "#__codelineno-35-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // 交换两结点< / span >
< a id = "__codelineno-35-17" name = "__codelineno-35-17" href = "#__codelineno-35-17" > < / 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-35-18" name = "__codelineno-35-18" href = "#__codelineno-35-18" > < / a > < span class = "w" > < / span > < 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 = "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-35-20" name = "__codelineno-35-20" href = "#__codelineno-35-20" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-35-21" name = "__codelineno-35-21" href = "#__codelineno-35-21" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-02-11 18:21:51 +08:00
< div class = "highlight" > < span class = "filename" > my_heap.c< / span > < pre > < span > < / span > < code > < a id = "__codelineno-36-1" name = "__codelineno-36-1" href = "#__codelineno-36-1" > < / 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" > push< / span > < span class = "p" > }< / span >
< a id = "__codelineno-36-2" name = "__codelineno-36-2" href = "#__codelineno-36-2" > < / a >
< a id = "__codelineno-36-3" name = "__codelineno-36-3" href = "#__codelineno-36-3" > < / 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 >
2023-02-08 14:54:41 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-02-15 21:48:29 +08:00
< div class = "highlight" > < span class = "filename" > my_heap.cs< / 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 = "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 >
< a id = "__codelineno-37-3" name = "__codelineno-37-3" href = "#__codelineno-37-3" > < / a > < span class = "p" > {< / span >
< a id = "__codelineno-37-4" name = "__codelineno-37-4" href = "#__codelineno-37-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 添加结点< / span >
< a id = "__codelineno-37-5" name = "__codelineno-37-5" href = "#__codelineno-37-5" > < / 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-37-6" name = "__codelineno-37-6" href = "#__codelineno-37-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 从底至顶堆化< / span >
< a id = "__codelineno-37-7" name = "__codelineno-37-7" href = "#__codelineno-37-7" > < / 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-37-8" name = "__codelineno-37-8" href = "#__codelineno-37-8" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-37-9" name = "__codelineno-37-9" href = "#__codelineno-37-9" > < / a >
< a id = "__codelineno-37-10" name = "__codelineno-37-10" href = "#__codelineno-37-10" > < / a > < span class = "cm" > /* 从结点 i 开始，从底至顶堆化 */< / span >
< a id = "__codelineno-37-11" name = "__codelineno-37-11" href = "#__codelineno-37-11" > < / 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 >
< a id = "__codelineno-37-12" name = "__codelineno-37-12" href = "#__codelineno-37-12" > < / a > < span class = "p" > {< / span >
< a id = "__codelineno-37-13" name = "__codelineno-37-13" href = "#__codelineno-37-13" > < / 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 >
< a id = "__codelineno-37-14" name = "__codelineno-37-14" href = "#__codelineno-37-14" > < / a > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-37-15" name = "__codelineno-37-15" href = "#__codelineno-37-15" > < / a > < span class = "w" > < / span > < span class = "c1" > // 获取结点 i 的父结点< / span >
< a id = "__codelineno-37-16" name = "__codelineno-37-16" href = "#__codelineno-37-16" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > p< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > parent< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > );< / span >
< a id = "__codelineno-37-17" name = "__codelineno-37-17" href = "#__codelineno-37-17" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若“越过根结点”或“结点无需修复”，则结束堆化< / span >
< a id = "__codelineno-37-18" name = "__codelineno-37-18" href = "#__codelineno-37-18" > < / 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-37-19" name = "__codelineno-37-19" href = "#__codelineno-37-19" > < / a > < span class = "w" > < / span > < span class = "k" > break< / 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 = "c1" > // 交换两结点< / span >
< a id = "__codelineno-37-21" name = "__codelineno-37-21" href = "#__codelineno-37-21" > < / 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-37-22" name = "__codelineno-37-22" href = "#__codelineno-37-22" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环向上堆化< / span >
< a id = "__codelineno-37-23" name = "__codelineno-37-23" href = "#__codelineno-37-23" > < / a > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > p< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-37-24" name = "__codelineno-37-24" href = "#__codelineno-37-24" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-37-25" name = "__codelineno-37-25" href = "#__codelineno-37-25" > < / a > < 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" > my_heap.swift< / 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 = "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-38-3" name = "__codelineno-38-3" href = "#__codelineno-38-3" > < / a > < span class = "c1" > // 添加结点< / span >
< a id = "__codelineno-38-4" name = "__codelineno-38-4" href = "#__codelineno-38-4" > < / 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-38-5" name = "__codelineno-38-5" href = "#__codelineno-38-5" > < / a > < 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 = "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-38-7" name = "__codelineno-38-7" href = "#__codelineno-38-7" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-38-8" name = "__codelineno-38-8" href = "#__codelineno-38-8" > < / a >
< a id = "__codelineno-38-9" name = "__codelineno-38-9" href = "#__codelineno-38-9" > < / a > < span class = "cm" > /* 从结点 i 开始，从底至顶堆化 */< / span >
< a id = "__codelineno-38-10" name = "__codelineno-38-10" href = "#__codelineno-38-10" > < / a > < span class = "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-38-11" name = "__codelineno-38-11" href = "#__codelineno-38-11" > < / a > < span class = "kd" > var< / span > < span class = "nv" > i< / span > < span class = "p" > =< / span > < span class = "n" > i< / span >
< a id = "__codelineno-38-12" name = "__codelineno-38-12" href = "#__codelineno-38-12" > < / a > < span class = "k" > while< / span > < span class = "kc" > true< / span > < span class = "p" > {< / span >
< a id = "__codelineno-38-13" name = "__codelineno-38-13" href = "#__codelineno-38-13" > < / a > < span class = "c1" > // 获取结点 i 的父结点< / span >
< a id = "__codelineno-38-14" name = "__codelineno-38-14" href = "#__codelineno-38-14" > < / 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-38-15" name = "__codelineno-38-15" href = "#__codelineno-38-15" > < / a > < span class = "c1" > // 当“越过根结点”或“结点无需修复”时，结束堆化< / span >
< a id = "__codelineno-38-16" name = "__codelineno-38-16" href = "#__codelineno-38-16" > < / 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-38-17" name = "__codelineno-38-17" href = "#__codelineno-38-17" > < / a > < span class = "k" > break< / span >
< a id = "__codelineno-38-18" name = "__codelineno-38-18" href = "#__codelineno-38-18" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-38-19" name = "__codelineno-38-19" href = "#__codelineno-38-19" > < / a > < span class = "c1" > // 交换两结点< / span >
< a id = "__codelineno-38-20" name = "__codelineno-38-20" href = "#__codelineno-38-20" > < / 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-38-21" name = "__codelineno-38-21" href = "#__codelineno-38-21" > < / a > < span class = "c1" > // 循环向上堆化< / span >
< a id = "__codelineno-38-22" name = "__codelineno-38-22" href = "#__codelineno-38-22" > < / a > < span class = "n" > i< / span > < span class = "p" > =< / span > < span class = "n" > p< / span >
< a id = "__codelineno-38-23" name = "__codelineno-38-23" href = "#__codelineno-38-23" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-38-24" name = "__codelineno-38-24" href = "#__codelineno-38-24" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-02-09 22:55:35 +08:00
< div class = "highlight" > < span class = "filename" > my_heap.zig< / span > < pre > < span > < / span > < code > < a id = "__codelineno-39-1" name = "__codelineno-39-1" href = "#__codelineno-39-1" > < / a > < span class = "c1" > // 元素入堆< / span >
< a id = "__codelineno-39-2" name = "__codelineno-39-2" href = "#__codelineno-39-2" > < / 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-39-3" name = "__codelineno-39-3" href = "#__codelineno-39-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 添加结点< / span >
2023-03-15 03:13:04 +08:00
< a id = "__codelineno-39-4" name = "__codelineno-39-4" href = "#__codelineno-39-4" > < / 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 >
2023-02-09 22:55:35 +08:00
< a id = "__codelineno-39-5" name = "__codelineno-39-5" href = "#__codelineno-39-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 从底至顶堆化< / span >
< a id = "__codelineno-39-6" name = "__codelineno-39-6" href = "#__codelineno-39-6" > < / a > < span class = "w" > < / span > < span class = "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-39-7" name = "__codelineno-39-7" href = "#__codelineno-39-7" > < / a > < span class = "p" > }< / span > < span class = "w" > < / span >
< a id = "__codelineno-39-8" name = "__codelineno-39-8" href = "#__codelineno-39-8" > < / a >
< a id = "__codelineno-39-9" name = "__codelineno-39-9" href = "#__codelineno-39-9" > < / a > < span class = "c1" > // 从结点 i 开始，从底至顶堆化< / span >
< a id = "__codelineno-39-10" name = "__codelineno-39-10" href = "#__codelineno-39-10" > < / a > < span class = "k" > 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-39-11" name = "__codelineno-39-11" href = "#__codelineno-39-11" > < / 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-39-12" name = "__codelineno-39-12" href = "#__codelineno-39-12" > < / 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-39-13" name = "__codelineno-39-13" href = "#__codelineno-39-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 获取结点 i 的父结点< / span >
< a id = "__codelineno-39-14" name = "__codelineno-39-14" href = "#__codelineno-39-14" > < / 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-39-15" name = "__codelineno-39-15" href = "#__codelineno-39-15" > < / a > < span class = "w" > < / span > < span class = "c1" > // 当“越过根结点”或“结点无需修复”时，结束堆化< / span >
2023-03-15 03:13:04 +08:00
< a id = "__codelineno-39-16" name = "__codelineno-39-16" href = "#__codelineno-39-16" > < / 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 >
2023-02-09 22:55:35 +08:00
< a id = "__codelineno-39-17" name = "__codelineno-39-17" href = "#__codelineno-39-17" > < / a > < span class = "w" > < / span > < span class = "c1" > // 交换两结点< / span >
< a id = "__codelineno-39-18" name = "__codelineno-39-18" href = "#__codelineno-39-18" > < / 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-39-19" name = "__codelineno-39-19" href = "#__codelineno-39-19" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环向上堆化< / span >
< a id = "__codelineno-39-20" name = "__codelineno-39-20" href = "#__codelineno-39-20" > < / a > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > p< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-39-21" name = "__codelineno-39-21" href = "#__codelineno-39-21" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-39-22" name = "__codelineno-39-22" href = "#__codelineno-39-22" > < / a > < span class = "p" > }< / span >
2023-02-08 14:54:41 +08:00
< / 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 >
< p > 堆顶元素是二叉树根结点，即列表首元素，如果我们直接将首元素从列表中删除，则二叉树中所有结点都会随之发生移位（索引发生变化），这样后续使用堆化修复就很麻烦了。为了尽量减少元素索引变动，采取以下操作步骤：< / p >
< ol >
< li > 交换堆顶元素与堆底元素（即交换根结点与最右叶结点）；< / li >
< li > 交换完成后，将堆底从列表中删除（注意，因为已经交换，实际上删除的是原来的堆顶元素）；< / li >
< li > 从根结点开始，< strong > 从顶至底执行堆化< / strong > ； < / li >
< / ol >
< 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 > ，我们比较根结点的值与其两个子结点的值，将最大的子结点与根结点执行交换，并循环以上操作，直到越过叶结点时结束，或当遇到无需交换的结点时提前结束。< / 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 >
< p > 与元素入堆操作类似，< strong > 堆顶元素出堆操作的时间复杂度为 < span class = "arithmatex" > \(O(\log n)\)< / span > < / strong > 。< / p >
< div class = "tabbed-set tabbed-alternate" data-tabs = "7:10" > < 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" / > < 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 > < / div >
< div class = "tabbed-content" >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > my_heap.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-40-1" name = "__codelineno-40-1" href = "#__codelineno-40-1" > < / a > < span class = "cm" > /* 元素出堆 */< / span >
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< a id = "__codelineno-40-2" name = "__codelineno-40-2" href = "#__codelineno-40-2" > < / 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-40-3" name = "__codelineno-40-3" href = "#__codelineno-40-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 判空处理< / span >
< a id = "__codelineno-40-4" name = "__codelineno-40-4" href = "#__codelineno-40-4" > < / 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-40-5" name = "__codelineno-40-5" href = "#__codelineno-40-5" > < / 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" > EmptyStackException< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-40-6" name = "__codelineno-40-6" href = "#__codelineno-40-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 交换根结点与最右叶结点（即交换首元素与尾元素）< / span >
< a id = "__codelineno-40-7" name = "__codelineno-40-7" href = "#__codelineno-40-7" > < / 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-40-8" name = "__codelineno-40-8" href = "#__codelineno-40-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 删除结点< / span >
< a id = "__codelineno-40-9" name = "__codelineno-40-9" href = "#__codelineno-40-9" > < / 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-40-10" name = "__codelineno-40-10" href = "#__codelineno-40-10" > < / a > < span class = "w" > < / span > < span class = "c1" > // 从顶至底堆化< / span >
< a id = "__codelineno-40-11" name = "__codelineno-40-11" href = "#__codelineno-40-11" > < / 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-40-12" name = "__codelineno-40-12" href = "#__codelineno-40-12" > < / a > < span class = "w" > < / span > < span class = "c1" > // 返回堆顶元素< / span >
< a id = "__codelineno-40-13" name = "__codelineno-40-13" href = "#__codelineno-40-13" > < / 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-40-14" name = "__codelineno-40-14" href = "#__codelineno-40-14" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-40-15" name = "__codelineno-40-15" href = "#__codelineno-40-15" > < / a >
< a id = "__codelineno-40-16" name = "__codelineno-40-16" href = "#__codelineno-40-16" > < / a > < span class = "cm" > /* 从结点 i 开始，从顶至底堆化 */< / span >
< a id = "__codelineno-40-17" name = "__codelineno-40-17" href = "#__codelineno-40-17" > < / 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-40-18" name = "__codelineno-40-18" href = "#__codelineno-40-18" > < / 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-40-19" name = "__codelineno-40-19" href = "#__codelineno-40-19" > < / a > < span class = "w" > < / span > < span class = "c1" > // 判断结点 i, l, r 中值最大的结点，记为 ma< / span >
< a id = "__codelineno-40-20" name = "__codelineno-40-20" href = "#__codelineno-40-20" > < / 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-40-21" name = "__codelineno-40-21" href = "#__codelineno-40-21" > < / 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-40-22" name = "__codelineno-40-22" href = "#__codelineno-40-22" > < / 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-40-23" name = "__codelineno-40-23" href = "#__codelineno-40-23" > < / 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-40-24" name = "__codelineno-40-24" href = "#__codelineno-40-24" > < / 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-40-25" name = "__codelineno-40-25" href = "#__codelineno-40-25" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若结点 i 最大或索引 l, r 越界，则无需继续堆化，跳出< / span >
< a id = "__codelineno-40-26" name = "__codelineno-40-26" href = "#__codelineno-40-26" > < / 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-40-27" name = "__codelineno-40-27" href = "#__codelineno-40-27" > < / a > < span class = "w" > < / span > < span class = "c1" > // 交换两结点< / span >
< a id = "__codelineno-40-28" name = "__codelineno-40-28" href = "#__codelineno-40-28" > < / 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-40-29" name = "__codelineno-40-29" href = "#__codelineno-40-29" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环向下堆化< / span >
< a id = "__codelineno-40-30" name = "__codelineno-40-30" href = "#__codelineno-40-30" > < / 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-40-31" name = "__codelineno-40-31" href = "#__codelineno-40-31" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-40-32" name = "__codelineno-40-32" href = "#__codelineno-40-32" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > my_heap.cpp< / span > < pre > < span > < / span > < code > < a id = "__codelineno-41-1" name = "__codelineno-41-1" href = "#__codelineno-41-1" > < / a > < span class = "cm" > /* 元素出堆 */< / span >
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< a id = "__codelineno-41-2" name = "__codelineno-41-2" href = "#__codelineno-41-2" > < / 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-41-3" name = "__codelineno-41-3" href = "#__codelineno-41-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 判空处理< / span >
< a id = "__codelineno-41-4" name = "__codelineno-41-4" href = "#__codelineno-41-4" > < / 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 >
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< a id = "__codelineno-41-5" name = "__codelineno-41-5" href = "#__codelineno-41-5" > < / 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-41-6" name = "__codelineno-41-6" href = "#__codelineno-41-6" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-41-7" name = "__codelineno-41-7" href = "#__codelineno-41-7" > < / a > < span class = "w" > < / span > < span class = "c1" > // 交换根结点与最右叶结点（即交换首元素与尾元素）< / span >
< a id = "__codelineno-41-8" name = "__codelineno-41-8" href = "#__codelineno-41-8" > < / 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-41-9" name = "__codelineno-41-9" href = "#__codelineno-41-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 删除结点< / span >
< a id = "__codelineno-41-10" name = "__codelineno-41-10" href = "#__codelineno-41-10" > < / 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-41-11" name = "__codelineno-41-11" href = "#__codelineno-41-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 从顶至底堆化< / span >
< a id = "__codelineno-41-12" name = "__codelineno-41-12" href = "#__codelineno-41-12" > < / a > < span class = "w" > < / span > < span class = "n" > siftDown< / span > < span class = "p" > (< / span > < span class = "mi" > 0< / span > < span class = "p" > );< / span >
< a id = "__codelineno-41-13" name = "__codelineno-41-13" href = "#__codelineno-41-13" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-41-14" name = "__codelineno-41-14" href = "#__codelineno-41-14" > < / a >
< a id = "__codelineno-41-15" name = "__codelineno-41-15" href = "#__codelineno-41-15" > < / a > < span class = "cm" > /* 从结点 i 开始，从顶至底堆化 */< / span >
< a id = "__codelineno-41-16" name = "__codelineno-41-16" href = "#__codelineno-41-16" > < / 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-41-17" name = "__codelineno-41-17" href = "#__codelineno-41-17" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nb" > true< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-41-18" name = "__codelineno-41-18" href = "#__codelineno-41-18" > < / a > < span class = "w" > < / span > < span class = "c1" > // 判断结点 i, l, r 中值最大的结点，记为 ma< / span >
< a id = "__codelineno-41-19" name = "__codelineno-41-19" href = "#__codelineno-41-19" > < / 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-41-20" name = "__codelineno-41-20" href = "#__codelineno-41-20" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若结点 i 最大或索引 l, r 越界，则无需继续堆化，跳出< / span >
< a id = "__codelineno-41-21" name = "__codelineno-41-21" href = "#__codelineno-41-21" > < / 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 > < span class = "w" > < / span >
< a id = "__codelineno-41-22" name = "__codelineno-41-22" href = "#__codelineno-41-22" > < / 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-41-23" name = "__codelineno-41-23" href = "#__codelineno-41-23" > < / 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-41-24" name = "__codelineno-41-24" href = "#__codelineno-41-24" > < / 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-41-25" name = "__codelineno-41-25" href = "#__codelineno-41-25" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若结点 i 最大或索引 l, r 越界，则无需继续堆化，跳出< / span >
< a id = "__codelineno-41-26" name = "__codelineno-41-26" href = "#__codelineno-41-26" > < / 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 >
< a id = "__codelineno-41-27" name = "__codelineno-41-27" href = "#__codelineno-41-27" > < / a > < span class = "w" > < / span > < span class = "k" > break< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-41-28" name = "__codelineno-41-28" href = "#__codelineno-41-28" > < / 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-41-29" name = "__codelineno-41-29" href = "#__codelineno-41-29" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环向下堆化< / span >
< a id = "__codelineno-41-30" name = "__codelineno-41-30" href = "#__codelineno-41-30" > < / 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-41-31" name = "__codelineno-41-31" href = "#__codelineno-41-31" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-41-32" name = "__codelineno-41-32" href = "#__codelineno-41-32" > < / 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-42-1" name = "__codelineno-42-1" href = "#__codelineno-42-1" > < / 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 >
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< a id = "__codelineno-42-2" name = "__codelineno-42-2" href = "#__codelineno-42-2" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 元素出堆 " " " < / span >
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< a id = "__codelineno-42-3" name = "__codelineno-42-3" href = "#__codelineno-42-3" > < / a > < span class = "c1" > # 判空处理< / span >
< a id = "__codelineno-42-4" name = "__codelineno-42-4" href = "#__codelineno-42-4" > < / a > < span class = "k" > assert< / span > < span class = "ow" > not< / span > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > is_empty< / span > < span class = "p" > ()< / span >
< a id = "__codelineno-42-5" name = "__codelineno-42-5" href = "#__codelineno-42-5" > < / a > < span class = "c1" > # 交换根结点与最右叶结点（即交换首元素与尾元素）< / span >
< a id = "__codelineno-42-6" name = "__codelineno-42-6" href = "#__codelineno-42-6" > < / 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-42-7" name = "__codelineno-42-7" href = "#__codelineno-42-7" > < / a > < span class = "c1" > # 删除结点< / span >
< a id = "__codelineno-42-8" name = "__codelineno-42-8" href = "#__codelineno-42-8" > < / 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-42-9" name = "__codelineno-42-9" href = "#__codelineno-42-9" > < / a > < span class = "c1" > # 从顶至底堆化< / span >
< a id = "__codelineno-42-10" name = "__codelineno-42-10" href = "#__codelineno-42-10" > < / 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-42-11" name = "__codelineno-42-11" href = "#__codelineno-42-11" > < / a > < span class = "c1" > # 返回堆顶元素< / span >
< a id = "__codelineno-42-12" name = "__codelineno-42-12" href = "#__codelineno-42-12" > < / a > < span class = "k" > return< / span > < span class = "n" > val< / span >
< a id = "__codelineno-42-13" name = "__codelineno-42-13" href = "#__codelineno-42-13" > < / a >
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< a id = "__codelineno-42-14" name = "__codelineno-42-14" href = "#__codelineno-42-14" > < / 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-42-15" name = "__codelineno-42-15" href = "#__codelineno-42-15" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 从结点 i 开始，从顶至底堆化 " " " < / span >
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< a id = "__codelineno-42-16" name = "__codelineno-42-16" href = "#__codelineno-42-16" > < / a > < span class = "k" > while< / span > < span class = "kc" > True< / span > < span class = "p" > :< / span >
< a id = "__codelineno-42-17" name = "__codelineno-42-17" href = "#__codelineno-42-17" > < / a > < span class = "c1" > # 判断结点 i, l, r 中值最大的结点，记为 ma< / span >
< a id = "__codelineno-42-18" name = "__codelineno-42-18" href = "#__codelineno-42-18" > < / 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-42-19" name = "__codelineno-42-19" href = "#__codelineno-42-19" > < / 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-42-20" name = "__codelineno-42-20" href = "#__codelineno-42-20" > < / a > < span class = "n" > ma< / span > < span class = "o" > =< / span > < span class = "n" > l< / span >
< a id = "__codelineno-42-21" name = "__codelineno-42-21" href = "#__codelineno-42-21" > < / 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-42-22" name = "__codelineno-42-22" href = "#__codelineno-42-22" > < / a > < span class = "n" > ma< / span > < span class = "o" > =< / span > < span class = "n" > r< / span >
< a id = "__codelineno-42-23" name = "__codelineno-42-23" href = "#__codelineno-42-23" > < / a > < span class = "c1" > # 若结点 i 最大或索引 l, r 越界，则无需继续堆化，跳出< / span >
< a id = "__codelineno-42-24" name = "__codelineno-42-24" href = "#__codelineno-42-24" > < / 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-42-25" name = "__codelineno-42-25" href = "#__codelineno-42-25" > < / a > < span class = "k" > break< / span >
< a id = "__codelineno-42-26" name = "__codelineno-42-26" href = "#__codelineno-42-26" > < / a > < span class = "c1" > # 交换两结点< / span >
< a id = "__codelineno-42-27" name = "__codelineno-42-27" href = "#__codelineno-42-27" > < / 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-42-28" name = "__codelineno-42-28" href = "#__codelineno-42-28" > < / a > < span class = "c1" > # 循环向下堆化< / span >
< a id = "__codelineno-42-29" name = "__codelineno-42-29" href = "#__codelineno-42-29" > < / 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" >
< div class = "highlight" > < span class = "filename" > my_heap.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-43-1" name = "__codelineno-43-1" href = "#__codelineno-43-1" > < / a > < span class = "cm" > /* 元素出堆 */< / span >
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< a id = "__codelineno-43-2" name = "__codelineno-43-2" href = "#__codelineno-43-2" > < / 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-43-3" name = "__codelineno-43-3" href = "#__codelineno-43-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 判空处理< / span >
< a id = "__codelineno-43-4" name = "__codelineno-43-4" href = "#__codelineno-43-4" > < / 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-43-5" name = "__codelineno-43-5" href = "#__codelineno-43-5" > < / 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-43-6" name = "__codelineno-43-6" href = "#__codelineno-43-6" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "kc" > nil< / span >
< a id = "__codelineno-43-7" name = "__codelineno-43-7" href = "#__codelineno-43-7" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-43-8" name = "__codelineno-43-8" href = "#__codelineno-43-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 交换根结点与最右叶结点（即交换首元素与尾元素）< / span >
< a id = "__codelineno-43-9" name = "__codelineno-43-9" href = "#__codelineno-43-9" > < / 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-43-10" name = "__codelineno-43-10" href = "#__codelineno-43-10" > < / a > < span class = "w" > < / span > < span class = "c1" > // 删除结点< / span >
< a id = "__codelineno-43-11" name = "__codelineno-43-11" href = "#__codelineno-43-11" > < / 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-43-12" name = "__codelineno-43-12" href = "#__codelineno-43-12" > < / 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-43-13" name = "__codelineno-43-13" href = "#__codelineno-43-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 从顶至底堆化< / span >
< a id = "__codelineno-43-14" name = "__codelineno-43-14" href = "#__codelineno-43-14" > < / 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-43-15" name = "__codelineno-43-15" href = "#__codelineno-43-15" > < / a >
< a id = "__codelineno-43-16" name = "__codelineno-43-16" href = "#__codelineno-43-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // 返回堆顶元素< / span >
< a id = "__codelineno-43-17" name = "__codelineno-43-17" href = "#__codelineno-43-17" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > val< / span >
< a id = "__codelineno-43-18" name = "__codelineno-43-18" href = "#__codelineno-43-18" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-43-19" name = "__codelineno-43-19" href = "#__codelineno-43-19" > < / a >
< a id = "__codelineno-43-20" name = "__codelineno-43-20" href = "#__codelineno-43-20" > < / a > < span class = "cm" > /* 从结点 i 开始，从顶至底堆化 */< / span >
< a id = "__codelineno-43-21" name = "__codelineno-43-21" href = "#__codelineno-43-21" > < / 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-43-22" name = "__codelineno-43-22" href = "#__codelineno-43-22" > < / 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-43-23" name = "__codelineno-43-23" href = "#__codelineno-43-23" > < / a > < span class = "w" > < / span > < span class = "c1" > // 判断结点 i, l, r 中值最大的结点，记为 max< / span >
< a id = "__codelineno-43-24" name = "__codelineno-43-24" href = "#__codelineno-43-24" > < / 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-43-25" name = "__codelineno-43-25" href = "#__codelineno-43-25" > < / 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-43-26" name = "__codelineno-43-26" href = "#__codelineno-43-26" > < / 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-43-27" name = "__codelineno-43-27" href = "#__codelineno-43-27" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-43-28" name = "__codelineno-43-28" href = "#__codelineno-43-28" > < / 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-43-29" name = "__codelineno-43-29" href = "#__codelineno-43-29" > < / 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-43-30" name = "__codelineno-43-30" href = "#__codelineno-43-30" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-43-31" name = "__codelineno-43-31" href = "#__codelineno-43-31" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若结点 i 最大或索引 l, r 越界，则无需继续堆化，跳出< / span >
< a id = "__codelineno-43-32" name = "__codelineno-43-32" href = "#__codelineno-43-32" > < / 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-43-33" name = "__codelineno-43-33" href = "#__codelineno-43-33" > < / a > < span class = "w" > < / span > < span class = "k" > break< / span >
< a id = "__codelineno-43-34" name = "__codelineno-43-34" href = "#__codelineno-43-34" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-43-35" name = "__codelineno-43-35" href = "#__codelineno-43-35" > < / a > < span class = "w" > < / span > < span class = "c1" > // 交换两结点< / span >
< a id = "__codelineno-43-36" name = "__codelineno-43-36" href = "#__codelineno-43-36" > < / 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-43-37" name = "__codelineno-43-37" href = "#__codelineno-43-37" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环向下堆化< / span >
< a id = "__codelineno-43-38" name = "__codelineno-43-38" href = "#__codelineno-43-38" > < / 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-43-39" name = "__codelineno-43-39" href = "#__codelineno-43-39" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-43-40" name = "__codelineno-43-40" href = "#__codelineno-43-40" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > my_heap.js< / span > < pre > < span > < / span > < code > < a id = "__codelineno-44-1" name = "__codelineno-44-1" href = "#__codelineno-44-1" > < / a > < span class = "cm" > /* 元素出堆 */< / span >
2023-03-13 22:41:04 +08:00
< a id = "__codelineno-44-2" name = "__codelineno-44-2" href = "#__codelineno-44-2" > < / a > < span class = "nx" > 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 >
< 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 = "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 = "s2" > " 堆为空" < / span > < span class = "p" > );< / span >
< a id = "__codelineno-44-5" name = "__codelineno-44-5" href = "#__codelineno-44-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 交换根结点与最右叶结点（即交换首元素与尾元素）< / span >
< a id = "__codelineno-44-6" name = "__codelineno-44-6" href = "#__codelineno-44-6" > < / 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-44-7" name = "__codelineno-44-7" href = "#__codelineno-44-7" > < / a > < span class = "w" > < / span > < span class = "c1" > // 删除结点< / span >
< a id = "__codelineno-44-8" name = "__codelineno-44-8" href = "#__codelineno-44-8" > < / 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-44-9" name = "__codelineno-44-9" href = "#__codelineno-44-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 从顶至底堆化< / span >
< a id = "__codelineno-44-10" name = "__codelineno-44-10" href = "#__codelineno-44-10" > < / 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-44-11" name = "__codelineno-44-11" href = "#__codelineno-44-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 返回堆顶元素< / span >
< a id = "__codelineno-44-12" name = "__codelineno-44-12" href = "#__codelineno-44-12" > < / 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-44-13" name = "__codelineno-44-13" href = "#__codelineno-44-13" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-44-14" name = "__codelineno-44-14" href = "#__codelineno-44-14" > < / a >
< a id = "__codelineno-44-15" name = "__codelineno-44-15" href = "#__codelineno-44-15" > < / a > < span class = "cm" > /* 从结点 i 开始，从顶至底堆化 */< / span >
< a id = "__codelineno-44-16" name = "__codelineno-44-16" href = "#__codelineno-44-16" > < / 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-44-17" name = "__codelineno-44-17" href = "#__codelineno-44-17" > < / 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-44-18" name = "__codelineno-44-18" href = "#__codelineno-44-18" > < / a > < span class = "w" > < / span > < span class = "c1" > // 判断结点 i, l, r 中值最大的结点，记为 ma< / span >
< a id = "__codelineno-44-19" name = "__codelineno-44-19" href = "#__codelineno-44-19" > < / 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-44-20" name = "__codelineno-44-20" href = "#__codelineno-44-20" > < / 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-44-21" name = "__codelineno-44-21" href = "#__codelineno-44-21" > < / 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-44-22" name = "__codelineno-44-22" href = "#__codelineno-44-22" > < / 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-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 = "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-44-24" name = "__codelineno-44-24" href = "#__codelineno-44-24" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若结点 i 最大或索引 l, r 越界，则无需继续堆化，跳出< / span >
< a id = "__codelineno-44-25" name = "__codelineno-44-25" href = "#__codelineno-44-25" > < / 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-44-26" name = "__codelineno-44-26" href = "#__codelineno-44-26" > < / a > < span class = "w" > < / span > < span class = "c1" > // 交换两结点< / span >
< a id = "__codelineno-44-27" name = "__codelineno-44-27" href = "#__codelineno-44-27" > < / 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-44-28" name = "__codelineno-44-28" href = "#__codelineno-44-28" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环向下堆化< / span >
< a id = "__codelineno-44-29" name = "__codelineno-44-29" href = "#__codelineno-44-29" > < / 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-44-30" name = "__codelineno-44-30" href = "#__codelineno-44-30" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-44-31" name = "__codelineno-44-31" href = "#__codelineno-44-31" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > my_heap.ts< / span > < pre > < span > < / span > < code > < a id = "__codelineno-45-1" name = "__codelineno-45-1" href = "#__codelineno-45-1" > < / a > < span class = "cm" > /* 元素出堆 */< / span >
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< a id = "__codelineno-45-2" name = "__codelineno-45-2" href = "#__codelineno-45-2" > < / 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 >
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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 = "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-45-5" name = "__codelineno-45-5" href = "#__codelineno-45-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 交换根结点与最右叶结点（即交换首元素与尾元素）< / span >
< a id = "__codelineno-45-6" name = "__codelineno-45-6" href = "#__codelineno-45-6" > < / a > < span class = "w" > < / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "nx" > swap< / span > < span class = "p" > (< / span > < span class = "mf" > 0< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "nx" > size< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "p" > );< / span >
< a id = "__codelineno-45-7" name = "__codelineno-45-7" href = "#__codelineno-45-7" > < / a > < span class = "w" > < / span > < span class = "c1" > // 删除结点< / span >
< a id = "__codelineno-45-8" name = "__codelineno-45-8" href = "#__codelineno-45-8" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > val< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "nx" > maxHeap< / span > < span class = "p" > .< / span > < span class = "nx" > pop< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-45-9" name = "__codelineno-45-9" href = "#__codelineno-45-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 从顶至底堆化< / span >
< a id = "__codelineno-45-10" name = "__codelineno-45-10" href = "#__codelineno-45-10" > < / a > < span class = "w" > < / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "nx" > siftDown< / span > < span class = "p" > (< / span > < span class = "mf" > 0< / span > < span class = "p" > );< / span >
< a id = "__codelineno-45-11" name = "__codelineno-45-11" href = "#__codelineno-45-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 返回堆顶元素< / span >
< a id = "__codelineno-45-12" name = "__codelineno-45-12" href = "#__codelineno-45-12" > < / 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-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 >
< a id = "__codelineno-45-15" name = "__codelineno-45-15" href = "#__codelineno-45-15" > < / a > < span class = "cm" > /* 从结点 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 = "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 >
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< 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 = "kc" > true< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-45-18" name = "__codelineno-45-18" href = "#__codelineno-45-18" > < / a > < span class = "w" > < / span > < span class = "c1" > // 判断结点 i, l, r 中值最大的结点，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 = "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-45-20" name = "__codelineno-45-20" href = "#__codelineno-45-20" > < / 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-45-21" name = "__codelineno-45-21" href = "#__codelineno-45-21" > < / 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-45-22" name = "__codelineno-45-22" href = "#__codelineno-45-22" > < / 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-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 = "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-45-24" name = "__codelineno-45-24" href = "#__codelineno-45-24" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若结点 i 最大或索引 l, r 越界，则无需继续堆化，跳出< / span >
< a id = "__codelineno-45-25" name = "__codelineno-45-25" href = "#__codelineno-45-25" > < / 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-45-26" name = "__codelineno-45-26" href = "#__codelineno-45-26" > < / a > < span class = "w" > < / span > < span class = "c1" > // 交换两结点< / span >
< a id = "__codelineno-45-27" name = "__codelineno-45-27" href = "#__codelineno-45-27" > < / 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-45-28" name = "__codelineno-45-28" href = "#__codelineno-45-28" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环向下堆化< / span >
< a id = "__codelineno-45-29" name = "__codelineno-45-29" href = "#__codelineno-45-29" > < / 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-45-30" name = "__codelineno-45-30" href = "#__codelineno-45-30" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-45-31" name = "__codelineno-45-31" href = "#__codelineno-45-31" > < / 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.c< / span > < pre > < span > < / span > < code > < a id = "__codelineno-46-1" name = "__codelineno-46-1" href = "#__codelineno-46-1" > < / 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" > pop< / span > < span class = "p" > }< / span >
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< a id = "__codelineno-46-2" name = "__codelineno-46-2" href = "#__codelineno-46-2" > < / a >
< a id = "__codelineno-46-3" name = "__codelineno-46-3" href = "#__codelineno-46-3" > < / 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 class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > my_heap.cs< / 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 >
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< a id = "__codelineno-47-2" name = "__codelineno-47-2" href = "#__codelineno-47-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > pop< / 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 = "p" > {< / span >
< a id = "__codelineno-47-4" name = "__codelineno-47-4" href = "#__codelineno-47-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 判空处理< / span >
< a id = "__codelineno-47-5" name = "__codelineno-47-5" href = "#__codelineno-47-5" > < / 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-47-6" name = "__codelineno-47-6" href = "#__codelineno-47-6" > < / 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-47-7" name = "__codelineno-47-7" href = "#__codelineno-47-7" > < / a > < span class = "w" > < / span > < span class = "c1" > // 交换根结点与最右叶结点（即交换首元素与尾元素）< / span >
< a id = "__codelineno-47-8" name = "__codelineno-47-8" href = "#__codelineno-47-8" > < / 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-47-9" name = "__codelineno-47-9" href = "#__codelineno-47-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 删除结点< / span >
< a id = "__codelineno-47-10" name = "__codelineno-47-10" href = "#__codelineno-47-10" > < / 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-47-11" name = "__codelineno-47-11" href = "#__codelineno-47-11" > < / 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-47-12" name = "__codelineno-47-12" href = "#__codelineno-47-12" > < / a > < span class = "w" > < / span > < span class = "c1" > // 从顶至底堆化< / span >
< a id = "__codelineno-47-13" name = "__codelineno-47-13" href = "#__codelineno-47-13" > < / 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-47-14" name = "__codelineno-47-14" href = "#__codelineno-47-14" > < / a > < span class = "w" > < / span > < span class = "c1" > // 返回堆顶元素< / span >
< a id = "__codelineno-47-15" name = "__codelineno-47-15" href = "#__codelineno-47-15" > < / 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-47-16" name = "__codelineno-47-16" href = "#__codelineno-47-16" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-47-17" name = "__codelineno-47-17" href = "#__codelineno-47-17" > < / a >
< a id = "__codelineno-47-18" name = "__codelineno-47-18" href = "#__codelineno-47-18" > < / a > < span class = "cm" > /* 从结点 i 开始，从顶至底堆化 */< / span >
< a id = "__codelineno-47-19" name = "__codelineno-47-19" href = "#__codelineno-47-19" > < / 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 >
< a id = "__codelineno-47-20" name = "__codelineno-47-20" href = "#__codelineno-47-20" > < / a > < span class = "p" > {< / span >
< a id = "__codelineno-47-21" name = "__codelineno-47-21" href = "#__codelineno-47-21" > < / 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 >
< a id = "__codelineno-47-22" name = "__codelineno-47-22" href = "#__codelineno-47-22" > < / a > < 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" > // 判断结点 i, l, r 中值最大的结点，记为 ma< / span >
< a id = "__codelineno-47-24" name = "__codelineno-47-24" href = "#__codelineno-47-24" > < / 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" > 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-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 = "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-47-26" name = "__codelineno-47-26" href = "#__codelineno-47-26" > < / a > < span class = "w" > < / span > < span class = "n" > ma< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > l< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-47-27" name = "__codelineno-47-27" href = "#__codelineno-47-27" > < / 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-47-28" name = "__codelineno-47-28" href = "#__codelineno-47-28" > < / 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-47-29" name = "__codelineno-47-29" href = "#__codelineno-47-29" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若“结点 i 最大”或“越过叶结点”，则结束堆化< / span >
< a id = "__codelineno-47-30" name = "__codelineno-47-30" href = "#__codelineno-47-30" > < / 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-47-31" name = "__codelineno-47-31" href = "#__codelineno-47-31" > < / a > < span class = "w" > < / span > < span class = "c1" > // 交换两结点< / span >
< a id = "__codelineno-47-32" name = "__codelineno-47-32" href = "#__codelineno-47-32" > < / 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-47-33" name = "__codelineno-47-33" href = "#__codelineno-47-33" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环向下堆化< / span >
< a id = "__codelineno-47-34" name = "__codelineno-47-34" href = "#__codelineno-47-34" > < / 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-47-35" name = "__codelineno-47-35" href = "#__codelineno-47-35" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-47-36" name = "__codelineno-47-36" href = "#__codelineno-47-36" > < / a > < span class = "p" > }< / span >
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< / 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-48-1" name = "__codelineno-48-1" href = "#__codelineno-48-1" > < / a > < span class = "cm" > /* 元素出堆 */< / span >
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< a id = "__codelineno-48-2" name = "__codelineno-48-2" href = "#__codelineno-48-2" > < / 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 >
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< a id = "__codelineno-48-3" name = "__codelineno-48-3" href = "#__codelineno-48-3" > < / a > < span class = "c1" > // 判空处理< / span >
< a id = "__codelineno-48-4" name = "__codelineno-48-4" href = "#__codelineno-48-4" > < / a > < span class = "k" > if< / span > < span class = "bp" > isEmpty< / span > < span class = "p" > ()< / span > < span class = "p" > {< / span >
< a id = "__codelineno-48-5" name = "__codelineno-48-5" href = "#__codelineno-48-5" > < / a > < span class = "bp" > fatalError< / span > < span class = "p" > (< / span > < span class = "s" > " 堆为空" < / span > < span class = "p" > )< / span >
< a id = "__codelineno-48-6" name = "__codelineno-48-6" href = "#__codelineno-48-6" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-48-7" name = "__codelineno-48-7" href = "#__codelineno-48-7" > < / a > < span class = "c1" > // 交换根结点与最右叶结点（即交换首元素与尾元素）< / span >
< a id = "__codelineno-48-8" name = "__codelineno-48-8" href = "#__codelineno-48-8" > < / 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-48-9" name = "__codelineno-48-9" href = "#__codelineno-48-9" > < / a > < span class = "c1" > // 删除结点< / span >
< a id = "__codelineno-48-10" name = "__codelineno-48-10" href = "#__codelineno-48-10" > < / 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-48-11" name = "__codelineno-48-11" href = "#__codelineno-48-11" > < / a > < span class = "c1" > // 从顶至底堆化< / span >
< a id = "__codelineno-48-12" name = "__codelineno-48-12" href = "#__codelineno-48-12" > < / 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-48-13" name = "__codelineno-48-13" href = "#__codelineno-48-13" > < / a > < span class = "c1" > // 返回堆顶元素< / span >
< a id = "__codelineno-48-14" name = "__codelineno-48-14" href = "#__codelineno-48-14" > < / a > < span class = "k" > return< / span > < span class = "n" > val< / span >
< a id = "__codelineno-48-15" name = "__codelineno-48-15" href = "#__codelineno-48-15" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-48-16" name = "__codelineno-48-16" href = "#__codelineno-48-16" > < / a >
< a id = "__codelineno-48-17" name = "__codelineno-48-17" href = "#__codelineno-48-17" > < / a > < span class = "cm" > /* 从结点 i 开始，从顶至底堆化 */< / span >
< a id = "__codelineno-48-18" name = "__codelineno-48-18" href = "#__codelineno-48-18" > < / 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-48-19" name = "__codelineno-48-19" href = "#__codelineno-48-19" > < / a > < span class = "kd" > var< / span > < span class = "nv" > i< / span > < span class = "p" > =< / span > < span class = "n" > i< / span >
< a id = "__codelineno-48-20" name = "__codelineno-48-20" href = "#__codelineno-48-20" > < / a > < span class = "k" > while< / span > < span class = "kc" > true< / span > < span class = "p" > {< / span >
< a id = "__codelineno-48-21" name = "__codelineno-48-21" href = "#__codelineno-48-21" > < / a > < span class = "c1" > // 判断结点 i, l, r 中值最大的结点，记为 ma< / span >
< a id = "__codelineno-48-22" name = "__codelineno-48-22" href = "#__codelineno-48-22" > < / 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-48-23" name = "__codelineno-48-23" href = "#__codelineno-48-23" > < / 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-48-24" name = "__codelineno-48-24" href = "#__codelineno-48-24" > < / a > < span class = "kd" > var< / span > < span class = "nv" > ma< / span > < span class = "p" > =< / span > < span class = "n" > i< / span >
< a id = "__codelineno-48-25" name = "__codelineno-48-25" href = "#__codelineno-48-25" > < / 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-48-26" name = "__codelineno-48-26" href = "#__codelineno-48-26" > < / a > < span class = "n" > ma< / span > < span class = "p" > =< / span > < span class = "n" > l< / span >
< a id = "__codelineno-48-27" name = "__codelineno-48-27" href = "#__codelineno-48-27" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-48-28" name = "__codelineno-48-28" href = "#__codelineno-48-28" > < / 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-48-29" name = "__codelineno-48-29" href = "#__codelineno-48-29" > < / a > < span class = "n" > ma< / span > < span class = "p" > =< / span > < span class = "n" > r< / span >
< a id = "__codelineno-48-30" name = "__codelineno-48-30" href = "#__codelineno-48-30" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-48-31" name = "__codelineno-48-31" href = "#__codelineno-48-31" > < / a > < span class = "c1" > // 若结点 i 最大或索引 l, r 越界，则无需继续堆化，跳出< / span >
< a id = "__codelineno-48-32" name = "__codelineno-48-32" href = "#__codelineno-48-32" > < / 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-48-33" name = "__codelineno-48-33" href = "#__codelineno-48-33" > < / a > < span class = "k" > break< / span >
< a id = "__codelineno-48-34" name = "__codelineno-48-34" href = "#__codelineno-48-34" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-48-35" name = "__codelineno-48-35" href = "#__codelineno-48-35" > < / a > < span class = "c1" > // 交换两结点< / span >
< a id = "__codelineno-48-36" name = "__codelineno-48-36" href = "#__codelineno-48-36" > < / 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-48-37" name = "__codelineno-48-37" href = "#__codelineno-48-37" > < / a > < span class = "c1" > // 循环向下堆化< / span >
< a id = "__codelineno-48-38" name = "__codelineno-48-38" href = "#__codelineno-48-38" > < / a > < span class = "n" > i< / span > < span class = "p" > =< / span > < span class = "n" > ma< / span >
< a id = "__codelineno-48-39" name = "__codelineno-48-39" href = "#__codelineno-48-39" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-48-40" name = "__codelineno-48-40" href = "#__codelineno-48-40" > < / 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.zig< / span > < pre > < span > < / span > < code > < a id = "__codelineno-49-1" name = "__codelineno-49-1" href = "#__codelineno-49-1" > < / a > < span class = "c1" > // 元素出堆< / span >
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< a id = "__codelineno-49-2" name = "__codelineno-49-2" href = "#__codelineno-49-2" > < / 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 >
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< a id = "__codelineno-49-3" name = "__codelineno-49-3" href = "#__codelineno-49-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 判断处理< / span >
< a id = "__codelineno-49-4" name = "__codelineno-49-4" href = "#__codelineno-49-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > 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-49-5" name = "__codelineno-49-5" href = "#__codelineno-49-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 交换根结点与最右叶结点（即交换首元素与尾元素）< / span >
< a id = "__codelineno-49-6" name = "__codelineno-49-6" href = "#__codelineno-49-6" > < / 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-49-7" name = "__codelineno-49-7" href = "#__codelineno-49-7" > < / a > < span class = "w" > < / span > < span class = "c1" > // 删除结点< / 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 = "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 >
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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 >
< a id = "__codelineno-49-10" name = "__codelineno-49-10" href = "#__codelineno-49-10" > < / 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-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 >
< 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 = "n" > val< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-49-13" name = "__codelineno-49-13" href = "#__codelineno-49-13" > < / a > < span class = "p" > }< / span > < span class = "w" > < / span >
< a id = "__codelineno-49-14" name = "__codelineno-49-14" href = "#__codelineno-49-14" > < / a >
< a id = "__codelineno-49-15" name = "__codelineno-49-15" href = "#__codelineno-49-15" > < / a > < span class = "c1" > // 从结点 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 = "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-49-17" name = "__codelineno-49-17" href = "#__codelineno-49-17" > < / 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-49-18" name = "__codelineno-49-18" href = "#__codelineno-49-18" > < / 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-49-19" name = "__codelineno-49-19" href = "#__codelineno-49-19" > < / a > < span class = "w" > < / span > < span class = "c1" > // 判断结点 i, l, r 中值最大的结点，记为 ma< / span >
< a id = "__codelineno-49-20" name = "__codelineno-49-20" href = "#__codelineno-49-20" > < / 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-49-21" name = "__codelineno-49-21" href = "#__codelineno-49-21" > < / 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-49-22" name = "__codelineno-49-22" href = "#__codelineno-49-22" > < / 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 >
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< 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 = "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-49-24" name = "__codelineno-49-24" href = "#__codelineno-49-24" > < / 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 >
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< a id = "__codelineno-49-25" name = "__codelineno-49-25" href = "#__codelineno-49-25" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若结点 i 最大或索引 l, r 越界，则无需继续堆化，跳出< / span >
< a id = "__codelineno-49-26" name = "__codelineno-49-26" href = "#__codelineno-49-26" > < / 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-49-27" name = "__codelineno-49-27" href = "#__codelineno-49-27" > < / a > < span class = "w" > < / span > < span class = "c1" > // 交换两结点< / span >
< a id = "__codelineno-49-28" name = "__codelineno-49-28" href = "#__codelineno-49-28" > < / 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-49-29" name = "__codelineno-49-29" href = "#__codelineno-49-29" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环向下堆化< / span >
< a id = "__codelineno-49-30" name = "__codelineno-49-30" href = "#__codelineno-49-30" > < / 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-49-31" name = "__codelineno-49-31" href = "#__codelineno-49-31" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-49-32" name = "__codelineno-49-32" href = "#__codelineno-49-32" > < / a > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
< / div >
< / div >
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< h2 id = "814" > 8.1.4. 堆常见应用< a class = "headerlink" href = "#814" title = "Permanent link" > ¶ < / a > < / h2 >
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< ul >
< li > < strong > 优先队列< / strong > 。堆常作为实现优先队列的首选数据结构，入队和出队操作时间复杂度为 < span class = "arithmatex" > \(O(\log n)\)< / span > ，建队操作为 < span class = "arithmatex" > \(O(n)\)< / span > ，皆非常高效。< / li >
< li > < strong > 堆排序< / strong > 。给定一组数据，我们使用其建堆，并依次全部弹出，则可以得到有序的序列。当然，堆排序一般无需弹出元素，仅需每轮将堆顶元素交换至数组尾部并减小堆的长度即可。< / li >
< li > < strong > 获取最大的 < span class = "arithmatex" > \(k\)< / span > 个元素< / strong > 。这既是一道经典算法题目，也是一种常见应用，例如选取热度前 10 的新闻作为微博热搜，选取前 10 销量的商品等。< / li >
< / ul >
< h2 id = "__comments" > 评论< / h2 >
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