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< title > 7.4. < / title >
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跳转至
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Hello 算法
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7.4. AVL 树 *
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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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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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< a href = "../../chapter_computational_complexity/performance_evaluation/" class = "md-nav__link" >
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2.1. 算法效率评估
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< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_computational_complexity/time_complexity/" class = "md-nav__link" >
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2.2. 时间复杂度
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< / a >
< / li >
< li class = "md-nav__item" >
< 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 >
< / li >
< li class = "md-nav__item" >
< 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 >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_computational_complexity/summary/" class = "md-nav__link" >
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2.5. 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_4" >
< label class = "md-nav__link" for = "__nav_4" id = "__nav_4_label" tabindex = "0" >
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3. 数据结构简介
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< span class = "md-nav__icon md-icon" > < / span >
< / label >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_4_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_4" >
< span class = "md-nav__icon md-icon" > < / span >
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3. 数据结构简介
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< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "../../chapter_data_structure/data_and_memory/" class = "md-nav__link" >
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3.1. 数据与内存
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< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_data_structure/classification_of_data_structure/" class = "md-nav__link" >
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3.2. 数据结构分类
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< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_data_structure/summary/" class = "md-nav__link" >
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3.3. 小结
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< li class = "md-nav__item md-nav__item--section md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_5" >
< label class = "md-nav__link" for = "__nav_5" id = "__nav_5_label" tabindex = "0" >
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4. 数组与链表
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< span class = "md-nav__icon md-icon" > < / span >
< / label >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_5_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_5" >
< span class = "md-nav__icon md-icon" > < / span >
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4. 数组与链表
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< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "../../chapter_array_and_linkedlist/array/" class = "md-nav__link" >
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4.1. 数组
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< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_array_and_linkedlist/linked_list/" class = "md-nav__link" >
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4.2. 链表
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< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_array_and_linkedlist/list/" class = "md-nav__link" >
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4.3. 列表
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< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_array_and_linkedlist/summary/" class = "md-nav__link" >
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4.4. 小结
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< / 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_6" >
< label class = "md-nav__link" for = "__nav_6" id = "__nav_6_label" tabindex = "0" >
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5. 栈与队列
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< span class = "md-nav__icon md-icon" > < / span >
< / label >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_6_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_6" >
< span class = "md-nav__icon md-icon" > < / span >
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5. 栈与队列
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< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "../../chapter_stack_and_queue/stack/" class = "md-nav__link" >
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5.1. 栈
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< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_stack_and_queue/queue/" class = "md-nav__link" >
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5.2. 队列
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< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_stack_and_queue/deque/" class = "md-nav__link" >
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5.3. 双向队列
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< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_stack_and_queue/summary/" class = "md-nav__link" >
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5.4. 小结
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< / 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_7" >
< label class = "md-nav__link" for = "__nav_7" id = "__nav_7_label" tabindex = "0" >
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6. 散列表
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< span class = "md-nav__icon md-icon" > < / span >
< / label >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_7_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_7" >
< span class = "md-nav__icon md-icon" > < / span >
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6. 散列表
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< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "../../chapter_hashing/hash_map/" class = "md-nav__link" >
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6.1. 哈希表
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< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_hashing/hash_collision/" class = "md-nav__link" >
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6.2. 哈希冲突处理
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< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_hashing/summary/" class = "md-nav__link" >
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6.3. 小结
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< / a >
< / li >
< / ul >
< / nav >
< / li >
< li class = "md-nav__item md-nav__item--active md-nav__item--section md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_8" checked >
< label class = "md-nav__link" for = "__nav_8" id = "__nav_8_label" tabindex = "0" >
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7. 树
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< span class = "md-nav__icon md-icon" > < / span >
< / label >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_8_label" aria-expanded = "true" >
< label class = "md-nav__title" for = "__nav_8" >
< span class = "md-nav__icon md-icon" > < / span >
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7. 树
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< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "../binary_tree/" class = "md-nav__link" >
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7.1. 二叉树
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< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../binary_tree_traversal/" class = "md-nav__link" >
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7.2. 二叉树遍历
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< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../binary_search_tree/" class = "md-nav__link" >
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7.3. 二叉搜索树
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< / a >
< / li >
< li class = "md-nav__item md-nav__item--active" >
< input class = "md-nav__toggle md-toggle" type = "checkbox" id = "__toc" >
< label class = "md-nav__link md-nav__link--active" for = "__toc" >
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7.4. AVL 树 *
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< span class = "md-nav__icon md-icon" > < / span >
< / label >
< a href = "./" class = "md-nav__link md-nav__link--active" >
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7.4. AVL 树 *
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< / a >
< 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 = "#741-avl" class = "md-nav__link" >
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7.4.1. AVL 树常见术语
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< / a >
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< nav class = "md-nav" aria-label = "7.4.1. AVL 树常见术语" >
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< ul class = "md-nav__list" >
< li class = "md-nav__item" >
< a href = "#_1" class = "md-nav__link" >
结点高度
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "#_2" class = "md-nav__link" >
结点平衡因子
< / a >
< / li >
< / ul >
< / nav >
< / li >
< li class = "md-nav__item" >
< a href = "#742-avl" class = "md-nav__link" >
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7.4.2. AVL 树旋转
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< / a >
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< nav class = "md-nav" aria-label = "7.4.2. AVL 树旋转" >
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< ul class = "md-nav__list" >
< li class = "md-nav__item" >
< a href = "#case-1-" class = "md-nav__link" >
Case 1 - 右旋
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "#case-2-" class = "md-nav__link" >
Case 2 - 左旋
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "#case-3-" class = "md-nav__link" >
Case 3 - 先左后右
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "#case-4-" class = "md-nav__link" >
Case 4 - 先右后左
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "#_3" class = "md-nav__link" >
旋转的选择
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< / li >
< / ul >
< / nav >
< / li >
< li class = "md-nav__item" >
< a href = "#743-avl" class = "md-nav__link" >
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7.4.3. AVL 树常用操作
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< / a >
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< nav class = "md-nav" aria-label = "7.4.3. AVL 树常用操作" >
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< ul class = "md-nav__list" >
< li class = "md-nav__item" >
< a href = "#_4" class = "md-nav__link" >
插入结点
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "#_5" class = "md-nav__link" >
删除结点
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "#_6" class = "md-nav__link" >
查找结点
< / a >
< / li >
< / ul >
< / nav >
< / li >
< li class = "md-nav__item" >
< a href = "#744-avl" class = "md-nav__link" >
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7.4.4. AVL 树典型应用
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< / a >
< / li >
< / ul >
< / nav >
< / li >
< li class = "md-nav__item" >
< a href = "../summary/" class = "md-nav__link" >
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7.5. 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_9" >
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< label class = "md-nav__link" for = "__nav_9" id = "__nav_9_label" tabindex = "0" >
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8. 堆
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< span class = "md-nav__icon md-icon" > < / span >
< / label >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_9_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_9" >
< span class = "md-nav__icon md-icon" > < / span >
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8. 堆
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< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "../../chapter_heap/heap/" class = "md-nav__link" >
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8.1. 堆
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< / a >
< / li >
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< li class = "md-nav__item" >
< a href = "../../chapter_heap/build_heap/" class = "md-nav__link" >
8.2. 建堆操作 *
< / a >
< / li >
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< li class = "md-nav__item" >
< a href = "../../chapter_heap/summary/" class = "md-nav__link" >
8.3. 小结
< / a >
< / li >
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< / 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_10" >
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< label class = "md-nav__link" for = "__nav_10" id = "__nav_10_label" tabindex = "0" >
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9. 图
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< span class = "md-nav__icon md-icon" > < / span >
< / label >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_10_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_10" >
< span class = "md-nav__icon md-icon" > < / span >
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9. 图
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< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "../../chapter_graph/graph/" class = "md-nav__link" >
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9.1. 图
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< / a >
< / li >
< li class = "md-nav__item" >
< 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 >
< / li >
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< li class = "md-nav__item" >
< a href = "../../chapter_graph/graph_traversal/" class = "md-nav__link" >
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9.3. 图的遍历
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< / a >
< / li >
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< li class = "md-nav__item" >
< a href = "../../chapter_graph/summary/" class = "md-nav__link" >
9.4. 小结
< / a >
< / li >
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< / 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_11" >
< label class = "md-nav__link" for = "__nav_11" id = "__nav_11_label" tabindex = "0" >
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10. 查找算法
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< span class = "md-nav__icon md-icon" > < / span >
< / label >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_11_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_11" >
< span class = "md-nav__icon md-icon" > < / span >
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10. 查找算法
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< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "../../chapter_searching/linear_search/" class = "md-nav__link" >
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10.1. 线性查找
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< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_searching/binary_search/" class = "md-nav__link" >
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10.2. 二分查找
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< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_searching/hashing_search/" class = "md-nav__link" >
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10.3. 哈希查找
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< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_searching/summary/" class = "md-nav__link" >
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10.4. 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_12" >
< 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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< span class = "md-nav__icon md-icon" > < / span >
< / label >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_12_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_12" >
< span class = "md-nav__icon md-icon" > < / span >
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11. 排序算法
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< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "../../chapter_sorting/intro_to_sort/" class = "md-nav__link" >
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11.1. 排序简介
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< / a >
< / li >
< 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 >
< li class = "md-nav__item" >
< a href = "../../chapter_sorting/summary/" class = "md-nav__link" >
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11.6. 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 = "#741-avl" class = "md-nav__link" >
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7.4.1. AVL 树常见术语
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< / a >
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< nav class = "md-nav" aria-label = "7.4.1. AVL 树常见术语" >
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< ul class = "md-nav__list" >
< li class = "md-nav__item" >
< a href = "#_1" class = "md-nav__link" >
结点高度
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "#_2" class = "md-nav__link" >
结点平衡因子
< / a >
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< / ul >
< / nav >
< / li >
< li class = "md-nav__item" >
< a href = "#742-avl" class = "md-nav__link" >
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7.4.2. AVL 树旋转
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< / a >
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< nav class = "md-nav" aria-label = "7.4.2. AVL 树旋转" >
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< ul class = "md-nav__list" >
< li class = "md-nav__item" >
< a href = "#case-1-" class = "md-nav__link" >
Case 1 - 右旋
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "#case-2-" class = "md-nav__link" >
Case 2 - 左旋
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "#case-3-" class = "md-nav__link" >
Case 3 - 先左后右
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "#case-4-" class = "md-nav__link" >
Case 4 - 先右后左
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "#_3" class = "md-nav__link" >
旋转的选择
< / a >
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< / ul >
< / nav >
< / li >
< li class = "md-nav__item" >
< a href = "#743-avl" class = "md-nav__link" >
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7.4.3. AVL 树常用操作
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< / a >
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< nav class = "md-nav" aria-label = "7.4.3. AVL 树常用操作" >
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< ul class = "md-nav__list" >
< li class = "md-nav__item" >
< a href = "#_4" class = "md-nav__link" >
插入结点
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "#_5" class = "md-nav__link" >
删除结点
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "#_6" class = "md-nav__link" >
查找结点
< / a >
< / li >
< / ul >
< / nav >
< / li >
< li class = "md-nav__item" >
< a href = "#744-avl" class = "md-nav__link" >
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7.4.4. AVL 树典型应用
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< / a >
< / li >
< / ul >
< / nav >
< / div >
< / div >
< / div >
< 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_tree/avl_tree.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 = "74-avl" > 7.4. AVL 树 *< a class = "headerlink" href = "#74-avl" title = "Permanent link" > ¶ < / a > < / h1 >
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< p > 在「二叉搜索树」章节中提到，在进行多次插入与删除操作后，二叉搜索树可能会退化为链表。此时所有操作的时间复杂度都会由 < span class = "arithmatex" > \(O(\log n)\)< / span > 劣化至 < span class = "arithmatex" > \(O(n)\)< / span > 。< / p >
< p > 如下图所示，执行两步删除结点后，该二叉搜索树就会退化为链表。< / p >
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< p > < img alt = "AVL 树在删除结点后发生退化" src = "../avl_tree.assets/avltree_degradation_from_removing_node.png" / > < / p >
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< p align = "center" > Fig. AVL 树在删除结点后发生退化 < / p >
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< p > 再比如，在以下完美二叉树中插入两个结点后，树严重向左偏斜，查找操作的时间复杂度也随之发生劣化。< / p >
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< p > < img alt = "AVL 树在插入结点后发生退化" src = "../avl_tree.assets/avltree_degradation_from_inserting_node.png" / > < / p >
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< p align = "center" > Fig. AVL 树在插入结点后发生退化 < / p >
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< p > G. M. Adelson-Velsky 和 E. M. Landis 在其 1962 年发表的论文 "An algorithm for the organization of information" 中提出了「AVL 树」。< strong > 论文中描述了一系列操作， ， < / strong > ，进而使得各种操作的时间复杂度均能保持在 < span class = "arithmatex" > \(O(\log n)\)< / span > 级别。< / p >
< p > 换言之， ， < / p >
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< h2 id = "741-avl" > 7.4.1. AVL 树常见术语< a class = "headerlink" href = "#741-avl" title = "Permanent link" > ¶ < / a > < / h2 >
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< p > 「AVL 树」既是「二叉搜索树」又是「平衡二叉树」，同时满足这两种二叉树的所有性质，因此又被称为「平衡二叉搜索树」。< / p >
< h3 id = "_1" > 结点高度< a class = "headerlink" href = "#_1" title = "Permanent link" > ¶ < / a > < / h3 >
< p > 在 AVL 树的操作中，需要获取结点「高度 Height」， < code > height< / code > 变量。< / p >
< 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" > < pre > < span > < / span > < code > < a id = "__codelineno-0-1" name = "__codelineno-0-1" href = "#__codelineno-0-1" > < / a > < span class = "cm" > /* AVL 树结点类 */< / span >
< a id = "__codelineno-0-2" name = "__codelineno-0-2" href = "#__codelineno-0-2" > < / a > < span class = "kd" > class< / span > < span class = "nc" > TreeNode< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-0-3" name = "__codelineno-0-3" href = "#__codelineno-0-3" > < / a > < span class = "w" > < / span > < span class = "kd" > public< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > val< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 结点值< / span >
< a id = "__codelineno-0-4" name = "__codelineno-0-4" href = "#__codelineno-0-4" > < / a > < span class = "w" > < / span > < span class = "kd" > public< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > height< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 结点高度< / span >
< a id = "__codelineno-0-5" name = "__codelineno-0-5" href = "#__codelineno-0-5" > < / a > < span class = "w" > < / span > < span class = "kd" > public< / span > < span class = "w" > < / span > < span class = "n" > TreeNode< / span > < span class = "w" > < / span > < span class = "n" > left< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 左子结点< / span >
< a id = "__codelineno-0-6" name = "__codelineno-0-6" href = "#__codelineno-0-6" > < / a > < span class = "w" > < / span > < span class = "kd" > public< / span > < span class = "w" > < / span > < span class = "n" > TreeNode< / span > < span class = "w" > < / span > < span class = "n" > right< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 右子结点< / span >
< a id = "__codelineno-0-7" name = "__codelineno-0-7" href = "#__codelineno-0-7" > < / a > < span class = "w" > < / span > < span class = "kd" > public< / span > < span class = "w" > < / span > < span class = "nf" > TreeNode< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > x< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / 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" > x< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-0-8" name = "__codelineno-0-8" href = "#__codelineno-0-8" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-1-1" name = "__codelineno-1-1" href = "#__codelineno-1-1" > < / a > < span class = "cm" > /* AVL 树结点类 */< / span >
< a id = "__codelineno-1-2" name = "__codelineno-1-2" href = "#__codelineno-1-2" > < / a > < span class = "k" > struct< / span > < span class = "w" > < / span > < span class = "nc" > TreeNode< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-1-3" name = "__codelineno-1-3" href = "#__codelineno-1-3" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > val< / span > < span class = "p" > {};< / span > < span class = "w" > < / span > < span class = "c1" > // 结点值< / span >
< a id = "__codelineno-1-4" name = "__codelineno-1-4" href = "#__codelineno-1-4" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > height< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 结点高度< / span >
< a id = "__codelineno-1-5" name = "__codelineno-1-5" href = "#__codelineno-1-5" > < / a > < span class = "w" > < / span > < span class = "n" > TreeNode< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > left< / span > < span class = "p" > {};< / span > < span class = "w" > < / span > < span class = "c1" > // 左子结点< / span >
< a id = "__codelineno-1-6" name = "__codelineno-1-6" href = "#__codelineno-1-6" > < / a > < span class = "w" > < / span > < span class = "n" > TreeNode< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > right< / span > < span class = "p" > {};< / span > < span class = "w" > < / span > < span class = "c1" > // 右子结点< / span >
< a id = "__codelineno-1-7" name = "__codelineno-1-7" href = "#__codelineno-1-7" > < / a > < span class = "w" > < / span > < span class = "n" > TreeNode< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > default< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-1-8" name = "__codelineno-1-8" href = "#__codelineno-1-8" > < / a > < span class = "w" > < / span > < span class = "k" > explicit< / span > < span class = "w" > < / span > < span class = "n" > TreeNode< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > x< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "n" > val< / span > < span class = "p" > (< / span > < span class = "n" > x< / span > < span class = "p" > ){}< / span >
< a id = "__codelineno-1-9" name = "__codelineno-1-9" href = "#__codelineno-1-9" > < / a > < span class = "p" > };< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-2-1" name = "__codelineno-2-1" href = "#__codelineno-2-1" > < / a > < span class = "sd" > " " " AVL 树结点类 " " " < / span >
< a id = "__codelineno-2-2" name = "__codelineno-2-2" href = "#__codelineno-2-2" > < / a > < span class = "k" > class< / span > < span class = "nc" > TreeNode< / span > < span class = "p" > :< / span >
< a id = "__codelineno-2-3" name = "__codelineno-2-3" href = "#__codelineno-2-3" > < / a > < span class = "k" > def< / span > < span class = "fm" > __init__< / span > < span class = "p" > (< / span > < span class = "bp" > self< / span > < span class = "p" > ,< / span > < span class = "n" > val< / span > < span class = "o" > =< / span > < span class = "kc" > None< / span > < span class = "p" > ,< / span > < span class = "n" > left< / span > < span class = "o" > =< / span > < span class = "kc" > None< / span > < span class = "p" > ,< / span > < span class = "n" > right< / span > < span class = "o" > =< / span > < span class = "kc" > None< / span > < span class = "p" > ):< / span >
< a id = "__codelineno-2-4" name = "__codelineno-2-4" href = "#__codelineno-2-4" > < / a > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > val< / span > < span class = "o" > =< / span > < span class = "n" > val< / span > < span class = "c1" > # 结点值< / span >
< a id = "__codelineno-2-5" name = "__codelineno-2-5" href = "#__codelineno-2-5" > < / a > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > height< / span > < span class = "o" > =< / span > < span class = "mi" > 0< / span > < span class = "c1" > # 结点高度< / span >
< a id = "__codelineno-2-6" name = "__codelineno-2-6" href = "#__codelineno-2-6" > < / a > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > left< / span > < span class = "o" > =< / span > < span class = "n" > left< / span > < span class = "c1" > # 左子结点引用< / span >
< a id = "__codelineno-2-7" name = "__codelineno-2-7" href = "#__codelineno-2-7" > < / a > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > right< / span > < span class = "o" > =< / span > < span class = "n" > right< / span > < span class = "c1" > # 右子结点引用< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-3-1" name = "__codelineno-3-1" href = "#__codelineno-3-1" > < / a > < span class = "cm" > /* AVL 树结点类 */< / span >
< a id = "__codelineno-3-2" name = "__codelineno-3-2" href = "#__codelineno-3-2" > < / a > < span class = "kd" > type< / span > < span class = "w" > < / span > < span class = "nx" > TreeNode< / span > < span class = "w" > < / span > < span class = "kd" > struct< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-3" name = "__codelineno-3-3" href = "#__codelineno-3-3" > < / a > < span class = "w" > < / span > < span class = "nx" > Val< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "c1" > // 结点值< / span >
< a id = "__codelineno-3-4" name = "__codelineno-3-4" href = "#__codelineno-3-4" > < / a > < span class = "w" > < / span > < span class = "nx" > Height< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "c1" > // 结点高度< / span >
< a id = "__codelineno-3-5" name = "__codelineno-3-5" href = "#__codelineno-3-5" > < / a > < span class = "w" > < / span > < span class = "nx" > Left< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > TreeNode< / span > < span class = "w" > < / span > < span class = "c1" > // 左子结点引用< / span >
< a id = "__codelineno-3-6" name = "__codelineno-3-6" href = "#__codelineno-3-6" > < / a > < span class = "w" > < / span > < span class = "nx" > Right< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > TreeNode< / span > < span class = "w" > < / span > < span class = "c1" > // 右子结点引用< / span >
< a id = "__codelineno-3-7" name = "__codelineno-3-7" href = "#__codelineno-3-7" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-4-1" name = "__codelineno-4-1" href = "#__codelineno-4-1" > < / a > < span class = "kd" > class< / span > < span class = "w" > < / span > < span class = "nx" > TreeNode< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-4-2" name = "__codelineno-4-2" href = "#__codelineno-4-2" > < / a > < span class = "w" > < / span > < span class = "nx" > val< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 结点值< / span >
< a id = "__codelineno-4-3" name = "__codelineno-4-3" href = "#__codelineno-4-3" > < / a > < span class = "w" > < / span > < span class = "nx" > height< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > //结点高度< / span >
< a id = "__codelineno-4-4" name = "__codelineno-4-4" href = "#__codelineno-4-4" > < / a > < span class = "w" > < / span > < span class = "nx" > left< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 左子结点指针< / span >
< a id = "__codelineno-4-5" name = "__codelineno-4-5" href = "#__codelineno-4-5" > < / a > < span class = "w" > < / span > < span class = "nx" > right< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 右子结点指针< / span >
< a id = "__codelineno-4-6" name = "__codelineno-4-6" href = "#__codelineno-4-6" > < / a > < span class = "w" > < / span > < span class = "kr" > constructor< / span > < span class = "p" > (< / span > < span class = "nx" > val< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > left< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > right< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > height< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-4-7" name = "__codelineno-4-7" href = "#__codelineno-4-7" > < / a > < span class = "w" > < / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "nx" > val< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > val< / span > < span class = "w" > < / span > < span class = "o" > ===< / span > < span class = "w" > < / span > < span class = "kc" > undefined< / 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 = "nx" > val< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-4-8" name = "__codelineno-4-8" href = "#__codelineno-4-8" > < / a > < span class = "w" > < / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "nx" > height< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > height< / span > < span class = "w" > < / span > < span class = "o" > ===< / span > < span class = "w" > < / span > < span class = "kc" > undefined< / 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 = "nx" > height< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-4-9" name = "__codelineno-4-9" href = "#__codelineno-4-9" > < / a > < span class = "w" > < / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "nx" > left< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > left< / span > < span class = "w" > < / span > < span class = "o" > ===< / span > < span class = "w" > < / span > < span class = "kc" > undefined< / span > < span class = "w" > < / span > < span class = "o" > ?< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "w" > < / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "nx" > left< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-4-10" name = "__codelineno-4-10" href = "#__codelineno-4-10" > < / a > < span class = "w" > < / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "nx" > right< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > right< / span > < span class = "w" > < / span > < span class = "o" > ===< / span > < span class = "w" > < / span > < span class = "kc" > undefined< / span > < span class = "w" > < / span > < span class = "o" > ?< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "w" > < / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "nx" > right< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-4-11" name = "__codelineno-4-11" href = "#__codelineno-4-11" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-4-12" name = "__codelineno-4-12" href = "#__codelineno-4-12" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-5-1" name = "__codelineno-5-1" href = "#__codelineno-5-1" > < / a > < span class = "kd" > class< / span > < span class = "w" > < / span > < span class = "nx" > TreeNode< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-5-2" name = "__codelineno-5-2" href = "#__codelineno-5-2" > < / a > < span class = "w" > < / 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 = "w" > < / span > < span class = "c1" > // 结点值< / span >
< a id = "__codelineno-5-3" name = "__codelineno-5-3" href = "#__codelineno-5-3" > < / a > < span class = "w" > < / span > < span class = "nx" > height< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 结点高度< / span >
< a id = "__codelineno-5-4" name = "__codelineno-5-4" href = "#__codelineno-5-4" > < / a > < span class = "w" > < / span > < span class = "nx" > left< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > TreeNode< / span > < span class = "w" > < / span > < span class = "o" > |< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 左子结点指针< / span >
< a id = "__codelineno-5-5" name = "__codelineno-5-5" href = "#__codelineno-5-5" > < / a > < span class = "w" > < / span > < span class = "nx" > right< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > TreeNode< / span > < span class = "w" > < / span > < span class = "o" > |< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 右子结点指针< / span >
< a id = "__codelineno-5-6" name = "__codelineno-5-6" href = "#__codelineno-5-6" > < / a > < span class = "w" > < / span > < span class = "kr" > constructor< / 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 = "w" > < / span > < span class = "nx" > height?< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > left?< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > TreeNode< / span > < span class = "w" > < / span > < span class = "o" > |< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > right?< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > TreeNode< / span > < span class = "w" > < / span > < span class = "o" > |< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-5-7" name = "__codelineno-5-7" href = "#__codelineno-5-7" > < / a > < span class = "w" > < / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "nx" > val< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > val< / span > < span class = "w" > < / span > < span class = "o" > ===< / span > < span class = "w" > < / span > < span class = "kc" > undefined< / span > < span class = "w" > < / span > < span class = "o" > ?< / span > < span class = "w" > < / span > < span class = "nx" > 0< / span > < span class = "w" > < / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > val< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-5-8" name = "__codelineno-5-8" href = "#__codelineno-5-8" > < / a > < span class = "w" > < / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "nx" > height< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > height< / span > < span class = "w" > < / span > < span class = "o" > ===< / span > < span class = "w" > < / span > < span class = "kc" > undefined< / span > < span class = "w" > < / span > < span class = "o" > ?< / span > < span class = "w" > < / span > < span class = "nx" > 0< / span > < span class = "w" > < / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > height< / span > < span class = "p" > ;< / span > < span class = "w" > < / span >
< a id = "__codelineno-5-9" name = "__codelineno-5-9" href = "#__codelineno-5-9" > < / a > < span class = "w" > < / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "nx" > left< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > left< / span > < span class = "w" > < / span > < span class = "o" > ===< / span > < span class = "w" > < / span > < span class = "kc" > undefined< / span > < span class = "w" > < / span > < span class = "o" > ?< / span > < span class = "w" > < / span > < span class = "nx" > null< / span > < span class = "w" > < / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > left< / span > < span class = "p" > ;< / span > < span class = "w" > < / span >
< a id = "__codelineno-5-10" name = "__codelineno-5-10" href = "#__codelineno-5-10" > < / a > < span class = "w" > < / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "nx" > right< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > right< / span > < span class = "w" > < / span > < span class = "o" > ===< / span > < span class = "w" > < / span > < span class = "kc" > undefined< / span > < span class = "w" > < / span > < span class = "o" > ?< / span > < span class = "w" > < / span > < span class = "nx" > null< / span > < span class = "w" > < / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > right< / span > < span class = "p" > ;< / span > < span class = "w" > < / span >
< a id = "__codelineno-5-11" name = "__codelineno-5-11" href = "#__codelineno-5-11" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-5-12" name = "__codelineno-5-12" href = "#__codelineno-5-12" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < 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" >
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-7-1" name = "__codelineno-7-1" href = "#__codelineno-7-1" > < / a > < span class = "cm" > /* AVL 树结点类 */< / span >
< a id = "__codelineno-7-2" name = "__codelineno-7-2" href = "#__codelineno-7-2" > < / a > < span class = "k" > class< / span > < span class = "w" > < / span > < span class = "nc" > TreeNode< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-7-3" name = "__codelineno-7-3" href = "#__codelineno-7-3" > < / a > < span class = "w" > < / span > < span class = "k" > public< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > val< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 结点值< / span >
< a id = "__codelineno-7-4" name = "__codelineno-7-4" href = "#__codelineno-7-4" > < / a > < span class = "w" > < / span > < span class = "k" > public< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > height< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 结点高度< / span >
< a id = "__codelineno-7-5" name = "__codelineno-7-5" href = "#__codelineno-7-5" > < / a > < span class = "w" > < / span > < span class = "k" > public< / span > < span class = "w" > < / span > < span class = "n" > TreeNode< / span > < span class = "o" > ?< / span > < span class = "w" > < / span > < span class = "n" > left< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 左子结点< / span >
< a id = "__codelineno-7-6" name = "__codelineno-7-6" href = "#__codelineno-7-6" > < / a > < span class = "w" > < / span > < span class = "k" > public< / span > < span class = "w" > < / span > < span class = "n" > TreeNode< / span > < span class = "o" > ?< / span > < span class = "w" > < / span > < span class = "n" > right< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 右子结点< / span >
< a id = "__codelineno-7-7" name = "__codelineno-7-7" href = "#__codelineno-7-7" > < / a > < span class = "w" > < / span > < span class = "k" > public< / span > < span class = "w" > < / span > < span class = "nf" > TreeNode< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > x< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / 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" > x< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-7-8" name = "__codelineno-7-8" href = "#__codelineno-7-8" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-8-1" name = "__codelineno-8-1" href = "#__codelineno-8-1" > < / a > < span class = "cm" > /* AVL 树结点类 */< / span >
< a id = "__codelineno-8-2" name = "__codelineno-8-2" href = "#__codelineno-8-2" > < / a > < span class = "kd" > class< / span > < span class = "nc" > TreeNode< / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-3" name = "__codelineno-8-3" href = "#__codelineno-8-3" > < / a > < span class = "kd" > var< / span > < span class = "nv" > val< / span > < span class = "p" > :< / span > < span class = "nb" > Int< / span > < span class = "c1" > // 结点值< / span >
< a id = "__codelineno-8-4" name = "__codelineno-8-4" href = "#__codelineno-8-4" > < / a > < span class = "kd" > var< / span > < span class = "nv" > height< / span > < span class = "p" > :< / span > < span class = "nb" > Int< / span > < span class = "c1" > // 结点高度< / span >
< a id = "__codelineno-8-5" name = "__codelineno-8-5" href = "#__codelineno-8-5" > < / a > < span class = "kd" > var< / span > < span class = "nv" > left< / span > < span class = "p" > :< / span > < span class = "n" > TreeNode< / span > < span class = "p" > ?< / span > < span class = "c1" > // 左子结点< / span >
< a id = "__codelineno-8-6" name = "__codelineno-8-6" href = "#__codelineno-8-6" > < / a > < span class = "kd" > var< / span > < span class = "nv" > right< / span > < span class = "p" > :< / span > < span class = "n" > TreeNode< / span > < span class = "p" > ?< / span > < span class = "c1" > // 右子结点< / span >
< a id = "__codelineno-8-7" name = "__codelineno-8-7" href = "#__codelineno-8-7" > < / a >
< a id = "__codelineno-8-8" name = "__codelineno-8-8" href = "#__codelineno-8-8" > < / a > < span class = "kd" > init< / span > < span class = "p" > (< / span > < span class = "n" > x< / span > < span class = "p" > :< / span > < span class = "nb" > Int< / span > < span class = "p" > )< / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-9" name = "__codelineno-8-9" href = "#__codelineno-8-9" > < / a > < span class = "n" > val< / span > < span class = "p" > =< / span > < span class = "n" > x< / span >
< a id = "__codelineno-8-10" name = "__codelineno-8-10" href = "#__codelineno-8-10" > < / a > < span class = "n" > height< / span > < span class = "p" > =< / span > < span class = "mi" > 0< / span >
< a id = "__codelineno-8-11" name = "__codelineno-8-11" href = "#__codelineno-8-11" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-8-12" name = "__codelineno-8-12" href = "#__codelineno-8-12" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
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< div class = "tabbed-block" >
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-9-1" name = "__codelineno-9-1" href = "#__codelineno-9-1" > < / a >
< / code > < / pre > < / div >
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< p > 「结点高度」是最远叶结点到该结点的距离，即走过的「边」的数量。需要特别注意，< strong > 叶结点的高度为 0 ，空结点的高度为 -1< / strong > 。我们封装两个工具函数，分别用于获取与更新结点的高度。< / 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" > avl_tree.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-10-1" name = "__codelineno-10-1" href = "#__codelineno-10-1" > < / a > < span class = "cm" > /* 获取结点高度 */< / 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" > height< / span > < span class = "p" > (< / span > < span class = "n" > TreeNode< / span > < span class = "w" > < / span > < span class = "n" > node< / 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 = "c1" > // 空结点高度为 -1 ，叶结点高度为 0< / span >
< a id = "__codelineno-10-4" name = "__codelineno-10-4" href = "#__codelineno-10-4" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "w" > < / span > < span class = "o" > ?< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "w" > < / span > < span class = "p" > :< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "na" > height< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-10-5" name = "__codelineno-10-5" href = "#__codelineno-10-5" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-10-6" name = "__codelineno-10-6" href = "#__codelineno-10-6" > < / a >
< a id = "__codelineno-10-7" name = "__codelineno-10-7" href = "#__codelineno-10-7" > < / a > < span class = "cm" > /* 更新结点高度 */< / span >
< a id = "__codelineno-10-8" name = "__codelineno-10-8" href = "#__codelineno-10-8" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "nf" > updateHeight< / span > < span class = "p" > (< / span > < span class = "n" > TreeNode< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-10-9" name = "__codelineno-10-9" href = "#__codelineno-10-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 结点高度等于最高子树高度 + 1< / span >
< a id = "__codelineno-10-10" name = "__codelineno-10-10" href = "#__codelineno-10-10" > < / a > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "na" > height< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > Math< / span > < span class = "p" > .< / span > < span class = "na" > max< / span > < span class = "p" > (< / span > < span class = "n" > height< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "na" > left< / span > < span class = "p" > ),< / span > < span class = "w" > < / span > < span class = "n" > height< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "na" > right< / 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-10-11" name = "__codelineno-10-11" href = "#__codelineno-10-11" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > avl_tree.cpp< / span > < pre > < span > < / span > < code > < a id = "__codelineno-11-1" name = "__codelineno-11-1" href = "#__codelineno-11-1" > < / a > < span class = "cm" > /* 获取结点高度 */< / 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" > height< / span > < span class = "p" > (< / span > < span class = "n" > TreeNode< / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "n" > node< / 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 = "c1" > // 空结点高度为 -1 ，叶结点高度为 0< / span >
< a id = "__codelineno-11-4" name = "__codelineno-11-4" href = "#__codelineno-11-4" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "k" > nullptr< / span > < span class = "w" > < / span > < span class = "o" > ?< / span > < span class = "w" > < / span > < span class = "mi" > -1< / span > < span class = "w" > < / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "o" > -> < / span > < span class = "n" > height< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-11-5" name = "__codelineno-11-5" href = "#__codelineno-11-5" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-11-6" name = "__codelineno-11-6" href = "#__codelineno-11-6" > < / a >
< a id = "__codelineno-11-7" name = "__codelineno-11-7" href = "#__codelineno-11-7" > < / a > < span class = "cm" > /* 更新结点高度 */< / span >
< a id = "__codelineno-11-8" name = "__codelineno-11-8" href = "#__codelineno-11-8" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "nf" > updateHeight< / span > < span class = "p" > (< / span > < span class = "n" > TreeNode< / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-11-9" name = "__codelineno-11-9" href = "#__codelineno-11-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 结点高度等于最高子树高度 + 1< / span >
< a id = "__codelineno-11-10" name = "__codelineno-11-10" href = "#__codelineno-11-10" > < / a > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "o" > -> < / span > < span class = "n" > height< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > max< / span > < span class = "p" > (< / span > < span class = "n" > height< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "o" > -> < / span > < span class = "n" > left< / span > < span class = "p" > ),< / span > < span class = "w" > < / span > < span class = "n" > height< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "o" > -> < / span > < span class = "n" > right< / 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-11-11" name = "__codelineno-11-11" href = "#__codelineno-11-11" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > avl_tree.py< / span > < pre > < span > < / span > < code > < a id = "__codelineno-12-1" name = "__codelineno-12-1" href = "#__codelineno-12-1" > < / a > < span class = "sd" > " " " 获取结点高度 " " " < / span >
< a id = "__codelineno-12-2" name = "__codelineno-12-2" href = "#__codelineno-12-2" > < / a > < span class = "k" > def< / span > < span class = "nf" > height< / span > < span class = "p" > (< / span > < span class = "bp" > self< / span > < span class = "p" > ,< / span > < span class = "n" > node< / span > < span class = "p" > :< / span > < span class = "n" > Optional< / span > < span class = "p" > [< / span > < span class = "n" > TreeNode< / span > < span class = "p" > ])< / span > < span class = "o" > -> < / span > < span class = "nb" > int< / span > < span class = "p" > :< / span >
< a id = "__codelineno-12-3" name = "__codelineno-12-3" href = "#__codelineno-12-3" > < / a > < span class = "c1" > # 空结点高度为 -1 ，叶结点高度为 0< / span >
< a id = "__codelineno-12-4" name = "__codelineno-12-4" href = "#__codelineno-12-4" > < / a > < span class = "k" > if< / span > < span class = "n" > node< / span > < span class = "ow" > is< / span > < span class = "ow" > not< / span > < span class = "kc" > None< / span > < span class = "p" > :< / span >
< a id = "__codelineno-12-5" name = "__codelineno-12-5" href = "#__codelineno-12-5" > < / a > < span class = "k" > return< / span > < span class = "n" > node< / span > < span class = "o" > .< / span > < span class = "n" > height< / span >
< a id = "__codelineno-12-6" name = "__codelineno-12-6" href = "#__codelineno-12-6" > < / a > < span class = "k" > return< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-12-7" name = "__codelineno-12-7" href = "#__codelineno-12-7" > < / a >
< a id = "__codelineno-12-8" name = "__codelineno-12-8" href = "#__codelineno-12-8" > < / a > < span class = "sd" > " " " 更新结点高度 " " " < / span >
< a id = "__codelineno-12-9" name = "__codelineno-12-9" href = "#__codelineno-12-9" > < / a > < span class = "k" > def< / span > < span class = "nf" > __update_height< / span > < span class = "p" > (< / span > < span class = "bp" > self< / span > < span class = "p" > ,< / span > < span class = "n" > node< / span > < span class = "p" > :< / span > < span class = "n" > Optional< / span > < span class = "p" > [< / span > < span class = "n" > TreeNode< / span > < span class = "p" > ]):< / span >
< a id = "__codelineno-12-10" name = "__codelineno-12-10" href = "#__codelineno-12-10" > < / a > < span class = "c1" > # 结点高度等于最高子树高度 + 1< / span >
< a id = "__codelineno-12-11" name = "__codelineno-12-11" href = "#__codelineno-12-11" > < / a > < span class = "n" > node< / span > < span class = "o" > .< / span > < span class = "n" > height< / span > < span class = "o" > =< / span > < span class = "nb" > max< / span > < span class = "p" > ([< / span > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > height< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "o" > .< / span > < span class = "n" > left< / span > < span class = "p" > ),< / span > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > height< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "o" > .< / span > < span class = "n" > right< / span > < span class = "p" > )])< / span > < span class = "o" > +< / span > < span class = "mi" > 1< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > avl_tree.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-13-1" name = "__codelineno-13-1" href = "#__codelineno-13-1" > < / a > < span class = "cm" > /* 获取结点高度 */< / span >
2023-02-09 04:43:20 +08:00
< 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" > t< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > aVLTree< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "nx" > height< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > TreeNode< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
2023-02-08 14:54:41 +08:00
< a id = "__codelineno-13-3" name = "__codelineno-13-3" href = "#__codelineno-13-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 空结点高度为 -1 ，叶结点高度为 0< / span >
< a id = "__codelineno-13-4" name = "__codelineno-13-4" href = "#__codelineno-13-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "w" > < / span > < span class = "o" > !=< / span > < span class = "w" > < / span > < span class = "kc" > nil< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-13-5" name = "__codelineno-13-5" href = "#__codelineno-13-5" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > Height< / span >
< a id = "__codelineno-13-6" name = "__codelineno-13-6" href = "#__codelineno-13-6" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-13-7" name = "__codelineno-13-7" href = "#__codelineno-13-7" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-13-8" name = "__codelineno-13-8" href = "#__codelineno-13-8" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-13-9" name = "__codelineno-13-9" href = "#__codelineno-13-9" > < / a >
< a id = "__codelineno-13-10" name = "__codelineno-13-10" href = "#__codelineno-13-10" > < / a > < span class = "cm" > /* 更新结点高度 */< / span >
2023-02-09 04:43:20 +08:00
< a id = "__codelineno-13-11" name = "__codelineno-13-11" href = "#__codelineno-13-11" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > t< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > aVLTree< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "nx" > updateHeight< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > TreeNode< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-13-12" name = "__codelineno-13-12" href = "#__codelineno-13-12" > < / a > < span class = "w" > < / span > < span class = "nx" > lh< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nx" > t< / span > < span class = "p" > .< / span > < span class = "nx" > height< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > Left< / 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 = "nx" > rh< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nx" > t< / span > < span class = "p" > .< / span > < span class = "nx" > height< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > Right< / span > < span class = "p" > )< / span >
2023-02-08 14:54:41 +08:00
< a id = "__codelineno-13-14" name = "__codelineno-13-14" href = "#__codelineno-13-14" > < / a > < span class = "w" > < / span > < span class = "c1" > // 结点高度等于最高子树高度 + 1< / span >
< a id = "__codelineno-13-15" name = "__codelineno-13-15" href = "#__codelineno-13-15" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "nx" > lh< / span > < span class = "w" > < / span > < span class = "p" > > < / span > < span class = "w" > < / span > < span class = "nx" > rh< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-13-16" name = "__codelineno-13-16" href = "#__codelineno-13-16" > < / a > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > Height< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "nx" > lh< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-13-17" name = "__codelineno-13-17" href = "#__codelineno-13-17" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-13-18" name = "__codelineno-13-18" href = "#__codelineno-13-18" > < / a > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > Height< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "nx" > rh< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-13-19" name = "__codelineno-13-19" href = "#__codelineno-13-19" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-13-20" name = "__codelineno-13-20" href = "#__codelineno-13-20" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > avl_tree.js< / span > < pre > < span > < / span > < code > < a id = "__codelineno-14-1" name = "__codelineno-14-1" href = "#__codelineno-14-1" > < / a > < span class = "cm" > /* 获取结点高度 */< / span >
< a id = "__codelineno-14-2" name = "__codelineno-14-2" href = "#__codelineno-14-2" > < / a > < span class = "nx" > height< / span > < span class = "p" > (< / span > < span class = "nx" > node< / 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 = "c1" > // 空结点高度为 -1 ，叶结点高度为 0< / span >
< a id = "__codelineno-14-4" name = "__codelineno-14-4" href = "#__codelineno-14-4" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "w" > < / span > < span class = "o" > ===< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "w" > < / span > < span class = "o" > ?< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "mf" > 1< / span > < span class = "w" > < / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > height< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-14-5" name = "__codelineno-14-5" href = "#__codelineno-14-5" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-14-6" name = "__codelineno-14-6" href = "#__codelineno-14-6" > < / a >
< a id = "__codelineno-14-7" name = "__codelineno-14-7" href = "#__codelineno-14-7" > < / a > < span class = "cm" > /* 更新结点高度 */< / span >
< a id = "__codelineno-14-8" name = "__codelineno-14-8" href = "#__codelineno-14-8" > < / a > < span class = "nx" > updateHeight< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-14-9" name = "__codelineno-14-9" href = "#__codelineno-14-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 结点高度等于最高子树高度 + 1< / span >
< a id = "__codelineno-14-10" name = "__codelineno-14-10" href = "#__codelineno-14-10" > < / a > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > height< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nb" > Math< / span > < span class = "p" > .< / span > < span class = "nx" > max< / span > < span class = "p" > (< / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "nx" > height< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > left< / span > < span class = "p" > ),< / span > < span class = "w" > < / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "nx" > height< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > right< / 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-14-11" name = "__codelineno-14-11" href = "#__codelineno-14-11" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > avl_tree.ts< / span > < pre > < span > < / span > < code > < a id = "__codelineno-15-1" name = "__codelineno-15-1" href = "#__codelineno-15-1" > < / a > < span class = "cm" > /* 获取结点高度 */< / span >
< a id = "__codelineno-15-2" name = "__codelineno-15-2" href = "#__codelineno-15-2" > < / a > < span class = "nx" > height< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > TreeNode< / 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 = "c1" > // 空结点高度为 -1 ，叶结点高度为 0< / span >
< a id = "__codelineno-15-4" name = "__codelineno-15-4" href = "#__codelineno-15-4" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "w" > < / span > < span class = "o" > ===< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "w" > < / span > < span class = "o" > ?< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "nx" > 1< / span > < span class = "w" > < / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > node.height< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-15-5" name = "__codelineno-15-5" href = "#__codelineno-15-5" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-15-6" name = "__codelineno-15-6" href = "#__codelineno-15-6" > < / a >
< a id = "__codelineno-15-7" name = "__codelineno-15-7" href = "#__codelineno-15-7" > < / a > < span class = "cm" > /* 更新结点高度 */< / span >
< a id = "__codelineno-15-8" name = "__codelineno-15-8" href = "#__codelineno-15-8" > < / a > < span class = "nx" > updateHeight< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > TreeNode< / span > < span class = "p" > )< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "ow" > void< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-15-9" name = "__codelineno-15-9" href = "#__codelineno-15-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 结点高度等于最高子树高度 + 1< / span >
< a id = "__codelineno-15-10" name = "__codelineno-15-10" href = "#__codelineno-15-10" > < / a > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > height< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nb" > Math< / span > < span class = "p" > .< / span > < span class = "nx" > max< / span > < span class = "p" > (< / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "nx" > height< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > left< / span > < span class = "p" > ),< / span > < span class = "w" > < / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "nx" > height< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > right< / 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-15-11" name = "__codelineno-15-11" href = "#__codelineno-15-11" > < / 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" > avl_tree.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" > aVLTree< / 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" > height< / 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" > aVLTree< / 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" > updateHeight< / 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" > avl_tree.cs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-17-1" name = "__codelineno-17-1" href = "#__codelineno-17-1" > < / a > < span class = "cm" > /* 获取结点高度 */< / span >
2023-02-08 22:16:28 +08:00
< 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" > height< / span > < span class = "p" > (< / span > < span class = "n" > TreeNode< / span > < span class = "o" > ?< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > )< / span >
2023-02-08 14:54:41 +08:00
< 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 = "c1" > // 空结点高度为 -1 ，叶结点高度为 0< / span >
< a id = "__codelineno-17-5" name = "__codelineno-17-5" href = "#__codelineno-17-5" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "k" > null< / span > < span class = "w" > < / span > < span class = "o" > ?< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "m" > 1< / span > < span class = "w" > < / span > < span class = "p" > :< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "n" > height< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-17-6" name = "__codelineno-17-6" href = "#__codelineno-17-6" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-17-7" name = "__codelineno-17-7" href = "#__codelineno-17-7" > < / a >
< a id = "__codelineno-17-8" name = "__codelineno-17-8" href = "#__codelineno-17-8" > < / a > < span class = "cm" > /* 更新结点高度 */< / span >
2023-02-08 22:16:28 +08:00
< a id = "__codelineno-17-9" name = "__codelineno-17-9" href = "#__codelineno-17-9" > < / a > < span class = "k" > void< / span > < span class = "w" > < / span > < span class = "nf" > updateHeight< / span > < span class = "p" > (< / span > < span class = "n" > TreeNode< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > )< / span >
2023-02-08 14:54:41 +08:00
< a id = "__codelineno-17-10" name = "__codelineno-17-10" href = "#__codelineno-17-10" > < / a > < span class = "p" > {< / span >
< a id = "__codelineno-17-11" name = "__codelineno-17-11" href = "#__codelineno-17-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 结点高度等于最高子树高度 + 1< / span >
< a id = "__codelineno-17-12" name = "__codelineno-17-12" href = "#__codelineno-17-12" > < / a > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "n" > height< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > Math< / span > < span class = "p" > .< / span > < span class = "n" > Max< / span > < span class = "p" > (< / span > < span class = "n" > height< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "n" > left< / span > < span class = "p" > ),< / span > < span class = "w" > < / span > < span class = "n" > height< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "n" > right< / 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-17-13" name = "__codelineno-17-13" href = "#__codelineno-17-13" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > avl_tree.swift< / span > < pre > < span > < / span > < code > < a id = "__codelineno-18-1" name = "__codelineno-18-1" href = "#__codelineno-18-1" > < / a > < span class = "cm" > /* 获取结点高度 */< / span >
< a id = "__codelineno-18-2" name = "__codelineno-18-2" href = "#__codelineno-18-2" > < / a > < span class = "kd" > func< / span > < span class = "nf" > height< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > :< / span > < span class = "n" > TreeNode< / 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 = "c1" > // 空结点高度为 -1 ，叶结点高度为 0< / span >
< a id = "__codelineno-18-4" name = "__codelineno-18-4" href = "#__codelineno-18-4" > < / a > < span class = "n" > node< / span > < span class = "p" > ==< / span > < span class = "kc" > nil< / span > < span class = "p" > ?< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > :< / span > < span class = "n" > node< / span > < span class = "p" > !.< / span > < span class = "n" > height< / span >
< a id = "__codelineno-18-5" name = "__codelineno-18-5" href = "#__codelineno-18-5" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-18-6" name = "__codelineno-18-6" href = "#__codelineno-18-6" > < / a >
< a id = "__codelineno-18-7" name = "__codelineno-18-7" href = "#__codelineno-18-7" > < / a > < span class = "cm" > /* 更新结点高度 */< / span >
< a id = "__codelineno-18-8" name = "__codelineno-18-8" href = "#__codelineno-18-8" > < / a > < span class = "kd" > func< / span > < span class = "nf" > updateHeight< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > :< / span > < span class = "n" > TreeNode< / span > < span class = "p" > ?)< / span > < span class = "p" > {< / span >
< a id = "__codelineno-18-9" name = "__codelineno-18-9" href = "#__codelineno-18-9" > < / a > < span class = "c1" > // 结点高度等于最高子树高度 + 1< / span >
< a id = "__codelineno-18-10" name = "__codelineno-18-10" href = "#__codelineno-18-10" > < / a > < span class = "n" > node< / span > < span class = "p" > ?.< / span > < span class = "n" > height< / span > < span class = "p" > =< / span > < span class = "bp" > max< / span > < span class = "p" > (< / span > < span class = "n" > height< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > :< / span > < span class = "n" > node< / span > < span class = "p" > ?.< / span > < span class = "kr" > left< / span > < span class = "p" > ),< / span > < span class = "n" > height< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > :< / span > < span class = "n" > node< / span > < span class = "p" > ?.< / span > < span class = "kr" > right< / span > < span class = "p" > ))< / span > < span class = "o" > +< / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-18-11" name = "__codelineno-18-11" href = "#__codelineno-18-11" > < / 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" > avl_tree.zig< / span > < pre > < span > < / span > < code > < a id = "__codelineno-19-1" name = "__codelineno-19-1" href = "#__codelineno-19-1" > < / a > < span class = "c1" > // 获取结点高度< / 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" > height< / 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" > node< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "o" > ?*< / span > < span class = "n" > inc< / span > < span class = "p" > .< / span > < span class = "n" > TreeNode< / span > < span class = "p" > (< / span > < span class = "n" > T< / span > < span class = "p" > ))< / span > < span class = "w" > < / span > < span class = "kt" > i32< / 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 = "n" > _< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > self< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-19-4" name = "__codelineno-19-4" href = "#__codelineno-19-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 空结点高度为 -1 ，叶结点高度为 0< / span >
< a id = "__codelineno-19-5" name = "__codelineno-19-5" href = "#__codelineno-19-5" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "o" > ?< / span > < span class = "p" > .< / span > < span class = "n" > height< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-19-6" name = "__codelineno-19-6" href = "#__codelineno-19-6" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-19-7" name = "__codelineno-19-7" href = "#__codelineno-19-7" > < / a >
< a id = "__codelineno-19-8" name = "__codelineno-19-8" href = "#__codelineno-19-8" > < / a > < span class = "c1" > // 更新结点高度< / span >
< a id = "__codelineno-19-9" name = "__codelineno-19-9" href = "#__codelineno-19-9" > < / a > < span class = "k" > fn< / span > < span class = "w" > < / span > < span class = "n" > updateHeight< / 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" > node< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "o" > ?*< / span > < span class = "n" > inc< / span > < span class = "p" > .< / span > < span class = "n" > TreeNode< / span > < span class = "p" > (< / span > < span class = "n" > T< / span > < span class = "p" > ))< / span > < span class = "w" > < / span > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-19-10" name = "__codelineno-19-10" href = "#__codelineno-19-10" > < / a > < span class = "w" > < / span > < span class = "c1" > // 结点高度等于最高子树高度 + 1< / span >
< a id = "__codelineno-19-11" name = "__codelineno-19-11" href = "#__codelineno-19-11" > < / a > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "o" > ?< / span > < span class = "p" > .< / span > < span class = "n" > height< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > std< / span > < span class = "p" > .< / span > < span class = "n" > math< / span > < span class = "p" > .< / span > < span class = "n" > max< / span > < span class = "p" > (< / span > < span class = "n" > self< / span > < span class = "p" > .< / span > < span class = "n" > height< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "o" > ?< / span > < span class = "p" > .< / span > < span class = "n" > left< / span > < span class = "p" > ),< / span > < span class = "w" > < / span > < span class = "n" > self< / span > < span class = "p" > .< / span > < span class = "n" > height< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "o" > ?< / span > < span class = "p" > .< / span > < span class = "n" > right< / 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-19-12" name = "__codelineno-19-12" href = "#__codelineno-19-12" > < / a > < span class = "p" > }< / span >
2023-02-08 14:54:41 +08:00
< / code > < / pre > < / div >
< / div >
< / div >
< / div >
< h3 id = "_2" > 结点平衡因子< a class = "headerlink" href = "#_2" title = "Permanent link" > ¶ < / a > < / h3 >
< p > 结点的「平衡因子 Balance Factor」是 < strong > 结点的左子树高度减去右子树高度< / strong > ，并定义空结点的平衡因子为 0 。同样地，我们将获取结点平衡因子封装成函数，以便后续使用。< / 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" > avl_tree.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-20-1" name = "__codelineno-20-1" href = "#__codelineno-20-1" > < / a > < span class = "cm" > /* 获取平衡因子 */< / 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" > balanceFactor< / span > < span class = "p" > (< / span > < span class = "n" > TreeNode< / span > < span class = "w" > < / span > < span class = "n" > node< / 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 = "c1" > // 空结点平衡因子为 0< / span >
< a id = "__codelineno-20-4" name = "__codelineno-20-4" href = "#__codelineno-20-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-20-5" name = "__codelineno-20-5" href = "#__codelineno-20-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 结点平衡因子 = 左子树高度 - 右子树高度< / span >
< a id = "__codelineno-20-6" name = "__codelineno-20-6" href = "#__codelineno-20-6" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > height< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "na" > left< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "n" > height< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "na" > right< / span > < span class = "p" > );< / span >
< a id = "__codelineno-20-7" name = "__codelineno-20-7" href = "#__codelineno-20-7" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > avl_tree.cpp< / span > < pre > < span > < / span > < code > < a id = "__codelineno-21-1" name = "__codelineno-21-1" href = "#__codelineno-21-1" > < / a > < span class = "cm" > /* 获取平衡因子 */< / 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" > balanceFactor< / span > < span class = "p" > (< / span > < span class = "n" > TreeNode< / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "n" > node< / 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 = "c1" > // 空结点平衡因子为 0< / span >
< a id = "__codelineno-21-4" name = "__codelineno-21-4" href = "#__codelineno-21-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "k" > nullptr< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-21-5" name = "__codelineno-21-5" href = "#__codelineno-21-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 结点平衡因子 = 左子树高度 - 右子树高度< / span >
< a id = "__codelineno-21-6" name = "__codelineno-21-6" href = "#__codelineno-21-6" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > height< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "o" > -> < / span > < span class = "n" > left< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "n" > height< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "o" > -> < / span > < span class = "n" > right< / span > < span class = "p" > );< / span >
< a id = "__codelineno-21-7" name = "__codelineno-21-7" href = "#__codelineno-21-7" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > avl_tree.py< / span > < pre > < span > < / span > < code > < a id = "__codelineno-22-1" name = "__codelineno-22-1" href = "#__codelineno-22-1" > < / a > < span class = "sd" > " " " 获取平衡因子 " " " < / span >
< a id = "__codelineno-22-2" name = "__codelineno-22-2" href = "#__codelineno-22-2" > < / a > < span class = "k" > def< / span > < span class = "nf" > balance_factor< / span > < span class = "p" > (< / span > < span class = "bp" > self< / span > < span class = "p" > ,< / span > < span class = "n" > node< / span > < span class = "p" > :< / span > < span class = "n" > Optional< / span > < span class = "p" > [< / span > < span class = "n" > TreeNode< / span > < span class = "p" > ])< / span > < span class = "o" > -> < / span > < span class = "nb" > int< / span > < span class = "p" > :< / span >
< a id = "__codelineno-22-3" name = "__codelineno-22-3" href = "#__codelineno-22-3" > < / a > < span class = "c1" > # 空结点平衡因子为 0< / span >
< a id = "__codelineno-22-4" name = "__codelineno-22-4" href = "#__codelineno-22-4" > < / a > < span class = "k" > if< / span > < span class = "n" > node< / span > < span class = "ow" > is< / span > < span class = "kc" > None< / span > < span class = "p" > :< / span >
< a id = "__codelineno-22-5" name = "__codelineno-22-5" href = "#__codelineno-22-5" > < / a > < span class = "k" > return< / span > < span class = "mi" > 0< / span >
< a id = "__codelineno-22-6" name = "__codelineno-22-6" href = "#__codelineno-22-6" > < / a > < span class = "c1" > # 结点平衡因子 = 左子树高度 - 右子树高度< / span >
< a id = "__codelineno-22-7" name = "__codelineno-22-7" href = "#__codelineno-22-7" > < / a > < span class = "k" > return< / span > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > height< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "o" > .< / span > < span class = "n" > left< / span > < span class = "p" > )< / span > < span class = "o" > -< / span > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > height< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "o" > .< / span > < span class = "n" > right< / span > < span class = "p" > )< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > avl_tree.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-23-1" name = "__codelineno-23-1" href = "#__codelineno-23-1" > < / a > < span class = "cm" > /* 获取平衡因子 */< / span >
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< 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" > t< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > aVLTree< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "nx" > balanceFactor< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > TreeNode< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
2023-02-08 14:54:41 +08:00
< a id = "__codelineno-23-3" name = "__codelineno-23-3" href = "#__codelineno-23-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 空结点平衡因子为 0< / span >
< a id = "__codelineno-23-4" name = "__codelineno-23-4" href = "#__codelineno-23-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "kc" > nil< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-23-5" name = "__codelineno-23-5" href = "#__codelineno-23-5" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span >
< a id = "__codelineno-23-6" name = "__codelineno-23-6" href = "#__codelineno-23-6" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-23-7" name = "__codelineno-23-7" href = "#__codelineno-23-7" > < / a > < span class = "w" > < / span > < span class = "c1" > // 结点平衡因子 = 左子树高度 - 右子树高度< / span >
2023-02-09 04:43:20 +08:00
< a id = "__codelineno-23-8" name = "__codelineno-23-8" href = "#__codelineno-23-8" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > t< / span > < span class = "p" > .< / span > < span class = "nx" > height< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > Left< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "nx" > t< / span > < span class = "p" > .< / span > < span class = "nx" > height< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > Right< / span > < span class = "p" > )< / span >
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< a id = "__codelineno-23-9" name = "__codelineno-23-9" href = "#__codelineno-23-9" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > avl_tree.js< / span > < pre > < span > < / span > < code > < a id = "__codelineno-24-1" name = "__codelineno-24-1" href = "#__codelineno-24-1" > < / a > < span class = "cm" > /* 获取平衡因子 */< / span >
< a id = "__codelineno-24-2" name = "__codelineno-24-2" href = "#__codelineno-24-2" > < / a > < span class = "nx" > balanceFactor< / span > < span class = "p" > (< / span > < span class = "nx" > node< / 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 = "c1" > // 空结点平衡因子为 0< / span >
< a id = "__codelineno-24-4" name = "__codelineno-24-4" href = "#__codelineno-24-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "w" > < / span > < span class = "o" > ===< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "mf" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-24-5" name = "__codelineno-24-5" href = "#__codelineno-24-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 结点平衡因子 = 左子树高度 - 右子树高度< / span >
< a id = "__codelineno-24-6" name = "__codelineno-24-6" href = "#__codelineno-24-6" > < / 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" > height< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > left< / 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" > height< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > right< / span > < span class = "p" > );< / span >
< a id = "__codelineno-24-7" name = "__codelineno-24-7" href = "#__codelineno-24-7" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > avl_tree.ts< / span > < pre > < span > < / span > < code > < a id = "__codelineno-25-1" name = "__codelineno-25-1" href = "#__codelineno-25-1" > < / a > < span class = "cm" > /* 获取平衡因子 */< / span >
< a id = "__codelineno-25-2" name = "__codelineno-25-2" href = "#__codelineno-25-2" > < / a > < span class = "nx" > balanceFactor< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > TreeNode< / 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-25-3" name = "__codelineno-25-3" href = "#__codelineno-25-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 空结点平衡因子为 0< / span >
< a id = "__codelineno-25-4" name = "__codelineno-25-4" href = "#__codelineno-25-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "w" > < / span > < span class = "o" > ===< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "mf" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-25-5" name = "__codelineno-25-5" href = "#__codelineno-25-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 结点平衡因子 = 左子树高度 - 右子树高度< / span >
< a id = "__codelineno-25-6" name = "__codelineno-25-6" href = "#__codelineno-25-6" > < / 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" > height< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > left< / 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" > height< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > right< / span > < span class = "p" > );< / span >
< a id = "__codelineno-25-7" name = "__codelineno-25-7" href = "#__codelineno-25-7" > < / 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" > avl_tree.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" > aVLTree< / 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" > balanceFactor< / span > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > avl_tree.cs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-27-1" name = "__codelineno-27-1" href = "#__codelineno-27-1" > < / a > < span class = "cm" > /* 获取平衡因子 */< / span >
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< 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" > balanceFactor< / span > < span class = "p" > (< / span > < span class = "n" > TreeNode< / span > < span class = "o" > ?< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > )< / span >
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< 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 = "c1" > // 空结点平衡因子为 0< / span >
< a id = "__codelineno-27-5" name = "__codelineno-27-5" href = "#__codelineno-27-5" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "k" > null< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "m" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-27-6" name = "__codelineno-27-6" href = "#__codelineno-27-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 结点平衡因子 = 左子树高度 - 右子树高度< / span >
< a id = "__codelineno-27-7" name = "__codelineno-27-7" href = "#__codelineno-27-7" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nf" > height< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "n" > left< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "n" > height< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "n" > right< / span > < span class = "p" > );< / span >
< a id = "__codelineno-27-8" name = "__codelineno-27-8" href = "#__codelineno-27-8" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > avl_tree.swift< / span > < pre > < span > < / span > < code > < a id = "__codelineno-28-1" name = "__codelineno-28-1" href = "#__codelineno-28-1" > < / a > < span class = "cm" > /* 获取平衡因子 */< / span >
< a id = "__codelineno-28-2" name = "__codelineno-28-2" href = "#__codelineno-28-2" > < / a > < span class = "kd" > func< / span > < span class = "nf" > balanceFactor< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > :< / span > < span class = "n" > TreeNode< / 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 = "c1" > // 空结点平衡因子为 0< / span >
< a id = "__codelineno-28-4" name = "__codelineno-28-4" href = "#__codelineno-28-4" > < / a > < span class = "k" > guard< / span > < span class = "kd" > let< / span > < span class = "nv" > node< / span > < span class = "p" > =< / span > < span class = "n" > node< / span > < span class = "k" > else< / span > < span class = "p" > {< / span > < span class = "k" > return< / span > < span class = "mi" > 0< / span > < span class = "p" > }< / span >
< a id = "__codelineno-28-5" name = "__codelineno-28-5" href = "#__codelineno-28-5" > < / a > < span class = "c1" > // 结点平衡因子 = 左子树高度 - 右子树高度< / span >
< a id = "__codelineno-28-6" name = "__codelineno-28-6" href = "#__codelineno-28-6" > < / a > < span class = "k" > return< / span > < span class = "n" > height< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > :< / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "kr" > left< / span > < span class = "p" > )< / span > < span class = "o" > -< / span > < span class = "n" > height< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > :< / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "kr" > right< / span > < span class = "p" > )< / span >
< a id = "__codelineno-28-7" name = "__codelineno-28-7" href = "#__codelineno-28-7" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > avl_tree.zig< / span > < pre > < span > < / span > < code > < a id = "__codelineno-29-1" name = "__codelineno-29-1" href = "#__codelineno-29-1" > < / a > < span class = "c1" > // 获取平衡因子< / 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" > balanceFactor< / 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" > node< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "o" > ?*< / span > < span class = "n" > inc< / span > < span class = "p" > .< / span > < span class = "n" > TreeNode< / span > < span class = "p" > (< / span > < span class = "n" > T< / span > < span class = "p" > ))< / span > < span class = "w" > < / span > < span class = "kt" > i32< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-29-3" name = "__codelineno-29-3" href = "#__codelineno-29-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 空结点平衡因子为 0< / span >
< a id = "__codelineno-29-4" name = "__codelineno-29-4" href = "#__codelineno-29-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-29-5" name = "__codelineno-29-5" href = "#__codelineno-29-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 结点平衡因子 = 左子树高度 - 右子树高度< / span >
< a id = "__codelineno-29-6" name = "__codelineno-29-6" href = "#__codelineno-29-6" > < / 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" > height< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "o" > ?< / span > < span class = "p" > .< / span > < span class = "n" > left< / 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" > height< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "o" > ?< / span > < span class = "p" > .< / span > < span class = "n" > right< / span > < span class = "p" > );< / span >
< a id = "__codelineno-29-7" name = "__codelineno-29-7" href = "#__codelineno-29-7" > < / a > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
< / div >
< / div >
< div class = "admonition note" >
< p class = "admonition-title" > Note< / p >
< p > 设平衡因子为 < span class = "arithmatex" > \(f\)< / span > ，则一棵 AVL 树的任意结点的平衡因子皆满足 < span class = "arithmatex" > \(-1 \le f \le 1\)< / span > 。< / p >
< / div >
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< h2 id = "742-avl" > 7.4.2. AVL 树旋转< a class = "headerlink" href = "#742-avl" title = "Permanent link" > ¶ < / a > < / h2 >
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< p > AVL 树的独特之处在于「旋转 Rotation」的操作， < strong > 在不影响二叉树中序遍历序列的前提下，使失衡结点重新恢复平衡< / strong > 。换言之，旋转操作既可以使树保持为「二叉搜索树」，也可以使树重新恢复为「平衡二叉树」。< / p >
< p > 我们将平衡因子的绝对值 < span class = "arithmatex" > \(> 1\)< / span > 的结点称为「失衡结点」。根据结点的失衡情况，旋转操作分为 < strong > 右旋、左旋、先右旋后左旋、先左旋后右旋< / strong > ，接下来我们来一起来看看它们是如何操作的。< / p >
< h3 id = "case-1-" > Case 1 - 右旋< a class = "headerlink" href = "#case-1-" title = "Permanent link" > ¶ < / a > < / h3 >
< p > 如下图所示（结点下方为「平衡因子」），从底至顶看，二叉树中首个失衡结点是 < strong > 结点 3< / strong > 。我们聚焦在以该失衡结点为根结点的子树上，将该结点记为 < code > node< / code > ，将其左子结点记为 < code > child< / code > ，执行「右旋」操作。完成右旋后，该子树已经恢复平衡，并且仍然为二叉搜索树。< / p >
2023-02-22 00:57:11 +08:00
< div class = "tabbed-set tabbed-alternate" data-tabs = "4:4" > < 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" / > < 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 > < / div >
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< div class = "tabbed-content" >
< div class = "tabbed-block" >
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< p > < img alt = "右旋操作步骤" src = "../avl_tree.assets/avltree_right_rotate_step1.png" / > < / p >
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< / div >
< div class = "tabbed-block" >
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< p > < img alt = "avltree_right_rotate_step2" src = "../avl_tree.assets/avltree_right_rotate_step2.png" / > < / p >
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< / div >
< div class = "tabbed-block" >
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< p > < img alt = "avltree_right_rotate_step3" src = "../avl_tree.assets/avltree_right_rotate_step3.png" / > < / p >
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< / div >
< div class = "tabbed-block" >
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< p > < img alt = "avltree_right_rotate_step4" src = "../avl_tree.assets/avltree_right_rotate_step4.png" / > < / p >
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< / div >
< / div >
< / div >
< p > 进而，如果结点 < code > child< / code > 本身有右子结点（记为 < code > grandChild< / code > ），则需要在「右旋」中添加一步：将 < code > grandChild< / code > 作为 < code > node< / code > 的左子结点。< / p >
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< p > < img alt = "有 grandChild 的右旋操作" src = "../avl_tree.assets/avltree_right_rotate_with_grandchild.png" / > < / p >
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< p align = "center" > Fig. 有 grandChild 的右旋操作 < / p >
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< p > “向右旋转”是一种形象化的说法，实际需要通过修改结点指针实现，代码如下所示。< / 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" > avl_tree.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-30-1" name = "__codelineno-30-1" href = "#__codelineno-30-1" > < / a > < span class = "cm" > /* 右旋操作 */< / span >
< a id = "__codelineno-30-2" name = "__codelineno-30-2" href = "#__codelineno-30-2" > < / a > < span class = "n" > TreeNode< / span > < span class = "w" > < / span > < span class = "nf" > rightRotate< / span > < span class = "p" > (< / span > < span class = "n" > TreeNode< / span > < span class = "w" > < / span > < span class = "n" > node< / 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 = "n" > TreeNode< / span > < span class = "w" > < / span > < span class = "n" > child< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "na" > left< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-30-4" name = "__codelineno-30-4" href = "#__codelineno-30-4" > < / a > < span class = "w" > < / span > < span class = "n" > TreeNode< / span > < span class = "w" > < / span > < span class = "n" > grandChild< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > child< / span > < span class = "p" > .< / span > < span class = "na" > right< / 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" > // 以 child 为原点，将 node 向右旋转< / span >
< a id = "__codelineno-30-6" name = "__codelineno-30-6" href = "#__codelineno-30-6" > < / a > < span class = "w" > < / span > < span class = "n" > child< / span > < span class = "p" > .< / span > < span class = "na" > right< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-30-7" name = "__codelineno-30-7" href = "#__codelineno-30-7" > < / a > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "na" > left< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > grandChild< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-30-8" name = "__codelineno-30-8" href = "#__codelineno-30-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 更新结点高度< / span >
< a id = "__codelineno-30-9" name = "__codelineno-30-9" href = "#__codelineno-30-9" > < / a > < span class = "w" > < / span > < span class = "n" > updateHeight< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > );< / span >
< a id = "__codelineno-30-10" name = "__codelineno-30-10" href = "#__codelineno-30-10" > < / a > < span class = "w" > < / span > < span class = "n" > updateHeight< / span > < span class = "p" > (< / span > < span class = "n" > child< / 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 = "c1" > // 返回旋转后子树的根结点< / span >
< a id = "__codelineno-30-12" name = "__codelineno-30-12" href = "#__codelineno-30-12" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > child< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-30-13" name = "__codelineno-30-13" href = "#__codelineno-30-13" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > avl_tree.cpp< / span > < pre > < span > < / span > < code > < a id = "__codelineno-31-1" name = "__codelineno-31-1" href = "#__codelineno-31-1" > < / a > < span class = "cm" > /* 右旋操作 */< / span >
< a id = "__codelineno-31-2" name = "__codelineno-31-2" href = "#__codelineno-31-2" > < / a > < span class = "n" > TreeNode< / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "nf" > rightRotate< / span > < span class = "p" > (< / span > < span class = "n" > TreeNode< / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "n" > node< / 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 = "n" > TreeNode< / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "n" > child< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "o" > -> < / span > < span class = "n" > left< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-31-4" name = "__codelineno-31-4" href = "#__codelineno-31-4" > < / a > < span class = "w" > < / span > < span class = "n" > TreeNode< / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "n" > grandChild< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > child< / span > < span class = "o" > -> < / span > < span class = "n" > right< / 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" > // 以 child 为原点，将 node 向右旋转< / span >
< a id = "__codelineno-31-6" name = "__codelineno-31-6" href = "#__codelineno-31-6" > < / a > < span class = "w" > < / span > < span class = "n" > child< / span > < span class = "o" > -> < / span > < span class = "n" > right< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-31-7" name = "__codelineno-31-7" href = "#__codelineno-31-7" > < / a > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "o" > -> < / span > < span class = "n" > left< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > grandChild< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-31-8" name = "__codelineno-31-8" href = "#__codelineno-31-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 更新结点高度< / span >
< a id = "__codelineno-31-9" name = "__codelineno-31-9" href = "#__codelineno-31-9" > < / a > < span class = "w" > < / span > < span class = "n" > updateHeight< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > );< / span >
< a id = "__codelineno-31-10" name = "__codelineno-31-10" href = "#__codelineno-31-10" > < / a > < span class = "w" > < / span > < span class = "n" > updateHeight< / span > < span class = "p" > (< / span > < span class = "n" > child< / 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 = "c1" > // 返回旋转后子树的根结点< / span >
< a id = "__codelineno-31-12" name = "__codelineno-31-12" href = "#__codelineno-31-12" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > child< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-31-13" name = "__codelineno-31-13" href = "#__codelineno-31-13" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > avl_tree.py< / span > < pre > < span > < / span > < code > < a id = "__codelineno-32-1" name = "__codelineno-32-1" href = "#__codelineno-32-1" > < / a > < span class = "sd" > " " " 右旋操作 " " " < / span >
< a id = "__codelineno-32-2" name = "__codelineno-32-2" href = "#__codelineno-32-2" > < / a > < span class = "k" > def< / span > < span class = "nf" > __right_rotate< / span > < span class = "p" > (< / span > < span class = "bp" > self< / span > < span class = "p" > ,< / span > < span class = "n" > node< / span > < span class = "p" > :< / span > < span class = "n" > Optional< / span > < span class = "p" > [< / span > < span class = "n" > TreeNode< / span > < span class = "p" > ])< / span > < span class = "o" > -> < / span > < span class = "n" > TreeNode< / span > < span class = "p" > :< / span >
< a id = "__codelineno-32-3" name = "__codelineno-32-3" href = "#__codelineno-32-3" > < / a > < span class = "n" > child< / span > < span class = "o" > =< / span > < span class = "n" > node< / span > < span class = "o" > .< / span > < span class = "n" > left< / span >
< a id = "__codelineno-32-4" name = "__codelineno-32-4" href = "#__codelineno-32-4" > < / a > < span class = "n" > grand_child< / span > < span class = "o" > =< / span > < span class = "n" > child< / span > < span class = "o" > .< / span > < span class = "n" > right< / span >
< a id = "__codelineno-32-5" name = "__codelineno-32-5" href = "#__codelineno-32-5" > < / a > < span class = "c1" > # 以 child 为原点，将 node 向右旋转< / span >
< a id = "__codelineno-32-6" name = "__codelineno-32-6" href = "#__codelineno-32-6" > < / a > < span class = "n" > child< / span > < span class = "o" > .< / span > < span class = "n" > right< / span > < span class = "o" > =< / span > < span class = "n" > node< / span >
< a id = "__codelineno-32-7" name = "__codelineno-32-7" href = "#__codelineno-32-7" > < / a > < span class = "n" > node< / span > < span class = "o" > .< / span > < span class = "n" > left< / span > < span class = "o" > =< / span > < span class = "n" > grand_child< / span >
< a id = "__codelineno-32-8" name = "__codelineno-32-8" href = "#__codelineno-32-8" > < / a > < span class = "c1" > # 更新结点高度< / span >
< a id = "__codelineno-32-9" name = "__codelineno-32-9" href = "#__codelineno-32-9" > < / a > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > __update_height< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > )< / span >
< a id = "__codelineno-32-10" name = "__codelineno-32-10" href = "#__codelineno-32-10" > < / a > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > __update_height< / span > < span class = "p" > (< / span > < span class = "n" > child< / span > < span class = "p" > )< / span >
< a id = "__codelineno-32-11" name = "__codelineno-32-11" href = "#__codelineno-32-11" > < / a > < span class = "c1" > # 返回旋转后子树的根结点< / span >
< a id = "__codelineno-32-12" name = "__codelineno-32-12" href = "#__codelineno-32-12" > < / a > < span class = "k" > return< / span > < span class = "n" > child< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > avl_tree.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-33-1" name = "__codelineno-33-1" href = "#__codelineno-33-1" > < / a > < span class = "cm" > /* 右旋操作 */< / span >
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< 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" > t< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > aVLTree< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "nx" > rightRotate< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > TreeNode< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > TreeNode< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
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< a id = "__codelineno-33-3" name = "__codelineno-33-3" href = "#__codelineno-33-3" > < / a > < span class = "w" > < / span > < span class = "nx" > child< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > Left< / span >
< a id = "__codelineno-33-4" name = "__codelineno-33-4" href = "#__codelineno-33-4" > < / a > < span class = "w" > < / span > < span class = "nx" > grandChild< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nx" > child< / span > < span class = "p" > .< / span > < span class = "nx" > Right< / span >
< a id = "__codelineno-33-5" name = "__codelineno-33-5" href = "#__codelineno-33-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 以 child 为原点，将 node 向右旋转< / span >
< a id = "__codelineno-33-6" name = "__codelineno-33-6" href = "#__codelineno-33-6" > < / a > < span class = "w" > < / span > < span class = "nx" > child< / span > < span class = "p" > .< / span > < span class = "nx" > Right< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "nx" > node< / span >
< a id = "__codelineno-33-7" name = "__codelineno-33-7" href = "#__codelineno-33-7" > < / a > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > Left< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "nx" > grandChild< / span >
< a id = "__codelineno-33-8" name = "__codelineno-33-8" href = "#__codelineno-33-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 更新结点高度< / span >
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< a id = "__codelineno-33-9" name = "__codelineno-33-9" href = "#__codelineno-33-9" > < / a > < span class = "w" > < / span > < span class = "nx" > t< / span > < span class = "p" > .< / span > < span class = "nx" > updateHeight< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > )< / span >
< a id = "__codelineno-33-10" name = "__codelineno-33-10" href = "#__codelineno-33-10" > < / a > < span class = "w" > < / span > < span class = "nx" > t< / span > < span class = "p" > .< / span > < span class = "nx" > updateHeight< / span > < span class = "p" > (< / span > < span class = "nx" > child< / span > < span class = "p" > )< / span >
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< a id = "__codelineno-33-11" name = "__codelineno-33-11" href = "#__codelineno-33-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 返回旋转后子树的根结点< / span >
< a id = "__codelineno-33-12" name = "__codelineno-33-12" href = "#__codelineno-33-12" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > child< / span >
< a id = "__codelineno-33-13" name = "__codelineno-33-13" href = "#__codelineno-33-13" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > avl_tree.js< / span > < pre > < span > < / span > < code > < a id = "__codelineno-34-1" name = "__codelineno-34-1" href = "#__codelineno-34-1" > < / a > < span class = "cm" > /* 右旋操作 */< / span >
< a id = "__codelineno-34-2" name = "__codelineno-34-2" href = "#__codelineno-34-2" > < / a > < span class = "nx" > rightRotate< / span > < span class = "p" > (< / span > < span class = "nx" > node< / 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 = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > child< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > left< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-34-4" name = "__codelineno-34-4" href = "#__codelineno-34-4" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > grandChild< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > child< / span > < span class = "p" > .< / span > < span class = "nx" > right< / 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" > // 以 child 为原点，将 node 向右旋转< / span >
< a id = "__codelineno-34-6" name = "__codelineno-34-6" href = "#__codelineno-34-6" > < / a > < span class = "w" > < / span > < span class = "nx" > child< / span > < span class = "p" > .< / span > < span class = "nx" > right< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-34-7" name = "__codelineno-34-7" href = "#__codelineno-34-7" > < / a > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > left< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > grandChild< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-34-8" name = "__codelineno-34-8" href = "#__codelineno-34-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 更新结点高度< / span >
< a id = "__codelineno-34-9" name = "__codelineno-34-9" href = "#__codelineno-34-9" > < / a > < span class = "w" > < / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "nx" > updateHeight< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > );< / span >
< a id = "__codelineno-34-10" name = "__codelineno-34-10" href = "#__codelineno-34-10" > < / a > < span class = "w" > < / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "nx" > updateHeight< / span > < span class = "p" > (< / span > < span class = "nx" > child< / 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 = "c1" > // 返回旋转后子树的根结点< / span >
< a id = "__codelineno-34-12" name = "__codelineno-34-12" href = "#__codelineno-34-12" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > child< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-34-13" name = "__codelineno-34-13" href = "#__codelineno-34-13" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > avl_tree.ts< / span > < pre > < span > < / span > < code > < a id = "__codelineno-35-1" name = "__codelineno-35-1" href = "#__codelineno-35-1" > < / a > < span class = "cm" > /* 右旋操作 */< / span >
< a id = "__codelineno-35-2" name = "__codelineno-35-2" href = "#__codelineno-35-2" > < / a > < span class = "nx" > rightRotate< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > TreeNode< / span > < span class = "p" > )< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "nx" > TreeNode< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-35-3" name = "__codelineno-35-3" href = "#__codelineno-35-3" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > child< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > left< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-35-4" name = "__codelineno-35-4" href = "#__codelineno-35-4" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > grandChild< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > child< / span > < span class = "p" > .< / span > < span class = "nx" > right< / 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" > // 以 child 为原点，将 node 向右旋转< / span >
< a id = "__codelineno-35-6" name = "__codelineno-35-6" href = "#__codelineno-35-6" > < / a > < span class = "w" > < / span > < span class = "nx" > child< / span > < span class = "p" > .< / span > < span class = "nx" > right< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-35-7" name = "__codelineno-35-7" href = "#__codelineno-35-7" > < / a > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > left< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > grandChild< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-35-8" name = "__codelineno-35-8" href = "#__codelineno-35-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 更新结点高度< / span >
< a id = "__codelineno-35-9" name = "__codelineno-35-9" href = "#__codelineno-35-9" > < / a > < span class = "w" > < / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "nx" > updateHeight< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > );< / span >
< a id = "__codelineno-35-10" name = "__codelineno-35-10" href = "#__codelineno-35-10" > < / a > < span class = "w" > < / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "nx" > updateHeight< / span > < span class = "p" > (< / span > < span class = "nx" > child< / span > < span class = "p" > );< / span >
< a id = "__codelineno-35-11" name = "__codelineno-35-11" href = "#__codelineno-35-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 返回旋转后子树的根结点< / span >
< a id = "__codelineno-35-12" name = "__codelineno-35-12" href = "#__codelineno-35-12" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > child< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-35-13" name = "__codelineno-35-13" href = "#__codelineno-35-13" > < / 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" > avl_tree.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" > aVLTree< / 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" > rightRotate< / 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" > avl_tree.cs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-37-1" name = "__codelineno-37-1" href = "#__codelineno-37-1" > < / a > < span class = "cm" > /* 右旋操作 */< / span >
< a id = "__codelineno-37-2" name = "__codelineno-37-2" href = "#__codelineno-37-2" > < / a > < span class = "n" > TreeNode< / span > < span class = "o" > ?< / span > < span class = "w" > < / span > < span class = "n" > rightRotate< / span > < span class = "p" > (< / span > < span class = "n" > TreeNode< / span > < span class = "o" > ?< / span > < span class = "w" > < / span > < span class = "n" > node< / 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 = "n" > TreeNode< / span > < span class = "o" > ?< / span > < span class = "w" > < / span > < span class = "n" > child< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "n" > left< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-37-5" name = "__codelineno-37-5" href = "#__codelineno-37-5" > < / a > < span class = "w" > < / span > < span class = "n" > TreeNode< / span > < span class = "o" > ?< / span > < span class = "w" > < / span > < span class = "n" > grandChild< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > child< / span > < span class = "o" > ?.< / span > < span class = "n" > right< / 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" > // 以 child 为原点，将 node 向右旋转< / span >
< a id = "__codelineno-37-7" name = "__codelineno-37-7" href = "#__codelineno-37-7" > < / a > < span class = "w" > < / span > < span class = "n" > child< / span > < span class = "p" > .< / span > < span class = "n" > right< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-37-8" name = "__codelineno-37-8" href = "#__codelineno-37-8" > < / a > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "n" > left< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > grandChild< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-37-9" name = "__codelineno-37-9" href = "#__codelineno-37-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 更新结点高度< / span >
< a id = "__codelineno-37-10" name = "__codelineno-37-10" href = "#__codelineno-37-10" > < / a > < span class = "w" > < / span > < span class = "n" > updateHeight< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > );< / span >
< a id = "__codelineno-37-11" name = "__codelineno-37-11" href = "#__codelineno-37-11" > < / a > < span class = "w" > < / span > < span class = "n" > updateHeight< / span > < span class = "p" > (< / span > < span class = "n" > child< / span > < span class = "p" > );< / span >
< a id = "__codelineno-37-12" name = "__codelineno-37-12" href = "#__codelineno-37-12" > < / a > < span class = "w" > < / span > < span class = "c1" > // 返回旋转后子树的根结点< / span >
< a id = "__codelineno-37-13" name = "__codelineno-37-13" href = "#__codelineno-37-13" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > child< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-37-14" name = "__codelineno-37-14" href = "#__codelineno-37-14" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > avl_tree.swift< / span > < pre > < span > < / span > < code > < a id = "__codelineno-38-1" name = "__codelineno-38-1" href = "#__codelineno-38-1" > < / a > < span class = "cm" > /* 右旋操作 */< / span >
< a id = "__codelineno-38-2" name = "__codelineno-38-2" href = "#__codelineno-38-2" > < / a > < span class = "kd" > func< / span > < span class = "nf" > rightRotate< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > :< / span > < span class = "n" > TreeNode< / span > < span class = "p" > ?)< / span > < span class = "p" > -> < / span > < span class = "n" > TreeNode< / 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 = "kd" > let< / span > < span class = "nv" > child< / span > < span class = "p" > =< / span > < span class = "n" > node< / span > < span class = "p" > ?.< / span > < span class = "kr" > left< / span >
< a id = "__codelineno-38-4" name = "__codelineno-38-4" href = "#__codelineno-38-4" > < / a > < span class = "kd" > let< / span > < span class = "nv" > grandChild< / span > < span class = "p" > =< / span > < span class = "n" > child< / span > < span class = "p" > ?.< / span > < span class = "kr" > right< / span >
< a id = "__codelineno-38-5" name = "__codelineno-38-5" href = "#__codelineno-38-5" > < / a > < span class = "c1" > // 以 child 为原点，将 node 向右旋转< / span >
< a id = "__codelineno-38-6" name = "__codelineno-38-6" href = "#__codelineno-38-6" > < / a > < span class = "n" > child< / span > < span class = "p" > ?.< / span > < span class = "kr" > right< / span > < span class = "p" > =< / span > < span class = "n" > node< / span >
< a id = "__codelineno-38-7" name = "__codelineno-38-7" href = "#__codelineno-38-7" > < / a > < span class = "n" > node< / span > < span class = "p" > ?.< / span > < span class = "kr" > left< / span > < span class = "p" > =< / span > < span class = "n" > grandChild< / span >
< a id = "__codelineno-38-8" name = "__codelineno-38-8" href = "#__codelineno-38-8" > < / a > < span class = "c1" > // 更新结点高度< / span >
< a id = "__codelineno-38-9" name = "__codelineno-38-9" href = "#__codelineno-38-9" > < / a > < span class = "n" > updateHeight< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > :< / span > < span class = "n" > node< / span > < span class = "p" > )< / span >
< a id = "__codelineno-38-10" name = "__codelineno-38-10" href = "#__codelineno-38-10" > < / a > < span class = "n" > updateHeight< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > :< / span > < span class = "n" > child< / span > < span class = "p" > )< / span >
< a id = "__codelineno-38-11" name = "__codelineno-38-11" href = "#__codelineno-38-11" > < / a > < span class = "c1" > // 返回旋转后子树的根结点< / span >
< a id = "__codelineno-38-12" name = "__codelineno-38-12" href = "#__codelineno-38-12" > < / a > < span class = "k" > return< / span > < span class = "n" > child< / span >
< a id = "__codelineno-38-13" name = "__codelineno-38-13" href = "#__codelineno-38-13" > < / 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" > avl_tree.zig< / span > < pre > < span > < / span > < code > < a id = "__codelineno-39-1" name = "__codelineno-39-1" href = "#__codelineno-39-1" > < / a > < span class = "c1" > // 右旋操作< / 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" > rightRotate< / 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" > node< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "o" > ?*< / span > < span class = "n" > inc< / span > < span class = "p" > .< / span > < span class = "n" > TreeNode< / span > < span class = "p" > (< / span > < span class = "n" > T< / span > < span class = "p" > ))< / span > < span class = "w" > < / span > < span class = "o" > ?*< / span > < span class = "n" > inc< / span > < span class = "p" > .< / span > < span class = "n" > TreeNode< / span > < span class = "p" > (< / span > < span class = "n" > T< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-39-3" name = "__codelineno-39-3" href = "#__codelineno-39-3" > < / a > < span class = "w" > < / span > < span class = "kr" > var< / span > < span class = "w" > < / span > < span class = "n" > child< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "o" > ?< / span > < span class = "p" > .< / span > < span class = "n" > left< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-39-4" name = "__codelineno-39-4" href = "#__codelineno-39-4" > < / a > < span class = "w" > < / span > < span class = "kr" > var< / span > < span class = "w" > < / span > < span class = "n" > grandChild< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > child< / span > < span class = "p" > .< / span > < span class = "o" > ?< / span > < span class = "p" > .< / span > < span class = "n" > right< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-39-5" name = "__codelineno-39-5" href = "#__codelineno-39-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 以 child 为原点，将 node 向右旋转< / span >
< a id = "__codelineno-39-6" name = "__codelineno-39-6" href = "#__codelineno-39-6" > < / a > < span class = "w" > < / span > < span class = "n" > child< / span > < span class = "p" > .< / span > < span class = "o" > ?< / span > < span class = "p" > .< / span > < span class = "n" > right< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-39-7" name = "__codelineno-39-7" href = "#__codelineno-39-7" > < / a > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "o" > ?< / span > < span class = "p" > .< / span > < span class = "n" > left< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > grandChild< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-39-8" name = "__codelineno-39-8" href = "#__codelineno-39-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 更新结点高度< / span >
< a id = "__codelineno-39-9" name = "__codelineno-39-9" href = "#__codelineno-39-9" > < / a > < span class = "w" > < / span > < span class = "n" > self< / span > < span class = "p" > .< / span > < span class = "n" > updateHeight< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > );< / span >
< a id = "__codelineno-39-10" name = "__codelineno-39-10" href = "#__codelineno-39-10" > < / a > < span class = "w" > < / span > < span class = "n" > self< / span > < span class = "p" > .< / span > < span class = "n" > updateHeight< / span > < span class = "p" > (< / span > < span class = "n" > child< / 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 = "c1" > // 返回旋转后子树的根结点< / span >
< a id = "__codelineno-39-12" name = "__codelineno-39-12" href = "#__codelineno-39-12" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > child< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-39-13" name = "__codelineno-39-13" href = "#__codelineno-39-13" > < / a > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
< / div >
< / div >
< h3 id = "case-2-" > Case 2 - 左旋< a class = "headerlink" href = "#case-2-" title = "Permanent link" > ¶ < / a > < / h3 >
< p > 类似地，如果将取上述失衡二叉树的“镜像”，那么则需要「左旋」操作。< / p >
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< p > < img alt = "左旋操作" src = "../avl_tree.assets/avltree_left_rotate.png" / > < / p >
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< p align = "center" > Fig. 左旋操作 < / p >
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< p > 同理，若结点 < code > child< / code > 本身有左子结点（记为 < code > grandChild< / code > ），则需要在「左旋」中添加一步：将 < code > grandChild< / code > 作为 < code > node< / code > 的右子结点。< / p >
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< p > < img alt = "有 grandChild 的左旋操作" src = "../avl_tree.assets/avltree_left_rotate_with_grandchild.png" / > < / p >
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< p align = "center" > Fig. 有 grandChild 的左旋操作 < / p >
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< p > 观察发现，< strong > 「左旋」和「右旋」操作是镜像对称的，两者对应解决的两种失衡情况也是对称的< / strong > 。根据对称性，我们可以很方便地从「右旋」推导出「左旋」。具体地，只需将「右旋」代码中的把所有的 < code > left< / code > 替换为 < code > right< / code > 、所有的 < code > right< / code > 替换为 < code > left< / code > ，即可得到「左旋」代码。< / p >
< div class = "tabbed-set tabbed-alternate" data-tabs = "6:10" > < input checked = "checked" id = "__tabbed_6_1" name = "__tabbed_6" type = "radio" / > < input id = "__tabbed_6_2" name = "__tabbed_6" type = "radio" / > < input id = "__tabbed_6_3" name = "__tabbed_6" type = "radio" / > < input id = "__tabbed_6_4" name = "__tabbed_6" type = "radio" / > < input id = "__tabbed_6_5" name = "__tabbed_6" type = "radio" / > < input id = "__tabbed_6_6" name = "__tabbed_6" type = "radio" / > < input id = "__tabbed_6_7" name = "__tabbed_6" type = "radio" / > < input id = "__tabbed_6_8" name = "__tabbed_6" type = "radio" / > < input id = "__tabbed_6_9" name = "__tabbed_6" type = "radio" / > < input id = "__tabbed_6_10" name = "__tabbed_6" type = "radio" / > < div class = "tabbed-labels" > < label for = "__tabbed_6_1" > Java< / label > < label for = "__tabbed_6_2" > C++< / label > < label for = "__tabbed_6_3" > Python< / label > < label for = "__tabbed_6_4" > Go< / label > < label for = "__tabbed_6_5" > JavaScript< / label > < label for = "__tabbed_6_6" > TypeScript< / label > < label for = "__tabbed_6_7" > C< / label > < label for = "__tabbed_6_8" > C#< / label > < label for = "__tabbed_6_9" > Swift< / label > < label for = "__tabbed_6_10" > Zig< / label > < / div >
< div class = "tabbed-content" >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > avl_tree.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-40-1" name = "__codelineno-40-1" href = "#__codelineno-40-1" > < / a > < span class = "cm" > /* 左旋操作 */< / span >
< a id = "__codelineno-40-2" name = "__codelineno-40-2" href = "#__codelineno-40-2" > < / a > < span class = "n" > TreeNode< / span > < span class = "w" > < / span > < span class = "nf" > leftRotate< / span > < span class = "p" > (< / span > < span class = "n" > TreeNode< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-40-3" name = "__codelineno-40-3" href = "#__codelineno-40-3" > < / a > < span class = "w" > < / span > < span class = "n" > TreeNode< / span > < span class = "w" > < / span > < span class = "n" > child< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "na" > right< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-40-4" name = "__codelineno-40-4" href = "#__codelineno-40-4" > < / a > < span class = "w" > < / span > < span class = "n" > TreeNode< / span > < span class = "w" > < / span > < span class = "n" > grandChild< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > child< / span > < span class = "p" > .< / span > < span class = "na" > left< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-40-5" name = "__codelineno-40-5" href = "#__codelineno-40-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 以 child 为原点，将 node 向左旋转< / span >
< a id = "__codelineno-40-6" name = "__codelineno-40-6" href = "#__codelineno-40-6" > < / a > < span class = "w" > < / span > < span class = "n" > child< / span > < span class = "p" > .< / span > < span class = "na" > left< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-40-7" name = "__codelineno-40-7" href = "#__codelineno-40-7" > < / a > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "na" > right< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > grandChild< / 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" > // 更新结点高度< / span >
< a id = "__codelineno-40-9" name = "__codelineno-40-9" href = "#__codelineno-40-9" > < / a > < span class = "w" > < / span > < span class = "n" > updateHeight< / span > < span class = "p" > (< / span > < span class = "n" > node< / 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 = "n" > updateHeight< / span > < span class = "p" > (< / span > < span class = "n" > child< / span > < span class = "p" > );< / span >
< a id = "__codelineno-40-11" name = "__codelineno-40-11" href = "#__codelineno-40-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 返回旋转后子树的根结点< / span >
< a id = "__codelineno-40-12" name = "__codelineno-40-12" href = "#__codelineno-40-12" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > child< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-40-13" name = "__codelineno-40-13" href = "#__codelineno-40-13" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > avl_tree.cpp< / span > < pre > < span > < / span > < code > < a id = "__codelineno-41-1" name = "__codelineno-41-1" href = "#__codelineno-41-1" > < / a > < span class = "cm" > /* 左旋操作 */< / span >
< a id = "__codelineno-41-2" name = "__codelineno-41-2" href = "#__codelineno-41-2" > < / a > < span class = "n" > TreeNode< / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "nf" > leftRotate< / span > < span class = "p" > (< / span > < span class = "n" > TreeNode< / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-41-3" name = "__codelineno-41-3" href = "#__codelineno-41-3" > < / a > < span class = "w" > < / span > < span class = "n" > TreeNode< / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "n" > child< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "o" > -> < / span > < span class = "n" > right< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-41-4" name = "__codelineno-41-4" href = "#__codelineno-41-4" > < / a > < span class = "w" > < / span > < span class = "n" > TreeNode< / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "n" > grandChild< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > child< / span > < span class = "o" > -> < / span > < span class = "n" > left< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-41-5" name = "__codelineno-41-5" href = "#__codelineno-41-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 以 child 为原点，将 node 向左旋转< / span >
< a id = "__codelineno-41-6" name = "__codelineno-41-6" href = "#__codelineno-41-6" > < / a > < span class = "w" > < / span > < span class = "n" > child< / span > < span class = "o" > -> < / span > < span class = "n" > left< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > node< / 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 = "n" > node< / span > < span class = "o" > -> < / span > < span class = "n" > right< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > grandChild< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-41-8" name = "__codelineno-41-8" href = "#__codelineno-41-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 更新结点高度< / span >
< a id = "__codelineno-41-9" name = "__codelineno-41-9" href = "#__codelineno-41-9" > < / a > < span class = "w" > < / span > < span class = "n" > updateHeight< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > );< / span >
< a id = "__codelineno-41-10" name = "__codelineno-41-10" href = "#__codelineno-41-10" > < / a > < span class = "w" > < / span > < span class = "n" > updateHeight< / span > < span class = "p" > (< / span > < span class = "n" > child< / 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" > // 返回旋转后子树的根结点< / span >
< a id = "__codelineno-41-12" name = "__codelineno-41-12" href = "#__codelineno-41-12" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > child< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-41-13" name = "__codelineno-41-13" href = "#__codelineno-41-13" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > avl_tree.py< / span > < pre > < span > < / span > < code > < a id = "__codelineno-42-1" name = "__codelineno-42-1" href = "#__codelineno-42-1" > < / a > < span class = "sd" > " " " 左旋操作 " " " < / span >
< a id = "__codelineno-42-2" name = "__codelineno-42-2" href = "#__codelineno-42-2" > < / a > < span class = "k" > def< / span > < span class = "nf" > __left_rotate< / span > < span class = "p" > (< / span > < span class = "bp" > self< / span > < span class = "p" > ,< / span > < span class = "n" > node< / span > < span class = "p" > :< / span > < span class = "n" > Optional< / span > < span class = "p" > [< / span > < span class = "n" > TreeNode< / span > < span class = "p" > ])< / span > < span class = "o" > -> < / span > < span class = "n" > TreeNode< / span > < span class = "p" > :< / span >
< a id = "__codelineno-42-3" name = "__codelineno-42-3" href = "#__codelineno-42-3" > < / a > < span class = "n" > child< / span > < span class = "o" > =< / span > < span class = "n" > node< / span > < span class = "o" > .< / span > < span class = "n" > right< / span >
< a id = "__codelineno-42-4" name = "__codelineno-42-4" href = "#__codelineno-42-4" > < / a > < span class = "n" > grand_child< / span > < span class = "o" > =< / span > < span class = "n" > child< / span > < span class = "o" > .< / span > < span class = "n" > left< / span >
< a id = "__codelineno-42-5" name = "__codelineno-42-5" href = "#__codelineno-42-5" > < / a > < span class = "c1" > # 以 child 为原点，将 node 向左旋转< / span >
< a id = "__codelineno-42-6" name = "__codelineno-42-6" href = "#__codelineno-42-6" > < / a > < span class = "n" > child< / span > < span class = "o" > .< / span > < span class = "n" > left< / span > < span class = "o" > =< / span > < span class = "n" > node< / span >
< a id = "__codelineno-42-7" name = "__codelineno-42-7" href = "#__codelineno-42-7" > < / a > < span class = "n" > node< / span > < span class = "o" > .< / span > < span class = "n" > right< / span > < span class = "o" > =< / span > < span class = "n" > grand_child< / span >
< a id = "__codelineno-42-8" name = "__codelineno-42-8" href = "#__codelineno-42-8" > < / a > < span class = "c1" > # 更新结点高度< / span >
< a id = "__codelineno-42-9" name = "__codelineno-42-9" href = "#__codelineno-42-9" > < / a > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > __update_height< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > )< / 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" > __update_height< / span > < span class = "p" > (< / span > < span class = "n" > child< / span > < span class = "p" > )< / span >
< a id = "__codelineno-42-11" name = "__codelineno-42-11" href = "#__codelineno-42-11" > < / a > < span class = "c1" > # 返回旋转后子树的根结点< / span >
< a id = "__codelineno-42-12" name = "__codelineno-42-12" href = "#__codelineno-42-12" > < / a > < span class = "k" > return< / span > < span class = "n" > child< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > avl_tree.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-43-1" name = "__codelineno-43-1" href = "#__codelineno-43-1" > < / a > < span class = "cm" > /* 左旋操作 */< / 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" > t< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > aVLTree< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "nx" > leftRotate< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > TreeNode< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > TreeNode< / 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 = "nx" > child< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > Right< / span >
< a id = "__codelineno-43-4" name = "__codelineno-43-4" href = "#__codelineno-43-4" > < / a > < span class = "w" > < / span > < span class = "nx" > grandChild< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nx" > child< / span > < span class = "p" > .< / span > < span class = "nx" > Left< / span >
< a id = "__codelineno-43-5" name = "__codelineno-43-5" href = "#__codelineno-43-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 以 child 为原点，将 node 向左旋转< / span >
< a id = "__codelineno-43-6" name = "__codelineno-43-6" href = "#__codelineno-43-6" > < / a > < span class = "w" > < / span > < span class = "nx" > child< / span > < span class = "p" > .< / span > < span class = "nx" > Left< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "nx" > node< / span >
< a id = "__codelineno-43-7" name = "__codelineno-43-7" href = "#__codelineno-43-7" > < / a > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > Right< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "nx" > grandChild< / span >
< a id = "__codelineno-43-8" name = "__codelineno-43-8" href = "#__codelineno-43-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 更新结点高度< / span >
2023-02-09 04:43:20 +08:00
< a id = "__codelineno-43-9" name = "__codelineno-43-9" href = "#__codelineno-43-9" > < / a > < span class = "w" > < / span > < span class = "nx" > t< / span > < span class = "p" > .< / span > < span class = "nx" > updateHeight< / span > < span class = "p" > (< / span > < span class = "nx" > node< / 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 = "nx" > t< / span > < span class = "p" > .< / span > < span class = "nx" > updateHeight< / span > < span class = "p" > (< / span > < span class = "nx" > child< / span > < span class = "p" > )< / span >
2023-02-08 14:54:41 +08:00
< a id = "__codelineno-43-11" name = "__codelineno-43-11" href = "#__codelineno-43-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 返回旋转后子树的根结点< / span >
< a id = "__codelineno-43-12" name = "__codelineno-43-12" href = "#__codelineno-43-12" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > child< / span >
< a id = "__codelineno-43-13" name = "__codelineno-43-13" href = "#__codelineno-43-13" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > avl_tree.js< / span > < pre > < span > < / span > < code > < a id = "__codelineno-44-1" name = "__codelineno-44-1" href = "#__codelineno-44-1" > < / a > < span class = "cm" > /* 左旋操作 */< / span >
< a id = "__codelineno-44-2" name = "__codelineno-44-2" href = "#__codelineno-44-2" > < / a > < span class = "nx" > leftRotate< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-44-3" name = "__codelineno-44-3" href = "#__codelineno-44-3" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > child< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > right< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-44-4" name = "__codelineno-44-4" href = "#__codelineno-44-4" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > grandChild< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > child< / span > < span class = "p" > .< / span > < span class = "nx" > left< / 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" > // 以 child 为原点，将 node 向左旋转< / span >
< a id = "__codelineno-44-6" name = "__codelineno-44-6" href = "#__codelineno-44-6" > < / a > < span class = "w" > < / span > < span class = "nx" > child< / span > < span class = "p" > .< / span > < span class = "nx" > left< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > node< / 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 = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > right< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > grandChild< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-44-8" name = "__codelineno-44-8" href = "#__codelineno-44-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 更新结点高度< / span >
< a id = "__codelineno-44-9" name = "__codelineno-44-9" href = "#__codelineno-44-9" > < / a > < span class = "w" > < / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "nx" > updateHeight< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > );< / span >
< a id = "__codelineno-44-10" name = "__codelineno-44-10" href = "#__codelineno-44-10" > < / a > < span class = "w" > < / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "nx" > updateHeight< / span > < span class = "p" > (< / span > < span class = "nx" > child< / 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" > // 返回旋转后子树的根结点< / 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" > child< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-44-13" name = "__codelineno-44-13" href = "#__codelineno-44-13" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > avl_tree.ts< / span > < pre > < span > < / span > < code > < a id = "__codelineno-45-1" name = "__codelineno-45-1" href = "#__codelineno-45-1" > < / a > < span class = "cm" > /* 左旋操作 */< / span >
< a id = "__codelineno-45-2" name = "__codelineno-45-2" href = "#__codelineno-45-2" > < / a > < span class = "nx" > leftRotate< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > TreeNode< / span > < span class = "p" > )< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "nx" > TreeNode< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-45-3" name = "__codelineno-45-3" href = "#__codelineno-45-3" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > child< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > right< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-45-4" name = "__codelineno-45-4" href = "#__codelineno-45-4" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > grandChild< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > child< / span > < span class = "p" > .< / span > < span class = "nx" > left< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-45-5" name = "__codelineno-45-5" href = "#__codelineno-45-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 以 child 为原点，将 node 向左旋转< / span >
< a id = "__codelineno-45-6" name = "__codelineno-45-6" href = "#__codelineno-45-6" > < / a > < span class = "w" > < / span > < span class = "nx" > child< / span > < span class = "p" > .< / span > < span class = "nx" > left< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > node< / 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 = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > right< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > grandChild< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-45-8" name = "__codelineno-45-8" href = "#__codelineno-45-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 更新结点高度< / span >
< a id = "__codelineno-45-9" name = "__codelineno-45-9" href = "#__codelineno-45-9" > < / a > < span class = "w" > < / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "nx" > updateHeight< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > );< / 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" > updateHeight< / span > < span class = "p" > (< / span > < span class = "nx" > child< / 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" > // 返回旋转后子树的根结点< / 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" > child< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-45-13" name = "__codelineno-45-13" href = "#__codelineno-45-13" > < / 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" > avl_tree.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" > aVLTree< / 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" > leftRotate< / 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" > avl_tree.cs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-47-1" name = "__codelineno-47-1" href = "#__codelineno-47-1" > < / a > < span class = "cm" > /* 左旋操作 */< / span >
< a id = "__codelineno-47-2" name = "__codelineno-47-2" href = "#__codelineno-47-2" > < / a > < span class = "n" > TreeNode< / span > < span class = "o" > ?< / span > < span class = "w" > < / span > < span class = "n" > leftRotate< / span > < span class = "p" > (< / span > < span class = "n" > TreeNode< / span > < span class = "o" > ?< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > )< / span >
< 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 = "n" > TreeNode< / span > < span class = "o" > ?< / span > < span class = "w" > < / span > < span class = "n" > child< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "n" > right< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-47-5" name = "__codelineno-47-5" href = "#__codelineno-47-5" > < / a > < span class = "w" > < / span > < span class = "n" > TreeNode< / span > < span class = "o" > ?< / span > < span class = "w" > < / span > < span class = "n" > grandChild< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > child< / span > < span class = "o" > ?.< / span > < span class = "n" > left< / 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 = "c1" > // 以 child 为原点，将 node 向左旋转< / span >
< a id = "__codelineno-47-7" name = "__codelineno-47-7" href = "#__codelineno-47-7" > < / a > < span class = "w" > < / span > < span class = "n" > child< / span > < span class = "p" > .< / span > < span class = "n" > left< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-47-8" name = "__codelineno-47-8" href = "#__codelineno-47-8" > < / a > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "n" > right< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > grandChild< / 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" > // 更新结点高度< / span >
< a id = "__codelineno-47-10" name = "__codelineno-47-10" href = "#__codelineno-47-10" > < / a > < span class = "w" > < / span > < span class = "n" > updateHeight< / span > < span class = "p" > (< / span > < span class = "n" > node< / 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" > updateHeight< / span > < span class = "p" > (< / span > < span class = "n" > child< / 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" > // 返回旋转后子树的根结点< / span >
< a id = "__codelineno-47-13" name = "__codelineno-47-13" href = "#__codelineno-47-13" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > child< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-47-14" name = "__codelineno-47-14" href = "#__codelineno-47-14" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > avl_tree.swift< / span > < pre > < span > < / span > < code > < a id = "__codelineno-48-1" name = "__codelineno-48-1" href = "#__codelineno-48-1" > < / a > < span class = "cm" > /* 左旋操作 */< / span >
< a id = "__codelineno-48-2" name = "__codelineno-48-2" href = "#__codelineno-48-2" > < / a > < span class = "kd" > func< / span > < span class = "nf" > leftRotate< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > :< / span > < span class = "n" > TreeNode< / span > < span class = "p" > ?)< / span > < span class = "p" > -> < / span > < span class = "n" > TreeNode< / span > < span class = "p" > ?< / span > < span class = "p" > {< / span >
< a id = "__codelineno-48-3" name = "__codelineno-48-3" href = "#__codelineno-48-3" > < / a > < span class = "kd" > let< / span > < span class = "nv" > child< / span > < span class = "p" > =< / span > < span class = "n" > node< / span > < span class = "p" > ?.< / span > < span class = "kr" > right< / span >
< a id = "__codelineno-48-4" name = "__codelineno-48-4" href = "#__codelineno-48-4" > < / a > < span class = "kd" > let< / span > < span class = "nv" > grandChild< / span > < span class = "p" > =< / span > < span class = "n" > child< / span > < span class = "p" > ?.< / span > < span class = "kr" > left< / span >
< a id = "__codelineno-48-5" name = "__codelineno-48-5" href = "#__codelineno-48-5" > < / a > < span class = "c1" > // 以 child 为原点，将 node 向左旋转< / span >
< a id = "__codelineno-48-6" name = "__codelineno-48-6" href = "#__codelineno-48-6" > < / a > < span class = "n" > child< / span > < span class = "p" > ?.< / span > < span class = "kr" > left< / span > < span class = "p" > =< / span > < span class = "n" > node< / span >
< a id = "__codelineno-48-7" name = "__codelineno-48-7" href = "#__codelineno-48-7" > < / a > < span class = "n" > node< / span > < span class = "p" > ?.< / span > < span class = "kr" > right< / span > < span class = "p" > =< / span > < span class = "n" > grandChild< / span >
< a id = "__codelineno-48-8" name = "__codelineno-48-8" href = "#__codelineno-48-8" > < / a > < span class = "c1" > // 更新结点高度< / span >
< a id = "__codelineno-48-9" name = "__codelineno-48-9" href = "#__codelineno-48-9" > < / a > < span class = "n" > updateHeight< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > :< / span > < span class = "n" > node< / span > < span class = "p" > )< / span >
< a id = "__codelineno-48-10" name = "__codelineno-48-10" href = "#__codelineno-48-10" > < / a > < span class = "n" > updateHeight< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > :< / span > < span class = "n" > child< / span > < span class = "p" > )< / span >
< a id = "__codelineno-48-11" name = "__codelineno-48-11" href = "#__codelineno-48-11" > < / a > < span class = "c1" > // 返回旋转后子树的根结点< / span >
< a id = "__codelineno-48-12" name = "__codelineno-48-12" href = "#__codelineno-48-12" > < / a > < span class = "k" > return< / span > < span class = "n" > child< / span >
< a id = "__codelineno-48-13" name = "__codelineno-48-13" href = "#__codelineno-48-13" > < / 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" > avl_tree.zig< / span > < pre > < span > < / span > < code > < a id = "__codelineno-49-1" name = "__codelineno-49-1" href = "#__codelineno-49-1" > < / a > < span class = "c1" > // 左旋操作< / span >
< 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" > leftRotate< / 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" > node< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "o" > ?*< / span > < span class = "n" > inc< / span > < span class = "p" > .< / span > < span class = "n" > TreeNode< / span > < span class = "p" > (< / span > < span class = "n" > T< / span > < span class = "p" > ))< / span > < span class = "w" > < / span > < span class = "o" > ?*< / span > < span class = "n" > inc< / span > < span class = "p" > .< / span > < span class = "n" > TreeNode< / span > < span class = "p" > (< / span > < span class = "n" > T< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-49-3" name = "__codelineno-49-3" href = "#__codelineno-49-3" > < / a > < span class = "w" > < / span > < span class = "kr" > var< / span > < span class = "w" > < / span > < span class = "n" > child< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "o" > ?< / span > < span class = "p" > .< / span > < span class = "n" > right< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-49-4" name = "__codelineno-49-4" href = "#__codelineno-49-4" > < / a > < span class = "w" > < / span > < span class = "kr" > var< / span > < span class = "w" > < / span > < span class = "n" > grandChild< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > child< / span > < span class = "p" > .< / span > < span class = "o" > ?< / span > < span class = "p" > .< / span > < span class = "n" > left< / 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" > // 以 child 为原点，将 node 向左旋转< / span >
< a id = "__codelineno-49-6" name = "__codelineno-49-6" href = "#__codelineno-49-6" > < / a > < span class = "w" > < / span > < span class = "n" > child< / span > < span class = "p" > .< / span > < span class = "o" > ?< / span > < span class = "p" > .< / span > < span class = "n" > left< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > node< / 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 = "n" > node< / span > < span class = "p" > .< / span > < span class = "o" > ?< / span > < span class = "p" > .< / span > < span class = "n" > right< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > grandChild< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-49-8" name = "__codelineno-49-8" href = "#__codelineno-49-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 更新结点高度< / span >
< a id = "__codelineno-49-9" name = "__codelineno-49-9" href = "#__codelineno-49-9" > < / a > < span class = "w" > < / span > < span class = "n" > self< / span > < span class = "p" > .< / span > < span class = "n" > updateHeight< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > );< / span >
< a id = "__codelineno-49-10" name = "__codelineno-49-10" href = "#__codelineno-49-10" > < / a > < span class = "w" > < / span > < span class = "n" > self< / span > < span class = "p" > .< / span > < span class = "n" > updateHeight< / span > < span class = "p" > (< / span > < span class = "n" > child< / 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" > // 返回旋转后子树的根结点< / 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" > child< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-49-13" name = "__codelineno-49-13" href = "#__codelineno-49-13" > < / a > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
< / div >
< / div >
< h3 id = "case-3-" > Case 3 - 先左后右< a class = "headerlink" href = "#case-3-" title = "Permanent link" > ¶ < / a > < / h3 >
< p > 对于下图的失衡结点 3 ， < strong > 单一使用左旋或右旋都无法使子树恢复平衡< / strong > ，此时需要「先左旋后右旋」，即先对 < code > child< / code > 执行「左旋」，再对 < code > node< / code > 执行「右旋」。< / p >
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< p > < img alt = "先左旋后右旋" src = "../avl_tree.assets/avltree_left_right_rotate.png" / > < / p >
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< p align = "center" > Fig. 先左旋后右旋 < / p >
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< h3 id = "case-4-" > Case 4 - 先右后左< a class = "headerlink" href = "#case-4-" title = "Permanent link" > ¶ < / a > < / h3 >
< p > 同理，取以上失衡二叉树的镜像，则需要「先右旋后左旋」，即先对 < code > child< / code > 执行「右旋」，然后对 < code > node< / code > 执行「左旋」。< / p >
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< p > < img alt = "先右旋后左旋" src = "../avl_tree.assets/avltree_right_left_rotate.png" / > < / p >
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< p align = "center" > Fig. 先右旋后左旋 < / p >
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< h3 id = "_3" > 旋转的选择< a class = "headerlink" href = "#_3" title = "Permanent link" > ¶ < / a > < / h3 >
< p > 下图描述的四种失衡情况与上述 Cases 逐个对应，分别需采用 < strong > 右旋、左旋、先右后左、先左后右< / strong > 的旋转操作。< / p >
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< p > < img alt = "AVL 树的四种旋转情况" src = "../avl_tree.assets/avltree_rotation_cases.png" / > < / p >
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< p align = "center" > Fig. AVL 树的四种旋转情况 < / p >
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< p > 具体地，在代码中使用 < strong > 失衡结点的平衡因子、较高一侧子结点的平衡因子< / strong > 来确定失衡结点属于上图中的哪种情况。< / p >
< div class = "center-table" >
< table >
< thead >
< tr >
< th > 失衡结点的平衡因子< / th >
< th > 子结点的平衡因子< / th >
< th > 应采用的旋转方法< / th >
< / tr >
< / thead >
< tbody >
< tr >
< td > < span class = "arithmatex" > \(> 0\)< / span > （即左偏树）< / td >
< td > < span class = "arithmatex" > \(\geq 0\)< / span > < / td >
< td > 右旋< / td >
< / tr >
< tr >
< td > < span class = "arithmatex" > \(> 0\)< / span > （即左偏树）< / td >
< td > < span class = "arithmatex" > \(< 0\)< / span > < / td >
< td > 先左旋后右旋< / td >
< / tr >
< tr >
< td > < span class = "arithmatex" > \(< 0\)< / span > （即右偏树）< / td >
< td > < span class = "arithmatex" > \(\leq 0\)< / span > < / td >
< td > 左旋< / td >
< / tr >
< tr >
< td > < span class = "arithmatex" > \(< 0\)< / span > （即右偏树）< / td >
< td > < span class = "arithmatex" > \(> 0\)< / span > < / td >
< td > 先右旋后左旋< / td >
< / tr >
< / tbody >
< / table >
< / div >
< p > 为方便使用，我们将旋转操作封装成一个函数。至此，< strong > 我们可以使用此函数来旋转各种失衡情况，使失衡结点重新恢复平衡< / 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" > avl_tree.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-50-1" name = "__codelineno-50-1" href = "#__codelineno-50-1" > < / a > < span class = "cm" > /* 执行旋转操作，使该子树重新恢复平衡 */< / span >
< a id = "__codelineno-50-2" name = "__codelineno-50-2" href = "#__codelineno-50-2" > < / a > < span class = "n" > TreeNode< / span > < span class = "w" > < / span > < span class = "nf" > rotate< / span > < span class = "p" > (< / span > < span class = "n" > TreeNode< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-50-3" name = "__codelineno-50-3" href = "#__codelineno-50-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 获取结点 node 的平衡因子< / span >
< a id = "__codelineno-50-4" name = "__codelineno-50-4" href = "#__codelineno-50-4" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > balanceFactor< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > balanceFactor< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > );< / span >
< a id = "__codelineno-50-5" name = "__codelineno-50-5" href = "#__codelineno-50-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 左偏树< / span >
< a id = "__codelineno-50-6" name = "__codelineno-50-6" href = "#__codelineno-50-6" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > balanceFactor< / 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 = "p" > {< / span >
< a id = "__codelineno-50-7" name = "__codelineno-50-7" href = "#__codelineno-50-7" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > balanceFactor< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "na" > left< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-50-8" name = "__codelineno-50-8" href = "#__codelineno-50-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 右旋< / span >
< a id = "__codelineno-50-9" name = "__codelineno-50-9" href = "#__codelineno-50-9" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > rightRotate< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > );< / span >
< a id = "__codelineno-50-10" name = "__codelineno-50-10" href = "#__codelineno-50-10" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-50-11" name = "__codelineno-50-11" href = "#__codelineno-50-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 先左旋后右旋< / span >
< a id = "__codelineno-50-12" name = "__codelineno-50-12" href = "#__codelineno-50-12" > < / a > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "na" > left< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > leftRotate< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "na" > left< / span > < span class = "p" > );< / span >
< a id = "__codelineno-50-13" name = "__codelineno-50-13" href = "#__codelineno-50-13" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > rightRotate< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > );< / span >
< a id = "__codelineno-50-14" name = "__codelineno-50-14" href = "#__codelineno-50-14" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-50-15" name = "__codelineno-50-15" href = "#__codelineno-50-15" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-50-16" name = "__codelineno-50-16" href = "#__codelineno-50-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // 右偏树< / span >
< a id = "__codelineno-50-17" name = "__codelineno-50-17" href = "#__codelineno-50-17" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > balanceFactor< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-50-18" name = "__codelineno-50-18" href = "#__codelineno-50-18" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > balanceFactor< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "na" > right< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-50-19" name = "__codelineno-50-19" href = "#__codelineno-50-19" > < / a > < span class = "w" > < / span > < span class = "c1" > // 左旋< / span >
< a id = "__codelineno-50-20" name = "__codelineno-50-20" href = "#__codelineno-50-20" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > leftRotate< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > );< / span >
< a id = "__codelineno-50-21" name = "__codelineno-50-21" href = "#__codelineno-50-21" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-50-22" name = "__codelineno-50-22" href = "#__codelineno-50-22" > < / a > < span class = "w" > < / span > < span class = "c1" > // 先右旋后左旋< / span >
< a id = "__codelineno-50-23" name = "__codelineno-50-23" href = "#__codelineno-50-23" > < / a > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "na" > right< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > rightRotate< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "na" > right< / span > < span class = "p" > );< / span >
< a id = "__codelineno-50-24" name = "__codelineno-50-24" href = "#__codelineno-50-24" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > leftRotate< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > );< / span >
< a id = "__codelineno-50-25" name = "__codelineno-50-25" href = "#__codelineno-50-25" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-50-26" name = "__codelineno-50-26" href = "#__codelineno-50-26" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-50-27" name = "__codelineno-50-27" href = "#__codelineno-50-27" > < / a > < span class = "w" > < / span > < span class = "c1" > // 平衡树，无需旋转，直接返回< / span >
< a id = "__codelineno-50-28" name = "__codelineno-50-28" href = "#__codelineno-50-28" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-50-29" name = "__codelineno-50-29" href = "#__codelineno-50-29" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > avl_tree.cpp< / span > < pre > < span > < / span > < code > < a id = "__codelineno-51-1" name = "__codelineno-51-1" href = "#__codelineno-51-1" > < / a > < span class = "cm" > /* 执行旋转操作，使该子树重新恢复平衡 */< / span >
< a id = "__codelineno-51-2" name = "__codelineno-51-2" href = "#__codelineno-51-2" > < / a > < span class = "n" > TreeNode< / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "nf" > rotate< / span > < span class = "p" > (< / span > < span class = "n" > TreeNode< / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-51-3" name = "__codelineno-51-3" href = "#__codelineno-51-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 获取结点 node 的平衡因子< / span >
< a id = "__codelineno-51-4" name = "__codelineno-51-4" href = "#__codelineno-51-4" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > _balanceFactor< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > balanceFactor< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > );< / span >
< a id = "__codelineno-51-5" name = "__codelineno-51-5" href = "#__codelineno-51-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 左偏树< / span >
< a id = "__codelineno-51-6" name = "__codelineno-51-6" href = "#__codelineno-51-6" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > _balanceFactor< / 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 = "p" > {< / span >
< a id = "__codelineno-51-7" name = "__codelineno-51-7" href = "#__codelineno-51-7" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > balanceFactor< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "o" > -> < / span > < span class = "n" > left< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-51-8" name = "__codelineno-51-8" href = "#__codelineno-51-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 右旋< / span >
< a id = "__codelineno-51-9" name = "__codelineno-51-9" href = "#__codelineno-51-9" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > rightRotate< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > );< / span >
< a id = "__codelineno-51-10" name = "__codelineno-51-10" href = "#__codelineno-51-10" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-51-11" name = "__codelineno-51-11" href = "#__codelineno-51-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 先左旋后右旋< / span >
< a id = "__codelineno-51-12" name = "__codelineno-51-12" href = "#__codelineno-51-12" > < / a > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "o" > -> < / span > < span class = "n" > left< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > leftRotate< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "o" > -> < / span > < span class = "n" > left< / span > < span class = "p" > );< / span >
< a id = "__codelineno-51-13" name = "__codelineno-51-13" href = "#__codelineno-51-13" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > rightRotate< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > );< / span >
< a id = "__codelineno-51-14" name = "__codelineno-51-14" href = "#__codelineno-51-14" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-51-15" name = "__codelineno-51-15" href = "#__codelineno-51-15" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-51-16" name = "__codelineno-51-16" href = "#__codelineno-51-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // 右偏树< / span >
< a id = "__codelineno-51-17" name = "__codelineno-51-17" href = "#__codelineno-51-17" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > _balanceFactor< / 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 = "p" > {< / span >
< a id = "__codelineno-51-18" name = "__codelineno-51-18" href = "#__codelineno-51-18" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > balanceFactor< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "o" > -> < / span > < span class = "n" > right< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-51-19" name = "__codelineno-51-19" href = "#__codelineno-51-19" > < / a > < span class = "w" > < / span > < span class = "c1" > // 左旋< / span >
< a id = "__codelineno-51-20" name = "__codelineno-51-20" href = "#__codelineno-51-20" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > leftRotate< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > );< / span >
< a id = "__codelineno-51-21" name = "__codelineno-51-21" href = "#__codelineno-51-21" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-51-22" name = "__codelineno-51-22" href = "#__codelineno-51-22" > < / a > < span class = "w" > < / span > < span class = "c1" > // 先右旋后左旋< / span >
< a id = "__codelineno-51-23" name = "__codelineno-51-23" href = "#__codelineno-51-23" > < / a > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "o" > -> < / span > < span class = "n" > right< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > rightRotate< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "o" > -> < / span > < span class = "n" > right< / span > < span class = "p" > );< / span >
< a id = "__codelineno-51-24" name = "__codelineno-51-24" href = "#__codelineno-51-24" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > leftRotate< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > );< / span >
< a id = "__codelineno-51-25" name = "__codelineno-51-25" href = "#__codelineno-51-25" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-51-26" name = "__codelineno-51-26" href = "#__codelineno-51-26" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-51-27" name = "__codelineno-51-27" href = "#__codelineno-51-27" > < / a > < span class = "w" > < / span > < span class = "c1" > // 平衡树，无需旋转，直接返回< / span >
< a id = "__codelineno-51-28" name = "__codelineno-51-28" href = "#__codelineno-51-28" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-51-29" name = "__codelineno-51-29" href = "#__codelineno-51-29" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > avl_tree.py< / span > < pre > < span > < / span > < code > < a id = "__codelineno-52-1" name = "__codelineno-52-1" href = "#__codelineno-52-1" > < / a > < span class = "sd" > " " " 执行旋转操作，使该子树重新恢复平衡 " " " < / span >
< a id = "__codelineno-52-2" name = "__codelineno-52-2" href = "#__codelineno-52-2" > < / a > < span class = "k" > def< / span > < span class = "nf" > __rotate< / span > < span class = "p" > (< / span > < span class = "bp" > self< / span > < span class = "p" > ,< / span > < span class = "n" > node< / span > < span class = "p" > :< / span > < span class = "n" > Optional< / span > < span class = "p" > [< / span > < span class = "n" > TreeNode< / span > < span class = "p" > ])< / span > < span class = "o" > -> < / span > < span class = "n" > TreeNode< / span > < span class = "p" > :< / span >
< a id = "__codelineno-52-3" name = "__codelineno-52-3" href = "#__codelineno-52-3" > < / a > < span class = "c1" > # 获取结点 node 的平衡因子< / span >
< a id = "__codelineno-52-4" name = "__codelineno-52-4" href = "#__codelineno-52-4" > < / a > < span class = "n" > balance_factor< / span > < span class = "o" > =< / span > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > balance_factor< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > )< / span >
< a id = "__codelineno-52-5" name = "__codelineno-52-5" href = "#__codelineno-52-5" > < / a > < span class = "c1" > # 左偏树< / span >
< a id = "__codelineno-52-6" name = "__codelineno-52-6" href = "#__codelineno-52-6" > < / a > < span class = "k" > if< / span > < span class = "n" > balance_factor< / span > < span class = "o" > > < / span > < span class = "mi" > 1< / span > < span class = "p" > :< / span >
< a id = "__codelineno-52-7" name = "__codelineno-52-7" href = "#__codelineno-52-7" > < / a > < span class = "k" > if< / span > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > balance_factor< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "o" > .< / span > < span class = "n" > left< / span > < span class = "p" > )< / span > < span class = "o" > > =< / span > < span class = "mi" > 0< / span > < span class = "p" > :< / span >
< a id = "__codelineno-52-8" name = "__codelineno-52-8" href = "#__codelineno-52-8" > < / a > < span class = "c1" > # 右旋< / span >
< a id = "__codelineno-52-9" name = "__codelineno-52-9" href = "#__codelineno-52-9" > < / a > < span class = "k" > return< / span > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > __right_rotate< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > )< / span >
< a id = "__codelineno-52-10" name = "__codelineno-52-10" href = "#__codelineno-52-10" > < / a > < span class = "k" > else< / span > < span class = "p" > :< / span >
< a id = "__codelineno-52-11" name = "__codelineno-52-11" href = "#__codelineno-52-11" > < / a > < span class = "c1" > # 先左旋后右旋< / span >
< a id = "__codelineno-52-12" name = "__codelineno-52-12" href = "#__codelineno-52-12" > < / a > < span class = "n" > node< / span > < span class = "o" > .< / span > < span class = "n" > left< / span > < span class = "o" > =< / span > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > __left_rotate< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "o" > .< / span > < span class = "n" > left< / span > < span class = "p" > )< / span >
< a id = "__codelineno-52-13" name = "__codelineno-52-13" href = "#__codelineno-52-13" > < / a > < span class = "k" > return< / span > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > __right_rotate< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > )< / span >
< a id = "__codelineno-52-14" name = "__codelineno-52-14" href = "#__codelineno-52-14" > < / a > < span class = "c1" > # 右偏树< / span >
< a id = "__codelineno-52-15" name = "__codelineno-52-15" href = "#__codelineno-52-15" > < / a > < span class = "k" > elif< / span > < span class = "n" > balance_factor< / span > < span class = "o" > < < / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > :< / span >
< a id = "__codelineno-52-16" name = "__codelineno-52-16" href = "#__codelineno-52-16" > < / a > < span class = "k" > if< / span > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > balance_factor< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "o" > .< / span > < span class = "n" > right< / span > < span class = "p" > )< / span > < span class = "o" > < =< / span > < span class = "mi" > 0< / span > < span class = "p" > :< / span >
< a id = "__codelineno-52-17" name = "__codelineno-52-17" href = "#__codelineno-52-17" > < / a > < span class = "c1" > # 左旋< / span >
< a id = "__codelineno-52-18" name = "__codelineno-52-18" href = "#__codelineno-52-18" > < / a > < span class = "k" > return< / span > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > __left_rotate< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > )< / span >
< a id = "__codelineno-52-19" name = "__codelineno-52-19" href = "#__codelineno-52-19" > < / a > < span class = "k" > else< / span > < span class = "p" > :< / span >
< a id = "__codelineno-52-20" name = "__codelineno-52-20" href = "#__codelineno-52-20" > < / a > < span class = "c1" > # 先右旋后左旋< / span >
< a id = "__codelineno-52-21" name = "__codelineno-52-21" href = "#__codelineno-52-21" > < / a > < span class = "n" > node< / span > < span class = "o" > .< / span > < span class = "n" > right< / span > < span class = "o" > =< / span > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > __right_rotate< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "o" > .< / span > < span class = "n" > right< / span > < span class = "p" > )< / span >
< a id = "__codelineno-52-22" name = "__codelineno-52-22" href = "#__codelineno-52-22" > < / a > < span class = "k" > return< / span > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > __left_rotate< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > )< / span >
< a id = "__codelineno-52-23" name = "__codelineno-52-23" href = "#__codelineno-52-23" > < / a > < span class = "c1" > # 平衡树，无需旋转，直接返回< / span >
< a id = "__codelineno-52-24" name = "__codelineno-52-24" href = "#__codelineno-52-24" > < / a > < span class = "k" > return< / span > < span class = "n" > node< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > avl_tree.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-53-1" name = "__codelineno-53-1" href = "#__codelineno-53-1" > < / a > < span class = "cm" > /* 执行旋转操作，使该子树重新恢复平衡 */< / span >
2023-02-09 04:43:20 +08:00
< a id = "__codelineno-53-2" name = "__codelineno-53-2" href = "#__codelineno-53-2" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > t< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > aVLTree< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "nx" > rotate< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > TreeNode< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > TreeNode< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
2023-02-08 14:54:41 +08:00
< a id = "__codelineno-53-3" name = "__codelineno-53-3" href = "#__codelineno-53-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 获取结点 node 的平衡因子< / span >
2023-02-09 04:43:20 +08:00
< a id = "__codelineno-53-4" name = "__codelineno-53-4" href = "#__codelineno-53-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // Go 推荐短变量，这里 bf 指代 t.balanceFactor< / span >
< a id = "__codelineno-53-5" name = "__codelineno-53-5" href = "#__codelineno-53-5" > < / a > < span class = "w" > < / span > < span class = "nx" > bf< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nx" > t< / span > < span class = "p" > .< / span > < span class = "nx" > balanceFactor< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > )< / span >
2023-02-08 14:54:41 +08:00
< a id = "__codelineno-53-6" name = "__codelineno-53-6" href = "#__codelineno-53-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 左偏树< / span >
< a id = "__codelineno-53-7" name = "__codelineno-53-7" href = "#__codelineno-53-7" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "nx" > bf< / span > < span class = "w" > < / span > < span class = "p" > > < / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
2023-02-09 04:43:20 +08:00
< a id = "__codelineno-53-8" name = "__codelineno-53-8" href = "#__codelineno-53-8" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "nx" > t< / span > < span class = "p" > .< / span > < span class = "nx" > balanceFactor< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > Left< / span > < span class = "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 = "p" > {< / span >
2023-02-08 14:54:41 +08:00
< a id = "__codelineno-53-9" name = "__codelineno-53-9" href = "#__codelineno-53-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 右旋< / span >
2023-02-09 04:43:20 +08:00
< a id = "__codelineno-53-10" name = "__codelineno-53-10" href = "#__codelineno-53-10" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > t< / span > < span class = "p" > .< / span > < span class = "nx" > rightRotate< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > )< / span >
2023-02-08 14:54:41 +08:00
< a id = "__codelineno-53-11" name = "__codelineno-53-11" href = "#__codelineno-53-11" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-53-12" name = "__codelineno-53-12" href = "#__codelineno-53-12" > < / a > < span class = "w" > < / span > < span class = "c1" > // 先左旋后右旋< / span >
2023-02-09 04:43:20 +08:00
< a id = "__codelineno-53-13" name = "__codelineno-53-13" href = "#__codelineno-53-13" > < / a > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > Left< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "nx" > t< / span > < span class = "p" > .< / span > < span class = "nx" > leftRotate< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > Left< / span > < span class = "p" > )< / span >
< a id = "__codelineno-53-14" name = "__codelineno-53-14" href = "#__codelineno-53-14" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > t< / span > < span class = "p" > .< / span > < span class = "nx" > rightRotate< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > )< / span >
2023-02-08 14:54:41 +08:00
< a id = "__codelineno-53-15" name = "__codelineno-53-15" href = "#__codelineno-53-15" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-53-16" name = "__codelineno-53-16" href = "#__codelineno-53-16" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-53-17" name = "__codelineno-53-17" href = "#__codelineno-53-17" > < / a > < span class = "w" > < / span > < span class = "c1" > // 右偏树< / span >
< a id = "__codelineno-53-18" name = "__codelineno-53-18" href = "#__codelineno-53-18" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "nx" > bf< / span > < span class = "w" > < / span > < span class = "p" > < < / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
2023-02-09 04:43:20 +08:00
< a id = "__codelineno-53-19" name = "__codelineno-53-19" href = "#__codelineno-53-19" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "nx" > t< / span > < span class = "p" > .< / span > < span class = "nx" > balanceFactor< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > Right< / span > < span class = "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 = "p" > {< / span >
2023-02-08 14:54:41 +08:00
< a id = "__codelineno-53-20" name = "__codelineno-53-20" href = "#__codelineno-53-20" > < / a > < span class = "w" > < / span > < span class = "c1" > // 左旋< / span >
2023-02-09 04:43:20 +08:00
< a id = "__codelineno-53-21" name = "__codelineno-53-21" href = "#__codelineno-53-21" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > t< / span > < span class = "p" > .< / span > < span class = "nx" > leftRotate< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > )< / span >
2023-02-08 14:54:41 +08:00
< a id = "__codelineno-53-22" name = "__codelineno-53-22" href = "#__codelineno-53-22" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-53-23" name = "__codelineno-53-23" href = "#__codelineno-53-23" > < / a > < span class = "w" > < / span > < span class = "c1" > // 先右旋后左旋< / span >
2023-02-09 04:43:20 +08:00
< a id = "__codelineno-53-24" name = "__codelineno-53-24" href = "#__codelineno-53-24" > < / a > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > Right< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "nx" > t< / span > < span class = "p" > .< / span > < span class = "nx" > rightRotate< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > Right< / span > < span class = "p" > )< / span >
< a id = "__codelineno-53-25" name = "__codelineno-53-25" href = "#__codelineno-53-25" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > t< / span > < span class = "p" > .< / span > < span class = "nx" > leftRotate< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > )< / span >
2023-02-08 14:54:41 +08:00
< a id = "__codelineno-53-26" name = "__codelineno-53-26" href = "#__codelineno-53-26" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-53-27" name = "__codelineno-53-27" href = "#__codelineno-53-27" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-53-28" name = "__codelineno-53-28" href = "#__codelineno-53-28" > < / a > < span class = "w" > < / span > < span class = "c1" > // 平衡树，无需旋转，直接返回< / span >
< a id = "__codelineno-53-29" name = "__codelineno-53-29" href = "#__codelineno-53-29" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > node< / span >
< a id = "__codelineno-53-30" name = "__codelineno-53-30" href = "#__codelineno-53-30" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > avl_tree.js< / span > < pre > < span > < / span > < code > < a id = "__codelineno-54-1" name = "__codelineno-54-1" href = "#__codelineno-54-1" > < / a > < span class = "cm" > /* 执行旋转操作，使该子树重新恢复平衡 */< / span >
< a id = "__codelineno-54-2" name = "__codelineno-54-2" href = "#__codelineno-54-2" > < / a > < span class = "nx" > rotate< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-54-3" name = "__codelineno-54-3" href = "#__codelineno-54-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 获取结点 node 的平衡因子< / span >
< a id = "__codelineno-54-4" name = "__codelineno-54-4" href = "#__codelineno-54-4" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > balanceFactor< / 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" > balanceFactor< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > );< / span >
< a id = "__codelineno-54-5" name = "__codelineno-54-5" href = "#__codelineno-54-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 左偏树< / span >
< a id = "__codelineno-54-6" name = "__codelineno-54-6" href = "#__codelineno-54-6" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > balanceFactor< / 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 = "p" > {< / span >
< a id = "__codelineno-54-7" name = "__codelineno-54-7" href = "#__codelineno-54-7" > < / 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" > balanceFactor< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > left< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > > =< / span > < span class = "w" > < / span > < span class = "mf" > 0< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-54-8" name = "__codelineno-54-8" href = "#__codelineno-54-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 右旋< / span >
< a id = "__codelineno-54-9" name = "__codelineno-54-9" href = "#__codelineno-54-9" > < / 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" > rightRotate< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > );< / span >
< a id = "__codelineno-54-10" name = "__codelineno-54-10" href = "#__codelineno-54-10" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-54-11" name = "__codelineno-54-11" href = "#__codelineno-54-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 先左旋后右旋< / span >
< a id = "__codelineno-54-12" name = "__codelineno-54-12" href = "#__codelineno-54-12" > < / a > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > left< / 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" > leftRotate< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > left< / span > < span class = "p" > );< / span >
< a id = "__codelineno-54-13" name = "__codelineno-54-13" href = "#__codelineno-54-13" > < / 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" > rightRotate< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > );< / span >
< a id = "__codelineno-54-14" name = "__codelineno-54-14" href = "#__codelineno-54-14" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-54-15" name = "__codelineno-54-15" href = "#__codelineno-54-15" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-54-16" name = "__codelineno-54-16" href = "#__codelineno-54-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // 右偏树< / span >
< a id = "__codelineno-54-17" name = "__codelineno-54-17" href = "#__codelineno-54-17" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > balanceFactor< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "mf" > 1< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-54-18" name = "__codelineno-54-18" href = "#__codelineno-54-18" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "nx" > balanceFactor< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > right< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "mf" > 0< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-54-19" name = "__codelineno-54-19" href = "#__codelineno-54-19" > < / a > < span class = "w" > < / span > < span class = "c1" > // 左旋< / span >
< a id = "__codelineno-54-20" name = "__codelineno-54-20" href = "#__codelineno-54-20" > < / 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" > leftRotate< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > );< / span >
< a id = "__codelineno-54-21" name = "__codelineno-54-21" href = "#__codelineno-54-21" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-54-22" name = "__codelineno-54-22" href = "#__codelineno-54-22" > < / a > < span class = "w" > < / span > < span class = "c1" > // 先右旋后左旋< / span >
< a id = "__codelineno-54-23" name = "__codelineno-54-23" href = "#__codelineno-54-23" > < / a > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > right< / 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" > rightRotate< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > right< / span > < span class = "p" > );< / span >
< a id = "__codelineno-54-24" name = "__codelineno-54-24" href = "#__codelineno-54-24" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "nx" > leftRotate< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > );< / span >
< a id = "__codelineno-54-25" name = "__codelineno-54-25" href = "#__codelineno-54-25" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-54-26" name = "__codelineno-54-26" href = "#__codelineno-54-26" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-54-27" name = "__codelineno-54-27" href = "#__codelineno-54-27" > < / a > < span class = "w" > < / span > < span class = "c1" > // 平衡树，无需旋转，直接返回< / span >
< a id = "__codelineno-54-28" name = "__codelineno-54-28" href = "#__codelineno-54-28" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-54-29" name = "__codelineno-54-29" href = "#__codelineno-54-29" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > avl_tree.ts< / span > < pre > < span > < / span > < code > < a id = "__codelineno-55-1" name = "__codelineno-55-1" href = "#__codelineno-55-1" > < / a > < span class = "cm" > /* 执行旋转操作，使该子树重新恢复平衡 */< / span >
< a id = "__codelineno-55-2" name = "__codelineno-55-2" href = "#__codelineno-55-2" > < / a > < span class = "nx" > rotate< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > TreeNode< / span > < span class = "p" > )< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "nx" > TreeNode< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-55-3" name = "__codelineno-55-3" href = "#__codelineno-55-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 获取结点 node 的平衡因子< / span >
< a id = "__codelineno-55-4" name = "__codelineno-55-4" href = "#__codelineno-55-4" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > balanceFactor< / 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" > balanceFactor< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > );< / span >
< a id = "__codelineno-55-5" name = "__codelineno-55-5" href = "#__codelineno-55-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 左偏树< / span >
< a id = "__codelineno-55-6" name = "__codelineno-55-6" href = "#__codelineno-55-6" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > balanceFactor< / 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 = "p" > {< / span >
< a id = "__codelineno-55-7" name = "__codelineno-55-7" href = "#__codelineno-55-7" > < / 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" > balanceFactor< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > left< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > > =< / span > < span class = "w" > < / span > < span class = "mf" > 0< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-55-8" name = "__codelineno-55-8" href = "#__codelineno-55-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 右旋< / span >
< a id = "__codelineno-55-9" name = "__codelineno-55-9" href = "#__codelineno-55-9" > < / 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" > rightRotate< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > );< / span >
< a id = "__codelineno-55-10" name = "__codelineno-55-10" href = "#__codelineno-55-10" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-55-11" name = "__codelineno-55-11" href = "#__codelineno-55-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 先左旋后右旋< / span >
< a id = "__codelineno-55-12" name = "__codelineno-55-12" href = "#__codelineno-55-12" > < / a > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > left< / 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" > leftRotate< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > left< / span > < span class = "p" > );< / span >
< a id = "__codelineno-55-13" name = "__codelineno-55-13" href = "#__codelineno-55-13" > < / 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" > rightRotate< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > );< / span >
< a id = "__codelineno-55-14" name = "__codelineno-55-14" href = "#__codelineno-55-14" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-55-15" name = "__codelineno-55-15" href = "#__codelineno-55-15" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-55-16" name = "__codelineno-55-16" href = "#__codelineno-55-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // 右偏树< / span >
< a id = "__codelineno-55-17" name = "__codelineno-55-17" href = "#__codelineno-55-17" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > balanceFactor< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "mf" > 1< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-55-18" name = "__codelineno-55-18" href = "#__codelineno-55-18" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "nx" > balanceFactor< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > right< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "mf" > 0< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-55-19" name = "__codelineno-55-19" href = "#__codelineno-55-19" > < / a > < span class = "w" > < / span > < span class = "c1" > // 左旋< / span >
< a id = "__codelineno-55-20" name = "__codelineno-55-20" href = "#__codelineno-55-20" > < / 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" > leftRotate< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > );< / span >
< a id = "__codelineno-55-21" name = "__codelineno-55-21" href = "#__codelineno-55-21" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-55-22" name = "__codelineno-55-22" href = "#__codelineno-55-22" > < / a > < span class = "w" > < / span > < span class = "c1" > // 先右旋后左旋< / span >
< a id = "__codelineno-55-23" name = "__codelineno-55-23" href = "#__codelineno-55-23" > < / a > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > right< / 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" > rightRotate< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > right< / span > < span class = "p" > );< / span >
< a id = "__codelineno-55-24" name = "__codelineno-55-24" href = "#__codelineno-55-24" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "nx" > leftRotate< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > );< / span >
< a id = "__codelineno-55-25" name = "__codelineno-55-25" href = "#__codelineno-55-25" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-55-26" name = "__codelineno-55-26" href = "#__codelineno-55-26" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-55-27" name = "__codelineno-55-27" href = "#__codelineno-55-27" > < / a > < span class = "w" > < / span > < span class = "c1" > // 平衡树，无需旋转，直接返回< / span >
< a id = "__codelineno-55-28" name = "__codelineno-55-28" href = "#__codelineno-55-28" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-55-29" name = "__codelineno-55-29" href = "#__codelineno-55-29" > < / 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" > avl_tree.c< / span > < pre > < span > < / span > < code > < a id = "__codelineno-56-1" name = "__codelineno-56-1" href = "#__codelineno-56-1" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{< / span > < span class = "n" > aVLTree< / 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" > rotate< / 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" > avl_tree.cs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-57-1" name = "__codelineno-57-1" href = "#__codelineno-57-1" > < / a > < span class = "cm" > /* 执行旋转操作，使该子树重新恢复平衡 */< / span >
< a id = "__codelineno-57-2" name = "__codelineno-57-2" href = "#__codelineno-57-2" > < / a > < span class = "n" > TreeNode< / span > < span class = "o" > ?< / span > < span class = "w" > < / span > < span class = "n" > rotate< / span > < span class = "p" > (< / span > < span class = "n" > TreeNode< / span > < span class = "o" > ?< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > )< / span >
< a id = "__codelineno-57-3" name = "__codelineno-57-3" href = "#__codelineno-57-3" > < / a > < span class = "p" > {< / span >
< a id = "__codelineno-57-4" name = "__codelineno-57-4" href = "#__codelineno-57-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 获取结点 node 的平衡因子< / span >
< a id = "__codelineno-57-5" name = "__codelineno-57-5" href = "#__codelineno-57-5" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > balanceFactorInt< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > balanceFactor< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > );< / span >
< a id = "__codelineno-57-6" name = "__codelineno-57-6" href = "#__codelineno-57-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 左偏树< / span >
< a id = "__codelineno-57-7" name = "__codelineno-57-7" href = "#__codelineno-57-7" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > balanceFactorInt< / 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-57-8" name = "__codelineno-57-8" href = "#__codelineno-57-8" > < / a > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-57-9" name = "__codelineno-57-9" href = "#__codelineno-57-9" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > balanceFactor< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "n" > left< / span > < span class = "p" > )< / 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-57-10" name = "__codelineno-57-10" href = "#__codelineno-57-10" > < / a > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-57-11" name = "__codelineno-57-11" href = "#__codelineno-57-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 右旋< / span >
< a id = "__codelineno-57-12" name = "__codelineno-57-12" href = "#__codelineno-57-12" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nf" > rightRotate< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > );< / span >
< a id = "__codelineno-57-13" name = "__codelineno-57-13" href = "#__codelineno-57-13" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-57-14" name = "__codelineno-57-14" href = "#__codelineno-57-14" > < / a > < span class = "w" > < / span > < span class = "k" > else< / span >
< a id = "__codelineno-57-15" name = "__codelineno-57-15" href = "#__codelineno-57-15" > < / a > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-57-16" name = "__codelineno-57-16" href = "#__codelineno-57-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // 先左旋后右旋< / span >
< a id = "__codelineno-57-17" name = "__codelineno-57-17" href = "#__codelineno-57-17" > < / a > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "n" > left< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > leftRotate< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "o" > ?.< / span > < span class = "n" > left< / span > < span class = "p" > );< / span >
< a id = "__codelineno-57-18" name = "__codelineno-57-18" href = "#__codelineno-57-18" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nf" > rightRotate< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > );< / span >
< a id = "__codelineno-57-19" name = "__codelineno-57-19" href = "#__codelineno-57-19" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-57-20" name = "__codelineno-57-20" href = "#__codelineno-57-20" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-57-21" name = "__codelineno-57-21" href = "#__codelineno-57-21" > < / a > < span class = "w" > < / span > < span class = "c1" > // 右偏树< / span >
< a id = "__codelineno-57-22" name = "__codelineno-57-22" href = "#__codelineno-57-22" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > balanceFactorInt< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "m" > 1< / span > < span class = "p" > )< / span >
< a id = "__codelineno-57-23" name = "__codelineno-57-23" href = "#__codelineno-57-23" > < / a > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-57-24" name = "__codelineno-57-24" href = "#__codelineno-57-24" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > balanceFactor< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "n" > right< / span > < span class = "p" > )< / 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-57-25" name = "__codelineno-57-25" href = "#__codelineno-57-25" > < / a > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-57-26" name = "__codelineno-57-26" href = "#__codelineno-57-26" > < / a > < span class = "w" > < / span > < span class = "c1" > // 左旋< / span >
< a id = "__codelineno-57-27" name = "__codelineno-57-27" href = "#__codelineno-57-27" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nf" > leftRotate< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > );< / span >
< a id = "__codelineno-57-28" name = "__codelineno-57-28" href = "#__codelineno-57-28" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-57-29" name = "__codelineno-57-29" href = "#__codelineno-57-29" > < / a > < span class = "w" > < / span > < span class = "k" > else< / span >
< a id = "__codelineno-57-30" name = "__codelineno-57-30" href = "#__codelineno-57-30" > < / a > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-57-31" name = "__codelineno-57-31" href = "#__codelineno-57-31" > < / a > < span class = "w" > < / span > < span class = "c1" > // 先右旋后左旋< / span >
< a id = "__codelineno-57-32" name = "__codelineno-57-32" href = "#__codelineno-57-32" > < / a > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "n" > right< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > rightRotate< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "o" > ?.< / span > < span class = "n" > right< / span > < span class = "p" > );< / span >
< a id = "__codelineno-57-33" name = "__codelineno-57-33" href = "#__codelineno-57-33" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nf" > leftRotate< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > );< / span >
< a id = "__codelineno-57-34" name = "__codelineno-57-34" href = "#__codelineno-57-34" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-57-35" name = "__codelineno-57-35" href = "#__codelineno-57-35" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-57-36" name = "__codelineno-57-36" href = "#__codelineno-57-36" > < / a > < span class = "w" > < / span > < span class = "c1" > // 平衡树，无需旋转，直接返回< / span >
< a id = "__codelineno-57-37" name = "__codelineno-57-37" href = "#__codelineno-57-37" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-57-38" name = "__codelineno-57-38" href = "#__codelineno-57-38" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > avl_tree.swift< / span > < pre > < span > < / span > < code > < a id = "__codelineno-58-1" name = "__codelineno-58-1" href = "#__codelineno-58-1" > < / a > < span class = "cm" > /* 执行旋转操作，使该子树重新恢复平衡 */< / span >
< a id = "__codelineno-58-2" name = "__codelineno-58-2" href = "#__codelineno-58-2" > < / a > < span class = "kd" > func< / span > < span class = "nf" > rotate< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > :< / span > < span class = "n" > TreeNode< / span > < span class = "p" > ?)< / span > < span class = "p" > -> < / span > < span class = "n" > TreeNode< / span > < span class = "p" > ?< / span > < span class = "p" > {< / span >
< a id = "__codelineno-58-3" name = "__codelineno-58-3" href = "#__codelineno-58-3" > < / a > < span class = "c1" > // 获取结点 node 的平衡因子< / span >
< a id = "__codelineno-58-4" name = "__codelineno-58-4" href = "#__codelineno-58-4" > < / a > < span class = "kd" > let< / span > < span class = "nv" > balanceFactor< / span > < span class = "p" > =< / span > < span class = "n" > balanceFactor< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > :< / span > < span class = "n" > node< / span > < span class = "p" > )< / span >
< a id = "__codelineno-58-5" name = "__codelineno-58-5" href = "#__codelineno-58-5" > < / a > < span class = "c1" > // 左偏树< / span >
< a id = "__codelineno-58-6" name = "__codelineno-58-6" href = "#__codelineno-58-6" > < / a > < span class = "k" > if< / span > < span class = "n" > balanceFactor< / span > < span class = "o" > > < / span > < span class = "mi" > 1< / span > < span class = "p" > {< / span >
< a id = "__codelineno-58-7" name = "__codelineno-58-7" href = "#__codelineno-58-7" > < / a > < span class = "k" > if< / span > < span class = "kc" > self< / span > < span class = "p" > .< / span > < span class = "n" > balanceFactor< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > :< / span > < span class = "n" > node< / span > < span class = "p" > ?.< / span > < span class = "kr" > left< / span > < span class = "p" > )< / span > < span class = "o" > > =< / span > < span class = "mi" > 0< / span > < span class = "p" > {< / span >
< a id = "__codelineno-58-8" name = "__codelineno-58-8" href = "#__codelineno-58-8" > < / a > < span class = "c1" > // 右旋< / span >
< a id = "__codelineno-58-9" name = "__codelineno-58-9" href = "#__codelineno-58-9" > < / a > < span class = "k" > return< / span > < span class = "n" > rightRotate< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > :< / span > < span class = "n" > node< / span > < span class = "p" > )< / span >
< a id = "__codelineno-58-10" name = "__codelineno-58-10" href = "#__codelineno-58-10" > < / a > < span class = "p" > }< / span > < span class = "k" > else< / span > < span class = "p" > {< / span >
< a id = "__codelineno-58-11" name = "__codelineno-58-11" href = "#__codelineno-58-11" > < / a > < span class = "c1" > // 先左旋后右旋< / span >
< a id = "__codelineno-58-12" name = "__codelineno-58-12" href = "#__codelineno-58-12" > < / a > < span class = "n" > node< / span > < span class = "p" > ?.< / span > < span class = "kr" > left< / span > < span class = "p" > =< / span > < span class = "n" > leftRotate< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > :< / span > < span class = "n" > node< / span > < span class = "p" > ?.< / span > < span class = "kr" > left< / span > < span class = "p" > )< / span >
< a id = "__codelineno-58-13" name = "__codelineno-58-13" href = "#__codelineno-58-13" > < / a > < span class = "k" > return< / span > < span class = "n" > rightRotate< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > :< / span > < span class = "n" > node< / span > < span class = "p" > )< / span >
< a id = "__codelineno-58-14" name = "__codelineno-58-14" href = "#__codelineno-58-14" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-58-15" name = "__codelineno-58-15" href = "#__codelineno-58-15" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-58-16" name = "__codelineno-58-16" href = "#__codelineno-58-16" > < / a > < span class = "c1" > // 右偏树< / span >
< a id = "__codelineno-58-17" name = "__codelineno-58-17" href = "#__codelineno-58-17" > < / a > < span class = "k" > if< / span > < span class = "n" > balanceFactor< / span > < span class = "o" > < < / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > {< / span >
< a id = "__codelineno-58-18" name = "__codelineno-58-18" href = "#__codelineno-58-18" > < / a > < span class = "k" > if< / span > < span class = "kc" > self< / span > < span class = "p" > .< / span > < span class = "n" > balanceFactor< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > :< / span > < span class = "n" > node< / span > < span class = "p" > ?.< / span > < span class = "kr" > right< / span > < span class = "p" > )< / span > < span class = "o" > < =< / span > < span class = "mi" > 0< / span > < span class = "p" > {< / span >
< a id = "__codelineno-58-19" name = "__codelineno-58-19" href = "#__codelineno-58-19" > < / a > < span class = "c1" > // 左旋< / span >
< a id = "__codelineno-58-20" name = "__codelineno-58-20" href = "#__codelineno-58-20" > < / a > < span class = "k" > return< / span > < span class = "n" > leftRotate< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > :< / span > < span class = "n" > node< / span > < span class = "p" > )< / span >
< a id = "__codelineno-58-21" name = "__codelineno-58-21" href = "#__codelineno-58-21" > < / a > < span class = "p" > }< / span > < span class = "k" > else< / span > < span class = "p" > {< / span >
< a id = "__codelineno-58-22" name = "__codelineno-58-22" href = "#__codelineno-58-22" > < / a > < span class = "c1" > // 先右旋后左旋< / span >
< a id = "__codelineno-58-23" name = "__codelineno-58-23" href = "#__codelineno-58-23" > < / a > < span class = "n" > node< / span > < span class = "p" > ?.< / span > < span class = "kr" > right< / span > < span class = "p" > =< / span > < span class = "n" > rightRotate< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > :< / span > < span class = "n" > node< / span > < span class = "p" > ?.< / span > < span class = "kr" > right< / span > < span class = "p" > )< / span >
< a id = "__codelineno-58-24" name = "__codelineno-58-24" href = "#__codelineno-58-24" > < / a > < span class = "k" > return< / span > < span class = "n" > leftRotate< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > :< / span > < span class = "n" > node< / span > < span class = "p" > )< / span >
< a id = "__codelineno-58-25" name = "__codelineno-58-25" href = "#__codelineno-58-25" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-58-26" name = "__codelineno-58-26" href = "#__codelineno-58-26" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-58-27" name = "__codelineno-58-27" href = "#__codelineno-58-27" > < / a > < span class = "c1" > // 平衡树，无需旋转，直接返回< / span >
< a id = "__codelineno-58-28" name = "__codelineno-58-28" href = "#__codelineno-58-28" > < / a > < span class = "k" > return< / span > < span class = "n" > node< / span >
< a id = "__codelineno-58-29" name = "__codelineno-58-29" href = "#__codelineno-58-29" > < / 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" > avl_tree.zig< / span > < pre > < span > < / span > < code > < a id = "__codelineno-59-1" name = "__codelineno-59-1" href = "#__codelineno-59-1" > < / a > < span class = "c1" > // 执行旋转操作，使该子树重新恢复平衡< / span >
< a id = "__codelineno-59-2" name = "__codelineno-59-2" href = "#__codelineno-59-2" > < / a > < span class = "k" > fn< / span > < span class = "w" > < / span > < span class = "n" > rotate< / 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" > node< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "o" > ?*< / span > < span class = "n" > inc< / span > < span class = "p" > .< / span > < span class = "n" > TreeNode< / span > < span class = "p" > (< / span > < span class = "n" > T< / span > < span class = "p" > ))< / span > < span class = "w" > < / span > < span class = "o" > ?*< / span > < span class = "n" > inc< / span > < span class = "p" > .< / span > < span class = "n" > TreeNode< / span > < span class = "p" > (< / span > < span class = "n" > T< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-59-3" name = "__codelineno-59-3" href = "#__codelineno-59-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 获取结点 node 的平衡因子< / span >
< a id = "__codelineno-59-4" name = "__codelineno-59-4" href = "#__codelineno-59-4" > < / a > < span class = "w" > < / span > < span class = "kr" > var< / span > < span class = "w" > < / span > < span class = "n" > balance_factor< / 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" > balanceFactor< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > );< / span >
< a id = "__codelineno-59-5" name = "__codelineno-59-5" href = "#__codelineno-59-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 左偏树< / span >
< a id = "__codelineno-59-6" name = "__codelineno-59-6" href = "#__codelineno-59-6" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > balance_factor< / 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 = "p" > {< / span >
< a id = "__codelineno-59-7" name = "__codelineno-59-7" href = "#__codelineno-59-7" > < / 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" > balanceFactor< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "o" > ?< / span > < span class = "p" > .< / span > < span class = "n" > left< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-59-8" name = "__codelineno-59-8" href = "#__codelineno-59-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 右旋< / span >
< a id = "__codelineno-59-9" name = "__codelineno-59-9" href = "#__codelineno-59-9" > < / 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" > rightRotate< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > );< / span >
< a id = "__codelineno-59-10" name = "__codelineno-59-10" href = "#__codelineno-59-10" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-59-11" name = "__codelineno-59-11" href = "#__codelineno-59-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 先左旋后右旋< / span >
< a id = "__codelineno-59-12" name = "__codelineno-59-12" href = "#__codelineno-59-12" > < / a > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "o" > ?< / span > < span class = "p" > .< / span > < span class = "n" > left< / 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" > leftRotate< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "o" > ?< / span > < span class = "p" > .< / span > < span class = "n" > left< / span > < span class = "p" > );< / span >
< a id = "__codelineno-59-13" name = "__codelineno-59-13" href = "#__codelineno-59-13" > < / 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" > rightRotate< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > );< / span >
< a id = "__codelineno-59-14" name = "__codelineno-59-14" href = "#__codelineno-59-14" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-59-15" name = "__codelineno-59-15" href = "#__codelineno-59-15" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-59-16" name = "__codelineno-59-16" href = "#__codelineno-59-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // 右偏树< / span >
< a id = "__codelineno-59-17" name = "__codelineno-59-17" href = "#__codelineno-59-17" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > balance_factor< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-59-18" name = "__codelineno-59-18" href = "#__codelineno-59-18" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > self< / span > < span class = "p" > .< / span > < span class = "n" > balanceFactor< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "o" > ?< / span > < span class = "p" > .< / span > < span class = "n" > right< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-59-19" name = "__codelineno-59-19" href = "#__codelineno-59-19" > < / a > < span class = "w" > < / span > < span class = "c1" > // 左旋< / span >
< a id = "__codelineno-59-20" name = "__codelineno-59-20" href = "#__codelineno-59-20" > < / 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" > leftRotate< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > );< / span >
< a id = "__codelineno-59-21" name = "__codelineno-59-21" href = "#__codelineno-59-21" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-59-22" name = "__codelineno-59-22" href = "#__codelineno-59-22" > < / a > < span class = "w" > < / span > < span class = "c1" > // 先右旋后左旋< / span >
< a id = "__codelineno-59-23" name = "__codelineno-59-23" href = "#__codelineno-59-23" > < / a > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "o" > ?< / span > < span class = "p" > .< / span > < span class = "n" > right< / 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" > rightRotate< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "o" > ?< / span > < span class = "p" > .< / span > < span class = "n" > right< / span > < span class = "p" > );< / span >
< a id = "__codelineno-59-24" name = "__codelineno-59-24" href = "#__codelineno-59-24" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > self< / span > < span class = "p" > .< / span > < span class = "n" > leftRotate< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > );< / span >
< a id = "__codelineno-59-25" name = "__codelineno-59-25" href = "#__codelineno-59-25" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-59-26" name = "__codelineno-59-26" href = "#__codelineno-59-26" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-59-27" name = "__codelineno-59-27" href = "#__codelineno-59-27" > < / a > < span class = "w" > < / span > < span class = "c1" > // 平衡树，无需旋转，直接返回< / span >
< a id = "__codelineno-59-28" name = "__codelineno-59-28" href = "#__codelineno-59-28" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-59-29" name = "__codelineno-59-29" href = "#__codelineno-59-29" > < / a > < span class = "p" > }< / span >
2023-02-08 14:54:41 +08:00
< / code > < / pre > < / div >
< / div >
< / div >
< / div >
2023-02-24 18:46:22 +08:00
< h2 id = "743-avl" > 7.4.3. AVL 树常用操作< a class = "headerlink" href = "#743-avl" title = "Permanent link" > ¶ < / a > < / h2 >
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< h3 id = "_4" > 插入结点< a class = "headerlink" href = "#_4" title = "Permanent link" > ¶ < / a > < / h3 >
< p > 「AVL 树」的结点插入操作与「二叉搜索树」主体类似。不同的是，在插入结点后，从该结点到根结点的路径上会出现一系列「失衡结点」。所以，< strong > 我们需要从该结点开始，从底至顶地执行旋转操作，使所有失衡结点恢复平衡< / strong > 。< / p >
< div class = "tabbed-set tabbed-alternate" data-tabs = "8:10" > < input checked = "checked" id = "__tabbed_8_1" name = "__tabbed_8" type = "radio" / > < input id = "__tabbed_8_2" name = "__tabbed_8" type = "radio" / > < input id = "__tabbed_8_3" name = "__tabbed_8" type = "radio" / > < input id = "__tabbed_8_4" name = "__tabbed_8" type = "radio" / > < input id = "__tabbed_8_5" name = "__tabbed_8" type = "radio" / > < input id = "__tabbed_8_6" name = "__tabbed_8" type = "radio" / > < input id = "__tabbed_8_7" name = "__tabbed_8" type = "radio" / > < input id = "__tabbed_8_8" name = "__tabbed_8" type = "radio" / > < input id = "__tabbed_8_9" name = "__tabbed_8" type = "radio" / > < input id = "__tabbed_8_10" name = "__tabbed_8" type = "radio" / > < div class = "tabbed-labels" > < label for = "__tabbed_8_1" > Java< / label > < label for = "__tabbed_8_2" > C++< / label > < label for = "__tabbed_8_3" > Python< / label > < label for = "__tabbed_8_4" > Go< / label > < label for = "__tabbed_8_5" > JavaScript< / label > < label for = "__tabbed_8_6" > TypeScript< / label > < label for = "__tabbed_8_7" > C< / label > < label for = "__tabbed_8_8" > C#< / label > < label for = "__tabbed_8_9" > Swift< / label > < label for = "__tabbed_8_10" > Zig< / label > < / div >
< div class = "tabbed-content" >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > avl_tree.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-60-1" name = "__codelineno-60-1" href = "#__codelineno-60-1" > < / a > < span class = "cm" > /* 插入结点 */< / span >
< a id = "__codelineno-60-2" name = "__codelineno-60-2" href = "#__codelineno-60-2" > < / a > < span class = "n" > TreeNode< / span > < span class = "w" > < / span > < span class = "nf" > insert< / 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-60-3" name = "__codelineno-60-3" href = "#__codelineno-60-3" > < / a > < span class = "w" > < / span > < span class = "n" > root< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > insertHelper< / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > val< / span > < span class = "p" > );< / span >
< a id = "__codelineno-60-4" name = "__codelineno-60-4" href = "#__codelineno-60-4" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > root< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-60-5" name = "__codelineno-60-5" href = "#__codelineno-60-5" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-60-6" name = "__codelineno-60-6" href = "#__codelineno-60-6" > < / a >
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< a id = "__codelineno-60-7" name = "__codelineno-60-7" href = "#__codelineno-60-7" > < / a > < span class = "cm" > /* 递归插入结点（辅助方法） */< / span >
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< a id = "__codelineno-60-8" name = "__codelineno-60-8" href = "#__codelineno-60-8" > < / a > < span class = "n" > TreeNode< / span > < span class = "w" > < / span > < span class = "nf" > insertHelper< / span > < span class = "p" > (< / span > < span class = "n" > TreeNode< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > val< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-60-9" name = "__codelineno-60-9" href = "#__codelineno-60-9" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "w" > < / span > < span class = "n" > TreeNode< / span > < span class = "p" > (< / span > < span class = "n" > val< / span > < span class = "p" > );< / span >
< a id = "__codelineno-60-10" name = "__codelineno-60-10" href = "#__codelineno-60-10" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 1. 查找插入位置，并插入结点 */< / span >
< a id = "__codelineno-60-11" name = "__codelineno-60-11" href = "#__codelineno-60-11" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > val< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "na" > val< / span > < span class = "p" > )< / span >
< a id = "__codelineno-60-12" name = "__codelineno-60-12" href = "#__codelineno-60-12" > < / a > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "na" > left< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > insertHelper< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "na" > left< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > val< / span > < span class = "p" > );< / span >
< a id = "__codelineno-60-13" name = "__codelineno-60-13" href = "#__codelineno-60-13" > < / a > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > val< / span > < span class = "w" > < / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "na" > val< / span > < span class = "p" > )< / span >
< a id = "__codelineno-60-14" name = "__codelineno-60-14" href = "#__codelineno-60-14" > < / a > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "na" > right< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > insertHelper< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "na" > right< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > val< / span > < span class = "p" > );< / span >
< a id = "__codelineno-60-15" name = "__codelineno-60-15" href = "#__codelineno-60-15" > < / a > < span class = "w" > < / span > < span class = "k" > else< / span >
< a id = "__codelineno-60-16" name = "__codelineno-60-16" href = "#__codelineno-60-16" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 重复结点不插入，直接返回< / span >
< a id = "__codelineno-60-17" name = "__codelineno-60-17" href = "#__codelineno-60-17" > < / a > < span class = "w" > < / span > < span class = "n" > updateHeight< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 更新结点高度< / span >
< a id = "__codelineno-60-18" name = "__codelineno-60-18" href = "#__codelineno-60-18" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 2. 执行旋转操作，使该子树重新恢复平衡 */< / span >
< a id = "__codelineno-60-19" name = "__codelineno-60-19" href = "#__codelineno-60-19" > < / a > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > rotate< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > );< / span >
< a id = "__codelineno-60-20" name = "__codelineno-60-20" href = "#__codelineno-60-20" > < / a > < span class = "w" > < / span > < span class = "c1" > // 返回子树的根结点< / span >
< a id = "__codelineno-60-21" name = "__codelineno-60-21" href = "#__codelineno-60-21" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-60-22" name = "__codelineno-60-22" href = "#__codelineno-60-22" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > avl_tree.cpp< / span > < pre > < span > < / span > < code > < a id = "__codelineno-61-1" name = "__codelineno-61-1" href = "#__codelineno-61-1" > < / a > < span class = "cm" > /* 插入结点 */< / span >
< a id = "__codelineno-61-2" name = "__codelineno-61-2" href = "#__codelineno-61-2" > < / a > < span class = "n" > TreeNode< / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "nf" > insert< / 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-61-3" name = "__codelineno-61-3" href = "#__codelineno-61-3" > < / a > < span class = "w" > < / span > < span class = "n" > root< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > insertHelper< / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > val< / span > < span class = "p" > );< / span >
< a id = "__codelineno-61-4" name = "__codelineno-61-4" href = "#__codelineno-61-4" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > root< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-61-5" name = "__codelineno-61-5" href = "#__codelineno-61-5" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-61-6" name = "__codelineno-61-6" href = "#__codelineno-61-6" > < / a >
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< a id = "__codelineno-61-7" name = "__codelineno-61-7" href = "#__codelineno-61-7" > < / a > < span class = "cm" > /* 递归插入结点（辅助方法） */< / span >
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< a id = "__codelineno-61-8" name = "__codelineno-61-8" href = "#__codelineno-61-8" > < / a > < span class = "n" > TreeNode< / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "nf" > insertHelper< / span > < span class = "p" > (< / span > < span class = "n" > TreeNode< / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > val< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-61-9" name = "__codelineno-61-9" href = "#__codelineno-61-9" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "k" > nullptr< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "w" > < / span > < span class = "n" > TreeNode< / span > < span class = "p" > (< / span > < span class = "n" > val< / span > < span class = "p" > );< / span >
< a id = "__codelineno-61-10" name = "__codelineno-61-10" href = "#__codelineno-61-10" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 1. 查找插入位置，并插入结点 */< / span >
< a id = "__codelineno-61-11" name = "__codelineno-61-11" href = "#__codelineno-61-11" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > val< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "o" > -> < / span > < span class = "n" > val< / span > < span class = "p" > )< / span >
< a id = "__codelineno-61-12" name = "__codelineno-61-12" href = "#__codelineno-61-12" > < / a > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "o" > -> < / span > < span class = "n" > left< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > insertHelper< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "o" > -> < / span > < span class = "n" > left< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > val< / span > < span class = "p" > );< / span >
< a id = "__codelineno-61-13" name = "__codelineno-61-13" href = "#__codelineno-61-13" > < / a > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > val< / span > < span class = "w" > < / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "o" > -> < / span > < span class = "n" > val< / span > < span class = "p" > )< / span >
< a id = "__codelineno-61-14" name = "__codelineno-61-14" href = "#__codelineno-61-14" > < / a > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "o" > -> < / span > < span class = "n" > right< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > insertHelper< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "o" > -> < / span > < span class = "n" > right< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > val< / span > < span class = "p" > );< / span >
< a id = "__codelineno-61-15" name = "__codelineno-61-15" href = "#__codelineno-61-15" > < / a > < span class = "w" > < / span > < span class = "k" > else< / span >
< a id = "__codelineno-61-16" name = "__codelineno-61-16" href = "#__codelineno-61-16" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 重复结点不插入，直接返回< / span >
< a id = "__codelineno-61-17" name = "__codelineno-61-17" href = "#__codelineno-61-17" > < / a > < span class = "w" > < / span > < span class = "n" > updateHeight< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 更新结点高度< / span >
< a id = "__codelineno-61-18" name = "__codelineno-61-18" href = "#__codelineno-61-18" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 2. 执行旋转操作，使该子树重新恢复平衡 */< / span >
< a id = "__codelineno-61-19" name = "__codelineno-61-19" href = "#__codelineno-61-19" > < / a > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > rotate< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > );< / span >
< a id = "__codelineno-61-20" name = "__codelineno-61-20" href = "#__codelineno-61-20" > < / a > < span class = "w" > < / span > < span class = "c1" > // 返回子树的根结点< / span >
< a id = "__codelineno-61-21" name = "__codelineno-61-21" href = "#__codelineno-61-21" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-61-22" name = "__codelineno-61-22" href = "#__codelineno-61-22" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > avl_tree.py< / span > < pre > < span > < / span > < code > < a id = "__codelineno-62-1" name = "__codelineno-62-1" href = "#__codelineno-62-1" > < / a > < span class = "sd" > " " " 插入结点 " " " < / span >
< a id = "__codelineno-62-2" name = "__codelineno-62-2" href = "#__codelineno-62-2" > < / a > < span class = "k" > def< / span > < span class = "nf" > insert< / 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 = "o" > -> < / span > < span class = "n" > TreeNode< / span > < span class = "p" > :< / span >
< a id = "__codelineno-62-3" name = "__codelineno-62-3" href = "#__codelineno-62-3" > < / a > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > root< / span > < span class = "o" > =< / span > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > __insert_helper< / span > < span class = "p" > (< / span > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > root< / span > < span class = "p" > ,< / span > < span class = "n" > val< / span > < span class = "p" > )< / span >
< a id = "__codelineno-62-4" name = "__codelineno-62-4" href = "#__codelineno-62-4" > < / a > < span class = "k" > return< / span > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > root< / span >
< a id = "__codelineno-62-5" name = "__codelineno-62-5" href = "#__codelineno-62-5" > < / a >
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< a id = "__codelineno-62-6" name = "__codelineno-62-6" href = "#__codelineno-62-6" > < / a > < span class = "sd" > " " " 递归插入结点（辅助方法）" " " < / span >
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< a id = "__codelineno-62-7" name = "__codelineno-62-7" href = "#__codelineno-62-7" > < / a > < span class = "k" > def< / span > < span class = "nf" > __insert_helper< / span > < span class = "p" > (< / span > < span class = "bp" > self< / span > < span class = "p" > ,< / span > < span class = "n" > node< / span > < span class = "p" > :< / span > < span class = "n" > Optional< / span > < span class = "p" > [< / span > < span class = "n" > TreeNode< / 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 = "o" > -> < / span > < span class = "n" > TreeNode< / span > < span class = "p" > :< / span >
< a id = "__codelineno-62-8" name = "__codelineno-62-8" href = "#__codelineno-62-8" > < / a > < span class = "k" > if< / span > < span class = "n" > node< / span > < span class = "ow" > is< / span > < span class = "kc" > None< / span > < span class = "p" > :< / span >
< a id = "__codelineno-62-9" name = "__codelineno-62-9" href = "#__codelineno-62-9" > < / a > < span class = "k" > return< / span > < span class = "n" > TreeNode< / span > < span class = "p" > (< / span > < span class = "n" > val< / span > < span class = "p" > )< / span >
< a id = "__codelineno-62-10" name = "__codelineno-62-10" href = "#__codelineno-62-10" > < / a > < span class = "c1" > # 1. 查找插入位置，并插入结点< / span >
< a id = "__codelineno-62-11" name = "__codelineno-62-11" href = "#__codelineno-62-11" > < / a > < span class = "k" > if< / span > < span class = "n" > val< / span > < span class = "o" > < < / span > < span class = "n" > node< / span > < span class = "o" > .< / span > < span class = "n" > val< / span > < span class = "p" > :< / span >
< a id = "__codelineno-62-12" name = "__codelineno-62-12" href = "#__codelineno-62-12" > < / a > < span class = "n" > node< / span > < span class = "o" > .< / span > < span class = "n" > left< / span > < span class = "o" > =< / span > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > __insert_helper< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "o" > .< / span > < span class = "n" > left< / span > < span class = "p" > ,< / span > < span class = "n" > val< / span > < span class = "p" > )< / span >
< a id = "__codelineno-62-13" name = "__codelineno-62-13" href = "#__codelineno-62-13" > < / a > < span class = "k" > elif< / span > < span class = "n" > val< / span > < span class = "o" > > < / span > < span class = "n" > node< / span > < span class = "o" > .< / span > < span class = "n" > val< / span > < span class = "p" > :< / span >
< a id = "__codelineno-62-14" name = "__codelineno-62-14" href = "#__codelineno-62-14" > < / a > < span class = "n" > node< / span > < span class = "o" > .< / span > < span class = "n" > right< / span > < span class = "o" > =< / span > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > __insert_helper< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "o" > .< / span > < span class = "n" > right< / span > < span class = "p" > ,< / span > < span class = "n" > val< / span > < span class = "p" > )< / span >
< a id = "__codelineno-62-15" name = "__codelineno-62-15" href = "#__codelineno-62-15" > < / a > < span class = "k" > else< / span > < span class = "p" > :< / span >
< a id = "__codelineno-62-16" name = "__codelineno-62-16" href = "#__codelineno-62-16" > < / a > < span class = "c1" > # 重复结点不插入，直接返回< / span >
< a id = "__codelineno-62-17" name = "__codelineno-62-17" href = "#__codelineno-62-17" > < / a > < span class = "k" > return< / span > < span class = "n" > node< / span >
< a id = "__codelineno-62-18" name = "__codelineno-62-18" href = "#__codelineno-62-18" > < / a > < span class = "c1" > # 更新结点高度< / span >
< a id = "__codelineno-62-19" name = "__codelineno-62-19" href = "#__codelineno-62-19" > < / a > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > __update_height< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > )< / span >
< a id = "__codelineno-62-20" name = "__codelineno-62-20" href = "#__codelineno-62-20" > < / a > < span class = "c1" > # 2. 执行旋转操作，使该子树重新恢复平衡< / span >
< a id = "__codelineno-62-21" name = "__codelineno-62-21" href = "#__codelineno-62-21" > < / a > < span class = "k" > return< / span > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > __rotate< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > )< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > avl_tree.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-63-1" name = "__codelineno-63-1" href = "#__codelineno-63-1" > < / a > < span class = "cm" > /* 插入结点 */< / span >
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< a id = "__codelineno-63-2" name = "__codelineno-63-2" href = "#__codelineno-63-2" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > t< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > aVLTree< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "nx" > insert< / span > < span class = "p" > (< / span > < span class = "nx" > val< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > TreeNode< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-63-3" name = "__codelineno-63-3" href = "#__codelineno-63-3" > < / a > < span class = "w" > < / span > < span class = "nx" > t< / span > < span class = "p" > .< / span > < span class = "nx" > root< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "nx" > t< / span > < span class = "p" > .< / span > < span class = "nx" > insertHelper< / span > < span class = "p" > (< / span > < span class = "nx" > t< / span > < span class = "p" > .< / span > < span class = "nx" > root< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > val< / span > < span class = "p" > )< / span >
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< a id = "__codelineno-63-4" name = "__codelineno-63-4" href = "#__codelineno-63-4" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > t< / span > < span class = "p" > .< / span > < span class = "nx" > root< / span >
< a id = "__codelineno-63-5" name = "__codelineno-63-5" href = "#__codelineno-63-5" > < / a > < span class = "p" > }< / span >
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< a id = "__codelineno-63-6" name = "__codelineno-63-6" href = "#__codelineno-63-6" > < / a >
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< a id = "__codelineno-63-7" name = "__codelineno-63-7" href = "#__codelineno-63-7" > < / a > < span class = "cm" > /* 递归插入结点（辅助方法） */< / span >
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< a id = "__codelineno-63-8" name = "__codelineno-63-8" href = "#__codelineno-63-8" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > t< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > aVLTree< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "nx" > insertHelper< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > TreeNode< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > val< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > TreeNode< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-63-9" name = "__codelineno-63-9" href = "#__codelineno-63-9" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "kc" > nil< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-63-10" name = "__codelineno-63-10" href = "#__codelineno-63-10" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > NewTreeNode< / span > < span class = "p" > (< / span > < span class = "nx" > val< / span > < span class = "p" > )< / span >
< a id = "__codelineno-63-11" name = "__codelineno-63-11" href = "#__codelineno-63-11" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-63-12" name = "__codelineno-63-12" href = "#__codelineno-63-12" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 1. 查找插入位置，并插入结点 */< / span >
< a id = "__codelineno-63-13" name = "__codelineno-63-13" href = "#__codelineno-63-13" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "nx" > val< / span > < span class = "w" > < / span > < span class = "p" > < < / span > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > Val< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-63-14" name = "__codelineno-63-14" href = "#__codelineno-63-14" > < / a > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > Left< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "nx" > t< / span > < span class = "p" > .< / span > < span class = "nx" > insertHelper< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > Left< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > val< / span > < span class = "p" > )< / span >
< a id = "__codelineno-63-15" name = "__codelineno-63-15" href = "#__codelineno-63-15" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "nx" > val< / span > < span class = "w" > < / span > < span class = "p" > > < / span > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > Val< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-63-16" name = "__codelineno-63-16" href = "#__codelineno-63-16" > < / a > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > Right< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "nx" > t< / span > < span class = "p" > .< / span > < span class = "nx" > insertHelper< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > Right< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > val< / span > < span class = "p" > )< / span >
< a id = "__codelineno-63-17" name = "__codelineno-63-17" href = "#__codelineno-63-17" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-63-18" name = "__codelineno-63-18" href = "#__codelineno-63-18" > < / a > < span class = "w" > < / span > < span class = "c1" > // 重复结点不插入，直接返回< / span >
< a id = "__codelineno-63-19" name = "__codelineno-63-19" href = "#__codelineno-63-19" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > node< / span >
< a id = "__codelineno-63-20" name = "__codelineno-63-20" href = "#__codelineno-63-20" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-63-21" name = "__codelineno-63-21" href = "#__codelineno-63-21" > < / a > < span class = "w" > < / span > < span class = "c1" > // 更新结点高度< / span >
< a id = "__codelineno-63-22" name = "__codelineno-63-22" href = "#__codelineno-63-22" > < / a > < span class = "w" > < / span > < span class = "nx" > t< / span > < span class = "p" > .< / span > < span class = "nx" > updateHeight< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > )< / span >
< a id = "__codelineno-63-23" name = "__codelineno-63-23" href = "#__codelineno-63-23" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 2. 执行旋转操作，使该子树重新恢复平衡 */< / span >
< a id = "__codelineno-63-24" name = "__codelineno-63-24" href = "#__codelineno-63-24" > < / a > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "nx" > t< / span > < span class = "p" > .< / span > < span class = "nx" > rotate< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > )< / span >
< a id = "__codelineno-63-25" name = "__codelineno-63-25" href = "#__codelineno-63-25" > < / a > < span class = "w" > < / span > < span class = "c1" > // 返回子树的根结点< / span >
< a id = "__codelineno-63-26" name = "__codelineno-63-26" href = "#__codelineno-63-26" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > node< / span >
< a id = "__codelineno-63-27" name = "__codelineno-63-27" href = "#__codelineno-63-27" > < / a > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > avl_tree.js< / span > < pre > < span > < / span > < code > < a id = "__codelineno-64-1" name = "__codelineno-64-1" href = "#__codelineno-64-1" > < / a > < span class = "cm" > /* 插入结点 */< / span >
< a id = "__codelineno-64-2" name = "__codelineno-64-2" href = "#__codelineno-64-2" > < / a > < span class = "nx" > insert< / 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-64-3" name = "__codelineno-64-3" href = "#__codelineno-64-3" > < / a > < span class = "w" > < / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "nx" > root< / 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" > insertHelper< / span > < span class = "p" > (< / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "nx" > root< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > val< / span > < span class = "p" > );< / span >
< a id = "__codelineno-64-4" name = "__codelineno-64-4" href = "#__codelineno-64-4" > < / 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" > root< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-64-5" name = "__codelineno-64-5" href = "#__codelineno-64-5" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-64-6" name = "__codelineno-64-6" href = "#__codelineno-64-6" > < / a >
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< a id = "__codelineno-64-7" name = "__codelineno-64-7" href = "#__codelineno-64-7" > < / a > < span class = "cm" > /* 递归插入结点（辅助方法） */< / span >
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< a id = "__codelineno-64-8" name = "__codelineno-64-8" href = "#__codelineno-64-8" > < / a > < span class = "nx" > insertHelper< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > val< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-64-9" name = "__codelineno-64-9" href = "#__codelineno-64-9" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "w" > < / span > < span class = "o" > ===< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "ow" > new< / span > < span class = "w" > < / span > < span class = "nx" > TreeNode< / span > < span class = "p" > (< / span > < span class = "nx" > val< / span > < span class = "p" > );< / span >
< a id = "__codelineno-64-10" name = "__codelineno-64-10" href = "#__codelineno-64-10" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 1. 查找插入位置，并插入结点 */< / span >
< a id = "__codelineno-64-11" name = "__codelineno-64-11" href = "#__codelineno-64-11" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > val< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > val< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > left< / 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" > insertHelper< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > left< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > val< / span > < span class = "p" > );< / span >
< a id = "__codelineno-64-12" name = "__codelineno-64-12" href = "#__codelineno-64-12" > < / a > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > val< / span > < span class = "w" > < / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > val< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > right< / 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" > insertHelper< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > right< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > val< / span > < span class = "p" > );< / span >
< a id = "__codelineno-64-13" name = "__codelineno-64-13" href = "#__codelineno-64-13" > < / a > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 重复结点不插入，直接返回< / span >
< a id = "__codelineno-64-14" name = "__codelineno-64-14" href = "#__codelineno-64-14" > < / a > < span class = "w" > < / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "nx" > updateHeight< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 更新结点高度< / span >
< a id = "__codelineno-64-15" name = "__codelineno-64-15" href = "#__codelineno-64-15" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 2. 执行旋转操作，使该子树重新恢复平衡 */< / span >
< a id = "__codelineno-64-16" name = "__codelineno-64-16" href = "#__codelineno-64-16" > < / a > < span class = "w" > < / span > < span class = "nx" > node< / 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" > rotate< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > );< / span >
< a id = "__codelineno-64-17" name = "__codelineno-64-17" href = "#__codelineno-64-17" > < / a > < span class = "w" > < / span > < span class = "c1" > // 返回子树的根结点< / span >
< a id = "__codelineno-64-18" name = "__codelineno-64-18" href = "#__codelineno-64-18" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-64-19" name = "__codelineno-64-19" href = "#__codelineno-64-19" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > avl_tree.ts< / span > < pre > < span > < / span > < code > < a id = "__codelineno-65-1" name = "__codelineno-65-1" href = "#__codelineno-65-1" > < / a > < span class = "cm" > /* 插入结点 */< / span >
< a id = "__codelineno-65-2" name = "__codelineno-65-2" href = "#__codelineno-65-2" > < / a > < span class = "nx" > insert< / 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 = "nx" > TreeNode< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-65-3" name = "__codelineno-65-3" href = "#__codelineno-65-3" > < / a > < span class = "w" > < / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "nx" > root< / 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" > insertHelper< / span > < span class = "p" > (< / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "nx" > root< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > val< / span > < span class = "p" > );< / span >
< a id = "__codelineno-65-4" name = "__codelineno-65-4" href = "#__codelineno-65-4" > < / 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" > root< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-65-5" name = "__codelineno-65-5" href = "#__codelineno-65-5" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-65-6" name = "__codelineno-65-6" href = "#__codelineno-65-6" > < / a >
2023-02-10 01:03:44 +08:00
< a id = "__codelineno-65-7" name = "__codelineno-65-7" href = "#__codelineno-65-7" > < / a > < span class = "cm" > /* 递归插入结点（辅助方法） */< / span >
2023-02-08 14:54:41 +08:00
< a id = "__codelineno-65-8" name = "__codelineno-65-8" href = "#__codelineno-65-8" > < / a > < span class = "nx" > insertHelper< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > TreeNode< / span > < span class = "p" > ,< / span > < span class = "w" > < / 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 = "nx" > TreeNode< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-65-9" name = "__codelineno-65-9" href = "#__codelineno-65-9" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "w" > < / span > < span class = "o" > ===< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "ow" > new< / span > < span class = "w" > < / span > < span class = "nx" > TreeNode< / span > < span class = "p" > (< / span > < span class = "nx" > val< / span > < span class = "p" > );< / span >
< a id = "__codelineno-65-10" name = "__codelineno-65-10" href = "#__codelineno-65-10" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 1. 查找插入位置，并插入结点 */< / span >
< a id = "__codelineno-65-11" name = "__codelineno-65-11" href = "#__codelineno-65-11" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > val< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "nx" > node< / 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-65-12" name = "__codelineno-65-12" href = "#__codelineno-65-12" > < / a > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > left< / 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" > insertHelper< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > left< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > val< / span > < span class = "p" > );< / span >
< a id = "__codelineno-65-13" name = "__codelineno-65-13" href = "#__codelineno-65-13" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > val< / span > < span class = "w" > < / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "nx" > node< / 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-65-14" name = "__codelineno-65-14" href = "#__codelineno-65-14" > < / a > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > right< / 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" > insertHelper< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > right< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > val< / span > < span class = "p" > );< / span >
< a id = "__codelineno-65-15" name = "__codelineno-65-15" href = "#__codelineno-65-15" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-65-16" name = "__codelineno-65-16" href = "#__codelineno-65-16" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 重复结点不插入，直接返回< / span >
< a id = "__codelineno-65-17" name = "__codelineno-65-17" href = "#__codelineno-65-17" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-65-18" name = "__codelineno-65-18" href = "#__codelineno-65-18" > < / a > < span class = "w" > < / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "nx" > updateHeight< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 更新结点高度< / span >
< a id = "__codelineno-65-19" name = "__codelineno-65-19" href = "#__codelineno-65-19" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 2. 执行旋转操作，使该子树重新恢复平衡 */< / span >
< a id = "__codelineno-65-20" name = "__codelineno-65-20" href = "#__codelineno-65-20" > < / a > < span class = "w" > < / span > < span class = "nx" > node< / 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" > rotate< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > );< / span >
< a id = "__codelineno-65-21" name = "__codelineno-65-21" href = "#__codelineno-65-21" > < / a > < span class = "w" > < / span > < span class = "c1" > // 返回子树的根结点< / span >
< a id = "__codelineno-65-22" name = "__codelineno-65-22" href = "#__codelineno-65-22" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-65-23" name = "__codelineno-65-23" href = "#__codelineno-65-23" > < / 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" > avl_tree.c< / span > < pre > < span > < / span > < code > < a id = "__codelineno-66-1" name = "__codelineno-66-1" href = "#__codelineno-66-1" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{< / span > < span class = "n" > aVLTree< / 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" > insert< / span > < span class = "p" > }< / span >
< a id = "__codelineno-66-2" name = "__codelineno-66-2" href = "#__codelineno-66-2" > < / a >
< a id = "__codelineno-66-3" name = "__codelineno-66-3" href = "#__codelineno-66-3" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{< / span > < span class = "n" > aVLTree< / 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" > insertHelper< / 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" > avl_tree.cs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-67-1" name = "__codelineno-67-1" href = "#__codelineno-67-1" > < / a > < span class = "cm" > /* 插入结点 */< / span >
2023-02-08 22:16:28 +08:00
< a id = "__codelineno-67-2" name = "__codelineno-67-2" href = "#__codelineno-67-2" > < / a > < span class = "n" > TreeNode< / span > < span class = "o" > ?< / span > < span class = "w" > < / span > < span class = "n" > insert< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > val< / span > < span class = "p" > )< / span >
2023-02-08 14:54:41 +08:00
< a id = "__codelineno-67-3" name = "__codelineno-67-3" href = "#__codelineno-67-3" > < / a > < span class = "p" > {< / span >
< a id = "__codelineno-67-4" name = "__codelineno-67-4" href = "#__codelineno-67-4" > < / a > < span class = "w" > < / span > < span class = "n" > root< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > insertHelper< / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > val< / span > < span class = "p" > );< / span >
< a id = "__codelineno-67-5" name = "__codelineno-67-5" href = "#__codelineno-67-5" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > root< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-67-6" name = "__codelineno-67-6" href = "#__codelineno-67-6" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-67-7" name = "__codelineno-67-7" href = "#__codelineno-67-7" > < / a >
2023-02-10 01:03:44 +08:00
< a id = "__codelineno-67-8" name = "__codelineno-67-8" href = "#__codelineno-67-8" > < / a > < span class = "cm" > /* 递归插入结点（辅助方法） */< / span >
2023-02-08 22:16:28 +08:00
< a id = "__codelineno-67-9" name = "__codelineno-67-9" href = "#__codelineno-67-9" > < / a > < span class = "n" > TreeNode< / span > < span class = "o" > ?< / span > < span class = "w" > < / span > < span class = "n" > insertHelper< / span > < span class = "p" > (< / span > < span class = "n" > TreeNode< / span > < span class = "o" > ?< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > val< / span > < span class = "p" > )< / span >
2023-02-08 14:54:41 +08:00
< a id = "__codelineno-67-10" name = "__codelineno-67-10" href = "#__codelineno-67-10" > < / a > < span class = "p" > {< / span >
< a id = "__codelineno-67-11" name = "__codelineno-67-11" href = "#__codelineno-67-11" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "k" > null< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "w" > < / span > < span class = "n" > TreeNode< / span > < span class = "p" > (< / span > < span class = "n" > val< / span > < span class = "p" > );< / span >
< a id = "__codelineno-67-12" name = "__codelineno-67-12" href = "#__codelineno-67-12" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 1. 查找插入位置，并插入结点 */< / span >
< a id = "__codelineno-67-13" name = "__codelineno-67-13" href = "#__codelineno-67-13" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > val< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "n" > val< / span > < span class = "p" > )< / span >
< a id = "__codelineno-67-14" name = "__codelineno-67-14" href = "#__codelineno-67-14" > < / a > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "n" > left< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > insertHelper< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "n" > left< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > val< / span > < span class = "p" > );< / span >
< a id = "__codelineno-67-15" name = "__codelineno-67-15" href = "#__codelineno-67-15" > < / a > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "nf" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > val< / span > < span class = "w" > < / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "n" > val< / span > < span class = "p" > )< / span >
< a id = "__codelineno-67-16" name = "__codelineno-67-16" href = "#__codelineno-67-16" > < / a > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "n" > right< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > insertHelper< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "n" > right< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > val< / span > < span class = "p" > );< / span >
< a id = "__codelineno-67-17" name = "__codelineno-67-17" href = "#__codelineno-67-17" > < / a > < span class = "w" > < / span > < span class = "k" > else< / span >
< a id = "__codelineno-67-18" name = "__codelineno-67-18" href = "#__codelineno-67-18" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 重复结点不插入，直接返回< / span >
< a id = "__codelineno-67-19" name = "__codelineno-67-19" href = "#__codelineno-67-19" > < / a > < span class = "w" > < / span > < span class = "n" > updateHeight< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 更新结点高度< / span >
< a id = "__codelineno-67-20" name = "__codelineno-67-20" href = "#__codelineno-67-20" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 2. 执行旋转操作，使该子树重新恢复平衡 */< / span >
< a id = "__codelineno-67-21" name = "__codelineno-67-21" href = "#__codelineno-67-21" > < / a > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > rotate< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > );< / span >
< a id = "__codelineno-67-22" name = "__codelineno-67-22" href = "#__codelineno-67-22" > < / a > < span class = "w" > < / span > < span class = "c1" > // 返回子树的根结点< / span >
< a id = "__codelineno-67-23" name = "__codelineno-67-23" href = "#__codelineno-67-23" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-67-24" name = "__codelineno-67-24" href = "#__codelineno-67-24" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > avl_tree.swift< / span > < pre > < span > < / span > < code > < a id = "__codelineno-68-1" name = "__codelineno-68-1" href = "#__codelineno-68-1" > < / a > < span class = "cm" > /* 插入结点 */< / span >
< a id = "__codelineno-68-2" name = "__codelineno-68-2" href = "#__codelineno-68-2" > < / a > < span class = "p" > @< / span > < span class = "n" > discardableResult< / span >
< a id = "__codelineno-68-3" name = "__codelineno-68-3" href = "#__codelineno-68-3" > < / a > < span class = "kd" > func< / span > < span class = "nf" > insert< / 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 > < span class = "n" > TreeNode< / span > < span class = "p" > ?< / span > < span class = "p" > {< / span >
< a id = "__codelineno-68-4" name = "__codelineno-68-4" href = "#__codelineno-68-4" > < / a > < span class = "n" > root< / span > < span class = "p" > =< / span > < span class = "n" > insertHelper< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > :< / span > < span class = "n" > root< / span > < span class = "p" > ,< / span > < span class = "n" > val< / span > < span class = "p" > :< / span > < span class = "n" > val< / span > < span class = "p" > )< / span >
< a id = "__codelineno-68-5" name = "__codelineno-68-5" href = "#__codelineno-68-5" > < / a > < span class = "k" > return< / span > < span class = "n" > root< / span >
< a id = "__codelineno-68-6" name = "__codelineno-68-6" href = "#__codelineno-68-6" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-68-7" name = "__codelineno-68-7" href = "#__codelineno-68-7" > < / a >
2023-02-10 01:03:44 +08:00
< a id = "__codelineno-68-8" name = "__codelineno-68-8" href = "#__codelineno-68-8" > < / a > < span class = "cm" > /* 递归插入结点（辅助方法） */< / span >
2023-02-08 14:54:41 +08:00
< a id = "__codelineno-68-9" name = "__codelineno-68-9" href = "#__codelineno-68-9" > < / a > < span class = "kd" > func< / span > < span class = "nf" > insertHelper< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > :< / span > < span class = "n" > TreeNode< / 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 > < span class = "n" > TreeNode< / span > < span class = "p" > ?< / span > < span class = "p" > {< / span >
< a id = "__codelineno-68-10" name = "__codelineno-68-10" href = "#__codelineno-68-10" > < / a > < span class = "kd" > var< / span > < span class = "nv" > node< / span > < span class = "p" > =< / span > < span class = "n" > node< / span >
< a id = "__codelineno-68-11" name = "__codelineno-68-11" href = "#__codelineno-68-11" > < / a > < span class = "k" > if< / span > < span class = "n" > node< / span > < span class = "p" > ==< / span > < span class = "kc" > nil< / span > < span class = "p" > {< / span >
< a id = "__codelineno-68-12" name = "__codelineno-68-12" href = "#__codelineno-68-12" > < / a > < span class = "k" > return< / span > < span class = "n" > TreeNode< / span > < span class = "p" > (< / span > < span class = "n" > x< / span > < span class = "p" > :< / span > < span class = "n" > val< / span > < span class = "p" > )< / span >
< a id = "__codelineno-68-13" name = "__codelineno-68-13" href = "#__codelineno-68-13" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-68-14" name = "__codelineno-68-14" href = "#__codelineno-68-14" > < / a > < span class = "cm" > /* 1. 查找插入位置，并插入结点 */< / span >
< a id = "__codelineno-68-15" name = "__codelineno-68-15" href = "#__codelineno-68-15" > < / a > < span class = "k" > if< / span > < span class = "n" > val< / span > < span class = "o" > < < / span > < span class = "n" > node< / span > < span class = "p" > !.< / span > < span class = "n" > val< / span > < span class = "p" > {< / span >
< a id = "__codelineno-68-16" name = "__codelineno-68-16" href = "#__codelineno-68-16" > < / a > < span class = "n" > node< / span > < span class = "p" > ?.< / span > < span class = "kr" > left< / span > < span class = "p" > =< / span > < span class = "n" > insertHelper< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > :< / span > < span class = "n" > node< / span > < span class = "p" > ?.< / span > < span class = "kr" > left< / span > < span class = "p" > ,< / span > < span class = "n" > val< / span > < span class = "p" > :< / span > < span class = "n" > val< / span > < span class = "p" > )< / span >
< a id = "__codelineno-68-17" name = "__codelineno-68-17" href = "#__codelineno-68-17" > < / a > < span class = "p" > }< / span > < span class = "k" > else< / span > < span class = "k" > if< / span > < span class = "n" > val< / span > < span class = "o" > > < / span > < span class = "n" > node< / span > < span class = "p" > !.< / span > < span class = "n" > val< / span > < span class = "p" > {< / span >
< a id = "__codelineno-68-18" name = "__codelineno-68-18" href = "#__codelineno-68-18" > < / a > < span class = "n" > node< / span > < span class = "p" > ?.< / span > < span class = "kr" > right< / span > < span class = "p" > =< / span > < span class = "n" > insertHelper< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > :< / span > < span class = "n" > node< / span > < span class = "p" > ?.< / span > < span class = "kr" > right< / span > < span class = "p" > ,< / span > < span class = "n" > val< / span > < span class = "p" > :< / span > < span class = "n" > val< / span > < span class = "p" > )< / span >
< a id = "__codelineno-68-19" name = "__codelineno-68-19" href = "#__codelineno-68-19" > < / a > < span class = "p" > }< / span > < span class = "k" > else< / span > < span class = "p" > {< / span >
< a id = "__codelineno-68-20" name = "__codelineno-68-20" href = "#__codelineno-68-20" > < / a > < span class = "k" > return< / span > < span class = "n" > node< / span > < span class = "c1" > // 重复结点不插入，直接返回< / span >
< a id = "__codelineno-68-21" name = "__codelineno-68-21" href = "#__codelineno-68-21" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-68-22" name = "__codelineno-68-22" href = "#__codelineno-68-22" > < / a > < span class = "n" > updateHeight< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > :< / span > < span class = "n" > node< / span > < span class = "p" > )< / span > < span class = "c1" > // 更新结点高度< / span >
< a id = "__codelineno-68-23" name = "__codelineno-68-23" href = "#__codelineno-68-23" > < / a > < span class = "cm" > /* 2. 执行旋转操作，使该子树重新恢复平衡 */< / span >
< a id = "__codelineno-68-24" name = "__codelineno-68-24" href = "#__codelineno-68-24" > < / a > < span class = "n" > node< / span > < span class = "p" > =< / span > < span class = "n" > rotate< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > :< / span > < span class = "n" > node< / span > < span class = "p" > )< / span >
< a id = "__codelineno-68-25" name = "__codelineno-68-25" href = "#__codelineno-68-25" > < / a > < span class = "c1" > // 返回子树的根结点< / span >
< a id = "__codelineno-68-26" name = "__codelineno-68-26" href = "#__codelineno-68-26" > < / a > < span class = "k" > return< / span > < span class = "n" > node< / span >
< a id = "__codelineno-68-27" name = "__codelineno-68-27" href = "#__codelineno-68-27" > < / 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" > avl_tree.zig< / span > < pre > < span > < / span > < code > < a id = "__codelineno-69-1" name = "__codelineno-69-1" href = "#__codelineno-69-1" > < / a > < span class = "c1" > // 插入结点< / span >
< a id = "__codelineno-69-2" name = "__codelineno-69-2" href = "#__codelineno-69-2" > < / a > < span class = "k" > fn< / span > < span class = "w" > < / span > < span class = "n" > insert< / 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 = "n" > inc< / span > < span class = "p" > .< / span > < span class = "n" > TreeNode< / span > < span class = "p" > (< / span > < span class = "n" > T< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-69-3" name = "__codelineno-69-3" href = "#__codelineno-69-3" > < / a > < span class = "w" > < / span > < span class = "n" > self< / span > < span class = "p" > .< / span > < span class = "n" > root< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < 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" > insertHelper< / span > < span class = "p" > (< / span > < span class = "n" > self< / span > < span class = "p" > .< / span > < span class = "n" > root< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > val< / span > < span class = "p" > );< / span >
< a id = "__codelineno-69-4" name = "__codelineno-69-4" href = "#__codelineno-69-4" > < / 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" > root< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-69-5" name = "__codelineno-69-5" href = "#__codelineno-69-5" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-69-6" name = "__codelineno-69-6" href = "#__codelineno-69-6" > < / a >
2023-02-10 01:03:44 +08:00
< a id = "__codelineno-69-7" name = "__codelineno-69-7" href = "#__codelineno-69-7" > < / a > < span class = "c1" > // 递归插入结点（辅助方法）< / span >
2023-02-09 22:55:35 +08:00
< a id = "__codelineno-69-8" name = "__codelineno-69-8" href = "#__codelineno-69-8" > < / a > < span class = "k" > fn< / span > < span class = "w" > < / span > < span class = "n" > insertHelper< / 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" > node_< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "o" > ?*< / span > < span class = "n" > inc< / span > < span class = "p" > .< / span > < span class = "n" > TreeNode< / span > < span class = "p" > (< / span > < span class = "n" > T< / 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 = "n" > inc< / span > < span class = "p" > .< / span > < span class = "n" > TreeNode< / span > < span class = "p" > (< / span > < span class = "n" > T< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-69-9" name = "__codelineno-69-9" href = "#__codelineno-69-9" > < / a > < span class = "w" > < / span > < span class = "kr" > var< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > node_< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-69-10" name = "__codelineno-69-10" href = "#__codelineno-69-10" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-69-11" name = "__codelineno-69-11" href = "#__codelineno-69-11" > < / a > < span class = "w" > < / span > < span class = "kr" > var< / span > < span class = "w" > < / span > < span class = "n" > tmp_node< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < 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" > mem_allocator< / span > < span class = "p" > .< / span > < span class = "n" > create< / span > < span class = "p" > (< / span > < span class = "n" > inc< / span > < span class = "p" > .< / span > < span class = "n" > TreeNode< / span > < span class = "p" > (< / span > < span class = "n" > T< / span > < span class = "p" > ));< / span >
< a id = "__codelineno-69-12" name = "__codelineno-69-12" href = "#__codelineno-69-12" > < / a > < span class = "w" > < / span > < span class = "n" > tmp_node< / span > < span class = "p" > .< / span > < span class = "n" > init< / span > < span class = "p" > (< / span > < span class = "n" > val< / span > < span class = "p" > );< / span >
< a id = "__codelineno-69-13" name = "__codelineno-69-13" href = "#__codelineno-69-13" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > tmp_node< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-69-14" name = "__codelineno-69-14" href = "#__codelineno-69-14" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-69-15" name = "__codelineno-69-15" href = "#__codelineno-69-15" > < / a > < span class = "w" > < / span > < span class = "c1" > // 1. 查找插入位置，并插入结点< / span >
< a id = "__codelineno-69-16" name = "__codelineno-69-16" href = "#__codelineno-69-16" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > val< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "o" > ?< / span > < span class = "p" > .< / span > < span class = "n" > val< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-69-17" name = "__codelineno-69-17" href = "#__codelineno-69-17" > < / a > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "o" > ?< / span > < span class = "p" > .< / span > < span class = "n" > left< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < 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" > insertHelper< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "o" > ?< / span > < span class = "p" > .< / span > < span class = "n" > left< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > val< / span > < span class = "p" > );< / span >
< a id = "__codelineno-69-18" name = "__codelineno-69-18" href = "#__codelineno-69-18" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > val< / span > < span class = "w" > < / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "o" > ?< / span > < span class = "p" > .< / span > < span class = "n" > val< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-69-19" name = "__codelineno-69-19" href = "#__codelineno-69-19" > < / a > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "o" > ?< / span > < span class = "p" > .< / span > < span class = "n" > right< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < 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" > insertHelper< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "o" > ?< / span > < span class = "p" > .< / span > < span class = "n" > right< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > val< / span > < span class = "p" > );< / span >
< a id = "__codelineno-69-20" name = "__codelineno-69-20" href = "#__codelineno-69-20" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-69-21" name = "__codelineno-69-21" href = "#__codelineno-69-21" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 重复结点不插入，直接返回< / span >
< a id = "__codelineno-69-22" name = "__codelineno-69-22" href = "#__codelineno-69-22" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-69-23" name = "__codelineno-69-23" href = "#__codelineno-69-23" > < / a > < span class = "w" > < / span > < span class = "n" > self< / span > < span class = "p" > .< / span > < span class = "n" > updateHeight< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 更新结点高度< / span >
< a id = "__codelineno-69-24" name = "__codelineno-69-24" href = "#__codelineno-69-24" > < / a > < span class = "w" > < / span > < span class = "c1" > // 2. 执行旋转操作，使该子树重新恢复平衡< / span >
< a id = "__codelineno-69-25" name = "__codelineno-69-25" href = "#__codelineno-69-25" > < / a > < span class = "w" > < / span > < span class = "n" > node< / 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" > rotate< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > );< / span >
< a id = "__codelineno-69-26" name = "__codelineno-69-26" href = "#__codelineno-69-26" > < / a > < span class = "w" > < / span > < span class = "c1" > // 返回子树的根结点< / span >
< a id = "__codelineno-69-27" name = "__codelineno-69-27" href = "#__codelineno-69-27" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-69-28" name = "__codelineno-69-28" href = "#__codelineno-69-28" > < / a > < span class = "p" > }< / span >
2023-02-08 14:54:41 +08:00
< / code > < / pre > < / div >
< / div >
< / div >
< / div >
< h3 id = "_5" > 删除结点< a class = "headerlink" href = "#_5" title = "Permanent link" > ¶ < / a > < / h3 >
< p > 「AVL 树」删除结点操作与「二叉搜索树」删除结点操作总体相同。类似地，< strong > 在删除结点后，也需要从底至顶地执行旋转操作，使所有失衡结点恢复平衡< / strong > 。< / p >
< div class = "tabbed-set tabbed-alternate" data-tabs = "9:10" > < input checked = "checked" id = "__tabbed_9_1" name = "__tabbed_9" type = "radio" / > < input id = "__tabbed_9_2" name = "__tabbed_9" type = "radio" / > < input id = "__tabbed_9_3" name = "__tabbed_9" type = "radio" / > < input id = "__tabbed_9_4" name = "__tabbed_9" type = "radio" / > < input id = "__tabbed_9_5" name = "__tabbed_9" type = "radio" / > < input id = "__tabbed_9_6" name = "__tabbed_9" type = "radio" / > < input id = "__tabbed_9_7" name = "__tabbed_9" type = "radio" / > < input id = "__tabbed_9_8" name = "__tabbed_9" type = "radio" / > < input id = "__tabbed_9_9" name = "__tabbed_9" type = "radio" / > < input id = "__tabbed_9_10" name = "__tabbed_9" type = "radio" / > < div class = "tabbed-labels" > < label for = "__tabbed_9_1" > Java< / label > < label for = "__tabbed_9_2" > C++< / label > < label for = "__tabbed_9_3" > Python< / label > < label for = "__tabbed_9_4" > Go< / label > < label for = "__tabbed_9_5" > JavaScript< / label > < label for = "__tabbed_9_6" > TypeScript< / label > < label for = "__tabbed_9_7" > C< / label > < label for = "__tabbed_9_8" > C#< / label > < label for = "__tabbed_9_9" > Swift< / label > < label for = "__tabbed_9_10" > Zig< / label > < / div >
< div class = "tabbed-content" >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > avl_tree.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-70-1" name = "__codelineno-70-1" href = "#__codelineno-70-1" > < / a > < span class = "cm" > /* 删除结点 */< / span >
< a id = "__codelineno-70-2" name = "__codelineno-70-2" href = "#__codelineno-70-2" > < / a > < span class = "n" > TreeNode< / span > < span class = "w" > < / span > < span class = "nf" > remove< / 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-70-3" name = "__codelineno-70-3" href = "#__codelineno-70-3" > < / a > < span class = "w" > < / span > < span class = "n" > root< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > removeHelper< / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > val< / span > < span class = "p" > );< / span >
< a id = "__codelineno-70-4" name = "__codelineno-70-4" href = "#__codelineno-70-4" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > root< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-70-5" name = "__codelineno-70-5" href = "#__codelineno-70-5" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-70-6" name = "__codelineno-70-6" href = "#__codelineno-70-6" > < / a >
2023-02-10 01:03:44 +08:00
< a id = "__codelineno-70-7" name = "__codelineno-70-7" href = "#__codelineno-70-7" > < / a > < span class = "cm" > /* 递归删除结点（辅助方法） */< / span >
2023-02-08 14:54:41 +08:00
< a id = "__codelineno-70-8" name = "__codelineno-70-8" href = "#__codelineno-70-8" > < / a > < span class = "n" > TreeNode< / span > < span class = "w" > < / span > < span class = "nf" > removeHelper< / span > < span class = "p" > (< / span > < span class = "n" > TreeNode< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > val< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-70-9" name = "__codelineno-70-9" href = "#__codelineno-70-9" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-70-10" name = "__codelineno-70-10" href = "#__codelineno-70-10" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 1. 查找结点，并删除之 */< / span >
< a id = "__codelineno-70-11" name = "__codelineno-70-11" href = "#__codelineno-70-11" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > val< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "na" > val< / span > < span class = "p" > )< / span >
< a id = "__codelineno-70-12" name = "__codelineno-70-12" href = "#__codelineno-70-12" > < / a > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "na" > left< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > removeHelper< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "na" > left< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > val< / span > < span class = "p" > );< / span >
< a id = "__codelineno-70-13" name = "__codelineno-70-13" href = "#__codelineno-70-13" > < / a > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > val< / span > < span class = "w" > < / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "na" > val< / span > < span class = "p" > )< / span >
< a id = "__codelineno-70-14" name = "__codelineno-70-14" href = "#__codelineno-70-14" > < / a > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "na" > right< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > removeHelper< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "na" > right< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > val< / span > < span class = "p" > );< / span >
< a id = "__codelineno-70-15" name = "__codelineno-70-15" href = "#__codelineno-70-15" > < / a > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-70-16" name = "__codelineno-70-16" href = "#__codelineno-70-16" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "na" > left< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "w" > < / span > < span class = "o" > ||< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "na" > right< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-70-17" name = "__codelineno-70-17" href = "#__codelineno-70-17" > < / a > < span class = "w" > < / span > < span class = "n" > TreeNode< / span > < span class = "w" > < / span > < span class = "n" > child< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "na" > left< / span > < span class = "w" > < / span > < span class = "o" > !=< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "w" > < / span > < span class = "o" > ?< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "na" > left< / span > < span class = "w" > < / span > < span class = "p" > :< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "na" > right< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-70-18" name = "__codelineno-70-18" href = "#__codelineno-70-18" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子结点数量 = 0 ，直接删除 node 并返回< / span >
< a id = "__codelineno-70-19" name = "__codelineno-70-19" href = "#__codelineno-70-19" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > child< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > )< / span >
< a id = "__codelineno-70-20" name = "__codelineno-70-20" href = "#__codelineno-70-20" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-70-21" name = "__codelineno-70-21" href = "#__codelineno-70-21" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子结点数量 = 1 ，直接删除 node< / span >
< a id = "__codelineno-70-22" name = "__codelineno-70-22" href = "#__codelineno-70-22" > < / a > < span class = "w" > < / span > < span class = "k" > else< / span >
< a id = "__codelineno-70-23" name = "__codelineno-70-23" href = "#__codelineno-70-23" > < / a > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > child< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-70-24" name = "__codelineno-70-24" href = "#__codelineno-70-24" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-70-25" name = "__codelineno-70-25" href = "#__codelineno-70-25" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子结点数量 = 2 ，则将中序遍历的下个结点删除，并用该结点替换当前结点< / span >
< a id = "__codelineno-70-26" name = "__codelineno-70-26" href = "#__codelineno-70-26" > < / a > < span class = "w" > < / span > < span class = "n" > TreeNode< / span > < span class = "w" > < / span > < span class = "n" > temp< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > getInOrderNext< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "na" > right< / span > < span class = "p" > );< / span >
< a id = "__codelineno-70-27" name = "__codelineno-70-27" href = "#__codelineno-70-27" > < / a > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "na" > right< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > removeHelper< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "na" > right< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > temp< / span > < span class = "p" > .< / span > < span class = "na" > val< / span > < span class = "p" > );< / span >
< a id = "__codelineno-70-28" name = "__codelineno-70-28" href = "#__codelineno-70-28" > < / a > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "na" > val< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > temp< / span > < span class = "p" > .< / span > < span class = "na" > val< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-70-29" name = "__codelineno-70-29" href = "#__codelineno-70-29" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-70-30" name = "__codelineno-70-30" href = "#__codelineno-70-30" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-70-31" name = "__codelineno-70-31" href = "#__codelineno-70-31" > < / a > < span class = "w" > < / span > < span class = "n" > updateHeight< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 更新结点高度< / span >
< a id = "__codelineno-70-32" name = "__codelineno-70-32" href = "#__codelineno-70-32" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 2. 执行旋转操作，使该子树重新恢复平衡 */< / span >
< a id = "__codelineno-70-33" name = "__codelineno-70-33" href = "#__codelineno-70-33" > < / a > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > rotate< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > );< / span >
< a id = "__codelineno-70-34" name = "__codelineno-70-34" href = "#__codelineno-70-34" > < / a > < span class = "w" > < / span > < span class = "c1" > // 返回子树的根结点< / span >
< a id = "__codelineno-70-35" name = "__codelineno-70-35" href = "#__codelineno-70-35" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-70-36" name = "__codelineno-70-36" href = "#__codelineno-70-36" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-70-37" name = "__codelineno-70-37" href = "#__codelineno-70-37" > < / a >
< a id = "__codelineno-70-38" name = "__codelineno-70-38" href = "#__codelineno-70-38" > < / a > < span class = "cm" > /* 获取中序遍历中的下一个结点（仅适用于 root 有左子结点的情况） */< / span >
< a id = "__codelineno-70-39" name = "__codelineno-70-39" href = "#__codelineno-70-39" > < / a > < span class = "n" > TreeNode< / span > < span class = "w" > < / span > < span class = "nf" > getInOrderNext< / span > < span class = "p" > (< / span > < span class = "n" > TreeNode< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-70-40" name = "__codelineno-70-40" href = "#__codelineno-70-40" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-70-41" name = "__codelineno-70-41" href = "#__codelineno-70-41" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环访问左子结点，直到叶结点时为最小结点，跳出< / span >
< a id = "__codelineno-70-42" name = "__codelineno-70-42" href = "#__codelineno-70-42" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "na" > left< / span > < span class = "w" > < / span > < span class = "o" > !=< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-70-43" name = "__codelineno-70-43" href = "#__codelineno-70-43" > < / a > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "na" > left< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-70-44" name = "__codelineno-70-44" href = "#__codelineno-70-44" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-70-45" name = "__codelineno-70-45" href = "#__codelineno-70-45" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-70-46" name = "__codelineno-70-46" href = "#__codelineno-70-46" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > avl_tree.cpp< / span > < pre > < span > < / span > < code > < a id = "__codelineno-71-1" name = "__codelineno-71-1" href = "#__codelineno-71-1" > < / a > < span class = "cm" > /* 删除结点 */< / span >
< a id = "__codelineno-71-2" name = "__codelineno-71-2" href = "#__codelineno-71-2" > < / a > < span class = "n" > TreeNode< / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "nf" > remove< / 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-71-3" name = "__codelineno-71-3" href = "#__codelineno-71-3" > < / a > < span class = "w" > < / span > < span class = "n" > root< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > removeHelper< / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > val< / span > < span class = "p" > );< / span >
< a id = "__codelineno-71-4" name = "__codelineno-71-4" href = "#__codelineno-71-4" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > root< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-71-5" name = "__codelineno-71-5" href = "#__codelineno-71-5" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-71-6" name = "__codelineno-71-6" href = "#__codelineno-71-6" > < / a >
2023-02-10 01:03:44 +08:00
< a id = "__codelineno-71-7" name = "__codelineno-71-7" href = "#__codelineno-71-7" > < / a > < span class = "cm" > /* 递归删除结点（辅助方法） */< / span >
2023-02-08 14:54:41 +08:00
< a id = "__codelineno-71-8" name = "__codelineno-71-8" href = "#__codelineno-71-8" > < / a > < span class = "n" > TreeNode< / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "nf" > removeHelper< / span > < span class = "p" > (< / span > < span class = "n" > TreeNode< / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > val< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-71-9" name = "__codelineno-71-9" href = "#__codelineno-71-9" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "k" > nullptr< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "k" > nullptr< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-71-10" name = "__codelineno-71-10" href = "#__codelineno-71-10" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 1. 查找结点，并删除之 */< / span >
< a id = "__codelineno-71-11" name = "__codelineno-71-11" href = "#__codelineno-71-11" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > val< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "o" > -> < / span > < span class = "n" > val< / span > < span class = "p" > )< / span >
< a id = "__codelineno-71-12" name = "__codelineno-71-12" href = "#__codelineno-71-12" > < / a > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "o" > -> < / span > < span class = "n" > left< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > removeHelper< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "o" > -> < / span > < span class = "n" > left< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > val< / span > < span class = "p" > );< / span >
< a id = "__codelineno-71-13" name = "__codelineno-71-13" href = "#__codelineno-71-13" > < / a > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > val< / span > < span class = "w" > < / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "o" > -> < / span > < span class = "n" > val< / span > < span class = "p" > )< / span >
< a id = "__codelineno-71-14" name = "__codelineno-71-14" href = "#__codelineno-71-14" > < / a > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "o" > -> < / span > < span class = "n" > right< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > removeHelper< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "o" > -> < / span > < span class = "n" > right< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > val< / span > < span class = "p" > );< / span >
< a id = "__codelineno-71-15" name = "__codelineno-71-15" href = "#__codelineno-71-15" > < / a > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-71-16" name = "__codelineno-71-16" href = "#__codelineno-71-16" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "o" > -> < / span > < span class = "n" > left< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "k" > nullptr< / span > < span class = "w" > < / span > < span class = "o" > ||< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "o" > -> < / span > < span class = "n" > right< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "k" > nullptr< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-71-17" name = "__codelineno-71-17" href = "#__codelineno-71-17" > < / a > < span class = "w" > < / span > < span class = "n" > TreeNode< / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "n" > child< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "o" > -> < / span > < span class = "n" > left< / span > < span class = "w" > < / span > < span class = "o" > !=< / span > < span class = "w" > < / span > < span class = "k" > nullptr< / span > < span class = "w" > < / span > < span class = "o" > ?< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "o" > -> < / span > < span class = "n" > left< / span > < span class = "w" > < / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "o" > -> < / span > < span class = "n" > right< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-71-18" name = "__codelineno-71-18" href = "#__codelineno-71-18" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子结点数量 = 0 ，直接删除 node 并返回< / span >
< a id = "__codelineno-71-19" name = "__codelineno-71-19" href = "#__codelineno-71-19" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > child< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "k" > nullptr< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-71-20" name = "__codelineno-71-20" href = "#__codelineno-71-20" > < / a > < span class = "w" > < / span > < span class = "k" > delete< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-71-21" name = "__codelineno-71-21" href = "#__codelineno-71-21" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "k" > nullptr< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-71-22" name = "__codelineno-71-22" href = "#__codelineno-71-22" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-71-23" name = "__codelineno-71-23" href = "#__codelineno-71-23" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子结点数量 = 1 ，直接删除 node< / span >
< a id = "__codelineno-71-24" name = "__codelineno-71-24" href = "#__codelineno-71-24" > < / a > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-71-25" name = "__codelineno-71-25" href = "#__codelineno-71-25" > < / a > < span class = "w" > < / span > < span class = "k" > delete< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-71-26" name = "__codelineno-71-26" href = "#__codelineno-71-26" > < / a > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > child< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-71-27" name = "__codelineno-71-27" href = "#__codelineno-71-27" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-71-28" name = "__codelineno-71-28" href = "#__codelineno-71-28" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-71-29" name = "__codelineno-71-29" href = "#__codelineno-71-29" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子结点数量 = 2 ，则将中序遍历的下个结点删除，并用该结点替换当前结点< / span >
< a id = "__codelineno-71-30" name = "__codelineno-71-30" href = "#__codelineno-71-30" > < / a > < span class = "w" > < / span > < span class = "n" > TreeNode< / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "n" > temp< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > getInOrderNext< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "o" > -> < / span > < span class = "n" > right< / span > < span class = "p" > );< / span >
< a id = "__codelineno-71-31" name = "__codelineno-71-31" href = "#__codelineno-71-31" > < / a > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "o" > -> < / span > < span class = "n" > right< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > removeHelper< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "o" > -> < / span > < span class = "n" > right< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > temp< / span > < span class = "o" > -> < / span > < span class = "n" > val< / span > < span class = "p" > );< / span >
< a id = "__codelineno-71-32" name = "__codelineno-71-32" href = "#__codelineno-71-32" > < / a > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "o" > -> < / span > < span class = "n" > val< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > temp< / span > < span class = "o" > -> < / span > < span class = "n" > val< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-71-33" name = "__codelineno-71-33" href = "#__codelineno-71-33" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-71-34" name = "__codelineno-71-34" href = "#__codelineno-71-34" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-71-35" name = "__codelineno-71-35" href = "#__codelineno-71-35" > < / a > < span class = "w" > < / span > < span class = "n" > updateHeight< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 更新结点高度< / span >
< a id = "__codelineno-71-36" name = "__codelineno-71-36" href = "#__codelineno-71-36" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 2. 执行旋转操作，使该子树重新恢复平衡 */< / span >
< a id = "__codelineno-71-37" name = "__codelineno-71-37" href = "#__codelineno-71-37" > < / a > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > rotate< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > );< / span >
< a id = "__codelineno-71-38" name = "__codelineno-71-38" href = "#__codelineno-71-38" > < / a > < span class = "w" > < / span > < span class = "c1" > // 返回子树的根结点< / span >
< a id = "__codelineno-71-39" name = "__codelineno-71-39" href = "#__codelineno-71-39" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-71-40" name = "__codelineno-71-40" href = "#__codelineno-71-40" > < / a > < span class = "p" > }< / span >
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< a id = "__codelineno-71-41" name = "__codelineno-71-41" href = "#__codelineno-71-41" > < / a >
< a id = "__codelineno-71-42" name = "__codelineno-71-42" href = "#__codelineno-71-42" > < / a > < span class = "cm" > /* 获取中序遍历中的下一个结点（仅适用于 root 有左子结点的情况） */< / span >
< a id = "__codelineno-71-43" name = "__codelineno-71-43" href = "#__codelineno-71-43" > < / a > < span class = "n" > TreeNode< / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "nf" > getInOrderNext< / span > < span class = "p" > (< / span > < span class = "n" > TreeNode< / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-71-44" name = "__codelineno-71-44" href = "#__codelineno-71-44" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "k" > nullptr< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-71-45" name = "__codelineno-71-45" href = "#__codelineno-71-45" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环访问左子结点，直到叶结点时为最小结点，跳出< / span >
< a id = "__codelineno-71-46" name = "__codelineno-71-46" href = "#__codelineno-71-46" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "o" > -> < / span > < span class = "n" > left< / span > < span class = "w" > < / span > < span class = "o" > !=< / span > < span class = "w" > < / span > < span class = "k" > nullptr< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-71-47" name = "__codelineno-71-47" href = "#__codelineno-71-47" > < / a > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "o" > -> < / span > < span class = "n" > left< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-71-48" name = "__codelineno-71-48" href = "#__codelineno-71-48" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-71-49" name = "__codelineno-71-49" href = "#__codelineno-71-49" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-71-50" name = "__codelineno-71-50" href = "#__codelineno-71-50" > < / a > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > avl_tree.py< / span > < pre > < span > < / span > < code > < a id = "__codelineno-72-1" name = "__codelineno-72-1" href = "#__codelineno-72-1" > < / a > < span class = "sd" > " " " 删除结点 " " " < / span >
< a id = "__codelineno-72-2" name = "__codelineno-72-2" href = "#__codelineno-72-2" > < / a > < span class = "k" > def< / span > < span class = "nf" > remove< / 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-72-3" name = "__codelineno-72-3" href = "#__codelineno-72-3" > < / a > < span class = "n" > root< / span > < span class = "o" > =< / span > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > __remove_helper< / span > < span class = "p" > (< / span > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > root< / span > < span class = "p" > ,< / span > < span class = "n" > val< / span > < span class = "p" > )< / span >
< a id = "__codelineno-72-4" name = "__codelineno-72-4" href = "#__codelineno-72-4" > < / a > < span class = "k" > return< / span > < span class = "n" > root< / span >
< a id = "__codelineno-72-5" name = "__codelineno-72-5" href = "#__codelineno-72-5" > < / a >
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< a id = "__codelineno-72-6" name = "__codelineno-72-6" href = "#__codelineno-72-6" > < / a > < span class = "sd" > " " " 递归删除结点（辅助方法） " " " < / span >
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< a id = "__codelineno-72-7" name = "__codelineno-72-7" href = "#__codelineno-72-7" > < / a > < span class = "k" > def< / span > < span class = "nf" > __remove_helper< / span > < span class = "p" > (< / span > < span class = "bp" > self< / span > < span class = "p" > ,< / span > < span class = "n" > node< / span > < span class = "p" > :< / span > < span class = "n" > Optional< / span > < span class = "p" > [< / span > < span class = "n" > TreeNode< / 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 = "o" > -> < / span > < span class = "n" > Optional< / span > < span class = "p" > [< / span > < span class = "n" > TreeNode< / span > < span class = "p" > ]:< / span >
< a id = "__codelineno-72-8" name = "__codelineno-72-8" href = "#__codelineno-72-8" > < / a > < span class = "k" > if< / span > < span class = "n" > node< / span > < span class = "ow" > is< / span > < span class = "kc" > None< / span > < span class = "p" > :< / span >
< a id = "__codelineno-72-9" name = "__codelineno-72-9" href = "#__codelineno-72-9" > < / a > < span class = "k" > return< / span > < span class = "kc" > None< / span >
< a id = "__codelineno-72-10" name = "__codelineno-72-10" href = "#__codelineno-72-10" > < / a > < span class = "c1" > # 1. 查找结点，并删除之< / span >
< a id = "__codelineno-72-11" name = "__codelineno-72-11" href = "#__codelineno-72-11" > < / a > < span class = "k" > if< / span > < span class = "n" > val< / span > < span class = "o" > < < / span > < span class = "n" > node< / span > < span class = "o" > .< / span > < span class = "n" > val< / span > < span class = "p" > :< / span >
< a id = "__codelineno-72-12" name = "__codelineno-72-12" href = "#__codelineno-72-12" > < / a > < span class = "n" > node< / span > < span class = "o" > .< / span > < span class = "n" > left< / span > < span class = "o" > =< / span > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > __remove_helper< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "o" > .< / span > < span class = "n" > left< / span > < span class = "p" > ,< / span > < span class = "n" > val< / span > < span class = "p" > )< / span >
< a id = "__codelineno-72-13" name = "__codelineno-72-13" href = "#__codelineno-72-13" > < / a > < span class = "k" > elif< / span > < span class = "n" > val< / span > < span class = "o" > > < / span > < span class = "n" > node< / span > < span class = "o" > .< / span > < span class = "n" > val< / span > < span class = "p" > :< / span >
< a id = "__codelineno-72-14" name = "__codelineno-72-14" href = "#__codelineno-72-14" > < / a > < span class = "n" > node< / span > < span class = "o" > .< / span > < span class = "n" > right< / span > < span class = "o" > =< / span > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > __remove_helper< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "o" > .< / span > < span class = "n" > right< / span > < span class = "p" > ,< / span > < span class = "n" > val< / span > < span class = "p" > )< / span >
< a id = "__codelineno-72-15" name = "__codelineno-72-15" href = "#__codelineno-72-15" > < / a > < span class = "k" > else< / span > < span class = "p" > :< / span >
< a id = "__codelineno-72-16" name = "__codelineno-72-16" href = "#__codelineno-72-16" > < / a > < span class = "k" > if< / span > < span class = "n" > node< / span > < span class = "o" > .< / span > < span class = "n" > left< / span > < span class = "ow" > is< / span > < span class = "kc" > None< / span > < span class = "ow" > or< / span > < span class = "n" > node< / span > < span class = "o" > .< / span > < span class = "n" > right< / span > < span class = "ow" > is< / span > < span class = "kc" > None< / span > < span class = "p" > :< / span >
< a id = "__codelineno-72-17" name = "__codelineno-72-17" href = "#__codelineno-72-17" > < / a > < span class = "n" > child< / span > < span class = "o" > =< / span > < span class = "n" > node< / span > < span class = "o" > .< / span > < span class = "n" > left< / span > < span class = "ow" > or< / span > < span class = "n" > node< / span > < span class = "o" > .< / span > < span class = "n" > right< / span >
< a id = "__codelineno-72-18" name = "__codelineno-72-18" href = "#__codelineno-72-18" > < / a > < span class = "c1" > # 子结点数量 = 0 ，直接删除 node 并返回< / span >
< a id = "__codelineno-72-19" name = "__codelineno-72-19" href = "#__codelineno-72-19" > < / a > < span class = "k" > if< / span > < span class = "n" > child< / span > < span class = "ow" > is< / span > < span class = "kc" > None< / span > < span class = "p" > :< / span >
< a id = "__codelineno-72-20" name = "__codelineno-72-20" href = "#__codelineno-72-20" > < / a > < span class = "k" > return< / span > < span class = "kc" > None< / span >
< a id = "__codelineno-72-21" name = "__codelineno-72-21" href = "#__codelineno-72-21" > < / a > < span class = "c1" > # 子结点数量 = 1 ，直接删除 node< / span >
< a id = "__codelineno-72-22" name = "__codelineno-72-22" href = "#__codelineno-72-22" > < / a > < span class = "k" > else< / span > < span class = "p" > :< / span >
< a id = "__codelineno-72-23" name = "__codelineno-72-23" href = "#__codelineno-72-23" > < / a > < span class = "n" > node< / span > < span class = "o" > =< / span > < span class = "n" > child< / span >
< a id = "__codelineno-72-24" name = "__codelineno-72-24" href = "#__codelineno-72-24" > < / a > < span class = "k" > else< / span > < span class = "p" > :< / span > < span class = "c1" > # 子结点数量 = 2 ，则将中序遍历的下个结点删除，并用该结点替换当前结点< / span >
< a id = "__codelineno-72-25" name = "__codelineno-72-25" href = "#__codelineno-72-25" > < / a > < span class = "n" > temp< / span > < span class = "o" > =< / span > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > __get_inorder_next< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "o" > .< / span > < span class = "n" > right< / span > < span class = "p" > )< / span >
< a id = "__codelineno-72-26" name = "__codelineno-72-26" href = "#__codelineno-72-26" > < / a > < span class = "n" > node< / span > < span class = "o" > .< / span > < span class = "n" > right< / span > < span class = "o" > =< / span > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > __remove_helper< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "o" > .< / span > < span class = "n" > right< / span > < span class = "p" > ,< / span > < span class = "n" > temp< / span > < span class = "o" > .< / span > < span class = "n" > val< / span > < span class = "p" > )< / span >
< a id = "__codelineno-72-27" name = "__codelineno-72-27" href = "#__codelineno-72-27" > < / a > < span class = "n" > node< / span > < span class = "o" > .< / span > < span class = "n" > val< / span > < span class = "o" > =< / span > < span class = "n" > temp< / span > < span class = "o" > .< / span > < span class = "n" > val< / span >
< a id = "__codelineno-72-28" name = "__codelineno-72-28" href = "#__codelineno-72-28" > < / a > < span class = "c1" > # 更新结点高度< / span >
< a id = "__codelineno-72-29" name = "__codelineno-72-29" href = "#__codelineno-72-29" > < / a > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > __update_height< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > )< / span >
< a id = "__codelineno-72-30" name = "__codelineno-72-30" href = "#__codelineno-72-30" > < / a > < span class = "c1" > # 2. 执行旋转操作，使该子树重新恢复平衡< / span >
< a id = "__codelineno-72-31" name = "__codelineno-72-31" href = "#__codelineno-72-31" > < / a > < span class = "k" > return< / span > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > __rotate< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > )< / span >
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< a id = "__codelineno-72-32" name = "__codelineno-72-32" href = "#__codelineno-72-32" > < / a >
< a id = "__codelineno-72-33" name = "__codelineno-72-33" href = "#__codelineno-72-33" > < / a > < span class = "sd" > " " " 获取中序遍历中的下一个结点（仅适用于 root 有左子结点的情况） " " " < / span >
< a id = "__codelineno-72-34" name = "__codelineno-72-34" href = "#__codelineno-72-34" > < / a > < span class = "k" > def< / span > < span class = "nf" > __get_inorder_next< / span > < span class = "p" > (< / span > < span class = "bp" > self< / span > < span class = "p" > ,< / span > < span class = "n" > node< / span > < span class = "p" > :< / span > < span class = "n" > Optional< / span > < span class = "p" > [< / span > < span class = "n" > TreeNode< / span > < span class = "p" > ])< / span > < span class = "o" > -> < / span > < span class = "n" > Optional< / span > < span class = "p" > [< / span > < span class = "n" > TreeNode< / span > < span class = "p" > ]:< / span >
< a id = "__codelineno-72-35" name = "__codelineno-72-35" href = "#__codelineno-72-35" > < / a > < span class = "k" > if< / span > < span class = "n" > node< / span > < span class = "ow" > is< / span > < span class = "kc" > None< / span > < span class = "p" > :< / span >
< a id = "__codelineno-72-36" name = "__codelineno-72-36" href = "#__codelineno-72-36" > < / a > < span class = "k" > return< / span > < span class = "kc" > None< / span >
< a id = "__codelineno-72-37" name = "__codelineno-72-37" href = "#__codelineno-72-37" > < / a > < span class = "c1" > # 循环访问左子结点，直到叶结点时为最小结点，跳出< / span >
< a id = "__codelineno-72-38" name = "__codelineno-72-38" href = "#__codelineno-72-38" > < / a > < span class = "k" > while< / span > < span class = "n" > node< / span > < span class = "o" > .< / span > < span class = "n" > left< / span > < span class = "ow" > is< / span > < span class = "ow" > not< / span > < span class = "kc" > None< / span > < span class = "p" > :< / span >
< a id = "__codelineno-72-39" name = "__codelineno-72-39" href = "#__codelineno-72-39" > < / a > < span class = "n" > node< / span > < span class = "o" > =< / span > < span class = "n" > node< / span > < span class = "o" > .< / span > < span class = "n" > left< / span >
< a id = "__codelineno-72-40" name = "__codelineno-72-40" href = "#__codelineno-72-40" > < / a > < span class = "k" > return< / span > < span class = "n" > node< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > avl_tree.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-73-1" name = "__codelineno-73-1" href = "#__codelineno-73-1" > < / a > < span class = "cm" > /* 删除结点 */< / span >
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< a id = "__codelineno-73-2" name = "__codelineno-73-2" href = "#__codelineno-73-2" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > t< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > aVLTree< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "nx" > remove< / span > < span class = "p" > (< / span > < span class = "nx" > val< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > TreeNode< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-73-3" name = "__codelineno-73-3" href = "#__codelineno-73-3" > < / a > < span class = "w" > < / span > < span class = "nx" > root< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nx" > t< / span > < span class = "p" > .< / span > < span class = "nx" > removeHelper< / span > < span class = "p" > (< / span > < span class = "nx" > t< / span > < span class = "p" > .< / span > < span class = "nx" > root< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > val< / span > < span class = "p" > )< / span >
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< a id = "__codelineno-73-4" name = "__codelineno-73-4" href = "#__codelineno-73-4" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > root< / span >
< a id = "__codelineno-73-5" name = "__codelineno-73-5" href = "#__codelineno-73-5" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-73-6" name = "__codelineno-73-6" href = "#__codelineno-73-6" > < / a >
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< a id = "__codelineno-73-7" name = "__codelineno-73-7" href = "#__codelineno-73-7" > < / a > < span class = "cm" > /* 递归删除结点（辅助方法） */< / span >
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< a id = "__codelineno-73-8" name = "__codelineno-73-8" href = "#__codelineno-73-8" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > t< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > aVLTree< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "nx" > removeHelper< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > TreeNode< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > val< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > TreeNode< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
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< a id = "__codelineno-73-9" name = "__codelineno-73-9" href = "#__codelineno-73-9" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "kc" > nil< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-73-10" name = "__codelineno-73-10" href = "#__codelineno-73-10" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "kc" > nil< / span >
< a id = "__codelineno-73-11" name = "__codelineno-73-11" href = "#__codelineno-73-11" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-73-12" name = "__codelineno-73-12" href = "#__codelineno-73-12" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 1. 查找结点，并删除之 */< / span >
< a id = "__codelineno-73-13" name = "__codelineno-73-13" href = "#__codelineno-73-13" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "nx" > val< / span > < span class = "w" > < / span > < span class = "p" > < < / span > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > Val< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
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< a id = "__codelineno-73-14" name = "__codelineno-73-14" href = "#__codelineno-73-14" > < / a > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > Left< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "nx" > t< / span > < span class = "p" > .< / span > < span class = "nx" > removeHelper< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > Left< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > val< / span > < span class = "p" > )< / span >
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< a id = "__codelineno-73-15" name = "__codelineno-73-15" href = "#__codelineno-73-15" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "nx" > val< / span > < span class = "w" > < / span > < span class = "p" > > < / span > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > Val< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
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< a id = "__codelineno-73-16" name = "__codelineno-73-16" href = "#__codelineno-73-16" > < / a > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > Right< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "nx" > t< / span > < span class = "p" > .< / span > < span class = "nx" > removeHelper< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > Right< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > val< / span > < span class = "p" > )< / span >
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< a id = "__codelineno-73-17" name = "__codelineno-73-17" href = "#__codelineno-73-17" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-73-18" name = "__codelineno-73-18" href = "#__codelineno-73-18" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > Left< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "kc" > nil< / span > < span class = "w" > < / span > < span class = "o" > ||< / span > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > Right< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "kc" > nil< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-73-19" name = "__codelineno-73-19" href = "#__codelineno-73-19" > < / a > < span class = "w" > < / span > < span class = "nx" > child< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > Left< / span >
< a id = "__codelineno-73-20" name = "__codelineno-73-20" href = "#__codelineno-73-20" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > Right< / span > < span class = "w" > < / span > < span class = "o" > !=< / span > < span class = "w" > < / span > < span class = "kc" > nil< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-73-21" name = "__codelineno-73-21" href = "#__codelineno-73-21" > < / a > < span class = "w" > < / span > < span class = "nx" > child< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > Right< / span >
< a id = "__codelineno-73-22" name = "__codelineno-73-22" href = "#__codelineno-73-22" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-73-23" name = "__codelineno-73-23" href = "#__codelineno-73-23" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子结点数量 = 0 ，直接删除 node 并返回< / span >
< a id = "__codelineno-73-24" name = "__codelineno-73-24" href = "#__codelineno-73-24" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "nx" > child< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "kc" > nil< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-73-25" name = "__codelineno-73-25" href = "#__codelineno-73-25" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "kc" > nil< / span >
< a id = "__codelineno-73-26" name = "__codelineno-73-26" href = "#__codelineno-73-26" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-73-27" name = "__codelineno-73-27" href = "#__codelineno-73-27" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子结点数量 = 1 ，直接删除 node< / span >
< a id = "__codelineno-73-28" name = "__codelineno-73-28" href = "#__codelineno-73-28" > < / a > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "nx" > child< / span >
< a id = "__codelineno-73-29" name = "__codelineno-73-29" href = "#__codelineno-73-29" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-73-30" name = "__codelineno-73-30" href = "#__codelineno-73-30" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-73-31" name = "__codelineno-73-31" href = "#__codelineno-73-31" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子结点数量 = 2 ，则将中序遍历的下个结点删除，并用该结点替换当前结点< / span >
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< a id = "__codelineno-73-32" name = "__codelineno-73-32" href = "#__codelineno-73-32" > < / a > < span class = "w" > < / span > < span class = "nx" > temp< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nx" > t< / span > < span class = "p" > .< / span > < span class = "nx" > getInOrderNext< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > Right< / span > < span class = "p" > )< / span >
< a id = "__codelineno-73-33" name = "__codelineno-73-33" href = "#__codelineno-73-33" > < / a > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > Right< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "nx" > t< / span > < span class = "p" > .< / span > < span class = "nx" > removeHelper< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > Right< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > temp< / span > < span class = "p" > .< / span > < span class = "nx" > Val< / span > < span class = "p" > )< / span >
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< a id = "__codelineno-73-34" name = "__codelineno-73-34" href = "#__codelineno-73-34" > < / a > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > Val< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "nx" > temp< / span > < span class = "p" > .< / span > < span class = "nx" > Val< / span >
< a id = "__codelineno-73-35" name = "__codelineno-73-35" href = "#__codelineno-73-35" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-73-36" name = "__codelineno-73-36" href = "#__codelineno-73-36" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-73-37" name = "__codelineno-73-37" href = "#__codelineno-73-37" > < / a > < span class = "w" > < / span > < span class = "c1" > // 更新结点高度< / span >
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< a id = "__codelineno-73-38" name = "__codelineno-73-38" href = "#__codelineno-73-38" > < / a > < span class = "w" > < / span > < span class = "nx" > t< / span > < span class = "p" > .< / span > < span class = "nx" > updateHeight< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > )< / span >
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< a id = "__codelineno-73-39" name = "__codelineno-73-39" href = "#__codelineno-73-39" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 2. 执行旋转操作，使该子树重新恢复平衡 */< / span >
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< a id = "__codelineno-73-40" name = "__codelineno-73-40" href = "#__codelineno-73-40" > < / a > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "nx" > t< / span > < span class = "p" > .< / span > < span class = "nx" > rotate< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > )< / span >
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< a id = "__codelineno-73-41" name = "__codelineno-73-41" href = "#__codelineno-73-41" > < / a > < span class = "w" > < / span > < span class = "c1" > // 返回子树的根结点< / span >
< a id = "__codelineno-73-42" name = "__codelineno-73-42" href = "#__codelineno-73-42" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > node< / span >
< a id = "__codelineno-73-43" name = "__codelineno-73-43" href = "#__codelineno-73-43" > < / a > < span class = "p" > }< / span >
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< a id = "__codelineno-73-44" name = "__codelineno-73-44" href = "#__codelineno-73-44" > < / a >
< a id = "__codelineno-73-45" name = "__codelineno-73-45" href = "#__codelineno-73-45" > < / a > < span class = "cm" > /* 获取中序遍历中的下一个结点（仅适用于 root 有左子结点的情况） */< / span >
< a id = "__codelineno-73-46" name = "__codelineno-73-46" href = "#__codelineno-73-46" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > t< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > aVLTree< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "nx" > getInOrderNext< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > TreeNode< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > TreeNode< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-73-47" name = "__codelineno-73-47" href = "#__codelineno-73-47" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "kc" > nil< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-73-48" name = "__codelineno-73-48" href = "#__codelineno-73-48" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > node< / span >
< a id = "__codelineno-73-49" name = "__codelineno-73-49" href = "#__codelineno-73-49" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-73-50" name = "__codelineno-73-50" href = "#__codelineno-73-50" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环访问左子结点，直到叶结点时为最小结点，跳出< / span >
< a id = "__codelineno-73-51" name = "__codelineno-73-51" href = "#__codelineno-73-51" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > Left< / span > < span class = "w" > < / span > < span class = "o" > !=< / span > < span class = "w" > < / span > < span class = "kc" > nil< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-73-52" name = "__codelineno-73-52" href = "#__codelineno-73-52" > < / a > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > Left< / span >
< a id = "__codelineno-73-53" name = "__codelineno-73-53" href = "#__codelineno-73-53" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-73-54" name = "__codelineno-73-54" href = "#__codelineno-73-54" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > node< / span >
< a id = "__codelineno-73-55" name = "__codelineno-73-55" href = "#__codelineno-73-55" > < / a > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > avl_tree.js< / span > < pre > < span > < / span > < code > < a id = "__codelineno-74-1" name = "__codelineno-74-1" href = "#__codelineno-74-1" > < / a > < span class = "cm" > /* 删除结点 */< / span >
< a id = "__codelineno-74-2" name = "__codelineno-74-2" href = "#__codelineno-74-2" > < / a > < span class = "nx" > remove< / 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-74-3" name = "__codelineno-74-3" href = "#__codelineno-74-3" > < / a > < span class = "w" > < / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "nx" > root< / 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" > removeHelper< / span > < span class = "p" > (< / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "nx" > root< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > val< / span > < span class = "p" > );< / span >
< a id = "__codelineno-74-4" name = "__codelineno-74-4" href = "#__codelineno-74-4" > < / 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" > root< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-74-5" name = "__codelineno-74-5" href = "#__codelineno-74-5" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-74-6" name = "__codelineno-74-6" href = "#__codelineno-74-6" > < / a >
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< a id = "__codelineno-74-7" name = "__codelineno-74-7" href = "#__codelineno-74-7" > < / a > < span class = "cm" > /* 递归删除结点（辅助方法） */< / span >
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< a id = "__codelineno-74-8" name = "__codelineno-74-8" href = "#__codelineno-74-8" > < / a > < span class = "nx" > removeHelper< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > val< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-74-9" name = "__codelineno-74-9" href = "#__codelineno-74-9" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "w" > < / span > < span class = "o" > ===< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-74-10" name = "__codelineno-74-10" href = "#__codelineno-74-10" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 1. 查找结点，并删除之 */< / span >
< a id = "__codelineno-74-11" name = "__codelineno-74-11" href = "#__codelineno-74-11" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > val< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > val< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > left< / 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" > removeHelper< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > left< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > val< / span > < span class = "p" > );< / span >
< a id = "__codelineno-74-12" name = "__codelineno-74-12" href = "#__codelineno-74-12" > < / a > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > val< / span > < span class = "w" > < / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > val< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > right< / 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" > removeHelper< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > right< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > val< / span > < span class = "p" > );< / span >
< a id = "__codelineno-74-13" name = "__codelineno-74-13" href = "#__codelineno-74-13" > < / a > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-74-14" name = "__codelineno-74-14" href = "#__codelineno-74-14" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > left< / span > < span class = "w" > < / span > < span class = "o" > ===< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "w" > < / span > < span class = "o" > ||< / span > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > right< / span > < span class = "w" > < / span > < span class = "o" > ===< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-74-15" name = "__codelineno-74-15" href = "#__codelineno-74-15" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > child< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > left< / span > < span class = "w" > < / span > < span class = "o" > !==< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "w" > < / span > < span class = "o" > ?< / span > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > left< / span > < span class = "w" > < / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > right< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-74-16" name = "__codelineno-74-16" href = "#__codelineno-74-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子结点数量 = 0 ，直接删除 node 并返回< / span >
< a id = "__codelineno-74-17" name = "__codelineno-74-17" href = "#__codelineno-74-17" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > child< / span > < span class = "w" > < / span > < span class = "o" > ===< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-74-18" name = "__codelineno-74-18" href = "#__codelineno-74-18" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子结点数量 = 1 ，直接删除 node< / span >
< a id = "__codelineno-74-19" name = "__codelineno-74-19" href = "#__codelineno-74-19" > < / a > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > child< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-74-20" name = "__codelineno-74-20" href = "#__codelineno-74-20" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-74-21" name = "__codelineno-74-21" href = "#__codelineno-74-21" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子结点数量 = 2 ，则将中序遍历的下个结点删除，并用该结点替换当前结点< / span >
< a id = "__codelineno-74-22" name = "__codelineno-74-22" href = "#__codelineno-74-22" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > temp< / 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" > getInOrderNext< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > right< / span > < span class = "p" > );< / span >
< a id = "__codelineno-74-23" name = "__codelineno-74-23" href = "#__codelineno-74-23" > < / a > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > right< / 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" > removeHelper< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > right< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > temp< / span > < span class = "p" > .< / span > < span class = "nx" > val< / span > < span class = "p" > );< / span >
< a id = "__codelineno-74-24" name = "__codelineno-74-24" href = "#__codelineno-74-24" > < / a > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > val< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > temp< / span > < span class = "p" > .< / span > < span class = "nx" > val< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-74-25" name = "__codelineno-74-25" href = "#__codelineno-74-25" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-74-26" name = "__codelineno-74-26" href = "#__codelineno-74-26" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-74-27" name = "__codelineno-74-27" href = "#__codelineno-74-27" > < / a > < span class = "w" > < / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "nx" > updateHeight< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 更新结点高度< / span >
< a id = "__codelineno-74-28" name = "__codelineno-74-28" href = "#__codelineno-74-28" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 2. 执行旋转操作，使该子树重新恢复平衡 */< / span >
< a id = "__codelineno-74-29" name = "__codelineno-74-29" href = "#__codelineno-74-29" > < / a > < span class = "w" > < / span > < span class = "nx" > node< / 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" > rotate< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > );< / span >
< a id = "__codelineno-74-30" name = "__codelineno-74-30" href = "#__codelineno-74-30" > < / a > < span class = "w" > < / span > < span class = "c1" > // 返回子树的根结点< / span >
< a id = "__codelineno-74-31" name = "__codelineno-74-31" href = "#__codelineno-74-31" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-74-32" name = "__codelineno-74-32" href = "#__codelineno-74-32" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-74-33" name = "__codelineno-74-33" href = "#__codelineno-74-33" > < / a >
< a id = "__codelineno-74-34" name = "__codelineno-74-34" href = "#__codelineno-74-34" > < / a > < span class = "cm" > /* 获取中序遍历中的下一个结点（仅适用于 root 有左子结点的情况） */< / span >
< a id = "__codelineno-74-35" name = "__codelineno-74-35" href = "#__codelineno-74-35" > < / a > < span class = "nx" > getInOrderNext< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-74-36" name = "__codelineno-74-36" href = "#__codelineno-74-36" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "w" > < / span > < span class = "o" > ===< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-74-37" name = "__codelineno-74-37" href = "#__codelineno-74-37" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环访问左子结点，直到叶结点时为最小结点，跳出< / span >
< a id = "__codelineno-74-38" name = "__codelineno-74-38" href = "#__codelineno-74-38" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > left< / span > < span class = "w" > < / span > < span class = "o" > !==< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-74-39" name = "__codelineno-74-39" href = "#__codelineno-74-39" > < / a > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > left< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-74-40" name = "__codelineno-74-40" href = "#__codelineno-74-40" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-74-41" name = "__codelineno-74-41" href = "#__codelineno-74-41" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-74-42" name = "__codelineno-74-42" href = "#__codelineno-74-42" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > avl_tree.ts< / span > < pre > < span > < / span > < code > < a id = "__codelineno-75-1" name = "__codelineno-75-1" href = "#__codelineno-75-1" > < / a > < span class = "cm" > /* 删除结点 */< / span >
< a id = "__codelineno-75-2" name = "__codelineno-75-2" href = "#__codelineno-75-2" > < / a > < span class = "nx" > remove< / 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 = "nx" > TreeNode< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-75-3" name = "__codelineno-75-3" href = "#__codelineno-75-3" > < / a > < span class = "w" > < / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "nx" > root< / 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" > removeHelper< / span > < span class = "p" > (< / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "nx" > root< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > val< / span > < span class = "p" > );< / span >
< a id = "__codelineno-75-4" name = "__codelineno-75-4" href = "#__codelineno-75-4" > < / 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" > root< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-75-5" name = "__codelineno-75-5" href = "#__codelineno-75-5" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-75-6" name = "__codelineno-75-6" href = "#__codelineno-75-6" > < / a >
2023-02-10 01:03:44 +08:00
< a id = "__codelineno-75-7" name = "__codelineno-75-7" href = "#__codelineno-75-7" > < / a > < span class = "cm" > /* 递归删除结点（辅助方法） */< / span >
2023-02-08 14:54:41 +08:00
< a id = "__codelineno-75-8" name = "__codelineno-75-8" href = "#__codelineno-75-8" > < / a > < span class = "nx" > removeHelper< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > TreeNode< / span > < span class = "p" > ,< / span > < span class = "w" > < / 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 = "nx" > TreeNode< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-75-9" name = "__codelineno-75-9" href = "#__codelineno-75-9" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "w" > < / span > < span class = "o" > ===< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-75-10" name = "__codelineno-75-10" href = "#__codelineno-75-10" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 1. 查找结点，并删除之 */< / span >
< a id = "__codelineno-75-11" name = "__codelineno-75-11" href = "#__codelineno-75-11" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > val< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "nx" > node< / 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-75-12" name = "__codelineno-75-12" href = "#__codelineno-75-12" > < / a > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > left< / 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" > removeHelper< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > left< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > val< / span > < span class = "p" > );< / span >
< a id = "__codelineno-75-13" name = "__codelineno-75-13" href = "#__codelineno-75-13" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > val< / span > < span class = "w" > < / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "nx" > node< / 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-75-14" name = "__codelineno-75-14" href = "#__codelineno-75-14" > < / a > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > right< / 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" > removeHelper< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > right< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > val< / span > < span class = "p" > );< / span >
< a id = "__codelineno-75-15" name = "__codelineno-75-15" href = "#__codelineno-75-15" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-75-16" name = "__codelineno-75-16" href = "#__codelineno-75-16" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > left< / span > < span class = "w" > < / span > < span class = "o" > ===< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "w" > < / span > < span class = "o" > ||< / span > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > right< / span > < span class = "w" > < / span > < span class = "o" > ===< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-75-17" name = "__codelineno-75-17" href = "#__codelineno-75-17" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > child< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > left< / span > < span class = "w" > < / span > < span class = "o" > !==< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "w" > < / span > < span class = "o" > ?< / span > < span class = "w" > < / span > < span class = "nx" > node.left< / span > < span class = "w" > < / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > node.right< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-75-18" name = "__codelineno-75-18" href = "#__codelineno-75-18" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子结点数量 = 0 ，直接删除 node 并返回< / span >
< a id = "__codelineno-75-19" name = "__codelineno-75-19" href = "#__codelineno-75-19" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > child< / span > < span class = "w" > < / span > < span class = "o" > ===< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-75-20" name = "__codelineno-75-20" href = "#__codelineno-75-20" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-75-21" name = "__codelineno-75-21" href = "#__codelineno-75-21" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-75-22" name = "__codelineno-75-22" href = "#__codelineno-75-22" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子结点数量 = 1 ，直接删除 node< / span >
< a id = "__codelineno-75-23" name = "__codelineno-75-23" href = "#__codelineno-75-23" > < / a > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > child< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-75-24" name = "__codelineno-75-24" href = "#__codelineno-75-24" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-75-25" name = "__codelineno-75-25" href = "#__codelineno-75-25" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-75-26" name = "__codelineno-75-26" href = "#__codelineno-75-26" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子结点数量 = 2 ，则将中序遍历的下个结点删除，并用该结点替换当前结点< / span >
< a id = "__codelineno-75-27" name = "__codelineno-75-27" href = "#__codelineno-75-27" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > temp< / 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" > getInOrderNext< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > right< / span > < span class = "p" > );< / span >
< a id = "__codelineno-75-28" name = "__codelineno-75-28" href = "#__codelineno-75-28" > < / a > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > right< / 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" > removeHelper< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > right< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > temp< / span > < span class = "p" > .< / span > < span class = "nx" > val< / span > < span class = "p" > );< / span >
< a id = "__codelineno-75-29" name = "__codelineno-75-29" href = "#__codelineno-75-29" > < / a > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > val< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > temp< / span > < span class = "p" > .< / span > < span class = "nx" > val< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-75-30" name = "__codelineno-75-30" href = "#__codelineno-75-30" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-75-31" name = "__codelineno-75-31" href = "#__codelineno-75-31" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-75-32" name = "__codelineno-75-32" href = "#__codelineno-75-32" > < / a > < span class = "w" > < / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "nx" > updateHeight< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 更新结点高度< / span >
< a id = "__codelineno-75-33" name = "__codelineno-75-33" href = "#__codelineno-75-33" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 2. 执行旋转操作，使该子树重新恢复平衡 */< / span >
< a id = "__codelineno-75-34" name = "__codelineno-75-34" href = "#__codelineno-75-34" > < / a > < span class = "w" > < / span > < span class = "nx" > node< / 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" > rotate< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > );< / span >
< a id = "__codelineno-75-35" name = "__codelineno-75-35" href = "#__codelineno-75-35" > < / a > < span class = "w" > < / span > < span class = "c1" > // 返回子树的根结点< / span >
< a id = "__codelineno-75-36" name = "__codelineno-75-36" href = "#__codelineno-75-36" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-75-37" name = "__codelineno-75-37" href = "#__codelineno-75-37" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-75-38" name = "__codelineno-75-38" href = "#__codelineno-75-38" > < / a >
< a id = "__codelineno-75-39" name = "__codelineno-75-39" href = "#__codelineno-75-39" > < / a > < span class = "cm" > /* 获取中序遍历中的下一个结点（仅适用于 root 有左子结点的情况） */< / span >
< a id = "__codelineno-75-40" name = "__codelineno-75-40" href = "#__codelineno-75-40" > < / a > < span class = "nx" > getInOrderNext< / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > TreeNode< / span > < span class = "p" > )< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "nx" > TreeNode< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-75-41" name = "__codelineno-75-41" href = "#__codelineno-75-41" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "w" > < / span > < span class = "o" > ===< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-75-42" name = "__codelineno-75-42" href = "#__codelineno-75-42" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环访问左子结点，直到叶结点时为最小结点，跳出< / span >
< a id = "__codelineno-75-43" name = "__codelineno-75-43" href = "#__codelineno-75-43" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > left< / span > < span class = "w" > < / span > < span class = "o" > !==< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-75-44" name = "__codelineno-75-44" href = "#__codelineno-75-44" > < / a > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > .< / span > < span class = "nx" > left< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-75-45" name = "__codelineno-75-45" href = "#__codelineno-75-45" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-75-46" name = "__codelineno-75-46" href = "#__codelineno-75-46" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-75-47" name = "__codelineno-75-47" href = "#__codelineno-75-47" > < / 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" > avl_tree.c< / span > < pre > < span > < / span > < code > < a id = "__codelineno-76-1" name = "__codelineno-76-1" href = "#__codelineno-76-1" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{< / span > < span class = "n" > aVLTree< / 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" > remove< / span > < span class = "p" > }< / span >
< a id = "__codelineno-76-2" name = "__codelineno-76-2" href = "#__codelineno-76-2" > < / a >
< a id = "__codelineno-76-3" name = "__codelineno-76-3" href = "#__codelineno-76-3" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{< / span > < span class = "n" > aVLTree< / 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" > removeHelper< / span > < span class = "p" > }< / span >
< a id = "__codelineno-76-4" name = "__codelineno-76-4" href = "#__codelineno-76-4" > < / a >
< a id = "__codelineno-76-5" name = "__codelineno-76-5" href = "#__codelineno-76-5" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{< / span > < span class = "n" > aVLTree< / 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" > getInOrderNext< / 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" > avl_tree.cs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-77-1" name = "__codelineno-77-1" href = "#__codelineno-77-1" > < / a > < span class = "cm" > /* 删除结点 */< / span >
2023-02-08 22:16:28 +08:00
< a id = "__codelineno-77-2" name = "__codelineno-77-2" href = "#__codelineno-77-2" > < / a > < span class = "n" > TreeNode< / span > < span class = "o" > ?< / span > < span class = "w" > < / span > < span class = "k" > remove< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > val< / span > < span class = "p" > )< / span >
2023-02-08 14:54:41 +08:00
< a id = "__codelineno-77-3" name = "__codelineno-77-3" href = "#__codelineno-77-3" > < / a > < span class = "p" > {< / span >
< a id = "__codelineno-77-4" name = "__codelineno-77-4" href = "#__codelineno-77-4" > < / a > < span class = "w" > < / span > < span class = "n" > root< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > removeHelper< / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > val< / span > < span class = "p" > );< / span >
< a id = "__codelineno-77-5" name = "__codelineno-77-5" href = "#__codelineno-77-5" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > root< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-77-6" name = "__codelineno-77-6" href = "#__codelineno-77-6" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-77-7" name = "__codelineno-77-7" href = "#__codelineno-77-7" > < / a >
2023-02-10 01:03:44 +08:00
< a id = "__codelineno-77-8" name = "__codelineno-77-8" href = "#__codelineno-77-8" > < / a > < span class = "cm" > /* 递归删除结点（辅助方法） */< / span >
2023-02-08 22:16:28 +08:00
< a id = "__codelineno-77-9" name = "__codelineno-77-9" href = "#__codelineno-77-9" > < / a > < span class = "n" > TreeNode< / span > < span class = "o" > ?< / span > < span class = "w" > < / span > < span class = "n" > removeHelper< / span > < span class = "p" > (< / span > < span class = "n" > TreeNode< / span > < span class = "o" > ?< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > val< / span > < span class = "p" > )< / span >
2023-02-08 14:54:41 +08:00
< a id = "__codelineno-77-10" name = "__codelineno-77-10" href = "#__codelineno-77-10" > < / a > < span class = "p" > {< / span >
< a id = "__codelineno-77-11" name = "__codelineno-77-11" href = "#__codelineno-77-11" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "k" > null< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "k" > null< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-77-12" name = "__codelineno-77-12" href = "#__codelineno-77-12" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 1. 查找结点，并删除之 */< / span >
< a id = "__codelineno-77-13" name = "__codelineno-77-13" href = "#__codelineno-77-13" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > val< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "n" > val< / span > < span class = "p" > )< / span >
< a id = "__codelineno-77-14" name = "__codelineno-77-14" href = "#__codelineno-77-14" > < / a > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "n" > left< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > removeHelper< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "n" > left< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > val< / span > < span class = "p" > );< / span >
< a id = "__codelineno-77-15" name = "__codelineno-77-15" href = "#__codelineno-77-15" > < / a > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "nf" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > val< / span > < span class = "w" > < / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "n" > val< / span > < span class = "p" > )< / span >
< a id = "__codelineno-77-16" name = "__codelineno-77-16" href = "#__codelineno-77-16" > < / a > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "n" > right< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > removeHelper< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "n" > right< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > val< / span > < span class = "p" > );< / span >
< a id = "__codelineno-77-17" name = "__codelineno-77-17" href = "#__codelineno-77-17" > < / a > < span class = "w" > < / span > < span class = "k" > else< / span >
< a id = "__codelineno-77-18" name = "__codelineno-77-18" href = "#__codelineno-77-18" > < / a > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-77-19" name = "__codelineno-77-19" href = "#__codelineno-77-19" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "n" > left< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "k" > null< / span > < span class = "w" > < / span > < span class = "o" > ||< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "n" > right< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "k" > null< / span > < span class = "p" > )< / span >
< a id = "__codelineno-77-20" name = "__codelineno-77-20" href = "#__codelineno-77-20" > < / a > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-77-21" name = "__codelineno-77-21" href = "#__codelineno-77-21" > < / a > < span class = "w" > < / span > < span class = "n" > TreeNode< / span > < span class = "o" > ?< / span > < span class = "w" > < / span > < span class = "n" > child< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "n" > left< / span > < span class = "w" > < / span > < span class = "o" > !=< / span > < span class = "w" > < / span > < span class = "k" > null< / span > < span class = "w" > < / span > < span class = "o" > ?< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "n" > left< / span > < span class = "w" > < / span > < span class = "p" > :< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "n" > right< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-77-22" name = "__codelineno-77-22" href = "#__codelineno-77-22" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子结点数量 = 0 ，直接删除 node 并返回< / span >
< a id = "__codelineno-77-23" name = "__codelineno-77-23" href = "#__codelineno-77-23" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > child< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "k" > null< / span > < span class = "p" > )< / span >
< a id = "__codelineno-77-24" name = "__codelineno-77-24" href = "#__codelineno-77-24" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "k" > null< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-77-25" name = "__codelineno-77-25" href = "#__codelineno-77-25" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子结点数量 = 1 ，直接删除 node< / span >
< a id = "__codelineno-77-26" name = "__codelineno-77-26" href = "#__codelineno-77-26" > < / a > < span class = "w" > < / span > < span class = "k" > else< / span >
< a id = "__codelineno-77-27" name = "__codelineno-77-27" href = "#__codelineno-77-27" > < / a > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > child< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-77-28" name = "__codelineno-77-28" href = "#__codelineno-77-28" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-77-29" name = "__codelineno-77-29" href = "#__codelineno-77-29" > < / a > < span class = "w" > < / span > < span class = "k" > else< / span >
< a id = "__codelineno-77-30" name = "__codelineno-77-30" href = "#__codelineno-77-30" > < / a > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-77-31" name = "__codelineno-77-31" href = "#__codelineno-77-31" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子结点数量 = 2 ，则将中序遍历的下个结点删除，并用该结点替换当前结点< / span >
< a id = "__codelineno-77-32" name = "__codelineno-77-32" href = "#__codelineno-77-32" > < / a > < span class = "w" > < / span > < span class = "n" > TreeNode< / span > < span class = "o" > ?< / span > < span class = "w" > < / span > < span class = "n" > temp< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > getInOrderNext< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "n" > right< / span > < span class = "p" > );< / span >
< a id = "__codelineno-77-33" name = "__codelineno-77-33" href = "#__codelineno-77-33" > < / a > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "n" > right< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > removeHelper< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "n" > right< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > temp< / span > < span class = "p" > .< / span > < span class = "n" > val< / span > < span class = "p" > );< / span >
< a id = "__codelineno-77-34" name = "__codelineno-77-34" href = "#__codelineno-77-34" > < / a > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "n" > val< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > temp< / span > < span class = "p" > .< / span > < span class = "n" > val< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-77-35" name = "__codelineno-77-35" href = "#__codelineno-77-35" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-77-36" name = "__codelineno-77-36" href = "#__codelineno-77-36" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-77-37" name = "__codelineno-77-37" href = "#__codelineno-77-37" > < / a > < span class = "w" > < / span > < span class = "n" > updateHeight< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 更新结点高度< / span >
< a id = "__codelineno-77-38" name = "__codelineno-77-38" href = "#__codelineno-77-38" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 2. 执行旋转操作，使该子树重新恢复平衡 */< / span >
< a id = "__codelineno-77-39" name = "__codelineno-77-39" href = "#__codelineno-77-39" > < / a > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > rotate< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > );< / span >
< a id = "__codelineno-77-40" name = "__codelineno-77-40" href = "#__codelineno-77-40" > < / a > < span class = "w" > < / span > < span class = "c1" > // 返回子树的根结点< / span >
< a id = "__codelineno-77-41" name = "__codelineno-77-41" href = "#__codelineno-77-41" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-77-42" name = "__codelineno-77-42" href = "#__codelineno-77-42" > < / a > < span class = "p" > }< / span >
2023-02-08 22:16:28 +08:00
< a id = "__codelineno-77-43" name = "__codelineno-77-43" href = "#__codelineno-77-43" > < / a >
< a id = "__codelineno-77-44" name = "__codelineno-77-44" href = "#__codelineno-77-44" > < / a > < span class = "cm" > /* 获取中序遍历中的下一个结点（仅适用于 root 有左子结点的情况） */< / span >
< a id = "__codelineno-77-45" name = "__codelineno-77-45" href = "#__codelineno-77-45" > < / a > < span class = "n" > TreeNode< / span > < span class = "o" > ?< / span > < span class = "w" > < / span > < span class = "n" > getInOrderNext< / span > < span class = "p" > (< / span > < span class = "n" > TreeNode< / span > < span class = "o" > ?< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > )< / span >
< a id = "__codelineno-77-46" name = "__codelineno-77-46" href = "#__codelineno-77-46" > < / a > < span class = "p" > {< / span >
< a id = "__codelineno-77-47" name = "__codelineno-77-47" href = "#__codelineno-77-47" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "k" > null< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-77-48" name = "__codelineno-77-48" href = "#__codelineno-77-48" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环访问左子结点，直到叶结点时为最小结点，跳出< / span >
< a id = "__codelineno-77-49" name = "__codelineno-77-49" href = "#__codelineno-77-49" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "n" > left< / span > < span class = "w" > < / span > < span class = "o" > !=< / span > < span class = "w" > < / span > < span class = "k" > null< / span > < span class = "p" > )< / span >
< a id = "__codelineno-77-50" name = "__codelineno-77-50" href = "#__codelineno-77-50" > < / a > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-77-51" name = "__codelineno-77-51" href = "#__codelineno-77-51" > < / a > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "n" > left< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-77-52" name = "__codelineno-77-52" href = "#__codelineno-77-52" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-77-53" name = "__codelineno-77-53" href = "#__codelineno-77-53" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-77-54" name = "__codelineno-77-54" href = "#__codelineno-77-54" > < / 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" > avl_tree.swift< / span > < pre > < span > < / span > < code > < a id = "__codelineno-78-1" name = "__codelineno-78-1" href = "#__codelineno-78-1" > < / a > < span class = "cm" > /* 删除结点 */< / span >
< a id = "__codelineno-78-2" name = "__codelineno-78-2" href = "#__codelineno-78-2" > < / a > < span class = "p" > @< / span > < span class = "n" > discardableResult< / span >
< a id = "__codelineno-78-3" name = "__codelineno-78-3" href = "#__codelineno-78-3" > < / a > < span class = "kd" > func< / span > < span class = "nf" > remove< / 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 > < span class = "n" > TreeNode< / span > < span class = "p" > ?< / span > < span class = "p" > {< / span >
< a id = "__codelineno-78-4" name = "__codelineno-78-4" href = "#__codelineno-78-4" > < / a > < span class = "n" > root< / span > < span class = "p" > =< / span > < span class = "n" > removeHelper< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > :< / span > < span class = "n" > root< / span > < span class = "p" > ,< / span > < span class = "n" > val< / span > < span class = "p" > :< / span > < span class = "n" > val< / span > < span class = "p" > )< / span >
< a id = "__codelineno-78-5" name = "__codelineno-78-5" href = "#__codelineno-78-5" > < / a > < span class = "k" > return< / span > < span class = "n" > root< / span >
< a id = "__codelineno-78-6" name = "__codelineno-78-6" href = "#__codelineno-78-6" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-78-7" name = "__codelineno-78-7" href = "#__codelineno-78-7" > < / a >
2023-02-10 01:03:44 +08:00
< a id = "__codelineno-78-8" name = "__codelineno-78-8" href = "#__codelineno-78-8" > < / a > < span class = "cm" > /* 递归删除结点（辅助方法） */< / span >
2023-02-08 14:54:41 +08:00
< a id = "__codelineno-78-9" name = "__codelineno-78-9" href = "#__codelineno-78-9" > < / a > < span class = "kd" > func< / span > < span class = "nf" > removeHelper< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > :< / span > < span class = "n" > TreeNode< / 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 > < span class = "n" > TreeNode< / span > < span class = "p" > ?< / span > < span class = "p" > {< / span >
< a id = "__codelineno-78-10" name = "__codelineno-78-10" href = "#__codelineno-78-10" > < / a > < span class = "kd" > var< / span > < span class = "nv" > node< / span > < span class = "p" > =< / span > < span class = "n" > node< / span >
< a id = "__codelineno-78-11" name = "__codelineno-78-11" href = "#__codelineno-78-11" > < / a > < span class = "k" > if< / span > < span class = "n" > node< / span > < span class = "p" > ==< / span > < span class = "kc" > nil< / span > < span class = "p" > {< / span >
< a id = "__codelineno-78-12" name = "__codelineno-78-12" href = "#__codelineno-78-12" > < / a > < span class = "k" > return< / span > < span class = "kc" > nil< / span >
< a id = "__codelineno-78-13" name = "__codelineno-78-13" href = "#__codelineno-78-13" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-78-14" name = "__codelineno-78-14" href = "#__codelineno-78-14" > < / a > < span class = "cm" > /* 1. 查找结点，并删除之 */< / span >
< a id = "__codelineno-78-15" name = "__codelineno-78-15" href = "#__codelineno-78-15" > < / a > < span class = "k" > if< / span > < span class = "n" > val< / span > < span class = "o" > < < / span > < span class = "n" > node< / span > < span class = "p" > !.< / span > < span class = "n" > val< / span > < span class = "p" > {< / span >
< a id = "__codelineno-78-16" name = "__codelineno-78-16" href = "#__codelineno-78-16" > < / a > < span class = "n" > node< / span > < span class = "p" > ?.< / span > < span class = "kr" > left< / span > < span class = "p" > =< / span > < span class = "n" > removeHelper< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > :< / span > < span class = "n" > node< / span > < span class = "p" > ?.< / span > < span class = "kr" > left< / span > < span class = "p" > ,< / span > < span class = "n" > val< / span > < span class = "p" > :< / span > < span class = "n" > val< / span > < span class = "p" > )< / span >
< a id = "__codelineno-78-17" name = "__codelineno-78-17" href = "#__codelineno-78-17" > < / a > < span class = "p" > }< / span > < span class = "k" > else< / span > < span class = "k" > if< / span > < span class = "n" > val< / span > < span class = "o" > > < / span > < span class = "n" > node< / span > < span class = "p" > !.< / span > < span class = "n" > val< / span > < span class = "p" > {< / span >
< a id = "__codelineno-78-18" name = "__codelineno-78-18" href = "#__codelineno-78-18" > < / a > < span class = "n" > node< / span > < span class = "p" > ?.< / span > < span class = "kr" > right< / span > < span class = "p" > =< / span > < span class = "n" > removeHelper< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > :< / span > < span class = "n" > node< / span > < span class = "p" > ?.< / span > < span class = "kr" > right< / span > < span class = "p" > ,< / span > < span class = "n" > val< / span > < span class = "p" > :< / span > < span class = "n" > val< / span > < span class = "p" > )< / span >
< a id = "__codelineno-78-19" name = "__codelineno-78-19" href = "#__codelineno-78-19" > < / a > < span class = "p" > }< / span > < span class = "k" > else< / span > < span class = "p" > {< / span >
< a id = "__codelineno-78-20" name = "__codelineno-78-20" href = "#__codelineno-78-20" > < / a > < span class = "k" > if< / span > < span class = "n" > node< / span > < span class = "p" > ?.< / span > < span class = "kr" > left< / span > < span class = "p" > ==< / span > < span class = "kc" > nil< / span > < span class = "o" > ||< / span > < span class = "n" > node< / span > < span class = "p" > ?.< / span > < span class = "kr" > right< / span > < span class = "p" > ==< / span > < span class = "kc" > nil< / span > < span class = "p" > {< / span >
< a id = "__codelineno-78-21" name = "__codelineno-78-21" href = "#__codelineno-78-21" > < / a > < span class = "kd" > let< / span > < span class = "nv" > child< / span > < span class = "p" > =< / span > < span class = "n" > node< / span > < span class = "p" > ?.< / span > < span class = "kr" > left< / span > < span class = "o" > !=< / span > < span class = "kc" > nil< / span > < span class = "p" > ?< / span > < span class = "n" > node< / span > < span class = "p" > ?.< / span > < span class = "kr" > left< / span > < span class = "p" > :< / span > < span class = "n" > node< / span > < span class = "p" > ?.< / span > < span class = "kr" > right< / span >
< a id = "__codelineno-78-22" name = "__codelineno-78-22" href = "#__codelineno-78-22" > < / a > < span class = "c1" > // 子结点数量 = 0 ，直接删除 node 并返回< / span >
< a id = "__codelineno-78-23" name = "__codelineno-78-23" href = "#__codelineno-78-23" > < / a > < span class = "k" > if< / span > < span class = "n" > child< / span > < span class = "p" > ==< / span > < span class = "kc" > nil< / span > < span class = "p" > {< / span >
< a id = "__codelineno-78-24" name = "__codelineno-78-24" href = "#__codelineno-78-24" > < / a > < span class = "k" > return< / span > < span class = "kc" > nil< / span >
< a id = "__codelineno-78-25" name = "__codelineno-78-25" href = "#__codelineno-78-25" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-78-26" name = "__codelineno-78-26" href = "#__codelineno-78-26" > < / a > < span class = "c1" > // 子结点数量 = 1 ，直接删除 node< / span >
< a id = "__codelineno-78-27" name = "__codelineno-78-27" href = "#__codelineno-78-27" > < / a > < span class = "k" > else< / span > < span class = "p" > {< / span >
< a id = "__codelineno-78-28" name = "__codelineno-78-28" href = "#__codelineno-78-28" > < / a > < span class = "n" > node< / span > < span class = "p" > =< / span > < span class = "n" > child< / span >
< a id = "__codelineno-78-29" name = "__codelineno-78-29" href = "#__codelineno-78-29" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-78-30" name = "__codelineno-78-30" href = "#__codelineno-78-30" > < / a > < span class = "p" > }< / span > < span class = "k" > else< / span > < span class = "p" > {< / span >
< a id = "__codelineno-78-31" name = "__codelineno-78-31" href = "#__codelineno-78-31" > < / a > < span class = "c1" > // 子结点数量 = 2 ，则将中序遍历的下个结点删除，并用该结点替换当前结点< / span >
< a id = "__codelineno-78-32" name = "__codelineno-78-32" href = "#__codelineno-78-32" > < / a > < span class = "kd" > let< / span > < span class = "nv" > temp< / span > < span class = "p" > =< / span > < span class = "n" > getInOrderNext< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > :< / span > < span class = "n" > node< / span > < span class = "p" > ?.< / span > < span class = "kr" > right< / span > < span class = "p" > )< / span >
< a id = "__codelineno-78-33" name = "__codelineno-78-33" href = "#__codelineno-78-33" > < / a > < span class = "n" > node< / span > < span class = "p" > ?.< / span > < span class = "kr" > right< / span > < span class = "p" > =< / span > < span class = "n" > removeHelper< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > :< / span > < span class = "n" > node< / span > < span class = "p" > ?.< / span > < span class = "kr" > right< / span > < span class = "p" > ,< / span > < span class = "n" > val< / span > < span class = "p" > :< / span > < span class = "n" > temp< / span > < span class = "p" > !.< / span > < span class = "n" > val< / span > < span class = "p" > )< / span >
< a id = "__codelineno-78-34" name = "__codelineno-78-34" href = "#__codelineno-78-34" > < / a > < span class = "n" > node< / span > < span class = "p" > ?.< / span > < span class = "n" > val< / span > < span class = "p" > =< / span > < span class = "n" > temp< / span > < span class = "p" > !.< / span > < span class = "n" > val< / span >
< a id = "__codelineno-78-35" name = "__codelineno-78-35" href = "#__codelineno-78-35" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-78-36" name = "__codelineno-78-36" href = "#__codelineno-78-36" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-78-37" name = "__codelineno-78-37" href = "#__codelineno-78-37" > < / a > < span class = "n" > updateHeight< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > :< / span > < span class = "n" > node< / span > < span class = "p" > )< / span > < span class = "c1" > // 更新结点高度< / span >
< a id = "__codelineno-78-38" name = "__codelineno-78-38" href = "#__codelineno-78-38" > < / a > < span class = "cm" > /* 2. 执行旋转操作，使该子树重新恢复平衡 */< / span >
< a id = "__codelineno-78-39" name = "__codelineno-78-39" href = "#__codelineno-78-39" > < / a > < span class = "n" > node< / span > < span class = "p" > =< / span > < span class = "n" > rotate< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > :< / span > < span class = "n" > node< / span > < span class = "p" > )< / span >
< a id = "__codelineno-78-40" name = "__codelineno-78-40" href = "#__codelineno-78-40" > < / a > < span class = "c1" > // 返回子树的根结点< / span >
< a id = "__codelineno-78-41" name = "__codelineno-78-41" href = "#__codelineno-78-41" > < / a > < span class = "k" > return< / span > < span class = "n" > node< / span >
< a id = "__codelineno-78-42" name = "__codelineno-78-42" href = "#__codelineno-78-42" > < / a > < span class = "p" > }< / span >
2023-02-09 04:43:20 +08:00
< a id = "__codelineno-78-43" name = "__codelineno-78-43" href = "#__codelineno-78-43" > < / a >
< a id = "__codelineno-78-44" name = "__codelineno-78-44" href = "#__codelineno-78-44" > < / a > < span class = "cm" > /* 获取中序遍历中的下一个结点（仅适用于 root 有左子结点的情况） */< / span >
< a id = "__codelineno-78-45" name = "__codelineno-78-45" href = "#__codelineno-78-45" > < / a > < span class = "kd" > func< / span > < span class = "nf" > getInOrderNext< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > :< / span > < span class = "n" > TreeNode< / span > < span class = "p" > ?)< / span > < span class = "p" > -> < / span > < span class = "n" > TreeNode< / span > < span class = "p" > ?< / span > < span class = "p" > {< / span >
< a id = "__codelineno-78-46" name = "__codelineno-78-46" href = "#__codelineno-78-46" > < / a > < span class = "kd" > var< / span > < span class = "nv" > node< / span > < span class = "p" > =< / span > < span class = "n" > node< / span >
< a id = "__codelineno-78-47" name = "__codelineno-78-47" href = "#__codelineno-78-47" > < / a > < span class = "k" > if< / span > < span class = "n" > node< / span > < span class = "p" > ==< / span > < span class = "kc" > nil< / span > < span class = "p" > {< / span >
< a id = "__codelineno-78-48" name = "__codelineno-78-48" href = "#__codelineno-78-48" > < / a > < span class = "k" > return< / span > < span class = "n" > node< / span >
< a id = "__codelineno-78-49" name = "__codelineno-78-49" href = "#__codelineno-78-49" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-78-50" name = "__codelineno-78-50" href = "#__codelineno-78-50" > < / a > < span class = "c1" > // 循环访问左子结点，直到叶结点时为最小结点，跳出< / span >
< a id = "__codelineno-78-51" name = "__codelineno-78-51" href = "#__codelineno-78-51" > < / a > < span class = "k" > while< / span > < span class = "n" > node< / span > < span class = "p" > ?.< / span > < span class = "kr" > left< / span > < span class = "o" > !=< / span > < span class = "kc" > nil< / span > < span class = "p" > {< / span >
< a id = "__codelineno-78-52" name = "__codelineno-78-52" href = "#__codelineno-78-52" > < / a > < span class = "n" > node< / span > < span class = "p" > =< / span > < span class = "n" > node< / span > < span class = "p" > ?.< / span > < span class = "kr" > left< / span >
< a id = "__codelineno-78-53" name = "__codelineno-78-53" href = "#__codelineno-78-53" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-78-54" name = "__codelineno-78-54" href = "#__codelineno-78-54" > < / a > < span class = "k" > return< / span > < span class = "n" > node< / span >
< a id = "__codelineno-78-55" name = "__codelineno-78-55" href = "#__codelineno-78-55" > < / 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" > avl_tree.zig< / span > < pre > < span > < / span > < code > < a id = "__codelineno-79-1" name = "__codelineno-79-1" href = "#__codelineno-79-1" > < / a > < span class = "c1" > // 删除结点< / span >
< a id = "__codelineno-79-2" name = "__codelineno-79-2" href = "#__codelineno-79-2" > < / a > < span class = "k" > fn< / span > < span class = "w" > < / span > < span class = "n" > remove< / 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 = "n" > inc< / span > < span class = "p" > .< / span > < span class = "n" > TreeNode< / span > < span class = "p" > (< / span > < span class = "n" > T< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-79-3" name = "__codelineno-79-3" href = "#__codelineno-79-3" > < / a > < span class = "w" > < / span > < span class = "n" > self< / span > < span class = "p" > .< / span > < span class = "n" > root< / 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" > removeHelper< / span > < span class = "p" > (< / span > < span class = "n" > self< / span > < span class = "p" > .< / span > < span class = "n" > root< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > val< / span > < span class = "p" > );< / span >
< a id = "__codelineno-79-4" name = "__codelineno-79-4" href = "#__codelineno-79-4" > < / 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" > root< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-79-5" name = "__codelineno-79-5" href = "#__codelineno-79-5" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-79-6" name = "__codelineno-79-6" href = "#__codelineno-79-6" > < / a >
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< a id = "__codelineno-79-7" name = "__codelineno-79-7" href = "#__codelineno-79-7" > < / a > < span class = "c1" > // 递归删除结点（辅助方法）< / span >
2023-02-09 22:55:35 +08:00
< a id = "__codelineno-79-8" name = "__codelineno-79-8" href = "#__codelineno-79-8" > < / a > < span class = "k" > fn< / span > < span class = "w" > < / span > < span class = "n" > removeHelper< / 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" > node_< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "o" > ?*< / span > < span class = "n" > inc< / span > < span class = "p" > .< / span > < span class = "n" > TreeNode< / span > < span class = "p" > (< / span > < span class = "n" > T< / 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 = "n" > inc< / span > < span class = "p" > .< / span > < span class = "n" > TreeNode< / span > < span class = "p" > (< / span > < span class = "n" > T< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-79-9" name = "__codelineno-79-9" href = "#__codelineno-79-9" > < / a > < span class = "w" > < / span > < span class = "kr" > var< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > node_< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-79-10" name = "__codelineno-79-10" href = "#__codelineno-79-10" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-79-11" name = "__codelineno-79-11" href = "#__codelineno-79-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 1. 查找结点，并删除之< / span >
< a id = "__codelineno-79-12" name = "__codelineno-79-12" href = "#__codelineno-79-12" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > val< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "o" > ?< / span > < span class = "p" > .< / span > < span class = "n" > val< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-79-13" name = "__codelineno-79-13" href = "#__codelineno-79-13" > < / a > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "o" > ?< / span > < span class = "p" > .< / span > < span class = "n" > left< / 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" > removeHelper< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "o" > ?< / span > < span class = "p" > .< / span > < span class = "n" > left< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > val< / span > < span class = "p" > );< / span >
< a id = "__codelineno-79-14" name = "__codelineno-79-14" href = "#__codelineno-79-14" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > val< / span > < span class = "w" > < / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "o" > ?< / span > < span class = "p" > .< / span > < span class = "n" > val< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-79-15" name = "__codelineno-79-15" href = "#__codelineno-79-15" > < / a > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "o" > ?< / span > < span class = "p" > .< / span > < span class = "n" > right< / 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" > removeHelper< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "o" > ?< / span > < span class = "p" > .< / span > < span class = "n" > right< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > val< / span > < span class = "p" > );< / span >
< a id = "__codelineno-79-16" name = "__codelineno-79-16" href = "#__codelineno-79-16" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-79-17" name = "__codelineno-79-17" href = "#__codelineno-79-17" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "o" > ?< / span > < span class = "p" > .< / span > < span class = "n" > left< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "w" > < / span > < span class = "k" > or< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "o" > ?< / span > < span class = "p" > .< / span > < span class = "n" > right< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-79-18" name = "__codelineno-79-18" href = "#__codelineno-79-18" > < / a > < span class = "w" > < / span > < span class = "kr" > var< / span > < span class = "w" > < / span > < span class = "n" > child< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "o" > ?< / span > < span class = "p" > .< / span > < span class = "n" > left< / span > < span class = "w" > < / span > < span class = "o" > !=< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "o" > ?< / span > < span class = "p" > .< / span > < span class = "n" > left< / span > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "o" > ?< / span > < span class = "p" > .< / span > < span class = "n" > right< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-79-19" name = "__codelineno-79-19" href = "#__codelineno-79-19" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子结点数量 = 0 ，直接删除 node 并返回< / span >
< a id = "__codelineno-79-20" name = "__codelineno-79-20" href = "#__codelineno-79-20" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > child< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-79-21" name = "__codelineno-79-21" href = "#__codelineno-79-21" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-79-22" name = "__codelineno-79-22" href = "#__codelineno-79-22" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子结点数量 = 1 ，直接删除 node< / span >
< a id = "__codelineno-79-23" name = "__codelineno-79-23" href = "#__codelineno-79-23" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-79-24" name = "__codelineno-79-24" href = "#__codelineno-79-24" > < / a > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > child< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-79-25" name = "__codelineno-79-25" href = "#__codelineno-79-25" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-79-26" name = "__codelineno-79-26" href = "#__codelineno-79-26" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-79-27" name = "__codelineno-79-27" href = "#__codelineno-79-27" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子结点数量 = 2 ，则将中序遍历的下个结点删除，并用该结点替换当前结点< / span >
< a id = "__codelineno-79-28" name = "__codelineno-79-28" href = "#__codelineno-79-28" > < / a > < span class = "w" > < / span > < span class = "kr" > var< / span > < span class = "w" > < / span > < span class = "n" > temp< / 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" > getInOrderNext< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "o" > ?< / span > < span class = "p" > .< / span > < span class = "n" > right< / span > < span class = "p" > );< / span >
< a id = "__codelineno-79-29" name = "__codelineno-79-29" href = "#__codelineno-79-29" > < / a > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "o" > ?< / span > < span class = "p" > .< / span > < span class = "n" > right< / 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" > removeHelper< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "o" > ?< / span > < span class = "p" > .< / span > < span class = "n" > right< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > temp< / span > < span class = "p" > .< / span > < span class = "o" > ?< / span > < span class = "p" > .< / span > < span class = "n" > val< / span > < span class = "p" > );< / span >
< a id = "__codelineno-79-30" name = "__codelineno-79-30" href = "#__codelineno-79-30" > < / a > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "o" > ?< / span > < span class = "p" > .< / span > < span class = "n" > val< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > temp< / span > < span class = "p" > .< / span > < span class = "o" > ?< / span > < span class = "p" > .< / span > < span class = "n" > val< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-79-31" name = "__codelineno-79-31" href = "#__codelineno-79-31" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-79-32" name = "__codelineno-79-32" href = "#__codelineno-79-32" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-79-33" name = "__codelineno-79-33" href = "#__codelineno-79-33" > < / a > < span class = "w" > < / span > < span class = "n" > self< / span > < span class = "p" > .< / span > < span class = "n" > updateHeight< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 更新结点高度< / span >
< a id = "__codelineno-79-34" name = "__codelineno-79-34" href = "#__codelineno-79-34" > < / a > < span class = "w" > < / span > < span class = "c1" > // 2. 执行旋转操作，使该子树重新恢复平衡< / span >
< a id = "__codelineno-79-35" name = "__codelineno-79-35" href = "#__codelineno-79-35" > < / a > < span class = "w" > < / span > < span class = "n" > node< / 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" > rotate< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > );< / span >
< a id = "__codelineno-79-36" name = "__codelineno-79-36" href = "#__codelineno-79-36" > < / a > < span class = "w" > < / span > < span class = "c1" > // 返回子树的根结点< / span >
< a id = "__codelineno-79-37" name = "__codelineno-79-37" href = "#__codelineno-79-37" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-79-38" name = "__codelineno-79-38" href = "#__codelineno-79-38" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-79-39" name = "__codelineno-79-39" href = "#__codelineno-79-39" > < / a >
< a id = "__codelineno-79-40" name = "__codelineno-79-40" href = "#__codelineno-79-40" > < / a > < span class = "c1" > // 获取中序遍历中的下一个结点（仅适用于 root 有左子结点的情况）< / span >
< a id = "__codelineno-79-41" name = "__codelineno-79-41" href = "#__codelineno-79-41" > < / a > < span class = "k" > fn< / span > < span class = "w" > < / span > < span class = "n" > getInOrderNext< / 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" > node_< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "o" > ?*< / span > < span class = "n" > inc< / span > < span class = "p" > .< / span > < span class = "n" > TreeNode< / span > < span class = "p" > (< / span > < span class = "n" > T< / span > < span class = "p" > ))< / span > < span class = "w" > < / span > < span class = "o" > ?*< / span > < span class = "n" > inc< / span > < span class = "p" > .< / span > < span class = "n" > TreeNode< / span > < span class = "p" > (< / span > < span class = "n" > T< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-79-42" name = "__codelineno-79-42" href = "#__codelineno-79-42" > < / a > < span class = "w" > < / span > < span class = "n" > _< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > self< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-79-43" name = "__codelineno-79-43" href = "#__codelineno-79-43" > < / a > < span class = "w" > < / span > < span class = "kr" > var< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > node_< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-79-44" name = "__codelineno-79-44" href = "#__codelineno-79-44" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-79-45" name = "__codelineno-79-45" href = "#__codelineno-79-45" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环访问左子结点，直到叶结点时为最小结点，跳出< / span >
< a id = "__codelineno-79-46" name = "__codelineno-79-46" href = "#__codelineno-79-46" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "o" > ?< / span > < span class = "p" > .< / span > < span class = "n" > left< / span > < span class = "w" > < / span > < span class = "o" > !=< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-79-47" name = "__codelineno-79-47" href = "#__codelineno-79-47" > < / a > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "o" > ?< / span > < span class = "p" > .< / span > < span class = "n" > left< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-79-48" name = "__codelineno-79-48" href = "#__codelineno-79-48" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-79-49" name = "__codelineno-79-49" href = "#__codelineno-79-49" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-79-50" name = "__codelineno-79-50" href = "#__codelineno-79-50" > < / a > < span class = "p" > }< / span >
2023-02-08 14:54:41 +08:00
< / code > < / pre > < / div >
< / div >
< / div >
< / div >
< h3 id = "_6" > 查找结点< a class = "headerlink" href = "#_6" title = "Permanent link" > ¶ < / a > < / h3 >
< p > 「AVL 树」的结点查找操作与「二叉搜索树」一致，在此不再赘述。< / p >
2023-02-24 18:46:22 +08:00
< h2 id = "744-avl" > 7.4.4. AVL 树典型应用< a class = "headerlink" href = "#744-avl" title = "Permanent link" > ¶ < / a > < / h2 >
2023-02-08 14:54:41 +08:00
< ul >
< li > 组织存储大型数据，适用于高频查找、低频增删场景；< / li >
< li > 用于建立数据库中的索引系统；< / li >
< / ul >
< div class = "admonition question" >
< p class = "admonition-title" > 为什么红黑树比 AVL 树更受欢迎？< / p >
< p > 红黑树的平衡条件相对宽松，因此在红黑树中插入与删除结点所需的旋转操作相对更少，结点增删操作相比 AVL 树的效率更高。< / p >
< / div >
< h2 id = "__comments" > 评论< / h2 >
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